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Harte -

then why do some trees grow leaves in a fibonacci sequence?

cause, or effect?

my point is that mathematics is not immune.

there is no final, elegant, definitive "proof" anywhere, anytime.

past, present or future.



john

This is too deep for me.

there is no final, elegant, definitive "proof" anywhere, anytime.

Hey! Bush said that Iraq had Weapons of Mass Destruction and...........


uh.


Bad example.

Hey John,

This is the wrong place to look for the absence of absolute proof.

If you want some proof let us know. But quit your crying.

Or better yet what proof do you have?

I like John's post and I agree. We do spend a lot of time on semantics and on buulshit. We do demand proof of things and his assessment of same is accurate. I use the word evidence a lot, I had thought that I used it too much, but in light of John's definitive post I am glad I use it instead of "proof". There are a lot of very intelligent people who write for this forum, but occasionally it's difficult to tell who they are because of all the trivialities which invade. I can remember when much of what was posted here went over my head, but now either I'm a lot smarter or the IQ average for posters here has dropped. I'm sure it's a little of both. I have learned a lot here. Some of the discussion, however, deteriorates to childish squabbling rather abruptly. We do have a lot of freedom here and that's good as people's personalities are allowed to show through. Many times scientific discussions can become very dry and boring, especially to the layperson. Not much chance of that happening here. We must strive for some kind of halfway point between dry and boring and wild flaming. I gotta go home now. Bye!

john wrote:Harte -

then why do some trees grow leaves in a fibonacci sequence?

cause, or effect?

Neither.

The Fibonacci sequence is a model (though not originally intended as one - as much of the rest of mathematics has unintended applications) for how leaves and other things sometimes grow. The reality is only approximate, while the Fib. sequence is absolutely precise.

john wrote: my point is that mathematics is not immune.

there is no final, elegant, definitive "proof" anywhere, anytime.

past, present or future.

john

No, Mathematics is by definition immune. For the reasons I stated previously, namely because mathematics begins with the assertion of truths. From these assertions (axioms,) a vast number of extremely elegant, final and definitive proofs can easily be constructed.

But, they have no final, definitive meaning outside the field of Mathematics, other than their usefulness in manipulating scientific theories, which themselves are not "proofs" of anything at all.

Harte

Harte wrote:

john wrote:Harte -

then why do some trees grow leaves in a fibonacci sequence?

cause, or effect?

Neither.

The Fibonacci sequence is a model (though not originally intended as one - as much of the rest of mathematics has unintended applications) for how leaves and other things sometimes grow. The reality is only approximate, while the Fib. sequence is absolutely precise.

john wrote: my point is that mathematics is not immune.

there is no final, elegant, definitive "proof" anywhere, anytime.

past, present or future.

john

No, Mathematics is by definition immune. For the reasons I stated previously, namely because mathematics begins with the assertion of truths. From these assertions (axioms,) a vast number of extremely elegant, final and definitive proofs can easily be constructed.

But, they have no final, definitive meaning outside the field of Mathematics, other than their usefulness in manipulating scientific theories, which themselves are not "proofs" of anything at all.

Harte

Harte-

agree with you completely, save for one small point.

you define mathematics as a "separate universe", based on axioms.

good so far.

my question to you is

did fibonaccci's sequences arise "full blown from the thigh of zeus", i.e. independent from awareness of the physical universe

or were they a codification of observations, however subtle, OF the physical universe?

in short, what creates an axiom?

there are some interesting parallels to this question raging in the various biblical threads on this forum.



john

Wasn't Fibonacci a character in the Goldfather?

john wrote:...my question to you is

did fibonaccci's sequences arise "full blown from the thigh of zeus", i.e. independent from awareness of the physical universe

or were they a codification of observations, however subtle, OF the physical universe?

in short, what creates an axiom?

The sequence arose originally (in the Western world, anyway) as a way of measuring how many pairs of rabbits would be created in a year if you start with one pair, and each pair producing another pair each month, starting with the second month.

But the real origin, or at least the earliest record of it I know of, comes from around 300 BC, with some Hindu liguistics guy figuring out the cadences of sanskrit given the two vowel soundings in that tongue. The problem was eventually more clearly elucidated by later Indian mathemeticians several hundred years later.

So, what we call the Fibonacci numbers (or sequence) actually does have it's roots in counting, which, it may be argued, is a physical activity. But what I said still applies, since counting, and arithmetic itself, are based on certain axioms (like "two is the next number after one," for example.) It is the absolute and final definition of such things that make such a thing an axiom. And axioms themselves are based on logic, or in other words, what "seems" right but cannot be proven.

An excellent example is the axiom from Euclid's geometry which states that "Three points define a plane."

Try to prove that one in anything like a rigorous manner.

Harte

Why are we discussing math on an archaeological forum? Man, I freakin' hate math. Gives me a headache. Can we connect this to archaeology in some way? Bad enough we have to discuss religion here, but at least he tries to connect it to archaeology.....sorta.

unfortunately for you, according to the CBS t.v. show, NUMBERS, we are supposed to use math everywhere. in their eyes math belongs in archaeology as well.

by the way, that show is a crock.

Frank Harrist wrote:Why are we discussing math on an archaeological forum? Man, I freakin' hate math. Gives me a headache. Can we connect this to archaeology in some way? Bad enough we have to discuss religion here, but at least he tries to connect it to archaeology.....sorta.

frank -

connection is absolute. homo sapiens is the single and only author of mathematics. argument is still raging as to the absolute date of man's conception of abstract "numbers".

stay tuned for the news at "eleven".


john

Harte wrote:

john wrote:...my question to you is

did fibonaccci's sequences arise "full blown from the thigh of zeus", i.e. independent from awareness of the physical universe

or were they a codification of observations, however subtle, OF the physical universe?

in short, what creates an axiom?

The sequence arose originally (in the Western world, anyway) as a way of measuring how many pairs of rabbits would be created in a year if you start with one pair, and each pair producing another pair each month, starting with the second month.

But the real origin, or at least the earliest record of it I know of, comes from around 300 BC, with some Hindu liguistics guy figuring out the cadences of sanskrit given the two vowel soundings in that tongue. The problem was eventually more clearly elucidated by later Indian mathemeticians several hundred years later.

So, what we call the Fibonacci numbers (or sequence) actually does have it's roots in counting, which, it may be argued, is a physical activity. But what I said still applies, since counting, and arithmetic itself, are based on certain axioms (like "two is the next number after one," for example.) It is the absolute and final definition of such things that make such a thing an axiom. And axioms themselves are based on logic, or in other words, what "seems" right but cannot be proven.

An excellent example is the axiom from Euclid's geometry which states that "Three points define a plane."

Try to prove that one in anything like a rigorous manner.

Harte

harte -

back in high school i had this physics/mathematics teacher, a highly athletic guy, who would leap into the classroom and fill the blackboard with equasions for the fifty minutes. as students, we were mystified and regularly somewhat astounded. when we asked our poor questions, he would look at us, astonished, and say "don't you see? it's intuitively obvious!"

thus euclid.

but in my simplistic mind,

one point proves an entity

two points prove a line

three points prove a plane

and four points can prove just damn near anything!


cheers,


john

Ok lets keep it archaeological, guys.

Frank Harrist wrote:Ok lets keep it archaeological, guys.

sorry, frank -

just trying to figure out how the neandertals decided the number of holes to put into one of their flutes.

j