That Lucky Number Seven

We're coming up to St. Patrick's Day and it reminds us that we have an orientation towards luck.  It seems tome that mathematicians moved the term 'lucky number' into number theory.  The wikipedia entry says that it is a 'natural number' in a set which is generated by a certain 'sieve'. While the article describes a methodology that is usually seemingly obscure to us lay people, the origin isn't obscure.  It is termed the Josephus problem.   "The problem is named after Flavius Josephus, a Jewish historian living in the 1st century. According to Josephus' account of the siege of Yodfat, he and his 40 soldiers were trapped in a cave by Roman soldiers. They chose suicide over capture, and settled on a serial method of committing suicide by drawing lots. Josephus states that by luck or possibly by the hand of God, he and another man remained until the end and surrendered to the Romans rather than killing themselves." I found this an astounding story.  The wikipedia entry goes on to say that the details of the mechanism remained vague. Various mathematicians have suggested various methods - e.g. arranging the men in a circle and counting by threes to determine the order of elimination.   You can find the solution HERE. The answer is that the problem is solved when every second person is killed - but there is quite a few calculations to get to that. So a lucky number turns out to be Josephus and his companion's 'positions' in the circle.   Well, back to the social unconscious of us humans.  Here are some of the inputs to what make us humans consider some numbers to be lucky numbers: 7 - seven days of the week, 7 colours in the rainbow, 7 seas, 7 continents 3 - on the count of three, third time's the charm, three's a crowd, three strikes and you're out... 4 - four seasons, 4 elements, 4 points on the compass, four-leafed clover 8 - 8 planets, 8 notes in a musical octave See each number and its relevant luckiness summary HERE.  Today's a train day with a visit to the Sundance Layout.  Here's a picture with a person in the setting so you can get a sense of size.

Sundance Trains

There's a model layout tour in Niagara tomorrow.  This layout is Sundance. I must have thousands of images of the Sundance layout.  It has been to the narrow gauge conventions for the last several years.  It retired from travel this year and is on display in Orlando Florida.

So for those who love trains, here are more scenes from that beautiful layout.