Chapter 27 - Infinity

Portent

The wedding band: the use of a circle to represent infinity, an endless loop. But if the loop denies itself? That’s just the liar’s paradox. Easily represented as a NOT gate feeding back on itself. But what it you unroll this most basic of self-referential circuits? An endless sequence of NOT gates each feeding into the next, each accepting from the previous. The loop does not represent “add one more” it represents the entire infinity, infinite in both directions.

So now roll the infinity back up. But, you ask, “By how many gates at a time.?

Primary Docs

Paradigm Discourse:
Open the Title Without End discourse in the next tab

Technical Chapter:
Open the Infinity chapter in the next tab

Significance

Given an infinite sequence of NOT gates, one gets lost in the form. Am I on a true gate or a false gate? So the closed loop is paradoxical, if true it must be false, and if false it must be true.

Which is it? Is this one true or is this one false?

At first glance, don’t seem to have the same problem with an infinite sequence of BUF gates, they are either all true or all false, but that is just the flip side of the same problem.

Which is it? Are they all true, or are they all false?

But self-reference is not limited to loops. More complicated (nearly fractal) spatial expansions also show up.