From: John K Clark (johnkc@well.com)
Date: Tue Nov 19 1996 - 13:52:51 MST
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On Mon, 18 Nov 1996 Michael Lorrey <retroman@tpk.net> Wrote:
>you suffer from the hubris
Yes, I do have lot of hubris, but I think it's a virtue not a vice.
>you want your supper NOW DAMMIT. That sounds like a spoiled
>child talking.
I really don't care what it sounds like, and you have to give me one thing,
at least I know what I want.
>any experimental scientist working with animals like dolphins
>knows that the experiments they put their charges in to test
>them for intelligence, and teach them communication, or try
>to learnin their communication, will neccessarily impose
>sever hardship on the individual animals involved.
If so then there is no reason for those animals to love us and every reason
to hate us.
>>John:
>>"God" would know the basic laws of physics in the world
>>created by His computer, but that does NOT mean He "would
>>necessarily have a complete understanding of the entire
>>workings of that simulation". In the cellular automation
>>universe of the "Game of Life" the physics is very simple
>>yet it creates extraordinary patterns of great complexity,
>>and the only way to figure out what it will do next is to
>>run it and see. You can learn the physics (rules) of Chess
>>in a few minutes, and spend a lifetime learning just some
>>of its ramifications.
>Michael:
>True, but that is using your human mind. We are talking
>about hypothetical hyper-beings.
No, the implications are much wider that that, it's true for any finite being.
In 1930 Godel proven that any logical system, such as a computer or a finite
mind, can not be both consistent and complete. Most will insist on consistency
so there are some things no logical system with a finite number of axioms can
solve, or to put it another way, there are some problems no computer can solve
in a finite amount of time. If we could identify what those un solvable we
could then ignore them and concentrate on problems that do have a solution,
but in 1935 Turing proved we can't do that either. There are some statements
that are either false of true but have no proof and we (or a finite God)
can't even tell what those statements are.
For example, take the Goldbach Conjecture, it states that every even number
greater that 4 is the sum of two odd primes (all the primes except 1 and 2).
Let's try it for some numbers:
6=3+3
8=5+5
10=3+7
12=5+7
14=3+11
16=3+13
18=7+11
20=3+17
22=5+17
24=7+17
26=7+19
28=11+17
30=11+19
This all looks very promising, but is it true for ALL even numbers? Checking
all even numbers one by one would take an infinite number of steps, to test
it in finite number of steps we need a proof, but I don't have one, nobody
does. The Goldbach Conjecture was first proposed in 1742 ( 1742=1729+13 )
and since that time all the top minds in mathematics have looked for a proof
but have come up empty. Well, perhaps we can't prove it because it's not true,
however modern computers have looked for a counterexample, they've gone up to
a trillion or so and it works every time. Now a trillion is a big number but
it's no closer to being infinite than the number 1 is, so perhaps The Goldbach
Conjecture will fail at a trillion +2 or a trillion to the trillionth power.
It's also possible that some brilliant mathematician will come up with a proof
tomorrow, as recently happened with Fermat's last theorem , but there is yet
another possibility, it could be un- provable.
The Goldbach Conjecture is either true or it's not, Godel and Turing never
denied that, the question is, will ever know if it's true or not? According
to Godel some statements are un-provable, if The Goldbach Conjecture is one
of these it means that it's true so we'll never find a counterexample to prove
it wrong, and it also means we'll never find a proof to show it's correct.
Turing showed that if If it's un-provable we will never know it's un-provable,
Godel just said that such statements exists but we can never positively
identify one. A billion years from now, whatever hyper intelligent entities
we will have become will still be deep in thought looking, unsuccessfully,
for a proof and still grinding away at numbers looking, unsuccessfully,
for a counterexample.
We could avoid this fate if we at least prove that it's either untrue or
un-provable. If we could do that we still wouldn't know if it was true or not,
but it would tell us to stop spinning our wheels by trying to prove it and we
could turn to other things that we could prove. Unfortunately Turing showed 5
years after Godel that even that was not possible.
If we get frustrated enough could we just add Goldbach as an axiom? Not a
good idea, great care should be exercised before you add an axiom, otherwise
some day you could find out that The Goldbach conjecture is untrue but we
find a proof anyway: The conclusion is ...Disaster!!! Mathematics is in BIG,
BIG trouble, it's inconsistent, and that's much worse than just being
incomplete. Mathematicians must be incompetent, for they have utterly
botched the foundations of their science by building mathematics on a base
made of sand. They should be looking for a new line of work, something
they're better at, I hear there are openings at Burger King. Fortunately
this scenario is very unlikely. Consider the other possibilities:
1) The Goldbach conjecture is true and it is possible to find a proof:
In this case adding Goldbach as a Axiom is unnecessary and inelegant.
3) The Goldbach conjecture is untrue but we add it as an axiom: Bad idea, now
you've made mathematics inconsistent, think of the embarrassment when some
computer finds a number that violates Goldbach, your axiom.
3) The Goldbach conjecture is true but unprovable: In this case it would be
a great idea to add Goldbach as an axiom because then your axiomatic
system would be more complete and just as consistent. The only trouble is,
if it's unprovable you'll never know it, so it's just too dangerous to take
the chance.
>Words mean what you say they mean........
Yes, but if you're using a word it a unusual way you must define it for me.
On the other hand I will never ask you for a definition of the word
"definition" because If I already know then it would be a waste of time, and
if I don't your answer would be meaningless. If you use a word I'm unfamiliar
with, like klognee, I certainly won't ask you for the klognee of "klognee".
John K Clark johnkc@well.com
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