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Pi Is Wrong

math.utah.edu

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31–40 of 69 posts

Re: Pi Is Wrong

#31

Post by rquantz »

super_mario wrote: post #22
rquantz wrote: post #11

Earlier quoted context omitted.

Exactly -- nature isn't doing any calculations. The correct statement would be "it takes difficult calculations to describe what nature does using numbers."

Actually, if you look at the formal definition of computation (see for example "Introduction to the Theory of Computation" by Michael Sipser), a lot of natural processes are in fact a computation. An atom is a computer. Photons may hit an electron giving it extra quanta of energy and it shifts orbit (it skips further away from the nucleus), or it may emit a photon and shift its orbit closer to the nucleus of the atom…

I like this. Sipser is already on my reading list. I'll make sure I get to it once I finish working my way through SICP.

Re: Pi Is Wrong

#33

Post by jgw »

pwpwp wrote: post #2

Instead of whether we should use Pi or 2*Pi, I find much more interesting R. Buckminster Fuller's statements that "Pi is operationally irrelevant" and that "Nature is not using Pi". "Inasmuch as the kind of mathematics I had learned of in school required the use of the XYZ coordinate system and the necessity of placing π in calculating the spheres, I wondered, "to how many decimal places does nature carry out π befor…

I'm a dodgy mathematician at best, but doesn't the simple elegance of Euler's formula suggest that π is beyond merely "relevant" and indeed one of a handful of the most fundamental building blocks of the universe?

Re: Pi Is Wrong

#34

Post by brudgers »

FreakLegion wrote: post #29
brudgers wrote: post #20

Earlier quoted context omitted.

The description of a thing is not the thing itself.

Except in the case of performatives! http://en.wikipedia.org/wiki/Performative_utterance

Not exactly.

Austin's proposition is that the statement, "I promise," is a promise not a proposition.

But that does not make it a description of a state of affairs [or a picture of reality per Wittgensteinian]. A description would be, "You promised," and that is clearly not a promise.

YMMV.

Re: Pi Is Wrong

#35

Post by losvedir »

rquantz wrote: post #31
super_mario wrote: post #22

Earlier quoted context omitted.

Actually, if you look at the formal definition of computation (see for example "Introduction to the Theory of Computation" by Michael Sipser), a lot of natural processes are in fact a computation. An atom is a computer. Photons may hit an electron giving it extra quanta of energy and it shifts orbit (it skips further away from the nucleus), or it may emit a photon and shift its orbit closer to the nucleus of the atom…

I like this. Sipser is already on my reading list. I'll make sure I get to it once I finish working my way through SICP.

Oh, I heartily second super_mario's recommendation. You won't regret it.

I had the pleasure of taking Sipser's class a few years ago, and the man could explain things so clearly. We used his book as our textbook, and it was just as clear.

You should also check out Scott Aaronson's blog[1] if you're into this sort of thing.

[1]http://www.scottaaronson.com/blog/

Re: Pi Is Wrong

#36

Post by batista »

m_for_monkey wrote: post #16
lutorm wrote: post #12

Earlier quoted context omitted.

Hogwash. Mathematics is a way of describing nature, not the other way around. And doesn't Gödel's incompleteness theorem make it clear that any such attempt must necessarily be flawed?

"Hogwash" I wouldn't dare to say that about Dr Fuller... "Mathematics is a way of describing nature, not the other way around." He doesn't say otherwise, he says that our description of nature (that we are using pi) is flawed.

This is not mathematics though, nor science, it's just the meta-mathematical philosophical opinion of a guy (mostly self-taught, by the way, and know for his cool inventions and ideas, not for his deep mathematical insights).

He also use Pi in computers, e.g to draw circles, and computers (and displays) are even more discrete that nature.

Has he come up with something better to use in Pi's place?

That we don't use "all" of Pi to draw a circle doesn't matter, the "Pi" kind of circle is like the perfect archetype. We don't make the "perfect bridge" or the "perfect car" either, that doesn't mean the concept of bridges and cars is useless.

Re: Pi Is Wrong

#37

Post by batista »

brudgers wrote: post #34
FreakLegion wrote: post #29

Earlier quoted context omitted.

Except in the case of performatives! http://en.wikipedia.org/wiki/Performative_utterance

Not exactly. Austin's proposition is that the statement, "I promise," is a promise not a proposition. But that does not make it a description of a state of affairs [or a picture of reality per Wittgensteinian]. A description would be, "You promised," and that is clearly not a promise. YMMV.

Wait, what? "I promise" is as much a description as "You promised". A description can be made in the first person.

Re: Pi Is Wrong

#38

Post by brlewis »

pwpwp wrote: post #2

Instead of whether we should use Pi or 2*Pi, I find much more interesting R. Buckminster Fuller's statements that "Pi is operationally irrelevant" and that "Nature is not using Pi". "Inasmuch as the kind of mathematics I had learned of in school required the use of the XYZ coordinate system and the necessity of placing π in calculating the spheres, I wondered, "to how many decimal places does nature carry out π befor…

Why does he assume nature requires decimal representation for her calculations?

Re: Pi Is Wrong

#39

Post by keithnoizu »

lutorm wrote: post #12
pwpwp wrote: post #2

Instead of whether we should use Pi or 2*Pi, I find much more interesting R. Buckminster Fuller's statements that "Pi is operationally irrelevant" and that "Nature is not using Pi". "Inasmuch as the kind of mathematics I had learned of in school required the use of the XYZ coordinate system and the necessity of placing π in calculating the spheres, I wondered, "to how many decimal places does nature carry out π befor…

Hogwash. Mathematics is a way of describing nature, not the other way around. And doesn't Gödel's incompleteness theorem make it clear that any such attempt must necessarily be flawed?

My understanding of Godels is that it only implies that a super system will always be required to explain certain results in a base system.

Which does not refute out ability to model nature.

Re: Pi Is Wrong

#40

Post by Confusion »

brlewis wrote: post #38
pwpwp wrote: post #2

Instead of whether we should use Pi or 2*Pi, I find much more interesting R. Buckminster Fuller's statements that "Pi is operationally irrelevant" and that "Nature is not using Pi". "Inasmuch as the kind of mathematics I had learned of in school required the use of the XYZ coordinate system and the necessity of placing π in calculating the spheres, I wondered, "to how many decimal places does nature carry out π befor…

Why does he assume nature requires decimal representation for her calculations?

He doesn't; the entire argument is base independent.
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