Godels theorem

[Radical Edward]

I've just been reading The Emperor's New Mind by Rger Penrose (A damn fine book, and one you should read) and it mentions a theorem put forward by a chap called Godel.

Basically, what he showed was, any precise system of mathematical axioms and rules of procedure, provided that it is broad enough to contain descriptions of somple arithmeic propositions, and provided that it is free from contradiction must contain some statements that are neither provable nor disprovable by the means allowed within the system.

This got me thinking about the universe generally, which can be represented as a mathematical set of rules... would the same apply? would there be things that can not be proved within the system, or is my understanding of this theorem somewhat flawed? I haven't really been able to look it up anywhere, and if anyone could mention a decent source, that would be most helpful

[Ragnarak]

been a while since i read that book but what context is he talking about this in?

(the artificial intelligence/computer mind isn't it?)

 

wouldn't that be an example?

 

when i read it i understood it to imply the same as you

[Radical Edward]

he's talking about it in the sense of mathematical theorems, I don't think he really implied what I thought.. I could quote whole passages, but there wouldn't really be much point

[NSX]

Well, as far as we know, the Math works for us.

 

I'm reminded of a display in my Physics Text:

They talk about 2 experiments:

Both involve bombarding a golf ball with something or another to find out what it's like [mind you, we're not supposed to know its a golf ball].

 

1. They bombard it with balls roughly 1/10 the size of the golf ball; some of the balls hit @ an angle, causing them to change direction; thus, we know there is a curvature.

 

2. They bombard it with balls roughly 1/1000 the size of the golf ball; balls also hit @ an angle, but this time, we are able to detect the small indentations on the golf ball, as well as realise its' curvature.

 

Anyways, long story cut short:

I think that our mathematical / arithmetical / geometrical view on our Universe is like trying to travel @ the speed of light:

THat is, we can get ever & ever so close, but never the actual thing.

[JaKiri]

Eh NSX?

[NSX]

Originally posted by MrL_JaKiri

Eh NSX?

 

Well, in a nutshell, I was saying how we can only get a picture of things around us based on what we are given. There is no way [currently] for us to gain an absolute view on the world around us.

[liarliarpof]

If you like Sir Roger's work, perhaps consider simply moving on to his 2004 book, 'The Road To Reality'. Godel receives rather short schrift, but there is much rich fodder in this 1,000p. tome. For a well done, and quite accessible introduction to Godel & his work, try Rebecca Goldstein's outstanding book, 'INCOMPLETENESS The Proof and Paradox of Kurt Godel'.