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Anonymous Mon 08 Feb 01:37:46 2021 No.12679891 View Reply Original Report

Quoted By: >>12679917 >>12679983 >>12680065 >>12680075 >>12680253 >>12680465 >>12680494

Why does pi need to be 3.1415... etc. why can't it be a different ratio? I know it's because that's the ratio of the circumference over the diameter but why didn't our universe have the ratio be different? Couldn't we have very well been born in a universe where the circumference over the diameter was a different ratio like 4 or something for example? We can't conceive of such a scenario as possible but that's only because we were born in a universe where it wasn't possible, but why couldn't we have been born in a universe where it was possible?

Anonymous

Anonymous Mon 08 Feb 2021 01:44:52 No.12679917 Report

Quoted By: >>12679932 >>12679993

>>12679891
yes anon, the fact that the ratio of circumference to diameter is equal to pi is something that could change depending on the curvature of space. in fact, since our space is not perfectly flat (it is slightly hyperbolic because of the cosmological constant) a sufficiently accurate measurement would show that the circumference is actually slightly larger than pi times the diameter (we do not live in perfectly euclidean space)

however, the definition of pi in advanced books is different. usually it is defined in terms of the periodicity of trigonometric functions which are in turn defined not geometrically but rather something like cos(x) = 1-x^2/2!+x^4/4!-x^6/6!... in that case you define pi as half the period of that function and it doesn’t depend on geometry at all. it is not conceivable that such a definition could vary in another universe unless somehow mathematics and set theory and logic could somehow be different

Anonymous

Anonymous Mon 08 Feb 2021 01:49:41 No.12679932 Report

Quoted By: >>12679956 >>12679968 >>12682268

>>12679917
>unless somehow mathematics and set theory and logic could somehow be different
Yeah that's what I'm talking about. Our world is particular but why couldn't math have just been different?

Anonymous

Anonymous Mon 08 Feb 2021 01:56:58 No.12679956 Report

Quoted By: >>12679972

>>12679932
Why can't arithmetic be different?

Anonymous

Anonymous Mon 08 Feb 2021 02:00:39 No.12679968 Report

Quoted By: >>12679977

>>12679932
well, keep in mind that now we’re talking about philosophy. you are perfectly allowed in mathematics to use different axioms. and in philosophy, set theory is just one theory. i could for example change the laws of set theory so that {C} is a subset of {A B} and try to create a mathematics from that kind of nonsense. it might work in some other universe, our ours, maybe even by luck, but this is a philosophical question — to ask “could logic have been any other way?” from my scientific standpoint these philosophical questions are silly because one could regard math as a part of science and the fact that it works means it must be right, and i don’t see any alternative math that normal math needs to compete with (at least at the basic level of what is pi. you have things like the axiom of choice and whatnot but that’s not something science ever needs to worry about)

Anonymous

Anonymous Mon 08 Feb 2021 02:01:13 No.12679972 Report

Quoted By: >>12679988 >>12680043

>>12679956
We can't conceive of 1+1=3 but if you change the "code," of the universe if you will to make 1+1=3 then we wouldn't be able to conceive of anything else, and everything would work differently. We couldn't conceive of it in the same way we can't conceive of 'i' the imaginary constant or 4th spacial dimension, but that doesn't mean it can't exist. So, why doesn't it? Kinda weird we got such a specific world huh.

Anonymous

Anonymous Mon 08 Feb 2021 02:02:14 No.12679977 Report

Quoted By:

>>12679968
Yes you are right, but philosophy still has implications in science, even though they are completely different fields, every once in a while science and philosophy have to acknowledge each other though.

Anonymous

Anonymous Mon 08 Feb 2021 02:05:09 No.12679983 Report

Quoted By:

>>12679891
Math is the way it is out of necessity. There are no alternative facts, multiverse is an unfalsifiable idea.

Anonymous

Anonymous Mon 08 Feb 2021 02:07:13 No.12679988 Report

Quoted By:

>>12679972
1=s(0)
3=s(s(s(0)))
1+1=s(0)+s(0)=s(s(0))+0=s(s(0))
s(s(0)) =/= s(s(s(0)))

Anonymous

Anonymous Mon 08 Feb 2021 02:08:19 No.12679993 Report

Quoted By: >>12680036 >>12680560

>>12679917
>our space is not perfectly flat
[citation needed]

Anonymous

Anonymous Mon 08 Feb 2021 02:20:33 No.12680036 Report

Quoted By: >>12680089

>>12679993
this is a meme-ish source but it the first one google popped up that had a clear discussion about how the cosmological constant determines whether or not space is flat:
https://www.preposterousuniverse.com/encyc/

Anonymous

Anonymous Mon 08 Feb 2021 02:22:41 No.12680043 Report

Quoted By:

>>12679972
1+1=3 in modulo 1 arithmetic, which is just as valid algebraic structure as the ring of integers, it's just a much less useful construction

Anonymous

Anonymous Mon 08 Feb 2021 02:27:42 No.12680065 Report

Quoted By:

>>12679891
Write program for laser to cut perfactly cardioid conus.

Anonymous

Anonymous Mon 08 Feb 2021 02:31:46 No.12680075 Report

Quoted By: >>12680083

>>12679891
Pi is defined as the ratio of the circumference over the diameter therefore those two are numbers that are exactly equal and only have different names.
It could not have been 4 because that would make it deviate from its original definition
You cannot insist that pi is both 4 AND of the ratio of circumference over the diameter because that makes as much sense as saying "can a number be two numbers at the same time?" which is impossible under axioms that define how numbers work.

As for why IS the ratio of circumference over the diameter the number that it comes from the way circumference and diameter are defined.
The number could not have been different if you kept the same definitions for circumference and diameter.
You cannot insist that it's different if you keep the same definitions because that would be like defining the rules for addition in the usual way but INSISTING 1+1=3.

Anonymous

Anonymous Mon 08 Feb 2021 02:34:50 No.12680083 Report

Quoted By: >>12680150

>>12680075
anon, hate to break it to you but you’re retarded

Anonymous

Anonymous Mon 08 Feb 2021 02:37:01 No.12680089 Report

Quoted By: >>12680098

>>12680036
Yes, the cosmological constant determines WHETHER space is flat. It doesn't claim that space is flat.

Anonymous

Anonymous Mon 08 Feb 2021 02:39:49 No.12680098 Report

Quoted By:

>>12680089
yes, it determines the large scale curvature of space. the cosmological constant has now been measured many times and all the latest measurements rule out a zero or negative cosmological constant at a very high confidence level (i believe over 5 sigma). so science is telling us the cosmological constant is positive which implies that space is slightly hyperbolic and not flat or negatively curved

Anonymous

Anonymous Mon 08 Feb 2021 02:54:23 No.12680150 Report

Quoted By: >>12680243

>>12680083
I'm sorry that you are too stupid to understand that a number can't be two different numbers.
What's next? Why is 1 1 and not 2? Why is 1 not 1 and 2 at the same time but also neither?

Anonymous

Anonymous Mon 08 Feb 2021 03:23:11 No.12680243 Report

Quoted By: >>12680246 >>12680247 >>12680305

>>12680150
the reason you are retarded is because the definition of pi in terms of anything geometric is going to fail if you don’t restrict to euclidean geometry. for example it would be possible to have a literal “circle” in a lobachevskyan space where the ratio of circumference to diameter is actually 4. you are just too retarded to understand noneuclidean geometry which

Anonymous

Anonymous Mon 08 Feb 2021 03:25:02 No.12680246 Report

Quoted By: >>12680278

>>12680243
No...

Imagine said: Triangle, with radius of 1 one point in circle divided by lenght of part of diameter with line perpendicular to diameter going to point on a circle.

Anonymous

Anonymous Mon 08 Feb 2021 03:25:36 No.12680247 Report

Quoted By: >>12680942

>>12680243
>which
forget i said “which”. that should just end at “geometry”

Anonymous

Anonymous Mon 08 Feb 2021 03:26:21 No.12680253 Report

Quoted By: >>12680272

>>12679891
>Why does pi need to be 3.1415...

Because it just does

Anonymous

Anonymous Mon 08 Feb 2021 03:31:10 No.12680272 Report

Quoted By:

>>12680253
angry_soijak.jpg

Anonymous

Anonymous Mon 08 Feb 2021 03:32:21 No.12680278 Report

Quoted By:

>>12680246
all i could envision was a bowl with some lettuce and cucumbers and tomatoes with a lingonberry vinaigrette

Anonymous

Anonymous Mon 08 Feb 2021 03:36:48 No.12680294 Report

Quoted By: >>12680339

Three is amount of sides needed for first angular shape.

Anonymous

Anonymous Mon 08 Feb 2021 03:38:30 No.12680299 Report

Quoted By: >>12680341

Thought about it for a while and it’s basically a system of preventions meant to stave off contradiction of order of figure

Anonymous

Anonymous Mon 08 Feb 2021 03:41:24 No.12680305 Report

Quoted By: >>12680308 >>12680310

>>12680243
>definition of pi in terms of anything geometric is going to fail if you don’t restrict to euclidean geometry.
And? Yes, pi is defined as ratio of diameter and circumference of a *flat* circle where where triangles add up to 180 degrees, not in a curved space where they don't so I don't understand what your point is.

Anonymous

Anonymous Mon 08 Feb 2021 03:43:08 No.12680308 Report

Quoted By:

>>12680305
Topography applies?

Anonymous

Anonymous Mon 08 Feb 2021 03:43:38 No.12680310 Report

Quoted By: >>12680329

>>12680305
so if you lived in a curved space then your definition of pi would be useless, right? give me a definition that would work for anybody

Anonymous

Anonymous Mon 08 Feb 2021 03:53:07 No.12680329 Report

Quoted By: >>12680335

>>12680310
There are trillions of equivalent ways to define pi because it's a number that's found everywhere but its value is always going to be the same regardless how useful you find any particular definition.

Anonymous

Anonymous Mon 08 Feb 2021 03:55:02 No.12680335 Report

Quoted By: >>12680368 >>12680373

>>12680329
we’ll give me just ONE that is independent of some dependence on geometry. if it’s so easy then you could come up with one right?

Anonymous

Anonymous Mon 08 Feb 2021 03:58:28 No.12680339 Report

Quoted By:

>>12680294
Yes that is how things ARE, but not necessarily how things HAVE to be.

Anonymous

Anonymous Mon 08 Feb 2021 03:59:28 No.12680341 Report

Quoted By:

>>12680299

True...

Anonymous

Anonymous Mon 08 Feb 2021 04:10:26 No.12680368 Report

Quoted By:

>>12680335
>give me just ONE that is independent of some dependence on geometry
$<br />\pi = 6\sqrt{\sum_{n=1}^{\infty}\frac{1}{n^2}}<br />$

Now what?

Anonymous

Anonymous Mon 08 Feb 2021 04:13:38 No.12680373 Report

Quoted By: >>12680394 >>12680410 >>12680461

>>12680335
>give me just ONE that is independent of some dependence on geometry
$\pi=\sqrt{\sum_{n=1}^{\infty}\frac{6}{n^2}}$
Now what?

Anonymous

Anonymous Mon 08 Feb 2021 04:25:01 No.12680394 Report

Quoted By: >>12680965

>>12680373
great, if that is indeed a definition of pi, then you have confirmed that pi is a constant that is independent of geometry. that’s my point. the constant pi is independent of geometry and the fact that in general geometry is noneuclidean and pi doesn’t dictate geometry is something people should get used to

you should also appreciate that somehow a constant that exists independent of geometry plays a big role in geometry is a wonderful curiosity

Anonymous

Anonymous Mon 08 Feb 2021 04:31:24 No.12680410 Report

Quoted By: >>12680438

>>12680373
Well to be fair that Euler formula relies on the power series expansions for sin and cos so arguably how independent on geometry those are. Since how the Leibniz formula relies on the power series for arctan.

Anonymous

Anonymous Mon 08 Feb 2021 04:41:03 No.12680438 Report

Quoted By: >>12680461

>>12680410
the power series expansion of sin and cos has nothing to do with geometry, unless you are confusing yourself by looking at plots on 2D paper in your 3D space. it is all analytic and has nothing to do with geometry

Anonymous

Anonymous Mon 08 Feb 2021 04:49:36 No.12680461 Report

Quoted By: >>12680476

>>12680438
Well the proof for >>12680373 relies on the roots of sin/cos which are factors of $\pi$ . Is that geometry or pure maths?

Anonymous

Anonymous Mon 08 Feb 2021 04:51:11 No.12680465 Report

Quoted By:

>>12679891
Its all arbitrary anyway
Make a number system where pi = 1

Anonymous

Anonymous Mon 08 Feb 2021 04:54:48 No.12680476 Report

Quoted By: >>12680481

>>12680461
again, in most advanced books the trigonometric functions are DEFINED like e^ix := 1+ix-x^2/2!-3ix^3/3!+x^4/4!... and you can find zeroes and the periodicity of that function purely analytically

Anonymous

Anonymous Mon 08 Feb 2021 04:57:36 No.12680481 Report

Quoted By:

>>12680476
oops typo there, no 3 before x^3/3! my bad. but that’s an obvious typo i hope

Anonymous

Anonymous Mon 08 Feb 2021 05:02:38 No.12680494 Report

Quoted By: >>12680518

>>12679891
Pi in other bases.

https://www.virtuescience.com/pi-in-other-bases.html

Anonymous

Anonymous Mon 08 Feb 2021 05:17:30 No.12680518 Report

Quoted By: >>12680987

>>12680494
That doesn't mean it's a different number.

Anonymous

Anonymous Mon 08 Feb 2021 05:37:04 No.12680560 Report

Quoted By:

>>12679993
General relativity says that mass curves spacetime.

Anonymous

Anonymous Mon 08 Feb 2021 08:43:08 No.12680942 Report

Quoted By:

>>12680247
Too late, we all saw it. You're the retard now

Anonymous

Anonymous Mon 08 Feb 2021 09:02:00 No.12680965 Report

Quoted By:

>>12680394
do you also appreciate that the length of the diagonal in a unit Euclidean square is sqrt(2) but sqrt(2) exists independent of geometry?

Anonymous

Anonymous Mon 08 Feb 2021 09:18:35 No.12680987 Report

Quoted By:

>>12680518
its definitely got a pattern to it in binary though, probably worth analyzing

Anonymous

Anonymous Mon 08 Feb 2021 18:26:24 No.12682268 Report

Quoted By:

>>12679932
it could have but if you had a mathematical language based on pi you would have a really hard time counting your fingers

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