I thought I'd add another spin, that hasn't been used here.
Kathryn Blackmond Laskey wrote:
>
> Ronald,
>
> >When you apply Bayes rule, you are assuming that future outcomes will be
> >drawn from the same distribution as past outcomes, i.e. you are assuming
> >that induction works.
>
> Not true! ALL I am assuming is basic, timeless Bayes Rule.
>
> I am beginning with a prior distribution which places some mass on "simple
> universe," some mass on "unlearnable universe," and some mass on "edge of
> chaos universe evolving a self-understanding."....
No. You are assuming that there are propositions that are independent of
time.
Suppose you changed the example, so that you used the propositions
simple_universe(t), (that the universe is simple at time t). Then you
want to claim evidence for simple_universe at times t1..tk can be used
as evidence for for-all t simple_universe(t) - i.e., your "simple
universe" proposition. I think this is what Ron was objecting to.
This is very much like Nelson Goodman's Grue-Bleen paradox (for those
who don't know this, green is the colour that starts off as grue till
the year 2000 and then changes to bleen, and blue is the colour that
starts off as bleen till the year 2000 and then changes to grue). All of
the evidence that emeralds are green is exactly the same evidence that
emeralds are grue. Maybe the universe is changing from simple to complex
(or the other way around). Maybe the meaning of your propositions change
(just like the meaning of "green" and "blue" just seem to flip at some
arbitrary date for no good reason). Maybe there are no atemporal
propositions like "simple universe".
The evidence of cosmology (which I am not an expert in by any means) is
that there isn't a property of the universe that persists infinitely
forward and backwards and backwards in time. In particular infinitely
backwards, before the big bang. This suggests that Kathy's atemporal
hypotheses should all be rejected!!
> >Not true! ALL I am assuming is basic, timeless Bayes Rule.
> ~~~~~~~~
> But isn't it strange to reason about causes and effects without
> the notion of time? Isn't it a major gap in Bayesian (causal!)
> networks that the notion of time is not the part of the formalism?
>
No. It is the power of the formalism that it can represent both temporal
and atemporal causation. You can represent a(t) & a(t') as different
variables. The thing you can't do is represent dense time (where there
are infinitely many variables of the form a(t) for t in some dense
interval), but whether you need this is debatable.
On the hypothesis of a learnable universe: The dinosaurs learnt that the
universe isn't as learnable as they may have liked. They adapted to
their environment, but when it changed they all died out. (Those that
didn't adapt to their environment (learned) died out much earlier.) So I
suppose the right answer is to learn & adapt, but not to learn and adapt
too much!!! Or alternatively be able to respond to changes quickly,
which seems to preclude using the timeless hypotheses.
David
