Matti Pitkanen (matpitka@pcu.helsinki.fi)
Thu, 22 Jul 1999 18:29:49 +0300 (EET DST)
On Thu, 22 Jul 1999, Stephen P. King wrote:
> Dear Matti,
>
> Umm, I wish we could spend some time talking about the computational
> issue. It is the crux of my reasoning! It is said by mystics that we are
> the Universe "experiencing it-self". I find this notion to be directly
> reflected in the fact that the behaviour of the world as it is observed
> can not be considered as "existing a priori". The ideas involved in
> Plato's cave are useful in illustrating that the experience's of
> individuals are "mere shadows of an external Reality", but the
> ontological status of this "Reality" is very much in need of discussion!
> Reality can not be an a priori given! (See Kant's discussion of "a
> priori synthetic", he has to appeal to divinity to allow for them!
> http://www.bu.edu/wcp/Papers/Meta/MetaBurg.htm)
I am actually ending up with something resembling computational
picture in some respects. I am not sure whether I really
managed to send the small digression about selves and thoughts.
In any case, I send a polished version as separate mail.
>
> Here is the comment of experts:
> ***
> On 29 Apr 1999 08:08:52 GMT,
> Peter Hines wrote:
> > I vaguely remember that the problem for the next dimension up (4-manifolds)
> > is Turing machine equivalent, so no classification procedure can exist
> > (although this was a long time ago - I'm not sure about that).
>
> This is true; it's because a 4-manifold can have an arbitrary group
> as its fundamental group, and the question of whether two infinite
> groups
> are equivalent is undecidable.
>
> - Cris Moore, Santa Fe Institute
> ***
>
> This property of "equivalence" is, to me, what an observation is all
> about! The notion that "observations" are mappings between subsets of
> the Universe U seems appropriate (it gives us a way to account for the
> existence of non-equilibria!) and thus the consideration that properties
> of objects are given only in the context of a finite mapping between
> subsets of U seems to follow.
> It seems that Time is a subjective notion derived from the sequences of
> observations that each subset of the Universe goes through in its
> "experiencing of itself". To postulate that the properties are given
> prior to the observations is to postulate that somehow the Universe
> pre-computed the classification of the 4-manifold involved in all
> possible experiences. (It seems obvious that any experience involves a
> spatial-temporal framing, thus a 4-manifold!)
> I am trying to advance the notion that what we are trying to model in
> physics is the very computation of the Universe! To assume that it is
> already somehow "out there" is to assume that knowledge can be gotten
> for free, and this is clearly WRONG!
> I will respond to the [time 464] post in detail shortly. :-)
We have opposite aims and starting points. I try to understand how some
computational aspects result from my own picture!
Best,
MP
> Later,
>
> Stephen
>
> PS, I got your responce about the embeding space as I wrote this and my
> point is very more strongly in my mind!
>
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