1. Background
2. Detecting new, non-chance associations
3. Insight from the information sciences
4. Three aspects of intelligence
5. Summary
1. Background
Intelligence is a quality easily recognizable in other people's actions, talk, or writing, yet the current trend among psychologists is to deny that it can be accurately defined or described. This has mainly resulted from the many ways in which intelligence manifests itself, but there is also concern at the arrogance of regarding the IQ as the only adequate measure of an individual's mind, and at the degradation and insult to racial groups that resulted from the intelligence-testing movement. Furthermore the early discussions of the topic were singularly inconclusive and unproductive (Thorndike et al. 1921), so many wished to draw a line under them and pursue the topic no further. Some even accepted the infamous definition given by Boring (1923) — intelligence is what the tests test — but to let the matter rest there surely belittles the status of psychology as a science. Heat, like intelligence, shows itself in many ways, but where would physics be if it had simply been accepted that heat was what thermometers respond to and that its theoretical nature was not a problem worth tackling? There have been great theoretical advances in the information sciences since the early days of intelligence tests; because intelligence is something to do with the way the brain handles information, it is time for another look at the problem.The suggestion pursued in this article is that intelligence is the art of guessing right. 'Guessing' is sometimes used as a pejorative term, and of course it is not intelligent to guess blindly when sound knowledge is available. But only bad guesswork ignores sound knowledge; good guesswork uses all the knowledge and evidence that are available, and it is the science behind the art of guessing right that illuminates the nature of intelligence.
2. Detecting new, non-chance, associations
We can start with the suggestion that intelligence is the capacity to detect new, non-chance, associations (see Barlow 1970, Fatmi and Young 1970). Consider the hungry dog that leaps from its comfortable rug in front of the fire when it hears the sound of the refrigerator door being opened. That sound has often been experienced as the precursor of food, and the recognition of this association by the dog deservedly earns it some reputation for intelligence. This is not, however, an easy task: first the sound of a refrigerator door opening is not a simple sound like a whistle or a bird's alarm call, with much acoustic energy concentrated in easily defined frequency bands; it is a series of sounds spread over a wide bandwidth, and it is likely to vary greatly according to the vigour with which the door is pulled open and the rattling of objects inside and on top of the fridge. Furthermore it is heard against a background of other complex sounds that are in some ways similar — the opening and closing of other doors, the pad of feet along corridors, and perhaps the sounds of traffic from outside the house.Communication engineers now know exactly how to design an optimal detector for such a sound, but to do so they would need a great deal of information about the sounds produced by the fridge door and the other sounds from which it must be discriminated, as well as the technical knowledge about how to use this information to construct the detector. It would be hard work to provide this information to the engineers, but the dog's behaviour shows that it has automatically acquired the necessary information about the acoustic environment, and that its brain has the technical means to produce some approximation to an optimal filter for the detection task.
3. Insight from the information sciences
Initially the dog's feat seemed a simple example of learning a new association, but the modern statistical viewpoint tells us something quite different. It says that the environment is complicated and uncertain, but that knowledge of the complexity (in this case statistical aspects of the sounds produced by the fridge door and of other sounds in the acoustic environment) can be used to reduce uncertainty about likely sources of food and thus help the dog to guess right. One can see immediately that, if the general role of intelligence is to master similar complexity in all other aspects of the environment, it faces a truly stupendous task. It should assess the frequencies of all the sensory messages from the environment, the ways they are associated with each other, and the ways they fail to behave as random, independent elements. That may seem a tall order, but a dog does have considerable knowledge of its environment and can detect many other acoustic patterns that have significance for it, such as that of the postman opening the garden gate or of its mistress's car returning home. For humans the task is even more stupendous, for no one can doubt that through language, books, libraries, academies, and now the internet, the world we are in touch with is truly complex.Those familiar with the rudiments of information theory will appreciate that it defines two quantities in a collection of messages such as those a dog or a person receives about the environment — information and redundancy. Our hypothesis about the art of guessing right could be restated thus: intelligence exploits redundancy to make predictions more certain. This relation between redundancy and intelligence was appreciated early in the history of information theory (Barlow 1959, Watanabe 1960) and an account, updated with the benefit of hindsight, can be found elsewhere (Barlow 2001). The importance of the statistical structure of natural stimuli in problems of perception is now widely recognized (Simoncelli and Olshausen 2001). Macphail (1982) reviewed evidence on the learning abilities of many species of animal, and was surprised to find that there was apparently no correlation with their supposed intelligence. He concluded that intelligence was not closely linked to learning, but this is just as the current hypothesis predicts; most learning tests are carefully designed to prevent test animals benefiting from knowledge of the associative structure of their environment — precisely the knowledge intelligence is thought to exploit to improve guesswork.
4. Three aspects of intelligence
What do these insights from the information sciences tell us about its measurement? In order to guess right there are three conceptually distinct tasks, namely formulating possible guesses (i.e. hypotheses about new association), testing them to find if they are acceptable, and working out the implications of those that escape disproof.Associative efficiency. Of these three, it is easiest to imagine an objective measure of the testing process, because the theory and practice of statistical tests for associations are well developed, and in principle this makes it possible to compare an individual's performance at an associative task with an 'ideal statistician's'. The ideal statistician will devise tests that make the best possible use of all the evidence, and a measure of 'associative efficiency' is obtainable from the ratio of the amounts of evidence required for these tests and for the individual being tested, when each performs at the same level of reliability. This is an absolute measure of how well the subject utilizes the information available — how well he guesses in fact. This concept of statistical efficiency (Fisher 1925) has been used to measure human perceptual tasks (Rose 1942, Tanner and Birdsall 1958, Barlow and Reeves 1979, Barlow and Tripathy 1997), but has not yet been applied to the associative tasks that underlie intelligence (nor to learning for that matter).It is satisfying that the definition enables one to specify one aspect of intelligence that could in principle be measured objectively and in absolute terms, knowing precisely what one was measuring. The idea that there is an absolute zero of intelligence, where none of the available information about a new association is used, or 100 per cent intelligence, where all of it is used, may be new to some people, as will be the idea that one aspect of intelligence is in principle measurable on an absolute scale, free of reference to population norms.Imaginative intelligence. The next question is; 'How does the possibility of a particular association enter someone's mind?' One naturally attributes intelligence to a mind that generates its own array of plausible possibilities, and stupidity to a mind that produces inappropriate ones or has to be fed with suggestions in every new circumstance. Seeing possible solutions is an essential part of good guesswork, and the nature of this imaginative ability may be a more interesting question than that of assessing statistically whether a given association is present or not. The main difficulty here is the astronomical number of possible associations: it is certainly not intelligent to point to any or all of them for testing, whereas it would, for instance, show a glimmer of intelligence to start looking for associations between events that occur with approximately the same frequency. It seems likely that numeric measures of imaginative inventiveness would have to depend upon comparisons with population norms, as with the standard IQ. One must also pay attention to the third distinctive part of intelligence.Deductive intelligence. It is not intelligent to claim as a new association something that can readily be deduced from associations that are already known. Every moment we see sights and hear sounds that can be predicted from associations already established by our own minds, or implanted in them by others. To distinguish what is new, knowledge of these pre-existing associations must be organized so that they are taken into account. Thus the deductive reasoning required to use a background of general knowledge is a necessary part of intelligence on the current definition.
5. Summary
The suggestion that intelligence is complex and requires imagination, judgement, and reasoning will surprise no one. But insight from the information sciences leads to two novel conclusions: first, the part concerned with statistical judgement can in principle be measured on an absolute scale, using theoretical limits as references rather than population norms; and second, the basis for efficient use of information in guessing right comes from processes that are part of perception, rather than learning. The diversity of minds and their aptitudes should not conceal the fact that there is a recognizable unity behind all manifestations of intelligence, namely the goal of improving the reliability of predictions by exploiting the redundancy of sensory messages — in other words, intelligence helps us to guess right.(Published 1987)
— Horace B. Barlow
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