Summer of Math Exposition

The concept of Mass being described as a mathematical outcome of symmetries is very interesting. I wonder looking at physics as symmetries might change how we perceive nature

Nice video! I think as its setup, it makes a for a nice YouTube math hook (“Are force and mass fundemental?”) but the part that would be useful for students is de-emphasized. (And indeed, trying to tell students not to worry about force and mass might do more harm than good). The key thing that could have been useful for students I think is the pipeline from symmetries to properties, which could lead into Noether’s theorem nicely. The actual little mini-proofs could be stated as “if there is time symmetry then… ” to make this type of thing work.

Well thought out, I really liked the explanation and was great to see the logic behind the idea come to life.

Excellent idea. The implementation can be improved:

1. The framing is misleading. You are not tackling the question of whether forces and mass are fundamental, but rather giving an alternative presentation of this idea, starting with other concepts. Moreover, you say that you did not postulate mass, but in fact you did by saying that it is equivalent to several identical moving particles, which is more or less the standard way to present mass.

2. The claim that in Newtonian mechanics the multi-body problem is undeterministic is wrong. It is chaotic but very deterministic. Moreover, the fact that it is chaotic will not change when you change the point of view, even under the (beautiful) point of view presented in the video.

3. The animation is a bit too monotonous, and so is the tone in general.

Phenomenal video, and a great way to to explain mechanics from the ground up that I had never realized. It was really helpful to use different colors for the different postulates, and having all of the equations on the screen as they were used.

Overall, this is an interesting and thought-provoking video, but I fear it is too simple for what it is trying to do. It’s not convincing that you have derived any meaningful mechanics from conservation principles.

Take Newton’s First Law, for example. You have round-aboutly shown that “an object will continue in motion if not acted upon by a force”, but not explored what happens if there is a force, the meaning of force and so on. You have argued using macro-scale postulates, such as a gas in a perfectly insulated box (in fact, real gases in boxes do lose or gain energy as they heat up and cool down).

As you may be aware, pre-Newtonians like Plato believed that a force was actually required to maintain constant motion. This is probably because they would always experience friction in practice. Plato could critique your argument by saying that there is no time symmetry, hence why a chariot would slow down if not pushed. And, on the macro scale, he would be right! The Second Law of Thermodynamics breaks time symmetry; friction is one example of the Second Law in action.

For the scope of what you are trying to do, I would like to see these ideas greatly expanded upon.

I would say that it is not super well motivated, or novel, since this is a reduced discussion of Noether’s Theorem, which is otherwise well-known. I think this theorem should have been mentioned by name.

Nonetheless, it was enjoyable and quite memorable!

This is really a great idea! I’ve been looking for something like this. I guess this will eventually explain Emmy Noether’s ideas.

The production quality can be improved a lot. There is no mathematical typesetting (except the mechanical laws, probably a screenshot). There is a reason why mathematical symbols are typeset differently. When it is the same as the main text, they are pretty unreadable. The animations have some countdowns, that grab the attention.

The topic was quite unique and interesting!

The way you started with one particle and built up to three particles helped with the clarity. But I think overall the equations were solved too quickly for the viewer to follow along.

I believe this could have been better in a written down format instead of a video because it had a lot of formulas but not as many visuals.

Regardless, I thought the problem was well motivated because it can offer students a deeper understanding of interactions!!

I am wondering about the time symmetry postulate - since entropy always increases. But that is out of scope here.

Great job!!

Its is a different take on the idea of mass

I might have missed the point, but I do not think this is correct. From scale invariance, we could conclude that any physical event has linear effects. That is not true. Events remaining the same with reversal of time goes against the concept of entropy. There are good animations, and a lot of interesting points are raised (noticing that physics do not care about right and left, understanding that changing units does not change the physical event, that exchanging two identical particles changes nothing, an introduction to different frames of references, how to use physical intuitions to remember equations and discard wrong hypotheses…) but it is too simplistic and could be misleading to students.

Rough at the start, but has a great ahha moment in the last five minutes. Lots of techincal stuf, but it isnt necessary to keep track anyway, he explains the motivation and intuition well enough. Thick accent though.

I like the animations!

A lot of arguments seem oversimplified and other seem to assume that we know advanced physics (e.g. perfect gaz and how they react to perfect vacuum and isolation) to derive Newton’s law. I am really not sure I understand that one can really use such a reasoning.