When Numbers Get Too Large

There is a concept in probability called the Law of Large Numbers.  Basically, it says that the more attempts you make at a measured activity, the more accurately you will understand the distribution of that activity.  For example, you may get a lucky streak at a casino or racetrack and come out ahead on a given day; but if you play long enough, you will lose.  The rules of the game stack the odds slightly against you.  Short term streaks occur, but results are predictable in the long run.

If you toss a coin ten times, you will get an equal number of heads and tails only about one in four tries.  More than 75% of the time you would get a different result.  But toss it a thousand times and the chance of getting closer to 50% heads and 50% tails is much better.  As you increase the number of coin tosses (or any similar activity), you are much more likely to be close to the expected outcome.  The same is true of experiments and studies as I have fussed about many times in the past when writing about science and medicine.  The bigger the sample size or number of trials, the more likely the results will be consistent with real life.

But I have created a different law of large numbers.  It states that it is almost impossible for anyone to really understand numbers greater than one million.  To most people numbers commonly tossed around in politics and science, like billions and trillions, are just words designating a big number or a whole bunch.  Even one million is beyond the grasp of most.

A million is a thousand thousands.  Counting to one million at one number per second nine hours a day would take a month – not time very well spent.  A stack of a million one dollar bills would stand almost 360 feet high and weigh over 1.1 tons.  A million of anything (or one chance in a million) is extremely hard to picture.  Such a large number means very little to most of us in real terms.

Now a billion is a thousand millions.  Politicians in Washington talk about a billion dollars as if it’s pocket change – a billion here, a billion there.  Here is an example given by a teacher to a class of seventh graders.  “If I gave you $1,000 a day, seven days a week, how long would it take you to collect 1 billion dollars?”   Most guessed around 4 years.  The answer is 2,737 years, 10 months, 7 days.  If this exercise started in the manger on the first Christmas, you would still be over 700 years away from collecting your billionth dollar.

A trillion is a thousand billion.  Count all the hairs on all the heads of everyone in a football stadium.  That’s a measly 6 billion or so.  To get a trillion of anything, load 38 and a half dump trucks like the one shown here with fine sand and count all the grains of sand – incomprehensible!

 Photo Credit:   http://www.earthhaulers.com

Today our national debt hovers above 20 trillion dollars.  How big is that number?  If everyone in the US cancelled holiday shopping and sent all that money to pay off the debt, American children would be without Christmas for over 30 years – no tree, no lights, no presents, no special meal, just empty stockings for a generation and a half.

Perhaps the lack of urgency about government spending is due to the fact that those numbers are so big, bigger than anyone is able to grasp or imagine.