patrick honner

Math teacher in Brooklyn, New York

I, RuBot

RuBotThis 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.

By patrick honner, ago

Are Stock Prices Random? Part II

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?

Stock Graphs

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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By patrick honner, ago

Are You Related to Confucius?

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:

family tree 1

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

binary tree

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 2^{99}, or 633,825,300,114,114,700,748,351,602,688 (thanks, WolframAlpha).

A reasonable estimate is that at the time of Confucius there were around 250 million total people in existence.  Each of those 2^{99} spots in your family tree has to be filled by someone, which means that, on average, each person in existence at that time had to fill roughly

\frac {2^{99}} {250,000,000} =  2,535,301,200,456,458,802,993

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?

By patrick honner, ago

Math at the Boundary

While in Maine, I took some nice photos of the boundary between the beach and the sea:

Shoreline

It made me think of something I saw a long time ago (maybe on 60 Minutes?) about a scientist who thought deeply about coffee spills on his countertop. The power of the internet helped me locate Sidney Nagel, a physicist who studies the physics of drops, why things get “jammed”, and why a coffee spill leaves a dark ring after it dries.

Is there any way to predict the kind of edge this water will make as it crawls up the beach? Is there any order in this chaos? If this inspires you to great scientific accomplishment, please remember where you got your start.

By patrick honner, ago

The Levytator

LevytatorFrom the “Why Didn’t I Think of This?” files comes the Levytator,

http://www.youtube.com/watch?v=iC_se2zrmLM

The Levytator is a more efficient and flexible take on the escalator.  It runs in a circuit, instead of conveyor-belt style, so you don’t lose half your steps to the useless, upside-down underground path, like in a traditional escalator.  Thus, you get more transportation per square foot of step.

In addition, the interlocking steps are curved and not rectangular, meaning that not only can the Levytator turn around corners, but essentially it can be designed to follow any kind of path a planner might need.

Be sure to check out the video for some cool demonstrations (which remind me a lot of closed-loop integrals).

By patrick honner, ago
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