This is Wednesday, so, at the request of someone, I will try to explain Bayes' Theorem and Peirce Abduction. I'll get there, but let me begin with a question: Who invented mathematics?
- As primates began to appear almost 100 million years ago, some form of math capability began then because:
- a whole host of animals can count, with some monkeys more capable than college students
- alas, Clever Hans, a horse, did not have any math skill, but answered questions based on observing facial and body cues
- Thus, the earliest humans already had this talent for basic math 300,000 years ago, but only barely.
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| Geometry | Trigonometry | Differential geometry |
- It was around 3000 BC that arithmetic, algebra and geometry were developed in Mesopotamia.
- Egyptian math texts as far back as 2000 BC have been found.
- Greek mathematician Pythagoras (right), born around 570 BC, is known for a theorem by his name: for a right-angled triangle, the square of the length of the hypotenuse (longest side), is equal to the sum of the square of the other two sides.
- Along came another Greek mathematician, Euclid, born in 325 BC, who is known as the father of geometry, even though the concept was invented almost three millennia earlier.
- Islamic and Indian scholars further developed mathematics so that by 1500 AD, Nicolaus Copernicus of Prussia and Galileo Galilei of Italy applied them to study the Universe.
- In the 1600's, French philosopher Rene Descartes (right) became the father of analytical geometry, and is noted for: I think, therefore I am.
- Pierre Fermat from France helped develop calculus, which was used in the 1700's by Isaac Newton of Great Britain for his works on optics and gravitation. Blame him for differential calculus.
- In the mid-1700's Reverend Thomas Bayes (right) became famous for his theorem in probability, the equivalent of Pythagoras in geometry.
- In the later 1800's, American philosopher Charles Sanders Peirce introduced abduction into logic. Abduction and deduction can be combined to provide the hypothesis. All related to induction and the scientific movement linked to Galileo of Italy and Bacon of England.
Here I was planning to introduce you to Bayes' Theorem and Peirce Abduction. Let me start with one graphic. I came to a conclusion that anything more I try will only confuse you.
I was a terrific math student into geometry and trigonometry in high school. Then in college, mathematics lost me, for I could not picture something physical in my mind. So much so that I felt compelled to audit Non-Linear Differential Equations to prepare me for graduate school. It was taught by Christopher Gregory, the first chairman of the Math Department at the University of Hawaii. This is the only course I ever took there.
Professor Gregory might have been the smartest teacher I ever had. But, then again, there is something dominant about being at the podium of a university class. As a professor, you have a mystique that transcends actual intelligence. For one, we know more about a subject than any smart student. I have talked to colleagues about this factor, and we all agree that we haven't yet taught a genius in our courses.
Interestingly enough, the math department in Hawaii was only founded in 1954 as part of the School of Engineering, whose dean was Wilfred Jasper Holmes, famous for helping crack the Imperial Japanese ciphers during World War II. His wife was early on an instructor in the math program. I spent most of my professional life in Holmes Hall, and chaired the first open house when this building became available in 1973, an annual tradition that carries on till today. As part of my educational administrative career, I worked in the Manoa Chancellor's office during the late 1970's with Ruth Wong, who from 1962 to 1993 served as associate chair of mathematics.
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Tropical Storm Mitag battered South Korea and is headed for northern Honshu.
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