How to Arrive at ‐1 and 1 from Spaces or Zeroes

You will learn of a theory of how the Universe might have started, i.e. arrived at Oneness from Emptiness, as came via investigation of the Theory of Neutral Operations, which creates sets of numbers that satisfy the condition that say a+b = a*b, a+b = a/b, a-b = a*b, a-b = a/b, a*b = a^b and a+b = a^b, etc. -- one operator is held neutral versus another operator while the values a and b are constant, as calculated.

Let a+b = a*b = c. Let a+b-b = (a*b)-b. Let a = b*(a-1) factoring out b on the right after simplifying the left side. Then a/(a-1) = b and b has been isolated and defined in terms of a and 1 after dividing both sides by (a-1) and simplifying. Neither a nor b may equal 1 or there would be division by 0 in the denominator, and the operations of addition and multiplication which were started with are commutative, and one might just as easily have stated out by subtracting a from both sides instead of b. 5/4 = b then, if we let a=5, since a/(a-1) = b. Testing the original hypothesis, a+b = a*b = c? 5+ 5/4 = 5* 5/4 = 25/4 = c; correct. And a^2/(a-1) and b^2/(b-1); both = c since a*b = c. That is Neutral Operations, demonstrated. Now on to Creation.

Watch the 6.5 minute video by clicking on the green text below, not on the photo below it, and going to YouTube, then using your Esc key or Back Button when done in order to return here: <iframe src="../" allowfullscreen="" frameborder="0" height="315" width="420"></iframe>


  1. Image titled SPACES in Neutral RELATION
    Investigate the steps of the Theory of Neutral Operations as they apply to spaces or zeroes arriving at negative and positive 1, from the point of view of an early Universe trying to create something from nothing (purely logically). Do so by going to the Desktop and selecting the green X (for XL), starting the app, and then select File Open New Workbook. Take notes of the Conditions and Formulas below onto the workbook worksheet and save the file into a logical folder.
  2. 2
    Let there be at least 3 spaces (or zeroes), such that O>0>o and all are unequal or equal to the Null Set, {ø}, i.e. they are exactly empty space or space-time, without energy, differentiable only by imagined size. To restate: in this primordial reality or existence, the zero symbol, 0, is less than than the capital O symbol and both are greater than the small o symbol.
  3. 3
    Notice that sometimes O+o = 0, that is when two spaces sum to make a third space. Let a multiplicity of these be noticed also, i.e. O*o = 0. What is noticed is that space may be proportioned into parts, and brought again together into wholes. You may also think about O*o as if they were each squares and the smaller square was unit inches or square inches; in that case, multiplying the larger square (space) by the smaller one (an abstract unit) would result in the larger space being measurable in terms of abstract inches, all of which are zeroes, not things. When we say 'One foot = 12", we do not need a ruler or a thing to have a good idea of what is meant in terms of space. The space still equals zero since nothing occupies it yet. It's just an abstract "overlay" of a sort.
  4. 4
    Regard that stating "what is noticed" sounds like one is talking about an Awareness in the Primordial Universe. Let it suffice that Truth = Comprehension, such that if a state is True, it is Comprehended by the Bounds of Reality since certainly human comprehension exists within the Bounds of Reality at least, and perhaps Universal Mind does as well. Therefore, if it is more proper to say "space-time" instead of "space", then that is what is meant by each symbol, including (one supposes) the operators, equality and inequalities. In other words, everything is being accomplished by pure logic and the only "matter" involved is empty space-time. That sort of abstraction connotes that logic is a property of space or space-time itself, or perhaps a property of different sorts of space or space-time -- just as air is different than outer space and the space around a neutron star is different than the space around other types of stars. Yes, those conditions require matter while instead a matter-less reality for the beginning of the Universe is supposed, but differences in the quality of matter may arise from differences in the quality of sub-space, e.g. in spin operators even where no particles are spinning, only where waves of space are somehow differentiable, if only by size. Because all the theory actually depends upon is O>o and O+o=0=O*o. That is to say, a difference in size existed in the Primary Universe, and that this difference had a Cause. What that Cause was matters less than the Logic it gives rise to for this case under consideration.
  5. 5
    Now do the Neutral Operation O+o = O*o = 0. Proceed as before with a and b, and when arriving at division, mean it geometrically, i.e. proportionally, i.e. a/b = a:b as a simple proportion, rather than as a mathematical operation that is performed. That is, the great space is greater in proportion to the smaller space, rather then physically divided by it (though that is possible as well, as in the ruler example).
  6. 6
    Do O+o-o = (O*o)-o by subtracting o from both sides of the equation.
  7. 7
    Do O = o*(O-1)... an admittedly great step for the Universe to take, to factor out o on the right after simplifying the left, but Nature has a way of trying all possibilities, so consider it at least a possibility. The raw logic of this may have taken eons or billions of eons, but time is on our side when attempting to create something as tremendous as a Universe. Carl Sagan once said that proving 1, or the Identity Principle, takes 28 steps in logic. Those 28 or so steps are being assumed.
  8. 8
    Do O:o = O/o = (O-1) .... now here is taken a step not taken with a and b. Then, both sides were divided by the parenthetical term in order to isolate a single term. Now, isolate -1. O/o = O:o, i.e. the greater space is in proportional relation to the lesser space.
  9. 9
    Do O:o - O = O/o - O = -1 and negative 1 has been isolated and defined.
  10. Image titled SPACES in Neutral RELATION 631
    Do O - O:o = O - O/o = +1 after multiplying through by negative 1, and the result is positive 1 has been isolated and defined. There now exists in the Universe 1, 1 thing, 1 unit, a counted thing in the Universe, and its antithesis, -1 as well from the previous step. Both require the "know how" to do O/o = O:o, i.e. hold two spaces of different size in ratio to one another -- that's the key. Let's suppose the larger O = 3 and the smaller o = 2. 3 > 3:2 and 3 > 3/2. Here what we have supposed is that the smaller space is 1/2 as large as the larger space. If we look at the final step, we have 3 - 3/2, which = 3/2, so it would not be true that 0>O, unless 0 is the very concept of "zero-ness", and includes all zeroes. It, strangely enough, also equals the Null Set, which is the absence of anything, even zeroes I believe. Thus, it is All and it is Nothing. It comprehends everything and exists nowhere in particular -- not even in empty Space-Time. It is the greatest and the least of all things ... being both Everything and Nothing, simultaneously. Conclude then, that it is beyond comprehension, yet contains comprehension, and thus all perception and reason, including this possible theory for the formation of its existence.

Helpful Guidance

See the Related wikiHows below and the article How to Do the Sub Steps of Neutral Operations for a list of articles related to Excel, Geometric and/or Trigonometric Art, Charting/Diagramming and Algebraic Formulation relating to Neutral Operations.

For more art charts and graphs, you might also want to click on Category:Algebra, Category:Mathematics, Category:Spreadsheets or Category:Graphics to view many Excel worksheets and charts where Trigonometry, Geometry and Calculus have been turned into Art, or simply click on the category as appears in the upper right white portion of this page, or at the bottom left of the page.


  • It is true that the tangent of 0 degrees times the tangent of 90 degrees, being their slopes, equals -1, and the x and y axes are perpendicular to each other. But the tangent y/x of 90 degrees = y/0, which is either Infinite, else Undefined. Trigonometry tables book lists it as Infinity. So Infinity * 0 = -1, to state the matter plainly. And that has other ramifications. It is mentioned here only to demonstrate that division by zero is sometimes acceptable.
  • If the square root of the x axis, equal to 0 degrees, equals 0, then what does the square root of the y axis equal, since it itself equal Infinity? And what is the Infinite Root of Infinity? Might it be some Transcendental Number like π, for example, or phi, or e? IDK!!
  • n.b. A new Part, The Quadratic Relation of Neutral Operations / Symmetry by Commutation, has been added to the article *How to Convert a Quadratic Formula to Roots Form by Completing the Square


  • Taking the square root of a number is an involved process, so it's dubious whether sqrt(Infinity*0) = sqrt(-1) is practical, even by either the Babylonian method or Newton-Raphson. One could well be wrong. It may be possible genetically, and the Universe may have been created on the sperm and ovum model, but that involves a level of complexity here avoided. Using simple raw space and the 4 simple arithmetic operators, a little algebra, all from Boolean comparison -- that gives rise to the Equality the Neutral Operation utilizes. It seems hardly doable without a divisive agent of Energy like Dark Energy -- some sort of inherent binary-ness to begin with. Or Matter and Anti-Matter. However, very, very simple thinking trying to stick with the simplest course of events imaginable is the goal here.
  • Normally, the steps of the Neutral Operation are as follows:
  • O+o = O*o = 0 ≥ {ø}
  • O+o-o = (O*o)-o
  • O = o(O-1) simplifying the left and factoring out o on right.
  • O/(O-1) = o and now o has been isolated and defined. One could just as easily have started out by subtracting O instead of o, and since both Addition and Multiplication are Commutative, it's also true that o/(o-1) = O, so O has also been isolated and defined. Since O*o = 0, o^2/(o-1) = O^2/(O-1) = 0 ≥ {ø}.
  • Now in each case, the 1 stands for something it replaced, which may be substituted back in, but that's left for another wikiHow.
  • Suffice it to say that, as in the following picture, some 0's may be more substantial than others once the Universe arrives at particles:

    Different Zeroes or Spaces

Article Info

Categories: Algebra | Mathematics