Trick and Truth: The Natural Effectiveness of Math in Fundamental Science by Alma Ionescu

Dear Alma,

Thank you for your comments. It will be great if someone took to investigating common emergence in physical phenomena and the in the mathematics used to describe it. For instance, there are concrete studies which derive quantum theory as an emergent phenomenon, and gravity as an emergent phenomenon, and they use precise mathematics at all levels. It will be interesting to explore if the corresponding mathematics can be described as emergent.

Just one small correction Alma ...one of us (Anshu) is female :-) We understand of course that it is not always easy to deduce gender from foreign names.

Kind regards,

Anshu, Tejinder

I don't know to what extent theorems have emergent properties as it might be the things theorem refer to. I have been working on how spacetime is a coarse grained manifestation of large N entanglements, which have a period 8 structure. In this way the basic SLOCC structure is 4-bit or 8-bit even if there are 2^n = N large number of quantum bits. The geometry of spacetime time then comes about from event horizons that are measures of these entanglements. This in part goes in favor of those who say that time is a sort of illusion, but as I think space is a bit of an illusion also.

On this basis we could say that distance measures, say the Pythagorean theorem, is not emergent so much as the underlying constructions of points, lines, planes and so forth. Given that those elements exist, even if they are emergent, then Pythagoras was right as is so much of other mathematics. Of course we are talking about physical emergence, not so much mathematical. Mathematics as an idealized system of models does not seem to my mind emerge as such, but rather the underlying natural system the mathematics models is emergent.

LC

Dear Alma,

It is fine, no need to feel sorry. We brought to your notice in order to avoid further confusion. As is reflected from our earlier correspondence, I too have enjoyed your insightful essay.

Regards,

Anshu

Dear Alma,

I spent a few hours this morning reading your essay and preparing a non trivial comment for you. You will have a very good comment and appreciation from me by the end of the day. May be this is an instance of distant entanglement between brains at least not a pure coincidence. My thoughts during the two hour fast walk I just had was about rivalry between the two hemispheres that you might be call Phys and Math., a kind of quantum superposition that collapses one side or the other depending on context.

Have a good afternoon.

Michel

Dear Alma,

Great essay! You have an engaging writing style that is enjoyable and accurately expresses your arguments. I particularly liked the section "Simplicity and What Follows" and "The Shape of Things to Come" and I share your optimism. I also discussed the role of simplicity in my essay; I would like to take your opinion.

All the best,

Mohammed

Dear Alma,

In simple sentences and well chosen pieces you gave a relevant hint of what relates maths and physics, a proof of maturity that some experts either never had or have lost. Let me quote you "When one makes the (upper-half) complex plane, fractals grow in it uninvited", "Einstein's cosmological constant and black holes - mere second-handunwanted consequences of his theory - and Higgs' field were firstly miraculous ideas based on physical intuition, not lucky attempts to search the whole of math in the hope of a chance finding" and "It may very well be a gap in our total knowledge of the world, not of the physical, or biological or mathematical fields in isolation."

I had more time than you to think about the power of mathematical physics and always found this remarkable coincidence between maths and physics in several fields from electronic engineering to quantum information. About 20 years ago, I have been fascinated by the possible connection between cognition and the quantum: I gave a few references at Vincent Douzal blog. At the the same time, I attended a school on Grothendieck's dessin d'enfants that remained "dormant" until very recently.

You are the first to acknowledge me of introducing modular forms in the program! May the moonshine topic is no longer as fashionable as it was, or just too abstract!

I don't want to be too long, but reading you revitalized my forgotten quest of putting our cognitive ability into the picture. I remembered me reading the Nobel winner in Physiology or Medicine: John Eccles "I here express my efforts to understand with deep humility a self, myself, as an experiencing being. I offer it in the hope that we human selves may discover a transforming faith in the meaning and significance of this wonderful adventure that each of us is given on this salubrious Earth of ours, each with our wonderful brain, which is ours to control and use for our memory and enjoyment and creativity and with love for other human selves." --How the Self Controls Its Brain, pp. 180-1 (1994).

I suspect that the gap in our knowledge of the world lies in our neglect of other fields such as those concerning ourselves. I also suspect that maths can be as much effective there with enough imagination.

I wish you all the best and keep ready for further interaction.

Michel

Dear Alma,

As I told you in my Essay page, I have read your intriguing Essay. You made an excellent and original work. Here are some comments/questions:

1) I see your pretty statement that "the belief that math has an independent existence beyond our daily lives is based on the observation that even a child can intuitively understand math" confirmed every day by my son David, 4 years old, who plays with numbers...

2) Your aphorisms "Physics is the only science that can work with spherical cows in a void", "As opposed to an engine, one can't fix math", "Mathematical physics is only as good as physical insight.", "We can't expect math to work on its own", "Physics is simple", "There is still time for math", "You know you're missing something when there's just too much you can't explain" and "Just wait to see our children" are fantastic! For the last one, see my point 1).

3) Your stress we don't have a quantitative match between theories in pure math and the description of nature. I think we will never have it.

4) Do you think physics is not scale invariant?

5) I agree with you that the Langlands program sounds like good news for physics, but it must be handled very carefully. I know two possibilities to translate an intractable problem into another framework which sometimes generate confusion: the Maldacena conjecture, which, in my opinion, does nor resolve the black hole information paradox as it is often claimed, and the "Einstein frame versus Jordan frame" controversy in astrophysics observations.

Finally, I found the reading of your beautiful Essay very interesting and enjoyable. Thus, I am giving you a deserved highest rate.

I wish you best luck in the contest.

Cheers, Ch.