Hawking Up Hairballs

Tuesday, January 22, 2008

Nerdy By The Digits

In college, I majored in mathematics, and I worked for many years programming PC's, so it's no surprise that I'm a bit of a nerd. Not that I ever used a pocket protector or wore big glasses with black, plastic frames, but those are just media cliches anyway. The Nobel Prize winning physicist Richard Feynman was known as a womanizer, and a quite successful one at that. Another Nobel physicist, Sheldon Glashow, upon visiting Turkey for reasons of physics, was most interested in finding some good hashish. (For those of you who doubt me, I refer you to the following two books. For Feynman, there's Genius: The Life and Science of Richard Feynman by James Gleick. For Glashow, there's The Second Creation: The Makers of the Revolution in Twentieth-Century Physics by Robert P. Crease and Charles C. Mann. I recommend the latter book to anyone who is interested in twentieth-century physics. It does a good job of walking the fine line between explicating the physics and talking about the scientists themselves.)

This is all by way of prefacing a neat little trick that appeals to the nerd in me. Now, everyone knows that you can represent any number between one and ten with your fingers. Just raise the number of fingers that correspond to the number you want to represent. Okay, then, ask yourself this. Is there another way to use your ten fingers to represent numbers and, if so, what's the largest number that you can represent? The answer is, yes, grasshopper, there is another way to do it, a way in which you can represent any number all the way up to 1,023.

Okay, now for the details. Here's how it works. Place both of your hands palms down on a flat surface, then make fists. Lift the little finger on your right hand. That's the number one. Now, back to the fists again. This time, raise the finger next to that little one. That's two. Bring up the little one, so both are showing. That's three. The middle finger alone, the proverbial bird, represents four. (It may here occur to some of you that one could hence use the word "four" as equivalent to the bird. That's really heavy duty though and, if you think that's neat, there's only one word to describe you, NERD, in all caps.) Bring up that little finger with the middle one and you've got five. By now you should be able to see what I'm doing. I'm using the ten fingers of the hands to represent binary digits. The little finger of the right hand is two to the zero power, which is one. The little finger of the left hand is two to the ninth power, which is 512. Hence, the largest number that can be represented is twice that 512 minus one, namely, 1023. Now, how about that, huh?


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