Smith, Steven B. The Great Mental Calculators: The Psychology, Methods, and Lives of Calculating Prodigies, Past and Present. Columbia University Press, 1984. "Intelligence is as intelligence does!" as Forrest Gump would say. It is through our hands, our communication with language and symbols, and our ability to cooperate, that the fruits of culture and civilization are experienced and extended for better or worse, by each member of Homo Sapiens. For Arthur Jensen, intelligence cannot be defined without employing the mysterious "g-factor". The g or General Factor is that which is at the root of intelligence itself, but no one, including Jensen, seems to be able to tell us what that is. Some say it is Abstract Reasoning, others say its general problem solving ability...it remains an unknown entity as of this writing. Being active in the world, learning about the world, and making a living in addition to seeking answers to our questions about reality, defines intelligence at the human level of existence. The problem with "G" can be meaningfully understood by a little side journey into the Mathematics of "Lie Algebras". Lets call "G" a faithfull representation of a Lie Group, with structural constants. Knowledge of the structural constants give us knowledge of some open region of G. Whatever G is, we only know some small region of it "N", surrounding the identity element "I". knowing the region N, does not tell us about the global nature of G. We can symbolize I within N, but N is always a "patch" on G, whatever that is. Over time, we can extend the patch to get more of an idea of how G is structured, only Guilford has made this attempt. Guilford was attempting to extend this "patch" on G, untill we could see its total structure. What is common to all of Guilfords Factors?? Can we somehow geometricaly isolate the commonality in all of Guilfords Factors? If we could, we would be looking at G. There does not seem to be a "G" Factor at all, other than what we do with our minds, from day to day and as a sum total of human history.
TESTING INTELLIGENCE
According to the late Mathematician, Alan Turing, it would be possible someday, to be fooled by a machine. That is we could be having a conversation with this machine, and not know it was a computer. This taps into what we are referring to in this article as the Meaning function, and even though it may be possible to dupe a human into thinking the computer is sentient, it is doubtful that any computer will be aware of itself as an intelligent entity. (see, Alan Turing, the Turing Test). This test is basically an imitation of human conversation, that has been programmed to respond to humans. When a computer can make decisions based on its conversations with an intelligent human, and continue to learn from experience.....we may have a sentient being, the so called "Blue Brain", touted by the Artificial Intelligence community. The debate rages about the possibility of Electronic Life, the Blue Brain and whethor or not we as humans, will be replaced by a more powerful intellect, coming out of the order of Computers. Computers that program and repair themselves, and learn from experience, may be very near in the future. (see Levels and Loops: The future of Artificial Intelligence and Neuroscience). If our intelligence is a kind of "noise" or after effect of our wet brains, then it follows that electronic or atomic brains could exist, that claim to be conscious. Intelligence for a Blue Brain would be a function of its inherent order, and that order would allow for some expression of an entity that can express a sensitivity to order, as well as to its own existence. If this is the case, then one level of order expresses itself as a plant, another level of order brings the animal mind and yet another complexity yields human consciousness. Is the brain making consciousness?, or is it simply a receiver for some deeper dimension of being, most likely at the Quantum level, that we call consciousness? (See the Emporers New Mind, by Sir Roger Penrose). The debate proceeds on.
When we really examine Intelligence, it appears to fall into two broad categories: EXECUTIVE FUNCTIONS, like memory, reading, calculating and things we have learned and do automatically, and MEANING FUNCTIONS, as in reading and understanding a philosophy paper, or understanding an idea in Physics. A computer is an example of a device that can outstrip humans in almost all Executive Functions. However, no device has ever outdone us in MEANING. Meaning, Understanding, is the true mark of Intelligence, and its measurement by intelligence tests, remains somewhat elusive. The accepted tests of Intelligence designed by Cognitive Scientists and Psychologists, like the Stanford Binet 5, the Wechsler Adult Intelligence Scale-1V, and a host of others, claim to measure both the Executive and the Meaning functions of Human Intelligence, but their labels for these two broad categories of ability differ. http://www.riverpub.com/products/sb5/details.html . David Wecshler's Idea of how to measure Intelligence differs from that of Lewis Terman, or Alfred Binet, or other test creators. The test makers themselves, only agree that Intelligence can in fact, be measured. Broadly defining: Beings or machines that calculate, or use algorithms, or store information, are using Executive Functions. Activities like Law, Philosophy, Literature, and Science at most levels, are using the Meaning Function of intellect. According to Professor J.R.Flynn, people all over the world have shown an increase in IQ. Obviously Flynn does not believe in a static IQ, and he offers advice to test developers. (see: What is Intelligence? James R. Flynn,Cambridge University press, 2007)
Opinions vary on what constitutes a valid intelligence test. www.sushkin.com/connecttext/psy.ch08/what.mhtml Most Psychologists agree that standardization and item analysis is essential to constructing a valid instrument. Tests abound on the Internet, that are guesses, at best, as to what makes a good measure of intelligence. Until the Stanford Binet 5 came out with the incredible top of 220 (an extended scale), intelligence tests were hard pressed to accurately measure an IQ over 155. For all practical purposes, the limit of measurable Human Intelligence is around 160. Scores above this figure have very little meaning, as meaning itself still cannot be measured as a mental ability with scales that seperate people. Someone with a photographic or super auditory memory may be able to push high into the new Stanford Binet extended scale up to 200, and not really understand the writings of Bertrand Russell. Trying to find a human being who is twice as intelligent as a normal human being is madness, and vanity on the part of those who claim these scores. Sir Roger Penrose, Steven Hawking, Thomas Edison, Albert Einstein...and others showed us their working Meaning Function Intellects,by their output and contribution to mans knowledge. To assigen a number to their intelligence is sophomoric at best. The mathematician and Physicist Edward Whitten, is probably more intelligent than 99.99999 % of people on earth, yet his scores on one of these tests could fall almost anywhere between 115 and 160. His work IS his intelligence. Pick up THE ROAD TO REALITY, by Sir Roger Penrose, and you will read the words of a true Genius!. Its folly to put these people into a box with a number on it. The Standard Curve, or Gaussian Curve indicates that beyond an IQ of 137, these scores may not have much meaning, in terms of what they tell us about the people who earn them. As the normal curve shows that on a good standardized test, an IQ of 137 is the top 1% of the population. Statistically, IQ's over 137 have little meaning, as the population is very thin beyond the 99th percentile.

There seems to be an innate dislike with many, for being simply average. You almost never hear anyone tell you that they have an average IQ. Their reports often put them above that 1% in population, which, mathematically, we know for most of the people reporting these scores, that they simply must be falsehoods. A man 7 feet tall is rare, and just about as rare, is an IQ of 165. An examination of the above diagrams will show that an SAT score of 700 falls into the area of 2% of the testing population. This does NOT translate to an IQ of 130 or better, as the two instruments measure different abilities and skills. The SAT is an achievement test, and although it must correlate somewhat with IQ scores, the pure cross reference for percentiles, is not valid. A score of 700 on the Verbal part of the SAT does not mean that the examined has a Verbal IQ of 130. An average IQ is between 90 and 109, and this accounts for 68.8% of the population. http://iq-test.learninginfo.org/iq04.htm .Looking at the top curve depicting IQ scores, it can be seen that scores of 85 to 115 take up 68% of that curve. This is because 15 points is considered one Standard Deviation from the mean (100), on each side of 100. We often demand to much of ourselves, out of ignorance of the numbers involved. The average person, for example will tell you that the average age for an infant to walk is about 12 months, or even earlier. In fact, the average age for starting to walk unaided, in human infants is 15 months, the range is 9 to 18 months. www.parenting.com . We exaggerate height, intelligence, strength, and even income and longevity, based in part on our sense of inadequacy, and in part due to being innumerate. The average man is not 6 feet tall, and the average income, as of this writing, is not 75 thousand a year. Knowledge of what is average, seems to belong to the few who have a sense of numbers and are not innumerate. Developing a test of "Knowledge of the Mean", may be an interesting project for a Cognitive Psychologist. (See INNUMERACY, Mathematical illiteracy and its consequences, by John Allen Paulos, 1989. )
It is noteworthy that one common test found in all intelligence tests that test more than just reasoning or general knowledge, seems to correlate higher with overall IQ than any of the others and that test is VOCABULARY. Most psychologists will agree that ones vocabulary seems to be the best single measure of ability, if you had nothing else to use to estimate intelligence. When we develop our vocabulary, for the most part, its is done unconsciously, as we pass through school and life. It is a function of our working memory and our ability to pick up information from our surroundings, our culture and our specific cohort. For this reason, the PEABODY PICTURE VOCABULARY TEST, correlates very highly with other tests that claim to measure intelligence. The Peabody simply asks the examinee to pick out one of four pictures that best portrays a given word. This test is very easy to give, and gives a very good estimate of how the subject will perform on other tests with more tasks and sub tests to measure the dimensions of intelligence. Words as common as "Ball" and as uncommon as "Cenotaph", are given, and there are several forms and word lists. In our Seperation of Intelligence into Executive and Meaning Functions, the following examples will be helpful:
Examples of tests that call on the EXECUTIVE FUNTION of intelligence are:
1. What are the next two numbers in this series? 77,49,36,__,__ ( 18,8)
2. Arrange the following numbers and letters in order: 7,9,c,4,g,v,t,3,q. (this is tested from memory)
3. Collect the following into their respective categories: ALLIGATOR, CHAIR, PARIS,SNAKE, CINCINATTI,SOFA,LIZARD,TABLE,CUBA.
4. You buy a roll of 40 cent stamps for 20 Dollars, approximately how many stamps are on the roll?
5. Recall the following words after 10 minutes (other tasks given in the interim): Ball, Shirt, Peace, Turkey, Handsome, Pencil, Thief. (note that not all the words are objects).
6. Replicate a design from a card from one inch cubes: This is Kohs Block Design Test. (see Encylopedia of Psychology, Google)
7. You are sent to a river to measure out exactly 2 pints of water, given only a 5 pint can and a 4 pint can. Explain how to arrive at 2 pints of water, begin by filling the 5 pint can. (no measurements or markings are involved).
Which 3 of these pieces go together to make this puzzle? (sample from the new WAIS-IV)

Here are some samples of test items that tap into the MEANING FUNCTION of intelligence:
1. How are a WATERFALL and the SUN alike?
2. If you find someones unopened mail on the sidewalk, what should you do?
3. What is the exact Opposite of an Island? ( Lake. Peninsula is not the correct answer).
4. Why do we have immigration laws?
5. Explain the Meaning of this short sentence: EXTREME CAUSAL EFFECT. (note that we want the meaning of the entire sentence, not each individual word).
6. Why does our Constitution insist on a separation of Church and State?
7. What does this saying mean?: "Shallow brooks are noisy?"
8. place a single word in the blank to give this sentence meaning: "We find, that in the long run, most of our______ bear fruit." (efforts, labors, etc).
You will notice how the Meaning questions tap into our cultural knowledge as well as our common sense and understanding. For many reasons, the Meaning dimension of Human Intelligence is the most difficult to measure, and yet the most important function of the Human Mind, and a salient part of Law. A course in Set Theory and Logic would go a long way toward helping young people develop clearer thought, and be able to utilize the Executive Functions of their Intelligence to augment their Meaning Functions. High schools should provide the basis for meaningful thought on a variety of issues. Upon graduation, a test of general knowledge, along with essays on various subjects, may well be a way to augment our present testing programs in Amercan Schools. We may not make future generations more intelligent, but we certainly can provide an environment that will make them more thoughtful. At present, American High School Graduates are deficient in Mathematics, knowledge of World Religions and Civics. Schools in Europe and on the other side of the world in Japan, do not allow these deficits. (See: IES National Center for Educational Statistics): sample link: http://nces.ed.gov/PUBSEARCH/pubsinfo.asp?pubid=200407
In line with education and testing, no discussion of Intelligence and its measurement would be complete without including the great J.P. Guilford.
J.P.GUILFORD AND THE MULTIPLE FACTORS THEORY: J.P. Guilford (1897-1987), worked for decades to define all of the parameters of human mental abilities. He believed that intelligence was made up of clusters of aptitudes, which he labeled "factors". Guilford classified these factors and concluded that there were at least 180 of them. Most intelligence instruments on the market today will test anywhere from 7 to 10 factors. One of the most accurate and cheap tests out, the Shipley Intelligence Scale, tests only vocabulary and simple problem solving. Yet this simple pencil paper test has proven to be an accurate instrument for understanding the intelligence level of inmates in prisons and mental hospitals all over the United States. What will we gain by comming up with tests for all 180+ factors that Guilford proposes? Perhaps better ways to help people decide on various careers, or to aid in our ongoing research into the Mind and Brain. Certainly a test that measured all of these factors would be unusualy long and cumbersome. The Differential Aptitude Battery, (DAT) has been in service for a long time, testing junior high school and high school children to help them make decisions on future careers. The GATB, or General Aptitude Test Battery is another aptitude series that assigns an IQ like score for each aptitude and even comes up with a General Score. Guilfords Factors interact with one another to produce aptitudes in isolation, and are classified into OPERATIONS, CONTENTS and PRODUCTS. A test desigened to test Symbolic Convergent Production, for example, is from combining the Products and Contents sub factors...Symbolic, with Convergent Production. These various factors or aptitudes can be modeled as a 3 dimensional cube. There are tests out now, that measure up to 26 of Guilfords Factors. http://rer.sagepub.com/cgt/pdf_29/1/96 It is hoped that people will stop being labeled by IQ, and the multi-factor idea will catch on and the various strenghts and weakness's that everyone has, will be known to them personaly through proper testing and proper interpretation of the scores, as a part of their normal education. If it turns out that a child is very good at Symbolic Operations, this may mean that Mathematics orComputer Programming or a related field would be approriate. The Childs school record would indicate the high score on Symbolic Operations and the scores on various other factors, without a global or general score. Gifted Children who score high on many of these factors could be accomodated by chosing the right areas to emphasize with further counseling and personality and interest testing. What is the difference between someone with an IQ of 132 and someone with an IQ of 188? Since the number of people drop off beyond 132, the differences would have to be less and less as the scores increase. A single score, simply has very little meaning. But if the child is told that he or she is good at Symbolic Operations and is not as good at Semantic Evaluation, it has more meaning than a global score, when these factors are known and explained. The great Richard Feynman, Nobel Laureatte and a Theoretical Physicist, had a high school pencil paper IQ test score of 125. (see GENIUS, the biography of Dr.Richard Feynman, by James Gleick). This score is in the 95%tile, but is it what anyone would expect of a genius who worked on the Atomic Bomb and won a nobel prize in physics? An IQ of 125 is about the average for Physicians according to the Wechsler Scale. Feynman was a Genius and that is not disputed by either his work or anyone that knew him. Most Psychologists save the Genius category for people who test in the neighborhood of 155 and above. Our definition of Genius must not be exclusive to an IQ score alone. If Dr. Feynman ever had himself re-tested on a bonified individual test, it is not known.Test scores and Genius must not always correlate highly. Global scores, especialy on pencil paper tests are not of any lasting value, especialy when it comes to assessing future contributers to human knowledge.
IMPROVING YOUR INTELLIGENCE
Neuroplasticity is the reason you can improve your intelligence. Both your executive and meaning functions improve when you give yourself a new experience or learn a new task. Learning to play the piano, forcing you to learn with both hands is among the best ways to make your brain wiring denser and your overall intellect will feel the positive effect.Take up any musical instrument, learn a second language, pick up that old algebra book and re-wire your brain on how to solve word problems. Learn short cuts in mental arithmetic, you can find many books on this subject that will exercise and improve your mind. Put away that calculator and estimate the answers in your head. You will dust off the cob webs and make yourself smarter. Do you exercise frequently? How good is your balance? your cerebellum tells your muscles how to operate to walk or sit or any physical activity. How long can you balance on one foot? Balance daily and practice untill you can balance on one foot and bend down and touch the floor with your hands with one leg up in the air. Exercise to the point where you are breathing hard at least 3 times a week, or more....this is excellent for your brain. So is Tai Chi, Chi Kung, and any of the mind-body exercises discovered and practiced in the east.
When is the last time you engaged in a discussion that involves thought and meaning? What is the highest number? We never see a brown light, why? Just what is Gravity? Why is the speed of light, the speed that it is? Can you slow down light? Are there an infinite number of sets of things? What would the set that contains all sets be called? What is free will? Do we really have free will? Could our Universe have come from some other Universe? What IS space? Does it have an end? What is the difference between justice and the present execution of our laws? What is the value of Capital Punishment? If there are intelligent beings on other planets, what would they look like? Are UFO's real, or just wishful thinking? Pick up a good philosopher and read him/her. Read Kierkegaard, David Hume, Bishop Berkeley, Bertrand Russell. Identify erronious thinking and reporting in the news. Take a course in logic or set theory or both. All of these things will expand the meaning function of your intellect. Best of all, challange your own cherished beliefs. Other people in other parts of the world do not believe in God the way you do, why? Is there a God? What evidence do we have of such a concept? Do you really understand the Theory of Evolution? What is the evidence for evolution? What does the word "Theory" really mean to scientists as oppossed to laymen? Challenge what you have been taught as true, and you will find that you are expanding your mind in many directions. Is everything written in the newspaper true? Do Republicans always really cut back on the Government? Do Democrats always really spend to much? Are Democrats Socialists and Repubicans Imperialists? Was the Civil War in America necessary? Look into things you have been told and dont just accept them at face value. And yes, you can watch the History channel, the Discovery channels and all the Science channels. Watch "how its made" and the "myth busters". As they said in school long ago..."put on your thinking cap" .Your mind can be expanded, your Intelligence can be improved.
OF RELATED INTEREST
- Artificial Intelligence
- Systems Intelligence
- Theories of Intelligence
- Educational Psychology
- Intelligence and Race
- Memory Systems
- Short cuts in Math
- Human Factors Studies
- Exercise and the Brain
- Giftedness
- Chi Kung and Tai Chi
- Meditation and Yoga
- Brain Physiology
- Holographic Theory






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