Honey, I Shrunk the Universe…

... or, "What if we were totally wrong?" Inside-Out Universe To say that the Universe 'exploded' from a 'thing smaller than an electron' in what's commonly called "The Big Bang" could be a complete misunderstanding of the data we've gathered from our observations of the galaxies and 'stuff out there around us'. Let me show…

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! Imagine a sphere upon which you've written the…

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…

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…