Math Fail

Make a triangle of numbers in which the leftmost column is the sequence of prime numbers and each other number is the absolute value of the difference of the two numbers to its left:

  2
  3 1
  5 2 1
  7 2 0 1
 11 4 2 2 1
 13 2 2 0 2 1
 17 4 2 0 0 2 1
 19 2 2 0 0 0 2 1
 23 4 2 0 0 0 0 2 1
 29 6 2 0 0 0 0 0 2 1
 31 2 4 2 2 2 2 2 2 0 1
 37 6 4 0 2 0 2 0 2 0 0 1
 41 4 2 2 2 0 0 2 2 0 0 0 1
 43 2 2 0 2 0 0 0 2 0 0 0 0 1
 47 4 2 0 0 2 2 2 2 0 0 0 0 0 1
 53 6 2 0 0 0 2 0 2 0 0 0 0 0 0 1
 59 6 0 2 2 2 2 0 0 2 2 2 2 2 2 2 1
 61 2 4 4 2 0 2 0 0 0 2 0 2 0 2 0 2 1
 67 6 4 0 4 2 2 0 0 0 0 2 2 0 0 2 2 0 1
 71 4 2 2 2 2 0 2 2 2 2 2 0 2 2 2 0 2 2 1
 73 2 2 0 2 0 2 2 0 2 0 2 0 0 2 0 2 2 0 2 1
 79 6 4 2 2 0 0 2 0 0 2 2 0 0 0 2 2 0 2 2 0 1
 83 4 2 2 0 2 2 2 0 0 0 2 0 0 0 0 2 0 0 2 0 0 1
 89 6 2 0 2 2 0 2 0 0 0 0 2 2 2 2 2 0 0 0 2 2 2 1
 97 8 2 0 0 2 0 0 2 2 2 2 2 0 2 0 2 0 0 0 0 2 0 2 1

Notice the pattern of 1′s running down the right side? Gilbreath’s conjecture states that it continues like that forever.

If you want to see proof of another sequence of integers that continues forever, go to http://11011110.livejournal.com/212920.html and you will find the Python source code used to make it happen and the reasoning behind it.

Baseball isn’t that interesting in and of itself, but if you add a speed variable into it, it’s a whole other story.

What would happen if you tried to hit a baseball pitched at 90% the speed of light?

Let’s set aside the question of how we got the baseball moving that fast. We’ll suppose it’s a normal pitch, except in the instant the pitcher releases the ball, it magically accelerates to 0.9c. From that point onward, everything proceeds according to normal physics.

The answer turns out to be “a lot of things”, and they all happen very quickly, and it doesn’t end well for the batter (or the pitcher). I sat down with some physics books, a Nolan Ryan action figure, and a bunch of videotapes of nuclear tests and tried to sort it all out. What follows is my best guess at a nanosecond-by-nanosecond portrait:

The ball is going so fast that everything else is practically stationary. Even the molecules in the air are stationary. Air molecules vibrate back and forth at a few hundred miles per hour, but the ball is moving through them at 600 million miles per hour. This means that as far as the ball is concerned, they’re just hanging there, frozen.

The ideas of aerodynamics don’t apply here. Normally, air would flow around anything moving through it. But the air molecules in front of this ball don’t have time to be jostled out of the way. The ball smacks into them so hard that the atoms in the air molecules actually fuse with the atoms in the ball’s surface. Each collision releases a burst of gamma rays and scattered particles.

These gamma rays and debris expand outward in a bubble centered on the pitcher’s mound. They start to tear apart the molecules in the air, ripping the electrons from the nuclei and turning the air in the stadium into an expanding bubble of incandescent plasma. The wall of this bubble approaches the batter at about the speed of light—only slightly ahead of the ball itself.

The constant fusion at the front of the ball pushes back on it, slowing it down, as if the ball were a rocket flying tail-first while firing its engines. Unfortunately, the ball is going so fast that even the tremendous force from this ongoing thermonuclear explosion barely slows it down at all. It does, however, start to eat away at the surface, blasting tiny particulate fragments of the ball in all directions. These fragments are going so fast that when they hit air molecules, they trigger two or three more rounds of fusion.

After about 70 nanoseconds the ball arrives at home plate.

Want to know what happens next? Go to XKDC.