Ack! Well... I guess now we're in the muck of what the heck probability and statistics are for mathematicians vs. scientists. Of note, my understanding is that statistics was a field for at least a few decades before it was specified in a formal enough way to be invited into the hallows of mathematics departments, and that it is still frequently viewed with suspicion there.
Glen states: *We talk of "selecting" or "choosing" subsets or elements from larger sets. But such "selection" isn't an action in time. Such "selection" is an already extant property of that organization of sets.* I find such talk quite baffling. When I talk about selecting or choosing or assigning, I am talking about an action in time. Often I'm talking about an action that I personally performed. "You are in condition A. You are in condition B. You are in condition A." etc. Maybe I flip a coin when you walk into my lab room, maybe I pre-generated some random numbers, maybe I look at the second hand of my watch as soon as you walk in, maybe I write down a number "arbitrarily", etc. At any rate, you are not in a condition before I put you in one, and whatever it is I want to measure about you hasn't happened yet. I fully admit that we can model the system without reference to time, if we want to. Such efforts might yield keen insights. If Glen had said that we can usefully model what we are interested in as an organized set with such-and-such properties, and time no where to be found, that might seem pretty reasonable. But that would be a formal model produced for specific purposes, not the actual phenomenon of interest. Everything interesting that we want to describe as "probable" and all the conclusions we want to come to "statistically" are, for the lab scientist, time dependent phenomena. (I assert.) ----------- Eric P. Charles, Ph.D. Supervisory Survey Statistician U.S. Marine Corps <echar...@american.edu> On Wed, Dec 14, 2016 at 12:16 PM, glen ☣ <geprope...@gmail.com> wrote: > > Thanks! Everything you say seems to land squarely in my opponent's camp, > with the focus on the concept of an action or event, requiring some sort of > partially ordered index (like time). But you included the clause "but > doesn't have to be". I'd like to hear more about what you conceive > probability theory to be without events, actions, time, etc. > > For the sake of this argument, anyway, my concept is affine to Grant's: > "the study of probability spaces". Probability, to me, is just the study > of the sizes of sets where all the sizes are normalized to the [0,1] > interval. We talk of "selecting" or "choosing" subsets or elements from > larger sets. But such "selection" isn't an action in time. Such > "selection" is an already extant property of that organization of sets. > Likewise, the "events" of probability are merely analogous to the events we > experience in subjective time. Those "events" are (various) properties or > predicates that hold over whatever set of sets is under consideration. > Those "events" don't _happen_. They simply _are_. > > Since your language seems to depend on the idea that those predicates must > _happen_ (i.e. at one point, they are potential or imaginary, and the next > they are actual or factual), yet you say they don't have to, I'd like to > hear you explain how "they don't have to". What are these "events" absent > time (or another such partially ordered index)? > > p.s. FWIW, I have the same problem with the concept of "function" and > asymmetric transformations. I accept the idea of a non-invertible > function. But by accepting that, am I forced to admit something like > time? Or, asked another way: As all the no-go theorem provers keep telling > us (Tarski, Gödel, Wolpert, Arrow, ...), are we doomed to a "turtles all > the way down" perspective? > > > On 12/13/2016 05:03 PM, Robert Wall wrote: > > At the risk of exposing my own ignorance, I'll also say your question > has to do with the ontological status of any random "event" when treated in > any estimation experiments or likelihood computation; that is, are proposed > probability events or measured statistical events real? > > > > For example--examples are always good to help clarify the question--is > the likelihood of a lung cancer event given a history of smoking pointing > to some reality that will actually occur with a certain amount of > uncertainty? In a population of smokers, yes. For an individual smoker, > no. In the language of probability and statistics, we say that in a > population of smokers we /expect /this reality to be observed with a > certain amount of certainty (probability). To be sure, these tests would > likely involve several levels of contingencies to tame troublesome > confounding variables (e.g., age, length of time, smoking rate). Don't want > to get into multi-variate statistics, though. > > > > Obviously, time is involved here but doesn't have to be (e.g., the > probability of drawing four aces from a trial of five random draws). An > event is an observation in, say, a nonparametric Fisher exact test of > significance against the null hypothesis of, say, a person that smokes will > contract lung cancer, which we can make contingent on, say, the number of > years of smoking. Epidemiological studies can be very complex, so maybe not > the best of examples ... > > > > So, since probability and statistics both deal with the idea of an > event--as your "opponent" insists--events are just observations that the > event of interest [e.g., four of a kind] occurred; so I would say > epistemologically they are real experiences with a potential (probability) > based on either controlled randomized experiments of observational > experience. But is a potential ontologically real? 🤔 > > > > Asking if those events come with ontologically real probabilistic > properties is another, perhaps, different question? This gets into > worldview notions of determinism and randomness. We tend to say that if a > human cannot predict the event in advance, it is random ... enough. If it > can be predicted based, say, on known initial conditions, then using > probability theory here is misplaced. Still, there are chaotic non-random > events that are not practically predictable ... they seem random ... > enough. Santa Fe science writer and book author George Johnson gets into > this in his book /Fire in the Mind/. > > -- > ☣ glen > > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com > FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove >
============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove
