Most of this blog seems to be about what I call “mystical” thinking which is offered as anti-logic or contradictory. It only seems that way. While I make claims like stupid is smart, raw is cooked, warmth is cold and any number of other kinds of nonsense, I don’t actually believe these things. The goal is to understand the failure of ideation, and so this post is a Buddhist disclaimer. Like a human body, ideas are beautiful in some ways but also stink in some places and have disgusting aspects. There is no escape from this problem except to strive away from ideation. I show paradox in the most eternal aspect of our knowledge- mathematics. It is a tremendous egoism to believe in mathematics in spite of these paradoxes. I do not think we should accept the failure of our minds and efforts to grasp the truth, but rather to reject paradox, mathematics and logic in its present state as a way to understand truth.

I would like to begin a new direction for this blog, guided by questions like “What conception of number will lead you naturally to reject the conception of number?” “How to make number imperfect in a gradual, pedagogical way?” Like the dying sound of a gong, good ideas lead you to peace of mind.

Numbers seem to march on towards infinity in a regular and perfect progression, like a straight highway to the horizon. However, the size of the highway changes as the eye looks into the distance, the distant numbers are different from the near ones. It is very much related to the relative difference between large numbers and small numbers- so that the difference between 1 and 2 is relatively larger than the difference between a thousand and 1,001. This aspect of number should not be concealed, but suggested rhetorically at every turn. The idea that numbers progress evenly and regularly is an abstraction that forgets the “size” or “numerousness” of the number. Without this context of the size of each number in the progression, the progression eventually loses cognizance of its subject – number. Eventually what the progression is about can barely be called number at all. The concept of the natural numbers, its progression of “always one more” does not live forever, but degrades and loses its meaning. Number theory is mortal.

Posing that an improbable event is a chaotic one- that when something happens that probably should happen it is at least in a certain sense orderly, and, when something happens that is very improbable, it is an “accident” as Aristotle would put it.

Now, take an event A that repeats itself over and over. If there is any chance that something else could happen besides event A, the probability that event A would repeat itself over and over would get rather small rather quickly, making a large number of repetitions a chaotic event. But a repeatable event is the very definition of order, the fundament of any scientific theory or law. Even probability itself follows rules, if these rules have any exceptions at all (including the rules about exceptions), using them repeatedly over and over again to measure everything is actually a chaotic way to behave- particularly if you happen to believe that the vast majority of things are unknown- making any known laws very likely to have a lot of unknown exceptions.

A person who really believes probability is the sort of person that thinks he knows most everything, or most everything “is known,” and the possibilities can be counted out and calculated.

Education that involves a lot of repetition actually creates instability, since in a long view of the life of an ‘educated’ person, it is very likely he will reject everything he was made to repeat as fact.

Culture that is not in some sense like a wild beast, will not restrain its people.

Control, following a ruler (whether it is a yard stick or otherwise), comes at a price- that (technically before the control is exerted and over a very long view) the ruled will rebel. But how often?

Belief in rules, in the sense of rules carrying on indefinitely—be it the rule for calculating square-root of two or otherwise, is belief in chaos.