Anatomy of a Pattern of Very Very Large Numbers

What happens when you take a number and raise it to the power of itself, then increase that number by one and raise it to the power of the new number, and keep increasing like that? You quickly start to get very very large numbers. Surprisingly, the ratios of those increasing numbers converges on a well-known mathematical constant. This video examines not only that convergence, but also the computational requirements for proving it.