CAN SCIENCE AND RELIGION EVER MIX?
I have had two very interesting careers -- as a marine physicist working for 35 years with the Canadian Department of National Defence, and as ordained clergy in the United Church of Canada, to which I came quite late in my life. The writings in "In The Beginning" come out of a synthesis of these two disciplines, on the one hand recognizing the historical and spiritual value of the biblical Genesis account, and on the other hand recognizing the very clear value of the great amount of "origins" knowledge we human beings have acquired in the past two millenia (and most much more recently).
Two versions are given, one in which metaphorical-theological expresssions are explicit and one in which they are not (
implicit).
No statement of this kind is ever the last word, but I hope these speak to some people as they do to me.
WHY KLONDIKE SOLITAIRE?
My motivation for this is more personal. I don't find playing the game of Klondike Solitaire very engaging — having another purpose for playing the game makes it much more interesting.
In my early teen years I remember one time when the oldest brother of a good friend of mine was ill and needed to stay home to recover. He decided to play solitaire, the Klondike kind, and his mother (I think) suggested that he keep track of the number of cards he got into the foundation stacks at the end of each game (the number of cards “up”). I was quite taken by that idea but never did it myself – until much later. About 10-12 years ago I was in a period in my life when I was also recovering (from a loss) and played Klondike solitaire to help in the healing. I then did begin to keep track of the number of cards in the “up” stacks at the end of each game. I played 220 games at that time using a deck of cards. Shortly after that I played solitaire on my computer using a game which has since become unusable due to OS updates, but I played 197 games and again kept a record of the number of cards in the stacks at the end of each game.
My life moved on and although I kept the records I didn’t do anything with them. A number of months ago one of my friends referred to playing solitaire and I told him about my having kept track of the results of all those games. That brought it back to mind and I decided then to complete this endeavour and so to enter the results into my computer and determine some statistics for all the games.
After looking at a few histograms of the results I realized that to achieve some semblance of stability more data were needed. The computer game I had used earlier was not available any more so I downloaded a new one. I played 823 games with this new software version, and with 40 more games played by cards at about the same time, the overall total came to 1,280.
The analysis followed --
TESTS ON SHUFFLING
For Klondike Solitaire, and most other card games, the effectiveness of the shuffling process is of major importance. Without a good shuffling technique, the randomization of the cards within a shuffle will be incomplete, and there will not be statistical independence of one game to the next. In order to make some statement about the reliablity of the probability distribution function of the end game results given in
Klondike Solitaire Probabilities, and of the applicability of the probabilities and frequencies of the patterns in the initial layouts, also given in
Kondike Solitaire Probabilities, I decided to test the shuffling effectiveness of the process used to produce a randomized sequence of 52 consecutive integers (representing cards).
A large amount of research has been devoted to the randomizing effectiveness of various numerical random number generators. This focusses on the initial basic programming steps needed to produce the random variables. I chose instead to test the end result, i.e. the quality of the randomization apparent in the shuffled "cards" themselves including the sorting process necessary for the final production of a 52 "card" set.
The simplest randomizing process I had access to was Excel's RAND() function, so I began with that, and used correlational techniques to produce the statistics to be tested. The results are provided in
Tests on Shuffled Data.