Physics And Mathematics As Abstraction Or Reality

Reality is an abstraction in that we have no direct experience of the stuff. Even ZenMasters stub their toes. Not once but over and over.

Isn't stubbing your toe a direct experience of reality?

No, it's a direct experience of your toe. Your toe is an empirical device. Your interpretation of the signals coming from it as "stubbing" is a theory. You can frame the stubbing-theory in terms of math and physics, but that doesn't make it any more real. Or help you avoid stubbing it again.

But there are a lot of scientists who accept math and physics descriptions of phenomena, including toe-stubbing, without question, as reality.

No, there are no scientists who do that because scientists by definition employ the ScientificMethod. Scientists keep an open mind and accept that any theory can be refuted by new empiricism. In other words, they accept that sometime, somewhere, when they least expect it, they'll stub their toes.

rubbish, scientists can be as close minded as any other group of people. And the other point, there have often been long abstraction vs reality debates in science, consider the long battles over what QuantumMechanics actually means.


(Originally spawned as a side-argument from CloudsInMyIceCream)
ThichNhatHanh is not talking about clouds or ice cream at all. Debating the existence or non-existence of the clouds in the ice cream is absolutely missing the point. -- StevenNewton

The claim is that clouds exist even after they are destroyed. It's a very subtle claim aimed at undermining ObjectIdentity.

Water molecules do exist, and one could go from being in a cloud to being in your ice cream. Or is that missing the point?

Yes, it is missing the point. Abstractions exist, and they exist objectively. They are physically real. A car is an abstraction, yet it is a physically real object.

Abstractions exist objectively? What abstractions exist independently of an abstractor? When is a car no longer a car? When you remove a wheel? A door? If it's in pieces in a large box? If you melt it down? Where one decides to draw the line is arbitrary, and very much subjective. (see also TheLawOfFives)

ALL abstractions exist independently of an abstractor. All mathematics exists independently of people, yet all mathematics is abstractions.

That mathematics is internally consistent, does not imply that it is independent of people. You obviously believe this, but that does not make it fact.

Mathematics isn't internally consistent since different theories are inconsistent with each other. This is the central fact established by Goedel's incompleteness theorem. And it is precisely this fact (multiple mathematics, most mutually inconsistent) which distinguishes neo-platonism from mere mathematical realism.

Mathematics is independent of people, independent of whoever believes it at any point in time. This is as true as that software is independent of computers. And these aren't esoteric facts but unambiguously self-evident truths which every single mathematician in the whole of human history has accepted.

Quick note from a set theorist: there are indeed multiple mutually contradictory strands of maths, at least where infinite collections are concerned. A good example is the Axiom Of Choice. There are incompatible axioms (for instance, the Axiom Of Determinancy) which have a fair degree of currency. So infinite cardinality set-theoretic maths, at least, does not exist as a single mutually consistent ideal.

You're confusing abstractions with perceptions, it's the latter that can't exist without a perceiver.

No, you are missing that abstractions are based on perceptions, neither can exist without someone to observe them. It is comforting to think that Mathematics and Physics are reality, and it's true that they are very useful models for guiding us through life, but that doesn't make them equal life - what a boring world this would be if they were all that was to reality.

First is your inability to distinguish between our physical reality, another physical reality, and the whole of mathematics (a meta-reality). Then is your inability to distinguish reality as it is from how it is experienced subjectively from the inside (ie, perception).

It should be obvious to everyone that you don't understand the first thing about reality, whether that means mathematics, physics or even "life" and so any opinion you might form on the matter is grossly misinformed.

[I think he was hinting that mathematics is boring in comparison to "life". However, many find mathematics fascinating - a welcome relief from the boredom of life.]

The moment you claim that abstractions don't exist, you can't do any physics because molecules, atoms, and even quarks are all abstractions of more fundamental objects. And in fact, those "more fundamental" objects are themselves only abstractions which people postulate to exist in order to explain perceptions. In a weird turnaround, even superstrings are only abstractions.

Science is not reality - it is a model for us to understand reality. Just as Buddhism (Hahn is a Buddhist monk) is a finger pointing at the moon, and not the moon itself, so too is Science. Neither the Buddhist explanation, nor Physics is reality - just a way for us humans to try and make sense of things (get it to make sense?). The validity of one does not preclude the validity of the other - in fact, they must both be true if people can live by them - which they have.

You're wrong - physics is reality. To be precise, physical reality is nothing but a branch of mathematics which happens to have subjective perceivers within its theorems, and 'physics' is our explorations of that mathematics. And of course, math is a representation of other math only so long as it's incomplete, because the moment it's complete it becomes the real thing. There is no magical ontological asymmetry between one type of math and another, the one being real where the other is "merely representational".

There is no other intelligible definition of reality. There's actually a good article in May 2003's issue of ScientificAmerican about the meaning of 'multiverse' which talks about this issue.

And why that reality has to be intelligible?

[It doesn't have to be. Indeed, it doesn't have to be anything in particular, but thus far there's no evidence to suggest it isn't intelligible.]
You're wrong, physics is reality.

Physics models reality. Physics changes with each new theory but we don't pretend reality changes along with it. Believing that physics is reality is like eating the menu. TheMapIsNotTheTerritory. DontEatTheMenu. -- EricHodges

To be precise, physical reality is nothing but a branch of mathematics which happens to have subjective perceivers within its theorems and 'physics' is our explorations of that mathematics.

Mathematics is a creation of domesticated primate nervous systems. If physical reality was a branch of mathematics then physical reality would have to be incomplete or inconsistent due to GoedelsTheorem. -- EricHodges

For something to be created, it must be possible for its creator to determine its structure, or at the very least its existential status, it must have been possible for the created object to not exist. Such is not the case with mathematics since mathematicians have absolutely no power at all over their "creation". Thus, all agree that mathematics is real, that it is discovered, and not a creation at all. To believe otherwise is to be an absolute loony on a par with creationists.

I agree that mathematics is real, but I don't agree that mathematics is reality. Math is a model we created. There is no evidence that any other organism created it independently before us, but the possibility exists. -- EricHodges

I interpret your saying "mathematics is reality" as "physical reality is a branch of mathematics". And as I already explained, the only evidence we need for physical reality being a branch of math is that math works in physics. Besides, the notion that there is something "out there" which is neither our perceptions nor math because it possesses some inexpressible mystical quality that makes it different from both of them, is ludicrous and in direct contradiction to OccamsRazor.

I didn't say "mathematics is reality", so I'm not sure who you're talking to here. OccamsRazor is violated all the time, so I'm not worried if believing in an absolute external reality violates it. If there isn't anything outside you and me that we each observe independently it doesn't matter to model building or verification. Science ignores solipsism.

''I'm tempted to remove the above paragraph as too confused and besides the point but it seems to be honest, which can't be said of, say:

"Well then, are we creating this paragraph or merely discovering a particular word-sequence? (I assume that the binary representation of this paragraph occurs somewhere in the decimal expansion of pi.)"

To answer your question, math is independent from you and me. It isn't "outside" us, it transcends us completely. Since physics is a branch of math, that particular branch which best explains our perceptions, it too is independent from you and me. There doesn't need to be anything completely "apart from" us the way that most people assume physical reality to be in order to avoid solipsism completely.

In fact, the existence of anything completely "outside" us cannot ever be proved from our subjective perceptions so its existence must be assumed. Any such assumption is an attempt to "create" reality and hence the act of a solipsist.


[Do we make cars, or just discover certain possible structures (which when assembled we call cars)? Exactly! It is possible for cars to not exist physically because we could choose to not make them. In contrast, it's impossible to say that we created internal combustion anymore than someone can say they created pi. As a mathematician, you can choose to not construct a proof but the theorem's existence is independent of your actions.]

As for physical reality being subject to the GIT, well so what? If physics is the set of all self-consistent theories, it is inconsistent; if not, it is incomplete. This is neither untenable nor absurd, it is self-evident just as the GIT is self-evident. To believe that physical reality isn't subject to the GIT is to believe the supernatural, the mystical, without any proof at all, without even the possibility of a proof. You are denying the power of mathematics to model physical reality, a power that can only be due to physical reality being mathematics. This is entirely analogous to the creationists denying the power of science. Your mystical distinction between physical reality and mathematics is not supported by a single factoid but only the sheer power of your delusions, your Faith.

To address your earlier point, if physics changes, so does the past, retroactively. Each time physics changes, reality does so as well. Of course, you can't tell this has happened because the change is outside of your perception of time, a perception which is embedded within reality. This is one way of looking at things. The other way of looking at it I have already described: physics is never invented by human beings but only discovered and we just haven't discovered all physics yet.

Of course, this is a question of semantics. And it is completely tangential to the question of abstractions. You have never addressed the fact that abstractions exist in physical reality just as they do in mathematics. You claimed that they only exist in science, but this is errant nonsense.


Can you discuss math and physics without insulting me? -- EricHodges

Can you accept as fact what everyone of any import in the field, in all of human history, has believed to be self-evident? Can you show proper respect for facts everyone accepts as true instead of casually dismissing them? Can you ask why your misinformed opinion is wrong instead of stating it as fact? Can you refrain from using "but I wouldn't like the outcome" as an argument? It seems not, and that's pretty much why I can't discuss philosophy of math and physics without insulting you.

No, no, no, and yes. You can discuss the philosophy of math and physics without insulting me by omitting the insults. -- EricHodges

The closest valid position to your view of math is called Constructivism and while it was alive for a few years, it's been dead for many. Your position is so deader than dead that its name has been recycled by educators to mean something else. And I'm pretty sure Constructivists never claimed that math was a creation of mathematicians.

So the closest "valid position" is invalid and isn't really my position? Then let's ignore it. -- EricHodges

Let's ignore you.

That should be easy since nothing exists outside of you.

Furthermore, can I suggest safely that a molecule is not an 'abstraction' of quarks, &c, but rather an amalgamation? And... also may I suggest that 'physics' in this mode refers to the physics as understood by people as being dynamic, and not the fundamental nature of what is real? It seems to me that a couple of minor linguistic differences were not ironed out early on, and we are really ArguingSemantics? or imagining a conflict. -- JoeOsborn

Can you suggest that molecules aren't abstractions? No, you can't because it's false. The only way you could suggest this would be if you don't understand what the word "abstraction" means. Something is an abstraction if it has supervenient (in the abstract layer) properties which can't be traced back to any subvenient (in the concrete layer) properties but only to the interrelationships between subvenient objects. A neutron star is an abstraction since it is a stable state of zillions of neutrons all of which are unstable on their own. A molecule is an abstraction of atoms which are abstractions of nucleons and electrons, which are in turn abstractions of quarks. A molecule isn't simply an "amalgamation", it's an abstraction to the third power.

I really don't get how people can misunderstand abstractions on a forum full of programmers.

There are linguistic differences, but that's inevitable since Eric doesn't possess the concepts necessary to talk about the subject.

If you really think about it, you'll realize that it would be impossible for programmers to understand the concept of "abstraction". That's because it's a fuzzy concept, and when you stretch it to its pathological extreme, you get amalgamation. Programmers love pathological cases.


I wonder who the proponent of "physical reality is a branch of math" is. This page is an interesting mix of things I've written elsewhere and things that are exactly like I would have written them, once upon a time. Makes me wonder who the other voice that sounds like me is. -- RichardKulisz


This page has entered a LaynesLaw debate over the definition of "abstraction".
So I can invent a new formalism, call it Mathematics, and pretend it is reality. No need to start arguing since it is self-evident. Interesting food for a solipsist. -- PhilippeDetournay
See ThereIsNoInfinity, InfiniteStateMachine, DefinitionOfLife, WhatsaDistinction, LeibnizianDefinitionOfConsciousness, FindMeaCircle, ObjectIdentity, SoftwareGivesUsGodLikePowers, UsefulLie
CategoryAbstraction CategoryMath CategoryPhysics

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