Logic sometimes breeds monsters. Henri Poincaré In math, we often speak of things being “nice,” “well behaved,” “elegant,” or even “beautiful.” The flip side of this is those things in math which often remain in shadow: the unfriendly, the unruly, the awkward, and the ugly. In some cases, inelegant solutions are apparently unavoidable. In other…
Tag: Math
Probability estimation vs probability calculation
If I take the bus downtown today, what are the chances I’ll run into my friend (let’s call her Alice)? Suppose I’m on the bus for an hour. According to the local metro, there are approximately 31 people using a single bus per hour of operation. Assume that during the hour I’m on the bus…
The language of balanced parentheses
Grammatically, parentheses must be balanced, meaning every open parenthesis ‘(‘ must eventually be followed by a close parenthesis ‘)’. Parentheses can be nested, meaning there can be parentheses inside parentheses. If we were to take a piece of writing and remove all letters and punctuation except parentheses, we might end up with something like: ()()()(())()(),…
thoughts on mind 