Intelligence, creativity and genius are generally regarded as highly valuable assets of the human mind. As a strong positive correlation exists between IQ and the median earned income, most people would gladly boost their IQ, improve creativity or accept being called a genius. Exceptions to this rule are few and most revolve around a claim that intelligence may be an obstacle on the way towards universal happiness. Here are a few exemplary arguments against human intelligence listed by the detractors of genius:
- high intelligence reveals existential truths and as such is highly depressive
- high intelligence prevents atavistic enjoyment of relationships
- high intelligence is a source of envy and other bad feelings in others
- high intelligence leads to inhuman behaviors and most sophisticated forms of evil
In this article, I will tacitly ignore the above claims and assume that you would gladly become more intelligent, creative or innovative. I believe it can be shown that an increase in knowledge and creative power can statistically leads to more "goodness" (see: Goodness of knowledge). I will tacitly assume throughout this text that achieving creative genius is a desirable goal.
Many books on psychology put a substantial emphasis on the nature-vs-nurture debate. Psychologist ask which factors are decisive in developing human behavioral characteristics: genetic background or education and upbringing? As far as intelligence is concerned, both genetics and upbringing determine the final outcome. Using reductio ad absurdum we quickly notice that we have not yet recorded a case of a success in science by an individual affected with Down syndrome, i.e. we can easily show that genetics can stifle intellectual development. At the same time, we notice that individuals deprived of education and human contact may be deprived of the ability to read, speak or conduct abstract reasoning, i.e. we can show that lack of education may be equally devastating to the human mind (see: Feral children).
The power of genetics on the functioning of the brain is illustrated by afflictions such as Down syndrome (mental retardation), dyslexia (reading problems), amusia (problems with recognizing sounds and music), unipolar and bipolar disorders (depression and manic-depressive disorder), and many more. These factors on one hand illustrate that we may at birth be handicapped in the quest for genius. At the same time, behavioral therapies used in all listed cases, show the tremendous power of training in developing compensation for disability.
If you look at the human brain from 100,000 years ago, you will not see much difference when compared with today's brains. Yet training and education, as well as the ability to communicate and work collectively, has lifted the human potential to unimaginable levels. See gray insets for more insights on the potential and limitations of the human brain.
|Throughout this article, gray inserts will provide additional illustrative material. All inserts are optional! These are stories that can either explain major points by example or simply serve as a source of additional inspiration. The order of inserts is arbitrary. Each insert makes a separate and independent reading. Some may require more knowledge in a given field (e.g. biology, computing sciences, etc.). You do not need to read gray inserts to understand the text. You can read all inserts now, later, or not at all|
Of the inborn disorders that affect intellectual capacity, Down syndrome is the most prevalent and best studied. Down syndrome is a term used to encompass a number of genetic disorders of which trisomy 21 is the most representative (95% of cases). Trisomy 21 is the existence of the third copy of the chromosome 21 in cells throughout the body of the affected person. Other Down syndrome disorders are based on the duplication of the same subset of genes (e.g. various translocations of chromosome 21). Depending on the actual etiology, the mental retardation may range from mild to severe. Trisomy 21 results in over-expression of genes located on chromosome 21. One of these is superoxide dismutase gene. Some (but not all) studies have shown that the activity of the superoxide dismutase enzyme (SOD) is elevated in Down syndrome. SOD converts oxygen radicals to hydrogen peroxide and water. Oxygen radicals produced in cells can be damaging to cellular structures; hence the important role of SOD. However, the hypothesis says that once SOD activity increases disproportionately to enzymes responsible for removal of hydrogen peroxide (e.g. glutathione peroxidase), the cells will suffer from a peroxide damage. Some scientists believe that the treatment of Down syndrome neurons with free-radical scavengers can substantially prevent neuronal degeneration. Oxidative damage to neurons results in rapid brain aging similar to that of Alzheimer's disease. Another chromosome 21 gene that might predispose Down syndrome individuals to develop Alzheimer's pathology is the gene that encodes the precursor of the amyloid protein. Neurofibrillary tangles and amyloid plaques are commonly found in both Down syndrome and Alzheimer's individuals. Layer II of the entorhinal cortex and the subiculum, both critical for memory consolidation, are one of the first affected by the damage. A gradual decrease in the number of nerve cells throughout the cortex follows. A few years ago, the Johns Hopkins scientists created a genetically engineered mouse called Ts65Dn (segmental trisomy 16 mouse) as an excellent model for studying the Down syndrome. Ts65Dn mouse has genes on chromosomes 16 that are very similar to the human chromosome 21 genes. With this animal model, the exact causes of Down syndrome neurological symptoms will soon be elucidated (for the amazing genetic science in action see: Cytogenetics Resources Ts65Dn including pictures of "Down syndrome mouse"). Naturally, Ts65Dn research is also likely to highly benefit Alzheimer's research.
Whatever the actual molecular reason, over-expression of chromosome 21 genes puts children with Down syndrome at immediate disadvantage as compared with normal kids. Their IQ rarely goes beyond 60. The brain of children with Down syndrome is usually small and underweight. The cerebellum and brain stem are unusually small. So is the superior temporal gyrus. Their intellectual potential is further limited by a number of ailments such as recurring infections diseases, heart problems, poor eyesight, etc. Genetics is a true roadblock here. People with Down syndrome have (until now) never become great scientists, novelists, politicians, etc.
At the same time, medical treatment, conducive family environment, vocational training, etc. can increasingly produce excellent improvement in the overall development of Down syndrome kids. On one hand, Down syndrome shows that we cannot jump over genetic limitations; on the other, it shows that intense training can produce miracles whatever the starting point. In conclusion, the optimum path to excellence goes via the mental training independent of genetic limitations
You will find many definitions of human intelligence of which three make the most of the daily use of the word:
- problem solving ability - the power of the human mind to process information and solve problems. When you see a bright scientist with wide knowledge and numerous discoveries to his credit, you may say: This person is really intelligent! Look at his record! To use a computer metaphor, the scientist is endowed with the best hardware and software money can buy. He or she is optimally equipped for problem solving
- processing power - the raw nimbleness and agility of the human mind. When you see a smart student quickly learn new things, think logically, solve puzzles and show uncanny wit, you may say: This guy is really intelligent! See how fast his brain reacts! The student has a fast processor installed and his RAM has a lightning access time. He may though still need a couple of years to "build" good software through years of study. IQ tests attempt to measure this sort of intelligence in abstraction of knowledge. The difficulty of improving processing power by training comes for similar reasons as the fact that programming cannot speed up the processor
- intelligence potential - the potential to develop intelligence in senses listed above. When you see a young child that shows a number of talents and seems to be on a straight path to become a nimble student or a prolific scientist, you may say: This kid is really intelligent! The sky is the limit for him. The kid is equipped with high quality extensible hardware infrastructure. He is on the best path to reach highest intelligence both in terms of processing power (Definition 2) and problem solving ability (Definition 1)
In this article, I will focus on ways towards developing the intelligence in the sense of problem solving ability (i.e. Definition 1). After all, the whole purpose of education is to improve our problem solving ability, i.e. the ability to optimally answer questions such as What to eat for dinner? What job to take? How to build a better mouse-trap? What should my position on abortion be? Which party should I vote for? etc.
High IQ is welcome but it makes up for only a fraction of intelligence (Definition 1). As much as a fast processor stands only for a fraction for what we expect of a good computer.
Later in the article, I will argue in support for the scientifically obvious statement: well-designed training can produce amazing results in enhancing intelligence (Definition 1). However, this statement is surprisingly little understood in general population. It falls into the category of scientific facts that may find more skeptics than believers. Naturally, vox populi does not detract from the merits of evolution, genetic engineering, human cloning, Big Bang theory, sociocybernetics, neuropsychological interpretation of the thought and consciousness, etc. However, to make the obvious more digestible, I will use the computer metaphor to illustrate the building blocks of intelligence and genius
The neural network of the brain can be seen as mental hardware. It includes inborn ROM memory as well as highly plastic RAM. The inborn wiring and structure of the brain may roughly be compared to a ROM memory. If you stop eating for a day, program stored in your ROM will make you experience hunger. Things we learn in life can be considered software that is stored in your RAM.
If you doubt a mental ROM exists try the following experiment: look at the computer screen, keep your eyes open, stay conscious and yet try not to perceive the picture of the screen. Seems impossible? Now try to superimpose the face of a loved person by using the power of your imagination. This is easy for most people. Here is your RAM in action superimposing over a ROM-enforced perception. You can even imagine touching parts of the imaginary face. Yet the screen underneath does not seem ready to go away. The impulses from the retina hit the visual cortex, and you can do little about it.
Knowledge is encoded in the modifiable strength of connections between neurons in a similar way as bits are stored by electrical charges in cells of RAM memory. Our software can roughly be compared to an expert system. An expert system is a software application that can be used in problem solving such as producing a medical diagnosis. An expert system is built of two components: factual knowledge and an inference engine. They roughly correspond to data and software in a computer or to knowledge and reason in the human brain.
| Expert systems
Expert systems are computer programs that take over the job of an expert in a highly specialized field such as medical diagnosis, production management, criminal profiling, etc.. An expert system is fed with data and it's job is to answer questions such as: "What is the list of the most likely diseases the patient is suffering from?", "Which supplies need to be ordered next?", or "Which offenders in the database match the profile of the described crime?". Expert systems provide an excellent metaphor for studying human problem solving and provide clues for enhancing creativity.
An expert system is usually built of a knowledge base (collection of facts representing factual knowledge) and an inference engine (collection of rules representing inferential knowledge). An expert system may store facts such as "E. coli bacteria is not resistant to norfloxacin" and "E.coli can cause urinary tract infections". It can also store updateable facts such as: "Pain during during urination is associated in X% of cases with urinary tract infection" (where X is a number regularly updated as the expert system improves its knowledge), or "E. coli is a cause of Y% of urinary tract infections". The expert system can also store rules such as "If (A is an antibiotic) and (B is a bacteria) and (patient is infected with B) then (suggest administration of A)". Some rules can be fuzzy, i.e. applicable with a degree of probability or producing a given outcome with a given probability, for example, "If (patient infected with E. coli) then (probability of success with norfloxacin is P%)" or "If (probability of E. coli infection is greater than P%) then (use norfloxacin)". By analyzing the facts stored in the database and facts fed into the expert system, the expert system can use its inference rules to answer questions on the optimum antibiotic therapy. It can also generate the probability profile of the successful application of individual antibiotics. Although the difference between static facts and if-then rules in an expert system is very clear-cut, there is no sharp fact-rule distinction in the human brain which uses neural representations for storing knowledge. However, the difference between facts and rules is very valuable in explaining the difference between smart and dumb learning.
Expert systems are always based on storing large amounts of information. They are built by peeking at human experts in action and concluding about their reasoning. A knowledge engineer or an expert himself needs to formulate the rules that are used in arriving at a solution to a problem. Consequently, there is a very direct parallel between an expert system and a human expert in action.
Much of expert thinking is much simpler than what happens in a child's brain in the course of ordinary play! The reason for this is that we are inborn with powerful computing machinery for visual processing, for association, for analyzing motion, for spatial orientation, for phonological analysis, for language parsing, etc. A child recognizing a simple ba-ba language may be harder to imitate in a computer than an expert botanist recognizing one of a thousand species of plant. As Marvin Minsky put it: It can be harder to be a novice than to be an expert! A program written in 1961 by James Slagle could solve calculus problems that are normally given to college students. This program was able to score an A on an MIT exam. This program needed only about a hundred algebraic rules to solve all the required calculus problems! Calculus permeates engineering and forms part of the foundation of the industrial world. It is also a classroom nightmare to many students. Yet in essence it is very simple and compact. Simplicity of calculus powerfully illustrates what our brains were not born to do. It also shows what new powers our brains can acquire with relatively little effort if the new knowledge is selected in the right way. Algebra can serve as a model of abstractness of rules. After all, it is based on symbols that can mean anything: a plane or a bird or just anything. As stated throughout this article, abstractness of rules stored in the human brain lays at the foundation of creative thinking.
What an expert needs to know can indeed be simple. However, it is often not simple to discover or explicitly formulate it in the first place. Many students may have problems with calculus because of the simple fact that some rules of calculus are highly heuristic and cannot be found in math books. Good (or rather hard working) students acquire those rules implicitly by solving a large number of calculus tasks. Poor students could easily catch up if their books or teachers explicitly formulated those hazy rules, e.g. if you see those two symbols on the left, go for the rule X rather than wasting time on the remaining five other possibilities that can cost you an hour each. Human experts seem more intuitive than computers. But this only comes from the fact that they apply rules that they themselves have hard time formulating. There is no qualitative difference between human or computer expert in that respect. Intuition is not a magic power. Intuition is an inability to explicitly express knowledge that is already wired in the neural network of the brain.
As with the haziness of the rules, similar uncertainty may concern the actual application of inference rules: the problem solving strategy. A creative individual will often not be able to clearly say how and why he or she arrived at the solution. When later writing a scientific paper on the solution to the problem, the creator will often need to look for a clear path towards the solution even though he has definitely arrived at the goal before. Expert systems may use various strategies such as data-driven derivation called forward chaining (going from the facts to a conclusion, e.g. deriving symptoms from a disease database), goal-driven derivation called backward chaining (going back from the goal to test a hypothesis, e.g. testing for a disease given the symptoms), search (applying simple rules repetitively over a large number of combinations that could yield a solution), and various combinations of these strategies. As for the problem solving strategy, the human brain is even harder to simulate. Usually the search space for major problems is huge and no simple strategy can be used (otherwise the problem would not be a problem in the first place). Then the lucky genius stroke, the brilliant association, insight, breakthrough, etc. is nothing else than applying the right rule to the right data at the right time. The "right time" here refers to the different states of the brain at different moments of time. The brain works associatively and two or more neuronal assemblies must be active at the same time for the association to be formed. Archimedes could have thought of volume when entering his bathtub before he yelled: Eureka! Newton's brain must have been sensitized to gravity when he was struck by a falling fruit. James Watt must have had his engine-power neurons potentiated when looking at a rattling kettle. Millions of people see kettles daily but they rather do not think about a steam engine as a result. The genius breakthrough comes from an association of ideas in the brain. In terms of an expert system, the right rule must be applied to the right set of facts. The best term to describe human problem solving is heuristic search. We apply available rules using the best-search rules which may be subject to another layer of meta-rules that are implicitly interwoven in the intricacies of the neural circuitry of the brain.
In conclusion, knowledge is the key to problem solving. In particular, highly abstract inferential knowledge is central to a creative search for solutions. The disassociation of the link between knowledge and genius can be harmful. The confusion usually comes from the fact that memorizing worthless data is not differentiated from memorizing useful rules. Many people mistakenly fail to recognize the associative power of human memory and conclude that relying on external sources of information may suffice in their particular field of activity. As a result, memorizing is perceived as a dumb act. Some articles at supermemo.com illustrate this problem:
The most important things we learn from expert systems is that extensive knowledge helps solve problems. We also learn that the way we represent knowledge may determine the successful outcome of problem solving. Conclusions: we need to keep on learning and we need to pay special attention to how we represent things in our memory to ensure we understand the implications of the things we learn.
For a quick course on basic concepts of Expert Systems and Artificial Intelligence see: ABC of AI
Factual knowledge is made of facts. A fact may have a form of "Jimmy Carter was elected the US president in 1976" or "Abraham Lincoln was assassinated in 1865". Inference engine is based on inferential knowledge. Inferential knowledge is made of a set of rules. Unlike static facts, rules can be applied to facts to produce more facts, assertions, statements, theorems, formulas, etc. For example, a rule may say "Since the 22nd Amendment, a US president cannot serve for more than ten years" (i.e. two terms plus two years of possible succession). From a fact "Jimmy Carter was the president" and from a rule "President cannot serve for more than 10 years" we can derive new knowledge: "President Carter served no more than 10 years". In mathematics, a fact may say that x=3 and a rule may say that x+x=2*x. By applying the rule to the fact we can conclude that 3+3=2*3. Rules can then be used to derive new facts and new rules. If we know that x+x>x (for x>0) then we also derive a new rule: 2*x>x. In the course of problem solving, our brain will often develop new rules and store them in memory. These new rules will form a highly valuable component of your knowledge and will decide on your creative powers. Rene Descartes said: "Each problem that I solved became a rule which served afterwards to solve other problems"
Apart from declarative facts and rules which we can learn in a textbook, our nervous system also includes other forms of knowledge. For our analysis we will mostly need to discern: inborn knowledge and procedural knowledge. Inborn knowledge can be compared to rules stored in our ROM. For example, when feeling a burning pain in fingers, retract the arm. Procedural knowledge is knowledge that is acquired by trial and error via punishment-reward stimuli. For example, when we ride a bicycle, each time we lose balance, an information is sent to the motor system not to repeat the recent moves that should be considered an error. At the same time, the elation of smooth ride, reinforces the circuits responsible for sequential stimulation of muscles involved in cycling.
Apart from inference engine, our brain is equipped with a sort of "interference engine". Our brain was programmed for survival. It is supposed to make you search for sources of water when you are thirsty or react with interest to an attractive representative of the opposite sex. We are driven by instincts and emotions. Emotions helped humans survive thousands of years of evolution. However, emotions also interfere with the intellectual effort. Isaac Newton might be the brightest scientific mind of the 17th century, yet the last 25 years of his life were marred by a bitter battle with Leibnitz over their claim to having invented the calculus. Alan Turing, the father of the famous Turing Test, committed suicide by cyanide poisoning under the burden of intolerance brought forth by his homosexuality. His mind might have been affected by a hormonal therapy that was supposed to "cure" him of homosexuality. Even the greatest mind may be incapacitated by a strong interference from hormones or lower-level brain circuits. Emotions can literally kill genius.
Here is the summary of the computer metaphor of the human mind. Terminology defined here will be used throughout the rest of this article:
Hardware - the brain
Infrastructure - brain components: cortex, thalamus, cerebellum, basal ganglia, etc.
ROM - inborn knowledge (e.g. acrophobia)
Software - knowledge
Declarative knowledge - textbooks knowledge
Facts - e.g. Mary is a pilot
Rules - e.g. All snakes are reptiles, formula for solving quadratic equations, etc.
Procedural knowledge - skills (e.g. playing piano, touch typing, swimming, etc.)
Interference - emotions, instincts, reflexes (e.g. hunger, thirst, orgasm, etc.)
positive emotions (e.g. passion, laugh, elation, zeal, energy, etc.)
negative emotions, instincts, reflexes (e.g. anger, envy, hate, malice, etc.)
In the above light, we can simplify genius to the following:
Genius is based on good hardware, excellent knowledge, strong motivation, and minimum negative interference.
In other words:
- it is helpful to be blessed with a healthy brain (hardware)
- this brain must be subject to a lifelong training in acquiring useful knowledge (software); esp. problem solving knowledge
- knowledgeable brain must be driven by strong motivational factors (drive), including positive emotions (passion, enthusiasm, love, etc.)
- well-driven knowledgeable brain must avoid negative interference from inborn weaknesses and destructive emotions (e.g. few things cloud judgment as badly as anger, and few things are as distracting as love)
Using the "simplified brain model" above, I will try to look for factors that determine a genius brain and how these factors could be influenced.
A genius brain in action will tackle a problem, quickly find an appropriate set of rules, and derive a solution. Actually, the speed of processing the rules is not as critical as the skill in choosing the appropriate rules at hand. For a genius breakthrough, the speed is usually quite unimportant. It took Darwin five years to collect data during his Beagle trip to come up with a vision of the evolutionary process. Yet it took him another 20 years collecting all necessary material, and opinions before mustering courage to publish On the origin of species. The book has changed our view of the human species for ever. It is hard to pinpoint a single breakthrough or a stroke of genius. Darwin's reasoning wasn't blindingly fast neither. Yet Darwin's impact on the ways of the mankind was monumental
|Biological basis of genius
Humans do differ in their brain power. Some get a biological head start, others get handicapped from early childhood. In cannot be stressed enough though that the optimum path towards maximum achievement is always through training. The starting point is not relevant for choosing hard-work learning trajectory. It is also important to know, that in majority of cases, mental limitations can be overcome. Some major disabilities, such as Down syndrome or brain injury can pose a formidable challenge. However, practice shows that a huge proportion of the population see a problem where it does not exist. Many people write to me about their memory problems just to discover (e.g. with SuperMemo analytical tools) that qualitatively their memory does not differ from their peers. What usually prevents people from reaching intellectual heights is personality and the environment (school, family, etc.). Many do not live up to their potential simply because of insufficient motivation or belief in their own powers. Others fail due to parental inattention. Those factors are statistically by far more important than inborn limitations.
Scientists have studied Einstein's brain to look for the clues as to his genius. On cursory examination, they could hardly find any. Later it transpired that some areas of his brain were indeed better developed and nourished by a rich fabric of glial cells, i.e. brain cells that are, among others, responsible for the right environment for neurons to work in. Yet it is difficult to predicate as to whether all these differences were inborn or were rather a result of his training in abstract thinking.
Anatomical studies show that various areas of the human brain may substantially differ in size between individuals. Yet it is not easy to find correlations between these difference and mental powers. In people with a normal range of IQ, the volume of cerebral cortex may vary twice between one person and the next. So may the extent of differences in metabolic rates in the same organ. Similar differences have been found between such critical brain structures as the hippocampus, entorhinal cortex, and the amygdala. Connections between the hemispheres can dramatically differ in volume (e.g. seven-fold difference for the anterior commissure). The left inferior-parietal lobule (located just above the level of the ears in the parietal cortex) is larger in men, and was also found to be larger in Einstein's brain as well as in the brains of mathematicians and physicists. On the other hand, the two language area of the cortex: Broca and Wernicke areas are larger in women, which may explain why women might be superior in language processing and verbal tasks. Bigger men have bigger brains but are not smarter.
A racially sensitive subject of lower SAT test scores among blacks and Hispanics in the US has been a matter of debate for a number of years. The differences could not be explained by the material status of families or the neighborhood factor. Stanford psychology professor Claude Steele has conducted revealing experiments in which black students could do equally well on the test as long as they were not told they are being scored.
Although we can point to differences based on sex or ethnicity, the ultimate difference in the creative potential is by far more dependent on the upbringing, education and student's personality. As explained in Genius in Chess, despite chess being a "male game", female chess player, Judit Polgar, developed skills that are superior to those of 99.99997% of the male population.
When we tried to see if student IQ makes it easier to do well in learning and in exams, we found that some personality factors matter more. A small group of students learned with SuperMemo, and the main success factor was the perfectionism trait, not the actual IQ (Wozniak 1994, Gorzelanczyk et al. 1998). Most optimistically, SuperMemo and memory research show that our memory works in the same way at the very basic molecular and synaptic level. Our forgetting is described by the same forgetting curve whose steepness is mostly determined by knowledge representation. As the analysis of success stories with SuperMemo shows, main learning differences between individuals can be found in (1) personality (perseverance, delayed gratification, optimism, etc.) and (2) knowledge representation skills. A week-long course in mnemonic techniques immediately illustrates that knowledge representation skills can be learn very fast indeed. Those skills also develop in proportion to the amount of learning as demonstrated by differences between primary, secondary, undergraduate and graduate levels. All users of SuperMemo, unless primed beforehand, start with building clumsy collections of learning material that is quite difficult to retain in memory. Within months, most users develop reasonable strategies on how knowledge should be represented to minimize the effort of learning (see: 20 rules of formulating knowledge in learning).
To produce breakthrough ideas, most valuable rules are those that are highly abstract (i.e. detached from a particular subject matter). They should be applicable to a wide range of problems. This is why various branches of mathematics should be taught to students of all professions. Logic, probability calculus, or statistics are highly abstract and highly applicable. The same formula of logic may be the basis of dozens of other highly abstract rules. Surprisingly, many professionals find it hard to differentiate between conjunctions such as AND, OR, AND/OR, or XOR. Let alone the difference between deduction and induction which forms the basis of scientific investigation, as well as the basis of logical (read "correct") thinking about such simple choices in life as selecting the appropriate brand of cereals for breakfast
Rule abstractness: If you learn the rule "Wheat contains 340 kcal per 100 grams" its is only applicable to wheat. If you narrow the term wheat to a single concept (i.e. not grain of all species of plan called "wheat"), this rule can be interpreted as a fact. However, the rule "Most cereals contain 330-360 kcal per 100 grams" is probabilistically applicable to both wheat and maize. The latter rule is more abstract and statistically more valuable in problem solving (i.e. you can use cereal rule in more circumstances than the wheat rule)
The applicability of rules does not only depend on their express meaning. The actual representation of the rule in the human brain is paramount! The same rule in the mind of a genius can find a dozen more applications than can be borne out of an effort of a plain crammer. The skill of learning the rules the right way is a critical component of genius. Genetic component may play a minor role here. Many individuals find it difficult to represent knowledge in their minds in a way that can lead to a genius breakthrough. Understanding the right forms of training for abstract representation of rules in the human mind may bring untold benefits to mankind in years to come.
Let us use our computer metaphor to illustrate the problem:
If we take this rule: "if HardDiskSpace<5MB then raise(HardwareAlert('Running out of hard disk space')"
If you type this rule to MS Word and save it in a doc file, the rule will be as useless as any rule crammed into your memory without understanding. Yet the same rule encoded in a hardware monitor DLL can be a blessing to the security of data stored in your computer. The way we represent rules in our brain determines their applicability.
For the same reason, I started this article with a computer metaphor. This way I tried to represent the foundation knowledge of this text in a form that is easily understood by everyone. The rules I am expressing can hopefully be easier to digest and store in your mind with a more tangible long-term benefit. With the appropriate representation, no scientific theory is complex. All great theories were born in the human mind. Einstein, Turing, G�� or Heisenberg did not have to be inherently brighter than you. However, they were able to arrange the pieces of the puzzle in their mind in such a way that they could easily see the light. There is nothing inherently complex in the theory of relativity, the theorem of incompleteness or the uncertainty principle. Some theories may be more voluminous than others. Some may be voluminous enough, in their digestible simple representation, to discourage many from digging in. An important conclusion: No product of human thought is inherently complex or incomprehensible. The difference between easy subjects and difficult once can always be explained by the representation and volume.
Abstractness calls for particularly well-chosen representation. The fact that dinosaurs became extinct 65 million years ago may require no special approach. Abstract mathematics, on the other hand, may be introduced to a student in a number of ways that differ in their effectiveness by many orders of magnitude. There are many more students who fear algebra than those who tremble before a literature class. Symbols of algebra do not have specialized brain circuits to process and simplify them. Student problems with algebra can usually be tracked down to insufficient training in math at primary and secondary levels. Consequently, a motivation factor builds up another inhibitory layer. The gratification from reading an excellent novel is instant. The benefits of math require good command of the raw basics, starting with the multiplication table and the sums. We have not been able to find many shortcuts from the basic level math towards solving differential equations. However, yet a few years ago, you could hear from many: Computers? That's not for me. I have never been good at technical subjects. Today, the same people surf the net for hours. Seniors are flocking to the net in droves. We have succeeded in simplifying the way people see and use the computers. We have changed the way computing is represented in public mind.
|Blue inserts in this article are dedicated solely to users of SuperMemo. If you are not a user, you can skip these|
|Popularity of SuperMemo vs.
SuperMemo is still far from being widely accepted. It still awaits a moment to be packaged in a way that is digestible for an average citizen. Its problem is its representation in the public mind. It is surprisingly difficult to explain the benefits of SuperMemo. Try to convince your classmates or colleagues at work to use SuperMemo to experience this difficulty first hand. It is even more difficult to explain the program itself and how to use it. And it is by far the hardest to illustrate the destruction committed on learned knowledge by giving up spaced repetition. Without finding a formula for simplicity and popular appeal, SuperMemo will for long remain a tool for only those with the highest intellectual aspirations
In acquiring knowledge, never say "this article or book is too hard for me". When listing books he read in his youth, Charles Babbage, the inventor of the first mechanical computer, wrote "Amongst these were Humphry Ditton's 'Fluxions', of which I could make nothing". We know that Babbage was the last person you would suspect of having problems with mathematical texts. If you see the text of which "you could make nothing", go to the first sentence and analyze it. Most often than not, it is just the author who uses the language or structure that is either inappropriate or not matching your present knowledge in the field. If you encounter problems, and there is no explanation, no introduction, or if specialist terminology runs out of the field without a suitable glossary, you may safely excuse your comprehension problems. Do not attempt to dig into advanced chemistry article without the basic chemistry background. Every fourth word may fall out of your vocabulary range. It may take months or years to build a necessary background! Least of all, blame your own perception. Just keep on working harder and one day you will see the light.
If you find difficult material, do not waste time for depression or despair. Abstractness is inherently harder to digest than plain facts. Methodically analyze the reasons for which you cannot comprehend given material. Either the material is badly presented or you need new knowledge that will resolve your problem. Be patient and remember: Everything is difficult before it becomes easy!If you are a user of SuperMemo 2004, see Dealing with complexity in SuperMemo 2004 later in this article
High achievements in all fields require hours of training. This refers to music, chess, sciences, sports and what not. I wholeheartedly subscribe to the famous statement by Edison: "Genius is 1% inspiration and 99% perspiration". Training can have a miraculous impact on the human brain. It does not matter much how well you were endowed by the genetics. You got no better choice than to commit yourself to a lifelong course of learning. If you are in a minority that shows identifiable genetic limitations, you may need to hone your routine to your particular needs; however, if you have already arrived to this point in this article, health permitting, you are highly likely to be equipped with all the basic intellectual components for building genius.
| Genius in chess
It is a pity that not all those genius chess brains had been sufficiently employed in the betterment of this planet. However, they all provide highly valuable material for studying the human brain power. There are a couple of reasons for chess being so valuable to study. Chess rules are clear-cut. The competitive achievement is measurable. Individual games are available for study move-by-move on the Internet. Last but not least, chess is often associated with aura of genius, and world champions generate lots of excitement that results in numerous books and studies on scientific and popular-scientific platforms. In those conditions, we can study factors that help some people reach processing power that is hard to match with the present computing technology.
Chess is a great metaphor for creativity. Chessboard positions roughly correspond to facts and applicable moves correspond to inferential rules (see: facts and rules). The more abstract the rules, the more positions they can resolve. The more abstract the rules you acquire, the less sheer computation your brain needs to do in the game of chess. Consequently, the better your chess score. The move rules will often be based on pattern recognition rules who can filter complex position into simply identifiable patterns. The better your arsenal of pattern recognition rules, the more applicable your move rules become. The rules are the key to chess genius.
British chess player and author Jonathan Levitt proposed a formula linking chess scores with IQ (The Levitt Equation: Elo ~ (10 x IQ) + 1000). Although the formula does not represent exact science, it is a good illustration of the difference between the two concepts of intelligence and genius: one of the true mental processing power and the other of the potential to develop it. Levitt's formula determines the approximate maximum chess score for a given IQ assuming years of extensive training. The purpose of IQ is to distil innate mental skills from expertise. Although this is never entirely possible, people with little expertise in any selected field may still show high IQ which is indicative of high intellectual potential. In chess, adding new recognition and move rules to memory will plateau with time, and the quality of reshuffling them in conditions of maximum concentration will determine the champion. However, there is no substitute for hard work on the way to success in chess. No amount of lateral thinking or transcendental mediation will help. The chess player's brain needs to be equipped with the arsenal of thousands position patterns. The chess scores reflect the true processing power of a players brain in the narrow specialty of chess. In real life, high IQ is welcome; however, what will determine a person's success in a given field is the actual ability to solve problems in that given field. This ability is always related to knowledge, skills and expertise. One of the greatest geniuses of the past century, Herbert Simon (Nobel prize in economics, 1978) has devoted his whole life to studying expertise and proposed another (very rough) formula: it takes 10 years for an individual to reach the top-rank level in any field of expertise (be it chess, medical diagnosis or botany). This number reflects the fact that we tend to measure human accomplishments relative to the accomplishments other individuals in the same class. With classical learning methods, acquired knowledge tends to plateau after a period of time in which the forgetting rate becomes comparable with the acquisition rate. Today, this plateau can be overcome with spaced repetition (see: SuperMemo) that linearizes the acquisition of knowledge in lifetime. Simon's 10-year period reflects the approximate acquisition plateau in non-linear learning. If an individual works hard enough, he will sail close to his maximum knowledge acquisition potential in more or less ten years. His knowledge and skills, as compared with his peers, will then be most noticeable. Due to the law of diminishing returns, the increase in expertise will not be as easy to notice later on. Levitt's formula links the intellectual potential expressed by IQ with the maximum level of expertise in the field expressed by chess score. Herbert Simon's "formula" fits well with chess. The brightest stars of chess, Bobby Fischer and Judit Polgar both got their grand master titles in just under ten years. Some estimates put the number of position patterns recognized by a grandmaster at 50,000. This is more or less as much knowledge as you accumulate with several-hours-per-day extensive learning in the period of ten years in any field (or in a much shorter period in SuperMemo).
An important component of success in chess is the way chess knowledge is represented in the brain. Optimum representation cannot be described verbally, but it is acquired with time via the inherent properties of neural networks employed in processing of the chessboard configurations. Herbert Simon noticed that grandmasters show huge advantage over amateur players in their ability to memorize or recognize meaningful positions in chess. At the same time, their advantage all but evaporates when it comes to memorizing meaningless positions (i.e. those that are not likely to result from a real game). Grandmasters see the chessboard in their special way. They use their own representation. Their own language. Their own pattern recognition. This special representation is the key to getting away from the complexity of chess and reducing games to (relatively) simple game of applying thousands of memorized rules of the winning strategy. As with memorizing the result of 199 x 199, good rules make it possible to replace lengthy computation with a quick retrieval of a solution or applying a succession of just a few well-fitting rules. This is also why it is so difficult to write computer programs that could match grandmaster skills. Those non-verbal skills are difficult to convert to unfailing algorithms.
In essence, chess training is based on memorizing positions and moves (see: smart vs. dumb learning if the word memorizing raises an opposition here). A chess player's brain subconsciously develops a specific chess language in which it expresses the events on the chessboard. This language is a form of knowledge representation which, as it is always the case in learning, plays a central role in success. Once this internal language develops and becomes the player's second nature, all games analyzed and played, leave a trace of memorized chess knowledge in player's memory. Over years, player's memory acts like an efficient pattern recognition computer. One look at the chessboard results in a quick retrieval of relevant patterns from memory and a quick analysis of not-so-many applicable move rules and their outcomes. Unlike Deep Blue beating Kasparov by juggling 200 millions positions per second in its digital memory, a chess player, with a high error rate, quickly guesses best moves in a process that is hard to replicate in a computer.
Of numerous interlinking factors, the personality of a chess player may be one of the most important factors for his or her ultimate success. The baseline IQ may determine the realistic ceiling of achievement. However, it is hard work and training that makes a great chess player. For this, you need a truly neurotic personality with an extreme obsession for the game. Scrupulous analysis of the game and highly competitive spirit are crucial ingredients. It is the personality that turns a budding player into a computer-like achieving machine where chess permeates all aspects of an individual's life. Training, tournaments, game analysis and the highest accomplishment are central points of a chess champion's mind throughout his day. With training, further qualities develop: the art of concentration, and chess expertise. On-demand concentration plays a greater role in chess than in other areas of creative activity. A chess player must reach top concentration at the right moment and sustain a high-level of game processing power until the next move is chosen. On the other hand, success in sciences, engineering, business, etc. will rely on the quality of the creative output independent of the speed at which it is reached. More like in correspondence chess. If you can produce a better result in 3 hours of thinking than another genius in 3 minutes of thinking, you can still arrive to a better business plan, better scientific theory, better algorithm, better design, better marketing idea, etc. Your creation over many years will accumulate those incremental points. In creativity, quality counts more than speed
In chess, it is easy to notice that statistically it better to be Jewish, middle-class, and male for top achievement. The Jewish factor is more to do with home environment and family values rather than with genetics. The male factor may have more to do with the genes; however, Judit Polgar could still beat 99.99997% males of this planet (i.e. just about all of them except few). Additionally, women's incentives to enter the chess world are miserable (judging by less glamour and offensive prize offers), and disincentives to leave it are by far greater (see the issue of marriage and children in Polgar sisters insert). Probably, the sex and race, as baseline IQ, can influence the hard to measure ceiling of achievement; however, in practical terms they appear inconsequential. It is the quality and the amount of training that will determine the outcome
Ultimately the short formula for genius in chess is: (1) the right competitive personality that makes one work hard and able to reach the peaks of concentration at critical times, and (2) the resulting hard work that leads to mastering thousands of highly abstract chessboard rules
A well-planned training regimen has been shown to lead to a remarkable progress in people suffering from various inborn limitations to the functioning of the brain. The brain's amazing ability to compensate for the limited functionality of its components can be well illustrated by an excellent prognosis for kids with hemispherectomy (i.e. surgery in which half of the brain is removed). If hemispherectomy is conducted early enough, the kid is likely to return to normal life. Due to the brain's symmetry, a damage to the same area on both sides of the brain may be harder to compensate but still not impossible. Dyslexia is a genetically based condition in which reading may pose particular challenge in otherwise bright people. Dyslectics show reduced activity in their language center on the left side of their brain. In dyslexia, training can be very frustrating but the right hemisphere can compensate for the limitations of the left side. To experience the hardship of dyslectic training, pick up the pen in your non-dominant hand and write now the letter that has waited years to be written. Don't just slug it away, try to match the speed of your dominant hand. See the pain? Incidentally, Edison was a dyslectic too. And so was Einstein
People who experience reading difficulty without being otherwise intellectually disabled are said to suffer from dyslexia. Studying dyslexia is very valuable for understanding intelligence and creativity. It illustrates the power of inborn wiring of the brain in developing mental skills. At the same time it can show how inborn limitations can be overcome by using the compensatory power of the brain. Dyslexia is caused by an inability to handle linguistic information in visual form.
5-15% of the population can be diagnosed as suffering from various degrees of dyslexia. Its main manifestation is a difficulty in developing reading skills in elementary school children. Those difficulties result from reduced ability to link up visual symbols with sounds. In the past, dyslexia was mistakenly thought to have a motivational background. Researchers studying the brains of dyslectics have, however, found that in reading tasks dyslexics show reduced activity in the left inferior parietal cortex. Otherwise, dyslectics are known to often show higher than average intelligence. A number of bright brains are said to have suffered from varying degree of dyslexia. Those include Einstein, Edison, Alexander Graham Bell, Faraday and many others. Dyslectics may show a natural dislike of reading and, in consequence, compensate by developing unique verbal communication skills, inter-personal and leadership skills. Hence so many prominent CEOs list minor to severe dyslexia among their childhood disabilities. Those include Richard Branson (Virgin Enterprises), Henry Ford, Ted Turner (AOL - Time Warner), John Chambers (Cisco), as well as prominent statesmen: Winston Churchill, George Washington, Thomas Jefferson, John F. Kennedy and others. Perhaps for similar reasons, many dyslexics tend to take on arts (e.g. Tom Cruise or Whoopi Goldberg)
The list above indicates that those who show reading difficulties in childhood can also cope well with their deficiency later in life and become avid readers and skilled writers. Research shows that intense training in dyslectics helps them use the right part of their brain to take over the limited functionality in the left part. Even a few weeks of intense phonological training (e.g. breaking down and rearranging sounds to produce different words) can help noticeably improve reading skills. Unlike normal adults, phonological training shows increase in the activity in the right temporoparietal cortex. This part of the brain works in spatial tasks and may be the main compensatory structure in phonological training. This is the sister region of the left temporoparietal cortex responsible for visual motion processing which is underactive in many dyslexics. The earlier the phonological regimen is taken on, the better the overall result. Advanced brain scans could identify children at risk of dyslexia before they can even read.
In 1979, anatomical differences in the brain of a young dyslexic have been documented. Albert Galaburda of Harvard Medical School noticed that language centers in dyslectic brains showed microscopic flaws known as ectopias and mycrogyria. Both affect the normal six-layer structure of the cortex. An ectopia is a collection of neurons that have pushed up from lower cortical layers into the outermost one. A microgyrus is an area of cortex that includes only four layers instead of six. These flaws affect connectivity and functionality of the cortex in critical areas related to sound and visual processing. These and similar structural abnormalities may be the basis of the inevitable and hard to overcome difficulty in reading.
Several genetic regions on chromosomes 1 and 6 have been found that might be linked to dyslexia. In all likelihood, dyslexia is a conglomeration of disorders that all affect similar and associated areas of the cortex. With time, science is likely to identify and classify all individual suborders with benefits to our understanding of how low-level genetic flaws can affect the wiring of the brain and enhance or reduce a particular component of human mental capacity.
Whether today's models of dyslexia are correct or not, the main lesson of dyslexia is that minor genetic changes affecting the layering of the cortex in a minor area of the brain may impose inborn limitation on the overall intellectual function. At the same time, dyslexia shows that the brain exhibits a strong ability to compensate for its inborn or acquired limitations, and intense training can often result in miraculous turnabouts
Smart lifelong training is an essential component of the formula for genius! Even though genetic background or health may handicap a minority, the optimum strategy for maximizing the intellectual power is still the same: as much quality learning as possible. Learning is your genius brain work-out. Commit yourself to heavy learning for life today! Be sure that this is smart learning (as emphasized in the next section). Genius of spatial symmetry, Buckminster Fuller said: I'm not a genius. I'm just a tremendous bundle of experience. See also: Practice can make a perfect genius
Most average students today could amaze Aristotle with their ability to draw conclusions in many areas of science. They would laugh at the great philosopher's theories. Their brains are better primed for scientific thinking than the brain of the greatest philosopher of the 4th century B.C. In today's world, your IQ or the folding of your cerebral cortex are valuable assets but they are ultimately less important than your ability to solve problems. This ability is based on knowledge. And knowledge is inherently acquirable. One thing you must not forget though: Make your learning smart:
To build genius, your learning program must be based on high applicability of newly acquired skills and knowledge. If you memorize the whole phone book (i.e. a big set of facts), you won't be much closer to a genius mind and your problem solving ability will increase only slightly (mostly through the beneficial effect of memory training on the health of your brain). On the other hand, a simple formula for expected payoff may affect all decisions you make in problem solving and in life in general. It can, for example, save you years of wasted investment in lottery tickets. Millions of people are enticed with huge lottery jackpots, yet they would never agree to give up their whole income for life in order to get it back at retirement in one-off payment, which is a frequent probabilistic payoff equivalent of taking part in lotteries. Using the terminology defined above, you will find most benefit in mastering and understanding highly abstract rules of logical thinking and decision making.
To accomplish smart learning, you will need to constantly pay utmost attention to what material you decide to study. You must avoid short term gratification at the cost of long-term learning. It may be great fun to learn all Roman emperors and details of their interesting lives and rule. However, unless you study with a big picture in mind (e.g. in an attempt to understand why civilizations thrive or fall), your genius may benefit less than by slogging through less funny but highly applicable formulas of operation research (those can for example help you optimize your diet, investment, daily schedule, etc.). In other words, you cannot be guided just by the fun of learning but by your goals and needs. In time, you will learn to see the link between long-term learning and long-term benefits. You will simply conditions yourself to love beneficial learning. Hard study material can still provide instant gratification.
While you focus on your goals, you cannot forget about the overall context of human life. You cannot dig solely into studying car engines only because this happens to be your profession. This would put you at risk of developing a tunnel vision. Your genius could be severely handicapped. You might spend years improving liquid fuel engine efficiency while others would leap years by getting involved in hydrogen engines. Their decisions would not come from genius itself but from an extensive knowledge of the field, relevant sciences and the human endeavor in general. One of the main reasons for which companies go bankrupt is that their leadership fails to spot the change. As corporate darwinism eliminates short-sighted teams, future society will witness more and more intellectual darwinism. To understand the trends and the future, you need to study human nature, economics, sociology, history, neurophysiology, mathematics and computing sciences, and more. The more you lick the stronger your predictive powers and your problem solving capacity and creative strength.
A bright 25-year-old Microsoft programmer has suggested to me recently that I use wrong examples in my articles on learning. He specifically referred to the question "Which year was the Internet born?", which he classified as a piece of trivia. He implied I should use more "useful" examples to encourage readers. Here my own tunnel vision showed up as I found his position very surprising. I misjudged the concept of trivia in the eyes of people that do meet the criteria of genius. The term trivia excellently reflects the sort of knowledge we do not want to learn in the quest for genius. These are not-so-useful facts or rules of low applicability. However, the concept of trivia is highly relative. To a child in a kindergarten, the birth of the Internet is rather meaningless. At this stage of development, the child may find it difficult to grasp the concept of the Internet itself. Most of parents will wait until the primary school before showing a child a web browser (esp. that reading skills may be needed to appreciate the concept). The value of putting the date on the birth of the Internet probably develops only in the context of an effort to understand the history of technological development. In this context, 1969 may be as important as the years of Gutenberg. Only when multiple events of the 1960s and the 1970s dovetail together, the commissioning of ARPANET becomes meaningful. When we figure out that we landed the man on the moon before making the first connection via the net, 1969 looms larger. If we dig deeper, we may find it inspiring to know that when Charley Kline tried to log in on October 29, 1969, the network crashed as he typed the letter G. This little detail may still contribute to your genius! Say you work on commissioning a major installation you worked on for several years. You know that the installation implements revolutionary concepts yet it keeps on crashing. You are about to lose hearth. This may not necessarily be an emotional event, after all you also need to apply probability to deciding when to give up blind-alley pursuits even after years of investment. The juxtaposition of the small letter G and the groundbreaking concept of the interconnected world will help you see the big picture. If your concept is great enough, you will go on through another 100 crashes in hope of diagnosing the reason. If you win, your measure of genius will be enhanced.
Listen to other people's advice and valuations. The younger you are the more you should listen. In the end though, it must be you who determines the criteria for sifting golden knowledge from trivia. Only you can measure the value of knowledge in the light of your own goals.
Remember that not all knowledge can easily be formulated in a declarative manner. Remember then to use the power of your own neural networks: solve problems, practice your skills, compute, abstract, associate, etc. You and others may not be able to see or verbalize some rules but your brain will extract them in the course of practice. Once the rules have been developed, try to formulate them and write them down. This can be of benefit to you and others
|Sifting trivia in SuperMemo
In early versions of SuperMemo, your decisions related to sifting trivia from valuable knowledge would be binary in nature: memorize or forget. In 1991, the concept of the forgetting index made it possible to memorize items with a given probability of recall. In SuperMemo 2004, with incremental reading, there is a continuous transition from trivia to your platinum genius-building knowledge. Apart from the forgetting index, you can use ordinals and rescheduling tools to manage unheard-of quantities of knowledge
The ability to "see" the future is one of the best tests for genius. The nature of spacetime does not seem to make it possible to probe the future like we can probe the past via historical records. However, the laws of physics provide a strong platform for peeking into what may happen. A ball falling freely to earth may be an easy guess based on the Newtonian laws of gravity. However, the true difficulty in predicating the winner of Gore-Bush clash in October 2000 came out only after the election day on November 7. Guessing the winner of the 2004 election today would be yet harder. Guessing on the state of mankind beyond 2100 is a game reserved for only the best-equipped futurist minds. Predictive powers are so good in probing genius because they test all of these: (1) nimbleness of the mind, (2) extensive knowledge on the mechanics of the universe and the society, and (3) the abstractness of reasoning rules. Write down your predictions of the future today. In five years you will be amazed with your own predictive lapses. When will we be able to cure AIDS or cancer? When will we talk freely to computers? What job will you land after graduation? Would you predict the web explosion in 1990 (i.e. before the publishing of the web protocols)? Or in 1994 (i.e. already after Filo and Yang started collecting their Yahoo links)? What knowledge do you think you lack today to make your predictions more accurate?
Predictive powers are the cornerstone of success in business. Those who can see the technologies and trends that will shape a market in 3-5 years are posed to do well. Here comes the value of basic sciences such as math and physics in extracting trends from the chaos of the modern world. The value of math and physics comes from the fact that it equips you with highly abstract rules with a wide range of applications. This is why it pays highly to learn artificial intelligence, neural networks, sociology, neurophysiology, systems theory, statistics, evolutionary psychology, history, etc. Those sciences formulate rules that make it possible to better understand the reality, and most of all, draw conclusions about the reality. Those rules are the tools of computation for processing the picture of reality in your mind.
Here is an example: when Alan Turing developed the concept of his Turing machine, he equipped his genius brain with the tool for understanding computation. The Turing machine is a sort of a toy computer that scans a tape of symbols and stamps the tape depending on the currently read symbols and its own state. Turing's early intuition was that his toy computer, given enough time, could compute everything that is computable. If future was deterministically computable from the quantum states of subatomic particles, the Turing machine could compute it. If future was non-deterministic, the density function of individual outcomes could be computed too. The Turing machine became the simplest possible metaphor for the human brain. Turing could see the parallel between the shifting states of the Turing machine and the states of the human mind, including emotional states and the most complex computations of the human thought. Turing could then state boldly that one day machines will be as intelligent as humans. The famed Turing test is based on putting a computer in one room, a human in another, and testing if outside observers could distinguish between the two by means of a conversation (e.g. via a computer terminal). Once computers become indistinguishable from humans, they will have been said to have passed the Turing test. Most of people living at Turing's time (the 1930s) would disagree, but their predictive powers were limited by lack of tools for understanding the mind and computation. Turing machine and basic truths about its properties, equipped Turing's brain with tools that made it easy for him to see the simple parallel between the mind and the machine. For most researchers in the area of artificial intelligence, it is obvious that the Turing test will be passed sooner or later. Perhaps in 2010, perhaps in 2040, but it will happen. In the 1950s, Herbert Simon, using the same abstract rules related to computation, spoke loudly about his belief that the computer will beat the world chess champion within ten years. He was off by thirty years. This illustrates the difficulty in predicting the future, as well as the power of some basic abstract rules. In this case, Simon concluded that given the appropriate objective function for evaluating chess positions, it is only the matter of the number of moves the computer can process before it can produce better moves than a human being. He underestimated the power of human brain in simplifying (read: repre