::Okay, so unpack “ungrounded” for me. You’ve used the phrases “probability” and “calculated or measured likelihood of heads coming up”, but I’m not sure how you’re defining them.::
Ungrounded: That was a good movie. Grounded: That movie made money for the investors. Alternatively: I enjoyed it and recommend it. -- is for most purposes grounded enough.
::I’m going to do two things. First, I’m going to Taboo “probability” and “likelihood” (for myself—you too, if you want). Second, I’m going to ask you exactly which specific observable event it is we’re talking about. (First toss? Twenty-third toss? Infinite collection of tosses?) I have a definite feeling that our disagreement is about word usage.::
You yourself said that we’re dealing with one throw of a rigged coin, of unknown riggage. I don’t think we have have a disagreement, exactly, except it looks to me like the discussion’s moot.
But look: if I can back up a bit, the notion that we can be dealing with a rigged coin, know that it’s rigged, and say that the—er, chances—of getting a heads is “really” 50%, because we Just Don’t Know, is useless. At that point you’re using 50-50 because we have two possible known outcomes:
But in fact we deal with unknown probabilities all the time. Probabilities are by default unknown, until we measure them by repeated trial and a lot of scratch-work. What about when you’re dealing with a medication that might kill someone, or not: in the absence of any information, do you say that’s 50-50?
Conrad.
GBM:: ..That said, when I say a die has a 1⁄6 probability of landing on a 3, that means: Over a series of rolls in which no effort is made to systematically control the outcome (e.g. by always starting with 3 facing up before tossing the die), the die will land on a 3 about 1 in 6 times.::
--Well, no: it does mean that, but don’t let’s get tripped up that a measure of probability requires a series of trials. It has that same probability even for one roll. It’s a consequence of the physics of the system, that there are 6 stable distinguishable end-states and explosively many intermediate states, transitioning amongst each other chaotically.
Conrad.