Unnecessary Obstacles Make Games

As a golfer, you have a clear goal: to get a ball in a series of very small holes, with fewer tries than anyone else. If you weren’t playing a game, you’d achieve this goal the most efficient way possible: you’d walk right up to each hole and drop the ball in with your hand. What makes golf a game is that you willingly agree to stand really far away from each hole and swing at the ball with a club. Golf is engaging exactly because you, along with all the other players, have agreed to ma...

 Proof That the Set of Prime Numbers is Infinite

Theorem: There are infinitely many prime numbers. Proof: Suppose, contrary to the theorem, that there is only a finite number of primes. Thus, there will be a largest which we can call p. Now define a number n as 1 plus the product of all the primes: n = (2 X 3 X 5 X 7 X 11 X...X p) 1 Is n itself prime or composite? If it is prime then our original supposition is false, since n is larger than the supposed largest prime p. So now let’s consider it composite. This means that it must be div...

 Definition of Plank's Constant

Just as you can't have one-third of a penny or two and a half quarters, Planck declared that when it comes to energy, no fractions are allowed. Now, our monetary denominations are determined by the United States Treasury. Seeking a more fundamental explanation, Planck suggested that the energy denomination of a wave—the minimal lump of energy that it can have—is determined by its frequency. Specifically, he posited that the minimum energy a wave can have is proportional to its frequency: ...