Arithmetic, Population, and Energy - by Albert A. Bartlett - Fascinating yet simple illustration of why continued growth (of the population, of oil consumption, etc.) cannot go on forever. Intuitively, that much is obvious. Not so obvious is how near impossible it is for us (as a society) to recognize when we've gone too far, when our resources have been consumed to the point that it's too late to do anything about it.
The reason it's hard to recognize that point has everything to do with the simple yet profound implications of how compounding growth rates behave. Compounding growth rates are our friend when receiving interest. Compounding growth rates are our enemy when it comes to consumption and population growth.
This third video of the series carries a devastating message. The core problem of our unsustainable economy is the rate of population growth and the rate of resource consumption. When we think about China and India and their impact on global consumption in the coming years, it's essential to remember that what brought us to this point was U.S. consumption.
Euclid's Proof - Prime Numbers are Infinite - Found this on Burton MacKenzie's blog post Prime Motivation. I marveled at the simplicity of the Euclid's proof that there are an infinite number of prime numbers-- or more precisely, that there cannot be a largest prime number. The bonus is the Euclid proves this point by assuming there is a finite number of prime numbers. Actually, as I think about it, the only way to prove anything is to structure the hypothesis in such a way that it's antithesis can be disproved. Nassim Nicholas Taleb got into the in his book The Black Swan. Below is Burton's summary of the proof.