The answer to this question will significantly affect the idea of my previous post. I have a feeling that in general they discover. For example, a Tyrannosaurus Rex probably couldn't count, but that doesn't change the fact that it had 2 arms, 2 legs, 1 tail, and "x" razor-sharp teeth. So numbers "existed", but they weren't really being thought about carefully.

If mathematicians always discover (rather than create) mathematics, then my analogy in the previous post becomes quite weak. However, my faulty analogy might not change my acceptance of the (rather unlikely) possibility that an advanced civilization had a hand in the creation of the universe.

I should do some reading on the philosophy of mathematics and then post what I've learned. Stay tuned.

## Saturday, January 30, 2010

## Sunday, January 10, 2010

### Oh my god. Did I just become a deist?

I just had an idea about the plausibility of some form of creator, which is quite odd as I'm a diehard atheist (and quite possibly an anti-theist.) I was brushing my teeth, and suddenly I conceived of an idea that, unlike all other arguments I've heard for deism, seemed to have non-zero probability.

To get a grip on my idea, I must introduce some relatively simple concepts from mathematics. Mathematicians typically don't deal explicitly with numbers, they deal with objects. They are very good at converting practical ideas into abstract concepts for the purposes of research. For example, take the integers: ..., -3, -2, -1, 0, 1, 2, 3, ... along with simple addition '+'. (The ellipses, by the way, imply an endless continuation to the left and right.) Mathematicians take the integers and addition and abstract them into an object which they call a "group". (Please completely divorce this mathematical term from the normal definition of the word "group" which you are thinking of right now.)

In mathematics, a "group" is a set of things (possibly finite, possibly infinite) along with an operation which describes how the things can be combined, resulting in other things from within the same group. In groups, there's one very special thing called an "identity", which actually doesn't do much of anything. Also, for each thing in the set, there exists exactly one other thing called an "inverse", and when a thing and its inverse are combined, the result is the "identity".

Making this a bit more concrete, consider the group of the integers along with addition. The special thing called the identity is zero (i.e. 0) which clearly doesn't do anything since 5 + 0 = 5. For each integer, there is one inverse. For example, the inverse of 3 is -3, since 3 + (-3) = 0. (Remember, 0 is the identity of this particular group.) As another example, the inverse of -897 is 897, since (-897) + 897 = 0.

The integers are a very large set of numbers, in fact it is an infinite set. But this infinite set can be generated by only the number 1. 1 is called a "generator" of this group. [Just continue adding 1 to itself to get all of the positive integers: 1, 2, 3, 4, ... . Then take the inverse of 1, namely -1, and continue adding it to itself to get the negative integers. To generate 0, simply add 1 + (-1).] The idea of a generator is important as it shows that a very large set can be generated by very few members (and sometimes only one).

Groups seem like quite simple things, and they sometimes are. But their simple definition can be misleading. Once we cast away numbers and just focus on the abstract definition and objects, we start to uncover many very interesting properties. Shelves and shelves of books have been written on Group Theory and current mathematicians are expanding the theory monthly in numerous journals on the subject. (There are one or two other properties of a group, but in the interest of concision, I hope you will trust me when I say they are not very important to this argument.)

So, what is my point. How does this relate to the possibility of a creator? Well, when mathematicians first started thinking about groups, they had relatively little idea of the complexity, unexpected features, or beauty of the characteristics and theorems that would result after intense study. In a similar way, it is not so difficult to imagine a creator establishing its own kind of "cosmic group": a small set of elementary particles or energies (the generators), coupled with some initial rules dictating how these particles and energies interact (the operation). Over billions of years, the world we see today could have evolved from this very simple beginning, as the generators interact with each other, creating new matter and new energy.

This idea does not do away with the infinite regress question: if there was a creator, who created it? And who created the creator of that creator, and so on ad infinitum. This idea does however alleviate a concern I've always had with the idea of a creator. Looking around me, I've always wondered why our omnipotent God (assuming one exists) didn't create a much simpler universe, with no evil, no disease, and no mosquitos. Well, perhaps a creator did create the simplest of universes, using only simple initial conditions, but really had nothing to do with any of its evolution into the current complex and mosquito-infested universe we call home. I'm in no way saying that I could believe in any of the man-made gods that my fellow humans worship. But I could see myself contemplating the possibility of an incredibly advanced alien civilization (probably indistinguishable from God, as Asimov puts it) seeding our universe with the requisite primeval elements.

Of course, this is all a mathematical analogy, and doesn't prove a single thing. It has simply allowed me to consider (however minute) the remote possibly of some kind of creator. Since there is absolutely no evidence for such a creator, I could never bring myself to "believe" what I have just described. However, I will certainly not deny its possibility until a philosopher or mathematician pokes holes in my reasoning.

To get a grip on my idea, I must introduce some relatively simple concepts from mathematics. Mathematicians typically don't deal explicitly with numbers, they deal with objects. They are very good at converting practical ideas into abstract concepts for the purposes of research. For example, take the integers: ..., -3, -2, -1, 0, 1, 2, 3, ... along with simple addition '+'. (The ellipses, by the way, imply an endless continuation to the left and right.) Mathematicians take the integers and addition and abstract them into an object which they call a "group". (Please completely divorce this mathematical term from the normal definition of the word "group" which you are thinking of right now.)

In mathematics, a "group" is a set of things (possibly finite, possibly infinite) along with an operation which describes how the things can be combined, resulting in other things from within the same group. In groups, there's one very special thing called an "identity", which actually doesn't do much of anything. Also, for each thing in the set, there exists exactly one other thing called an "inverse", and when a thing and its inverse are combined, the result is the "identity".

Making this a bit more concrete, consider the group of the integers along with addition. The special thing called the identity is zero (i.e. 0) which clearly doesn't do anything since 5 + 0 = 5. For each integer, there is one inverse. For example, the inverse of 3 is -3, since 3 + (-3) = 0. (Remember, 0 is the identity of this particular group.) As another example, the inverse of -897 is 897, since (-897) + 897 = 0.

The integers are a very large set of numbers, in fact it is an infinite set. But this infinite set can be generated by only the number 1. 1 is called a "generator" of this group. [Just continue adding 1 to itself to get all of the positive integers: 1, 2, 3, 4, ... . Then take the inverse of 1, namely -1, and continue adding it to itself to get the negative integers. To generate 0, simply add 1 + (-1).] The idea of a generator is important as it shows that a very large set can be generated by very few members (and sometimes only one).

Groups seem like quite simple things, and they sometimes are. But their simple definition can be misleading. Once we cast away numbers and just focus on the abstract definition and objects, we start to uncover many very interesting properties. Shelves and shelves of books have been written on Group Theory and current mathematicians are expanding the theory monthly in numerous journals on the subject. (There are one or two other properties of a group, but in the interest of concision, I hope you will trust me when I say they are not very important to this argument.)

So, what is my point. How does this relate to the possibility of a creator? Well, when mathematicians first started thinking about groups, they had relatively little idea of the complexity, unexpected features, or beauty of the characteristics and theorems that would result after intense study. In a similar way, it is not so difficult to imagine a creator establishing its own kind of "cosmic group": a small set of elementary particles or energies (the generators), coupled with some initial rules dictating how these particles and energies interact (the operation). Over billions of years, the world we see today could have evolved from this very simple beginning, as the generators interact with each other, creating new matter and new energy.

This idea does not do away with the infinite regress question: if there was a creator, who created it? And who created the creator of that creator, and so on ad infinitum. This idea does however alleviate a concern I've always had with the idea of a creator. Looking around me, I've always wondered why our omnipotent God (assuming one exists) didn't create a much simpler universe, with no evil, no disease, and no mosquitos. Well, perhaps a creator did create the simplest of universes, using only simple initial conditions, but really had nothing to do with any of its evolution into the current complex and mosquito-infested universe we call home. I'm in no way saying that I could believe in any of the man-made gods that my fellow humans worship. But I could see myself contemplating the possibility of an incredibly advanced alien civilization (probably indistinguishable from God, as Asimov puts it) seeding our universe with the requisite primeval elements.

Of course, this is all a mathematical analogy, and doesn't prove a single thing. It has simply allowed me to consider (however minute) the remote possibly of some kind of creator. Since there is absolutely no evidence for such a creator, I could never bring myself to "believe" what I have just described. However, I will certainly not deny its possibility until a philosopher or mathematician pokes holes in my reasoning.

Labels:
alien,
anti-theism,
deism,
group theory,
math,
mathematics,
science

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