Probably more insufferable rambling- Part I

          Just in case you were wondering, there is, in fact, a compelling, logical argument for the postulation that we create our own realities.  That we do is a common refrain from numerous corners of the contemplative world like spiritual seekers and philosophers.  These types spend time wondering how it is that we exist.  Now there’s also a refrain about creating our own realities coming from those who wonder not how it is that we exist, but how we exist: scientists.  Most physicists you have the opportunity to ask would pretty vigorously deny that the contemplative types are asking the same questions as scientists are in their algorithmic world, much less getting the same answers.  Physicists’ stock and trade is in hard physical facts – unless they get into quantum issues, where the facts are physical all right, but a lot harder – to understand, anyway.  Quantum facts are hardly the nailed down, stalwart, sensible facts that make up Newtonian physics like those we know about apples falling from trees. Quantum facts hover in a cloud of probability.

          The way we generally think about probability is not very precise.  We think of it as being like chance or luck, but it’s better to think of it as a measure of ignorance.  One way to understand it is through the Monty Hall conjecture.  Picture yourself on Let’s Make a Deal, standing up there in front of doors #s 1,2 and 3. Monty tells you that there’s a car behind one of the doors, and goats behind the other two.  You get to pick a door, so you choose door #1.  Monty knows where the car is, and he says to open door #3, behind which is a goat. Then he asks you if you’d like to change your choice from #1 to #2.

          According to the Monty Hall conjecture, you absolutely should change your choice because it doubles your chances of getting the car. Most of us think, quite sensibly, that it doesn’t matter if you change your mind and choose door #2, since the car isn’t behind door #3 it must be behind either 1 or 2, so your chances of getting it are now 50/50. But that’s not true because a change in your knowledge of the system changes your expectations of the probable results of subsequent measurements of it. Your knowledge of what’s behind door #1 hasn’t changed, and the selection by Monty of door #3 to open was not random, so your chances with door #1 are still 1/3, but they’re 2/3 for door #2!

At first there was a 1/3 chance that door #3 had the car, but when the door was opened, the probability collapsed to 0. This is tricky stuff. Your knowledge about the system didn’t actually change the system:  the car didn’t leap from behind door #1 to #2 when the probability of it being there jumped from 1/3 to 1/2. There is still a 1/3 chance it could be behind #1. It’s just more probable that its behind #2, so you should change your choice.

          Another thought experiment that demonstrates how probability is a measure of ignorance is this one: You are a scientist and you have a hypothesis that you want to test. You think snow is cold. You write some grant proposals up, gather your team together, purchase some lab coats and clipboards and now you’re ready to rumble!  Your hypothesis that snow is cold has a probability of being correct of roughly 1/2. You might  find that you’ve awoken in a parallel universe where the physical laws allow objects to not have any temperature. That is very, very improbable, but it has not been ruled impossible. It’s possible you’ll find that snow has an indeterminate temperature of not-really-all-that-cold, and there are numerous other possibilities which will determine the probability that your hypothesis is correct, but its going to come out to be pretty near 50/50, so we’ll just call it that (by the way, the same holds true for the Monty Hall conjecture: there could be three goats back there because someone stole the car, but that isn’t very probable. Even so, it skews the chances away from a simple 1/3.).

          So the day comes for your experiment to test your hypothesis, and you and your team march out to a snow bank and stick your fingers in. Yep. It’s cold. The probability just collapsed to 1.  Simple enough, but you’re a good scientist, so you’re going to try to duplicate your results in another experiment. Next day you’re ready to march out there to that snow bank, but you pause for a minute to calculate the probability that your hypothesis is correct. Today, since your knowledge about the system of snow has changed, the probability that your hypothesis is correct has changed, too. It’s no longer (pretty darn close to) 50-50, but much higher. Nothing about the nature of snow has changed, just your ignorance about the nature of snow.