Is Mathematics Fundamental? by Ajay Pokhrel

Dear Ajay,

I think FQXi.org might be trying to find out if there could be a Natural fundamental. I am surprised that so many of the contest's entrants do not appear to know what am fundamental to science, or mathematics, or quantum histrionics.

Joe Fisher, Realist

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.

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

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聽cannot聽be聽derived聽from聽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

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 theory.....

............. very nice essay.... I highly appreciate your essay and hope for reciprocity ....You may please spend some of the valuable time on Dynamic Universe Model also and give your some of the valuable & esteemed guidance

Some of the Main foundational points of Dynamic Universe Model :

-No Isotropy

-No Homogeneity

-No Space-time continuum

-Non-uniform density of matter, universe is lumpy

-No singularities

-No collisions between bodies

-No blackholes

-No warm holes

-No Bigbang

-No repulsion between distant Galaxies

-Non-empty Universe

-No imaginary or negative time axis

-No imaginary X, Y, Z axes

-No differential and Integral Equations mathematically

-No General Relativity and Model does not reduce to GR on any condition

-No Creation of matter like Bigbang or steady-state models

-No many mini Bigbangs

-No Missing Mass / Dark matter

-No Dark energy

-No Bigbang generated CMB detected

-No Multi-verses

Here:

-Accelerating Expanding universe with 33% Blue shifted Galaxies

-Newton's Gravitation law works everywhere in the same way

-All bodies dynamically moving

-All bodies move in dynamic Equilibrium

-Closed universe model no light or bodies will go away from universe

-Single Universe no baby universes

-Time is linear as observed on earth, moving forward only

-Independent x,y,z coordinate axes and Time axis no interdependencies between axes..

-UGF (Universal Gravitational Force) calculated on every point-mass

-Tensors (Linear) used for giving UNIQUE solutions for each time step

-Uses everyday physics as achievable by engineering

-21000 linear equations are used in an Excel sheet

-Computerized calculations uses 16 decimal digit accuracy

-Data mining and data warehousing techniques are used for data extraction from large amounts of data.

- Many predictions of Dynamic Universe Model came true....Have a look at

http://vaksdynamicuniversemodel.blogspot.in/p/blog-page_15.html

I request you to please have a look at my essay also, and give some of your esteemed criticism for your information........

Dynamic Universe Model says that the energy in the form of electromagnetic radiation passing grazingly near any gravitating mass changes its in frequency and finally will convert into neutrinos (mass). We all know that there is no experiment or quest in this direction. Energy conversion happens from mass to energy with the famous E=mC2, the other side of this conversion was not thought off. This is a new fundamental prediction by Dynamic Universe Model, a foundational quest in the area of Astrophysics and Cosmology.

In accordance with Dynamic Universe Model frequency shift happens on both the sides of spectrum when any electromagnetic radiation passes grazingly near gravitating mass. With this new verification, we will open a new frontier that will unlock a way for formation of the basis for continual Nucleosynthesis (continuous formation of elements) in our Universe. Amount of frequency shift will depend on relative velocity difference. All the papers of author can be downloaded from "http://vaksdynamicuniversemodel.blogspot.in/ "

I request you to please post your reply in my essay also, so that I can get an intimation that you replied

Best

=snp

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.pdf 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.

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

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

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!

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 area overpowered. Ordinarily I would have reduced sail, but this day I felt differently. My contemplations were on the forces of nature, and I was ventured seaward increasingly amongst them. As the wind and the waves rose, my boat came under strain, but I was exhilarated. All the while I considered, how might I communicate the role of natural forces in understanding of the world around us. For they are surely it's central theme.

Beyond my essay's introduction, I place a microscope on the subjects of universal complexity and natural forces. I do so within context that clock operation is driven by Quantum Mechanical forces (atomic and photonic), while clocks also serve measure of General Relativity's effects (spacetime, time dilation). In this respect clocks can be said to possess a split personality, giving them the distinction that they are simultaneously a study in QM, while GR is a study of clocks. The situation stands whereby we have two fundamental theories of the world, but just one world. And we have a singular device which serves study of both those fundamental theories. Two fundamental theories, but one device? Please join me in questioning this circumstance?

My essay goes on to identify natural forces in their universal roles, how they motivate the building of and maintaining complex universal structures and processes. When we look at how star fusion processes sit within a "narrow range of sensitivity" that stars are neither led to explode nor collapse under gravity. We think how lucky we are that the universe is just so. We can also count our lucky stars that the fusion process that marks the birth of a star, also leads to an eruption of photons from its surface. for if they didn't then nebula gas accumulation wouldn't be halted and the star would again be led to collapse.

Could a natural organisation principle have been responsible for fine tuning universal systems? Faced with how lucky we appear to have been, shouldn't we consider this possibility?

For our luck surely didnt run out there, for these photons stream down on earth, liquifying oceans which drive geochemical processes that we "life" are reliant upon. The Earth is made up of elements that possess the chemical potentials that life is entirely dependent upon. Those chemical potentials are not expressed in the absence of water solvency. So again, how amazingly fortunate we are that these chemical potentials exist in the first instance, and additionally within an environment of abundant water solvency such as Earth, able to express these potentials.

My essay is an attempt at something audacious. It questions the fundamental nature of the interaction between space and matter Guv = Tuv, and hypothesizes the equality between space curvature and atomic forces is due to common process. Space gives up an energy potential in exchange for atomic forces in a conversion process, which drives atomic activity. And furthermore, that Baryons only exist because this energy potential of space exists, and is available for exploitation. Baryon characteristics and behaviours, complexity of structure and process might then be explained in terms of being evolved and optimised for this purpose and existence. Removing need for so many layers of extraordinary luck to eventuate our own existence. It attempts an interpretation of the above mentioned stellar processes within these terms, but also extends much further. It shines a light on molecular structure that binds matter together, as potentially being an evolved agency that enhances rigidity and therefor persistence of universal system. We then turn a questioning mind towards Earths unlikely geochemical processes, (for which we living things owe so much) and look at its central theme and propensity for molecular rock forming processes. The existence of chemical potentials and their diverse range of molecular bond forming activities? The abundance of water solvent on Earth, for which many geochemical rock forming processes could not be expressed without? The question of a watery Earth? is then implicated as being part of an evolved system that arose for purpose and reason, alongside the same reason and purpose that molecular bonds and chemical process arose.

By identifying process whereby atomic forces draw a potential from space, we have identified means for their perpetual action, and their ability to deliver perpetual work. Forces drive clocks and clock activity is shown by GR to dilate. My essay details the principle of force dilation and applies it to a universal mystery. My essay raises the possibility, that nature in possession of a natural energy potential, will spontaneously generate a circumstance of Darwinian emergence. It did so on Earth, and perhaps it did so within a wider scope. We learnt how biology generates intricate structure and complexity, and now we learn how it might apply for intricate structure and complexity within universal physical systems.

To steal a phrase from my essay "A world product of evolved optimization".

Best of luck for the conclusion of the contest

Kind regards

Steven Andresen

Darwinian Universal Fundamental Origin

Dear Ajay聽Pokharel聽 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.

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,