Monday, November 17, 2008

incompleteness theorem

Grad pictures took years! I think it was cause of all my cards moves and such.

Owned: hey, I don't think i've been owned yet! =D

It seems like I did pretty well on my physics test part 2. Also, I must finish all 56 math identity questions for 1 bonus mark on my test. Also,... there's magic club tomorrow after school!

Ok, I'll be getting into the Incompleteness Theorem by Gödel. This theorem basically states that for any branch of mathEmatics (maple...) there is always something that is an exception. Let's see, umm, I guess an example would be something squared should always give an positive. But than we were all proven wrong by unreal numbers. So, this also reflects on generally anything, there is always an exception, so just think about it. When you think you won't be accepted into a university, you might be an exception. chew on that... So now, we can all go and prove our math teachers wrong when he/she says "this will work for ANY case!".

Here's an actual example from Gödel's page. This is pretty confusing.

"The proof of Gödel's Incompleteness Theorem is so simple, and so sneaky, that it is almost embarassing to relate. His basic procedure is as follows:

  1. Someone introduces Gödel to a UTM, a machine that is supposed to be a Universal Truth Machine, capable of correctly answering any question at all.
  2. Gödel asks for the program and the circuit design of the UTM. The program may be complicated, but it can only be finitely long. Call the program P(UTM) for Program of the Universal Truth Machine.
  3. Smiling a little, Gödel writes out the following sentence: "The machine constructed on the basis of the program P(UTM) will never say that this sentence is true." Call this sentence G for Gödel. Note that G is equivalent to: "UTM will never say G is true."
  4. Now Gödel laughs his high laugh and asks UTM whether G is true or not.
  5. If UTM says G is true, then "UTM will never say G is true" is false. If "UTM will never say G is true" is false, then G is false (since G = "UTM will never say G is true"). So if UTM says G is true, then G is in fact false, and UTM has made a false statement. So UTM will never say that G is true, since UTM makes only true statements.
  6. We have established that UTM will never say G is true. So "UTM will never say G is true" is in fact a true statement. So G is true (since G = "UTM will never say G is true").
  7. "I know a truth that UTM can never utter," Gödel says. "I know that G is true. UTM is not truly universal."

Think about it - it grows on you ..." - http://www.miskatonic.org/godel.html

Song/weird stuff: http://www.youtube.com/watch?v=3awjDvHNg8M

Some weird talent: http://www.youtube.com/watch?v=ea-ZqPvoQrg

Question of the day: Is there a number when multiplied by 2, the last 2 digits are still the same? Is it possible? Is there more than one answer (obviously...).(and does not end with zeros, thanks victoria)

4 comments:

xoSimple_Mindedxo said...

ROFLMAO! "Is there are number where when" Nice english there buddy...xD owned..

Jeffrey Tong said...

... don't buddy me!

J said...

What equation did you get for sin 18?

Jeffrey Tong said...

use sin(72)=blah blah blah.