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#2 Re: Help Me ! » Solving systems of DEs » 2011-03-07 00:05:44

If you did a change of variables

remains unchanged.
You know how to solve

(eigenvectors right?)
so what would that change of variables have to be to put the equation in this form?

So we only need:

So if
is invertible, let:

Then you can solve
and then go back to the original variables by sending:

#3 Re: Help Me ! » Group Theory: Symmetric group and Alternating group » 2011-03-06 07:47:18

Consider the two groups as permutations of points on a plane or something.
You could visualise A6 as all the even permutations of the points of a hexagon.
Take 4 of the points on a hexagon, then can you get all permutations of those 4 points in A6?
All the even permutations are obvious, and the odd ones can be made even by swapping the extra 2 points you didn't choose!

#4 Re: Puzzles and Games » SETI Decoding Challenge » 2011-03-06 07:38:25

Would you even need an auditory organ to get music? It would be transmitted as an electromagnetic wave, so it isn't a given that it should be converted into sound. It could be converted into a visualisation or vibrations or something else. It's conceivable that a biological organ could exist which can directly pick up radio waves.
I don't think music could send any practical message other than- hey we exist and we like this kind of patterns. It's not even necessary that an ETI would appreciate music...

#5 Re: Puzzles and Games » SETI Decoding Challenge » 2011-03-06 07:23:55

That reminds me of an interesting question.
Would there be any value in sending a signal of music to an extra terrestrial intelligence?

#6 Re: Puzzles and Games » SETI Decoding Challenge » 2011-03-06 07:20:26

Thanks for the welcome!
What do you mean? Is that a satirical comment about modern music?!

#7 Re: Puzzles and Games » Let's make triangular numbers. » 2011-03-06 02:21:55


note these triangular numbers go:
...,45,55,66,78,91, quite cool that 4,5,6,7,8,9 appear in order with no interruptions!

#8 Puzzles and Games » SETI Decoding Challenge » 2011-03-06 02:10:40

Replies: 7


Check out the SETI Challenge:
It has some decoding challenges, where you are presented with a made up signal from an extra terrestrial source, and you must try to decode what it means.
Good luck!

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