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FQXi FORUM

October 18, 2019

CATEGORY:
Trick or Truth Essay Contest (2015)
[back]

TOPIC: A Mystery Demystified: The Connection between Mathematics and Physics by roberto mangabeira unger [refresh]

TOPIC: A Mystery Demystified: The Connection between Mathematics and Physics by roberto mangabeira unger [refresh]

The effectiveness of mathematics in physics is reasonable because it is relative. We should reject the view, predominant in the history of modern physics, that mathematics offers a shortcut to eternal truth, and serves as the oracle of nature and the prophet of science. We can better understand mathematics as an exploration of a simulacrum of the world from which time and particularity have been sucked out. The radical selectivity of mathematical reasoning helps explain its power, its limits, and its dangers in physics. Mathematics is good at some things, and bad at others, especially at those that are historical. That limitation matters if the most important fact about the universe is that it is what it is as a result of its history. Mathematics cannot replace physical intuition or empirical discovery. In return for the immense service that it renders, it offers science a poisoned chalice: the idea of immutable laws of nature.

Philosopher, social and legal theorist, and political activist. Author, most recently, of The Singular Universe and the Reality of Time, with Lee Smolin, in which each of us presents separately the entire argument of the work. Professor of Law, Harvard University. Member of the American Academy of Arts and Sciences. Minister of Strategic Affairs in the government of President Lula, Brazil.

Dear Mr. Mangabeira Unger,

Thank you for your enjoyable and well written essay.

You mentioned that "Mathematics gives us no royal road to truth about nature", myself share also this view. Math may intersect with physics and in some cases only in rough manner. The truth is that part of the math world can be unphysical similarly the physical world can sometimes be non-mathematical.

We have tangible circumstances in the physical world, i.e. where life is generated in particles and this phenomenon doesn't fit into math at all, I have touched many more examples of this sort in my article. One essential fact the bridges us to math and physics is "quantity" that can be measured, anything else in our world not obeying this rule is omitted as unphysical, this is one of the big dilemmas of contemporary physics.

Warm regards

Koorosh

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Thank you for your enjoyable and well written essay.

You mentioned that "Mathematics gives us no royal road to truth about nature", myself share also this view. Math may intersect with physics and in some cases only in rough manner. The truth is that part of the math world can be unphysical similarly the physical world can sometimes be non-mathematical.

We have tangible circumstances in the physical world, i.e. where life is generated in particles and this phenomenon doesn't fit into math at all, I have touched many more examples of this sort in my article. One essential fact the bridges us to math and physics is "quantity" that can be measured, anything else in our world not obeying this rule is omitted as unphysical, this is one of the big dilemmas of contemporary physics.

Warm regards

Koorosh

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Dear Mr. Mangabeira Unger,

It was a real pleasure to read your essay. It was interesting and accessible.

It opens up questions. For example: when you highlight whether any mathematical construction will have no assured application to the real world.

I have a different view on mathematics and time. I might be wrong but time exists in mathematics. Probabilities are inside time. Could probabilities exist without time?

In my view, the representation of time is different in mathematics. In probability, time is represented as a discontinuity. I find this property interesting.

Regards,

Christophe

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It was a real pleasure to read your essay. It was interesting and accessible.

It opens up questions. For example: when you highlight whether any mathematical construction will have no assured application to the real world.

I have a different view on mathematics and time. I might be wrong but time exists in mathematics. Probabilities are inside time. Could probabilities exist without time?

In my view, the representation of time is different in mathematics. In probability, time is represented as a discontinuity. I find this property interesting.

Regards,

Christophe

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Dear Roberto Unger,

In your essay you state that "causal explanations make no sense outside time; causal connections can exist only in time." This I agree with. But then you say "…*the moves in a mathematical or logical chain of argument do occur outside time*." I'm not so sure of that. A mathematical argument goes from step to step in sequential fashion which seems to...

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In your essay you state that "causal explanations make no sense outside time; causal connections can exist only in time." This I agree with. But then you say "…

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Dear Roberto Unger,

To be sincere I am wondering what exactly is going on here? I look forward to the book you are co-authoring with Lee Smolin to know exactly how the course of scientific truth will be advanced. If you have time, you may take a look at my essay and comment.

Regards,

Akinbo

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To be sincere I am wondering what exactly is going on here? I look forward to the book you are co-authoring with Lee Smolin to know exactly how the course of scientific truth will be advanced. If you have time, you may take a look at my essay and comment.

Regards,

Akinbo

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Dear Sir,

Mathematics is the quantitative description of Nature. It is linear (explication) or nonlinear (including recursive reasoning) accumulation and reduction in numbers. Number are concepts that differentiate between similars – if there are no similars, it is one; otherwise many; depending upon the sequence of perception of one’s. Being a concept, number has no physical existence...

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Mathematics is the quantitative description of Nature. It is linear (explication) or nonlinear (including recursive reasoning) accumulation and reduction in numbers. Number are concepts that differentiate between similars – if there are no similars, it is one; otherwise many; depending upon the sequence of perception of one’s. Being a concept, number has no physical existence...

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Dear Prof Unger:

You will not recall, but I once attended a seminar you gave. That person who kept asking what you mean with "real". I will not bother you with that again for I know it's an unfair question and in a way I was pleased you didn't pretend to have an answer. Let me thus get straight to the point of my essay and how it touches upon the topic of yours. You write:

"Mathematics deals with nature as well as with itself."

I've never seen "mathematics" dealing with anything. We deal. Note the difference. It doesn't matter whether you believe mathematics is invented or discovered. I find this a pointless discussion. The relevant point is that WE use mathematics FOR science. But what if we find out that mathematics has limits? Can we still do science? In my essay I argue that yes, we can, and that we already do.

-- Sophia

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You will not recall, but I once attended a seminar you gave. That person who kept asking what you mean with "real". I will not bother you with that again for I know it's an unfair question and in a way I was pleased you didn't pretend to have an answer. Let me thus get straight to the point of my essay and how it touches upon the topic of yours. You write:

"Mathematics deals with nature as well as with itself."

I've never seen "mathematics" dealing with anything. We deal. Note the difference. It doesn't matter whether you believe mathematics is invented or discovered. I find this a pointless discussion. The relevant point is that WE use mathematics FOR science. But what if we find out that mathematics has limits? Can we still do science? In my essay I argue that yes, we can, and that we already do.

-- Sophia

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Dear Madam,

Reality is whatever exists (has a confined structure that evolves in time and is perceptible), is intelligible (perceptible/knowable) and communicable (describable using a language as defined in our essay). Number is a perceivable property of all substances by which we differentiate between similars. If there are no similars, it is one. If there are similars, it is many. Many can be 2,3,..n depending upon the sequence of perception of one’s. Mathematics is the quantitative description of Nature. Thus, it explains only one part. Another part is described by physics, which has meaning only when observed (perceived).

Thus, mathematics can be figuratively said to deal with quantitative aspect of Nature and because of logical consistency, deal with itself. However, since it is we, who perceive the numbers - hence mathematics, we agree with you that we deal with it.

Regards,

basudeba

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Reality is whatever exists (has a confined structure that evolves in time and is perceptible), is intelligible (perceptible/knowable) and communicable (describable using a language as defined in our essay). Number is a perceivable property of all substances by which we differentiate between similars. If there are no similars, it is one. If there are similars, it is many. Many can be 2,3,..n depending upon the sequence of perception of one’s. Mathematics is the quantitative description of Nature. Thus, it explains only one part. Another part is described by physics, which has meaning only when observed (perceived).

Thus, mathematics can be figuratively said to deal with quantitative aspect of Nature and because of logical consistency, deal with itself. However, since it is we, who perceive the numbers - hence mathematics, we agree with you that we deal with it.

Regards,

basudeba

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Lots of physical-mathematical activities and perceptions doing the rounds.

Great, way to go!

Respectfully,

Miss. Sujatha Jagannathan

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Great, way to go!

Respectfully,

Miss. Sujatha Jagannathan

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Dear Mr. Unger,

Congratulations. Mathematics is indeed a misrepresentation of the real world if it claims to describe the whole as the sum of its parts. There is no evidence (upon which mathematics relies) that nature shares in the timelessness of mathematical propositions. Change is the only constant in nature - a provocative idea when applied to the pursuit of mathematical truths.

In question is whether or not there is discontinuity between natural fact and mathematical truth. We represent the former with words and the latter with numbers. In the world of nature truth is transient while in mathematics facts are represented as being true and constant. Numbers don’t lie unless they are improperly related, as is the case when they are intended to "trick" others.

I identify with your "most decisive and astonishing feature of mathematics, and the one by virtue of which it can be neither invention nor discovery, as they are conventionally understood. This trait -- the fourth attribute of mathematics -- is the study of a counterfeit version of the world, of the only world that there is". Mathematics is a distorted representation of the world because it only addresses those aspects of nature that can be enumerated. "Deception" is a heavy word but, used intentionally or otherwise, mathematics is correctly identified as such.

Mathematical reasoning is a self-chosen format for inquiring into the world whereby we brush away any unmanageable considerations, e.g. time and phenomenal variation in nature, in the interest of gaining certainty. However the only certainty that is so-gained is that mathematics does not represent nature the way it actually is.

Gary Hansen

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Congratulations. Mathematics is indeed a misrepresentation of the real world if it claims to describe the whole as the sum of its parts. There is no evidence (upon which mathematics relies) that nature shares in the timelessness of mathematical propositions. Change is the only constant in nature - a provocative idea when applied to the pursuit of mathematical truths.

In question is whether or not there is discontinuity between natural fact and mathematical truth. We represent the former with words and the latter with numbers. In the world of nature truth is transient while in mathematics facts are represented as being true and constant. Numbers don’t lie unless they are improperly related, as is the case when they are intended to "trick" others.

I identify with your "most decisive and astonishing feature of mathematics, and the one by virtue of which it can be neither invention nor discovery, as they are conventionally understood. This trait -- the fourth attribute of mathematics -- is the study of a counterfeit version of the world, of the only world that there is". Mathematics is a distorted representation of the world because it only addresses those aspects of nature that can be enumerated. "Deception" is a heavy word but, used intentionally or otherwise, mathematics is correctly identified as such.

Mathematical reasoning is a self-chosen format for inquiring into the world whereby we brush away any unmanageable considerations, e.g. time and phenomenal variation in nature, in the interest of gaining certainty. However the only certainty that is so-gained is that mathematics does not represent nature the way it actually is.

Gary Hansen

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Dear Professor Unger,

In your essay you state many important truths. Things in nature are thoroughly time-bound. We ourselves and our thinking processes are not exceptions. Mathematics cannot describe or represent all aspects of time, and therefore it is a serious error to suppose that the world is fully mathematical. With all this I agree.

My concern, however, is with denying...

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In your essay you state many important truths. Things in nature are thoroughly time-bound. We ourselves and our thinking processes are not exceptions. Mathematics cannot describe or represent all aspects of time, and therefore it is a serious error to suppose that the world is fully mathematical. With all this I agree.

My concern, however, is with denying...

view entire post

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Dear Professor Ungar,

I posted a comment at your site that was unnecessarily contemptuous and devoid of the civility all contributors are entitled to. I deeply regret having done so, and I do hope that you can forgive my slurring of your fully deserved reputation.

I suspect that I may be suffering a relapse of Asperger’s Disorder. While this might explain my distasteful action, it cannot in any way justify it.

Respectfully,

Joe Fisher

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I posted a comment at your site that was unnecessarily contemptuous and devoid of the civility all contributors are entitled to. I deeply regret having done so, and I do hope that you can forgive my slurring of your fully deserved reputation.

I suspect that I may be suffering a relapse of Asperger’s Disorder. While this might explain my distasteful action, it cannot in any way justify it.

Respectfully,

Joe Fisher

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Dear Professor Unger,

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

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

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

Joe Fisher

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

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

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

Joe Fisher

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1. Dear Roberto,

I read our essay with the ease that a clearly flowing exposition adds to finding ideas congruent with my own.

The aim of my essay was to outline a formal system that is consistent with much of what you argue for, but looking back at it, I see it is probably very hard to follow the thread of too many ideas packed into a few pages.

Here...

view entire post

I read our essay with the ease that a clearly flowing exposition adds to finding ideas congruent with my own.

The aim of my essay was to outline a formal system that is consistent with much of what you argue for, but looking back at it, I see it is probably very hard to follow the thread of too many ideas packed into a few pages.

Here...

view entire post

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Dear Roberto,

It is certainly true that, as you are saying, “mathematics … addresses a nature from which time and, together with time, all phenomenal distinction have been sucked out.” However, your conclusion that “mathematics gives us no royal road to truth about nature” contradicts to the tremendous success of fundamental physics. Your essay misses the questions about the fine-tuned universe, why there are life and thought in the world and why the world is so impressively theoretizable. Simplicity and “naturalness” of the laws of nature cannot explain why they are so simple as to be cosmically discoverable and at the same time why they are open to a possibility for living and conscious beings to emerge. On the other hand, I cannot but agree with you in what I would call an abuse of mathematics, or, wider, an abuse of reason, to use Hayek’s term. Physics is mathematical, and there is nothing but nectar in that (rather than poison). What is not nectar, is absolutization of that approach to all of reality, which already lead and continues to lead humanity not only to epistemological mistakes, but to massive tragedies.

Best Regards,

Alexey and Lev Burov.

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It is certainly true that, as you are saying, “mathematics … addresses a nature from which time and, together with time, all phenomenal distinction have been sucked out.” However, your conclusion that “mathematics gives us no royal road to truth about nature” contradicts to the tremendous success of fundamental physics. Your essay misses the questions about the fine-tuned universe, why there are life and thought in the world and why the world is so impressively theoretizable. Simplicity and “naturalness” of the laws of nature cannot explain why they are so simple as to be cosmically discoverable and at the same time why they are open to a possibility for living and conscious beings to emerge. On the other hand, I cannot but agree with you in what I would call an abuse of mathematics, or, wider, an abuse of reason, to use Hayek’s term. Physics is mathematical, and there is nothing but nectar in that (rather than poison). What is not nectar, is absolutization of that approach to all of reality, which already lead and continues to lead humanity not only to epistemological mistakes, but to massive tragedies.

Best Regards,

Alexey and Lev Burov.

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The viability of arithmetic in material science is sensible on the grounds that it is relative. We ought to dismiss the view, dominating ever, that arithmetic offers an alternate way to unceasing truth, and serves as the prophet of nature and the prophet of science, which I prove when do my math homework. We can better comprehend science as an investigation of a simulacrum of the world from which time and identity have been sucked out.

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Conducting essay contests are very helpful to the individuals to improve their quality of writing and also to increase the skills. Mainly they will get an opportunity to deal with different topics and we can see how they treat each topic.

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In question is whether or not there is discontinuity between natural fact and mathematical truth. We represent the former with words and the latter with numbers. In the world of nature truth is transient while in mathematics facts are represented as being true and constant. Numbers don’t lie unless they are improperly related, as is the case when they are intended to "trick" others. ccnp dumps 300-101

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