In putting together our public opinions, not only do we have to picture more space than we can see with our eyes, and more time than we can feel, but we have to describe and judge more people, more actions, more things than we can ever count, or vividly imagine. We have to summarize and generalize. We have to pick out samples, and treat them as typical.
To pick fairly a good sample of a large class is not easy. The problem belongs to the science of statistics, and it is a most difficult affair for anyone whose mathematics is primitive, and mine remain azoic in spite of the half dozen manuals which I once devoutly imagined that I understood. All they have done for me is to make me a little more conscious of how hard it is to classify and to sample, how readily we spread a little butter over the whole universe.
Some time ago a group of social workers in Sheffield, England, started out to substitute an accurate picture of the mental equipment of the workers of that city for the impressionistic one they had. [Footnote: The Equipment of the Worker.] They wished to say, with some decent grounds for saying it, how the workers of Sheffield were equipped. They found, as we all find the moment we refuse to let our first notion prevail, that they were beset with complications. Of the test they employed nothing need be said here except that it was a large questionnaire. For the sake of the illustration, assume that the questions were a fair test of mental equipment for English city life. Theoretically, then, those questions should have been put to every member of the working class. But it is not so easy to know who are the working class. However, assume again that the census knows how to classify them. Then there were roughly 104,000 men and 107,000 women who ought to have been questioned. They possessed the answers which would justify or refute the casual phrase about the "ignorant workers" or the "intelligent workers." But nobody could think of questioning the whole two hundred thousand.