[time 531] RE: [time 530] Surreal numbers

Youlian Troyanov (youlian@intelligenesis.net)
Thu, 12 Aug 1999 12:50:51 -0400

"Construction by games" ? Sounds way cool.
Have you checked yet the still unfinished (as far as I know) "meaning"
series of papers by J-Y Girard ? They expand on game semantics and boldly
go further. I have used the following address http://iml.univ-mrs.fr/ftp/
to access them, but it doesn't seem to work lately.


> -----Original Message-----
> From: owner-time@kitada.com [mailto:owner-time@kitada.com]On Behalf Of
> Stephen P. King
> Sent: Thursday, August 12, 1999 11:56 AM
> To: time@kitada.com
> Subject: [time 530] Surreal numbers
> Hi All,
> Perhaps this might spark a discussion!
> http://www.innerx.net/personal/tsmith/surreal.html
> "Surreal Numbers are just sequences of binary choices, and
> constructing them is something of a game. It begins with the
> simplest surreal number, an empty sequence made up of nothing
> at all: this is written as 0, and is the starting place of what
> mathematician Martin Kruskal calls the Binary Number Tree."
> It is this notion of "contruction by games" that I am proposing is
> occuring when I say "LSs interact with each other by bisimulating each
> other". Here we think of a bisimulational action as a mutual labeling of
> properties. This, I tenatively propose is that happens in an
> observation...
> I am thinking of how it is that we can think about labeling
> "points" in
> our spaces with numbers; how is it that the orderings are manifested?
> Are orderings ontologically a priori, or are they ex post facto defined
> by the interactions of the subsets of the Universe, or something else? I
> do not think that "objects" exist a priori with labels attached. It
> seems that the act of labeling is implicit in any observation and that
> the particular order of labels is "subjective"...
> Onward,
> Stephen

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