Intelligence is an "I know it when I see it" phenomenon, but psychologists have formed no consensus on what abilities combine to produce the appearance of great intelligence. Despite this, the lure of condensing a person's "intelligence" into a simple "intelligence quotient" (IQ) has proven irresistible to many in the field.
Measuring intelligenceThe first IQ test was introduced by Alfred Binet in 1905. While in principle an IQ score is meant to be 100 x (mental age)/(chronological age), this definition only applies to children, as mental abilities tend to stabilize at about 16 years of age.
IQ tests for adults are developed so that their scores fall on a bell curve, the peak of the curve being defined as an IQ of 100.
The standard deviation of the test results is then evaluated. One standard deviation equals 15 IQ points, so that a person scoring one standard deviation below average will be assigned an IQ of 85, while scoring one standard deviation above average yields an IQ of 115. In this way the results from competing approaches for the measurement of IQ can be easily compared.
Of particular interest is development of IQ tests which are free of cultural, linguistic, and other biases - tests that can cut to a "pure" IQ. Such tests are generally based on questions which are based on pictures or on numbers, these being thought to be relatively constant from culture to culture.
In progressive matrix tests, a large incomplete image is shown, and several options are given for patterns which will "properly" complete the main image. While the test designers often encounter difficulties in deciding which option is the best, testing the quiz on large groups of participants will reveal flaws in the questions.
Another class of nominally unbiased IQ test questions is prediction of number sequences. For example, if you are given [1,2,3,5,?], you are supposed to answer 8, as each number is the sum of the two preceding numbers. On the other hand, if given [2,24,720,?], the correct option is 40320, as each number is 2n factorial, with n taking on the consecutive values of the natural numbers. Another possible answer is 54000, which is correct if the sequence is a(i) = 4.8 x 2.5^(i-1) x a(i-1). There is nothing wrong mathematically with this answer, but it seems "clumsier" to humans.
An example of a number sequence that is not acceptable in such tests is [2,7,1,8,?], where the answer is 2, that being the next number in the base 10 expression of the transcendental number e. This is clearly not culture-invariant, as it tests knowledge instead of reasoning.
Testing a computer's IQWell, it happens that computers can handle both of these classes of problems, so are able to take non-verbal IQ tests. The tests are not based on speed of completion - the assumption is that some people will never figure out some of the answers. Neither will the computers.
Recent programs which handle these types of problems generally score below 100. Claes Strannegård, researcher at the Gothenburg Department of Philosophy, Linguistics and Theory of Science, recently achieved a breakthrough by deciding to design a smarter program, one which was designed with a model of certain traits of human psychology as well as pattern recognition algorithms. "We're trying to make programs that can discover the same types of patterns that humans see." he says.
Strannegård explains this point: "1, 2, ..., what comes next? Most people would say 3, but it could also be a repeating sequence like 1, 2, 1 or a doubling sequence like 1, 2, 4. Neither of these alternatives is more mathematically correct than the others. What it comes down to is that most people have learned the 1-2-3 pattern." People are attracted to an elegant or beautiful solution to a problem, which is not a mathematical concept. Thus, human modes of thinking are biased by psychological factors, which may not lead to optimal choices in problem-solving.
The Gothenburg group has developed a psychological model of patterns as seen and selected by humans, and incorporated it in their IQ test solving programs. The result is a program that attacks abstract problems using approaches similar to those a very smart person would use.
The psychology of the image completion problems is the most difficult to model, and the program scores an average IQ on such problems. The remarkable factor is that the computer is not presented with selection options. Rather, it solves for the missing piece of the image based on logic and human psychology models alone. The same program, when optimized for number sequence problems, attains an IQ of at least 150, again without the assistance of selection options.
"Our programs are beating the conventional math programs because we are combining mathematics and psychology. Our method can potentially be used to identify patterns in any data with a psychological component, such as financial data. But it is not as good at finding patterns in more science-type data, such as weather data, since then the human psyche is not involved," says Strannegård.
Having developed an initial understanding of how people approach the solution of IQ test problems. Strannegård's group is now aiming at developing new IQ tests. Their goal is to extend the capability of the psychological solution module to include other psychological factors for problem solving as they are uncovered through comparison with results generated by a general population.
In the end, the Gothenburg group's models may not only allow more accurate testing of human problem-solving ability, but may also yield programs whose purpose is to train people to include non-human approaches to problem solving, with the purpose of more effectively interacting with a Universe which is not strongly biased toward human thought patterns. Witness the enormously difficult problem of really understanding quantum mechanics. Our thought processes evolved to handle Newtonian physics quite readily (throw and catch a ball!), but we are largely adrift in the quantum world.
Eventually? We might create a new Renaissance driven by novel modes of thinking. Alternatively, we may find that mental chaos results from having too little selectivity in our mental processes. The original goal of Binet and his academic descendants may evolve so that a person's IQ reflects their ability to profitably use new modes of thought without getting lost in a chaotic maze of alternatives. Time will tell ...
Source: University of Gothenburg