Breadth is measured by how many different things a person knows that are relatively easy to know; that is they are not highly complex, abstruse, esoteric, or profound. There are many words, for excample, that are known by about 50 percent of the general population. Therefore they are fairly common and simple words. The number of such words that a person knows is an indication of his mental breadth. The same goes for items of general information. There are great individual differences in the "breadth of intellect" as so measured.
Altitude is measured by the most difficult and complex problems a person can solve, or the most difficult words in a vocabulary test or the most difficult general information questions he can get right. A test item's difficulty is indexed by the percentage of the standardization population that fails the item. So items can be ranked in difficulty, from very difficult items that are failed by more than 99 percent of the population to very easy items that are failed by fewer than 1 percent. The average of the most difficult items in several types of tests that a person can pass is an indication of that person's alititude. There are great individual differences in "altitude of intellect" just as in "breadth of intellect".
But the really interesting fact discovered by Thorndike is that measures of individual differences in breadth and altitude are allmost perfectly correlated. That is, these two seemingly different aspects of mental ability are both indices of one and the same general ability, or g. People who know rare or difficult things or can solve very complex problems also generally know a lot more than do most people of the rather ordinary kinds of words and facts that many people know. Persons with poor reasoning and problem-solving ability also possess much less common knowledge about the world around them. Brighter persons automatically pick up more information from any experience afforded by their environment.
I recall once interviewing a young man who tested out as borderline retarded, in the range of IQ 75, to get some idea of his fund of general information. I decided to begin by trying to find out how much he knéw about whatever topic he claimed to have the greatest interest in and to know the most about. It was baseball. He frequently went to baseball games with his father or watched them on television, and found them very exciting. Yet when I questioned him about baseball, I discovered that he didn't know for sure how many players are on a team, couldn't name all the positions on the team, and had only vague and at times incorrect notions of the rules of the game. He knew the names of three or four players on the local team but didn't know any of the world's most famous players or even the names of any of the Big League teams. When I probed other topics in which he claimed an interest - automobiles and gardening - I found that he possessed even less information about these than about baseball. It was evident that his quite low score on the General Information subtest of the Wechsler Adult Intelligence Scale, on which I had tested him, gave an accurate assessment of his level of general knowledge of the world around him. On the other hand, just out of curiosity, I later put the same baseball questions to a learned professor who, I happend to know, had no interest in any sport whatever. He even had positive disdain for spectator sports and claimed never to have seen a baseball game in his life. Yet he had no trouble answering the several baseball questions I asked him, and could name three Big League teams and several famous baseball players. Interestingly, he was quite surprised to discover that he knew anything at all about baseball and seemed puzzled as to where he could have learned facts about something he cared nothing about. But conversations with him revealed that he knew a great deal about a great many things, in science, literature, the arts, economics, politics, and world affairs. In his own field he is an acknowledged world authority.
These striking differences that are so obvious between the extremes of the IQ scale exist in smaller degrees between less extreme IQ differences. But when the differences are fairly small - less than 10 points or so - they cannot be dependably recognized by casual observation. Without very carefully designed tests we cannot reliably discriminate between the g levels of persons whose IQs are within ten or so points of each other. Within that range, the more obvious differences between persons involve their special talents, developed skills, interests, personal experiences, and educational backgrounds. The ordinarily observed differences between persons, then, are a poor basis for subjective judgments about differences in intelligence or g. In general, however, someone who knows a lot about something is more intelligent than one who doesn't know much about anything.<
Arthur Jensen, Straight Talk About Mental Tests, 1981
[Jensen wrote this book for the general public. Allthough old it seems to be a very readable, generally intelligible introduction to intelligence.]