Ontological Mathematics 101 by Joseph E Postma

What is the difference between the abstract concept of nothing versus the nothing of the mathematical ontological zero that represents the basis of reality?

Source: http://climateofsophistry.com/2014/06/10/ontological-mathematics-for-the-lay-person-part-1/

This is one of the most important things, probably the most important thing of all if you want to understand what we’re trying to say and to understand reality, is the difference between abstract mathematics versus what is called ontological mathematics. Ontological means “referring to existence and the nature of being”, and so we use that term for philosophical precision, and to distinguish from ideas and mathematics which are truly “abstract”, meaning just imagined or arbitrary. This is an important concept to wrap your head around: what is real or ontological math, and what is arbitrary or imaginary math?

Do you remember the Pythagorean Equation? That equation was for calculating the length of the hypotenuse of a right angled triangle. If you know the length of the sides of the triangle, then you can calculate the length of the hypotenuse of the triangle. This is an ontological equation. It works all the time, everywhere, and construction companies use it every day for real-world buildings and they never have to wonder if it will work correctly or not. Say someone is building a wall, but the wall needs a diagonal brace to help keep it strong. If you’re looking at the wall, the brace might go from the bottom left corner to the top right corner. That’s a diagonal, a hypotenuse, and the floor and right hand side of the wall make up the sides of the triangle. Well if you want to use a single length of lumber or steel for that diagonal, you have to know how long it is, and so you can just use the Pythagorean Equation to calculate it since you’ll already know the length and height of the wall. If some construction engineer is drawing up the plans for this wall, the worker can’t just go measure the length of the hypotenuse because the floor and sides of the wall don’t exist yet. So you calculate it ahead of time with the Pythagorean Equation, and this ontological equation will always work, because it really describes how reality works at a basic unavoidable level. The math of the Pythagorean Equation really exists, it is truly ontologically at the basis of triangular relationships in everything in nature.


So then what is abstract or imaginary math? Abstract math that doesn’t really represent reality would be, say, you losing 3 pounds in one week, and then extrapolating that loss to two more weeks ahead into the future so that you’ll have lost 9 pounds by the end of the third week. Truly wishful, imaginary thinking! Now it was totally mathematical, you used totally valid mathematics to make that prediction because you just multiplied 3 pounds by 3 weeks. But was the essence of that prediction ontological, did it really correspond to reality and take into account all of the factors that might prevent you from achieving that goal? No it wasn’t, and no it didn’t. The mathematical prediction was just imaginary, and abstract, even though the mathematical operation used to do so was perfectly valid.

So, we see that there is mathematics which truly corresponds with reality and which can never be wrong, such as the Pythagorean Equation, and we would call this “ontological” mathematics. On the other hand, there is valid mathematics but which is abstract, imaginary, and while it might work in some limited cases, like describing your weight loss for one week, the math won’t work for predicting your weight loss for the next two weeks.

Ontological mathematics can never be wrong, because it really describes the essence of reality. Abstract mathematics can be correct as far as adding and multiplying things the right way, but the results don’t necessarily correspond to what reality is actually doing or will do. This type of mathematics is what science is currently fixated upon, because most scientists haven’t yet realized that there are these two types of mathematics. They just haven’t thought about it yet. Science should orient its research methods around understanding and figuring out ontological mathematics, rather than just coming up with arbitrary equations to describe empirical data, if it truly wants to claim the position of being the method to understand reality. Illuminism seeks to understand the very basis of reality, the very fabric of existence, and its unavoidable reason for being. This difference between ontological math and abstract math therefore could not be any more important, because it is only ontological math which corresponds with fundamental reality. And so only Illuminism, not science as it currently exists, truly provides the answer as to why we’re here at all.

Equally important is understanding and developing the “mindset” of purely logical thinking. Unfortunately, this just isn’t taught to people in school any more, but, it isn’t that difficult to learn. The basic nature of logical thinking could be described as letting concepts and ideas dictate their own results. A logical thinker wants a totally justifiable and even unavoidable answer for everything. Now, the idea that “God” created the universe sounds like a valid answer to a lot of people. However, the logical thinker asks: “what created God”? The people who believe in a creator God will just say things like “well God has always existed”, and things like that, but answers like that explain away the question, rather than logically answering it! Why has God always existed? What is God made of? What did he do before he created the universe? Why did he bother creating the universe? You can’t just explain away these questions – rational and logical people want all the answers, and will not accept the idea that no final answers are possible. The existence of a creator God is a truly arbitrary assumption, and a logical rational person is not satisfied with simply assuming something that pretends to provide an answer. Unfortunately, materialist empirical science has also taken the position of traditionally religious people in concluding that no final answers are possible, but it goes even further and says that there’s no such thing as a meaning to your life, either. And that’s because science has not yet caught up to Illuminism, in distinguishing between ontological vs. abstract mathematics.  Your life does have a purpose, and it does have intrinsic value.


Here is the logical way to question the basis of reality, to distinguish between abstract nothing vs. ontological mathematical zero, and to then understand the basis of existence:

We must first realize that there has to be a basis of existence, there must be something which is the essence of existence. Whatever this something is, it has to be perfectly logical, and it has to satisfy a few basic logical requirements. So, whatever this basis is, it can’t be divided up. If you could split apart “the basis” or divide it up, then whatever you split it into would be even more basic, and so this would be a logical mistake for the thing you had believed to be the basis. So we see that the logically ultimate basis cannot be divided at all, in order to be a true logical basis. That’s one perfectly logical, totally justified requirement for whatever it is that is the basis of existence. Secondly, whatever this basis of existence is, it can’t be created nor derived from anything else. It can’t be created by something else, because if something else created it, well then whatever that “creator-thing” was would be even more basic, and so we would logically have to wonder and ask where this “creator-thing” came from. Obviously this would be another violation of whatever it is we consider as the basis. So if the basis of reality can not be created, a logical consequence is that the the basis has existed permanently.

So we have a completely logically “tight” set of requirements here, that are totally logically justified and totally rational. By definition, the basis of reality cannot be divided or split apart, and, it cannot have been created by something else. There are no assumptions being made here, but these are simple, totally justifiable logical requirements. What’s the answer to satisfy these requirements as the basis of reality?

Zero is the only possible logical answer. We have searched long and hard for other answers, we have looked for any other possible alternative that can satisfy and be as perfectly logical as required. For thousands of years, no one else has ever been able to provide a better answer, or even an answer at all.

Zero, when divided, results in zero, meaning that division didn’t have any effect on the zero. Zero can’t be split apart, because it is as small as you can possibly get. Zero is actually the infinitely small – you can’t get any smaller than zero, and so you can’t split it apart. So this perfectly satisfies the first requirement, and there is nothing else that is so logically perfect of an answer. Zero! Get it?

What about permanent existence, the logical requirement that zero can not have been created by anything else, if it is the true ultimate basis of existence? Well just what is zero? Here is the beauty between abstract and ontological mathematics. In the abstract, zero represents “nothing”. Nothing doesn’t require creation! Nothing doesn’t need to be created because it doesn’t represent anything. You don’t need to create nothing! No effort is required for zero to exist. However, logically, zero has to be “something”, because “something” has to be the logical indivisible basis of existence. Zero is the “something” that is perfectly indivisible. In the abstract, zero represents nothing, but logically, and ontologically, we also know that zero has to be the indivisible logical basis of existence, because it is the only thing that satisfies that requirement. So, is zero solely “nothing” in the abstract, or, is it “something” in fact?

The answer is that it is both! That is the amazing nature of zero. Zero is both abstractly nothing, and logically something. Zero is nothing and something united. Zero is ontological, meaning it truly exists, as the logical requirement for the basis of existence. Zero is “something” because it is the thing which is indivisible; zero is “nothing” also because it is the thing which is indivisible. Once you’ve identified the two essential logical requirements for the basis of existence, the only solution can be in uniting nothing with something, and the ontological mathematical zero is the only concept that can logically do it. There’s no way to get around this, and no other logical concept or answer which can be found.

In the abstract, doing mathematics on paper or just in our head, we calculate zeros that represent the absence of something. If you lost 5 pounds one excellent week, but then gained 5 pounds the next terrible week, your weight will have changed 0 pounds – nothing.  But what does this “nothing” refer to? It refers to pounds of fat, to something. Likewise, ontological zero is nothing because it is indivisible, and infinitely small, and it doesn’t require creation, however, it is also something because is the thing which is indivisible, and it is the thing which doesn’t require creation.

This concept might be initially upsetting for many people because of the need to reconcile what seems to be opposites into a single thing. However, there are many real-world tangible examples of things which contain and imply their opposites. Take good and evil, for example. Can we recognize good without being able to recognize evil? The concept of good “contains” evil, and the concept of evil “contains” good. Or another example of love and hate. The deepest love can and has, too many times to count, turned into the most scornful and vitriolic hate when that love gets violated with infidelity or any other number of issues. In this case, love literally turns into hate, and so, love really does seem to contain its opposite. Likewise, to hate one thing is to love its opposite. Ideas and concepts contain their opposite as a necessity of their existence, and concepts contain their opposites in any manner of examples we are intimately familiar with. That the nothing of zero is also the something of zero should become intuitively and logically obvious if you just think of how much you implicitly accept that logical reality in more tangible everyday aspects of your life. This logic, of concepts which necessarily contain their opposites, actually has a name, and is called “dialectical logic”, and was most clearly and fully developed by Georg Wilhelm Friedrich Hegel, a philosopher of the late 18’th and early 19’th Centuries. Dialectical logic also goes by the name of Hegelian logic or the Hegelian Dialectic. Dialectical logic couldn’t be any more important because it is all about understanding and resolving the apparent contradictions of things containing their opposites, such as love and hate, good and evil, and the ontological zero’s nothing and something. The dialectic forms the very basis of the energy or movement of existence, and within the zero and its innate dialectic of something vs. nothing, it creates all of the activity of reality at the elementary level.


Mathematically, the nothing and something of zero is united and demonstrated in what is now called the “God Equation”, which you might know as Euler’s Equation:

e = cos(θ) + i*sin(θ)

This equation contains all possible numbers – positive and negative real and positive and negative imaginary numbers, and it shows that they are all balanced around zero because the average of the sin or cosine function over a wave cycle is zero.  This equation shows that zero contains everything, because “everything” balances out to zero.  And indeed we should expect this, because logically we already know that zero should contains its opposite, infinity, because zero is the infinitely small, and because dialectically, everything contains its opposite.  Zero already contains the quality of infinity because it is implicitly the infinitely small.   Zero is the perfect basis for existence because by pure logic, it contains its opposite of infinity, and there is nothing beyond infinity, and within infinity, anything can be created, as long as it all balances out to zero.  However, whatever is created has to obey Euler’s Equation because that is the only ontological equation which governs how all numbers must relate to one another.  For example, space and time exist, and you can read here how space and time perfectly obey Euler’s Equation, and how that equation explains relativity theory.  That equation is also at the heart of Quantum Mechanics, and even things like heat flow.  Once science discovers this, if science ever becomes philosophically informed, radical new discoveries and simplifications of pedagogy will ensue, and a massive transformation and Golden Age of Man will begin.

Euler’s Equation is literally the boundary condition of existence, and everything that exists can be traced back to it.  There is nothing outside of it.  It is the prototypical Ontological Equation.  It is literally the equation of your soul!  The Prime Number sequence itself is hidden somewhere within the properties of Euler’s Equation.

In summary, abstract nothing can not have the quality of existence, because if it did have such a quality, then it would have an existent quality, and any existent quality is something.  Hence, something must exist.  The only thing which can exist without requiring creation (thus not requiring a pre-existent creator), and without being divisible (thus not being reducible to something else), is the nothing represented by the ontological zero.  No effort is required to create zero.  However, zero implicitly contains its opposite, infinity, because zero means the infinitely small, and also because if one zero can exist, then it makes no difference, and there is no sufficient reason, why an infinite number of other zeros can not exist, since none of them require any effort to exist.  There is a single governing equation which describes the set of all possible numbers balancing to zero, and this is Euler’s Equation, otherwise known as the God Equation, and this equation can be found at the heart of all of fundamental physical science such as relativity, quantum mechanics, and thermodynamics.

Euler complete


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