If you are aware of an interesting new academic paper (that has been published in a peer-reviewed journal or has appeared on the arXiv), a conference talk (at an official professional scientific meeting), an external blog post (by a professional scientist) or a news item (in the mainstream news media), which you think might make an interesting topic for an FQXi blog post, then please contact us at forums@fqxi.org with a link to the original source and a sentence about why you think that the work is worthy of discussion. Please note that we receive many such suggestions and while we endeavour to respond to them, we may not be able to reply to all suggestions.

Please also note that we do not accept unsolicited posts and we cannot review, or open new threads for, unsolicited articles or papers. Requests to review or post such materials will not be answered. If you have your own novel physics theory or model, which you would like to post for further discussion among then FQXi community, then please add them directly to the "Alternative Models of Reality" thread, or to the "Alternative Models of Cosmology" thread. Thank you.

Please also note that we do not accept unsolicited posts and we cannot review, or open new threads for, unsolicited articles or papers. Requests to review or post such materials will not be answered. If you have your own novel physics theory or model, which you would like to post for further discussion among then FQXi community, then please add them directly to the "Alternative Models of Reality" thread, or to the "Alternative Models of Cosmology" thread. Thank you.

Contests Home

Current Essay Contest

*Contest Partners: Nanotronics Imaging, The Peter and Patricia Gruber Foundation, and The John Templeton Foundation*

Media Partner: Scientific American

Previous Contests

**Undecidability, Uncomputability, and Unpredictability Essay Contest**

*December 24, 2019 - April 24, 2020*

Contest Partners: Fetzer Franklin Fund, and The Peter and Patricia Gruber Foundation

read/discuss • winners

**What Is “Fundamental”**

*October 28, 2017 to January 22, 2018*

*Sponsored by the Fetzer Franklin Fund and The Peter & Patricia Gruber Foundation*

read/discuss • winners

**Wandering Towards a Goal**

How can mindless mathematical laws give rise to aims and intention?

*December 2, 2016 to March 3, 2017*

Contest Partner: The Peter and Patricia Gruber Fund.

read/discuss • winners

**Trick or Truth: The Mysterious Connection Between Physics and Mathematics**

*Contest Partners: Nanotronics Imaging, The Peter and Patricia Gruber Foundation, and The John Templeton Foundation*

Media Partner: Scientific American

read/discuss • winners

**How Should Humanity Steer the Future?**

*January 9, 2014 - August 31, 2014*

*Contest Partners: Jaan Tallinn, The Peter and Patricia Gruber Foundation, The John Templeton Foundation, and Scientific American*

read/discuss • winners

**It From Bit or Bit From It**

*March 25 - June 28, 2013*

*Contest Partners: The Gruber Foundation, J. Templeton Foundation, and Scientific American*

read/discuss • winners

**Questioning the Foundations**

Which of Our Basic Physical Assumptions Are Wrong?

*May 24 - August 31, 2012*

*Contest Partners: The Peter and Patricia Gruber Foundation, SubMeta, and Scientific American*

read/discuss • winners

**Is Reality Digital or Analog?**

*November 2010 - February 2011*

*Contest Partners: The Peter and Patricia Gruber Foundation and Scientific American*

read/discuss • winners

**What's Ultimately Possible in Physics?**

*May - October 2009*

*Contest Partners: Astrid and Bruce McWilliams*

read/discuss • winners

**The Nature of Time**

*August - December 2008*

read/discuss • winners

Current Essay Contest

Media Partner: Scientific American

Previous Contests

Contest Partners: Fetzer Franklin Fund, and The Peter and Patricia Gruber Foundation

read/discuss • winners

read/discuss • winners

How can mindless mathematical laws give rise to aims and intention?

Contest Partner: The Peter and Patricia Gruber Fund.

read/discuss • winners

Media Partner: Scientific American

read/discuss • winners

read/discuss • winners

read/discuss • winners

Which of Our Basic Physical Assumptions Are Wrong?

read/discuss • winners

read/discuss • winners

read/discuss • winners

read/discuss • winners

Forum Home

Introduction

Terms of Use

RSS feed | RSS help

Introduction

Terms of Use

*Posts by the author are highlighted in orange; posts by FQXi Members are highlighted in blue.*

RSS feed | RSS help

RECENT POSTS IN THIS TOPIC

**Cristinel Stoica**: *on* 4/21/15 at 15:09pm UTC, wrote Dear David, I enjoyed reading your essay. Indeed, non-Euclidean geometries...

**Joe Fisher**: *on* 4/8/15 at 15:35pm UTC, wrote Dear David, I think Newton was wrong about abstract gravity; Einstein was...

**Marc Séguin**: *on* 4/1/15 at 1:41am UTC, wrote Dear David, In your concise, well argued essay, I think you perfectly...

**Ed Unverricht**: *on* 3/14/15 at 20:29pm UTC, wrote Dear Professor Garfinkle, Enjoyed your essay, learned some things about...

**Tejinder Singh**: *on* 3/8/15 at 9:39am UTC, wrote Dear David, We found your essay enjoyable and reasonably convincing: old...

**Alan Kadin**: *on* 3/7/15 at 12:30pm UTC, wrote Dear Prof. Garfinkle: I agree with your clear argument that the common...

**Mark Thomas**: *on* 3/7/15 at 1:42am UTC, wrote As a layman I appreciate your concise and classical writing approach...

**Bob Shour**: *on* 3/7/15 at 1:26am UTC, wrote Dear David Garfinkle, Well written and interesting. The idea of Euclidean...

RECENT FORUM POSTS

**Georgina Woodward**: "Hi Vesuvius Now, Not an A theorist OR B theorist. I want both series under..."
*in* The Nature of Time

**Vesuvius Now**: "Woodward, are you an A-theorist or a B-theorist? And a Presentist or an..."
*in* The Nature of Time

**Franco Nori**: "Non-Hermitian Systems / Open Quantum Systems are not only of fundamental..."
*in* A Summary of Some of our...

**John Cox**: "Georgi, I don't know."
*in* The Present State of...

**Georgina Woodward**: "Hi john, I've watched a video explaining that the 'pinball' idea of current..."
*in* The Present State of...

**Amrit Sorli**: "We have only 2 times in the universe: - psychological time that has its..."
*in* Can Time Be Saved From...

**Lorraine Ford**: "The minimum requirement for any mathematical system. Remember? Remember all..."
*in* Consciousness and the...

**olivier denis**: ""I d like to know more about your general philosophy of this universe, what..."
*in* Alternative Models of...

RECENT ARTICLES

*click titles to read articles*

**Good Vibrations**

Microbead 'motor' exploits natural fluctuations for power.

**Reconstructing Physics**

New photon experiment gives new meta-framework, 'constructor theory,' a boost.

**The Quantum Engineer: Q&A with Alexia Auffèves**

Experiments seek to use quantum observations as fuel to power mini motors.

**The Quantum Clock-Maker Investigating COVID-19, Causality, and the Trouble with AI**

Sally Shrapnel, a quantum physicist and medical practitioner, on her experiments into cause-and-effect that could help us understand time’s arrow—and build better healthcare algorithms.

**Connect the Quantum Dots for a New Kind of Fuel**

'Artificial atoms' allow physicists to manipulate individual electrons—and could help to reduce energy wastage in electronic devices.

RECENT FORUM POSTS

RECENT ARTICLES

Microbead 'motor' exploits natural fluctuations for power.

New photon experiment gives new meta-framework, 'constructor theory,' a boost.

Experiments seek to use quantum observations as fuel to power mini motors.

Sally Shrapnel, a quantum physicist and medical practitioner, on her experiments into cause-and-effect that could help us understand time’s arrow—and build better healthcare algorithms.

'Artificial atoms' allow physicists to manipulate individual electrons—and could help to reduce energy wastage in electronic devices.

FQXi FORUM

December 7, 2021

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

TOPIC: The Language of Nature by David Garfinkle [refresh]

TOPIC: The Language of Nature by David Garfinkle [refresh]

Galileo considered mathematics the language of nature. However, Wigner thought the effectiveness of mathematics in physics "miraculous" and noted that much of the mathematics needed for quantum mechanics had been previously developed by mathematicians for purposes having nothing to do with physics. I argue that Galileo's view is correct; but that the examples cited by Wigner in support of his view can be explained using two deep truths, one about mathematics and the other about physics. These truths are: (1) Since the advent of non-Euclidean geometry, new mathematics has been developed by abstracting and generalizing old mathematics. (2) New physical theories have old physical theories as limiting cases.

David Garfinkle is a Professor of Physics at Oakland University, in Rochester, Michigan. He has a BA in physics (Summa cum laude) from Princeton University and a PhD in physics from The University of Chicago. His field of research is Einstein's general theory of relativity, especially the study of spacetime singularities. He is the author (along with his brother Richard Garfinkle) of "Three Steps to the Universe" a book for general readers on black holes and dark matter.

Dear David,

I think your lucid essay gave a succinct and nearly complete answer to the theme question. The only thing I would add is that when presented with physical phenomena that lend themselves to the application of already discovered/invented mathematics, it still takes some imagination to 1)realize that there is "off the shelf" available mathematics that will be useful in describing these phenomena (it is easy to underestimate the flash of insight it takes after such usefulness has already been recognized), and 2) to apply the mathematics in such a way that otherwise unavailable new physical insights are gained.

The role of imagination is even more acute in those situations where there is no "off the shelf" mathematics available, and I am sure we agree that these situations occur in the physical sciences also quite often.

In my own essay, I focused the part devoted to answering the theme question on the latter kinds of situation, but if someone were to ask me about those involving the unreasonable usefulness of already existing mathematics, I would give essentially the same answer as you did.

Best wishes,

Armin

PS. I saw you at a recent Math Colloquium at UM about general relativity. As an expert in this field, what was your opinion about the new proposed definition of angular momentum?

report post as inappropriate

I think your lucid essay gave a succinct and nearly complete answer to the theme question. The only thing I would add is that when presented with physical phenomena that lend themselves to the application of already discovered/invented mathematics, it still takes some imagination to 1)realize that there is "off the shelf" available mathematics that will be useful in describing these phenomena (it is easy to underestimate the flash of insight it takes after such usefulness has already been recognized), and 2) to apply the mathematics in such a way that otherwise unavailable new physical insights are gained.

The role of imagination is even more acute in those situations where there is no "off the shelf" mathematics available, and I am sure we agree that these situations occur in the physical sciences also quite often.

In my own essay, I focused the part devoted to answering the theme question on the latter kinds of situation, but if someone were to ask me about those involving the unreasonable usefulness of already existing mathematics, I would give essentially the same answer as you did.

Best wishes,

Armin

PS. I saw you at a recent Math Colloquium at UM about general relativity. As an expert in this field, what was your opinion about the new proposed definition of angular momentum?

report post as inappropriate

Dear David Garfinkle,

Well written and interesting. The idea of Euclidean geometry as, in effect, a limiting case of more general geometries seems to me both relevant to the essay theme and insightful. The two paragraphs on page 4 beginning, "But why do we discover the limiting cases first?' are pearls.

Based on your essay, you might find mine interesting.

Best wishes.

Bob Shour

report post as inappropriate

Well written and interesting. The idea of Euclidean geometry as, in effect, a limiting case of more general geometries seems to me both relevant to the essay theme and insightful. The two paragraphs on page 4 beginning, "But why do we discover the limiting cases first?' are pearls.

Based on your essay, you might find mine interesting.

Best wishes.

Bob Shour

report post as inappropriate

As a layman I appreciate your concise and classical writing approach (readable). Another example of mathematics that was discovered before it was put to use is Ramanujan's 'mock modular functions' which is now used in black hole physics. More surprises await.

report post as inappropriate

report post as inappropriate

Dear Prof. Garfinkle:

I agree with your clear argument that the common nature of discovery of new physics and math explains much of the mutual effectiveness of the two. I would take it one step further; some of this effectiveness is an illusion created by inappropriate application of abstract mathematical models in certain cases. The general acceptance of such a model can create an established scientific dogma, which may actually discourage the development of more appropriate models.

The example that I present in my essay is Quantum Mechanics and the Hilbert Space Model. "Remove the Blinders: How Mathematics Distorted the Development of Quantum Theory" presents a simple realistic picture that makes directly testable experimental predictions, based on little more than Stern-Gerlach measurements. Remarkably, these simple experiments have never been done.

The accepted view of QM is that the physics (and mathematics) of the microworld are fundamentally different from those of the macroworld, which of course creates an inevitable boundary problem. I take the radical (and heretical) view that the fundamental organization is the same on both scales, so that the boundary problem immediately disappears. Quantum indeterminacy, superposition, and entanglement are artifacts of the inappropriate mathematical formalism. QM is not a universal theory of matter; it is rather a mechanism for distributed vector fields to self-organize into spin-quantized coherent domains similar to solitons. This requires nonlinear mathematics that is not present in the standard formalism.

Alan Kadin

report post as inappropriate

I agree with your clear argument that the common nature of discovery of new physics and math explains much of the mutual effectiveness of the two. I would take it one step further; some of this effectiveness is an illusion created by inappropriate application of abstract mathematical models in certain cases. The general acceptance of such a model can create an established scientific dogma, which may actually discourage the development of more appropriate models.

The example that I present in my essay is Quantum Mechanics and the Hilbert Space Model. "Remove the Blinders: How Mathematics Distorted the Development of Quantum Theory" presents a simple realistic picture that makes directly testable experimental predictions, based on little more than Stern-Gerlach measurements. Remarkably, these simple experiments have never been done.

The accepted view of QM is that the physics (and mathematics) of the microworld are fundamentally different from those of the macroworld, which of course creates an inevitable boundary problem. I take the radical (and heretical) view that the fundamental organization is the same on both scales, so that the boundary problem immediately disappears. Quantum indeterminacy, superposition, and entanglement are artifacts of the inappropriate mathematical formalism. QM is not a universal theory of matter; it is rather a mechanism for distributed vector fields to self-organize into spin-quantized coherent domains similar to solitons. This requires nonlinear mathematics that is not present in the standard formalism.

Alan Kadin

report post as inappropriate

Dear David,

We found your essay enjoyable and reasonably convincing: old physics and old maths relate to each other; new maths generalises from old maths, older physical theories are limiting cases of newer theories, and hence it is not surprising that the newer theory is built on some of the new maths. We were just wondering if there is any way to make this argument more quantitative / precise. In the sense: is there some tangible way to see that the abstraction / generalisation in mathematics precisely parallels the abstraction / generalisation in physical theories.

Maybe one could add here that in the development of a new physical theory, the transition from new data to a new mathematical formulation often involves an intermediate step - great conceptual leaps / unifications. Just to take some very simple examples: the unifying idea that the force that makes the apple fall to the earth is the same as the force that makes the moon go round the earth; that electricity and magnetism are two facets of the same force; the black-body radiation spectrum compels the proposal that radiation is emitted and absorbed in discrete units; the photoelectric effect suggests that the energy of radiation is quantised in units of its frequency, etc. It would seem that the introduction of a new concept is often an important intermediate step between the new data and the new mathematical description.

Thanks for putting up a very nicely written and lucid essay.

Best regards,

Anshu, Tejinder

report post as inappropriate

We found your essay enjoyable and reasonably convincing: old physics and old maths relate to each other; new maths generalises from old maths, older physical theories are limiting cases of newer theories, and hence it is not surprising that the newer theory is built on some of the new maths. We were just wondering if there is any way to make this argument more quantitative / precise. In the sense: is there some tangible way to see that the abstraction / generalisation in mathematics precisely parallels the abstraction / generalisation in physical theories.

Maybe one could add here that in the development of a new physical theory, the transition from new data to a new mathematical formulation often involves an intermediate step - great conceptual leaps / unifications. Just to take some very simple examples: the unifying idea that the force that makes the apple fall to the earth is the same as the force that makes the moon go round the earth; that electricity and magnetism are two facets of the same force; the black-body radiation spectrum compels the proposal that radiation is emitted and absorbed in discrete units; the photoelectric effect suggests that the energy of radiation is quantised in units of its frequency, etc. It would seem that the introduction of a new concept is often an important intermediate step between the new data and the new mathematical description.

Thanks for putting up a very nicely written and lucid essay.

Best regards,

Anshu, Tejinder

report post as inappropriate

Dear Professor Garfinkle,

Enjoyed your essay, learned some things about Galileo’s view right off the start, "*the image of nature and its laws as a book and asserted that that book was written in the language of mathematics*".

Your comment "*.. abstraction and generalization generated a great number of new mathematical objects and led to another pursuit of modern mathematicians: classification. For each new type of object (group, vector space, manifold, Lie Algebra, etc.) one would aim to produce a complete classification of all possible objects of that type.*" and argument that follows was very clear and thought provoking.

I hope you get a chance to have a look at my essay here. I try to build on these classifications and provide visual models of objects that match the proven mathematical models of the particles of the standard model and would be very interested in your comments.

Best of luck in the contest, you deserve a high rating and thank you for the essay.

Regards,

Ed Unverricht

report post as inappropriate

Enjoyed your essay, learned some things about Galileo’s view right off the start, "

Your comment "

I hope you get a chance to have a look at my essay here. I try to build on these classifications and provide visual models of objects that match the proven mathematical models of the particles of the standard model and would be very interested in your comments.

Best of luck in the contest, you deserve a high rating and thank you for the essay.

Regards,

Ed Unverricht

report post as inappropriate

Dear David,

In your concise, well argued essay, I think you perfectly answer Wigner's question when you say:

"Thus the new mathematics was related to the old mathematics, which was in turn related to the old physics. But why was the new mathematics just what was needed for the new physics? Here the answer has to do with the fact that old physical theories are limiting cases of new physical theories."

There's not much more to say... as long as we interpret this year's question as the relationship between known (or potentially known) mathematics and the observable (or potentially observable) universe. But there's another deeper question (perhaps too deep for science, and destined to remain in the realm of philosophy): what is the relationship between "all of mathematics" (in the limit that would be accessible to an infinitely intelligent mathematician) and the totality of all that physically exists?

Thank you for your essay, and good luck in the contest!

Marc

report post as inappropriate

In your concise, well argued essay, I think you perfectly answer Wigner's question when you say:

"Thus the new mathematics was related to the old mathematics, which was in turn related to the old physics. But why was the new mathematics just what was needed for the new physics? Here the answer has to do with the fact that old physical theories are limiting cases of new physical theories."

There's not much more to say... as long as we interpret this year's question as the relationship between known (or potentially known) mathematics and the observable (or potentially observable) universe. But there's another deeper question (perhaps too deep for science, and destined to remain in the realm of philosophy): what is the relationship between "all of mathematics" (in the limit that would be accessible to an infinitely intelligent mathematician) and the totality of all that physically exists?

Thank you for your essay, and good luck in the contest!

Marc

report post as inappropriate

Dear David,

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

report post as inappropriate

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

report post as inappropriate

Dear David,

I enjoyed reading your essay. Indeed, non-Euclidean geometries originated from a question of pure mathematical, or rather logical interest, and constituted the (temporary) departure of mathematics from physics. Axiomatic systems emancipated mathematics, making it its own raison d'être, and leading to the maths that, unexpectedly, will be needed someday by quantum theory and general relativity. Your arguments demystify this apparent miracle. If I understand well, it goes like this: physics and mathematics were once siblings, then they developed independently, and then, their progenies turned out to be cousins. Add to this that mathematics evolved by generalization, and physics was bound by Ockham's razor to find first limiting cases, this effectiveness is no longer unreasonable. I liked very much your writing and your arguments.

Best wishes,

Cristi Stoica

report post as inappropriate

I enjoyed reading your essay. Indeed, non-Euclidean geometries originated from a question of pure mathematical, or rather logical interest, and constituted the (temporary) departure of mathematics from physics. Axiomatic systems emancipated mathematics, making it its own raison d'être, and leading to the maths that, unexpectedly, will be needed someday by quantum theory and general relativity. Your arguments demystify this apparent miracle. If I understand well, it goes like this: physics and mathematics were once siblings, then they developed independently, and then, their progenies turned out to be cousins. Add to this that mathematics evolved by generalization, and physics was bound by Ockham's razor to find first limiting cases, this effectiveness is no longer unreasonable. I liked very much your writing and your arguments.

Best wishes,

Cristi Stoica

report post as inappropriate

Login or create account to post reply or comment.