I’m zrkrlc (pronounced ˈzɜːkəlɒk (in British IPA) or ‘zer-ker-lock’ in approximate English). I don’t do stuff for a living yet (fortunately) so I write about whatever tickles my pickle. And yes, that sounds as wrong as it reads so don’t say it out loud.
My life’s accomplishments include:
- 12 000+ hours of Internet use since 2007
- turned eight without burning the house down
- learned how to wiggle both my eyebrows
- bought 36 jars of made-in-the-mountains strawberry jam on a single trip
- got lost in a citadel for over two hours when I was in second grade
I also write code in Haskell, Python, and C# to varying degrees of proficiency.
I laid some prohibitions for myself in my first post, Things I will try NOT to do.
I will try to write as much as my time would allow. Being unemployed is a difficult commitment to keep so I try to let off steam here as much as I have to. Oh, and don’t worry: I don’t plan on inundating you with funsies all the time. Sometimes things have to get licking-your-face serious and I hope that doesn’t turn you off.
The Header Image
Pictured at the beginning of every page on this site is the topologist’s sine curve, so named because it’s a textbook example of why pedestrian’s don’t bother with such abstract nonsense. It’s the graph of the function plus the origin defined by . If we define the following notions:
Fig. 1: Examples and non-examples of topological spaces. Note that these are sets. Illustration taken from Wikipedia1..
- DEF: (topological space)
- a set of points together with a function whose elements we shall call the neighborhoods of , such that:
- If and are , then is also .
- If and such that , then .
- DEF: (connectedness)
- a topological space is connected if it is inexpressible as a union of disjoint nonempty open sets
- DEF: (neighborhood system)
- the set of all neighborhoods of a point
- DEF: (local connectedness)
- a topological space is locally connected if there exists a neighborhood system for all points which are composed entirely of open, connected sets
- DEF: (path)
- a path from a point x to a point y in a topological space X is a continuous function such that and
- DEF: (pathwise connectedness)
- a topological space X is pathwise connected if there exists a path between any two points in X
Then it can be shown that f is connected but neither locally connected nor pathwise connected. I like maths.
This also brings us to the title.
Fig. 2: A homotopy. GIF taken from Jim.belk2.
- DEF: (homotopy)
- Let and be topological spaces and f and g mappings between them. A function is a homotopy if .
Which basically means, if you pick up a path, beat it with a sledgehammer (without breaking it) and put it down again, then you just did a homotopy. Did I tell you I like maths?