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RECENT POSTS IN THIS TOPIC

**vincent douzal**: *on* 4/22/15 at 9:24am UTC, wrote Dears Anshu and Tejinder, I fully agree that a connection between...

**ABDELWAHED BANNOURI**: *on* 4/21/15 at 17:33pm UTC, wrote Dear Sing Tejinder : Certainly, your essay shows a great comprehension of...

**Tejinder Singh**: *on* 4/20/15 at 17:55pm UTC, wrote Dear Cristi, Greetings! It is a pleasure to meet you here again. Thank...

**Cristinel Stoica**: *on* 4/20/15 at 7:18am UTC, wrote Dear Anshu and Tejinder, Thank you for the beautiful and insightful essay....

**Tejinder Singh**: *on* 4/19/15 at 5:48am UTC, wrote Dear Alma, It is fine, no need to feel sorry. We brought to your notice in...

**Alma Ionescu**: *on* 4/18/15 at 15:24pm UTC, wrote Dear Anshu, I'm so sorry for the confusion I made and I'm very glad you...

**Alma Ionescu**: *on* 4/17/15 at 12:44pm UTC, wrote Dear Tejinder, Anshu, Thank you for your insightful comment! I enjoyed...

**Alma Ionescu**: *on* 4/16/15 at 20:10pm UTC, wrote Oh, I see, thank you very much for explaining it, now it makes perfect...

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A meditating mathematician is developing a theory of conscious experience to help understand the boundary between the quantum and classical world.

Underground experiments in the heart of the Italian mountains are testing the links between consciousness and collapse theories of quantum physics.

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.

Using neural networks to test definitions of 'autonomy.'

FQXi FORUM

May 26, 2022

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

TOPIC: Cognitive Science and the Connection between Physics and Mathematics by Anshu Gupta Mujumdar and Tejinder Singh [refresh]

TOPIC: Cognitive Science and the Connection between Physics and Mathematics by Anshu Gupta Mujumdar and Tejinder Singh [refresh]

The human mind is endowed with innate primordial perceptions such as space, distance, motion, change, flow of time, matter. The field of cognitive science argues that the abstract concepts of mathematics are not Platonic, but are built in the brain from these primordial perceptions, using what are known as conceptual metaphors. Known cognitive mechanisms give rise to the extremely precise and logical language of mathematics. Thus all of the vastness of mathematics, with its beautiful theorems, is human mathematics. It resides in the mind, and is not `out there’. Physics is an experimental science in which results of experiments are described in terms of concrete concepts – these concepts are also built from our primordial perceptions. The goal of theoretical physics is to describe the experimentally observed regularity of the physical world in an unambiguous, precise and logical manner. To do so, the brain resorts to the well-defined abstract concepts which the mind has metaphored from our primordial perceptions. Since both the concrete and the abstract are derived from the primordial, the connection between physics and mathematics is not mysterious, but natural. This connection is established in the human brain, where a small subset of the vast human mathematics is cognitively fitted to describe the regularity of the universe. Theoretical physics should be thought of as a branch of mathematics, whose axioms are motivated by observations of the physical world. We use the example of quantum theory to demonstrate the all too human nature of the physics-mathematics connection: it is at times frail, and imperfect. Our resistance to take this imperfection sufficiently seriously [since no known experiment violates quantum theory] shows the fundamental importance of experiments in physics. This is unlike in mathematics, the goal there being to search for logical and elegant relations amongst abstract concepts which the mind creates.

Anshu Gupta Mujumdar is a freelance researcher and visiting faculty in Mathematics/Physics for IB diploma program at the Fazlani L'Academie Globale, Mumbai. She holds a doctorate from the Physical Research Laboratory, Ahmedabad (1997) in the field of general relativity. She has held several postdoctoral positions and was a recipient of a post-doctoral fellowship award in Mathematical Physics (in memory of S. Chandrasekhar, 1998) and Peter Gruber post-doctoral fellowship in 2001. Her research interests are in inflationary cosmology, quantum effects in biological systems, and history of Mathematics. Tejinder Singh is Professor of Physics at the Tata Institute of Fundamental Research, Mumbai.

Dear Tejinder Singh and Anshu,

Your essay contains a numer of insights. Of course elementary counting, or number sense, is hardwired into the brain, but counting exists at almost every level of reality, from three quarks per baryon to the number of telomeres on chromosomes, and a significant number of lower lifeforms. Our own hardwired structures are extremely high level.

As for...

view entire post

Your essay contains a numer of insights. Of course elementary counting, or number sense, is hardwired into the brain, but counting exists at almost every level of reality, from three quarks per baryon to the number of telomeres on chromosomes, and a significant number of lower lifeforms. Our own hardwired structures are extremely high level.

As for...

view entire post

report post as inappropriate

Dear Madam/Sir,

Mathematics describes quantitative aspects of Nature; whereas physics describes its qualitative aspect (interaction is chemistry). Thus their relationship is like the chicken-egg problem or rather like electricity and magnetism. However, there is the danger of over-emphasizing some aspects like extra-dimensions, which could not be discovered even after more than a century,...

view entire post

Mathematics describes quantitative aspects of Nature; whereas physics describes its qualitative aspect (interaction is chemistry). Thus their relationship is like the chicken-egg problem or rather like electricity and magnetism. However, there is the danger of over-emphasizing some aspects like extra-dimensions, which could not be discovered even after more than a century,...

view entire post

report post as inappropriate

Dear Basudeba,

Thank you very much for reading our essay and for your comments above. There seems to be much that we disagree about! We cannot agree that physics describes *qualitative* aspects of nature, or that there is a chicken-egg problem here. Also, why do you say extra dimensions are a gospel truth? Surely they are till not accepted as confirmed by experiments. Also, we would not say that mathematics is all about certainties. Stochastic dynamics is very real, in various settings, at least in an emergent sense. Nor can we agree with what you conclude about the Michelson-Morley experiment.

Nonetheless, thanks for pointing us to your essay, which we look forwarding to reading in due course.

Best regards,

Tejinder, Anshu

Thank you very much for reading our essay and for your comments above. There seems to be much that we disagree about! We cannot agree that physics describes *qualitative* aspects of nature, or that there is a chicken-egg problem here. Also, why do you say extra dimensions are a gospel truth? Surely they are till not accepted as confirmed by experiments. Also, we would not say that mathematics is all about certainties. Stochastic dynamics is very real, in various settings, at least in an emergent sense. Nor can we agree with what you conclude about the Michelson-Morley experiment.

Nonetheless, thanks for pointing us to your essay, which we look forwarding to reading in due course.

Best regards,

Tejinder, Anshu

Your work circulates in primordial features of mathematics which signifies the emergence of indistinguishable notions simmering hypothetical notions.

Good Luck!

Best Regards,

Miss. Sujatha Jagannathan

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Good Luck!

Best Regards,

Miss. Sujatha Jagannathan

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Thank you for your remark Sujatha. We wonder what you meant by your use of the word `simmering' here?

Regards,

Tejinder, Anshu

Regards,

Tejinder, Anshu

Simmering in the sense 'Strong feeling'

Sincerely,

Miss. Sujatha Jagannathan

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Sincerely,

Miss. Sujatha Jagannathan

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Anshu and Tejinder,

It might be fair to say that mathematics was born out of a qualitative or cognitive analogue that grouped objects together. It took probably a bit to figure out how to really count beyond one, two three, many. The tendency of the human brain is to count in a sort of logarithmic sense. People from cultures without arithmetic will often say the number 3 is the middle number of a set of 10 objects, or that 6 is the middle of 20 objects.

You are correct I think in stating that our cognitive abilities underlie arithmetic. This might be compared to David Hume who said that reason is ultimately a slave to our passions.

Cheers LC

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It might be fair to say that mathematics was born out of a qualitative or cognitive analogue that grouped objects together. It took probably a bit to figure out how to really count beyond one, two three, many. The tendency of the human brain is to count in a sort of logarithmic sense. People from cultures without arithmetic will often say the number 3 is the middle number of a set of 10 objects, or that 6 is the middle of 20 objects.

You are correct I think in stating that our cognitive abilities underlie arithmetic. This might be compared to David Hume who said that reason is ultimately a slave to our passions.

Cheers LC

report post as inappropriate

Dear Lawrence,

Thanks for reading our essay and commenting on it. It is heartening that we agree on the role of cognition. Especially interesting is your remark on the tendency to count logarithmically...we learnt from Dehaene's book about Amazon tribes which tend to think of 1 and 2 being farther apart than 8 and 9 are [mental compression of a logarithmic nature]. It seems even young children, when asked to place say the number 10 on the number line, between 1 and 100, tend to put it near the middle of the line [like you suggest], and compress the larger numbers on the right half of the line. The linear equi-spaced ordering of numbers is learnt culturally through education as we grow up. This is perhaps another useful example of innate arithmetic versus learnt arithmetic.

We look forward to reading your essay.

Thanks and regards,

Anshu, Tejinder

Thanks for reading our essay and commenting on it. It is heartening that we agree on the role of cognition. Especially interesting is your remark on the tendency to count logarithmically...we learnt from Dehaene's book about Amazon tribes which tend to think of 1 and 2 being farther apart than 8 and 9 are [mental compression of a logarithmic nature]. It seems even young children, when asked to place say the number 10 on the number line, between 1 and 100, tend to put it near the middle of the line [like you suggest], and compress the larger numbers on the right half of the line. The linear equi-spaced ordering of numbers is learnt culturally through education as we grow up. This is perhaps another useful example of innate arithmetic versus learnt arithmetic.

We look forward to reading your essay.

Thanks and regards,

Anshu, Tejinder

Dear Tejinder Singh and Anshu,

Thank you for your essay. It was a real pleasure to read it, especially when you described how mathematical and physical concepts were built on each other over time.

I had great expectations on your essay and I felt a little bit disappointed. On one side, the perspective you introduced on mathematics and physics history is superb. On the other, I felt you went too much into relativism. Relativism and accepting that we know little or nothing might be accurate but it is not constructive.

I wish you could have shown that by changing our cognitive axioms, we could have developed different views of the world (very simple examples would have been enough). Maybe this task is impossible for us, humans, to do.

Wish you the best in this contest.

Regards

Christophe

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Thank you for your essay. It was a real pleasure to read it, especially when you described how mathematical and physical concepts were built on each other over time.

I had great expectations on your essay and I felt a little bit disappointed. On one side, the perspective you introduced on mathematics and physics history is superb. On the other, I felt you went too much into relativism. Relativism and accepting that we know little or nothing might be accurate but it is not constructive.

I wish you could have shown that by changing our cognitive axioms, we could have developed different views of the world (very simple examples would have been enough). Maybe this task is impossible for us, humans, to do.

Wish you the best in this contest.

Regards

Christophe

report post as inappropriate

Dear Christophe,

Many thanks for reading our essay and for your insightful comments. We would like to discuss further your constructive criticism. For that, it will be great if you could kindly elaborate and expand on your following remark:

"On the other, I felt you went too much into relativism. Relativism and accepting that we know little or nothing might be accurate but it is not constructive."

We are interested in understanding what you imply by relativism here.

Your remarks about changing cognitive axioms to get a different view are also very interesting. We implicitly had in mind a unique set of axioms for theoretical physics, which should lead to a theory consistent with experiments. In the sense that physicists are inclined to believe there is only one correct theoretical description of a phenomenon. And if it seems there are more than one description, we make every effort to find out which is the right one. This is perhaps different from mathematics where one could start from differing sets of axioms.

Did you have in mind different possible sets of starting axioms for theoretical physics?

As for different cognitive axioms, we will be indeed hard put to come up with a proposal, having assumed that cognitive axioms draw intimately on our motor-sensory perceptions and are hence unique. But this needs further thought and discussion, which we are certainly happy to continue with you.

Thanks and regards,

Anshu, Tejinder

Many thanks for reading our essay and for your insightful comments. We would like to discuss further your constructive criticism. For that, it will be great if you could kindly elaborate and expand on your following remark:

"On the other, I felt you went too much into relativism. Relativism and accepting that we know little or nothing might be accurate but it is not constructive."

We are interested in understanding what you imply by relativism here.

Your remarks about changing cognitive axioms to get a different view are also very interesting. We implicitly had in mind a unique set of axioms for theoretical physics, which should lead to a theory consistent with experiments. In the sense that physicists are inclined to believe there is only one correct theoretical description of a phenomenon. And if it seems there are more than one description, we make every effort to find out which is the right one. This is perhaps different from mathematics where one could start from differing sets of axioms.

Did you have in mind different possible sets of starting axioms for theoretical physics?

As for different cognitive axioms, we will be indeed hard put to come up with a proposal, having assumed that cognitive axioms draw intimately on our motor-sensory perceptions and are hence unique. But this needs further thought and discussion, which we are certainly happy to continue with you.

Thanks and regards,

Anshu, Tejinder

Dear Anshu, Tejinder,

I read your essay again and I find your case convincing.

I suspect my hope is that understanding the connection between mathematics and physics would tell us something about the world. Reading your essay, it tells us something about us. That’s probably where comes from my little disappointment, what I implied by relativism.

I agree with you that evolution has shaped our abilities. For example, driving a car implies processing hundreds of dynamic variables. Everyone does it easily. On the other side, an equation with the same number of variables is inaccessible to us.

If you have time, I have a short essay in this context. Your comments or criticisms will be appreciated. http://fqxi.org/community/forum/topic/2322

I wish I would have introduced my arguments in more details. Funny how one can get caught in the game!

Regards,

Christophe

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I read your essay again and I find your case convincing.

I suspect my hope is that understanding the connection between mathematics and physics would tell us something about the world. Reading your essay, it tells us something about us. That’s probably where comes from my little disappointment, what I implied by relativism.

I agree with you that evolution has shaped our abilities. For example, driving a car implies processing hundreds of dynamic variables. Everyone does it easily. On the other side, an equation with the same number of variables is inaccessible to us.

If you have time, I have a short essay in this context. Your comments or criticisms will be appreciated. http://fqxi.org/community/forum/topic/2322

I wish I would have introduced my arguments in more details. Funny how one can get caught in the game!

Regards,

Christophe

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Dear Profs. Majumdar and Singh,

I read your essay with great interest. I noticed that you briefly address the foundations of quantum theory, by identifying four "oddities", essentially logical paradoxes and inconsistencies.

In that regard, you might be interested in reading my essay: ("Remove the Blinders: How Mathematics Distorted the Development of Quantum Theory"

I argue that premature adoption of an abstract mathematical framework prevented consideration of a simple, consistent, realistic model of quantum mechanics, avoiding paradoxes of indeterminacy, entanglement, and non-locality. What’s more, this realistic model is directly testable using little more than Stern-Gerlach magnets.

Alan Kadin

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I read your essay with great interest. I noticed that you briefly address the foundations of quantum theory, by identifying four "oddities", essentially logical paradoxes and inconsistencies.

In that regard, you might be interested in reading my essay: ("Remove the Blinders: How Mathematics Distorted the Development of Quantum Theory"

I argue that premature adoption of an abstract mathematical framework prevented consideration of a simple, consistent, realistic model of quantum mechanics, avoiding paradoxes of indeterminacy, entanglement, and non-locality. What’s more, this realistic model is directly testable using little more than Stern-Gerlach magnets.

Alan Kadin

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Thank you Alan, for making time to read our essay. We had a first read of your essay, and look forward to reading it again for better understanding, and discussing it with you on your page.

In this context, we wonder if it might be of help for the sake of comparing your quantum viewpoint with ours, if you could critically examine the popular video `Does nature play dice'?' which one of us posted in the recent FQXi video contest. Understandably, we have quite different outlooks, but I am sure the comparative discussion will be stimulating. In particular, it would be interesting to know how you evaluate your proposal with the other modifications / reinterpretations of quantum theory discussed in the video.

Thanks and best regards,

Anshu, Tejinder

In this context, we wonder if it might be of help for the sake of comparing your quantum viewpoint with ours, if you could critically examine the popular video `Does nature play dice'?' which one of us posted in the recent FQXi video contest. Understandably, we have quite different outlooks, but I am sure the comparative discussion will be stimulating. In particular, it would be interesting to know how you evaluate your proposal with the other modifications / reinterpretations of quantum theory discussed in the video.

Thanks and best regards,

Anshu, Tejinder

Dear Authors,

I’ve read two times your essay, and what I find very nice in it is the perceivable ‘pleasure’ by which you move up and down the history of physics and mathematics, mentioning the most important milestones in both areas.

At a first sight, I also found quite interesting the idea to make the ‘unreasonable’ effectiveness of maths in physics become reasonable, or even inevitable, by identifying the roots of both in human primordial perceptions. But on a second though I am still left with much doubts about the validity of this explanation.

Imagine an other universe similar to ours, with galaxies, stars, planets, but where the phenomenon of conscious life (humans) has not emerged. Planet trajectories still follow the beautiful equation of the ellipsis and most phenomena still match the beautiful and simple patterns described so effectively by math. How could you explain this match in that case?

One could exclude this scenario, claiming that there is no reality without a conscious entity (say a human) that perceives it, but I had the impression that you are not a follower of this (rather extreme) school of thought. Then we are left with a universe nicely describable by compact math formulas (Tegmark’s External Reality Hypothesis) - although no brain is there to formulate and enjoy its mathematical description. But in case a conscious alien came to visit it from a parallel universe, he would probably enjoy the matching between math and physics, and find it ‘unreasonable’ indeed.

How to fix the problem? Or did I miss some crucial element in your reasoning?

Thanks

Tommaso

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I’ve read two times your essay, and what I find very nice in it is the perceivable ‘pleasure’ by which you move up and down the history of physics and mathematics, mentioning the most important milestones in both areas.

At a first sight, I also found quite interesting the idea to make the ‘unreasonable’ effectiveness of maths in physics become reasonable, or even inevitable, by identifying the roots of both in human primordial perceptions. But on a second though I am still left with much doubts about the validity of this explanation.

Imagine an other universe similar to ours, with galaxies, stars, planets, but where the phenomenon of conscious life (humans) has not emerged. Planet trajectories still follow the beautiful equation of the ellipsis and most phenomena still match the beautiful and simple patterns described so effectively by math. How could you explain this match in that case?

One could exclude this scenario, claiming that there is no reality without a conscious entity (say a human) that perceives it, but I had the impression that you are not a follower of this (rather extreme) school of thought. Then we are left with a universe nicely describable by compact math formulas (Tegmark’s External Reality Hypothesis) - although no brain is there to formulate and enjoy its mathematical description. But in case a conscious alien came to visit it from a parallel universe, he would probably enjoy the matching between math and physics, and find it ‘unreasonable’ indeed.

How to fix the problem? Or did I miss some crucial element in your reasoning?

Thanks

Tommaso

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Dear Tommaso,

Thanks so much for reading our essay and thanks for your interesting comments. In particular, you say:

"Imagine an other universe similar to ours, with galaxies, stars, planets, but where the phenomenon of conscious life (humans) has not emerged. Planet trajectories still follow the beautiful equation of the ellipsis and most phenomena still match the beautiful and...

view entire post

Thanks so much for reading our essay and thanks for your interesting comments. In particular, you say:

"Imagine an other universe similar to ours, with galaxies, stars, planets, but where the phenomenon of conscious life (humans) has not emerged. Planet trajectories still follow the beautiful equation of the ellipsis and most phenomena still match the beautiful and...

view entire post

Dear Sirs,

You claim in your essay the following:

"Next, mathematics is introduced by way of the second law, which encodes the experimentally verified inter-relation between the concrete concepts of mass and force, and the abstract entity from calculus (acceleration as the second time derivative of position). The second equality, the force law of gravitation, is motivated, amongst other things, by the necessity to deduce Kepler's empirical inference that the orbit is an ellipse."

The task of Newton, assigned to him by his peers, was to prove that given the law, the known orbits hold, called the "inverse problem". The law was known long ago before Newton. He proved that if the law is true, the orbit can be one of four conical sections, not only an ellipse. This cannot be reduced to some "motivation". This was a difficult task that changed science forever. Your approach to this subject is emotive. Newton made many abstract considerations to reach the final result that could not be made by mathematicians. You obviously have not read his books. I suggest you do so. Thank you for the effort but completely disagree with both the motivation and the conclusions.

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You claim in your essay the following:

"Next, mathematics is introduced by way of the second law, which encodes the experimentally verified inter-relation between the concrete concepts of mass and force, and the abstract entity from calculus (acceleration as the second time derivative of position). The second equality, the force law of gravitation, is motivated, amongst other things, by the necessity to deduce Kepler's empirical inference that the orbit is an ellipse."

The task of Newton, assigned to him by his peers, was to prove that given the law, the known orbits hold, called the "inverse problem". The law was known long ago before Newton. He proved that if the law is true, the orbit can be one of four conical sections, not only an ellipse. This cannot be reduced to some "motivation". This was a difficult task that changed science forever. Your approach to this subject is emotive. Newton made many abstract considerations to reach the final result that could not be made by mathematicians. You obviously have not read his books. I suggest you do so. Thank you for the effort but completely disagree with both the motivation and the conclusions.

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Dear Alex,

Thank you for reading our essay and for your comments, though it is not clear to us whether your last remark

"Thank you for the effort but completely disagree with both the motivation and the conclusions."

pertains to the entire essay or only to the example of planetary orbits. If you have a different view on the connection between physics and mathematics we will...

view entire post

Thank you for reading our essay and for your comments, though it is not clear to us whether your last remark

"Thank you for the effort but completely disagree with both the motivation and the conclusions."

pertains to the entire essay or only to the example of planetary orbits. If you have a different view on the connection between physics and mathematics we will...

view entire post

Dear Tejinder and Anshu,

You have done a good review of the theme of this year's essay. Even though it can be difficult to fault your finding that mathematics originates "from the brain", and is not "out there". However, if you will entertain my alternative view, I believe it cannot be ruled out that mathematical objects are 'out there', and the human brain evolved to meet them. It is my...

view entire post

You have done a good review of the theme of this year's essay. Even though it can be difficult to fault your finding that mathematics originates "from the brain", and is not "out there". However, if you will entertain my alternative view, I believe it cannot be ruled out that mathematical objects are 'out there', and the human brain evolved to meet them. It is my...

view entire post

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Dear Akinbo,

Thanks so much for reading our essay and for your kind comments. We respect the Platonic view even though it is essentially the opposite of ours. It is that we do not yet see how one could scientifically establish, without appealing to some yet unknown extra-sensory perceptions, the brain making contact with a Platonic `out there' mathematics. Maybe when the field of neurobiology has made further significant advances we will know the answer.

Regarding your comments on the extended point: we readily agree that an extended point can represent a physical reality. But we make a clear distinction between the `thing itself' and `mathematical representation of the thing'. The former is out there and the latter is in our mind, according to our viewpoint.

Unfortunately we could not understand your remarks about velocity of light. We certainly agree that the motion of the earth through space can be detected say via the cosmic microwave background dipole, but you will agree that such a detection does not imply that the speed of light is not a universal invariant independent of the choice of inertial frames.

Thanks for pointing us to your essay - we look forward to reading it in the next few days.

Best regards,

Anshu, Tejinder

Thanks so much for reading our essay and for your kind comments. We respect the Platonic view even though it is essentially the opposite of ours. It is that we do not yet see how one could scientifically establish, without appealing to some yet unknown extra-sensory perceptions, the brain making contact with a Platonic `out there' mathematics. Maybe when the field of neurobiology has made further significant advances we will know the answer.

Regarding your comments on the extended point: we readily agree that an extended point can represent a physical reality. But we make a clear distinction between the `thing itself' and `mathematical representation of the thing'. The former is out there and the latter is in our mind, according to our viewpoint.

Unfortunately we could not understand your remarks about velocity of light. We certainly agree that the motion of the earth through space can be detected say via the cosmic microwave background dipole, but you will agree that such a detection does not imply that the speed of light is not a universal invariant independent of the choice of inertial frames.

Thanks for pointing us to your essay - we look forward to reading it in the next few days.

Best regards,

Anshu, Tejinder

While looking forward to your comments on my essay, I wish to clarify my remarks regarding the velocity of light. It is a very common and very crucial misinterpretation what the statement "the speed of light is a universal invariant/ constant" means.

What is implied in special relativity is that the**resultant** velocity of light is invariant, c + v = c or c - v = c, where c is...

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What is implied in special relativity is that the

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Dear Anshu and Tejinder,

I am intrigued to know where mathematics and our language of physics comes from. That this starts with the human brain is a very reasonable working hypothesis and some scientists like Roger Penrose and Stuart Hameroff have even tried to locate our consciousness in brain microtubules. I am curious to learn your opinion about such a controversial subject.

My own mathematical impregnation led me to favour concepts that simultaneously and potentially contain maths and physical aspects like non linear models (and the resulting chaos, fractals, solitons...). For QM and its paradoxes, I was pushed to Grothendieck's "dessins d'enfants" (two-permutation groups possessing cosets, topology, a Riemann surface, algebra over the rationals and geometry). You mention some of these aspects in your paper and you may be interest to read what I have to say in connection to the Monstrous Moonshine.

To conclude, I found your essay stimulating and very well written. I agree with the goal of relating cognition and mathematical physics. I like that you insist that a basic level is that of complex numbers.

Michel

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I am intrigued to know where mathematics and our language of physics comes from. That this starts with the human brain is a very reasonable working hypothesis and some scientists like Roger Penrose and Stuart Hameroff have even tried to locate our consciousness in brain microtubules. I am curious to learn your opinion about such a controversial subject.

My own mathematical impregnation led me to favour concepts that simultaneously and potentially contain maths and physical aspects like non linear models (and the resulting chaos, fractals, solitons...). For QM and its paradoxes, I was pushed to Grothendieck's "dessins d'enfants" (two-permutation groups possessing cosets, topology, a Riemann surface, algebra over the rationals and geometry). You mention some of these aspects in your paper and you may be interest to read what I have to say in connection to the Monstrous Moonshine.

To conclude, I found your essay stimulating and very well written. I agree with the goal of relating cognition and mathematical physics. I like that you insist that a basic level is that of complex numbers.

Michel

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Dear Michel,

Thank you for reading our essay and for your kind remarks.

We have a little bit [though not much] familiarity with the work of Penrose and Hameroff, proposing that quantum coherence and collapse of the wave function in the microtubule environment is the source of consciousness, somehow. With due respect to these great scientists it is our opinion that much more work needs to be done to make this proposal credible. The first issue has to do with the proposal by Penrose, and others, that gravity is responsible for the collapse of the wave-function during a quantum measurement. If you would like to have a look, a recent review can be found here. We find this a very attractive idea but it needs to be developed into a concrete mathematical model first and tested in the laboratory. Only then can we consider applying it to an environment as complex and sophisticated as the brain. Even then, one would have to make a sound mathematical model of the quantum to classical transition in a microtubule. We did not find something like that in the works of Penrose and Hameroff. From what we know, biologists are probably not even agreed on whether microtubules are at all involved in consciousness (open question). Thus while definitely worthy of further study, the idea has a long way to go before becoming believable - so we think.

We had a first look at your very elegant essay on the maths-physics dialogue, and hope to get back to you soon.

Best regards,

Anshu, Tejinder

Thank you for reading our essay and for your kind remarks.

We have a little bit [though not much] familiarity with the work of Penrose and Hameroff, proposing that quantum coherence and collapse of the wave function in the microtubule environment is the source of consciousness, somehow. With due respect to these great scientists it is our opinion that much more work needs to be done to make this proposal credible. The first issue has to do with the proposal by Penrose, and others, that gravity is responsible for the collapse of the wave-function during a quantum measurement. If you would like to have a look, a recent review can be found here. We find this a very attractive idea but it needs to be developed into a concrete mathematical model first and tested in the laboratory. Only then can we consider applying it to an environment as complex and sophisticated as the brain. Even then, one would have to make a sound mathematical model of the quantum to classical transition in a microtubule. We did not find something like that in the works of Penrose and Hameroff. From what we know, biologists are probably not even agreed on whether microtubules are at all involved in consciousness (open question). Thus while definitely worthy of further study, the idea has a long way to go before becoming believable - so we think.

We had a first look at your very elegant essay on the maths-physics dialogue, and hope to get back to you soon.

Best regards,

Anshu, Tejinder

Dear Anshu and Tejinder,

Thank you for the easy to read and thought provoking essay. I like how you start with a definition of math "*Mathematics is a precise language in which true statements can be proved starting from a set of axioms, using logic.*" and a definition of physics "*Physics, on the other hand, is an experimental science of the world we observe, where experiments couple with great leaps of conceptual unification.*" and make a solid argument towards "*... it is experiments and concepts first, and then the mathematical formulation.*"

I have a small question where you point out for both math and physics, "*shape, pattern recognition, counting, space, time, and change.*" but missing in math is "*.. no place in mathematics for matter (material substance), and by extension, for light!*". What about the Dirac electron where the mass of the electron is the coupling constant of a pair of spinors, or the more recent work on defining mass through mathematical properties of the Higgs Boson?

That said, I very much enjoyed how you tied mathematics and physics to cognitive mechanisms in our own human brain. You left lots of things for the reader to ponder, a mark of a well done essay.

Best of luck in the contest and I hope you get a chance to have a look at my essay here where I take a different approach to our minds understanding of the concepts behind the standard model.

Thank you for the enjoyable read.

Regards, Ed Unverricht

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Thank you for the easy to read and thought provoking essay. I like how you start with a definition of math "

I have a small question where you point out for both math and physics, "

That said, I very much enjoyed how you tied mathematics and physics to cognitive mechanisms in our own human brain. You left lots of things for the reader to ponder, a mark of a well done essay.

Best of luck in the contest and I hope you get a chance to have a look at my essay here where I take a different approach to our minds understanding of the concepts behind the standard model.

Thank you for the enjoyable read.

Regards, Ed Unverricht

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Dear Ed,

Thanks so much for reading our essay and for your kind remarks.

Regarding your question, you of course have a good point. However we are making a distinction between physical reality (in this case the mass), and its mathematical representation. It would be like saying that if we hold a ball in our hand and squeeze it, we can feel and appreciate its `materialness' through our senses. On the other hand when we make the statement `We are holding a ball of mass M in our hand' this sort of lingual / mathematical representation of the physical reality is lacking in `materialness' even though we can perceive in our mind what we mean. We do not question the possibility that there can be an elegant mathematical explanation for the origin of mass. We hope (not sure though) this addresses your enquiry.

We enjoyed your essay and left a post on your page.

Best regards,

Anshu, Tejinder

Thanks so much for reading our essay and for your kind remarks.

Regarding your question, you of course have a good point. However we are making a distinction between physical reality (in this case the mass), and its mathematical representation. It would be like saying that if we hold a ball in our hand and squeeze it, we can feel and appreciate its `materialness' through our senses. On the other hand when we make the statement `We are holding a ball of mass M in our hand' this sort of lingual / mathematical representation of the physical reality is lacking in `materialness' even though we can perceive in our mind what we mean. We do not question the possibility that there can be an elegant mathematical explanation for the origin of mass. We hope (not sure though) this addresses your enquiry.

We enjoyed your essay and left a post on your page.

Best regards,

Anshu, Tejinder

Dear Dr. Anshu Gupta Mujumda

& Dr.Tejinder Singh

It's really a pleasure for me to read your nice essay.

You probably emphasized on a "primordial" logical connection which links both physic and mathematics originated from the "brain perceptions" of "at least one planet full of intelligent beings".

You also wrote: "The mathematics used in physics comes in only at a...

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& Dr.Tejinder Singh

It's really a pleasure for me to read your nice essay.

You probably emphasized on a "primordial" logical connection which links both physic and mathematics originated from the "brain perceptions" of "at least one planet full of intelligent beings".

You also wrote: "The mathematics used in physics comes in only at a...

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Dear Dipak,

Thank you for reading our essay and for your kind remarks.

You have raised some very nice points. We surely agree that the natural evolution of intelligent beings involves physical hardware (the brain) in which the software (mind, cognition) are operational. For the purpose of the essay, we are compelled to take the brain / mind as given; you will agree perhaps that not enough is known in neurobiology to answer how and why nature evolves hardware and software which then acts back to `understand' nature.

We agree there maybe fundamental limitations to the efficiency of the observer - observed interaction, but how to explore that scientifically? We also did not quite follow what you meant by `quantised' in this context. Hope to understand this from your essay.

You also suggest that cognition has a causal / deterministic aspect and a non-causal / probabilistic aspect. Is there a formal construction of this kind in cognitive science? We would have thought that probabilities are attributed to randomness / ignorance of initial conditions, rather than being a limitation of cognition. But you raise an interesting aspect which we need to think more about, and perhaps learn from your essay.

Best regards,

Anshu, Tejinder

Thank you for reading our essay and for your kind remarks.

You have raised some very nice points. We surely agree that the natural evolution of intelligent beings involves physical hardware (the brain) in which the software (mind, cognition) are operational. For the purpose of the essay, we are compelled to take the brain / mind as given; you will agree perhaps that not enough is known in neurobiology to answer how and why nature evolves hardware and software which then acts back to `understand' nature.

We agree there maybe fundamental limitations to the efficiency of the observer - observed interaction, but how to explore that scientifically? We also did not quite follow what you meant by `quantised' in this context. Hope to understand this from your essay.

You also suggest that cognition has a causal / deterministic aspect and a non-causal / probabilistic aspect. Is there a formal construction of this kind in cognitive science? We would have thought that probabilities are attributed to randomness / ignorance of initial conditions, rather than being a limitation of cognition. But you raise an interesting aspect which we need to think more about, and perhaps learn from your essay.

Best regards,

Anshu, Tejinder

"The failure of the Michelson-Morley experiment to detect the motion of the earth through the hypothesised ether led Einstein and others to abandon the ether, and look for a set of mathematical coordinate transformations which allow the speed of light to be the same for all inertial observers."

That was a dishonest step that eventually ruined physics. In 1887 (prior to FitzGerald and...

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That was a dishonest step that eventually ruined physics. In 1887 (prior to FitzGerald and...

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Dear Pentcho,

Thank you for your comments. It was my understanding that many many different experiments, carried out independently and using different set-ups, terrestrial as well as astronomical, rule out the emission theory of light to a very high precision.

With regards,

Tejinder

Thank you for your comments. It was my understanding that many many different experiments, carried out independently and using different set-ups, terrestrial as well as astronomical, rule out the emission theory of light to a very high precision.

With regards,

Tejinder

Dear Tejinder,

Your statement "many many different experiments (...) rule out the emission theory of light to a very high precision" is unfalsifiable - how can I oppose it? We can only discuss the experiments one by one. I hope you agree now that the Michelson-Morley experiment did confirm the variable speed of light predicted by the emission theory, and refuted the constant (independent of the speed of the light source) speed of light predicted by the ether theory and adopted by Einstein as his second postulate. The Pound-Rebka experiment also confirmed the variable (in a gravitational field) speed of light predicted by Newton's emission theory of light:

Albert Einstein Institute: "One of the three classical tests for general relativity is the gravitational redshift of light or other forms of electromagnetic radiation. However, in contrast to the other two tests - the gravitational deflection of light and the relativistic perihelion shift -, you do not need general relativity to derive the correct prediction for the gravitational redshift. A combination of Newtonian gravity, a particle theory of light, and the weak equivalence principle (gravitating mass equals inertial mass) suffices. (...) The gravitational redshift was first measured on earth in 1960-65 by Pound, Rebka, and Snider at Harvard University..."

Pentcho Valev

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Your statement "many many different experiments (...) rule out the emission theory of light to a very high precision" is unfalsifiable - how can I oppose it? We can only discuss the experiments one by one. I hope you agree now that the Michelson-Morley experiment did confirm the variable speed of light predicted by the emission theory, and refuted the constant (independent of the speed of the light source) speed of light predicted by the ether theory and adopted by Einstein as his second postulate. The Pound-Rebka experiment also confirmed the variable (in a gravitational field) speed of light predicted by Newton's emission theory of light:

Albert Einstein Institute: "One of the three classical tests for general relativity is the gravitational redshift of light or other forms of electromagnetic radiation. However, in contrast to the other two tests - the gravitational deflection of light and the relativistic perihelion shift -, you do not need general relativity to derive the correct prediction for the gravitational redshift. A combination of Newtonian gravity, a particle theory of light, and the weak equivalence principle (gravitating mass equals inertial mass) suffices. (...) The gravitational redshift was first measured on earth in 1960-65 by Pound, Rebka, and Snider at Harvard University..."

Pentcho Valev

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Dear Pentcho,

My understanding is that both emission theory and special relativity are consistent with the Michelson Morley experiment, but the former is refuted by subsequent experiments. From what I know, Einstein himself did consider an emission theory of his own, before discarding it in favour of special relativity. As regards the multitude of experiments that refute emission theory, I...

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My understanding is that both emission theory and special relativity are consistent with the Michelson Morley experiment, but the former is refuted by subsequent experiments. From what I know, Einstein himself did consider an emission theory of his own, before discarding it in favour of special relativity. As regards the multitude of experiments that refute emission theory, I...

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Dear Anshu and Tejinder,

I just red your reply following my very positive appreciation of your essay.

There is another essay about science and cognition by Vincent Douzal that you should not miss.

Me too I am not yet convinced by Hameroff and Penrose, I met them sometimes ago at a Tucson conference.

I am now rating your essay highly. I hope it will not be balanced by a stupid 1 as usual. Myself I already got 1 three times.

Best,

Michel

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I just red your reply following my very positive appreciation of your essay.

There is another essay about science and cognition by Vincent Douzal that you should not miss.

Me too I am not yet convinced by Hameroff and Penrose, I met them sometimes ago at a Tucson conference.

I am now rating your essay highly. I hope it will not be balanced by a stupid 1 as usual. Myself I already got 1 three times.

Best,

Michel

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Dear Michel,

Greetings, and thanks for pointing us to Vincent Douzal's paper, which we read and liked. Indeed there are a few papers in the contest emphasising the importance of cognition in the present context (though perhaps too few!). The research works of Lukaff, Nunez, Dehaene, Hestenes, amongst others, are noteworthy.

Kind regards,

Anshu, Tejinder

Greetings, and thanks for pointing us to Vincent Douzal's paper, which we read and liked. Indeed there are a few papers in the contest emphasising the importance of cognition in the present context (though perhaps too few!). The research works of Lukaff, Nunez, Dehaene, Hestenes, amongst others, are noteworthy.

Kind regards,

Anshu, Tejinder

Tejinder and Anshu,

Congratulations on a weighty discussion. As a modeller in the urbane, offensive and defensive weapons cost and support, and as a teacher of English, I see human mathematics as building on metaphors, not being an entity itself. My background lends that prejudice.

You do not burden yourself with this question, but do state your feeling: "tempting but erroneous to conclude that the beautiful math description is resident in the physical world."

I also believe that Cognition draws on the physical world to invent the stable human language of math. Such modelling has led us to discoveries quantum biology, DNA, and LHC through what I see as the connections of math, mind, and physics.

Thanks for the opportunity to share your views.

Jim

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Congratulations on a weighty discussion. As a modeller in the urbane, offensive and defensive weapons cost and support, and as a teacher of English, I see human mathematics as building on metaphors, not being an entity itself. My background lends that prejudice.

You do not burden yourself with this question, but do state your feeling: "tempting but erroneous to conclude that the beautiful math description is resident in the physical world."

I also believe that Cognition draws on the physical world to invent the stable human language of math. Such modelling has led us to discoveries quantum biology, DNA, and LHC through what I see as the connections of math, mind, and physics.

Thanks for the opportunity to share your views.

Jim

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Dear Jim.

Thank you for reading our essay and for your kind comments. Happy to know we are in agreement.

Best regards,

Anshu, Tejinder

Thank you for reading our essay and for your kind comments. Happy to know we are in agreement.

Best regards,

Anshu, Tejinder

Anshu and Tejinder,

Time grows short and I am revisiting essays I have read to determine if I've rated them. Yours I did on 3/28.

I would like to see your thoughts on mine.

Jim

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Time grows short and I am revisiting essays I have read to determine if I've rated them. Yours I did on 3/28.

I would like to see your thoughts on mine.

Jim

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Anshu and Tejinder,

"And Jim we do not seem to find in your essay an explanation for the central question as to why mathematics is so successfully employed in physics. Wonder what your thoughts on this are."

First there was the equation on page 3 that represent P, M, and B (physics, math and the human brain), showing their integral interconnection. I provide examples on page 3 & 5 in "Math's Applications" and "Math's Quantum Modeling" section on how math's use in modeling and algorithms, including lines of programming code containing the algorithms that mathematically tie physics concepts together with the LHC, DNA and quantum biology studies and successes.

My conclusion on page 7 shows how these connections of the brain, math and physics are vital in the stellar progress we've had in all physics but especially in those areas I cite.

Thank you both for reading my essay.

Jim

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"And Jim we do not seem to find in your essay an explanation for the central question as to why mathematics is so successfully employed in physics. Wonder what your thoughts on this are."

First there was the equation on page 3 that represent P, M, and B (physics, math and the human brain), showing their integral interconnection. I provide examples on page 3 & 5 in "Math's Applications" and "Math's Quantum Modeling" section on how math's use in modeling and algorithms, including lines of programming code containing the algorithms that mathematically tie physics concepts together with the LHC, DNA and quantum biology studies and successes.

My conclusion on page 7 shows how these connections of the brain, math and physics are vital in the stellar progress we've had in all physics but especially in those areas I cite.

Thank you both for reading my essay.

Jim

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Dear Anshu,

Dear Tejinder,

You are anti-Platonists (or rather non-Platonists), and I am a Platonist aware of all difficulties this option represents. But similar difficulties do undermine ALL options that could be discussed within the framework of this contest. Personally I see (i) this contest as a philosophical one and (ii) philosophy as the choice to focus on issues that do not...

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Dear Tejinder,

You are anti-Platonists (or rather non-Platonists), and I am a Platonist aware of all difficulties this option represents. But similar difficulties do undermine ALL options that could be discussed within the framework of this contest. Personally I see (i) this contest as a philosophical one and (ii) philosophy as the choice to focus on issues that do not...

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Dear Peter,

Many thanks for your kind remarks, and your detailed and incisive comments. We will respond after understanding them carefully and reading your essay, by later next week.

Kind regards,

Anshu, Tejinder

Many thanks for your kind remarks, and your detailed and incisive comments. We will respond after understanding them carefully and reading your essay, by later next week.

Kind regards,

Anshu, Tejinder

Dear Peter,

After leaving a post on your essay, we returned again to your comments above and re-read them...you undoubtedly express your stance very clearly - namely that using cognition to understand cognition is also metaphysics. We respectfully tend to disagree, and made some remarks to this effect on your page and perhaps one could avoid repeating them here. Principally we are saying that in considering a cognitive basis for the physics-maths connection there is at least hope for making a scientific model. As opposed to when one half, the mathematical half, is an immaterial reality - at least for now, until and unless, as you say, brains develop channels to communicate directly with such mathematical reality.

One further remark ... if we ask why does the world NOT exist rather than existing, we feel one day physics will give us an answer to that. Thus instead of relegating this question to a metaphysical realm, we want to think of it as a currently unsolved problem in physics.

Your criticism of the cognitive approach as being metaphysical is incisive and very clear, and trying to defend it has helped us understand our position better. We appreciate the dialogue you have initiated and will be happy to carry it further. Thank you.

Best regards,

Anshu, Tejinder

After leaving a post on your essay, we returned again to your comments above and re-read them...you undoubtedly express your stance very clearly - namely that using cognition to understand cognition is also metaphysics. We respectfully tend to disagree, and made some remarks to this effect on your page and perhaps one could avoid repeating them here. Principally we are saying that in considering a cognitive basis for the physics-maths connection there is at least hope for making a scientific model. As opposed to when one half, the mathematical half, is an immaterial reality - at least for now, until and unless, as you say, brains develop channels to communicate directly with such mathematical reality.

One further remark ... if we ask why does the world NOT exist rather than existing, we feel one day physics will give us an answer to that. Thus instead of relegating this question to a metaphysical realm, we want to think of it as a currently unsolved problem in physics.

Your criticism of the cognitive approach as being metaphysical is incisive and very clear, and trying to defend it has helped us understand our position better. We appreciate the dialogue you have initiated and will be happy to carry it further. Thank you.

Best regards,

Anshu, Tejinder

I did enjoy reading this essay which covers a wide ranging scope of topics in Mathematics, Physics and Cognitive Science.

I also enjoyed reading your technical end notes on Quantum Theory and completely agree with your assessment that quantum theory might be incomplete. I think you will enjoy reading my essay: 'solving the mystery' which addresses the four oddities that you mention in your essay. The problem is treated from a different conceptual viewpoint (the spacetime wave theory).

Best wishes

Richard Lewis

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I also enjoyed reading your technical end notes on Quantum Theory and completely agree with your assessment that quantum theory might be incomplete. I think you will enjoy reading my essay: 'solving the mystery' which addresses the four oddities that you mention in your essay. The problem is treated from a different conceptual viewpoint (the spacetime wave theory).

Best wishes

Richard Lewis

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Dear Anshu & Tejinder,

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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Dear Anshu and Tejinder,

I will start off with what will appear to be irrelevant observations (at least irrelevant to the shared subject matter).

Your writing style reflects a commitment to writing “flawlessly.” I don’t correct grammar or spelling of people who are committed to their thought, and let their writing be as it may.

In future issues of your essay (or parts...

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I will start off with what will appear to be irrelevant observations (at least irrelevant to the shared subject matter).

Your writing style reflects a commitment to writing “flawlessly.” I don’t correct grammar or spelling of people who are committed to their thought, and let their writing be as it may.

In future issues of your essay (or parts...

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Dear En,

Thank you for your candid remarks, and for pointing out the typos. We regret these errors and will correct them in a subsequent version. [We edited the essay together; and you are absolutely right - we were educated in India, with the medium of instruction being English (which is essentially British English), and then of course followed by lot of US texts in higher education! How you figure out something like that is beyond us :-)].

We are glad that we agree on the primitive origin of the force concept, and indeed we appreciate your remark that this captures the essence of our stance.

Kind regards,

Anshu, Tejinder

Thank you for your candid remarks, and for pointing out the typos. We regret these errors and will correct them in a subsequent version. [We edited the essay together; and you are absolutely right - we were educated in India, with the medium of instruction being English (which is essentially British English), and then of course followed by lot of US texts in higher education! How you figure out something like that is beyond us :-)].

We are glad that we agree on the primitive origin of the force concept, and indeed we appreciate your remark that this captures the essence of our stance.

Kind regards,

Anshu, Tejinder

Dear Anshu and Tejinder,

I have read your reply, and can now see that I did a terrible job of promoting your essay.

It was not my intention to make any subsequent readers think (and hopefully they will not) that your essay’s message could be abridged to something like what my (the relevant) paragraph says.

On the contrary. Your essay offers interesting and valuable insights, and yes, there is a ‘need to go into further details.’ Much is to be gained from reading every line of your essay, and consider the thoughts “contained” therein.

You were too polite in saying “…indeed we appreciate your remark that this captures the essence of our stance.” A less “polished” Westerner might have told me to go take a hike.

There is one question that you may still want to consider (and answer it to yourselves, or in a comment). It concerns this quote taken from page 1 of your essay: “Physics, on the other hand, is an experimental science (hence dependent on technology) of the world we observe, where experiments couple with great leaps of conceptual unification. The mathematics used in physics comes in only at a later stage, when we seek a precise language to describe the observed physical phenomena.”

The question that I had in mind is this. When you talk about physics in the quoted segment, are you thinking about physics as it is actually practiced, or as an idealized discipline (“that’s what physics ought to be”)? I am only asking whether you would like to make this distinction explicit.

I enjoyed your essay. It keeps the reader keen to learn more from each new observation you make.

En

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I have read your reply, and can now see that I did a terrible job of promoting your essay.

It was not my intention to make any subsequent readers think (and hopefully they will not) that your essay’s message could be abridged to something like what my (the relevant) paragraph says.

On the contrary. Your essay offers interesting and valuable insights, and yes, there is a ‘need to go into further details.’ Much is to be gained from reading every line of your essay, and consider the thoughts “contained” therein.

You were too polite in saying “…indeed we appreciate your remark that this captures the essence of our stance.” A less “polished” Westerner might have told me to go take a hike.

There is one question that you may still want to consider (and answer it to yourselves, or in a comment). It concerns this quote taken from page 1 of your essay: “Physics, on the other hand, is an experimental science (hence dependent on technology) of the world we observe, where experiments couple with great leaps of conceptual unification. The mathematics used in physics comes in only at a later stage, when we seek a precise language to describe the observed physical phenomena.”

The question that I had in mind is this. When you talk about physics in the quoted segment, are you thinking about physics as it is actually practiced, or as an idealized discipline (“that’s what physics ought to be”)? I am only asking whether you would like to make this distinction explicit.

I enjoyed your essay. It keeps the reader keen to learn more from each new observation you make.

En

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Dear En,

Greetings. No, we were not being polite! :-) We certainly thought you made a very good point by highlighting (using the example of force) that physical and mathematical concepts are built using metaphors based on primordial perceptions, and are not out there. But yes indeed we do expect and hope that an interested reader will read other parts of the essay too.

Regarding your latter question, we only had / have in mind physics as it is actually practiced, and not an idealized discipline. We honestly do not have much thought on what the idealised discipline should / would be like. Same for mathematics. It is more like: what is, is.

Best regards,

Anshu, tejinder

Greetings. No, we were not being polite! :-) We certainly thought you made a very good point by highlighting (using the example of force) that physical and mathematical concepts are built using metaphors based on primordial perceptions, and are not out there. But yes indeed we do expect and hope that an interested reader will read other parts of the essay too.

Regarding your latter question, we only had / have in mind physics as it is actually practiced, and not an idealized discipline. We honestly do not have much thought on what the idealised discipline should / would be like. Same for mathematics. It is more like: what is, is.

Best regards,

Anshu, tejinder

Dear Anshu,

Dear Tejinder,

I just have answered your post on my own page.

Best regards

Peter

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Dear Tejinder,

I just have answered your post on my own page.

Best regards

Peter

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Dear Tejinder, Anshu,

This was definitely one of my favorite essays in the contest. Although I'd say - and I'm sure you agree - that the patterns underlying the natural world are observer independent, I agree that the written part of math which makes up the totality of human research in this domain, can only become manifest through development brought by intelligent beings. I enjoyed a lot the part in which you bring evidence about the pattern recognition hard-wiring in the brain from cognitive science as I was unaware by some of the research you mentioned, research which is extremely interesting.

However for me the icing on the cake were the technical notes. With those alone and you would have had, in my opinion, more than enough material to participate in this contest. In there I found a very mature and original treatment of long lingering problems. I will have to read at least a couple of references, namely 21 and 22 as they sound extremely interesting. One naive question if I may, can I ask which theorem is referenced here: "* However, a no-go theorem forbids that, so long as X is an ordinary (commutative) manifold*"?

Thank you again for a most interesting read and wish you good luck in the contest! Should you have the time to read my essay, your comments are much appreciated.

Warm regards,

Alma

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This was definitely one of my favorite essays in the contest. Although I'd say - and I'm sure you agree - that the patterns underlying the natural world are observer independent, I agree that the written part of math which makes up the totality of human research in this domain, can only become manifest through development brought by intelligent beings. I enjoyed a lot the part in which you bring evidence about the pattern recognition hard-wiring in the brain from cognitive science as I was unaware by some of the research you mentioned, research which is extremely interesting.

However for me the icing on the cake were the technical notes. With those alone and you would have had, in my opinion, more than enough material to participate in this contest. In there I found a very mature and original treatment of long lingering problems. I will have to read at least a couple of references, namely 21 and 22 as they sound extremely interesting. One naive question if I may, can I ask which theorem is referenced here: "

Thank you again for a most interesting read and wish you good luck in the contest! Should you have the time to read my essay, your comments are much appreciated.

Warm regards,

Alma

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Dear Alma,

Thank you for reading our essay, and for your very kind remarks. Yes, we very much agree with you on the observer independence of the physical world.

The no-go theorem is due to John Mather - the original reference is his paper

"Simplicity of certain groups of diffeomorphisms" Bulletin of the American Mathematical Society 80, 271 (1974).

It is briefly discussed in context by Connes on p. 39-40 of his elegant review (our Ref. 29):

http://arxiv.org/pdf/math/0011193v1.pdf

The theorem's content being that the diffeorphism group of a connected ordinary manifold is simple, and hence cannot have a nontrivial normal subgroup, thereby disallowing the desired semi-direct product structure one is seeking.

We look forward to reading your essay within the next few days, and if possible, leave our comments on your page.

Thank you again, and kind regards,

Anshu, Tejinder

Thank you for reading our essay, and for your very kind remarks. Yes, we very much agree with you on the observer independence of the physical world.

The no-go theorem is due to John Mather - the original reference is his paper

"Simplicity of certain groups of diffeomorphisms" Bulletin of the American Mathematical Society 80, 271 (1974).

It is briefly discussed in context by Connes on p. 39-40 of his elegant review (our Ref. 29):

http://arxiv.org/pdf/math/0011193v1.pdf

The theorem's content being that the diffeorphism group of a connected ordinary manifold is simple, and hence cannot have a nontrivial normal subgroup, thereby disallowing the desired semi-direct product structure one is seeking.

We look forward to reading your essay within the next few days, and if possible, leave our comments on your page.

Thank you again, and kind regards,

Anshu, Tejinder

Oh, I see, thank you very much for explaining it, now it makes perfect sense! And thank you for the reference!

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Dear Tejinder, Anshu,

Thank you for your insightful comment! I enjoyed very much answering to your question!

Warm regards,

Alma

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Thank you for your insightful comment! I enjoyed very much answering to your question!

Warm regards,

Alma

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Dear Anshu,

I'm so sorry for the confusion I made and I'm very glad you realize it was a slip. I'm especially sorry for it since I appreciate your work. Thank you very much for being so nice and understanding :)

Alma

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I'm so sorry for the confusion I made and I'm very glad you realize it was a slip. I'm especially sorry for it since I appreciate your work. Thank you very much for being so nice and understanding :)

Alma

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Dear Anshu and Tejinder,

Thank you for the beautiful and insightful essay. While most essays discussed the unreasonable effectiveness of mathematics in physics, your essay comes with the fresh view that the effectiveness in both math and physics is due to the human mind. I fully agree with what you said, "Theoretical physics should be thought of as a branch of mathematics, whose axioms are...

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Thank you for the beautiful and insightful essay. While most essays discussed the unreasonable effectiveness of mathematics in physics, your essay comes with the fresh view that the effectiveness in both math and physics is due to the human mind. I fully agree with what you said, "Theoretical physics should be thought of as a branch of mathematics, whose axioms are...

view entire post

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Dear Sing Tejinder :

Certainly, your essay shows a great comprehension of the world of mathematics and physics. I agree with you on many points.

The human brain is divided into two hemispheres, the left is masculine, active, extroverted. called "rational". while, the right is female, passive, introverted, called "irrational,"

the same thing can be said about courage and fear, which are two primitive moods .

The most important thing is that these two opposite positions, are always present.

in mathematical term (X + 1) and (X - 1) are two limits, represent the needle of the scale.

You wrote: "Einstein and Bohr on a firm mathematical footing, in their extremely elegant and universal equations".

The standard Bohr's atomic model is not complete, because it does not explain the origin of the polarìzation, pace, time and force..... The General relativity, in addition to this, explains the GRAVITY incorrectly, "the mere presence of a massive body can not bend the space".

The answer to this question leads us inside of the "theory of everything".

The Bi-iterative model has already the answer, the theory of everything exist and real.

Sincerly yours

Bannouri

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Certainly, your essay shows a great comprehension of the world of mathematics and physics. I agree with you on many points.

The human brain is divided into two hemispheres, the left is masculine, active, extroverted. called "rational". while, the right is female, passive, introverted, called "irrational,"

the same thing can be said about courage and fear, which are two primitive moods .

The most important thing is that these two opposite positions, are always present.

in mathematical term (X + 1) and (X - 1) are two limits, represent the needle of the scale.

You wrote: "Einstein and Bohr on a firm mathematical footing, in their extremely elegant and universal equations".

The standard Bohr's atomic model is not complete, because it does not explain the origin of the polarìzation, pace, time and force..... The General relativity, in addition to this, explains the GRAVITY incorrectly, "the mere presence of a massive body can not bend the space".

The answer to this question leads us inside of the "theory of everything".

The Bi-iterative model has already the answer, the theory of everything exist and real.

Sincerly yours

Bannouri

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Dears Anshu and Tejinder,

I fully agree that a connection between physics and mathematics, if to be explained, must be rooted in cognitive science.

Your essay makes very important remarks, not often seen, notably that the mathematics involved in physics are relatively simple (and many current theoretical physics explorations seem to be just picking randomly in the...

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I fully agree that a connection between physics and mathematics, if to be explained, must be rooted in cognitive science.

Your essay makes very important remarks, not often seen, notably that the mathematics involved in physics are relatively simple (and many current theoretical physics explorations seem to be just picking randomly in the...

view entire post

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