RE: Bayes

From: Charles Goodwin <cgoodwin.domain.name.hidden>
Date: Thu, 6 Sep 2001 12:11:45 +1200

> -----Original Message-----
> From: Jacques Mallah [mailto:jackmallah.domain.name.hidden]
>
> The "1st world" / "3rd world" case is an excellent
> example. Suppose
> that 90% of people live in world #3, while 10% live in world
> #1. If you had
> no other information, then indeed the best you could do is to
> guess that you
> are 90% likely to be in #3.
> That's your a priori Bayesian probability of being in #3,
> but you do
> have additional information. In my case for example (which
> I'll use becuase
> I don't know where you are located), I can look out my window
> and see vast
> stretches with nothing but fast food restaurants, churches,
> cattle, and
> bales of hay. These things correlate very strongly with
> being in North
> Dakota. Let's say that only 1% of world #3 is like that,
> while 50% of world
> %1 is like that.
>
> So now I will guess my location: (here "see" is short for
> "what I see")
>
> p(me in world #1)
> = p(see|#1) p_0(#1) / [p(see|#1) p_0(#1) + p(see|#2) p_0(#2)]
> = (.50) (.1) / [ (.50) (.1) + (.01) (.9) ]
> = .05 / (.05 + .009) = 0.847
>
> So I now think I am about 85% likely to be in world #1.
> Using the
> additional information gained by observation, I realized that
> my location is
> probably not typical.

OK, but since I currently see myself as young (in QTI terms) then similar reasoning can be applied to arrive at the (QTI-compatible)
result that I'm at (or near) the start of my worldline, just as you aren't in the Third world.

In other words, looking out the window and seeing fast food joints etc skews your probability distribution away from being in the
third world (assuming you've got amnesia and don't KNOW where you live :-) while me looking in the mirror and seeing someone middle
aged (sigh) skews the probability away from me being any QTI type oldster at this point in my life (whatever the *** that is
supposed to look like! I'm kinda hoping QTI is wrong, or 'die young stay pretty' takes on a lot more significance...)

Also . . . I *still* don't see how I can treat my current OM as a typical sample, or whatever you want to call it. If I was
magically dropped into my worldline at a random position, like Kurt Vonnegut's Billy Pilgrim, then I would be able to use the
reasoning you give to figure out the likelihood that QTI is correct. But since I haven't "come adrift in time" I'm stuck with
plodding along my worldline starting from age 0 and carrying on to the point when I die (or to future timelike infinity, according
to QTI). Even if QTI is correct I would still have to do that, so my present experience isn't incompatible with QTI . . . . . I
mean, every journey starts with the 1st step, etc!

Anyway! Are there *other* objections to QTI (for those of us who don't accept the probability argument but still have a feeling
there must be something wrong with it?)

Charles
Received on Wed Sep 05 2001 - 17:45:10 PDT