31–40 of 46 posts
You can also calculate pi by throwing frozen hot dogs: http://www.wikihow.com/Calculate-Pi-by-Throwing-Frozen-Hot-D...
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Yeah I gotta think about that one. If we assume that there is some smallest discrete base unit of space (which I think is plausible), then all string lengths could only be some integer multiple of that base unit. Therefore length pi is out of the question. Now presumably 1 meter will be equivalent to some integer multiple of base units, though that may turn out not to be the case. Perhaps the current definition of a…
See my reply here: http://news.ycombinator.com/item?id=2667461 There is no discrete base unit of space, and on top of that objects do not have determinate sizes.
Next question: Is it possible for a piece of string to be pi units long? How do transcendental numbers translate to the real world?
Just as difficult a question: Is it possible for piece of string to be 2 units long? In the real world, you always run into limits on how finely you can measure things before you run into quandaries about number theory.
How does number theory relate to this?
(I think you just misused the term, and are thinking more about the philosophy of mathematics and not about that specific discipline.)
Pi is the wrong constant. That animation looks great, but it's misleading: the fundamental measurement of the circle is the radius, not the diameter. Measured with a unit radius, we'd see 2*pi for a full "turn" of the wheel. Twice pi, or tau, is the magic number. See http://tauday.com/ for details.
Pi is the right unit because it represents the largest irreducible radian size. It is the fundamental unit of 2 dimensional angles.
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Yeah I gotta think about that one. If we assume that there is some smallest discrete base unit of space (which I think is plausible), then all string lengths could only be some integer multiple of that base unit. Therefore length pi is out of the question. Now presumably 1 meter will be equivalent to some integer multiple of base units, though that may turn out not to be the case. Perhaps the current definition of a…
See my reply here: http://news.ycombinator.com/item?id=2667461 There is no discrete base unit of space, and on top of that objects do not have determinate sizes.
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>Pi is the wrong constant. Seems a bit pedantic. The post was about illustrating pi after all. I do enjoy the argument for tau though.
Actually I found that the animation showed a clear example demonstrating that pi is wrong. I don't know about you, but when I looked at it I immediately recognized the blue arrow and the centre of the wheel. That's a radius. There's no easy way to determine that a diameter was in the picture. As it rolls over the circumference, it's the radius line we follow. Therefore, I agree that pi is truly the wrong constant to…
I've read the Tau Manifesto before, and I think it makes some really good points. I'm probably 60-75% in agreement with it. But this animation is fine.
It's amazing just how much seeing something move makes a difference.
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Just as difficult a question: Is it possible for piece of string to be 2 units long? In the real world, you always run into limits on how finely you can measure things before you run into quandaries about number theory.
> number theory How does number theory relate to this? (I think you just misused the term, and are thinking more about the philosophy of mathematics and not about that specific discipline.)
So it doesn't matter if we're talking about lengths that are integer, rational, algebraic, transcendental, computable, or otherwise. The end of the string is fuzzy at many different scales, so even defining its length at high precision becomes a problem, and at very high precisions, you actually change the length when you measure it.
If that sounds like me ducking the question it's because nature itself ducks the question.
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See my reply here: http://news.ycombinator.com/item?id=2667461 There is no discrete base unit of space, and on top of that objects do not have determinate sizes.
I thought the Planck length (1.616252×10−35) was the discrete unit of length. Is that not true? http://en.wikipedia.org/wiki/Planck_length
So although it's a fun thought experiment to think about strings that that are precisely 4998997308233 base units long, actually measuring such a thing is too expensive or even impossible due to Heisenberg.
Nevertheless, mathematics has demonstrated that it's useful to think of "real numbers" as infinitely precise things, because that way your number system doesn't impose any preordained limits on your measurements -- even though nature itself does.
By far most real numbers are actually non-computable, meaning that there is no finitely expressible procedure for listing their digits to any desired length.
Now it's always seemed clear to me that if a thing is fundamentally unobservable and unidentifiable in any way, you might as well say that thing does not exist at all. Nevertheless, the theory of real numbers implies that the uncomputable numbers "exist" in some sense.
That actually simplifies the theory. Otherwise you'd have to confine yourself to the computable numbers, namely all strings of binary digits that can be produced by some Fexl function (see http://fexl.com/). For example, the number .1010... could be expressed as:
\number == (1; 0; number)
That might make the strict constructivists happy, but it might also hamper the free reigning thought processes of mathematicians.
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I think something could be two units long. Two is discrete, and at a microscopic level, things can be exactly discrete values (i.e. two angstroms...). I think asking if something could be exactly pi long is a different question.
Actually, no they can't. At a quantum level things do not have definitive sizes. They have sort of "clouds", where the center of the cloud is more likely to be their size, and the edges are less likely - but still possible.