a sense of perspective: how large is one thousand? one million? one billion? one trillion?
Large numbers are difficult for us to grasp the magnitude of. Oh, we can use logic and mathematics to intellectually designate their size, but emotionally, anything above the "thousand" designation tends to fall into a general "really really really big" category. Exactly how large is one thousand? one million? one billion? one trillion? It's difficult to have an emotional sense of just how big each of these numbers really are.
But then I started doing some math on the smallest unit of time we're all generally familiar with: the second. Whether it's the numbers on a digital clock, or the second hand of an analog wristwatch, or the closing moments of a sports game, we all have a sense of both how long and how short a second can be. So, in terms of familiarity, this would be a good way of giving us an emotional, as well as logical, sense of how big these numbers are, by converting the numbers of seconds into the other time units we're familiar with - minutes, hours, days, and years.
- one thousand seconds (103) =
- 16 2/3 minutes
- ~ 1/4 hour
This one feels straightforward enough - it's not difficult to think of a thousand seconds adding up to around a quarter of an hour. "One thousand" is a large number, but still one that "feels" within reach.
- one million seconds (106) =
- 16,666 2/3 minutes
- ~ 277.8 hours
- ~ 11.6 days
This is quite a bit larger, but still "feels" within reach. I can somewhat feel how a million seconds could come out to around 11-12 days. It's approximately the span of two work weeks, starting from Monday and ending with the next Friday, including the weekend in between. Large, but not unfathomable.
- one billion seconds (109) =
- ~ 277,777.8 hours
- ~ 11,574 days
- ~ 31.7 years
Okay... this is where my "feel" for the numbers completely broke down. There's no way I even remotely had the sense that one billion seconds would come out to nearly 32 years. It seems such an enormous jump from the 11-12 days at the million mark that I had to re-check my math twice to be sure I was doing it properly. (In fact, I had to suppress the urge to re-check it again as I write this!) It's interesting to think of myself as more than a billion seconds old at the age of 32... interesting, but (at least for me) still somewhat incomprehensible. I can't quite wrap my head around just how large one billion really is here.
Another try: my dad recently turned 61. In a couple years, nearly halfway through his 63rd year, he'll be over two billion seconds old. Again, I can do the math, and intellectually conclude it must be true, but emotionally I just can't quite grasp the magnitude of what a large number one billion truly is.
- one trillion seconds (1012) =
- ~ 31,688 years
This merely serves to drive the point home even further. This is approximately five to ten times greater than the entire span of recorded human history. There's no possible way I could even remotely wrap my head around just how much "one trillion" of anything would be.
In conclusion? I've been trying to think of one. This particular exercise is tied to our sense of time, and how long we've been alive, which helps to bring the true magnitude of these numbers within better reach of comprehensibility. Or at least defines exactly where our comprehension of these numbers breaks down.
For me, this was an eye-opener for just how wide the gulf between one million and one billion really is. And yet it seems these days we're surrounded by references to billions all the time. We hear about the rich billionaires running the multi-billion dollar companies that shape our lives... we hear about how there are over six billion people living on the planet... modern 120 gigabyte hard drives are able to store around 120 billion bytes (one gigabyte ~= a billion bytes)... and yet, none of that really makes it clear just how large one billion really is. But one billion seconds adding up to 31.7 years - that makes a dent.
I hope you all enjoyed this excursion into the realms of applied mathematics. Let me know if you come up with alternative ways of putting these large numbers into perspective, I'd love to hear them!