6 ms·
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 "Nat
by pwpwp 15y ago
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 before she decides that the computation can't be concluded?" Next I wondered, "to how many aribtrary decimal places does nature carry out the transcendental irrational before she decides to say it's a bad job and call it off?" If nature uses π she has to do what we call fudging of her design which means improvising, compromisingly. I thought sympathetically of nature's having to make all those myriad frustrated decisions each time she made a bubble. I didn't see how she managed to formulate the wake of every ship while managing the rest of the universe if she had to make all those decisions. So I said to myself, "I don't think nature uses π. I think she has some other mathematical way of coordinating her undertakings.""
From http://content.stamen.com/buckminster_fuller_and_the_beauty_of_bubbles http://content.stamen.com/buckminster_fuller_and_the_beauty_...
- lmm 15y agoAll 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.
- bunderbunder 15y agoWe 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 same time. So there's the possibility that any or all of that difficulty could turn out to be epicycles.
- rquantz 15y agoExactly -- nature isn't doing any calculations. The correct statement would be "it takes difficult calculations to describe what nature does using numbers."
- super_mario 15y agoActually, 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. So, basically it changes states predictably as it "sees" symbols (photons). It could be said it recognizes a language where alphabet are photons. Entire universe can be thought of as a computer.
- rquantz 15y agoI 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.
- losvedir 15y agoOh, 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/ http://www.scottaaronson.com/blog/
- loup-vaillant 15y ago> 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 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 http://wiki.lesswrong.com/wiki/Absolute_certainty
- abecedarius 15y agoFeynman 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.)
- lutorm 15y agoHogwash. 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?
- m_for_monkey 15y ago"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.
- backprojection 15y ago"he says that our description of nature (that we are using pi) is flawed" Every description we'll ever have will probably be flawed to some degree. I concur that it's hogwash
- sev 15y agoAgreed. Forget Pi, maybe the way we count is flawed!
- nodemaker 15y agoI think any way of counting will have the same basic axioms (http://en.wikipedia.org/wiki/Peano_axioms http://en.wikipedia.org/wiki/Peano_axioms) Also See What are numbers, and what is their meaning?: Dedekind http://www.math.uwaterloo.ca/~snburris/htdocs/scav/dedek/dedek.html http://www.math.uwaterloo.ca/~snburris/htdocs/scav/dedek/ded...
- batista 15y agoThis 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.
- nodemaker 15y agoWell according to http://en.wikipedia.org/wiki/Pi http://en.wikipedia.org/wiki/Pi Practically, one needs only 39 digits of π to make a circle the size of the observable universe accurate to the size of a hydrogen atom In my opinion trying to answer the question "to how many decimal places does nature carry out π before she decides that the computation can't be concluded" naturally leads us to what is known as Heisenberg's uncertainty principle
- jgw 15y agoI'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?
- abecedarius 15y agoexp(i tau) = 1
- lurker17 15y agoEuler'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.
- brlewis 15y agoWhy does he assume nature requires decimal representation for her calculations?