I think most of these have the same limitation. When the numbers are to big, such as 1000 comparable cases or a 1 in 1000 chance, the human brain cannot intuitively grasp what to do. We are really only optimized for things in a central range (and, obviously, not even that under many circumstances). Rarer events, at least ones that do not occur in aggregate, do not produce sufficient optimization pressures. At some point, all the hard parts must be reduced to purely mathematical questions. If you can actually think of 10 corresponding situations, or remember the average of 100 past situations, you can use that, but picturing yourself dealing with 10 000 of something does not feel very different than picturing 100 000.
That’s definitely a problem; a million is a statistic. I think we can try to work around it in some cases, though. You mentioned the numbers 10,000 and 100,000; one might convert these into a car and a house, respectively, by estimating costs. By interpreting such large numbers in terms of these real concepts, we get a more concrete sense of the difference between such large numbers. You can then think of the issue in terms of how often you use the car vs. the house, or even how much time you’re going to spend paying them off. That reduces the difference to something manageable. Obviously, this won’t work in all cases, and the weight or cost of even a real concept can vary based on the person and their location (spatial and temporal), but it can be worth trying.
For another example, consider the way people sometimes talk about government budgets. Someone might be outraged at $100 million going to a certain area, out of the overall budget of $50 billion. “Million” and “billion” are usually processed by our brains as just “big,” so we focus on the 100 and the 50, and 100 is bigger than 50, so… outrage! But if we divide by a million, we have $100 (a new cell phone) vs. $50,000 (a year of college tuition, or an expensive car). The difference is much clearer.
A technique I use to get around this problem is to think in terms of orders of magnitude. What you can do is ask yourself (for example) about being in ten corresponding situations, then ask yourself about that (i.e. the set of ten situations) happening ten times, then about that happening ten times. This is also, with a little practice, an effective way to develop a visceral (and accordingly mind-blowing) sense of cosmic/microscopic scales, long periods of time, and so forth—cf. the Powers of Ten video.
I think most of these have the same limitation. When the numbers are to big, such as 1000 comparable cases or a 1 in 1000 chance, the human brain cannot intuitively grasp what to do. We are really only optimized for things in a central range (and, obviously, not even that under many circumstances). Rarer events, at least ones that do not occur in aggregate, do not produce sufficient optimization pressures. At some point, all the hard parts must be reduced to purely mathematical questions. If you can actually think of 10 corresponding situations, or remember the average of 100 past situations, you can use that, but picturing yourself dealing with 10 000 of something does not feel very different than picturing 100 000.
That’s definitely a problem; a million is a statistic. I think we can try to work around it in some cases, though. You mentioned the numbers 10,000 and 100,000; one might convert these into a car and a house, respectively, by estimating costs. By interpreting such large numbers in terms of these real concepts, we get a more concrete sense of the difference between such large numbers. You can then think of the issue in terms of how often you use the car vs. the house, or even how much time you’re going to spend paying them off. That reduces the difference to something manageable. Obviously, this won’t work in all cases, and the weight or cost of even a real concept can vary based on the person and their location (spatial and temporal), but it can be worth trying.
For another example, consider the way people sometimes talk about government budgets. Someone might be outraged at $100 million going to a certain area, out of the overall budget of $50 billion. “Million” and “billion” are usually processed by our brains as just “big,” so we focus on the 100 and the 50, and 100 is bigger than 50, so… outrage! But if we divide by a million, we have $100 (a new cell phone) vs. $50,000 (a year of college tuition, or an expensive car). The difference is much clearer.
A technique I use to get around this problem is to think in terms of orders of magnitude. What you can do is ask yourself (for example) about being in ten corresponding situations, then ask yourself about that (i.e. the set of ten situations) happening ten times, then about that happening ten times. This is also, with a little practice, an effective way to develop a visceral (and accordingly mind-blowing) sense of cosmic/microscopic scales, long periods of time, and so forth—cf. the Powers of Ten video.