Mike, here's something for you to chew on: I like to think of the term "random" as meaning the absence of a *detectable * pattern, due to biases and/or blind spots of the observer or perspective. Under this definition, it is implicit that anything can be seen as random or non-random given an appropriate observer or perspective.
I think our minds are simply filters for reality, designed to pluck out the most common and useful patterns through appropriate biases. We look for the patterns we do because they help us accomplish our evolutionary purpose. When something looks random to us, it simply means we can't identify a pattern, not that there isn't one. Mathematics is a language for representing the sort of patterns the human mind tends to perceive. It is, in other words, a language for representing reality in terms of our intrinsic human perceptual biases. We have integer arithmetic because we perceive discrete, countable units in the universe. We have calculus because we perceive continuous phenomena such as curves, areas, volumes, and flows in the universe. We have geometry and topology because we perceive shapes and invariances of shape in the universe. We have logic because we perceive a mapping between situations and their descriptions (language, including math) in the universe. And we find commonalities and relationships between the various branches of mathematics, described in the terms of logic because logic is the language we use to talk about languages, including those of mathematics. Much of the confusion and failure generated by Boolean logic, the most commonly used and least versatile form of "fully functional" logic, arises from the failure of Boolean logic to recognize the distinction between different kinds of false statements (pieces of language). Boolean logic only recognizes statements that are false because their opposites are true. But it completely disregards the existence of statements which cannot be mapped to reality to verify their truth. These sorts of statements are not false because their opposites are true, but because they are meaningless. This lack of distinction (a bias towards perceiving truth and falsehood but not meaninglessness) is the source of many mathematical and logical paradoxes. As for your "irregular forms", Mike, what all this boils down to is that if the regularity of some aspect of the world isn't visible to mathematics, it isn't visible to *people*. Mathematics simply codifies what our brains already do. When we notice a regularity in reality, we create a branch of mathematics to describe it. If we don't see a regularity in a portion of reality, we call it random and mentally disregard it. I am identifying concepts themselves as human-perceivable regularities in the world, in case that isn't readily apparent. Thus if we can conceptualize something, it must be regular in our minds, and either a branch of mathematics exists to describe those regularities, or we can create one. (These new branches of math always start out as human language and become steadily more formalized as we become more certain about what the regularities are and how to more effectively describe them in language.) So, in summary: 1) A concept is a human-perceivable regularity. 2) Mathematics is a highly refined language for describing human-perceivable regularities. Therefore: 3) Mathematics is a highly refined language for describing concepts. Mathematics (and language in general) is how we tell each other about the world. If something can't be described in terms of mathematics, it's because it either can't be perceived, or we have identified a new branch of mathematics that needs to be created. Eventually, we will have covered all the filtering biases evolution has built into our minds, and mathematics will be sufficient to describe all concepts the human mind can perceive without further additions to the language. ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-c97d2393 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-2484a968 Powered by Listbox: http://www.listbox.com
