Connections: Physics, Math, & the Human Brain by James Lee Hoover

"You've not retired from your learning", I can witness that!

Best Wishes,

Miss. Sujatha Jagannathan

Dear Jim,

As you note, physics is a science that deals with "matter and energy and their interactions." (I consider the "matter" in this definition to include "anti-matter".) If one, barefooted, kicks a stone, one is left with a very strong feeling that the physical world is real - it matters! But you further note that the union of math and physics "offers more substance"; supplying proofs, furnishing structure, providing order, and clarifying and vivifying quests." Very well put!

You then focus on the Euler's identity. If I were ever tempted to be a Platonist, believing that mathematics existed in some realm outside time and space, I would probably use Euler's identity to prove my point. It is truly remarkable.

Instead, I tend to view it as follows. I see the essence of math as derived from physical reality and as a formal mapping or map overlaying abstract symbols in such a way as to reflect the order or structure of physical reality, say for example, a helix. If one then extracts the underlying reality from the mapped physical structure, one is left with only the map, which, apparently has existence only in our minds. Writing Euler's equation on paper would seem to mean nothing, if no one ever saw the paper.

I found your analogy of an interest formula, that shows the growth one expects from combining math, physics, and brains to be useful and to contain more than a grain of truth.

You tackle the big projects, like the LHC and the Human Genome Project. [I was present at the initial meeting, and you'd be amazed at how many of the participants were against the project - "big science" was foreign to biologists at the time.]

Your European Robin example is extremely interesting. As you know, from reading my essay, the study of one particle's spin interacting with a non-homogeneous magnetic field is overwhelmingly complex, and is currently quite controversial. My own opinion is that if we cannot understand and agree on this simple physics, it is quite a stretch to attribute bird navigation to entanglement in cytochrome. But that's what this essay contest is focused on.

You have written a wide-ranging, enjoyable essay, and I wish you the best. I certainly agree with your major points.

My very best regards,

Edwin Eugene Klingman

Jim,

Many thanks for an enjoyable read. I would make a revision to your equation for Gt by including $$$$$$ as one of the factors:-) You should read the essay by Shour. You both discuss something similar.

I'm a big fan of Euler but Euler's Equation does not have a zero value. Of course, the real part or the complex part can be zero (one or the other, not both). I tend to view Euler's Equation as a quaternion although it could operate on scalars.

You are completely correct regarding the bigger picture ... the whole is much greater than the sum of the parts ... without any one of the components, we would be limited. I cannot even imagine a level 1 civilization.

Best Regards and Good Luck,

Gary Simpson

I found your essay very interesting and very well written. Shows a lot

of thought went into preparation of this composition.

While you are correct in stating that "physics depends on the human

brain and accompanying senses to investigate the physical world around

us", the human brain also serves to quantify or describe the

mathematical interactions that describe physical reactions.

The digital computer operates under different conditions than does the

human brain, but this is due to digital computer pre-programming which

makes the computations of known mathematical interactions much more rapid.

The computer can't at this time observe "strange" phenomenon, conclude

that it is a "strange" phenomenon, then classify and perform an

analysis on its own. It can only record strange phenomenon, its limits

being set by programming efficiencies. The human brain however has no

limits to its exploration of the universe and the formation of theories,

although its ability to quantify or describe physical interactions may

suffer from the unknown properties, both mathematical and physical, of

the phenomenon observed.

Hi James,

Well done on your interesting contribution. While I agree with many aspects, I am reluctant to resign to the imaginary number в€љ-1 on the grounds that there aspects of physical reality beyond our comprehension. Unlike Newtonian hypotheses non fingo, I suggest we can be able to figure out hypotheses and test them.

All the best in the competition,

Akinbo

James,

Thanks for your comments on mine. I now see the basis of your questions. Yes, I agree that entanglement and Godel incompleteness are keys to improving understanding, also that it's the 'way we employ' maths that leads to flaws there, so indeed our minds/brains inadequately evolved, You'll recall my previous essays agree with your identification of the helix as fundamental. Indeed I've now found it even more important than we've realized; See this short video;

Time Dependent Redshift hypothesis.

I found your essay a nice easy read and a quite comprehensive well written eulogy on the merits of mathematics as a tool. You don't identify the abuses, but they are, hopefully, few. I see you seem to agree those I identify, including the great red/green sock switch con trick of QM, confounding logic!

I don't think your score represents the essay and think it should be higher. I'm certainly marking it so. Best of luck in the competition.

Peter

James,

I saw your note on mine. Someone's trolling. Mine just dived too - I'm sure without even being read! I've just added your (rather higher!) score now, in line with my honest comments (now 4.6).

Best wishes,

Peter

Jim,

Though it took me a while to get here, it was worth the trip. We find beauty in the same mathematical structures and equations, and largely for the same reasons.

Thanks for commenting in my forum. You get my top vote, and best wishes in the competition.

Best,

Tom

Dear James,

Always glad to detect people of this audience that have faith in mathematics and QM and ability for connecting the two. I like your reference to photosynthesis and entanglement, for QM and biology I also like http://arxiv.org/abs/1310.7761

As for the physical interpretation of Euler's identity, I propose the Bloch sphere representation of the single qubit, in which the south pole |1> and e^(i*pi)|1>=-|1> are the same. In group theoretical terms, this is the two to one homomorphism of SU(2) on SO(3). Yes mathematics is the right language for nature.

What you say about DNA and maths is very challenging and interesting. May be we already have enough maths that can be used in physics and biology to interpret some paradoxes and mysteries.

Best.

Michel

Dear James,

Thank you for your positive feedback. You deserve a similar compliment. You gave me to think about Euler's identity. About chemistry and biology, I have a few ideas based on the same free group (of Grothendieck) that I use for my monstrous topic.

All the best,

Michel

Jim,

thanks for writing this essay. It contains a lot of ideas and conclusions to agree with. As you know from ym essay, I'm really interesting into the relation between the disciplines like biology, sociology, physics, math etc. Your essay covered all these question.

It reminds me on a discussion with a biophysicist about consciousness and quantum mechanics. New experiments seem to imply that quantum mechanics is needed to get consciousness and higher brain functions. You explained it also at the example of birds finding their route.

Therefore you will also get a high rate from me.

Best

Torsten

Dear Jim

I really enjoyed your well thought out and lucidly written essay. Your ideas were presented so well the essay may well have been enjoyed as an after-dinner convention lecture for a group of engineers. As you noted in your comment on my page many of our ideas overlap, for example the highlighting of the Math Brain Physics trinity, or of biological phenomena exhibiting and mediating mathematical functions.

I learned some interesting things from the essay, for example why the Euler formula converts to sine cosine curves when adding a z dimension - or about quantum coherence (entanglement) in photosynthesis - wonderful.

You stress rather too strongly the difference between mathematics and computers while one can argue that digital computation is just a mathematical 'trick' discretizing continuous functions, and utilizing logical operations that are at the base of all mathematics.

As you may know my ideas of physical reality and the theories describing it are rather at odds with what is accepted unconditionally by the physics community, particularly regarding foundational concepts of quantum mechanics. Interpreted from the realism of my Beautiful Universe theory, Bell's Theorem appears as an unnecessary obfuscation of simple transfer of angular momentum across space with the local, causal and realistic interactions of the ether nodes acting like a slippery 'gear train'. Please read Edwin Eugene Klingman's essay debunking Bell.

In a similar vein I also highlight that mathematics, as a product of the mind, can be tricky, supporting multiple scenarios of the same phenomena, whilst physical reality should only have one. Hmmmm.

With best wishes

Vladimir

Dear James,

Can you explain "The cat map reminds me of machinations of Euler's Identity" ? Before I passed to QM I worked a lot on chaos in relation to the understanding of 1/f noise that I finally saw as number theory in experiments. Thanks to you, this year, I realized that Euler's identity has to be kept in mind in relation to the Bloch sphere. As Riemann sphere R is just another representation (a la Felix Klein) of the Bloch sphere, Euler's identity also has a meaning in this context. I just gave a reference on Zivlak's blog. My today favorite objects correspond to three punctures on R or other Riemann surfaces with genus (dessins d'enfants). I spent some time seing them as the molecules of chemistry and biology with moderate success until now (unpublished work).

Cheers,

Michel

ps/ I also rated your work highly a few day ago following our interaction.

Dear James,

Thanks for your note.

There is a blog at the Mathematics Stack Exchange under the title "Euler's identity: why is the e in e^ix? What if it were some other constant like 2^ix?" reminding that a^ix is a logarithmic spiral.

Myself, at the moment, I start from the Riemann sphere R= Complex numbers union infinity as a way to approach the multivaluedness of mathematical knowledge following the giants: Henri Poincaré, Felix Klein and Alexandre Grothendieck. There is the online book by Lando and Zwonkin "Graphs on surfaces and their applications" (2004) where many aspects of this subject are explained. You may be interested to read it.

Best,

Michel

Dear James Lee Hoover,

I thought that your engrossing essay was exceptionally well written and I do hope that it fares well in the competition.

I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

Joe Fisher

Dear James L. Hoover

I see that you deepen in quantum biology. It is necessary to mention that theory of quantum smell of Luca Turin exist also. Besides, a presumption exists also, that number of four base pairs in DNA is a consequence of quantum mechanics. Quantum photosyntesis or quantum smell was already confirmed with a sure result of experiment, I do not know which one. What do you think about Tegmark's proof, that quantum consciousness does not exist. Do you think that Tegmark's proof is still valid?

When it will be proven, that consciousness is a quantum phenomenon, the model for it still ever will be necessary. One model is written by me. But it is speculatively, how quantum consciousness changes randomness of quantum measurement. Thus, it is a speculation, that spin 1 of photon can happen more frequently that spin -1. But, Slvain Poirer claims in his essay that he read articles which claims this.

You really gave interestion Euler's formula.

But, I do not believe that your mentioned telescope will observe antigalaxies. Namely, in Feynman's ''Lectures On Gravitation'' it is proved that antimatter moves in gravitational field on the same way as the common matter. I hope that experiment in CERN will show, how it is with this.

My essay

Best regards

Janko Kokosar

James Lee Hoover,

A very informative essay. This is not a criticism, it is an admission on my part, I don't yet recognize the central importance assigned to Euler's identity. I will look into it more and think more about it. I do assign central importance to the fine structure constant definition that contains constants that connect major theoretical subdivisions. I feel that Euler's identity must be theoretically important because you point it out. I will work on it. Your essay deserves a high mark.

James Putnam