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AI explanation

^{Show image generation prompt} Model: dalle-3
Prompt: Generate an image of a high-tech scene in a lush, vibrant Burmese forest. Show tall bamboo and towering teak trees thriving under the warm sun. In the background, include a sleek, modern biomass power plant that hums, converting the forest's natural energy into sustainable electricity. As the plant's output increases, visualize an energetic wave of numbers, equations, and math symbols dancing through the air, swirling and sparking with creativity. Additionally, depict a nearby studio bustling with activity as the Numberphile team crafts captivating video titles, each one brimming with mathematical intrigue. Finally, illustrate the symbiotic relationship between Burmese biomass power and Numberphile's captivating titles in a dynamic cycle of renewable energy and mathematical inspiration. 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: How good Numberphile YouTube video titles are and Biomass power generated in Burma. 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: An image that looks like it is a scene from A Disney Movie High-tech Steampunk Voxel art Macabre
ChatGPT: High-tech

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 How good Numberphile YouTube video titles are and Biomass power generated in Burma, in the following situation: The more biomass power generated in Burma, the greater the positive energy flow in the universe, leading to an influx of number-related creativity. As the power output grows, so does the exponential titling prowess of Numberphile, creating a renewable cycle of electrifying math content. With each new video, the synergy between Burmese biomass and numerical knowledge becomes a prime factor in sparking excitement for both renewable energy and mathematics. It's a logarithmic match made in comedic and educational heaven, proving that when it comes to YouTube titles, Burma's biomass power is the real powerhouse behind Numberphile's magnetic math mania!. Keep the description simple.
ChatGPT: In a lush, vibrant Burmese forest, tall bamboo and towering teak trees thrive under the warm sun. A sleek, modern biomass power plant hums in the background, converting the natural energy of the forest into sustainable electricity. As the plant's output increases, an energetic wave of numbers, equations, and math symbols dance through the air, swirling and sparking with creativity. Meanwhile, a nearby studio bustles with activity as the Numberphile team crafts captivating video titles, each one brimming with mathematical intrigue. The symbiotic relationship between Burmese biomass power and Numberphile's captivating titles generates a dynamic cycle of renewable energy and mathematical inspiration, igniting a captivating fusion of sustainability and numerical wonder.

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: [ High-tech ] and depicting this scene: In a lush, vibrant Burmese forest, tall bamboo and towering teak trees thrive under the warm sun. A sleek, modern biomass power plant hums in the background, converting the natural energy of the forest into sustainable electricity. As the plant's output increases, an energetic wave of numbers, equations, and math symbols dance through the air, swirling and sparking with creativity. Meanwhile, a nearby studio bustles with activity as the Numberphile team crafts captivating video titles, each one brimming with mathematical intrigue. The symbiotic relationship between Burmese biomass power and Numberphile's captivating titles generates a dynamic cycle of renewable energy and mathematical inspiration, igniting a captivating fusion of sustainability and numerical wonder. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Generate an image of a high-tech scene in a lush, vibrant Burmese forest. Show tall bamboo and towering teak trees thriving under the warm sun. In the background, include a sleek, modern biomass power plant that hums, converting the forest's natural energy into sustainable electricity. As the plant's output increases, visualize an energetic wave of numbers, equations, and math symbols dancing through the air, swirling and sparking with creativity. Additionally, depict a nearby studio bustling with activity as the Numberphile team crafts captivating video titles, each one brimming with mathematical intrigue. Finally, illustrate the symbiotic relationship between Burmese biomass power and Numberphile's captivating titles in a dynamic cycle of renewable energy and mathematical inspiration.

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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 Power of a Good Numberphile Title: A Correlative Examination of YouTube Videos and Biomass Power Generation in Burma The Journal of Numberphile Studies Jan 2024 Reminder: This paper is AI-generated. Not real!

Problem variable:	Which variable has a problem? How good Numberphile YouTube video titles are Biomass power generated in Burma 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([6.5556,7.5053,7.5256,7.4286,7.5753,7.5294,7.5,7.6471,7.8542,7.725,7.6341,])
array_2 = np.array([0.003,0.191,0.209,0.225,0.206,0.212,0.231,0.251,0.26,0.261,0.26308,])
array_1_name = "How good Numberphile YouTube video titles are"
array_2_name = "Biomass power generated in Burma"

# 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 How good Numberphile YouTube video titles are
• Line chart for only Biomass power generated in Burma
• AI-generated correlation image
• The spurious research paper: The Power of a Good Numberphile Title: A Correlative Examination of YouTube Videos and Biomass Power Generation in Burma