I was explaining to my daughter how grotesquely big is the national debt. But how does one explain how big is twenty trillion dollars? Because trillion sounds like million, billion, and gazillion we tend to lose the significance of the number. Saying it is “a two followed by thirteen zeroes” does not capture the magnitude very well. Each zero adds an order of magnitude to the number. Yea, OK. That does not really help.
Take one. Add a zero you get ten. Ten is easy to comprehend–look at your fingers. Now add a zero to get one hundred. That is comprehensible. It is the number of yards on a football field, the points on a test. The number is comprehensible because it is countable.
(All numbers are written out. I am deliberately avoiding digits because adding zeroes is easy, which downplays the significance of an order of magnitude increase.)
Add another zero you get one thousand. Uh-oh. One could count it but no one does. In practical terms a thousand is not countable. Consequently, it is hard to comprehend a thousand individual items.
Think of a million things. A million is a thousand thousands. It is an uncountable number of sets of uncountable things.
Now think of a trillion. A trillion is a million millions. It is an uncountable number of sets of an uncountable number of sets of an uncountable number of sets of of uncountable things. It is so far beyond comprehension that “incomprehensible” hardly fits.
While we do not count seconds we experience time and have some sense of it. So let us use time to help understand the magnitude of large numbers. Start with one second. We have a good idea how big that is.
Increase that time to a thousand seconds—an increase of three orders of magnitude. A thousand seconds is seventeen minutes. That is about how long it takes to bake a frozen pizza.
Another three orders of magnitude (three more zeroes) gets us to a million seconds or twelve days. Again, we can comprehend twelve days. Twelve days (a million seconds) is a very long vacation, not quite two weeks.
Increase a million by three orders of magnitude to get a billion. This goes from twelve days to thirty-two years. Three orders of magnitude takes us from a long vacation to our first mid-life crisis. My dog might live a half billion seconds.
Another three orders yields a trillion. A trillion seconds is 317 centuries. (I lied about no digits). That is a long time. Christ lived twenty centuries ago and Socrates twenty five centuries. The pyramids are forty-five centuries old. In fact, the entire recorded history of humanity is less than a trillion seconds. This again illustrates how big is an increase of three orders of magnitude. It takes us from half a human life time to past the beginning of civilization.
Our national debt is nearly twenty trillion dollars. Twenty trillion seconds is more than six thousand centuries (633,762 years). Human life began two thousand centuries ago.
How big is the national debt? Well, if the very first proto-human being put one dollar in a bucket every second of every day–no sleep or weekends off (24/7)–then today the bucket would contain enough dollars to retire about one-third of the US national debt.
|Thousand||1,000 ÷ 60 = 17 minutes|
|Million||1,000,000 ÷ 60 ÷ 60 ÷ 24 = 12 days|
|Billion||1,000,000,000 ÷ 60 ÷ 60 ÷ 24 ÷ 365.25 = 32 years|
|Trillion||1,000,000,000,000 ÷ 60 ÷ 60 ÷ 24÷ 365.25 ÷ 100 = 317 centuries|
|20 trillion||20,000,000,000,000 ÷ 60 ÷ 60 ÷ 24 ÷ 365.25 ÷ 100 = 633,762 centuries|