Archive for Billions and Billions

Quadrillions and Quadrillions

Posted in Politics with tags , , , , , , , , on October 2, 2008 by njmalhq

This blog post is dedicated to the memory of Carl Sagan.  It appears that the last month before the next election will be dominated by talks of some very large numbers.  Within weeks numerical magnitudes in public discourse have grown from billions, to trillions to quadrillions.  I was reminded of Sagan’s last book,  Billions & Billions: Thoughts on Life and Death at the Brink of the Millennium, which opened with contemplations on very large numbers, and the big questions that come with them.  I am sure if he was still around and saw the enormous digits being plastered across the news channels, he would have had something intelligent to say about them.

He might have criticized the lack of any attempt to clarify the magnitude of these numbers.  The biggest number that has been thrown around so far is half a quadrillion ($513 trillion to be precise).  Apparently it is the size of the speculative-economy hole dug by the private financial system, which the administration and congress are trying to fill with another very large but much smaller number, the so called $700 billion bailout (or is it $1.2 trillion?).  But how big are these numbers really?  By the way they are written, with their zeroes stripped off, one could mistake them for something much smaller.  Like the monthly wages of an under-the-table immigrant worker in some unknown currency.

What does half a quadrillion really look like?  Let us write it in its un-abbreviated form, the way the numbers we usually deal with in our daily lives are written down:

500,000,000,000,000

Looks bigger than half quadrillion, or even 500 trillion.  But the gut response is still a little weak. Is that a soul sapping number, or merely a foot flattening one?  Sure enough the zeroes have made it appear larger, but by only a little.  Visually it seems only about 5 times bigger than 500 trillion.  There is an illusion here that results from exponential increase rendered linearly.  Adding a zero to a number makes its visual appearance grow by a unit, while its magnitude grows by a factor of 10.

To better appreciate the enormity of this number, it will have to be unfolded further.  Maybe into something more concrete, so we can visualize it.  I am writing this on a computer screen, so what better rendition than the smallest elements that make up the screen?  The tiny point of light that is called the pixel.  How big would a screen with half a quadrillion pixels be?

Without the bezel, my screen is 13.5 inches wide.  There are 1024 pixels across.  I’ll keep the calculations simple, and assume the pixels are square.  Dividing 13.5 by 1024 gives 0.013 inches.  So each pixel is about 0.013 pixels high and wide, or 0.00017 square inches, or 0.0000012 square feet.  So the screen would have an area of 500,000,000,000,000 * 0.0000012 , which is 600,000,000 square feet.

That is one huge screen.  How huge?  About 24,495 feet wide by 24,495 feet tall.  I went up Kilimanjaro, took me 6 days to get up there, and that gigantic mountain is just over 19,000 feet high.  The tallest building in Portland, one that is ironically named after a financial institution, is only 546 feet tall.  And remember, these are pixels, not dollars.

Dollars are thinner than the height of our pixel, but are much bigger on the sides.  I’ll avoid writing down the calculations.  Assuming the sources on the physical size of the dollar bill are accurate, the side of a cube of half a quadrillion dollars would be about 3000 feet.  That would be 6 times taller than the Wells Fargo Center, Portland’s tallest building, and little over half a mile wide and deep.  Laid out in a single row, it would circumscribe the entire planet to a height of about 10,000 feet. Now that is a veritable mountain of cash!

500 trillion dollars.  Enough to line the pockets of every living human being with about 100,000 dollars each.  The end of poverty as we know it.  There are after all only 5 billion of us.  Or, how about establishing human settlement on mars?  My guess is an entire martian nation can be erected with ease with that much money.  I won’t do the calculations on that.  Interstellar space travel is a little easier to estimate.  In his TV series Cosmos, Sagan mentioned  Project Orion and Project Daedalus.  I haven’t been able to find cost estimate numbers on the latter, but the former has a an upper estimate of $24 billion somewhere.  That would be a fleet of 21,000 Orion spaceships dispatched in every direction.

So who’s got them, all those quadrillions and quadrillions of dollars?  I am sure there is a thing or two we can do with them.