Since we didn’t go up to Shawnee this weekend as planned, and since most of my Sunday was spent cleaning my office and writing code for the “Big Secret Project” we had some time to discuss a new book that arrived: Mathematics 1001: Absolutely Everything That Matters About Mathematics in 1001 Bite-Sized Explanations.
Elaine had opened the book to the page (2/3rd’s) of the way into the book in which a simple discussion of the Monty Hall Problem was being discussed among the finer points of Probability and Statistics.
The Wikipedia entry on the Monty Hall Problem runs down the set-up this way:
The Monty Hall problem is a brain teaser, in the form of a probability puzzle (Gruber, Krauss and others), loosely based on the American television game show Let’s Make a Deal and named after its original host, Monty Hall. The problem was originally posed in a letter by Steve Selvin to the American Statistician in 1975 (Selvin 1975a), (Selvin 1975b). It became famous as a question from a reader’s letter quoted in Marilyn vos Savant‘s “Ask Marilyn” column in Parade magazine in 1990 (vos Savant 1990a):
Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?
Vos Savant’s response was that the contestant should switch to the other door (vos Savant 1990a). Under the standard assumptions, contestants who switch have a 2/3 chance of winning the car, while contestants who stick to their choice have only a 1/3 chance.
However clear this application of Bayes Theory is, Elaine wasn’t buying it.
To her was of thinking, if the contestant on the television show can now pick either door out of a Universe of two doors, the odds are down to 50-50.
Of course, that’s not right…switching doors will “win the car” 0.66 of the time. Not the 50% which would be the case if the contestant just picked from an initial Universe of two doors.
The contrast in probabilities, a 2/3rd’s chance of winning the car if you switch) versus a 50-50 chance if you look at the problem wrong, brings to light a fascinating aspect of Bayes theories that (extended out to infinity) have some really shocking spiritual implications.
At the core of it is something I can “event-chaining” in real-life. The concept of “event-chaining” is already well known in computing, it’s just that most of humans are right on the front steps of computer science and haven’t grasped that computers are teaching us about some very subtle aspects of Reality, if we’d only be quiet long enough to pick up on it.
The difference between the host and contestant and two doors, two outcomes being a 50-50 and a host and contestant grappling with three doors is just this little matter of event-chaining which is not well-described in spiritual matters.
Chains matter immensely, however.
Accident chains, specifically: And there’s a little form you can use to see how what people do results in “accidents” but this is almost always a series of chained events. Which gets us back to the Monty Hall Problem in statistics.
Accident-chains are very big in aeronautics, too, by the way.
The usefulness of Bayes is that it views the world (even after Monty opens a door) as still being part of an event-chain. The choice problem does not “reframe” just because it now looks like a two factor two-door choice.
So in addition to everything else you do this morning, on your way to work, see what happens when you go through the implications of this statement:
“If by opening a door, the Monty Hall Problem results in a pro-change shift of adds, does that mean that other factors in Life may be working the same way in my life?
Or, as I got to on Saturday…
“Am I facing a Bayes choice problem because I am fighting a Firewire from hell problem in my studio while I have the Secret Project still pending? Is Universe trying to bias me (my activity choices) from my natural inclination to do one thing (fix the damn Firewire problem) before doing the other (finish the Secret Project Server mods)?”
I decided (since Universe wasn’t budging on the Firewire problem) that I’d move to the Linux problem (hairy Squid proxy issues related to mixing content from eth0 and wlan1 in a secure way.
I should know in a week, or less how this will work out, but in the meantime, it’s yet another one of those “off moments in Life of George” when I frame something up (Universe shoving me this way or that) and the next day, UPS has left us a book which we happen to open and which happens to frame the Monty Hall problem and that happens to deal with how this Universe pushes topic.
So the ponder is (if Elaine and my sensibilities about reframing aren’t correct) Just how many discrete chain-steps removed are we from the set-up for the game of Life?
And then (depending on how far back you can see Bayes at work) is there any probability or is Free Will really not more of an illusion that we previously have been led to believe.
Or (weirder still) is this just a further hint verging on mathematical evidence that Life is a Big Game and we are nothing more than The Bayesian Blind” not being able to see back up the causative chains far enough in real-time “play” to really grasp more personal control over the Outcome of the Game?
I wrote this on Sunday immediately before firing up the Linux server. I’ll make a note in a few hours on how programming went (sparing you the details). The question before me is “Is finishing the Linux project a key “event-chain” that needs to be done right now?