Stephen, your notion about Bruno's "0-dimensional" reminds me of Isaac Asimov's BEST book (not sci-fi): "From Earth To Heaven" in which he deposits his scientific (in his own sense, of course) credo of 'Earthly' sciences (bio, geo, chemo related) and the 'Cosmo' related scineces, all in the observable (cf: dimensional) aspects, AND the word in between: ""to"" as an abstgract (call it dimensionless?) part of the title: for mathematics. This is of course an Asimovian humor, but very showing

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I usually object to expressing everything mathematically (number theory et al.) because I consider the world (totatlity) as a delectable varietas of unaccountable 'dimensions' (not meaning here only 'physical' Ds) while math I called a "one plane idea" indeed: rather a dimensionless imaging of the perceived and not perceived reality. I go here beyond Bruno's '3' (even '4'+) talking about ideational dimensions unrestricted. Which provides me with my habitual vagueness I enjoy. Varietas delectat. John Mikes --- Stephen Paul King <[EMAIL PROTECTED]> wrote: > Hi Bruno, > > That is a fascinating claim! "...we could argue > the UD is 0 dimensional: it computes an undefined > function with 0 arguments." > > What is the quantity of computational resources > required for such a computation? > > A new question is born from your comment: Is > your notion of a "dimension" flow from linear > independence, like that of vectors? How does one > define the notion of a "basis" in this computational > dimension? > > Onward! > > Stephen > > ----- Original Message ----- > From: Bruno Marchal > To: Stephen Paul King > Cc: everything-list@eskimo.com > Sent: Saturday, November 05, 2005 8:47 AM > Subject: Re: Let There Be Something > > > > Le 05-nov.-05, à 04:52, Stephen Paul King wrote( > to George): > > > It seems to me that the notion of "storing" > and communication 1 bit explicitly requires some > form of stable structure over multiple queries. Does > this not lead to the requirement of some form of > physicality, a physicality that is epiphenomena at > best in the ideal monism (everything is Numb3rs) > theory? > > > George, I agree with Stephen here. > > > > As to the question of the smallest dimension > that can support life and consciousness; this has > been considered by many people. My own ideas > consider the smallest dimension that allows for the > greatest diversity of forms, forms available to > instantiate and represent ideal Forms. We find that > in 3 dimensions there exists at least a countable > infinity of topologically distinct objects that > require non-trivial computational resources to sort > and categorize. > > > Hard question. Trivial at the 3-person level > description in the sense that we could argue the UD > is 0 dimensional: it computes an undefined function > with 0 arguments. > > > Bruno > > > http://iridia.ulb.ac.be/~marchal/ >