TPF : Mathematical Reality

[Gnomon]

We Are Math?

Which suggests that reality—that me, you, Earth, universe, etc.—is fundamentally some sort of abstract object existing outside spacetime. Hm. — Art48

Yes, we humans are essentially "abstract mathematical objects"*1 in space-time. I have arrived at a similar conclusion, except I typically use a more general term for reference to both the subjective objects of minds, and the objective things of physical senses : Information. From a scientific perspective, Mathematics*2 may be the fundamental aspect (essence) of reality. But, for Philosophical purposes Information*3 may be more broadly applicable. Math seems to be the most abstract form of Generic Information*4, yet it is the logical structure of the physical world.

Abstract objects*1 are not knowable by physical senses, but only by mental introspection or by communication with other minds. So, they are in the space-time world, but not of the physical world. Space-time is itself an abstract concept, that we measure indirectly by observing physical changes in the environment. Even the causes of change, Energy & Forces, are abstract concepts, not material things. We only know them indirectly by their effects on matter.

In my personal thesis, I refer to the universal power-to-enform (causation) as EnFormAction*5. And the logically necessary First Cause (the Enformer, the Programmer, the Great Mathematician, etc) is the only abstract thing that exists prior-to and outside the evolving (self-enforming) space-time world. I assume that you lean toward Platonism instead of Nominalism. Can you see the connection between Enformationism and your own proposal of a Mathematical universe?

*1. Abstract Object :
One doesn’t go far in the study of what there is without encountering the view that every entity falls into one of two categories: concrete or abstract. . . . Though there is a pervasive appeal to abstract objects, philosophers have nevertheless wondered whether they exist. The alternatives are: platonism, which endorses their existence, and nominalism, which denies the existence of abstract objects across the board.
https://plato.stanford.edu/entries/abstract-objects/
Note : while Mathematical Objects are typically accepted as real, in some sense, by pragmatic physicists & mathematicians, their Ideal (abstract ; non-concrete) existence puts them in the same ontological category as Souls & Ghosts. Hence, philosophically controversial.

*2. Mathematical universe hypothesis :
The theory can be considered a form of Pythagoreanism or Platonism in that it proposes the existence of mathematical entities; a form of mathematicism in that it denies that anything exists except mathematical objects; and a formal expression of ontic structural realism.
https://en.wikipedia.org/wiki/Mathemati ... hypothesis

*3. Information :
Information is an abstract concept that refers to that which has the power to inform. At the most fundamental level information pertains to the interpretation of that which may be sensed.
https://en.wikipedia.org/wiki/Information

*4. Information :
Knowledge and the ability to know. Technically, it's the ratio of order to disorder, of positive to negative, of knowledge to ignorance. It's measured in degrees of uncertainty. Those ratios are also called "differences". So Gregory Bateson* defined Information as "the difference that makes a difference". The latter distinction refers to "value" or "meaning". Babbage called his prototype computer a "difference engine". Difference is the cause or agent of Change. In Physics it’s called "Thermodynamics" or "Energy". In Sociology it’s called "Conflict".
http://blog-glossary.enformationism.info/page11.html
Note -- Information (EnFormAction) is generic in the sense of causing all forms of being in the universe.

*5. EnFormAction : The creative act of enforming; to give form to the formless.
Ententional Causation. A proposed metaphysical law or principle of the universe that causes random interactions between forces and particles to produce novel & stable arrangements of matter & energy. It’s the creative force of the universe. AKA : The innovative power of Evolution; the power to enform; Logos; Change.
http://blog-glossary.enformationism.info/page8.html

[Gnomon]

We have quantum entanglement, which says that signals can travel faster than light. — Art48

You'll get some negative feedback for that assertion. Actually, at first experimenters were baffled by the "entanglement effect" which seemed to imply faster than light communication. Since then though, other explanations for the instantaneous correlation between particles have been proposed. I'm not a physicist, so I prefer a model that fits into my personal information-theoretic worldview. From that perspective, there is no movement of matter, energy, or information between entangled particles. Instead, the opposite spins are metaphorically two sides of one particle. And all particles in the universe are non-local & unreal (virtual) until triggered by an interaction to manifest with physical properties. In other words, the world is a single holistic (non-space-time) reservoir of infinite Potential, until transformed into Actual bits of matter/energy. The particle doesn't have to go anywhere, because it's already there.

Unfortunately, that holistic description will not make sense to those with a Reductive scientific paradigm of reality. But it fits neatly into the philosophical Enformationism worldview, in which abstract (non-concrete) Information is the fundamental substance (essence) of the world. Another way to look at it is to say that abstract Mathematics is the logical structure (interrelationships) of reality. Mathematics (numbers ; ratios ; equivalences), like Logic, exists only ideally, with no physical properties at all. The science of mathematics is a product of human inference & imagination, hence Idealistic instead of Realistic -- a theory instead of an observation.

However, the human brain is programmed, by pragmatic evolution, to interpret abstract relationships in concrete terms. Consequently, our worldviews are seen through a matter-based frame. So, Materialists and Nominalists are merely saying what they are seeing with their eyes. But, as cognitive scientist Donald Hoffman has proposed, those real things we think we see are merely "icons" or symbols (mental representations) of the underlying reality, which is mathematical or informational. So, Realists are seeing their own conceptual models of reality, not ultimate reality.

Hoffman uses the metaphor of a computer interface to describe how our brains are deceived by our own pre-conceptions. But, in keeping with the Enformationism thesis, I like to use The Matrix movie as a metaphor. In one scene, Cypher is showing Neo the green raining code, and remarks that "I don't even see the code anymore". Like computer screen icons, the code is an abstraction of an underlying reality -- or in this case a simulated reality. Perhaps the real world your senses perceive is a simulation of the true reality : the mathematical information (code) that constructs the world of the senses.


The Evolutionary Argument Against Reality :
The world presented to us by our perceptions is nothing like reality
https://www.quantamagazine.org/the-evol ... -20160421/

Don Hoffman :
The Case Against Reality
https://en.wikipedia.org/wiki/Donald_D._Hoffman

SEMIOLOGY : REFERENCE vs REFERENT
3-s2.0-B9780444889232500185-f15-01-9780444889232.gif

Simulated Reality Code :
Matrix digital rain, Matrix code or sometimes green rain, is the computer code featured in the Matrix series. The falling green code is a way of representing the activity of the simulated reality environment of the Matrix on screen by kinetic typography.
https://en.wikipedia.org/wiki/Matrix_digital_rain
Don't see the code anymore :
https://kugelmass.wordpress.com/2012/03 ... e-anymore/

SEE THE REFERENT (the object being described) NOT THE REFERENCE (the code, symbol, model)
matr.jpg?w=300

[Gnomon]

↪Gnomon
Have you looked at ↪Art48's book? What do you make of it? — Banno

No. But I did look at another of his long essays, and he seems to be generally well-informed. In this thread, I'm only responding to the concepts expressed in this thread, not to Art's book. I'm aware that some of his ideas are fringey, but so are mine. That's why I try to encourage him to explore beyond the known into terra incognita, despite negative feedback.

For philosophical purposes, I'm not concerned about compatibility with "settled science", as long as the general idea makes sense to me (sounds logical). The notion of Mathematics as the foundation of physical reality, corresponds to my own understanding that General Information (which includes Math & Energy) may be the essential structure of Reality. That's not "settled science", but some prominent scientists are enthusiastic about such non-physical (abstract) aspects of Nature/Culture.

PS__I don't think that the mathematics of physics & minds is "outside of space-time". But, as non-physical abstractions, mathematical concepts only exist mentally & ideally, so not directly affected by the causal changes that we interpret as space-time. However, I do go so far as to postulate a timeless First Cause to explain the existence of our physical -- and meta-physical (mental) -- world. But I don't presume to speak for that hypothetical entity.

[Gnomon]

Put otherwise, anyone can make shit up. We need an evaluative eye that can spot the crap. . . . Along side a desire for stories of breadth and completeness, we need to foster a critical attitude. That seems to be missing here. — Banno

Sure. And philosophers tend to be good at "making sh*t up". Some of it turns out to be pragmatically useful, in which case science takes over to make use of the ideas. And this forum is an arena for presenting ideas to a wide variety of critical eyes. Some here find Hegel's ideas useful for their insights into the "teleology of history", while others find fault for the same "sh*t". Suum cuique."To each his own"

But all too often what we get is not constructive criticism, but censorious or condemnatory attacks on ideas that don't conform to a personal belief system. My comments in this thread are not intended to be scientific criticism, since I'm not a scientist with expertise in the mathematical concepts presented here. Instead, I'm try to be supportive of philosophical exploration of ideas that are of interest to me personally --- especially the philosophical implications of Information Theory and Quantum Theory, which are ripe targets for both positive & negative criticism.

PS__FWIW, I did quibble about his notion of Mathematical objects as existing "outside spacetime". Does that count as critique, from your perspective? Math is indeed something that humans "make up", but based on observations of relationships that exist or persist within space & time. But then, space-time is also an abstract concept (mental model), which is intended to describe observed changes in location and in relation. Yet the generalized or universalized concept of Mathematics seems to point beyond any particular brain/mind. So, where could it be located in space-time?

Critique vs. Criticism :
In general, criticism is judgmental and focused on finding fault, while critique is descriptive and balanced.
https://medium.com/storygarden/critique ... ddf0d191ff

Was mathematics invented or discovered? :
Both discovered and invented. When humans perceive the world through consciousness, everything is an abstract entity without a pre-defined representation. When we discover something in the world (such as ability, physical object, event, causality, pattern, etc.), we start to use our minds to describe it. Our consciousness will create personal ‘representations’ of everything for reasoning and thinking
https://www.quora.com/Was-mathematics-i ... scovered-1
Note -- We "discover" consistent patterns of inter-relationships between objects & actions, and then we "invent" formal symbols & language to allow us to discuss the invisible Logic that serves as the underlying inter-connection structure of the physical world.

[Gnomon]

Was mathematics invented or discovered? :
Both discovered and invented — Gnomon
More or less, although most math people give this question little thought. In my case, I was introduced to a notion years ago in my PhD studies. A little later on I decided to extend this idea to a more general realm - a sort of creative step. Once the basic ideas of the concept were set, then came the acts of discovery - finding what flows forth logically. — jgill

Math is usually associated with numerical Quanta, while Logic is associated with semantic Qualia. Ironically, both are expressed in "values" (numerical & meaning), and both are forms of Consciousness. That may help to explain why math overlaps both classes of experience. We become aware of individual objects, and infer their quantitative relationship to a collection of objects. Then we can deal with the group as-if it was a singular object (set ; whole system ; holism). So, maybe once we discover the "basic idea" of objective things & groups, we can discover (create) their subjective value (meaning) to the observer.

Sorry, I'm just riffing on your "creative step" notion. Our senses become aware of non-self things, that have only numerical value. But then, rational inference discovers a possible (logical) connection between thing and self. Hence, external objective Quanta (impersonal value) is transformed into personal Qualia via the "creative step" of inference (imagining thing & self together). The Measurement problem of Quantum Physics may be a case of crossing the line between Quanta/Qualia, numerical/personal, object/subject. I have to go now, but I may try to "extend this idea" at a later time.

[Gnomon]

Sorry, good try, but an appreciation of creativity and discovery comes with involvement, not philosophical chatter. — jgill

Sorry, I was just jotting down some preliminary ideas related to the OP, and to your notion of "Creative Step" and "Discovery". When you "decided to extend this idea to a more general realm" (specific-to-general) you were doing Inductive Reasoning, which is one kind of creative act in Philosophy, and in Mathematics. But, another approach is to break-down a broad general concept into more particular applications (general-to-specific) Deductive Reasoning. I suppose both can be creative, depending on their practical or theoretical implementation (involvement??).

It seems that the OP is an attempt to generalize from spacetime observations to something beyond spacetime : specifically Mathematics & Mental Images. The abstract concepts of Mathematics exist "beyond" space-time in the sense that Math objects are not affected by the physical laws that govern the behavior of material objects. I suppose that ↪Art48 is trying to extend that spaceless & timeless aspect of Math, to the abstractions that we humans create to represent the Self (or Soul, if you prefer). That is not exactly a new idea, except for the connection to immaterial Mathematics & Logic, which some thinkers imagine existing eternally out-there beyond the limits of space-time (Ideality instead of Reality).

So, he seems to be expressing an ancient concept (we are souls) in more modern language : "we are math". Whether that's a creative step may depend on how he develops the basic notion into a philosophical position. Unfortunately, even the Ontological status of Mathematics is subject to philosophical debate. So, the notion of a soul-man is not a slam-dunk.

PS__"Philosophical Chatter", as you put it, seems to be how philosophers get involved in discovering new ways to look at old ideas. Are the mathematician's chalk-marks on the blackboard more involved than text-marks on a philosophical forum?


"More or less, although most math people give this question little thought. In my case, I was introduced to a notion years ago in my PhD studies. A little later on I decided to extend this idea to a more general realm - a sort of creative step. Once the basic ideas of the concept were set, then came the acts of discovery - finding what flows forth logically." ___jgill

"Which suggests that reality—that me, you, Earth, universe, etc.—is fundamentally some sort of abstract object existing outside spacetime. Hm." ___Art48

[Gnomon]

The chief difficulty with Platonism is that while proposing a distinct type of reality of mathematical entities, it must then explain how this reality interacts with everyday things. — Banno
Good question What do you think of the following explanation for explaining interaction? . . . . In this view, mathematical entities are not a distinct type of reality. They are ideas, just like “tree.” — Art48

My tentative explanation of how Ideas interact with Real things is similar, but based on a philosophical simulation of Quantum & Information Theory. The dual entities are distinct only in the sense that the same mind can distinguish between a Thing and the idea of the Thing. Real & Ideal things are conceptually distinctive, but not epistemologically exclusive -- they are not in parallel worlds, but in the same world. You don't have to go out of this world to create an imaginary replica of a physical object.

Plato's Ideals are often portrayed as existing in some aethereal heavenly realm. But they are differentiated from mundane Reality only in the sense that mental Meta-Physics is distinct from material Physics. The human brain is physical, and interacts (communicates) with its own material body via electro-chemical signals (material information). Meanwhile, the brain also interacts (communicates) with its own ideas via something like Quantum Signal Processing : conversion of physical processes to mathematical ratios & algorithms.

In other words, specific physical energy patterns are converted into coded information functions -- in this case, the function we call "imagination" or "conception". This transformation from physical Energy to Meta-physical Information happens within the holistic system of a Person, not in some parallel world. Of course, the detailed "how" is far over my pointy little head. So, this is just a crude macro description of the micro mechanics of Thinking. Perhaps it could only be really/ideally understood by a Mathematical Physicist.

PS__The Brain deals with Material neuro-logical patterns while the Mind works with Logical/Mathematical patterns : inter-relationships.

Quantum Signal Processing is a Hamiltonian simulation algorithm
https://en.wikipedia.org/wiki/Quantum_signal_processing

The Hamiltonian of a system specifies its total energy—i.e., the sum of its kinetic energy (that of motion) and its potential energy (that of position)
https://www.britannica.com/science/Hamiltonian-function