Since the dawn of civilization, we have attempted to restrict our attention to the palpable world, but we have failed to do so miserably. Anybody with some intellect always ends up with questions about his existence, usually with no solution in sight. This presentation gives some answers provided by our ancestors.

1. Mathematical and Spiritual
Universes
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.
with millennia old mantras

2. Universal Hierarchy
• Physical universe
• Mathematical universe
• Spiritual universe
Here, physical universe is part of the mathematical
universe and spiritual universe is what lies beyond
the known mathematical universe. But remember
that it would be a folly to neglect the spiritual
universe for this reason.

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 that “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.

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… , where the x’s
represent a 0 or 1.
So, here is our visualization of an infinitesimal:
Corresponding to every real number, there is an
infinitesimal (white hole) 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 include
exactly 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 will call it 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. 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.

9. 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.

10. The MahaVakyas
The four mahavakyas of the vedas:
• TatTvamAsi (That Thou Art)
• PrajnamBrahma (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.

11. 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

12. 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.

13. 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!

14. 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 will be
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.

15. 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 humans 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.”

16. The End
United with fellow-men by the strongest of all ties, the
tie of common doom, … be it ours to shed sunshine on
their path. Let us remember that they are fellow-
sufferers in the same darkness, actors in the same
tragedy with ourselves.
---Bertrand Russell