Mathematics is Physical by Sara Walker

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

PS! I think the two fundamental descriptions of the world are very related to the two figures I drew in my essay! I found an extremely interesting bridge between them from Marr: http://psych.colorado.edu/~oreilly/cecn/node11.html

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

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

Hi Sara,

A wonderful, thought-provoking essay. You describe two distinct descriptions of nature: 1) the mathematical formulation of laws (e.g. Newton's laws), and 2) the algorithmic view. For the mathematical formalism, laws apply to initial states. They are deterministic, they are fixed, and they are independent of physical reality. Mathematical formulations typically interpret physical change as deterministic. This applies to classical mechanics, relativity, and to isolated (and unobserved) quantum systems.

For the algorithmic formalism, in contrast, you state that "the laws often depend, in part, on the current state of the system." Algorithms update their description of physical state at each iteration and redefine the physical state at each time step. Updating a state for a probabilistic algorithm describes irreversible and random change at each time step. This leads to the "path-dependent, historical narratives characteristic of the object-dependent dynamics of the biosphere" that you describe.

You state that "unification of these two formalisms ... is essential for some of the most difficult frontiers in science such as the emergence of life..." However, both algorithmic and mathematical formalisms are fundamentally deterministic descriptions, whether their predictions are definite or probabilistic. As deterministic descriptions, both formalisms therefore apply to initial states, are fixed, and are independent of physical reality. The fundamental difference between the mathematical and algorithmic formulations is not in their formalisms; it is with their different interpretations of time and change. Unifying their formalisms is not the difficulty; the difficulty is unifying their interpretations.

In my essay, I argue that it is physical reality itself, not physical laws, that are contextually defined. Empirical observations of physics are best interpreted by invoking a contextual reality that is defined with respect to its positive-temperature ambient surroundings. Absolute zero is an unattainable idealization, as is its implication of fundamental determinism. Nature resets a system's contextual state every time the system interacts with its ambient surroundings. In the case of measurements, a system's actual ambient surroundings is the measurement apparatus (or observer), and this resets the system's state upon measurement or observation. This interpretation is compatible with the algorithmic interpretation, and it enables the unification of the two formalisms and their interpretations.

I would love to hear your thoughts on this.

Best,

Harrison

Dear Professor Walker,

Thank you for your thought provoking essay!

The line that really stuck with me was this:

"The power of mathematics is precisely in that it is information that can berobustly copied, meaning we can readily see its structure across very different systems, giving it'sumph in the scientific arena."

It left me wondering if this could be an explanation of the difficulties biologists encounter when applying mathematics to the living world (at least compared with the glaring success of mathematics in physics). For what one never sees in biology is precisely this copy fidelity. No child cell is an exact duplicate of its parent.

Best of luck in the contest!

Rick Searle

Hope you will reply your comments and have a look at my essay please

Best

=snp

Hi Sara,

As a follow-up to my previous comment, a logical consequence of the contextual interpretation that I described is a definition of functional complexity and a principle of spontaneous self-organization. See my Medium essay, The Arrow of Functional Complexity. I use the term homeostate in the essay, but it is identical to David Deutsch's constructor.

Harrison

'Whereas I cannot take charge and separate it from an electron.' The theory of weak quantum measurements can lead to so-called Cheshire cat states, where the electron is over here and the charge over there. But only in a statistical post-selection context. Not sure if this affects your argument. Second comment: the concept of infinity has an uncertain status. Does it have causal power? Example: Hawking predicted black hole radiance with a Bogoliubov transformation between in and out modes of a quantum field. To get his famous thermal result, he had to integrate to infinity. If the integral is truncated at, say, the Planck frequency, the black hole just emits a puff of radiation and not a steady flux. So all the paraphernalia of black hole entropy and the associated research flowed from the use of infinity as if it is a real thing operating in the real world. Is this an act of faith, a pragmatic assumption or a comment on the deep nature of physical reality?

Dear Sara,

I greatly appreciated your work and discussion. I am very glad that you are not thinking in abstract patterns.

"While unification of these two formalisms is not necessary for the domains of science where each is independently valid, it is essential for some of the most difficult frontiers in science such as the emergence of life, which arguably occurs when our traditional Newtonian approach to physics based on initial states and fixed, deterministic "laws" of physics must yield the to path-dependent, historical narratives characteristic of the object-dependent dynamics of the biosphere. We need to explain a transition from a physics where abstractions and relations are descriptive to one where they are also causal. She expounds on all of this to me and then asks "When can you do the math and explain this to me?""

While the discussion lasted, I wrote an article: "Practical guidance on calculating resonant frequencies at four levels of diagnosis and inactivation of COVID-19 coronavirus", due to the high relevance of this topic. The work is based on the practical solution of problems in quantum mechanics, presented in the essay FQXi 2019-2020 "Universal quantum laws of the universe to solve the problems of unsolvability, computability and unpredictability".

I hope that my modest results of work will provide you with information for thought.

Warm Regards, `

Vladimir

Hi Sara,

Good story, nice idea. My comments are partly covered in your essay, yet I wish to extend it for further clarification.

> .. that information, or abstractions have causal consequences. It is however difficult to explain this beyond mere anecdote.

No, it is not so difficult to see why information has causal consequence, only that we have to understand reality of information differently. From the first principles of constancy of causal relation in the nature of change, if an interaction among physical systems results in an observable state S of a physical system P, then S of P must remain congruent with, or correlate with the information of the causal context effecting the change. Otherwise, measurements do not have an interpretation relating to the cause. Causal context includes precursor state descriptions of interacting systems. For example, mass of a physical system Q denotes its causal power in an interaction, which constitutes Q's function or the basis of its relation with other systems. If a system P interacts with Q and gains a state S due to this causal function of Q, then S of P is said to correlate with this information; `mass' is mere label for the causal function of Q, which constitutes primitive of semantics, upon which more structured and abstract semantics can be constructed.

For the same reasons of natural causal dependence, S of P also must correlate with what the observed precursor states of interacting systems correlate with. This is a second order correlation which inductively takes into account all causal descriptions responsible for S of P. It is the second order correlation that allows construction of structured and abstract semantics as shown in Fundamentals of Natural Representation Would you like if I state that reality of all information arises only from causal correlation of states of matter? Therefore, all information has causal consequence. Of course, most of them could be limited to the neural system of the brain without external action.

> What separates information from other physical attributes such as charge or mass? Take for example the charge of an electron. It is often considered to be a physical attribute because every electron in the universe has a charge and because the charge cannot be separated from the electron.

The concept of an electron as an isolated entity is not driven from any ontological first principles, but rather it depends on what consequences are observable due to the associated causal qualities (charge, mass, spin). So, the electron is defined as an entity that has rest mass of 0.511 MeV, charge of 1 negative electronic charge, and spin of one half. That is, the very identity of an electron (or any physical system) is defined in terms of constancy of certain observable causal powers. As it is so, the charge cannot even be conceptualized to be separated from its identity. In fact, causal states (observable qualities) are fundamental (primary), identity of an entity emergent (secondary / dependent). This distinction is crucial in associating the causal reality of information with the observable states rather than with the entity as is mistakenly done in physics.

I agree with your assertion, "If mathematics were not copiable there would be no way to build mathematical models of any physical phenomenon". If we consider two extents of physical system, one that is limited to an individual system like brain, and another that involves many. Indeed, the neuronal system of a brain does exchange the semantic values of information that has consequence in the physical world due to the causal dependence of neurons on each other. But, for the lack of such causal dependence or constraints, inter-personal transmission must be coded. Mathematical coding is far more precise as you mentioned, yet it has it limits Kako, E.; Wagner, L. The semantics of syntactic structures.

In my essay, I take a dig on, "The unreasonable effectiveness of mathematics in describing physical reality", which might entertain you for a moment or longer depending on your tolerance.

> These mathematical descriptions have a different property than the systems they are intended to describe. They can readily be copied between different physical media. .. I can take Coulomb's law and formulate it in my mind, write it on a piece of paper.

Coulomb's law in the mind has a semantic content, structure, and function, it does not require an interpretation. But what we copy from one medium to the next is not the information, but the bits that encode the information under certain scheme. I strongly felt that you were talking about the causal reality of semantics of information, not the artificial mechanism of coding. This treatment of information that entails storing, copying, transmitting in bits, has come at a cost; the cost is the formation of a mental image that information may come into play only when encoded, interpreted, and stored in bits etc., in some manner. This mental frame has kept the generations of researchers away from dealing with the semantics of information, and how causally they come into existence without a need for an interpreter. We know a device (brain) exists that processes semantics of information, but we never attempted to shed the Shannon's idea of quantity of information, or statistical properties of information to get to the semantics of information. So much so that even when such a mechanism is presented from first principles, Fundamentals of Natural Representation , it remains ignored.

Since your awareness has a causal basis, it can cause consequences. Though, states of registers (bits) may also cause consequences in physical universe, but without human constructor they would not be relevant to the mathematical idea because of the artificial coding involved.

Rajiv