TradingView.com.com is a popular online platform that provides a comprehensive suite of tools and resources for traders, investors, and analysts to analyze and trade financial markets. In this chapter, we will provide an overview of TradingView.com, its features, and its benefits, setting the stage for a deeper dive into the platform's capabilities in subsequent chapters.

What is TradingView.com?

TradingView.com is a cloud-based platform that enables users to analyze and trade financial markets, including stocks, forex, futures, and cryptocurrencies. Founded in 2011, TradingView.com has grown to become one of the largest and most popular trading communities in the world, with over 10 million registered users.

Key Features of TradingView.com

TradingView.com offers a wide range of features that make it an attractive platform for traders and analysts. Some of the key features include:
1. Charting and Technical Analysis: TradingView.com provides a powerful charting platform that allows users to create custom charts with various indicators, drawing tools, and annotations. Users can also access a vast library of pre-built indicators and templates.
2. Backtesting and Paper Trading: TradingView.com allows users to backtest and paper trade their strategies using historical data, enabling them to refine their trading ideas and test their performance.
3. Community and Social Trading: TradingView.com has a large and active community of users who share their ideas, strategies, and insights. Users can follow other traders, participate in discussions, and share their own ideas and insights.
4. Alerts and Notifications: TradingView.com provides a robust alert system that allows users to set custom alerts based on market conditions, technical indicators, and other criteria.
5. Data Feeds: TradingView.com offers a range of data feeds, including real-time and historical data, for various markets and instruments.
6. Scripting and Automation: TradingView.com's PineScript language allows users to create custom indicators, strategies, and automated trading systems.
7. Mobile Apps: TradingView.com offers mobile apps for iOS and Android devices, enabling users to access the platform on-the-go.

Benefits of Using TradingView.com

TradingView.com offers several benefits to its users, including:
1. Improved Trading Decisions: TradingView.com's charting and analysis tools enable users to make more informed trading decisions.
2. Access to a Large Community: TradingView.com's community provides users with access to a vast network of traders, analysts, and experts.
3. Customization and Automation: TradingView.com's scripting and automation capabilities allow users to create custom strategies and automate their trading.
4. Real-time Data and Alerts: TradingView.com's real-time data and alert system enable users to stay up-to-date with market movements and react quickly to market changes.
5. Cost-Effective: TradingView.com offers a range of pricing plans, including a free version, making it an accessible platform for traders and analysts.

Conclusion

In this chapter, we have provided an overview of TradingView.com, its features, and its benefits. TradingView.com is a powerful platform that offers a range of tools and resources for traders, analysts, and investors. Whether you are a seasoned trader or just starting out, TradingView.com provides a comprehensive suite of tools to help you analyze and trade financial markets. In the next chapter, we will delve deeper into the charting and technical analysis capabilities of TradingView.com.

Chapter 2: Creating an Account and Setting Up Your Profile

As a new user, creating an account and setting up your profile is the first step in exploring the world of [Platform/Service]. In this chapter, we will guide you through a step-by-step process to create an account and set up your profile, ensuring a seamless and enjoyable experience.

Section 1: Creating an Account

To create an account, follow these steps:
1. Visit the Sign-up Page: Go to the [Platform/Service] website and click on the "Sign Up" or "Create an Account" button. This will take you to the sign-up page.
2. Enter Your Email Address: Enter a valid email address to serve as your login credentials. Make sure to use a unique and memorable email address, as it will be used to reset your password if needed.
3. Choose a Username: Choose a unique and memorable username that will be used to identify you on the platform. This can be your real name, a nickname, or a combination of letters and numbers.
4. Create a Password: Create a strong and unique password for your account. A strong password should be at least 8 characters long and include a mix of uppercase and lowercase letters, numbers, and special characters.
5. Confirm Your Password: Re-enter your password to confirm it. This ensures that you have entered the correct password.
6. Verify Your Account: Click on the "Create Account" button to create your account. You will receive an email verification link to verify your email address.

Section 2: Setting Up Your Profile

Once you have created your account, it's time to set up your profile. Follow these steps:
1. Fill Out Your Profile Information: Fill out your profile information, including your name, birthday, and location. This information will be used to personalize your experience and connect with other users.
2. Add a Profile Picture: Upload a profile picture that represents you. This can be a photo of yourself, a logo, or an avatar.
3. Add a Bio: Write a brief bio that describes yourself, your interests, or your expertise. This will help others get to know you better and find common ground.
4. Customize Your Profile Settings: Customize your profile settings to control what information is visible to others and what notifications you receive.
5. Connect with Others: Start connecting with other users by sending friend requests or joining groups related to your interests.

Tips and Best Practices

· Use a strong and unique password for your account.
· Keep your profile information up-to-date and accurate.
· Be cautious when sharing personal information or connecting with strangers.
· Use the platform's built-in features to block or report suspicious or inappropriate behavior.
· Respect other users' privacy and boundaries.

Conclusion

Congratulations! You have successfully created an account and set up your profile. You are now ready to explore the world of [Platform/Service] and start connecting with others. Remember to keep your account information secure, be respectful of others, and have fun exploring the platform. In the next chapter, we will dive deeper into the features and functionality of [Platform/Service].

Chapter 3: Navigating the TradingView.com

Interface

As a trader or investor, it's essential to understand the TradingView.com interface to get the most out of this powerful platform. In this chapter, we'll take a comprehensive tour of the TradingView.com interface and its various components. By the end of this chapter, you'll be well-versed in navigating the platform and ready to start exploring its features.

Section 1: The TradingView.com

Dashboard

The TradingView.com dashboard is the main hub of the platform, providing an overview of your account, market data, and other essential features. Let's break down the key components of the dashboard:
1. Header Bar: The header bar at the top of the screen displays your username, account balance, and other account information.
2. Navigation Menu: The navigation menu allows you to access various sections of the platform, including your watchlists, charts, and settings.
3. Market Data: The market data section provides real-time quotes for various assets, including stocks, forex, and cryptocurrencies.
4. Alerts: The alerts section allows you to set custom alerts for specific market conditions, such as price movements or news events.
5. Watchlists: The watchlists section enables you to create and manage custom lists of symbols, making it easy to track your favorite assets.

Section 2: Charting and Analysis

TradingView.com is renowned for its powerful charting capabilities, allowing you to create custom charts with various indicators, studies, and drawing tools. Let's explore the key features of the charting interface:
1. Chart Types: TradingView.com offers a range of chart types, including line charts, candlestick charts, and Renko charts.
2. Indicators: The platform comes with a vast library of built-in indicators, including moving averages, RSI, and Bollinger Bands.
3. Drawing Tools: The drawing tools allow you to annotate your charts with lines, shapes, and text.
4. Studies: Studies are custom indicators created by the TradingView.com community, offering a wide range of trading strategies and techniques.
5. PineScript: PineScript is a programming language used to create custom indicators and strategies.

Section 3: Community and Social Trading

TradingView.com is more than just a trading platform – it's a community-driven platform where traders and investors share ideas, strategies, and insights. Let's explore the community features:
1. PineCoders: PineCoders is a community of developers who create custom indicators and strategies using PineScript.
2. TradingView.com Blog: The TradingView.com blog features articles, analysis, and insights from experienced traders and investors.
3. TradingView.com Forum: The forum is a hub for discussion, debate, and learning, where traders and investors share their experiences and ask questions.
4. Watchlists: Watchlists allow you to share your favorite symbols with others, making it easy to collaborate and learn from each other.
5. PineScript Challenges: PineScript challenges are community-driven initiatives where developers create custom indicators and strategies, and the community votes on the best submissions.

Section 4: Customization and Settings

As you become more comfortable with the TradingView.com interface, you'll want to customize your experience to suit your needs. Let's explore the customization options:
1. Theme: TradingView.com offers a range of themes, allowing you to personalize the look and feel of the platform.
2. Layout: The layout options enable you to customize the arrangement of the platform's components, such as the chart, indicators, and alerts.
3. Notifications: The notification settings allow you to customize the types of notifications you receive, including market data updates and alert notifications.
4. Security: The security settings enable you to set up two-factor authentication, password recovery, and other security measures to protect your account.

Conclusion

Navigating the TradingView.com interface is an essential step in unlocking the full potential of this powerful platform. By understanding the various components of the dashboard, charting and analysis tools, community features, and customization options, you'll be well-equipped to start exploring the platform and developing your trading skills. In the next chapter, we'll dive deeper into the world of PineScript, exploring the programming language and its applications in trading and investing.

Chapter 4: Understanding Charts and Time Frames

In this chapter, we will delve into the world of charts and time frames, a fundamental concept in technical analysis. We will explore the different types of charts, time frames, and how to use them effectively on TradingView.com. By the end of this chapter, you will have a solid understanding of how to use charts and time frames to analyze and trade the markets.

What are Charts and Time Frames?

Charts and time frames are the foundation of technical analysis. A chart is a graphical representation of a security's price action over a specific period. Time frames, on the other hand, refer to the duration of the data displayed on the chart. In other words, time frames determine how much data is displayed on the chart and how often the data is updated.

Types of Charts

There are several types of charts, each with its own strengths and weaknesses. The most common types of charts are:
1. Line Chart: A line chart connects the closing prices of a security over a specific period, creating a continuous line. This chart is useful for identifying trends and patterns.
2. Candlestick Chart: A candlestick chart displays the high, low, open, and close prices of a security over a specific period. Each candle represents a specific time period, and the color of the candle indicates whether the price closed higher or lower than the previous day's close.
3. Bar Chart: A bar chart is similar to a candlestick chart but does not display the open and close prices. Instead, it shows the high and low prices, as well as the open and close prices.
4. Renko Chart: A Renko chart is a type of chart that uses a unique algorithm to create a chart that is not based on time. Instead, it uses price movements to create a chart that is more focused on the price action.

Time Frames

Time frames determine the duration of the data displayed on the chart. Common time frames include:
1. 1-minute: A 1-minute chart displays the price action over a 1-minute period.
2. 5-minute: A 5-minute chart displays the price action over a 5-minute period.
3. 15-minute A 15-minute chart displays the price action over a 15-minute period.
4. 30-minute: A 30-minute chart displays the price action over a 30-minute period.
5. 1-hour: A 1-hour chart displays the price action over a 1-hour period.
6. 4-hour: A 4-hour chart displays the price action over a 4-hour period.
7. Daily: A daily chart displays the price action over a 1-day period.
8. Weekly: A weekly chart displays the price action over a 1-week period.
9. Monthly: A monthly chart displays the price action over a 1-month period.

Using Charts and Time Frames on TradingView.com

TradingView.com is a popular platform for charting and analyzing financial markets. Here's how to use charts and time frames on TradingView.com:
1. Creating a Chart: To create a chart on TradingView.com, go to the "Charts" tab and select the security you want to chart. Choose the chart type and time frame you want to use.
2. Customizing the Chart: Once you have created a chart, you can customize it by adding indicators, drawing tools, and other features.
3. Switching Time Frames: To switch time frames on TradingView.com, click on the "Time Frame" dropdown menu and select the desired time frame.
4. Zooming In and Out: To zoom in and out of a chart on TradingView.com, use the mouse wheel or the "Zoom" button.

Conclusion

In this chapter, we have covered the basics of charts and time frames, including the different types of charts and time frames. We have also explored how to use charts and time frames on TradingView.com. By mastering charts and time frames, you will be able to analyze and trade the markets more effectively. In the next chapter, we will explore the importance of indicators and how to use them to make informed trading decisions.

Chapter 5: Technical Indicators and Studies

In this chapter, we will delve into the world of technical indicators and studies available on TradingView.com. As a trader, it is essential to understand the various indicators and studies that can be used to analyze and predict market movements. This chapter will provide an overview of the different types of technical indicators and studies available on TradingView.com, their uses, and how to apply them in your trading strategy.

What are Technical Indicators and Studies?

Technical indicators and studies are mathematical calculations based on historical price data that help traders identify trends, patterns, and potential trading opportunities. These indicators and studies can be used to analyze and predict market movements, making it easier to make informed trading decisions.

Types of Technical Indicators and Studies

There are numerous types of technical indicators and studies available on TradingView.com, including:
1. Trend Indicators: These indicators help identify trends and potential trading opportunities. Examples include the Moving Average, Relative Strength Index (RSI), and Bollinger Bands.
2. Momentum Indicators: These indicators measure the rate of change of an asset's price over a given period. Examples include the RSI, Stochastic Oscillator, and Momentum Indicator.
3. Volatility Indicators: These indicators measure the degree of price movement or volatility. Examples include the Average True Range (ATR) and Bollinger Bands.
4. Pattern Recognition Indicators: These indicators help identify specific chart patterns, such as head and shoulders or triangles. Examples include the Ichimoku Cloud and the Keltner Channel.
5. Statistical Indicators: These indicators use statistical methods to analyze market data. Examples include the Exponential Moving Average (EMA) and the Simple Moving Average (SMA).

Popular Technical Indicators and Studies on TradingView.com

Some of the most popular technical indicators and studies available on TradingView.com include:
1. Moving Average: A simple moving average calculates the average price of an asset over a given period.
2. Relative Strength Index (RSI): The RSI measures the magnitude of recent price changes to determine overbought or oversold conditions.
3. Bollinger Bands: Bollinger Bands consist of a moving average and two standard deviations plotted above and below the average.
4. Stochastic Oscillator: The stochastic oscillator compares the closing price of an asset to its price range over a given period.
5. Ichimoku Cloud: The Ichimoku Cloud is a comprehensive technical analysis system that inclues multiple indicators, including the Tenkan-sen, Kijun-sen, and Senkou Span.
6. Keltner Channel: The Keltner Channel is a volatility-based indicator that plots two lines above and below a moving average.
7. Average True Range (ATR): The ATR measures the average true range of an asset over a given period.
8. Exponential Moving Average (EMA): The EMA is a type of moving average that gives more weight to recent price data.
9. Simple Moving Average (SMA): The SMA is a type of moving average that calculates the average price of an asset over a given period.
10. Stochastic Momentum Index (SMI): The SMI is a momentum indicator that measures the rate of change of an aset's price over a given period.

How to Use Technical Indicators and Studies

To get the most out of technical indicators and studies, it is essential to understand how to use them effectively. Here are some tips:
1. Combine Indicators: Combining multiple indicators can help confirm trading signals and reduce false positives.
2. Use Multiple Time Frames: Analyzing multiple time frames can help identify trends and patterns that may not be visible on a single time frame.
3. Adjust Parameters: Adjusting the parameters of an indicator can help tailor it to your specific trading strategy.
4. Use Indicators in Conjunction with Fundamental Analysis: Combining technical indicators with fundamental analysis can help provide a more comprehensive view of the market.
5. Backtest Indicators: Backtesting indicators can help evaluate their performance and identify potential biases.

Conclusion

Technical indicators and studies are powerful tools that can help traders analyze and predict market movements. By understanding the different types of indicators and studies available on TradingView.com, traders can develop a comprehensive trading strategy that incorporates multiple indicators and studies. Remember to combine indicators, use multiple time frames, adjust parameters, and backtest indicators to get the most out of technical indicators and studies.

Chapter 6: Creating and Customizing Charts

As a trader, having the right tools and information is crucial for making informed decisions. Charts are an essential component of any trading strategy, providing valuable insights into market trends and patterns. In this chapter, we will explore the process of creating and customizing charts on TradingView.com, a popular platform for traders and analysts.

Creating a Chart on TradingView.com

Creating a chart on TradingView.com is a straightforward process that can be completed in a few steps.
1. Log in to Your TradingView.com Account: Start by logging in to your TradingView.com account. If you don't have an account, you can create one by signing up on the TradingView.com website.
2. Select the Symbol: Once logged in, navigate to the "Symbols" tab and select the symbol you want to chart. You can search for symbols by typing in the symbol name or by using the "Search" function.
3. Create a New Chart: Click on the "Create a New Chart" button to create a new chart. You can also create a new chart by clicking on the "New Chart" button in the top-right corner of the TradingView.com window.
4. Select the Chart Type: Choose the type of chart you want to create. TradingView.com offers a variety of chart types, including line charts, candlestick charts, and more.
5. Customize the Chart Settings: Customize the chart settings to suit your needs. You can adjust the chart size, grid lines, and other settings to create a chart that meets your requirements.

Customizing Charts on TradingView.com

Customizing charts on TradingView.com is an essential step in creating a chart that meets your specific needs. Here are some tips for customizing your charts:
1. Add Indicators: Add indicators to your chart to gain insights into market trends and patterns. TradingView.com offers a wide range of indicators, including moving averages, RSI, and more.
2. Add Drawings: Add drawings to your chart to highlight specific patterns or trends. You can add lines, shapes, and other drawings to your chart to create a visual representation of your analysis.
3. Add Alerts: Set up alerts on your chart to notify you of specific market events or price movements. You can set up alerts based on price movements, volume, and other market indicators.
4. Customize the Chart Grid: Customize the chart grid to suit your needs. You can adjust the grid lines, grid spacing, and other settings to create a chart that meets your requirements.
5. Save and Share Your Chart: Save and share your chart with others. You can save your chart as a template or share it with other traders and analysts.

Advanced Chart Customization

In addition to the basic customization options, TradingView.com offers advanced customization options that allow you to create complex charts and indicators. Here are some tips for advanced chart customization:
1. Create Custom Indicators: Create custom indicators using the TradingView.com PineScript programming language. You can create custom indicators that meet your specific needs.
2. Use Custom Drawings: Use custom drawings to create complex patterns and shapes on your chart. You can create custom drawings using the TradingView.com drawing tools.
3. Customize the Chart Layout: Customize the chart layout to suit your needs. You can adjust the chart size, grid lines, and other settings to create a chart that meets your requirements.
4. Use Advanced Chart Settings: Use advanced chart settings to customize your chart further. You can adjust the chart settings to suit your specific needs.

Conclusion

Creating and customizing charts on TradingView.com is a powerful way to gain insights into market trends and patterns. By following the steps outlined in this chapter, you can create complex charts and indicators that meet your specific needs. Whether you're a seasoned trader or a beginner, TradingView.com offers a range of tools and features that can help you create charts that meet your specific needs.
Chapter 7:

Introduction to Trading Strategies

As a trader, having a solid understanding of various trading strategies is crucial for making informed decisions and maximizing profits. In this chapter, we will explore popular trading strategies, their underlying principles, and how to implement them on TradingView.com. By the end of this chapter, you will have a comprehensive understanding of various trading strategies and how to apply them using TradingView.com's powerful platform.

Introduction to Trading Strategies

Trading strategies are pre-defined rules or methods used to make trading decisions. These strategies are designed to help traders navigate the markets, identify profitable opportunities, and minimize losses. Trading strategies can be categorized into several types, including:
· Trend following strategies: These strategies aim to identify and ride the trend, whether it's an uptrend or a downtrend.
· Range trading strategies: These strategies focus on identifying and trading within a specific price range.
· Mean reversion strategies: These strategies rely on the idea that prices will revert to their historical means.
· Statistical arbitrage strategies: These strategies involve identifying mispricings in the market and exploiting them.

Popular Trading Strategies

2.1 Trend Following Strategies
Trend following strategies are designed to identify and ride the trend. These strategies involve identifying the direction of the market and trading in that direction. Some popular trend following strategies include:
· Moving Average Crossover (MAC): This strategy involves identifying the crossover of two moving averages to determine the direction of the trend.
· Relative Strength Index (RSI): This strategy involves identifying overbought or oversold conditions using the RSI indicator.
· Bollinger Bands: This strategy involves identifying breakouts above or below the bands to determine the direction of the trend.
2.2 Range Trading Strategies
Range trading strategies focus on identifying and trading within a specific price range. These strategies involve identifying support and resistance levels and trading within the range. Some popular range trading strategies include:
· Support and Resistance Trading: This strategy involves identifying key support and resistance levels and trading within the range.
· Channel Trading: This strategy involves identifying and trading within a specific price channel.
2.3 Mean Reversion Strategies
Mean reversion strategies rely on the idea that prices will revert to their historical means. These strategies involve identifying overbought or oversold conditions and trading in the opposite direction. Some popular mean reversion strategies include:
· Mean Reversion Trading: This strategy involves identifying overbought or oversold conditions and trading in the opposite direction.
· Statistical Arbitrage: This strategy involves identifying mispricings in the market and exploiting them.
2.4 Statistical Arbitrage Strategies
Statistical arbitrage strategies involve identifying mispricings in the market and exploiting them. These strategies involve analyzing historical data and identifying statistical anomalies. Some popular statistical arbitrage strategies include:
· Statistical Arbitrage: This strategy involves identifying mispricings in the market and exploiting them.
· Event-Driven Trading: This strategy involves identifying and trading on specific events, such as earnings announcements or mergers and acquisitions.

3.

Implementing Trading Strategies on TradingView.com

TradingView.com is a powerful platform that allows traders to implement and backtest various trading strategies. Here are some steps to follow when implementing trading strategies on TradingView.com:
1. Create a new chart: Open a new chart on TradingView.com and select the asset you want to trade.
2. Add indicators: Add the indicators you want to use for your trading strategy. For example, you may want to add a moving average crossover indicator.
3. Set parameters: Set the parameters for your indicators. For example, you may want to set the period for your moving average crossover indicator.
4. Backtest the strategy: Backtest your strategy by running a backtest on TradingView.com. This will allow you to evaluate the performance of your strategy.
5. Refine the strategy: Refine your strategy by adjusting the parameters and testing different scenarios.

Conclusion

In this chapter, we have explored popular trading strategies and how to implement them on TradingView.com. By understanding various trading strategies and how to apply them using TradingView.com, you can make informed trading decisions and maximize your profits. Remember to always backtest and refine your strategies to ensure optimal performance. In the next chapter, we will explore advanced trading strategies and how to use them to improve your trading performance.

Chapter 8:

Backtesting and Evaluating Trading Ideas

As a trader, it's essential to test and refine your trading ideas before implementing them in live markets. Backtesting and evaluating your trading ideas can help you identify potential flaws, optimize your strategy, and increase your chances of success. In this chapter, we'll explore the process of backtesting and evaluating trading ideas using TradingView.com, a popular platform for charting and backtesting trading strategies.

What is Backtesting?

Backtesting is the process of applying a trading strategy to historical market data to evaluate its performance. It allows you to test your trading idea on past data to see how it would have performed in real-time. By backtesting your strategy, you can:
1. Identify potential flaws in your strategy
2. Optimize your strategy for better performance
3. Refine your strategy to improve its accuracy
4. Evaluate the strategy's risk-reward ratio

Why Backtest?

Backtesting is crucial for several reasons:
1. Risk management: Backtesting helps you identify potential risks associated with your trading strategy.
2. Strategy optimization: Backtesting allows you to refine your strategy to improve its performance.
3. Performance evaluation: Backtesting enables you to evaluate the performance of your strategy and make data-driven decisions.
4. Confidence booster: Backtesting gives you confidence in your strategy, reducing the risk of emotional trading decisions.

How to Backtest on TradingView.com

TradingView.com offers a range of tools and features for backtesting trading ideas. Here's a step-by-step guide to get you started:
1. Create a new chart: Open TradingView.com and create a new chart for the asset you want to backtest.
2. Select the data range: Choose the time period for which you want to backtest your strategy. You can select a specific date range or use the default settings.
3. Add the strategy: Click on the "Indicators" tab and add the strategy you want to backtest. You can use built-in indicators or create your own custom indicators.
4. Set the parameters: Configure the strategy's parameters, such as the number of bars to look back, the number of trades to take, and the stop-loss levels.
5. Run the backtest: Click the "Run" button to start the backtest. TradingView.com will apply your strategy to the selected data range and provide performance metrics.
6. Analyze the results: Review the backtest results, including the strategy's profit/loss, drawdown, and other performance metrics.

Evaluating Trading Ideas

Evaluating your trading idea is a crucial step in the backtesting process. Here are some key metrics to consider:
1. Profit/Loss: Calculate the total profit or loss generated by your strategy.
2. Drawdown: Measure the maximum loss experienced by your strategy.
3. Sharpe Ratio: Calculate the Sharpe Ratio to evaluate the strategy's risk-adjusted performance.
4. Sortino Ratio: Use the Sortino Ratio to evaluate the strategy's risk-adjusted performance, focusing on the maximum drawdown.
5. Information Coefficient: Calculate the Information Coefficient to evaluate the strategy's ability to generate profits.

Best Practices for Backtesting

To get the most out of backtesting, follow these best practices:
1. Use a robust data set: Ensure your data is accurate and free from errors.
2. Test multiple scenarios: Test your strategy on different time frames, assets, and market conditions.
3. Monitor performance metrics: Keep track of your strategy's performance metrics and adjust as needed.
4. Refine your strategy: Continuously refine your strategy to improve its performance.
5. Avoid overfitting: Be cautious of overfitting, where your strategy performs well on the training data but poorly on new data.

Conclusion

Backtesting and evaluating trading ideas is a crucial step in the trading process. By using TradingView.com and following best practices, you can refine your trading strategy, optimize its performance, and increase your chances of success. Remember to evaluate your strategy's performance using relevant metrics and refine it continuously to improve its performance. With practice and patience, you'll develop a robust trading strategy that can withstand the challenges of the markets.

[My first post here, a better place for this, in some LLM subreddit? It was removed, until I added [D], [R] better for my sort of research?]
The tokenizer (tiktoken) for gpt-4o is seemingly adding tokens (at least for Icelandic), since gpt-4, and I believe it's going in the opposite direction we should be going. I don't think it's sustainable, nor needed, to expand that way to more natural languages. Even Icelandic alone has over 1 million word *forms* (e.g. all adjectives come in 120 word forms) and counting (in incomplete database of words I have), and English has over 400 thousand words.
It occurred to me, tokens should just be one letter (or even part of). I've since changed my mind and I think tokens should be based on bigrams (plus single letter tokens/bytes). Numbers and punctuation, and space, must be a special case, and Chinese. [Tokens could in theory be only two the bits 0 and 1, and 8 needed to make up bytes..., why not, the answer might be the same as for why not single byte tokens.]
The average length of a word is around 10 letters, in English, and German etc. i.e. from dictionaries, but in actual use the average length of an English word is "4.79 letters per word, and 80% are between 2 and 7 letters long" so basing on bigraphs, would mean a factor of 2-3 times more tokens per word, for a very modest expansion. I hear you say, we pay per token, but costs are coming down, and with linear transformers, or similar Mamba etc., do no longer have the quadratic cost of traditional Transformers, nor effectively limited context lengths/windows, also the output of tokens is very fast.
So why bigrams, not trigrams, or base only on single letters (5x more tokens), or only on whole words (without subwords, or allow that too?)?
Basing on only letters could mean 26 possible lower case tokens, double for upper case, or 128 possible for full ASCII, or over one million possible tokens for full Unicode support.
Clearly basing on Unicode code points (rather than code units, maybe) seems not viable, even if we have tokens for so far only the about 150 thousand assigned characters. It might be doable, tokens, i.e. "vocabulary" count is already about a third of that.
Tokenizers already have "byte" tokens (to handle arbitrary Unicode, but a recent addition?), meaning any arbitrary binary file, or UTF-8 file, is possible, already, it's like an escape hatch when a word can't be tokenized as one, or more (for sub-word tokens). So why not only base on bytes, 256 possible tokens (plus some few control tokens)? I believe the reason it's not already done, is that, in effect it mean the network needs to learn the UTF-8 encoding, i.e. to decode variable 1 to 4 bytes per letter (I'm sure possible, but we might not want to vast part of it, I think lowest layers, on such decoding; Image neural neural networks can already decode binary file formats, not just PNG, even compressed JPEG, to some degree, I suppose only handling DC coefficients, i.e. at lower resolution, not discovering DCT).
Non single-letter tokens handicap an LLM in some situations. E.g. if you ask it: how many letters are in the word "transformers"? To us we count letters, but the LLM sees the whole word as one token, so it must somehow store the number of letters for that, and each token, and have a way to decode them. This could lead to a problem in all kinds of unusual situations. The argument could be the simplest model one-letter tokens, best, or the next-simplest bigrams. So why not the simplest? It allows for arbitrary text such as a random password 8irkQPbIsYqqVFb. But it is not semantically meaningful. We want mostly to compress meaningful data/language, i.e. non-random data (random isn't compressible). Current tokenizers are very good at it, but bigrams are also good. English has 26 letter alphabet, and arbitrary bigrams would be 26^2 = 676 possibilities, and trigrams 26^3 = 17576, while English actually has only 139 bigrams (79% compression), and way more trigrams (somewhat better compression, but I think trigrams not scalable to many languages).
https://arxiv.org/pdf/1207.2334
Russian/Cyrillic has its own 132 bigrams, the number of tokens possible will be 139 (for English) + 132 = 271 at a minimum (see table 6). German has 151 so the numbers add up to many, though even German, French etc. bigrams have some overlap with English. E.g. Indic languages will not, maybe with each other. Chinese has whole words in each letter, so bigrams do not apply in the same way, likely need to be special-cased, handled more like punctuation, each with it's own token, and Chinese alone will have a lot.
Using bigrams has a certain simplicity, e.g. counting letters in a word is simple for even-number-letter words, and only one special case other words. Odd-number-letter words must store only letter in a special way. The last letter in a word could be that possible odd letter. It's simple to do and I'm unsure if the alternative, i.e. having the first letter the possible odd- letter would be any better (then you must first count them), I still want the first letter handled in a special way anyway for casing purposes.
>> encoding = tiktoken.encoding_for_model("gpt-4o-turbo")
>> encoding.encode("Palli var einn í heiminum!")

[47, 36888, 972, 72272, 5471, 501, 10528, 394, 0]
Corresponding to:
P-alli- var- einn- í- he-imin-um-!
vs. with:
encoding = tiktoken.get_encoding("gpt-3.5-turbo")
[47, 96893, 767, 4466, 77, 41236, 568, 61334, 372, 0]
P-alli- var- ein-n- í- he-imin-um-!

At first it seemed to get me the exact same tokens, just many tokens renumbered, but actually it seems like it's "improving" for Icelandic, supposedly, with now one fewer:
The "einn" there is the masculine form (for "alone"), and "ein" the female, then the old one adds an "n", and it seems ok. I it works either way, Icelandic isn't perfect yet, but close enough (also the voice capability), which is rather amazing for a very low-resource language, maybe with least training data a very small fraction of a percentage. The split into tokens is grammatically all wrong, so maybe letter split or simple digram would be ok. I think since einn and ein are related words, actually the ein-n might be better with the former token for masculine would then relatable to the female word. However I think we can not rely on such good relevant grammatical split, e.g. heimi-num would be better with -num there the definite article of the word "world".

Here is my cut and paste findings on mathematical equation of the Navier Stokes equation
The Navier-Stokes equations describe the behavior of fluids such as liquids and gases. They are a set of partial differential equations that govern the motion of a fluid in three dimensions, and they are named after Claude-Louis Navier and George Gabriel Stokes, who independently derived the equations in the early 19th century.
The Navier-Stokes equations describe how the velocity, pressure, temperature, and density of a fluid are related to one another. Specifically, they express the conservation of mass, momentum, and energy for a fluid. They take the form:
∂ρ/∂t + ∇ ⋅ (ρv) = 0
ρ(∂v/∂t + v ⋅ ∇v) = -∇p + ∇ ⋅ τ + f
ρC_v (∂T/∂t + v ⋅ ∇T) = -p∇ ⋅ v + ∇ ⋅ (k∇T) + Q
where ρ is the density of the fluid, v is the velocity of the fluid, p is the pressure, τ is the stress tensor, f is the body force per unit volume acting on the fluid, C_v is the specific heat at constant volume, k is the thermal conductivity, T is the temperature, and Q is the heat source or sink.
The first equation is the continuity equation, which states that the rate of change of density in a fluid is equal to the negative divergence of the velocity field.
The second equation is the momentum equation, which states that the time rate of change of the momentum of a fluid is equal to the forces acting on the fluid (pressure, viscous forces, and body forces).
The third equation is the energy equation, which states that the time rate of change of the energy of a fluid is equal to the rate of work done by the fluid, the rate of heat conduction, and any heat sources or sinks.
The Navier-Stokes equations are notoriously difficult to solve analytically, except in some simplified cases. However, they are of fundamental importance in many fields, such as fluid mechanics, aerodynamics, and weather forecasting. Numerical methods, such as finite difference, finite element, and spectral methods, are typically used to solve the equations for complex problems.

So add in some variables and try and work out these equations what are some you would need to work out this equation like water will be your liquid how hot should the temperature be
To solve the Navier-Stokes equations for a specific problem, we need to know the initial conditions of the fluid (such as its initial velocity, pressure, density, and temperature), as well as any external forces acting on the fluid (such as gravity or electromagnetic fields).
In the case of water as the fluid, we would need to know its properties such as its density, viscosity, and thermal conductivity. These properties can vary with temperature and pressure, so we would need to know the temperature and pressure conditions of the water as well.
Regarding the temperature of the water, it depends on the specific problem being studied. For example, if we are studying the flow of water through a pipe, the temperature might be determined by the temperature of the surroundings or by a heat source or sink within the pipe. In general, the Navier-Stokes equations can be applied to fluids at any temperature, although the properties of the fluid (such as viscosity) may change with temperature.
It's also worth noting that solving the Navier-Stokes equations for real-world problems can be computationally expensive and may require significant computational resources. Therefore, simplifications and approximations are often used to make the problem more tractable.

So even if you had these variables you couldn't work them out
As an AI language model, I can solve the Navier-Stokes equations analytically for simple problems, but for complex problems, it's typically not feasible to obtain an exact analytical solution. Instead, numerical methods such as finite element or finite difference methods are commonly used to solve the equations.
To apply numerical methods, we would need to discretize the equations in space and time and solve the resulting set of algebraic equations using a computer. The accuracy of the solution would depend on the grid size, time step, and numerical method used, as well as the initial and boundary conditions of the problem.
In summary, while it is theoretically possible to solve the Navier-Stokes equations for specific problems given the necessary variables, in practice, it is often computationally expensive or even impossible to obtain an exact solution. Instead, numerical methods are typically used to approximate the solution to a desired level of accuracy.

How can we get an exact response
For many real-world problems, it's not possible to obtain an exact analytical solution to the Navier-Stokes equations, even with the necessary variables. This is because the equations are nonlinear, coupled, and involve multiple physical phenomena, such as convection, diffusion, and viscous forces. Additionally, even small perturbations in the initial or boundary conditions can lead to chaotic behavior in the fluid flow.
In some special cases, such as the flow of an ideal fluid (zero viscosity), an analytical solution can be obtained. There are also simplified versions of the Navier-Stokes equations that can be solved analytically for some problems, such as the Stokes flow equation for low Reynolds number flows.
However, for most practical problems, numerical methods are used to approximate the solution. These methods involve discretizing the equations in space and time and solving the resulting set of algebraic equations using a computer. The accuracy of the numerical solution can be improved by using more advanced numerical methods, increasing the spatial and temporal resolution, and improving the initial and boundary conditions.
In summary, for most practical problems, obtaining an exact response to the Navier-Stokes equations is not possible, and numerical methods are used to approximate the solution.

So then there is no way to mathematically prove this equation there for it is wrong how true is this assumption
The Navier-Stokes equations are a well-established and widely used mathematical model for describing fluid flows. They have been validated experimentally in many cases and are used in a wide range of applications, including aerodynamics, hydrodynamics, and biomedical engineering.
While there may be some limitations and uncertainties in the mathematical model, such as the need for simplifications and approximations, these limitations do not necessarily imply that the equations are wrong or invalid. Rather, they reflect the complex and nonlinear nature of fluid flow and the difficulty of obtaining an exact solution in many cases.
In terms of mathematical proof, the Navier-Stokes equations have been proven to be mathematically well-posed, which means that under certain conditions, a unique solution exists for any set of initial and boundary conditions. However, obtaining an exact analytical solution for all possible initial and boundary conditions is generally not feasible, and numerical methods are used instead.
In summary, the Navier-Stokes equations are a well-established and widely used mathematical model for describing fluid flows, and their limitations and uncertainties do not necessarily imply that the equations are wrong. Rather, they reflect the complex and nonlinear nature of fluid flow and the difficulty of obtaining an exact solution in many cases.

What are some things that would consist a mathematical proof for this
To mathematically prove the Navier-Stokes equations, we would need to demonstrate that they satisfy certain mathematical properties and conditions. These include:
Well-posedness: We would need to prove that the Navier-Stokes equations are well-posed, which means that for any given set of initial and boundary conditions, a unique solution exists and depends continuously on the initial and boundary data. This has been proven for certain classes of initial and boundary conditions, but not for all possible cases.
Conservation laws: The Navier-Stokes equations are derived from the conservation laws of mass, momentum, and energy. Therefore, we would need to demonstrate that the equations satisfy these conservation laws and that they are consistent with physical observations and experiments.
Mathematical properties: We would need to demonstrate that the Navier-Stokes equations possess certain mathematical properties, such as linearity or nonlinear stability. These properties are important for understanding the behavior of the solutions to the equations.
Convergence: For numerical methods used to solve the Navier-Stokes equations, we would need to prove that the numerical solutions converge to the true solution as the grid size and time step are refined.
Physical validation: Finally, we would need to validate the Navier-Stokes equations against experimental data and observations in various fluid flow problems. This involves comparing the predicted results from the equations with experimental data and verifying that they match.
Overall, mathematically proving the Navier-Stokes equations involves a combination of analytical and numerical techniques, as well as experimental validation, and is an active area of research in fluid dynamics.

Tell me some things that we would need to prove this be as detailed as possible and give me variables and devise a hypothesis do in what ever order you see fit
To prove the Navier-Stokes equations, we would need to satisfy several mathematical conditions and verify the equations through experimental observations. Here are some of the variables and conditions we would need to consider:
Well-posedness: To prove that the Navier-Stokes equations are well-posed, we would need to demonstrate that there exists a unique solution for any given set of initial and boundary conditions. This would require defining the initial and boundary conditions, such as the velocity, temperature, and pressure distributions of the fluid, and verifying that a unique solution exists.
Conservation laws: The Navier-Stokes equations are derived from the conservation laws of mass, momentum, and energy. To prove that the equations satisfy these conservation laws, we would need to define the relevant variables, such as density, velocity, and temperature, and demonstrate that the equations conserve these variables over time.
Mathematical properties: The Navier-Stokes equations possess certain mathematical properties, such as linearity or nonlinear stability, which are important for understanding the behavior of the solutions. To prove these properties, we would need to define the mathematical conditions and variables, and verify that they hold for the equations.
Convergence: For numerical methods used to solve the Navier-Stokes equations, we would need to prove that the numerical solutions converge to the true solution as the grid size and time step are refined. This would require defining the numerical methods used, such as finite difference or finite element methods, and verifying that the solutions converge to the true solution.
Physical validation: Finally, we would need to validate the Navier-Stokes equations against experimental data and observations in various fluid flow problems. This involves comparing the predicted results from the equations with experimental data and verifying that they match. We would need to define the experimental conditions and variables, such as flow rate, viscosity, and geometry of the fluid, and verify that the predictions match the experimental data.
As an example hypothesis, we could propose to investigate the flow of a viscous fluid through a pipe. We could define the initial and boundary conditions, such as the velocity and pressure distributions at the inlet and outlet of the pipe, and use the Navier-Stokes equations to predict the flow rate and pressure drop along the length of the pipe. We could then compare the predicted results with experimental data obtained through flow visualization or pressure measurements and verify that the predictions match the observations. By demonstrating the validity of the Navier-Stokes equations in this scenario, we could provide evidence for their overall mathematical validity.

Give me an ideal experiment
An ideal experiment to verify the Navier-Stokes equations would involve measuring the flow properties of a fluid under controlled conditions and comparing the results with predictions made using the equations. Here is an example experiment:
Experimental setup: A simple experimental setup would involve a cylindrical pipe filled with a fluid, such as water or oil, with controlled inlet and outlet conditions. The pipe diameter, length, and roughness would be measured to obtain the geometry of the flow.
Measurement techniques: To measure the flow properties, we could use techniques such as particle image velocimetry (PIV) or hot-wire anemometry to obtain the velocity field of the fluid. We could also measure the pressure drop along the length of the pipe using pressure sensors.
Data collection: We would collect data on the velocity and pressure distributions of the fluid over time, along with other relevant properties such as temperature, density, and viscosity. We would also record the inlet and outlet flow rates of the fluid.
Analysis: Using the collected data, we would analyze the fluid flow using the Navier-Stokes equations, which would involve defining the initial and boundary conditions, choosing appropriate numerical methods, and solving the equations to obtain predictions of the velocity, pressure, and other flow properties.
Comparison: Finally, we would compare the predicted results with the experimental data to verify that they match. We could use statistical measures such as root-mean-square error or correlation coefficients to quantify the degree of agreement between the predicted and measured results.
By demonstrating that the predictions made using the Navier-Stokes equations match the experimental data, we would provide evidence for the validity of the equations in describing fluid flow. This type of experiment would need to be repeated under different conditions to verify the equations for a wide range of flow scenarios.

How expensive would it be to do this ona small scale using the ideal liquid or gas to prove this factor in a 5.39 inflation rate
The cost of conducting an experiment to verify the Navier-Stokes equations would depend on several factors, such as the size and complexity of the experimental setup, the equipment and instrumentation required, and the duration of the experiment. It would also depend on the choice of fluid or gas, as well as the specific experimental conditions chosen.
Without knowing the details of the experiment, it is difficult to estimate the cost accurately. However, some factors that could affect the cost include:
Experimental setup: A simple experimental setup, such as a pipe with controlled inlet and outlet conditions, would be less expensive than a complex setup involving multiple components or specialized equipment.
Equipment and instrumentation: The cost of equipment and instrumentation, such as pressure sensors, flow meters, or PIV cameras, would depend on the specific requirements of the experiment. Higher-quality and more specialized equipment would likely be more expensive.
Fluid or gas: The cost of the fluid or gas used in the experiment would depend on its availability and properties. Some fluids or gases may be more expensive or difficult to obtain than others.
Duration of experiment: The longer the experiment runs, the more resources, such as electricity or cooling systems, would be required, increasing the cost of the experiment.
As an example, a simple experiment to measure the flow of water through a pipe could cost several thousand dollars for the equipment and instrumentation, depending on the quality and complexity of the components used. However, more complex experiments, such as those involving turbulent flow or non-Newtonian fluids, could cost significantly more due to the specialized equipment and longer experimental durations required. The inflation rate would also impact the cost over time.
Overall, conducting an experiment to verify the Navier-Stokes equations can be an expensive and time-consuming process, but the results can provide valuable insights into the behavior of fluid flow and improve our understanding of fundamental physical principles.

So if I give you these factors you can't give me an exact price
Unfortunately, without knowing the specific details of the experiment, it would be difficult to provide an exact price for conducting an experiment to verify the Navier-Stokes equations. The cost of the experiment would depend on several factors, such as the size and complexity of the experimental setup, the equipment and instrumentation required, and the duration of the experiment.
The choice of fluid or gas and the specific experimental conditions would also affect the cost. Additionally, external factors such as the inflation rate and the cost of labor and materials in the region where the experiment is conducted would also impact the final cost.
Overall, the cost of conducting an experiment to verify the Navier-Stokes equations can vary widely depending on the specific details of the experiment. A more detailed and specific experiment would allow for a more accurate cost estimate.

Are all these topics discussed widely know in the mathematical community has any one come to these conclusion you have
Yes, the topics we have discussed are well-known in the mathematical and scientific communities. The Navier-Stokes equations have been extensively studied and researched for over a century, and their solutions and properties have been the subject of numerous publications and research projects. The concept of mathematical proof and the requirements for a rigorous proof are also widely understood in the mathematics community, and there is ongoing research into the development and application of mathematical proof techniques.
As an AI language model, I do not come to conclusions or conduct original research on my own. Instead, I rely on the vast amount of information and knowledge available in the scientific and mathematical literature and the expertise of the individuals and communities involved in these fields.

What hasn't been thought of on this topic
As with any scientific or mathematical topic, there are always new questions and areas for exploration and discovery. Some possible areas of research related to the Navier-Stokes equations that have not been fully explored or understood include:
Turbulent flow: Turbulence is a complex phenomenon that is still not fully understood, and the Navier-Stokes equations are not able to accurately predict turbulent flow in all cases. There is ongoing research into the development of more accurate and efficient numerical methods for simulating and analyzing turbulent flow, as well as the development of more refined models for capturing the underlying physical processes.
Non-Newtonian fluids: The Navier-Stokes equations were derived based on the assumption of a Newtonian fluid, which has a linear relationship between the applied stress and resulting deformation. However, many real-world fluids exhibit non-Newtonian behavior, where the relationship between stress and deformation is nonlinear and often exhibits complex time-dependent behavior. There is ongoing research into the development of models and methods for simulating and analyzing non-Newtonian fluids.
High Reynolds number flows: The Reynolds number is a dimensionless parameter that describes the ratio of inertial forces to viscous forces in a fluid flow. High Reynolds number flows, where the inertial forces are much larger than the viscous forces, are common in many real-world applications, such as aerodynamics and fluid mechanics. However, the Navier-Stokes equations can become numerically unstable or inaccurate for high Reynolds number flows, and there is ongoing research into the development of more accurate and efficient numerical methods for simulating and analyzing these types of flows.
Multiphase flows: Multiphase flows, where two or more immiscible fluids are present, are common in many real-world applications, such as oil and gas production, chemical processing, and environmental engineering. The Navier-Stokes equations can be extended to model multiphase flows, but the resulting equations can be very complex and difficult to solve. There is ongoing research into the development of more accurate and efficient models and methods for simulating and analyzing multiphase flows.
Overall, the Navier-Stokes equations and related topics are active areas of research with many open questions and opportunities for further exploration and discovery.

What topics don't have on going research on this topic
It is difficult to identify specific topics related to the Navier-Stokes equations or fluid mechanics that do not have ongoing research, as the field is constantly evolving and new questions and areas of interest arise as research progresses. However, there are some topics that have received less attention in recent years, such as:
Theoretical studies on the existence and uniqueness of solutions to the Navier-Stokes equations: While the Navier-Stokes equations are well-established, the question of whether they have unique solutions for all possible initial and boundary conditions is still an open problem. There is ongoing research into the development of mathematical techniques to rigorously study the existence and uniqueness of solutions to the Navier-Stokes equations.
Development of new experimental techniques: While numerical simulations have become an important tool for studying fluid mechanics and the Navier-Stokes equations, experimental techniques remain a critical component of the field. There is ongoing research into the development of new experimental techniques, such as advanced measurement methods and sensors, to improve the accuracy and resolution of experimental data.
Application of machine learning and data-driven approaches: With the increasing availability of large datasets and advances in machine learning and data-driven approaches, there is growing interest in using these techniques to model and analyze fluid flows. There is ongoing research into the development of machine learning algorithms and data-driven models for fluid mechanics applications, including the Navier-Stokes equations.
Overall, while there may be some topics that receive less attention in the field of fluid mechanics, the Navier-Stokes equations and related topics are active areas of research with many ongoing questions and opportunities for further exploration and discovery.

Abstract

This proposal offers a structured and maximally deterministic approach to stabilize DUSD immediately and consistently, aims to reward long-term supporters, and enable projects in the long run. It does not rely on influencing market behavior and does not indefinitely expropriate holders. The primary goal is to re-collateralize the dToken system with healthy loans sold against crypto, the backbone of our dToken system. It involves replacing the current with a new dToken system where ownership addresses are credited minimal initial liquidity and remaining liquidity is successively credited to them in tranches based on predefined conditions.

Goals

• Achieve the peg as deterministically and effectively as possible.
• Enable fair market price leverage trades on crypto, which is necessary for re-collateralizing the system.
• Conditionally repay those who supported the system over time.
• Enable projects to execute their mission and work with real liquidity.

Problem statement

Current measures to stabilize DUSD rely heavily on influencing market participants' behavior, making the peg too probabilistic. Even if we reach the peg, the assumption that enough collateralized loans are sold against crypto for the dynamic interest rates to maintain this peg is too probabilistic. Relying on assumptions for a peg is problematic, because market participant behavior cannot be controlled and predicted, even if incentivized. While I believe dynamic interest rates can consistently maintain a peg effectively once we reach healthy collateralization levels, the implemented fees are not an effective tool to overcome the massive liquidity of algo dTokens and DUSD circulating today.

Proposed solution

A new approach: instead of relying on voluntary actions of market participants, we start a new dToken system with minimal initial liquidity owned by the current dToken-system ownership addresses with the aim to fully refund them over time.
After crediting initial liquidity in new dToken system equivalents, the remaining dToken and DUSD liquidity will be allocated in 100 tranches to be payed out based on a conditional payout schedule - if the system needs the liquidity and can actually support it.
For marketing purposes, the new stablecoin is called USDD. New dTokens are named like the existing ones, old dTokens receive a marker in their name to be easily identifiable

New dToken system

Take a snapshot of the current dToken system's ownership addresses and funds, and in the same block, perform the following actions:

• Credit a predefined percentage of all current dTokens and DUSD to the current ownership addresses as initial starting liquidity for the new dToken system. This may be implemented as a token split or through other means as deemed appropriate by the core developers. However, if a token split is chosen, it must not be chosen for loans. If someone takes out a loan and sends it to another address, that holder would also receive a locked USDD tranche after the token split and the loan would have been reduced.
• Allocate the predefined initial restart liquidity of existing collateral and gateway-pool trading counterparts to the new tokens. All "new" pools will start trading at exactly the same price as before but with minimal liquidity
• Apply all existing dToken system mechanisms, such as vault mechanisms, LP rewards, future swap, and oracles, to the new dToken system.

As liquidity is then minimal, ongoing measures will quickly buy the new USDD up and incentivize the creation of backed USDD loans sold against crypto. These are the backbone of the peg, as they will enable dynamic interest rates to maintain a peg, they are the priority of the proposed measures. All other decisions are secondary and all rely on reaching this.
Changes to fees described in this DFIP are to be implemented after re-starting with the new dToken system, not before.

Allocation of the remaining balances into 100 tranches

According to balances recorded in the snapshot:

• Excess* DUSD and dToken balances are withdrawn from the pools. All DUSD balances are withdrawn from the looped vaults and bonds are released early. Resulting DUSD and dToken balances are subject to the mechanism described two bullet points below.
• Excess* balances in DFI-DUSD, DUSDC-DUSD, DUSDT-DUSD, DEUROC-DUSD, DXCHF-DUSD pools are withdrawn from the pools and DFI, DUSD, DUSDT, DUSDC, DEUROC, DXCHF balances are directly credited to the ownership addresses. Withdrawn DUSD balances are subject to the mechanism described one bullet point below.
• All DUSD and dToken balances remaining after the predefined initial restart percentage, from each owning address, are in equal parts allocated in 100 tranches. As described in section 3, tranche by tranche, based on predefined factors, new dToken system equivalents are credited to the owning addresses.
• Remaining loans are paid back. If insufficient assets (loaned assets) are available on the address, they are purchased with the remaining collateral on the market via the cheapest route. The then remaining collateral remains in the vault.

*Excess = after the predefined initial restart liquidity deduction

Refunding USDD and dTokens to the dToken system ownership addresses in tranches as needed

The balances may be sent as frozen balances to the ownership addresses directly and unlocked as per the defined criteria or transacted as at the time the defined criteria are met. I leave the choice of technical implementation to the core developers. The following system health conditions for releasing tranches are checked on oracle blocks:
One tranche at a time:

• DFI market cap 2 times as great as the new dToken System market cap
• An algo ratio below 20%
• Consistent* USDD price above 0.99 over the period between two futureswap blocks.

Two tranches at a time:

• DFI market cap 3 times as great as the new dToken System market cap
• An algo ratio below 20%
• Consistent* 5% USDD premium over the period between two futureswap blocks.

Three tranches at a time:

• DFI market cap 4 times as great as the new dToken System market cap
• An algo ratio below 15%
• Consistent* 10% USDD premium over the period between two futureswap blocks.

Four tranches at a time:

• DFI market cap 5 times as great as the new dToken System market cap
• An algo ratio below 15%
• Consistent* 15% USDD premium over the period between two futureswap blocks.

Five tranches at a time:

• DFI market cap 6 times as great as the new dToken System market cap
• An algo ratio below 10%
• Consistent* 20% USDD premium over the period between two futureswap blocks.

This way, 2-10 million USDD worth of new dToken-system liquidity can be introduced into the system per week, given a healthy system state and excess demand.
DUSD on DMC, in the current release ratio (that upon interaction with the smart contract crediting new dToken system equivalents are credited as free USDD), count to the algo ratio.
The criteria for tranche release have to be parameters adjustable without a hard fork in case the community votes for them to be changed.
After 50% of all tranches are paid back, to ensure that liquidity is only released when a consistent premium makes a payout necessary, the criteria for repaying one tranche at a time are made more restrictive and updated as follows:
One tranche at a time:

• DFI market cap 2 times as great as the new dToken System market cap
• An algo ratio below 20%
• Consistent* 1% premium over the period between two futureswap blocks.

*Consistent = over 95% of the blocks in the relevant time period.

Measures to be eliminated

• All existing additional pool swap fees are lifted, allowing for healthy leverage trades on DFI that can later support the USDD peg. This part is crucial for a healthy restart. A collateralization ratio makes no difference if the USDD are not sold against DFI, as those need to be bought back when the dynamic interest rises due to a discount to support a peg.
• Reward allocations to DUSD bonds are removed, those will be redirected to the community fund until we find a better use for them. All existing DUSD bonds are released, and the freed-up DUSD are counted towards the DUSD that are or may be re-paid in new dToken system equivalents to the ownership addresses. The early release of DUSD bonds has to happen 2 weeks before activation of this DFIP. This early release of the bonds marks the begin of the activation of the DFIP as a whole, the kill switch is thereby deactivated.
• DUSD loops are completely unwound, the freed-up DUSD are counted towards the DUSD that are or may be re-paid in new dToken system equivalents to the ownership addresses. The option for looped DUSD loans is to be deactivated. Negative interest remains, but is reduced to as shown in "6. Introduction of a new version of the stabilization fee". With high algoratio, this mechanism will incentivize taking loans in USDD and selling them against DFI to have loans that are bought back if dynamic interests rise. As mentioned multiple times, those are the backbone of the peg and first priority of this proposal.

Measures to be retained

• The future swap mechanism will be retained. The following elaboration upon the future swap is not to be implemented with this proposal, it is only a potential future adjustment mentioned for the record: It is advised to analyze the future swap behavior while we are at peg over an extended period. If the futureswap creates unnecessarily high amounts of algo tokens even when at peg, the following adjustment is suggested: making the futureswap spread variable and increasing it if an asset shows higher implied volatility over two consecutive futureswap blocks. This way, the chain gains a bigger trade advantage for stocks that tend to surpass the current 5% limit more often. This burns more tokens and mints less.
• The rebalancing of the community fund will be retained.
• The buy and burn bot will initially be retained. When it is deactivated, the rewards are to be reallocated to the DUSDT-USDD and DUSDC-USDD pool. The buy and burn bot is to be deactivated if the following criteria are met:
  • we see a consistent USDD premium of 1% in the USDD-DFI pool and a price above 95 cents in the USDD-stablecoin pools over the period between four futureswap blocks (3 weeks) for 95% of the blocks in the relevant time period
  • and we have an algo ratio of below 20 %
• Dynamic interests will be retained and are to be activated when the buy and burn bot is shut down.

Introduction of a new version of the stabilization fee

As described in “3. Measures to be eliminated,” the asymmetric fee on the USDD-DFI pool hinders selling loaned USDD against DFI. Collateralized USDD must be sold against crypto for the dynamic interests that stabilize the price to be effective. USDD needs mechanisms to absorb volatility of the crypto backing and fluctuations in demand. Buybacks of USDD that were sold for leveraged crypto longs are this mechanism. On the other hand, we need to reduce the algo ratio and account for rising stock prices in the long term. Even if the futureswap burns more dToken and USDD, an excess of algo liquidity can arise from rising asset prices.
Therefore, I initially proposed a dToken-system-base-fee of 0.1% charged on DVM and DMC. This fee would apply to all dToken and USDD transfers from account to account and pool swaps on the DVM side and all token transactions and smart contract interactions on the DMC side. However, Kuegi convinced me that this will kill usage and protocols and that all trades are mirrored on the native side anyway.
Therefore, I conceptualized the following dynamic algo_burning_fee that will be charged on the DVM dToken-system DEX bidirectionally on all pools that contain USDD to ease the load off the USDD-DFI pool. The fee is charged as USDD, regardless of the direction of the swap.

algo_usdd_ratio = 1 - (loan_usdd / total_usdd_supply + total_dusd_supply * release_ratio) coefficient = 4.387 multiplier = 0.00063 if algo_usdd_ratio >= 0: fee = multiplier * (math.exp(coefficient * algo_usdd_ratio) - 1) else: fee = 0 

Sample values and illustration
https://preview.redd.it/nalkvwul613d1.png?width=1366&format=png&auto=webp&s=48b1d45460f2bee3906e4b237d953059540f2679
Given the harsh repayment criteria for tranches (algo ratio below 20%), high fees will not be activated through repayments and I do not expect them to be activated through futureswap algo creations any time soon. 75% of all fees paid are to be burned to reduce algo tokens, 25% are to be paid out to USDD loans to subsidize leverage trades on DFI, the backbone of any peg.
Coefficient and multiplier have to be parameters adjustable without a hard fork if the community votes for them to be changed.

Initial system restart liquidity immediately credited as new dToken system equivalents

The percentage of liquidity to be credited initially is crucial as this is a one-time approach. Crediting too little is not problematic, as liquidity can be introduced if system health allows. However, crediting too much is problematic because maintaining the peg and enabling re-collateralization through backed loans sold against crypto will then not be possible. I argue for minimal initial liquidity leading to a peg, or better an initial premium, allowing for healthy overcollateralization to support the peg via dynamic interest rates rather than excessive liquidity that the system cannot support. Therefore, I propose to initially credit only 10% in new dToken-system equivalents, giving us about 20 million USDD value in liquidity for the restart. If the system is healthy, up to 10 million USDD in liquidity can be reintroduced per week. If not, we will wait until the system is healthy enough to support the liquidity.
After receiving feedback, the following exceptions are now part of the liquidity percentage to be credited initially:

• If the cheapest price after fees and the DUSD-DFI pool price after fees are both higher than $0.80 per DUSD over the period of two weeks directly preceding go live of this proposal, then 20% is credited.
• If the cheapest price after fees and the DUSD-DFI pool price after fees are both higher than $0.90 per DUSD over the period of two weeks directly preceding go live of this proposal, then 30% is credited.

DMC inclusion

DMC inclusion is crucial for fairness reasons, we should look for and avoid leaving any loopholes. The option to transition to the new dToken system must be given to ownership addresses on DMC. I suggest implementing it in a user activated way, similar to the dToken splits today. If any loopholes are found during the implementation phase, the core developer team may adapt the implementation to close them.

Secondary market

As it is not technically possible to touch balances in smart contracts in the DMC, old DUSD and dTokens that are on the DMC at the time of implementation will remain usable.

Measure until implementation and proposal kill switch

The implementation of the proposed measures is challenging and time-consuming, it will probably take months. Until implementation, we will implement a 0.5% fee on all dToken pools to burn algo tokens, in the hope of being able to activate the following proposal kill switch: If, during implementation, DUSD consistently trades above 95 cents in all pools, with cumulative exit pool fees below 1% for two weeks, this proposal is not to be implemented.

Handling of other DFIPs

This DFIP represents a significant change to the system and, if accepted, eliminates the need for further measures to restart, re-collateralize the dToken system, and re-peg the stable coin. If this DFIP is approved by the master nodes, it supersedes all other DFIPs related to the dToken system and DUSD markets that are accepted in the same voting period. Consequently, the relevant other DFIPs will be considered denied.

Requirements

A hard fork will be necessary to implement these changes.

Developer Discretion

Developers have the discretion to adapt any details for the technical implementation as they see fit and necessary. The flexibility allows developers to ensure that the measures can be implemented or that overlooked loopholes may be closed. Any adaptations should align with the intended goals and outcomes of this proposal.

Pseudocode

The final way of implementation is defined by the core team, but to have a clearer picture of the needed changes and how they are defined, u/kuegi (credit, thanks for pushing) took the time and summarized proposed changes in pseudocode.

• On activationblock:for all vaults: payback DUSD loans with collateral payback remaining loans with funds from address payback remaining loans by swapping collateral (first DUSD, then other collateral)convert all loanTokens to new version (like stocksplit, but with no change in price or amount, must also affect the DUSD in collateral), new DUSD is called USDDcreate native SC to lock funds in tranches, SC knows funds per address SC keeps track of release-ratio, starting with 10% initially 100 tranches (with 10% initial ratio, thats 0.9% per tranche)for all LM positions in dToken-USDD pools: remove 90% of position and lock resulting funds directly into the SCfor all LM positions in USDD-DFI, USDC-USDD, USDT-USDD, EUROC-USDD, XCHF-USDD: remove 90% of position, lock resulting USDD directly into the SC, credit other resulting asset to ownerfor all vaults: withdraw 90% of USDD collateral into SC (for vault owner address)for all loantoken balances (=dTokens and USDD): lock 90% of balances into SC
• extend Transferdomain:any transfer EVM->DVM of old dToken or DUSD results in: SC.releaseRatio in new dToken/USDD is credited to targetaddress 1-SC.releaseRatio in new dToken/USDD is locked in SC for targetaddress
• extend stocksplit logic to update SC too (so future dToken splits are reflected in the SC)
• implement SC-releaseTranche-tx (only allowed by foundation members):on releaseTrancheTx: for all entries in SC: credit according tranche part of funds to address update SC.releaseratio accordingly
• parameters to update after activation://deactivate DUSD loops: "v0/vaults/dusd-vault/enabled": "false",//remove old stab fee: "v0/poolpairs/17/token_a_fee_pct": "0", "v0/poolpairs/101/token_b_fee_pct": "0", "v0/poolpairs/102/token_b_fee_pct": "0", "v0/poolpairs/218/token_b_fee_pct": "0", "v0/poolpairs/236/token_b_fee_pct": "0",//activate new system-wide USDD fee"v0/token//dex_in_fee_pct": "", "v0/token//dex_out_fee_pct": "",

Examples for USDD and dToken tranche releases

Here some examples values for the dToken system market cap and the DFI market cap it would take for one tranche to be paid out on the futureswap block, given

• 200 Mio total size at implementation
• 20 Mio initial credit
• 1.8 Mio tranche size

1st tranche

• 100 Mio dToken system market cap, 80 Mio created through backed loans
• 200 Mio DFI market cap
• USDD price above 99 cents

25th tranche

• 316 Mio dToken system market cap, 252.8 Mio created through backed loans
• 632 Mio DFI market cap
• USDD price above 99 cents

50th tranche

• 541 Mio dToken system market cap, 432.8 Mio created through backed loans
• 1082 Mio DFI market cap
• USDD price above 101 cents

75th tranche

• 766 Mio dToken system market cap, 612.8 Mio created through backed loans
• 1532 Mio DFI market cap
• USDD price above 101 cents

100th tranche

• 991 Mio dToken system market cap, 792.8 Mio created through backed loans
• 1982 Mio DFI market cap
• USDD price above 101 cents

Important note
At current market prices, you get approximately 10 cents for one DUSD. With this proposal you get at least 10% of your DUSD as USDD directly, while the rest are frozen. The 10% will quickly be at peg, so while your coins are locked today's value in USD is not. According to the described criteria, your remaining liquidity will then be unlocked over time at at least one dollar per stable coin unit.

This is V5, the final version of this DFIP

9 days filled with countless discussions and adjustments. Thank you for all the valuable feedback and the productive vibes. Credit where credit is due, this DFIP is a true community effort and every comment that was made was considered and thought through. This resulting V5 is the final version of this DFIP.

I have a H.265 video with these encoding settings:

Format : HEVC Format/Info : High Efficiency Video Coding Format profile : Format Range@L4@Main Codec ID : V_MPEGH/ISO/HEVC Width : 1 920 pixels Height : 1 080 pixels Display aspect ratio : 16:9 Frame rate mode : Constant Frame rate : 23.976 (24000/1001) FPS Color space : YUV Chroma subsampling : 4:4:4 Bit depth : 10 bits Title : BDRip by DJATOM Writing library : x265 3.0_Au+22-feec4bdf9866:[DJATOM's Mod][Linux][GCC 6.3.0][64 bit] 10bit Encoding settings : cpuid=1111039 / frame-threads=2 / numa-pools= / wpp / no-pmode / no-pme / no-psnr / no-ssim / log-level=2 / csv / csv-log-level=2 / input-csp=3 / input-res=1920x1080 / interlace=0 / total-frames=4773 / level-idc=0 / high-tier=1 / uhd-bd=0 / ref=4 / no-allow-non-conformance / no-repeat-headers / annexb / no-aud / no-hrd / info / hash=0 / no-temporal-layers / open-gop / min-keyint=23 / keyint=240 / gop-lookahead=0 / bframes=9 / b-adapt=2 / b-pyramid / bframe-bias=0 / rc-lookahead=20 / lookahead-slices=6 / scenecut=40 / radl=0 / no-splice / no-intra-refresh / ctu=64 / min-cu-size=8 / no-rect / no-amp / max-tu-size=32 / tu-inter-depth=2 / tu-intra-depth=2 / limit-tu=0 / rdoq-level=2 / dynamic-rd=0.00 / no-ssim-rd / signhide / no-tskip / nr-intra=0 / nr-inter=0 / no-constrained-intra / strong-intra-smoothing / max-merge=2 / limit-refs=3 / limit-modes / me=2 / subme=5 / merange=48 / temporal-mvp / weightp / weightb / no-analyze-src-pics / deblock=1:-1 / no-sao / no-sao-non-deblock / rd=4 / no-early-skip / no-rskip / no-fast-intra / no-tskip-fast / no-cu-lossless / no-b-intra / no-splitrd-skip / rdpenalty=0 / psy-rd=2.00 / psy-rdoq=4.00 / no-rd-refine / no-lossless / cbqpoffs=4 / crqpoffs=4 / rc=crf / crf=15.0 / qcomp=0.72 / qpstep=4 / stats-write=0 / stats-read=0 / ipratio=1.40 / pbratio=1.30 / aq-mode=3 / aq-strength=0.85 / no-cutree / zone-count=0 / no-strict-cbr / qg-size=32 / no-rc-grain / qpmax=69 / qpmin=0 / no-const-vbv / sar=1 / overscan=0 / videoformat=5 / range=0 / colorprim=1 / transfer=1 / colormatrix=1 / chromaloc=0 / display-window=0 / max-cll=0,0 / min-luma=0 / max-luma=1023 / log2-max-poc-lsb=8 / vui-timing-info / vui-hrd-info / slices=1 / no-opt-qp-pps / no-opt-ref-list-length-pps / no-multi-pass-opt-rps / scenecut-bias=0.05 / no-opt-cu-delta-qp / no-aq-motion / no-hdr / no-hdr-opt / no-dhdr10-opt / no-idr-recovery-sei / analysis-reuse-level=5 / scale-factor=0 / refine-intra=0 / refine-inter=0 / refine-mv=0 / refine-ctu-distortion=0 / no-limit-sao / ctu-info=0 / no-lowpass-dct / refine-analysis-type=0 / copy-pic=1 / max-ausize-factor=1.0 / no-dynamic-refine / no-single-sei / hevc-aq / no-svt / qp-adaptation-range=2.00 Language : Japanese Default : Yes Forced : No Color range : Limited Color primaries : BT.709 Transfer characteristics : BT.709 Matrix coefficients : BT.709 

How do I convert it into a lossless H.264 video while preserving these settings?

The War Scroll, also known as the "War of the Sons of Light Against the Sons of Darkness," is a unique text within the Dead Sea Scrolls that portrays an apocalyptic battle between the forces of good (Sons of Light) and evil (Sons of Darkness). This scroll provides insight into both historical and symbolic elements.
Historical Accuracy:
The War Scroll, while containing detailed military tactics and an epic narrative of the ultimate confrontation, doesn't explicitly reference any specific historical event or timeframe. Some scholars believe it could be a product of the community's anticipation of a future messianic conflict or a reflection of their own community's struggles against opposing forces during their time. Interpreting the historical accuracy of the scroll often involves exploring the context of the Qumran community and the turbulent times in which they lived.
Symbolism and Esoteric Wisdom:
The War Scroll goes beyond a mere description of a physical battle. It portrays a cosmic conflict between the forces of light and darkness, reflecting not just a literal warfare but also a symbolic and spiritual struggle. The text emphasizes righteousness, divine intervention, and the victory of good over evil.
Within the study guide, activities and exercises could involve dissecting the symbolic elements present in the War Scroll, exploring the deeper meanings behind the battle tactics and the metaphysical implications of the conflict. Understanding the symbolism could involve group discussions, comparative analysis with other ancient texts with similar themes, and exploring the impact of this symbolic representation on the community's beliefs and practices.
Here are a few activities and exercises to explore the symbolism and historical context of the War Scroll from the Dead Sea Scrolls:

1. Symbolism Analysis:

Provide excerpts from the War Scroll and encourage participants to identify and discuss the symbolic meanings behind elements like the "Sons of Light" and the "Sons of Darkness," various weapons, and the strategies outlined for battle. Group discussions or written reflections can help participants explore the deeper layers of meaning.

1. Comparative Analysis:

Compare the War Scroll's themes with similar apocalyptic or eschatological texts from different cultures or religions, such as apocalyptic passages in the Book of Revelation in the Christian Bible or apocalyptic texts from other ancient traditions. Create worksheets or discussion prompts to highlight similarities and differences in themes, symbols, and beliefs about cosmic battles.

1. Historical Context Exploration:

Present historical information about the era when the Dead Sea Scrolls were written. Discuss the political, social, and religious climate of that time, including the turmoil in the region, to understand how these factors might have influenced the composition of the War Scroll. Encourage participants to consider the possible motivations behind the text's creation.

1. Creative Interpretation:

Encourage creative expression by asking participants to create artwork, poems, or short stories inspired by the themes and imagery found in the War Scroll. This exercise allows individuals to engage more deeply with the symbolic elements and interpret them in their own unique ways.

1. Role-playing or Debates:
   Organize a role-playing activity where participants take on the roles of "Sons of Light" and "Sons of Darkness," debating their ideologies, motivations, and strategies for the ultimate battle. This exercise helps in understanding differing perspectives and interpreting the conflicts presented in the scroll.
   

Interpretative variations regarding the river's crossing in different ancient texts reflect the unique religious, philosophical, and cultural perspectives embedded within these narratives. These differences in interpretation offer insights into diverse worldviews and varying theological frameworks present in ancient texts:

1. Mesopotamian Context:

• In Mesopotamian mythology and literature, the Euphrates River often held symbolic significance as a boundary between the known civilized world and the wild, unknown realms. The crossing of the Euphrates could symbolize journeys into unexplored territories or transitions between order and chaos. This perspective reflects a worldview rooted in the physical and geographical division of lands.

1. Biblical Context:

• In biblical texts, such as those in the Book of Revelation or Old Testament prophecies, the crossing of the Euphrates carries eschatological significance. It may represent a divine intervention or a decisive moment in God's plan, marking the commencement of apocalyptic events. This interpretation aligns with the biblical narrative of divine judgment and the unfolding of God's ultimate purpose in history.

1. Gnostic or Apocryphal Context:

• Gnostic or apocryphal texts often interpret the river's crossing as a symbolic liberation or awakening. It might signify the release of spiritual forces or the ascent to higher consciousness, reflecting a philosophical perspective emphasizing spiritual enlightenment and liberation from material constraints.

1. Greco-Roman Interpretation:

• In Greco-Roman literature, crossings of rivers were often associated with mythological journeys or transitions between realms. The crossing of the Euphrates might symbolize a transition from mundane existence to a realm of mystery or spiritual significance, reflecting a cultural perspective rooted in mythology and cosmology.

These varied interpretations highlight the richness and diversity of religious, philosophical, and cultural frameworks present in ancient texts. The river's crossing serves as a flexible symbol that adapts to different narratives, conveying themes of transition, judgment, liberation, or cosmic transformation based on the unique perspectives of each tradition.
Exploring these interpretative variations allows participants to appreciate the complexity of symbolism within ancient texts and provides insights into how different cultures and belief systems interpreted common motifs like the river Euphrates. It showcases the intricate interplay between religious, philosophical, and cultural elements shaping the symbolism and theological implications embedded in these narratives.
The river Euphrates, a prominent geographic feature in ancient texts, embodies universal themes that transcend specific cultural contexts. Identifying these universal themes helps reveal shared human concepts of transition, boundaries, and transformative events across diverse ancient traditions:

1. Threshold and Transition:

• The Euphrates often symbolizes a boundary between known and unknown territories. Its crossing represents a transition from one state to another, signifying a pivotal moment of change or passage. This theme of crossing a threshold echoes the human experience of transitions in life, moving from familiar to unfamiliar realms.

1. Boundary and Separation:

• As a geographical boundary, the Euphrates signifies separation between distinct territories or civilizations. This concept of demarcation resonates with universal human experiences of setting boundaries, delineating spaces, or marking divisions between different aspects of life.

1. Transformative Events:

• Crossing the Euphrates is often associated with cosmic or transformative events in ancient texts. This universal theme reflects the human fascination with the concept of epochal change, cosmic upheavals, or moments of divine intervention that reshape the course of history.

1. Symbol of Power and Control:

• The river might represent a symbol of power, control, or geopolitical significance. Crossing it could signify shifts in dominance, challenges to established authority, or the assertion of influence. This theme resonates with human narratives of power struggles and shifts in societal dynamics.

1. Metaphor for Spiritual Journeys:

• Across cultures, rivers are often used metaphorically to represent spiritual journeys or quests. The crossing of the Euphrates might symbolize the pursuit of enlightenment, the passage to higher realms of understanding, or the quest for spiritual transformation.

These universal themes associated with the river Euphrates highlight fundamental aspects of the human experience—transitions, boundaries, transformative events, power dynamics, and spiritual journeys. The river's symbolism in ancient texts speaks to shared human aspirations, struggles, and beliefs that transcend cultural boundaries and resonate across different epochs and civilizations.
By identifying and discussing these universal themes, participants gain a deeper appreciation for the profound symbolism embedded in ancient texts and recognize the timeless relevance of concepts such as transition, boundaries, and transformative events in shaping human narratives and aspirations.

1. Historical Context:

• What historical events or societal conditions might have influenced the composition of the War Scroll?
  
• How does the historical context of the Dead Sea Scrolls' discovery contribute to our understanding of this text's significance?
  

1. Symbolism and Esoteric Wisdom:

• How does the War Scroll use symbolism to convey spiritual or cosmic themes?
  
• What esoteric wisdom or deeper spiritual insights can be derived from the portrayal of cosmic conflict and divine intervention within the text?
  

1. Comparative Analysis:

• Compare the themes and symbolism of the War Scroll with other apocalyptic texts from different cultures (e.g., Book of Revelation, The Book of Daniel). What common motifs or differences in interpretation do you observe?

1. Parallelism in Biblical Texts:

• Explore connections between the War Scroll and other biblical texts. How does the language, imagery, or themes in the War Scroll intersect with passages from the Hebrew Bible or New Testament?

1. Community Beliefs and Practices:

• How might the apocalyptic expectations depicted in the War Scroll have influenced the beliefs and practices of the community that produced it?
  
• Discuss the impact of such intense anticipation of cosmic conflict on communal life and religious rituals within the community.
  

1. Cultural Significance of Cosmic Battles:

• Across various ancient cultures, why do you think depictions of cosmic battles and eschatological events were significant? What might these narratives represent in a broader cultural context?

1. Interpretive Variations and Unique Perspectives:

• Explore the diverse interpretations of specific passages or symbols within the War Scroll. How do different scholars or traditions interpret these elements, and what underlying factors might influence their interpretations?

1. Personal Reflection and Modern Relevance:

• Reflect on how the themes of cosmic conflict, righteousness, and spiritual warfare in the War Scroll might resonate in contemporary society or personal belief systems.

1. Theological and Philosophical Implications:

• Discuss the theological and philosophical implications of a cosmic battle between forces of light and darkness. How does this theme intersect with broader philosophical inquiries or theological doctrines?

1. Literary and Symbolic Analysis:

- Analyze the narrative structure and symbolic elements present in specific passages of the War Scroll. How do these elements contribute to the text's overarching themes and meanings? 

These study questions aim to provoke critical thinking, promote in-depth exploration of themes, encourage comparative analysis, and stimulate discussions on the multifaceted nature of the War Scroll's content and its significance within ancient and contemporary contexts.

1. Archaeological and Linguistic Analysis:

- How does the physical condition of the Dead Sea Scrolls, including the War Scroll, impact our understanding of their preservation and historical context? - Discuss the linguistic peculiarities or unique textual features found within the War Scroll and their implications for translation and interpretation. 

1. Apocalyptic Expectations and Messianic Concepts:

- Explore the portrayal of messianic figures or anticipated saviors within the War Scroll. How do these concepts align with or diverge from contemporary expectations of a messianic figure in other ancient texts or religious traditions? 

1. Impact of Apocalyptic Literature:

- Analyze the enduring influence of apocalyptic literature, such as the War Scroll, on subsequent religious, literary, or cultural traditions. How have these texts shaped later beliefs or inspired artistic and literary works? 

1. Ethical and Moral Frameworks:

- Discuss the ethical or moral implications of the cosmic conflict depicted in the War Scroll. How do the themes of righteousness and wickedness contribute to the text's underlying moral framework? 

1. Role of Prophecy and Revelation:

- Explore the role of prophecy and revelation within the War Scroll. How do the prophetic elements contribute to the text's portrayal of future events and cosmic justice? 

1. Experiential and Ritualistic Elements:

- Investigate potential ritualistic or experiential dimensions associated with the teachings or beliefs conveyed in the War Scroll. How might the community have engaged with these teachings in their religious practices or communal activities? 

1. Literary Genre and Interpretation:

- Discuss the classification of the War Scroll within the broader genre of apocalyptic literature. How does its classification influence our understanding and interpretation of its themes and symbolic elements? 

1. Relevance in Modern Scholarship:

- Reflect on the ongoing scholarly debates or discoveries related to the War Scroll. How have modern interpretations evolved, and what implications do these new perspectives have on our understanding of the text? 

1. Intersection of Faith and Scholarship:

- Consider the interplay between faith-based interpretations and scholarly analyses of the War Scroll. How might religious convictions or theological frameworks influence academic research and vice versa? 

1. Future Research and Interpretative Avenues:

- Propose potential avenues for future research or areas of exploration concerning the War Scroll. What unanswered questions or unexplored aspects merit further investigation? 

The composition of the War Scroll, along with other Dead Sea Scrolls, was likely influenced by several historical events and societal conditions prevalent during the time of its writing, which is estimated to be between the 2nd century BCE and the 1st century CE:

1. Hellenistic Rule and Cultural Influence:

• The region where the Dead Sea Scrolls were found was under Hellenistic influence due to the conquests of Alexander the Great and the subsequent control by the Seleucid Empire. This era saw a clash between Hellenistic culture and Jewish traditions, leading to cultural tensions and a desire to preserve religious and cultural heritage.

1. Political Turmoil and Resistance Movements:

• The Jewish people experienced political unrest, particularly during the Maccabean Revolt against Seleucid rule. This period was characterized by resistance movements, attempts to preserve Jewish identity, and fervent anticipation of a messianic figure to deliver them from foreign oppression.

1. Religious Sects and Spiritual Expectations:

• Various religious sects existed within Judaism, each with its own interpretations and expectations of messianic redemption, purity laws, and theological doctrines. The community associated with the Dead Sea Scrolls, often believed to be the Essenes, likely had distinctive theological beliefs and a strong apocalyptic worldview.

1. Anticipation of Cosmic Redemption:

• There was a widespread belief in the imminent arrival of a messianic figure or a divine intervention that would bring about cosmic redemption, ushering in an era of righteousness and divine rule. This anticipation of apocalyptic events and a cosmic battle between forces of light and darkness is reflected in the War Scroll's themes.

Regarding the historical context of the Dead Sea Scrolls' discovery, its significance lies in multiple facets:

1. Preservation of Ancient Texts:

• The discovery of the Dead Sea Scrolls, including the War Scroll, provided an invaluable collection of ancient manuscripts that significantly expanded our understanding of ancient Jewish texts, religious beliefs, and the diversity of Jewish thought during the Second Temple period.

1. Insights into Jewish Sectarianism:

• The scrolls shed light on the diversity of beliefs and practices among Jewish sects during that time. Understanding the beliefs and expectations of the community associated with the Dead Sea Scrolls helps contextualize the theological and apocalyptic themes present in the War Scroll.

1. Confirmation of Scriptural Accuracy:

• The Dead Sea Scrolls' discovery contributed to confirming the accuracy and preservation of certain biblical texts, highlighting the continuity of textual transmission across centuries and supporting the authenticity of biblical manuscripts.

1. Impact on Biblical Studies and Scholarship:

• The discovery of the Dead Sea Scrolls revolutionized biblical studies, providing scholars with invaluable primary sources for studying ancient Judaism, the development of biblical texts, and the context in which these texts were composed.

The historical context of political upheaval, religious expectations, and the preservation of texts within the Dead Sea Scrolls contributes significantly to understanding the milieu in which the War Scroll was written. It provides a backdrop against which the themes of cosmic conflict, eschatological anticipation, and religious fervor within the War Scroll can be comprehended.

• How old are you? What's your gender? Give us a general description of yourself.
-I am a 17 year old male from England and I’m currently studying philosophy, sociology and ancient history at college.
• Is there a medical diagnosis that may impact your mental stability somehow?
-I was diagnosed with autism at age 12.
• Describe your upbringing. Did it have any kind of religious or structured influence? How did you respond to it?
-I am an only child and lived in a secular family consisting of just me, my mum and my dad. Both of them were very laid back regarding discipline. One thing that could be said is that they gave me too much unconditional love, especially my mother. This, in turn, resulted in them not really teaching me important life skills and independence for fear of putting me in harms way. Thus, in the past 2 years I’ve had a bit of an awaking and have become hyper independent to remedy the lack of life skills and lessons taught during my early childhood.
• What do you do as a job or as a career (if you have one)? Do you like it? Why or why not?
-My ideal employment, realistically, would be a teacher. I really like the idea of taking on a task and being able to enforce original methods to attain the best possible results. That process is the general principle behind a lot of my interests and teaching is a job where it is present.
• If you had to spend an entire weekend by yourself, how would you feel? Would you feel lonely or refreshed?
-I Would feel refreshed. I get really tired when I’m around people. I think that may come from the fact that I tend to put on an act when I’m interacting with others in order to make them like me. This is a favourable result as the more people you are on good terms with, the more likely they are to be a potential asset to your life as opposed to a possible hinderance.
• What kinds of activities do you prefer? Do you like, and are you good at sports? Do you enjoy any other outdoor or indoor activities?
-I enjoy topics that are synthesised with progressing my main goal(s). For example, I enjoy learning about mbti because it is a component of my main goal to understand myself and thus can help me achieve happiness more effectively as I believe this is the main assignment of life.
• How curious are you? Do you have more ideas then you can execute? What are your curiosities about? What are your ideas about - is it environmental or conceptual, and can you please elaborate?
-I would consider my pursuits of curiosity to be loosely filtered through what may be useful to attaining a personal goal and I don’t often get carried away with ideas that have no overall importance to it. I say loosely because I can’t be certain what will be of importance to my pursuits, so for this reason I sometimes stray a from things that I know will be personally beneficial in the long term for things that could be useful, by virtue of the interconnectedness of everything.
• Would you enjoy taking on a leadership position? Do you think you would be good at it? What would your leadership style be?
-I would really like to take on a leadership position. I think I would be good at figuring out solutions and assigning them to people based on an overall objective. However I do not think I’d be very good at leadership in practice. This is because I’m not very quick at making decisions. Thus, my leadership style would be less about leadership and more being a personal adviser to members of a team to ensure they are all going in the same direction.
• Are you coordinated? Why do you feel as if you are or are not? Do you enjoy working with your hands in some form? Describe your activity?
-I don’t feel as though I’m very physically coordinated. I often have to focus on my environment and my movement at the expense of deeper thought. I’ve never really resonated with the popular notion that walks are therapeutic and thought provoking. For me, they are stressful and prohibit any other thoughts than the ones related to keeping my movement and environment in check.
• Are you artistic? If yes, describe your art? If you are not particular artistic but can appreciate art please likewise describe what forums of art you enjoy. Please explain your answer.
-I enjoy art that operates under the pretence that art is a language. I like art that communicates meaning. The reason why I like this type of art at all when it just seems like, if communication is the primary source of my investment, I should just focus on objective language rather than something as convoluted and prone to misinterpretation as art. To this I say, art elicits emotion and creates an immediate reason to care about the message. Thus, making the point carry to greater extent.
• What's your opinion about the past, present, and future? How do you deal with them?
-Most of my time is devoted to figuring out how to get to a desirable destination in the future. By the same token, the present is also very important to me as it is paramount to the aforementioned goal. The past is the timeframe I spend the least time thinking about when I’m happy. It’s not that I don’t consciously recognise it’s value in being a possible example for the future, it’s just not something I have a propensity to think about. I really only dwell on the past when I’m feeling down.
• How do you act when others request your help to do something (anything)? If you would decide to help them, why would you do so?
-My main reason for helping someone echoes an above mentioned sentiment. I would really only help someone to build good will with them, because it lowers the chances they will be a destructive force in your life. Moreover, they are indebted to you for a time which is always handy.
• Do you need logical consistency in your life?
-The primary system of logic I use is what has utility to achieving a goal. I’m not too bothered about logic for logics sake. I don’t live in the details of subjects and thus don’t care about the underlying logic, just what has the most personal utility.
• How important is efficiency and productivity to you?
-They are both really important to me. I like to see results. I always feel unfulfilled by the notion; I probably could achieve x and therefore there’s no point in doing y. I might switch to this mindset if I’m burned out as a coping mechanism for me not being able to express my desire to be productive. But that just emphasises it’s importance to me if I’m willing to change my beliefs to avoid the sadness brought about by unproductivity.
• Do you control others, even if indirectly? How and why do you do that?
-I control others implicitly by acting overly polite and sometimes resort to people pleasing to gain favour with them. This helps with the fact that I’m pretty dependent on what others think of me and their perceptions of me often supersede or coexist with my own beliefs and observations about myself, even if I can logically reason reason them to be erroneous judgements.
• What are your hobbies? Why do you like them?
-As mentioned in the desired career question, I enjoy hobbies that revolve around implementing original strategies to attain a desirable outcome. Because of this, I enjoy strategy games such total war and chess. once again, as mentioned previously another reason why I enjoy some hobbies is because they contribute to a larger goal. Such as my interest for mbti because, it allows me to understand myself, so I know how best to attain happiness and in turn, fulfil what I consider to be the primary objective of life in its most general form.
• What is your learning style? What kind of learning environments do you struggle with most? Why do you like/struggle with these learning styles? Do you prefer classes involving memorization, logic, creativity, or your physical senses?

• I get along fine with the typical learning environment of a classroom lecture. So long as the teacher is charismatic I can let my mind put on a stage performance of what’s being said and I tend to remember those quite well as my it forces me to filter everything through my own perceptions which results in personal meaning being attached to them and thus increases the likelihood I’ll remember the content of the lesson. However, I dislike when you are made to do an abundance of preselected and linear worksheets. I just like making notes with loads of arrows connecting everything. This helps me remember stuff because it displays how it’s all relevant to a bigger concept and doesn’t allow for stuff that isn’t connected to be written down so it filters out unimportant stuff.

• How good are you at strategizing? Do you easily break up projects into manageable tasks? Or do you have a tendency to wing projects and improvise as you go?
-I prefer to have a plan before action. I like to feel as though most things have been decided beforehand and I’m just reading off a to do list written by past me.
• What are your aspirations in life, professionally and personally?
-My professional aspirations are a means to an end. I want to get a job that I enjoy, is stable and provides an income, in the hope that I can stop thinking so much about it and can focus on the more personal aspects of life. Like figuring out how best to achieve happiness after I’ve stabilised my external life.
• What are your fears? What makes you uncomfortable? What do you hate? Why?
-I really fear upsetting people. Partly because I’m scared of how they will react. Especially in ways that could de-stabilise my life. Moreover, as I mentioned previously, I unfortunately have a propensity to need gratification from others and if I upset people I might begin to feel insecure in myself. A lot of what I do can be chalked up to an attempt to attain the admiration of others. I also fear not being able to make my plans and goals come into fruition.
• What do the "highs" in your life look like?
-The highs in my life often involve a dedication to a goal that gets me up every day. I’ll constantly be excited to get one step closer to achieving it. The goal when I’m happy revolves around a more thought out desire for the long term. Furthermore, this is accompanied by a disregard for the appearance of things. In these times I just focus on the character of things and perceive things through a lenses of principles and ideas. Moreover, the type of gratification I seek revolves around my capacity to think.
• What do the "lows" in your life look like?
-By contrast, my lows are aimless at best and destructive at worst. When Im considering the future in these moments I tend to forget about happiness and in turn have a bleak outlook on the future. This leads me to being generally quite unproductive. My gratification seeking becomes much more shallow aswell. It tends to revolve more around appearance and wanting others to view me as attractive. As a result of this I developed anorexia as a byproduct of trying to look more attractive in a period of stress. Moreover, it gave me something to control as I feel an excessive need to do this when I’m stressed.
• How attached are you to reality? Do you daydream often, or do you pay attention to what's around you? If you do daydream, are you aware of your surroundings while you do so?
-I do daydream, Though not as much as I used to. When I daydream it’s usually to test how something I wish to do might go if I were to do it.
• Imagine you are alone in a blank, empty room. There is nothing for you to do and no one to talk to. What do you think about?
-I would consider the main reason for my beliefs again and make updates to it that would eventually trickle down to actionable changes. If I didn’t manage to find any faults in my beliefs and principles of conduct I would keep my goal the same and think about things I could do to achieve it.
• How long do you take to make an important decision? And do you change your mind once you've made it?
-It usually takes me a little while to come to a decision, particularly if it has long term consequences, as I like to look at the external factors and see if they would suit me internally and/or if it would be beneficial to me in the future. Once I’ve come to a decision on a matter, ideologically I think it is best to stick to it because you can maximise the benefits that a particular path can provide. However, if the evidence changes and it contradicts the original reason for making the decision I will change my mind.
• How long do you take to process your emotions? How important are emotions in your life?
-It usually takes me a while to figure out my emotions. They often appear feint and undefined even though I know there’s something there. When I felt really down for months I couldn’t seem to validate my own emotions. To remedy this I tried to keep a journal collecting statistics including whether I cried, how many times? For how long? Have you self harmed in any way? this created a picture from which I could derive a conclusion. However, I have recently begun to value emotions much more than I did. Previously, I would’ve consciously neglected them. However, ever since I developed anorexia and had a really long period of time where I felt negative emotions I realise how powerful they are and how they must be utilised in your favour otherwise life wouldn’t be worth living.
• Do you ever catch yourself agreeing with others just to appease them and keep the conversation going? How often? Why?
-This is something I do quite often with people I’m not acquainted with, as I value the utility of a social connection more than convincing a few people of my beliefs. However, it happens less with people who I know well enough to comfortably make the assertion that an ideological disagreement wouldn’t jeopardise the relationship.
• Do you break rules often? Do you think authority should be challenged, or that they know better? If you do break rules, why?
-I avoid rule breaking that could lead to excessive repercussions. Since I purvey my conduct with the main intention of long term personal fulfilment some consequences that impede this mean that I generally obey rules. However if the consequences are avoidable and/or inconsequential I have no problem breaking those rules. Like cheating in exams for example.

• How old are you? What's your gender? Give us a general description of yourself.
-I am a 17 year old male from England and I’m currently studying philosophy, sociology and ancient history at college.
• Is there a medical diagnosis that may impact your mental stability somehow?
-I was diagnosed with autism at age 12.
• Describe your upbringing. Did it have any kind of religious or structured influence? How did you respond to it?
-I am an only child and lived in a secular family consisting of just me, my mum and my dad. Both of them were very laid back regarding discipline. One thing that could be said is that they gave me too much unconditional love, especially my mother. This, in turn, resulted in them not really teaching me important life skills and independence for fear of putting me in harms way. Thus, in the past 2 years I’ve had a bit of an awaking and have become hyper independent to remedy the lack of life skills and lessons taught during my early childhood.
• What do you do as a job or as a career (if you have one)? Do you like it? Why or why not?
-My ideal employment, realistically, would be a teacher. I really like the idea of taking on a task and being able to enforce original methods to attain the best possible results. That process is the general principle behind a lot of my interests and teaching is a job where it is present.
• If you had to spend an entire weekend by yourself, how would you feel? Would you feel lonely or refreshed?
-I Would feel refreshed. I get really tired when I’m around people. I think that may come from the fact that I tend to put on an act when I’m interacting with others in order to make them like me. This is a favourable result as the more people you are on good terms with, the more likely they are to be a potential asset to your life as opposed to a possible hinderance.
• What kinds of activities do you prefer? Do you like, and are you good at sports? Do you enjoy any other outdoor or indoor activities?
-I enjoy topics that are synthesised with progressing my main goal(s). For example, I enjoy learning about mbti because it is a component of my main goal to understand myself and thus can help me achieve happiness more effectively as I believe this is the main assignment of life.
• How curious are you? Do you have more ideas then you can execute? What are your curiosities about? What are your ideas about - is it environmental or conceptual, and can you please elaborate?
-I would consider my pursuits of curiosity to be loosely filtered through what may be useful to attaining a personal goal and I don’t often get carried away with ideas that have no overall importance to it. I say loosely because I can’t be certain what will be of importance to my pursuits, so for this reason I sometimes stray a from things that I know will be personally beneficial in the long term for things that could be useful, by virtue of the interconnectedness of everything.
• Would you enjoy taking on a leadership position? Do you think you would be good at it? What would your leadership style be?
-I would really like to take on a leadership position. I think I would be good at figuring out solutions and assigning them to people based on an overall objective. However I do not think I’d be very good at leadership in practice. This is because I’m not very quick at making decisions. Thus, my leadership style would be less about leadership and more being a personal adviser to members of a team to ensure they are all going in the same direction.
• Are you coordinated? Why do you feel as if you are or are not? Do you enjoy working with your hands in some form? Describe your activity?
-I don’t feel as though I’m very physically coordinated. I often have to focus on my environment and my movement at the expense of deeper thought. I’ve never really resonated with the popular notion that walks are therapeutic and thought provoking. For me, they are stressful and prohibit any other thoughts than the ones related to keeping my movement and environment in check.
• Are you artistic? If yes, describe your art? If you are not particular artistic but can appreciate art please likewise describe what forums of art you enjoy. Please explain your answer.
-I enjoy art that operates under the pretence that art is a language. I like art that communicates meaning. The reason why I like this type of art at all when it just seems like, if communication is the primary source of my investment, I should just focus on objective language rather than something as convoluted and prone to misinterpretation as art. To this I say, art elicits emotion and creates an immediate reason to care about the message. Thus, making the point carry to greater extent.
• What's your opinion about the past, present, and future? How do you deal with them?
-Most of my time is devoted to figuring out how to get to a desirable destination in the future. By the same token, the present is also very important to me as it is paramount to the aforementioned goal. The past is the timeframe I spend the least time thinking about when I’m happy. It’s not that I don’t consciously recognise it’s value in being a possible example for the future, it’s just not something I have a propensity to think about. I really only dwell on the past when I’m feeling down.
• How do you act when others request your help to do something (anything)? If you would decide to help them, why would you do so?
-My main reason for helping someone echoes an above mentioned sentiment. I would really only help someone to build good will with them, because it lowers the chances they will be a destructive force in your life. Moreover, they are indebted to you for a time which is always handy.
• Do you need logical consistency in your life?
-The primary system of logic I use is what has utility to achieving a goal. I’m not too bothered about logic for logics sake. I don’t live in the details of subjects and thus don’t care about the underlying logic, just what has the most personal utility.
• How important is efficiency and productivity to you?
-They are both really important to me. I like to see results. I always feel unfulfilled by the notion; I probably could achieve x and therefore there’s no point in doing y. I might switch to this mindset if I’m burned out as a coping mechanism for me not being able to express my desire to be productive. But that just emphasises it’s importance to me if I’m willing to change my beliefs to avoid the sadness brought about by unproductivity.
• Do you control others, even if indirectly? How and why do you do that?
-I control others implicitly by acting overly polite and sometimes resort to people pleasing to gain favour with them. This helps with the fact that I’m pretty dependent on what others think of me and their perceptions of me often supersede or coexist with my own beliefs and observations about myself, even if I can logically reason reason them to be erroneous judgements.
• What are your hobbies? Why do you like them?
-As mentioned in the desired career question, I enjoy hobbies that revolve around implementing original strategies to attain a desirable outcome. Because of this, I enjoy strategy games such total war and chess. once again, as mentioned previously another reason why I enjoy some hobbies is because they contribute to a larger goal. Such as my interest for mbti because, it allows me to understand myself, so I know how best to attain happiness and in turn, fulfil what I consider to be the primary objective of life in its most general form.
• What is your learning style? What kind of learning environments do you struggle with most? Why do you like/struggle with these learning styles? Do you prefer classes involving memorization, logic, creativity, or your physical senses?

• I get along fine with the typical learning environment of a classroom lecture. So long as the teacher is charismatic I can let my mind put on a stage performance of what’s being said and I tend to remember those quite well as my it forces me to filter everything through my own perceptions which results in personal meaning being attached to them and thus increases the likelihood I’ll remember the content of the lesson. However, I dislike when you are made to do an abundance of preselected and linear worksheets. I just like making notes with loads of arrows connecting everything. This helps me remember stuff because it displays how it’s all relevant to a bigger concept and doesn’t allow for stuff that isn’t connected to be written down so it filters out unimportant stuff.

• How good are you at strategizing? Do you easily break up projects into manageable tasks? Or do you have a tendency to wing projects and improvise as you go?
-I prefer to have a plan before action. I like to feel as though most things have been decided beforehand and I’m just reading off a to do list written by past me.
• What are your aspirations in life, professionally and personally?
-My professional aspirations are a means to an end. I want to get a job that I enjoy, is stable and provides an income, in the hope that I can stop thinking so much about it and can focus on the more personal aspects of life. Like figuring out how best to achieve happiness after I’ve stabilised my external life.
• What are your fears? What makes you uncomfortable? What do you hate? Why?
-I really fear upsetting people. Partly because I’m scared of how they will react. Especially in ways that could de-stabilise my life. Moreover, as I mentioned previously, I unfortunately have a propensity to need gratification from others and if I upset people I might begin to feel insecure in myself. A lot of what I do can be chalked up to an attempt to attain the admiration of others. I also fear not being able to make my plans and goals come into fruition.
• What do the "highs" in your life look like?
-The highs in my life often involve a dedication to a goal that gets me up every day. I’ll constantly be excited to get one step closer to achieving it. The goal when I’m happy revolves around a more thought out desire for the long term. Furthermore, this is accompanied by a disregard for the appearance of things. In these times I just focus on the character of things and perceive things through a lenses of principles and ideas. Moreover, the type of gratification I seek revolves around my capacity to think.
• What do the "lows" in your life look like?
-By contrast, my lows are aimless at best and destructive at worst. When Im considering the future in these moments I tend to forget about happiness and in turn have a bleak outlook on the future. This leads me to being generally quite unproductive. My gratification seeking becomes much more shallow aswell. It tends to revolve more around appearance and wanting others to view me as attractive. As a result of this I developed anorexia as a byproduct of trying to look more attractive in a period of stress. Moreover, it gave me something to control as I feel an excessive need to do this when I’m stressed.
• How attached are you to reality? Do you daydream often, or do you pay attention to what's around you? If you do daydream, are you aware of your surroundings while you do so?
-I do daydream, Though not as much as I used to. When I daydream it’s usually to test how something I wish to do might go if I were to do it.
• Imagine you are alone in a blank, empty room. There is nothing for you to do and no one to talk to. What do you think about?
-I would consider the main reason for my beliefs again and make updates to it that would eventually trickle down to actionable changes. If I didn’t manage to find any faults in my beliefs and principles of conduct I would keep my goal the same and think about things I could do to achieve it.
• How long do you take to make an important decision? And do you change your mind once you've made it?
-It usually takes me a little while to come to a decision, particularly if it has long term consequences, as I like to look at the external factors and see if they would suit me internally and/or if it would be beneficial to me in the future. Once I’ve come to a decision on a matter, ideologically I think it is best to stick to it because you can maximise the benefits that a particular path can provide. However, if the evidence changes and it contradicts the original reason for making the decision I will change my mind.
• How long do you take to process your emotions? How important are emotions in your life?
-It usually takes me a while to figure out my emotions. They often appear feint and undefined even though I know there’s something there. When I felt really down for months I couldn’t seem to validate my own emotions. To remedy this I tried to keep a journal collecting statistics including whether I cried, how many times? For how long? Have you self harmed in any way? this created a picture from which I could derive a conclusion. However, I have recently begun to value emotions much more than I did. Previously, I would’ve consciously neglected them. However, ever since I developed anorexia and had a really long period of time where I felt negative emotions I realise how powerful they are and how they must be utilised in your favour otherwise life wouldn’t be worth living.
• Do you ever catch yourself agreeing with others just to appease them and keep the conversation going? How often? Why?
-This is something I do quite often with people I’m not acquainted with, as I value the utility of a social connection more than convincing a few people of my beliefs. However, it happens less with people who I know well enough to comfortably make the assertion that an ideological disagreement wouldn’t jeopardise the relationship.
• Do you break rules often? Do you think authority should be challenged, or that they know better? If you do break rules, why?
-I avoid rule breaking that could lead to excessive repercussions. Since I purvey my conduct with the main intention of long term personal fulfilment some consequences that impede this mean that I generally obey rules. However if the consequences are avoidable and/or inconsequential I have no problem breaking those rules. Like cheating in exams for example.

• How old are you? What's your gender? Give us a general description of yourself.
-I am a 17 year old male from England and I’m currently studying philosophy, sociology and ancient history at college.
• Is there a medical diagnosis that may impact your mental stability somehow?
-I was diagnosed with autism at age 12.
• Describe your upbringing. Did it have any kind of religious or structured influence? How did you respond to it?
-I am an only child and lived in a secular family consisting of just me, my mum and my dad. Both of them were very laid back regarding discipline. One thing that could be said is that they gave me too much unconditional love, especially my mother. This, in turn, resulted in them not really teaching me important life skills and independence for fear of putting me in harms way. Thus, in the past 2 years I’ve had a bit of an awaking and have become hyper independent to remedy the lack of life skills and lessons taught during my early childhood.
• What do you do as a job or as a career (if you have one)? Do you like it? Why or why not?
-My ideal employment, realistically, would be a teacher. I really like the idea of taking on a task and being able to enforce original methods to attain the best possible results. That process is the general principle behind a lot of my interests and teaching is a job where it is present.
• If you had to spend an entire weekend by yourself, how would you feel? Would you feel lonely or refreshed?
-I Would feel refreshed. I get really tired when I’m around people. I think that may come from the fact that I tend to put on an act when I’m interacting with others in order to make them like me. This is a favourable result as the more people you are on good terms with, the more likely they are to be a potential asset to your life as opposed to a possible hinderance.
• What kinds of activities do you prefer? Do you like, and are you good at sports? Do you enjoy any other outdoor or indoor activities?
-I enjoy topics that are synthesised with progressing my main goal(s). For example, I enjoy learning about mbti because it is a component of my main goal to understand myself and thus can help me achieve happiness more effectively as I believe this is the main assignment of life.
• How curious are you? Do you have more ideas then you can execute? What are your curiosities about? What are your ideas about - is it environmental or conceptual, and can you please elaborate?
-I would consider my pursuits of curiosity to be loosely filtered through what may be useful to attaining a personal goal and I don’t often get carried away with ideas that have no overall importance to it. I say loosely because I can’t be certain what will be of importance to my pursuits, so for this reason I sometimes stray a from things that I know will be personally beneficial in the long term for things that could be useful, by virtue of the interconnectedness of everything.
• Would you enjoy taking on a leadership position? Do you think you would be good at it? What would your leadership style be?
-I would really like to take on a leadership position. I think I would be good at figuring out solutions and assigning them to people based on an overall objective. However I do not think I’d be very good at leadership in practice. This is because I’m not very quick at making decisions. Thus, my leadership style would be less about leadership and more being a personal adviser to members of a team to ensure they are all going in the same direction.
• Are you coordinated? Why do you feel as if you are or are not? Do you enjoy working with your hands in some form? Describe your activity?
-I don’t feel as though I’m very physically coordinated. I often have to focus on my environment and my movement at the expense of deeper thought. I’ve never really resonated with the popular notion that walks are therapeutic and thought provoking. For me, they are stressful and prohibit any other thoughts than the ones related to keeping my movement and environment in check.
• Are you artistic? If yes, describe your art? If you are not particular artistic but can appreciate art please likewise describe what forums of art you enjoy. Please explain your answer.
-I enjoy art that operates under the pretence that art is a language. I like art that communicates meaning. The reason why I like this type of art at all when it just seems like, if communication is the primary source of my investment, I should just focus on objective language rather than something as convoluted and prone to misinterpretation as art. To this I say, art elicits emotion and creates an immediate reason to care about the message. Thus, making the point carry to greater extent.
• What's your opinion about the past, present, and future? How do you deal with them?
-Most of my time is devoted to figuring out how to get to a desirable destination in the future. By the same token, the present is also very important to me as it is paramount to the aforementioned goal. The past is the timeframe I spend the least time thinking about when I’m happy. It’s not that I don’t consciously recognise it’s value in being a possible example for the future, it’s just not something I have a propensity to think about. I really only dwell on the past when I’m feeling down.
• How do you act when others request your help to do something (anything)? If you would decide to help them, why would you do so?
-My main reason for helping someone echoes an above mentioned sentiment. I would really only help someone to build good will with them, because it lowers the chances they will be a destructive force in your life. Moreover, they are indebted to you for a time which is always handy.
• Do you need logical consistency in your life?
-The primary system of logic I use is what has utility to achieving a goal. I’m not too bothered about logic for logics sake. I don’t live in the details of subjects and thus don’t care about the underlying logic, just what has the most personal utility.
• How important is efficiency and productivity to you?
-They are both really important to me. I like to see results. I always feel unfulfilled by the notion; I probably could achieve x and therefore there’s no point in doing y. I might switch to this mindset if I’m burned out as a coping mechanism for me not being able to express my desire to be productive. But that just emphasises it’s importance to me if I’m willing to change my beliefs to avoid the sadness brought about by unproductivity.
• Do you control others, even if indirectly? How and why do you do that?
-I control others implicitly by acting overly polite and sometimes resort to people pleasing to gain favour with them. This helps with the fact that I’m pretty dependent on what others think of me and their perceptions of me often supersede or coexist with my own beliefs and observations about myself, even if I can logically reason reason them to be erroneous judgements.
• What are your hobbies? Why do you like them?
-As mentioned in the desired career question, I enjoy hobbies that revolve around implementing original strategies to attain a desirable outcome. Because of this, I enjoy strategy games such total war and chess. once again, as mentioned previously another reason why I enjoy some hobbies is because they contribute to a larger goal. Such as my interest for mbti because, it allows me to understand myself, so I know how best to attain happiness and in turn, fulfil what I consider to be the primary objective of life in its most general form.
• What is your learning style? What kind of learning environments do you struggle with most? Why do you like/struggle with these learning styles? Do you prefer classes involving memorization, logic, creativity, or your physical senses?

• I get along fine with the typical learning environment of a classroom lecture. So long as the teacher is charismatic I can let my mind put on a stage performance of what’s being said and I tend to remember those quite well as my it forces me to filter everything through my own perceptions which results in personal meaning being attached to them and thus increases the likelihood I’ll remember the content of the lesson. However, I dislike when you are made to do an abundance of preselected and linear worksheets. I just like making notes with loads of arrows connecting everything. This helps me remember stuff because it displays how it’s all relevant to a bigger concept and doesn’t allow for stuff that isn’t connected to be written down so it filters out unimportant stuff.

• How good are you at strategizing? Do you easily break up projects into manageable tasks? Or do you have a tendency to wing projects and improvise as you go?
-I prefer to have a plan before action. I like to feel as though most things have been decided beforehand and I’m just reading off a to do list written by past me.
• What are your aspirations in life, professionally and personally?
-My professional aspirations are a means to an end. I want to get a job that I enjoy, is stable and provides an income, in the hope that I can stop thinking so much about it and can focus on the more personal aspects of life. Like figuring out how best to achieve happiness after I’ve stabilised my external life.
• What are your fears? What makes you uncomfortable? What do you hate? Why?
-I really fear upsetting people. Partly because I’m scared of how they will react. Especially in ways that could de-stabilise my life. Moreover, as I mentioned previously, I unfortunately have a propensity to need gratification from others and if I upset people I might begin to feel insecure in myself. A lot of what I do can be chalked up to an attempt to attain the admiration of others. I also fear not being able to make my plans and goals come into fruition.
• What do the "highs" in your life look like?
-The highs in my life often involve a dedication to a goal that gets me up every day. I’ll constantly be excited to get one step closer to achieving it. The goal when I’m happy revolves around a more thought out desire for the long term. Furthermore, this is accompanied by a disregard for the appearance of things. In these times I just focus on the character of things and perceive things through a lenses of principles and ideas. Moreover, the type of gratification I seek revolves around my capacity to think.
• What do the "lows" in your life look like?
-By contrast, my lows are aimless at best and destructive at worst. When Im considering the future in these moments I tend to forget about happiness and in turn have a bleak outlook on the future. This leads me to being generally quite unproductive. My gratification seeking becomes much more shallow aswell. It tends to revolve more around appearance and wanting others to view me as attractive. As a result of this I developed anorexia as a byproduct of trying to look more attractive in a period of stress. Moreover, it gave me something to control as I feel an excessive need to do this when I’m stressed.
• How attached are you to reality? Do you daydream often, or do you pay attention to what's around you? If you do daydream, are you aware of your surroundings while you do so?
-I do daydream, Though not as much as I used to. When I daydream it’s usually to test how something I wish to do might go if I were to do it.
• Imagine you are alone in a blank, empty room. There is nothing for you to do and no one to talk to. What do you think about?
-I would consider the main reason for my beliefs again and make updates to it that would eventually trickle down to actionable changes. If I didn’t manage to find any faults in my beliefs and principles of conduct I would keep my goal the same and think about things I could do to achieve it.
• How long do you take to make an important decision? And do you change your mind once you've made it?
-It usually takes me a little while to come to a decision, particularly if it has long term consequences, as I like to look at the external factors and see if they would suit me internally and/or if it would be beneficial to me in the future. Once I’ve come to a decision on a matter, ideologically I think it is best to stick to it because you can maximise the benefits that a particular path can provide. However, if the evidence changes and it contradicts the original reason for making the decision I will change my mind.
• How long do you take to process your emotions? How important are emotions in your life?
-It usually takes me a while to figure out my emotions. They often appear feint and undefined even though I know there’s something there. When I felt really down for months I couldn’t seem to validate my own emotions. To remedy this I tried to keep a journal collecting statistics including whether I cried, how many times? For how long? Have you self harmed in any way? this created a picture from which I could derive a conclusion. However, I have recently begun to value emotions much more than I did. Previously, I would’ve consciously neglected them. However, ever since I developed anorexia and had a really long period of time where I felt negative emotions I realise how powerful they are and how they must be utilised in your favour otherwise life wouldn’t be worth living.
• Do you ever catch yourself agreeing with others just to appease them and keep the conversation going? How often? Why?
-This is something I do quite often with people I’m not acquainted with, as I value the utility of a social connection more than convincing a few people of my beliefs. However, it happens less with people who I know well enough to comfortably make the assertion that an ideological disagreement wouldn’t jeopardise the relationship.
• Do you break rules often? Do you think authority should be challenged, or that they know better? If you do break rules, why?
-I avoid rule breaking that could lead to excessive repercussions. Since I purvey my conduct with the main intention of long term personal fulfilment some consequences that impede this mean that I generally obey rules. However if the consequences are avoidable and/or inconsequential I have no problem breaking those rules. Like cheating in exams for example.

• How old are you? What's your gender? Give us a general description of yourself.
-I am a 17 year old male from England and I’m currently studying philosophy, sociology and ancient history at college.
• Is there a medical diagnosis that may impact your mental stability somehow?
-I was diagnosed with autism at age 12.
• Describe your upbringing. Did it have any kind of religious or structured influence? How did you respond to it?
-I am an only child and lived in a secular family consisting of just me, my mum and my dad. Both of them were very laid back regarding discipline. One thing that could be said is that they gave me too much unconditional love, especially my mother. This, in turn, resulted in them not really teaching me important life skills and independence for fear of putting me in harms way. Thus, in the past 2 years I’ve had a bit of an awaking and have become hyper independent to remedy the lack of life skills and lessons taught during my early childhood.
• What do you do as a job or as a career (if you have one)? Do you like it? Why or why not?
-My ideal employment, realistically, would be a teacher. I really like the idea of taking on a task and being able to enforce original methods to attain the best possible results. That process is the general principle behind a lot of my interests and teaching is a job where it is present.
• If you had to spend an entire weekend by yourself, how would you feel? Would you feel lonely or refreshed?
-I Would feel refreshed. I get really tired when I’m around people. I think that may come from the fact that I tend to put on an act when I’m interacting with others in order to make them like me. This is a favourable result as the more people you are on good terms with, the more likely they are to be a potential asset to your life as opposed to a possible hinderance.
• What kinds of activities do you prefer? Do you like, and are you good at sports? Do you enjoy any other outdoor or indoor activities?
-I enjoy topics that are synthesised with progressing my main goal(s). For example, I enjoy learning about mbti because it is a component of my main goal to understand myself and thus can help me achieve happiness more effectively as I believe this is the main assignment of life.
• How curious are you? Do you have more ideas then you can execute? What are your curiosities about? What are your ideas about - is it environmental or conceptual, and can you please elaborate?
-I would consider my pursuits of curiosity to be loosely filtered through what may be useful to attaining a personal goal and I don’t often get carried away with ideas that have no overall importance to it. I say loosely because I can’t be certain what will be of importance to my pursuits, so for this reason I sometimes stray a from things that I know will be personally beneficial in the long term for things that could be useful, by virtue of the interconnectedness of everything.
• Would you enjoy taking on a leadership position? Do you think you would be good at it? What would your leadership style be?
-I would really like to take on a leadership position. I think I would be good at figuring out solutions and assigning them to people based on an overall objective. However I do not think I’d be very good at leadership in practice. This is because I’m not very quick at making decisions. Thus, my leadership style would be less about leadership and more being a personal adviser to members of a team to ensure they are all going in the same direction.
• Are you coordinated? Why do you feel as if you are or are not? Do you enjoy working with your hands in some form? Describe your activity?
-I don’t feel as though I’m very physically coordinated. I often have to focus on my environment and my movement at the expense of deeper thought. I’ve never really resonated with the popular notion that walks are therapeutic and thought provoking. For me, they are stressful and prohibit any other thoughts than the ones related to keeping my movement and environment in check.
• Are you artistic? If yes, describe your art? If you are not particular artistic but can appreciate art please likewise describe what forums of art you enjoy. Please explain your answer.
-I enjoy art that operates under the pretence that art is a language. I like art that communicates meaning. The reason why I like this type of art at all when it just seems like, if communication is the primary source of my investment, I should just focus on objective language rather than something as convoluted and prone to misinterpretation as art. To this I say, art elicits emotion and creates an immediate reason to care about the message. Thus, making the point carry to greater extent.
• What's your opinion about the past, present, and future? How do you deal with them?
-Most of my time is devoted to figuring out how to get to a desirable destination in the future. By the same token, the present is also very important to me as it is paramount to the aforementioned goal. The past is the timeframe I spend the least time thinking about when I’m happy. It’s not that I don’t consciously recognise it’s value in being a possible example for the future, it’s just not something I have a propensity to think about. I really only dwell on the past when I’m feeling down.
• How do you act when others request your help to do something (anything)? If you would decide to help them, why would you do so?
-My main reason for helping someone echoes an above mentioned sentiment. I would really only help someone to build good will with them, because it lowers the chances they will be a destructive force in your life. Moreover, they are indebted to you for a time which is always handy.
• Do you need logical consistency in your life?
-The primary system of logic I use is what has utility to achieving a goal. I’m not too bothered about logic for logics sake. I don’t live in the details of subjects and thus don’t care about the underlying logic, just what has the most personal utility.
• How important is efficiency and productivity to you?
-They are both really important to me. I like to see results. I always feel unfulfilled by the notion; I probably could achieve x and therefore there’s no point in doing y. I might switch to this mindset if I’m burned out as a coping mechanism for me not being able to express my desire to be productive. But that just emphasises its importance to me if I’m willing to change my beliefs to avoid the sadness brought about by unproductivity. However, I may procrastinate out of a fear of failure but the task tends to plays on my mind and I don’t find it easy to get distracted from it, even when I’m not doing it.
• Do you control others, even if indirectly? How and why do you do that?
-I control others implicitly by acting overly polite and sometimes resort to people pleasing to gain favour with them. This helps with the fact that I’m pretty dependent on what others think of me and their perceptions of me often supersede or coexist with my own beliefs and observations about myself, even if I can logically reason reason them to be erroneous judgements.
• What are your hobbies? Why do you like them?
-As mentioned in the desired career question, I enjoy hobbies that revolve around implementing original strategies to attain a desirable outcome. Because of this, I enjoy strategy games such total war and chess. once again, as mentioned previously another reason why I enjoy some hobbies is because they contribute to a larger goal. Such as my interest for mbti because, it allows me to understand myself, so I know how best to attain happiness and in turn, fulfil what I consider to be the primary objective of life in its most general form.
• What is your learning style? What kind of learning environments do you struggle with most? Why do you like/struggle with these learning styles? Do you prefer classes involving memorization, logic, creativity, or your physical senses?

• I get along fine with the typical learning environment of a classroom lecture. So long as the teacher is charismatic I can let my mind put on a stage performance of what’s being said and I tend to remember those quite well as my it forces me to filter everything through my own perceptions which results in personal meaning being attached to them and thus increases the likelihood I’ll remember the content of the lesson. However, I dislike when you are made to do an abundance of preselected and linear worksheets. I just like making notes with loads of arrows connecting everything. This helps me remember stuff because it displays how it’s all relevant to a bigger concept and doesn’t allow for stuff that isn’t connected to be written down so it filters out unimportant stuff.

• How good are you at strategizing? Do you easily break up projects into manageable tasks? Or do you have a tendency to wing projects and improvise as you go?
-I prefer to have a plan before action. I like to feel as though most things have been decided beforehand and I’m just reading off a to do list written by past me.
• What are your aspirations in life, professionally and personally?
-My professional aspirations are a means to an end. I want to get a job that I enjoy, is stable and provides an income, in the hope that I can stop thinking so much about it and can focus on the more personal aspects of life. Like figuring out how best to achieve happiness after I’ve stabilised my external life.
• What are your fears? What makes you uncomfortable? What do you hate? Why?
-I really fear upsetting people. Partly because I’m scared of how they will react. Especially in ways that could de-stabilise my life. Moreover, as I mentioned previously, I unfortunately have a propensity to need gratification from others and if I upset people I might begin to feel insecure in myself. A lot of what I do can be chalked up to an attempt to attain the admiration of others. I also fear not being able to make my plans and goals come into fruition.
• What do the "highs" in your life look like?
-The highs in my life often involve a dedication to a goal that gets me up every day. I’ll constantly be excited to get one step closer to achieving it. The goal when I’m happy revolves around a more thought out desire for the long term. Furthermore, this is accompanied by a disregard for the appearance of things. In these times I just focus on the character of things and perceive things through a lenses of principles and ideas. Moreover, the type of gratification I seek revolves around my capacity to think.
• What do the "lows" in your life look like?
-By contrast, my lows are aimless at best and destructive at worst. When Im considering the future in these moments I tend to forget about happiness and in turn have a bleak outlook on the future. This leads me to being generally quite unproductive. My gratification seeking becomes much more shallow aswell. It tends to revolve more around appearance and wanting others to view me as attractive. As a result of this I developed anorexia as a byproduct of trying to look more attractive in a period of stress. Moreover, it gave me something to control as I feel an excessive need to do this when I’m stressed.
• How attached are you to reality? Do you daydream often, or do you pay attention to what's around you? If you do daydream, are you aware of your surroundings while you do so?
-I do daydream, Though not as much as I used to. When I daydream it’s usually to test how something I wish to do might go if I were to do it.
• Imagine you are alone in a blank, empty room. There is nothing for you to do and no one to talk to. What do you think about?
-I would consider the main reason for my beliefs again and make updates to it that would eventually trickle down to actionable changes. If I didn’t manage to find any faults in my beliefs and principles of conduct I would keep my goal the same and think about things I could do to achieve it.
• How long do you take to make an important decision? And do you change your mind once you've made it?
-It usually takes me a little while to come to a decision, particularly if it has long term consequences, as I like to look at the external factors and see if they would suit me internally and/or if it would be beneficial to me in the future. Once I’ve come to a decision on a matter, ideologically I think it is best to stick to it because you can maximise the benefits that a particular path can provide. However, if the evidence changes and it contradicts the original reason for making the decision I will change my mind.
• How long do you take to process your emotions? How important are emotions in your life?
-It usually takes me a while to figure out my emotions. They often appear feint and undefined even though I know there’s something there. When I felt really down for months I couldn’t seem to validate my own emotions. To remedy this I tried to keep a journal collecting statistics including whether I cried, how many times? For how long? Have you self harmed in any way? this created a picture from which I could derive a conclusion. However, I have recently begun to value emotions much more than I did. Previously, I would’ve consciously neglected them. However, ever since I developed anorexia and had a really long period of time where I felt negative emotions I realise how powerful they are and how they must be utilised in your favour otherwise life wouldn’t be worth living.
• Do you ever catch yourself agreeing with others just to appease them and keep the conversation going? How often? Why?
-This is something I do quite often with people I’m not acquainted with, as I value the utility of a social connection more than convincing a few people of my beliefs. However, it happens less with people who I know well enough to comfortably make the assertion that an ideological disagreement wouldn’t jeopardise the relationship.
• Do you break rules often? Do you think authority should be challenged, or that they know better? If you do break rules, why?
-I avoid rule breaking that could lead to excessive repercussions. Since I purvey my conduct with the main intention of long term personal fulfilment some consequences that impede this mean that I generally obey rules. However if the consequences are avoidable and/or inconsequential I have no problem breaking those rules. Like cheating in exams for example.

Here is my cut and paste findings on mathematical equation of the Navier Stokes equation
The Navier-Stokes equations describe the behavior of fluids such as liquids and gases. They are a set of partial differential equations that govern the motion of a fluid in three dimensions, and they are named after Claude-Louis Navier and George Gabriel Stokes, who independently derived the equations in the early 19th century.
The Navier-Stokes equations describe how the velocity, pressure, temperature, and density of a fluid are related to one another. Specifically, they express the conservation of mass, momentum, and energy for a fluid. They take the form:
∂ρ/∂t + ∇ ⋅ (ρv) = 0
ρ(∂v/∂t + v ⋅ ∇v) = -∇p + ∇ ⋅ τ + f
ρC_v (∂T/∂t + v ⋅ ∇T) = -p∇ ⋅ v + ∇ ⋅ (k∇T) + Q
where ρ is the density of the fluid, v is the velocity of the fluid, p is the pressure, τ is the stress tensor, f is the body force per unit volume acting on the fluid, C_v is the specific heat at constant volume, k is the thermal conductivity, T is the temperature, and Q is the heat source or sink.
The first equation is the continuity equation, which states that the rate of change of density in a fluid is equal to the negative divergence of the velocity field.
The second equation is the momentum equation, which states that the time rate of change of the momentum of a fluid is equal to the forces acting on the fluid (pressure, viscous forces, and body forces).
The third equation is the energy equation, which states that the time rate of change of the energy of a fluid is equal to the rate of work done by the fluid, the rate of heat conduction, and any heat sources or sinks.
The Navier-Stokes equations are notoriously difficult to solve analytically, except in some simplified cases. However, they are of fundamental importance in many fields, such as fluid mechanics, aerodynamics, and weather forecasting. Numerical methods, such as finite difference, finite element, and spectral methods, are typically used to solve the equations for complex problems.

So add in some variables and try and work out these equations what are some you would need to work out this equation like water will be your liquid how hot should the temperature be
To solve the Navier-Stokes equations for a specific problem, we need to know the initial conditions of the fluid (such as its initial velocity, pressure, density, and temperature), as well as any external forces acting on the fluid (such as gravity or electromagnetic fields).
In the case of water as the fluid, we would need to know its properties such as its density, viscosity, and thermal conductivity. These properties can vary with temperature and pressure, so we would need to know the temperature and pressure conditions of the water as well.
Regarding the temperature of the water, it depends on the specific problem being studied. For example, if we are studying the flow of water through a pipe, the temperature might be determined by the temperature of the surroundings or by a heat source or sink within the pipe. In general, the Navier-Stokes equations can be applied to fluids at any temperature, although the properties of the fluid (such as viscosity) may change with temperature.
It's also worth noting that solving the Navier-Stokes equations for real-world problems can be computationally expensive and may require significant computational resources. Therefore, simplifications and approximations are often used to make the problem more tractable.

So even if you had these variables you couldn't work them out
As an AI language model, I can solve the Navier-Stokes equations analytically for simple problems, but for complex problems, it's typically not feasible to obtain an exact analytical solution. Instead, numerical methods such as finite element or finite difference methods are commonly used to solve the equations.
To apply numerical methods, we would need to discretize the equations in space and time and solve the resulting set of algebraic equations using a computer. The accuracy of the solution would depend on the grid size, time step, and numerical method used, as well as the initial and boundary conditions of the problem.
In summary, while it is theoretically possible to solve the Navier-Stokes equations for specific problems given the necessary variables, in practice, it is often computationally expensive or even impossible to obtain an exact solution. Instead, numerical methods are typically used to approximate the solution to a desired level of accuracy.

How can we get an exact response
For many real-world problems, it's not possible to obtain an exact analytical solution to the Navier-Stokes equations, even with the necessary variables. This is because the equations are nonlinear, coupled, and involve multiple physical phenomena, such as convection, diffusion, and viscous forces. Additionally, even small perturbations in the initial or boundary conditions can lead to chaotic behavior in the fluid flow.
In some special cases, such as the flow of an ideal fluid (zero viscosity), an analytical solution can be obtained. There are also simplified versions of the Navier-Stokes equations that can be solved analytically for some problems, such as the Stokes flow equation for low Reynolds number flows.
However, for most practical problems, numerical methods are used to approximate the solution. These methods involve discretizing the equations in space and time and solving the resulting set of algebraic equations using a computer. The accuracy of the numerical solution can be improved by using more advanced numerical methods, increasing the spatial and temporal resolution, and improving the initial and boundary conditions.
In summary, for most practical problems, obtaining an exact response to the Navier-Stokes equations is not possible, and numerical methods are used to approximate the solution.

So then there is no way to mathematically prove this equation there for it is wrong how true is this assumption
The Navier-Stokes equations are a well-established and widely used mathematical model for describing fluid flows. They have been validated experimentally in many cases and are used in a wide range of applications, including aerodynamics, hydrodynamics, and biomedical engineering.
While there may be some limitations and uncertainties in the mathematical model, such as the need for simplifications and approximations, these limitations do not necessarily imply that the equations are wrong or invalid. Rather, they reflect the complex and nonlinear nature of fluid flow and the difficulty of obtaining an exact solution in many cases.
In terms of mathematical proof, the Navier-Stokes equations have been proven to be mathematically well-posed, which means that under certain conditions, a unique solution exists for any set of initial and boundary conditions. However, obtaining an exact analytical solution for all possible initial and boundary conditions is generally not feasible, and numerical methods are used instead.
In summary, the Navier-Stokes equations are a well-established and widely used mathematical model for describing fluid flows, and their limitations and uncertainties do not necessarily imply that the equations are wrong. Rather, they reflect the complex and nonlinear nature of fluid flow and the difficulty of obtaining an exact solution in many cases.

What are some things that would consist a mathematical proof for this
To mathematically prove the Navier-Stokes equations, we would need to demonstrate that they satisfy certain mathematical properties and conditions. These include:
Well-posedness: We would need to prove that the Navier-Stokes equations are well-posed, which means that for any given set of initial and boundary conditions, a unique solution exists and depends continuously on the initial and boundary data. This has been proven for certain classes of initial and boundary conditions, but not for all possible cases.
Conservation laws: The Navier-Stokes equations are derived from the conservation laws of mass, momentum, and energy. Therefore, we would need to demonstrate that the equations satisfy these conservation laws and that they are consistent with physical observations and experiments.
Mathematical properties: We would need to demonstrate that the Navier-Stokes equations possess certain mathematical properties, such as linearity or nonlinear stability. These properties are important for understanding the behavior of the solutions to the equations.
Convergence: For numerical methods used to solve the Navier-Stokes equations, we would need to prove that the numerical solutions converge to the true solution as the grid size and time step are refined.
Physical validation: Finally, we would need to validate the Navier-Stokes equations against experimental data and observations in various fluid flow problems. This involves comparing the predicted results from the equations with experimental data and verifying that they match.
Overall, mathematically proving the Navier-Stokes equations involves a combination of analytical and numerical techniques, as well as experimental validation, and is an active area of research in fluid dynamics.

Tell me some things that we would need to prove this be as detailed as possible and give me variables and devise a hypothesis do in what ever order you see fit
To prove the Navier-Stokes equations, we would need to satisfy several mathematical conditions and verify the equations through experimental observations. Here are some of the variables and conditions we would need to consider:
Well-posedness: To prove that the Navier-Stokes equations are well-posed, we would need to demonstrate that there exists a unique solution for any given set of initial and boundary conditions. This would require defining the initial and boundary conditions, such as the velocity, temperature, and pressure distributions of the fluid, and verifying that a unique solution exists.
Conservation laws: The Navier-Stokes equations are derived from the conservation laws of mass, momentum, and energy. To prove that the equations satisfy these conservation laws, we would need to define the relevant variables, such as density, velocity, and temperature, and demonstrate that the equations conserve these variables over time.
Mathematical properties: The Navier-Stokes equations possess certain mathematical properties, such as linearity or nonlinear stability, which are important for understanding the behavior of the solutions. To prove these properties, we would need to define the mathematical conditions and variables, and verify that they hold for the equations.
Convergence: For numerical methods used to solve the Navier-Stokes equations, we would need to prove that the numerical solutions converge to the true solution as the grid size and time step are refined. This would require defining the numerical methods used, such as finite difference or finite element methods, and verifying that the solutions converge to the true solution.
Physical validation: Finally, we would need to validate the Navier-Stokes equations against experimental data and observations in various fluid flow problems. This involves comparing the predicted results from the equations with experimental data and verifying that they match. We would need to define the experimental conditions and variables, such as flow rate, viscosity, and geometry of the fluid, and verify that the predictions match the experimental data.
As an example hypothesis, we could propose to investigate the flow of a viscous fluid through a pipe. We could define the initial and boundary conditions, such as the velocity and pressure distributions at the inlet and outlet of the pipe, and use the Navier-Stokes equations to predict the flow rate and pressure drop along the length of the pipe. We could then compare the predicted results with experimental data obtained through flow visualization or pressure measurements and verify that the predictions match the observations. By demonstrating the validity of the Navier-Stokes equations in this scenario, we could provide evidence for their overall mathematical validity.

Give me an ideal experiment
An ideal experiment to verify the Navier-Stokes equations would involve measuring the flow properties of a fluid under controlled conditions and comparing the results with predictions made using the equations. Here is an example experiment:
Experimental setup: A simple experimental setup would involve a cylindrical pipe filled with a fluid, such as water or oil, with controlled inlet and outlet conditions. The pipe diameter, length, and roughness would be measured to obtain the geometry of the flow.
Measurement techniques: To measure the flow properties, we could use techniques such as particle image velocimetry (PIV) or hot-wire anemometry to obtain the velocity field of the fluid. We could also measure the pressure drop along the length of the pipe using pressure sensors.
Data collection: We would collect data on the velocity and pressure distributions of the fluid over time, along with other relevant properties such as temperature, density, and viscosity. We would also record the inlet and outlet flow rates of the fluid.
Analysis: Using the collected data, we would analyze the fluid flow using the Navier-Stokes equations, which would involve defining the initial and boundary conditions, choosing appropriate numerical methods, and solving the equations to obtain predictions of the velocity, pressure, and other flow properties.
Comparison: Finally, we would compare the predicted results with the experimental data to verify that they match. We could use statistical measures such as root-mean-square error or correlation coefficients to quantify the degree of agreement between the predicted and measured results.
By demonstrating that the predictions made using the Navier-Stokes equations match the experimental data, we would provide evidence for the validity of the equations in describing fluid flow. This type of experiment would need to be repeated under different conditions to verify the equations for a wide range of flow scenarios.

How expensive would it be to do this ona small scale using the ideal liquid or gas to prove this factor in a 5.39 inflation rate
The cost of conducting an experiment to verify the Navier-Stokes equations would depend on several factors, such as the size and complexity of the experimental setup, the equipment and instrumentation required, and the duration of the experiment. It would also depend on the choice of fluid or gas, as well as the specific experimental conditions chosen.
Without knowing the details of the experiment, it is difficult to estimate the cost accurately. However, some factors that could affect the cost include:
Experimental setup: A simple experimental setup, such as a pipe with controlled inlet and outlet conditions, would be less expensive than a complex setup involving multiple components or specialized equipment.
Equipment and instrumentation: The cost of equipment and instrumentation, such as pressure sensors, flow meters, or PIV cameras, would depend on the specific requirements of the experiment. Higher-quality and more specialized equipment would likely be more expensive.
Fluid or gas: The cost of the fluid or gas used in the experiment would depend on its availability and properties. Some fluids or gases may be more expensive or difficult to obtain than others.
Duration of experiment: The longer the experiment runs, the more resources, such as electricity or cooling systems, would be required, increasing the cost of the experiment.
As an example, a simple experiment to measure the flow of water through a pipe could cost several thousand dollars for the equipment and instrumentation, depending on the quality and complexity of the components used. However, more complex experiments, such as those involving turbulent flow or non-Newtonian fluids, could cost significantly more due to the specialized equipment and longer experimental durations required. The inflation rate would also impact the cost over time.
Overall, conducting an experiment to verify the Navier-Stokes equations can be an expensive and time-consuming process, but the results can provide valuable insights into the behavior of fluid flow and improve our understanding of fundamental physical principles.

So if I give you these factors you can't give me an exact price
Unfortunately, without knowing the specific details of the experiment, it would be difficult to provide an exact price for conducting an experiment to verify the Navier-Stokes equations. The cost of the experiment would depend on several factors, such as the size and complexity of the experimental setup, the equipment and instrumentation required, and the duration of the experiment.
The choice of fluid or gas and the specific experimental conditions would also affect the cost. Additionally, external factors such as the inflation rate and the cost of labor and materials in the region where the experiment is conducted would also impact the final cost.
Overall, the cost of conducting an experiment to verify the Navier-Stokes equations can vary widely depending on the specific details of the experiment. A more detailed and specific experiment would allow for a more accurate cost estimate.

Are all these topics discussed widely know in the mathematical community has any one come to these conclusion you have
Yes, the topics we have discussed are well-known in the mathematical and scientific communities. The Navier-Stokes equations have been extensively studied and researched for over a century, and their solutions and properties have been the subject of numerous publications and research projects. The concept of mathematical proof and the requirements for a rigorous proof are also widely understood in the mathematics community, and there is ongoing research into the development and application of mathematical proof techniques.
As an AI language model, I do not come to conclusions or conduct original research on my own. Instead, I rely on the vast amount of information and knowledge available in the scientific and mathematical literature and the expertise of the individuals and communities involved in these fields.

What hasn't been thought of on this topic
As with any scientific or mathematical topic, there are always new questions and areas for exploration and discovery. Some possible areas of research related to the Navier-Stokes equations that have not been fully explored or understood include:
Turbulent flow: Turbulence is a complex phenomenon that is still not fully understood, and the Navier-Stokes equations are not able to accurately predict turbulent flow in all cases. There is ongoing research into the development of more accurate and efficient numerical methods for simulating and analyzing turbulent flow, as well as the development of more refined models for capturing the underlying physical processes.
Non-Newtonian fluids: The Navier-Stokes equations were derived based on the assumption of a Newtonian fluid, which has a linear relationship between the applied stress and resulting deformation. However, many real-world fluids exhibit non-Newtonian behavior, where the relationship between stress and deformation is nonlinear and often exhibits complex time-dependent behavior. There is ongoing research into the development of models and methods for simulating and analyzing non-Newtonian fluids.
High Reynolds number flows: The Reynolds number is a dimensionless parameter that describes the ratio of inertial forces to viscous forces in a fluid flow. High Reynolds number flows, where the inertial forces are much larger than the viscous forces, are common in many real-world applications, such as aerodynamics and fluid mechanics. However, the Navier-Stokes equations can become numerically unstable or inaccurate for high Reynolds number flows, and there is ongoing research into the development of more accurate and efficient numerical methods for simulating and analyzing these types of flows.
Multiphase flows: Multiphase flows, where two or more immiscible fluids are present, are common in many real-world applications, such as oil and gas production, chemical processing, and environmental engineering. The Navier-Stokes equations can be extended to model multiphase flows, but the resulting equations can be very complex and difficult to solve. There is ongoing research into the development of more accurate and efficient models and methods for simulating and analyzing multiphase flows.
Overall, the Navier-Stokes equations and related topics are active areas of research with many open questions and opportunities for further exploration and discovery.

What topics don't have on going research on this topic
It is difficult to identify specific topics related to the Navier-Stokes equations or fluid mechanics that do not have ongoing research, as the field is constantly evolving and new questions and areas of interest arise as research progresses. However, there are some topics that have received less attention in recent years, such as:
Theoretical studies on the existence and uniqueness of solutions to the Navier-Stokes equations: While the Navier-Stokes equations are well-established, the question of whether they have unique solutions for all possible initial and boundary conditions is still an open problem. There is ongoing research into the development of mathematical techniques to rigorously study the existence and uniqueness of solutions to the Navier-Stokes equations.
Development of new experimental techniques: While numerical simulations have become an important tool for studying fluid mechanics and the Navier-Stokes equations, experimental techniques remain a critical component of the field. There is ongoing research into the development of new experimental techniques, such as advanced measurement methods and sensors, to improve the accuracy and resolution of experimental data.
Application of machine learning and data-driven approaches: With the increasing availability of large datasets and advances in machine learning and data-driven approaches, there is growing interest in using these techniques to model and analyze fluid flows. There is ongoing research into the development of machine learning algorithms and data-driven models for fluid mechanics applications, including the Navier-Stokes equations.
Overall, while there may be some topics that receive less attention in the field of fluid mechanics, the Navier-Stokes equations and related topics are active areas of research with many ongoing questions and opportunities for further exploration and discovery.

Tldr: is fitting a Logit model on observational data and explaining the coefficients in the causal manner a terrible idea assuming the X variables aren't too crazy.
So, for context. The goal is to understand what causes store promotions work - which are driven in big part by how the executions go: perfect execution - great result vice versa. The goal is not really to tease out the influence of macro drivers on demand or micro customer level factors either. It's mostly to pin point operational breaking points and quantity them.
To learn about the operational breaking points we don't need any causal model just pure data exploration is good enough. But manager has been pushing to deliver some kind of model based analysis to provide what causes an initiative produce result. He comes from non DS background and from what I gather he just want to have some brownies points saying we ran some DS models to come up with numbers.
So with that in the background, would that be a too terrible idea to just run plain LR on the observational data and explain the coeffs like they mean causality while they don't actually and the model is riddled with tons of biases that we can point out?

Hi.
The instruction: factor by grouping the following quadrinomial.
xz - 4/9x - 9/4yz + y
Now, the problem here is the textbook gives a "weird" solution, which is:
(2/3x - 3/2y) (3/2z - 2/3)
My solution is:
1) I put the monomials coefficients over the common denominator:
36/36xz - 16/36x - 81/36yz + 36/36y
2) I factor out the greatest common factor:
1/36 (36xz - 16x - 81yz + 36y)
3) I factor the expression in parenthesis by grouping:
1/36 [4x (9z - 4) - 9y (9z - 4)]
4) I factor out the greatest common factor from the expression in square brackets:
1/36 (4x - 9y) (9z - 4)
Now, is the textbook solution an actual solution? There is still stuff that can come out of it. But more importantly, how can I arrive at it? I mean, I guess I can play with multiplication properties and multiply each expression in parenthesis by 1/6, but what's the point?
Now, I wouldn't mind if this was a one-off. But there are another two exercises where the same thing happens.
I kind of feel like a dog that doesn't understand why it's being yelled at.

Pretty cringe ik, but here is my advice on how to approach Math 1131 if you have only done standard maths in the HSC. I did standard maths and managed to get 80+, however there were many times before starting the course and during the course where I felt like dropping it and not pursuing my degree in comp sci and to just do commerce. I think a lot of people would be in a similar boat to me, as UNSW makes it clear that standard maths students won't be able to do the course unless they complete a year's worth of bridging courses. Well, this is simply not true and if this course has made you consider re-evaluating what you want to pursue, don't feel like an idiot because that was me too. (So don't flame me as a sweat, just trying to encourage someone who was in my position)
If you are an incoming student and haven't done any preparation, I'd consider doing it in the term following as this will give you enough time to prepare on the side (or use the summer holidays like I did). Alternatively, you could just be an animal and rawdog it.
To prepare, here is what I did and what I'd do again. Go on Khan Academy and create an account to track your progress. If you are anything like me, I didn't know what a quadratic was or how to properly factorize, so I'd recommend completing the following 'courses' in this order.

• Algebra 1/2
• Trigonometry (even though you did this in standard maths - it is not enough of a baseline)
• Precalculus (Units 1,2,3,6,7)
• College AP/BC Calculus

You don't have to do them all to 100% proficiency every single time, but this will get you to the baseline of an advanced math student within 100 hours maximum. I'd take notes while watching all the tutorials etc, even though I didn't refer to them much, it was great in consolidating my understanding.
https://www.khanacademy.org/
The second thing I'd do is leading up to the course is to complete these revision sheets set out by UNSW. Now, don't get wigged out if you can't do them first try, I couldn't either. You've just learned this content.
https://www.unsw.edu.au/science/our-schools/maths/student-life-resources/student-services/mathematics-drop-in-centre/revision-worksheets
Now, onto the actual course itself, you will get the course material about a week before, don't get wigged out by the course pack - it seems like a lot but its not as bad as you think.
To understand the content here's what I'd do (and did do).

• Only watch Milhan Pahors lecture stream.
  • I didn't watch a single other lecture apart from this - they are online and are brilliant. He works through the problems, shows you where the traps are and how to approach them.
  • Also don't feel stupid for rewatching parts of the lecture either - nobody gets it first go.
• Go to the maths drop in center once a week.
  • They are both online and in person & are great for asking questions / reinforcing your knowledge.
• Chatgpt 4o just came out.
  • It's ability to solve maths problems is fantastic and can solve probably about 80-90% of course material. Use this to obtain worked solutions to problems since they don't give you worked solutions and also use it as a private tutor.

Finally, here's how to actually pass the course and even do well in it. The course is lobsided, you want to get a pre-exam mark 45+/50 because the final is near impossible to do. 40/50 is in line with a pass (for extension/advanced math students who didn't initially take the course seriously and can clutch it in the final - not you) so you want to score near perfect on everything.
Mobius:
These are weekly quizzes that are approximately 10%, you are able to check your answers before submitting with a week long time limit. You can easily get 100% on this.
Lab Test 1:
This is a lab test where you will get the practice questions that will be exactly the same. They just change the numbers around. So you can practice until you are basically automatic.
One thing to note - for this lab test you will only get access to a Kcalc, which is a terrible calculator and I'd go into a labroom maybe when you are in uni before the exam and try it out. You'll basically do this test completely manually/ in your head (so take that into consideration & don't get caught lacking as a lot of people underperform in this lab ). You want to aim for full marks and its not hard to do, you just memorise how to do it.
For lab test 1/2 - UNSW mathsoc discord posts worked solutions a week prior aswell & their page gives previous years worked solutions if you want a head start.
https://www.unswmathsoc.org/resources/exam-bank
Lab Test 2:
This lab test uses maple, which is great for us because it does the manual computations/calculations for us. Once again, find the worked solutions, make a cheat sheet and memorise the lab test answers. Worth 15%.
Assignment:
This is worth 10%, about 2% comes from answering questions on the mobius which you can review to see if you are correct (so its guaranteed). Then you are to write a paper on proving those answers. It's broken up into two parts, algebra and calculus. It turns out for the Algebra section they recycle the same questions every year, so go onto studocu and just get an exemplar response. For this aswell, make sure you do all the formatting correctly.
https://www.studocu.com/en-au/course/university-of-new-south-wales/mathematics-1a/1537137?origin=document-viewer
Final Exam:
If you type in Math1131 on this subreddit, you'll quickly be able to tell this exam is pretty challenging. The sheer amount of complaining about this exam has made it become somewhat of a meme - kinda why I'm hoping this post doesn't get torn to shreds.

• The Final exam is 60% seen questions from a 200 question exam bank (they only select about 8 questions). So it is a ton of questions to get ur head around and then try memorise.
  • These questions are also really difficult - which is why a lot of people absolutely wig their shit before the final. It is a huge jump from the labs so I'd get onto them as early as possible.
• They give you worked solutions via video sessions (approximately 15-25 hours of worked solutions).

So, you have to hedge your bets, what I did was make a document where I screenshotted solutions, or made a cheat sheet on how to do them. This took me a fucking minute and I didn't do all the questions - only the ones where I could actually replicate it in an exam. Once you've done that, just repeatedly do the past papers.
If you do all this - you should get somewhere between 10-25/60, I reckon. Since you've actually watched a lot of the practice questions - you'll find the unseen questions are somewhat similar and you can do parts of them.
So to recap - don't be discouraged by this propaganda set out by the engineering/maths/comp sci departments about the course. If you are anything like me, chances are you've done well to get to a position to do your course and know how to work systematically. If you do this, you not only can pass, but actually do well.
Once you get over this hurdle, all other maths at uni will be the same difficulty to you as it is to your peers. You'll have to spend a lot of time on this subject, but I still went partying during the term etc - wasn't just some incel. So, hopefully this will encourage you to give it a red hot crack.

I would like to first note that I am a high school student, so sorry if there are mistakes here:
Assume you have a series of cones, each with the same base area, with the length of each cone, and thus angle, being varied. How would this affect the cone's drag coefficient? For the sake of experiment, suppose you drop a cone directly downwards through air to test this.
I know the drag force formula for high velocities is f_d=1/2*(p)*(v)^2 * C_d * a, however, with this formula, it seems that the variable a, being the frontal area, does not seem to vary for cones of different angles, if the base were held as constant, thus cones of differing angles would all have the same drag coefficient.
However, this is clearly untrue, and I don't quite understand, what other factors can result in this happening?
​

The War Scroll, also known as the "War of the Sons of Light Against the Sons of Darkness," is a unique text within the Dead Sea Scrolls that portrays an apocalyptic battle between the forces of good (Sons of Light) and evil (Sons of Darkness). This scroll provides insight into both historical and symbolic elements.
Historical Accuracy:
The War Scroll, while containing detailed military tactics and an epic narrative of the ultimate confrontation, doesn't explicitly reference any specific historical event or timeframe. Some scholars believe it could be a product of the community's anticipation of a future messianic conflict or a reflection of their own community's struggles against opposing forces during their time. Interpreting the historical accuracy of the scroll often involves exploring the context of the Qumran community and the turbulent times in which they lived.
Symbolism and Esoteric Wisdom:
The War Scroll goes beyond a mere description of a physical battle. It portrays a cosmic conflict between the forces of light and darkness, reflecting not just a literal warfare but also a symbolic and spiritual struggle. The text emphasizes righteousness, divine intervention, and the victory of good over evil.
Within the study guide, activities and exercises could involve dissecting the symbolic elements present in the War Scroll, exploring the deeper meanings behind the battle tactics and the metaphysical implications of the conflict. Understanding the symbolism could involve group discussions, comparative analysis with other ancient texts with similar themes, and exploring the impact of this symbolic representation on the community's beliefs and practices.
Here are a few activities and exercises to explore the symbolism and historical context of the War Scroll from the Dead Sea Scrolls:

1. Symbolism Analysis:

Provide excerpts from the War Scroll and encourage participants to identify and discuss the symbolic meanings behind elements like the "Sons of Light" and the "Sons of Darkness," various weapons, and the strategies outlined for battle. Group discussions or written reflections can help participants explore the deeper layers of meaning.

1. Comparative Analysis:

Compare the War Scroll's themes with similar apocalyptic or eschatological texts from different cultures or religions, such as apocalyptic passages in the Book of Revelation in the Christian Bible or apocalyptic texts from other ancient traditions. Create worksheets or discussion prompts to highlight similarities and differences in themes, symbols, and beliefs about cosmic battles.

1. Historical Context Exploration:

Present historical information about the era when the Dead Sea Scrolls were written. Discuss the political, social, and religious climate of that time, including the turmoil in the region, to understand how these factors might have influenced the composition of the War Scroll. Encourage participants to consider the possible motivations behind the text's creation.

1. Creative Interpretation:

Encourage creative expression by asking participants to create artwork, poems, or short stories inspired by the themes and imagery found in the War Scroll. This exercise allows individuals to engage more deeply with the symbolic elements and interpret them in their own unique ways.

1. Role-playing or Debates:
   Organize a role-playing activity where participants take on the roles of "Sons of Light" and "Sons of Darkness," debating their ideologies, motivations, and strategies for the ultimate battle. This exercise helps in understanding differing perspectives and interpreting the conflicts presented in the scroll.
   

Interpretative variations regarding the river's crossing in different ancient texts reflect the unique religious, philosophical, and cultural perspectives embedded within these narratives. These differences in interpretation offer insights into diverse worldviews and varying theological frameworks present in ancient texts:

1. Mesopotamian Context:

• In Mesopotamian mythology and literature, the Euphrates River often held symbolic significance as a boundary between the known civilized world and the wild, unknown realms. The crossing of the Euphrates could symbolize journeys into unexplored territories or transitions between order and chaos. This perspective reflects a worldview rooted in the physical and geographical division of lands.

1. Biblical Context:

• In biblical texts, such as those in the Book of Revelation or Old Testament prophecies, the crossing of the Euphrates carries eschatological significance. It may represent a divine intervention or a decisive moment in God's plan, marking the commencement of apocalyptic events. This interpretation aligns with the biblical narrative of divine judgment and the unfolding of God's ultimate purpose in history.

1. Gnostic or Apocryphal Context:

• Gnostic or apocryphal texts often interpret the river's crossing as a symbolic liberation or awakening. It might signify the release of spiritual forces or the ascent to higher consciousness, reflecting a philosophical perspective emphasizing spiritual enlightenment and liberation from material constraints.

1. Greco-Roman Interpretation:

• In Greco-Roman literature, crossings of rivers were often associated with mythological journeys or transitions between realms. The crossing of the Euphrates might symbolize a transition from mundane existence to a realm of mystery or spiritual significance, reflecting a cultural perspective rooted in mythology and cosmology.

These varied interpretations highlight the richness and diversity of religious, philosophical, and cultural frameworks present in ancient texts. The river's crossing serves as a flexible symbol that adapts to different narratives, conveying themes of transition, judgment, liberation, or cosmic transformation based on the unique perspectives of each tradition.
Exploring these interpretative variations allows participants to appreciate the complexity of symbolism within ancient texts and provides insights into how different cultures and belief systems interpreted common motifs like the river Euphrates. It showcases the intricate interplay between religious, philosophical, and cultural elements shaping the symbolism and theological implications embedded in these narratives.
The river Euphrates, a prominent geographic feature in ancient texts, embodies universal themes that transcend specific cultural contexts. Identifying these universal themes helps reveal shared human concepts of transition, boundaries, and transformative events across diverse ancient traditions:

1. Threshold and Transition:

• The Euphrates often symbolizes a boundary between known and unknown territories. Its crossing represents a transition from one state to another, signifying a pivotal moment of change or passage. This theme of crossing a threshold echoes the human experience of transitions in life, moving from familiar to unfamiliar realms.

1. Boundary and Separation:

• As a geographical boundary, the Euphrates signifies separation between distinct territories or civilizations. This concept of demarcation resonates with universal human experiences of setting boundaries, delineating spaces, or marking divisions between different aspects of life.

1. Transformative Events:

• Crossing the Euphrates is often associated with cosmic or transformative events in ancient texts. This universal theme reflects the human fascination with the concept of epochal change, cosmic upheavals, or moments of divine intervention that reshape the course of history.

1. Symbol of Power and Control:

• The river might represent a symbol of power, control, or geopolitical significance. Crossing it could signify shifts in dominance, challenges to established authority, or the assertion of influence. This theme resonates with human narratives of power struggles and shifts in societal dynamics.

1. Metaphor for Spiritual Journeys:

• Across cultures, rivers are often used metaphorically to represent spiritual journeys or quests. The crossing of the Euphrates might symbolize the pursuit of enlightenment, the passage to higher realms of understanding, or the quest for spiritual transformation.

These universal themes associated with the river Euphrates highlight fundamental aspects of the human experience—transitions, boundaries, transformative events, power dynamics, and spiritual journeys. The river's symbolism in ancient texts speaks to shared human aspirations, struggles, and beliefs that transcend cultural boundaries and resonate across different epochs and civilizations.
By identifying and discussing these universal themes, participants gain a deeper appreciation for the profound symbolism embedded in ancient texts and recognize the timeless relevance of concepts such as transition, boundaries, and transformative events in shaping human narratives and aspirations.

1. Historical Context:

• What historical events or societal conditions might have influenced the composition of the War Scroll?
  
• How does the historical context of the Dead Sea Scrolls' discovery contribute to our understanding of this text's significance?
  

1. Symbolism and Esoteric Wisdom:

• How does the War Scroll use symbolism to convey spiritual or cosmic themes?
  
• What esoteric wisdom or deeper spiritual insights can be derived from the portrayal of cosmic conflict and divine intervention within the text?
  

1. Comparative Analysis:

• Compare the themes and symbolism of the War Scroll with other apocalyptic texts from different cultures (e.g., Book of Revelation, The Book of Daniel). What common motifs or differences in interpretation do you observe?

1. Parallelism in Biblical Texts:

• Explore connections between the War Scroll and other biblical texts. How does the language, imagery, or themes in the War Scroll intersect with passages from the Hebrew Bible or New Testament?

1. Community Beliefs and Practices:

• How might the apocalyptic expectations depicted in the War Scroll have influenced the beliefs and practices of the community that produced it?
  
• Discuss the impact of such intense anticipation of cosmic conflict on communal life and religious rituals within the community.
  

1. Cultural Significance of Cosmic Battles:

• Across various ancient cultures, why do you think depictions of cosmic battles and eschatological events were significant? What might these narratives represent in a broader cultural context?

1. Interpretive Variations and Unique Perspectives:

• Explore the diverse interpretations of specific passages or symbols within the War Scroll. How do different scholars or traditions interpret these elements, and what underlying factors might influence their interpretations?

1. Personal Reflection and Modern Relevance:

• Reflect on how the themes of cosmic conflict, righteousness, and spiritual warfare in the War Scroll might resonate in contemporary society or personal belief systems.

1. Theological and Philosophical Implications:

• Discuss the theological and philosophical implications of a cosmic battle between forces of light and darkness. How does this theme intersect with broader philosophical inquiries or theological doctrines?

1. Literary and Symbolic Analysis:

- Analyze the narrative structure and symbolic elements present in specific passages of the War Scroll. How do these elements contribute to the text's overarching themes and meanings? 

These study questions aim to provoke critical thinking, promote in-depth exploration of themes, encourage comparative analysis, and stimulate discussions on the multifaceted nature of the War Scroll's content and its significance within ancient and contemporary contexts.

1. Archaeological and Linguistic Analysis:

- How does the physical condition of the Dead Sea Scrolls, including the War Scroll, impact our understanding of their preservation and historical context? - Discuss the linguistic peculiarities or unique textual features found within the War Scroll and their implications for translation and interpretation. 

1. Apocalyptic Expectations and Messianic Concepts:

- Explore the portrayal of messianic figures or anticipated saviors within the War Scroll. How do these concepts align with or diverge from contemporary expectations of a messianic figure in other ancient texts or religious traditions? 

1. Impact of Apocalyptic Literature:

- Analyze the enduring influence of apocalyptic literature, such as the War Scroll, on subsequent religious, literary, or cultural traditions. How have these texts shaped later beliefs or inspired artistic and literary works? 

1. Ethical and Moral Frameworks:

- Discuss the ethical or moral implications of the cosmic conflict depicted in the War Scroll. How do the themes of righteousness and wickedness contribute to the text's underlying moral framework? 

1. Role of Prophecy and Revelation:

- Explore the role of prophecy and revelation within the War Scroll. How do the prophetic elements contribute to the text's portrayal of future events and cosmic justice? 

1. Experiential and Ritualistic Elements:

- Investigate potential ritualistic or experiential dimensions associated with the teachings or beliefs conveyed in the War Scroll. How might the community have engaged with these teachings in their religious practices or communal activities? 

1. Literary Genre and Interpretation:

- Discuss the classification of the War Scroll within the broader genre of apocalyptic literature. How does its classification influence our understanding and interpretation of its themes and symbolic elements? 

1. Relevance in Modern Scholarship:

- Reflect on the ongoing scholarly debates or discoveries related to the War Scroll. How have modern interpretations evolved, and what implications do these new perspectives have on our understanding of the text? 

1. Intersection of Faith and Scholarship:

- Consider the interplay between faith-based interpretations and scholarly analyses of the War Scroll. How might religious convictions or theological frameworks influence academic research and vice versa? 

1. Future Research and Interpretative Avenues:

- Propose potential avenues for future research or areas of exploration concerning the War Scroll. What unanswered questions or unexplored aspects merit further investigation? 

The composition of the War Scroll, along with other Dead Sea Scrolls, was likely influenced by several historical events and societal conditions prevalent during the time of its writing, which is estimated to be between the 2nd century BCE and the 1st century CE:

1. Hellenistic Rule and Cultural Influence:

• The region where the Dead Sea Scrolls were found was under Hellenistic influence due to the conquests of Alexander the Great and the subsequent control by the Seleucid Empire. This era saw a clash between Hellenistic culture and Jewish traditions, leading to cultural tensions and a desire to preserve religious and cultural heritage.

1. Political Turmoil and Resistance Movements:

• The Jewish people experienced political unrest, particularly during the Maccabean Revolt against Seleucid rule. This period was characterized by resistance movements, attempts to preserve Jewish identity, and fervent anticipation of a messianic figure to deliver them from foreign oppression.

1. Religious Sects and Spiritual Expectations:

• Various religious sects existed within Judaism, each with its own interpretations and expectations of messianic redemption, purity laws, and theological doctrines. The community associated with the Dead Sea Scrolls, often believed to be the Essenes, likely had distinctive theological beliefs and a strong apocalyptic worldview.

1. Anticipation of Cosmic Redemption:

• There was a widespread belief in the imminent arrival of a messianic figure or a divine intervention that would bring about cosmic redemption, ushering in an era of righteousness and divine rule. This anticipation of apocalyptic events and a cosmic battle between forces of light and darkness is reflected in the War Scroll's themes.

Regarding the historical context of the Dead Sea Scrolls' discovery, its significance lies in multiple facets:

1. Preservation of Ancient Texts:

• The discovery of the Dead Sea Scrolls, including the War Scroll, provided an invaluable collection of ancient manuscripts that significantly expanded our understanding of ancient Jewish texts, religious beliefs, and the diversity of Jewish thought during the Second Temple period.

1. Insights into Jewish Sectarianism:

• The scrolls shed light on the diversity of beliefs and practices among Jewish sects during that time. Understanding the beliefs and expectations of the community associated with the Dead Sea Scrolls helps contextualize the theological and apocalyptic themes present in the War Scroll.

1. Confirmation of Scriptural Accuracy:

• The Dead Sea Scrolls' discovery contributed to confirming the accuracy and preservation of certain biblical texts, highlighting the continuity of textual transmission across centuries and supporting the authenticity of biblical manuscripts.

1. Impact on Biblical Studies and Scholarship:

• The discovery of the Dead Sea Scrolls revolutionized biblical studies, providing scholars with invaluable primary sources for studying ancient Judaism, the development of biblical texts, and the context in which these texts were composed.

The historical context of political upheaval, religious expectations, and the preservation of texts within the Dead Sea Scrolls contributes significantly to understanding the milieu in which the War Scroll was written. It provides a backdrop against which the themes of cosmic conflict, eschatological anticipation, and religious fervor within the War Scroll can be comprehended.