Could a God Change the Value of Pi?

In summary, the conversation discusses the possibility of a god being able to alter the value of Pi, a transcendental number that exists only as an idea and does not occur in nature. The argument presents the idea that mathematics and logic are transcendental and could potentially exist without the need for a creator, rendering omnipotence impossible. The conversation also touches on the limitations of a god's power and the idea that different deities in different cultures may have different abilities.
  • #1
peter0302
876
3
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?
 
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  • #2
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.
 
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  • #3
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
Moridin said:
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.
 
  • #5
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
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.
 
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  • #7
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?
 
  • #8
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
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
Evo said:
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.
 
  • #11
I don't like the old fashioned geometrical definition of [itex]\pi[/itex]. 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 [itex]2\pi\mathbb{R}[/itex].

This definition of [itex]\pi[/itex] 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 ? :smile:
 
  • #12
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
Cale Carter said:
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.
 
  • #14
peter0302 said:
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.
 
  • #15
humanino said:
The kernel of this homeomorphism (a subgroup of R) cannot be dense in R, therefore it must be of the form [itex]2\pi\mathbb{R}[/itex].
Sorry, I obviously meant [itex]2\pi\mathbb{Z}[/itex] !
peter0302 said:
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.
 
  • #16
Evo said:
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 [itex]\pi[/itex] ?" 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
humanino said:
But the question "does general relativity changes the value of [itex]\pi[/itex] ?" 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?
 
  • #18
Evo said:
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 [itex]\pi[/itex] 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
humanino said:
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 [itex]\pi[/itex] 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. :tongue2:
 
  • #20
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.
 
  • #21
peter0302 said:
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.
 
  • #22
I'm disappointed by the confidence people seem have when tackling this problem.
 
  • #23
jostpuur said:
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.
 
  • #24
This:

Moridin said:
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

Werg22 said:
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.

Cale Carter said:
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..

Evo said:
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.
 
  • #25
jostpuur said:
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.
 
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  • #26
peter0302 said:
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.
 
  • #27
Werg22 said:
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*
 
  • #28
jostpuur said:
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.
 
  • #29
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.
 
  • #30
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.
 
  • #31
Yes, I am also sure that 2 + 2 = 4. That's a theorem.
 
  • #32
OAQfirst said:
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 [itex]\pi[/itex]. 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.
 
  • #33
humanino said:
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 [itex]\pi[/itex]. 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.
 
  • #34
OAQfirst said:
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.
 
  • #35
2+2 = 2+2
 
<h2>1. Could a God actually change the value of Pi?</h2><p>As a scientist, I cannot definitively answer this question as it is a matter of personal belief. However, according to the laws of mathematics and physics, Pi is a constant value that cannot be altered by any external force or entity.</p><h2>2. Is there any scientific evidence to suggest that a God could change the value of Pi?</h2><p>No, there is no scientific evidence to support the idea that a God could change the value of Pi. The laws of mathematics and physics have consistently shown Pi to be a constant value.</p><h2>3. What would be the implications if a God did change the value of Pi?</h2><p>If a God were to change the value of Pi, it would completely disrupt our understanding of mathematics and the physical world. It would also raise questions about the reliability and consistency of scientific laws.</p><h2>4. Are there any religious or cultural beliefs that suggest a God could change the value of Pi?</h2><p>There are some religious and cultural beliefs that may suggest a God has the power to change the value of Pi. However, these beliefs are not supported by scientific evidence and are based on faith and personal interpretation.</p><h2>5. How does the concept of a God changing the value of Pi relate to the concept of an unchanging and perfect God?</h2><p>The concept of a God changing the value of Pi contradicts the idea of an unchanging and perfect God. If a God were to change the value of Pi, it would suggest that this God is not all-knowing and all-powerful, as a perfect being would not need to alter a constant value.</p>

1. Could a God actually change the value of Pi?

As a scientist, I cannot definitively answer this question as it is a matter of personal belief. However, according to the laws of mathematics and physics, Pi is a constant value that cannot be altered by any external force or entity.

2. Is there any scientific evidence to suggest that a God could change the value of Pi?

No, there is no scientific evidence to support the idea that a God could change the value of Pi. The laws of mathematics and physics have consistently shown Pi to be a constant value.

3. What would be the implications if a God did change the value of Pi?

If a God were to change the value of Pi, it would completely disrupt our understanding of mathematics and the physical world. It would also raise questions about the reliability and consistency of scientific laws.

4. Are there any religious or cultural beliefs that suggest a God could change the value of Pi?

There are some religious and cultural beliefs that may suggest a God has the power to change the value of Pi. However, these beliefs are not supported by scientific evidence and are based on faith and personal interpretation.

5. How does the concept of a God changing the value of Pi relate to the concept of an unchanging and perfect God?

The concept of a God changing the value of Pi contradicts the idea of an unchanging and perfect God. If a God were to change the value of Pi, it would suggest that this God is not all-knowing and all-powerful, as a perfect being would not need to alter a constant value.

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