Define, Observe, change and resolve Chaos.

Current Problem

To define it, we'll take the definition State of total confusion with no order, but as we also consider a dice throw as random we can se that we've made a mistake somewhere, like how something that we create can't be define properly, as long as 1 + 1 will always be equal to 2, we can state that two things added together will produce the same thing over and over, but in this case apparently not, so, what are we missing ?

Lazy avoided calculus, define the Chaos

When i throw a dice or a coin, i state that the face on which it will drop is random, but also we know that if the object is perfectly shaped, it has a fixed chance to drop on a certain face and if we throw it over and over the number of times the face drop should come along a fixed value.

Now we know that two thing mixed together will always produces the same thing, and that the result is a fix value that can be "predicted" before any throw, but the thing in between is fully random and that is causing a disturbance in the result.

How is that possible ? How can we manage to know all the data from a throw but manage to be completely blind about the result ?

Blindfolded resolution

To figure this out, i'll take as an exemple two people on each side of the door, one looking from the hole and the other one looking 1m away.

We've all been in this situation and we know that we know much more when we're directly sticked to the door than far from it. And so as someone who know that the 2 peoples don't have the same information due to our statement, we can statue that the far one don't know that the other can see him. and so we don't have 2 but 3 points of view :

• Close one
• Far one
• Spectator

The Far one don't know anything beside his space, but don't even know there is 2 space.

The Close one know there is 2 spaces and know each one.

The Spectator knows what the twos know.

So if the far one is us, throwing a dice, the close one is something we're looking for, and the spectator is the world "computing" the throw.

We know that it truly exist something that we don't take in our calculus when we try to predict the dice throw. And thus lead to the theory that if something rules a throw, it therefore know all the rules it put in it, which is pretty logic.

And in our case, the dice is being pulled over by gravity and a thousand other forces that changes our variable and false our result.

This is why we had the wrong answer when we try to predict the result, we didn't take every variable into consideration because we were not looking from the good point of view.

This mean that the random part, were only something that we didn't consider before.

So we can now state that random or chaos is :

1st Law : Chaos is sum of all thing we don't consider in a process.

So we can guess what's random ? Observing other Chaos

This statement is not completely dumb nor it is truly false, i mean if we look at it, we said that we could guess something as random as a dice throw, so if we took the time to take in our calculus every forces, guess on which side a dice would roll. What's really usefull is to think that when we don't know theses parameters we assume that every face have a chance to be land on. And therefore that every state are plausible, which lead to the next important part.

MVD, the MultiVerse of the Dice

Let's have a look at the multiverse, a theory that say that it exist paralel universe where thing get a little bit different, by the time we can assume that like the Hilbert hotel, more and more multiverse are created or already exist (same thing there), because as we go forward in time, event goes by and multiples solution too, if i get a new car, each color could be a new multiverse with only this difference.

Now let's go back to our dice, before we throw the dice we state our probabilities to land on each face, which mean even if the probability is 1% , it exist, this lead to 6 different univers. And now a tricky things is that if i throw a coin beside that, we could say that it exist 24 univers, 6 for the dice times 2 for the coin, and times 2 for the order of the throw (dice - coin, coin - dice).

This part is interesting because if we look at the event as major thing, there is clearly 24 univers. But if we only look at the interesting part we only land with 12 univers. This mean that :

2nd Law : 2 univers can be the same from the data we're choosing.

So it's mean that in the lottery when all numbers are picked up, the next one could be one out of 44 different, it doesn't matter as long as we only need 45, and therefore all numbers after the fifth would be the same, because it's not apart of our calculus.

Take a rest, Changing Chaos

Now, if we look at a series of random number, like :

-1 -2 -3 -4 ...

At first sight you may be thinking that it's not random, if so it mean that you forget our first law Random is sum of all thing we don't consider in a process., and there we don't took the next number in the process. This mean that our series might as well be followed by a -5 than a -6, and this would not be random, because we would know that.

So what it mean is that every random series of number are random because we don't know the rules that state them as the Spectator would do.

But ! As our 2nd law says, 2 univers can be the same from the data we're choosing., and so we could change of univers to make the hole in the door more obvious to see, for exemple :

Consider that we're adding 2 series of numbers :

- 2 4 6 8 10 12 14 16 18 20

- 1 2 3 4   5   6   7   8   0  0

There we can easily define the first function as : f(x) = 2x in [ 1 ; 10 ]

The second one is a little trickier to guess, as the last numbers are 0, and we all se the straight function f(x) = x.

But what our laws tell us is that : 1st law allow us to define our random, that we will state as the 2 last Zeros.

And our 2nd laws say that every univers are built on the same base and can be mixed up as long as the data we're choosing stay the same. So i can say that we're only taking the first 8 numbers and change the last ?

Like this i can rewrite my sum of numbers series as :

- 2 4 6 8 10 12 14 16 18 20

- 1 2 3 4   5   6   7   8   9 10

And define my second function as : f(x) = x in [ 1 ; 8 ]

Thus i ended up being able to add 2 series of number i didn't knew the definition just by swapping one of them for another ! I know this one might be a little easy but let's have a look at something more tricky.

Sit down and take a coffee. Resolving Chaos

Now it's time for us to end our journey by manipulating a number sequence to be readable only by us Spectator of our self chaos ! That's sound great. So let's get deep further in our univers manipulation and let's set a new univers for each number we choose.

Let's get this clear, let's put some more specific rules to state number in our sequence, imagine that we're getting this sequence :

x :    0 1 2 3

f(x) : 1 0 0 0

This one is pretty easy, when x = 0, f(x) = 1, otherwise it's equal to 0. So we can define the function by :

f(x) = - ⌈ x / (x+1) ⌉ + 1

but it's working for our local function, if we try to extend it a bit to the right it work as the limit of the function in +infinity is 0, but we juste move the function a little bit to the left.

So as our 1st law says that it exist another function that do the same, so let's says we don't know it and we don't know of to get it. What can we do ?

We can look at the number that compose X, and says that the sum of every digit has to be 0.

Look everything like the previous but now we can manipulate it as we want and add near empty universe to make a custom one.

You can rest now, Goal of that

Like this we can achieve the success to find the function that look like :

- 1 2 3 5

But we can go far away as is we use binary over base 10, we can use Karnaugh table to make easier to format. Then with a little bit of format and optimisation we ended up with a script that can turn any series of number, into multiple univers that we define by making Karnaugh table out of it to sum into a single one.

As i said with a little bit of optimisation we can find more obvious function and prettier one too, like this one, which is the sequence of negative number :

The Equation i'm most proud of, beside the prime numbers.

The main goal is to create logic where we can't find one, like if we take some unsolved problem like the division or the absolute value in binary which run through a whole program in your computer, we can define a function for the first 8 bits (256 values), and then look a the schema the function does, and make it general for the whole infinity ! And so, we ended up turning a whole program into a physically O(1) program going electricity speed.

And it work for any series of number, and as we can anything as a series of number, this can optimize everything or find a way to link any series into a logical way, i used it to make a CPU and GPU with this as i turn the Bresenham algorithm into a O(1) algorithm and it turn out it make the process 20 to 30 times faster only for the line calculation part. This could improve our computer by the same ratio if we used it.