Summer of Math Exposition

The video made a good point in a streamlined and intuitively clear way. Giving concrete examples with dollars helped add intuition.

Directly mentioning social and political implications for this could put off some viewers, but I applaud you for saying it anyway—you’re absolutely correct.

The content wasn’t super groundbreaking, but it was addressed in a friendly and down-to-earth way that made this nice to watch.

The utility functions were quite confusing.

Very nice video. Quick and simple, gives some thoughts to the viewer.

Thank you for this great video. It was a really interesting perspective, looking at math from this “human” perspective. There are some minor flaws in the animation, but nothing major, definitely not for your 5th videos. The rest of your videos were added to my watchlist immediately after this. Thank you!

This video is well done and really highlights something that is usually not present in probability courses. That is that the expected value can be misleading in real world applications. The video does that by using a simple but effective model. Thank you for this very illustrative video.

The only improvement that I could give is that the section Another perspective: converting back is a little confusing. I do not understand exactly how the graph $w_0 \mapsto W$ is drawn because $U$ also change in the formulas at the bottom of the screen. So how did you choose $w_0 \mapsto U$?

Bonus points right off the back for ‘it’s not a flaw in our intuition — it’s a flaw in our model.’ I thought this was excellent; it motivated its topic with a perfect example, the math was always relevant but never overwhelming, it stayed connected to its topic the whole time, and even pointed out some consequences (like details of how safety nets can mitigate risk) that I hadn’t tied to this model before. If there’s anything I wanted to see that the video didn’t go into, it would’ve been (a) how the logarithmic model approximates the linear one in the regime where W >> 𝛿W (it does, right?) and (b) whether and how the base of logarithms matters; presumably it’s mostly just a scaling constant on the whole thing but it seems like it would impact e.g. the precise slope in that lower-change area and it’d be interesting to see some discussion of how to derive a ‘correct’ one. But those are just my personal desires for the video, not what I expect out of it, and it met and exceeded any expectations across the boad — to me it’s a testament to how good it was that I had to go so far afield to find things I wish it had done.

There seems to be a typo at 5:29, where the utility of both option A and option B are listed as 10.000, whereas I’m pretty sure that option B should be higher.

I thought this was a very good video. The pacing was spot on, the narration was smooth, and the ideas were communicated well. I also really appreciated the use of graphics, which helped clarify much of what was being said. I suspect graduate students might find this a bit simplistic, but by and large I think the target audience would have been very pleased with this video. Overall, I think the creator did a great job!

Nice visuals and neat presentation

Very nice explanation of decisions under uncertainty with utility functions

This introduced a novel concept to me of expected utility, and I think it helped me reframe some of my real life choices in a better light, that expected value had felt wrong on.

I really liked the “converting back” section, which gave nice insights.

Students might not be able to identify with the amounts of money. How many students have $10K, which is the starting value he uses for his initial example.

A very nice and interesting video. Try not to take all the formulas for granted - for example, you could remind viewers of the formula for the expected value in the discrete case (I’m putting myself in the student’s perspective). As for the initial problem, I think the choice depends more on ‘risk’ than on ‘utility’; I believe many people would accept even just $500 without risk… However, I understand the educational purpose of the video and I find it very interesting!

A very good entry. While the mathematics are trivial — just take a log to model diminishing returns — I liked the conclusions that you drew from it. Surprisingly, your application to social security did not feel as out of place here as these things usually do.

While all of the concepts covered in this video made intuitive sense, your explanations and visualizations really helped to me to ground that intuition in mathematical terms and apply it to real-life examples. One new thing I learned was the concept of utility functions, and how we can use them to make more informed decisions in our lives (what options will bring the most utility?).

Fantastic mixture of math and sociology. Please make more like this.

Very interesting. I’ve never seen this topic before on YouTube

Excellent Presentation and Conceptual Subject. Very practical application in real life.

This is a simple and concise video explaining simple statistics in a good way. I like the visuals too.

That was a cool concept and I felt like it was explained very elegantly.

A few pointers.

1. Could have included “High income improves evaluation of life but not emotional well-being” by Kahneman and Deaton. That would have worked as a perfect empirical example
2. Maybe dwell on the fact that expected value only works if you can repeat the experiment. Maybe 1 Mil vs a Billion Dollars with 1-in-100 odds or Death.
3. Could’ve been smoother with the transition about Free Healthcare, totally agree with the general point but it felt a bit jarring. Also Swedish billion dollar companies might not exploit local populations, but the global south is still affected.