Kevin's Watch

Hashi Lebwohl wrote:Yes, when I say "constant" in terms of math I am referring to something which will not change even if we all stop believing in it or will continue to be true even after we are all dead.

Well, the thing that the math describes won't change and will still exist. The math itself however will not.

--A

There is something about the 'purity' of a circle that works for us. It's a line where every point on it is equidistant from a single central point and it works. It doesn't 'exist' - it's a mental construct and the rules that pertain to it are mental constructs as well. They have no independant existence beyond the 'idea' of the circle. Lets say you are an Alien from another universe. For you what works is not a circle, but a circle with a flat bottom to stand on. You see *this* in the way we see a circle. To you this shape is the one that ticks all the boxes and when you do the math you find that the value of a different 'constant' that describes the relationships within this area equals 3. You don't question it, nor do you think it could ever be any different. It just is - and it satisfies you just in the way that pi satisfies us.

Vraith - is it the trancendential nature of pi that captures the imagination. This almost mystical 'goes on forever' thing (never mind the 'can't be described by an equation with a finite nuber of terms' thing added in) that makes it so 'right' in our eyes.

[Finally as we have a few mathemeticians gathered in one place, can I bounce the following off you. The 'Powertrain'. Developed by professor John Horton Conway at Princeton in 2007 it is the idea that for any number written abcdef it's powertrain is a(b)c(d)e(f) where the bracketed numbers are 'to the power' [sorry guys - I don't know how to do this on my computer but I'm sure it's possible]. So abcdef bcomes a(to the power b)c(to the power d)e(to the power f) etc. Now the thing is that they collapse. Take 3462 - it becomes 3(4)6(2), which becomes 81 x 36 = 2916. Apply the 'powertrain' to this and it becomes 2(9)1(6) = 512 x 1 = 512 = 5(1)2 =10 =1(0) = 1.
Conway began to search for indestructable digits, ie digits that could not be rediced to a single digit under the 'powertrain' and could find only one - 2592. [2(5)9(2) = 32 x 81 = 2592]. Neil Sloane, curator of "The Online Encyclopedia of integer sequences" has found a second - 24547284284866560000000000 (and this one depends on the convention that 0 to the power 0 = 1, since if it was taken to be zero then the number would vanish immediately). Both Sloane and Conway are convinced that that is it - that there are no other numbers that will not collapse under the 'powertrain'. Now how weird is this; that of all the infinite numbers of integers only 2, seemingly unrelated numbers resist the unbridled might of the 'powertrain' to resist destruction.]

Wikipedia has a pretty good summary of all the various positions philosophers have taken on this issue.

My position would fall under mathematical realism, specifically the Platonism subcategory ... though structuralism has a strange appeal to me. I suppose if you substitute the structures/relations within math for the actual numbers, then I'm more of a Platonist for the former rather than the latter.

Hashi's, Cozarkian's, and Orlion's positions sound like the empiricism subcategory of mathematical realism (correct me if I'm wrong). It sounds like WF is still open and questioning on this issue, but his questions seem most often to leave open the possibility of some form of psychologism, whereas math is built upon the workings of our own minds rather than anything objective in the world. And Avatar seems to have a more resolute position in this direction, perhaps even the embodied mind position.

Some of the other positions here are harder to pin down. And sometimes it seems many of us are holding contradictory pieces of several of these positions.

Fictionalism is quite fascinating. I'll have to give that one some thought.

Orlion wrote:Yeah, I'm going to have to rebuke Vraith about his Pi rant ("Get thee behind me, Satan!" )

Heh...well thanks for the winky in the rebuke.
So, I was a little too hard on Pi [I think the movie about his life pretty much blows chunks, too], it's a bit more hardworking than I gave it credit for...but I as having fun.

My only real problem with math being real is the ordering/hierarchy and what's left out.

As I said, it is real [heh...and you agreed with me, I note] in a similar way to words.

What it is NOT is some perfect, pure, superior truth/reality.

I don't think its effectiveness is at all ridiculous, all things considered.
I would expect that for every stable universe there will be maths that describe it accurately...but it may require completely different maths to do so, just as we require different maths for different purposes in our universe.
Reverse side of that is, as I've said before in various ways: for every aspect of math that touches the material in some way, there are other aspects that can never be anything BUT math, that contradict the material.
Things that are necessary for the math to work.
To return to apples [but avoid pi, this time]
In its way, at a primitive/intuitive level, 1 IMPLIES 0 and also -1, etc.
An apple may imply [especially for those who have eaten one before, and know how tasty it is] zero apples. But it in no way suggests negative apples. And where -1 is necessary for 1 to function properly for multiple, maybe infinite, purposes, negative apples are ridiculous at first blush...and if "real" would be as hazardous as, or worse, than the "Original Apple" for the world.

Vraith wrote: So, I was a little too hard on Pi [I think the movie about his life pretty much blows chunks, too]

Never saw the movie, but was not a huge fan of the book.

Zarathustra wrote:And Avatar seems to have a more resolute position in this direction, perhaps even the embodied mind position.

Thanks for the link, some interesting stuff. Looks pretty close, although to be perfectly honest, my position comes simply from "feeling" and certainly not from any real knowledge of math.

--A

Hashi Lebwohl wrote:The only movie about pi you need to see is this one, which is actually named "pi". Really good movie even if the high-contrast black/white filming is a little difficult to watch at times.

Yes - now that is a strange couple of hours of viewing!

Hashi Lebwohl wrote:The only movie about pi you need to see is this one, which is actually named "pi". Really good movie even if the high-contrast black/white filming is a little difficult to watch at times.

Hmmm....I'm gonna have to take a look at that.

I assume from your recommendation that it's better than...what was it? Was it "Contact?" Where at the very end, pi becomes zeroes and ones of varying lengths, and if you arrange them in a grid or something it creates a picture, or has communication coded in it or something??? Been too long...I think it was. In the book anyway...I don't recall movie? I think I saw it? Some things are really forgettable??

Edited to add...yea, Z, cool link...lots of stuff to cogitate.

Vraith wrote:
I assume from your recommendation that it's better than...what was it? Was it "Contact?" Where at the very end, pi becomes zeroes and ones of varying lengths, and if you arrange them in a grid or something it creates a picture, or has communication coded in it or something??? Been too long...I think it was. In the book anyway...I don't recall movie? I think I saw it? Some things are really forgettable??

I think that was in the novel but not the movie; it has been too long since I saw the movie. Yes, the advanced aliens had uncovered this apparent quirk in pi--I think the arrangement formed a circle made of ones in a field of zeroes or something like that--and even they didn't understand it. They also didn't create the wormholes, they only discovered them and used them for travel and making contact.

If math has no objective reality why does it translate across all human cultures? Why are there not cultures that don't have the idea of 3 or, more interestingly, for whom the idea of 3 cannot be described within their language because it will not translate.

Yes, Indian's developed "Zero" but "Zero" then easily translated into every human culture. If mathematics is not objective why can all mathematical concepts be understood by all cultures?

SerScot, you can make the same argument about G/god. And dragons.

I think you've shown us that there is a distinction between what is real and what has meaning. Does everything to which we ascribe meaning need to be real? (Real in a way other than being a real symbol for which we ascribe meaning?)

Math, if anything, is a Model. A Model can be conveyed from one person to another, one culture to another, perhaps even one species to another. But it doesn't require that the Model be real. Just that it make sense and be coherent.

Wayfriend,

And that's where I disagree. For a concept or an imagining to have universal applicablity, as mathematical concepts do they must be grounded in some universal reality. If not why can there not be mathematical concepts in different cultures that don't translate. The universal translatibilith of mathematics suggests objective reality to me.

What other concepts have universally identical translations?

SerScot wrote:Wayfriend,

And that's where I disagree. For a concept or an imagining to have universal applicablity, as mathematical concepts do they must be grounded in some universal reality. If not why can there not be mathematical concepts in different cultures that don't translate. The universal translatibilith of mathematics suggests objective reality to me.

What other concepts have universally identical translations?

I've said this before, I'm sure.
It isn't a matter of real vs. unreal.
It's just a matter of different KINDS of real.
And it is universally translatable because every materially sound universe will be describable by some kind of mathematics. [actually, many kinds are necessary it seems...math is contextual, too. At this point any kind of "metamath" to cover it all seems impossible...stay tuned, though...was it Heinlein story of a corp with the motto "the difficult we do now, the impossible takes a little longer?" or somesuch??]
And some physical/material facts will be experienced universally, have effects on everyone/thing.

Many things are universally translatable, though, I think.
The idea of language/communication itself, for instance.
And every culture understands "me" and "you," [which abstracts to "2," among other things]....
What they DO with that "me" and "you" concept may vary.

Vraith wrote:was it Heinlein story of a corp with the motto "the difficult we do now, the impossible takes a little longer?" or somesuch??

I don't know about that but it is featured in the classic Billie Holliday song "Crazy He Calls Me", as featured on Galaxy News Radio by its host, the inestimable and unparalleled Three Dog.

Math is real

I got a 60 something % in gr 12 math, alas math is always there to thwart my average.

Vraith,

What, other than mathematics, is universally translatable without variation for language and culture?

SerScot wrote:Vraith,

What, other than mathematics, is universally translatable without variation for language and culture?

Almost everything sensible/material to begin with.
Much of that doesn't even need to be translated, doesn't even need conceptualizing or naming unless one wants to use/alter/oppose it.
And as I already said communication/language itself is one. [and the ability to DO communication/language is the only reason one can talk about mathematics and translation.]
The main reason math works the way it does is because it is the simplest, most reduced of things [which is not the same as easy, of course] and almost all of it is true by definition.
It is not metaphysical, or some controlling superstructure. It is the lowest of the lowest common denominators.

There's a difference between objective and real.

--A