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RECENT POSTS IN THIS TOPIC

**Peter Jackson**: *on* 4/26/15 at 12:14pm UTC, wrote Donald, A truly great essay. Massive shame I missed it earlier, and...

**Joe Fisher**: *on* 4/8/15 at 15:39pm UTC, wrote Dear Donald, I think Newton was wrong about abstract gravity; Einstein was...

**Vladimir Rogozhin**: *on* 4/1/15 at 11:21am UTC, wrote You're absolutely right, Donald. Can be called "trialektika". But the...

**Donald Palmer**: *on* 4/1/15 at 3:25am UTC, wrote Thank you for reading and responding Edwin, While mathematics applies...

**Donald Palmer**: *on* 4/1/15 at 3:11am UTC, wrote Thank you for reading and responding to my essay, Vladimir You have chosen...

**Edwin Klingman**: *on* 3/31/15 at 20:56pm UTC, wrote Dear Donald Palmer, I enjoyed your essay, and some of your comments have...

**Vladimir Rogozhin**: *on* 3/30/15 at 10:18am UTC, wrote Dear Donald, Very interesting analytical essays in the spirit of deep...

**Donald Palmer**: *on* 3/12/15 at 10:04am UTC, wrote Thank you for your response, Mr. Blumschein I think you are missing the...

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Calculating the energy needed to acquire and compute information could help explain the (in)efficiency of human brains and guide the search for extra-terrestrial intelligence.

Using precision thermometry to make mini heat engines, that might, momentarily, bust through the thermodynamic limit.

FQXi FORUM

August 9, 2022

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Trick or Truth Essay Contest (2015)
[back]

TOPIC: Can Mathematics Reasonably Represent Nature? by Donald Palmer [refresh]

TOPIC: Can Mathematics Reasonably Represent Nature? by Donald Palmer [refresh]

Starting with Eugene Wigner’s 1960 article, an expansion of natural science is made to study both inanimate and animate nature. Further expanding the goal of science to the full description of nature, the uniqueness of all objects and events is introduced shifting this goal of science to the description of unique objects and events. As our current scientific methodology and tools attempt to eliminate uniqueness, we cannot use current scientific methodology or current mathematical tools to describe such a unique world. Therefore we must retreat to science being the study of general laws. Given the importance of our mathematical tools to science, the question of whether our current tools are sufficient is asked. Bringing in historical analogies, a need for inventing new numeric tools is presented.

Trained as a mathematician, Donald Palmer has followed the world of computers in his career. He received a BA in Mathematics from Earlham College, then a Masters in Mathematics from Villanova University. He ran his own computer services and software development company for 11 years, before entering the bio-pharmaceutical world, where he now works designing software. He has worked on numeric representational concepts and written a short book on modeling of scale in the physical world.

Well done. I agree and have suggested this in 2014 contest paper and in Survival is the only moral goal of life] Survival is the only moral goal of life.

For inanimate matter, the survival measure takes a form of growth such as mass attracts mass to grow in size and strength. But also note the politics reject the predictions goal of physics. This is the cause of not applying math to these areas.

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For inanimate matter, the survival measure takes a form of growth such as mass attracts mass to grow in size and strength. But also note the politics reject the predictions goal of physics. This is the cause of not applying math to these areas.

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Thank you for your response, Mr. Hodge:

Having been trained as a mathematician, I have also noticed the tendency for emotion to pull stronger than logic at many levels, not the least the political level. While I agree that math, and even more, logic, needs to be applied 'better' to many areas, the importance of the distinction of 'wisdom', taking account of emotion and the human condition, over 'logic' should not be lost.

It would seem the internet and discussions using this medium (such as this essay forum) are causing an evolution of communication and thought that is unprecedented. Maybe this aspect of connection between many different people can influence the scientific and political levels in a 'positive' direction.

Donald

Having been trained as a mathematician, I have also noticed the tendency for emotion to pull stronger than logic at many levels, not the least the political level. While I agree that math, and even more, logic, needs to be applied 'better' to many areas, the importance of the distinction of 'wisdom', taking account of emotion and the human condition, over 'logic' should not be lost.

It would seem the internet and discussions using this medium (such as this essay forum) are causing an evolution of communication and thought that is unprecedented. Maybe this aspect of connection between many different people can influence the scientific and political levels in a 'positive' direction.

Donald

This is an interesting and thought provoking essay. In particular, I find myself provoked to make the following points: (1) There is a difference between fundamental laws and useful approximations. Even if we have a fundamental law describing the motion of particles, the direct application of that law to 10^23 particles won't be something we can do. If the motions are random then a statistical...

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I would like to respectfully disagree with your first point. It may be difficult to model 10^23 particles at once, but why cant we develop proper animations of say 10^3 particles and test these animation by proving they properly model nature? Would not proper models of small groups of particles provide additional insight into these particles?

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Thank you for your feedback, Prof. Garfinkle

A couple quick responses: I hope we will move forward on including more animate situations into science and learn from previous discussions - not move backward into those old discussions.

I hope you are not missing the main emphasis of the discussion on numbers - that the concern is with how we represent numbers, not the numbers themselves. It can be very difficult to separate these items, since most any reference is made via a representation of a number In terms of manipulation of quantities, we could essentially remain with Rationals, but we could not remain with only fractions. It is the power of decimals (and positional-based numeric systems) which has allowed us such technological prowess way beyond previous ages. The ability to calculate is tremendously enhanced using decimals over fractions. In a forward looking direction, might there be a more powerful numeric system that could make calculations currently too difficult or even impossible with our current tools? Such numeric tools could produce technology our tools cannot.

Thank you for reading my essay,

Donald

A couple quick responses: I hope we will move forward on including more animate situations into science and learn from previous discussions - not move backward into those old discussions.

I hope you are not missing the main emphasis of the discussion on numbers - that the concern is with how we represent numbers, not the numbers themselves. It can be very difficult to separate these items, since most any reference is made via a representation of a number In terms of manipulation of quantities, we could essentially remain with Rationals, but we could not remain with only fractions. It is the power of decimals (and positional-based numeric systems) which has allowed us such technological prowess way beyond previous ages. The ability to calculate is tremendously enhanced using decimals over fractions. In a forward looking direction, might there be a more powerful numeric system that could make calculations currently too difficult or even impossible with our current tools? Such numeric tools could produce technology our tools cannot.

Thank you for reading my essay,

Donald

Dear Donald Palmer,

It looks like we may have a similar computer background so it is perhaps not surprising that I loved your essay. Your comment "animate objects need to be studied in a ‘timely’ manner, where the growth and movement of an animate object is crucial to understanding it." match my view.

Your argument leading to the comment "to achieve a full description of nature means to be able to describe individual situations, in all their individuality and uniqueness" was very solid.

I have written a lot of computer modelling and animation software using very small distances and time steps, so I would be very interested in "a short book on modeling of scale in the physical world" if it is something that is easy to post online.

Hope you get a chance to have a look at my essay and I would be interested in your comments on my models of the particles of the standard model. The models are meant to be built on and to allow to more complex computer modelling of the interaction of these particles in both chemistry and solid state physics.

Best of luck in the essay contest and you deserve a great rating.

Regards, Ed Unverricht

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It looks like we may have a similar computer background so it is perhaps not surprising that I loved your essay. Your comment "animate objects need to be studied in a ‘timely’ manner, where the growth and movement of an animate object is crucial to understanding it." match my view.

Your argument leading to the comment "to achieve a full description of nature means to be able to describe individual situations, in all their individuality and uniqueness" was very solid.

I have written a lot of computer modelling and animation software using very small distances and time steps, so I would be very interested in "a short book on modeling of scale in the physical world" if it is something that is easy to post online.

Hope you get a chance to have a look at my essay and I would be interested in your comments on my models of the particles of the standard model. The models are meant to be built on and to allow to more complex computer modelling of the interaction of these particles in both chemistry and solid state physics.

Best of luck in the essay contest and you deserve a great rating.

Regards, Ed Unverricht

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Dear Donald Palmer,

Perhaps you were mainly motivated by curiosity as a teacher when you dealt e.g. with numbers. I am an old engineer and when I will read your essay, I expect that you might have arrived at similar ideas and also at different conclusions.

For instance, I don't see any reason to distinguish between fractions like 0.5, 1/2 and 4/8. Likewise I don't distinguish between, 100, 2 times 50 and 4 times 25.

I even expect experts like you having difficulties to accept my reasoning. Please don't forget, I was motivated by practical problems and found valuable historic details already in the second edition of Mückenheim's History of Infinity.

David Joyce commented on an earlier essay of mine that I made some interesting points. I hope you will agree.

Sincerely,

Eckard Blumschein

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Perhaps you were mainly motivated by curiosity as a teacher when you dealt e.g. with numbers. I am an old engineer and when I will read your essay, I expect that you might have arrived at similar ideas and also at different conclusions.

For instance, I don't see any reason to distinguish between fractions like 0.5, 1/2 and 4/8. Likewise I don't distinguish between, 100, 2 times 50 and 4 times 25.

I even expect experts like you having difficulties to accept my reasoning. Please don't forget, I was motivated by practical problems and found valuable historic details already in the second edition of Mückenheim's History of Infinity.

David Joyce commented on an earlier essay of mine that I made some interesting points. I hope you will agree.

Sincerely,

Eckard Blumschein

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Thank you for your response, Mr. Blumschein

I think you are missing the very practical aspects of what I am proposing. While we have conceptions of Integers, Rationals, Reals, Complex, even Quaternions, these are theoretical definitions. When we perform calculations we cannot use these theoretic definitions, we must use a numeric representational system for them - such as fractions or decimals. I submit that, even if we had some concept of Real and Complex numbers, we could not produce our technology (and science) without a numeric system like the decimals. The ability to calculate with this system far outstrips that of fractions.

In a similar situation, I believe there exists a more powerful numeric system that has the ability to perform calculations significantly beyond what we can do today with our current systems. It goes hand-in-hand with expanding our theoretic conception of Complex numbers and also what we can measure - which expands what science can handle.

Take care,

Donald

I think you are missing the very practical aspects of what I am proposing. While we have conceptions of Integers, Rationals, Reals, Complex, even Quaternions, these are theoretical definitions. When we perform calculations we cannot use these theoretic definitions, we must use a numeric representational system for them - such as fractions or decimals. I submit that, even if we had some concept of Real and Complex numbers, we could not produce our technology (and science) without a numeric system like the decimals. The ability to calculate with this system far outstrips that of fractions.

In a similar situation, I believe there exists a more powerful numeric system that has the ability to perform calculations significantly beyond what we can do today with our current systems. It goes hand-in-hand with expanding our theoretic conception of Complex numbers and also what we can measure - which expands what science can handle.

Take care,

Donald

Dear Donald,

Very interesting analytical essays in the spirit of deep Cartesian doubt. I note your particular important ideas, conclusions and fundamental questions for the "fundamental science" that I liked:

"If we use Wigner’s limitation of the study of nature to that of physics, then we immediately remove a huge swath of nature and knowledge – that of animate (or living)...

view entire post

Very interesting analytical essays in the spirit of deep Cartesian doubt. I note your particular important ideas, conclusions and fundamental questions for the "fundamental science" that I liked:

"If we use Wigner’s limitation of the study of nature to that of physics, then we immediately remove a huge swath of nature and knowledge – that of animate (or living)...

view entire post

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Thank you for reading and responding to my essay, Vladimir

You have chosen the critical parts of the essay, which I appreciate.

I read your essay, however there were enough terms I was not familiar that I do not think I could do the same with yours - my lack of knowledge.

Grasping to understand your comments, I think you are suggesting a three-sided dialectic, that gets beyond the two-sided situation of opposites, in order to get out of our current 'crisis of understanding'.

I suppose I am of the persuasion that, in some sort of cyclic process, we have been at such a crisis before and will get to another such crisis in the future. So we are at a 'current crisis of understanding'. It is imperative that we resolve this crisis, however such a resolution will not provide an underlying understanding of why we get into these crises and how to resolve or avoid them in future.

Again, thank you for responding and I hope to better understand your perspective.

Take care,

Donald

You have chosen the critical parts of the essay, which I appreciate.

I read your essay, however there were enough terms I was not familiar that I do not think I could do the same with yours - my lack of knowledge.

Grasping to understand your comments, I think you are suggesting a three-sided dialectic, that gets beyond the two-sided situation of opposites, in order to get out of our current 'crisis of understanding'.

I suppose I am of the persuasion that, in some sort of cyclic process, we have been at such a crisis before and will get to another such crisis in the future. So we are at a 'current crisis of understanding'. It is imperative that we resolve this crisis, however such a resolution will not provide an underlying understanding of why we get into these crises and how to resolve or avoid them in future.

Again, thank you for responding and I hope to better understand your perspective.

Take care,

Donald

You're absolutely right, Donald. Can be called "trialektika". But the "wave" is like "Figaro" - she carries two basic states of matter, "linear" and "vortex".

I totally agree with you - "a current crisis of understanding ... It is imperative that we resolve this crisis, however such a resolution will not provide an underlying understanding of why we get into these crises and how to resolve or avoid them in future."

Thanks for your comment on my forum - I gave my answer and explanation of my ontological structure.

With great respect,

Vladimir

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I totally agree with you - "a current crisis of understanding ... It is imperative that we resolve this crisis, however such a resolution will not provide an underlying understanding of why we get into these crises and how to resolve or avoid them in future."

Thanks for your comment on my forum - I gave my answer and explanation of my ontological structure.

With great respect,

Vladimir

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Dear Donald Palmer,

I enjoyed your essay, and some of your comments have helped clarify your points.

You focus on number 'systems' [i.e., decimal versus fraction, and real versus complex versus quaternion, etc.], pointing out that actual calculations depend strongly on the system chosen. You also note that modeling 'animated' systems shifts the focus to 'uniqueness'. You discuss using mathematical systems to model nature and seem to suggest that even more appropriate number systems may be discoverable/inventable. In my essay I discuss the use of AND and NOT gates (at all scales, from RNA/DNA to neural organism, to silicon machines) to evolve theories based on measurement data. It would seem that any future numeric system would still be implemented as combinations of these gates, regardless of the specific numeric representation (a sort of 'existence theorem'.)

You focus on the power of decimals for modeling reality, noting that

"*Even if we had some concept of real and complex numbers, we could not produce our technology (and science) without a numeric system like the decimals*."

That is an excellent point that is often overlooked in discussions of Wigner. As a result of reading your essay and your comments I also have new awareness of the distinction between the*symbolic* aspects of math and the *numerical* aspects of math, a distinction that is usually glossed over.

I invite you to read my essay and welcome your comments.

Best regards,

Edwin Eugene Klingman

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I enjoyed your essay, and some of your comments have helped clarify your points.

You focus on number 'systems' [i.e., decimal versus fraction, and real versus complex versus quaternion, etc.], pointing out that actual calculations depend strongly on the system chosen. You also note that modeling 'animated' systems shifts the focus to 'uniqueness'. You discuss using mathematical systems to model nature and seem to suggest that even more appropriate number systems may be discoverable/inventable. In my essay I discuss the use of AND and NOT gates (at all scales, from RNA/DNA to neural organism, to silicon machines) to evolve theories based on measurement data. It would seem that any future numeric system would still be implemented as combinations of these gates, regardless of the specific numeric representation (a sort of 'existence theorem'.)

You focus on the power of decimals for modeling reality, noting that

"

That is an excellent point that is often overlooked in discussions of Wigner. As a result of reading your essay and your comments I also have new awareness of the distinction between the

I invite you to read my essay and welcome your comments.

Best regards,

Edwin Eugene Klingman

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Thank you for reading and responding Edwin,

While mathematics applies symbols in nearly aspects, values and calculations fall more on the 'Applied' side. However our representations of number are also used on the 'Theoretic' side, so representations of number seem to me to lie on the boundary of Theoretic and Applied math, impacting both plus many areas using either one (eg. Physics).

The fundamental aspects of AND and NOT gates to logic would suggest they should apply in most all situations where logic is applied, including mathematical models of nature. Applying them to animate nature seems an interesting direction, which I hope to understand by reading your essay.

Take care,

Donald

While mathematics applies symbols in nearly aspects, values and calculations fall more on the 'Applied' side. However our representations of number are also used on the 'Theoretic' side, so representations of number seem to me to lie on the boundary of Theoretic and Applied math, impacting both plus many areas using either one (eg. Physics).

The fundamental aspects of AND and NOT gates to logic would suggest they should apply in most all situations where logic is applied, including mathematical models of nature. Applying them to animate nature seems an interesting direction, which I hope to understand by reading your essay.

Take care,

Donald

Dear Donald,

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 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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Donald,

A truly great essay. Massive shame I missed it earlier, and tragedy it's not a finalist. My score would have been 10.

Thanks for your extraordinarily perceptive comments on mine. I've replied in detail there.

Great to make contact.

Peter

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A truly great essay. Massive shame I missed it earlier, and tragedy it's not a finalist. My score would have been 10.

Thanks for your extraordinarily perceptive comments on mine. I've replied in detail there.

Great to make contact.

Peter

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