A Mind/Mathematics Dualistic Foundation of Physical Reality by Sylvain Poirier

You wrote : The halting problem (what can/cannot be computed) arises due to a wrong question: "How long are you willing to wait"?

This is not a wrong question. At first sight it may look not very serious, like the liar paradox or the Berry paradox, but further examination of the foundations of mathematics shows that it is crucial and cannot be eliminated. Namely, once added up Goedel's completeness and incompleness theorems, we discover that the provability of some formulas happens to be undecidable, as the question of their provability, that is the "existence of a finite proof", begs the question "what is finiteness ?" which cannot be defined in the absolute as there are mathematical "universes" where a given formula (that we can write !) is "provable" but the length of its shortest "proof" is a nonstandard number, that the system mistakes as finite according to its definitions but which is actually infinite. In this universe, the proof "exists" but "the time we need to wait" to find it is infinite. If we wait long and do not find it, it may be because the time we need to wait has non-standard length, i.e. is infinite, so that we are right to stop searching and conclude we have no proof (as we are sure to do it before non-standard times) instead of taking the abstract "existence of a much longer proof" as meaningful, whose truth value in a non-standard universe does not conform to the real truth about provability.

Then, your remark about irrational numbers and precision is a particular of computation that does not answer the halting problem in its generality, in case we were interested with the halting problem in its generality.

The precise properties of quantum physics refuted since long ago the naive classical expectations that unpredicability only came from the limited precision of measurements. Such explanations cannot account for the precise form of quantum randomness which turned out to be irreducible in such terms.

"mathematics is only the quantitative description of Nature, whereas physics describes its qualitative aspects" This is not what I meant. I mentioned the hypothetical concept of a universe with only qualities and no quantities, but this is not the one where we live.

"there are many problems with relativity" : it depends. There are many people who imagine much more problem with relativity than there really are because they failed to understand it.

"there is no standard interpretation of quantum physics. " If you paid attention to my text you would have seen that I offer a precise interepretation of quantum physics, which seems to me by far the most coherent, and in agreement with observations.

I have ideas in geometry indeed and how to use it to understand theoretical physics, but this was not the topic of my essay, as I had more important and on-topic things to put there instead. You can find in my site some of my ideas on geometry and its axiomatization, and how to understand Special Relativity and quantum physics in geometric terms. There are also algebraic aspects of geometry, such as more deeply using duality in linear algebra, seen as a particular case of a much more general concept of duality in algebra involving the concept of polymorphism, and giving a clean introduction to the formalism of tensors. Long ago I also wrote other things on geometry in French (on affine, projective and conformal geometries, and geometries with a constant curvature). Unfortunately, I am still far from completing and cleaning up all things I wish to write on the topic, as I had many other things to write on, such as in the foundations of maths and in philosophy.

"Is very, very, very high probability the same as certainty?" : it all depends on context and how accurately we need to discuss. For example in a star, colliding atoms have every time a very low probability of undergoing some nuclear reaction, however there are so many collisions and each reaction releases so much energy that it suffices to provide the power of stars. Similarly, the chance of winning at Lotto is very low, but so many people are playing that the chances of existence of a winner becomes significant. Also, as free will operates by deviations from physical probabilities, it can make happen some possibilities that had very low "probability" as defined by quantum physics.

"Is it very, very, very probable that 2 3 = 5 or is it a certainty? When adding 2 and 3 apples together, can any of the apples perish as you go about doing your summation to see what you get?"

Of course, the formula 2 3 = 5 is a certainty but what is uncertain is whether its correspondence with apples is a valid one, in case an apple might perish.

"When adding 2 quantum particles to 3 of same, is it more or less likely the results you will get will be same as for apples?" Again, it all depends on the specific kind of particles you work with; and on the time passing between when you introduce the particles and when you count how many are still there. We cannot seriously go anywhere with such childish pseudo-examples. It is of course very easy to "prove that science isn't valid" by introducing some ridiculously naive way of pretending to do some experiment and apply a mathematical model, and victoriously failing to do so properly. The validity of mathematical theories to describe physics has been verified with an amazing degree of accuracy, but of course this requires to have done the very hard and professional work of finding out which theories are applicable and in which conditions. And generally I don't buy any "argument against reason" such as "it is possible to victoriously fail to reason (or experiment something) correctly, thus all reasonings (or experiments) must be incorrect as well". More comments on this topic here.

"Give this a thought." Do you think I waited for your invitation to do so ?

Hello. By "lowly mathematical" I meant "of a low mathematical kind" though it remains 100% mathematical. Moreover, not all algorithmic worlds are equal. Some, like Conway's Game of Life, have a low density of interesting possible behaviors lost in an ocean of chaotic ones, as I once verified by systematically testing hundreds of initial configurations, so that imaginative tips are most often impossible.

Indeed I concentrated here lots of ideas, so it may be hard to follow. It may look clearer reading the longer exposition of my interpretation of quantum physics from which the main ideas here are extracted, and maybe other texts on other aspects (introduction to quantum physics, problems with other interpretations, foundations of maths)

The last part touches last year's contest that I missed as I was busy trying to get people implement my project (but I actually failed to do so). But I stayed here at such a level of generality that I still see it on-topic: rather cosmological and related with the rest of ideas of the essay, without entering the details of how things can work. But for last year I am not sure what I could have explained in 9 pages. Maybe just a few key ideas and cases of functions, longer explained in my site. As a substitute, I undertook in the last few weeks to write a much longer comment on many ideas found in other essays of that contest.

About the relation between the "spheres" of the mathematical, the physical and the conscious, I think I was clear already in the title, and more details are expressed for example by the diagram on page 7.

The mathematical systems best suited to describe the physical world are well-known. There is no wonder what they are. Much of the competition is already past and now over. Possible candidates were already reviewed, and the ones that best fit were selected and very well verified. They are of course the established theories of physics : as far as we can tell now, they are the theories of General Relativity (with the Least Action Principle), Quantum Field Theory with the Standard Model, and the concept of density operator. Or, to take the main effective theories respectively resulting from them that more directly appear in practice : Newtonian gravitation, electromagnetism and thermodynamics. For more details on these lists, see in my essay, and in my site.

The word "entanglement" may be ambiguous. The formalism of quantum physics makes no fundamental distinction between entanglement and classical correlations. Usually, classical correlations are entanglements that macroscopically behave as mere classical correlations due to decoherence (that destroy the practical ability to measure observables not commuting with a specific one). And decoherence is an emergent phenonenon.

In my opinion, wave function collapse is caused by conscious observation (a non-physical condition) which requires decoherence (an emergent condition from physics). And time arrow is a property of consciousness, which causes the time arrow of thermodynamics.

Yes, not only entanglement times (i.e. before decoherence) are very short, but I see the idea of letting decoherence a precondition for observation (or free choice) a more logical way to articulate physics with metaphysics, for the reasons I explained in my site.

See my reply about U(1) symmetry in comment to Peter Woit's essay.

Best regards

Sylvain

Dear Joe Fisher,

Sorry for you but I have several reasons to consider the review of other essays a higher priority than yours, and one of them is your ridiculous claim to think that all essays in this competition are exceptionally well written, and that you do hope that they all fare well in the competition.