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.