A Metaphorical Chart of Our Mathematical Ontology by Philip Gibbs

Philip Gibbs

Alinbo, I will of course read your essay. For the last few weeks I have been enbroiled in some non-physics matters and only have time to answer a few questions but there is still plenty of time.

Tommaso Bolognesi

Dear Philip,

a central point in your essay is universality. A mathematical structure is more universal - more discovered than invented - when it is instantiated in more structures that superficially appear different from one another; and a physical law is more universal when it describes more physical systems that appear different from one another in some aspects (e.g. different particle types in systems that obey the same thermodynamical laws).

A dense spectrum of universality degrees is envisaged, for which we still lack formal treatment and measure. And yet, the idea to navigate the mathematical universe guided by this compass and reach the top of the hill (or the bottom of the valley), with the idea that the most universal mathematical structure coincide with the meta-laws of physics, is very appealing.

We have another interesting notion of universality, however, more advanced in terms of possibilities of formal treatment, and simply of a True/False type (no spectrum of degrees): that's of course computational universality (Turing universality) - the ability of a model of computation to reproduce any computation of any other conceivable model of computation.

To those who attribute a fundamentally algorithmic nature to the universe (thus justifying its mix of order and disorder better, in my opinion, than any other approach) this would be the first choice for a notion of universality. Then, the democratic idea that all vacua, or all mathematical structures, enjoy some form of existence, could perhaps also apply to the multiplicity of universal models of computation.

There seems to be a very large gap between the idea of an algorithmic uni/multiverse and the scenario that you describe. You place 'algorithms' in your picture below 'games', but still far from the 'point of universality'. I agree that individual algorithms are more invented than discovered, but what about the Universal Turing machine?

Thanks and best regards

Tommaso

P.S. In case the algorithmic paradigm gained credibility in the future, I suggest to replace the elephant with an ant, for its 'minimality', as a metaphor for the head of a Turing machine, and as a reminder of the variety of properties that emerge from the computations of 'turmites' (2D Turing machines), including Langton ant.

Philip Gibbs

Tommaso, thank you for your comment. It is good to see you in the contest again.

You have made a very astute point which is not lost on me although space constraints meant I did not say much about it in the essay. If you look at the paper by Seth Lloyd "The universal path integral" which I have cited you will see that he concentrates on algorithms. This may be very close to the kind of approach you are thinking of.

There are a couple of reasons why I did not want to focus on algorithms myself even though the universaltiy of computing is certainly very relevant here. One thing is that computers tend to run calculations forward in one direction. A normal sequential program has a time ordering in its calculations. This may be relaxed in a parallel programming architecture but there is still a partial ordering which people will inevitably try to link to temporal causality. As I said in my essay I dont think this kind of causality is important. I aknowledge that you could work with algroithms without making this connection.

The other thing is that path integrals are not just sums over configurations. When you have fermions the sum is replaced with an algebraic integral over grassman varuables. I suspect that the universality we see in maths and physics is also more general in this way. It is an algebraic principle that we do not understand and the kind of universality you get in statistical ensembles is just a good metaphor for that. The universality in computing is a little different again and it fits in somewhere, but here I tried to convey the idea of some other kind of self-referntial, self-organising universality that we understand very little about.

I look forward to reading your essay a little later

[deleted]

Dear Philip,

I read your essay with great interest. I totally agree with you: we need a new paradigm in basic science. To do this, need to consider the "universal point" as ontological "proto- existential - extremum". But not "meta-laws", only one "law of laws" - "Logos". My high score.I think that we must first to consider the proto-structure of the Universum (matter) from the point of view of eternity ("sub specie aeternitatis"), that is, to carry out the ontological structure of matter in the proto-era, "time before times began". When we "grab" (understand) the primordial (ontological) structure of space, then we will understand the nature of time. Therefore, we must move from the concept of "space-time" to the concept of "space-matter-time", which represents the ontological unity of the Universum. The primordial structure of matter determines the structure of the language in which Nature speaks to us, single language for mathematicians, physicists and poets , ie, language that contains all the meanings of the "LifeWorld" (E.Husserl).I invite you to read my essay .

Kind regards,

Vladimir

Philip Gibbs

Thank you Vladimir, I will read your essay, sounds intriguing.

Alan Kadin

Dear Dr. Gibbs,

I read your essay with great interest.

I note your citing of the parable of the blind men and the elephant, as a metaphor for incomplete knowledge. However, I think that abstract theories inferred from incomplete knowledge can be more pernicious than the lack of knowledge itself. Such mathematical theories can act to narrow the mind and blind the vision.

You might be interested in reading my own 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.

But questioning the foundations in this way is considered heretical, and is unpublishable in physics journals.

Alan Kadin

Efthimios Harokopos

Interesting essay. You frame a hypothesis of the existence of meta-laws. You write:

"At the same time technological progress will enable new empirical observations to help us understand inflation, dark matter, proton decay and other subtle phenomena that help to chart our course through the ontological realm to where we stand in it. They will enable us to pick out the universe's particular solution to the algebraic meta-laws."

AFAIK< and I may be wrong, so far science works the other way around (Higgs particle for example):our models make a prediction and we try to falsify in or verify it.

You allude to a procedure in which experiments will determine the selection of meta-laws. How can we look for something we do not know what it is? (Knowledge Paradox). Besides, we are far from making experiments at the Planck scale. If meta-laws exist, you think we will find them by experimentation without a formal framework of what we are looking for? Thanks.

Philip Gibbs

Science works both ways. Sometimes theorists make predictions that are then verified by scinece, but sometimes experienters find things that were not predicted and theorists have to find the right theory for them. There are plenty of examples of the latter e.g. the muon, law of black body radiation, constancy of the speed of light etc.

Particle accelerators search for predicted particles but they can also find things that were not predicted. This is done by continually measuring every quatity at higher and higher energies and checking to see whether they match predictions from accepted theory.

While accelerators are limited in energy scale, the other experiments I mentioned are not. proton decay could give us information about the GUT scale for example.

You dont need a formal framework to find something new. As soon as something does not match the existing framwork you can start looking for what might explain it.

Jose Koshy

Dear Dr. Gibbs,

I think the meadow of physics is marred by mathematical demons. So I was happy when FQXI announced the subject for this year's essay competition. The first essay I read was yours. Instantly, I identified you as a 'mathematicalist' trying to impose the rule of mathematics in the domain of physics.

The way you have written, however, is impressive that any one reluctant will jump into the 'mathematicalist' wagon. That I think is the beauty of the mathematics-oriented thinking coming from somebody who knows the intricacies of both mathematics and physics.

Your statement "geometry is an angel and algebra is a demon .......... the signs are that the devil rules at the deepest levels of existence" is thought provoking. Can I say that the rules of mathematics are essentially algebraic, and geometry just represents its emergent structures. Then the universality of mathematics is in its rules, not in its structures. Regarding the question, whether mathematics is invented or discovered, I think the rules are discovered, but the structures are invented. For example, in chess the properties of the pieces are invented, but the emergence follows mathematical rules and the overall structure of the game is thus invented. Starting with another set of arbitrary properties, you will obtain a different structure.

Again I would like to quote another statement "the theory you get by recursively iterating quantisation should be unique" . Without referring to existing Quantum Mechanics, your statement can be construed to be implying that fundamental particles, just because they are quanta, may be obeying a unique law, which is universal. Does it simply mean that starting from qunatised entities, you cannot have an infinite number of emergent structures?

The 'physicalist' idea that I propose in my essay is this: physics decides the properties, mathematics decides the rules. For the given properties, mathematics decides the emergent structures; for that emergent structures, physics again decides the emergent properties, and so on. Thus, the equations are mathematical, but the variables are physical. Starting from a finite number of variables having finite properties, the number of variables will soon come to the minimum that further emergent structures are impossible. That final structure is the physical world that we observe.

Somewhere above, you have stated that 'physics emerges from mathematics'. This I think tantamount to saying that 'the physical world emerges from mathematics'. Or, given the basic properties of matter, mathematics decides the final emergent structure. That way, I will have to call you a physicalist. So I am just confused. I have just submitted my essay, and expect it to be available within a few days. I would be awaiting for your comments.

I claim myself to be an independent researcher. And I find solace in the free-for-all 'VIXRA'. I take this opportunity to express my sincere thanks to you for providing an asylum for people like me.

susanne kayser-schillegger

Dear Dr. Gibbs,

after a second try I still have to admit not to understand most of your certainly excellent statements. It is a fact that mathematical constructs are difficult to translate into comprehensible physical meaning. Or, is it a trick to confuse those with a desire to understan?

Anyway, the theoreticians have an easy life. Nobody can refute your theories such as multiverses since there are no empirical facts. It sounds to me more like philosophy or clairvoyance.

I wish you good luck with your further work

Best

Lutz

Philip Gibbs

Susanne, the audience here has a wide range of levels of expertise so it is difficult to get it right for everyone. I have never seen these essays as an exercise in science popularization, but I have not included any equations as some people do here. That is my best compromise. I want to say something substantive to people who are familiar with the subject. If I did not mention the specific concepts I am referring to everything would be too vague, and if I attempted to explain them for those less familiar the essay would be ten times as long. Any of the terms used can be skipped and just accepted as something you don't know about, or they can be looked up. I hope you managed to get something out of it.

The topic for this essay is deeply philosophical so I make no apologies for the fact that my essay is philosophical and meta-physical. This kind of thinking is very important at the frontiers of theoretical physics where strongly help assumptions sometimes need to be given up to make progress. It is not testable in its own right but the idea is that it should guide thinking towards new ideas that would be testable. The route from foundational thinking to experimental checking is very long these days and will take many steps and many years. To complain that each step cannot be empirically tested or refuted misses the point of how science is being done. Note that my essay does not use the word multiverse which has been used to describe too many different things.

The other thing that philosophical thinking does is to provide an interpretation of physical theories. I think that is important too if we want to understand where we fit in the grand scheme of things, rather than merely finding practical uses for science.

Michael Rios

Philip

A very nice essay on cutting edge topics that reflect the current unreasonable effectiveness of mathematics in physics. The hidden structure behind the amplituhedron, sporadic groups, noncommutative geometry and M-theory is rapidly being revealed. I gave an overview in my essay, through the lens of motives.

Leo Vuyk

Dear Philip,

A very interesting approach of the ontology of math indeed.

As an architect I fully support the idea that it is the geomtrical aspects of the universe we should focuss more.

Then more thinkig out of the box seem to be possible, which even could lead to our understanding of the golden mean of the penta dodecahedron multiverseAttachment #1: Big_Bang_MWI_1.jpg

Alex Newman

Dear Sir,

Thank you for the essay but for someone like me who is trained in another field of science is was quite incomprehensible. I thought that FQXi essays target a general audience. Someone once said that if a scientist cannot explain what he means in a few sentences then he probably lack understanding of what he means. I get the impressions you are trying to impress people more than to educate them. With all respect of course...

Alex Newman

Philip Gibbs

Sorry, but I dont see this contest as an exercise in popularisation. If we had to write for people who dont know any fundamental physics we could not explain very much in nine pages.

Leo Vuyk

Dear Philip,

You wrote:

"Thus we learn finally that there is no mysterious force that defines our consciousness.

We have no existence beyond our journey in this material world."

However, No extra mysterious force is needed to understand local or universal entanglement between mirror symmetric particles at large distances right?

So if the universe has mirror symmetry, from the start, then we live in one of the two ( or even more) instant entangled symmetric universes.

Then Max Tegmark is right if he suggest that there is a copy person over there who also read these letters ! at the same moment.

See: Democratic Free Will in the Instant Entangled Multiverse.

http://vixra.org/pdf/1401.0071v2.pdf

Philip Gibbs

Hi leo, good to see you here. Are you doing an essay this year?

Leo Vuyk

Hi Philip,

Sorry I was not able to cope with the subject.

Perhaps an other time or perhaps ablog post

However indeed the relation between Math and physics for me is sort of a problem.

Pehaps you remember that Gerard 't Hooft my topological string model declined because my model did not fit into known math sustems.

I believe that OUR COMPLEX WORLD can not be described by FORMULAS ALONE. WHY? Because we don't know why the universe is as it is. An example: "Finetuning": Why are the "fundamental constants" constant? My suggestion: because the sub-quantum FORM of particles and the Higgs vacuum lattice have a certain form and play a game with us.. So I designed simple convertible shapes for real QUANTUM particle information use. At the same time I realized that black holes should also have some nuclear form and as a result I found that dark matter is related to black holes and Higgs particles have only energetic mass inside an oscillating Higgs vacuum lattice. Multiverse based mirror symmetric consciousness (entanglement) is assumed to be the base for all particle- wave -and human guidance or wavefunction collapse. SEE: https://www.flickr.com/photos/93308747@N05/?details=1and: http://vixra.org/author/leo_vuyk

I am an architect who is interested in the possible sub-quantum particle FORM as information medium and building blocks in nature. I also focus on the possible dynamical FORM transformation aspects in micro- and macro physics as a base for dark matter black holes, the Higgs field vacuum and the Big bang. see also:Attachment #1: STEPHEN_HAWKING_1.jpg Attachment #2: YELLOW_BALLS_2.jpg

basudeba mishra

Dear Sir,

Dimension is the perception of differentiation between the internal structural space and external relational space of objects. Since we perceive through electromagnetic interaction, where the electric and magnetic fields are perpendicular to each other and both move perpendicularly, we have three mutually perpendicular dimensions. These are invariant under mutual transformation (if we treat length as breadth or height, the object is not affected) and can be resolved into 10 different combinations. But even after more than a century of failures to find extra-large or compact dimensions; you still subscribe to such fiction perpetuated by the novel FLAT LANDS!

There are many unexplained questions relating to the strings. For example, given the measurement problem of quantum mechanics, what happens when a string is measured? Does the uncertainty principle apply to the whole string? Or does it apply only to some section of the string being measured? Does string theory modify the uncertainty principle? If we measure its position, do we get only the average position of the string? If the position of a string is measured with arbitrarily high accuracy, what happens to the momentum of the string? Does the momentum become undefined as opposed to simply unknown? What about the location of an end-point? If the measurement returns an end-point, then which end-point? Does the measurement return the position of some point along the string? (The string is said to be a Two dimensional object extended in space. Hence its position cannot be described by a finite set of numbers and thus, cannot be described by a finite set of measurements.) How do the Bell's inequalities apply to string theory? We must get answers to these questions first before we probe more and spend (waste!) more money in such research.

We have discussed Wigner's paper in our essay "REASONABLE EFFECTIVENESS OF MATHEMATICS" to point out the fallacy. In conformity with the second law of thermodynamics, arrow of time is well established - Past, Present and future are segments of sequences of intervals between events that are strictly ordered - all of future always follows present. The same sequence is not true for past, because any past event can be linked to the present bypassing the specific sequence of its occurrence but you cannot move from past to future violating the sequence. Further, we can remember events of the past and not of future. Thus positrons travelling backwards in time, is fiction. True, time and space are emergent properties, but not because of M theory or LQG. There are simpler explanations based on empirical principles that explain these.

Obviously, this new way of thinking is "giving up" on fundamental physics!

Regards,

basudeba

Philip Gibbs

basudeba, the "unexplained" questions you ask about string theory are very ordinary questions whose answers are well understood by string theorists. I am afraid you will just have to accept that it is only to you that they are not explained or understood.

The "new way of thinking" is not "giving up" . That is just the opinion of the old guard who does not understand the unexpected truths that new discoveries are telling us. That has always been the way science has progressed.

Leo Vuyk

Dear Pilip,

I like your statement: "layers of speculations" are needed etc. because I also think that this out of the box thinking could be productive.

IMHO:

I think that Stephen Hawking did not calculate with the possibility of a chiral oscillating Higgs field vacuum lattice combined with propeller shaped Fermions. Then, Electrons and positrons could both pushed away from the BH horizon at different distances, forming two charged separated spheres. With quark ( plasma) formation in between So Black Holes could be charge splitters violating the 2e law. Combined with a continuous microscopic big bang plasma creation process!

The result I try to describe :

1: Dark Matter is the same as Black Holes, they all consume photons and even gravitons but REPEL Fermions due to their propeller shape.

2: Dark Energy is the oscillating ( Casimir) energy of the Higgs Field equipped with a tetrahedron lattice structure.

3: Quantum Gravity = Dual Push= Attraction (Higgs-Casimir opposing Graviton push).

4: The Big Bang is a Splitting Big Bang Black Hole (BBBH), splitting into smaller primordial Splinters and evaporating into a zero mass Higgs particle based Higgs field.

5: So Primordial Big Bang Black Hole splinters (PBBS) evaporate partly into the energetic oscillating Dark Energy Higgs field.

6: Dual PBBSs hotspots, produce central plasma concentration in electric Herbig Haro systems as a base for stars in open star clusters as a start for Spiral Galaxies or later in Super Nova Nebula as a start for a planetary star system.

7: Spiral Galaxies will keep both Primordial Dark Matter Black Holes as Galaxy Anchor Black Holes (GABHs) at long distance.

8: After Galaxy Merging these GABHs are the origin of

Galaxy- and Magnetic field complexity and dwarf galaxies .

9: Dual Black Hole systems produce Plasma direct out of the

Higgs field because two Higgs particles are convertible into symmetric electron and positron (or even dual quark-) propellers (by BH horizon fluctuations).

10: The chirality of the (spiralling) vacuum lattice is the origin our material universe. (propeller shaped positrons merge preferentially first with gluons to form (u) Quarks.

11: The first Supernovas produce medium sized Black Holes as the base for secondary Herbig Haro systems.

12: last but not least ALL Dark Matter Black Holes are supposed to be CHARGE SEPARATORS with internal positive charge and an external globular shell of negative charged Ions and electrons.

Donald Palmer

Thank you for an interesting essay, Philip Gibbs

I agree strongly with the position you take on universality being the common bond between mathematics and physics. I do wonder if a universal property is that everything is unique, if we get precise enough in our measurements.

And I am responding to this sub-thread regarding foundations of mathematics mentioned by Prof. Crowell. We might need to consider the assumptions in the foundations of mathematics- especially as mathematics is applied to physics. In particular we assume our system of representing quantities (numeric representations) are adequate for what we can measure. What about things we might be unable to measure (today)? While we might be able to accomplish much of technology today using Rational numbers (we can only approximate Real numbers), we would be completely unable to build our technology with only fractions - a representational system for Rationals. The calculational power of decimals (and like based systems) far outstrips that of fractions. Might there be a more powerful system than the single-based numeric systems we use today that could manage calculations unthinkable today? Such a system would likely apply to a larger set of numbers and encompass operations not in our current systems (more universal). Being on the boundary of theoretic and applied mathematics, it could have a major impact on science as well.

Philip Gibbs

I am not sure if comments are working here. I had two notifications of comments but nothing has appeared.

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