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The Legacy of Sir Galton: from the Bean Machine to Social Sciences

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Tags: probabilitycentral-limit-theoremsocial-science

Many aspects of our society are shaped by the repeated occurrence of small, random events. This idea that the persistent repetition of random events can profoundly impact individuals was insightfully captured by Sir Francis Galton. In this video, we revisit the mathematical principles underlying Galton's board and leverage them to go further the Central Limit Theorem (CLT) and see what can happen when the hypothesis of the CLT are not satisfied. Given a different perspective of the same object in math can lead to a better understanding of it, and sometimes lead to new results or a broader understanding and this is what we are going to do in this video.

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5.28 Overall score*

102 Rank

7 Votes

3 Comments

Comments

6.7

The motivation is ok. You’ve motivated this in terms of looking deeper into statistical principles, and while that did appeal to me as a generally curious person, I think the motivation would be stronger if you started from the practical applications and then show why they necessitate changes to the CLT from the usual form.

The clarity here is pretty good for students with the appropriate background, very straightforward narration. The Manim looks good, although there are a few small issues that could use improvement, such as items not being aligned, or things appearing onscreen before you start describing them, which can be distracting. One more thing that was a bit confusing is that you motivate the Beta etc. distributions from your practical applications, but then when you plot those distributions, they are in terms of an arbitrary parameter, instead of the parameters from the actual example, which is what I was curious about at that point.

I think the novelty is good too, these topics get less coverage on YouTube than the basic CLT, and I like your choices for practical applications.

On memorability, I think the distorted Galton board visuals are very positive here, although you went a little too fast through the Beta etc. distributions for a new student to remember them from this video. This topic might be better as a series where you take the different aspects a little more slowly. But still, I learned things.

One more suggestion that you’ve probably already considered is that you might invest in a nicer microphone.

Generally nice job overall, and thanks for this illuminating contribution.

5.3

The part with dice could have been trimmed down. The main point of the video was about the galton board and a generalization. Might have been better to use that as an example to start the video rather than dice.

Quite a bit of the video was formula’s used to describe a picture that was no longer showing. Might have helped to keep the picture on one side of the screen and have the formula’s on the other. Just to keep the picture somewhere were I could see it. You did this at the 22 minute mark with Galton interaction vs Kaptein interaction and it was much easier to follow that part.

6.2

At first I was intimidated by the length of the video, but it turned out to be very entertaining.

I would suggest adding how the parameters alpha and beta in the Beta distribution relate to the original parameters in the Free thinking and consensus model and the same for the wealth trade model.