-Gerald O'
(see: http://www.enterprisemission.com/hyper1.html)
Bradley Scott wrote:
>
> Hi Gerald,
>
> At 08:42 AM 4/8/98 -0400, you wrote:
> >Brad,
> >I count 24. It is unclear to me from viewing your link why they are
> >talking about 27.
> >
> >First I thought this quote contained a typo: "Arthur Cayley's
> >hyperdimensional geometry (the "27 lines on the general cubic surface"
> >problem -- see diagram, right);"
>
> Yes, it is definitly not a typo.
>
> >
> >Yep only 24 major lines unless you just count segments then there's 42.
> >So the diagram doesn't seem to help. Is this some classical puzzle that
> >we haven't heard of?
>
> That is why I'm asking the question. I would like to know what the puzzle is.
>
> >
> >Now in some metaphysical doctrines, the numerology of threes and nines
> >has symbolical significance. Maybe thats the tie-in. 3^3 is 27. Three or
> >(3^1) is the minumum number of points needed to define a plane surface.
> >A surface squared becomes a 3d volume. Raise that 3d to the next
> >dimension and I guess we have the 4rth dimension or hyperspace?
>
> I see what you are getting at. But, it says "27 lines on the general cubic
> surface". So, just dealing with a 3d cube, where are the other 3 lines?
> Maybe, joining the centre of each surface with its opposite side would give
> 3 more lines, but they are not on the surface.
>
> I wish I could think more laterally!
>
> Cheers,
>
> Brad
>
> Dr Bradley W. Scott
> Saltbush Software
> Agricultural Business Research Institute
> University of New England, NSW
> Australia, 2350.