Skillful Observer

Archive for April, 2008

Free will … yeah right.

Montag, April 14th, 2008

Many people take free will for granted. In fact, many legal systems around the world are based heavily on it. But see, i have a problem with that. Noone can tell what free will actually is and in what cases it is blocked (migitation of punishment) or how it work’s or is formed.
I read an article today about scientists that use brain scanners to see how decisons are buildt. They claim that they can’t find anything related to free will at all, because they can detect and even predict decisions way before people think they made them. This leads to the severe question what the hell this free will thing is everyone is talking about. If it doesn’t exist, what the hell do judges rule upon?

But what really concearns me the most is, that people at the very source of this research are in themselfs so insecure about their findings that they are throwing all kinds of apologetic statements at journalists interviewing them. Want an example? Here you are:

Maybe free will enters at the last moment, allowing a person to override an unpalatable subconscious decision.

What the hell man? You just found out what people are speculating for a long time and try to debase it in the same breath? What’s wrong with drawing logical conclusions?

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Maths WTF?

Mittwoch, April 2nd, 2008

You know complex numbers right? Where a
complex number
$i=sqrt(-1)$
Now what happens if you want to know the outcome of
$sqrt(-1)^{\tiny{\sqrt(-1)}}=??$

This is where the fun begins. Euler gave us this great tool
$e^{i \pi} = -1$
which becomes
$e^{\frac{i \pi}{2}}=-{1}^{1/2}$
simpyfies to
$e^{{\frac{i \pi}{2}}}=i$
and because the logarithm is valid for complex numbers
$\frac{i \pi}{2}=ln(i)$

Because power works a litte different for complex numbers
$z^\omega=e^{\omega \ln(z)}$
you end up with
$i^{i}=e^{i ln(i)}$
and we know that
$i\frac{\pi}{2}=ln(i)$