Monday, September 22

Trillions

The Federal bailouts of the Wall Street and Mortgage robber morons that you and I, our kids and their kids have been tagged to pay for, without, I might add, any prospect of immediate benefit to our own well-being, are hovering around 1.3 trillion dollars. (Assuming two hundred million taxpayers, that's $6500 a head for the principal.) Looks like it's time for another tea party

$1,300,000,000,000

This is too hard to imagine as a real number. Let's instead stack up the numbers in terms of how long it would take to count the money or how long it would take to drive that distance at 55 m.p.h.


THOUSANDS

One thousand is pretty easy.
Write it out as 1,000
It equals ten times ten times ten (10 x 10 x 10)
In scientific notation, the cube of ten is 1x10 to the third power - 1x10^3 (A one with three zeros)
You can count to one thousand in about seventeen minutes.
You can drive a thousand miles at 55MPH in about eighteen hours.

MILLIONS

Take the now-seemingly paltry sum of "one million".
Write it out numerically, and it's 1,000,000.
It equals one thousand time one thousand.
In scientific notation, it's 1x10 to the 6th power -1x10^6. (A one with six zeros)
Or (10 x 10 x 10 x 10 x 10 x 10)
If someone gave you a million dollars, you could actually count it, given enough time. Counting one dollar a second, twenty-four hours a day - sorry, no time off to eat, sleep go to the bathroom or even a moovie - it would take you
twelve days to count your money. If you want to take it easy, and only work eight hours a day - you are, after all, a millionaire now, you could get the job done in 36 days. 

To drive a million miles at 55 MPH will take you about two years, non-stop.

BILLIONS

Now, lets try the same thing for a "billion" dollars.
Numerically, we're up to 1,000,000,000.
It equals one thousand times one million.
Or, one thousand times one thousand times one thousand again.
(10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10)
In scientific notation, it's 1x10 to the 9th power - 1x10^9. (A one with nine zeros)
Counting one dollar a second with no time off, it will take you 32 years to count your billion dollars. 

Counting eight hour days will take it up to 96 years. 

Your billion mile drive will take you about 2,000 years. Are we there yet?

TRILLIONS

The next step is trillions of dollars.
It's getting a bit awkward to write numerically - 1,000,000,000,000 - probably won't even fit on that little line in your checkbook.
It equals one thousand thousand thousand thousand.
We're up to 1x10 to the twelfth power - 1x10^12 (A one with twelve zeros)
(10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10)
If you're going to count a trillion dollars, get a comfortable chair and a big bag of Doritos, you're going to be counting 24 hours a day for
32,000 years.

As a point of reference, there hasn't been civilization on the Earth for anywhere near 32,000 years. Don't even think about the drive - a two million year road trip is beyond my ability to comprehend.

QUADRILLIONS

You've got waaay more money than you'll ever need, now. You ought to think about sharing some of that filthy lucre with the less fortunate - like me, for instance.
Try this one - 1,000,000,000,000,000
Now it's one thousand thousand thousand thousand thousand.
1x10 to the fifteenth power - 1x10^15 (A one with fifteen zeros)
(10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10)
We've entered the realm of the ridiculous - it would take you
32 MILLION YEARS to count a quadrillion - way longer than there have been humans on the Earth, but only half the time back toward the extinction of the dinosaurs.

AND SO ON

Keep adding exponents and you'll wind up with "quintillions" - one with eighteen zeros, "sextillions" - one with twenty-one zeros, "septillions" - one with twenty four zeros, "octillions" - one with twenty-seven zeros, "nonillions" - one with thirty zeros, and "decillions" - one with thirty-three zeros.

As an obtuse point of reference, the Earth has a mass of roughly six octilion grams - 6x10^27 g

THE LARGEST NUMBER

Ha! Made you look! Any likely candidate for the largest number can always be increased by simply adding "one". When I was in Junior High School, I was introduced to the concept of the googol - someone obviously ran out of "illions". The googol is the number 1 followed by one hundred zeros - 1x10^100 - it looks like this:

10,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000

For what it's worth, the actual name for a googol in American nomenclature is
"ten duotrigintillion".

You can use the googol as a convenient jumping-off point to start counting again - just add one. But there is really no reason to - you can use the googol as an exponent and create a "googolplex" - one times ten to to the googol power - 1x10^10x100. I can't show you what it looks like - a piece of paper large enough to write a googolplex would be larger than the known universe.

Asimov explains:

The googolplex, however, cannot be written out -- literally cannot. it is a 1 followed by a googol zeros, and this book will not hold as many as a googol zeros, no matter how small, within reason, those zeros are printed. In fact, you could not write the number on the entire surface of the earth if you made each zero no larger than an atom. In fact, if you represented each zero by a nucleon, there wouldn't be enough nucleons in the entire known universe or in a trillion like it to supply you with sufficient zeroes.

--Isaac Asimov, T-Formation, Magazine of Fantasy and Science Fact, Aug 1963
[reprinted in the collection of essays Asimov On Numbers, pg 45]


I need some coffee.

This spake the rabbit.

2 comments:

Applecart T. said...

i like that you took the time to figure all that out. beats my english-major math anyday!

Le Grand Lapin said...

We cipher so you don't have to.