Could a God Change the Value of Pi?

[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?

 

[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.

 

[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".

 

[Werg22]

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.

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.

 

[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.

 

[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.

 

[peter0302]

I think the question refers to if a god could chance that which mathematics is describing.

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?

 

[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...

 

[Evo]

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.

 

[Cale Carter]

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.

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.

 

[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 ?

 

[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.

 

[Evo]

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.

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.

 

[Evo]

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.

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.

 

[humanino]

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}.

Sorry, I obviously meant 2\pi\mathbb{Z} !

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?

I just re-interpreted it as "can God create something which would be different from itself ?", a type of self-contradictory statement.

 

[humanino]

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.

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 !")

 

[Evo]

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 !")

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?

 

[humanino]

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?

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.

 

[Evo]

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.

That's how I feel about it.

 

[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.

 

[baywax]

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?

Lets say that the idea of what a god can do changes dramatically in a few centuries if not faster. Just look up the different versions of "god" in the different versions of "religion" and you will see what I mean.

Whether this idea of a god can do anything to change anything is up to the people who believe in it. For instance, a person who believes their god has asked that the value of pi be changed will do so, somehow.. even if it means suicide or something as drastic. This is because people who think they know there is a "god" also think they know everything else and so its ok to change things when the voices in their head tell them to.

 

[jostpuur]

I'm disappointed by the confidence people seem have when tackling this problem.

 

[humanino]

I'm disappointed by the confidence people seem have when tackling this problem.

Sorry but I'm disappointed by you saying we tackle it with confidence. For instance, do you see anything wrong with the statement that the original question is not different from "could God contradict Itself ?" ? I would be happy if somebody could point out the subtlety I am missing here.

 

[jostpuur]

This:

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

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.

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..

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

is confidence. When I'm checking more carefully, I don't see you humanino stating anything excessively confident.

 

[Evo]

I'm disappointed by the confidence people seem have when tackling this problem.

The whole "problem" is based on personal belief, myth, not a real thing. So based on what you want this 'god" to be capable of, the answer will be different.

 

[Werg22]

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.

We're not even sure if two objects are brought together give 4 in our universe. We just know that we haven't observed otherwise.

 

[OAQfirst]

We're not even sure if two objects are brought together give 4 in our universe. We just know that we haven't observed otherwise.

?

You'd have a pretty hard time finding anyone without the confidence enough in that equation to not be willing to bet one's life on it. So I'd say just about everyone is sure. Even my CASIO fx-260 is sure of it.

EDIT: ah what the 'ell. *checks to be sure*

 

[peter0302]

I'm disappointed by the confidence people seem have when tackling this problem.

Funny, I'm disappointed with some of the views expressed here to the effect of "it's simple because God can do anything." No, that's a cop out. I'm asking about whether we have identified logical truths through math that are as powerful as any religious belief or perhaps even moreso. This is philosophy, not religion.

 

[Werg22]

2 + 2 = 4 is not a statement about the universe. It's a theorem of arithmetic. We believe that the base axioms of arithmetic hold of the several concretions we have of the terms of the theory and that, furthermore, the universe behaves rationally and so "2 objects joined with 2 objects gives 4" is accepted. But there is no way of definitively establishing the validity of our assumptions, and so we cannot be certain that there aren't times at which 2 objects joined with 2 other give 5.

 

[OAQfirst]

a·b will always equal b·a. Right?

In 1843, Sir William R Hamilton demonstrated that is is possible for algebra to be noncommutative, for a·b≠b·a to be true.

It's probably still to early to assume that a god can not make 2+2=5. We're still discovering rules. And how to break them.

However, I was replying to the matter of certainty. I am --sure-- that 2+2=4.

 

[Werg22]

Yes, I am also sure that 2 + 2 = 4. That's a theorem.

 

[humanino]

a·b will always equal b·a. Right?

This is a very bad example. Commutativity is valid for real numbers, period.

There are objects beyond commutativity, no problem, we just did not know that at that time. But that has not changed the commutativity of real numbers, neither has it changed the value of \pi. By the same token, the fundamental principles of elementary logic are valid independently of the fact that one can construct other forms of logical systems, such as fuzzy logic for instance.

 

[OAQfirst]

This is a very bad example. Commutativity is valid for real numbers, period.

There are objects beyond commutativity, no problem, we just did not know that at that time. But that has not changed the commutativity of real numbers, neither has it changed the value of \pi. By the same token, the fundamental principles of elementary logic are valid independently of the fact that one can construct other forms of logical systems, such as fuzzy logic for instance.

Not the point I was making. What seemed impossible at one time was found quite possible later.

 

[humanino]

Not the point I was making. What seemed impossible at one time was found quite possible later.

Still wrong. Mathematical theorems are true and period. If we have one think on this Earth we know is true, it's mathematical theorems !

IF A THEN B

It might appear to us later that A is unnecessary. But

IF A THEN B

remains true. Even if A is false.

 

[baywax]

2+2 = 2+2

 

[Werg22]

Still wrong. Mathematical theorems are true and period. If we have one think on this Earth we know is true, it's mathematical theorems !

IF A THEN B

It might appear to us later that A is unnecessary. But

IF A THEN B

remains true. Even if A is false.

I'd like to add a little something to this. Theorems are true by sole virtue of us declaring the axioms of the theories in which they occur as true. An axiom is, however, not true in by itself - there is no truth to be acquired about undefined terms - but rather purely assumed to be true; i.e. we assign the truth value 1 to the axioms of a theory by convention. The convention is obviously not arbitrary; this allows us the great flexibility of separating between "true" and "false" statements in mathematics (true if valid, false if the contrary is valid), which gives way to the method of reductio ad absurdum.

 

[jostpuur]

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

The whole "problem" is based on personal belief, myth, not a real thing. So based on what you want this 'god" to be capable of, the answer will be different.

You cannot make a mythical creature capable of changing the value of pi, unless you know what it means to change the value of pi. Nobody here knows what it means to change the value of pi, so there's one problem.

One possible interpretation for the word "God" in this context would be, that if we can figure out what it means to change the value of pi, then the procedure of changing its value exists in some sense, and we can say that the God could do it. Or at least that's the way I would like it. Then we don't need to yet solve what God is, and dealing with the pi is enough.

 

[Evo]

You cannot make a mythical creature capable of changing the value of pi, unless you know what it means to change the value of pi. Nobody here knows what it means to change the value of pi, so there's one problem.

One possible interpretation for the word "God" in this context would be, that if we can figure out what it means to change the value of pi, then the procedure of changing its value exists in some sense, and we can say that the God could do it. Or at least that's the way I would like it. Then we don't need to yet solve what God is, and dealing with the pi is enough.

If you have circles, I'd agree that the value of PI would be constant. Of course that means that your God cannot be all powerful.

A God could change the universe so that circles, etc... did not exist, then you would have no PI.

 

[humanino]

A God could change the universe so that circles, etc... did not exist, then you would have no PI.

You see, I am so closed minded I can't understand that. It does not matter that kids have no clue what a differential equation is, and it does not make them impossible if nobody knew about them. They are a logical construction, ready to be discovered by anybody willing to look at them. I can understand if you tell me, God could have prevented us from constructing the concept of circle. But making the construction impossible, I just don't see how it can make sense.

 

[peter0302]

Humanino you and I are on precisely the same page :)

And I beg to differ with those that say that the axioms of math are not necessarily true. What makes them axioms is the fact that they are self-evident. That is different than a postulate, which is an assumption not necessarily self evident.

For instance, it is an axiom that when you one thing together with another thing, you get two. In fact, that is essentially definitional. "2" is defined as what you get when you put "1" and "1" together. "3" is defined as what you get when you put "1" and "1" and "1" together. It is therefore self-evident that when you put "2" together with "1" you also get "3" because "2" is defined to be the same as "1" and "1".

These are not theorems that require assumptions; these are axiomatic / definitional constructs that cannot be falsified under any circumstances because they are self-evident.

What if God said "When you put one thing together with another thing, a third thing will magically appear"? Well that'd be quite a feat, but it would not change the above.

 

[OAQfirst]

Still wrong. Mathematical theorems are true and period. If we have one think on this Earth we know is true, it's mathematical theorems !

IF A THEN B

It might appear to us later that A is unnecessary. But

IF A THEN B

remains true. Even if A is false.

I think we need to skip back and reexamine what I was saying. Werg22 wrote, "We're not even sure if two objects are brought together give 4 in our universe. We just know that we haven't observed otherwise." I replied, "You'd have a pretty hard time finding anyone without the confidence enough in that equation to not be willing to bet one's life on it. So I'd say just about everyone is sure." If there is an exception to 2+2=4, then wouldn't the rules of the universe be jeopardized? That's why I draw a certainty. I probably shouldn't have used quaternions as an example to support the other view, as I was just playing Devil's advocate. So to get back to my original point, I am sure 2+2=4. And I'm sure most everyone else has the same impression.

 

[baywax]

If there is an exception to 2+2=4, then wouldn't the rules of the universe be jeopardized? That's why I draw a certainty. I probably shouldn't have used quaternions as an example to support the other view, as I was just playing Devil's advocate. So to get back to my original point, I am sure 2+2=4. And I'm sure most everyone else has the same impression.

Not me.

2 apples plus 2 apples = 1 trillion cells + 1 trillion cells + 5 or more seeds (per apple).

The number of pixels in the digitally imaged number "2" plus the same = approx. 26


etc... (eg. 2 oranges + 2 oranges = marmalade)

 

[Werg22]

An axiom is self-evident? Only in the case we are in the realm of material axiomatics, in which case the subject matter of the theory is a physical concretion with definite properties. In formal axiomatics, an axiom is nothing but a statement declared as true about some undefined, primitive terms of the theory. Example:

My theory will consist of a set of objects S, and a dyadic relation R and a binary operation # on S. Here are my axioms:

1. a R b -> b R a
2. a R b and b R c -> a R c
3. a # b = b # a
4. There exists a unique element 0 such that a # 0 = a for every a
5. a R b and a R c -> a R (b # c)

Now tell me a little, which one of these, exactly, is self-evident to you?

I think we need to skip back and reexamine what I was saying. Werg22 wrote, "We're not even sure if two objects are brought together give 4 in our universe. We just know that we haven't observed otherwise." I replied, "You'd have a pretty hard time finding anyone without the confidence enough in that equation to not be willing to bet one's life on it. So I'd say just about everyone is sure." If there is an exception to 2+2=4, then wouldn't the rules of the universe be jeopardized? That's why I draw a certainty. I probably shouldn't have used quaternions as an example to support the other view, as I was just playing Devil's advocate. So to get back to my original point, I am sure 2+2=4. And I'm sure most everyone else has the same impression.

There is no one in their right mind that functionally doubts that when two groups of two objects are brought together we obtain four. That is not the point. 2 + 2 = 4 is, repeating myself once again, is a theorem of arithmetic! Whether or not the interpretation of 2, + and 4 to real objects make it a true proposition or not is none of the pure mathematician's concern!

 

[Evo]

Ok, if a God can't create a Universe where circles would not exist, then this thread is completely pointless and should be deleted, correct?

 

[OAQfirst]

@Werg22: Then would you be kind enough to expand on your reply in post #26?

 

[Evo]

@Werg22: Then would you be kind enough to expand on your reply in post #26?

May I ask what the point is in discussing what everyone agrees is impossible? Because I don't see it.

I have tried making this obvious in every way I know aside from just saying "No" and closing the thread after the first post.

 

[peter0302]

Simply because you do not understand/appreciate the topic does not justify locking the thread which has (I am happy to see) generated quite a lot of interest.

The answer to your question:

Ok, if a God can't create a Universe where circles would not exist, then this thread is completely pointless and should be deleted, correct?

is that no one has suggested that god cannot create a universe in which circles do not exist. I have explicitly stated that that is fine. My question is whether god can create a universe in which the _idea_ of a circle cannot exist, which also implicitly asks whether mathematical ideas can be altered by any higher power or if they themselves are the highest power.

It is a perfectly legitimate philosophical question and I think that your locking threats miss the point and are uncalled for.


Weg22:
We're talking about the difference between an axiom and a postulate. Mathematical axioms are self-evident. What you're listing are postulates.

 

[Evo]

No one has agreed that it is possible from a valid scientific viewpoint, even bending the rules to allow for a mythical supreme being, which I did not have to allow, I tried to help you see if you could "construct" a "god" that would have such powers, but no one agreed such a god could be created.

To quote just one of many that have said no to your question.

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 !")

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[jostpuur]

Funny, I'm disappointed with some of the views expressed here to the effect of "it's simple because God can do anything." No, that's a cop out. I'm asking about whether we have identified logical truths through math that are as powerful as any religious belief or perhaps even moreso. This is philosophy, not religion.

I didn't get clear to me if there was misunderstanding between us, but to me it seems we were annoyed by the same thing. Your original post deals with a genuine philosophical question, and then people come in posting simple truths like "yes" or "no" in a hope, that they would make the problem seem easy and already solved.

 

[jostpuur]

If you have circles, I'd agree that the value of PI would be constant. Of course that means that your God cannot be all powerful.

A God could change the universe so that circles, etc... did not exist, then you would have no PI.

Ok, if a God can't create a Universe where circles would not exist, then this thread is completely pointless and should be deleted, correct?

That is not obvious. The real question is that could God create a universe where circles existed, and where pi had a different value. This is the difficult question, which I believe is little bit too difficult for humans, but which is suitable for a topic of a philosophical discussion.