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Pi Is Wrong

math.utah.edu

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Re: Pi Is Wrong

#51

Post by FreakLegion »

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.

Austin doesn't say performatives aren't propositions. Note that there are still truth-evaluable performatives, and that as Austin and others continued down the il/perlocutionary rabbit hole, they came to regard all language as essentially performative.

Don't get me wrong though, I see the point you want to make; but it misses the mark in statements like Rimbaud's "Je est un autre." Writers, poets especially, do this a lot, pushing performativity to some limit where the form accomplishes what the meaning merely asserts.

Which totally reminds me of a line from Marshall McLuhan:

Just before an airplane breaks the sound barrier, sound waves become visible on the wings of the plane. The sudden visibility of sound just as sound ends is an apt instance of that great pattern of being that reveals new and opposite forms just as the earlier forms reach their peak performance.

Re: Pi Is Wrong

#52

Post by FreakLegion »

brudgers wrote: post #50
batista wrote: post #37

Earlier quoted context omitted.

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... ]

He didn't say "You promised" is also a promise. Rather, he said "I promise" is also a description.

Re: Pi Is Wrong

#53

Post by m_for_monkey »

batista wrote: post #36
m_for_monkey wrote: post #16

Earlier quoted context omitted.

"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 "a…

Yes, it's "only" philosophy, but that doesn't mean it's utter BS.

Look we either talk about the exact pi, or not pi at all. In my computer there's no pi.

As for the alternative, at least he tried something:

"Fuller also claimed that the natural analytic geometry of the universe was based on arrays of tetrahedra. He developed this in several ways, from the close-packing of spheres and the number of compressive or tensile members required to stabilize an object in space. One confirming result was that the strongest possible homogeneous truss is cyclically tetrahedral."

http://en.wikipedia.org/wiki/Buckminster_Fuller#Philosophy_a...

Re: Pi Is Wrong

#54

Post by mattheww »

loup-vaillant wrote: post #44
dexen wrote: post #28

Earlier quoted context omitted.

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 th…

Actually, it's you who is doing the over interpreting. The Heisenberg uncertainty principle is a physical constraint that wave functions obey. If you define a state with an infinitely precise location, then the range of momentums is infinite. This result is fairly easy to reproduce, so it would probably be instructive to try it.

The measurement interpretation of the Heisenberg uncertainty principle is both a useful way to understand it, and historically, a way to ease experimentalists into accepting and believing it.

Re: Pi Is Wrong

#55

Post by Sniffnoy »

adeelk wrote: post #17

See also [1], where Terence Tao suggests that 2 pi i may be even more fundamental than both 2 pi and pi , and [2] for some explanation on why. [1] http://blog.computationalcomplexity.org/2007/08/is-pi-define... [2] http://qchu.wordpress.com/2011/03/14/pi-is-still-wrong/

Of course tau * i is what's really fundamental; however it's much more convenient to have the notation refer to a real constant. Firstly, one might be working in a context where complex numbers are not present, and to have to use them just to even refer to a real constant would be an annoyance. Secondly, if one defines a real constant tau, it is then easy to talk about the imaginary version i * tau; whereas one defining an imaginary constant, and having to divide by i or multiply by -i to get the real version would be somewhat annoying. Thirdly, if one went with the complex version, there'd be the whole "i or -i" problem due to the symmetry of the complex numbers -- OK, I guess this is not really an actual problem, but it would be slightly annoying, especially in context where dealing with complex numbers at all isn't really necessary. Whereas defining tau to be a positive real number gets rid of that problem.

Re: Pi Is Wrong

#56

Post by arctangent »

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?

> Mathematics is a way of describing nature, not the other way around.

I think this comes down to whether you are of the "realist" or the "Platonist" school of thought:

[1] http://en.wikipedia.org/wiki/Philosophy_of_mathematics

Re: Pi Is Wrong

#57

Post by pbhjpbhj »

loup-vaillant wrote: post #49
bunderbunder wrote: post #5

Earlier quoted context omitted.

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

Occam's Razor itself actually says that you mustn't multiply entities beyond necessity. It gives no clues as to the necessity and so is, IM[not very popular it seems]O, absolutely of no worth.

Of course if you can prove whether an entity is necessary to describe an outcome then you've no use of Occam's Razor, so it seems rather to excise itself from being useful.

Re: Pi Is Wrong

#58

Post by sixbrx »

mattheww wrote: post #54
loup-vaillant wrote: post #44

Earlier quoted context omitted.

> 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 th…

Actually, it's you who is doing the over interpreting. The Heisenberg uncertainty principle is a physical constraint that wave functions obey. If you define a state with an infinitely precise location, then the range of momentums is infinite. This result is fairly easy to reproduce, so it would probably be instructive to try it. The measurement interpretation of the Heisenberg uncertainty principle is both a useful w…

I'm not sure what your argument really is here. Your very invocation of "the wave function" implies continuity in the evolution of the state vectors, described by the wave equation - it matters not that results of macroscopic measurements will only produce quantized results. You still used continuity of the more abstract (but no less "real") state vector evolution.

Re: Pi Is Wrong

#60

Post by lurker17 »

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?

Euler's formula is a mathematical law, not a physical one. There is no proof that the Earth is perfectly round, and plenty of evidence to the contrary.
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