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AI explanation

^{Show image generation prompt} Model: dalle-3
Prompt: Create an image that embodies the following scene: In a cozy theater in Pennsylvania, a group of actors gracefully performs on a dimly lit stage. The gentle ambiance of the theater is contrasted by the glow of a large screen displaying the 3Blue1Brown YouTube channel's distinctive logo. As the actors passionately convey their characters, mathematical motifs subtly intertwine with the narrative, captivating the audience. The length of the performances steadily grows, echoing the surge in demand for theater productions and the increasing length of 3Blue1Brown videos. The scene is imbued with an aura of creativity and intertwining passions. This prompt aims to explore the unique concept of the interplay between traditional theater and innovative educational content through a captivating and visually engaging image. The depiction should include only scenes, people, and objects, it should not include text or speech bubbles.

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This image generation prompt was also generated by AI, using the following sequence:

Model: gpt-3.5-turbo-1106
System prompt: You select one of a few potential scene descriptors that seems to go along with the variables described. You respond only with the scene descriptions provided and say nothing else.
User prompt: Here are two variables: The number of actors in Pennsylvania and Average length of 3Blue1Brown YouTube videos. Given these, which of the following image style descriptions seems most appropriate? Pick the one that seems to be related to one of the variables at hand. Please respond with only one of the following potential descriptions: Realistic A TIME magazine cover image Charcoal Data cyber art High-tech
ChatGPT: A TIME magazine cover image

Model: gpt-3.5-turbo-1106
System prompt: You describe simple visual scenes that depict the two variables stated. You combine both variables into one scene.
User prompt: Please describe a visual scene that prominently depicts both The number of actors in Pennsylvania and Average length of 3Blue1Brown YouTube videos, in the following situation: As the number of actors in Pennsylvania increased, there was a corresponding spike in demand for local theater productions. This surge in demand led to a shortage of available venues, prompting 3Blue1Brown to create longer videos to serve as makeshift theater performances, complete with dramatic mathematical explanations and the occasional plot twist. After all, when the show must go on, so must the mathematical insights! "The length of these videos is like a prime number - it just keeps getting longer and longer with no end in sight!". Keep the description simple.
ChatGPT: I see a scene in Pennsylvania where a group of actors is performing on a stage in a local theater, while in the background, the 3Blue1Brown YouTube channel's logo is displayed on a large screen. The actors are doing a dramatic scene, and the average length of their performances seems to be increasing as the demand for theater productions surges. The 3Blue1Brown videos, usually known for their mathematical explanations, are now getting longer, serving as makeshift theater performances. Math concepts are creatively integrated into the videos, and the length of the videos seems to keep growing like an ever-expanding prime number.

Model: gpt-3.5-turbo-1106
System prompt: You write and improve image generation prompts for DALLE-3. You maintain the same subjects, but enhance the visuals.
User prompt: Please respond with an image generation prompt that would be likely to create an interesting visual using DALLE-3, using the following style: [ A TIME magazine cover image ] and depicting this scene: I see a scene in Pennsylvania where a group of actors is performing on a stage in a local theater, while in the background, the 3Blue1Brown YouTube channel's logo is displayed on a large screen. The actors are doing a dramatic scene, and the average length of their performances seems to be increasing as the demand for theater productions surges. The 3Blue1Brown videos, usually known for their mathematical explanations, are now getting longer, serving as makeshift theater performances. Math concepts are creatively integrated into the videos, and the length of the videos seems to keep growing like an ever-expanding prime number. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Create an image that embodies the following scene: In a cozy theater in Pennsylvania, a group of actors gracefully performs on a dimly lit stage. The gentle ambiance of the theater is contrasted by the glow of a large screen displaying the 3Blue1Brown YouTube channel's distinctive logo. As the actors passionately convey their characters, mathematical motifs subtly intertwine with the narrative, captivating the audience. The length of the performances steadily grows, echoing the surge in demand for theater productions and the increasing length of 3Blue1Brown videos. The scene is imbued with an aura of creativity and intertwining passions. This prompt aims to explore the unique concept of the interplay between traditional theater and innovative educational content through a captivating and visually engaging image.

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*Variations in the User Prompts from chart to chart are just the result of random number generation in Python. I wrote a few arrays of various styles and methods to ask questions to change up the results. Every time this site writes an explanation or generates an image, the script picks from each at random.

I sequence the requests into multiple prompts because I find GPT 3.5 to perform much better with short, well-managed contexts. Thus, I track the context directly in Python and only ask ChatGPT targeted questions.

AI academic paper

The Theatrical Tailor: Analyzing the Relationship Between the Number of Actors in Pennsylvania and the Average Length of 3Blue1Brown YouTube Videos The Journal of Theatrical Statistics and YouTube Analysis Jan 2024 Reminder: This paper is AI-generated. Not real!

Problem variable:	Which variable has a problem? The number of actors in Pennsylvania Average length of 3Blue1Brown YouTube videos Neither / both
Issue:	What is the issue? The data is incorrect The chart isn't displaying properly There is a typo The source link is incorrect A calculation is wrong Something else
Additional details: Optional
Confirm you are a human:

Data details

Why this works

1. Data dredging: I have 25,153 variables in my database. I compare all these variables against each other to find ones that randomly match up. That's 632,673,409 correlation calculations! This is called “data dredging.” Instead of starting with a hypothesis and testing it, I instead abused the data to see what correlations shake out. It’s a dangerous way to go about analysis, because any sufficiently large dataset will yield strong correlations completely at random.
2. Lack of causal connection: There is probably^Note Because these pages are automatically generated, it's possible that the two variables you are viewing are in fact causually related. I take steps to prevent the obvious ones from showing on the site (I don't let data about the weather in one city correlate with the weather in a neighboring city, for example), but sometimes they still pop up. If they are related, cool! You found a loophole.
   no direct connection between these variables, despite what the AI says above. This is exacerbated by the fact that I used "Years" as the base variable. Lots of things happen in a year that are not related to each other! Most studies would use something like "one person" in stead of "one year" to be the "thing" studied.
3. Observations not independent: For many variables, sequential years are not independent of each other. If a population of people is continuously doing something every day, there is no reason to think they would suddenly change how they are doing that thing on January 1. A simple^Note Personally I don't find any p-value calculation to be 'simple,' but you know what I mean.
   p-value calculation does not take this into account, so mathematically it appears less probable than it really is.
4. Confounding variable: 2020 is particularly different from the other years on this graph. Confounding variables (like global pandemics) will cause two variables to look connected when in fact a "sneaky third" variable is influencing both of them behind the scenes.
5. Very low n: There are not many data points included in this analysis. Even if the p-value is high, we should be suspicious of using so few datapoints in a correlation.

Try it yourself

# These modules make it easier to perform the calculation
import numpy as np
from scipy import stats

# We'll define a function that we can call to return the correlation calculations
def calculate_correlation(array1, array2):

    # Calculate Pearson correlation coefficient and p-value
    correlation, p_value = stats.pearsonr(array1, array2)

    # Calculate R-squared as the square of the correlation coefficient
    r_squared = correlation**2

    return correlation, r_squared, p_value

# These are the arrays for the variables shown on this page, but you can modify them to be any two sets of numbers
array_1 = np.array([1110,1550,2070,2050,1830,3350,2410,])
array_2 = np.array([407,651.25,1015.82,971.75,897.533,2429.1,1467,])
array_1_name = "The number of actors in Pennsylvania"
array_2_name = "Average length of 3Blue1Brown YouTube videos"

# Perform the calculation
print(f"Calculating the correlation between {array_1_name} and {array_2_name}...")
correlation, r_squared, p_value = calculate_correlation(array_1, array_2)

# Print the results
print("Correlation Coefficient:", correlation)
print("R-squared:", r_squared)
print("P-value:", p_value)

Reuseable content

• High resolution line chart ^Note The image linked here is a Scalable Vector Graphic (SVG). It is the highest resolution that is possible to achieve. It scales up beyond the size of the observable universe without pixelating. You do not need to email me asking if I have a higher resolution image. I do not. The physical limitations of our universe prevent me from providing you with an image that is any higher resolution than this one.
  
  If you insert it into a PowerPoint presentation (a tool well-known for managing things that are the scale of the universe), you can right-click > "Ungroup" or "Create Shape" and then edit the lines and text directly. You can also change the colors this way.
  
  Alternatively you can use a tool like Inkscape.
  
• High resolution line chart, optimized for mobile
• Alternative high resolution line chart
• Scatterplot
• Portable line chart (png)
• Portable line chart (png), optimized for mobile
• Line chart for only The number of actors in Pennsylvania
• Line chart for only Average length of 3Blue1Brown YouTube videos
• AI-generated correlation image
• The spurious research paper: The Theatrical Tailor: Analyzing the Relationship Between the Number of Actors in Pennsylvania and the Average Length of 3Blue1Brown YouTube Videos