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

Previous Contests

**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 Fnd.

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

Previous Contests

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

Contest Partner: The Peter and Patricia Gruber Fnd.

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

**Joe Fisher**: *on* 4/9/15 at 16:08pm UTC, wrote Dear Nicolas, I think Newton was wrong about abstract gravity; Einstein...

**Sujatha Jagannathan**: *on* 4/5/15 at 18:44pm UTC, wrote You've mentioned it very rightly, "We" human minds cannot understand this...

**Harry Ricker III**: *on* 4/5/15 at 13:51pm UTC, wrote Dear Nic, I thought this was one of the better attempts to deal with this...

**Constantinos Ragazas**: *on* 3/14/15 at 20:47pm UTC, wrote Nicolas, you write "Concerning time travel, however, I want to say that...

**Nicolas Fillion**: *on* 3/14/15 at 6:50am UTC, wrote Dear Ed, Thanks for your comment, and your criticism is very well-taken....

**Nicolas Fillion**: *on* 3/14/15 at 6:46am UTC, wrote Dear Constantinos (if I may), Thanks for taking the time to read my essay,...

**Edward MacKinnon**: *on* 3/14/15 at 4:41am UTC, wrote The author focuses on the rational reconstruction of scientific theories...

**Anonymous**: *on* 3/14/15 at 3:06am UTC, wrote Dear Nicolas, Like you, I see no mystery here. Math is Math and Physics...

RECENT FORUM POSTS

**kurt stocklmeir**: "em drive metamaterials at 1 end that create negative radiation pressure -..."
*in* Alternative Models of...

**jiya joseph**: "I guess a workshop is conducted by the people that are favorable for the..."
*in* Schrödinger’s Cat...

**mono joli**: "thanks a lot for such a great topic. Scary Maze Games Basketball Legends..."
*in* The Race to Replace the...

**Joe Fisher**: "Dear Dr. Brendan Foster, Of course: “We Are All Connected .” My..."
*in* We Are All Connected

**Caroline v**: "Thanks for informing us about FQXi-sponsored workshop which aim was to..."
*in* Schrödinger’s Cat...

**Yelena Hopper**: "Training is the way toward encouraging learning, or the procurement of..."
*in* Wandering Towards a Goal:...

**Yelena Hopper**: "This article is such a pleasant and intriguing one, I'm exceptionally happy..."
*in* We Are All Connected

**Yelena Hopper**: "Pushing the points of confinement of hypothesis and creative energy in..."
*in* Review of “A Big Bang...

RECENT ARTICLES

*click titles to read articles*

**Our Place in the Multiverse**

Calculating the odds that intelligent observers arise in parallel universes—and working out what they might see.

**Sounding the Drums to Listen for Gravity’s Effect on Quantum Phenomena**

A bench-top experiment could test the notion that gravity breaks delicate quantum superpositions.

**Watching the Observers**

Accounting for quantum fuzziness could help us measure space and time—and the cosmos—more accurately.

**Bohemian Reality: Searching for a Quantum Connection to Consciousness**

Is there are sweet spot where artificial intelligence systems could have the maximum amount of consciousness while retaining powerful quantum properties?

**Quantum Replicants: Should future androids dream of quantum sheep?**

To build the ultimate artificial mimics of real life systems, we may need to use quantum memory.

RECENT FORUM POSTS

RECENT ARTICLES

Calculating the odds that intelligent observers arise in parallel universes—and working out what they might see.

A bench-top experiment could test the notion that gravity breaks delicate quantum superpositions.

Accounting for quantum fuzziness could help us measure space and time—and the cosmos—more accurately.

Is there are sweet spot where artificial intelligence systems could have the maximum amount of consciousness while retaining powerful quantum properties?

To build the ultimate artificial mimics of real life systems, we may need to use quantum memory.

FQXi FORUM

October 18, 2017

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

TOPIC: Demystifying the Applicability of Mathematics by Nicolas Fillion [refresh]

TOPIC: Demystifying the Applicability of Mathematics by Nicolas Fillion [refresh]

Essential tensions remain in our understanding of the reasons underlying the striking success achieved in science by applying mathematics. Wigner and many likeminded scientists and philosophers conclude that this success is a miracle, a ``wonderful gift which we neither deserve nor understand.'' This essay seeks to dissipate that aura of mystery and bring the factors underlying the success of applied mathematics into the fold of scientific rationality.

Nic is an assistant professor of philosophy and member of the center for scientific computing at Simon Fraser University, Canada. His work focuses on philosophy of science, philosophy of mathematics, logic, and numerical analysis.

Dear Nicolas Fillion,

A very interesting a readable essay. Your comment "A model or theory that contained “the whole truth and nothing but the truth” would quite simply be too true to be good." hit the exact theme I started my essay with.

As an aside, from your comment "Let me first illustrate the point with a modern approach to understanding the impact of computational error as it occurs in computer simulations.", I wonder if you have consider cumulative errors. The error that makes many computer simulations so difficult is the compounding errors of using the output of one calculation as the input of the next calculation, ie. errors that result from f(f(f(x))). Modelling the "trajectory of Uranus" or the expect path of a space craft under the influence of several masses (where they cannot be solved as a n-body problem) require an amazing level of accuracy for the initial conditions and tend to diverge pretty rapidly.

My argument concentrated more on the "usefulness" of a model rather then the "accuracy" of the model, but I certainly enjoyed detailed reading of your essay. Hope you get a chance to have a look at mine here.

Best of luck in the contest.

Regards,

Ed Unverricht

report post as inappropriate

A very interesting a readable essay. Your comment "A model or theory that contained “the whole truth and nothing but the truth” would quite simply be too true to be good." hit the exact theme I started my essay with.

As an aside, from your comment "Let me first illustrate the point with a modern approach to understanding the impact of computational error as it occurs in computer simulations.", I wonder if you have consider cumulative errors. The error that makes many computer simulations so difficult is the compounding errors of using the output of one calculation as the input of the next calculation, ie. errors that result from f(f(f(x))). Modelling the "trajectory of Uranus" or the expect path of a space craft under the influence of several masses (where they cannot be solved as a n-body problem) require an amazing level of accuracy for the initial conditions and tend to diverge pretty rapidly.

My argument concentrated more on the "usefulness" of a model rather then the "accuracy" of the model, but I certainly enjoyed detailed reading of your essay. Hope you get a chance to have a look at mine here.

Best of luck in the contest.

Regards,

Ed Unverricht

report post as inappropriate

Dear Ed (if I may),

Thanks for reading my essay and for your comment and question! I will certainly return the favour some time next week as I'll have a bit more time by then. Your worry about cumulative errors is very relevant, and I have have a long story to tell about that! In fact, I've come to the philosophical argument included in my essay mostly by thinking about accumulating...

view entire post

Thanks for reading my essay and for your comment and question! I will certainly return the favour some time next week as I'll have a bit more time by then. Your worry about cumulative errors is very relevant, and I have have a long story to tell about that! In fact, I've come to the philosophical argument included in my essay mostly by thinking about accumulating...

view entire post

Dear Nicolas,

Like you, I see no mystery here. Math is Math and Physics should be too!

I have argued in past and present essays all Basic Laws of Physics are Mathematical Truisms. It is our physical interpretations of these mathematical truths (based on the 'physical view' we have) that "trick" us into believing non-sense. We do not need to know the "magician's trick", however, to know the magic is not real!

There is something perverse and corrupting when we start believing in "magic tricks" like "time travel". Ultimately, our lives get distorted and confused. This idea is encapsulated in the following principle:

**The Anthropocentric Principle : Our Knowledge of the Universe is such as to make Life possible.**

"The 'man-made' Universe"

Constantinos

report post as inappropriate

Like you, I see no mystery here. Math is Math and Physics should be too!

I have argued in past and present essays all Basic Laws of Physics are Mathematical Truisms. It is our physical interpretations of these mathematical truths (based on the 'physical view' we have) that "trick" us into believing non-sense. We do not need to know the "magician's trick", however, to know the magic is not real!

There is something perverse and corrupting when we start believing in "magic tricks" like "time travel". Ultimately, our lives get distorted and confused. This idea is encapsulated in the following principle:

"The 'man-made' Universe"

Constantinos

report post as inappropriate

Dear Constantinos (if I may),

Thanks for taking the time to read my essay, and I will make sure to return the favour next week as I'll have a bit more time then, and I'll write some comment. I fully agree with you concerning the "magic tricks". I almost included a quote attributed to Einstein, but I couldn't trace it to verify the context in which it was said (if indeed it was said): "There are only two ways to live your life, as if everything is a miracle, or as if nothing is a miracle." (That's from memory, so the phrasing might be off a bit.) Concerning time travel, however, I want to say that it's not entirely to be associated with magic tricks, as there's a meaningful physical notion associated with it, as you probably know, namely the closed timeline curves. But that's for another story! :)

Best,

Nic

Thanks for taking the time to read my essay, and I will make sure to return the favour next week as I'll have a bit more time then, and I'll write some comment. I fully agree with you concerning the "magic tricks". I almost included a quote attributed to Einstein, but I couldn't trace it to verify the context in which it was said (if indeed it was said): "There are only two ways to live your life, as if everything is a miracle, or as if nothing is a miracle." (That's from memory, so the phrasing might be off a bit.) Concerning time travel, however, I want to say that it's not entirely to be associated with magic tricks, as there's a meaningful physical notion associated with it, as you probably know, namely the closed timeline curves. But that's for another story! :)

Best,

Nic

The author focuses on the rational reconstruction of scientific theories rather than on an analysis of particular branches of physics. This abstract approach has a distinct advantage. It is possible to use the sork that philosophers of science have done on modelling, testing theories, perturbation, and epistemology. I think that the generaal position presenrted at thks level is quite reasonable. The disadvantage to this abstract approach is that it does not allow a discussion of differences between the role of mathematics in classical physics, quantum physics, and general relativity. These are significant.

Ed. MacKinnon

report post as inappropriate

Ed. MacKinnon

report post as inappropriate

Dear Ed,

Thanks for your comment, and your criticism is very well-taken. In fact, I was myself hesitating about which approach to utilize, as I thought that in such a short paper it wouldn't really be possible to use both. As you point out, it has its strengths and weaknesses, and in any case I didn't see a way to present things without the associated shortcomings. And it is certainly true that much is different between classical physics, quantum physics, and GR, but at the same time some key methods are shared and some of their methodological underpinnings are also shared. That's what I tried to emphasize, and hopefully I haven't failed too miserably! :)

I look forward to reading your essay! Best,

Nic

Thanks for your comment, and your criticism is very well-taken. In fact, I was myself hesitating about which approach to utilize, as I thought that in such a short paper it wouldn't really be possible to use both. As you point out, it has its strengths and weaknesses, and in any case I didn't see a way to present things without the associated shortcomings. And it is certainly true that much is different between classical physics, quantum physics, and GR, but at the same time some key methods are shared and some of their methodological underpinnings are also shared. That's what I tried to emphasize, and hopefully I haven't failed too miserably! :)

I look forward to reading your essay! Best,

Nic

Nicolas, you write

*"Concerning time travel, however, I want to say that it's not entirely to be associated with magic tricks, as there's a meaningful physical notion associated with it, as you probably know, namely the closed timeline curves."*

What is a "closed timeline curve"?

The problem always is, we can always give meaning to anything we give thought to. But the question is and always should be, "does it make sense". That is, does it agree with our "sense experience". The proverbial "man in the street" is the "expert" here! Theoretical physicists, no matter how clever they might be, often get it wrong. In fact the more clever, the more wrong!

I see you are a 'philosopher of science'. Please don't tell me you believe in the "spacetime continuum"!

Oh! I get it! All "tongue in check"!

Constantinos

report post as inappropriate

What is a "closed timeline curve"?

The problem always is, we can always give meaning to anything we give thought to. But the question is and always should be, "does it make sense". That is, does it agree with our "sense experience". The proverbial "man in the street" is the "expert" here! Theoretical physicists, no matter how clever they might be, often get it wrong. In fact the more clever, the more wrong!

I see you are a 'philosopher of science'. Please don't tell me you believe in the "spacetime continuum"!

Oh! I get it! All "tongue in check"!

Constantinos

report post as inappropriate

Dear Nic,

I thought this was one of the better attempts to deal with this topic. However, at the end I was entirely unsatisfied. In the first place, there is not much evidence to justify the claim of the miracle like effectiveness of mathematics in the first place. You fail to mention Aristotle who I think explains the problem very well in that math deals with quantity in terms of numbers. Nature can be modeled in terms of measurement of quantity. That is all there is to it basically. Physics is making measurements. Once measured in terms of quantity, nature is amenable to math modeling. You don't deal with the counter examples of how physics does a bad job with the math. We have special relativity riddled with paradoxes which are caused by math mistakes yet such is the power of the math over the mind of physics that they can not see that the math is entirely false, while the math errors scream that they are mistaken. They don't see a problem and think it is beautiful and perfect. There is a human problem here. Another problem is unipolar induction where physics can calculate the current but the physics underlying the math result is entirely without justification. In other words they don't have a clue why the math seems to work as it does. You don't address these very real and pressing problems of human failure in science.

report post as inappropriate

I thought this was one of the better attempts to deal with this topic. However, at the end I was entirely unsatisfied. In the first place, there is not much evidence to justify the claim of the miracle like effectiveness of mathematics in the first place. You fail to mention Aristotle who I think explains the problem very well in that math deals with quantity in terms of numbers. Nature can be modeled in terms of measurement of quantity. That is all there is to it basically. Physics is making measurements. Once measured in terms of quantity, nature is amenable to math modeling. You don't deal with the counter examples of how physics does a bad job with the math. We have special relativity riddled with paradoxes which are caused by math mistakes yet such is the power of the math over the mind of physics that they can not see that the math is entirely false, while the math errors scream that they are mistaken. They don't see a problem and think it is beautiful and perfect. There is a human problem here. Another problem is unipolar induction where physics can calculate the current but the physics underlying the math result is entirely without justification. In other words they don't have a clue why the math seems to work as it does. You don't address these very real and pressing problems of human failure in science.

report post as inappropriate

You've mentioned it very rightly, "We" human minds cannot understand this miracle. It is beyond comparison.

Great!

- Sincerely,

Miss. Sujatha Jagannathan

report post as inappropriate

Great!

- Sincerely,

Miss. Sujatha Jagannathan

report post as inappropriate

Dear Nicolas,

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

Login or create account to post reply or comment.