Bayes' Theorem

Notation:
Events are designated by capital letters
P(A) represents the probability that event A occurs
P(A,B) represents the probability that both A and B occur
P(A|B) represents the probability that A occurs given that B occurs

P(A,B) = P(A)xP(B|A) [intuitively obvious]
also P(A,B) = P(B)xP(A|B)
so P(A)xP(B|A) = P(B)xP(A|B) because both are equal to P(A,B)
divide both sides by P(A) giving

P(B|A) = P(B)xP(A|B)/P(A) qed

actually often stated with A and B reversed

P(A|B) = P(A)xP(B|A)/P(B)

P(A) is often determined by the sum of P(Bi)xP(A|Bi) over all i.

For continuous functions the sum is replaced by an integral.

No more searching for photo club judges

I resigned from this position. They found two women to share this duty for the next club year. I meet with them Monday to give them my papers and what advice I can (other than "Don't do it!"). Actually, the only problems I had were judges on the list who didn't answer calls, judges who didn't provide requested bio information for their introductions, and judges who didn't show (two). Oh, there were complaints about some of the judging. Being asked was an honor (I thought) and the experience was character building (I think). Resigning means I have to give up my Vice President title. The truly good thing about it was I got to know other club members better.

Tea Leaf Update

I located the web site of Tea Leaf Club International. They have over 800 members and lots of cool stuff. I'm sending them $30 for a membership. Now if I could find the equivalent for Lenox (Mystic pattern).

Math & AI - Part I

Saturday, June 13, 2009

Math and AI

First, a little background;

I am 82 years old. I got my masters in math in 1950 with courses in analysis and probability but no group theory. Working in insurance, I passed actuarial exams with the self-study methods common for actuaries at the time. I learned to program from IBM seminars (a whole week) and the manuals.

My reading hobby covered such things as Simon and Newell's work on computer problem solving and later the four-color problem, an interest I return to periodically to this day.
My interest in advanced math was recently reignited by The Problem That Couldn't Be Solved which led me to other books including Abel's Proof and Galois Group Theory and books on symmetry (The Monster) and Lie Groups.

I am curious about how much math can be taught to a computer and whether it could follow or even rediscover the proofs in these books. After all, they have been taught high-school geometry and symbolic logic.

Today's Journal

"Saturday, June 13, 2009 10:56am McD(N) Wt.: 178.25

"Finished arranging and counting tealeaf. Got big folding table into garage and started collecting. Stopped at an estate sale out of curiousity. Bought an abacus for $8. Resisted a spinet piano for $175. Got an e-mail from Krissy about her Mom. Actuarial yearbooks reduced to cover pages with pages with me. It provides a history of employment. Cold and rainy today. Finished book on oil depletion."

See, I told you it was dull.

What The Hey

When I started this blog I certainly didn't have tealeaf in mind. I was thinking more about mathematics, artificial intelligence, liberterianism, and other things to dazzle, confuse, and offend you with. I need to prepare treatises off-line. Also, I keep a dull daily journal which could contribute something. My apologies.

Tealeaf

Tealeaf is a design of Royal Ironstone China made by several manufacturers, especially Alfred Meakin but also Wedgewood among others. My wife's mother and later my wife conspired to corner the market. It is something I see in historical houses such as Lincoln's home in Springfield, IL. I've been sorting what must be 150 pieces. The major exception to Meakin is the cups and saucers which are Adams plus a few unmarked. Now my problem is, What on earth do I do with them?