Strictly speaking, this is not a commentary on Quantum Integer Programming (QuIP), but rather a prequel.
And an exemplar of the interplay of elementary mathematics and unusual insights in physics.
You may recall an earlier post of mine on Wicked Problems.
I introduced my concept of maximally inverse in my talk at the Collective Intelligence conference.
In the context of inertial frames of reference (“constant velocity” frames):
Newton: Time is the same; Speed is relative.
Einstein: Speed (of light) is the same; Time is relative.
As you can see from the simple math I worked out at the top of the post:
A Ferrari passes a standing observer, and at that instant of passing, the Ferrari driver shoots a pellet of light towards the ceiling of the car.
Newton would have analyzed the situation with the light pellet (he called it corpuscle) assuming that its x-velocity in the Ferrari is v larger than it would have been if it was instead shot by the standing observer.
Not so, says Einstein. It is just c, not c+v. It does not matter what v is.
So, if c is the same as v changes, something else has to give. What?
This is Special Relativity in a nutshell.
Everything else that follows (including E = mc2) is a straightforward consequence of this unusual insight by Einstein.
If you want to see the steps to get to the most famous equation ever, I have also included it in the gallery at the top of the post (scroll right).