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 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

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 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.

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 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.

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 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.

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 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.

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 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.

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 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.

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 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.

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 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.

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 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.

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 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 otherworldly being, in Deo, where I call
it the Absolute Infinite or simply Absolute.
 Gesammelte Abhandlungen

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 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.

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 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!

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 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.

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 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.

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