Mathematics is Physical by Sara Walker

Dear Sara:

The title of your essay "Mathematics is Physical" instantly grabbed my attention and made it the first essay I read. It was so because my idea is that we are math -- this is the title of my essay, in fact. Thus, I also believe math is physical, but in a more profound and complete way: we and all reality are made of mathematics. Since the mathematicians Cantor, Gödel and Turing showed that non-computable numbers and mathematics are uncountably infinitely more than computable numbers and math, they allow for non-computable phenomena that could explain everything from radioactive decay to life, consciousness, feelings and intelligence. Please read my essay and let me know what you think.

Best,

Luis F Patino

Dear Prof Sara Walker...

Your wonderful analysis in your essay is simple and straight forward... Your words.......... The first emerged in the scientific revolution of the 17th century with Newton's mathematical formulation of laws of physics in terms of an initial state and fixed, deterministic laws.Here the laws/math is immutable and unchanging and are not part of the structure of reality.

The second emerged in the 20th century with an algorithmic view of nature, where the "laws" often depend, in part, on the current state of the system in a computational view, or the current objects in a more physical one.Thus far, these two perspectives have been applied to different domains of science: the Newtonian legacy for physical systems, and the more recent "algorithmic" or "state/object -dependent" view for complex biological and technological systems. .................

using the first part, Dynamic Universe Model gave lot os good results and prediction using it as a N-Body problem solution. May please have look at my essay A properly deciding, Computing and Predicting new theory's Philosophy

In an similar way I want to do second part for quantum physics and consciousness...

Sara come on, lets do math for the 15 th model

Best Regards

=snp

Hi Sara,

"To parallel the hard problem of consciousness, this is considered to be the hard problem of matter - we do not know in of itself what matter is beyond our mathematical descriptions of its interactions."

Also from within the hard problem of consciousness, we do know for sure that phenomenal matter is what it is--it has a phenomenal thatness and a whatness such that knowing it directly we can categorise it, count it, put it in different piles and manipulate it. And that is all phenomenal information, or phenomenal patterns, that we can remember and pass on to the next gen and the next until suddenly we've gone from stone axes to ejecting matter into space!

I really enjoy your open minded take on information, evolutionary biology, and physics, and it's fascinating how phenomenal patterns can be communicated over and over via so many different material media, from the neuronal structure of our CNS to body language, vocal acoustic patterns, rock markings to the latest online quirk circuits emulating a quantum computer. I understand mathematical patterns as the most abstract and so the most cross-cultural of phenomenal pattern making in general. And I'd like to think of 'physical reality' as somehow fundamentally a reality of patterns/information that requires pattern observers in order for the universe to become a real pattern. So the potential for patterns must pre-exist biology but somehow also need biology to organise the patterns ...!

How far have you got thinking through the relation between our observed information structures and a new physics that can describe that observational feedback loop?

Cheers,

Malcolm Riddoch

Dear professor Walker,

concluding your essay you state:

"We need to explain a transition from physics where abstractions and relations are descriptive to one where they are also causal."

Permit my lengthy response.

Now, assuming that Newtonian physics is a "descriptive" model of nature and quantum mechanics is a "causal" model, my response to your task has been to assume that in a Wheelarian participatory universe we as different minds are actually different norms (normals) for describing the evolutions of light. Meaning, we are parts of the same cosmic system of wave we are attempting to describe/measure. And we each are unique probe energies (e.g. a unique Planckian quantum or Einsteinian photon) for describing nature.

This should make a mind actually a Markov property i.e. own initial and final condition of physical information.

It becomes clear why a mind cannot possibly renormalize gravitation, this is precisely because it as the norm/normal in the first place the unit for categorizing observable nature as either constructive or destructive interference (matter or antimatter; classical or quantum). The mind is by definition therefore the point of transition you seek.

This can become somewhat a case of the egg versus the hen, which came first. But the point I make now is that modelled as by definition the operative norm of gravitation (e.g. as the holographic vent horizon or graviton or quantum vacuum or cosmological constant proper), the mind/observer actually is source and sink of the difference it seeks to explain.

What then is required to bridge the gap between classical and quantum descriptions of nature is to first accept this. Accept that a mind is by definition a unique norm of gravitation i.e. physically speaking the self-referencing state proper of Gödel's theorem (and therefore own Landauer limit or "entropy").

Changing oneself or changing one's mind (to the extent this actually is possible) is equivalent to changing one's perspective of what constitute classical versus quantum physics; these classifications are then relative as must be in principle any arrow of time or any distinction between classical and quantum physics.

Progress in the physics of quantum gravity will consist then in the mind (life) accepting itself as being by definition a unique de facto definition of "nothing" namely per se the quantum vacuum (entropy).

In dispersion terms a mind would be perhaps a unique constant/unit refractive index (free space) of primordial speed of light. In own ranking of interferences a mind will be thus own unique undecidable of Gödel's theorem -- neither quite constructive nor destructive interference (neither quite wave nor corpuscular nature; neither quite matter nor antimatter). One can otherwise think of a mind as the birefringent -- the so-called "graviton".

In the specific sense then that it is at once the natural unit and natural limit of physical information the mind represents actually the quantum gravity scale. This may actually hint at the non-linear electromagnetism of Yang-Mills theory.

Mathematically, I think thus of a mind as the number basis (the imaginary unit) wherein the observable(s) are the so-called natural or real numbers. Physically, I think of a mind as in any observable dispersion relation i.e. spectral line of primordial speed of light actually the operative constant/unit refractive index. It is indeed same termed the holographic event horizon or "free space" -- strictly, the quantum vacuum.

Chidi Idika (forum topic: 3531)

This may sound crass, but I actually submitted my essay this year in the hope that you will perhaps find the time to read it, seriously. And, may be, give me your piece of judgement (forum topic: 3531).

Dear Professor. I. S. Walker

It's nice to participate again on this contest with an excellent essay, like the one you wrote some years ago with the title "Is life Fundamental", I keep it in my record and read it again and again.

Your new essay reminds me the Platonic world of ideas or to put it differently the Platonic world of mathematical forms, which as you write "being driven into existence by technology"

I wonder if mathematics is a human invention or they exist by themselves and remain to be discovered by us? Does a perfect circle exist somewhere in the world of ideas? Does the number pi (π) exist by itself or is an Archimedean artifice?

Your essay opens new perspectives and ideas to be discuss.

Best Regards

Basileios Grispos

Hi Sara,

I really enjoyed the format of your essay. I completely forgot it was a dialogue until the last sentence.

You mentioned that ``a transformation that cannot be caused... amounts to the physical equivalent of an uncomputable function''. If I understand correctly, a universal constructor cannot construct the necessary physical transformation---given it's resources---without violating a particular symmetry, then this is equivalent to an uncomputable function? In this sense, a universal constructor abides by the Church-Turing-Deutsch principle?

If so, do you think a local universal constructor exist without violating the second law of thermodynamics, which for an open system does not exhibit time reversal symmetry?

I had touched on some very similar ideas in my essay Noisy Machines.

Thanks!

Michael

Dear Sara Walker,

It is quite a relief to read an essay about insightful thoughts. Unfortunately much theoretical physics is influenced by the masculine nature. Too much focused on irrelevant details, in combination with the bad habit to uplift these details - with the help of the authority of previous physicists - to the desired status of a hypothetical "new corner stone" (actually, it is too much influenced by the love of competition). This in contrast with the opinion of ancient meta-physicists who argued that every thought must be true (in relation to the properties of the creating underlying reality).

It is the scientific culture that forces everyone to express the own thoughts in a way that can be exchanged as "valid information". But it is a hindering straitjacket too and it is limiting scientific progress. So I really like your essay! ;-))

With kind regards, Sydney

Dear Sara,

Congratulations on such a fine essay. Your essay is information dense and deserves a second reading. I kept picking up on ideas that I had previously missed or hadn't fully connected.

Tegmark suggests the Universe is a mathematical structure. I, on the other hand, believe the Universe is purely physical, and it is our job to discern the laws, which we do by constructing ontologies that are both mathematical and conceptual. In my area of interest, particle physics, the scale makes the force laws simpler to handle. At the scale of humans complexity reaches its limits as we currently know. At lesser scales emergent phenomena occur in a myriad of ways, which we generally quantify successfully with mathematics. But logic and math have their limitations, which our purely physical Universe ignores. Whilst our scientific method shines as a beacon for discovery, our experiments and their interpretations are generally flawed, but are slowly improving. At the scale of sub-atomic particles the going gets tough as our current best tools are quantum field theories that do not allow us to see clearly through the fog of accelerator data. The particle ontology needs a shake-up. Wolfram is trying a new way, by using 3D cellular automata, to visualise structure at these scales. His efforts can be short tracked by using rules that correctly manage the true symmetries of charge and spin.

Your essay touches on many of these ideas. I discuss the idea of relative presentism, which covers how 'abstractions exist and interact with the material world'. You say "we do not know in of itself what matter is beyond our mathematical descriptions of its interactions.". I would argue that to describe matter (say a fundamental particle) we need to describe both its properties (volume, charge, spin) and its force laws (attraction, repulsion, strength of action), which is a point that you also cover later in your essay. I enjoyed reading about constructor theory which you detailed very well.

We both have common ground in the notion of causality, which is where my idea of presentism shines.

I hope you can also comment on my essay.

Best wishes,

Lockie Cresswell

Sara interesting essay -- "caused" me to think about causes and other items in your essay. 1.your desire to "probe the Intersections of mathematics and physical matter. In my essay I introduce a self creating process that produces "all ordered existence" which includes all intelligence, the complete physical world and the self creation that produces all three. It is a very different process. It begins with the conversion of chaos to order. It overcomes entropy. The originating process is a C*s to SSCU conversion. It is described in the appendix of my essay. Subsequent self replication/self organization of that foundation eventually scales up to become the physical world, all intelligence and their interwoven SSC processing. For point 1. The important aspect is that this originating transformation is also the "foundation-fundamentals" of SSC mathematics, computations, philosophy, life, humanity, language, etc. and its scale up then becomes them. SSC processing produces its own mathematics and computations and "maps" them to the physical constructs as it progresses. That is why they are so useful in explaining physics. 2. The C*s described in my essay can change shape without changing value. So accumulations of C*s shape changing can "blend" to become a perfect circle or perfect sphere. This gets rid of the need for impossible computer pathways to attain perfection. 3.,Abstractions generalize information for transfer. So specifics to abstractions to transfer needs an equivalent process to retrieve the original specifics. If you have the transformation codes and the transfer routes you never lose the original information. That is why the the two sets of equivalent and opposites processes of SSCU and self it's scale up to become the universe never loses its information 4. the entire SSC processing is based on inverse logic 5.,The C*s to SSCU processing origination followed by self replication and self organizing is the primordial ancestor of "living processes. It is analogous to the processing that created the biological and psychological processes worlds and their integration in the progressive processing that became humanity. Is the universe alive? Are we descendants of the original SSCU? I would appreciate your comments on my essay and how it fits with your essay. Thanks John Crowell

Hi Sara!

This is a wonderfully written essay! I very much enjoyed the thought experiment as well, that was very funny. Actually, last year I had been led down a similar coding problem that says "Write the best algorithm that exactly calculates pi." But on a computer, or in physical reality, a perfect circle doesn't really exist so any answer would be an approximation.

I wonder if the discrepancy between our mathematical laws and ideas and physical reality is due to the state space we choose. I'd almost argue that physical reality does not have an inherent state space, but instead humans and other biological entities create their own state spaces to interact with reality. I'd be really interested to see what you think about these ideas that I outline in my essay.

In general, I think that constructor theory hints at a need to embed "knowledge", which I interpret as being a way to encode states in a particular state space. Do you have any thoughts about this? Particularly if constructor theory could offer insight on how humans/agents create these state spaces and encode states within them?

Cheers!

Alyssa

Dear Sara,

I like the style of the essay. On the concept "Information is physical", this topics was discussed in the previous essay contest "It From Bit or Bit From It?". I wrote the essay as the selected essay of the publication finally. As pointed out in the previous essay, this concept was developed in Leon Brillouin, who wrote the book "Science and Information Theory". What do you think about this concept?

In this time, I wrote the similar sense of the thought as seen my essay. This was pointed from the viewpoint between computation (not math) and physics. I hope that you enjoy reading my essay as well.

Best wishes,

Yutaka

I agree that mathematics/information is physical, and want to note something I thought of while reading your essay (that I'm sure you already thought of long before me).

It's easy to argue endlessly about whether mathematics or mathematical objects exist in some Platonic realm. But our ideas about mathematical objects are most certainly physical, in the following sense. When I think of a perfect circle, the neurons in my brain fire a certain way: there is some physical configuration of my brain associated with thinking about a perfect circle, or any other mathematical object I'm familiar with. When other people think about perfect circles, their neurons might fire in a different way, so that the 'same' information is stored differently. Regardless of how each of us stores that information, we can all access and output it in different forms, like as lines on paper or algebraic equations on a blackboard. Someone else can learn about circles by studying these different representations, and store their own representation of one. The mathematical idea of a perfect circle physically exists as the collection of all instantiations of the associated information.

How much energy is spent every day on the storage, retrieval, and communication of some mathematical idea? I wonder.

It's a little mind-bendy to think about abstract ideas having causal power in a physical universe. But it makes more sense to me when I remember that information, mathematical or otherwise, must be stored in some physical configuration of matter. Only physical things can have causal power in a physical universe, I think.

Appreciate the beautiful, deliberate writing. The beginning felt like a novel, and I got 'hooked' for the rest of your essay.

John

Dear Sara,

thanks for thought-provoking, stimulating essay. I am glad to notice that there are also several elements of agreement between our ideas, mostly based on the fundamental limitation of information (if you have time, I would be glad to receive your feedback on my essay). But your idea that mathematical abstraction can have causal consequesnces is indeed very interesting, although not spelled out in full detail.

Anyways, great job, I hope you will get the visibility your essay deserves. From my side, I gave you the highest rate.

All good wishes!

Flavio

Beautiful essay there on Human cognition.rated you accordingly.Does cognitive selection Bias play a role.in our view of the universe ? please read here https://fqxi.org/community/forum/topic/3525.All the Best in the contest.

Dear Sara,

This essay is well written. You help the reader by setting up a scene, introducing characters and telling a story in the course of explaining complex concepts. There are still points I need help understanding.

Please tell me if I have this correct. Current physics is deterministic as an example; two objects collide due to their speed and direction. Life is not deterministic as an example; two birds or two humans with the same speed and direction as inanimate objects destine for a collision miss, because of knowing action. Ideas have a physical component be it brain chemistry, marks on a page or electrical states of a silicon chip. Mathematics is physical and therefore must reflect the physical world. Physics of inanimate objects, such as Newtonian mechanics, falls short because the actions of life (Biology) are not included. Instead of working Physics up to life, we should work Biology down to Physics.

I have not yet rated this (or any other essay), but I will give your essay high marks.

Sincerely,

Jeff Schmitz

Dear Prof Sara

I got a very nice introduction to you from Prof. Malcolm Riddoch, this post is about furthering that discussion...

This is my second post

I mainly worked in cosmology , I am yet to enter into the world of Quantum Physics, i will do that in discussion with you and your friends...

Meanwhile he asked me about my possible fundamental concepts??

These are the Fundamental concepts of Dynamic Universe Model taken from my essay, Have a look at my essay for further details....

C.1. Logical and Physical 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

C.2. Main ETHICAL foundational principles of Dynamic Universe Model:

-Human Accrued knowledge should be free to all

-Concept should come out from the depth of truth;

-Authors / Scientists thinking should go towards perfection;

-Logic should be simple

-Theory's predictions should be verifiable experimentally, by anyone and anywhere with the same conditions

-Computations / computer programs should be simple

-ontological realism of senses produced information

-New theory lead us forward into ever-widening thought and action experiments

-Let the new theory lead us into that heaven of freedom.

C.3. Main PHYSICAL and COSMOLOGICAL foundational principles of "N-Body problem solution: Dynamic Universe Model":

-Natural universe regularly undergoes change in shape due to mutual Dynamical

Gravitational forces.

-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.

Best wishes to your essay

=snp

Dear Professor Walker,

This was a delightful and thought provoking essay.

Sincerely,

Rastin Reza

Sara,

I'd like to remark only that such sort of ideas of Nature as Symmetry and Homochirality can be easy found even in pure number theory ( Riemann problem and problem of nonexistence of odd perfect number). It could be considered as additional arguments for your thesis?

Best

Michael Popov

Dear Sara,

I really enjoyed your essay! You got me thinking and changed my thinking, for which I am extremely grateful.

To be honest, I had a difficult time accepting your title. I think of mathematics as a precise description, a precise language. Later in your essay, you discuss this. But I couldn't accept mathematics as being physical.

But you really got me to think more carefully about what it means to be physical. Your focus on causality was brilliant as it was undeniable. Can non-physical things be causal? I would have to argue they couldn't be. Conclusion reached! Bravo!

Near the end of your essay, you discuss CPT and the second law, and note that the constraints placed by physics are not quite comparable to constraints placed by Godel, because "the laws of physics are formulated by us." I don't think that it is that simple. In some cases, the laws of physics are so constrained by mathematical symmetries (eg. associativity and distributivity) that they are essentially dictated by those symmetries. (see my essay for example as well as the paper by John Skilling and myself: https://arxiv.org/abs/1712.09725).

And with that understanding, it strikes me that perhaps it is possible that Godel's theorem could constrain our physical laws. This is a fascinating thought that had not really sunk in until after reading and thinking about your essay. I am surprised that it hadn't occurred to me at that level because I go as far in my essay to discuss how Tarskii's Theorem makes probability theory generally applicable. But understanding comes in degrees or levels, and after reading your essay, I feel that I have a deeper understanding.

Thank you again!

Kevin Knuth