Stephen P. King (stephenk1@home.com)
Fri, 22 Oct 1999 14:28:46 -0400
Dear Hitoshi
Hitoshi Kitada wrote:
>
> Dear Stephen,
>
> Thanks for your comments.
You are welcome! ;^)
snip
[SPK]
> > It is my pleasure to help! :-) One final editorial note: Perhaps the
> > word "general" would be better that "generic" in the phrase: "Thus [P_L,
> > P] = P_L P - P P_L = 0. But in generic this does not hold because ..."
[HK]
> In mathematics, the word "generic" may be used in a slightly different way
> than the usual one (I might be wrong as I am not an English speaker): In this
> case, "in generic" means that
>
> [P_L, P] = 0 is "almost" equivalent to [H_L, H] = 0, but is slightly different
> in the sense that in some "special" cases, [P_L, P] = 0 and [H_L, H] not = 0
> hold simultaneously.
I see this does make a difference! I have been puzzled by the use of
"almost" and almost all" in math. Might this have to do with measure
zero or measure one situations?
[HK]
> As I think I am essentially a mathematician who does not think physically, I
> would prefer to follow mathematical usage rather than the usual one :-)
:-)
[SPK]
> > The final sentence of the paper is especially dear to me: "...time is
> > an indefinite desire to reach the balance that only the Universe [in
> > itself] has." I see this as being the key to the phenomenology of time
> > as expressed in the 'tension' of dissimilarity between the whole of the
> > Universe as a totality and the parts thereof. I am reminded of my
> > definitions of the word universe:
> >
> > 1) The Totality of Existence, All that exists. (This is the "objective"
> > definition")
> > 2) The sum, set or class of all observables that a given observer may be
> > aware, measure, etc. of. (This is the "subjective definition")
[HK]
> Yes, the discrepancy between the "objective" universe and the "subjective"
> universe is the cause that time exists subjectively (i.e locally).
I have though for a long time that "experiences" or the content of
subjective experience is constructed/simulated/generated/computed by the
never ending mapping between the Whole and the Part. This, in my strange
visual way of thinking, is what constitutes action/movement/etc. in
general...
[SPK]
> > These two aspects, I believe are expressions of the fundamental
> > dichotomy at the heart of observation and the reason why time is a
> > subjective phenomena. There is also the possibility that the difficult
> > issues of entropy and potentials will be better understood in the light
> > of this brilliant statement by Hitoshi!
[HK]
> It would be pleasure if it could be a help for us to understand those
> problems.
:-)
snip
[SPK]
> > > > We need to make this solid! I agree completely with the notion, having
> > > > independently arrived at a similar conclusion, but it appears that the
> > > > applicability of Goedel's Incompleteness theorem (GIT) to the Universe
> > > > is controversial to many people. I fail to see the problem that such
> > > > would have except perhaps they would like a solid, read "explicit",
> > > > mathematical relationship between physics and logic, which is the domain
> > > > of GIT]
> > > > We need to show that "observer cannot know that $E$ exists" follows
> > > > explicitly from "The theory of physics therefore includes an undecidable
> > > > proposition";
[HK]
> > > This should be read
> > >
> > > > "observer cannot know that $E$ exists" contradicts
> > > > "The theory of physics therefore includes an undecidable
> > > > proposition"
> > >
> > > The point in this problem would be to show that one i.e. observer can
> > > construct a proposition that proves the existence of the exterior $E$. I
> > > changed the descriptions in sections 2 and 5 as in the attached file.
[SPK]
> > I agree! This is excellent.
[HK]
> I hope that a "proof of the existence" of the exterior system E *implies* the
> "existence" of E.
It would seem to if we apply the notion that the "consistency (of the
proof) implies the existence of the object of the proof"!
snip
> > > The understanding here seems typical for physicists who do not understand
> > > what
> > > is formal theory or system. Even in Princeton when Goedel was an
> > > associated
> > > professor yet many years after his proof of incompletness, some professor
> > > said
> > > in front of him that logic did not make any progress since the age of
> > > Aristotle. Many of today's physicists are the same as that "some (stupid)
> > > professor."
[SPK]
> > I completely agree! It is sad that the Truth is ignored when it is not
> > convenient! I am still puzzled by the total apathy that is being shown
> > to thinkers such as yourself and Michael C. Mackey!
[HK]
> This may be because "their" purpose is not the Truth. Just to get a position
> is their purpose.
Unfortunately this is usaully the case! :-(
Later,
Stephen
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