Summer of Math Exposition

Clear description, nice visuals.

Obviously a very well executed web presentation. However, I think that the devil is in the organization of the content. Starting with magnets is a crazy shot when you could have chosen one of the two other examples to lead with. Now, I understand why you wanted to start with the physics approach: it helps to build a clear physical model without needing to question the wants or desires of animals. However, to explain how magnets work is already a lot to take in as a student, and it almost feels like the latter explanations are obligatory add-on’s to the presentation required by the introduction. I think you’ve done such a wonderful job of describing the magnetic aspect that you could focus down the presentation to just that. By reducing down the content, you might be able to get a more clear, engaging piece. Great work, I love the motivation and the novel approach, but it needs a pass at the concept level to make sure it’s easy to digest.

A beautifully crafted piece!

Amazing interactive widgets, each serving an actual purpose! Very memorable article.

Some of the highlighting of words was a bit over the top for me.

Excellent visualizations, interesting topic, love the color coding in the equations

Excellent article! The visualizations are very cool, and the explanation and modelling are also very nice.

This was super interesting and engaging! I really liked seeing the different colors, the boxes, and the simulation demonstrations. I think those are great to keep students engaged and it definitely contributes to this explainer’s merit for use in the classroom.

I really enjoyed this one. It was a focused reading, and I did it with pleasure. Because I realized how well prepared this was, I thought it deserves a longer feedback with my thought process while reading. Don’t try to relate the high vote with the long feedback. I think even really good articles deserve it to make them even better. Also, apologies for being a bit disorganized. Consider it as linear feedback as I read through the post and take notes.

Right from when I started reading, the use of colored text felt distracting. The only one that I think is justified is the red/blue north/south tip/tail. Maybe also spin/tiny arrow. But then why is ‘move around’ also yellow, same as spin/arrow?

Finally, we describe the evolution of our system over time by saying that each spin prefers to align with its nearest neighbors

OK but what do you mean by evolution of the system? Why would the spins change? (after reading everything, I’m not sure what I meant here. Probably asking why is ‘aligning with neighbors’ a good choice of modeling, as opposed to, say, nothing?)

And… voilà! We can now summarize our model into a simple algorithm

This caught me off guard. I still don’t know what exactly we are trying to model. We seem to be modeling a magnet. Out of what? Any piece of matter? Doesn’t make sense. After reading more on the article, maybe it does make sense when adding temperature. It would mean that most matter needs a small temperature to destroy the magnetic effect and only some require a larger temperature, so at a given temperature, some matter will produce a magnetic field and other won’t. Of course I’m just writing my thought process in case it helps, because of the lack of explanation in the article.

If the flip increases alignment with neighbors, accept it.

How do we define alignment to know if it’s more or less? Is it using the energy/hamiltonian? But that’s in an optional read box, I might be confused.

Magnets simulation is amazing but I think it starts when I load the page so by the time the reader reaches that part it might be confusing. Can you add play button?

When defining the rate of change of angle, why do we need the sine of the angle differences? Why not just the differences? This seems to be taken for granted. I don’t know the answer either.

2D Ising model with interaction strength simulation. Again same problem, by the time I get there, all arrows are aligned, so I’m confused. Better adding a play button.

Boxes should have useful names to tell the reader if it’s worth to open them or not. For example, instead of “Temperature dependence” I would use “Why square root of T?” (this was actually my question, and I didn’t know it would be answered in the box until I opened it). For the next one “BKT transition” I don’t know what I would choose, but certainly not that, because the reader likely doesn’t know what that is, so they don’t know if they should open the box or not.

For the fish example, we are modeling that they end up moving in the same direction. In reality, is that everything? I don’t know how fish dynamics work but maybe they also tend to approach each other? Since we only model the direction, I was wondering this. I’m sure this is just an example to build on the Ising model and more complex models exist, so maybe just mention something.

There is only one thing to say really: Bravo. This is a really good work. The structure is good, you differentiated well for different levels in the audience and the simulations are fantastic.

In my opinion, there is only one thing where you should try to improve: As a non-native speaker myself, I know that it is not always easy to verify oneself the language part. But perhaps, you can either ask a friend that is a native speaker or you might want to use tools that are now more widely available to check the language.

Side notes: a) maybe note at some point that you are using radians and not degrees. especially if the article is meant (also) for highschool students.

This entry leverages the format well and the interactive elements are employed meaningfully. A reset button would have been nice on some of them since they can end up in a local minimum. I found the first (and maybe second) one a bit off-putting, which might turn people away, especially at the start.

Structure wise, the sections build meaningfully on top of each other, but I think they could have been tied more closely together at the end — maybe by putting the different Hamiltonians next to each other and cross-referencing equivalent terms or something similar.

This entry ties together some nice examples from different fields. While it enriches them with useful interactive elements, I unfortunately don’t see much novelty in it.

Visuals are great, links to further investigate are highly appreciated and the topic is very interesting.

This was a really clear explanation and stepped through in such an organized logical manner. The interactive elements were well utilized.