Bob,

Thanks for the book. Am still getting through the prerequisites for the prerequisite (about page 77 in Multidimensional Man). But been thinking about the concept and want to try out a metaphor on you.

I had a dream last night. It involved something 10 dimensional and I was working through an analysis of this thing from a 9 and an 11 dimensional view (contrasting one dimension up vs. one dimension down)... also 2 dimensions (who knows why, you know how dreams are). When I woke up I couldn't remember the details but thought I might understand how probability collapses under higher dimensional views.

Please bear with me. For you I could jump straight to the punchline, but I want to recreate my thought pattern to help it crystallize in my mind and to help me communicate it to those who haven't soaked in what you have. (PS: Since I haven't finished the reading, I could be completely whacked out and missed the point entirely... still I find these thoughts intriguing).

You've no doubt played with scalene triangles and realized that when constrained to two dimensions, these are, unlike isoceles, chiral. But in three dimensions, scalene images are identical. In general, chirality defined for dimension 'n' is moot in 'n+1.' Likewise our seemingly immutable views of l-amino acids or d-glucose are wiped out by a half turn in 4-space. So imagine we have an achiral synthesis of carvone. We plan to make one molecule. What is the chance that it will be d-carvone? 50%. Not if we carry the reaction out in 4 dimensions. There, the question has no meaning. We'll get carvone, plain and simple.

Going further, recall that d-carvone tastes like dill and l-carvone tastes like spearmint. Well if I turn one flip in 4-space and return here with all my chiral centers reversed, now d- is spearmint and l- is dill. Aha, what if I am a four dimensional being and I import some l-carvone (or d-) from the 3rd dimension. What's it taste like? Well, with four spatial degrees of freedom for both me and the liquid, I have to assume that all receptor/ligand arrangements occur and so, there is NO difference between dill and spearmint in four dimensions. The distinction we make between these two flavors is a dimensional fluke, not a 'real' distinction.

I can't draw on more metaphors, but it is very tempting to suggest that, with high enough dimensionality, distinctions become impossible. How far could this go? Well, if it is limited to 'chirality' it has pretty far reaching implications for biology but since chirality is geometry and you know there are geometric speculations about the underlying fabric of existence, I might be tempted to argue that if 'reality' is infinitely dimensional then all things may be "the same" -- l-carvone/d-carvone, protons/neutrons, bread/butter, friends/enemies, me/you.

Weird! Weird enough to have some meaning or just too much Chinese food on Saturday night?

-alph-