In his famous tragedy, William Shakespeare has Julius Caesar say, "Let me have men about me that are fat: Sleek-headed men and such as sleep o' nights: Yond Cassias has a lean and hungry look; He thinks too much: such men are dangerous."

With rare exceptions, those who seek or hold political power usually control men with their emotions rather than their minds. They prefer people who can be easily manipulated by oration, by imagery, and by fear, greed, and envy.

The media-produced emotional world of vicarious violence, trivialized sex, primitive primal "music," and nonexistent morality and ethics of today is ideal for those who seek to manipulate unthinking Americans. The television-addicted public is saturated with whatever "thoughts" the controllers want them to "think," and polls are continually taken to see whether their propaganda is having the desired effect. This is the "education" that is most desired.

Of course, our government does maintain about 4 million tax-financed employees to educate American youth in government schools. These schools are wonderful indeed. A newly announced federal program has set as its goal that, 10 years from now, the students in these institutions will all be able to - read.

Still, there is also a need for men of the mind. Somewhere in the basement of each power plant, there must be an engineer who knows how the plant works. Moreover, even for the political manipulators, it is especially important to have engineers and scientists who keep the country at the forefront of military technology. Weapons are essential in the international contest between governments. Therefore, men who can think are tolerated, so long as they keep in their place and do not seek political power.

Yet, the fact is that every human mind does think to some extent. Understanding the ways in which the mind works is important to educators, to students, and to every individual who prefers to be among those who use their minds effectively. While no one can claim to thoroughly understand the mind, some useful generalizations are possible. I will summarize some of these with respect to scientists, but, in fact, the processes are substantially the same for everyone and in all occupations.

First, the mind has a capacity to memorize facts. The speed with which facts can be memorized and the number of facts that can be learned and easily recalled varies greatly between individuals. While a great storehouse of facts can easily impress one's audience and more importantly, can convince the memorizer that he is very well educated, facts alone are not especially useful.

First, there is the problem of verifying facts. Will Rogers famously commented that, "It ain't what we don't know, but what we know that ain't so" that causes trouble for us. Second, facts, by themselves, usually provide little basis for action. Unless we have some organizing principle for facts, they provide poor guidance.

Science depends entirely upon experimental observations. These observations are facts, but they have little utility by themselves. Unless experimental observations can be fitted into a framework of hypothesis and theory that successfully predicts further observations, they are considered interesting but not yet understood.

Innumerable demonstrations have been made that were predicted by Isaac Newton's laws of mechanics, so these laws are considered verified, within the framework of current experience. In contrast, no demonstration has ever been made of the process of "spontaneous origin of life." Many facts have been observed that can be explained by this hypothesis, but these facts can also be explained by alternative hypotheses. Verification of this hypothesis is difficult unless one happens to have a spare planet and a few hundred million years to wait. So, contrary to media-generated opinion, spontaneous origin is an interesting but unproved "hypothesis," not a verified "theory."

Ah, some will say. We knew this guy is a nut. Everybody "knows" that spontaneous origin is a verified theory. They "know" this because they have repeatedly heard it. Yet, I know several outstanding contemporary scientists who do not accept this theory, even though they are professed atheists. They keep quiet because this position is unpopular and would cause trouble for them

What is going on here? There seems to be something at work other than the facts. That something is a "model." Science requires that a self-consistent, verifiable, and testable model be constructed to explain experimental observations. This requirement is derived from the way in which the human mind works.

In addition to its capacity to memorize facts, the mind has the capacity to organize those facts into simplifying models that can be extrapolated to useful conclusions. These models are far more valuable than the facts themselves. They must, however, be verified by means of further observations.

A chemist builds in his mind a self-consistent model of the nature of molecules and the way they work. That model is the result of several centuries of experimentally observed facts and the theoretical organization of those facts by a great many very smart scientists. The model does not contain the facts. It is, however, consistent with most of the known facts and can predict the results of many further observations. There are facts that do not seem to fit the current chemical model, but these are regarded, for the most part, as involving refinements that will later be added to the model, rather than things that are not consistent with it.

A research chemist usually works to apply a new model to an old problem or an old model to a new problem For examples, he may have a new hypothesis about the cause of biological aging, an old problem for which is there is, as yet, no verified explanation, or he may seek to synthesize a new drug by means of the standard model of synthetic organic chemistry. Always, he is using the models in his mind and comparing his observations to them.

Many remarkable advances occur simply when a chemist - or physicist or other scientist - notices something that does not fit the currently accepted model. If he has sufficient curiosity to pursue this observation until he understands it, he may make a valuable addition to the model, or, perhaps, identify some error within it.

Model building is far more important than memorizing facts or procedures. First, there are so many facts and procedures that even a certified genius cannot memorize a significant fraction of them. Second, unorganized facts do not lead to further directed thoughts.

A good scientist requires an excellent model and a well-developed ability to, by thinking, organize new facts into additional models or meld them with existing models.

This is the reason that problem solving is a substantial part of a scientific education. From the simplest problem in arithmetic to the most complicated problems in physics, problem solving is the organization of facts into useful models.

Most teachers and students do not understand this. They think that problem solving consists of "getting the answer." They seek solutions manuals that show the student how to work each problem. Newtonian mechanics, the principal subject of first-year high school and college physics, affords an excellent example.

Most high school texts provide a formula that allows a student to calculate the length of time required for an apple to fall from a specified position in a tree to the ground .The student plugs numbers into the formula and computes the answer.A properly educated 8-Year-old child should be able to do this just fine -which is about the level of math skills of many tax-financed high school students. 

This is not problem-solving. Since there are essentially uncountable variations of this problem that require different equations, it is not even useful .The student will never be able to memorize all of these different equations.

 

In an appropriate course,the student is presented with the problem and required to apply Newton's laws of motion to derive the necessary equation. If a numerical solution is required, he will, indeed, plug the numbers into his equation, but this is a final and essentially trivial part of the exercise. The student must apply the Newtonian model to the necessary facts in his derivation.

 

This derivation, however, requires calculus. Since most tax-financed high school students do not know calculus, they cannot learn to solve physics problems. So, the school provides a non-calculus "physics" course. The school pretends to teach physics, and the students pretend to learn.

 

Newtonian mechanics involves primarily objects that can be seen and that move in ways that are consistent with ordinary experience. This makes it easier to comprehend the scientific model that Newton invented.

 

Most of modern science, however, involves the submicroscopic molecular world that cannot be seen by the unaided eye and obeys rules that are often not consistent with ordinary experience.In this world, therefore, models are especially important. It is essentially impossible to work productively in such a field without well-developed models.

 

To be sure, the simplest models are often eventually reduced to automatic memory. After understanding the concepts, a six-year-old should commit the simple arithmetic operations to memory. "Seven times eight equals fifty six" should be memorized by unthinking instant rote memory. This result will be used so often that its repeated derivation would slow the student down in later work. It should not be memorized, however, until the student knows that he can derive the result from his logical model and has done so.

 

The acquisition of problem-solving ability - the skill to apply logic and an appropriate model to determine the correct solution of a problem - requires many, many years of practice involving the unaided solution of tens of thousands of problems. Gradually the student builds both the requisite ability and also self-confidence in his ability. Both are required for successful problem solving. He is unlikely to solve difficult problems unless he is confident that he can do so.

 

Tax-financed schools are uninterested in ability, but they have noticed the part about self-confidence. The students and parents must "believe"that the students are doing well, so "self-esteem" is promoted. Misplaced self-esteem without real ability is, however, a cruel fraud. It holds negative value for the student.

 

The teacher can aid the student by selecting a good course of study and by example in demonstrating good study habits and methodical intellectual techniques. When, however, the teacher actually works a problem for the student he deprives the student of the problem. Its value is gone. The student will only develop skills with those problems he actually solves. Teacher solutions also harm self-confidence and discipline because the idea that, if the problem is difficult, he can refer it to the teacher will always be lurking in the student's mind.

 

The school must provide 1) a good study environment, 2) good study habits, and 3) a superb course of study that is appropriate for all students and also for the best of students. Not even one of these three requirements is met in today's tax-financed schools.

Moreover, problem-solving ability - the ability to move with facility back and forth between a mental model and the facts that relate to it and to apply the model and the facts to the discovery of new facts and new models - is an essential part of virtually all human higher mental activity. It is best taught with introductory mathematics, physics, and chemistry, but it is applicable to all endeavors.

Economists have a model. If parts of that model are omitted, odd conclusions are the result. It is intuitively obvious, for example, that tax revenues will be zero if the tax rate is 0 % and also if it is 100%. At 100%, there is zero incentive to produce. Fear of death or torture can, of course, elicit some work from slaves, but this is not taxation. So, the boundary conditions of a graph of governmental income from taxes require that the curve pass through zero income at 0% and at 100% taxation. In between, income rises from zero at 0%, reaches a maximum, and then declines to zero at 100%.

This is commonly known as the Laffer curve, but it should be trivially obvious to any good problem solver even with no economics training. Yet, with taxation well beyond the maximum of the Laffer curve, politicians and the media continually claim to the public that raising taxes will "soak the rich" and result in more money for distribution to the public. The public supports this for two reasons. First, they have adopted the unethical view that stealing is right if the majority votes for the government to do it. Second, most of them have almost no problem-solving ability and cannot therefore realize that higher taxes are not even in the economic self-interests of the thieves.

In addition to mental models, facts, and the capacity to meld them in thought, the mind also needs a frame of reference - an anchor - a location for itself in the universe. It needs to know the answers to questions that are beyond the capacity of the human mind. That anchor and those answers are best supplied by Christian faith. Faith is combined with facts and models in the mind by means of the human spirit. All three - facts, models, and faith - are entirely self-consistent, but this consistency cannot be proved by science or other constructs of human reason.

This is unsurprising. Walk outside on a dark, clear night. Look up at the stars - and try to tell yourself that your mind is capable of understanding all of that and its origins. A well-trained mind can do much. Humility can help it to keep its balance.

Another currently popular economic belief is that the United States can continue to tax, regulate, and litigate its industry and workers into bankruptcy and then expect the industry and workers of other countries to produce the goods it needs. This model involves a world in which the citizens of other countries do the work and Americans reap the benefits - through an apparently clever process of printing money to exchange for the goods and then borrowing it back to spend again.

This belief seems to be intertwined with a belief that superior military power - American hegemony as the "world's only super power" - will permit the United States to force the world to accept this system. This is the currently prevailing foreign affairs model. It requires only modest problem-solving ability to realize that a country with less than 5% of the world's population and a rapidly declining industrial base will not be able to sustain such a military empire.

Only the people of a country controlled by thieves who receive subsidies paid for by a government that steals the property of their neighbors could adopt such a model. An ordinary 10-year-old problem solver should readily see that this system will ultimately fail.

Marriage and family also involve a model. This model has served civilizations well for thousands of years. It is not difficult to predict that the advantages of this model cannot be obtained if key aspects of the model are abandoned The mental processes required to understand this are no different from those required to solve scientific problems. In this case, a relatively low level of problem-solving ability is needed to reach sensible conclusions. Yet, the news about new marital "innovations" and statistics regarding American families show that the majority of our people now lack even that low level of ability.

Education programs are often advertised as means for teaching the student to "think," but one rarely sees a definition of "thinking" in this context. A reasonable definition of such a program may be as follows:

First, it imparts to the student an extensive set of excellent mental models - models of mathematics, science, history, economics, personal affairs, ethics, morality, and other essential subjects.

Second, it provides the student with a sufficient body of facts with which to test these models and to conduct his own initial verification of them.

Third, and most importantly, it teaches the student to derive new conclusions from old models, to create new models, and to continually and intuitively move back and forth between mental models and facts in order to check the accuracy of both.

How are these skills taught? They are best taught in the way that most students learn - by example. The student will emulate the study environment, study habits, and mental methodology of his teacher. In addition, the student will follow the example of the person he knows best - himself.

If the student is required to solve problems - beginning with easy problems when he is five or six years old and increasing in difficulty as he becomes older -by himself and with no specific help from his teacher, the student will gradually teach his mind to flow productively between mental models and their underlying facts and to subconsciously compare all new and old facts to his current collection of mental models. As he observes himself, formally and consciously engaged in this activity several hours each day during school and informally and subconsciously engaged the rest of the time, the student will emulate himself and thereby rise in both ability and justified self-confidence.

Since the fundamental thought processes required for modeling in mathematics and science are the same as for any other mental modeling process, math and science provide excellent material for teaching this ability, regardless of the student's ultimate goals.

The three older members of our family illustrate the effects of independent problem solving on rapidity of thinking. I estimate that the three of us have comparable innate abilities. Our future accomplishments are, of course, subject to human fragility, and our good fortune is a blessing, not a reward.

I am 61 years old, attended public schools, and solved only the problems required in public school courses. I required four years to complete a BS in chemistry and four years to complete a PhD. I think much more slowly than my sons. I partially make up for this when working with them because I am older and have had more time to think. I did not take GRE, graduate record exams.

Zachary is 27 Years old. He began intense self-teaching problem solving at about the age of 13. He has however, a partially photographic mind and reads with very high speed, so he diverted himself somewhat by the memorization of unusual numbers of facts. Zachary required only two years to complete his BS in chemistry, scored an average of 95 percentile on his GRE exams, and completed his doctorate in veterinary medicine in four years. This is a structured program that cannot be taken in less than four years.

Noah is 25 Years old. He began intense self-teaching problem solving at the age of 11 and worked problems about 4 hours per day, 6 days per week, without distraction. Noah completed his BS in chemistry in two years, scored 800, 800, and 770 on his GRE exams - two perfect scores and a third of 99 percentile, and completed his PhD in chemistry at Caltech in 3 years.

Both of these young men move back and forth between models and facts far more rapidly than I (even when I was their age), and their relative performance reflects their problem-solving experience.

When Zachary and Noah were in their home school, each day (six days per week) began with a fixed number of math problems. Until they had worked those correctly without help, the rest of their day could not begin. After they finished calculus, physics and chemistry problems were solved. The younger four Robinsons are successfully using the same method.

A child who learns in this way approaches all aspects of his life differently. Beginning one's day by working correctly, without help except from self-reading of the text, an appropriate set of math or science problems requiring two to four hours of effective thought, imparts a similar mental approach to the remaining activities of the day. Many letters that we have received from parents of some of the 60,000 children who use our curriculum verify our experiences. The same things that happened within our school and family have happened within many others when using these techniques.

Every human mind acts in accordance with a set of learned mental models. The mind chooses among the presented models by comparing them to the available facts. The ability to make this comparison effectively is an acquired skill. This skill can be learned by a process of directed self-help problem solving.

If the models - mathematical, physical, personal, moral, and ethical- are well-chosen and the mind is skilled in the use and checking of its models, that person's mind is well equipped to deal with both the opportunities and the vicissitudes of life.

If, alternatively, the models are chosen by televised media and the degraded culture that surrounds it, socialist schools, race-baiting and envy-saturated political propagandists, and the other false prophets of our time and model evaluation through problem solving is not taught, that person has little chance in life. The pathetic results can be seen on almost every street in America.