If HE (not It:rolleyes:) really wanted to He could change it to whatever in a way that we didn’t even realize it.
It’s more a matter of faith then what we know as fact though.
This question could be refined down to “might the properties of the universe have been different?” - if the initial conditions of the universe had been different (God or Big Bang - it doesn’t really matter), could the periodic table have looked different? Might the physical and chemical properties of matter have been different? Might mechanics and geometry operate under different rules? Might the energy of the universe have become organised into a completely different class of discrete units than we currently see?
I suspect that the universe couldn’t be any way other than what it is.
But if we thought the universe could be different, how could we tell? It’s not like we can compare…
Mangetout, I do not think the questions are the same. It is easy to imagine that the laws of physics that govern the universe might be different, leading to different properties of the chemical elements or other changes, but it is logically impossible that <pi> have any other value than it does given the axioms of euclidian geometry and the definition of a circle.
It seems to me that postulating the existence of a being able to create logical contradictions is tantamount to postulating a logical contradiction, which is a priori known to be incorrect. Thus God, if S/He exists, could not create a logical contradiction, so could not change the value of <pi>.
Hey, if Q could change the gravitational constant of the universe…
Before people start going off into non-planar geometry and the like, you should remember that pi is DEFINED on a plane surface. Its an abstract relation which doesnt care for what surface its on. Extrapolating from that relationship, we can determine the value as an infinite sum of rational fractions. ie: 1/3 + 1/5 - 1/7 + 1/9 etc. To alter the value of pi would mean that god would have to alter the notion of “oneness”. While it may not be IMPOSSIBLE, it is certainly inconceviable for one to be anything other than what it is.
Of course He could.
But, why should he ruin everyone else’s day, just for you?
Sheesh.
People ask for the dumbest stuff.
Tris
The value of [symbol]p[/symbol] is independent of the properties of the physical universe. It’s defined by the basic axioms of algebra and Euclidian geometry and the definition of a circle. For God to change that would be like for God to make a not equal a.
Math is a language to describe the real world, not a property of the real world itself. If God changed the properties of the universe in the way you described, then our math would still be valid, it just might not have any real-world applications.
It depends on if God sets the laws or God is limited by them. When Our Lord changed water into wine it might be argued that He was limited by the conservation of mass and energy. The Miracle of Chanukah where the oil lasted 7(8?) days does not violate that law as there was certainly enough mass to be converted into energy to fuel a lamp so long.
G and read Contact by Carl Sagan, it was made into a film a few years ago with Jodie Foster.
In the book Ellie, an astronomer detects an alien signal from vega and gets instructed to build a machine which takes her to them.
In the book one of the aliens tells her that if you continue working out pi eventually you come to 10 0’s in a row, just waiting for a 10 fingered race (working in base 10) to come and find it.
“…it is logically impossible that <pi> have any other value than it does given the axioms of euclidian geometry and the definition of a circle…”
JasonFin, would you amplify on this?
In what sense to these axioms and definitions stipulate that the ratio of the circumference of a circle to its diameter shall be the certain string of numbers we now have?
Remember, the issue is not whether Pi could be any old string of numbers, but whether it might have been other than it in fact is.
In the sort of uniformly curved universe I mention in my post, dwellers therein DON’T KNOW that what they are embedded in is not “flat.” They find no discontinuities. But when they measure across a circle with what is TO THEM a straight line, the ratio is slightly different…maybe it terminates at the 4000th digit. Or maybe after a certain point it just varies by 1–and that’s enough!
Their idea of an idealized straight line is an abstraction from what they actually experience–isn’t it? How do you measure (to an infinite decimal expansion!) an idea?
“If it is the sum of an infinite series then no.”
Erislover,
I did wonder about that; I’m aware that Pi has significances beyond its ordinary use. One can only speculate about a Reality of which both of the following are true:
(1) ALL the arithmetical constants (such as Euler’s) are “tweaked” and yet all fit together as well as our set; and
(2) we, as we are, can genuinely conceive of the situation, and thus make (genuine) reference to it–as I am purporting to do.
I’m not sure.
But at the moment my inclination is to emphasize, not restrict, the (possible) powers of a (possible) deity. Remember St. Anselm–even a possible God is somebody you don’t want to piss off!
If God changed the value, it would no longer be pi.
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Because you cannot have your pi and edict too.
Scott Dickerson: I believe that the axioms of Euclidian geometry and number theory completely determine the value of Pi. However, I havn’t been able to find any proof of this that does not assume that the sine and cosine functions have certain features (ex: this pdf file). To complete such a proof, one would also need to show from basic geometry that the sine and cosine functions, when defined based on a circle, must have those features. I suspect this is possible, but don’t have a cite at the moment.
God, when come back, change pi.
The proof of this is obvious: If God changed the value of pi, pi would be archaic …
You can prove all of the properties of the sine and cosine function geometrically, but it’s not pleasant.
But that’s not the stumbling block you might think it is. What I would do is show that R[sup]2[/sup] is a model for Euclidean geometry, and then you can use anything you know to be true about the real numbers as well as anything from Euclidean geometry.
Pi is a constant defined by humans.
There is no being that can change the constant, just the definition.
I thought this was obvious.
Ah, but could God actually change the nature of mathematics so that, when we performed the proof a second time, we found that it was invalid?
I strongly suspect that such a thing isn’t possible (or at least that doing so would destroy the universe as it must be for any kind of sentience to exist in it)… but I can’t think of a way to prove it.
Metamathematics may be necessary.
Mathematics is a tool invented by man, not some gift from on high. I can change the rules if I like.
But that’s irrelevant. Given the current axioms and the current rules of inference, [symbol]p[/symbol] is a constant, and there’s nothing that can change that fact or the value that [symbol]p[/symbol] has.
Fatwater Fewl
Ow. That really frosts it! I think you should be panned for that!