The Platonic Mathematical World

[Avatar]

So, could another species that has had no contact with Humans determine "prime" numbers are not "prime"? Is the mathematical concept of "prime numbers" dependent upon human intellect and culture?

Maybe they could. Or maybe everybody recognises the same quality of certain counting words. That doesn't mean they have an independent existence though. Any mathematical concept depends on intellect. And maybe on culture. Because mathematical concepts are just descriptions of a perceived (or imagined (theoretical)) phenomenon.

--A

[SerScot]

Avatar,

If mathematical concepts are "just descriptions of a perceived (or imagined (theoretical)) phenomenon" why are there no variations between cultures of irreducable mathematical concepts? If Math is a creation of the human mind why do people keep coming up with the same ideas. Calculus was invented by two men, Newton and Leibniz, at the same time completely independent of each other. If they both imagined it without reference to some concrete reality how did two men who spoke different languages and came from fairly different cultural backgrounds come up with the same thing at the same time?

Jungian collective memory? Seriously. Further, if mathematics is purely a construct of the human mind it is pointless to attempt to use digital signals to attempt to send mathematical concepts out in the universe to "prove" we are intelligent life forms. Other civilizations will not be able to understand what we are saying if Mathematics has no existence outside our own.

Therefore, because Mathematics is universal I believe the concepts within Mathematics must have some existence outside our own existence. After all the Universe itself exists whether we do or not. Why don't Mathematical concepts exist whether we do or not? You say the are descriptive that implies they are describing something that exists before we do.

[Vraith]

I'm saying neither is it "real," nor invented by minds.
It is an artifact/reflection of what does exist. Invert the Platonic.
It is meaningless without something to work on/apply to.
It is grammar [context] without language [content].
And lets not forget that the math, applied to reality, is always wrong: it only works cuz it is close enough.
You need pi to calculate, say, the circumference of a circle. But pi is irrational, it will never tell you the exact circumference...yet the circumference has an exact value.
And lets not forget the math you use depends on what you are looking at.
Lets say I have a Pie. In one system it weighs 10 dorks. In my system, it weights 12 geeks. Dividing the pie exactly into 3 is impossible for those who use dorks [repeatin 3's forever]...so they go to war over who gets the heavier slice. But it divides up perfectly into 3 pieces of 4 geeks-weight.

[SerScot]

Vraith,

That's variation in language and systems of measurement not the formulae that underlie the concepts themselves. It's the formulae and the concepts of numbers themselves that have universality and thus existence outside of human conciousness.

[Avatar]

Avatar,

If mathematical concepts are "just descriptions of a perceived (or imagined (theoretical)) phenomenon" why are there no variations between cultures of irreducable mathematical concepts?

Hmmm, pretty sure that western mathematics had no concept of "0" for quite a while.

If Math is a creation of the human mind why do people keep coming up with the same ideas.

Because they observe the same phenomena?

If they both imagined it without reference to some concrete reality how did two men who spoke different languages and came from fairly different cultural backgrounds come up with the same thing at the same time?

See above. I'm not saying it doesn't reference a concrete reality...quite the opposite. It does. But it's only a reference.

Further, if mathematics is purely a construct of the human mind it is pointless to attempt to use digital signals to attempt to send mathematical concepts out in the universe to "prove" we are intelligent life forms. Other civilizations will not be able to understand what we are saying if Mathematics has no existence outside our own.

Perhaps other minds have constructed it as well?

Therefore, because Mathematics is universal I believe the concepts within Mathematics must have some existence outside our own existence.

How do you know it's universal?

After all the Universe itself exists whether we do or not.

Sure?

Why don't Mathematical concepts exist whether we do or not? You say the are descriptive that implies they are describing something that exists before we do.

Whatever it is that they describe exists. But that doesn't mean our description has an independant reality. Like the six blind men and the elephant, right?

--A

[SerScot]

Avatar,

My wife and I started this discussion last night. Her point is close to yours. She thinks the universality of mathematical concepts is irrelevant as well. She thinks mathematics is universal but our descriptions, as Vraith pointed out, are simply the vagaries of language.

What I explained to her is this. I turn 40 next year. I've always been a Christian of one form or another. As my 40th year has approached, particularly in the last six months, I've become much more keenly aware that I may have more days behind me than before me. It has been somewhat disconcerting. I still have faith but I'm more aware than ever that my faith is without concrete evidence. The idea of Platonic realism, that mathematics is somehow more real than the universe in which I and all of us exist is the first time in my life that I've experienced an idea, outside my own personal experiences, that could stand as possible evidence of an existence beyond our own.

Does that make any sense? If the Platonists are right and the Universality of Mathematics stands as evidence of something beyond our own world couldn't that be taken a step further and be evidence of God's existence as well. That mathematics is simply the imprint of God's perfection on an imperfect universe?

I know that's a stretch and that religious belief is tied up in the Kierkigarrdian idea of the "leap of faith" but the idea that there may be some direct evidence of God's presence in or outside our Universe is very appealing to me right now.

[Avatar]

Hahaha, it makes sense. I don't agree with you, but it makes sense. And I appreciate the honesty too.

I pretty much think the opposite...mathematics are largely imaginary. In general, mathematics is derived from a prior assumption. They argue from their conclusions, as it were.

Nobody sits down and starts doing maths randomly, only to discover the theory or formula for something. They start off by saying "This is what happens" and then they play around with mathematics until they find a formula that "equals" what happened.

If mathematics is universal, at best it would demonstrate that the universe (or physical reality) as we know it adheres to certain principles which govern its properties.

But then, I'm an atheist so...

--A

[SerScot]

Avatar,

I do see your point. I simply hope otherwise. I see the the purity of mathematical concepts and ideas as God's fingerprints. It's an encouraging idea for me. That said by belief is not without skepticism.

[wayfriend]

If mathematics is universal, at best it would demonstrate that the universe (or physical reality) as we know it adheres to certain principles which govern its properties.

I would emphasize the "as we know it".

The universe may not adhere to any principles at all. It may be only that we think it does, based on our perceptions. Principles may arise, not from what we observe, but from what we use to observe it, and what we use to interpret what we observe.

Therefore, the universal applicability of mathematics may only mean that something arising from our minds (mathematics) corresponds to something arising from our minds (our perceptions).

Which isn't saying much at all.

[Vraith]

Avatar,

I do see your point. I simply hope otherwise. I see the the purity of mathematical concepts and ideas as God's fingerprints. It's an encouraging idea for me. That said by belief is not without skepticism.

The funny thing is, Plato was pretty much just hoping, too. He just plain didn't like uncertainty/change.

It's interesting why you want the math to be so, though.

For me, Math isn't that way...it's not a higher/purer/absolute truth. It's just the lowest common denominator of a particular field. I think I have a way to say it finally that's both easy and accurate:
IF you were God-like, at least in the aspect of knowledge, and knew/understood ALL of this universe's reality, one of the things [among many others] you would know/understand would be all of mathematics.
IF, however, you had the same all-encompassing intelligence but "existed" in the "math world" you would know only the math, nothing else, because nothing in the math world, as an inherent property, provides for, describes, or even implies, the universe of forces and matter. [even some of the math you couldn't know because you would have no basis to examine them: from what do the equations that describe pendulums or orbital mechanics arise in a place where neither is even theoretically possible?...Listen: no examination of pure number yields the concept of a clock ticking.]

I'm actually, little by little, coming to think that all metaphysical fields/beliefs/structures/philosophies/what-have-you, are really lowest-common-denominator things. Even morality, even souls.

[Fist and Faith]

Pffffffff... You guys...

For Av.
If one chair and another chair makes two chairs; one star and another star makes two stars; one tree and another tree makes two trees........ It doesn't matter who looks at the objects, what the objects are, whether they're not the same thing, or any other factor we care to name. Well, let's take away the objects, and say one plus one equals two.

What's wrong with this? What's inaccurate about it? If a situation comes up where it's wrong, we'll have to find the bigger picture that encompasses the gajillions of situations where it's right and the one where it's wrong. Then we'll see how 1+1=2 is only a true statement under certain conditions. What's the prior assumption that makes it imaginary? No, math is not a physical face. It's a way of describing physical facts. But that doesn't make it less true.


To wf.
No principles at all? Is it even conceivable that we could even exist if there were none? I don't even know how to begin contemplating the possibility. I don't know how to consider how we could consider at all if there were no principles. Can you get me started?

[Vraith]

It's a way of describing physical facts. But that doesn't make it less true.

Not the point. The argument is about it's heirarchical place in relation to our universe. And other universes.

[Fist and Faith]

I'm not sure that's Av's point. He's been bad-mouthing math forever! But seriously, Av, I've never been really clear on exactly how you object to math.

[SerScot]

Wayfriend,

If mathematics is universal, at best it would demonstrate that the universe (or physical reality) as we know it adheres to certain principles which govern its properties.

I would emphasize the "as we know it".

The universe may not adhere to any principles at all. It may be only that we think it does, based on our perceptions. Principles may arise, not from what we observe, but from what we use to observe it, and what we use to interpret what we observe.

Therefore, the universal applicability of mathematics may only mean that something arising from our minds (mathematics) corresponds to something arising from our minds (our perceptions).

Which isn't saying much at all.

Okay are you speculating there are parts of the universe where prime numbers are divisible by numbers other than themselves and one? Isn't that precisely the same argument that young Earth creationists use to claim carbon and other forms of radioactive decay dating are not reliable simply because we can't know for certian time didn't flow differently in the past?

[Avatar]

What's the prior assumption that makes it imaginary? No, math is not a physical fact. It's a way of describing physical facts. But that doesn't make it less true.

That's not math, that's arithmetic.

My point on this score is always that it begins with an observation, and then the math is juggled until the answer comes out at what is observed.

My favourite example is M-theory. They couldn't get the math to come out at the answer they wanted. So, in order to get that answer, they hypothesised an additional "dimension" (for a total of 11 IIRC, compared to the 10 of string theory) and suddenly the math worked. They made up another dimension so that they got the answer they wanted.

Imaginary.

--A

[Fist and Faith]

In your example, they didn't change the math. They speculated on the nature of reality based on the math. If they said, "The only way to get the math to come out at the answer we want is to say 2+2=5, so that's what we'll do" I'd have a problem.

As for actually changing math itself, let me quote myself. From ZatAoMM:

"Well, it's quite a bootstrap operation. It's analogous to the kind of hang-up Sir Isaac Newton had when he wanted to solve the problems of instantaneous rates of change. It was unreasonable in his time to think of anything changing within a zero amount of time. Yet it's almost necessary mathematically to work with other zero quantities, such as points in space and time that no one thought were unreasonable at all, although there was no real difference. So what Newton did was say, in effect, 'We're going to presume there's such a thing as instantaneous change, and see if we can find ways of determining what it is in various applications.' The result of this presumption is the branch of mathematics known as the calculus, which every engineer uses today. Newton invented a new form of reason..."

I don't really know, but I assume that's how calculus got its start. And even if not, the principle is: If the newly invented math doesn't stand up the next time its needed, it has to be thrown out, or refined. Either Newton got it all right the first time around and his math held in all following times of need, or it was corrected and refined through the years. But, I'm told, calculus is an accurate tool.

[wayfriend]

To wf.
No principles at all? Is it even conceivable that we could even exist if there were none? I don't even know how to begin contemplating the possibility. I don't know how to consider how we could consider at all if there were no principles. Can you get me started?

You can consider that our perceptions are filtered. And that it's been demonstrated that we humans have an innate tropism to seeing patterns even when none exists. Also, you can consider how readily we humans like to fit what we perceive into prefabricated hypotheses, and resist noticing what doesn't fit. The brain is as much built for imposing order and for filtering out chaos as it is for finding order in the chaos.

[Vraith]

In your example, they didn't change the math. They speculated on the nature of reality based on the math. If they said, "The only way to get the math to come out at the answer we want is to say 2+2=5, so that's what we'll do" I'd have a problem.

As for actually changing math itself, let me quote myself. From ZatAoMM:

"Well, it's quite a bootstrap operation. It's analogous to the kind of hang-up Sir Isaac Newton had when he wanted to solve the problems of instantaneous rates of change. It was unreasonable in his time to think of anything changing within a zero amount of time. Yet it's almost necessary mathematically to work with other zero quantities, such as points in space and time that no one thought were unreasonable at all, although there was no real difference. So what Newton did was say, in effect, 'We're going to presume there's such a thing as instantaneous change, and see if we can find ways of determining what it is in various applications.' The result of this presumption is the branch of mathematics known as the calculus, which every engineer uses today. Newton invented a new form of reason..."

I don't really know, but I assume that's how calculus got its start. And even if not, the principle is: If the newly invented math doesn't stand up the next time its needed, it has to be thrown out, or refined. Either Newton got it all right the first time around and his math held in all following times of need, or it was corrected and refined through the years. But, I'm told, calculus is an accurate tool.

I've occasionally wondered if Calculus and its variations would have changed Plato's mind about some things, since it is both Ideal, and a mathematics of change, but Plato denies change in the Ideal.

[SerScot]

wayfriend,

To wf.
No principles at all? Is it even conceivable that we could even exist if there were none? I don't even know how to begin contemplating the possibility. I don't know how to consider how we could consider at all if there were no principles. Can you get me started?

You can consider that our perceptions are filtered. And that it's been demonstrated that we humans have an innate tropism to seeing patterns even when none exists. Also, you can consider how readily we humans like to fit what we perceive into prefabricated hypotheses, and resist noticing what doesn't fit. The brain is as much built for imposing order and for filtering out chaos as it is for finding order in the chaos.

So, is it possible for a prime number to be not prime? For the idealized concept of 3, not a measurment of something, to be more or less than 3?

[wayfriend]

So, is it possible for a prime number to be not prime?

I would say 'no'. But does that say something about the real world?

Did you ever wonder how to explain 'red' to a blind person ... and then wonder if every sighted person's perception of red is the same? Soon you realize that it doesn't matter ... as long as red is red to you, and red is red to me, it doesn't matter if how I see red is the same as how you see red.

For the same reason, it doesn't matter if how I see red now is the same as how I see red one second from now. As long as my brain says 'it's red', everything works for me. Red may have become green ... but as long as my brain's perception of red changed along with it, I wouldn't notice the difference.

The idea that red is a constant could therefore be an illusion. All that I know is that my perception of what is red seems constant. Red may be constantly changing ... and my perceptual mechanisms may be constantly adjusting it give it the appearance of constance.

We may perceive changing reality as constant. We may perceive constant reality is changing.

So in the end, we may even perceive a correlation between mathematics and reality that isn't really there.