ABSTRACT
Atoms are the building blocks of matter. Our axioms for numbers are the basic patterns from which the patterns of numbers, many of which you have learned earlier in your career, are built. It turns out that atoms can be torn down into even more elementary building blocks.1 It also happens that our axioms of numbers can be broken down further into other patterns from which they can be constructed. Just as breaking atoms down leads us to advanced physics, further removed from everyday observations of patterns, breaking our 7 axioms for numbers down into patterns of set theory and logic leads us to more advanced mathematics and farther from the patterns of counting easily observed in everyday life. I am not going to explore set theory or logic in this text any more than I am going to study elementary particle physics. I just want you to know that there is more to learn, in case you get curious. There also exist other parts of mathematics with their own fundamental patterns that have little or nothing to do with numbers! I will introduce you to one such system when we study the Warlpiri Aborigines of Australia, cf., III. We are studying numbers deeply enough so that we can use them with a
solid understanding and without making too many technical errors. I won’t be telling you everything that I know about numbers, which honestly, is less than is known-which in turn is a lot less than is knowable.2
