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By using the tag Popular songs I am able to trace the development of my short and unsuccessful songwriting efforts. I started in September &...

Thursday, February 18, 2016

Engineering

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.

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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.