Literary Discussions

Excerpt: Mathematics is study of patterns: geometry is the study of shape, arithmetic is the study of counting, calculus is the study of change, probability is the study of chance. Everybody is intuitively aware of such patterns, so everybody is a mathematician, even if they don't realize it. Mathematics has been part of our cultural heritage for over 2,500 years. The door to Plato's Academy in ancient Athens had inscribed over it "Let none enter here who is ignorant of mathematics."

Albert Einstein made one curious casual remark which caught my attention. Einstein said that no one could possible inductively arrive at the theory of relativity simply by observation and measurement of observable phenomena (I am paraphrasing his remark from memory.)

I realized or guessed that what Einstein might have meant is that the human imagination (at least of a gifted mathematician) is like a kaleidoscope of axiomatic systems which eventually, serendipitously stumbles across a mathematical model which seems to match physical phenomena. Of course then one must determine if the model actually tells us something about being/reality or is it simply a tool which measures and predicts to within a certain degree of accuracy.

People fret over the fact that Pi (the ratio of a circle's circumference to its diameter) is an IRRATIONAL number, a number whose decimal places never repeat and never end but are only an approximation. But given the limits of accuracy of our instruments the integers are no better or worse than Pi.  Pi taken to 10 decimal places can measure the sensible universe to withing an accuracy of one foot. And if you desire greater accuracy, use 20 decimal places, but the number of decimal places that you use will soon exceed the accuracy of your equipment.

Mathematicians were never pleased with Euclid's Fifth Postulate regarding parallel lines. "Postulo" means "I demand" (that you accept as intuitively obvious without proof). One word in monasteries for novices is "postulants" who are tested by the demands placed upon them.  

Geometers decided to ASSUME that parallel lines DO meet at infinity, hoping to reason to a contradiction and thereby PROVE the fifth postulate by reductio ad absurdum.  Instead to their amazement they discovered Hyperbolic and Elliptical geometry. Euclidean geometry states that the three interior angles of any triangle add up to EXACTLY two right angles (180 degrees). Hyperbolic (meaning to throw beyond) says the interior angles must be ever so slightly GREATER than 180 while Elliptical (meaning to fall short) says that the three angles must be ever so slightly less than two right angles.

Gauss took the measurements of a triangle formed by three mountain peaks to determine experimentally what the true nature of space is but this cannot be done because of the lack of accuracy of our measuring devices.

Einstein had to use something called Riemannian geometry which says that all of space is finite but unbounded.

Mathematics can be deceptive. One woman's college had two male professors and one professor married one of his students. The newspaper headlines read "50 per cent of male faculty marry their students" which of course was true in this case but misleading.