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”

# Tag: spaces

## The Circle in the Plane: How bizarre is this?

The circle is a strange creature, and most definitely not as simple as it seems. In fact, you will see that a circle in the plane doesn’t enclose anything – that ‘inside’ and ‘outside’ are completely arbitrary and in the end, meaningless. Hold on to your seats!

Continue reading “The Circle in the Plane: How bizarre is this?”

## Adjacent Existents – A Theory

These ideas are a work in progress.

Axiom 1: A Thing “exists” if and only if it also defines what it is “not”, which is also a Thing.

## Mathematics and the Real

To my previous post, Louis Kauffman, himself, generously took the time to reply. I have included his reply in the comments section of that post. In that comment, I’d promised to continue the discussion in a new post. Here it is, with the brief continuation of the dialogue I had begun with Mr. Kauffman. I have copied the discussion here below:

Continue reading “Mathematics and the Real”

## On rotations as continuously-reflected translations

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?

Hmmm….