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Pi Is Wrong

math.utah.edu

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41–50 of 69 posts

Re: Pi Is Wrong

#41

Post by abecedarius »

jgw wrote: post #33
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?

exp(i tau) = 1

Re: Pi Is Wrong

#42

Post by abecedarius »

lmm wrote: post #4
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…

All the evidence is that nature does implausibly difficult computations all the time. Multiplying by pi has nothing on calculating the evolution of a quantum system.

Feynman said in his talk on quantum computing (IIRC) that this bugged him -- how according to our best understanding of physics it takes an infinite amount of computation to predict what happens in an arbitrarily small volume. And that was part of what set him to thinking about quantum-mechanical computers. (I should look up the actual quote, though.)

Re: Pi Is Wrong

#44

Post by loup-vaillant »

dexen wrote: post #28
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?

http://en.wikipedia.org/wiki/Heisenberg_uncertainty_principl... describes nature's limit to precision of measurement of position and speed vector of objects. In physics, it does not make sense to discuss position (nor boundaries) of object with infinite or absolute precision. There are suggestions that http://en.wikipedia.org/wiki/Planck_distance is the smallest distance (or size) nature handles. You could say nature…

> In physics, it does not make sense to discuss position (nor boundaries) of object with infinite or absolute precision.

No, no, no, you are over interpreting. The fact that you cannot measure with infinite precision doesn't mean it doesn't even makes sense to talk infinitely precisely about positions. You can for instance make thoughts experiments, by imagining an initial state infinitely precisely, then conclude that subsequent measures will give such and such results, this time with finite precision.

According to current models, nature runs on infinitely precise mathematics. (And according to most sensible current models, that math is also deterministic.) The fact that your access to those maths lack infinite precision doesn't mean the math itself is imprecise.

Re: Pi Is Wrong

#45

Post by softbuilder »

Notation aside, I like the term "turn" used for the whole unit. If you say 2 pi or 1 tau, it's still cloaked in traditional mathspeak. That kills opportunities for intuitive understanding, which can be a foothold for some.

Re: Pi Is Wrong

#46

Post by rmk »

If only more articles like this made it to the frontpage... Instead articles about the MPAA and RIAA seem to make it to the frontpage more and more.

Re: Pi Is Wrong

#47

Post by lutorm »

brudgers wrote: post #20
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?

The description of a thing is not the thing itself.

Isn't that what I said?

Re: Pi Is Wrong

#48

Post by lutorm »

keithnoizu wrote: post #39
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?

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.

I never said it refutes our ability to model nature. I said it seems to refute the idea that nature itself runs on mathematics. Because what is the super system of nature?

Re: Pi Is Wrong

#49

Post by loup-vaillant »

bunderbunder wrote: post #5
lmm wrote: post #4

Earlier quoted context omitted.

All the evidence is that nature does implausibly difficult computations all the time. Multiplying by pi has nothing on calculating the evolution of a quantum system.

We don't really have any evidence at all of exactly what nature computes or how it does it. We do have models that mimic observations in nature, and those models do include some very difficult calculations. However the map is not the territory. We can't be sure that the models' inner workings mimic nature's inner workings, any more than you can conclude that two watches have identical mechanisms because they keep the…

> We can't be sure that the models' inner workings mimic nature's inner workings

William of Ockham says we have reasonable hope of coming damn close. http://en.wikipedia.org/wiki/Occam%27s_razor

Anyway, infinite certainty doesn't exist. Not even for 2+2=4. http://wiki.lesswrong.com/wiki/Absolute_certainty

Re: Pi Is Wrong

#50

Post by brudgers »

batista wrote: post #37
brudgers wrote: post #34

Earlier quoted context omitted.

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.

Austin's argument is that "I promise" is unique because saying "I promise" is the act of promising.

"You promised" is not a promise, it is a description of the act of promising (carried out by someone else).

[see How to Do Things with Words: http://www.amazon.com/How-Do-Things-Words-Lectures/dp/067441... ]

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