# Could a God Change the Value of Pi?

1. Aug 12, 2008

### peter0302

I assert that an omnipotent creator (calling it God just for the sake of convenience) could not change the value of Pi, and therefore omnipotence itself is impossible, that there are some universal laws that are immutable and exist purely by virtue of logic, neither requiring a creator nor allowing one to have dominion over them.

Let's start with the obvious. God of course can eliminate all circles in nature and replace them all with ovals. That's not what I mean by change the value of Pi. God also could trick every human into calculating Pi incorrectly. That's also not what I mean.

I mean can God change the ratio of a perfect circle to its diameter? A perfect circle being a purely logical construct, it can exist in the abstract without there being any such thing as a circle in the physical world. Indeed, since Pi itself is a transcendental number, there can be *no* truly mathematically exact perfect circle in nature because infinite precision would be required (which we all know is impossible in quantum mechanics).

A circle is the equation x^2 + y^2 = r^2. That's it. God cannot change the properties or behavior of that equation any more than he can make 2+2 equal 5.

Mathematics and logic are transcendental of the physical world. Perhaps they, themselves, are the creator, existing before and after time, immutable, and supreme. Were it possible to derive the empirical laws of physics using pure math and logic - no empirical observation required - would that not moot the need for anything more?

2. Aug 12, 2008

### Moridin

A god is generally defined as a very powerful and transcendent entity. If such an entity existed, it could change mathematics, logic, empirical data and morality arbitrarily on a whim at any time which of course would be completely unpredictable to humans. Thus, if such a god exists, everything goes, and mathematics (along with most parts of reality, if such a concept is still meaningful) is untrustworthy, irrelevant or both.

Also, mathematics and logic are hardly transcendental to a materialist; mathematics can be considered a precise language with a large component simplicity for describing quantities, relations and similar concepts, whereas logic is merely a method for non-contradictory communication. There is no need to go any further than the physical world. Before one ponders if something is out of this world, make sure they are not inside it first.

Last edited: Aug 12, 2008
3. Aug 12, 2008

### Moridin

Naturally, a supernaturalist could simply argue that mathematics is a necessary part of the nature or identity of this god (whatever that is) and therefore not contingent on this god, or simply change the definition of "omnipotent".

4. Aug 12, 2008

### Werg22

But logic is formalized. It's purely a "game" that we play by some rules. Whether or not a god could change the real logic of our universe, it wouldn't have an effect on mathematics, it would only make it inapplicable to any real world model.

5. Aug 13, 2008

### Moridin

Yes, most highly useful methods are, in fact, formalized. I don't see your objection. Let's be careful to distinguish 'mathematics' as the specific language we use, and 'mathematics' as the quantities, relations and so on that the specific language refers to. I think the question refers to if a god could chance that which mathematics is describing.

6. Aug 13, 2008

### Werg22

Sorry, I didn't fully understand what you were conveying at first, now I do. In final analysis, I would think the answer to the question depends on whether one adopts the idealist or the materialist thesis, with the obvious consequences once one sees the question this way.

Last edited: Aug 13, 2008
7. Aug 13, 2008

### peter0302

Yes and no. Mathematics can be used to describe and predict the physical world, or it can be used in the abstract simply to talk about relations and quantities that have no physical basis in reality. Pi is one of those things - the number cannot, by definition, occur in nature. Therefore it cannot be changed, even by God, because it doesn't really exist except as an idea.

Maybe the question is broader - can God alter an idea? God can prevent humans from *having* that idea, but does he actually have any power over the idea itself?

8. Aug 18, 2008

### Cale Carter

Pi is a construct of this reality.

GOD by definition is outside this time/space continum and reality.

Pi in another reality may be a different value.. in this value we have it's present state.

"Could GOD change the value of Pi in this reality?" Maybe he has...

9. Aug 18, 2008

### Staff: Mentor

A "god" can do whatever you want to pretend it can do. You can make any mythical creature capable of anything.

For you to have an argument, you would first have to say what your God is capable of and what restrictions it has. There are many supernatural deities in different cultures that have different mythical powers.

Do you want to limit your "God" to this Universe and obey the laws of physics of this Universe? You need to be more specific about the deity you are creating.

10. Aug 18, 2008

### Cale Carter

Actually from a theological perspective the Judeo and Christian gods are the only ones who are defined as existing outside our time/space and not being "in" this time space limitation per se.

It's been a long time since my classes on this subject, so correct me if I am wrong.

11. Aug 18, 2008

### humanino

I don't like the old fashioned geometrical definition of $\pi$. Bourbaki's algebraic definition is better.

It does something like this (check it, I don't have the book right here) :
There is a unique homeomorphism of period 1 from the group (R,+) to the group (C1,x) where C1 is the unit complex circle.
The kernel of this homeomorphism (a subgroup of R) cannot be dense in R, therefore it must be of the form $2\pi\mathbb{R}$.

This definition of $\pi$ is so outrageously wrong that it is obviously the best one.

Anyway, if you want to go into this, it has been solved for a long time : God cannot create a stone so heavy that He could not lift it...
Or can He ?

12. Aug 18, 2008

### peter0302

We seem to be at an empasse here which is why I think the thread was dying.

For those of you who think the answer is yes, you haven't addressed my question, which is how could any force change the laws of math and logic? Because they do not require physical reality in order to exist - in the abstract - they exist unto themselves. God could change the size of an atom or the gravitatinal constant, but how can he change something that _has_ to be true?

Humanino touched on it - can God make a stone so heavy he cannot lift it. That's close to, but not exactly, what I'm getitng at. What I'm getting at is really the following: are the laws of math and logic so fundamental that they - themselves - *are* the all-powerful force that we would typically impute to God?

Let's look at it this way. What are the properties we typically assign to God:
- Exists outside of time and space
- Predated the Universe and will post-date it
- All-powerful and incapable of being cheated or circumvented or deceived
- Governs everything we experience

Can we not say all of those things about math and logic? Can we not say that Pi is immutable even if there were no such thing as a circle or the number "3.14" never occurred naturally - anywhere - in nature?

It is a cop-out to simply say "god can do anything," I'm sorry.

13. Aug 18, 2008

### Staff: Mentor

Since we don't get into any specific religions here, the "god" can be anything, and therefore the OP needs to be specific about what it can do.

The question is "Could a God change the value of Pi?" He needs to describe the God in enough detail so that people can make a guess.

The Judeo-Christian god is the same, btw.

14. Aug 18, 2008

### Staff: Mentor

Couldn't such a God change the universe to something so completely different that the laws of physics that we know don't exist? If it can't, then the God's powers are limited to what works in this Universe.

15. Aug 18, 2008

### humanino

Sorry, I obviously meant $2\pi\mathbb{Z}$ !
I just re-interpreted it as "can God create something which would be different from itself ?", a type of self-contradictory statement.

16. Aug 18, 2008

### humanino

But the question "does general relativity changes the value of $\pi$ ?" has always been considered a "wrong" question. A mathematical constant does not depend on how we actually measure it. In the case at hand, euclidean circles still are euclidean, even if they would not be realized geometrically in our Universe, the constant stays itself. That's why I don't see how the original question is any different from "could God contradict Itself ?" (a well-known question, such as Q: "what was God doing before time ?" A: "preparing Hell for those who would wonder !")

17. Aug 18, 2008

### Staff: Mentor

But if "god lives outside of time and space', therefor is not limited to what we know to be possible, then is it possible for this God to wipe out the Universe as we know it and replace it with something unimaginable? To believe in a god like this means we have to be willing to throw out what we believe is possible, no?

18. Aug 18, 2008

### humanino

Yes, you are right in principle. Just, in that case, I don't think the "unimaginable" is linked to a "God living outside time and space", because $\pi$ is outside time and space, what I find unimaginable is to throw away logic (no surprise for a scientist). It's not that it's impossible to throw away logic, but if you accept it, then the original question (or any discussion or even action) certainly is moot.

19. Aug 18, 2008

### Staff: Mentor

That's how I feel about it. :tongue2:

20. Aug 19, 2008

### peter0302

Yes, I think I agree with you Humanino. If you accept the validity of logic, then any question regarding god's ability to alter logic is answered in the negative.

Could there be a universe in which 2+2 = 5? Well, I suppose that god could play a trick such that any time two things were brought together with two of the same thing, there would suddenly be five of them, but I still don't think that changes the metaphysical laws of logic, which don't concern themselves with counting or measuring real things.