[ewzimm]

Most of this makes sense, but I have a problem with the often-repeated assertion that humans can't handle large numbers. We might not have an intuitive sense of astronomical odds, but that's why we developed mathematics. We have the ability to compensate for our lack of numeracy by thinking through problems with structured languages. We can do much stranger things than calculate whether we should play the lottery. With math, we can calculate what it would be like to navigate in four-dimensional space.

When I hear that people act irrationally when it comes to probability, I feel like it should be replaced with the assertion that people tend to act irrationally when they have not been trained to think methodically in a particular situation or because of circumstances rely on primitive approximations. The first assertion sounds like an immutable property of human nature, when it is more of a cultural and educational issue.

[corysama]

> The first assertion sounds like an immutable property of human nature

If you are not reading a formal thesis, you should not interpret statements formally. Doing so will only lead to a lifetime of frustration. The author probably agrees with you. The vast majority of the audience probably understands that the author is simply being brief and does not have the "audience attention span" budget to more formally describe the assertion that you take issue with.

My interpretation of the author's intent with the statement "humans can't handle large numbers" is "Large numbers of humans have been presented with large numbers of problems involving large numbers. In practice, the vast majority of them fail. Thus, humanity at large does not handle large numbers well." I.e. "humans" refers to the current mass of humanity, not the theoretical possibilities of an individual.

[ewzimm]

You might be right, but I have seen this trend before without mention that people tend to handle these things badly because of the environments they live in. Most people seem to have pretty poor training when it comes to probability, but the reason for this is presented as an evolutionary trait. I'm sure evolution plays a part, but I think it's mostly in terms of initial, untrained states. When people talk about how people do things because they evolved to do them that way, it sounds like something insurmountable. Humans have been bad at probability for hundreds of thousands of years, so of course they are now. But people are constantly the victim of marketers trying to confuse them with numbers. The lottery is just one of many ways this happens. It's no wonder that people are bad with numbers when there's so much obvious manipulation to try to get people to make irrational purchases. This isn't avoided by the article, but I feel like any mention of a trait people have inherited by evolution needs to be accompanied by an analysis of just how immutable it is. For example, desire for sex or food are pretty difficult to train out of, though not impossible. Poor aptitude with probability is pretty easily remedied. The fact is, not many organizations are motivated to fix it, and lots are more than willing to exploit it.

[JoeAltmaier]

Its not about how we think; its about how we feel. Some people feel safe without wearing a bicycle helmet or seatbelt, because they perceive the chances of an accident to be small or zero. The decision is made without thinking; get in the car, skip the seatbelt 'just this once, I'm not going far' and never consider the odds analytically at all.

[ewzimm]

I can definitely see feelings overriding an opportunity for thought. Personally, I have never bought a lottery ticket. I always wear a bike helmet or a seatbelt. I don't really feel anything about these issues. It just makes sense to do or not do them. I could see myself buying lottery tickets if there was a mathematical argument for doing so, as is the case in some lotteries where if you buy a certain number of tickets you are pretty much guaranteed a win, but not in any other case.

If I'm picking something to eat, however, there's definitely an emotional component in addition to the nutrition. I won't just optimize for nutrition. Maybe I'm just the same as the lottery ticket people, but I have different priorities. An emotional attachment to making rational decisions maybe. If that's the case, could a person override irrational emotions with more powerful emotional impulses toward rationality? It would come back to a cultural issue in that case.