1	WhiteHole, BlackWhole, and The Book Kannan Nambiar Physical and intellectual spaces are visualized making use of concepts from Intuitive Set Theory.
2	Introduction Intuitive Set Theory (IST) provides a conceptually simple and clear visualization of the physical space of the universe. Also, if we consider all the proofs of mathematics as our intellectual or mental space, it is possible to conceive of a book in which all the transfinite ordinals of Cantor has a corresponding page and the proofs are arranged in the lexical order. Intuitive Set Theory is the axiomatic theory we get when we add Axiom of Combinatorial Sets and Axiom of Infinitesimals (defined elsewhere, visit the Web) to Zermelo-Fraenkel Theory.
3	WhiteHole We need the concept of a DedekindKnife (dknife) to define a WhiteHole (whitehole). Dknife can cut an interval, exactly in the middle, without bruising it in any way. When the dknife operates on a unit interval, an infinite (Cantor’s first transfinite cardinal) number of times, the infinitely small pieces (infinitesimals) we get are called whiteholes. Thus the unit interval is nothing but a set of whiteholes with very little embellishments.
4	About the WhiteHole The first transfinite cardinal of Cantor is called aleph-null. Recursive function theory tells us that the cardinality of the set of infinite recursive subsets (IRS) of natural numbers is aleph-null. Since every IRS corresponds to a nonterminating binary sequence (NBS) and since every NBS corresponds to an infinite sequence of cuts by dknife, it follows that the cardinality of the set of whiteholes in a unit interval is aleph-null.
5	Axiom of Infinitesimals The elements of a whitehole we will call figments. We want to maintain that the axiom of choice cannot choose a figment from a whitehole. Here is a plausible argument: For zeroing in to a location in a unit interval, we have already done our best, by specifying a nonterminating binary sequence. Hence, it is better to consider it as axiomatic, that we cannot pick or choose a figment from a whitehole.
6	BlackWhole To describe what is beyond the finite space, we need the concept of a CantorRocket (crocket) which can travel horizontally, out in space, even at transfinite velocities. The space through which crocket travels after it has crossed Cantor’ first transfinite cardinal distance is called the BlackWhole (blackwhole). There is a duality (visit the Web) between the unit interval and the blackwhole. Each whitehole in a unit interval corresponds to a BlackStretch (blackstretch) in the blackwhole. Thus, we can consider blackwhole as the set of blackstretches.
7	About the BlackWhole Whatever we have said about whiteholes can be said about blackstretches also. The blackstreches contain figments which cannot be accessed by the axiom of choice. Just as the visible part of space is filled up with whiteholes, the invisible part is filled up with blackstretches. We will assume that the crocket will stop with a flash when it can no longer conform with IST. An examination of the figments in a whitehole (visit the Web) suggests that a crocket which starts towards the right, should finally end up on the left side with a flash.
8	The Book The Book is an invention of Paul Erdos, perhaps, the most prolific mathematician of the twentieth century. In this book, The Almighty has written in lexical order the proofs of all the theorems of mathematics. Of course, this is a job a computer can be setup to do, but the big difference is that The Almighty has finished the job, unlike the computer. Note that the lexical order is with respect to proofs, not with respect to theorems, a cruel joke by The Almighty. Incidentally, Hilbert wanted to list the theorems in lexical order!
9	Anatomy of The Book The Book is altogether three millimeters thick, with the front and back covers, each one millimeter thick. The first sheet is half millimeter thick, the second sheet is half thick as the first, the third sheet is half thick as the second, and so on. Each odd page has a full proof written on it and the proofs are in the lexical order. The even page contains the corresponding theorem. The last sheet is stuck with the back cover, which means we will never know what His Last Theorem is, let alone the proof.
10	Conclusion Invisible is The Absolute, visible is The Absolute Universe comes from The Absolute Dispensing even the infinite The Absolute ever remains the same ---BrihadAranyaka Upanishad Some philosophers say that there is no difference between The Almighty, The Absolute, and The Book. They believe that an individual is A Book containing a subset of proofs from The Book. When a person starts insisting on a proof not in The Book, that is the time when the holocaust starts!
11	The End