Tuesday, March 14, 2006

Fred's Theorem

Fred's Theorem: It is impossible for a mathematical function to generate new symbolic information.


Proof
  1. Assume it is possible to create a function f(x) that creates new information.
  2. This function would take as input data from the set s1 and give resulting values within set s2
  3. Because the function generates new information, the amount of information of s2 would be greater than that in s1
  4. Therefore there must be some information in s2 that is not a function of the data in s1
  5. #4 contradicts #1.
  6. QED
Several corollaries follow out of these theorem proving:
  • The existance of God
  • The existance of the Human soul
  • The impossibility of evolution
  • The failure of Artificial Intelligence

2 comments:

Tim said...

I enjoyed reading your function proof however am unconvinced and confused.

In reference to part 1 and 3:

We don’t know what new means. Let’s assume that the function is f(x) = x2 and s1 contains the values .5 and 5. Then our s2 contains .25 and 25. We have different numbers in the second set than in the first set. Are those new?

What if the function involved things other than numbers like atoms? In a function, we do something to our input that changes our input in some way right? Assuming that I’m not too far off on this, could we then say that our function goes like this: f(x)= (x)O + 2H(x) where x=number of oxygen, O=oxygen, and H=hydrogen? If we did this simple thing, we would just describe how we make water H2O. Then, every number we put into our s1 would create x molecules of water, and we would have water in s2 and only numbers in s1. It seems to me that what the function does is very important because it manipulates its input and relates it to something which may be real. Additionally it seems important to ask again the question in a different way:

If we have a more simple function which is f(x)= 2x, and our set contains a single atom of oxygen and a single atom of hydrogen, then wouldn’t we get an s2 that contains some water (or hydrogen peroxide) and an s1 without water? Is the water new, or do we not think of it as different since it is still made of 2 hydrogen and 1 oxygen?

I also don’t understand what you mean by greater. In my example of the water molecule we have different form but do we have greater?

In reference to part 4:
In my example we have water in set 2 and no water in set 1. If we assume that it the water in s2 is new and greater compared with that of set 1, we can still see that it is a function of s1. In this case with the single atom of H and of O in s1, we end up with an s2 that contains one molecule of water and one oxygen molecule (H2 + O2 equals H2O +H). The function, which manipulates the input of s1 by multiplying it not only changes the amount of things, but changes the structure of things. We could also have the case where we end up with hydrogen peroxide in s2 and just hydrogen and oxygen in s1. In this case s2 would be the function of s1 directly and nothing would exist in s2 that wasn’t a function of the input s1.

If we accept that hydrogen peroxide or water is new, or that the numbers .25 and 25 in s2 are new compared to their s1 input of .5 and 5, then isn’t part 5 no longer applicable?

How do your corollaries relate to the proof? Maybe you could expand in your next blog entry.

Thanks!

Fritz the Cat said...

"Several corollaries follow out of these theorem proving:

* The existance of God
* The existance of the Human soul
* The impossibility of evolution
* The failure of Artificial Intelligence"

First off, the logical fallibility of one thing does not prove the logical accuracy of another. You couldn't say that Fred's Impossible Theorem proves the existEnce of God any more than you could say that it proves the existence of an all-knowing orangutan.

Disproving Darwinism does not mean that God exists. It just means that Darwinism is wrong. If you believe something to be true, the onus is on you to provide the proof.