© May, 1976 & Jan, 2011
Does anyone know the ultimate cause of all existence? One may answer that "unanswerable" question by probing into mathematical and religious concepts that lead to an explantion of the universe.
Existence is the universe and everything that might be beyond. All existence is an endless manifestation, whole and complete in itself, and controlled by an infinite "master mind" (system of principles) consisting of all the laws that maintain and create.
Everything exists because there is one supreme law that transforms nothing into a manifold creation by purely relative means. To understand how creation comes about it is important to know the nature of infinity.
George Gamow, author of a number of far-reaching books on science and astronomy, states that one kind of numerical infinity is stronger than another kind: (1)
Thus it is impossible to establish a one-to-one correspondence between the points on a line and the integer numbers, which means that the infinity of points on a line is larger (stronger) than the infinity of all integer or fractional numbers. (2)
Gamow points out the fact that an infinity, one step stronger than the infinity of integer or fractional numbers, is actually an infinite number of infinities. He proves this statement by the following experiment:
To prove this statement let us try to establish one to-one correspondence between the points on a line, say one inch long, and the sequence of integer numbers.
Each point on the line is characterized by its distance from one end of the line, and this distance can be written in the form of an infinite decimal fraction, like 0.7350624780056 .... or 0.38250375632 .... Thus we have to compare the number of all integers with the number of all possible infinite decimal fractions. (3)
It turns out that the number of infinite fractions can be represented only by the distances of points on a line, not by periodic decimal fractions or integers alone. (4) There are an infinite number of different infinite fractions between every terminating decimal, periodic decimal and whole number. (5) Therefore, the infinity of points on a line is actually an infinite number of infinities. Gamow goes on to say that there are many infinities even stronger:
According to George Cantor, the creator of the "Arithmetics of Infinity", infinite numbers are denoted by the Hebrew letter "N" (aleph) with a little number in the lower right corner that indicates the order of the infinity. The sequence of numbers (including the infinite ones!) now runs:
1, 2, 3, 4, 5........... N 1, N 2, N 3...........
and we say "there are "N 1 points in a line" or "there are N 2 different curves" just as we say that "there are 7 parts to the world" or "52 cards in a pack." (6)
For every infinity there is another, stronger infinity. While "N 0" designates the number infinity (corresponds to the first dimension), "N 1" is an infinite number of infinities (corresponds to the second dimension) and "N 2" is an infinite number of an infinite number of infinities (corresponds to the third dimension). (7) What is the largest possible infinity? The principle of the slope-intercept equation, y = mx + b (9) will help to answer the above question:
... the number "m" determines how much of a change there will be in the value of "y" for every change of one unit in the value of "x." For example, if m = 2, y will increase by two units whenever x increases by one unit. (10)
If m = O, then the line will be horizontal and would therefore have a "zero" slope, If m = 1, then y will equal x and for every unit across there will be one unit rise. The line would then be exactly between vertical and horizontal. If m = 1/0, which is the reciprocal of zero, then an exact mirror image of the horizontal line (a vertical line) is produced with the line x = y (11) as the mirror or line of symmetry. All pairs of lines that have each other's reciprocals are reflections of each other, with x = y as the line of symmetry.
A line becoming horizontal has a slope approaching zero in the same way a line becoming vertical has a slope becoming infinite. A vertical line has a slope of the strongest possible infinity, which is designated 1/0 because its exact reciprocal is zero, which is the slope of the horizontal line. 1/0 is definitely the largest possible of all infinities. What can be more vertical than a vertical line? 1/0is the reciprocal or multiplicative inverse of its "twin sister" zero, which is likewise the smallest infinitesimal possible. What could be more level than a horizontal line?
The ultimate, infinite whole, or set of all objects, is existence itself. Any whole can be represented by a fraction, such as 1/1, 2/2, 1,000,000/1,000,000 (which equals one) or infinity/infinity and 0/0 (even though considered "undefined" can still equal any quantity or value). The pie sections of a circle (which is a good example for a whole) are used in the following paragraph as an example to demonstrate the principals of the infinite integral (13) utilized in calculus to figure out the exact areas within curved boundaries. (14) David Bergamini, an author specializing in scientific subjects, states that the whole is nothing but the summation of an infinite number of infinitesimal parts: (15)
As a triangle becomes infinitely narrow, exactly when does it cease to be triangular shaped and start to behave as if it were a pie-shaped sliver of pie? Surely it does not take on the shape of a proper pie slice until it is infinitely narrow and then, surely, it is no longer something, but nothing. How can an infinite number of nothings be added up to produce a something such as a circle? (16)
The circle is not exactly an infinite amount of nothings, but an infinite amount of infinitesimally small parts that make up the circle. An infinitesimal amount is closer to nothing than any decimal fraction can be, but it is still not absolutely nothing. (17) However, If we take the strongest infinity (1/0 from the slope intercept equation), and if a 1/0 amount of nothing (1/0 x 0) was used in making the circle, then there would have to be the division of zero into itself (0/0) which would have to produce something however ambiguous that "something" might be--perhaps enough "something" to create some numerical value, a circle, anything? The multiplication goes like this:
1/0 x 0/1 = 0/0 = any value
Any number times its reciprocal equals one. (18) Any object or set of objects can equal zero divided by zero. 1/0 times zero could equal one whole set of anything, whether it be all the atoms in a rock or all the stars in the universe.
To those who have pondered the existence of God or wondered if there must be some universally aware Principle of creation, you might find thefollowing interesting; we are now hopping beyond the frontiers of science into the mystical and spiritual.
Awareness seems basic to existence and the creation of matter. Physicist, Bob Toben, states: "The incomprehensible unaware oneness beyond space-time becomes aware of itself, creating light...." (19) which "chases itself in gravitational collapse" (20) forming "a quantum (mini) blackhole (21) which is the fundamental unit of matter." (22)
This "unaware oneness" must be nothing because nothing can exist until it becomes aware of itself. (23) Existence is awareness. (24) From an absolute (rather than relative) perspective, nothing really exists, because beyond space-time is everywhere. (25) Nothing "becomes aware of itself" only when it divides into itself (when the perspective of itself changes from absolute to relative), which is a constant, inevitable process. Zero divides by zero, creating all relative existence. 0/0 is just the two opposite forces, 1/0 and 0/1 in combination with each other. The universal forces, 1/0 , 0/1 and their combination is remarkably similar to the Trinity.
In support of the above theory, Paramahansa Yogananda, author of Autobiography of a Yogi and founder of SRF, states:
God the Father is the Absolute, Unmanifested, existing beyond vibratory creation. God the Son is the Christ Consciousness (Brahma or Kutastha Chaitanya ) existing within vibratory creation; this Christ Consciousness is the "only begotten" or sole reflection of the Uncreated Infinite. The outward manifestation of the omnipresent Christ Consciousness, its "witness" (Revelation 3:14), is Aum, the Word or Holy Ghost: invisible divine power, the only doer, the sole causative and activating force that upholds all creation through vibration. (26)
Zero becomes the "Holy Ghost" or "invisible divine power, the only doer, the sole causative and activating force that upholds all creation through vibration" (27) when it (through changing its perspective--awarness of itself--from absolute to relative) divides by itself or, in effect, multiplies with its reciprocal, 1/0. Then from the perspective created by the equation, 0/0 = reality, "Son" or "creation," 1/0 appears to be an equivalent to the infinite "Father", "the Absolute, Unmanifested existing beyond vibrating creation" (28) beyond space-time. The infinite "Father", by relativity or perspective, might be an effect of the original zero that zero divides into:
0 (infinite "Father") is divided by: 0 ("Holy Ghost")
The quotient of 0/0 is the "Son" or creation itself. It could be defined as the "only begotten sole reflection of the Uncreated Infinite." (29)
The underliying principles (laws) of creation (existence) never began, nor will they ever end. The beginning of creation lies in every moment, arising directly from the virtual existence of eternal, permanent, "Unmanifested" mathematical principles (1/0 or infinite intelligence--"Father").
In essence, all existence is a relative phenomenon of vibration that dances between the opposites, 1/0 and 0/1. Like the sequence of counting numbers, there is also a sequence of infinities, the strongest and largest being the reciprocal of zero. The slope-intercept equation demonstrates the validity of the number 1/0 . There are exactly as many zeros in zero as there are parts in a whole. 1/0, 0/0 and 0/1 seem to play the same unifying roles as the "Father," "Son" and "Holy Ghost" as explained in Yogananda's Autobiography of a Yogi. Zero divided by zero, in the context explained above, could be the ultimate cause of all Existence.
1 George Gamow, One Two Three...Infinity (New York,
Viking press, Inc. 1971), p. 20.
2 Ibid., p. 20.
3 Ibid., pp. 18 - 19.
4 Ibid., p. 19.
5 Ibid., p. 20.
6 Ibid., p. 23.
9 Gardner Cowles, The Cowles Commrehensive Encyclopedia (New York, Cowles Educational Books, Inc. 1965), Book 9, p. ll66.
10 Ibid., Book 9, p. 1166.
13 David Bergamini. Mathematics (New York, Time Inc., 1963, p. 107.
14 Ibid., p. 107.
15 Ibid., p. 44.
17 Ibid., pp. 108 - 109.
18 Mary P. Dolciani, Modern School Mathematics Algebra One (Sacramento, California State Department of Education, 1967), p. 637.
19 Bob Toben, Space - Time and Beyond, (New York, P.O. Dutton and Co. Inc., 1975), p.47.
24 Ibido, p. 88.
25 Ibid., pO 54.
26 Paramahansa Yogananda, Autobiography of a Yogi (Los Angeles, California, Self-Realization Fellowship publishers, 1973), p. 169. See Footnote n.
Bergamini, David. Mathematics. New York: Time Inc., 1963.
Cowles, Gardner. The Cowles Comprehensive Encyclopedia. New York: Cowles Educational Books, Inc., 1965.
Dolciani, Mary P. Modern School Mathematics Algebra One. Sacramento: California State Department of Education, 1967.
Gamow, George. One Two Three....Infinity. New York: Viking Press, Inc., 1971.
Meyer, Jerorne S. Fun with Mathematics. New York: Fawcett World Library, 1966.
Toben, Bob. Space-Time and Beyond. New York: E.P. Dutton and C o. Inc., 1975.
Yogananda, Paramahansa. Autobiography of a Yogi. Los Angeles, California: Self-Realization Fellowship Publishers, 1973.
REFLECTIONS OF ETERNITY: (The Image is massive and opens in a separate window)
CLICK HERE and let us reflect for a few moments on how awesome our universe really is.
Hubble Telescope image provided by NASA. Applet program provided by Fabio Ciucci.