Skillful Observer
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Ludwig Boltzmann > Albert Einstein

Dienstag, November 18th, 2008

Seriously!
Einstein taught us that time is just another space dimension. This showed us how gravity works and that our space in reality has 4 dimensions rather than 3. After hearing of this in school smart kids will feel like their eyes have been opened to a whole new world.

Almost unnoticed Ludwig Boltzmann slips by. Years befor Einstein he found the fundamental connection between the speed of the molecules and the temperature of a material. Previously, temperature has always been considered almost a mystical hidden variable. Slowly physicists discovered that temperature and physical work seem to be connected. But it took Boltzmann to find out that temperature of a material is nothing more than the kinetic energy of it’s microscopic parts. This picture seems so simple to us now that it’s kinda hard to understand what revelation this must have been. In my opinion, it’s certainly the least publicized breakthrough in physics.

So for me
Boltzmann > Einstein

video test

Montag, September 8th, 2008

A little test

(mehr …)

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)

HOORAY
i^{i}=e^{i (i \frac{\pi}{2})}=e^{-\frac{\pi}{2}}
and
i^{i}=0,207879576

Owned by Wikipedia.
Math is fun again o/