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Irek Defee

Dear Prof. Landsman,

You essay is brilliant, very important for closing loopholes and final ending with determinism in QM. The question now is where the fundamental indeterminism or randomness plus undecidability comes from. You state that theory of the Planck scale would derive QM as emergent, then hopefully we may know. Such theory, or an ultimate theory of everything should also be able to tell emerging 'why' and from 'what' and this 'what' should be then kind of irreducible or self-referential. Such topics are obviously rather mind-blowing. In my essay I am focusing on the 'why' and 'what' and it turns out it is uncomputable sequences which have curious relation with nothingness. Material in my essay is rather compressed and concepts are not stated precisely but I hope the essence can be grasped.

Best regards,

Irek

Dear Peter,

Thank you for your valuable comments on my essay. I read your essay and I am greatly impressed by the depth and width of your knowledge and thoughts. The title of your essay is most attractive and eye catching of all. Questioning binary logic is very promising, there is stuff called quantum logic. Noticing that laws of ancient Greeks are valid for metaphysical but not for nature is brilliant. You correctly see that applying fuzzy logic is the way and that should be standard for the future. I wish you very fruitful research along these lines.

Best regards,

Irek

Dear George,

Thank you for reading my essay, you really grasped its essence which I tell you is rare and remarkable. But my lesson from it is that I have to expand it greatly to present concepts with utmost clarity.

Your essay is well written and obviously it touches absolutely fundamental problems. When looking into the relation between consciousness, physics and mathematics I see consciousness as total enigma. We know much more about physics and mathematics which makes that it is very hard to connect all these three areas.

I also looked into your 2015 essay, I see now what you mean by hole in the center of creation. About paradoxes I suggest reading brilliant essay by Hippolyte Dourdent here.

Personally my taste is not to refer to any religion since this is very subjective topic as there are so many of them, some claim Asian religions grasp aspects of consciousness better than others and that would mean cultural bias is entering our thinking which does not sound good.

I wish you to continue you fruitful investigations.

Br,

Irek

Dear Hippolyte,

This is by far the best essay I read until now. It is highly illuminating, it is possible to understand it without a deep dig into literature first and one learns why becoming meta-observer is not a good thing:). 10/10.

Dear Markus Mueller,

Your essay is extremely well written with sharply presented arguments. One can agree that the world which is open for opportunities (unpredictable) provides generally optimistic perspective though sometimes reality bites painfully as one can see. Questions which remain are of deeper foundational nature: why it is as it is, e.g. your hypothesis about the quantum world. It has to be originating from an underlying structure unless one accepts that every possible world exists and we just happened in this one.

As this essay has the word 'uncomputability' in the title which also appears in my essay I had to read it. I see some issues with the concept:

spin-half is represented by uncomputable number, more precisely it should be spin direction but the direction depends on the frame of measurement and there is no absolute frame, how to deal with that?

pure state is represented by an uncomputable number with 1 for the digit which corrseponds to direction n. I have difficulty understanding this, this number has only single one and all the rest are zero? Then it would be computable.

Is this number fixed?

measurement is respresented by the calculation of one single digit. But how the position of this digit is selected?

The second part of the essay looks unrelated to the first part.

Dear Authors,

Your essay is written in good style and provides excellent review of issues. I would like to comment on the part concerning uncomputability since this word appears in the title of my essay. You provide account of different number systems which could have potential for physics but in my view there will be always question why these? In other words we have to go below the level of number systems when thinking about deepest foundations, the systems have to be emerging from something. In my essay this is done by considering uncomputable sequences from which the mathematical fields and other mathematical structures emerge due to the action of infinite permutation groups, there is enough headroom there for physics to be one to them. Physics would be then emerging from uncomputable substrate which means an ultimate theory without the baggage of assumptions and notions.

Best regards,

Irek Defée

Dear Prof. Hossenfelder,

Your essay is sharply written which makes it pleasure to read. I would like to focus on the 'uncomputability' aspect since my essay has this word in the title. In connection to it, you say among others that in science we really don't deal with real numbers which of course is true. But the problem is that real numbers are indispensable for theory, QM breaks up without them, QM based only on rationals is impossible. One can brush this away as an artifical issue which would be unscientific, or treat it as a signal that something deeper might be lurking there. Thinking probably along these lines Tegmark proposed radical thesis that physics is just a mathematical structure but this is seen more as belief since there are no constructive arguments for supporting it. In my essay I am sketching a constructive way via uncomputability in the form of uncomputable sequences which are giving rise to the emergence of mathematical structures due to the action of permutation groups. The groups are enormous, uncountably and countably infinite ones which provides headroom for extremely complex structures and physics could be one among them.

Best regards,

Irek Defée

Dear Israel,

Thank you for your comments placed in my thread, they are valuable as I can see from them where my arguments should be clarified and sharpened to make them clear. I am replying here to reach you easier.

You write "I also support the view that we should develop a physical understanding to have a complete view of reality." This of course is fundamental issue. Position of the majority of physicists (put eloquently by Hossenfelder) is that there is physical reality which is something different or beyond math. It stems from long tradition of seeing physics as concerned with 'material' and also from our perception of the world in which reality bites but mathematical abstractions can not bite. Problems with this position is that mathematics is so 'unreasonably effective' and getting ever more abstract for the description of reality confirmed in experiments that this can not be treated anymore as a coincidence or invention of human mind.

I am not fully convinced about your examples for the argument how physical understanding have to be put on top of the mathematical one. The problem as I see it is that models and mathematics used in these case might be too simplified. For your example of the wave number of electron. It obviously assumes that electron is a wave but is it really? According to quantum field theory electron is field excitation and there are creation and anihilation operators, quantum vacuum, and so on. Thus there might be mathematics in the QFT which eliminates the need for such physical understanding. It would thus be enlightening to ask experts in the sizable area of 'Electron in QFT' what they think about this.

In general it be could that the need for any physical understanding is due to limited math models we have and not that math is just an imperfect tool for physics. It could then also be that any time we need the 'physical understanding' it points that underlying math theory is simply incomplete and insufficient.

That leads to the issue of relation of mathematics and physics which is the topic in my essay. The argument of Tegmark is rather thin, assuming all math structures exist. In my essay I am trying to derive arguments that the fundamental structure have to be uncomputable sequences which are intrinsically tied with nothingness. Symmetry requires then that infinite permutations groups have to act on these sequences and this gives rise to emerging mathematical structures, physics is one of them. From this, support for the Tegmark claim that all math structures 'exist' comes with addition that this will be very intermittent structures, just appearing and disappearing due to the action of permutation groups. Physics from this point will be exceptional in the sense of created by rare special group whose symmetry will be dissolving in a huge number of actions. Also from my elaborations it results what is the relation of infinities and real numbers to physics. Infinity is appearing only in the uncomputable substrate from which physics emerge, there is no need for infinity in the physics itself and real numbers are only emerging as apparent but they both are done there in the substrate. I have to prepare expanded version of the essay to make all this clear, there was too much compression and only now I am getting valuable comments.

Br,

Irek

Dear Cristian,

Thank you for replying in my thread. You have quotes from famous scientists in your essay: Poincare, Wiener, von Neumann, Deutsch etc. You could just take a look into their published work to have idea about the topics and style of their writing. You will notice then that it is as much math as there is graphics in your essay:) In scientific literature one should reference any previous work related to the work being presented and explain the relation. Reason for this is a) to show that the work presented is original that is there is something new and not only repeating the previous work, b) to give credit to authors of previous work on which the presented work is based. If a) is not fulfilled than there are doubts if the work is original, in worse case it may happen that the problem was solved earlier and thus the presented work makes no sense. If b) is not fulfilled it may mean that the author is not aware about the previous work in the area or is neglecting contributions of other people on which his work is based. Thus, one has to be extremely careful about references which typically first hard step to prepare a paper. One can learn how all this should be done by reading papers produced by other people.

However, your essay is more of artistic genre. Artistic work should be original, not copying others. Your work looks original and it does not need references.

Br,

Irek

Dear Torsten,

I replied to your comments about my essay in my thread. Here are some thoughts about your essay. I think the undecidability and uncomputability as they are usually considered have nothing to deal with physics. This sounds provocative but the reason I see it like this is if we take e.g. this paper about undecidability of spectral gap. So the gap is undecidable but it is decided by physical matter all the time. One thus ask how is that possible but after a moment of reflection this is trivial: undecidability deals with a model of computation but matter is not computing according to this model. Matter conforms to the requirements of symmetry and these have form reflected by mathematics which is about symmetries. But nothing is computed in the sense of computers.

Uncomputability is similar since its stuff is infinite and that is questionable for physics. Idea of essay is based on uncomputable sequences from which math and physics emerge, and thus physics can be finite but running on uncomputable substrate.

Unpredictability is another issue and a very important question is where is the source at the most fundamental level, maybe it is in the incompletness of arithmetic and thus math?

By the way, you mention brain and consciousness in your essay. I think these items are much worse than physics, quantum field theory and quantum gravity:) in the sense that absolutely nothing can be said about anything there with any degree of certainty. One can take single neurons as example, they are modelled as threshold elements but real neurons are by far not like this. All the time there are coming new data showing they are extremely complicated, dendrites and axons are not only simple wires, synapses are not simple switches, cellular scaffolding aorund neurons is not passive and so and so on. So we do not even know what is really single neuron doing, assemblies of neurons are much more complicated. I've been in the area of image processing and pattern recognition and things there are really ad hoc.

Br,

Irek

Dear Torsten,

Thank you for your remarks. They are very valuable since my essay introduces notions which are outside of standard thinking and thus they have to be explained with utmost clarity and examples to be understood the way I intended, otherwise it be seen as a junk. In the essay explanations were compressed to minimum and thus clarity is not at the highest level. This obviously implies that I must prepare extended exposition of these ideas and I am looking into it.

P-adic numbers are covered recently by Tim Palmer in an interesting way and he also has an essay here. However my questions are more fundamental: If p-adic then where they are emerging from? In particular there will be issue, why this particular p?

Uncomputable sequences appear in my essay due to critical problem of theory baggage and background which is critical for TOE. TOE is very tricky in this respect, if somebody claims having developed TOE and starts with e.g. 'assume Minkowski space' there is immediate question why this and where it is coming from? Even the usage of real numbers can not be taken for granted in the TOE. In this sense QM is at a significant distance from TOE since it assumes huge amount of background stuff.

So I am starting from the level below real numbers, everything should be emerging due to symmetries.

I will be happy to discuss the issues further, if you wish you can contact me directly to my email which is in the essay headline.

Br,

Irek

There is missing one highly relevant reference.

At present even the assumption of "time evolution of a quantum system is deterministic" is not obvious and is subject to investigation as the temporal order might in principle be entangled.

When invoking Turing machines in the QM context one has to resist temptation that QM is like a computer and 'computing'. In QM dealing with qubits there are indeed computations going one and quantum computers are possible. But this is trivial QM as the real QM is inherently infinitely dimensional and the really real QM is quantum field theory.

Best regards,

Irek

Dear Torsten,

Thank you for your reply and promise to comment on my essay. Then I can add few words about how I see uncomputability and undecidability from the perspective of physics.

Best regards,

Irek

Dear Israel,

Your essay is very interesting and well written. The relation of mathematics and physics is a fundamental issue. Tegmark is championing radical thesis that physics is mathematics. This of course sounds like a metaphysical belief but the "unreasonable effectiveness of mathematics" when applied to physics can not be just brushed away. Thinking along these lines I developed approach in which uncomputability is foundational, Theory of Everything has to be founded on it but in a very peculiar way. This is sketched in my essay.

Best regards,

Irek

Dear Torsten,

There is only a couple of essays with the word Uncomputability in the title worth mentioning. Your essay is excellent and I read it with interest since it explains the concept very well. I got idea there is more to it and in my essay I take a radical vantage point with Uncomputability becoming absolutely central to everything, Theory of Everything has to be based on it. Why and how this is done is in my essay.

Best regards,

Irek

Dear Arto,

In your essay you raise the hard question about something rather than nothing which has been asked many times but no answer whatsoever been in sight. I got an idea how to tackle this by the TOE based on uncomputability and sketched some answer in my essay.

Yståvällisin Terveisin,

Irek

Dear Carl,

You write: Everything we know in physics is fundamentally time-symmetrical...

It is not so, please search 'CPT symmetry' as there is only CPT symmetry invariance.

Dear Dr Batista

You raise absolutely fundamental questions in your essay. However there is a problem with your premise that Nature can be viewed as a computing system, in particular operating with finite numbers. The first problem is that theory requires real numbers in full, e.g. quantum mechanics fall apart without real numbers. So we have an issue what is the relation of quantum mechanics to reality. Another problem is excessive simplification, you write "A free electron can be fully described by its charge, mass, spin. Therefore it can can be easily represented". But there is another level here if one asks why this value of charge and mass and how it interacts with surrounding space. Then it becomes a hellish issue which even after 100 years is still not fully rigorousl solved and it seems to exceed by far reality based on finite numbers. To get a glimpse on it search e.g. 'baez struggles with the continuum'.

Dear Alexandru,

Your essay is very funny in artistic way proving you really have far from standard imagination. However, I think expectations of this contest are more formal and preferred style is like submission to scientific journals.

Best regards,

Irek