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Thread: Topology of 0: The Mathematics of Nothing

  1. #1
    Join Date
    May 2010
    New Jersey

    Topology of 0: The Mathematics of Nothing


    "0²=2 simply states, that the surface of 'nothing', in a very real, arithmetical sense, has an inherent twoness at it's surface, it has it's In'side' and it's Out'side'."


    Possibly relevant excerpts from Buckminster Fuller’s Synergetics:

    100.010 Awareness of the Child: The simplest descriptions are those expressed by only one word. The one word alone that describes the experience "life" is "awareness." Awareness requires an otherness of which the observer can be aware. The communication of awareness is both subjective and objective, from passive to active, from otherness to self, from self to otherness.

    Awareness = self + otherness
    Awareness = observer + observed

    100.011 Awareness is the otherness saying to the observer, "See Me." Awareness is the observer saying to self, "I see the otherness." Otherness induces awareness of self. Awareness is always otherness inductive. The total complex of otherness is the environment.

    100.012 Universe to each must be All that is, including me. Environment in turn must be All that is, excepting me.

    264.02 At minimum, life involves awareness, self involves otherness, and otherness involves somethingness. Awareness is of otherness: awareness of the outside superficiality of the observer’s “finger” by the externality-searching optical system of the observer. Indeed, the externality-searching for the nipple of its mother’s breast by the olfactorily guided external nose-mouth of the newborn constitutes initial otherness awareness. As a fertilized ovum of an integrally evolving female organism umbilically circuited with the female organism, no otherness awareness is involved except that of the mother even as she may be sensorially aware of a sore spot on her arm.

    264.03 Otherness involves somethingness: This brings us to the consideration of the nature of the epistemographic evolution of experience that__at one historical moment__evolved the misconceptioning of a nothingness__ergo, dimensionless__point.

    264.10 Prime Othernesses: Single and Plural Otherness

    264.11 While environment plus me equals Universe, Universe minus me does not equal environment.

    264.12 Environment does not exist without me. I the observer am the living human experience. Life is the present experience. Experience begins with awareness. No otherness: No awareness.

    264.13 I am one of the two prime othernesses: I am the single otherness; environment is the plural otherness. I am the present otherness; environment is the past otherness. By the time I have become aware, other as-yet-untuned-in events of nonunitarily conceptual Universe have transpired. Environment is inherently historical. Universe is eternally inclusive of all past, present, and future experiences plus all the at- present-untune-inable otherness of Universe. Universe is eternally general; environment is always special case.

    415.10 Even at zero frequency of the vector equilibrium, there is a fundamental twoness that is not just that of opposite polarity, but the twoness of the concave and the convex, i.e., of the inwardness and outwardness, i.e., of the microcosm and of the macrocosm. We find that the nucleus is really two layers because its inwardness turns around at its own center and becomes outwardness. So we have the congruence of the inbound layer and the outbound layer of the center ball.

    10F2 + 2

    F = 0

    10 × 0 = 0

    0 + 2 = 2 (at zero frequency)

    Because people thought of the nucleus only as oneness, they for long missed the significant twoness of spherical unity as manifest in the atomic weights in the Periodic Table of the Elements.

    415.11 When they finally learned that the inventory of data required the isolation of the neutron, they were isolating the concave. When they isolated the proton, they isolated the convex.

    986.164 One by itself is nonexistent. Existence begins with awareness. Awareness begins with observable otherness.

    986.165 Understanding means comprehending the interrelationship of the observer and the observed. Definitive understanding of interrelationships is expressed by ratios.

    986.166 At the outset of my explorations I made the working assumption that unity is two, as combined with the experimentally demonstrable fact that every system and every systemic special case sphere is at once both a concave and a convex sphere__ergo, always inherently two spheres. Reflective concave surfaces convergently concentrate all impinging radiation, and reflective convex surfaces divergently diffuse all impinging radiation. Though concave and convex are inherently congruent as they are always-and- only coexisting, they are also diametrically opposed physical behavior phenomena__ergo, absolutely different because the one diffuses the energies of Universe, producing macrocosmic dispersion, and the other concentrates the energies of Universe, producing microcosmic convergence. Concave and convex are explicitly two opposites cosituate (congruent) geometrically as one. This led me to the working assumption at the outset of my__thus far__60-year exploration for nature's own coordinate system, that unity is inherently plural and at minimum is to be dealt with as the value two, which twoness might well coexist with other numbers of inherent properties of primary-existence systems.
    Last edited by Albion; 12-27-2010 at 09:44 PM.

  2. #2
    Join Date
    May 2010
    New Jersey
    The Trouble with Spacetime: The Rise of the Planck Length, The Fall of a System of Theory, And What Comes Next

    “…That the explanation of space, time and matter must also generate the mathematical structures it uses is no doubt a profound observation, akin to the intuitionism of mathematicians like Kronecker, Atiyah and Woit. Einstein, evidently disillusioned with the explanation of space, time and matter, using the continuum mathematics of the field, long before anybody else ever was, privately pined for a true mathematical structure of the discretium, upon which to build a unified theory. He wrote to Walter Dällenbach:

    The problem seems to me [to be] how one can formulate statements about a discontinuum without calling upon a continuum (space-time) as an aid; the latter should be banned from the theory as a supplementary construction, not justified by the essence of the problem, [a construction] which corresponds to nothing “real.” But we still lack the mathematical structure unfortunately. How much have I already plagued myself in this way.

    Clearly, the phase space of quantum mechanics, based on the ad hoc invention of complex numbers, via imaginary numbers, producing the conundrum that fills Sir Atiyah with such wonder, does just what Einstein felt should be banned from the unified theory: It calls upon the continuum (the infinite set of complex numbers of size one), as a supplementary construction, which certainly is not justified by the essence of the challenge to find a unified theory of nature, since it is a construction that does not correspond to anything real. Not only does quantum theory incorporate such a construction, but even Einstein’s own concept of the fourth dimension of spacetime, as he originally conceived it, is given as x4 = ict, and as such is something he insisted we should always regard as “purely imaginary.”

    Imagine Einstein’s delight, then, had he been able to find a discrete principle of fundamental physics, which was able to “generate the mathematical structures it uses,” but, alas, it was not to be in his time. Today, though, Rowlands believes he has found such a principle in the truism that nothing is perfect. His idea is that zero, or nothing, must be the starting and ending point for constructing a unified theory, because, since it is obvious that “nothing…comes from nothing,” he has to agree with Peter Atkins, a science writer he quotes as stating that “the seemingly something” of reality must be “elegantly organized nothing.”

    While this might sound like mumbo-jumbo, it’s actually consonant with most modern theories of physics, because it is now recognized that the most perfect symmetry obtainable is nothing, and since the universe is something, its current state must represent the broken symmetry of nothing. K.C. Cole explains it this way:

    …our universe could once have been so symmetrical that it amounted to nothing at all. “Nothing” is as perfect a symmetry as you can imagine, since there’s nothing you can do to it that makes a difference. This nothing would have been unstable, however— like a pencil balanced perfectly (which is to say, symmetrically) on its tip. And that means— as Frank Wilczek has put it—the answer to the question “Why is there something rather than nothing?” would simply be that “nothing” is unstable.

    As Rowlands states it, “the universe and everything we can possible experience or conceive is also conceptually nothing. No other position is extreme or uncompromising enough to be able to explain everything.”

    There is much to say about this figure, but most of it will have to wait for a subsequent essay. Suffice it to say now that the expansion of the pseudoscalars, at unit speed, constitutes a physical and mathematical starting point of infinite degeneracy, for a physical system consisting of nothing but space/time; that is, n/n = 1/1 = 0, in terms of motion, because unit motion, or a space/time ratio of 1/1, is perfectly symmetrical, or balanced, and only nothing is perfectly symmetrical, as Cole and Rowlands explained.
    However, introducing a unit vibration, wherein a parity transformation of the pseudoscalars occurs at the end of each temporal unit, or vice versa, breaks the symmetry of the 1/1 space/time ratio, and produces a unit temporal, or a unit spatial, speed displacement, a unit speed-displacement from unit speed, we might say. In this way, three, and only three, space/time ratios emerge: 1/2, 1/1, 2/1, equivalent to three integers, -1, 0, 1, algebraically, corresponding to the n-dimensional properties of the three circles (spheres) of figure 2 above, geometrically speaking (i.e. in terms of π).

    Since the unit integers are the foundation of all mathematics and physics, and given that they are generated by the simple physical processes of space/time, as order in progression, the consequences that follow portend an exciting new system of physical theory.

    So, recognizing this, particle physicists are looking for evidence of Supersymmetry and the Higgs particle, while Rowlands is looking for evidence of infinite degeneracy, which are physical and mathematical manifestations of duality, the chief characteristic of symmetry, and the key to understanding how the imperfections of something can come from the perfection of nothing.

    Meanwhile, taking Larson’s derivation of natural units of space and time, from the observed constants of the speed of light, c, and the Rydberg constant, R, a new, non-paradoxical, means for quantizing space and time, through the folding of continuous motion by vibration, provides a perfect example of nothing becoming something, while preserving nothing in the process. To briefly explain how this can be developed requires only that we recognize that order in progression provides a basis for a new algebra, not of time alone, but of physical space/time.


    ZERO TO INFINITY The Foundation of Physics - Peter Rowland [A book referred to in the (anonymous?) article above]

    [Peter Rowland is a Uni-Phi co-collaborator with Nassim Haramein]

    Excerpt from chapter 1

    "A ‘unified’ theory, however, means something very particular. It means a
    theory which derives all its results from a single source, not simply one in which
    we put all our known results into a single comprehensive package. This is a
    crucial distinction which is not always made in discussions of the subject; but, in
    principle, a truly unified theory cannot come from an act of unification; that is,
    we cannot, for example, create a truly unified theory simply by combining
    quantum mechanics and general relativity in a new mathematical superstructure.

    Such attempts have always failed in the past, and will continue to do so in the
    future, because the concept of unification as combination is invalid. Unification
    is really about finding descent from a common origin. Creating a sophisticated
    mathematical superstructure will not provide answers to the fundamental
    questions that we would expect from a truly unified theory, a theory of

    Many physicists believe that we can assume concepts such as space, time and
    matter to be fundamental and even inexplicable. Many also believe that we must
    assume that the fundamental ideas will be expressed in a mathematical language
    that already exists independently of the physical principles we are expressing.
    Others again are prepared to believe that the unifying mathematical structure,
    whatever it is, will be a sophisticated one which only a few will be able to truly
    understand. I do not believe in any of these things. If physics is to prove itself the
    most fundamental possible way of understanding the ‘natural world’, then it must
    explain space, time and matter, as well as use them, and it must generate the
    mathematical structures it uses; it must also show how all things that are
    sophisticated arise from things that are much more simple. In principle, all
    possible complications must be removed from the ultimate starting point. It has
    to be intrinsically simple and absolutely single.

    So, how do we construct such a theory? What would be left after we have
    removed all the complications? What could be our single and simple starting
    point? There is only one possible answer: zero, absolutely nothing, or perhaps
    ‘no thing’. This is the only thing in all our experience which has no structure and
    includes no complication. So, zero must be our starting point. It must also be
    where we finish, for nothing, as we all know, comes from nothing – nihil ex
    nihilo fit. The idea that the universe may be a totality of ‘nothing’, in some sense,
    has been discussed for quite a number of years, especially in the context of the
    ‘big bang’ theory of creation, where the total energies of matter (positive) and
    gravitation (negative) could cancel each other out. This is the kind of reasoning
    behind the statement of the science-writer, Peter Atkins, that ‘the seemingly
    something is elegantly reorganized nothing, and … the net content of the
    universe is … nothing’.1 However, to find the most fundamental possible theory,
    we must go even further, and state that the universe and everything we can
    possible experience or conceive is also conceptually nothing. No other position is
    extreme or uncompromising enough to be able to explain everything.

    1.2 The Genesis of Number
    As we have said, many scientists today believe that the concept of nothing has a
    fundamental role to play in an understanding of the universe and its contents. It
    is, for example, often stated that the universe itself could have emerged as a
    quantum fluctuation from an essentially zero state, and that the total zero energy
    is maintained by the total positive mass energy being equated numerically to the
    negative gravitational energy generated by this mass through a special
    application of Mach’s principle (the idea that the inertia or mass of physical
    objects is determined by their interactions with the rest of the matter in the
    universe). However, the concept of nothing may be even more powerful than
    this, for it may be that the nothingness applies also to the entire conceptual
    scheme of which matter and the universe are merely components. Nothing is
    unique among conceptual ideas in being infinitely degenerate (infinitely capable
    of reinterpretation) and it may be that this infinite degeneracy is the key to an
    understanding of its special power.

    However, since ‘nothing comes from nothing’, we are left with the question
    of how we preserve the total nothingness in the presence of the seemingly
    ‘something’ which we call ‘the universe’. Both mathematics and physics suggest
    that the answer lies in the concept of duality, the idea that to every fundamental
    concept there exists some kind of partnership or relationship with another that is
    its ‘dual’. As Nicholas Young has noted, ‘the idea of duality pervades
    mathematics’, the pairing of positive and negative numbers being only the most
    obvious example. So we might well expect that the scheme required for
    preserving the conceptual nothingness of mathematical physics, is essentially a
    dualistic one. (This will be discussed in the next chapter.) But we still have to
    identify the origin of such processes, and it is here that we will need the concept
    of infinite degeneracy, for we have a logical analogy in the rewrite systems
    which are fundamental to computing.

    Obviously, we cannot generate a fundamental theory by imagining in advance
    that computers actually exist or that the universe is structured like a computer,
    but the ‘rewrite’ concept is independent of any connection with software or
    hardware, and can be conceived as a purely abstract process. If we could develop
    a universal system which endlessly rewrote itself, superveniently (that is, without
    any sense of temporal progression), we would also have a system which was, by
    definition, infinitely degenerate; and, if at every rewriting, the dualistic principle
    (or, in the first instance, zero totality) applied, we would have a universal process
    relevant to mathematics, physics and all such attempts at a fundamental
    description of ultimate ‘reality’."

    A related article...

    Last edited by Albion; 11-24-2011 at 01:09 AM.

  3. #3
    Join Date
    May 2009
    1/2, 1/1, 2/1, equivalent to three integers, -1, 0, 1, algebraically
    Am I missing something here?

    Should that read 1-2,1-1,2-1?

    based on the ad hoc invention of complex numbers
    Rafael Bombelli first set down the rules for multiplication in the complex numbers in 1572. Complex Number Arithmetic

    Today complex numbers are used widely in engineering and electronics ...were they aware then of what we were going to know now?

    For example, because of the sinusoidal property of ac emf over capacitors and inductors and their reactance the calculations for the
    performance of these components use Complex Number Arithmetic. These components didn't exist in 1572.

    Gerolamo Cardano (24 September 1501 – 21 September 1576) acknowledged the existence of what are now called
    imaginary numbers, although he did not understand their properties (described for the first time by his
    Italian contemporary Rafael Bombelli, although mathematical field theory was developed centuries later).
    How does one come up with a complete set of mathematical principles with non existant application?

    "ad hoc invention of complex numbers" I call it just plain wierd or wyrd

    1 = 2 :

    With the following assumptions:

    0 x 1 = 0
    0 x 2 = 0

    The following must be true:

    0 x 1 = 0 x 2

    Dividing by zero gives:

    0/0 x 1 = 0/0 x 2

    Simplified, yields:

    1 = 2

    The fallacy is the implicit assumption that dividing by 0 is a legitimate operation.

    The above post fits very well with the theory of solipsism

    solipsism (slp-szm, slp-)

    n. Philosophy
    1. The theory that the self is the only thing that can be known and verified.
    2. The theory or view that the self is the only reality.
    Everything else is nothing \o/ maybe?

    I found the above a little hard to follow so I may have the wrong end of the stick.

    Albion, is there a way of putting that post into laymans terms?

    Androgynus gave me a link to a good video on Solipsism, but I am not sure where it is now...
    perhaps he will be kind enough to post it here


    Edit: A similar concept perhaps:

    Quote Originally Posted by Ghislain View Post
    Imagine the One, a single entity that encompasses everything; the creator and destroyer of all
    things, a being alone in blissful wonder. This being feels no pain, sorrow, happiness or anxiety; it
    doesn’t sense heat or cold, rough or smooth...and all the other experiences we take for granted, so it
    creates vessels that can and platforms where all this can take place. One of the platforms is here
    and we are some of the vessels. There is no good or evil just experience.
    Or maybe it can't exist as one.

    Bowie spoke about a star man blowing our mind...imagine finding out you are just a thought in the imagination of another...I guess that would blow your mind
    Last edited by Ghislain; 11-24-2011 at 02:13 AM.
    Open Book
    "Dogmatic Assumption Inhibits Enquiry" Rupert Sheldrake

  4. #4
    Join Date
    May 2010
    New Jersey

    1) Despite the occurrence of posts like these, I am not Mathematically literate. Logic is more my strong suit - which I employ when attempting to intuitively explore areas [such as this] which are otherwise beyond my ken.

    2) At the core of my current, active conceptual arena, I am not actually working with “zero” as a literal, utter void somehow cancelling the validity of existence, individuality and otherness. And, as I take it from Rowland, et al, I don’t even see zero as a negation of number. However, I am fascinated with it all the same as a means of conceptually clearing the field as it were, and, as such, wonder if it might not be, as Rowland claims, a better starting premise for Physics.

    3) I am not a solipsist, and consider the premises of solipsism, despite (or even because of) its apparent non-falsifiability, to be flawed.

    The arguments of solipsism remind me of the Aristotelian/Ptolemaic, geocentric theories of planetary motion, wherein the proposed apparently aberrant orbits were justified with circuitous additions [epicycles upon epicycles]. In other words, solipsists’ have to keep explaining away data that would otherwise clearly support the reality of “others” by employing tortuous logical circumlocutions - all the while seeking refuge in the unfalsifiability of their premise.

    Wikipedia Entry: Geocentric Model

    The Universe of Aristotle and Ptolemy

    Solipsism and the problem of other Minds

    Wikipedia Entry: Solipcism [see “Responses” section]

    I guess I submitted that last post because I felt it had a certain value that I’m not really qualified to back up. So, it sort of just is what it is. But I’m sorry for any confusion it might have generated. Also sorry that I don’t have the time to respond more thoroughly to your post as I’m caught up in something else this evening. Maybe that about covers it anyway.

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