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Dizhechko Semyonovich: on 3/31/20 at 14:38pm UTC, wrote Dear Sabina, it is difficult to argue with your mathematical essay. With...

Peter Jackson: on 3/25/20 at 17:42pm UTC, wrote Dear Sabine, A novel, beautifully written and slightly irreverent set of...

Andrew Knight: on 3/22/20 at 18:58pm UTC, wrote Hi Sabine, I very much enjoyed reading your essay. I love love LOVE how...

Martin Staveren: on 3/22/20 at 10:15am UTC, wrote The Navier-Stokes equation has already been mentioned. Thus we have the...

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Satyavarapu Gupta: on 3/21/20 at 21:24pm UTC, wrote Hi Sabine Your wonderful words..........And yet, physics isn’t math....

Roger Schlafly: on 3/19/20 at 1:58am UTC, wrote You say: "the future is already determined, up to the occasional random...

Dale Gillman: on 3/16/20 at 2:29am UTC, wrote Hello Dr. Hossenfelder, I will admit that I am humbled to write a...


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FQXi FORUM
April 5, 2020

CATEGORY: Undecidability, Uncomputability, and Unpredictability Essay Contest (2019-2020) [back]
TOPIC: Math Matters by Sabine Hossenfelder [refresh]
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This essay's rating: Community = 7.8; Public = 6.8


Author Sabine Hossenfelder wrote on Mar. 11, 2020 @ 01:23 GMT
Essay Abstract

Gödel taught us that mathematics is incomplete. Turing taught us some problems are undecidable. Lorenz taught us that, try as we might, some things will remain unpredictable. Are such theorems relevant for the real world or are they merely academic curiosities? In this essay, I first explain why one can rightfully be skeptical of the scientific relevance of mathematically proved impossibilities, but that, upon closer inspection, they are both interesting and important.

Author Bio

Sabine Hossenfelder is a physicist at the Frankfurt Institute for Advanced studies.

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Amrit Srecko Sorli wrote on Mar. 11, 2020 @ 04:26 GMT
Godel on math incompleteness view is mathematical philosophy. It has nothing to do with physics. Math has destroyed physics. That's why I introduced BIJECTIVITY.

attachments: 2_Cosmology_based_on_measured_data_and_observation.pdf

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Jochen Szangolies wrote on Mar. 11, 2020 @ 06:36 GMT
Dear Sabine,

thanks for an engaging and well-written essay. It's good to introduce a skeptical point of view to the applicability of limitative metamathematical theorems to physics, or at least, one tinged with a healthy dose of realism.

However, I find your initial argument somewhat spurious. While it's true that, no matter how much we like a certain mathematical formalism, this...

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Jochen Szangolies replied on Mar. 11, 2020 @ 06:41 GMT
"...applying instead to wide classes of theorems." should have been "applying instead to wide classes of formalisms.", sorry.

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Author Sabine Hossenfelder replied on Mar. 11, 2020 @ 06:53 GMT
Jochen,

Thanks for your feedback which is much appreciated. However, you are mixing together two separate things that I discussed separately. Goedel-like theorems are not relevant to scientific practice because of their axiomatic structure. Theorems that rely on something being infinite and so result in something being uncomputable or undedidable are not relevant for science because they don't apply to the real world.

"While it's true that, no matter how much we like a certain mathematical formalism, this doesn't tell us anything regarding whether nature actually avails herself of that formalism, perhaps much to our chagrin, the theorems of Gödel, Turing et al are not limited to some formalism, but rather, are metamathematical theorems applying instead to wide classes of theorems."

I don't know what you mean by that. These theorems apply to classes of axiomatic systems. I am saying that in physics we can never tell whether the axioms are actually the correct ones, so why worry about it.

"Furthermore, I'm not quite sure if I agree with you that these questions really only apply in infinitary contexts."

This isn't a matter of opinion. Just look at the derivation.

I am happy to hear you liked my essay. With best wishes,

Sabine

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Jochen Szangolies replied on Mar. 11, 2020 @ 07:04 GMT
Sabine,

thanks for your quick reply. The point I was making with my example above, however, is that while we may never be able to 'tell which axioms are actually the correct ones', we may be able to tell what class of axiomatic system is best in line with the data we observe, and whether that is a system to which the limitative theorems apply.

As I showed, it may very well be the case that we observe finite data and find a law such that the most reasonable explanation is that the underlying function is noncomputable. Sure: it could be that the agent above is wrong, and that their success in predicting future observations is accidental, or that they have not yet found the true fundamental law; but such is all the certainty we get in science. Quantum mechanics' predictive successes could be accidental, or there could be an underlying deterministic theory; then again, there might not be, and as our failure to find one drags on, it becomes more and more reasonable to believe so.

Cheers

Jochen

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Satyavarapu Naga Parameswara Gupta wrote on Mar. 11, 2020 @ 09:34 GMT
Well Said Sabine,

...................physics isn’t math. Physics is science and as such has the purpose of describing observations of natural phenomena. Yes, we use mathematics in physics, and plenty of that, as I’m sure you have noticed. But we do this not because we know the world is truly mathematics. It may be mathematics, but Platonism is a philosophical position, not a scientific one...........

What we do is describing Physics and nature by using mathematics. Some setup is more successful in explaining it mathematically, some setup cannot. It is all depends on true open thinking oppurtunity available to the researcher is it not?

I just elaborated what should be the freedom available to an author when the “ real open thinking” is supported. Have a look at my essay please.

“A properly deciding, Computing and Predicting new theory’s Philosophy”

=snp.gupta

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Author Sabine Hossenfelder replied on Mar. 11, 2020 @ 15:09 GMT
Thanks for the kind words. I will have a look at your essay. With best wishes,

Sabine

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Manfred U.E. Pohl wrote on Mar. 11, 2020 @ 10:37 GMT
Dear Sabine Hossenfelder,

i rate your essay as the best one in the contest so far. Perfect on all points.

Regarding the weatherforecast and Navier Stokes: Golbal Temperatur is an intense property in physics. So a physicist knows we can't measure average temperature with many measurements at different places at same time or with many measurements at different times but a single place. Both does not tell us anything about the Global temperature.

How to measure Global temperature in physics?

We know that if earth gets hotter, within the CO2 circulation more of the distribution should be in light atmosphere than in water, as if oceans get warmer the CO2 level in water decreases while in atmosphere rises.

So to measure the temperature of a living planet earth we measure with the Keeling curve at Mauna Loa : https://de.wikipedia.org/wiki/Messstation_Mauna_Loa

So an intense property in Physics we can only measure indirect. As far as i identified the key problem of the Measurement-Problem it is the detailed reasoning for space, time, velocity and speed at what stage where and how we have to deal with intensive and extensive quantities of space-time plasma to fuse mathematics- with physics in a new way.

Best regards and much thanks for the Essay.

Manfred U.E. Pohl

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Author Sabine Hossenfelder replied on Mar. 11, 2020 @ 15:06 GMT
Dear Manfred Pohl,

Thanks for this interesting remark, I will keep it in mind! With best regards,

Sabine

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Martin van Staveren replied on Mar. 22, 2020 @ 09:57 GMT
I saw above the question whether nature avails itself of a formalism. This is a misunderstanding. An electron does not calculate anything. A theory May be a representation of a data collection, in the algebraic sense. The objective is to obtain a sufficient level of isomorphism. Thus an effective model may represent the data, even when there is no one-to-one correspondence between the terms of the model with elements of reality. See e.g. the Bogoliubov and Froehlich transformations or the old fashioned normal mode transformations. Is a normal mode a physical object?

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Martin van Staveren replied on Mar. 22, 2020 @ 10:15 GMT
The Navier-Stokes equation has already been mentioned. Thus we have the hydrodynamic regime: low energy excitations, long wavelengths. The matter density is a continuous function of space, which is of course not true. But in the hydrodynamic regime this is good enough; when we sit in the bath tub then we do not see molecules. Foundational physics should look at condensed matter physics; these systems are usually so complicated (mainly due to many particle interactions) that all models are only effective.

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Mihai Panoschi Panoschi wrote on Mar. 11, 2020 @ 12:51 GMT
Dear Sabine, I happen to disagree with most of your essay's statements right form the outset. For instance: 'Godel taught us that mathematics is incomplete' I would say that's an overstatement and that rather, his results proved unambiguously that mathematics (or rather its particular branches such as geometry, algebra, topology, etc) can never be grounded on formal, symbolic logic, as per...

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Author Sabine Hossenfelder replied on Mar. 11, 2020 @ 15:08 GMT
"In other words you're saying that Platonism, Aristotelianism, Cartesianism, Kantianism, Hegelianism, etc. played no role in the history of human mind and its quest for scientific knowledge and certainty?"

I didn't say anything like that.

As to your picking on my introductory sentence. I know what the theorem says. That's a brief summary of the gist of it and not a formal statement.

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Mihai Panoschi Panoschi replied on Mar. 11, 2020 @ 17:13 GMT
I think it is one thing to say the the grounds/the foundations of various mathematical branches such as arithmetic, geometry, anylysis, algebra, topology, probability, ststistics, etc and even physics are incomplete/logically inconsistent and a totally different thing to say that mathematics, in general, if there is such a thing, is incomplete, wouldn't you say?,,,I doubt that Godel ever stated the latter even as a 'gist' of his celebrated theorems, As their gist more accurately reflects the former, in my opion.

As to Platonism as a mere philosophical position and not a scientific one,let's just pose for a minute and ask ourselves the following question: would for instance be a science today called 'Cosmology ' if the mankind didn't have such a profound dialogue written by Plato, viz. Timaeus handed down through time to us?...Moreover, where would our science and culture of today with its main branches such as Physics, Mathematics,Logic, Ethics,Aesthetics, Metaphysics, etc be without the ancient Greeks?...

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Robert H McEachern wrote on Mar. 11, 2020 @ 14:15 GMT
"Any proof is only as good as its assumptions" All too true.

And as Max Planck observed a century ago, the problem is, theoretical physicists are not particularly adept at identifying that some things, even are assumptions; with the result that "self evidently true" facts, lead to long periods of stagnation, until those "facts" are eventually shown to be just idealistic, false assumptions. The seldom stated assumptions underlying Bell's theorem are a case in point.

Rob McEachern

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Author Sabine Hossenfelder replied on Mar. 11, 2020 @ 15:10 GMT
I entirely agree with that.

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David Brown wrote on Mar. 11, 2020 @ 15:15 GMT
"... Einstein’s Field Equations are widely believed to break down near the singularity because quantum gravitational effects should become important. And since the singularity is hidden behind the event horizon ..." In physical reality, is there such a thing as an event horizon? Consider the following question: After quantum averaging, are Einstein's field equations 100% correct?

Consider the following:

Einstein's Field Equations: 3 Criticisms

Can you cite empirical evidence that shows that any of 3 suggested modifications are wrong? I claim the following: Merely on the basis of mathematics, the alleged Rañada-Fernández-Milgrom effect is approximately equivalent to Milgrom's MOND — whenever and wherever the MOND approximation is empirically valid. Do you agree or disagree with the preceding claim?

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Wilhelmus de Wilde de Wilde wrote on Mar. 11, 2020 @ 16:00 GMT
Dear Sabine;

I have read with great interest your essay and concluded that I agree with most of the deductions and conclusions. Only we are using different “words”. Some remarks while reading your essay.

“A theory may have given us the most extraordinarily accurate predictions until today, and still tomorrow we could discover that it doesn’t explain the next measurement.”...

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Author Sabine Hossenfelder replied on Mar. 13, 2020 @ 05:11 GMT
Wilhelmus,

Thanks for your thoughtful comment. I largely agree except on your remark about the black hole horizon. A black hole horizon is a global property of space-time. It's a macroscopic feature and has nothing to do with the Planck scale. For large black holes the curvature at the horizon can be arbitrarily small. I will have a look at your essay. With best regards,

Sabine

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Flavio Del Santo wrote on Mar. 11, 2020 @ 16:24 GMT
Dear Prof. Hossenfelder,

congratulations on a beautiful essay indeed! (like many of your writings with which I am familiar). I agree with most of your arguments and overall with your program against the (arrogant) reductionist view of physicists.

You might find some resonance with my essay, based on a work carried out with Nicolas Gisin, where we further developed the argument against the physical significance of real numbers. This seems to entail this almost Platonistic standpoint on mathematics, having its really existing entities and physics relies on them at an ontic level. As you also say, of course nobody questions the great power of mathematics in modelling physics, but math is not physics, nevertheless.

I wish you to get to the prize range, top rate from my side!

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Flavio Del Santo replied on Mar. 11, 2020 @ 21:01 GMT
I am sorry, wrong link :) I meant my essay: https://fqxi.org/community/forum/topic/3436

(Although, Eric's essay is a good one!)

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Author Sabine Hossenfelder replied on Mar. 13, 2020 @ 05:06 GMT
Hi Flavio,

Thanks for pointing out, I will have a look at your essay! With best regards,

Sabine

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Flavio Del Santo wrote on Mar. 11, 2020 @ 16:26 GMT
Dear Prof. Hossenfelder, congratulations on a beautiful essay indeed! (like many of your writings with which I am familiar). I agree with most of your arguments and overall with your program against the (arrogant) reductionistic view of physicists.

You might find some resonance with my essay, based on a work carried out with Nicolas Gisin, where we further developed the argument against the physical significance of real numbers. This seems to entail this almost Platonistic standpoint on mathematics, having its really existing entities and physics relies on them at an ontic level. As you also say, of course nobody questions the great power of mathematics in modelling physics, but math is not physics, nevertheless.

I wish you to get to the prize range, top rate from my side!

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H.H.J. Luediger wrote on Mar. 11, 2020 @ 22:00 GMT
Sabine,

while I agree that the three 'uns' aren't physical problems, they yet pose a problem to physics. Gödel's theorems don't say that mathematics is either incomplete or inconsistent, they say that logic cannot deal even with traces of mathematics. In plain words they say that logic doesn't belong to mathematics and hence to physics.

Heinz

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Lorraine Ford replied on Mar. 11, 2020 @ 22:51 GMT
That is true Heinz: "logic doesn't belong to mathematics and hence to physics".

Physics represents "laws of nature" with equations, but you can't derive logic from equations. This is where Sabine is missing something in her otherwise excellent essay: physics can't explain the existence of logic. If physics can't explain the existence of logic then physics cannot explain the nature of the world.

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Mihai Panoschi Panoschi replied on Mar. 13, 2020 @ 10:58 GMT
That was precisely my point above too Heinz. Frege used to refer to logic as "the third realm" as distinct from maths/ideal and physics/real. If Physics can't explain Logic then physics can't explain the human mind and its thinking structures which is an integral part of nature/Universe as a whole, yes Lorraine, I would agree with that. Interesting, in this context, is of course Heidegger's attempt to ground logic on ontology in Being and Time.

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Branko L Zivlak wrote on Mar. 12, 2020 @ 08:19 GMT
Dear Sabine Hossenfelder,

Your views are very clear and helpful. They certainly do not fall into the phraseology that is common and leads nowhere.

I fully agree with your statement:

“Nothing realis infinite [4], therefore the whole formulation of the problem is scientifically meaningless. Inpractice, we never need an algorithm that can correctly answer infinitely many questions.”

Not only are there no endless physical phenomena in reality, but thanks to Planck, many of the limits of these phenomena are well known to us.

My comment on:

“Again, we conclude that impossibility-theorems are mathematical curiosities without scientific relevance.”

If I understand you well, we should not waste our time solving difficult problems that are scientifically meaningless. In my essay, I have pointed out three trivial problems that are great obstacles to understanding reality, and can be easily solved.

I cannot fully agree with your position:

“The major difficulty we face in making predictions is that we either don’t have sufficient data or don’t have the math for handling the data, not that there’s a mathematical theorem preventing us from making predictions.”

The fact is that the giants of natural philosophy in the past, came to a remarkable predictions that did not even have the information about the existence of other galaxies than the Milky Way. I even argue that the abundance of data has greatly confused scientists, who have failed to understand some phenomena. I particularly emphasize here what is related to the works of Hubble and Lemaitre.

As a meteorologist I read with interest your rational explanations of the butterfly effect and chaos theory. Thank you for that.

I can agree with your point of view “Physics Isn’t Math”, but contrary to you I claim: Reality is math, and surely can be well described by math. I claim that because I got it by compiling the results of Newton, Kepler, Planck, partly Einstein ...

Regards Branko

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Steve Dufourny wrote on Mar. 12, 2020 @ 08:28 GMT
Hi, It is a beautuful general essay , I see the maths and physics like this. The maths are very important indeed, they permit to prove assumptions and this tool is foundamental when they respect the logic. We need these maths to prove simply.That said we must be prudent about the mathematical extrapolations, sometimes they imply confusions , it seems that all is a question of limits in the interpretations, the maths indeed imply many assumptions, like the multiverses, the whormholes or the time travel or this or that. But after all only the proved works are accepted inside the sciences Community. The physics and maths converge when the pure determinism, rationalism or logic are respected. About the predictions and computabilities, we are limited I beleive, we know so few still and we have still many secrets to add. We cannot predict all of course , just because we are not sure about what are our foundamental mathematical and physical objects, are they points , or strings or in my model 3D coded spheres ? we don t know and we cannot affirm, the sanme for the philosophy of main causes, have we a 1D main field like in the strings or this or that, we don t know, all what we have are just assumptions and they must be proved simply by experiments or mathematical proofs.

Regards

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Lawrence B. Crowell wrote on Mar. 12, 2020 @ 11:44 GMT
Gödel’s theorem does require an infinite number of predicates and Gödel numbers that are the subject of a predicate. The diagonal or self-reference and the Cantor trick leads to the lack of enumerability and unprovability. The first of Gödel’s theorem then explicitly appeals to infinity. Physics of course avoids infinity the way most now try to avoid Covid-19. Clearly, we do not measure infinite quantities.

Invoking Gödel’s theorems in quantum mechanics is not easy. As I have argued decoherence is a process where quantum phase is taken up by auxiliary quantum states, and a needle state in a measurement is then as a result at least analogous to a Gödel numbering of quantum states.

Quantum mechanics in principle has an infinite number of states in Hilbert space. This then means at least in a formal sense this can be done. Physically this is a bit more problematic, and often I think of quantum systems as finite, accessing some finite subset of Hilbert space, but where there is no fundamental upper bound.

Physics has plenty of instances where infinity is appealed. Calculus with its lim_{x-->∞} has been used for centuries since the time Leibnitz struggled with this. We learn this and then teach this without batting an eye. Yet I, and I think many of us, regard this as a sort of idealization cast in symbolic form. The application of Gödel’s theorems in physics, in particular quantum mechanical foundations is a similar move.

A benefit of doing this is to end this nonsensical kerfuffle over quantum interpretations. If these are really just unprovable auxiliary postulates, analogous to axioms, then these are really just formal statements we impose, and that nature ignores. We could put all of this trash over quantum interpretations where they below, the basura.

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Lawrence B. Crowell replied on Mar. 12, 2020 @ 15:06 GMT
I wrote this in MS Word and did not copy all of it.

On balance your paper is reasonable, at least precautionary. We do all to often frame physics according to mathematical systems, which can lead to expectations about nature that are not correct.

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John C Hodge wrote on Mar. 12, 2020 @ 15:42 GMT
Dr. Hossenfelder:

Historically, when physics models have limits in predictability, changing the fundamental physics postulates results in better predictability. For example, your weather analogy with all the sensors on Earth would still be limited as you suggest. But some model of the Sun activity would be required and could increase predictability more effectively than a model of...

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Author Sabine Hossenfelder replied on Mar. 13, 2020 @ 05:05 GMT
John Hodge,

Whether physics is fundamentally predictable or not is a question we will never be able to answer. The only thing we can tell is whether our currently best theories are or aren't predictable. What I argue in my essay is that even though the impossibility theorems cannot tell us anything about nature per se -- because we will never know whether the math is ultimately the right one -- they are important in practice simply because we use specific types of math.

Thanks for your interest,

Sabine

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Steve Dufourny replied on Mar. 13, 2020 @ 10:23 GMT
All rational deterministic thinkers understand this simple fact, we have limits in knowledges and even the best theories are limited , we cannot explain several things , that is why a TOE cannot exist, not need to discourse about this truth I beleive, it is the same with our assumptions, we cannot affirm them without proofs simply. The maths I repeat is a tool permitting sometimes to prove an assumption, and when it is proved, so it is accepted, it is only simple than this. All is not predictable and computable simply because we dont know several things, like the foundamental objects or others, even the philosophy is not proved generally about our main causes. Maths and physics matter indeed if and only if they are proved with their laws, equations, axioms. It is even easier to predict and prove the Vanity of thinkers inside the sciences Community than other unknowns lol spherically yours

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Dale Carl Gillman wrote on Mar. 16, 2020 @ 02:29 GMT
Hello Dr. Hossenfelder,

I will admit that I am humbled to write a response to your essay:

“…Reality may not be math, but it surely can be well described by math…” I am unsure if you have read Tegmark’s Our Mathematical Universe (2014)- he addressed this already.

You went on to state “…You are free to believe that reality is math, but since this belief is...

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Roger Schlafly wrote on Mar. 19, 2020 @ 01:58 GMT
You say: "the future is already determined, up to the occasional random interference from quantum events."

This is a very strange view. It sounds as if you believe the true laws of physics as non-quantum, and quantum mechanics is just making it sloppy. Your footnote says that this refutes any sensible notion of free will. So do you think humans are governed by physical laws that do not include quantum mechanics?

I know from your blog that you don't even believe in quantum randomness, because you subscribe to superdeterminism. So why even bring it up? Why not stick to your superdeterminism beliefs?

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Satyavarapu Naga Parameswara Gupta wrote on Mar. 21, 2020 @ 21:24 GMT
Hi Sabine

Your wonderful words..........And yet, physics isn’t math. Physics is science and as such has the purpose of describing observations of natural phenomena. Yes, we use mathematics in physics, and plenty of that, as I’m sure you have noticed. But we do this not because we know the world is truly mathematics.It may be mathematics, but Platonism is a philosophical position, not a scientific one. You are free to believe that reality is math, but since this belief is scientifically indefensible I will not defend it. We also don’t need it: Physicists use mathematics simply because it is useful. Reality may not be math, but it surely can be well described by math......

Same thing i expressed in my essay to.......

Best

=snp

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Andrew Knight wrote on Mar. 22, 2020 @ 18:58 GMT
Hi Sabine,

I very much enjoyed reading your essay. I love love LOVE how you clarify the nature of physics (relating specifically to experiments and observations), as well as why mathematical theorems must be “taken with a grain of salt.” Further, your discussion of the irrelevance of infinity (and even real numbers) to the real world was apt and led me to read your cited reference...

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Peter Jackson wrote on Mar. 25, 2020 @ 17:42 GMT
Dear Sabine,

A novel, beautifully written and slightly irreverent set of valid insights as usual. But am I right feeling low ambition pervades it? Do you really think that aiming high has the same chance of hitting heights than aiming low?

Your description of physics purpose as "describing" observations seems just a mathematical view, but do you not consider...

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Dizhechko Boris Semyonovich wrote on Mar. 31, 2020 @ 14:38 GMT
Dear Sabina, it is difficult to argue with your mathematical essay. With the statement that they cannot control the thermonuclear reaction because of the inability to predict its progress at all stages large and small, I completely agree. We cannot do this because of the lack of a deeper understanding of the essence of matter at all stages of its behavior. I invite you to discuss my essay, in which I show the successes of the neocartesian generalization of modern physics, based on the identity of Descartes’ space and matter: “The transformation of uncertainty into certainty. The relationship of the Lorentz factor with the probability density of states. And more from a new Cartesian generalization of modern physics. by Dizhechko Boris Semyonovich ". At the very beginning of the essay, I repeat twice the idea that rectilinear motion, in essence, is a motion around a circle of infinitely large radius and, if this radius is reduced, then in infinitesimal, the laws of motion of the theory of relativity will go over to the laws of quantum mechanics.

Next come mathematical formulas that only spoil my essay, but without them in any way. I will be pleased if you catch their main meaning and bless me for the further generalization of modern physics.

Sincerely, Dizhechko Boris Semyonovich.

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