Posted by
Frank Wimberly-2 on
URL: http://friam.383.s1.nabble.com/Model-of-induction-tp7588431p7588470.html
Don't think about choosing. The axiom of choice says that there is a function from each set (subset) to an element of itself, as I recall.
Frank
Frank C. Wimberly
140 Calle Ojo Feliz
Santa Fe, NM 87505
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-----Original Message-----
From: Friam [mailto:
[hidden email]] On Behalf Of glen ?
Sent: Wednesday, December 14, 2016 11:36 AM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] probability vs. statistics (was Re: Model of induction)
Ha! Yay! Yes, now I feel like we're discussing the radicality (radicalness?) of Platonic math ... and how weird mathematicians sound (to me) when they say we're discovering theorems rather than constructing them. 8^)
Perhaps it's helpful to think about the "axiom of choice"? Is a "choosable" element somehow distinct from a "chosen" element? Does the act of choosing change the element in some way I'm unaware of? Does choosability require an agent exist and (eventually) _do_ the choosing?
On 12/14/2016 10:24 AM, Eric Charles wrote:
> 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.)
--
☣ glen
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