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      Welcome!   03/05/2016

      Welcome, everyone, to the new 910CMX Community Forums. I'm still working on getting them running, so things may change.  If you're a 910 Comic creator and need your forum recreated, let me know and I'll get on it right away.  I'll do my best to make this new place as fun as the last one!

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15 hours ago, WR...S said:
22 hours ago, hkmaly said:

You can, if you don't insist on parallel lines not crossing. I mean, "world where this number were equal to pi" sounds very similarly to description of non-euclidean space.

You can come up with geometries where the ratio of circumference to diameter of a circle isn't equal to pi, but that doesn't mean that pi is different, only that the circle is different.  The difference in the circle will have other consequences precisely because pi is still the same.  (And, in fact, you can't have that ratio be a constant other than pi, because non-Euclidean geometries are still locally Euclidean, meaning that as the circle gets smaller the ratio approaches pi.)

It depends on what you take as definition of π. It's true that the equation e = -1 would never work with anything rational. You can develop the math behind this without inputing anything from real world, so if you define π based on that geometry wouldn't matter.

But good point about the locally Euclidean stuff: constructing geometry which would make circles with constant ratio different than π no matter size of circle will likely be impossible - or at least the results will be totally unusable in some other way. Both elliptic and hyperbolic geometry definitely wouldn't qualify.

15 hours ago, WR...S said:

It's true that IC manufacture requires extraordinary precision, but that the tolerance at any step, let alone any step involving pi, is less than 0.0000000000007% is something of which I'd need more substantial evidence to be convinced of than "because Einstein and quantum."

You don't need tolerance of manufacturing being lower than 0.0000000000007%. But in the mathematics of design? I was actually reacting to

On 05/11/2016 at 9:20 AM, WR...S said:

 Sure, there are a few cases where the phases of something-or-other would be noticeably off,

... well, if the phases are off, that means interference. With the speed modern CPUs are operating, length of signal paths is actually close to how fast signal is required to get from one end to other by speed of light. I must admit I don't actually know enough about it to know how much is π needed there, but it appears very easily around signal processing, and if it's somewhere on start of computation, the difference in result might be multiplied.

By the way, quantum physic? SSD contain flash NAND, which uses tunnel injection for writing. Specifically, Fowler–Nordheim tunneling ... totally impossible under classical mechanics. Also, there is π several times on the page talking about it (although I'm not sure if those needs to be computed when constructing the SSD).

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It's true that if everyone on Earth decided suddenly that pi were exactly 3.14159265359 we'd be climbing into a handbasket as small errors accrued, but individually, immediately, even that designer you mention is working within a margin of error, since someone will have to build what's being designed.  That was really mostly meant to stress just how small a contradiction is still a contradiction.

As for the definition of pi - maybe.  I probably should have gone with e instead, due to pi's roots in Euclidean geometry, and Euclidean geometry's roots in our own perception.  So let's say for the sake of argument that pi is indeed defined as the lowest positive real number for which Euler's identity holds - its place in Euclidean geometry, once Euclidean geometry is defined, follows without contingency, and that utter lack of contingency was the point.

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