Outside the Blur

About 3 years ago I begun listening the weekly show of Armin van Buuren, A State Of Trance. I remember that it was ASOT 182 when the ritm caught me. I was amazed by his style and extraordinary capacity to compile such many compositions in one show of 2 hours. I was in a very difficult period and I believe that his music has improved my mind and my psychic.

After I while I observed that when I’m listening the brain make new connections, and new ideas comes to me. It was a very stimulating, very optimizing source. And it was a very good quality music. Before I listened also many genders of music beginning from classics and opera to heavy metal. The progressive trance of A State of Trance is very powerful, it has many elements of classic, pop, and rock music combined with a good style and sense being in the same time also euphoric and relaxing.

It seems that you escape for a while from this world, from this reality and a new temporary reality it is formed just by listening this music. The advantage is that when you take of your headphones all this world disappears. The effect will not last and it will not harm your own reality or the interactions with other people. Is just a music for the spirit, It will not harm your brain.

I discovered so many things just by listening this music that I am still amazed. I believe that this new style of music is a revolution in music and it is one of the most advanced. It’s a source of inspiration and a liberty of thinking.

Look here for a small mathematical problem that was concerning me somewhere in the high school.

It is called Zeeman’s problem. But i think that the problem was also posed by some antic philosophers.

The problem sounds as follows :

Suppose you want to pass accros the street. You pass a half. So it rests you another half to pass. You pass another half of this half and it rests you one quarter. You pass a half of this quarter and it rests you an eighth of the total distance. You pass a half of this eighth and it rests you a 16th part of the road.

It seems that you’ll never reach the destination and some car will hit you because you didn’t passed the road.

But how can we solve this interesting problem? It’s obvious that we’ll always have a small part to cross, even if it is very very small. The mathematics resolved this problem centuries ago (16 th century).

Look here for a Solution (there are of course others) :

We observe that we always have halves. We have :

1/2, 1/4, 1/8, 1/16, …, 1/n

So basically they are powers of 2 :

2^-1, 2^-2, 2^-3, 2^-4,…, 2^-n

Or :

1/2^1, 1/2^2, 1/2^3, 1/2^4,…, 1/2^n

If we add them arithmetically we see that it’s always missing a unit of a number power of 2 :

for example : 15/16+… . It is missing a 1/16.

If we have n=8. We’ll find that we have crossed 255/256. It rests 1/256 still to cross

But we want to find which is this small part when the n increase to infinity.

We must prove that when n increase to infinity this small part is 0. The part that it rests us can be written as 1/2^n.

And the mathematics has a way to say this :

lim 1/2^n = ?

n->oo

Well, the answer is very simple. The result is 0. The missing part is 0 if n increase to infinity.

So the answer is :

lim 1/2^n = 0

n->oo

And you have passed the road. You are safe now. No car will hurt you.