There seems to be a logical disconnect in our brains when it comes to very large numbers. We have ten fingers and ten toes. We are fine counting to ten. When it comes to counting to 100, we don’t have big problem either. However, I note that I can put myself to sleep counting down from 100 by “1’s” or “2.5’s.” One hundred seems a natural barrier, and because we are a tens based society, ten times our natural barrier is still comprehendible. However, as we go further from hundreds our understanding of scale diminishes. When we start counting in thousands, we may as well go back to the childhood counting, saying “One, two, many, lots, and whole bunches!”
We can intellectually go beyond a thousand, but I note that when we do, we group things so that we are counting the groups again, never going beyond the hundreds. For example, 530,253,063 is said “five hundred thiry million, two hundred fifty-three thousand, and sixty-three.” We have kept our counting to the hundreds of a group. That seems a natural cognitive limit of our intuitive understanding.
I think this inability to think beyond hundreds inhibits some of our intuitive understanding of scale. I see this all the time even amongst those of us dealing with numbers all the time. At my work, a group of us play the lottery when the winnings are big enough for all of us to retire. We call it the “stupid people’s tax” because we all know the expected return for our money is nothing and we pay anyway. The odds of one in hundreds of millions feels like one in hundreds with the millions only understood intellectually.
It is with this in mind that I read much of the news about the Syrian refugees. I see reports where countries take in thousands or even tens of thousands, and it feels impressive for some group to advocate increasing the number of refugees from one thousand to ten thousand. It feels like the group advocating for ten thousand is much more heroic. I submit this thinking is at least partially the result of our inability to comprehend the number of refugees is estimated at 10.8 million. Again, we focused on the wrong parts when thinking about the scale of the crisis. Like the examples above, we thought about the numbers I underlined instead of the description after them. It is very hard to get to 10.8 million (number of refugees) when we are dealing with them a thousand to maybe ten thousand at a time. When I think about the true scale of the problem, it feels like the responses are akin to trying to put out California forest fires with one spoon full of water at a time. Some may bring the teaspoon while others bring a ladle, but how effective are either?
Don’t take this wrong, our minds inability to grasp large numbers has advantages. I take a drug that has a chance to cause severe brain infections and possibly kill me. The published odds I get on that happening to me are changing all the time. My neurologist asks at every visit if I am concerned by the odds and want to switch medications. My most recent numbers were one in seven hundred, and I told him again I will be concerned when my odds worsen to below one in two hundred. Above that, my mind treats the risk like the odds of being struck by lightening or dying in a car crash on the way to work. These things happen all the time, but the odds are not worth worrying about because my mind puts them all in the remote risk category. My minds inability to internalize the risk helps me live my day to day life. I justify my thinking about taking Tysabri by noting my odds are still better than a Cancer patient taking Chemo which has a mortality rate of one in two hundred. I do not think about the large number that is my odds of getting the brain infection. Rather I think about it in comparison to something else.
The comparison method is the only way I think most of us truly attach meaning to large numbers. This is what I am doing when I compare the mortality rate taking Tysbari with the mortality rate of a cancer taking chemo. When we release data on the United States economy, most people care more about the direction of the change in numbers and how fast they are changing rather than how big the actual base number was. Most of us really cannot intuit the GDP reports talking about trillions of dollars.
When it comes to large numbers, we just need to be careful to be mindful of what the large numbers are for which we see differences and the differences in scale between different large numbers. If we can manage these two obstacles, we might avoid some of the common mistakes in our perceptions of the universe in which we live. Maybe then we can stop comparing “many” to “whole lots.”