Can God change the value of Pi?

Great Debates
1

Of course, if this has already been talked to death, there’s no way to find it because the search engine won’t look for God (three letters) or pi.

The thread that is (presently) in GQ brought to mind another debate I had some time back… if there is a God, can It alter some mathematical constants? Or is the ratio of a circle (on a plane) to its diameter something that can only be 3.1415926…

Put another way, did God invent that thing that we observe as mathematics? Or does it have independent existence?

2

Two theories I would suppose:

  1. No, God did not invent it, he does not exist.

  2. God does exist and he invented it in some form or another. If God is the creator then on some level he would have HAD to have had some part in it’s existence.

3

Engywook wrote:

Kant argured, convincingly in my opinion, that knowledge of pi (actually, mathematical knowledge in general) is synthetic, not analytic.

4

I don’t think the question has much meaning no matter how you phrase it. I suppose if God was in the mood for some fun he could alter the dimensions of space but how would we know? I think it’s kind of like relativity. I can put the pedal to the metal on my spaceship until it reaches 0.99c but my tape measure is still going to tell me the plastic Jesus on my dash is just as tall as when we were sitting in the garage.

5

My obviously IMHO response.

Two ways to approach this.

First way:

Let us accept as our premisses that:
(a) there exists such an entity as “God”
(b) this entity has the traditional attribute of omnipotence
© to be omnipotent is to be able to bring about any condition whatsoever, where
(d) “any condition,” a collective reference, is stipulated to subsume “condition-1, condition-2, condition-3…condition-N” such that [only (NOT (any one of: conditions))] is excluded. (That last one just means that “any condition” is defined as including “every condition individually”!)

Pi is the name of a certain string of numbers that begins, as I recall, 3.1416. (Or–that’s a useful approximation.) It is defined as the ratio of the circumference of a circle to its diameter.

No one of the terms “3.1415…” or “circle” or “diameter” or even “string of numbers” is directly synonymous with any one of the rest. They are all logically independent; in the old terminology, they are related synthetically, not analytically.

It follows from the premisses, then, that God can alter the particular relationship under discussion.

I will add only this proviso, from my metaphysical stance: we are allowed to claim that God can do anything however DIFFICULT, but we can’t claim that he can do that which is so profoundly inconceivable that our attempts to refer to it are unintelligible. The notion that a VISIBLE diameter of a VISIBLE circle is shorter than its circumference is, I think, part of what we mean when we say, “Look, that’s a circle!” God can adjust the part after the decimal point, but I’m not so sure about the 3.

Second approach:

Take “flat” space, and curve it uniformly, like the surface of a sphere. The sphere can have a radius as large as you like–how about a hundred trillion light years?

Now a circle is unaffected by such a change, but the ratio of the diameter to the circumference IS affected. Thus God could alter Pi by bending the universe.

I would prefer to have Pi exactly 3, thank you.

6

Pi is exactly 3, if you’re looking at a hexagon. Remember, pi is a ratio, not a fixed number. Pi as regards a circle is 3.14…, regarding a hexagon it’s 3, regarding a square it’s sqr2/4, and so on and so forth.

Meaning, of course, that your everyday average human being can change the value of pi - it just depends on what he draws.

7

Good answer. I was about to launch into a description of Riemannian geometry, but you answer is so much more elegant, I think I’ll just leave off of it. :slight_smile:

leaves off

8

[symbol]p[/symbol] is the ratio of the circumference of a circle to its diameter, and is therefore fixed (a little calculus will get you the easy proof).

Fact is, given the axioms of Euclidean geometry and the rules of inference that we all know and love, the value of [symbol]p[/symbol] is determined and can’t be otherwise.

9

“Given the axioms of Euclidian geomtery” being the key phrase. [symbol]p[/symbol] can change once you change those axioms.

10

A good answer indeed. It also depends on what sort of surface he draws it on, whether a flat plane, or a plane with positive or negative curvature. A circle not on a flat plane will have a ratio other than pi (although pi will be a factor).

11

Ah, but if we change the axioms of Euclidean geometry, it’s not Euclidean geometry any longer, is it?

[The True Scotsman]: “Och aye, laddie, 'tis Euclidean no longer.”

12

:smiley:

13

Isn’t it obvious that He’s making it up as he goes along?

14

Sure, he could. He could made humans with 12 fingers and twelve toes.

*Hey little twelvetoes, I hope you’re thriving.
Some of us ten-toed folks are still surviving.
If you help me with my twelves, I’ll help you with your tens.
And we could all be friends.
Little twelvetoes, please come back home.
*

15

But if it isn’t Euclidian geometry it isn’t [symbol]p[/symbol].

16

the OP specifies circle (on a plane).

I dont see how the ratio could ever change as we know it. A perfect circle on a plane will always have its relative characteristics. Changing the way we measure it or draw it is cheating.

17

I thought pi was the ratio of any figure’s circumference to its diameter. If not, what symbol do they use for, say, pentagons?

18

No special symbol, because that number doesn’t show up as often.

19

>> If not, what symbol do they use for, say, pentagons?

The Rumsfeld.

20

It depends on what you mean by pi. If it is the ratio etc as an idealized case of the real world, then I should imagine so. If it is the sum of an infinite series then no.

My answer would be “No.”