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**barry gilbert**: *on* 5/19/20 at 12:31pm UTC, wrote Nice stimulating essay Dr. Hossenfelder [ in running out of time I'll be...

**Neil Bates**: *on* 5/19/20 at 2:50am UTC, wrote Dear Sabine, Your essay is almost a flip side in foundational beliefs...

**Jonathan Dickau**: *on* 5/18/20 at 22:58pm UTC, wrote An excellent addition to the field Dr. Hossenfelder... I like that you...

**Steven Brock**: *on* 5/18/20 at 11:19am UTC, wrote A fine essay appreciating the practical importance of what might seem...

**Ian Durham**: *on* 5/17/20 at 0:22am UTC, wrote I'm often torn on this. I do think that this "unreasonable effectiveness"...

**Ian Durham**: *on* 5/17/20 at 0:16am UTC, wrote I'm purely speculating here, but I would bet that Sabine is simply...

**Ian Durham**: *on* 5/17/20 at 0:12am UTC, wrote "And really all of science is just a sloppy version of physics." That was...

**Emily Adlam**: *on* 5/16/20 at 16:59pm UTC, wrote I very much enjoyed your essay (as indeed I enjoy all of your writing!)....

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Investigating how quantum memory storage could aid machine learning and how quantum interactions with the environment may have played a role in evolution.

FQXi FORUM

September 23, 2020

CATEGORY:
Undecidability, Uncomputability, and Unpredictability Essay Contest (2019-2020)
[back]

TOPIC: Math Matters by Sabine Hossenfelder [refresh]

TOPIC: Math Matters by Sabine Hossenfelder [refresh]

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.

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

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

post approved

attachments: 2_Cosmology_based_on_measured_data_and_observation.pdf

post approved

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...

view entire post

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...

view entire post

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"...applying instead to wide classes of theorems." should have been "applying instead to wide classes of formalisms.", sorry.

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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

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

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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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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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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...................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

report post as inappropriate

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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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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Dear Manfred Pohl,

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

Sabine

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

Sabine

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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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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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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"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.

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.

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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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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"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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And as Max Planck observed a century ago, the problem is, theoretical physicists are not particularly adept at identifying that some things,

Rob McEachern

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"... 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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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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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.”...

view entire post

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.”...

view entire post

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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

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

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!

post approved

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!

post approved

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

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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!

report post as inappropriate

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!

report post as inappropriate

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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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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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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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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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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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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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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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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Regards

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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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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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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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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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Hi Lawrence,

Yes, infinity is a useful mathematical concept and as such has a place in the toolkit of physicists. It is not that I question its operational usefulness, but (as others have said before, see references in my essay), one should not forget that it is really just a stand-in for something very large. With best wishes,

Sabine

Yes, infinity is a useful mathematical concept and as such has a place in the toolkit of physicists. It is not that I question its operational usefulness, but (as others have said before, see references in my essay), one should not forget that it is really just a stand-in for something very large. With best wishes,

Sabine

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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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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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

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

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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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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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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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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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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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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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

post approved

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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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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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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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

Your description of physics purpose as

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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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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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Sabine:

Very well argued. Having studied CS Peirce for 30 years, you seem to be converging to many of his views. Now, you like many might not be very aware of his work but it's been spreading for a while.

Regardless, what you are getting across is very important. Thanks.

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Very well argued. Having studied CS Peirce for 30 years, you seem to be converging to many of his views. Now, you like many might not be very aware of his work but it's been spreading for a while.

Regardless, what you are getting across is very important. Thanks.

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Sabine I do believe that math matters and I appreciate your interest in reduction and unpredictability. In my revised essay, I describe the lowest level of Successful Self Creation and how it converts chaos to order. This level is also the lowest level of reduction and it converts unpredictability to predictability. You may find this “level” interesting to consider in your research. Also, in the revised essay, I describe how the SSC processing produces and “incorporates“ its own mathematics and algorithms into its processing and results. My essay gives credence to Tegmark’s statement-“ The Universe is Mathematics” and Lloyd’s statement- “The Universe is a (Quantum) Computer. It also provides a “why” to your statement- “Mathematics has worked incredibly well for physicists”. It shows why mathematics is a reliable tool to describe physics. I feel that my essay is pertinent to both your research and your essay. I would appreciate your comments. John Crowell

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Hello Mr Crowell,

If I can, you cannot affirm this about a pure mathematical universe, but I respect your points of vue about this physicality and the philosophy correclated. Like Max Tegmark , you consider so a kind of pure mathematical universe.

I beleive that nobody can affirm the generality of this universe, we have just assumptions about the main cause. The problem is this one...

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If I can, you cannot affirm this about a pure mathematical universe, but I respect your points of vue about this physicality and the philosophy correclated. Like Max Tegmark , you consider so a kind of pure mathematical universe.

I beleive that nobody can affirm the generality of this universe, we have just assumptions about the main cause. The problem is this one...

view entire post

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Dear Professor Hossenfelder,

Thank you for this highly original contribution to this contest, which reminded me of Wittgenstein's last philosophical thoughts, collected in "On Certainty", to the effect that most discussions take place within a 'container', but some discuss the container (which he calls the set of hinge propositions) itself. Your essay seems to belong to the latter category,...

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Thank you for this highly original contribution to this contest, which reminded me of Wittgenstein's last philosophical thoughts, collected in "On Certainty", to the effect that most discussions take place within a 'container', but some discuss the container (which he calls the set of hinge propositions) itself. Your essay seems to belong to the latter category,...

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Dear Sabine,

Thank you for your very good and well-written essay. I mostly agree with your main contributions. There is however one point that I have to disagree with which is expressed by your sentence: "Physics isn’t math, and Godel’s theorem is irrelevant for scientific practice". I agree that physics isn't math, but I think scientific practice, as opposed to a scientific, falsifiable theory, embodies more than things that have testable consequences. As a computer scientist, I think all my CS and math colleagues would agree that Gödel's theorem is indeed relevant for scientific practice in their respective fields, although not having any testable consequences. I think it would have been more correct to talk about "scientific practice in the physical sciences" instead of "scientific practice" in general.

Best regards,

Ruben

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Thank you for your very good and well-written essay. I mostly agree with your main contributions. There is however one point that I have to disagree with which is expressed by your sentence: "Physics isn’t math, and Godel’s theorem is irrelevant for scientific practice". I agree that physics isn't math, but I think scientific practice, as opposed to a scientific, falsifiable theory, embodies more than things that have testable consequences. As a computer scientist, I think all my CS and math colleagues would agree that Gödel's theorem is indeed relevant for scientific practice in their respective fields, although not having any testable consequences. I think it would have been more correct to talk about "scientific practice in the physical sciences" instead of "scientific practice" in general.

Best regards,

Ruben

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Hey Sabine —

Thanks for the really fun essay.

A few years ago there was a fad for predicting critical collapse. Some of this was really good, but other pieces I thought had a big flaw: you could not predict a singularity using an analytic approximation! (More correctly, the a singularity means an inability to use prior data to “extrapolate through” the pole.) You can have signatures of a singularity to come, but only conditional on a good model.

I wonder how this might play out in your suggestion for steering clear of Lorentz horizons. In the plasma case I’m going to guess that our best models are phenomenological. The pattern recognition system they used had some even more phenomenological model yet. Knowing what patterns it was picking up on could tell us a lot about the underlying dynamics.

It reminds me of some simulations we did years ago to measure critical indices in phase transitions. Our systems were finite, so no real singularity. But one way to think about it was that there was a singularity, in the complex plane, and as N got larger (the simulation more accurate) it rotated around and got closer and closer to the real axis.

Simon

Simon

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Thanks for the really fun essay.

A few years ago there was a fad for predicting critical collapse. Some of this was really good, but other pieces I thought had a big flaw: you could not predict a singularity using an analytic approximation! (More correctly, the a singularity means an inability to use prior data to “extrapolate through” the pole.) You can have signatures of a singularity to come, but only conditional on a good model.

I wonder how this might play out in your suggestion for steering clear of Lorentz horizons. In the plasma case I’m going to guess that our best models are phenomenological. The pattern recognition system they used had some even more phenomenological model yet. Knowing what patterns it was picking up on could tell us a lot about the underlying dynamics.

It reminds me of some simulations we did years ago to measure critical indices in phase transitions. Our systems were finite, so no real singularity. But one way to think about it was that there was a singularity, in the complex plane, and as N got larger (the simulation more accurate) it rotated around and got closer and closer to the real axis.

Simon

Simon

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Dear Sabine Hossenfelder:

You note in the beginning of your essay that:

“Physicists use mathematics simply because it is useful. Reality may not be math, but it surely can be well described by math.”

I must submit that math can and does obstruct –

especially when that math describes things not observed in real life that becomes the basis of physics – as in de Sitter’s expanding space – Friedman’s creation of the world from nothing – and Lemaître notation – “If the world has begun with a single quantum…” these all obscure applicable common 3D physics hiding the physics of the Big Bang.

It is proposed that any evidence describing the Big Bang is beyond science’s reach and yet this essay of mine entered January 18th*Common 3D Physics Depicts Universe Emerging From Chaos* presents a plausible explanation with plenty of current replicable evidence describing ‘Reality.’ Check it out.

Regards

Charles Sven

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You note in the beginning of your essay that:

“Physicists use mathematics simply because it is useful. Reality may not be math, but it surely can be well described by math.”

I must submit that math can and does obstruct –

especially when that math describes things not observed in real life that becomes the basis of physics – as in de Sitter’s expanding space – Friedman’s creation of the world from nothing – and Lemaître notation – “If the world has begun with a single quantum…” these all obscure applicable common 3D physics hiding the physics of the Big Bang.

It is proposed that any evidence describing the Big Bang is beyond science’s reach and yet this essay of mine entered January 18th

Regards

Charles Sven

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Dear Sabine:

Excellent essay that clarifies: Physics is not math. But math matters.

Your essay is bold, powerful and correct:

(i) “…. physics isn’t math. ….For this reason, the topic of this essay contest – undecidability, uncomputability, and unpredictability – sounds very academic indeed. Who cares whether a big-brained scientist proved that a certain mathematical problem is unsolvable if we can never know whether this math is fundamentally the correct description of nature?”

(ii) “Looking for patterns that allow us to express data in simpler ways is pretty much all that scientists have ever done.” –So far.

In praise of math assisting the practical world of achieving inexhaustible energy:

(iii) Modeling and finding the onset of instability a few millisecond ahead of time, allows for the incorporation of corrective plasma parameters in a fusion plasma chamber. This helps scientists to prevent the instability by proactively readjusting the necessary parameters.

The discussion around “Reductionism” is excellent and succinct.

I have also read your book, “Lost in Math”. I consider your book to be an extremely timely and valuable “social service” for the physics community.

Chandra

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Excellent essay that clarifies: Physics is not math. But math matters.

Your essay is bold, powerful and correct:

(i) “…. physics isn’t math. ….For this reason, the topic of this essay contest – undecidability, uncomputability, and unpredictability – sounds very academic indeed. Who cares whether a big-brained scientist proved that a certain mathematical problem is unsolvable if we can never know whether this math is fundamentally the correct description of nature?”

(ii) “Looking for patterns that allow us to express data in simpler ways is pretty much all that scientists have ever done.” –So far.

In praise of math assisting the practical world of achieving inexhaustible energy:

(iii) Modeling and finding the onset of instability a few millisecond ahead of time, allows for the incorporation of corrective plasma parameters in a fusion plasma chamber. This helps scientists to prevent the instability by proactively readjusting the necessary parameters.

The discussion around “Reductionism” is excellent and succinct.

I have also read your book, “Lost in Math”. I consider your book to be an extremely timely and valuable “social service” for the physics community.

Chandra

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Dear Dr. Hossenfelder,

Thank you for your wonderful essay. The work was written in a style that was clear and approachable which is remarkable given the complexity of the subject.

If you claim there is no free will, then that is your choice.

If you claim that large-scale events are fully dependent on smaller scale events than the following points should be address:

A sound of 20 dB has an energy of 10^-10 Watts/m^3, which works out to around 3*10^13 J/m^3 = 1.9*10^6 J/m^3 which is far too low of an energy density for an atomic transition for an atomic volume around 10^-30 m^3. Sound within the human range of hearing exists, but cannot be explained on the atomic or molecular scales.

Laminar and turbulent flow of a liquid and the ordered and glass states of solids have the same wavelength and energy density issues.

Electrical resistance (mostly) following Ohm’s law is difficult to explain with quantum mechanics.

Nuclear decay is independent of chemical state and temperature. If this smaller scale is the engine of atomic change, why does it not change rate as it powers or slows a reaction?

Perhaps the wavelength difference between a butterfly and a storm front are enough so that they are independent.

Sincerely,

Jeff Schmitz

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Thank you for your wonderful essay. The work was written in a style that was clear and approachable which is remarkable given the complexity of the subject.

If you claim there is no free will, then that is your choice.

If you claim that large-scale events are fully dependent on smaller scale events than the following points should be address:

A sound of 20 dB has an energy of 10^-10 Watts/m^3, which works out to around 3*10^13 J/m^3 = 1.9*10^6 J/m^3 which is far too low of an energy density for an atomic transition for an atomic volume around 10^-30 m^3. Sound within the human range of hearing exists, but cannot be explained on the atomic or molecular scales.

Laminar and turbulent flow of a liquid and the ordered and glass states of solids have the same wavelength and energy density issues.

Electrical resistance (mostly) following Ohm’s law is difficult to explain with quantum mechanics.

Nuclear decay is independent of chemical state and temperature. If this smaller scale is the engine of atomic change, why does it not change rate as it powers or slows a reaction?

Perhaps the wavelength difference between a butterfly and a storm front are enough so that they are independent.

Sincerely,

Jeff Schmitz

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I should first mention that I am "a fan" and that I am here and wrote an essay for this contest because you made me aware of this contest by mentioning it on your YouTube channel.

You wrote: "Nothing real is infinite, therefore the whole formulation of the problem is scientifically meaningless. In practice, we never need an algorithm that can correctly answer infinitely many questions."

Your criticism in this regard is entirely misplaced. Although infinity is certainly a valid target of criticism, the concept isn't*obviously* wholly spurious. (Personally, I prefer Feferman's "unfolding infinity.") For example, addition is an algorithm that works for any infinite class (i.e., every *n* + *m*). Clearly, the infinite class includes numbers for which addition has never *actually* been verified to hold. But we take it *on faith* that the numbers do not get so large that addition ceases to work.

Speaking of faith, you wrote: "Science shouldn’t rest on faith."

But it does. Or are you one of those*true believers* that claims that it rests on *Truth*? If so, I would like to introduce you to the *Liar*! (pun intended)

These are minor criticisms. Overall, as usual, I enjoyed hearing your thoughts and I generally agree with your conclusion. I think it is obvious that, at the very least, the impossibility theorems represent a limitation on the tools that we use. However, if you are arguing that the three un's (as you call them) are absolutely*nothing more than* limitations on the tools we use, then I do not think you sufficiently presented that argument.

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You wrote: "Nothing real is infinite, therefore the whole formulation of the problem is scientifically meaningless. In practice, we never need an algorithm that can correctly answer infinitely many questions."

Your criticism in this regard is entirely misplaced. Although infinity is certainly a valid target of criticism, the concept isn't

Speaking of faith, you wrote: "Science shouldn’t rest on faith."

But it does. Or are you one of those

These are minor criticisms. Overall, as usual, I enjoyed hearing your thoughts and I generally agree with your conclusion. I think it is obvious that, at the very least, the impossibility theorems represent a limitation on the tools that we use. However, if you are arguing that the three un's (as you call them) are absolutely

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Hi Jason,

Thanks for your comment. Science rests on evidence-based arguments, not on faith. I didn't say anything about "truth" (a word I generally avoid) and therefore, with apologies, I do not know what you are getting at.

As to infinity, I didn't write it's "spurious", I wrote nothing real is infinite and this is exactly what I meant. If you want to disagree, then please show me a measurement value that came out to be infinity. With best regards,

Sabine

Thanks for your comment. Science rests on evidence-based arguments, not on faith. I didn't say anything about "truth" (a word I generally avoid) and therefore, with apologies, I do not know what you are getting at.

As to infinity, I didn't write it's "spurious", I wrote nothing real is infinite and this is exactly what I meant. If you want to disagree, then please show me a measurement value that came out to be infinity. With best regards,

Sabine

Hi Sabine!

Wonderful essay! I love your point that "We may simply want to avoid situations in which it becomes unpredictable for us" since this is a very true and practical approach to many physical problems. I also wonder if you've considered that, even if we DID have all accurate information about things like the weather, the physical load it would take to compute would be too much to bear. Since there is a real, physical cost to computation, it could be that such systems might not be capable of even performing the computation needed to make a prediction. I talk about this a bit in my own essay, and I'd be very curious to hear your thought on it!

Cheers!

Alyssa

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Wonderful essay! I love your point that "We may simply want to avoid situations in which it becomes unpredictable for us" since this is a very true and practical approach to many physical problems. I also wonder if you've considered that, even if we DID have all accurate information about things like the weather, the physical load it would take to compute would be too much to bear. Since there is a real, physical cost to computation, it could be that such systems might not be capable of even performing the computation needed to make a prediction. I talk about this a bit in my own essay, and I'd be very curious to hear your thought on it!

Cheers!

Alyssa

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I always enjoy your essays, Sabine. Please keep writing! This one inspired me to enter this contest too.

In your signature style, you continue to emphasize two points physicists need to be continually reminded of: physics is not math, and experiment is the ultimate arbiter of truth in physics.

Some great turns of phrase I liked:

"If it’s not a deadline that sets an end to...

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In your signature style, you continue to emphasize two points physicists need to be continually reminded of: physics is not math, and experiment is the ultimate arbiter of truth in physics.

Some great turns of phrase I liked:

"If it’s not a deadline that sets an end to...

view entire post

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Dear Sabine,

Excellent essay. I loved for example the incisive one-line bluntness of "Nothing real is infinite, therefore the whole formulation of the [halting] problem is scientifically meaningless," Hah! So much for all of our wordy pontificating in ever-so-many other essays!

Cheers,

Terry

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Excellent essay. I loved for example the incisive one-line bluntness of "Nothing real is infinite, therefore the whole formulation of the [halting] problem is scientifically meaningless," Hah! So much for all of our wordy pontificating in ever-so-many other essays!

Cheers,

Terry

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Dear Sabine,

I really enjoyed reading your essay. Thank you so much for the point of "real butterfly effect". I did not consider it. On the Lorenz perspective, what do you think to reduce the computational cost in quantum-computing era? How much universality of "real butterfly effect" can we discuss?

Best wishes,

Yutaka

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I really enjoyed reading your essay. Thank you so much for the point of "real butterfly effect". I did not consider it. On the Lorenz perspective, what do you think to reduce the computational cost in quantum-computing era? How much universality of "real butterfly effect" can we discuss?

Best wishes,

Yutaka

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Dear Sabine Hossenfelder.

Great economy of thought and words

You state:

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

I beg to differ. Even physics has its own no-go theorems. Plus you concur that they can be a guide.

Indeed, what should worry us in the moment is the uncanny similarity if not parallelism between physics and math. Take for instance the Gödel second incompleteness theorem and what we may call its parallel in physics the Heisenberg uncertainty principle or the Landauer limit. For me, importance of the no-go theorems are not so much about their stated or otherwise tacit limitations to human knowledge (in math as well as in physics) as it is about making the unreasonable effectiveness between math and physics reasonable instead.

Secondly, you assert that “Nothing real is infinite”

But I consider that we may actually live in an infinite world. To tame this infinity we must then presume ourselves as minds to represent a particular norm (axioms) within the infinity. This will be analogous to how the ZF Axiomatic set theory must tame Russell’s Paradox or how physically the Planck constant must tame the ultra-violet catastrophe.

Taming infinity remains a persistent problem. Modern physics has, for instance, a clear and present danger in the so-called vacuum catastrophe and then mathematics has, among others, declared what it terms the mass gap existence problem.

Doesnt it upset your argument that ironical modern mathematics is worrying about explaining some actual** existence ** (the mass gap) while modern physics is worrying about specifying correctly the idea of ** “nothing” ** (the vacuum)?

Chidi Idika (forum topic: 3531)

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Great economy of thought and words

You state:

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

I beg to differ. Even physics has its own no-go theorems. Plus you concur that they can be a guide.

Indeed, what should worry us in the moment is the uncanny similarity if not parallelism between physics and math. Take for instance the Gödel second incompleteness theorem and what we may call its parallel in physics the Heisenberg uncertainty principle or the Landauer limit. For me, importance of the no-go theorems are not so much about their stated or otherwise tacit limitations to human knowledge (in math as well as in physics) as it is about making the unreasonable effectiveness between math and physics reasonable instead.

Secondly, you assert that “Nothing real is infinite”

But I consider that we may actually live in an infinite world. To tame this infinity we must then presume ourselves as minds to represent a particular norm (axioms) within the infinity. This will be analogous to how the ZF Axiomatic set theory must tame Russell’s Paradox or how physically the Planck constant must tame the ultra-violet catastrophe.

Taming infinity remains a persistent problem. Modern physics has, for instance, a clear and present danger in the so-called vacuum catastrophe and then mathematics has, among others, declared what it terms the mass gap existence problem.

Doesnt it upset your argument that ironical modern mathematics is worrying about explaining some actual

Chidi Idika (forum topic: 3531)

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Dear Sabine,

Your essay, thoughts and conclusions are extremely important for finding a way to overcome the crisis of understanding in the philosophical basis of fundamental science. I have some questions and comments for discussion:

*"Physics Isn’t Math"*

Yes, it's true. But mathematics is the "language of Nature." Physics without mathematics is dumb and blind. In no...

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Your essay, thoughts and conclusions are extremely important for finding a way to overcome the crisis of understanding in the philosophical basis of fundamental science. I have some questions and comments for discussion:

Yes, it's true. But mathematics is the "language of Nature." Physics without mathematics is dumb and blind. In no...

view entire post

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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

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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

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Dear Sabine,

Thank you for writing this enjoyable essay.

I agree with you that physics isn’t math. This implies many things. One is that all uses of infinities in physics are mathematical constructs. This applies to so many domains in physics: the definition of pure states in quantum mechanics, these exercises where we are given two infinite plates and have to compute the electric...

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Thank you for writing this enjoyable essay.

I agree with you that physics isn’t math. This implies many things. One is that all uses of infinities in physics are mathematical constructs. This applies to so many domains in physics: the definition of pure states in quantum mechanics, these exercises where we are given two infinite plates and have to compute the electric...

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Hi Sabine,

Very nice reading experience. I had a niggling issue that followed me throughout:

The essay seemed to present a view of science as essentially a black box; we don't know why it works, but it often keeps giving us numbers that match our experiments.

But a philosopher might wonder why it is that "maths works" and why reality can be so well described by it. Why do our "observations of natural phenomena" fit? You don't give any clues to this and on the whole it reads as quite a stark instrumentalism. Obviously, one of the reasons behind treating physics as math in some sense is precisely this (unreasonable) effectiveness: there seems to be be a structural mapping, so facts about one apply to the other. The fit seems to give us a *reason* that "this math is fundamentally the correct description of nature".

Moreover, when you write "mathematical theorems are not of much use for the messy science of real-world systems", this ignores the fact that much (if not most) of the science we have of real-world systems, originated in some mathematical theorems - e.g. the steps from differential geometry to GPS or analytical mechanics to holonomic robotics. So, even if only to discredit it, I think you have to say something about the business of why math works when considering the kinds of issue you discuss in order to show that such things as mathematical theorems are relevant or not.

Best

Dean

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Very nice reading experience. I had a niggling issue that followed me throughout:

The essay seemed to present a view of science as essentially a black box; we don't know why it works, but it often keeps giving us numbers that match our experiments.

But a philosopher might wonder why it is that "maths works" and why reality can be so well described by it. Why do our "observations of natural phenomena" fit? You don't give any clues to this and on the whole it reads as quite a stark instrumentalism. Obviously, one of the reasons behind treating physics as math in some sense is precisely this (unreasonable) effectiveness: there seems to be be a structural mapping, so facts about one apply to the other. The fit seems to give us a *reason* that "this math is fundamentally the correct description of nature".

Moreover, when you write "mathematical theorems are not of much use for the messy science of real-world systems", this ignores the fact that much (if not most) of the science we have of real-world systems, originated in some mathematical theorems - e.g. the steps from differential geometry to GPS or analytical mechanics to holonomic robotics. So, even if only to discredit it, I think you have to say something about the business of why math works when considering the kinds of issue you discuss in order to show that such things as mathematical theorems are relevant or not.

Best

Dean

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I'm often torn on this. I do think that this "unreasonable effectiveness" of mathematics in the sciences is something that is worthy of an explanation. And as someone whose PhD is in *pure mathematics*, I am inclined to be sympathetic to mathematical explanations. That said, the fact that I also possess a degree in engineering tells me that there's an awful lot that we can do without questioning why it works.

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Sabine,

Turing had different ideas on Undecidability, in particularly in his computer search for counterexample for Riemann problem ,he used generalized definition where Undecidability is merely a part of some UUU - computational construction.

My essay attempts to reconstruct such sort of approach,also. May be it could be interesting for further development of your provocative idea.

Respectfully

Michael Popov

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Turing had different ideas on Undecidability, in particularly in his computer search for counterexample for Riemann problem ,he used generalized definition where Undecidability is merely a part of some UUU - computational construction.

My essay attempts to reconstruct such sort of approach,also. May be it could be interesting for further development of your provocative idea.

Respectfully

Michael Popov

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I very much enjoyed your essay (as indeed I enjoy all of your writing!). Godel's incompleteness theorem and other similar results do tend to get brought up in many contexts in physics, often in fairly dubious ways, and so what you have done here by taking a step back and examining the actual practical consequences of these results for physics is extremely useful, thank you!

I did have one minor question - at one point you suggest that '(if the renormalisation flow ran into a singular point) reductionism would be demonstrably false, and other scientific disciplines would count as equally fundamental as physics.' Is it your intention here to suggest that physics is inextricably tied to reductionism, and that non-reductionist approaches (e.g. top-down causation) wouldn't count as physics at all? Or is this just a reference to the fact that our current best physical theories are reductionist in character?

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I did have one minor question - at one point you suggest that '(if the renormalisation flow ran into a singular point) reductionism would be demonstrably false, and other scientific disciplines would count as equally fundamental as physics.' Is it your intention here to suggest that physics is inextricably tied to reductionism, and that non-reductionist approaches (e.g. top-down causation) wouldn't count as physics at all? Or is this just a reference to the fact that our current best physical theories are reductionist in character?

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I'm purely speculating here, but I would bet that Sabine is simply referencing the fact that our current best physical theories are reductionist. I think if she were presented with a sufficiently well-supported downwardly causal theory, she would probably accept it. But that's just my gut feeling...

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"And really all of science is just a sloppy version of physics."

That was my favorite line. You remain one of the best contrarians in the business. Excellent essay.

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That was my favorite line. You remain one of the best contrarians in the business. Excellent essay.

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A fine essay appreciating the practical importance of what might seem purely theoretical limits on scientific inquiry. Gödel reportedly never understood why his theories did not transform the practice of mathematics and logic the way that relativity transformed physics, but perhaps that change is now beginning. Indeed, I think you understate the limits of predictability, focusing on the Lorenz...

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An excellent addition to the field Dr. Hossenfelder...

I like that you balanced the disproof of relevance and showing the importance of some limitations. But for the record; the Halting Problem is a practical not just a mathematical problem that was well known to indigenous people long before Church or Turing came on the scene. See the book by my friend Evan Pritchard "No Word for Time" for details. It was long a part of Algonquin culture that things take as long as they take. They knew that as one adds steps and complexity to any process it becomes more and more unpredictable. That is the reason why they reject our sense of clock time as "White man's craziness," and why their language has no word for time as we normally think of it.

My research calls into question some of the statement early in your essay, and the subject of your book. All those things are true of Maths invented to describe Physics, that are in fact only models of nature, and miss important details. But I've been saddled for more than 30 years with a problem like that of Haldane, coming into a remarkable insight almost by accident, or while looking for something else, and over time coming to grips with the fact that it has broad applicability and deep significance. So if you want a peek at what the hyper-Platonist view looks like; have a look at my essay.

All the Best,

Jonathan

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I like that you balanced the disproof of relevance and showing the importance of some limitations. But for the record; the Halting Problem is a practical not just a mathematical problem that was well known to indigenous people long before Church or Turing came on the scene. See the book by my friend Evan Pritchard "No Word for Time" for details. It was long a part of Algonquin culture that things take as long as they take. They knew that as one adds steps and complexity to any process it becomes more and more unpredictable. That is the reason why they reject our sense of clock time as "White man's craziness," and why their language has no word for time as we normally think of it.

My research calls into question some of the statement early in your essay, and the subject of your book. All those things are true of Maths invented to describe Physics, that are in fact only models of nature, and miss important details. But I've been saddled for more than 30 years with a problem like that of Haldane, coming into a remarkable insight almost by accident, or while looking for something else, and over time coming to grips with the fact that it has broad applicability and deep significance. So if you want a peek at what the hyper-Platonist view looks like; have a look at my essay.

All the Best,

Jonathan

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Dear Sabine,

Your essay is almost a flip side in foundational beliefs about the 3uns compared to that of Paul Davies here. You consider the limitations of computability to not be so physically material, so to speak. And yet you realize that of course the issues matter to what we can actually predict about things, whether it's worth trying etc.

I wonder why you state that "quantum mechanics is unpredictable by assumption, not by theorem." My understanding of the basis of our knowing it is that way, is empirically based: "identically prepared systems" give probabilistic results which cannot be narrowed down more and more by perfecting the similarity of the systems or entities in question. Hence, apparently-identical muons decay at different times, apparently identical patterns of light intensity result in different specific patterns of hits - even though the numbers of them tend to certain statistical averages.

Also: readers might want to take at look at my own essay, addressing the issue of the strong correlations of entanglement and how neo-mechanistic models of quantum physics aren't enough to explain them. (https://fqxi.org/community/forum/topic/3548)

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Your essay is almost a flip side in foundational beliefs about the 3uns compared to that of Paul Davies here. You consider the limitations of computability to not be so physically material, so to speak. And yet you realize that of course the issues matter to what we can actually predict about things, whether it's worth trying etc.

I wonder why you state that "quantum mechanics is unpredictable by assumption, not by theorem." My understanding of the basis of our knowing it is that way, is empirically based: "identically prepared systems" give probabilistic results which cannot be narrowed down more and more by perfecting the similarity of the systems or entities in question. Hence, apparently-identical muons decay at different times, apparently identical patterns of light intensity result in different specific patterns of hits - even though the numbers of them tend to certain statistical averages.

Also: readers might want to take at look at my own essay, addressing the issue of the strong correlations of entanglement and how neo-mechanistic models of quantum physics aren't enough to explain them. (https://fqxi.org/community/forum/topic/3548)

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Nice stimulating essay Dr. Hossenfelder [

in running out of time I'll be brief.

maths is part of the problem, not the solution, It is simply another language albeit precise, much better in the hands of engineers than physicists or philosophers' good for analysis dangerous for synthesis. If you can't explain you thoughts to your mother you don't understand what your talking about. It enables people to shield their lacking true understanding. Qm is theistic nonsense hiding behind mathematical facade, engineers have to be insured against erroneous design, QM's are rewarded for convoluted drivel. There are more supercomputers grinding away Maxwellian EM simulators than QM voodooism after all the wonders of modern technologies are Maxwellian. The transistor was discovered by accident, not by QM. I'll give you are ten if I make it?

more expansion less curt next year.

good luck

Barry

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in running out of time I'll be brief.

maths is part of the problem, not the solution, It is simply another language albeit precise, much better in the hands of engineers than physicists or philosophers' good for analysis dangerous for synthesis. If you can't explain you thoughts to your mother you don't understand what your talking about. It enables people to shield their lacking true understanding. Qm is theistic nonsense hiding behind mathematical facade, engineers have to be insured against erroneous design, QM's are rewarded for convoluted drivel. There are more supercomputers grinding away Maxwellian EM simulators than QM voodooism after all the wonders of modern technologies are Maxwellian. The transistor was discovered by accident, not by QM. I'll give you are ten if I make it?

more expansion less curt next year.

good luck

Barry

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