All of us gain a set of thoughts and beliefs about the world through the normal process of growing up. Some people are lucky enough to find that the beliefs they grew up with work well for them throughout their lives, needing only minor adjustments. Others find that their thoughts and beliefs don’t do a good enough job of helping them navigate the world, and they are forced to reject their old beliefs and find or create new ones. In any case, it can be very useful to go about thought formation consciously and deliberately, rather than just letting it happen on its own.
Random errors and the wisdom of crowds
We aren’t perfect: if a person is asked to guess another person’s height she might get it exactly right, but she might guess a couple of inches too high or too low.
Suppose ten people are asked to guess an eleventh person’s height (and they aren’t allowed to look at each-others’ answers). Some will guess too high, some will guess too low, and some will get it dead on. How to get the best estimate? Add all ten answers together and divide by ten. With random errors, some guesses are too high and some are too low, so when you take the average of many guesses, the mistakes tend to cancel each-other out.
Systematic errors (bias)
Systematic errors aren’t random: most people will make the same mistake, so the mistakes don’t tend to cancel each-other out. Systematic error, or bias, is much harder to detect and correct than random error, so we’ll explore this topic further in a later chapter.