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"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.
"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
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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…
Exactly -- nature isn't doing any calculations. The correct statement would be "it takes difficult calculations to describe what nature does using numbers."
Just slightly a link-bait-esque title. Can we rename it to e.g. “Tau: Why 2π Would Be a Better Constant than Pi”?
"Pi is wrong!" also makes for a pithier rallying cry. Can you imagine Braveheart yelling "Tau: Why 2π Would Be a Better Constant than Pi!" Neither can I.
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…
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
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"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
Agreed. Forget Pi, maybe the way we count is flawed!
Also See What are numbers, and what is their meaning?: Dedekind http://www.math.uwaterloo.ca/~snburris/htdocs/scav/dedek/ded...
Unfortunately, mathematical notation has tons of historical cruft like this. And there will be people who will fight tooth and nail to preserve all those artificial complexities. Personally, I always believed that improving the notation would have huge benefits in the future.
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?
There are suggestions that http://en.wikipedia.org/wiki/Planck_distance is the smallest distance (or size) nature handles.
You could say nature has no concept of real numbers.
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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.