This is a thoughtful and hilarious satire of old-school, British public television-style educational videos.
http://www.youtube.com/watch?v=Pj2NOTanzWI
I laughed repeatedly throughout. Watch the video, and give it a minute or so to win to you over. It’s worth it.
P.S. Students–please do not bring razor blades, Garry Gum, or Anti-Garry Gum to class in your pencil case.
Thanks to Ivan R. for showing me this!
This is a nice resource from Erich Friedman, a math professor at Stetson University: it’s a list of distinctive characteristics of [most of] the numbers between 1 and 9999:
http://www2.stetson.edu/~efriedma/numbers.html
Now, maybe knowing that 215 is equivalent to 555 in base 6 isn’t that useful, but there are a lot of great ideas woven throughout this list of integers. If you can fill in any of the gaps (do you know anything distinctive about 6821?), I’m sure Dr. Friedman would love to hear from you.
This is a great video of RuBot, the Rubik’s cube solving robot!
http://www.youtube.com/watch?v=pOhU3WP7zXw
This video was shot at the Maker Faire, a sort of do-it-yourself science fair recently held in NYC.
Apparently you can scramble up the cube any way you like, and set it on RuBot’s platform. RuBot picks it up, inspects the sides to determine the configuration, and then solves the cube! RuBot must have been happy when it was recently announced that every position of the Rubik’s cube can be solved in 20 moves or less.
I’m not sure if Rubot can solve 4×4’s or 5×5’s cubes. And I’m not sure why they made him look so creepy.
Last week, I challenged readers to identify which graph was the stock market and which graph was random. The purpose of the exercise was to highlight a fundamental question in economics and finance–are the valuations of things (like stocks and equities) predictable, or are they essentially random? Can you beat the market, or is it all just a crap-shoot?
I predicted that it would be hard for people to tell the stock prices from the random prices, thereby suggesting that stock prices are random. I don’t claim that the exercise was rigorous or exhaustive, but the results seem to agree with my prediction: 54% thought Graph A was the stock market, and 46% though Graph B was the stock market. Whichever is the correct answer, it doesn’t appear obvious.
Some people noted that the variations of the two graphs make it easy to tell which was which. Highlighted below, we see that Graph A has more places where the graph jumps or drops quickly; mathematically, this would be measured as variation. But is this an indication of randomness or reality?
What I found most interesting about the process was how challenging it was to make a sequence of numbers that were essentially “random” but looked like the stock market. It was harder than I thought, and the few people who knew how I did it seemed to have an easier time picking the correct graph.
Stay tuned for more graph-picking!
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Are all of us descendants of Confucius? Here’s a curious mathematical argument that suggests just that.
No matter who you are, you came from a mother and a father (I won’t go into details). So, in your family tree, the part behind you has two branches, like this:
The same goes for your mother and father, and their mothers and fathers, and so on. Thus, continuing on back the line, you see a family tree like this
And it just keeps going and going and going. An interesting mathematical feature of this tree is that, as your move backward in time, each generation has twice as many branches as the previous generation, roughly speaking. Thus, when you go back a hundred or so generations, to the time of Confucius, the number of branches in your family tree is roughly 
A reasonable estimate is that at the time of Confucius there were around 250 million total people in existence. Each of those
of the spots in your family tree. It seems like a statistical impossibility that Confucius wasn’t one of them. So, I guess that makes us cousins?