1	The Mathematical Universe in a Nutshell Kannan Nambiar The mathematical universe is discussed in some detail, so that we may have a better understanding of the physical universe and a greater appreciation for the spiritual universe
2	Universal Hierarchy Physical universe: Visible Reality Mathematical universe: Visualizable Reality Spiritual universe: Ultimate Reality Here, physical universe is part of the mathematical universe and spiritual universe is what lies beyond the known mathematical universe. Planets go in elliptical orbits because the equations of Newton force them. Mathematical logic says that we will never be satisfied with our knowledge of Ultimate Reality.
3	Mathematical Logic Logicians are not as sure about their logic as some of us might think. Goedel tells us that there is no logical way to prove that any given significant theory is consistent. The inevitable conclusion is that God wants us to be permanently on tenterhooks, when it comes to serious matters. This means that tomorrow, if we find that 2+2=5 or the sun rises from the west, we will have nobody to complain to. Logicians will gleefully tell you: we told you so.
4	Continuum Hypothesis Many consider set theory as the most complex and the most beautiful creation of mathematical logic. But there are insurmountable problems when it deals with infinite sets. One of them is the Continuum Hypothesis. A possible solution: Take aleph_1 as the set of all subsets of aleph_0 of cardinality aleph_0. A plausible argument: The set of subsets of aleph_0 of cardinality aleph_0 is the largest set of subsets possible within aleph_0. Hence, aleph_1 = 2^aleph_0. For a rigorous proof, click here.
5	White Hole: The Infinitesimal In binary notation the number 2/3 can be written as an infinite sequence 0.1010101*(up to aleph_0). But, Cantor tells us that, in principle, we can extend this to 0.1010101(up to aleph_0)xxxxxxx**(up to aleph_1), where the x represents a 0 or 1. So, here is our visualization of an infinitesimal: Corresponding to every real number, there is an infinitesimal (white hole, dedekind edge) sitting on the real line, and that infinitesimal has a nonzero, but infinitely small, length. Thus, the infinitesimal corresponding to 2/3 is the set of subsets of aleph_1 which contain all the odd integers.
6	Black Stretch: The Transfinite When a real number written as an infinite sequence is flipped around the binary point, we define it as a supernatural number. Thus, ***1010101.0 is a supernatural number. From symmetry considerations, we claim that corresponding to every supernatural number there is a black stretch. If we make use of the concept of point at infinity of complex analysis, we can visualize the black stretch as the usual black hole. Note that a supernatural number is no more supernatural than the transcendental number is transcendental, and corresponding to every transcendental number there is a supernatural number.
7	The Black Whole The set of black stretches we may call the black whole and the set of white holes, the real line or white whole. With this terminology, we can visualize the finite part of our physical universe as the white whole and the infinite space beyond as the black whole.
8	About Creator: A Malayalam Poem
9	Expanding Universe Entire potential universe, compacted into Effulgent Form Affected by nothing, detached from everything Revealed to the discerning as the One Kept from the ignorant as none, the one and only spirit The one without the second, the one that is free That One, they say, created the universe. Again, when all merge back into One There is no universe, only void. ---Poomthanam, a sixteenth century Malayalam poet. The poem seem to come very close to the description of exploding a white hole into a black stretch and vice versa. Here, void represents what we have after the big crunch, when not even the empty space (set) is there.
10	Anthropic Principle Many consider the problem of existence as the most serious concern of humankind. This leads us to seek a proper definition of consciousness and other related matters like the Ultimate Reality. While everybody agrees that (s)he is conscious, it is hard to say what is here is. The question that comes to the forefront is the following: which one should be given the dominant role, your self or the universe around you. Anthropic principle is made up by humans and not surprisingly the principle gives the dominant role to your self. The view is that the universe you see is the part of Ultimate Reality that you are capable of seeing.
11	The MahaVakyas The four mahavakyas of the vedas: TatTvamAsi (That Thou Art) PrajnanamBrahma (Perception is Brahman) AhamBrahmasmi (I am Brahman) AyamAtmaBrahma (Atman is Brahman) The nearest English translation of Brahman is what the philosopher would call the Ultimate Reality. All the four mahavakyas emphasize the fact that the perceiver, the perception, and the perceived are the same. Some thinkers, like Ervin Schrodinger and Aldous Huxley, consider this as the most basic fact of physics.
12	The Absolute 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 Upanishad gets total support from Cantor: The actual infinite arise *** when it is realized in the most complete form, in a fully independent other-worldly being, in Deo, where I call it the Absolute Infinite or simply Absolute. ---Gesammelte Abhandlungen
13	The Book The Book is an invention of Paul Erdos, generally considered, the most prolific mathematician of the twentieth century. In this book, The Almighty has written the proofs of all the theorems of mathematics, arranged according their length and in lexical order. 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 which, of course, turned out to be an unworkable idea. Click here for the anatomy of The Book.
14	A Book 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. It is generally agreed that when a person starts insisting on a proof not in The Book, a holocaust is the result!
15	Ultimate Court Many scientists believe in pantheism, which says that the complex working of the nature around us is the only palpable God that we can deal with. For these scientists The Book is everything and they know that any issue in nature can be resolved, if it can be resolved, by patiently scanning through The Book. They are acutely aware of the limitations of their intellect and the utility of The Book, so that their guarded oath in the ultimate court of nature is somewhat as follows: I solemnly swear that if I am sane, I will tell the truth, nothing but the truth, however, not the whole truth.
16	Divine Light Absolute over physical, astral, and celestial, THAT supreme divine light, The Radiant Savior, we meditate, Who awaken our intellect. ---Gayatri Mantra This mantra, chanted by millions for millennia, is nothing but an expression of gratitude to God for providing the human beings with consciousness and perception. J.B.S. Haldane opines that the Gayatri Mantra should be carved on the doors of every laboratory in the world.
17	The End