Infinite complexity

[El_Machinae]

Okay, is pi really an infinitely [wrong]complex[/wrong] (edit: irrational) number? Or do we just pretend it is?

It seems to me that significant digits come into play.

Do due the Heisenberg Uncertainty Principal, the radius and circumference of any real circle can only be 'known' so accurately. This means that when you divide the two, you will run into significant digits.

Heck, even the biggest circle we know, the visible universe, must have a margin of error. And once you have a limit to your accuracy, you have to limit your calculations to significant digits.

So pi could actually be the circumference divided by radius of the visible universe, limited by significant digits. You'll note that the circle gets continually bigger, but is still finite.

KnowwhatImean?

 

[Shaihulud]

It seems clear to me that for a perfect circle the pi must be infinite, thats just for mathematical exercise. Realistically, noone expects any "real" circle to contain perfect dimensions.

 

[EdCase]

Your argument is flawed.
Pi is a measurement in two dimensional space.Even using conventional wisdom the Universe is quite obviously existant in 3 dimensions.
Therefore no quantifiable size can be defined for the Universe using pi.

 

[The Last Conformist]

A circle is a mathematical construct, that realworld phenomena may more-or-less closely construct. If you will, an abstraction.

You are, incidentally, misusing the term "complex" badly.

 

[Shaihulud]

Any shapes possesing 3D qualities should be measurable in the 2D. Such as the diameter of a sphere.

 

[Irish Caesar]

Wouldn't this problem only become an issue in measurement purposes? Pi would still be an infinite irrational decimal, but we would have no way of calculating it past a certain point without uncertainty. Of course, we have yet to reach that point...

 

[Leifmk]

Uh.

Pi is not a measurement. It has a clear mathematical definition. It coincides with the ratio between a circle's circumference and its diameter in the ordinary Euclidean plane.

 

[The Last Conformist]

Pi can be calculated to arbitrary precision without reference to any circle realized in spacetime, which is just as good, since spacetime isn't Euclidean, which means that the relationship between the radius and the circumference isn't actually pi, altho for most pragmatically interesting cases it's close enough.

 

[El_Machinae]

Crap, I mean irrational number. I'll edit it above.

 

[EdCase]

Any shapes possesing 3D qualities should be measurable in the 2D. Such as the diameter of a sphere.

Agreed...but at no point did I mention the Universe being spherical and/or perfectly regular.
The "real" world has a bad habit of being different to theories

 

[Heretic_Cata]

Correct me if i am wrong but aren't "pi", "e" and ... gamma smthing (this had smthing to do with the Riemann dude) transcendent numbers ... damn it why was i sleeping in the classroom when the teacher explained this

 

[The Last Conformist]

Correct me if i am wrong but aren't "pi", "e" and ... gamma smthing (this had smthing to do with the Riemann dude) transcendent numbers ... damn it why was i sleeping in the classroom when the teacher explained this

Pi and e are transcendent numbers (transcendent numbers being a subset of the reals). Gamma is not a number at all - it's a function.

 

[El_Machinae]

My biggest point is that there is an error of margin in the biggest real pi we can calculate, so isn't any extrapolation of the true 'pi' a guess after that?

 

[Markus6]

I'm lost but I wonder what the biggest true pie we can make is?

 

[El_Machinae]

Depends on what you're willing to count as an ingredient.

To paraphrase Sagan "We're all made of pie stuff"

 

[Ayatollah So]

El Mac, are you trying to get at the question whether the physical universe is truly continuous, or at some very small level discrete? For any two real numbers which are different, there is another between them. But, perhaps the same does not apply for any two spatial locations. Most (all?) physical theories use continuous mathematics, but maybe this is a mistake. mumble mumble Planck scale mumble mumble...

Suppose for the sake of argument that it does turn out that discrete mathematics, rather than continuous, provides the best description of the real world. In that case is continuous mathematics just a bunch of lies, even if it's occasionally convenient to pretend they're true?

 

[Heretic_Cata]

Gamma is not a number at all - it's a function.

I was refering to the number ... (let me get my seminars) c = 0,517... (the "gamma smthing" was a series part of the Riemann's Series - i don't know if you call them series in english ...) I didn't write down what and who's number is this , i just know it was as important as "e" ...

 

[The Last Conformist]

My biggest point is that there is an error of margin in the biggest real pi we can calculate, so isn't any extrapolation of the true 'pi' a guess after that?

No, because the "real" pi's you are refering to aren't what determines the value of pie.

 

[Erik Mesoy]

FYI: Pi to 80 decimals or so is enough to calculate the circumference of the Universe with the error margin of a subatomic particle. 100 decimals were calculated back in 1709. So we passed "significant digits" long ago.

 

[El_Machinae]

How much math would I need to learn, then, how we know that the digits past 100 are 'true'?