Author Topic: Neo-Pythagoreans are at least half wrong ...  (Read 263 times)

Offline Cavebear

Re: Neo-Pythagoreans are at least half wrong ...
« Reply #15 on: October 04, 2018, 04:02:21 AM »
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Sorry.  My bad.  Substituted algebraic for computational.  But the argument still holds, even though an algebraic number (saw square root of two) is easier to compute that Pi, but they both can be computed.  Not all transcendental numbers (which Pi is) can be computed.

"easier to compute that Pi, but they both can be computed".  You can compute Pi?
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Re: Neo-Pythagoreans are at least half wrong ...
« Reply #16 on: October 04, 2018, 02:01:48 PM »
No, pi can't be computed, only approximated.
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Offline Cavebear

Re: Neo-Pythagoreans are at least half wrong ...
« Reply #17 on: October 04, 2018, 02:22:11 PM »
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No, pi can't be computed, only approximated.

Thank you.  I was pretty sure an irrational number couldn't be computed (by definition), but math discoveries surprise me frequently.  If I read that someone found a way to prove calculating primes, I wouldn't be too surprised. 
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Offline Baruch

Re: Neo-Pythagoreans are at least half wrong ...
« Reply #18 on: October 04, 2018, 07:06:49 PM »
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"easier to compute that Pi, but they both can be computed".  You can compute Pi?

One digit at a time.  Not the whole of it.  For a non-computable transcendental number, you can't even compute one digit at time (convergence is too slow).
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Offline Baruch

Re: Neo-Pythagoreans are at least half wrong ...
« Reply #19 on: October 04, 2018, 07:10:24 PM »
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No, pi can't be computed, only approximated.

Bad use of synonyms.  An approximation isn't the same as a computation.  You can with finite time, compute the millionth digit of Pi.  An approximation is ... Baruch is approximately 6 ft tall.  Rational numbers are simply easier to compute than algebraic numbers, and algebraic numbers are easier to compute than computable transcendental numbers like Pi.  Non-computable transcendental numbers are harder still, so hard you can't get an approximation of any of the digits (infinitely slow convergence).
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Offline Cavebear

Re: Neo-Pythagoreans are at least half wrong ...
« Reply #20 on: October 07, 2018, 06:40:52 AM »
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Bad use of synonyms.  An approximation isn't the same as a computation.  You can with finite time, compute the millionth digit of Pi.  An approximation is ... Baruch is approximately 6 ft tall.  Rational numbers are simply easier to compute than algebraic numbers, and algebraic numbers are easier to compute than computable transcendental numbers like Pi.  Non-computable transcendental numbers are harder still, so hard you can't get an approximation of any of the digits (infinitely slow convergence).

I think it was obvious he was speaking both geometrically and fractionally.  Fractionally, Pi is close to 22/7 but closer to the fraction 355/113.  Geometrically, such things can often be described by enclosing larger and smaller polygrams but at upper limits, the maths get hideous.
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Offline Baruch

Re: Neo-Pythagoreans are at least half wrong ...
« Reply #21 on: October 07, 2018, 08:51:24 AM »
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I think it was obvious he was speaking both geometrically and fractionally.  Fractionally, Pi is close to 22/7 but closer to the fraction 355/113.  Geometrically, such things can often be described by enclosing larger and smaller polygrams but at upper limits, the maths get hideous.

Correct on what you say.  But I think he implied something else.
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Offline Cavebear

Re: Neo-Pythagoreans are at least half wrong ...
« Reply #22 on: October 07, 2018, 10:14:04 AM »
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Correct on what you say.  But I think he implied something else.

OK, what was it?
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Offline Baruch

Re: Neo-Pythagoreans are at least half wrong ...
« Reply #23 on: October 07, 2018, 11:41:11 AM »
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OK, what was it?

He hasn't bothered to respond, so we must wait ...
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Offline Cavebear

Re: Neo-Pythagoreans are at least half wrong ...
« Reply #24 on: October 07, 2018, 12:22:23 PM »
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He hasn't bothered to respond, so we must wait ...

OK, what do you THINK he implied?
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Offline Baruch

Re: Neo-Pythagoreans are at least half wrong ...
« Reply #25 on: October 07, 2018, 01:41:56 PM »
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OK, what do you THINK he implied?

Lack of education in number theory.  Something that applied to me, only a few years ago.  Though earlier in this string, I had a faux pas.

There is the old joke about approximation ... a mathematician and an engineer are trapped in a room with an attractive other person.  The rule is, you can approach the attractive person, by dividing the remaining distance in half.  The mathematician gives up immediately.  The engineer knows that an approximation is good enough.  Mathematicians are bound by rigor in their work, like that example.

Or we can say that Unbeliever was speaking like an engineer.  I one-upped with the rigorous version.
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Offline Cavebear

Re: Neo-Pythagoreans are at least half wrong ...
« Reply #26 on: October 07, 2018, 02:02:33 PM »
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Lack of education in number theory.  Something that applied to me, only a few years ago.  Though earlier in this string, I had a faux pas.

There is the old joke about approximation ... a mathematician and an engineer are trapped in a room with an attractive other person.  The rule is, you can approach the attractive person, by dividing the remaining distance in half.  The mathematician gives up immediately.  The engineer knows that an approximation is good enough.  Mathematicians are bound by rigor in their work, like that example.

Or we can say that Unbeliever was speaking like an engineer.  I one-upped with the rigorous version.

The old fractional approach argument was nonsense to begin with.  When it got to a fraction of a second, all you had to do was measure the next full second.  Problem solved.
Atheist born, atheist bred.  And when I die, atheist dead!

Offline Baruch

Re: Neo-Pythagoreans are at least half wrong ...
« Reply #27 on: October 07, 2018, 02:44:47 PM »
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The old fractional approach argument was nonsense to begin with.  When it got to a fraction of a second, all you had to do was measure the next full second.  Problem solved.

Spoken like an engineer.  Not a logician/mathematician.  The other guy is playing for the other team.
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Offline Cavebear

Re: Neo-Pythagoreans are at least half wrong ...
« Reply #28 on: October 07, 2018, 02:51:05 PM »
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Spoken like an engineer.  Not a logician/mathematician.  The other guy is playing for the other team.

Engineers build bridges;  math guys calculate Pi.  And that's a softball comment for you...
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Offline Baruch

Re: Neo-Pythagoreans are at least half wrong ...
« Reply #29 on: October 07, 2018, 02:55:19 PM »
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Engineers build bridges;  math guys calculate Pi.  And that's a softball comment for you...

It is said that just 7 digits of Pi would be enough to make a sphere as smooth as a ball bearing, the size of the Earth.  Math is more nerdy.
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