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AI explanation

^{Show image generation prompt} Model: dalle-3
Prompt: [ Hyper-realistic ] Generate an image of a football stadium filled with cheering fans, the field containing the Denver Broncos' defensive players. Show the players visibly straining to maintain their formation as invisible gravitational forces, represented as distorted ripples in the air, create gaps in their defense around them. Depict the players in slow motion, with their movements appearing stretched and distorted, highlighting their struggle due to the distant influence of Mercury. The colors and textures should emphasize the hyper-realistic portrayal of the chaotic scene. 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 distance between Uranus and Mercury and Points allowed by the Denver Broncos. 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: Scalar art Pop art Surrealism Hyper-realistic Brutalism
ChatGPT: Hyper-realistic

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 distance between Uranus and Mercury and Points allowed by the Denver Broncos, in the following situation: The gravitational pull from Uranus was disrupting the Broncos' defensive formation, creating gaps for the opposing team to exploit. Meanwhile, the distance from Mercury was affecting the Broncos' agility and reaction time on the field.. Keep the description simple.
ChatGPT: In a football stadium, the Denver Broncos' defensive players are struggling to maintain their formation as invisible gravitational forces from Uranus create gaps in their defense. Simultaneously, the players seem to be moving in slow motion, their agility and reaction time hindered by the distant influence of Mercury.

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: [ Hyper-realistic ] and depicting this scene: In a football stadium, the Denver Broncos' defensive players are struggling to maintain their formation as invisible gravitational forces from Uranus create gaps in their defense. Simultaneously, the players seem to be moving in slow motion, their agility and reaction time hindered by the distant influence of Mercury. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: [ Hyper-realistic ] Generate an image of a football stadium filled with cheering fans, the field containing the Denver Broncos' defensive players. Show the players visibly straining to maintain their formation as invisible gravitational forces, represented as distorted ripples in the air, create gaps in their defense around them. Depict the players in slow motion, with their movements appearing stretched and distorted, highlighting their struggle due to the distant influence of Mercury. The colors and textures should emphasize the hyper-realistic portrayal of the chaotic scene.

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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

Are the Denver Broncos Playing Defense... in the Solar System? A Correlational Analysis of the Distance between Uranus and Mercury and Points Allowed on the Football Field The Journal of Intergalactic Sports Science Jan 2024 Reminder: This paper is AI-generated. Not real!

Problem variable:	Which variable has a problem? The distance between Uranus and Mercury Points allowed by the Denver Broncos 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. Y-axis doesn't start at zero: I truncated the Y-axes of the graph above. I also used a line graph, which makes the visual connection stand out more than it deserves. ^Note Nothing against line graphs. They are great at telling a story when you have linear data! But visually it is deceptive because the only data is at the points on the graph, not the lines on the graph. In between each point, the data could have been doing anything. Like going for a random walk by itself!
   Mathematically what I showed is true, but it is intentionally misleading. Below is the same chart but with both Y-axes starting at zero.

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([18.3876,18.4437,18.4985,18.5425,18.5867,18.6291,18.6976,18.7541,18.8374,18.9128,18.9759,19.0281,19.0862,19.1513,19.2154,19.3048,19.3787,19.4518,19.5005,19.5626,19.6169,19.6735,19.7482,19.8059,19.857,19.8835,19.9236,19.9438,19.9796,20.0244,20.0611,20.0844,20.0915,20.1032,20.0939,20.1052,20.1119,20.1222,20.1024,20.0804,20.0533,20.0051,19.9857,19.9598,19.9414,19.8976,19.8571,19.7988,19.7327,])
array_2 = np.array([307,206,148,198,262,323,289,226,327,241,329,327,288,352,226,374,235,329,284,396,345,275,287,309,318,369,339,344,301,304,258,305,409,448,324,471,390,289,399,354,296,297,382,349,316,446,322,359,351,])
array_1_name = "The distance between Uranus and Mercury"
array_2_name = "Points allowed by the Denver Broncos"

# 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 distance between Uranus and Mercury
• Line chart for only Points allowed by the Denver Broncos
• AI-generated correlation image
• The spurious research paper: Are the Denver Broncos Playing Defense... in the Solar System? A Correlational Analysis of the Distance between Uranus and Mercury and Points Allowed on the Football Field