A gentle re-introduction
So I've decided to try and blog more frequently about the great and interesting world around me, and what I learn from it.
I'll very gently start my engines by saying that I heard something interesting from E. today that divide-and-conquer algorithms differ from things like Gauss' kindergarten adding technique* insofar that the divide-and-conquer algorithms perform the same trick on progressively smaller buckets while Gauss' technique involves an intellectual re-expression of the problem. This feels like a subtle but interesting view on the topic.
"You can entertain, confuse, and make small children cry with this problem."
(with regard to the Bridges of Konigsberg Problem)
I've also learned about innate learning modules in animals (Bees! All of my linguistic readings are indeed covered in BEES.) and how there is a hierarchy between senses (odor > color > shape) for the bees. Additionally, it is difficult train animals into behaviors that are misaligned with their "functions". For example, pigeons can be trained to peck at things for food, but it is harder to train them to hop for food. (The opposite goes for noises and whatnot.)
C. told me about the Cantor set today, where you take a line segment between the closed interval [0, 1], cut out the middle 1/3, and continue to do so for the remaining segments ad infinitum. You can sum up the remaining segments as a geometrical progression... and get 1. Additionally, in spite of removing chunks of line segments, the set has the same amount of points after as before, and is thus an uncountable set. The Cantor set is apparently useful for breaking people's theories.
There . I still remember Prof. H. bringing up Cantor's diagonalization during a lecture in Syntax II last semester, which is tantalizingly on the tip of my tongue. Must find it in my pile of notes.
Additionally, I learned that when water mains are repaired, the water pressure will be higher after the fact. Unpleasant things may happen as a result.
*For numbers 1..n, the sum can be expressed as (n(n+1)) / 2
