Advanced Summer Program for students age 11-14
who show high promise and love mathematics

Message of Executive Director to Alumni

Address delivered by the Executive Director at the closing ceremonies in MathPath 2007

July 28, 2007
Colorado College
Colorado Springs, CO

Parents, students, staff, and faculty:


This is the happiest moment of my year – looking on the students and parents at the closing ceremony. I would like to dedicate this occasion to the parents of campers in MathPath 2006, for their endurance and understanding, for believing in us even while we had to raise the camp fee in 2006 with only a month from that camp’s start date. They have contributed to the financial stability of this independent non-profit camp. Some of those parents are present here as parents of the returning students. Will the parents of returning students rise? [Applause]

I thank Mr. Kip Sumner and his staff for another good camp. I thank the world-class faculty who despite the other ways they could have chosen to spend a month of the summer chose to help these students see mathematical concepts and do mathematics. Above all, I thank Professor Stephen Maurer for his meticulous, tireless, and professional work as Academic Director. Often I feel that he is not a man but a machine!

Rather than talk about the mathematical experience you just had, I shall dwell on a matter that I believe is relevant to living your life. It is the topic of sympathetic projection. It is connected with the concept of “good.”


“What is good for man?” is perhaps the most important question for a human being to ask, for by knowing the answer to this question one could direct one’s life to good and thus have a more rewarding life than otherwise.

The answer to this lies in the answer to “What is good?”. Students in their early years do not think long on this question. And most adults “feel” they have the answer. They do not!

It is a difficult question whose answer occurred partly to Protagoras and more fully to William James. Yet, the approbation of the world, including some major religions, went to Kant and many others who though profound were profoundly wrong in their answer to the question of what is good.

For early Greek thinkers the idea of something being good meant that it was useful or efficient in performing its function. So they asked what a good man is. Their answer was: A good man is one who performs efficiently the function of a man. This led them to ask: What is the function of a man? They settled on the idea that man’s function is the use of rational powers. Thus a good man is a rational man and virtue – the possession of the good - is the exercize of reason.

Socrates sought not what was assumed by a particular culture as good but what was good by nature. He could not discover it but believed that this natural moral goodness, once discovered, can be taught so people can possess it. In other words virtue can be taught.

Socratic doctrine: If a man knows the good, he cannot choose evil. In other words, no man voluntarily chooses evil. So men who do bad things are acting from ignorance. This is delineated by his parable of a man coming to drink from a well of poisoned water.

Moral ethics delineated in this way by pure reason is called moral rationalism. On the other hand, moral empiricism assumes that the truth of things is learned through perception and experience. If we experience the world as different from what it ought to be by reason, then the reason should be modified to fit the experience and not vice versa. Protagoras adhered to this philosophy. He summed up thus: Man is the measure of all things, of things that are, that they are, and of things that are not, that they are not. So moral goodness is by convention, not by nature. There is no natural morality, justice, or law. That is, the veracity of anything can not be judged by virtue of its being measured against nature. This is indeed true of mathematics. One can build up a mathematical theory in which what one wants is true – like 2 + 3 = 6.

Epicurus believed that what is felt to be good is good. So pleasure is always good and pain always bad. Further, pleasure is the only ultimate good. If pleasure is the only good then a good life is a life of pleasure. Strive for the greatest total pleasure with the least pain.

Hedonism is any philosophy in which pleasure is the good. Further pleasure is good for its own sake and the only good that is good for its own sake.

J.S.Mill’s modern hedonism adds to hedonism. It is every man’s duty to increase to the utmost the total amount of pleasure in the world and to reduce to the utmost the total amount of pain.

Kant, the champion of the concept of duty, believed that we are to do always what duty requires for no other reason than that Duty requires it. According to him, the good then is the doing of the dictates of duty. And a will governed solely by the sense of duty is the only good in nature.


William James departed from these axiomatic approaches. He reasoned that a thing is good by virtue of its being sought and evil because it is shunned. The seeking and shunning gives rise to the distinction between good and evil. This I call the modern view of the good. Richard Taylor, a James proponent, explains this by noting that in a world devoid of even one sentient being, there is neither good nor evil. When one such being is introduced, the good and the bad appear. Those things it desires are the good.

When just one more sentient being is introduced, right and wrong appear. For instance, the two conative beings may want the same thing and only one can get it. Then rules are introduced. The right is the adherence to the rule.

The modern view is difficult to argue against and it has the following consequences:
(1) The injunction that men ought to pursue the good amounts to saying that they should seek what they seek. So it is an empty principle.
(2) The greatest good for man is the total satisfaction of all his desires to the extent it is possible to satisfy them.
(3) The common good is the maximum satisfaction of all men’s desires, to the extent it is possible. That is, maximum satisfaction at the minimum cost of evil to all.

When two or more conative beings inhabit a world the good of one can be the bad for another and thus conflicting aims arise. [Pause]

For conflicting aims in a multiplicity of humans, “sympathetic projection” can be used to make them conflicting aims in the same individual and the preferred aim for the individual can be established. Sympathetic projection is the adoption of other people’s predicaments as one’s own. What you think of bad can then become good. Sympathetic projection is advocated in the main scriptures of most religions.

The Hindu religious text, Mahabharata, teaches: "One should not behave towards others in a way which is disagreeable to oneself. This is the essence of morality.” Jainist scripture says: "A man should wander about treating all creatures in the world as he himself would be treated." When Confucius was asked to sum up the rules of life, he answered: " What you do not want done to yourself, do not do to others." The Taoists taught: "Regard your neighbor's gain as your own gain, and regard your neighbor's loss as your own loss." In the generation before Jesus a man asked the great Rabbi Hillel to teach him the Law. Hillel answered: "What thou thyself hatest, do not to thy neighbor. This is the whole Law. The rest is commentary. Go and learn it." The discourses of Buddha contain this: A state that is not pleasing or delightful to me, how could I inflict upon another? Judaism and Christianity have this (Bible, Leviticus 19:18): You shall love your neighbor as yourself.
In Christianity, the golden rule of the Gospels is this: In everything do to others what you would have them to you, for this sums up the law and the Prophets.

This is sympathetic projection. I sometimes think of it mathematically as the scalar projection of a vector on a given axis. It can make you a better professor, for mathematics is boring only by virtue of bad presentation. Project yourself on to your students. ......... Sympathetic projection is of practical importance for modern life, for in one’s interaction with superiors, colleagues, and assistants it makes for a smoother way. It is equally important in how you treat the most important people in your lives – your future children and spouse. You will likely achieve much in life. But it is how you treat your close family members that will determine the peace you will have in the last days and moments of your life. In this your own parents have been the example. They have raised you well and even cared so much for your academic future that they sent you to this camp. I am grateful to them. [Pause]

When you need me, I shall try to be prompt and useful for you. Keep in touch with the friends you made at camp. Now go! This is the beginning!

-- George Rubin Thomas


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