Re: [s-d] [s-b] Consultation: the Field

["Geoffrey Spear" <geoffspear@xxxxxxxxx>]

On Jan 2, 2008 11:29 AM, 0x44 <bnomic@xxxxxxxxxxxxxx> wrote:
>
> Geoffrey Spear wrote:
> > On Jan 2, 2008 11:12 AM, Roger Hicks <pidgepot@xxxxxxxxx> wrote:
> >
> >> On Jan 2, 2008 4:49 AM, Geoffrey Spear <geoffspear@xxxxxxxxx> wrote:
> >>
> >>> I submit the following Consultation:
> >>>
> >>> {{ Does the fact that the Field is geometrically impossible mean that
> >>> it doesn't exist? }}
> >>>
> >>>
> >> Arguments:
> >>
> >> No one (including the Referee) is required to create an accurate
> >> geometric display of the Field. The Referee's public display of the
> >> field can be an approximation; All other public displays are
> >> approximations of the data they represent.
> >>
> >
> > The display isn't my issue.  The platonic description of the Field is,
> > in my opinion, impossible without positing a non-trivial and
> > heretofore (to the best of my knowledge) nonexistent form of
> > non-Euclidean geometry where there's something called a "square" that
> > can be used to tile the surface of a torus.
> >
> >
> You can tile a sphere with squares, from the perspective of the surface
> of the sphere they are square, from the perspective of an observer they
> are curved. In a Field Match participants exist upon the field,
> therefore the squares are square, even if they're saddle-shaped so as to
> tile the torus.

Sure, but spherical geometry is a well-established field where the
term "square" has a precise meaning.  I'd argue that the rules
creating new fields of geometry implicitly is stretching things a bit.

-- 
Geoffrey Spear
http://www.geoffreyspear.com/
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