The second law of desk dynamics is a ruthless master.
I wasn’t familiar with Usage #2 until my mid-twenties. It comes from “form,” as in, “you’re manipulating the symbolic forms on the page, without necessarily ensuring that the manipulations make conceptual sense.”
The Mach 4
This sounds like a very painful razor to me. Like, there’s the direction of down my cheek, and the direction of across, but the next direction after that will consist of burrowing into my cheek… and I neither can nor wish to imagine the fourth direction.
Zorro vs. Zero
Harder to slash with your sword, but a much cooler conversation starter.
Boole’s Periodic Table
I thought there wasn’t suppose to be any memorization in math!
“The Social Network” needs a topology-themed sequel.
C’mon, right ant! Put it in perspective!
For what it’s worth, it can be tricky to identify, in any given scenario, whether you should be thinking about the percentage or the actual value. E.g., at the grocery store, should you buy more of an object than you planned because of a sale that lowers the unit price? Or should you stick to your original plan, which will have a lower absolute cost?
I mean connections like this conversation. But they’re meaningless, also like this conversation.
Intuition and Rigor
As with many things in mathematical mastery (skill vs. concept, technique vs. insight, standard procedure vs. creative solution) it’s not either-or. It’s both-and.
Evolution of Square
Mathematical archaeologists are just now coming across another transitional fossil called the rectangle. The phylogeny of squares is tricky!
Inspired by a true story. A horror story.
(For the record, 13 million seconds is just under 5 months. ACCURATE.)
I think about this a lot and have come to no definitive solution.
Maybe I should try to look it up instead of drawing comics about it, you say?
“Oh, a comic about hotdogs!” -Literally everyone’s reaction to seeing this picture
I find continued fractions very cool and rather mind-bending. They’d make for a fun slightly-off-the-beaten-path exploratory project for a high-schooler or undergrad.
I’m probably revealing too much of my own psychology here. As they say, Freud feeds on friends’ feuds.
Teaching vs. Comedy
I have since been informed that my teaching involves too few celebrity impressions.
It seems like a weird job to think professionally about things no one understands.
An astute commenter pointed out that this bizarre creature, although self-similar, is not really fractal for most definitions of fractal (e.g., shapes of non-integer dimension).
A Random Walk
Random walks in 2D are really weird. They return to their starting point with probability 1; the number of expected returns is infinite; but the expected time until the starting point is infinite.
I wanted to draw the y-axis with little arms and legs instead of numerals, but I’ll leave that to someone whose blog is “Math with Competent Drawings.”
Those who have seen me dance acknowledge that I’m getting pretty close.
8 thoughts on “I’m Going on a Random Walk”
As usual, your post stirs my mental pot in numerous ways. Two thoughts bubbled up. 1) On the matter of 70% chance of rain: when I lived in Tucson, the local weatherman gently explained one day that a 70% chance of rain there meant that 70% of the local area might see rain, so stop complaining if you see no rain in your backyard even though your neighbor got drenched!! 2) On the matter of teaching undergrads, I took organic chemistry from a PhD who was perennially annoyed at having to teach in a podunk back country college in Vermont. He once drew a huge circle on the board, saying this represented all he knew about chemistry. He then drew a tiny circle inside the huge one, and said this was all he was allowed to teach in this class He declared that he was sick of talking about the stuff in the tiny circle and longed to talk about all the rest of the circle, then glared at us like that was our fault, and stormed out of the classroom. We rejoiced, as class was over for the day with far less pain than usual!
Most folks hope to die of a heart attack in their sleep; I’m imagining dying of laughter reading a Ben Orlin post…
…came close today 8-/
Chance of rain is figured out by multiplying how confident you are with your prediction of rain by what percentage of the area it covers. So a 70% chance of rain could mean that the meteorologist thinks there is a 70% chance of rain over 100% of the area, or a 100% chance of rain over 70% of the area, or somewhere in between those extremes.
A 70% chance it will rain some place in the area at some time in the day!
Expanding the area or the time window, the probability approaches 1.
I have a sneaking suspicion, if I saw you on the dance floor, I would be able do differentiate your un-smooth moments.
I need to know about the entropy of my anemone – Is it the entirety of my anemia, or a double-entendre entree?
Clearly the Mach^4 razor’s time dimension is its most important selling point: shave once, and you’re shaved for the rest of your life. (Why does this sound like “Build someone a fire, and they are warm for an hour; set someone on fire, and they are warm for the rest of their life”?)
The intuition/rigor dichotomy reminds me of Kant saying that percepts without concepts are blind, whereas concepts without percepts are deaf. Only better, because pictures.
I think that fractals come in two flavors, those which are self-similar at every (real) scale, and those that are only self-similar by steps, which I dub “integral”. The Sierpinski curve (triangles made of triangles made of …) is an integral fractal, as are your two examples here; the Mandelbrot set and the shoreline are non-integral fractals.