0.999… repeating (or 0.9‾0.\bar{9}) is equal to 1. It’s a fact. To some, this is highly counterintuitive, unbelievable even. I’ve seen various explanations for how it works, from informal explanations to formal proofs. I recently found an interesting (not original) proof, but first I’ll give a couple less rigorous explanations. Informal arguments Tripling a third…
Tag: explained
The barber shop pole illusion explained with math
This is a well known optical illusion in which rotation appears to be vertical motion. There are several aspects of the barber pole design which make the illusion more effective, including having multiple stripes, making the stripes different colors, and using rotation. We will strip these things away in order to see what is happening…
What is the Second Law of Thermodynamics?
The Second Law of Thermodynamics is one of the most misunderstood scientific laws. Stated briefly, the law says that entropy increases over time in an isolated system. The misunderstanding can come partly from not knowing what an isolated system is, but mostly comes from not knowing what entropy is. What is entropy? First, entropy is…
thoughts on mind 