Really Big Numbers… Really
Jim’s recent blog entry prodded me into thinking about scale and numbers, concepts fundamental to understanding the world around us that many of us tend to use and repeat without really thinking about them. Between the war, the recession and the election cycle, the idea of billions and trillions of dollars are tossed around regularly. But what do those numbers mean? How can we bring those numbers home?
A billion is already a pretty big number. A recent list from an advertisement puts it this way:
- A billion seconds prior to 2006 it was 1959.
- A billion minutes ago Jesus was alive.
- A billion hours ago our ancestors were living in the Stone Age.
- A billion days ago no one walked on the earth on two feet.
- A billion dollars ago was only 8 hours and 20 minutes, at the rate our
government is spending it.
In my comment to Jim I cited one way of thinking about a trillion dollars, courtesy of AIGA:
"It’s the year 0, the beginning of the first millennium, and you have a trillion dollars to spend, at the rate of a million dollars a day. At just before three years, you’ve reached a billion. You keep spending, and now you are in the year 2001. You still have 737 years to go, spending a million every day, before you reach the end of your trillion dollar pile."
Or another way, from Richard Wurman’s book Understanding USA:
"If you counted to a trillion out loud, one number per second, you’d have to clear your calendar for the next 31,688 years just to complete the task."
That seems crazy, so let’s make it easier:
"If you were to go back to the Miocene Age, when mammals reached their greatest variety (19 millions years ago), spending one dollar every minute, day and night, seven days a week ($526,000 each year) you would just now run through your trillion dollars [give or take a few hundred thousand]"
Trying to internalize numbers of this magnitude ripples through our apprehension. Man’s dominion over the earth? Less than a sliver… literally (from Bill Bryson’s A Short History of Nearly Everything– a fine, fun read about the history of science):
‘Perhaps an even more effective way of grasping our extreme recentness as part of this 4.5 billion-year-old picture is to stretch your arms to their fullest extent and imagine that width as the entire history of the Earth. On this scale, according to John McPhee in Basin and Range, the distance from the fingertips of one hand to the wrist of the other is Precambrian. All of complex life is in one hand, "and in a single stroke with a medium-grained nail file you could eradicate human history."’
As an avid reader of science fiction, I relish the thought that someday we might reach the stars, but it remains a practical impossibility due to the sheer distances involved to travel even to our sun’s closest neighbor:
"The fastest speed recorded for any existing spacecraft is 241,000km per hour. At this speed it would still take almost 19,000 years to reach Proxima Centauri. Put in perspective – 19,000 years ago we lived in caves."
But we will struggle for many decades to even hope to get a person to Mars safely, much less out of our solar system, whose own scale is something to consider. A scale model of the solar system with the Earth reduced to the size of a common classroom globe would result in Mars being placed 4.5 miles away at a diameter of 9 inches, while Neptune (not to mention poor Pluto, demoted to a minor planet) would be 61 inches in diameter and nearly 90 miles away… the Sun would have to be nearly 146 feet in diameter!
Many of the systems of measurement don’t help us much. The 1964 Anchorage, Alaska earthquake was 9.2 on the Richter scale, while the 1989 Loma Prieta, California earthquake was 7.1. Not too different, many think, but because the Richter scale is based on magnitude, the 1964 quake was actually 100 times the 1989 quake (which itself caused over 10 billion dollars worth of property damage).
We (must) deal with these numbers in cavalier fashion all the time: China’s population is over a billion, the US national debt is edging toward 6 trillion dollars, a common DVD-R has the capacity for 37 billion bits. How do you comprehend the kind of scale involved in economics, astronomy, physics, geology and others? What examples bring the numbers home in a way that you really understand?