Sunday, September 14, 2014

64 x 39 (Thirty-Nine)

Thirty-nine consists of two digits, a 3 and a 9. One is a prime, the other is the square of that prime. 39 itself is not a prime, but it is the multiple of two primes, 3 and 13. Legend has it that good things come in threes. Thirteen, on the other hand, is supposed to be bad luck. Thirty-nine has a split personality.

Process Reflection: When I sat down to write tonight I did not have anything in particular lined up. I opened up the master file for the sequence of sixty-four word posts I've been working on and typed in XXXIX. Then I sat looking at the screen, and the shape of that roman numeral (especially in contrast the previous one, XXXVIII) got me thinking about the shape or iconography of 39 both as a roman numeral and and as an arabic numeral, and so I thought I'd just try to say something true about the number 39 in exactly sixty words. Which turned out to be harder than I thought it would be. I wrote four sentences, and was just getting warmed up, and was already up to 71 words. So I cut a bunch of stuff and got back down to 51, then started adding again and eventually landed on 64. 

So yeah, okay, it's not a post of any particular insight or importance. But this project is of its nature more about lateral thinking than depth: I haven't done anything like that before. And just to dip my toe into that water conjures oceans of questions that it would take a lifetime to navigate. 

One obliquely relevant question that came up as I was writing this process reflection was whether or not the terms Roman numeral and Arabic numeral should be capitalized. And it turns out that there is some disagreement about that, in honor of which disagreement I've done it both ways here. 

A better question has to do with how the way we represent numbers to ourselves in our minds directs and shapes the mathematical thinking we do. For example, anyone reading this probably isn't using roman numerals anymore. You probably use arabic numerals almost exclusively, or think you do. The digits are deployed in groups of ten: 0123456789. But most of the real work being done with numbers today is being done in base two, binary code. This actually came up today in conversation with my granddaughter, the question of how streams of 1s and 0s can make it possible do something as miraculous (and invisible and easy to take for granted) as providing a voice to give us accurate directions over the phone to the volleyball game in Terra Linda. I mean, what's up with that?

During the time I was in school I had mostly very bad math teachers. I didn't realize how bad until my sixties, when I started getting involved with professional development programs for math teachers run by people who actually were very good math teachers. Dan Meyer, for example. Then I wound up reading stuff by Joanne Boaler and Paul Lockhart and Karen Economopoulos and many others and basically wound up wishing I could rewind the clock and go back and do it all over again.

Anyway, here we are, once again. Sixty-four words have led us into the maelstrom. If you think that I thought, when I started, that we would be getting into all of this, you have another think coming. Go for it.

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