Essay—The New Math (49)

Summary—This essay argues that we should teach a new brand of mathematics and physics so that children are not left behind and may use mathematics and physics as a concrete way of life.

Cardassians are a humanoid species from the Star Trek television and movie franchise. The Cardassian legal system is based on the notion that the defendant is always guilty beforehand and the purpose of the trial is simply to confirm his guilt. Christianity is also based on such a preconceived approach. Christians believe that, with the Second Coming of Christ, He will validate all of their existing beliefs. But what if Christ were to arrive on the scene and reveal to the Christian world that they have built their castles on sand? Similarly, if the Canadian government were to tell us that 2 + 2 = 5, then our objective would be to make it so. The physicist Edward Witten said that string theory will occupy the world of physics for the next fifty years. String theorists have thus made plans for the next fifty years. But fifty years of normal science does not add up to a single nanosecond of paradigm-shifting science like with my theory of one (2001).

Against the Gods. In his 1998 book Against the Gods—The Remarkable Story of Risk, Peter Bernstein tells stories about the history of risk. By remembering the past we can attempt to predict what will happen in the future and thus make good choices in the face of uncertainty. But too often we find ourselves at the mercy of the gods who tend to take control of us. While driving in the country I came across a farmer standing under an apple tree with some pigs. I watched the farmer while he held a pig above his head as the pig ate an apple from the tree. He put the pig down and picked up another pig, only to perform the same mesmerizing act once again. I approached the farmer and began speaking with him. I asked him whether he might be better off taking some of the apples from the tree and putting them on the ground for the pigs to eat there—suggesting that this could save time—for which he responded—What’s time to a pig? We have a habit of letting the pigs and the government become our gods so we only see reality through their eyes. Our challenge then is to go against the gods and see reality through our own eyes.

Historized Mathematics. According to the Greek Plato (427-347 BC) true or a priori knowledge must be certain and infallible and it must be of real objects or Forms like the Pythagorean Form. Mathematics is the systematic treatment of Forms and relationships between Forms. It is the science of drawing conclusions and is the primordial foundation of all other science. High school students are taught mathematics from a current perspective. We dump a bunch of complicated equations on them that they forget moments after completing their exams. I would argue that we should supplement existing mathematics and physics courses with history courses on mathematics, physics and risk. We could tell them stories that would last a lifetime like that of the Bernoulli brothers who challenged each other to find the optimal curve that a bead could slide down in the shortest time.

Risk Theory. Probability theory is the branch of mathematics that deals with the quantitative measuring of likelihood that an experiment will have a specific outcome. Statistical theory is the branch of mathematics that deals with the algebraic analysis of random variables. Probability theory and statistical theory were first used in answering queries arising from games of chance. Utility theory defines the value of assets internally rather than from external market values. Risk (or portfolio) theory in organizations is all about bringing the moving parts (eg. oil prices, gas prices and foreign exchange rates) together into one probability distribution like the normal curve. Risk managers use a process known as value-at-risk to define acceptable levels of risk exposure. Risk is associated with reward so that organizations seek to receive the appropriate rewards for given levels of risk. For example, one expects high-reward from high-risk assets. Risk, probability, statistical and utility theory are all vitally important in decision-making.

Schrödinger and Einstein. I recently tried to explain the dead simple algebra involved in the Pythagorean Form to a woman—to which she immediately disconnected. The Pythagorean Form is the basis of special relativity theory (1905). In that she could not understand the Pythagorean Form, she was unable to see my theory of one conclusions that the universe is bounded, that there is only one photon (a particle of light), and that one photon is God. I recently asked a man, who has a science degree, whether he had heard of the Schrödinger’s cat thought problem—to which he replied no. He could thus not comprehend the main thrust of the thought problem which asserts that consciousness determines physical reality. This in turn made him unable to understand the Einstein’s moon thought problem—which asks whether the moon really exists when no one is looking at it. By applying Schrödinger’s cat to Einstein’s moon, we see that consciousness once again determines physical reality—revealing that the moon does not exist when no one is looking at it. These are the problems that arise when people do not understand mathematics, physics and their attendant stories.

Descartes and Arguments. René Descartes (1596-1650) was a French philosopher, scientist and mathematician. He was the father of modern philosophy and the father of modern mathematics—ie. algebra plus geometry equals analytic geometry. Descartes insisted on the primacy of the individual and the analysis of human consciousness. This starting point for existential philosophy is the Cartesian cogito—I think, therefore I exist. Descartes formulated his famous model for constructing arguments which is—Order thoughts from simple to complex—Only accept clear and distinct ideas as true—Divide arguments into as many parts as necessary—Check thoroughly for oversights—And, using reversibility, rehearse, examine and test arguments over and over until they can be grasped with a single act of intuition or faith. Initially, one faithfully or intuitively senses truth, which is followed up by constructing rational arguments and then intuitively capturing completed arguments. In other words, faith leads us to reason and then reason leads us back to faith. Descartes also formulated the theory of systematic doubt whereby one says no to any argument no matter how plausible so long as he saw the possibility of doubting the argument.

Strong and Free? The Canadian national anthem tells us that we are the true north strong and free. But the Canadian government has repeatedly turned down challenges to answer my arguments—which is clearly a sign of weakness. As for being free, we are free to walk in line like animals in a zoo. Canada feeds us well with the nonrenewable resources of our country and we have God to thank for this abundance of nonrenewable resources. We also have the United States to thank for watching our backs. Without them we would probably all be speaking German now. The time has come for Canada to take a leadership role on the world stage which begins by rethinking the education of mathematics and physics. Consider the facts that the universe is sixteen billion years old and that we will use up the nonrenewable resources in three hundred years. If we translate the sixteen billion years to the six days of Creation, we find that we will run out of nonrenewable resources in less than a second. Friedrich Nietzsche (1844-1900) said that my enemies are those who destroy the world without creating themselves. I am arguing that we must create ourselves while using the nonrenewable resources. Creating ourselves means to seek the higher consciousness found in self-awareness.

Totalitarianism. Totalitarianism is the practice of governance that attempts to monopolize all possible influences affecting the behavior of individuals. It atomizes people and existentially alienates them from themselves and each other, thus forcing them to capitulate to the external authority of government in order to survive. Totalitarianism depends upon the masses to control the masses by either physical or metaphysical force. Sir James Jeans (1877-1946) said that God is a mathematician. I would argue that the Canadian government is totalitarian in that it denies children access to the mind of God by inflicting on them a wrongheaded education that is founded on dehistorized versions of mathematics and physics. The Canadian government uses positive reinforcement rather than the negative reinforcement commonly associated with totalitarianism. But the net result is the same—total governmental control over the behavior of people. Albert Camus (1913-60) said that memory is the enemy of totalitarianism. And memory is just another word for history. I would thus argue that we should teach the history of mathematics and physics so they are accessible to everyone.

Conclusion. Our current system of mathematics and physics education leaves many of the children behind. I would advocate three new high school history courses on mathematics, physics and risk—based on Philosophymagazine and books like Against the Gods. This new math would be taught from a historical perspective and would enable people to use mathematics, physics and risk in their daily lives. Plato and Socrates both employed philosophy and mathematics as a regular way of life. Socrates said we must follow the argument wherever it leads. The process of drawing conclusions with philosophy and mathematics is a touchstone of human existence. Remembering the past enables us to better get ready for the future. Preparing for the future using the new math takes on a whole new meaning if one believes in reincarnation. Everybody should learn the new math and seriously concern themselves with their own eternal destiny.