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Sorry, my mistake, I was distracted when I wrote that reply. Yes, I did write that, but it's not actually essential to the point I was trying to make, which wa
by lisper 2y ago
Sorry, my mistake, I was distracted when I wrote that reply. Yes, I did write that, but it's not actually essential to the point I was trying to make, which was: what could the result of measuring anything to an infinite precision possibly look like?
- JumpCrisscross 2y ago> what could the result of measuring anything to an infinite precision possibly look like? Depends on what you're measuring. To illustrate why that isn't a facetious response, consider the difference between 'measuring' pi, 'measuring' a meter and 'measuring' the mass of a proton. (Or, for that matter, the relative mass of three of something to one of it.)
- lisper 2y agoHow do you measure pi?
- JumpCrisscross 2y ago> How do you measure pi? Pick your method. It’s the ratio of a circle’s circumference to its diameter.
- winwang 2y agoConsidering that we don't know the value of pi (not that we could write it out nor read it), I'm not sure your definition of "measure" is the same as mine or most people's.
- Dylan16807 2y agoI think your definition of "know" is unreasonably strict. Especially because we can write out pieces of algebra that are exactly pi. I think it's reasonable to say we can't truly measure pi, though. And you can neither know nor measure a random real.
- lisper 2y ago> we can write out pieces of algebra that are exactly pi Sure, but how would you compare those against a measurement?
- Dylan16807 2y agoThat depends on how you're measuring. But the second paragraph of that post already says you can't truly measure pi.
- winwang 2y agoHmm, I should say "the numerical value of pi in base 10" (or really any rational base), even if we were to weaken that with the qualifier "a to arbitrary degree of precision". We know pi in the sense of "a unique real number satisfying many useful properties".
- Dylan16807 2y agoIsn't "3.14" pi to an arbitrary degree of precision? Or am I misreading that. > We know pi in the sense of "a unique real number satisfying many useful properties". We know it a lot better than that. We have efficient programs that output the numerical value of pi for as many digits as you want. There's a bunch of real numbers we can identify that are far harder to make use of or approximate, and don't have easy exact description of their value.
- PeterisP 2y agoYou can calculate or 'measure' an arbitrary approximation of that ratio by various methods, but calculating all of it takes infinite time, which I don't have and thus can't do it.
- skirmish 2y agoBy repeatedly throwing a needle on a striped pattern: [1]. Obviously, you will need an infinite number of throws for an infinitely precise measurement of pi. [1] https://en.wikipedia.org/wiki/Buffon%27s_needle_problem https://en.wikipedia.org/wiki/Buffon%27s_needle_problem
- lisper 2y ago> you will need an infinite number of throws It's worse than that: you also need an unambiguous way of determining whether the needle is overlapping a stripe.
- skirmish 2y agoThat would affect only a few borderline trials and would average out with subsequent throws. It would be much more worrisome that the length of a needle or the width of a stripe is not infinitely precise, that would consistently affect all the trials.
- d_tr 2y agoYou'd need to somehow record refinements endlessly? I don't get what you're getting at.