…is always light

Author Archives: Markus

Just a short post on my and my girlfriend’s Christmas together in 2017.

It’s been almost a year and we are planning in piece and quiet our next Christmas.

The most important thing in the coming Christmas is, that we spend it together. Our plans are to make it some kind of quiet Christmas with lots of reading.

At the moment there is snow in here, but let us hope, that there is snow in the land also in Christmas. 🙂


Two shows what even is;
everywhere where it fits evenly,
it exists;
and so is even that,
where two evenly fits.

So many are there twos in a number,
than the relation possible with two evenly is;
if that possible is.

For if it impossible is,
even number not is.

To eight goes two four times;
To six slips it three times;
To four it fits twice;
To zero it doesn’t fit;
No pairs are there in zero.
No trace of two.
”Where’s my pair?”
Zero asks…

Sometime in 2008 I heard music while sleeping. In fact it was me composing music in a dream. I always manage to do things in my dreams better than when I’m awake. The first time I composed music in my dream while sleeping, was when I was 15 years old.

The Amiga has only 4 hardware music channels. In my dream I had more advanced Amiga, that had 5 hardware channels and I composed with it music that I can’t really even imagine, when I’m awake — the music composed in my dream was beyond my ability to make music…

In 2008 I tried to put the notes together that I had heard in my dream. This is the result:

Sometimes when I’m programming in my dreams I feel that there is something, that I must program. I see the result of programming while sleeping, also the code and I experience myself thinking how to program something..

Sometimes when I’m over stressed in programming when I’m in fact sleeping, I suddenly realize that I’m not awake — I’m sleeping and I don’t have to do anything at all! …or do I still have to do all that? …even stress myself while sleeping and having a dream.

Those are moments when I experience somehow, that I have control over my dreams while sleeping…

Sometimes while sleeping and having a dream it takes a while to realize that I’m now  not awake, this is only a dream. Though, I’ve started to think, that can I really say about my dreams, that they are only dreams…

I’ve had many nightmares where I’m haunted by demons.. Often in those nigthmares I’m also blind and can’t see my enemies — the demons — who attack me in number of ways… Once I fell off my bed to the floor and I woke up. In my dream I was dodging a demon impaling me…

It’s over midnight here.. Since the source code in one of my videos is not very readable, I decided to publish the Python source code of the video in this blog post.

import turtle

def draw_curve():  
   window = turtle.Screen()  

def vonKoch(turt,depth,length):
    if depth == 0: turt.forward(length)


That’s it for now. Time to go to sleep.

There are finite number of letters. If we limit the length of a word to finite amount of letters, the number of all possible words is also finite.

If there were infinite number of letters in a word and this word consisted of infinite amount of sounds, the pronunciation of a word would never end.

As there are finite number of words, also the number of consepts formed from these words is finite.


On the other hand, if we would create consepts in mathematical way, we could have infinite number of consepts. Though, all of them couldn’t be explicitly ever written nor said in finite amount of time.

I’ve sometimes wonderd, that how many meaningful natural languages of humans’ from all of these finite number of words could be formed — also how many grammars. What we understand by “meaningful language” might be hard to define…

Let us examine numbers as distances from some number.

If we choose as starting point the zero (0), we have the usual case.

0 = |0 – 0|
1 = |0 – 1|
2 = |0 – 2|

n = |0 – n|

Each distance can be divided into parts, let’s think the number space as the familiar set R. For example the distance from zero to two can be divided in n parts, we get distances 2 / n between zero and two.

The point from which we started isn’t a distance but — like said — a point, that can’t be divided into smaller parts. Philosophically speaking this point is now in words of Democritus “atomos”, the smallest unit.

In the book “The way to geometry” it is said: “The magnitude of a point is zero.”

When we founded the numbers as distances in relation to zero, the zero point is indivisible; because in question is a point not a distance, dividing zero (a point) by any number, we get zero. Zero doesn’t get smaller by dividing.

Of course zero can’t be divided by itself. In distance interpretation philosophically speaking indivisible would be divided by indivisible.

Now zero is different from other numbers so that it is a point, the other numbers are distances from this point.


As distance interpretation we could start the numbers also in relation for example to number eight (8).

Now eight is a point, we get the other numbers as distances to number eight.

0 = ||8 – 8| – 0||
1 = ||8 – 8| – 1||
2 = ||8 – 8| – 2||

n = ||8 – 8| – n||

Here from number eight is “created new zero”. First we determine the distance of number eight from itself, then the distance of examined number from the determined distance earlier..

We could get the numbers (distances) and the zero point also by denoting:

0 = |8 – (8 + 0)|
1 = |8 – (8 + 1)|
2 = |8 – (8 + 2)|

n = |8 – (8 + n)|

When we see the numbers as distances from some number, we notice, that the distance can be divided into smaller parts, but the point from which we started, we can’t divide into smaller parts.

In our example when we started from eight, we examine first the distance of eight from itself, |8 – 8| = 0, which is and remains as zero.

The distance can be even or uneven, but the point from which the distance is determined can’t be even or uneven, that is the whole point of this post.

If we want also the negative numbers as distance interpretation, we simply put the minus sign before the determined distance, for example -2 = -|0 – 2| and this is how we can get the entire set R so that the distances from zero point can be divided into smaller parts, but zero point is and remains zero and is not a distance but a point. In the words of Euclid that which has no part. In my own words: “Indivisible”.

In this way the specialty of zero can be seen better.