Which suggests that reality—that me, you, Earth, universe, etc.—is fundamentally some sort of abstract object*1 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? :smile:

*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/Mathematical_universe_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

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

This makes no sense to me. A category error at least. "Existing" north of the North Pole ... :roll:

If this is actually the case, however, I also don't see what non-trivial difference being "fundamentally some sort of abstract object" would make with respect to (our) human existence (pace M. Tegmark).

To think, I might be sitting next to unactualized possibles, the conversations to be ……

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

No it doesn't! From the physics stack exchange:

Entanglement between two qubits means that if a measurement is made on one of them, the other one is decided instantaneously.

This is true, but this does not allow for faster than light communication. If you have one qubit with you and I have one qubit with me and you make a measurement on your qubit, that will mean my qubit is decided . But how does that send any signal ?

Later on, when I make a measurement on my qubit, I get a measurement, just as I would have got some measurement had you not measured first. There is no way for me to know that I got this measurement after you had measured yours or before you have measured yours. Hence, no signal can be sent faster than light using entanglement

This makes no sense to me. A category error at least. — 180 Proof

Definitely, but one that is made repeatedly hereabouts. Folk want this sort of nonsense to be the case. What's that about, then?

I tried to understand quantum entanglement using my own following thought experiment:
If the distance between us was 1 light year. Then I could send you a message that says.
Measure your entangled particle the moment you receive this message.
I would then have to know very precisely (I think) when to measure my item just before you do, 1 light year away. I would then send a message to you 1 light year away, asking you what your measurement was. If I had measured a 1 then you will have read a 0.
But it will take 2 years after the actual event, for me to confirm this, so no signal is travelling faster than light in this thought experiment.

I don't know if this is correct but it's what I understand as quantum entanglement at the moment.

What's that about, then? — Banno

Defibrillation for dying theosophies imo.

The contradiction can be resolved if we restate Einstein’s relativity theory as “nothing can travel through spacetime faster than light.” If the signals somehow bypass spacetime, then the contradiction is resolved. Hm. — Art48

Sorry, I didn't read this part carefully enough before responding. I speculate that there is no travelling needed in certain conditions, due to QFT. Every 'point' in space can manifest any particle/excitation at any moment of time. So the entangled state does not 'travel' as it is already there and only requires measurement.

When we drill down to the deepest level of matter, we get the quantum wavefunction, a mathematical object that uses regular numbers (“real” numbers) and “complex” numbers which are based on “i”, the square root of negative one. We begin with matter, trace its source, and end up with a complex-valued mathematical wavefunction — Art48

Which is not matter, just a way to predict changes in matter, energy, etc.

I keep bringing up my late Corgi, Jake, and his inability to understand algebra, though I'm sure he tried. Humans may never "understand" matter and energy at some ultimate level, but, like Jake, they can enjoy chasing metaphysical sticks and learn how to manipulate physical entities. (He learned how to manipulate me)

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. :smile:


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

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

SEMIOLOGY : REFERENCE vs REFERENT


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/2012/03/29/i-dont-even-see-the-code-anymore/

SEE THE REFERENT (the object being described) NOT THE REFERENCE (the code, symbol, model)

Have you looked at 's book? What do you make of it?

reality—that me, you, Earth, universe, etc.—is fundamentally some sort of abstract object existing outside spacetime. — Art48
This makes no sense to me. — 180 Proof

Does it make sense to you that our deepest description of matter is the wavefunction?
Does it make sense that the wavefunction is a mathematical function?
Does is make sense that mathematical functions exists outside spacetime?

Does it make sense to you that our deepest description of matter is the wavefunction? — Art48

"Deepest description" so far ... Why wouldn't that "make sense"?

Does it make sense that the wavefunction is a mathematical function?

This question, Art, doesn't make much sense. What else would / should "the wavefunction" be if not a mathematical function?

Does is make sense that mathematical functions exists outside spacetime?

Another incoherent question. Abstract objects subsist in minds and minds exist – are embodied – spatiotemporally.

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

What book?

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

No, quantum entanglement says measurements will be correlated - a very different thing. As physicist Asher Peres noted, "relativistic quantum field theory is manifestly local." (longer quote here).

[From Physics Stack Exchange] Entanglement between two qubits means that if a measurement is made on one of them, the other one is decided instantaneously.

This is true, but this does not allow for faster than light communication. If you have one qubit with you and I have one qubit with me and you make a measurement on your qubit, that will mean my qubit is decided . But how does that send any signal ?

Later on, when I make a measurement on my qubit, I get a measurement, just as I would have got some measurement had you not measured first. There is no way for me to know that I got this measurement after you had measured yours or before you have measured yours. Hence, no signal can be sent faster than light using entanglement — universeness

Yes though the term "instantaneously" can be misleading. The other qubit has to be measured and the results compared. As Peres also noted, "unperformed experiments have no results" (see counterfactual definiteness).

I tried to understand quantum entanglement using my own following thought experiment:
If the distance between us was 1 light year. Then I could send you a message that says.
Measure your entangled particle the moment you receive this message.
I would then have to know very precisely (I think) when to measure my item just before you do, 1 light year away. I would then send a message to you 1 light year away, asking you what your measurement was. If I had measured a 1 then you will have read a 0.
But it will take 2 years after the actual event, for me to confirm this, so no signal is travelling faster than light in this thought experiment.

I don't know if this is correct but it's what I understand as quantum entanglement at the moment. — universeness

That's correct. But note that, per relativity of simultaneity, the order of the measurements can potentially differ in each particle's reference frame. The point is that each measurement is local. One measurement doesn't cause or influence the other measurement.

Does it make sense to you that our deepest description of matter is the wavefunction? — Art48

How do you know it's not interdimensional vibrating superstrings?
How do you know our universe is not a result of interacting branes?

That's correct. But note that, per relativity of simultaneity, the order of the measurements can potentially differ in each particle's reference frame. The point is that each measurement is local. One measurement doesn't cause or influence the other measurement. — Andrew M

:up: But if the two items 1 light year apart are entangled, then surely "However, if the events are causally connected, precedence order is preserved in all frames of reference." From the wikipedia article: https://en.wikipedia.org/wiki/Relativity_of_simultaneity applies?

Does is make sense that mathematical functions exists outside spacetime?
Another incoherent question. Abstract objects subsist in minds and minds exist – are embodied – spatiotemporally. — 180 Proof

Good point. Some philosophers say that material objects exist but abstract objects subsist.
So, let's change the third question.

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

This makes no sense to me. — 180 Proof

Does it make sense to you that our deepest description of matter is the wavefunction?
Does it make sense that the wavefunction is a mathematical function?
Does is make sense that mathematical functions SUBSIST outside spacetime? — Art48

Does it make sense to you now?

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

No, quantum entanglement says measurements will be correlated - a very different thing. As physicist Asher Peres noted, "relativistic quantum field theory is manife — Andrew M

My understanding is that Einstein's famous "spooky action at a distance" concern was about something going faster than the speed of light. Here a quote from an article of Astronomy.com
- https://astronomy.com/news/2022/10/what-is-quantum-entanglement

"The strange part of quantum entanglement is that when you measure something about one particle in an entangled pair, you immediately know something about the other particle, even if they are millions of light years apart. This odd connection between the two particles is instantaneous, seemingly breaking a fundamental law of the universe. Albert Einstein famously called the phenomenon “spooky action at a distance.”

↪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. :smile:

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.

Does is make sense that mathematical functions SUBSIST outside spacetime?
— Art48
Does it make sense to you now? — Art48

No. "Outside spacetime" is as incoherent as north of the North Pole. And to subsist is to be thought by minds which are, as I've pointed out already, embodied spatiotemporally; so the question remains doubly nonsensical to me.

No. "Outside spacetime" is as incoherent as north of the North Pole. And to subsist is to be thought by minds which are, as I've pointed out already, embodied spatiotemporally; so the question remains doubly nonsensical to me. — 180 Proof

OK, I suppose that's one view of abstract objects. Another view is that they exist subsist outside spacetime. For instance, "two plus two equals four" subsisted and was true before the big bang.
In your view (if I understand it correctly) the thought "two plus two equals four" didn't exist immediately after the big bang because there were no minds to think it. Is that right?

More or less.

That's why I try to encourage him to explore beyond the known into terra incognita, despite negative feedback. — Gnomon

People like to make up stories. We pass them from one person to another, keeping the bits we like and adding new stuff as we go. The talk "grows in the telling", as Tolkien put it.

We've found, over time, that there are ways in which we can make our stories of how things are more useful. So we find that a story that is liked by more folk will make it easier for folk to work together, for example. A story that explains a wider variety of situations or circumstances will have more uses than one that explains only a small part of the world. We've also found that we can check our stories, one agains the other, and modify them so that they are more consistent.

Where the story is about how the world is, this leads to taking a conservative approach to story telling, Small changes are preferred, because it is easier to see what their repercussions are, how they effect the other parts of the story as a whole.

On the other hand a desire for excitement or entertainment might lead one to posit large-scale changes to the story. Their ramifications will be greater, and their flaws more easily seen.

Either way, one evaluates changes in the story in terms of the other parts of the story. The process is holistic, consisting in a critique of the web of belief.

Put otherwise, anyone can make shit up. We need an evaluative eye that can spot the crap.

's suggestion that reality is an abstract object fumbles the clear and happy distinctions that we make between abstract or concrete, on the one hand, and real or not real, on the other. It muddles ideas from the every day and ideas from quantum theory. It is far more direct and reasonable to posit that abstractions such as property, marriage, and complex numbers are stuff we made up than to imagine them exiting in the way chairs and trees do, but in some parallel reality.

Along side a desire for stories of breadth and completeness, we need to foster a critical attitude. That seems to be missing here.

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"

Yet 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 trying 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. :smile:

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. Then again, 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-vs-criticism-36ddf0d191ff

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-invented-or-discovered-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.

It is far more direct and reasonable to posit that abstractions such as property, marriage, and complex numbers are stuff we made up than to imagine them exiting in the way chairs and trees do, but in some parallel reality. — Banno

As an ultimately abstract entity, I enjoy the company of so many numerous abstract entities. We often discuss if there really are concrete objects, but conclude they are just grammatical fictions.

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.

The varied origins of mathematical concepts involve both complicated regressions and sheer moments of genius. My advisor would say there are no original ideas in the subject - they all trace back to antiquity (I would disagree). Take the way we measure distances (Euclidean); some time back the notion of an abstract "distance" was conceived, in a space of "objects". Thus was born the study of metric spaces, which eventually led to or coincided with the development of topological spaces. And on and on . . .

Interesting points of view. I suppose the Universe or mass and energy are composite; pluralist builds of all things, yet sentience of course does work- it's more than a different state off matter. One shouldn't be rashly reductionist about mind arising from matter. The wavefunction, Shrodinger equation, Hilbert Space quantum paradigm etc; does it all require different ways of viewing things if one substitutes Hugh Everett's paradigm of what Tegmark named a level 4 Multiverse instead of the Copenhagen Interpretation/Schrodinger wavefunction collapse? Or does the Higgs field effects slowing down two dimensional particles so they pick up a third dimension and allow the appearance of three dimensional mass to exist mean that items like quantum entanglement are secondary, contingent phenomena too?

I would think that reality is everything that exists including appearances of it sentient beings are aware of and everything they aren't aware of too. Even so these days I tend to regard the two dimension, massless particle-wave realm 'outside' or beyond the Higgs field as more fundamental than the three-dimension world of experience.

Tegmark speculated the Multiverse is made of math; that a logical structure exists in it that corresponds to reality and is based on oure math. THe idea of a mathematical universe brings one to think that there is a logical structure to the universe including the quantum world that seems necessary for temporality, motion, being and nothingness, change, evolution and so for th yet of course it could all be in the thought of God. An infinite Multiverse pre-existing from eternity in an Everett-Tegmark Level 4 Mutliverse construction perhaps. It's interesting to consider. String theoriy's Mutliverse paradigm with mathematical, logical structure would be interesting for mathematicians to consider and for others like myself to read about.

:up: But if the two items 1 light year apart are entangled, then surely "However, if the events are causally connected, precedence order is preserved in all frames of reference." From the wikipedia article: https://en.wikipedia.org/wiki/Relativity_of_simultaneity applies? — universeness

The particle measurement events aren't causally connected (i.e., correlation is not causation). So the precedence order need not be preserved in all frames of reference.

In quantum field theory, observables of events with a spacelike relationship, "elsewhere", have to commute, so the order of observations or measurements of such observables do not impact each other. — Causality (physics) - Wikipedia

My understanding is that Einstein's famous "spooky action at a distance" concern was about something going faster than the speed of light. — Art48

Yes, that was his concern (which, more generally, was about wavefunction collapse). However QM neither specifies nor requires non-locality. Further, locality is one of the axioms of quantum field theory.

Locality is one of the axioms of relativistic quantum field theory, as required for causality. The formalization of locality in this case is as follows: if there are two observables, each localized within two distinct spacetime regions which happen to be at a spacelike separation from each other, the observables must commute. Alternatively, a solution to the field equations is local if the underlying equations are either Lorentz invariant or, more generally, generally covariant or locally Lorentz invariant. — Principle of locality - Wikipedia

I suppose that's one view of abstract objects. Another view is that they exist subsist outside spacetime. — Art48

How is two plus two equals four subsisting outside space-time different to two plus two equals four existing outside space-time ?