# [time 951] Re: [time 950] Re: [time 949] Re: [time 944] Goedel's incompleteness implies the existence of time

Sat, 23 Oct 1999 02:36:13 +0900

Dear Stephen,

----- Original Message -----
From: Stephen P. King <stephenk1@home.com>
Cc: Time List <time@kitada.com>; Paul Hanna <phanna@ghs.org>
Sent: Saturday, October 23, 1999 12:07 AM
Subject: [time 950] Re: [time 949] Re: [time 944] Goedel's incompleteness
implies the existence of time

> Dear Hitoshi,
>
> >
> > Dear Stephen,
> >
> > Thanks for your comments and helps in English. I corrected some points as
in
> > the LaTeX file attached.
>
> 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 ..."

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.

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 :-)

>
> 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")

Yes, the discrepancy between the "objective" universe and the "subjective"
universe is the cause that time exists subjectively (i.e locally).

>
> 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!

It would be pleasure if it could be a help for us to understand those
problems.

>
> > ----- Original Message -----
> > From: Stephen P. King <stephenk1@home.com>
> > Sent: Friday, October 22, 1999 5:21 AM
> > Subject: [time 944] Goedel's incompleteness implies the existence of time
> >
> > > Hi Hitoshi,
> > >
> > > I am presenting this version of your paper with some editorial comments
> > > and pointers in [boxes] Egrammatical suggestions are not labeled EUmm,
> > > it looks like I messed up the formatting of the original! :-(
> > >
> > >
> > > >>Here is some excerpt from time_VI.tex. LaTeX file is attached, which
is
> > > available also at
> > >
> > > index.html)
> > >
> > > A key is Goedel's incompleteness theorem, which assures the existence of
> > > (local) time.>>
> > >
> > > [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";
> >
> > 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.
>
> I agree! This is excellent.

I hope that a "proof of the existence" of the exterior system E *implies* the
"existence" of E.

> For all Time List readers there is a
> discussion of the implications of Goedel's Incompleteness Theorem at:
>
PS&CONTEXT=940602804.2060124203&HIT_CONTEXT=940602804.2060124203&HIT_NUM=0&rec
num=%3c36CC02E1.167E@cns.mpg.de%3e%231/1&group=sci.physics.research&frpage=get
doc.xp&back=clarinet
>
> > > this must be air-tight! I believe that your idea here is
> > > correct, but I believe that we must be able to defend against the
> > > skepticism. Here is an example:
> > >
> >
http://members.home.net/stephenk1/Outlaw/Chicken%20Little%20and%20Group%20Theo
> > ry.html
> >
> > 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."
>
> 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!

This may be because "their" purpose is not the Truth. Just to get a position
is their purpose.

>
> Later,
>
> Stephen
>

I add a correction of the acknowledgements that owes to my wife who teaches
English (her page is http://www.kitada.com/~keiko/ ):

{\bf Acknowledgements.} I wish to express my appreciation to
the members of Time Mailing List at http://www.kitada.com/
for giving me the opportunity to consider the present problem.
Special thanks are addressed to Lancelot R. Fletcher, Stephen
Paul King, Benjamin Nathaniel Goertzel, Matti Pitkanen, who have
been making stimulating discussions with me on the list and
leading me to consider the present problem. I especially thank
Stephen for his comments on the earlier draft to improve my
English and descriptions.

Best wishes,
Hitoshi

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