Thursday, 1 December 2016

In response to the question "Are there differences in brains of men and women".

Imagine that you have two types of dice, yellow ones and pink ones. Both types have six consecutive numbers on their six faces as usual. However, in this case we don't know what the lowest and highest numbers are, or the colour, because we are blindfolded. Now we throw 1000 of each type and get someone, who isn't blindfolded, to add up the total number of spots for both colours.

If the total for yellow dice is around 3,500 we would have some justification for thinking that these dice are the normal 1 to 6 version; 3.5 is the average score for standard dice. If the total for the pink type, after a thousand throws, is 4,500 then it would be fair to conclude that pink dice were numbered 2 to 7 and that the two types of dice are indeed different.

So far so good. But if you have one throw only, without knowing which colour you have thrown, then the chances you will find out the colour, on that single trial, is only 1 in 6. Five times out of six a single trial is not enough to tell which type you have thrown. And the more faces your dice have the less likely it is that one throw will tell you which type it is.

It gets worse. A small number of yellow dice are known to have a 7 rather than a 6. And a small number of pink dice have a 1 rather than a 2. So now it is never possible to know for certain which colour from a single blindfold trial just by being told the number you have thrown.

So looking at a single brain is like looking at a single throw of a dice type with many hundreds of faces, and where it is certain that many of the faces are not typical.

The sentence 'pink dice have more spots than yellow dice' remains true - but only of the population. What you can discover by looking at a single dice is almost nothing.