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

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.

Dear Alma,

It was my pleasure. He is myself who thanks you for your kind words on my little son David. I think to have understood your point on scale invariance. It is nice and sharable.

Cheers, Ch.

Dear Alma,

You essay and comments are insightful and you seem to be a charming person. I was also interested in Leifer's essay viewing the whole of knowledge as a scale-free network. Your idea of looking at possible phase transitions is developed in his Ref. [13], Sec. G, p. 63 where you can read that "the critical exponents of the phase transition equal the critical exponents of the infinite-dimensional percolation". On my side, in my Neuroquantology paper quant- ph/0403020, I wrote in the abstract "Time perception is shown to depend on the thermodynamics of a quantum algebra of number and phase operators already proposed for quantum computational tasks, and to evolve according to a Hamiltonian mimicking Fechner's law. The mathematics is Bost and Connes quantum model for prime numbers. The picture that emerges is a unique perception state above a critical temperature and plenty of them allowed below, which are parametrized by the symmetry group for the primitive roots of unity." We recently revisited the BC model in the context of Riemann hypothesis and quantum computation http://iopscience.iop.org/1751-8121/labtalk-article/45421. This is a good sign that a good mathematical theory may have many inequivalent applications.

Today I have in mind to approach the subject of cognition with the tools I am advocating in my essay, it may take a while. I already mentioned that rivalry between the two cerebral hemisphres looks like a qubit.

Thank you very much Alma for the stimulus you are giving me. My very best regards.

Michel

Dear Alma,

A beautiful essay in all ways, original, insightful and with perfect English and logic, well argued.

I feel I should reproduce the phrases that I felt hit the target most perfectly;

'We can't expect math to work on its own'

'You know you're missing something when there's just too much you can't explain.'

'We've carefully chosen bits of math that resemble the phenomena we wanted to study'

'In pure math, any inconsistency is shot dead on sight.'

'Math requires us to be very careful when shaping a theory because the slightest false step will bring down the whole edifice that we've carefully built by creating a contradiction.'

'when we lose the correct track we have no way to find it again without more new insights.'

No time now, or even need, for detailed questions, time for scoring. i hope you may have time to read mine, which identifies a specific and important case of loosing the correct track but accepting illogicality by being satisfied that maths is enough. I'd love to hear your views.

Very well done, and thank you.

Peter

Alma Ionescu wrote on Apr. 18, 2015 @ 15:08 GMT stub

Dear En,

This is nice and to the point. Your writing displays an interesting personal stance and I'm sure you enjoyed the exercise. I think that you're right when you're saying, in the third paragraph, that Wigner's expression should not be taken literally as it was more a metaphorical way of encouraging new lines of thought and maybe a feeling of delight in the face of the best known parts of the natural world.

Warm regards,

Alma

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Author En Passant replied on Apr. 21, 2015 @ 07:32 GMT stub

Dear Alma,

I actually have many contacts with Romanians. They are extremely good at programming, and (in fact) BitDefender (the best antivirus program) is programmed by Romanians.

Don't worry, the NSA can "get in" anyway. But their interests are not what we worry about (banking, etc.).

En

Hi Alma--

Your essay was a joy to read. There is a wonderful lyrical quality to your writing style. I loved your sayings, especially "You know you're missing something when there's just too much you can't explain". I shall incorporate that one into my daily lexicon.

Quick question, admittedly somewhat off-point: Which philosopher has influenced you the most?

Very best regards and luck in the contest,

Bill.

Hi Alma--

I admire your preferences for thinkers and philosophers. If you haven't already, I urge to read Jim Holt's book, "Why does the world exist"?. It's a wonderful book. Furthermore, Holt devotes an entire section to Weinberg (chapter 9). Reading Weinberg's views on philosophy, the multiverse, etc., was fascinating.

Best regards,

Bill.

Alma,

You're a winner. I do not exaggerate when I say that in my opinion, your essay ranks near Wigner's own, in its breadth of knowledge and depth of insight.

A couple of confessions I have to make: I have followed and enjoyed your intelligent commentary in other forums, so I knew I would get to your essay eventually. And the other confession is that I checked on the internet to verify how young you are; I would never have believed it from your mature postings. I do hope your circumstances permit you to go on to higher academic pursuits -- it's obvious that you have the "right stuff."

I didn't know the story of von Neumann and the engine. I do recall another one, though, of his lightning-fast calculating skill -- mathematicians like to try and fool each other with problems that seem complicated, but can be made simple with "tricks". One of them concerns two trains approaching each other, with a fly flying back and forth between the engines -- how far does the fly travel before getting squashed when the trains collide? One can get a quick answer by knowing the short cut of averaging -- otherwise, calculating the series by brute force is long and tedious. It is said that when the problem was put to von Neumann, he gave the solution almost immediately. Asked if he knew the short cut, he looked puzzled and replied, "What could be easier than summing the infinite series?" The Wolfram site has an article on the two-train problem.

Highest marks, and good luck!

Tom

Dear Alma,

Your essay is extremely insightful and directly addresses this forum topic. I really enjoyed the development of your conclusions, in particular "mathematical physics is only as good as physical insight." My essay makes the exact same point, and discusses how changing the physical insight subsequently effects the mathematical abstraction, and how changing mathematical representation affects physical explanation. Your examples are excellent and very pertinent, in fact exciting. In particular, your juxtaposition of the Langlands program with Godel is brilliant. The Taniyama-Shimura-Weil conjecture is an incredible connection of different mathematical areas, and I absolutely agree that an equivalent to the Langlands program applies to physics; indeed it is a cornerstone in physical explanation. Schroedinger is perhaps one immediate example, though there are many more, and I'm familiar with some university programs specifically designed to connect different areas of physics for this very reason. As I mentioned, I liked how you juxtaposed this with your discussion of Gödel, and how you distinguished mathematical physics when countering the consequences of incompleteness. My essay too shows how what was considered a limitation can actually be expanded when attempting to physically model undecidability, and thus consider the physical requirements resulting from incompleteness. Finally, your appreciation of the humanity and lives of some of the greats, coupled with your optimism for the future is quite noble. This essay is a great contribution and I give it a 10.

Please check out my essay as well, and we have many things in common and our ideas very well support each other.

Thanks,

Steve Sax

Dear Alma

nicely written essay. I agree on many points, and especially about complexity, about which you say that "That our knowledge manifests gaps around emergent phenomena seems to be an indication that we lack some insight of the mathematical description itself, not just of what happens physically." And I agree that that this limits our knowledge in fields as biology, along with phys. and math themselves.

My best wishes for your essay and for you

Mauro