By the value of Pi I mean the ratio between the circumfrence of a circle and the diameter of the same circle on a flat plane. Assuming standard mathematical definitions of circle, diameter and flat plane.
So did God set the value to 3.1415…? Could God have (assuming omnipotence and creation of the Universe) given this ratio some other value?
Pi is derived from man-made measurements.
If the measurements were different, so would be the ratio.
And yes, in non-euclidian math (rubber-sheet geometry), pi can be smaller, as when a circle has a bump in the middle that lengthens the diameter but not the circumference.
I think it’s just a quirk of mathematics - there’s a real ratio there; we just can’t finitely represent it in our system of math. If one assumes there is a God, and that God is omnipotent, then He could have made the value anything he felt like. What’s your point?
JohnBarleycorn, note first that Bippy explicitly defined p on a plane, so non-Euclidian geometry is irrelevant. Note second that p has an exact value; it is no more a measured quantity than is 2, or e, or any other number. That we can measure it says nothing about whether it must be measured.
Thus, I am forced to conclude that God cannot change the value of p: once we define the concepts of “circle” and “diameter” and “plane,” the value of p falls out.
I am also forced to agree with blowero, in that I’m not quite seeing the point. Perhaps you could elaborate?
I would say that “God can no more change the value of pi than the value of 1+1” - that is, both depend on a simple set of axioms. I don’t see anything in the extra axioms required to get a circle that differs philosophically from those needed to get 1+1.
Whether God can change 1+1 I wouldn’t like to say.
I don’t have a cite, but I believe St. Augustine said it is a sin to believe God’s omnipotence is any the less because God cannot do logically impossible things, such as dividing something into three equal halves. This would also cover changing the value of pi.
My own view is that it is possible to envision an alternate universe where the laws of physics and chemistry are different, but it is not possible to imagine an alternate universe where the laws of mathematics are different. (Whether the universe is “Euclidean” or “non-Euclidean” is a question in physics and cosmology, not mathematics.) Mathematics are universal and transcultural. Two and two always make four, assuming we are using the standard definitions of these whole numbers and the operation of addition.
I think it’s nifty that Pi contains the social security number, birthdate, phone number and credit card number – listed right together – of every member of this message board.
The reason for the question is this. If God did not choose Pi to have its particular value, then the value of Pi is something that exists without God creating it. This then links in with the questions about God creating a three sided square, an integer between 0 and 1, etc.
BrainGlutton then hints at the thrust of my thoughts. What are the things that are not defined by God, but are existant through purely logical reasoning?
This lead from my thinking of the relationships of calculus, the relationship between curve, area under a curve between any two points, and gradient of a curve at any point. This relationship seems to me similarly defined by pure logic.
If on the other hand, God could have chosen a different value for Pi is a Universe with any other value of Pi even imaginable?
That would be true if π is normal — that is, contains every sequence of digits with equal frequency among sequences of the same length. I don’t believe π is known to be normal, however. (If it is, I’d be interested to read the announcement, which must be relatively recent.)
Of course, the number of SDMB board members is finite, hence the number of their “ID” strings is finite, and so π might contain all those strings anyway even if it isn’t normal.
But I’m skeptical that you’ve checked this. 
Hmm. I’d wondered if this was where you were going. 
I, for one, agree. But then, I’m one of those people who thinks math was discovered and not invented.
Not mine! (the UK National Insurance ID is alphanumeric).
Nitpick: in a sense, so is a phone number alphanumeric.
Nitpick: nobody specified base 10 not base 36 yet, did they?
As I see it, if it’s just the only way something can be, then if there is a god, God set it that way. Could pi be anything else? If people used a different sort of mathematical system, yes. With the numbers most people use? Not in this universe.
Welcome to the boards Princess Ana, though pi could be translated into any different numerical systems, it would still have the same value when converted to decimal. Could another different Universe have a different value for pi, could a Universe exist where a flat plane cannot be theorized, and a notion of a point on that plane and a distance from that point not be discribed? Maybe in a zero or one dimensional universe such abstraction would be incredibly hard for that Universes enhabitants.
If mathematics is existant without God’s intervention of creating it, do some of the more esoteric aspects of math effect God? Is God subject to the Godel incompleteness theorem, and does this have any implications, I wonder.
It also contains MP3s and OGGs of every song ever recorded, in any bitrate you want. Let’s hope the RIAA doesn’t figure that out!
The key concept here is that of a formal system, which is a collection of axioms,rules of inference, and some other stuff.
Basically, given the axioms of our math, and its rules of inference, the value of [symbol]p[/symbol], the ratio of the circumference of a circle to its diameter in the Euclidean plane, must be equal to the standard value. Given a different formal system, [symbol]p[/symbol] might have a different value, or be non-constant.
More importantly, if it’s normal then it contains an MP3 of every song, whether or not it’s been recorded (or written) yet. It also has all stock prices, past present and future.
So, does all that mean Euclid is God? Or at least the God of Flatland?
Since I’ve always preferred the God described in Job, the mildly sociopathic regular guy who makes bar bets with Satan, I imagine him looking at pi and thinking how cool it is that it just keeps going. Maybe that’s what kept him occupied while Adam and Eve were still playing nice. You know, before things got TOO quiet down here and he knew they were up to no good.
OTOH, Augustine’s stern daddy dope slapping people who ask dumb questions has some appeal.
Are you quite certain of that? Has the distribution of digits been demonstrated to be perfectly random and even?
This has come up a couple of times before and people seem to get hung up about the representation of pi rather than the value. It doesn’t matter what base its in or whether space is curved. That merely changes how we represent things, but doesn’t change the essential platonic ideal.
The point is that the value pi is so essential in almost every branch of mathematics and so interrelated you literally have to change the definition of equality before your allowed to change pi. In short, you need to imagine a universe where 1 != 1.
The thing that really brought Contact (Carl Sagan) alive for me was the implication that it contained. There were creatures out there that could literally twist the fabric of reality on such a profound level. It was probably the closest I ever got to a religious experience.