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The edges are broken Where it has fallen And lies face down Like an ice-cream cone I dropped Long empty chambers flecked A papery brown: exposed I pick it up and take it home Set it on the steps and watch The last thin white cap shimmer As a blackness moves below My friends gather, grab for it Wanting to pull the nest apart But I guard it till they have gone A flicker pushes against the cap A black spindly mandible brakes through The edge, ripping at the seal The cap pushed open, hangs Then falls away As the wasp tries to climb out The paper nest holds The slick, black body tight It bites and pushes with fore arms That move like little fingers over keys With quick, clicking strokes It pushes with mid-legs Then stumbles, twists and shimmers free I wait for it to fly away But it sits, wings beating slowly Thorax rhythmically expanding Like the sides of my dog Waiting for me The wings stop Its body as still as mine Then suddenly it

The famous French mathematician Henri Poincare (1854-1912) said that Cantor’s set theory was a malady, a perverse illness from which some day mathematicians would be cured. ~Amir D Aczel, The Mstery of the Aleph, (Pocket Books New York, N. Y., 2000) p. 111 When Cantor published his revised proof, some— like the French mathematician Paul Du Bois-Reymond— objected that it was “repugnant to common sense.” ~Robert Kaplan and Ellen Kaplan, The Art of the Infinite, (Oxford University Press, New York, N. Y., 2003) p. 245 Since Cantor’s work on infinite sets is generally accepted—and (more importantly) since it is entirely antithetical to the principles of the DS theory, I will take some time in this chapter to include a few (slightly more formal) arguments that (I believe) demonstrate why Cantor’s conclusions are not valid. Before I deal with Cantor’s specific arguments, however, I want to review a few beliefs about mathematics that are generally held to be true. These were covered in

A slight variation in the axioms at the foundations of a theory can result in huge changes at the frontier. ~Stanley P. Gudder An interesting (and very important) things about the way the DS theory understands set theory and mathematics is that it doesn’t really change anything about the practical ways we use math in our everyday lives. When we add [2 +2] using the DS theory of mathematics, we still get the answer [4]. All that changes is our conscious understanding about what that [4] means. Despite this, the DS theory does have some rather huge implications when it comes to the frontiers of mathematical thought. It’s sort of like the proverbial claim that the flap of a butterfly’s wings (which barely makes any local disturbance) can cause a thunderstorm or a tornado to appear months or years later, in a place far away. In much the same way, the early DS principles of mathematics can go completely unnoticed; but by the time we get to infinity, a number of principles which have

An Introduction to the DS Theory of Truth and Knowledge It is easy to be certain. One has only to be sufficiently vague. ~Charles Sanders Peirce. In previous chapters, I’ve looked at the reciprocal way the brain works, how the brain learns, the structures of an expression and how we use the built-in redundancies to express the reciprocal aspects of reality. Now I want to look at the reciprocal nature of the truths we express. Absolute vs. Relative Truth Like everything else, the DS theory understands truth to be most accurately defined by reciprocal properties. The first pair I want to look at is the distinction between [absolute truth] and [relative truth]. According to the DS theory, an [absolute truth] is very similar to a state-of-being, except that, instead of being the state-of-being itself, it is the completely accurate expression (or understanding) of that state-of-being. In the diagram below, the meme-form in the leftmost box and the object in the rightmost box are

Just as kneading bread dough turns the simple elements of flower and water into something more complex, so too the folding of ideas that occurs when we repeatedly invert the conceptual and physical aspects of numbers, has the ability to turn very simple numbers into a series of more and more complex numbers, each with distinctly unique characteristics and properties. ~Antone The Ordinal Number Sequence In the DS theory, the [power set of an abstraction set] is constructed by placing the [abstraction set] inside of itself. For example, the power set of: {x│x is nothing} is" {x│x is {x’│x’ is nothing}. In other words, the power set of [the idea of nothing] is [the idea of the idea of nothing]. Like all other abstract sets, this "idea" is a singular idea, but ironically, it can be said to contain two elements, much the way that the number two is a singular idea but is necessarily composed of two distinct things. If I'm holding two quarters in my hand, they become a singular

ECONOMICS: A BRIEF HISTORICAL BACKGROUND According to Lionel Robbins, a British economist, Economics is the study of the use of scarce resources which have alternative uses. The term, [scarce resources] is the universal condition of virtually all existence—or to paraphrase Thomas Robert Malthus, nature does not provide the means of existence for everyone. Humans exist in an environment of scarce resources. This means that all men are in competition for the means of survival, for a share of the world’s wealth. According to Malthus, the aim of man is to remove the scarcity and make it possible for a greater number of people to survive. Ironically, having scarce resources is actually a positive thing in the long run. It’s the driving force behind social evolution, a fact that is reflected in the saying, “Necessity is the mother of all invention.” In fact, I believe it is the driving force behind all evolution: if every animal could get everything it wanted from nature without any