Known limitations, why it does not always works?

Imagine you have a speed and you add speed because you want to know the speed of a bullet fired at .5*c in a space ship travelling at .9*c.

What happens?

Well, you have a problem by finding a speed greater than the speed of light in a fixed referential.

The big question is: is the bug located in the composition of the vectors or located in the norm?.

We have a very fast answer::

>>> ### let's compose the speed and see
>>> bullet.speed= .5 # expressed in ratio of c
>>> spaceship.speed = .9 # expressed in ratio of c
>>> spaceship.speed + bullet.speed

The problem should be solved at composition level. We have left euclidian geometry, and we know work in a space were transaltion of vector are bound by Lorentz transformation.

So, the limitation is in the substraction/addition?

Well not.

Well, this example not as funny as measuring the distance at which you place the army in case of a zombie invasion in a square city (looking like a matrix).

Given a speed of 1 block per hour (zombies are slow), we want to where to post our valiant anti-zombie task force. We want to be able to test if a given human will be in zombie range in n hours.

Given that I am lazy person, I only make a nice draw to illustrate the problem:

And I give the solution. In this case: you change abs for any given vector.

Instead of::

>>> abs = lambda x,y: ( x**2 + y**2 ) ** .5

You write::

>>> abs = lambda x,y:abs(x) + abs(y)

I am really speaking of zombies only?

Well, no.

If you push hard enough the precision of your computer, your reachable values are discretized, thus, it is also how your 2D vector will look.

Have you noticed that the stuff I draw are circles.

These are squares.

Thus the value of Pi is changed (when a circle is a square there are odds that pi is not an irrational number anymore), so is the distance logic.

Most time, you don’t care. I guess only 1 out of 100 000 developers will be bitten by this problem in their whole life.

So cool down, it is just an illustration of computers limitation.