Summer of Math Exposition

Nice topic, interesting. Nice pacing. Clear.

Questions:

• Where do bias (namely 15) comes from? What role do it play in floats and what would happen if we just don’t add it?

Tips:

• When explaining that points closer to zero are more precise, a linear scale would really help understand that point.

Really interesting topic/animations! I like to see that it was a team effort too.

It would have been nice to get a deeper explanation of why Posits are more accurate that Floats. Is it just because they don’t round to 0 or infinity? By doing that you could also have motivated all the things that make up Posits like the regime and exponent. Because in the video all these changes to Floats felt a little random. Maybe with this you could also explain some of the shapes in the plots.

I like the video, the animations are very clear and the content was also interesting. But in the end, comparison of floats and posits is very biased for posits: precision problems for floats are presented as a bigger problem than it is, and much worse performance of posits is ignored. For example, inaccuracy of floating point numbers is not a big problem in real computations in numerics because one usually does some normalization, orthogonalization, etc. to avoid growing errors. For example, most numerical linear algebra algorithms use orthogonal matrices, which is necessary to get good results anyway since there also are errors in the input data, and we do not want to amplify these error by running a wrong computation.

Good explanation of posits, though it really sounds like it came from a basis of not understanding floats. I suspect that that’s not your fault, it’s the original paper’s. For example, do posits adequately handle atan2 and its behaviours surrounding zero and infinity?

But this makes a good marketing video for posits.

Graphs were on screen to short a time. Explanation of base10 to binary was skipped, but moving radix was not. A bit more time on binary conversion would be nice. Moving around the graphs would be great without the mouse and with a key plan. Comparisons side by side would be even better. Also, use the full width of the video. Good pacing. Good introduction linking to real world example. I’m not sure I remember ‘why’ and when posits were created compared to floating point. I would also like to know why speed matters in relation to other factors.

Since you are comparing posits to floats, I would recommend taking more time explaining them. What is the bias in the exponent? When do overflow and underflow occur (you could give some examples for this)? You should even contemplate the possibility of explaining how to pass from decimal to binary in the simplest case, integers, if you are targeting a highschool audience.

However, I think your video is very well structured and I found it very interesting.

The length of the video does not allow average students to maintain attention, and the topic is very specialized and not within everyone’s reach. It might be suitable for computer science tracks (I suppose).

Very well done! Interesting non-trivial topic, great explanation and even some unexpected results like the fractals that appeared.

Just great! Great topic. Well motivated.

Really cool visuals at the end

Arguments and plots are coming from nowjere

The content in this video is very interesting to a wide audience while also being digestible and easy to follow in most parts.

When the posits were introduced a lot of the concepts (and computations) were left under or unexplained. For example, the es number.

Motivation was fairly clear. The topic was very unique and yet important. The style, however, was not very unique. It was well-executed but followed 3b1b’s a little too closely. The concept of a posit will definitely be memorable to those familiar with floats and computers already.