Summer of Math Exposition

The math itself is a bit rushed. But otherwise, a wonderful video!

Section summary is super helpful!!

I find the idea of studying human-seen colours via algebraic methods quite interesting, but do not completely understand what the targeted audience for this video is (in the context of this competition and not as a whole, as I see the channel has a fair amount of followers).

On the math part, if the viewer does not know the concept of “dimension” or “size” of a matrix, then the concept of SVD or singular values cannot be understood. On the other hand, if the viewer does know some basic linear algebra, then they would have likely seen the SVD, or at least be familiar with the concept and role of eigenvalues. Personally, I would recommend either moving the focus away from the singular values to simply talk about number of colours and effective dimension (concepts which I believe are fairly easy to understand), or explain the other conceptsin more details: how to normalize the matrices, how to precisely compute the effective dimension, how to find the number of possible colours, etc.

On the chromatic part, I understand that this channel has a base of viewers that are somewhat familiar with the concepts explored here, but as a first time viewer, still with some basic knowledge regarding colour theory (via website/code designs), some of the mentioned choices and rationals were difficult to understand. The concepts that overlapping colour curves reduces the dimension is interesting and the toy examples made that clear, but then the extensive discussions on what subtlety can be seen by tri or tetra-chromatic people lost me. I also appreciate the idea of comparing the different visions with side screens, but rather than explaining what would tetra-chromatic people see if one of their channel was removed, I would have preferred seeing what our vision would look like to them; what I mean, is reduce the number of standard colours by the same ratio between tetra and tri-chromatic, so that we can see how much tri-chromatic people loose to tetra-chromatic people. I also “conceptually” understand the concept explained at the end, where the red curve is split between left and right eyes to increase its clarity and resulting dimension, but do not have a sense of what this means in terms of vision comparatively to what normal people see.

Finally, and this is definitely more of a personal opinion, but I am not a super fan of the video narrative: 1 - Normal people are tri-chromatic. 2 - Some extremely rare genes lead to tetra-chromatic. 3 - Actually, tetra-chromatic people are kind of normal. 4 - Here is ME, actually tetra-chromatic and mathematically the best. I understand that the author is passionate about colour-vision and has (extensively) trained to see differently, but I would like to have some motivation as to why one might want to do that. As a general rule, I also prefer the video not to be so much about why the author is so great.

The cow and burning noise are distracting and I think leaving the math on the screen, with the cow in a corner would be better. Otherwise, a great physics video with some math.

good but not so intuitive.

Interesting.

Great job on your SoME5 entry. As it is a 40 minute video, it is clear that you spent a lot of effort in the research and evaluation of tetrachromacy. There were many different points made throughout the video and I learned a few interesting things.

I feel that the SVD needs to be more explained more clearly. If there is one thing you can improve that would make me give you a higher score, it would be this. Because the SVD is such a pivotal tool you used to evaluate all the different vision curves, like different kinds of trichromacy, with or without colour blindness, the “natural” SMQL tetrachromacy and the “artificial” tetrachromacy with tinted glasses, not understanding the SVD is like taking the foundation out of your beautiful house of explanations.

From linear algebra, the SVD of a matrix $A$ come from the eigenvalues and vectors of $A^TA$ and $AA^T$. But I don’t remember hearing about this in the video. So let’s say you have the matrix at 6:10 - doesn’t have to be that one, just giving an example. What are the interpretations of $A^TA$ and $AA^T$ and the singular values? If I had never learned about singular values, I would have be even more confused. If I had a clear understanding of what the singular values and vectors actually are in the context of your matrices, not just that they are a “standard tool”, this would’ve amplified my understanding for the rest of the video.

Overall I actually learned a lot of things. Like how a pure dichromacy is better than a “bad” trichromacy, why red/green colour blindness is so common---it’s due to L and M cones having really adjacent sensitivity curves, that tetrachromats even exist, and how you can get a better version of tetrachromacy with tinted glasses. I just wish the interpretations of SVD were crystal clear and left no room for doubt.

• After watching this video, I have very little intuition for how SVD tells you the “number of colors” that exist for a given set of cone sensitivities, and I studied computer science, so I do have some sense of the point of dimensionality reduction and information content in general. You get into the explanations very quickly without first taking a breath and giving some background for what the sensitivity plots represent, and what we even mean by two wavelengths being perceived as distinct “colors”.
• I don’t think you ever explained what the rotating 3D visualization to the right represented - at least I had no idea.
• Once you get into some examples I do /get/ the concept of effective dimensionality, but I don’t quite understand why SVD on the matrix of optimal sensitivities gives that to you.
• The use of commas as a decimal separator caused me to misinterpret and be confused by some of the numbers, until I remembered the European convention. This isn’t a ding against the video of course, since it’s how lots of places do it, but it does risk confusing a lot of the native English-speaking audience that uses dots to separate the decimal places.
• The script has a lot of reading numbers out loud, while the visuals have a lot of numbers in tables, which is hard to parse. It would be better to visualize things as plots/heatmaps/etc.

I think pretty interesting video that really dives deep into the technical details and aims to dissect it into a part that allows less technical people to understand it. I was also quite amazed about the new possibility of worlds this opened up in terms of being able to understand enhanced spaces. I liked how they used SVD to really establish a common language and intuition on how we should understand the graphs. I think for a SOME entry, it was a bit technical near the beginning, so would be good to give more recap to readers near the start and give some context on what’s going on.

I wish the math was explained in more detail. But the concept is very new.

Lots of information, but kind of hard to follow everything.

Is this your own research? It did not sound very well established. Also everything revolves around an svd… OF WHAT?

A very novel application of SVD, justifiable and relevant.

What I liked: you proposed a new (to me, at least) method of quantifying color visibility. You studied it and followed it to its logical conclusion, to describe and downplay the characteristics of a common tetrachromatic spectrum. The visuals were nice and colorful, and easy to follow. The narrative was structured nicely and was easily followed. On the pieces you thought were important, you spent a decent amount of time going over them.

What I disliked: You didn’t spend as much time as you might have needed to developing what SVD was, why it was appropriate, or what the numbers meant. Knowing a bit about SVD, I might understand why it’s applicable (every matrix is given by stretching in some orthogonal dimensions, plus some rotation; you’re just focused on that squishing, because the squishing directions are the axes we use to enumerate our choices), but it wasn’t well-enough explained for someone to compute it.

Additionally, it’s not exactly clear where the matrices you wrote down came from. The columns don’t add to 1, nor do the rows, and at the peaks of each color’s spectrum, their “auto-correlation” is not 1 as one might expect. So while you present a very nice story, the ability to compute these dimensions self-sufficiently doesn’t appear to be presented to the viewer. It may be in the other videos you present (as this does appear to be a part of a series) but I haven’t watched those.

In any case, though, your storytelling ability makes up for the lack of complete detail in describing the mathematics, and it makes it clear that if the values were presented, the same computations could be done, and the conclusions presented seem consistent with the computations. Well done!