The Question : is mathematics discovered or invented?

[oldman]

...Penrose ...Wigner (who both, by the way, are physicists, right?)

No. Not Penrose. He's a mathematician who writes superbly about speculative or mysterious parts of physics. But his work on tiling (Penrose tiling) did have a big impact on solid state physics when Schectman unexpectedly discovered (quasi) crystals with previously-thought-impossible five-fold symmetries, long ago.

Your later remark "Physics is the discipline that concerns itself with building perfect models of the universe, then falls continuously short in its Sisyphean effort" is lovely.

But this would be theoretical physics since about 1975. Not the physics that wins Nobel prizes e.g. for discovering the phenomenon of giant magnetoresistance that makes storing all this talk stuff compactly on disc so easy.

 

[Noone]

sorry but math was here before we were so the answer is no to both... it just wasnt called math nor did people know how to show it to others like how we use words. the world and the means of how it works and the ways to measure it were allways here or there, its just our thought is not. It was man the defines and lables all things for the means of communication to others. math was also difined for the same thing, to give understanding of how, what, and why the workings of the world work how they work. but then if you see it in a difrent way it would be yes to both... mainly philosophy is chaotic because the all most infinit ways of perception of the point of views of one kind of thought -.- but even now if all the math was never written down we could look to nature to unravel it again... just like how they did it back in the day of stick's and stone's :D

 

[Noone]

first you must discover the concept to invent somthing of that concept... so its like the question of which came frist the chicken or the egg... we all know one thing, and that's the chicken came from the egg... so the invention came from the discovery of the concept. its the answer is discoverd :D doesn't matter much were the egg came from maybe chickens didnt always lay eggs x.X silly question this one is. answer is logical. its discoverd. you must discover your invention be for you can invent somthing :P

 

[Noone]

are unknown start is the egg were the chickens. we know were we came from :D just don't know were the egg did

 

[Noone]

this question has been de-bunked by logical and reasonable thinking :P

 

[Noone]

Reasonable thought is what brings control over a chaotic philosophy, logic binds it by telling what must be true and what must be false.

 

[Noone]

so for us to invent somthing you must discover your inventions concept. aka the foundation for your invention to be made or said or shown

 

[CaptainQuasar]

Not exactly. We all adhere to the same physical reality, everybody doesn't get to invent their own physics... but scientists (like Newton) do invent the math (or symbolism/diagrams) to help them understand the physical world. We're pattern making creatures, it's absolutely in our nature. We invented supernatural things to explain phenomena so that the pattern could be fulfilled. Math is a more sophisticated version of this need for us to complete patterns to make sense of things.

There have been quite a few different and conflicting versions of physics!

And if you're talking about symbolism and diagrams, that's again something I've pointed out is common to all disciplines. The symbolism and diagrams of physics are just as invented.

Phenomena in the physical world were already constrained by the calculus Newton and Leibniz each independently discovered while trying to model it. They couldn't have simply invented any mathematics they desired to use to model it. And I would think there were conclusions they were forced into by the nature of the mathematics that they did not anticipate via physical observations - conclusions arrived at by examination of the congruences within the math itself, not through experimental inquiry.

You can make up any story you want to for explaining supernatural phenomena - witches, ghosts, UFOs, psychic abilities, etc. and there need not be any congruence or particular structure within the explanations. Not so with mathematics.

And as I pointed out, it's the history of physics which has been much more like a flawed theorizing about mysterious phenomena and retelling of a story, rather than mathematics. On the contrary, it's the mathematics which have been consistent and unchanging throughout human history - Euclid's axioms and your namesake formula have held against all scrutiny down through the ages and are still employed in modern mathematics. Try that with Aristotle's explanation of gravity or of the fundamental elements that make up all matter (ie. Earth, Air, Fire, Water, Aether to the ancient Greeks).

So, I hate to say it because it sounds imputing, but it still looks like you're projecting. Physics is the discipline where someone can make up whatever they want and if they're deft enough in speech and mathematical legerdemain and authoritative flair can get away with it. But in mathematics, if you try to simply make something up that isn't true, your symbols and diagrams prove themselves to be false all on their own. And false conclusions will break other parts of mathematics (often quite obviously) if any attempt is made to use them. In mathematics there is some external constraint that is more immediate and forceful than the experimental confirmation that science is limited to.

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[Pythagorean]

There have been quite a few different and conflicting versions of physics!

And if you're talking about symbolism and diagrams, that's again something I've pointed out is common to all disciplines. The symbolism and diagrams of physics are just as invented.

Phenomena in the physical world were already constrained by the calculus Newton and Leibniz each independently discovered while trying to model it. They couldn't have simply invented any mathematics they desired to use to model it. And I would think there were conclusions they were forced into by the nature of the mathematics that they did not anticipate via physical observations - conclusions arrived at by examination of the congruences within the math itself, not through experimental inquiry.

You can make up any story you want to for explaining supernatural phenomena - witches, ghosts, UFOs, psychic abilities, etc. and there need not be any congruence or particular structure within the explanations. Not so with mathematics.

And as I pointed out, it's the history of physics which has been much more like a flawed theorizing about mysterious phenomena and retelling of a story, rather than mathematics. On the contrary, it's the mathematics which have been consistent and unchanging throughout human history - Euclid's axioms and your namesake formula have held against all scrutiny down through the ages and are still employed in modern mathematics. Try that with Aristotle's explanation of gravity or of the fundamental elements that make up all matter (ie. Earth, Air, Fire, Water, Aether to the ancient Greeks).

So, I hate to say it because it sounds imputing, but it still looks like you're projecting. Physics is the discipline where someone can make up whatever they want and if they're deft enough in speech and mathematical legerdemain and authoritative flair can get away with it. But in mathematics, if you try to simply make something up that isn't true, your symbols and diagrams prove themselves to be false all on their own. And false conclusions will break other parts of mathematics (often quite obviously) if any attempt is made to use them. In mathematics there is some external constraint that is more immediate and forceful than the experimental confirmation that science is limited to.

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I wasn't really talking about physics, I was talking about our physical reality. Of course physics (the discipline) is an invention, but the physical relationships are what is discovered. In response to most of the rest of your post, I'll point this out again:

(keep in mind that the author also brings up your points, but neither him or I see the conflict that you purport)
ON MATH:

Somebody once said that philosophy is the misuse of a terminology which was invented just for this purpose. In the same vein, I would say that mathematics is the science of skillful operations with concepts and rules invented just for this purpose. The principal emphasis is on the invention of concepts. Mathematics would soon run out of interesting theorems if these had to be formulated in terms of the concepts which already appear in the axioms.

The principal point which will have to be recalled later is that the mathematician could formulate only a handful of interesting theorems without defining concepts beyond those contained in the axioms and that the concepts outside those contained in the axioms are defined with a view of permitting ingenious logical operations which appeal to our aesthetic sense both as operations and also in their results of great generality and simplicity.

ON PHYSICS:

The first point is that mathematical concepts turn up in entirely unexpected connections. Moreover, they often permit an unexpectedly close and accurate description of the phenomena in these connections. Secondly, just because of this circumstance, and because we do not understand the reasons of their usefulness, we cannot know whether a theory formulated in terms of mathematical concepts is uniquely appropriate. We are in a position similar to that of a man who was provided with a bunch of keys and who, having to open several doors in succession, always hit on the right key on the first or second trial. He became skeptical concerning the uniqueness of the coordination between keys and doors.

MATH IN PHYSICS:

Naturally, we do use mathematics in everyday physics to evaluate the results of the laws of nature, to apply the conditional statements to the particular conditions which happen to prevail or happen to interest us. In order that this be possible, the laws of nature must already be formulated in mathematical language. However, the role of evaluating the consequences of already established theories is not the most important role of mathematics in physics. Mathematics, or, rather, applied mathematics, is not so much the master of the situation in this function: it is merely serving as a tool.

A possible explanation of the physicist's use of mathematics to formulate his laws of nature is that he is a somewhat irresponsible person. As a result, when he finds a connection between two quantities which resembles a connection well-known from mathematics, he will jump at the conclusion that the connection is that discussed in mathematics simply because he does not know of any other similar connection. It is not the intention of the present discussion to refute the charge that the physicist is a somewhat irresponsible person. Perhaps he is. However, it is important to point out that the mathematical formulation of the physicist's often crude experience leads in an uncanny number of cases to an amazingly accurate description of a large class of phenomena. This shows that the mathematical language has more to commend it than being the only language which we can speak; it shows that it is, in a very real sense, the correct language.

all from http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

In other words... the fact that we fail so much using math in physics should be a big hint that mathematics is not some shining grail that holds the universe together. The universe would still be here if math wasn't, we just wouldn't understand it the way we do. Math is a perfect world, the universe is not. It's absolutely spontaneous, random, and diverse.

A punch in the nose is much more real than the laplacian. However, we can both agree that the laplacian is more useful.

 

[Pythagorean]

also, here's a post I found that was made independent of this discussion here at PF:

https://www.physicsforums.com/showthread.php?t=221532#7

 

[CaptainQuasar]

Math is a perfect world, the universe is not. It's absolutely spontaneous, random, and diverse.

I again think that you're focusing on simplifications and learning devices made to ease human understanding within the field of mathematics.

To say that the universe is spontaneous and random is a rather strident assertion, correct me if I'm wrong. By my understanding, QM and the Bell's Inequalities tests et cetera simply state that we're unable to predict certain phenomena and thereby do not attempt to posit a deterministic mechanism behind them - which is not the same thing as positively asserting that the universe is random or that the particular outcomes of quantum-scale interactions are uncaused.

If the physical universe is filled with uncaused events as you appear to be positing then that very discontinuity or disjointedness, that lack of congruence, is dissimilar to the structure within mathematics that I've been talking about, I agree (but again, only under the assumption that your claim is true.) But if you're simply trying to imply that the physical universe is more complicated than what mathematics could possibly contain I think that's an untenable assertion; the closer we analyze things the more it appears there's an infinity of fractal complexity in every direction and on every scale, as it were.

And I'll reiterate again, since both your own arguments and the people you're quoting are repeatedly mentioning cases where physicists crudely, ineptly, or unsuccessfully try to use mathematics as a tool - that reflects poorly on physicists and physics, not on the subject of study of mathematics. As I said before mathematics isn't there because humans want to do calculations or because physicists want to make models of the physical universe. A wrench is a poor tool for banging nails into wooden planks but that doesn't really say anything about the wrench. (But that's just an analogy, I don't think that the subject of study of mathematics is a tool.)

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[Pythagorean]

I again think that you're focusing on simplifications and learning devices made to ease human understanding within the field of mathematics.

I'm really trying to make the point that I'm not. I mean to say that what you see as mathematics is a consequence of your brain having developed in the macroscopic world, where there's so many millions of thousands of things going on at once (considering each particle in its state around you and making you up) that you can't observe 99.99999% of the universe (rough estimate, probably too low). It's very natural for you to think mathematics was there all along, waiting just for you, because of how consistent it is with itself (something we don't get out of real life... something we crave... oh, how I loved answering math problems in high school... there was no ambiguity there.)

To say that the universe is spontaneous and random is a rather strident assertion, correct me if I'm wrong. By my understanding, QM and the Bell's Inequalities tests et cetera simply state that we're unable to predict certain phenomena and thereby do not attempt to posit a deterministic mechanism behind them - which is not the same thing as positively asserting that the universe is random or that the particular outcomes of quantum-scale interactions are uncaused.If the physical universe is filled with uncaused events as you appear to be positing then that very discontinuity or disjointedness, that lack of congruence, is dissimilar to the structure within mathematics that I've been talking about, I agree (but again, only under the assumption that your claim is true.) But if you're simply trying to imply that the physical universe is more complicated than what mathematics could possibly contain I think that's an untenable assertion; the closer we analyze things the more it appears there's an infinity of fractal complexity in every direction and on every scale, as it were.

I wouldn't say it's a strident assertion; it may be even be a logical assumption at this point This would be a whole 'nother topic to argue about that we could go on for hours about: "Is the Universe Spontaneous or Determinisitc?" But if this is a dealbreaker, it may be worth it.

And I wasn't referring to belles inequalities particularly, more the spontaneous decay of atoms. There's no way to tell which atom will decay in a sample, there's (as far as anyone can tell) no cause and effect related to this phenomena. But If I remember correctly, belle's inequality did prove the Copenhagen Interpretation to be correct.

Schroedinger's Cat is the most obvious example I can think of.

I can tell you right off that I'm not a determinist, though. I was early in my science career. I thought everything could be predicted in every way because I assumed everything worked Newtonian. That becomes harder and harder to accept as I delve into QM.

And I'll reiterate again, since both your own arguments and the people you're quoting are repeatedly mentioning cases where physicists crudely, ineptly, or unsuccessfully try to use mathematics as a tool - that reflects poorly on physicists and physics, not on the subject of study of mathematics. As I said before mathematics isn't there because humans want to do calculations or because physicists want to make models of the physical universe. A wrench is a poor tool for banging nails into wooden planks but that doesn't really say anything about the wrench. (But that's just an analogy, I don't think that the subject of study of mathematics is a tool.)

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I don't think it does reflect poorly on physicists and physics. They've done a mighty awesome job. We don't care though, whether it's perfect... that's the mathematicians obsession (as you display). We are lucky to be able to make predictions and answer our own questions about our environment. It's about satisfying our own curiosity about things; not some holy grail scientific method like politicians try to sell you on. Physics IS NOT reality. It is a representation of it.

So when you say:

"mentioning cases where physicists crudely, ineptly, or unsuccessfully try to use mathematics as a tool - that reflects poorly on physicists and physics, not on the subject of study of mathematics."

I'm wondering why you associate negativity with this. It's not like we're looking back and seeing where physicists screwed up (there's that too...) we're talking about excellent, elegant, working theories even today, that will never be able to fully describe reality alone. It's a patchwork quilt, and I have the feeling it will always be that way.

I don't mean to say this as a complaint either. I don't think you really understand how grateful physicists are that mathematics can be used in this way.

 

[CaptainQuasar]

I'm really trying to make the point that I'm not. I mean to say that what you see as mathematics is a consequence of your brain having developed in the macroscopic world,

How so? Mathematics doesn't fail to work at a quantum level so I don't see what the macroscopic world thing has to do with it - unless you're restricting your scope of consideration to the more easily-human-comprehensible mathematics that are most straightforward at a macroscopic level (which is what I meant about focusing on learning devices).

Before your thing was that mathematics is a consequence of self-consciousness - where did the connection to the macroscopic world come in? What if you put a brain in a vat and only gave it sensory input from quantum-scale measurement instruments - would that mind be unable to comprehend mathematics? I just don't see that there's any reason that would follow.

It's very natural for you to think mathematics was there all along, waiting just for you, because of how consistent it is with itself (something we don't get out of real life... something we crave... oh, how I loved answering math problems in high school... there was no ambiguity there.)

Well, it's also very natural of you to think that the subject you're studying puts you in closer touch with the “real” universe than any other field of study. Belief that our occupations have significance and reveal truth, there's something we crave too.

I wouldn't say it's a strident assertion; it may be even be a logical assumption at this point

Ah, well, if you don't think making the sort of declaration that Einstein and Bohr and Heisenberg were unwilling to make is strident, you won't mind me asserting that the universe is deterministic and therefore everything about it obeying mathematical rules I've been saying must be true.

And I wasn't referring to belles inequalities particularly, more the spontaneous decay of atoms. There's no way to tell which atom will decay in a sample, there's (as far as anyone can tell) no cause and effect related to this phenomena. But If I remember correctly, belle's inequality did prove the Copenhagen Interpretation to be correct.

But my point is that the CI does not positively state there is no deterministic mechanism producing the outcomes of QM - it simply fails to posit one because there's no basis upon which to theorize either way.

Even when you say “spontaneous decay of atoms” - there isn't anybody out there claiming for certain, or even proposing an experimental test to show, that atomic decay is uncaused, is there? That would seem rather unscientific to me.

I can tell you right off that I'm not a determinist, though. I was early in my science career. I thought everything could be predicted in every way because I assumed everything worked Newtonian. That becomes harder and harder to accept as I delve into QM.

I find it strange that physicists and others match up “deterministic” and “non-deterministic” with “Newtonian” and “QM” - both of those pairings seem like leaping to conclusions to me. The reason I think the universe might be deterministic has nothing to do with Newtonian mechanics - it's because stopping at “oh, that part's just uncaused” is silly, it's deus ex machina. Even if some phenomenon at some level is uncaused we'll never know for certain because you wouldn't be able to analyze or investigate something like that - the answer will never get better than “we don't know.”

But anyways, even if you're willing to close the case on the count of determinism versus non-determinism - I don't think it really matters. Even if it's a non-deterministic universe where things conform to statistical distributions rather than discrete values (which I never asserted was part of it, anyways), I still don't buy your thesis that mathematics is somehow an unreal thing unconnected to reality that it just so happens any self-conscious mind may develop.

I don't think it does reflect poorly on physicists and physics. They've done a mighty awesome job. We don't care though, whether it's perfect... that's the mathematicians obsession (as you display)...

I'm wondering why you associate negativity with this. It's not like we're looking back and seeing where physicists screwed up (there's that too...) we're talking about excellent, elegant, working theories even today, that will never be able to fully describe reality alone.

I would point out that you were the one who mentioned how “we fail so much using math in physics”. That's why in my response I was talking about your citing of cases “where physicists crudely, ineptly, or unsuccessfully try to use mathematics as a tool.”

In what way am I displaying an obsession with perfection? If you're simply defining math as being an obsession with perfection, it's rather circular logic to say that I'm obsessed with perfection because I like math.

I apologize if you feel I was getting too personal in talking about projecting, but you really have been attributing characteristics of physics to mathematics.

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[Pythagorean]

How so? Mathematics doesn't fail to work at a quantum level so I don't see what the macroscopic world thing has to do with it - unless you're restricting your scope of consideration to the more easily-human-comprehensible mathematics that are most straightforward at a macroscopic level (which is what I meant about focusing on learning devices).

Yes, mathematics does fail (on all levels) to describe things if you use the math alone. Mathematics doesn't really say anything about reality unless a human is there to ascribe meaning to the operations and values.

Before your thing was that mathematics is a consequence of self-consciousness - where did the connection to the macroscopic world come in? What if you put a brain in a vat and only gave it sensory input from quantum-scale measurement instruments - would that mind be unable to comprehend mathematics? I just don't see that there's any reason that would follow.

You're dramatically simplifying the human brain and you're thought experiment is vague. You might have been better of not to include this paragraph. Brain in a vat is a story about a boy who couldn't accept reality, so came up with arguments as to why it's not real.

Well, it's also very natural of you to think that the subject you're studying puts you in closer touch with the “real” universe than any other field of study. Belief that our occupations have significance and reveal truth, there's something we crave too.

That's just where your repeated fallacy is coming from. I don't. I think physics and math are both inadequate in this regard. You're the one who seems to attribute some omnipresent property to mathematics. Humans have a very narrow scope of perception and even then our brains are always adjusting them. (For instance, most indoor lighting is pea green, but your brain adjusts for this for better vision)

Ah, well, if you don't think making the sort of declaration that Einstein and Bohr and Heisenberg were unwilling to make is strident, you won't mind me asserting that the universe is deterministic and therefore everything about it obeying mathematical rules I've been saying must be true.

Why would I mind? You can assert what you want. I find it only fitting that we both make our own assertions based on our own experiences.

Everyone developing quantum mechanics was confused and maddened by it in one way or another (reading some of their philosophical mindlings on it) I don't necessarily trust your opinion of what Einstein, Bohr, and Heisenberg think either, since people often like to claim that Einstein was religious, too.

"God does not play dice"... well, this is what stopped the progress of QM. Einstein refusing to believe that their is randomness in the universe. It kind of hurt his feelings and made him depressed.

Even when you say “spontaneous decay of atoms” - there isn't anybody out there claiming for certain, or even proposing an experimental test to show, that atomic decay is uncaused, is there? That would seem rather unscientific to me.

There would be no way to prove it as far as I can tell. Our discussion is largely philosophical though... and it may seem this is the source of disagreement here. This deterministic vs. non-deterministic bit.

I find it strange that physicists and others match up “deterministic” and “non-deterministic” with “Newtonian” and “QM” - both of those pairings seem like leaping to conclusions to me. The reason I think the universe might be deterministic has nothing to do with Newtonian mechanics - it's because stopping at “oh, that part's just uncaused” is silly, it's deus ex machina. Even if some phenomenon at some level is uncaused we'll never know for certain because you wouldn't be able to analyze or investigate something like that - the answer will never get better than “we don't know.”

Well... it's like this. The whole point of science is to be able to determine things. For a long time we expected this. We, as humans, naturally assume 'cause and affect' (that's why we invent gods and supernatural phenomena)

QM seems to imply that there may be no such thing as cause and affect. And you may argue that this is a shortcoming of human perception and that we'll never be able to know about cause and effect... but then that would be a non-deterministic system simply because we can't determine it. That's good enough for me. It's useless for me build a theory based on the perception of a space alien that sees causes and affects that I'll never be able to see and therefore, have nothing to say about.

But anyways, even if you're willing to close the case on the count of determinism versus non-determinism - I don't think it really matters. Even if it's a non-deterministic universe where things conform to statistical distributions rather than discrete values (which I never asserted was part of it, anyways), I still don't buy your thesis that mathematics is somehow an unreal thing unconnected to reality that it just so happens any self-conscious mind may develop.

Truth be told, there's probably no such thing as deterministic and non-deterministic. There's no reason why there should be a conflict between them. (Consider... a path-independent integral... we may arrive at some deterministic end because of the brute force (large number of particles in the universe) but the path we take to get there is non-deterministic because of the spontaneity of identical particles.

In what way am I displaying an obsession with perfection? If you're simply defining math as being an obsession with perfection, it's rather circular logic to say that I'm obsessed with perfection because I like math.

Because you keep associating negativity when I talk about imperfection (which I happen to be proud of, personally).

I don't blame math for physics failures as you might have read, and I don't mean fail in the emotional way that you ascribe to it. In my opinion, you have to play with an idea for a finite amount of time, and apply it, and keep playing with, and it will never ever be perfect, but it will asymptotically approach perfection. (If, of course, the idea of perfection is a) accuracy and b) not having to switch the math with hand-waving in the middle of the theory to make it consistent with observation)

This perfection I describe is not important to me. The math doesn't have to be exclusive. As long as theory makes predictions within a given accuracy, it's fine.

Physics would get nowhere with math alone, but it wouldn't get anywhere without math. Math is the best thing we got... it's a very articulate language, and we need to articulate on the order of our observations and predictions.

The important part of physics is observation (which is interaction). If you can't physically interact with something, then it may as well not exist. I'm not talking about math here, because (as I've stated) math is very real and does exist, and does have a physical interaction (in our brain).

The issue here, of course, is when people think they can't interact with something, but it's in fact just a very weak interaction.

NOTE:

I also notice you tend to think I'm using an argument as a point to persuade you or something, when in fact, I'm not. For instance, the last three paragraphs (to me) don't seem to make a point one way or another... It's just interesting stuff that's popped up in my mind as a result of this discussion (i.e. the point of the discussion).

 

[CaptainQuasar]

You're dramatically simplifying the human brain and you're thought experiment is vague. You might have been better of not to include this paragraph. Brain in a vat is a story about a boy who couldn't accept reality, so came up with arguments as to why it's not real.

Ah, but “what you see as mathematics is a consequence of your brain having developed in the macroscopic world,” - that's a perfectly non-vague, non-simplifying hypothetical statement to make about the human brain and mathematics, I guess. Don't you think you're striking a little bit of a double standard to refuse to engage my arguments and dismiss them as simplifying and naïve, and talk about not accepting reality, while you're going to hypothesize about how the human brain develops and make assertions about what the mental consequences of self-consciousness are?

Everyone developing quantum mechanics was confused and maddened by it in one way or another (reading some of their philosophical mindlings on it) I don't necessarily trust your opinion of what Einstein, Bohr, and Heisenberg think either, since people often like to claim that Einstein was religious, too.

I wasn't trying to state my opinion, though - I haven't come across, and I do not think exists, statements by any of them or by any prominent scientists positively stating that QM indicates un-causedness of quantum phenomena. And it's not simply my opinion that the CI doesn't say that - I'm pretty sure it literally does not say anything like that.

That's good enough for me. It's useless for me build a theory based on the perception of a space alien that sees causes and affects that I'll never be able to see and therefore, have nothing to say about.

Except of course when you want to say that mathematics is a non-existent consequence of self-consciousness - then speculating about the significance of a space alien's perceptions is admissible evidence, eh?

All right, well, it seems to me that your position on whether mathematics is discovered or invented is amounting to saying that nothing is real, so mathematics isn't either. Or maybe not, since you just said “math is very real and does exist”... but then you qualified that statement with “the last three paragraphs (to me) don't seem to make a point one way or another.”

But I know what you mean about ideas popping into your head. This is continuing to be an interesting discussion in any case.

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[Pythagorean]

I'll respond in detail later. In the meantime, have you seen this talk? (it pertains to the marcoworld I brought up earlier... Dawkins calls it "middle world")

http://video.google.com/videoplay?docid=6308228560462155344

 

[CaptainQuasar]

I'll respond in detail later. In the meantime, have you seen this talk? (it pertains to the marcoworld I brought up earlier... Dawkins calls it "middle world")

Yes, I've seen it, though I'm not recalling its content in particular. I'll have to check it out again.

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[Pythagorean]

Yes, I've seen it, though I'm not recalling its content in particular. I'll have to check it out again.

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Dawkins doesn't bring up mathematics any, but it has a sort of influence over my opinion.

Ah, but “what you see as mathematics is a consequence of your brain having developed in the macroscopic world,” - that's a perfectly non-vague, non-simplifying hypothetical statement to make about the human brain and mathematics, I guess. Don't you think you're striking a little bit of a double standard to refuse to engage my arguments and dismiss them as simplifying and naïve, and talk about not accepting reality, while you're going to hypothesize about how the human brain develops and make assertions about what the mental consequences of self-consciousness are?

I don't think they're on the same level. It's my impression you've claimed that we could duplicate a human brain with a computer (even, perhaps, a quantum computer). I don't think we can. I think you could fool a lot of people with a well-designed application of quantum computing, but for it to actually "think on it's own" (or at least to the point that we might fool ourselves about thinking on our own...)

I wasn't trying to state my opinion, though - I haven't come across, and I do not think exists, statements by any of them or by any prominent scientists positively stating that QM indicates un-causedness of quantum phenomena. And it's not simply my opinion that the CI doesn't say that - I'm pretty sure it literally does not say anything like that.

Actually, Einstein did say that QM meant indeterminism (of course, this was an intuitive feeling of his, not a proof). That is the whole reason he didn't like QM, because he believed in determinism. There is a quote from one of his letters that details this in "The Consequences of Determinism" (you can view it in Google Books) which also has a statement reading "QM does not unseat determinism"

And it's true, of course, it really doesn't. I treat a lot of situations in my everyday life with some form of determinism, but not so much as a scientist (or pseudoscientist as an undergrad). QM is very suggestive of indeterminism, though, in my opinion.

Except of course when you want to say that mathematics is a non-existent consequence of self-consciousness - then speculating about the significance of a space alien's perceptions is admissible evidence, eh?

All right, well, it seems to me that your position on whether mathematics is discovered or invented is amounting to saying that nothing is real, so mathematics isn't either. Or maybe not, since you just said “math is very real and does exist”... but then you qualified that statement with “the last three paragraphs (to me) don't seem to make a point one way or another.”

But I know what you mean about ideas popping into your head. This is continuing to be an interesting discussion in any case.

I didn't say mathematics is a non-existent consequence of self-consciousness. Mathematics EXISTS as a consequence of self-consciousness. I also never said anything about evidence. You used the alien analogy first posts ago so I thought it would be more comprehensive.

I also never claimed that nothing is real. Why don't we trial some other subjects, for argument's sake, and I'll tell you whether I think they're a product of self-consciousness or whether they physically exist (outside of the human brain).

 

[2banon]

A new question

Hello,
I recently started asking a question concerning whether math was discovered or invented in my graduate social science class, as well as in stats. My social psyc instructor led me to this thread which I have enjoyed experiencing. I thought for a moment there might emerge some bad feelings from the topic, but was happy to witness humans acting nice.
So, here is a new question. Do we ever have a completely original idea/thought? I believed I invented that question about math, but it is historical.
Do we ever have an original thought?
Thank you for being here.
2b

 

[CaptainQuasar]

Sorry, been busy for a few days.

I don't think they're on the same level. It's my impression you've claimed that we could duplicate a human brain with a computer (even, perhaps, a quantum computer). I don't think we can. I think you could fool a lot of people with a well-designed application of quantum computing, but for it to actually "think on it's own" (or at least to the point that we might fool ourselves about thinking on our own...)

I didn't intend to say anything about duplicating human brains... was it the “brain in a vat” thing? I don't get the connection but I think that's the only thing I've said about brains.

The reason I mentioned that is because you said “what you see as mathematics is a consequence of your brain having developed in the macroscopic world”. I was pointing out that there's no reason why a brain experiencing a quantum-level world would not comprehend mathematics - your connection between mathematics and brains developing in a macroscopic world doesn't make sense to me.

Actually, Einstein did say that QM meant indeterminism (of course, this was an intuitive feeling of his, not a proof). That is the whole reason he didn't like QM, because he believed in determinism. There is a quote from one of his letters that details this in "The Consequences of Determinism" (you can view it in Google Books) which also has a statement reading "QM does not unseat determinism"

And it's true, of course, it really doesn't. I treat a lot of situations in my everyday life with some form of determinism, but not so much as a scientist (or pseudoscientist as an undergrad). QM is very suggestive of indeterminism, though, in my opinion.

I'm not an Einstein biographer or anything but it seems like you may have this backwards; the statement “QM does not unseat determinism” to me sounds as though it's saying the same thing I am, that QM does not overturn or rule out determinism.

And isn't the other classic Einstein quote on this subject “God does not play dice with the universe” ?

Any phenomenon where we do not understand the deterministic mechanism is going to appear random and suggest indeterminism. Inheritance of traits looked completely indeterminate until Mendeleev demonstrated that many traits obey narrow rules... at that point it looked like inheritance was a matter of flipping a coin or rolling a four-sided die, 1:2 or 1:4 or odds based on some other power of 2, etc. Now we've preceeded to the point where we very precisely understand many of the mechanisms by which genes combine or mutate.

But it seems to me that these things have little to do with each other. Mathematics is just as external to humans whether or not the universe is deterministic. Probabilities are equally as mathematical as discrete deterministic rules would be (or analog deterministic rules, for that matter! No reason why the mathematics of a deterministic universe is any simpler than a non-deterministic one.)

I didn't say mathematics is a non-existent consequence of self-consciousness. Mathematics EXISTS as a consequence of self-consciousness.

At this point in the conversation you know that what I mean by “exists” is not compatible with mathematics being simply thoughts or speech or whatever of self-conscious beings.

I also never said anything about evidence. You used the alien analogy first posts ago so I thought it would be more comprehensive.

Okay, replace “evidence” in my statements with whatever you'd use to build a theory. You said “It's useless for me build a theory based on the perception of a space alien”.

Basically I'm ticked off that you flat out rejected my reasoning based on whether non-human intelligence would arrive at mathematics as well as humans do, yet you're willing to toss out what appear to be completely hypothetical statements about the relationship of self-consciousness to mathematics or the relationship of some theoretical property of the development of brains to mathematics.

I also never claimed that nothing is real.

Not technically, no, but calling “real” something which exists only because of self-conscious minds thinking about it gets pretty close. You could make these claims of anything, any phenomena at all, that our perception of them is a consequence not of external reality but of a complicated internal reality we all share (and even space aliens would share, is what your talk of self-consciousness seems to entail.)

―​

2banon, if by original you mean novel, then I think that thoughts can be as novel as anything else, like the forms galaxies take or the forms that organic life takes. If you mean original as in the classical "the sum is greater than the parts" sense I'd say the same - insofar as galactic formation or the development of life is a sum greater than its parts, our thoughts can be as well.

⚛​

 

[2banon]

CQ, what I was getting at with my "new idea" question is the Jung's universal conscious concept. Did I invent my question about math from my own mind even though others have asked it apparently, or was it just one of the thoughts floating around for many to ponder when the time was right? It is the same thought that I have about music, it seems like there are not many new tunes to be had. It is getting harder to come up with an original beat that some other band has never put into a song before as can possibly be seen in lawsuits claiming stolen songs. Have all the things to be thought about been thought about, have all the tunes been arraigned? As technology continues to create new things there will be opportunity for new thoughts there, but I wonder about new thoughts concerning old ideas.

 

[Schrodinger's Dog]

I never have really understood how mathematics could be discovered, and I've not seen a particularly good argument for that. That said as is often the way with philosophy neither side has an answer and it's easily possible to argue on either side.

 

[2banon]

Hello Dog, if I may call you that. Where is it that there is no path? This fits right in with my questioning originality of idea, how can we be sure ours is a new path and not just one grown over waiting to be rediscovered?
2b

 

[siphon]

Math is equivalent to a logic language that uses numbers instead of words. It is sort of the language that makes it easier to explain the relationships of nature. Math is more of a written language than a spoken one. The odds are it did not appear until people began to read and write using traditional languages.

 

[Schrodinger's Dog]

Hello Dog, if I may call you that. Where is it that there is no path? This fits right in with my questioning originality of idea, how can we be sure ours is a new path and not just one grown over waiting to be rediscovered?
2b

Yeah sorry I've only really read the last page, so if I've missed a lot apologies. How can we be sure any knowledge is new? I mean the only way we could be sure is to find out at which point such knowledge was created, categorise it as an abstract and then say this was discovered. It needn't be original in terms of the whole universe just independently found, rather like calculus by Liebniz and Newton say. I think maths is an abstraction and I don't hold dear the idea that it exists as an entity in and of itself. There is no 2 in the universe without a consciousness to define it. 2 the number does not exist any more than i does.

 

[siphon]

According to Jung, similar ideas can spontaneously appear in different people at different places. He tried to prove this by showing how many cultures with no known connection developed similar myths and symbols, independently. The study is quite remarkable and suggest the unconscious mind forming the concepts first. These then come into conscious awareness. The unconscious is more collective, so it will generate the same basic type of output schema. While consciousness is more distinct and will flavor this output to reflect culture.

This is not surprising if you think about it logically. The conscious mind is more cerebral using the mass of the cerebral cortex. But the center of the brain is far more integrated being the place where all the cerebral connections integrate. Relative to computer power, the core would need a faster processor since the data density is higher. This trickles back to cerebral for more processing, but at a lower processing speed capable or spoken and written communication.

An analogy is one's life flashing before their eyes in a near death experience. In a matter of seconds tons of data is processed. It happens too fast, such that one would not be able to speak that fast in real time. You got to rely on the after image that the data output burned into the cerebral. Then you can take it apart and spread that 2 seconds of core processing over several hours so one can communicate it. But in the process of translation there will be data lost or maybe even misunderstood. Math may have formed the same way, with it first being formulated with the higher processor speed of the core. The core then kicks the result up to the cerebral for gradual unfolding.

The original gut feelings of the earliest mathematicians would have been too high in data density or data speed to be able to put it directly into words. It could have been like hearing a recording at high speeds to where one hears a hum with only a few words becoming conscious here and there, but not enough to gather any solid meaning. They had to wait for the data to slow down and/or spread out into the cerebral so they could use language to process the data.

 

[octelcogopod]

On the face of things it seems pretty obvious that there is quantity in the universe right?
You have two apples, three oranges, and so forth.
At the most basic level math is about adding, subtracting, dividing etc, but we wouldn't be able to do any of this without an external world, or even internal world (same thing.)
The problem is, it appears to me that the relations, the logic and the math behind the quantity of this world is not inherent in the physical reality itself.
So you have two apples, but what will happen to them without a conscious mind?
Nothing. If there is nothing that is capable of creating the math that could arise from 2 apples and 3 oranges, then the math doesn't exist.

It's kind of like putting a glass of water next to an animal, it might drink it, it might not, but there's no logic in saying the water is made for being drinked, or that somehow the concept of drinking exists if there is no animal to drink it.
I would argue that you need both a brain, and a world, to have math.

 

[oldman]

Posts here seems to be swinging back to basics, in simplifying discussion of the titular question down to whether counting numbers, like "two", are invented or discovered. See recent views posted by Schroedinger's Dog:

There is no 2 in the universe without a consciousness to define it. 2 the number does not exist any more than (1?) does.

and Octelcogopod:

So you have two apples, but what will happen to them without a conscious mind?
Nothing. If there is nothing that is capable of creating the math that could arise from 2 apples and 3 oranges, then the math doesn't exist.

Here is two cents worth of my "philosophy": I strongly believe that when one is faced with difficult questions about complicated subjects (which is what philosophers are supposed to tackle), the way to start is to go back to the fundamentals and worry about sophistications later on. In this case don't start by worrying about "math" as a generality --- most people are intimidated by this very word, anyway --- settle the basics, like arithmetic and the counting numbers, first.

It's nice to see this thread turning back to such matters, after much "hanna-hanna" and "wurra-wurra" as heavy discussions are called in this far neck of the woods.

This is not to say that in these forums one should be intimidated into avoiding discussions about sophisticated topics, say https://www.physicsforums.com/showthread.php?p=1656605"

 

[octelcogopod]

oldman I see..

I'm not sure if this topic can be deduced to something simple, because I don't have all the knowledge, but from the looks of it, if you have two apples, which is one apple and one apple, then the concept of "two" is something which arises in the brain.
It seems clear to me you need some entity to say 'two apples.'

I'm not sure if one can deduce from this that all math is the same, that every logical relationship - and in turn the math that one can calculate from these - is equal to arithmetic and counting.
This would include the most advanced quantum math to whatever.
The nature of the universe and logic is difficult, and the way everything fits together so nicely is a persuasive indication that it is discovered, and that one day we might have a theory of everything.
On the other hand, that theory of everything may just be a model of perception after all, with hints of discovered math, or maybe just one of many ways one can correctly perceive reality.

Bottom line - this is complicated and I do not know :)

 

[JoeDawg]

The nature of the universe and logic is difficult, and the way everything fits together so nicely is a persuasive indication that it is discovered...

Think of it this way, if I create a model of an airplane... then throw it... it will probably break.

But if I go into greater detail, create a model plane with a real working engine... with flaps and a steering mechanism...etc... etc... If I include enough detail into my model, then at least theoretically it would fly.

If I then put this plane in a wind tunnel, I could then use the model to predict what actual planes might do.

This is essentially what math is doing. Its a very finely tuned model, and we can learn about the world from it, because its such a damn good simulation of the actual thing. It took a long time to build and there were many dead ends with regards to design, but math has had this great error correction method... its called reality. We continue to fine tune it, or, rather others do... I suck at math.

 

[octelcogopod]

Yep, but here's my question as well.. If we in theory create a model that is exactly correct, if possible, would this model be discovered or would it be that we designed the same thing as reality from scratch?

The obvious limit to why math would be created would be that our math model can never include everything, that it fundamentally can only describe certain interactions and forms in the universe.
But if this is the case and we have to create a new language for those new things, what would that mean?

It seems to me that if we had a true theory of everything with math, then we had simply combined puzzle pieces together, because in the end we'd be some kind of creator/god characters, and nothing would be a mystery anymore. We'd simply just know everything.
I guess my point is that if we can have math that describes everything, then it is discovered(because that would mean everything is mathematical and that math is perfect), and if it can never do so, then it is more of a created model.

Excuse me if this is too crackpot and extreme, but I did this to make my point, hope it came out clear.

 

[Pythagorean]

Sorry, been busy for a few days.

happens to the best of us :P I'm kind of disoriented from my points and arguments (just getting over flu too). But having developed more thoughts and ideas on this, I don't mind starting over.

I'm not an Einstein biographer or anything but it seems like you may have this backwards; the statement “QM does not unseat determinism” to me sounds as though it's saying the same thing I am, that QM does not overturn or rule out determinism.

And isn't the other classic Einstein quote on this subject “God does not play dice with the universe” ?

Einstein didn't say that. Einstein was quoted by the author who said that. And yes, I was conceding that QM does not unseat determinism (as I said in that particular post).

The classic Einstein quote you bring up though, "God does not play dice" was his reaction to QM. In fact, he spent his last days on his death bed trying to come up with an alternative to QM because he didn't like it. The point not that it disproves determinism but that it's very suggestive of something like this to people raised on Newtonian physics.

Any phenomenon where we do not understand the deterministic mechanism is going to appear random and suggest indeterminism. Inheritance of traits looked completely indeterminate until Mendeleev demonstrated that many traits obey narrow rules... at that point it looked like inheritance was a matter of flipping a coin or rolling a four-sided die, 1:2 or 1:4 or odds based on some other power of 2, etc. Now we've preceeded to the point where we very precisely understand many of the mechanisms by which genes combine or mutate.

Yes, you can say that generally about many sciences. Unfortunately, as octelco said above, there's no universal math that perfectly describes everything (as far as we can tell). You have to betray and contradict the math for different cases. You can zoom in on the details and lose the general picture or you can zoom out to the general picture and lose the details (or go somewhere in between).

Basically I'm ticked off that you flat out rejected my reasoning based on whether non-human intelligence would arrive at mathematics as well as humans do, yet you're willing to toss out what appear to be completely hypothetical statements about the relationship of self-consciousness to mathematics or the relationship of some theoretical property of the development of brains to mathematics.

Well, it's fair enough that we drop all that, as it's gotten somewhat convoluted.

What I'm really saying is that the burden of proof is on you to show me how mathematics exists inherently in the universe. But it's more difficult than that... I've received some programming in mathematics myself, so you'll have to prove it to my grandmother, who has not been brainwashed by mathematics.

Something else to consider: I don't know if you're religious or not, but I'm atheist. The gods in religions are still very real to me. Take, for example, the Christian God. Whether he truly exists as a separate entity is impossible to prove, but look how much he has physically manifested into our life (evangelists on ch. 4, church buildings, congregations of political warriors a.k.a God's Warriors, crusades).

I feel somehow that you take it lightly when I insist that mathematics is very real, regardless of whether it exists separate of the human mind. I don't believe that either God or mathematics exists independent of human thought despite their physical manifestations.

I guess my point is that if we can have math that describes everything, then it is discovered(because that would mean everything is mathematical and that math is perfect), and if it can never do so, then it is more of a created model.

Excuse me if this is too crackpot and extreme, but I did this to make my point, hope it came out clear.

That's pretty much what I would expect if math were invented, and I seriously doubt we'll ever have a theory of everything that isn't very patchwork.