ROBERTS I think that if you take the different things that happened to you and you measured their effect, the effects will have a power-law distribution. A tiny number will have a huge effect . . .
ROBERTS . . . and a large number will have very little effect. But I guess you could shift the slope of that power-law distribution if you were smart. My research with rats has involved measuring how long they hold the bar down when they press the bar and it turns out that has a power-law distribution.
MLODINOW That’s interesting. Why is it that they hold it down with a power-law distribution rather than, letâ€™s say, a normal distribution?
ROBERTS Why? I think itâ€™s because the way the cerebellum is constructed. I think it has to do with . . . the brain is a network and itâ€™s much easier to get a power-law distribution out of a network than out of a non-network and itâ€™s revealing of the mechanism that produces the bar presses. Itâ€™s revealing that it comes from a very networked structure and a little bit more than that, too. Itâ€™s not only networked, itâ€™s also chain reactioning and it sheds some light on the mechanism thatâ€™s producing the bar presses and that mechanism is not so far from what we see in the cerebellum, which has these incredible density of neurons, highly interconnected neurons. So thatâ€™s the connection.
ROBERTS Thatâ€™s the best I can say as to the why. Clearly evolution designed the brain to solve the problems that animals encounter and why does the cerebellum have the structure it does? Because this power-law distribution is a good idea. Normal distribution is probably too conservative, whereas the power-law distribution is . . . every now and then itâ€™s searching much more widely.
MLODINOW Searching for . . . to see if holding it down less or more amount of time will have any effect, so the power-law you will have some of those explorations into holding it down not long or extra long and therefore sometimes discover something new, rather than really more narrow . . . in a narrow band holding it down a certain number of milliseconds or whatever.
ROBERTS I would guess that the brain has been shaped to produce the power-law distribution in those operations and I think thereâ€™s probably other patterns of variability in other aspects of behavior but this is the one we measured.