Spencer-Brown: Cataphatist

George Spencer-Brown (GSB) did some wonderful work for a system of logic that has us consistently painting ourselves into a corner. That’s the problem. His work contributes to a system of reasoning that is consistent but incomplete.
What he doesn’t see (and few who I’ve encountered who understand his work) is that he is stuck within a cataphatic mode of thought. When he says “Let us take the form of distinction for the form.” he effectively merges the boundary between things with one of the spaces that boundary ‘encloses’.
So he takes ‘the mark’ as being indicative of what it encloses. This is wrong – or maybe it’s better that I say it’s ‘too eager’. Continue reading “Spencer-Brown: Cataphatist”

On rotations as continuously-reflected translations

Image of PDF file - single page

rotatn_is_reflected_translatns.pdf is a pdf of a little diagram I created this morning, where I muse with the ideas of transformations and how we can express Rotations (and circularity or curvature) using “not” – the ‘omni-dimensional’ Reflection (how would you describe a zero-yet-infinity-dimensional thing? “multi-“? or “trans-“?).

I don’t know why I called those vectors in the diagram ‘rays’  – they’re vectors which describe a translation transformation.

If this is right, why would we need ‘curved’ non-Euclidean spaces?