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RECENT POSTS IN THIS TOPIC

**Ajay Pokhrel**: *on* 3/3/18 at 6:50am UTC, wrote Hello Kamal, In that case, I will certainly like to read your essay. I...

**Ajay Pokhrel**: *on* 3/3/18 at 6:47am UTC, wrote Hello Dizhechko Boris Semyonovich, Thank you for reading and commenting on...

**Ajay Pokhrel**: *on* 3/3/18 at 6:45am UTC, wrote Hello Steven, I will certainly look into your essay. Sorry to get back to...

**Kamal Rajpal**: *on* 2/26/18 at 17:34pm UTC, wrote Dear Ajay Pokhrel, I have read your essay but, disagree that maths is...

**Dizhechko Semyonovich**: *on* 2/25/18 at 18:04pm UTC, wrote Dear Ajay Pokharel your essay is the scientific picture of the world....

**Steven Andresen**: *on* 2/23/18 at 13:08pm UTC, wrote Dear Ajay If you are looking for another essay to read and rate in the...

**Ajay Pokhrel**: *on* 2/8/18 at 5:09am UTC, wrote Hello Jouko, Thank you for your motivating comment. Math is used to build...

**Ajay Pokhrel**: *on* 2/8/18 at 5:06am UTC, wrote Hello Don, Thank you for reading and commenting on my essay. I will visit...

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The impossibility of building a perfect clock could help explain away microscale weirdness.

FQXi FORUM

May 24, 2019

CATEGORY:
FQXi Essay Contest - Spring, 2017
[back]

TOPIC: Is Mathematics Fundamental? by Ajay Pokhrel [refresh]

TOPIC: Is Mathematics Fundamental? by Ajay Pokhrel [refresh]

Humans, from the beginning, have been trying to explain each phenomenon in the universe in the form of theories. We discovered Classical physics, Relativistic physics, Quantum Mechanics and several mysteries of the universe. Moreover, we are searching for something that unites every law of universe i.e. Theory Of everything (TOE). But what is it that we have really found between all these years and efforts? Isn’t it the mathematics and the patterns that we have actually developed? Indeed, yes! In this essay, I am going to discuss how our whole universe (Or multiverse), from tiny atoms to huge galaxies, depends on mathematics and numbers for its foundation and operation. The essay will discuss the strength of mathematics and patterns along with the breakthrough achieved with the help of these patterns. The essay will also try to show the relationship between several fields of science with the mathematics and numbers ultimately concluding that “Mathematics is fundamental”. The essay focuses on clarifying the physical laws and phenomena in the universe through mathematical perspective.

I am a high school student and an independent researcher from Nepal who is very enthusiastic in physics and mathematics. Last year, I submitted an essay named "Our Numerical Universe" which was still in top hundred among more than 200 essays. I participated to International Mathematics Olympiad from my country and am currently working on my own thesis. I look forward for your suggestions in the essay.

Dear Ajay Pokhrel,

Nature produced one single unified VISIBLE infinite surface occurring eternally in one single dimension that am always illuminated by mostly finite non-surface light millions of years before humanly contrived finite mathematical information ever became evident on earth.

Joe Fisher, Realist.

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Nature produced one single unified VISIBLE infinite surface occurring eternally in one single dimension that am always illuminated by mostly finite non-surface light millions of years before humanly contrived finite mathematical information ever became evident on earth.

Joe Fisher, Realist.

report post as inappropriate

Hello Joe Fisher,

Thank you for your comment.

I clearly understand that your thought is that the universe and its dimensions were created millions of years ago before the development of mathematics. I support your statement but what I meant by the essay is that our universe, even it was formed a long time ago, was formed with a pattern and exist as a pattern; a pattern of mathematics and numbers; a pattern of sequence and formulae, which concludes the fact that our universe might have mathematics as basis for its existence.

Kind regards

Ajay

Thank you for your comment.

I clearly understand that your thought is that the universe and its dimensions were created millions of years ago before the development of mathematics. I support your statement but what I meant by the essay is that our universe, even it was formed a long time ago, was formed with a pattern and exist as a pattern; a pattern of mathematics and numbers; a pattern of sequence and formulae, which concludes the fact that our universe might have mathematics as basis for its existence.

Kind regards

Ajay

Dear Ajay,

In your approach, I miss the efforts of Garrett Birkhoff and John von Neumann to establish a fundament that emerges into a suitable modeling platform. In their 1936 paper, they introduced a relational structure that they called quantum logic and that mathematicians call an orthomodular lattice. It automatically emerges into a separable Hilbert space, which also introduces a selected set of number systems into the modeling platform. Hilbert spaces can only cope with division rings and separable Hilbert spaces can store discrete values but no continuums. Each infinite dimensional separable Hilbert space owns a unique non-separable Hilbert space that embeds its separable partner. In this way, the structure and the functionality of the platform grow in a restricted way. After a few steps a very powerful and flexible modeling platform evolves. This model acts as a repository for dynamic geometric data that fit in quaternionic eigenvalues of dedicated operators. The non-separable part of the model can archive continuums that are defined by quaternionic functions.

In other words, the foundation that was discovered by Birkhoff and von Neumann delivers a base model that can offer the basement of well-founded theories and that puts restrictions on the dimensions which universe can claim.

Multiple Hilbert spaces can share the same underlying vector space and form a set of platforms that float on a background platform. On those platforms can live objects that hop around in a stochastic hopping path. This adds dynamics to the model.

The orthomodular lattice acts like a seed from which a certain kind of plant grows. Here the seed turns into the physical reality that we perceive.

The Wikiversity Hilbert Book Model Project investigates this approach.

https://en.wikiversity.org/wiki/Hilbert_Book_Model_

Project

http://vixra.org/author/j_a_j_van_leunen contains documents that treat some highlights of the project.

report post as inappropriate

In your approach, I miss the efforts of Garrett Birkhoff and John von Neumann to establish a fundament that emerges into a suitable modeling platform. In their 1936 paper, they introduced a relational structure that they called quantum logic and that mathematicians call an orthomodular lattice. It automatically emerges into a separable Hilbert space, which also introduces a selected set of number systems into the modeling platform. Hilbert spaces can only cope with division rings and separable Hilbert spaces can store discrete values but no continuums. Each infinite dimensional separable Hilbert space owns a unique non-separable Hilbert space that embeds its separable partner. In this way, the structure and the functionality of the platform grow in a restricted way. After a few steps a very powerful and flexible modeling platform evolves. This model acts as a repository for dynamic geometric data that fit in quaternionic eigenvalues of dedicated operators. The non-separable part of the model can archive continuums that are defined by quaternionic functions.

In other words, the foundation that was discovered by Birkhoff and von Neumann delivers a base model that can offer the basement of well-founded theories and that puts restrictions on the dimensions which universe can claim.

Multiple Hilbert spaces can share the same underlying vector space and form a set of platforms that float on a background platform. On those platforms can live objects that hop around in a stochastic hopping path. This adds dynamics to the model.

The orthomodular lattice acts like a seed from which a certain kind of plant grows. Here the seed turns into the physical reality that we perceive.

The Wikiversity Hilbert Book Model Project investigates this approach.

https://en.wikiversity.org/wiki/Hilbert_Book_Model_

Project

http://vixra.org/author/j_a_j_van_leunen contains documents that treat some highlights of the project.

report post as inappropriate

Dear Ajay,

I liked your Essay. You have pretty mature way of arguing about your point of view. I have also submitted my Essay in this context - wherein I have concluded Nature is too complex- and we human have a long way to go.

with regards

Brajesh Mishra

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I liked your Essay. You have pretty mature way of arguing about your point of view. I have also submitted my Essay in this context - wherein I have concluded Nature is too complex- and we human have a long way to go.

with regards

Brajesh Mishra

report post as inappropriate

Hello Ajay,

This is an excellent effort on your part. You argue your point very well.

While I do not think that Math is fundamental, many respected people do. They think of it as existing in the Platonic realm. I will concede that I think Math is the fundamental language of the universe. I also think that we will eventually have a one-to-one correspondence between Physics and Math.

Your youthful enthusiasm shines through much of your essay. Well done and good luck with your continued studies.

Best Regards,

Gary Simpson

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This is an excellent effort on your part. You argue your point very well.

While I do not think that Math is fundamental, many respected people do. They think of it as existing in the Platonic realm. I will concede that I think Math is the fundamental language of the universe. I also think that we will eventually have a one-to-one correspondence between Physics and Math.

Your youthful enthusiasm shines through much of your essay. Well done and good luck with your continued studies.

Best Regards,

Gary Simpson

report post as inappropriate

Dear Ajay Pokhrel,

a very good work, thank you for sharing, it was pleasurable to read – congratulations also being so young and yet insightful.

I'll be now a little provocative. You write that

> Mathematics cannot be derived from anything

but we learn mathematics through natural language (and gestures and so on), so couldn't it be this praxis even more fundamental?

Bests and good luck!

Francesco D'Isa

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a very good work, thank you for sharing, it was pleasurable to read – congratulations also being so young and yet insightful.

I'll be now a little provocative. You write that

> Mathematics cannot be derived from anything

but we learn mathematics through natural language (and gestures and so on), so couldn't it be this praxis even more fundamental?

Bests and good luck!

Francesco D'Isa

report post as inappropriate

Hello Francesco,

Thank you for reading and commenting on my essay.

To answer your question, I have already written something in my essay itself that mathematics is from the beginning and we are on the way to discover more things due to mathematics. I believe that mathematics cannot be derived and the natural language we used to discover numbers and patterns show that we are only discovering something that is already in existence.

Thank you

Best

Ajay Pokharel

Thank you for reading and commenting on my essay.

To answer your question, I have already written something in my essay itself that mathematics is from the beginning and we are on the way to discover more things due to mathematics. I believe that mathematics cannot be derived and the natural language we used to discover numbers and patterns show that we are only discovering something that is already in existence.

Thank you

Best

Ajay Pokharel

I understand your point, mine is that also mathematics has a relational nature, as I've written in my text. All the best, I enjoyed reading you!

Francesco

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Francesco

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Chi Ajay Pokhrel…

You discussed nicely… “I am going to discuss how our whole universe (Or multiverse), from tiny atoms to huge galaxies, depends on mathematics and numbers for its foundation and operation.” Now try these concepts of Dynamic Universe Model also…. Try to understand it ask me questions, I will guide you…dear Ajay Pokhrel, best wishes for your...

view entire post

You discussed nicely… “I am going to discuss how our whole universe (Or multiverse), from tiny atoms to huge galaxies, depends on mathematics and numbers for its foundation and operation.” Now try these concepts of Dynamic Universe Model also…. Try to understand it ask me questions, I will guide you…dear Ajay Pokhrel, best wishes for your...

view entire post

report post as inappropriate

Dear Ajay,

I've read with interest your Essay. I do understand that there is a strong consensus around the fact the mathematics is fundamental, but I've missed if this is because you can't do without to handle physics, or if it is believed to express some "intrinsic" property of Nature. If you refer to the second, I would suggest to reconsider this position. If you take for instance the work of D'Ariano (see just to make an example: http://www.qubit.it/research/publications/quant-ph0612162.pd

f but you may find many other references), mathematical structure is obtained as a consequence of information-related principles, which is a very different - and alternative - vision.

Anyway, congratulations for your work.

E.

report post as inappropriate

I've read with interest your Essay. I do understand that there is a strong consensus around the fact the mathematics is fundamental, but I've missed if this is because you can't do without to handle physics, or if it is believed to express some "intrinsic" property of Nature. If you refer to the second, I would suggest to reconsider this position. If you take for instance the work of D'Ariano (see just to make an example: http://www.qubit.it/research/publications/quant-ph0612162.pd

f but you may find many other references), mathematical structure is obtained as a consequence of information-related principles, which is a very different - and alternative - vision.

Anyway, congratulations for your work.

E.

report post as inappropriate

Hello Everyone,

Thank you for taking your time to read my essay.

As you can see that I am still a high school student and moving ahead with my passion for mathematics and physics, I would like all of you to criticise, suggest and give me ways to improve my essay.

You can vote whatever rate you think is suitable.

Kind Regards

Ajay Pokharel

Thank you for taking your time to read my essay.

As you can see that I am still a high school student and moving ahead with my passion for mathematics and physics, I would like all of you to criticise, suggest and give me ways to improve my essay.

You can vote whatever rate you think is suitable.

Kind Regards

Ajay Pokharel

Hi Ajay,

I would say that: Mathematical patterns exist and we discover them via language and a specialized symbolism. And they could be fundamental, and incomplete.

This is just a quibble. Your essay is super!

Do visit the essay of George Gantz and start a conversation with him. Do not be put off by the title of his essay. Read it, particularly the mathematics part.

You have a great future.

All the best,

Don Limuti

PS I believe calculus has been used beyond its usefulness. If interested see my website: digitalwavetheory.com

report post as inappropriate

I would say that: Mathematical patterns exist and we discover them via language and a specialized symbolism. And they could be fundamental, and incomplete.

This is just a quibble. Your essay is super!

Do visit the essay of George Gantz and start a conversation with him. Do not be put off by the title of his essay. Read it, particularly the mathematics part.

You have a great future.

All the best,

Don Limuti

PS I believe calculus has been used beyond its usefulness. If interested see my website: digitalwavetheory.com

report post as inappropriate

Hi Ajay

For a high school student your work is very well written and structured so that it is easy to understand.

I like how you connect your ideas and concepts. Though I think language itself is more fundamental than maths, it was an enjoyable read.

If maths is all then how do "numbers" become "flesh and blood" and the world we comprehend around, about and is us; and also how do you connect the purely maths with the purely physical. Maths has nothing that appears physical involved in it's construction yet it claims to be able to describe our reality.

Have you thought how a world without number or numbers would appear and then compare that with our world -- then you could really show if our world is fundamentally maths or not!

report post as inappropriate

For a high school student your work is very well written and structured so that it is easy to understand.

I like how you connect your ideas and concepts. Though I think language itself is more fundamental than maths, it was an enjoyable read.

If maths is all then how do "numbers" become "flesh and blood" and the world we comprehend around, about and is us; and also how do you connect the purely maths with the purely physical. Maths has nothing that appears physical involved in it's construction yet it claims to be able to describe our reality.

Have you thought how a world without number or numbers would appear and then compare that with our world -- then you could really show if our world is fundamentally maths or not!

report post as inappropriate

Hello Jouko,

Thank you for your motivating comment.

Math is used to build physical. For instance, the rocket we build is built using several laws of engineering and that also carries pattern and mathematics.

I tried to think of a world without numbers, but unfortunately, it does not exist because we cannot think of anything without math and number, from counting to inventing.

Thank you for your motivating comment.

Math is used to build physical. For instance, the rocket we build is built using several laws of engineering and that also carries pattern and mathematics.

I tried to think of a world without numbers, but unfortunately, it does not exist because we cannot think of anything without math and number, from counting to inventing.

Dear Ajay

If you are looking for another essay to read and rate in the final days of the contest, will you consider mine please?

A couple of days in and semblance of my essay taking form, however the house bound inactivity was wearing me. I had just the remedy, so took off for a solo sail across the bay. In the lea of cove, I had underestimated the open water wind strengths. My sail...

view entire post

If you are looking for another essay to read and rate in the final days of the contest, will you consider mine please?

A couple of days in and semblance of my essay taking form, however the house bound inactivity was wearing me. I had just the remedy, so took off for a solo sail across the bay. In the lea of cove, I had underestimated the open water wind strengths. My sail...

view entire post

report post as inappropriate

Dear Ajay Pokharel your essay is the scientific picture of the world. Try enter in it New Cartesian Physics, which is based on the principle of identity of space and matter of Descartes. You might like to look at the sky and it seems to you empty infinite space in which it moves large and small body. However, this impression is deceptive. According to the principle of identity of space and matter Descartes, space is matter that moves. When Copernicus asserted that the Earth revolves around the Sun, he had to add that along with the Earth revolves around the Sun, all the solar space. Space is what built the world. Space contains information about the development of the Universe . Take a look at my essay in which I showed how radically can change physics, if it will follow this principle. Leave your autograph. FQXi Fundamental in New Cartesian Physics by Dizhechko Boris Semyonovich

Do not allow New Cartesian Physics go away into nothingness, which can to be the theory of everything OO.

Sincerely, Dizhechko Boris Semyonovich.

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Do not allow New Cartesian Physics go away into nothingness, which can to be the theory of everything OO.

Sincerely, Dizhechko Boris Semyonovich.

report post as inappropriate

Dear Ajay Pokhrel,

I have read your essay but, disagree that maths is fundamental in physics. I believe that conceptual physics is more important than mathematical physics. If the concepts are not clear than we can end up with incorrect conclusions.

Quantum Mechanics claims that an electron can be both spin-up and spin-down at the same time. In my conceptual physics Essay on Electron Spin, I have proved that this is not true. Please read: https://fqxi.org/community/forum/topic/3145

We can be in touch even after this essay contest is over.

Kamal Rajpal,

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I have read your essay but, disagree that maths is fundamental in physics. I believe that conceptual physics is more important than mathematical physics. If the concepts are not clear than we can end up with incorrect conclusions.

Quantum Mechanics claims that an electron can be both spin-up and spin-down at the same time. In my conceptual physics Essay on Electron Spin, I have proved that this is not true. Please read: https://fqxi.org/community/forum/topic/3145

We can be in touch even after this essay contest is over.

Kamal Rajpal,

report post as inappropriate

Hello Kamal,

In that case, I will certainly like to read your essay. I think that mathematics is used to derive the laws of physics which of course exists already in the universe. Mathematics thus defines the universal law by giving form to it. Physics is what defines the law and mathematics is what represents these laws.

Good luck with your essay

Best Regards

Ajay Pokharel

In that case, I will certainly like to read your essay. I think that mathematics is used to derive the laws of physics which of course exists already in the universe. Mathematics thus defines the universal law by giving form to it. Physics is what defines the law and mathematics is what represents these laws.

Good luck with your essay

Best Regards

Ajay Pokharel

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