Formal Mathematical Proof

Red Roses Blue

Context Free Gramma

Neuroplasticity

Lispy Lisping Lovers

Platonic Love

The 5 platonic solids are tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron. They are the only 5 convex regular solids possible. Being convex means The solid doesn't cave in or protrude. A cube is convex, but a christmas star is not.

Plato thought the first 4 solids are related to the 4 classical elements, fire is tetrahedron, earth is hexahedron, air is octahedron, and water is icosahedron. Plato had his philosohical fantasy why this is so. He didn't really know what dodecahdron is related to.

Anorexia Nervosa

Pumping Life

The regular expression is a way to express patterns in a string of letters, like all strings alternating between a and b ("ab", "abab"). The "pumping lemma" means that certain kind of patterns if they describe a long enough string, it must be that it's a repeating pattern. So given a string that fits a pattern, it's possible to lengthen the string to however long you'd like, by repeating a smaller pattern within the larger pattern however many times you'd like.

In our example, the pattern "abab...", you can imagine any arbitrarily long string of letters that fits the pattern. The pumping lemma says that because there HAS to be a repeating sub pattern within the pattern "abab...", we can find an example that fits the pattern, and the example can be as long as we'd like.

Finite Love Machine

A finite state machine is a theoretical (and often practical) object in computer science. It has the ability to recognize certain class of patterns-- patterns that can be checked with finite amount of memory.

So given a pattern that asks you to keep track of increasing amount of information, it is impossible to construct a finite machine to recognize every instances of that pattern.

The pattern 10100100010000... is one such example, because it asks you to build a finite machine that can keep track of the increasing amount of zeroes that separate each ones.