QoW Update - comic for 12/20

There are no monkeys in here. Really.

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ACK!!

Postby Koukonei_crazy on Wed Dec 22, 2004 8:52 am

[color=darkred][/color][b]I really want Kestral to be with this guy!! she needs a nice boyfriend and somthing to work out for her!! please God let this be him. :o [/b]
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Welcome

Postby HiFranc on Wed Dec 22, 2004 3:55 pm

Welcome to Queen of Wands and the forums, Koukonei_crazy.

{edit} Sorry, wrong strip. :oops:
Last edited by HiFranc on Wed Dec 22, 2004 3:58 pm, edited 1 time in total.
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The new guy

Postby HiFranc on Wed Dec 22, 2004 3:56 pm

We don't know enough about him to know if he will be good for her. I still think she should be cautious considering their first encounter.
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Postby Ambystoma4 on Wed Dec 22, 2004 4:08 pm

I thik she should have her fun with it for the month that she is going to still be there.
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Postby Winkie on Wed Dec 22, 2004 5:59 pm

I'm not satisfied with his explanation of Godel. He's taking it to be all about relativism. I'm not saying that relativism has no place in mathematics -- it's kind of the basis of non-euclidean geometry -- but it's not what Godel's Incompleteness Theorem is about.

The essence of Godel's Incompleteness Theorem is this: No system of mathematical proof is complete. For every system of proof, there are things that are undecidable - things that the system in question can neither prove nor disprove. Other systems might have those undecidable propositions covered, but they'll have gaps of their own. It's not that there's no absolute truth, it's just that no system can describe the truth completely.

And this isn't just hippie philosophizing, either. Godel provides a recipe for constructing a statement that's true but not provable in a system of proof, given the system's rules. What it all comes down to is using the system to model itself mathematically, so you can construct statements about what the system can and cannot prove, and put those statement within the scope of the system itself. This way, you can construct a statement G that essentially says 'Statement G is not provable in this system', and there's your undecidable proposition. Note that G's undecidability does't mean that it's neither true nor false - in fact, because what it says is that it can't be proved within the system, its undecidability makes it true. But we only know that because we're reasoning outside the system.

There are life lessons we can draw from this. Mainly, humility. Godel reminds us that no one knows everything, not even in a field as sharply-defined as number theory.
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Postby GrassyNoel on Thu Dec 23, 2004 7:48 am

Winkie wrote:Other systems might have those undecidable propositions covered, but they'll have gaps of their own. It's not that there's no absolute truth, it's just that no system can describe the truth completely.

Aren't axioms supposed to fill the gaps? That is, assumed facts that can't be deduced from the theorems.
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Postby Sechen_Rob on Thu Dec 23, 2004 2:47 pm

GrassyNoel wrote:Aren't axioms supposed to fill the gaps? That is, assumed facts that can't be deduced from the theorems.

Axioms do fill in the gaps, but what Godel's incompleteness theorem says is that there are an infinate number of axioms. No matter how many you have, there are always more. The description in the comic is pretty close to how the proof works: if you have a set of axioms you can create a theorem that cannot be derived from them. Therefore, you can never have all the axioms.
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