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Dave Bacon is a theoretical ski bum who is also a pseudo professor. His research is on quantum computing, his scientific passions extend to everything in physics, mathematics, computer science and beyond, and his personal pleasures include making wine, playing poker, skiing, camping, and daydreaming (although not all of those at the same time.) Nothing he says on this blog should be construed as having anything to do with his employer or his dog.

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(1+p)(1-p)

Category: Mathematics
Posted on: October 14, 2008 11:15 AM, by Dave Bacon

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I wonder how many people this week realized that "ten percent down" followed by "ten percent up" does not equal "no change." Probably a few. And how many realized that "ten percent down" followed by "ten percent up" is the same as "ten percent up" followed by "ten percent down"? Or that up 5 percent, down 3 percent, up 2 percent, down 8 percent, and down 8 percent in that order is the same as down 8 percent, up 2 percent, down 3 percent, up 5 percent, down 8 percent in that order? Commutativity is cool. Yes, I am easily amused.

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This is exactly why I don't like descriptions of change that are posed solely in terms of percent change - I think they're hard to understand. Harder to understand than differential equations, I would argue.

Posted by: llewelly | October 14, 2008 12:20 PM

"I wonder how many people this week realized..."

We have a good swath of our country who believes that a large part of the rest of the world is praying against "our god" and "our god" should take action against those who think they are bigger than "our god." (Arnold Conrad.) (Kind of sounds like the my-dad-is-bigger-than-yours argument.) The same ones who think Sarah Palin would make a great president should it come to that. So, I'm starting to believe the collective IQ is much, much lower than I had imagined. I doubt many understand commutative property at all. (A few years ago I read about a test that was given to a number of top executives in the financial sector that asked to solve the most basic quadratic equation. Overwhelmingly the executives complained that they should not be expected to know such "advanced" concepts.)

Posted by: JohnQPublic | October 14, 2008 12:48 PM

Engineers like decibels. 10 dB down, followed by 10 dB up, gets you back where you started.

Posted by: Lemon Curry | October 14, 2008 3:11 PM

Yes, I am easily amused.

Or simply staving off insanity in the face of an evaporating retirement fund.

Posted by: Ian Durham | October 14, 2008 3:29 PM

I wonder how many journalists say "ten percent down" when they mean "ten percentage points down".

Posted by: Abie | October 15, 2008 4:36 AM

And yet if the stock market randomly goes up/down by 10% each with probability 1/2, the expected value is exactly its current value. Math is weird.

Posted by: james | October 16, 2008 11:27 PM

For this and other surprises see:
http://gilkalai.wordpress.com/2008/08/17/surprising-math/
My memories from an older stock market crash is that not many people fully understand that 'eighty percent down' can be followed by another 'eighty percent down.'

Posted by: gil kalai | November 11, 2008 3:24 AM