Wrapping your head around a trillion
In this financial crisis, there are tons of numbers being bandied about -- hundreds of billions of trillions of dollars used to stimulate, bailout and lose. Commentator K.C. Cole says these days, a big number like a trillion is something we can't even grasp.
K.C. Cole (http://annenberg.usc.edu/)
More on Commentaries, America's Financial Crisis
TEXT OF STORY
Tess Vigeland: That the figure Steve just mentioned -- $2 trillion. You know I remember back in the day when a million dollars seemed like a lot of money. Now it seems like every day we're talking billions -- the stimulus package, the bank bailout.. Add it all up and you've got those trillions. Commentator K.C. Cole says wonders how we're supposed to wrap our minds around such a ginormous number.
K.C. COLE: The fact is, you can't -- because your brain is constructed something like a chessboard.
There's an oft-told tale about the fellow who invented chess, so delighting his ruler that he got to choose his own prize. He asked that one piece of grain be placed on the first square of the chess board, two on the next, four on the next, and so forth -- doubling the number of grains for each square -- right on up to 64. The resulting "prize" added up to more wheat than could be produced if every arable acre of land on earth were dedicated to it.
Why is that so hard to see coming? Because our brains count the squares, not the grains.
In a sense, our brains count only the logarithms of large numbers -- the power they are raised to, rather than the number itself. Two to the 6th power is only 64 grains. But two to the 10th power is already more than a thousand.
If you only count the difference between the power 6 and 10, you'll be badly misled.
It's the same with millions and billions and trillions. We automatically "read" a billion as about a third of a trillion. After all, it's only three zeros off. But of course, a trillion is a thousand times a billion, and a thousand is a lot.
Decrease your salary by a factor of a thousand, and it could go from 200,000 dollars to 200. Increase class size by the same amount, and your 15 students would turn into 15,000. It's roughly what happens when the "m" in million becomes a "b."
Our brains haven't evolved to directly deal with such staggering numbers, but we can use stories and metaphors to retrain ourselves.
So the next time a trillion begins to sound just like a billion, think about how you'd fare on a $200 annual salary -- or survive teaching a class of 15,000 students instead of 15, in the same classroom, with the same number of books.
Comments
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From Los Angeles, CA, 02/21/2009
@Richard Johnston: You may understand simple math, but evidently not simple psychology, which is what KC is talking about. She's not telling you that you don't _know_ that 1 trillion is 1000 times a billion. She's saying that in our gut, that's not the comparison we're making. Next, you _do_ have a PhD, which makes you significantly more educated than the average listener. Finally, _my_ PhD _is_ in math, and I thought it was a great piece. Something along the lines of: "Space is big. You just won't believe how vastly, hugely, mind-bogglingly big it is."
02/19/2009
Somehow good music soothes even the worst of problems... and I do love Uncle Tupelo.
From Westfield, NJ, 02/19/2009
I'm sorry to the PHD, and the other non mathematicians who were insulted.
This is very telling, important to remember and next to impossible to grasp, she's right.
Oh, and when Tess says they think the banks are off by two TRILLION dollars, I would like to say, "wishful thinking Trish"!
Here :(http://sos-newdeal.blogspot.com/2009/02/proposal-jus-come-clean-admit-truth.html)
hidden in the first paragraph is a doozy.
I predict that the financial (banking crisis) will not be done until we get rid of all the CDO's that are STILL out there.
I say, "..(eventually...)...admit how big the problem is. (hint: I say it's closer to 20-70 TRILLION dollars (including sub-primes, CDO's and everything consumer (College Loans, credit card loans, car loans).
I also hypothesize that we've only seen 25% of the financial crisis.
care to comment on my predictions?
I predicted this "depression 2.0" that we're now in (but no one will take the lead and admit until next december) TWO YEARS ago!
From New York, NY, 02/19/2009
Excuse me, but what does this pretentious intellectual take us for, and what exactly is her point? My PhD may not be in mathematics or economics, but I can do simple math, and this stupid commentary is condescending and insulting.
From Hillsborough, NC, 02/19/2009
Imagine a bead. Then a row of 10 beads on a wire, about 3" long. Put 10 rows together to make a square of 100 beads, 3" on each side. Make a pile of 10 squares into a cube, for 1000 beads, 3" each dimension.
Make a row of ten of these cubes - 10,000, 30" long. Make a square of these, 100,000, 30" each side. Make a pile to form a cube of these cubes for 1,000,000, 30" on each side.
Use these big cubes to make a row of 10,000,000, 300" long, a square of 100,000,000 and a cube of 1,000,000,000, 300" per side
Repeat to make 10 billion, 100 billion, and then the cube of 1 trillion, which is 3000" per side or 83.33 yards each dimension, not as long as a football field but wider and higher.
I should credit Montessori teaching materials for the first cube.
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