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To begin a new project is to realize what one already knows about it (more than you think you do), as well as well as the overwhelming chall...

Thursday, February 18, 2016


We think of the humanities as antithetical to engineering, and that's true for how a lot of humanities are practiced. A lot of vague crap about what makes us human, etc... and the fuzzy postmodernism of "anything goes." A poem, though, is a machine made of words (William Carlos Williams) and can be spoken of with precision, the same way as a piece of music. What the humanities offers is not a reprieve from the hardcoreness of STEM fields, but a greater hermeneutic wealth. In other words, we can interpret things in greater depth and with greater sophistication.


I found a nice mathematical problem the other day. It involves the sequence

1 / 2 / 3 as exponents of 2.

2 the first power, 2 to the second power...

Running parallel the same sequence in the denominator of a fraction

1/2 1/4 1/8...

So you play a game in which the odds of winning decrease by one half each time, while the rewards winning increase exponentially by powers of 2 at the same time.

So you half the time you play it, you win $2, a quarter of the time, you'd win $4, once (on average) every 8 times you'd win $8. The question is how much you would pay to play the game? It is called the St. Petersburg lottery. It is paradoxical because you could win a huge sum, but most people would not pay very much to play it.

Suppose you played 16 times. On average, playing that many times you would get

$16 (half the time you win that)
$16 (a quarter of the time, or 4 times, you'd win $4)
$16 (1/8 of the time (twice), you'd earn 8.
$16 (1/16 of the time you'd earn 16).

Then one more time (on average) you'd get >$32. So you'd get >$96 (on average) playing 8 times. It's fascinating, because if you play enough, say 1,000,000 times, a certain percentage of those times will leads astronomical returns.