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Counting on your 1024 fingers

Last week I went to a conference given by Mathieu Hébert. He was showing off, and somewhat teaching, his ability to do mathematical operations on his fingers (article in French), using each one as a binary digit. Ten fingers makes for 1024 combinaisons, allowing to represent number as big as 1023 since it starts with 0.

Many numbers in the linked article are wrong, stick to your calculator for accuracy…

The idea is rather simple, though having thought of it in 1940 is really avant-garde. The Z1 computer was built only a few years before !

If you look on the Internet, you will find many resources showing how to represent a number on your fingers. What was cool was his ability to add, subtract, divide and multiply just by fiddling his fingers. He identified some patterns and he reproduces them at each calculation step, without really knowing what number he is at. When he is done, he just reads the binary number back in decimal for a usable answer.

If you have bc, set obase=2 and give a try. Start by reprenting easy, one-handed 2-bit numbers, like 10, 20 or 24. Then add one bit on your other hand, with numbers like 74, 84 or 88. You should see a pattern right about now…

Come up with a few numbers and represent them on your fingers. Aim for accuracy, not speed. Then start to look for numbers around you: license plates, subway car number, the time or date. You are surrounded by numbers…

I am at the point of trying to do simple operations. Subtracting looks like the easiest one to do. M. Hebert is 86, and he would like for his tricks to survive him. I will try to whip up a tutorial – my laptop was stolen, so all my other projects are on hold.

Until then, I give M. Hébert a 48 (that’s two thumbs up, in binary) 😉