A Metaphorical Chart of Our Mathematical Ontology by Philip Gibbs

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.

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.

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.

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

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

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

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

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

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.

See also: vixra.org/author/leo_vuyk

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.

Excellent paper Phil,

I like the way you would re-frame our treatment of the vacuum, and I agree that a multiplicity or landscape of vacuum state solutions is a feature of a large class of quantum gravity candidate theories, not only Strings. I like the way you informed us about how the concept of an algebra can be generalized, and about the free Lie algebra - which is new to me, but obviously significant. Also; I like that you weave in higher category theory, as I savvy that the category theoretic framework can subsume a lot of other Maths.

Well done!

Jonathan

Dear Philip,

In Grothendieck's 'dessins d'enfants' all is about a two-generator free group, as I am rediscovering step by step with Magma, motivated by the application to quantum observables and contextuality. Reading your wide range excellent essay, I start to be convinced that playing with free algebra over the appropriate rings, new territories of understanding may be reached.

As you refer to topics also investigated in my essay, e.g. Moonshine, modularity and groups, I suspect you may be interested to read me. I would love to have some comments from your side.

Best,

Michel

Dear Philip Gibbs,

"You talked about nature of physical laws and mathematical structures and then metaphysical structures to guide us in the development of physical theories. why we exist and why laws of physics are so steeped in mathematical abstraction.Uncovering the meta-laws is now the most important goal in our quest to understand the universe.

You also talked about referring Wigner that We don't know why complex numbers originally formulated in analysis and algebra became so useful in number theory and physics?

The deepest questions we can ask about existence are "How do we exist?" and "Why are things as they are?"The Mathematical Universe Hypotheses tells us that all logical possibilities are equal. It does not require a magic spell to bring one chosen system of equations into reality.

We will discover more about the relationships between algebra and geometry that determine the emergence of space and time in a universe governed by the laws of energy and entropy that are needed for life to evolve."

Let me quote Swami Vivekananda who had addressed World's Parliament of Religion held at Chicago in 1893. Swamiji was a man of higher consciousness.The great scientist Nicholas Tesla and many others were deeply influenced by him and used to take guidance from him by attending his lectures. He hinted at scientific theories decade before Albert Einstein formulated his relativity theories.

So, what did Swamiji say?

He made statements like, "Take

anything before you, the most material

thing--take one of the most material

sciences, as chemistry or physics, astronomy

or biology--study it, push the study forward

and forward, and the gross forms will begin

to melt and become finer and finer, until

they come to a point where you are bound to

make a tremendous leap from these material

things into the immaterial. The gross melts

into the fine, physics into metaphysics, in

every department of knowledge."[Please refer to the attached file for his detailed view on Cosmology,Universe,Matter,Existence.

Before asking the question why do I exist, one needs to be able to answer Who am 'I' and what is 'I' ? paradox of Self-Consciousness Albert Einstein rightly put(please refer to my essay for his quote) that the separation of human from the Universe as different entity is optical delusion and deep lack of consciousness. MUH,ERH claiming about "physical laws independent of human" & mathematical structures should explore what is human or say 'I'(for that human) ? Who creates mathematical structures used as language for physical reality because every language has certain structures behind its existence. If it asks the existence of mathematical equations,but what governs the physics of equation itself ? If Wigner said that complex number is advanced concept ? Complex numbers have been so useful in number theory to Quantum physics? Why so effective? Eugen Merzbacher in his QM book took the most general structure of wave and showed that in order to satisfy the condition that physical characteristics of the wave should remain invariant under the displacement in space-time directions, the parameter comes out to be'i'(complex number. Here is the laws of invariance behind complex number that makes it so useful . Why we defined (-)*(-)=(); why not ()*()=(-) also? It is this laws of invariance behind the mathematical structures, which makes it compatible in different physical and mathematical scenarios.

In context of Skolem's paradox - "A particular model fails to accurately capture every feature of the reality of which it is a model. A mathematical model of a physical theory, for instance, may contain only real numbers and sets of real numbers, even though the theory itself concerns, say, subatomic particles and regions of space-time. Similarly, a tabletop model of the solar system will get some things right about the solar system while getting other things quite wrong. So, for instance, it may get the relative sizes of the planets right while getting their absolute sizes (or even their proportional sizes) wrong"

Why so? Its not mathematics describing physics rather the laws of invariance behind mathematical structures(whether discovered /invented) describes the laws of invariance behind physical reality.

Mathematical Structure Hypothesis(which I have propounded) states that they both having no independent existence because they both originate from Vibration. So,its not that laws of energy and entropy governs only physics but also the mathematical abstractness,which can be seen in context of Poincare & Geometrization conjecture.

Anyway, you have written a great essay.

Regards,

Pankaj ManiAttachment #1: vivekanada_universe.pdf