Mathematical Proof Of God

[miekko]

Another problem comes up when one brings in the Aleph numbers which identify different orders of infinite magnitude. The statements made in the OP for infinity and zero don't apply the same way. In particular, the number 2 raised to the Aleph-0 power is Aleph-1, which is not contained in the lowest infinite order of Aleph-0.

 

On a side note, a lot of the problems we have with infinity is that we simply are not able to comprehend it. I can't help but wonder if quantum computers will change this.

 

To take that thought further, what would be the implications if quantum computers could deal with infinity? At the very least one would have to think about what it means for a finite entity (Man) to create something capable of understanding the infinite.

I realize this is slightly off topic, but no, quantum computers won't change that, and here's a somewhat long explanation why:

 

Quantum computers are probably the most overrated thing ever (not saying they're not a great concept, but people seem to think they're a lot of things they are not). When trying to understand the benefits quantum computing brings over classical computing, one benefits from thinking of problem-solving. Computers essentially appeared as a result of late 19th- and early 20th- century maths problems. Specifically, a sort of metaproblem, the problem of how to solve problems more generally. Ultimately, it was shown by a bunch of clever minds that there is no general problem-solving method that can solve all problems. Computers sort of are then a bit of the answer to 'well, what can we really solve'?

 

To figure out what generally can be solved, we need to come up with a reasonable mechanism for solving problems, and then trying to see what problems this mechanism can solve. In fact, we have several different mechanisms solving different kinds of problems, see e.g. the Chomsky hierarchy of automata. As far as we can tell, there are no realistic models surpassing the Turing machine. None surpass it, but many are equivalent to it - there's any number of formalisms that have basically the same properties, but for some reason, the Turing machine's the gold standard for research into these kinds of things. Any problem solvable in any formalism equal in power to the turing machine is solvable in any other formalism equal in power to the turing machine. 

 

(I would do good to get into a diversion on the Halting problem about here, as it's kind of central to why we can't have an universal problem solver. I won't get into that though.) 

 

Now, certain types of problems are relatively difficult to solve - but for this, we need to come up with some way of measuring difficulty. There are several ways to measure it, but one simple way is to pick some formalism - we pick the Turing machine now - and then pick some "resource". This resource may be how much memory is needed or how many instructions have to be carried out, or even how many times a memory cell is written to (altering the contents), or even the opposite: how many times a memory cell is overwritten with the same contents it previously had. The two main resources people tend to think of are time (number of operations needed to calculate the solution), and memory (number of memory cells needed to calculate the solution). 

 

There are a bunch of trivial kinds of problems where the "path of computation" never really splits - you don't have to guess whether the solution is down one path or the other. Simple calculations like "(50319311111189.31 * 6952342342.999999999999983222274 + 323.9239239) / 73.2120034" are among those. I call that a simple calculation because even if you add ten decimals to each number, the number of operations you need to carry out doesn't grow remarkably much, you could probably calculate all of it in a rather short time ultimately. In addition, you could reuse some of the calculations you've done - e.g. the long string of 1s or the long string of 9s in the two numbers give you a nice little shortcut - just multiply those results by ten, repeatedly - which is damn easy, by the way). You can predict how this calculation will go down, and you don't need to worry. Some problems, though, happen not to share this property - at some point you need to make a guess. And what's worse is that you cannot guarantee that the guess you take will ever reach a solution - your computation may get stuck in an infinite computational branch. So, you may have to do something like this:

---> reach a fork in the road

-------> start on fork 1, progress a bit into it

----------> after a while when no result has been obtained, save the progress, and

-------> start on fork 2, progress a bit into it

 

----------> after a while, when no result has been obtained, save the progress and resume progress on fork 1

----------> repeat and jump back to fork 2

 

 

So far so good, but what if fork 1 forks again? We have to repeat the same for fork 1.1 and fork 1.2, and there's a risk we'll keep forking - especially if the problem is large.

Forks of this kind are a terrible thing, as the numbers can grow quickly - 1, 2, 4, 8, 16, 32, 64 ... you get the point. With classical computing, parallelism can of course cut out a bit of this - say you have a very very demanding problem and you are in a hurry to find it, and you happen to have 64 cores to distribute the problem over. If there's only six forks, Bob's your uncle. Heck, even if there's twelve forks or so, that's no biggie, each core gets 2^6 forks to go over, and that's not that terribly bad - do keep in mind that if we're solving a problem of size N, it's not unlikely we'll soon want to solve a problem of size N+1, and soon we'll end up reaching the practical limits to what we can do with the machinery we have. 

 

Quantum computing utilizes another kind of parallelism - it essentially uses qubits to emulate having several cores, but this only shaves off a constant number of forks, and there's no big problem making a decidedly finite problem that even a huge quantum computer will choke on. It seems some problems have properties that make quantum computers relatively efficient on them - even more so than the above way of thinking of them would hint at, but these problems are a subset of all problems that exist. Prime factorization is probably one of those, and this might in part have some kind of connection to the fact that prime factorization always has a unique solution, and every other attempt at a solution will explicitly fail  - many other problems may not have an unique solution, and so even if the solution you have works there's no guarantee it's the best solution - which often is what we are looking for.

 

Compare figuring out the prime factors of 798444321 to partitioning {17, 9, 12, 32, 8, 14, 30, 11, 9, 7, 15, 15, 8, 9, 6, 15, 18, 19, 31, 7} into smaller groups whose sums are not to exceed 39, such that the number of such groups is as small as possible. In the first case, one number wrong gives you the wrong result - in the latter case, you are unlikely to get all groups to add up to 39, but sometimes for problems of that type, it is difficult to know whether there is a way to rearrange the numbers in such a way that the number of 'containers' can be reduced. Quantum computers seem to be good at the first kind of problem, and about as bad as classical computers at the latter.

 

The idea that a technology that improves the speed at which we can solve certain kinds of problems - problems whose search space tends to have certain properties, e.g. existence of one clear and undeniable solution - would improve our understanding of infinity seems rather far-fetched. There's no connection - either obvious or less than obvious - between the two things, and it all seems like just more of this naive idea that quantum is magic, albeit dressed in technological jargon. Quantum computing isn't a panacea for computational problems, and it's not a panacea for lack of understanding of mathematical concepts either.

[Guest nat]

 

 

 

The problem here arises from confusing infinity for an actual number.  It's just a placeholder for the phrase "as some variable increases without bound."  It really isn't that profound.

 

I already said that I can't debate this on the advanced level. I will leave that for others. But I still do think my logic is sound. And i don't confuse infinity with a number. Infinity is not a number. It is undefined. I like to think that division by 0 is infinity. I have already seen many uncomfortable with this. Even if it is not 0, the numbers as you get closer to 0 are getting so large, that it either reaches infinity or something like it. The semantics don't really interest me. infinity *0 is undetermined. Undetermined is not that same as undefined. Undetermined means that it can be this or that or anything. I don't want to argue semantics. The fact is that infinity times zero is not zero. That alone is an amazing fact! That alone is compelling. I think any logical person would agree. 

We will never understand God nor infinity. I think God gave us the gift of infinity in order to realize that He is also there even if we can't ever understand.

[Guest nat]

Concerning negative infinity. Could very well be that negative infinity is the past and positive infinity is the future.

[Margee]

Hi nat! welcome to Ex-c! I don't know mathematics so I won't even try but I do have one question. This god who has the mathematics perfect for earth....does 'he' also have the same mathematics for the billions of other planets out in the universe...or has these mathematics only have to do with the planet earth? This is a sincere question by the way!!   Glad you are here for discussion!!

 

Check out this website and tell me what you think please?  http://curiosity.discovery.com/question/other-planets-sustain-life

 

 

Quote: '' Professor, the universe is so big. Are we alone?" I don't think so. In fact, we now have some numbers that substantiate that. The Hubble Space Telescope orbiting in outer space right now has given us the first census of planets in the galaxy that may have life on them. It turns out that out of every 200 stars you see at night, one of those stars can have a planet in the habitable zone, the Goldilocks Zone -- not too close where the oceans would boil, not too far from where the oceans would freeze but just right to have liquid oceans. Why liquid oceans? Because water is the universal solvent. It dissolves most things including the organic materials of life like DNA.

 

Think about it. Our galaxy contains billions of stars. This means that perhaps 500 million planets in our own backyard, in our own Milky Way Galaxy may have planets carrying liquid oceans and perhaps even life. In the future, when you look at the night sky, you will have an existential shock knowing that here, there, there, there are twins of the Earth. When you look at the night sky, you will always wonder is anyone looking back.''

[new2me]

God is the infinite. The opposite of God is nothing. Judaism teaches that God made this world from nothing. God*0=all things.

 

And that is the mathematical proof to God.

Thank you.

 

The Flying Spaghetti Monster is also the infinite.  The opposite of the Flying Spaghetti Monster is nothing.  FSM*0 = all things.

 

And that is the mathematical proof to FSM.

 

Try it with any number of imaginary things - it really works!!

[♦ ficino ♦]

Nat, on second pass:

 

since your OP claims to offer a "proof to God" and not merely reflections on how we apply the term "infinite" to God in a way that is analogous to the way we apply it in some other contexts, I'll add:

 

1. I don't think that the God of Judaism or Christianity can be equated with "the infinite."  There are many things that God is not - or, many predicates that cannot be predicated of God.  You may know that some ancient Greek thinkers tended to associate the infinite with matter, not with God, who they thought imposed limit on matter.  We can say that God is not limited in certain respects, but to say that God is not limited in any respect would destroy the creator-creation relation to which you refer in your OP (i.e. God would just be everything).  It doesn't mean much to say "thou shalt have no other gods before me" if God is just everything.

 

but maybe you would agree.

 

2. In line with what new2me said, I think your "proof" collapses into one of these, depending on your tacit assumptions:

 

 either "I'm thinking of ways that God is infinite;  therefore, God"  (begs the question)

 

or  "I'm thinking of aspects of infinity;  therefore, God" (non sequitur)

[boftx]

Well, it looks like nat has been initiated.

[Guest nat]

 

God is the infinite. The opposite of God is nothing. Judaism teaches that God made this world from nothing. God*0=all things.

 

And that is the mathematical proof to God.

Thank you.

 

The Flying Spaghetti Monster is also the infinite.  The opposite of the Flying Spaghetti Monster is nothing.  FSM*0 = all things.

 

And that is the mathematical proof to FSM.

 

Try it with any number of imaginary things - it really works!!

 

Not true, A flying spaghetti monster cannot be infinite, because infinity cant be divided, while the flying spaghetti monster can.

[new2me]

 

 

God is the infinite. The opposite of God is nothing. Judaism teaches that God made this world from nothing. God*0=all things.

 

And that is the mathematical proof to God.

Thank you.

 

The Flying Spaghetti Monster is also the infinite.  The opposite of the Flying Spaghetti Monster is nothing.  FSM*0 = all things.

 

And that is the mathematical proof to FSM.

 

Try it with any number of imaginary things - it really works!!

 

Not true, A flying spaghetti monster cannot be infinite, because infinity cant be divided, while the flying spaghetti monster can.

 

Prove it.

[Guest nat]

I believe that God is infinite in all ways. Infinity is not all things. Infinity is never ending, and is not definable or understandable. So there is no way for me to explain it. Matter is not infinite because it can be divided. Infinity cannot be divided.

[Guest nat]

Prove what?

 

Infinity/2=infinity. Anyone who knows math knows that.

 

Flying spagetti monster/2=1/2 flying spaghetti monster.

[♦ ficino ♦]

I believe that God is infinite in all ways. Infinity is not all things. Infinity is never ending, and is not definable or understandable. So there is no way for me to explain it. Matter is not infinite because it can be divided. Infinity cannot be divided.

Surely you don't believe that God is infinite in that all predicates can be predicated of Him?

[Guest nat]

I don't know how math holds up on other planets. Havent been there. I hope its the same.

[Guest nat]

 

I believe that God is infinite in all ways. Infinity is not all things. Infinity is never ending, and is not definable or understandable. So there is no way for me to explain it. Matter is not infinite because it can be divided. Infinity cannot be divided.

Surely you don't believe that God is infinite in that all predicates can be predicated of Him?

 

Not sure what you mean. God is not of this realm. God is infinite endless, undefined, and unknown. God as he appears to us in the bible is not the same thing as God himself. The bible defines God as this or that for our benefit. According to Kabbalah, the infinite God created defined forms of himself to interact with this world. 

[boftx]

 

I believe that God is infinite in all ways. Infinity is not all things. Infinity is never ending, and is not definable or understandable. So there is no way for me to explain it. Matter is not infinite because it can be divided. Infinity cannot be divided.

Surely you don't believe that God is infinite in that all predicates can be predicated of Him?

 

 

If someone did accept that I would love to see OrdinaryClay get around "God is evil" as a consequence.

[midniterider]

 

 

 

 

The problem here arises from confusing infinity for an actual number.  It's just a placeholder for the phrase "as some variable increases without bound."  It really isn't that profound.

 

I already said that I can't debate this on the advanced level. I will leave that for others. But I still do think my logic is sound. And i don't confuse infinity with a number. Infinity is not a number. It is undefined. I like to think that division by 0 is infinity. I have already seen many uncomfortable with this. Even if it is not 0, the numbers as you get closer to 0 are getting so large, that it either reaches infinity or something like it. The semantics don't really interest me. infinity *0 is undetermined. Undetermined is not that same as undefined. Undetermined means that it can be this or that or anything. I don't want to argue semantics. The fact is that infinity times zero is not zero. That alone is an amazing fact! That alone is compelling. I think any logical person would agree. 

We will never understand God nor infinity. I think God gave us the gift of infinity in order to realize that He is also there even if we can't ever understand.

 

 

So if infinity is undetermined should it be considered a wave function? And upon collapse of the wave function we get a real number that we punch into a calculator, multiply it by zero and get: zero.

[midniterider]

 

God is the infinite. The opposite of God is nothing. Judaism teaches that God made this world from nothing. God*0=all things.

 

And that is the mathematical proof to God.

Thank you.

 

The Flying Spaghetti Monster is also the infinite.  The opposite of the Flying Spaghetti Monster is nothing.  FSM*0 = all things.

 

And that is the mathematical proof to FSM.

 

Try it with any number of imaginary things - it really works!!

 

 

Imaginary beings will not be mocked!  lol.

[midniterider]

 

 

God is the infinite. The opposite of God is nothing. Judaism teaches that God made this world from nothing. God*0=all things.

 

And that is the mathematical proof to God.

Thank you.

 

The Flying Spaghetti Monster is also the infinite.  The opposite of the Flying Spaghetti Monster is nothing.  FSM*0 = all things.

 

And that is the mathematical proof to FSM.

 

Try it with any number of imaginary things - it really works!!

 

Not true, A flying spaghetti monster cannot be infinite, because infinity cant be divided, while the flying spaghetti monster can.

 

 

Dont blaspheme the FSM please. He is above criticism. His ways are mysterious and we cannot understand his Noodliness. :-)

[midniterider]

Deleted for future fixing. 

[new2me]

Prove what?

 

Infinity/2=infinity. Anyone who knows math knows that.

 

Flying spagetti monster/2=1/2 flying spaghetti monster.

Prove that you can divide the Flying Spaghetti Monster.  He is infinite and indivisible because I believe that he is infinite in all ways.

 

I am well aware that infinity / 2 = infinity.

 

The point I am trying to make is that in a mathematical proof, you must be able to defend each step of the proof.  You make a GIANT leap when you say that God is the infinite just because you believe it to be so.  You are using circular logic if you are trying to define God as infinite, then applying mathematical calculations using infinity to 'prove' its existence.

[midniterider]

 

 

I believe that God is infinite in all ways. Infinity is not all things. Infinity is never ending, and is not definable or understandable. So there is no way for me to explain it. Matter is not infinite because it can be divided. Infinity cannot be divided.

Surely you don't believe that God is infinite in that all predicates can be predicated of Him?

 

Not sure what you mean. God is not of this realm. God is infinite endless, undefined, and unknown. God as he appears to us in the bible is not the same thing as God himself. The bible defines God as this or that for our benefit. According to Kabbalah, the infinite God created defined forms of himself to interact with this world. 

 

 

1. God is this.

2. God isn't this.

3. God is something else.

4. God isn't something else.

 

Makes perfect sense.

[Guest nat]

 

Prove what?

 

Infinity/2=infinity. Anyone who knows math knows that.

 

Flying spagetti monster/2=1/2 flying spaghetti monster.

Prove that you can divide the Flying Spaghetti Monster.  He is infinite and indivisible because I believe that he is infinite in all ways.

 

I am well aware that infinity / 2 = infinity.

 

The point I am trying to make is that in a mathematical proof, you must be able to defend each step of the proof.  You make a GIANT leap when you say that God is the infinite just because you believe it to be so.  You are using circular logic if you are trying to define God as infinite, then applying mathematical calculations using infinity to 'prove' its existence.

 

You miss my point. I am showing that there is something infinite out there. I call it God. You can call it what you want. There is infinity to the past and there is infinity to the future. Matter cannot be infinite because it can be divided. Matter was not there for infinity. The infinite is undefined, unknowable. I call it God. There is something infinite out there. You can decide for yourself what it is, but it isn't made of matter. 

Infinity times nothing is not nothing. You take nothing an infinite amount of times, you don't get nothing. That is a mathematical fact. How can it be? It can be because we don't know what infinity is, so we can't understand its affect on nothing.

infinity times nothing is undetermined, not undefined. Infinity times nothing can be this or that or anything.

Infinity is the boundless extreme on one end. Nothing is the extreme on the other end. Between the two can be anything.

This is the only way to explain how matter came into existence.

[Margee]

 

 

 

 

 I call it God. You can call it what you want.  You can decide for yourself what it is, but it isn't made of matter. 

 

 

 

 

 nat, so you call 'it' God? But arent' you a proud Jew? So your god must be old testament god? Am I wrong? And we who make up our own version of 'god'...are we saved....will we go to heaven? Will our god love us the same as 'it' loves you?

[Kurari]

 

Sorry, NULL is not 0, it is undefined, or undetermined, in the context I present. One has only to look at how many databases treat the terms "0", "" and NULL to see that.

 

It is true that in many cases one can consider NULL (or undefined) to be the logical equivalent of "FALSE" but not always. I'd have to refresh my memory on it, but I also believe that set theory makes a distinction between "0" and NULL.

Ok, we will never understand infinity or God, and if Null is undefined, we will never understand that as well. Undefined means that we cannot define or understand it. It should be humbling that math proves to us that we cannot understand something.

 

 

Then that really kind of leaves us back where we all started and nothing has changed. 

 

A big misconception about atheists is that we do not acknowledge what has not been discovered, defined, or understood and that our position is fixed. This just isn't true. "I don't know" is a fine position to have. This is what science is for. To discover. To learn. To think. 

 

I doubt I'm alone in that I'd be very interested in seeing and meeting and defining an actual "god." If that were to happen, I would have no issues with being a theist. 

 

But in the case of a "god" that is undefined or undiscovered, this has no impact on how I live my life. I have no reason to base or live by beliefs on something that we cannot define or understand. 

[par4dcourse]

If your god is all infinite and undefinable and not understandable, then I care even less whether he exists.