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Monthly Archives: February 2009

Definition of Paradox: A seemingly contradictory statement that may nonetheless be true.

A paradox is supposed to define what is false.

The statement below is false.

The statement above is true.

You can go around and around on this one. But most of us try to work it out a couple of times, say, “Oh, it’s a paradox.” and go about our business. Unlike a computer, which could cycle over this classic paradox until eternity, or Windows crashes, which ever comes first.

midieval

Mideival Thought

What is it about our brains that allow us to tolerate paradox as well as we do? In general, it is considered incompatible with good math or physics. Godel’s theorem,¬† discussed in a previous post, suggests that all mathematical systems, however rigorous, will turn up paradoxes, or fail to prove things that are true or both. How does Godel establish truth or falsity? By reference to common sense attributes of the real number system which we know to be true or false.

This is all related to the time-honored philosophical battle between ontology versus epistemology, or what is true versus what can be known. As they delve into relms of physics further removed from everyday experience, physicists have settled on the principal of falsifiability. A theory or hypothesis in physics may be considered true if it predicts the outcomse of experimental tests. Such tests accumulate and continue to be consistent with the hypothesis, the hypothesis is more likely to be true. If any such experiment fails, the hypothesis may be considered false. Read More »

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Sigmund Freud reportedly was once asked what make for a healthy mental life, and answered, “lieben und arbeiten,” to love and to work. In his book “The Power of Play” David Elkind argues that he should have included “spielen” … to play. As the developmental psychologist¬† Jean Piaget said,¬† “Play is the answer to the question, ‘How does anything new ever come about.'”

leaves1All children play. If toys are not available to children in primitive cultures or in areas of poverty, they will utilize whatever items are available. Imagination animates sticks, old cans, blocks of wood, and discarded cooking utensils. Dolls, toy animals, and imaginary playmates develop lives of their own. Children re-create the world and manipulate it in play, stimulating neurological development and creating the inner space which we call the mind and which will be used to understand the external world and plan for the future. Read More »