Mathematical and logical truths exist before we have discovered them, so

[Georgepowell]

So does that mean that a world can exist through purely a system of numbers, values and rules?

This system can exist without any physical matter, as it is only a mathematical pattern/system, and not an object.

The system can include such things as "time" and "dimensions", but only the mathematical interpretations behind them. As this system of rules and patterns evolves to deeper and deeper complexities, things resembling 'life' and 'objects' can exist. (It is still only the values and properties of these things that exist, and not the objects themselves).

I propose that humans and the universe are nothing more than one part of a mathematical system that can and always has existed without necessary "existing" any more than the number 4 'exists'.

This explains why there is no real analogy or familiarity to explain the phenomena in the quantum world, the particles and fields really are nothing more than values and numerical properties that follow rules.

This also means that every other possible (stable) system of values and rules does exist just as much as ours does (which links in with the multiple universes idea), which explains how life originated despite the improbabilities.

Furthermore, I think that if something is possible, then it has to 'exist', just because we are nothing but a set of values following a set of rules.

Tell me your thoughts, I haven't had too long to think about it, I just wanted to here someone else's view.

 

[epenguin]

"Mathematical and logical truths exist before we have discovered them"

Where?

 

[Alfinch]

Where?

We're assuming that if two independent civilisations were to develop mathematics, even on opposite sides of the universe, the mathematical rules they deduced would be identical. For example, prime numbers are always only divisible by one and themselves, regardless of your location in time and space.

A problem arises when you try to explain how an individual conscious entity can exist simply as a set of mathematical rules. If this were possible, if I wrote the algorithm for George on a piece of paper (presumably a very large piece of paper), it too would be conscious just as George is himself. Call it a hunch, but that can't be right, can it?

 

[Gear300]

A problem arises when you try to explain how an individual conscious entity can exist simply as a set of mathematical rules. If this were possible, if I wrote the algorithm for George on a piece of paper (presumably a very large piece of paper), it too would be conscious just as George is himself. Call it a hunch, but that can't be right, can it?

Wouldn't that mean our conscious has limits/boundaries?...it seems logical...after all, we can't really imagine anything beyond our conscious.

 

[epenguin]

We're assuming that if two independent civilisations were to develop mathematics, even on opposite sides of the universe, the mathematical rules they deduced would be identical. For example, prime numbers are always only divisible by one and themselves, regardless of your location in time and space.

That is not a very good example as that is just a definition (of prime numbers).
But I agree there are theorems about prime numbers that someone could independently discover elsewhere. They might have a handful of 20 stones and discover they could arrange them in a rectangular pattern

...
...
...
...

but that they could not make any rectangular pattern with one less stone.

Only in my view, and I think there is a philosophy that says this (constructivism?) until there are beings collecting stones, counting and arranging, "19 is prime" does not exist. Only the stones exist.

I think things exist independent of us, but not "truths". I am challenging your introductory premise.

However maybe this is not mainly what interests you, your ideas formulated a bit differently can perhaps be pursed independently of this quibble.

 

[turbo]

The "truths" don't exist as entities. They gain that authority as we try to make sense of the world, and come to realize that there are some rules that we can apply under a range of circumstances (perhaps even most or all circumstances) and obtain reliable and testable results. Many, many times we have discovered and promulgated "truths" that turned out not to be true at all, and there is absolutely no reason to believe that many cherished ideas in modern science will be shown to be inaccurate, incomplete, or "not even wrong".

 

[m.e.t.a.]

I feel like the exasperated parent whom a child has just played the "Why?" game with, except that you, George, have gone about 100 "Why?"s beyond the usual point of conclusion of the game! I find all that has been said so far interesting, but I won't lose any sleep thinking about it. The reason is that, to questions such as "What is Existence?", there is simply no answer which is simultaneously both rational and satisfactory. You can step outside of science and resort to supernatural explanations, thus feeling satisfied. Or you can deduce that the idea of an "answer" to the question of existence is meaningless, thus being rational. But you can't have both at the same time.

A problem arises when you try to explain how an individual conscious entity can exist simply as a set of mathematical rules. If this were possible, if I wrote the algorithm for George on a piece of paper (presumably a very large piece of paper), it too would be conscious just as George is himself. Call it a hunch, but that can't be right, can it?

There's a thought. I'm sure you don't really mean paper, of course. When you represent a mathematical truth on paper, you have made marks on paper, you have not Created a Truth. Can I assume that you refer to "paper" as an analogy for something else? And if so, the question becomes: what? Is the paper "Existence". If so, what is the ink -- and how do you define "Existence", for that matter? See how these questions quickly become utterly meaningless. Almost as quickly, it becomes impossible to even formulate the next question.

George, I think that you have posed a fascinating, if unanswerable, question; but it is my advice that you not spend too much time or effort in looking for an answer anyway. You might become rather depressed.

P.S. Incidentally, I can't believe that the thread has made it even this far without a Douglas Adams reference. Do you feel cheated?

- m.e.t.a.

 

[CaptainQuasar]

Many, many times we have discovered and promulgated "truths" that turned out not to be true at all, and there is absolutely no reason to believe that many cherished ideas in modern science will be shown to be inaccurate, incomplete, or "not even wrong".

But in mathematics and logic, though? Certainly that's happened in science but there aren't any civilizations that have concluded that 2 + 2 = 5 that I know of. Mathematical and logical principles, however they have been expressed between different cultures (like the Mayans using a base 5 number system or the Egyptians only being able to conceive of fractions with "1" in the denominator) have always turned out to be reconcilable.

⚛​

 

[turbo]

But in mathematics and logic, though? Certainly that's happened in science but there aren't any civilizations that have concluded that 2 + 2 = 5 that I know of. Mathematical and logical principles, however they have been expressed between different cultures (like the Mayans using a base 5 number system or the Egyptians only being able to conceive of fractions with "1" in the denominator) have always turned out to be reconcilable.

⚛​

You're right, of course. Mathematics is the most provable, testable science that there is, and it is simple in that we are dealing with concepts, not real-world observations with experimental errors. For the macroscopic world, it is a wonderful system. Once we get to the quantum scale, difficulties arise. It seems that our mathematics cannot be used to construct reasonable models of the quantum world. A fault of quantum theory or a limitation of mathematics? I lean toward the former, but the latter is not out of the question.

"I must say that I am very dissatisfied with the situation, because this so-called 'good theory' does involve neglecting infinities which appear in its equations, neglecting them in an arbitrary way. This is just not sensible mathematics. Sensible mathematics involves neglecting a quantity when it is small — not neglecting it just because it is infinitely great and you do not want it!"

 

[CaptainQuasar]

You're right, of course. Mathematics is the most provable, testable science that there is, and it is simple in that we are dealing with concepts, not real-world observations with experimental errors. For the macroscopic world, it is a wonderful system. Once we get to the quantum scale, difficulties arise. It seems that our mathematics cannot be used to construct reasonable models of the quantum world. A fault of quantum theory or a limitation of mathematics? I lean toward the former, but the latter is not out of the question.

What do you mean that mathematics cannot be used to construct reasonable models of the quantum world? What else is used to construct those models?

I don't understand why you appear to be suggesting that mathematics stops working at the quantum level. To my knowledge it does not, in fact it's so reliable that we pretty much explore the quantum world exclusively with mathematical modeling.

Nothing we have discovered relative to quantum phenomena has rendered invalid one iota of mathematics. Mathematics doesn't have some preference for the macroscopic over the quantum world any more than science deciding that the heavens were heliocentric rather than geocentric revealed any problems in mathematics.

IMO you are confusing mathematics with physics. The science of physics is what explodes due to paradigm shift every few centuries and has to be put back together from scratch... mathematics continues working through it all with at most some new notation being desirable.

P.S. I also do not regard mathematics to be some sort of science. They're completely different things. Mathematics isn't established or expanded by the scientific method nor are its conclusions tested by experimentation as those of science are.

⚛​

 

[Gear300]

George, I think that you have posed a fascinating, if unanswerable, question; but it is my advice that you not spend too much time or effort in looking for an answer anyway. You might become rather depressed.
- m.e.t.a.

A true philosopher's way of putting it.

 

[turbo]

What do you mean that mathematics cannot be used to construct reasonable models of the quantum world? What else is used to construct those models?

Mathematics has been used to model and test quantum theories, and the accordance with theory has been impressive. One need only audit a few of Roger Penrose's popular lectures to get a feel for this.

Mathematics started with simple enumeration, and advanced from there. Once we get to quantum scales, we have to start casting out infinities in order to get these great results. I don't think that it's a fault of our understanding of mathematics, but we cannot reject it out hand either.

One glaring problem is the 120 OOM too-small (is that a big enough disagreement?) prediction of the expansive force expected to arise from the energy of the quantum vacuum. It's not infinity, but we currently throw it away because it is convenient to do so. (Refer to Dirac) Do we have a fundamental defect in quantum theory (vs classical physics) or is there some defect in our application of mathematics to this field. Epistemology might help here, but it's honored more in the breach these days, it seems.

 

[CaptainQuasar]

...or is there some defect in our application of mathematics to this field.

Oh, sure. But physicists erroneously applying mathematics to a problem of science isn't the same thing as a flaw or limitation in mathematics itself.

In essence I'm pretty skeptical of assertions that mathematics is something that has no independent existence. Yeah, science is proven to be erroneous or the product of a fixated point of view over and over again down the centuries but mathematics has had an entirely different history. Yet it seems to me that scientists often try to surreptitiously gather mathematics into the failures of science, misery loves company don'cha know...

⚛​

 

[Pythagorean]

Oh, sure. But physicists erroneously applying mathematics to a problem of science isn't the same thing as a flaw or limitation in mathematics itself.

In essence I'm pretty skeptical of assertions that mathematics is something that has no independent existence. Yeah, science is proven to be erroneous or the product of a fixated point of view over and over again down the centuries but mathematics has had an entirely different history. Yet it seems to me that scientists often try to surreptitiously gather mathematics into the failures of science, misery loves company don'cha know...

⚛​

I'm detecting a bias...

Mathematics is sometimes necessary but always insufficient for accurately describing anything in the universe. 2+4 = 6 tells me nothing in the context of my experience in the universe. 2 apples + 4 tomatoes could be equivalent to 2 fruits or 6 fruits depending on who you talk to and how they define a fruit. These shortcomings are inherent to describing reality. Of course mathematics in its purest form is free of them... because mathematics in its purest form has nothing to do with reality (which itself is much less stable than the concept of mathematics)

An alien race might come up with an alternate method for manipulating their world that doesn't require mathematics. It seems anthrocentric to claim the human method of observation and manipulation is the only one.

Also, every human race has come up with theology independently too. If aliens were to be religious would we have to start considering the validity of religion as a universal truth as well?

 

[CaptainQuasar]

I'm detecting a bias...

I've certainly got a bias, but it's no more of one than when physicists or other scientists try to blame mathematics for things that go wrong in the course of their own discipline!

Mathematics is sometimes necessary but always insufficient for accurately describing anything in the universe. 2+4 = 6 tells me nothing in the context of my experience in the universe. 2 apples + 4 tomatoes could be equivalent to 2 fruits or 6 fruits depending on who you talk to and how they define a fruit. These shortcomings are inherent to describing reality. Of course mathematics in its purest form is free of them... because mathematics in its purest form has nothing to do with reality (which itself is much less stable then the concept of mathematics)

An alien race might come up with an alternate method for manipulating their world that doesn't require mathematics. It seems anthrocentric to claim the human method of observation and manipulation is the only one.

That would be anthropocentric if I claimed that, yes... but I didn't. I just said that it has existence separate from human contemplation of it, nothing about mathematics being the only way to do anything.

And if that's the case, that mathematics or its subject of study has some existence separate from human contemplation of it, it seems odd to say that it has nothing to do with reality. Introducing the problem of defining what a fruit is is again attempting to drag one of the problems of science into mathematics, btw.

Also, every human race has come up with theology independently too. If aliens were to be religious would we have to start questioning the validity of religion as well?

If aliens ended up developing the exact same theology, which hasn't even happened independently between separate cultures on Earth, that would be pretty notable, yes.

Whereas if aliens developed mathematics reconcilable with human mathematics, many aspects of which have been developed independently in Earth history, no one would be anywhere near as amazed as they would be if we encountered an alien civilization practing, say, Theravada Buddhism.

⚛​

 

[Pythagorean]

(1)I've certainly got a bias, but it's no more of one than when physicists or other scientists try to blame mathematics for things that go wrong in the course of their own discipline!


(2)That would be anthropocentric if I claimed that, yes... but I didn't. I just said that it has existence separate from human contemplation of it, nothing about mathematics being the only way to do anything.

(3)And if that's the case, that mathematics or its subject of study has some existence separate from human contemplation of it, it seems odd to say that it has nothing to do with reality. Introducing the problem of defining what a fruit is is again attempting to drag one of the problems of science into mathematics, btw.



(4)If aliens ended up developing the exact same theology, which hasn't even happened independently between separate cultures on Earth, that would be pretty notable, yes.

Whereas if aliens developed mathematics reconcilable with human mathematics, many aspects of which have been developed independently in Earth history, no one would be anywhere near as amazed as they would be if we encountered an alien civilization practing, say, Theravada Buddhism.

⚛​

(1) I think you have a huge misconception here and you're clumping and stereotyping based on what seems like a personal experience of yours (I also notice not much of your opinion has changed since I last talked to you, further enforcing your bias). I'm pointing this out because it may very well be impossible to have a progressive discussion with you at all.

(2) Fair enough.

(3) Actually, if you'd free yourself from your bias of my line of thought you'd see that I outright admitted that science has flaws inherent to it. But the point is that pure mathematics is void of reality. You have to attach qualitative meaning to it for it to describe reality at all. Of course science makes flaws describing reality and mathematics doesn't; mathematics doesn't attempt to describe reality. Science uses mathematics because it's more accurate than language, not because it perfectly describes anything.

(4) Do you see how you're expecting exact relationships (right down to the name of the religion) for theology, but you'll willing to be much more loose about the relationships between the mathematics of different species?

Just as cultures in Earth developed different theologies, they developed different mathematical theories and they compared and confirmed some of them, and found others to be erroneous, then they founded better axioms and reformed.

You will find mathematicians that disagree about math just as you will find theologists who disagree about theological principals. You will find different schools focused on different axioms in both cases.

Now, I'm not claiming mathematics and religion are the same. Mathematicians designed their axioms in favor of structure and self-consistency. You don't need the rest of the world to confirm mathematics. Religion, on the other hand, based their axioms on observations of reality. It stands more a chance of being wrong since it's actually daring to make a guess about reality.

Science is somewhere in between religion and mathematics, making guesses about the universe, but using the mathematics (like you'd use a man made wrench) to make sure the observations themselves are consistent enough to make predictions about similar observations.

 

[Phrak]

"Mathematical and logical truths exist before we have discovered them"

Where?

On Orion's Belt.

 

[Georgepowell]

"Mathematical and logical truths exist before we have discovered them"

Where?

Where? Well, I suppose that question is meaningless after you have presumed that time and dimensions are only mathematical systems. These systems do not exist in a 'place', because a 'place' only has any meaning when dimensions exist.

But I see what your saying, For something to exist, it needs to exist somewhere, right? Well that is only if it is a physical object. The number four exists, as does the feeling of happiness. But neither of them can be given a position in space or time.

A problem arises when you try to explain how an individual conscious entity can exist simply as a set of mathematical rules. If this were possible, if I wrote the algorithm for George on a piece of paper (presumably a very large piece of paper), it too would be conscious just as George is himself. Call it a hunch, but that can't be right, can it?

What I'm saying is that the algorithm for me already exists, and it is me. Of course it can not exist on its own, it needs the 'algorithms' for air, and the world, the universe, time and dimensions. Which if they are all stable and do not involve any mathematical contradictions or paradoxes, then they are mathematical truths and therefore "exist".

These truths and systems need not even be based on maths, there maybe a world who's fundamental language is not maths or 'logic', but of course it would be entirely impossible for us to imagine or comprehend such a world because our own minds are written fundamentally from mathematics. It's like, if your world does not have space, time, or dimensions, then how could someone from it possibly imagine them? Especially if there fundamental tool for predicting things or explaining things is completely different from maths.

 

[Georgepowell]

George, I think that you have posed a fascinating, if unanswerable, question; but it is my advice that you not spend too much time or effort in looking for an answer anyway. You might become rather depressed.
- m.e.t.a.

It is not my aim to answer it, or even argue that it is true. And no, I will not spend much time thinking about it; I am sure it is not an original idea, and as you said it is ultimately unanswerable. However, it is interesting to think about it at least.

 

[Pythagorean]

Where? Well, I suppose that question is meaningless after you have presumed that time and dimensions are only mathematical systems. These systems do not exist in a 'place', because a 'place' only has any meaning when dimensions exist.

But I see what your saying, For something to exist, it needs to exist somewhere, right? Well that is only if it is a physical object. The number four exists, as does the feeling of happiness. But neither of them can be given a position in space or time.

The number four and the feeling of happiness may exist, but the question is is whether they exist outside of the brain. If you say the number four and happiness are descriptions of the state of the system (the system being our physical brain) well that's hard to refute. But saying that the number four existed somehow outside of conscious thought doesn't seem like a falsifiable claim to me.

 

[Georgepowell]

The number four and the feeling of happiness may exist, but the question is is whether they exist outside of the brain. If you say the number four and happiness are descriptions of the state of the system (the system being our physical brain) well that's hard to refute. But saying that the number four existed somehow outside of conscious thought doesn't seem like a falsifiable claim to me.

Happiness is just a particular pattern inside the mathematical system in which we live. It is a pattern that happens inside our brain, and can ultimately be described and perhaps defined through mathematics. This pattern does exist, and so does the number four (which is a building block for all the different patterns found in this system).

The fact that everything in this world (so far) can be explained fundamentally using the tool of maths is a sign that our world is nothing more than a mathematical system. I don't think this is an original idea, but my contribution is that this system exists in exactly the same way that any other system 'exists'.

We could invent (or discover?) a new field of mathematics that cannot help us predict or explain anything in our world so far, but this system still exists in the same way that our world does.

 

[Pythagorean]

(1)Happiness is just a particular pattern inside the mathematical system in which we live. It is a pattern that happens inside our brain, and can ultimately be described and perhaps defined through mathematics. This pattern does exist, and so does the number four (which is a building block for all the different patterns found in this system).

(2)The fact that everything in this world (so far) can be explained fundamentally using the tool of maths is a sign that our world is nothing more than a mathematical system. I don't think this is an original idea, but my contribution is that this system exists in exactly the same way that any other system 'exists'.

(3)We could invent (or discover?) a new field of mathematics that cannot help us predict or explain anything in our world so far, but this system still exists in the same way that our world does.

(1) I don't really know what you're point is here. While things can be defined through mathematics that doesn't mean mathematics is some transient existence. Not everything can be described with mathematics, and there's plenty of mathematics that doesn't describe anything in reality. What about language? If this is your basis for mathematics existing outside of human thinking, you must also admit all other languages into the class, since they describe reality as well.

(2) That's false. Not everything can be described with mathematics. No math perfectly fits any observation. It's just more accurate than the English language (many times more accurate, but never spot on unless the person utilizing the math simplifies his observations through qualitative description.

(3) I disagree. It doesn't exist in the same way. It exists in our mind/brain whereas the physical world exists outside of our mind/brain.

 

[Alfinch]

I disagree. It doesn't exist in the same way. It exists in our mind/brain whereas the physical world exists outside of our mind/brain.

Aren't our minds part of the physical world?

 

[Pythagorean]

Aren't our minds part of the physical world?

yes, well, our brains specifically. I'm dividing physical realm between inside and outside the boundary layer of our skull (or at least our skin). The mind is more of a human concept itself than the brain is.

 

[CaptainQuasar]

(1) I think you have a huge misconception here and you're clumping and stereotyping based on what seems like a personal experience of yours (I also notice not much of your opinion has changed since I last talked to you, further enforcing your bias). I'm pointing this out because it may very well be impossible to have a progressive discussion with you at all.

I think it's rhetorical of you to declare that I'm the one exhibiting bias, misconceptions, and stereotyping. You aren't too bad at wielding bias yourself. For example, down below and in preceding comments you've made the statement "pure mathematics is void of reality": well this is simply assuming your own conclusions! The only reason to say this is if you're already assuming that mathematics is something derived from the human mind with no external existence.

And also I'm not making these criticisms out of the blue, I was responding to what turbo said. He proposed, "It seems that our mathematics cannot be used to construct reasonable models of the quantum world." And only when I resisted this did he refine the statement into a concern about the application of mathematics by physicists.

That's exactly the kind of behavior I'm talking about. Physics is what's concerned with describing the tangible world; that task is not a goal or objective of mathematics. That's why the proposal, "some physicists had difficulty describing what they're studying using mathematics - there must be something wrong with maths!" seems like a blame-shifting game to me.

Even if there are actually phenomena that can't be modeled with mathematics, that would have no bearing on the nature of mathematics; at least not so far as whether some aspect of mathematics is independent of the human mind. There's no reason why "must be able to describe everything in physics" would be a necessary attribute of a mathematics that is independent of the human mind.

If you really can't see how so many of these arguments are bent around physicist taking a utilitarian or instrumentalist perspective on mathematics - conceptually assuming that it is subordinate or otherwise incidental to physics - I think you are the one approaching this with bias.

(3) Actually, if you'd free yourself from your bias of my line of thought you'd see that I outright admitted that science has flaws inherent to it. But the point is that pure mathematics is void of reality. You have to attach qualitative meaning to it for it to describe reality at all. Of course science makes flaws describing reality and mathematics doesn't; mathematics doesn't attempt to describe reality. Science uses mathematics because it's more accurate than language, not because it perfectly describes anything.

Okay, that's great. It still doesn't explain why some difficulty scientists have in employing mathematics for modeling phenomena has any relevance on whether or not the subject of mathematics has existence outside of the human mind. (And, as I pointed out above, declaring mathematics to be void of reality is assuming your conclusion.)

I think it's just fine to say "science makes flaws" in this regard, it's when that's extended to mathematics, and pretenses are made such as suggesting that the development of quantum theory entailed some portion of mathematics being scratched out and rewritten - which it did not, it was science that had to be rewritten - that I take issue with and which appears to me to be a case of someone projecting the problems of science upon mathematics.

(4) Do you see how you're expecting exact relationships (right down to the name of the religion) for theology, but you'll willing to be much more loose about the relationships between the mathematics of different species?

No, I'm not. Buddhist theology contradicts Christian theology, for example, and even the most broad principles of theology of particular sects within a single religion are often completely contradictory. No matter what things were named if an alien culture posessed an independently-developed theology that in every metaphysical precept was in agreement with and compatible with a particular Earth religion that would be staggering.

Whereas conversely, however an alien culture expressed mathematics, even so specific an agreement as the fact they'd arrived at the exact same value of π would be unsurprising. Or, for example, even if they had never discovered the Pythagorean theorem and did not have the concept of triangles, we would expect nothing in the Pythagorean theorem to contradict anything within their mathematics and vice-versa. A small detail like 2 + 2 = 5, for example, would irreconcilably break the Pythagorean theorem and many other things; but we would not expect to encounter anything like that.

This is not a case of theology and mathematics being approximately similar and I'm simply being picky about details. They're fundamentally different things.

Science is somewhere in between religion and mathematics, making guesses about the universe, but using the mathematics (like you'd use a man made wrench) to make sure the observations themselves are consistent enough to make predictions about similar observations.

I think it's putting science on a rather high pedestal to assign it the role of mediator between religion and mathematics. I think most theologians (and I have known a few) would assert that they don't end up going anywhere near science if they need to apply principles of mathematics or logic to religion. (And you were criticizing me for bias? Mathematics is the wrench of science?)

And as I've said all along, it's wonderful that science finds mathematics so reliable that it invariably employs it this way. But that does not mean that the fundamental nature of mathematics is somehow integrally tied to its usefulness to scientists as a tool.

⚛​

 

[epenguin]

Where? Well, I suppose that question is meaningless after you have presumed that time and dimensions are only mathematical systems. These systems do not exist in a 'place', because a 'place' only has any meaning when dimensions exist.

But I see what your saying, For something to exist, it needs to exist somewhere, right? Well that is only if it is a physical object. The number four exists, as does the feeling of happiness. But neither of them can be given a position in space or time.

I will just limit to this, which was essentially in your introductory sentence and maybe your other ideas could be independent of it.

Pythagorean has got there before me. Still you have almost refuted yourself here. Happiness surely did not exist before there were beings to experience it, before we had discovered it. Less obvious, but I say the number four does not exist without us or conscious beings who count. Objects existed. Then we came along and mentally separated them in groups to which we applied comparison and categorised some of them as four. Planets existed. But they did not travel in conic sections, I don't think they even traveled they just were; if there is no-one to remember where you were yesterday you have not traveled. Certainly not according to a conic section, because it is we who have put the cone and the section there, there is nothing physical e.g. at the point of the cone, nor probably at the other focus of the ellipse where the sun isn't. Though our descriptuion by conic sections is quite objective.

 

[Phrak]

Since the number 4 exists and it's not physical, I'm wondering how many backup copies there are, just in case it gets changed. But if one of these trans-physical 4 gets changed and you have two of them, how do you know which one is the right 4?

And what if you have 5 of every number just to be safe, but the number 5 gets messed up?

 

[Gear300]

Since the number 4 exists and it's not physical, I'm wondering how many backup copies there are, just in case it gets changed. But if one of these trans-physical 4 gets changed and you have two of them, how do you know which one is the right 4?

And what if you have 5 of every number just to be safe, but the number 5 gets messed up?

I lost you there...please expand on this

 

[Pythagorean]

I think it's rhetorical of you to declare that I'm the one exhibiting bias, misconceptions, and stereotyping. You aren't too bad at wielding bias yourself. For example, down below and in preceding comments you've made the statement "pure mathematics is void of reality": well this is simply assuming your own conclusions! The only reason to say this is if you're already assuming that mathematics is something derived from the human mind with no external existence.

yes, I do have to restate that, "pure mathematics is void of the human experience of reality". Nobody can make claims about the reality we don't experience. That's my fundamental problem with the statement "mathematics exists independent of human thought". There's no way to know that. Note: it's just as ridiculous to make the claim that mathematics is completely dependent on human thought, but I'm not saying that. I'm showing it is dependent on human thought (barring the "completely" which I'm not able to comment on).

And also I'm not making these criticisms out of the blue, I was responding to what turbo said. He proposed, "It seems that our mathematics cannot be used to construct reasonable models of the quantum world." And only when I resisted this did he refine the statement into a concern about the application of mathematics by physicists.

I have no comment on this issue, I was picking on some of your supporting points. I may as well disagree with turbo here...

That's exactly the kind of behavior I'm talking about. Physics is what's concerned with describing the tangible world; that task is not a goal or objective of mathematics. That's why the proposal, "some physicists had difficulty describing what they're studying using mathematics - there must be something wrong with maths!" seems like a blame-shifting game to me.

But I didn't say that, and I've done my best to make the point against that. The flaws are intrinsic to science. You could say that science gets the lady because he actually pursues her while math isn't interested in the woman. This doesn't mean that math is intrinsic to the woman or that science is better with women. Both conclusions have no valid premises.

Even if there are actually phenomena that can't be modeled with mathematics, that would have no bearing on the nature of mathematics; at least not so far as whether some aspect of mathematics is independent of the human mind. There's no reason why "must be able to describe everything in physics" would be a necessary attribute of a mathematics that is independent of the human mind.

I agree. I guess hidden in here, I'm defending science where you have assaulted it.

If you really can't see how so many of these arguments are bent around physicist taking a utilitarian or instrumentalist perspective on mathematics - conceptually assuming that it is subordinate or otherwise incidental to physics - I think you are the one approaching this with bias.

It's true that I've been championing the other side in an effort to bring you to the middle. I should be focusing on showing you how you're wrong, not how the counter-argument is right.. because really I believe both sides are wrong... or at least that it's more complicated than that. I have held off for a long time on giving you my compromise though because of your bias (I guess I've tried fighting bias with bias or something). I fear that if I give you an inch, you'll take a mile. So I'll still hold off for now.

I think it's just fine to say "science makes flaws" in this regard, it's when that's extended to mathematics, and pretenses are made such as suggesting that the development of quantum theory entailed some portion of mathematics being scratched out and rewritten - which it did not, it was science that had to be rewritten - that I take issue with and which appears to me to be a case of someone projecting the problems of science upon mathematics.

Then we agree somewhat. But I still see no connection between reality and pure mathematics. Everytime I say this, it's an opportunity for you to show me the connection.I'm out of time right now, but I'll reply to the rest later.

 

[Pythagorean]

No, I'm not. Buddhist theology contradicts Christian theology, for example, and even the most broad principles of theology of particular sects within a single religion are often completely contradictory. No matter what things were named if an alien culture posessed an independently-developed theology that in every metaphysical precept was in agreement with and compatible with a particular Earth religion that would be staggering.

I absolutely disagree. The most broad principals in religion are:

1) there's an omnipotent entity (their used to be several, but that axiom must have led to more inconsistencies within the system of religion somehow and was eventually rejected).
2) there's an afterlife (reincarnation included... the fundamental concept being you don't die when you "die".)
3) there's an objective moral basis

By doing the right 3), 1) allows you into a 2) that you'll like better. If you don't obey 3), 1) decides you will have a remarkably uncomfortable 2).

Religion argues about who the 1) is and about what the 2)'s look like, and they even argue about the details of all the 3)'s but their 3)'s are remarkably similar for the most part.

And you can't pretend like everyone agrees on every aspect of mathematics today, either. Especially when you consider the edge of mathematics. Religion, like science, has the balls to go after the woman, but religion tends to make a lot of wrong guesses about the woman (even though their fundamental).

Given their fundamental axioms (both mathematics and religion) any fringe pseudoreligion (or pseudomath) that doesn't agree with the axioms isn't accepted by the community as it's a clear contradiction of the systems foundation.

The difference between religion and mathematics in this regards is that nearly all the solutions that will satisfy the axioms of religion are completely independent of each other. Infinite independent solutions. Mathematics is a much more complicated system of axioms.

And here's where my ultimate point comes in (I come out with my compromise here and give up defenses):

What you consider mathematics may be the tip of the iceberg of something much more fundamental to reality; what you consider the fundamental axioms of all mathematics could be laughable to an alien species as a skewed view of a special case, because you chose the axioms that were attractive to you, as a human, not seeing the most general case of the axiom.

The alien race may very well have some sort of dynamic axiom system, in which mathematics is one of a thousands of stable states in the system.

It would be like Hawking meeting Newton.

 

[Georgepowell]

(1) I don't really know what you're point is here. While things can be defined through mathematics that doesn't mean mathematics is some transient existence. Not everything can be described with mathematics, and there's plenty of mathematics that doesn't describe anything in reality. What about language? If this is your basis for mathematics existing outside of human thinking, you must also admit all other languages into the class, since they describe reality as well.

(2) That's false. Not everything can be described with mathematics. No math perfectly fits any observation. It's just more accurate than the English language (many times more accurate, but never spot on unless the person utilizing the math simplifies his observations through qualitative description.

(3) I disagree. It doesn't exist in the same way. It exists in our mind/brain whereas the physical world exists outside of our mind/brain.

(1) May I change my point slightly: Mathematics is our interpretation of the rules that govern our universe, and we may not have got it completely right. What i am sure of is that our universe does rely on a system of some sort. And some of it's rules may be solidly defined with mathematics.

"Not everything can be described with mathematics, and there's plenty of mathematics that doesn't describe anything in reality." What can't be described or explained using maths? And by this i don't mean some system that is so complex we still don't have the computing power or methods to calculate the mathematics, I mean is there some system in our universe who's basic laws are written in some other 'language'? As for the systems that do not describe anything in our universe; my point is, is that they exist as the rest of mathematics does, and they will explain/describe the phenomina that happen in that system.

(2) Correct me if I am wrong, but the only reason things are not explained perfectly using maths is that we either do not have the computing power to solve the equations, or we have only simplified/estimated versions of the origional data that we use.

(3) Happyness is a pattern that I think ultimatly can be described using maths, and so is any physical object. They exist in the same way, they are both a pattern, or set of values, that describe an observation.

 

[Chrisc]

...I propose that humans and the universe are nothing more than one part of a mathematical system that can and always has existed without necessary "existing" any more than the number 4 'exists'.

I think this is where your premise falls apart.
The "number" four does not exist without humans to qualify what numbers are.
The "quantity" four does not exist without humans to qualify what is being quantified.
Mathematics arises from quantification, setting a code or convention for the meaning of quantities such as four.
Before quantification can begin mathematics must devise axioms of qualification.
Two mortgages plus two universes equals four chickens.
This is a quantifiably accurate statement when the quantities are the numeric value of each entity, but clearly a qualifiably nonsensical statement with respect to the entities themselves.
When we realize the necessity of qualification in order to test what is being quantified we realize in its purest expression, qualification is an arbitrary, subjective and unquestionably an anthropocentric reality.
That mathematics exists without human qualification of its quantities is thus meaningless. To prove such a notion would require human intervention to qualify the quantities as holding to the axioms which are.. human constructs.
In other words, the universe may obey all our mathematical rules whether we ever existed to test such a theory or not. This is not because the universe has some deep design encoded in mathematics, but because mathematics is the language we create to express the deep encoded nature of the universe.

 

[Pythagorean]

(1) May I change my point slightly: Mathematics is our interpretation of the rules that govern our universe, and we may not have got it completely right. What i am sure of is that our universe does rely on a system of some sort. And some of it's rules may be solidly defined with mathematics.

"Not everything can be described with mathematics, and there's plenty of mathematics that doesn't describe anything in reality." What can't be described or explained using maths? And by this i don't mean some system that is so complex we still don't have the computing power or methods to calculate the mathematics, I mean is there some system in our universe who's basic laws are written in some other 'language'? As for the systems that do not describe anything in our universe; my point is, is that they exist as the rest of mathematics does, and they will explain/describe the phenomina that happen in that system.

(2) Correct me if I am wrong, but the only reason things are not explained perfectly using maths is that we either do not have the computing power to solve the equations, or we have only simplified/estimated versions of the origional data that we use.

(3) Happyness is a pattern that I think ultimatly can be described using maths, and so is any physical object. They exist in the same way, they are both a pattern, or set of values, that describe an observation.

(1) well, I suppose I can withdraw from this one, but it would have been emotions, behavior, purpose, etc. But I suppose you could argue that with advancements in brain science, we'd be able to apply maths to answer these kind of questions.

(2) This has always been a hard one to explain. The universe is so dynamic that once you use a model to describe something, you have to sacrifice generality for specifics, or specifics for generality. In this sense, the math you use to describe something is always wrong in some frame (but always right in another frame). You can never completely describe something on all frames at once, your statements about the system will always be incomplete. It's a lot like the English language int his regard.

(3) I agree somewhat, given the considerations above. But remember that the word happiness is loaded with subjectivity.

 

[Georgepowell]

(1) well, I suppose I can withdraw from this one, but it would have been emotions, behavior, purpose, etc. But I suppose you could argue that with advancements in brain science, we'd be able to apply maths to answer these kind of questions.

(2) This has always been a hard one to explain. The universe is so dynamic that once you use a model to describe something, you have to sacrifice generality for specifics, or specifics for generality. In this sense, the math you use to describe something is always wrong in some frame (but always right in another frame). You can never completely describe something on all frames at once, your statements about the system will always be incomplete. It's a lot like the English language int his regard.

(3) I agree somewhat, given the considerations above. But remember that the word happiness is loaded with subjectivity.

Well I'm happy to end the debate here, I think we have agreed as much as we can. In any case, nothing this 'deep' will ever be proved or agreed on, and it doesn't really have any real implications for science/maths anyway. So arguing about it is fruitless :p.

After changing my point slightly, my original idea no-longer rests on the title of this thread being true, and other people's and your arguments have made a difference on my views.

Thanks again,

George

 

[Georgepowell]

I lost you there...please expand on this

Ditto

 

[Chrisc]

Ditto

Phrak, please feel free to correct me as I am finding it a little scary that I understand such hyperbole.

The notion of numbers and what they represent must exist exclusive of humans if you hold to the idea that mathematics can define the universe before human existence.

But as numbers are not physical, all 4s are indistinguishable.
Therefore 4 represents anything and therefore nothing.

In other words, until humans attach significance to any 4, any equation it takes part in has no
meaning at all.
So to answer your OP, no logic, no truth and no reason exists before we discover them because
discovery in this sense is creation, the creation of reason.

 

[Georgepowell]

Phrak, please feel free to correct me as I am finding it a little scary that I understand such hyperbole.

The notion of numbers and what they represent must exist exclusive of humans if you hold to the idea that mathematics can define the universe before human existence.

But as numbers are not physical, all 4s are indistinguishable.
Therefore 4 represents anything and therefore nothing.

In other words, until humans attach significance to any 4, any equation it takes part in has no
meaning at all.
So to answer your OP, no logic, no truth and no reason exists before we discover them because
discovery in this sense is creation, the creation of reason.

Discovering a rule does not mean that the rule was not obeyed before we discovered it. So that rule has already existed. The mathematics that we use to describe that rule is only our interpretation of it, written in our own language of logic, and does not define it. (This might be slightly different to my OP, but my opinion has shifted slightly...)

The system/language that does define the 'rule' distinguishes between different types of 4, because as you said, 4 can have an infinite number of interpretations.

The 4 that is used in describing the pattern in our brain that creates happiness, is the same 4 that describes the width of an object. Untill we as humans mention the difference.
---------------
To summarise my changed idea (in a more logical order):

Our universe follows rules, these rules (as far as we can see) have always been obeyed. All of these rules so far can be defined through mathematics, so I presume that the fundamental rules of the universe are 'written' in a language similar to maths.

The place where maths must differ from the fundamental code of the universe is that in maths, one particular number can be used in a multitude of contexts. This inherent ambiguity of the different numbers means that the system of our universe must not be written in just maths. So far, the tool of maths has been sufficient in describing and predicting the ways of our universe, as it is easy to tell someone the necessary interpretation behind your numbers.

Dimensions, Time, objects and even emotions are just our own interpretations of the different patterns, phenomena, and types of values that exists in this fundamental system. For example, we interpret one type of 4 to mean distance, another type of 4 to mean electronic charge, and a third type of 4 to perhaps mean a distance in time. Maths does not distinguish between these fours, but the system of our universe does.

Other types of system that cannot be described using maths, and are completely different to the system of our own universe can exist, and may hold other amazing phenomena (like life in ours) that is so separate to our system that we can not imagine it. This endless amount of systems makes it less amazing that life originated, and perhaps makes something as unlikely as the origin of life not unlikely at all.

I don't know if we agree now or not... But reading our two posts it actually looks like I am on your side now.

Any more criticisms from anyone?

 

[CaptainQuasar]

yes, I do have to restate that, "pure mathematics is void of the human experience of reality". Nobody can make claims about the reality we don't experience.

I think that this is still assuming your conclusions, even if you tack on that "human experience" qualifier.

If mathematics has nothing to do with some fundamental reality, but it also does not arise from a human perspective or experience of anything, where the heck is it coming from? Surely at least our formulation of geometry has something to do with us experiencing flat three-dimensional space through our senses.

That's my fundamental problem with the statement "mathematics exists independent of human thought". There's no way to know that. Note: it's just as ridiculous to make the claim that mathematics is completely dependent on human thought, but I'm not saying that. I'm showing it is dependent on human thought (barring the "completely" which I'm not able to comment on).

If you were to refer back to oldman's [thread=215118]The Question : is mathematics discovered or invented?[/thread] thread where we first discussed this (sorry I never replied to your last post in that thread btw), you would see that I don't insist that mathematics is in its entirety independent of human thought either. It's not like I'm proposing that mathematics texts as a group are some infallible transcendent revelation the way Islam regards the Koran or a Christian Biblical fundamentalist regards the Bible.

Of course the human formulation of mathematics is going to be thoroughly human in its nature, colored and maybe even twisted by the human perspective on the universe, and undoubtedly encompassing only a portion - perhaps a tiny portion - of its subject matter. As I said [post=1618613]here[/post] the point is that the subject that human mathematics studies is something that has independent existence. It's not studying something that is a human creation like French Renaissance Literature is studying or scholars of Early 20th Century Film are studying.

But I didn't say that, and I've done my best to make the point against that. The flaws are intrinsic to science.

You haven't said so in this thread, but turbo said that bit I quoted above and in the other thread [post=1649585]you made[/post] what looks to me like an exactly parallel argument: you told me that "what you see as mathematics is a consequence of your brain having developed in the macroscopic world" and similarly to turbo above talked as though mathematics stops working at the quantum level, which as I've pointed out repeatedly it does not at all.

So I understand just fine if you're recanting that now but this is what I've been talking about: both you and turbo acted as though, since the development of understanding of quantum level phenomena was an Earth-shattering paradigm shift for physics and chemistry, it's had a similar impact on mathematics or as if the behavior of quantum-level phenomena invalidates some aspect of mathematics.

But that's not true at all; as I've emphasized before, not one iota of mathematics had to be scratched out and rewritten in the face of quantum phenomena the way that so much of physics had to be. This is why statements like the ones I've referenced look like psychological projection on physicists' part. Yes, quantum phenomena are incredible and rock-your-world type things but they don't have bearing on the nature of mathematics.

I guess hidden in here, I'm defending science where you have assaulted it.

I would say that if anything I have assaulted scientists if anything, not science itself. I think it's an entirely forgivable and understandable transference to have made. I only point it out because we're talking about the nature of mathematics, not the nature of physics, and the way that quantum phenomena forced such a revolution in the understanding of physics just doesn't have bearing on the nature of mathematics nor does it present any evidence regarding whether or not the things that mathematics studies have existence independent of human thought.

It's true that I've been championing the other side in an effort to bring you to the middle. I should be focusing on showing you how you're wrong...

Do you think maybe that the reason you're having so much trouble convincing me, and why you have to do things like apparently recant the quantum phenomena argument, is because I'm not wrong? That perhaps the things I'm saying are true and so would have to be incorporated into or accounted for in whatever this "middle" position is, which you've evidently been secretly holding all this time?

Then we agree somewhat. But I still see no connection between reality and pure mathematics. Everytime I say this, it's an opportunity for you to show me the connection.

I did quite a bit of showing you the connection in that previous thread, during which you mostly said that you were still formulating your thoughts on the subject. But it's an interesting topic so it's well worth re-hashing.

Okay - so, even if there were no humans around to see it, the universal gravitational constant averaged across all gravitational interactions in the universe would still approach

, right? Obviously the expression above is a human formulation of that value, but there is some constant ratio between that value and the averaging value of, say, all the weak nuclear force interactions in the universe, right?

Even if there were some group of aliens who had an innate understanding of GR spacetime geometry and to whom the concept of "gravity" never even arose, the universal gravitational constant we speak of and the way we use it would not contradict their understanding of physics - at worst it might appear as a silly and pointlessly arbitrary abstraction of marginal importance to them but it would be consistent with their knowledge of the way the universe works. So this is a scientific fact that I think we can say exists independent of humanity. At least it's more independent of humanity than some fact about French Literature or Early 20th Century Film.

In a nutshell, what I'm saying is that π, as a mathematical fact that is the limit to which the averaging ratio of the radius to the circumference of all circular objects in the universe approaches, is as independently real and existent as is G. And that there are a whole network of relationships underlying the human formulation of mathematics that are equally as independently real and existent.

Note that the π ratio being a fact from pure mathematics, from not only geometry but trigonometry as well, that has relevance in reality as experienced by humans, this is a counterargument to your "void of... reality" claim above.

I had all sorts of elaborate ways of expressing and refining the idea that I used in the other thread but I'll leave those aside until you've responded to the above.

I absolutely disagree. The most broad principals in religion are:

1) there's an omnipotent entity (their used to be several, but that axiom must have led to more inconsistencies within the system of religion somehow and was eventually rejected).
2) there's an afterlife (reincarnation included... the fundamental concept being you don't die when you "die".)
3) there's an objective moral basis

By doing the right 3), 1) allows you into a 2) that you'll like better. If you don't obey 3), 1) decides you will have a remarkably uncomfortable 2).

To me this looks like a crude attempt to paper over the extreme differences in human religion in an attempt to pound the round peg of religion into a square hole so that it has the similarities to mathematics that you want to claim it has.

1) simply is not universal - you're talking like someone from a Judeo-Christian religion. The Dali Lama talks about all sorts of different gods when he discusses Buddhist theology. But Islam says "There is no god but Allah."

Some Buddhists and Hindus and other polytheist say "One supreme god up above all the others? Uh... sure! That's kinda like bráhman." And I'm sure many of them have incorporated a single supreme being into their theology since exposure to Judeo-Christian religions. But the theological definition of bráhman is nothing like the omnipotent supreme being you are positing as common to all religions there.

And of course, going back in history there are many variations. In early Zoroastrianism, for example, there were two equally powerful beings, one that was pure good and one that was pure evil in modern terminology.

Even within Judeo-Christianity there's lots of conflicting theology. Jews, Trinitarian Christians, and Mormons all consider themselves to be monotheistic but Jews consider Trinitarian Christians to be polytheistic and they both consider Mormonism to be polytheistic.

I will grant you that 2) is pretty common but I would not say that it's universal. I have been told by some modern Jews that "For all we know, there is no afterlife. This life is a reward itself - that is the covenant with God."

Your 3) is definitely another attempt at mushing things from different religions together. Modern and Christian-influenced notions of sin and redemption and absolute good and evil just aren't the same thing as the notions of making sacrifices to please the gods in so many religions. Nor is it the same thing as the early Greek or Viking ideas that winning glory in battle might get you picked out as a sort of trophy by the gods to decorate their heavenly abodes.

And a way to win a good afterlife isn't universal either - some Greeks thought of Elysium as I mentioned there, but in the Odyssey, through sorcery Odysseus meets and speaks with the shade of Achilles in Hades. Achilles won more glory than any other figure in Greek mythology - but he was confined to the grey netherworld of Hades with everyone else, thirsting after the life he once had. Some scholars think that the afterworld in early Judaism, sheol, was like the Greek Hades - simply the place that dead people went, nothing good about it at all.

So yeah, I personally think that many if not most modern ideas of multicultural equivalence are politically correct reductionism that do not hold up under close examination. Yeah, there are some things that all people have in common, but definitely all religions are not equivalent and interchangeable at some level.

What you consider mathematics may be the tip of the iceberg of something much more fundamental to reality; what you consider the fundamental axioms of all mathematics could be laughable to an alien species as a skewed view of a special case, because you chose the axioms that were attractive to you, as a human, not seeing the most general case of the axiom.

The alien race may very well have some sort of dynamic axiom system, in which mathematics is one of a thousands of stable states in the system.

I've never said anything about there being some fundamental true axioms of mathematics. Nor that human understanding of mathematics is in any way comprehensive. So don't worry, you're not surrendering anything at all, if indeed you've really had the same secret position the whole time and your most recent statements aren't the result of me presenting evidence incompatible with your earlier views.

You really need to go back and re-read that other thread. The way in which I have proposed that mathematics has an independent existence is pretty abstract.

⚛​

 

[Pythagorean]

Well, I had a reply written out, but I somehow lost it in the log-in process, so I've lost motivation now. I will reply in more detail later, but I wanted to clear up something that I think is important to how you're interpreting my posts.

I've never said anything about there being some fundamental true axioms of mathematics. Nor that human understanding of mathematics is in any way comprehensive. So don't worry, you're not surrendering anything at all, if indeed you've really had the same secret position the whole time and your most recent statements aren't the result of me presenting evidence incompatible with your earlier views.

When I said my thoughts were undeveloped in the previous thread, perhaps I didn't make it clear that the whole point of my engagement in this discussion is to develop my thoughts, so of course my views change as you present logical arguments (and no evidence has been presented in my opinion, this is a philosophical debate, its comes down to logical arguments, not "evidence" in the scientific regard.)

If you're thoughts haven't changed during the course of the discussion, then you're still holding firmly to your bias (which is what I was pointing out). Just because I don't stop and validate your argument doesn't mean I still disagree with them. I'll usually just drop an argument if I see it's flaw and continue on with the rest. If I state that I agree it's usually because I don't see how it follows (i.e. your point was true, but not valid).

My thoughts have definitely moved more towards the middle through discussion with you (on a side note, nobody else has really contributed in this regard so there's a chance I"m just believe your flawed arguments because you've been persuasive). I will respond in detail to your finer points later. I'm intellectually exhausted from the reply I misplaced.

I also tend to play Devil's Advocate where I'm ignorant on a subject. This prompts more valuable (to me) discussion as replies tend to cut straight to the point.

I'm a conventional troll (as opposed to the modern trolls who just seek to insult and aggravate without any sort of interest in knowledge).

 

[CaptainQuasar]

Well, I had a reply written out, but I somehow lost it in the log-in process, so I've lost motivation now.

Oh, man, I hate it so much when that happens. My condolences.

But from what you said there, I have to maintain that your declarations that I am biased or that my arguments are generally flawed appear to simply be rhetorical with nothing to support them.

I mean, if not only am I able to point out specific flaws in your arguments, but I can now anticipate that your arguments and position are going to be changing over time, what reason at all do I have to be swayed by them? How is it being biased to not be swayed by that?

Anyways, I do hope you get the opportunity to re-write your response, but I know exactly what you mean about being exhausted and I'd understand if you didn't.

P.S. I do not think you're a troll, even though you've exhibited some contrarian behaviors (which I exhibit myself as well.) The thing about a troll is that a troll is contrary solely for the purpose of getting attention and keeping the argument going. I believe that you are earnestly interested in exploring the nature of mathematics.

P.P.S. My thoughts have changed during the course of the argument but it's that I have refined them in the course of articulating them.

⚛​

 

[Pythagorean]

Oh, man, I hate it so much when that happens. My condolences.

But from what you said there, I have to maintain that your declarations that I am biased or that my arguments are generally flawed appear to simply be rhetorical with nothing to support them.

I mean, if not only am I able to point out specific flaws in your arguments, but I can now anticipate that your arguments and position are going to be changing over time, what reason at all do I have to be swayed by them? How is it being biased to not be swayed by that?

I don't think your arguments are generally flawed; If I recall correctly, I was being picky about certain parts of your arguments. I'm not a mathematician, and the definition of mathematics is squirmy to me. I've never taken a proofs class. I've utilized plenty of math in many different forms, but it's very much a rugged tool to me, and like a lego set it can be manipulated into the shapes you need.

A sound argument is a sound argument no matter who it comes from or what their history with you is. There's no guarantee that the flaws you point are completely founded, either.

I also am not making an argument for your bias yet. I stated it as an intuitive guess. Another aspect of my debate technique is to make intuitive guesses so they can be analyzed later when argument has developed.

Also, you may be a better arguer than me (I suspect this is true), which itself does not validate your claims.

Lastly, I've noticed sometimes you'll assume comments I make are in support of the antithesis when they're not. I'm testing your claim, but I don't really have an alternative.

The thing about a troll is that a troll is contrary solely for the purpose of getting attention and keeping the argument going. I believe that you are earnestly interested in exploring the nature of mathematics.

Yes, I am interested in the nature of mathematics, but I'm also kind of blind on the topic so I feel like a troll when I'm fishing around in the dark for an argument.

(back to previous post...)

If mathematics has nothing to do with some fundamental reality, but it also does not arise from a human perspective or experience of anything, where the heck is it coming from? Surely at least our formulation of geometry has something to do with us experiencing flat three-dimensional space through our senses.

I did say "pure mathematics"

mathematics (minus the pure) arises the same way language arises. You want to learn more about an observation so you study it it, and you find relationships. At first, you may use words like "that's a lot, that's a little, that's none", but then as you become more accurate about your observations, you can use a numerical system.

But it also arises the same way rules in a board game arise. As long as you're careful enough when you define the system of rules, they won't contradict themselves. This doesn't mean the rules of the game were discovered.

"Pure mathematics" is the further exploring the implications of those other rules to make more rules. Just because we can use the rules to better articulate our observations doesn't mean that they inherently came from our observations.

As I said here the point is that the subject that human mathematics studies is something that has independent existence. It's not studying something that is a human creation like French Renaissance Literature is studying or scholars of Early 20th Century Film are studying.

ok, give me more.. what is that "subject" that mathematics is studying? I don't see the ghost, so I can only suspect that you're imagining things that aren't there.

you told me that "what you see as mathematics is a consequence of your brain having developed in the macroscopic world" and similarly to turbo above talked as though mathematics stops working at the quantum level, which as I've pointed out repeatedly it does not at all.

This argument: "what you see as mathematics is a consequence of your brain having developed in the macroscopic world" I can rearticuilate. The only real burden their is "macroscopic world".

I used plenty of math in QM, that's not my argument. My argument before was that the world is non-determinant (I had thought QM said this too, but you were right, it does not unseat determinism... which makes sense since ). If you want to have a discussion (heh,d ebate!) about how non-determinism implies mathematics is not discovered, we should start a new thread.

Anyway, I think what me and turbo are both trying to do is preemtively dismantle the argument that some mathematicians make (you're not the only one I've had this debate with... oddly it's always mathematicians defending this claim).

That argument suggests that mathematics describes all of reality on some universal level or that mathematics is somehow reality. The argument with QM is that we have to change frames. One math works in one frame, the other math works in another frame, and even then, you're still generalizing. The math reduces inaccuracy and uncertainty, but it does not eliminate it. Technically, this has nothing to do with our argument, but it's a common misconception of science-dumb mathematicians that can be the justification for their claim that math is discovered, not invented. (and yes, I realize that I'm a math-dumb scientist).

Ok, have some homework to do (applied analysis, no less!) so I'll do more later.

 

[CaptainQuasar]

I don't think your arguments are generally flawed; If I recall correctly, I was being picky about certain parts of your arguments. I'm not a mathematician, and the definition of mathematics is squirmy to me. I've never taken a proofs class. I've utilized plenty of math in many different forms, but it's very much a rugged tool to me, and like a lego set it can be manipulated into the shapes you need.

A sound argument is a sound argument no matter who it comes from or what their history with you is. There's no guarantee that the flaws you point are completely founded, either.

I also am not making an argument for your bias yet. I stated it as an intuitive guess. Another aspect of my debate technique is to make intuitive guesses so they can be analyzed later when argument has developed.

I think it's entirely fair to make intuitive guesses or even to mention them in an argument. It's just that when you broadly declare that I'm biased, without demonstrating how my bias is prejudicing my judgment or arguments, nor even specifically saying what you think I'm biased about, it certainly appears like a rhetorical technique and of course I'm going to respond.

(Technically it would be an ad hominem fallacy: it looks as though you're implying that there's something wrong with my arguments because there's something wrong with me, that I have an inherent bias which must be producing un-identified flaws in my arguments.

As an aside, I find that most people use the phrase ad hominem incorrectly, as if it's something to do with etiquette, that any criticism of another person or their behavior is somehow erroneous or wrong. But that has nothing to do with it. I think it's perfectly valid for someone else to advance personal criticisms of me, or vice versa, particularly if there's evidence to cite.)

Also, you may be a better arguer than me (I suspect this is true), which itself does not validate your claims.

Definitely not, you're right. An argument must stand on its own and is valid exclusively through its own virtues.

As far as me being a better arguer that you, I ought to mention that in picking theology as an analogy to mathematics you had the bad luck to hit on something that is sort of a hobby of mine, I have spent a great deal of time studying the various religions of the world.

I did say "pure mathematics"

mathematics (minus the pure) arises the same way language arises. You want to learn more about an observation so you study it it, and you find relationships. At first, you may use words like "that's a lot, that's a little, that's none", but then as you become more accurate about your observations, you can use a numerical system.

But it also arises the same way rules in a board game arise. As long as you're careful enough when you define the system of rules, they won't contradict themselves. This doesn't mean the rules of the game were discovered.

Hmmm. The thing is, it seems that people in widely disparate civilizations around the world have been able to consistently and repeatedly come up with sets of rules, independently, that do not contradict each other. In the case of mathematics it does not seem to require anywhere near as much care or caution to avoid coming up with contradictory rules.

For example, when you talk to people about the way that they perform simple arithmetic, you find that there are a widely varying array of algorithms that are used. But they all arrive at the same answer. And if someone were to arrive at a different answer, it's possible to objectively prove that the answer is incorrect, without needing to know the details of the algorithm used to derive it. (Though of course you might look at that algorithm if you're teaching someone arithmetic and trying to help them find where they're going wrong.)

"Pure mathematics" is the further exploring the implications of those other rules to make more rules. Just because we can use the rules to better articulate our observations doesn't mean that they inherently came from our observations.

I guess we're working with somewhat different definitions here: I would pretty much regard pure mathematics to be anything that is beyond the realm of applied mathematics. Simply, say, learning about prime numbers and looking at how they relate to factoring in the case of multiplication, for example, when you're sort of examining how the math works instead of using arithmetic to count physical things or measure physical quantities, seems like pure mathematics to me.

In any case, to get back to my geometry example - if, say, the Pythagorean theorem as something derived from the implications of other rules of Euclidean geometry qualifies as pure mathematics, the fact that it also works properly in the physical world seems to me to violate your assertion that pure mathematics is void of reality.

ok, give me more.. what is that "subject" that mathematics is studying? I don't see the ghost, so I can only suspect that you're imagining things that aren't there.

Wait, so are you saying that you don't believe there is a subject that mathematics is studying? When a mathematician is examining a problem and trying to find a proof or other solution, what is she examining? That's what I would say that mathematics is studying, the thing or things that mathematicians examine all the time and try to formulate rules about and descriptions of.

This argument: "what you see as mathematics is a consequence of your brain having developed in the macroscopic world" I can rearticuilate. The only real burden their is "macroscopic world".

I used plenty of math in QM, that's not my argument. My argument before was that the world is non-determinant (I had thought QM said this too, but you were right, it does not unseat determinism... which makes sense since ). If you want to have a discussion (heh,d ebate!) about how non-determinism implies mathematics is not discovered, we should start a new thread.

Okay... but can we at least agree that the discovery of QM did not result in any part of mathematics being invalidated, and that the effect, as far as invalidating anything, was entirely within physics?

Anyway, I think what me and turbo are both trying to do is preemtively dismantle the argument that some mathematicians make (you're not the only one I've had this debate with... oddly it's always mathematicians defending this claim).

I'm not a mathematician, btw, I'm a software engineer. Though my degree in school was a combination of pure mathematics and computer science.

That argument suggests that mathematics describes all of reality on some universal level or that mathematics is somehow reality.

Sort of along the lines of "the universe and the fundamental reality is an information matrix" kind of thing? I'm not advancing that, as I said I don't think that the existence of physics phenomena that are impossible to model or describe with mathematics would invalidate the sort of things I'm saying. I'm really just saying something along the lines of π and G are both real and existent independent of humanity (though not that they necessarily have the same nature.) I'll declare right now, that by no means entails that the fundamental nature of the universe is mathematical.

(I certainly find the notion that the universe is entirely mathematical at base tempting, but I don't think that would be anywhere near as demonstrable or supportable as what I'm saying and so that's not what I'm arguing in this context.)

The argument with QM is that we have to change frames. One math works in one frame, the other math works in another frame, and even then, you're still generalizing.

I don't think that's true of everything, is it? I thought that wave mechanics, for example, is equally applicable at both the macroscopic and quantum levels. And of course simple things like π work and appear in radial equations all over the place. And I know that there are massive differences in classical field theory versus quantum field theory, but I believe they're using as tools many of the same mathematical elements - scalar, vector, tensor, and spinor fields, of course, at the very least.

(and yes, I realize that I'm a math-dumb scientist).

I wouldn't be surprised, since I've been out of school for a few years and the opportunity to use any really good math stuff in my work is pretty infrequent, that you probably have a much better handle on many mathematical topics than I do right now.

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[Pythagorean]

(I've made two posts here, just fyi before you hit the quote button)

So I asked my math teacher today, and of course his view is that math is discovered. He drew on the analogy of language (which I consider math... a highly articulate language) before I even brought that metaphor up.

His argument was that even people of different languages have an objective basis and will eventually be able to correlate the languages (otherwise communication between different language-speaking peoples would be impossible).

This is aligned with your argument:

Wait, so are you saying that you don't believe there is a subject that mathematics is studying? When a mathematician is examining a problem and trying to find a proof or other solution, what is she examining? That's what I would say that mathematics is studying, the thing or things that mathematicians examine all the time and try to formulate rules about and descriptions of.

But to me, what you're effectively saying is that languages (math included) are used to describe something that is objectively real (i.e. reality). This does not seem to satisfy the claim that "math is discovered" for me. It seems to say instead, what you explicitly stated before:

As I said here the point is that the subject that human mathematics studies is something that has independent existence.

That sounds to me, like you're admitting that math itself is not discovered (which is what I thought we were debating). I feel that it is an abstraction that was invented to study that underlying thing.

The Physicist's Analogy:

I'll start with a quote from you:

I wouldn't be surprised, since I've been out of school for a few years and the opportunity to use any really good math stuff in my work is pretty infrequent, that you probably have a much better handle on many mathematical topics than I do right now.

I guess what I meant in my post to which this reply originated is that I'm math-dumb about the fundamental axioms of mathematics. I've never studies the formal foundation. It's been exclusively used as a tool in my experiences.

Now, tools are real, but they didn't exist before humans. In some cases, they can just be an abstaction of a real object. For instance, a shillelagh is a tool, but the real object is just a stick. Not much is done to make a stick into a shillelagh physically, but there's no such thing as a shillelagh without a human (or a primate in some cases) to see the stick as a weapon that can be used to hit things.

A spear is just a couple shavings away from a stick, but there's a physical interaction involved here.

Being physically trained, I've always viewed mathematics as a tool. Now, that tool may be made of things that were around before the human, but the tool itself was constructed (i.e. invented) out of those previously-existing substances.

Sort of along the lines of "the universe and the fundamental reality is an information matrix" kind of thing? I'm not advancing that

Well that kills a few arguments of mine then. I apologize for operating on this assumption, and also for not making the assumption clear before so that you could refute it.

 

[Pythagorean]

I'm really just saying something along the lines of π and G are both real and existent independent of humanity (though not that they necessarily have the same nature.) I'll declare right now, that by no means entails that the fundamental nature of the universe is mathematical.

I'm pretty sure there's no such thing as a straight line or a perfect circle anywhere in the universe. Space is also noneuclidian (G is based off of euclidian space). I realize pi has other applications, but these are just examples of where those constant work as a tool, but don't perfectly describe the reality.

(warning: intuition involved above!)

I don't think that's true of everything, is it? I thought that wave mechanics, for example, is equally applicable at both the macroscopic and quantum levels. And of course simple things like π work and appear in radial equations all over the place. And I know that there are massive differences in classical field theory versus quantum field theory, but I believe they're using as tools many of the same mathematical elements - scalar, vector, tensor, and spinor fields, of course, at the very least.

That example doesn't follow from what I'm talking about. Looking at a wave alone can be helpful in the specifics of a single, isolated wave (which doesn't exist in nature... or at least there's no way we could observe it if it did...). For instance, you can use it to model a guitar string, but if you try to model several guitar string in reality, you have to change the maths to get a decent prediction out of the whole system. In music, they have to use techniques like http://en.wikipedia.org/wiki/Equal_temperament" to get the instrument to act (disguise itself) like the beautiful math version. We actually can't hit the notes like we'd be able to in a math world, but the human ear is insensitive enough to be tricked by a system that is just slightly off the ideal.

This is what I mean when I say math doesn't have anything to do with reality. That statement is a bit extreme. What I really mean to say is that it takes creativity and "leaps of faith" to bridge the gap between reality and math.

In fact I remember a neurological argument made by Penrose (I think) that pure logic would have failed in making any predictions in science. It requires a leap of faith in the human brain for science to be useful at all.

 

[CaptainQuasar]

So I asked my math teacher today, and of course his view is that math is discovered. He drew on the analogy of language (which I consider math... a highly articulate language) before I even brought that metaphor up.

His argument was that even people of different languages have an objective basis and will eventually be able to correlate the languages (otherwise communication between different language-speaking peoples would be impossible).

This is not anything I'm saying. I would not regard language to be the same as mathematics any more than I would regard physics to be the same as mathematics. (I'd say that they're less similar, in fact.)

But to me, what you're effectively saying is that languages (math included) are used to describe something that is objectively real (i.e. reality). This does not seem to satisfy the claim that "math is discovered" for me.

*snip*...

That sounds to me, like you're admitting that math itself is not discovered (which is what I thought we were debating). I feel that it is an abstraction that was invented to study that underlying thing.

This is again something that got discussed extensively in the other thread. Of course all the words and symbols and things that humans use to express mathematics are invented. It's not the words and symbols and things, nor even the general human formulation of mathematics, that I am proposing as independent of humanity.

Physics is used to describe something that is objectively real; does that mean that physics is invented?

If you group physics, mathematics, and Swedish grammar together by the degree to which each examines something that exists independent of humanity, it's physics and mathematics that go together, not mathematics and Swedish grammar. As I said in the other thread this is what I believe the "discovered or invented" question is asking.

By bringing in things that your math professor says, or that you've heard other mathematicians say, and arguing against those things it seems like you're trying to avoid understanding or dealing with what I'm saying, which is different.

Now, tools are real, but they didn't exist before humans. In some cases, they can just be an abstaction of a real object. For instance, a shillelagh is a tool, but the real object is just a stick. Not much is done to make a stick into a shillelagh physically, but there's no such thing as a shillelagh without a human (or a primate in some cases) to see the stick as a weapon that can be used to hit things.

If a human picks up a rock and uses it as a doorstop or to pound a nail into a piece of wood, that tool existed before any humans existed. Humans using something as a tool does not change its fundamental nature, just as I've been saying that physicists using mathematics as a tool does not change the nature of mathematics.

And even besides that, this line of reasoning, like the "human mathematics is used to describe something" one above, does nothing to distinguish physics from mathematics. I could just as easily say that physics is a tool that mathematicians use when they want to apply mathematics to the more experiential parts of reality, hence physics is just a tool and it's invented.

I'm pretty sure there's no such thing as a straight line or a perfect circle anywhere in the universe. Space is also noneuclidian (G is based off of euclidian space). I realize pi has other applications, but these are just examples of where those constant work as a tool, but don't perfectly describe the reality.

See, you're again ignoring most of what I've already said. (Though I've said quite a bit, so it's understandable.) This is why up above I used the big clumsy phrase where I expressed π as the limit to which the ratio of the circumference to radius of all the circle-like things in the universe approaches as they approach the shape of a perfect circle.

There's no case where the value of G is perfectly exact either. That's why the value for G I listed above has a tolerance range appended to the end of it. You haven't demonstrated anything that disinguishes π as different from G, so I maintain that they are independently real to the same degree.

That example doesn't follow from what I'm talking about. Looking at a wave alone can be helpful in the specifics of a single, isolated wave (which doesn't exist in nature... or at least there's no way we could observe it if it did...). For instance, you can use it to model a guitar string, but if you try to model several guitar string in reality, you have to change the maths to get a decent prediction out of the whole system. In music, they have to use techniques like http://en.wikipedia.org/wiki/Equal_temperament" to get the instrument to act (disguise itself) like the beautiful math version. We actually can't hit the notes like we'd be able to in a math world, but the human ear is insensitive enough to be tricked by a system that is just slightly off the ideal.

This is what I mean when I say math doesn't have anything to do with reality.

Whoa, whoa, whoa, you're switching topics here. The reason I was talking about wave mechanics wasn't to prove anything about reality, it's because you claimed that the mathematics that must be used between the macroscopic and quantum frames is different. But it's not.

That statement is a bit extreme. What I really mean to say is that it takes creativity and "leaps of faith" to bridge the gap between reality and math.

I still maintain that this is assuming your conclusions. The only reason it requires any more of a leap of faith than anything else is if you assume that math is "void of" or unconnected to reality in the first place.

In fact I remember a neurological argument made by Penrose (I think) that pure logic would have failed in making any predictions in science. It requires a leap of faith in the human brain for science to be useful at all.

Well, if you want to say that mathematics is only as discovered as physics is, I'd accept that, it's pretty much what I'm proposing.

⚛​

 

[Pythagorean]

(note: two posts again... )

This is again something that got discussed extensively in the other thread. Of course all the words and symbols and things that humans use to express mathematics are invented. It's not the words and symbols and things, nor even the general human formulation of mathematics, that I am proposing as independent of humanity.

That's quite different to me. The term "mathematics" is not just the symbols and things that human use to express it. Mathematics is the system of axioms itself.

Physics is used to describe something that is objectively real; does that mean that physics is invented?

Absolutely! Physics is not reality! That's a common misconception! It's a collection of techniques used to model reality.

If you group physics, mathematics, and Swedish grammar together by the degree to which each examines something that exists independent of humanity, it's physics and mathematics that go together, not mathematics and Swedish grammar. As I said in the other thread this is what I believe the "discovered or invented" question is asking.

Once again you're making your argument by using the general terms (physics and mathematics) then being specific about the Swedish grammar (like you did with religion earlier). The general term would be language, not "Swedish grammar" is obviously not required. However, language is required if you want to describe physics. Mathematics alone just won't do it. You have to assign meaning from reality (from your observations) to the mathematics.

By bringing in things that your math professor says, or that you've heard other mathematicians say, and arguing against those things it seems like you're trying to avoid understanding or dealing with what I'm saying, which is different.

We both agreed a sound argument is a sound argument. I'm able to separate your arguments in my mind. One of our problems may have been the definition of mathematics. But I declared in this post, above, that mathematics is the system of axioms that humans (invented/discovered) that we're disputing (I thought) not the symbols.

If a human picks up a rock and uses it as a doorstop or to pound a nail into a piece of wood, that tool existed before any humans existed. Humans using something as a tool does not change its fundamental nature, just as I've been saying that physicists using mathematics as a tool does not change the nature of mathematics.

"Humans using something as a tool does not change its fundamental nature". Of course not! It's fundamental nature is a rock. The human was using it as a tool, ignoring its fundamental nature, giving meaning to it. The doorstop was invented. As were pet rocks. They may be lousy, cheap inventions, but they actually take ingenuity to come up (it may seem trivial to you, but you were raised in an educated society so you were handed plenty of prejudices before you ever started thinking for yourself... I'm not different of course, this is human nature.)

And even besides that, this line of reasoning, like the "human mathematics is used to describe something" one above, does nothing to distinguish physics from mathematics. I could just as easily say that physics is a tool that mathematicians use when they want to apply mathematics to the more experiential parts of reality, hence physics is just a tool and it's invented.

So we agree! I've never once claimed that physics is discovered. To me, a soon-to-be physicist, physics is a tool. It works.

Whoa, whoa, whoa, you're switching topics here. The reason I was talking about wave mechanics wasn't to prove anything about reality, it's because you claimed that the mathematics that must be used between the macroscopic and quantum frames is different. But it's not.

Er, no, I don't think I claimed that this thread. I've taken both semesters of QM since last thread and had time to digest the information (by the way, the wave equations are somewhat similar, but not the same as classically. In QM the operators are observables and the function that's operated on is the wave function. Classically, the observables are in the funciton and we don't consider the hilbert space.)

My argument above was not about macroscopic vs. quantum. It's about generalization vs. specifying. We were arguing two different things there.

I still maintain that this is assuming your conclusions. The only reason it requires any more of a leap of faith than anything else is if you assume that math is "void of" or unconnected to reality in the first place.

Well, if you want to say that mathematics is only as discovered as physics is, I'd accept that, it's pretty much what I'm proposing.

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It sounds like you want me to play fair or something. It was harsh of me to say "void of" or "unconnected to" reality. Let's scratch that from the record. "Is invented" is sufficient for now. But now we're on the level that they're even, eh? They're both invented!

Notice, I never once (not even in the last thread we discussed) claimed that physics is discovered. Physics is a human interface (and an abstraction) for reality and mathematics is a human interface for abstractions such as physics. Mathematics applies to a lot more things than science, granted, but all these things tend to focus on human inventions too (for instance, sudoko). NOTE, I'm saying this to the benefit of mathematics, I'm not saying the sudoko's couldn't be applied to reality, 100% of this discussion doesn't have to be debate. I realize now, looking back at your posts that you've gotten defensive on points that I wasn't even really debating. I am capable of mixing discussion with debate (as are you, when you're aware that I'm not attempting to tie a point into my argument.)

 

[Pythagorean]

Alien Argument:

By the way, every time I've said mathematics did not exist before humans, I've been absolutely anthrocentric.

I kind of assumed everyone agreed on this, but replace human with sentient life. I mean, "alien" can means space mites that will never develop mathematical axioms because they're completely instinctual (as far as we can tell).

Sentient life includes any alien that has a brain very similar to humans and learns and comprehends things the same way humans do. I wouldn't be surprised at all if they invented/discovered mathematics. I also wouldn't be surprised if they invented/developed a moral basis (reward/punishment), which is what's left of my religious analog (religion being different methods of practicing the perspective that morality as an objective/discovered thing).

But like I said, these aliens would have to have brains remarkably similar to ours for them to develop math in such a way that it can be compared to ours.

A monkey has a remarkably similar brain, but it has no concept of mathematics. It's brain does calculations, but he's obviously not doing mathematics in his head. We know this, because our brain does the same thing (a basket ball player taking a shot). He can build axioms to make the shot without mathematics/physics, based on his interactions with reality. His interactions on reality are all that is discovered. His axioms are invented in the most consistent way he can afford to understand those interactions. Those interactions/observations are not fundamentally mathematical in nature just because you can describe them that way (as I think you admitted, but I think that invalidates the alien argument.).

Why should any of the interactions/observations be fundamentally any of the ways we can describe them because a like-minded person comes up with the same idea?

Tool Analogy:

If physics were a chainsaw and the tree were reality, the sharpening tools, and the almighty chainsaw tool (and a plethora of other little tools and your bar oil, and your gasoline) would be mathematics. The chainsaw might go a little while without the tools, but you won't get very far through a single tree (and we're in a forest of a 10^100 trees at least). Mathematics and physics together come closer to pwning reality than either does separately, but I'd suspect things would be a lot less confusing if they actually reached reality.

 

[HallsofIvy]

Mathematical truths exist be for we "find" or prove them but not before we define them.

Is "the sum of the angles in a triangle is 180 degrees" a "mathematical truth"? It is in Euclidean geometry but not in non-Euclidean geometry. There exist an infinite number of "mathematical system" or "axiomatic structures". We create mathematical truth when we define a specific mathematical system. We then discover those truths when we prove them.

Whether or not "a world can exist through purely a system of numbers, values and rules" depends entirely upon what you mean by 'a world'. In any meaning of 'world' that I would use, the answer to your question is "certainly not"!

 

[CaptainQuasar]

Er, no, I don't think I claimed that this thread. I've taken both semesters of QM since last thread and had time to digest the information (by the way, the wave equations are somewhat similar, but not the same as classically. In QM the operators are observables and the function that's operated on is the wave function. Classically, the observables are in the funciton and we don't consider the hilbert space.)

My argument above was not about macroscopic vs. quantum. It's about generalization vs. specifying. We were arguing two different things there.

This is what I was talking about:

The argument with QM is that we have to change frames. One math works in one frame, the other math works in another frame, and even then, you're still generalizing.

That's why I was talking about things like wave mechanics and fields, because the math is the same in both frames. It seems to me like you're saying there's a particular kind of math that only works in the macroscopic frame or something like that. I don't think you've demonstrated how math stops working somewhere at some point. Even if you were examining some very tiny circular objects or circular regions of fields, quantum-scale-sized-ones, the ratio between their circumferences and their radii would still approach 2πr.

Perhaps you haven't been trying to say that, but if you haven't then I definitely still don't understand what the discussion of QM in this context is all about.

(And yes, as you sort of pointed out, I know that the "wave function" is a misnomer because what it's describing is not an application of wave mechanics. But it's my understanding that there are other areas of QM where wave mechanics gets applied, though I could be wrong.)

So we agree! I've never once claimed that physics is discovered.

Okay, we had hit on this again and again and again in the other thread, I thought you might remember. If all you're saying is that mathematics is invented and not discovered because anything that describes something else is invented, and that hence anything that is ever communicated between humans is invented, that seems like a pretty mundane meaning of the word "invented" and I do not think that's the meaning of "invented" in the question "Is mathematics discovered or invented?"

I thought that we had already gotten this out of the way about a hundred postings back in the overall discussion, though I guess not. I actually went out of my way to dig up where we discussed this in the previous thread and linked to it above, in the hopes that we wouldn't get mired in it again, but alas...

So of course, this is why I have been talking about the significant thing being whether the subject of mathematics is discovered or invented; I was referring back to that previous discussion of the meaning of "invented". But if you really consider even physics and the subject it studies to be wholly invented, an exercise in human navel-gazing as it were, as invented as Swedish grammar or the grammar of human languages in general^†, then yeah, I guess there's nothing to talk about.

† General grammar contains contradictions in a fashion that I think is different than anything in human mathematics and is not consistent in the same manner, which is why I would specify "Swedish" the same way I would specify a particular theology. For example, if you know everything about all human mathematics other than Mayan mathematics, you're going to be able to figure out the solution to a math problem expressed in Mayan notation even if you have never seen that problem solved before. You may even be able to correctly determine entire sets of rules that Mayan mathematics would have to contain.

But even if you know every human language other than, say, Basque (let's pick that one since it's a "language isolate" unrelated to other languages in the same way that Mayan mathematical notation is unrelated to other mathematical notations) you are not going to be able to figure out what the rules of grammar of Basque are, nor other conventions of the language like how to pluralize words, unless you have access to examples of that being done in the language.

But like I said, these aliens would have to have brains remarkably similar to ours for them to develop math in such a way that it can be compared to ours.

You keep making these statements about the human brain. First you said that there's some essential part of mathematics that is connected to human brains having evolved in the macroscopic world but I think I've demonstrated that our mathematics works just fine on the quantum level and nothing is invalidated by QM nor has to be corrected for that.

Now you're again making this sort of statement but I really don't think that you're presenting any sort of evidence or an argument for it; it again seems to me like something which simply assumes your conclusions. Is there anything in particular you can point to that would indicate what about our mathematics would be incomparable or incompatible with some other sort of mathematics? Or anything you can point to in mathematics that seems particularly dependent upon the human brain for it to be true?

Again, if they were presented with a definition of π, would they be unable to see how it had anything to do with circles or trigonometry or wave mechanics or whatever analogs of those things might exist in their mathematics? Would they conclude somehow that we had reached an incorrect value for π?

And does this all apply to their physics too? Would our physics seem to them like a bunch of nonsense unconnected to the physical world?

I don't think so. I think it would be just like I said above:

Even if there were some group of aliens who had an innate understanding of GR spacetime geometry and to whom the concept of "gravity" never even arose, the universal gravitational constant we speak of and the way we use it would not contradict their understanding of physics - at worst it might appear as a silly and pointlessly arbitrary abstraction of marginal importance to them but it would be consistent with their knowledge of the way the universe works. So this is a scientific fact that I think we can say exists independent of humanity.

And similarly, I think that π and its relationship to circles, trigonometric and other periodic functions, and wave mechanics is a mathematical fact that could not contradict anything within an alien's mathematics.

⚛​

 

[CaptainQuasar]

Mathematical truths exist be for we "find" or prove them but not before we define them.

Do you really think so? That would seem to mean that if, a million years before humans even existed, some alien on the other side of the universe just happened to mathematically define the same thing we call a triangle in Euclidean 2-space (though perhaps from its perspective Euclidean 2-space would be an exotic and counter-intuitive concept), then because that's before we've defined triangles the alien might arrive at the conclusion that the sum of a triangle's angles is something other than 180°.

I do not think that's true. I think that the sum of a triangle's angles being 180° is either a fact that exists independently from any intellect thinking about it, or a fact based upon some more fundamental mathematical relationships that exist independently from any intellect thinking about them. And hence the sum of 180° is something that could be reached by different humans not communicating with each other and even by aliens as well.

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