In this series, ontological mathematics is explored. Ontological mathematics means ‘real’ math which means it is reality rather then describing reality. Hence everything is mathematics! Ever gotten stuck on the reasoning why we exist, lets's answer it!
This article is based on the work of Morque in ontological mathematics but only the theoretical thesis. In the next article, I will go into the practical applications. I make this separation because in the second part Morque makes a leap into cultish thinking that I will not promote or support. Although, I do think there is value in the theoretical foundations he uncovers. It is worth noting that those ideas are based on a long history of ontological mathematics and were not invented by Morgue. He did write an excellent summary of this tradition going back to Pythagoras within his book. Certainly, check it out if you have not already.
1. How To Define Nature of Existence
Empirical, inductive, posterior can never logically be a foundation of reality. Rather, deductive reasoning is ‘necessary’ for building ‘necessarily’, a priori, conclusions. Empirical, inductive methods can be used to discover necessarily truths but can not describe reality with 100% absolute certainty.
2. Change Perspective
In order to follow this article, it is essential to start with no assumptions about reality. Forget all knowledge you have about reality. Step outside time, space, and its derivative. Ont (ontological) math starts with absolutely nothing and works towards absolute everything. Start from scratch! It is vital that everything that is proven to exist is based on previous deductive proven logic. The ground of existence has to be grounded in itself or be an infinite regress.
3. Pure Nothingness (that Exists)
We start with nothingness. What is nothing? No‘thing’! Not some‘thing’. No dimensions, no start, no end, eternal! Now. Nowhere. Undefined. No cause, not created. Something that is not, cannot be created!
There is no sufficient reason to prevent nothingness from existing, and therefore it MUST necessarily exist. Try to stop nothing from existing! IMPOSSIBLE. Notice the nothingness existence paradox.
Base rule: There is no sufficient reason to prevent nothingness from existing, and therefore it MUST exist
4. Aseity
Nothingness is equal to ‘0’, since ‘0’ in itself is nothing! Keep in mind the number ‘0’ is an arbitrage interpretation, symbol, of the meaning of ‘0’. An alien species could also mark it with ‘§’.
Grounding: If something depends on another thing for its existence, the dependent thing is said to be grounded in the other thing.
The ultimate ground of existence MUST be self-grounding, dependent on only itself. It is a self-referential, a strange loop. ‘0’ is the absolute self-grounding ground of existence, as it needs nothing. And is not dependent on anything!
Rule 1: ‘0’ is nothingness, self-contained, self-grounded, non-dependent, and therefore MUST exist.
Rule 2: Anything that is not equal to ‘0’, nothingness, is something thus for something to exist, it MUST be equal to ‘0’.
Debatable 1: 0 = nothingness
Debatable 2: Does a necessary self-grounding ground exclude infinite regress?
5. Infinite dual number pairs.
The next step is to find mathematical patterns that are encoded in ‘0’.
Does ‘0’ have any structure a.k.a a pattern? Yes:
-n + n = n + (-n) = 0 = nothingness
If a positive real number exists, a negative number MUST exist to cancel it out, thus we must have infinite numbers going into each side in the equality formula.
Rule 3: Any unions of opposites that sums to ‘0’ MUST exist. Formulated by `-n + n = n + (-n) = 0`
Debatable 2: Real numbers exist, which in itself cannot be proven due to Godel's incompleteness theorem. Morque instead uses the principle of sufficient reason, if something exists, there is a reason for it. With this rule, he escapes the need to define real numbers.
6. Complex Circle
In terms of geometrical shapes, the complex circle is the ONLY pattern in which every value is uniformly related and equidistant (mathematical, not spacial) from the origin, 0. Therefore the complex circle is used as the foundation for generating more patterns.
Any complex circle, when summed, totals to ‘0’. There are an infinite number of circles generatable from this complex circle pattern. The possible circles include both real numbers (positive, negative, zero, rational, and irrational numbers) and imaginary numbers like sqrt(-4).
Rule 4: The sum of any complex circle nets to ‘0’, and therefore MUST exist.
7. Euler’s Formula
The complex circle is formulated by Euler’s Formula:
The left side of the equation represents the complex circle, the right-hand side describes two sinusoidal waveforms. This opens up the concept of frequencies! Notice the ‘i’ for irrational numbers and the well-known cos/sinus for y and x.
Rule 5: By Euler’s formula, any wave pattern that is an integer multiple of the unit wave, is a ‘stable’ pattern that nets to ‘0’, and therefore MUST exist.
8. Frequencies
- A is the amplitude, it denotes how much of each frequency to add.
- f is a function to control the frequency.
- Frequency is the number of times a wave oscillates per natural revolution.
- A natural revolution is one full turn of a circle or one cycle of a wave. We should not use time and space in frequency definitions.
- ‘0’ is a phase-shifting value. This is basically how much a wave is shifted from its natural form.
sin(x+90)=cos(x).
The Eulers formula introduces sinusoidal waves, therefore, introducing frequencies, wavelengths, and oscillations. The complex circle deductively introduces any kind of frequency wave that nets zero. All frequencies are controlled by the Eulers formula. At any given integer value, stable waves are generated. A stable wave completes the pattern smoothly.
Rule 6: By Euler’s Formula any complex circle introduces a combination of stable sinusoidal waves (rule 6) and therefore both the complex circle and stable sinusoidal waves MUST exist.
9. Wave Shifting
A wave that’s phase shifted by 0.25 (45°) 0.50° (180°), 0.75 (270°), or 1 (360°) natural revolution (previous section) will lie directly on one of the axes and will not form a right triangle. Those have an orthogonal phase and can be called axial waves. Any other wave that does not create a right-angled triangle has a non-orthogonal phase a.k.a interaxial waves.
10. The Fourier Series
A Fourier series is a sum that represents a periodic function as a sum of sine and cosine waves. The sum is a complex waveform.
The Fourier series represents a summing of Euler's formula at different frequencies. The ‘integer’ n denotes how many variations of the Eulers formula and which frequencies are added. Adding sines and cosines of various frequencies produces a new wave of greater complexity!
Rule 7: By the Fourier series any complex wave can be created by summing stable frequency patterns generated by rule 6, which adheres to rule 7.
Rule 8: Whenever Rule 8 produces a complex wave that does not net to zero, a complementary wave is also produced that, when combined with the first wave, reduces it to zero ensuring that the total system nets to zero, which MUST exist.
11. A Monad
A monad is a collection of all possible wave frequencies that adhere to rule 10. A monad is the fundamental constituent of existence. It nets to zero, it is self-grounding, it is singularly, it is self-contained, it is nothingness!
Rule 9: A monad is a collection of all possible wave patterns generated by rule 10, and therefore sums to ‘0’, and therefore MUST exist.
Rule 11: Since one monad is possible a multitude of monads are possible since the sum of them is equal to 0, and therefore MUST exist.
12. Introduction of Motion without space
Reality as we know it, is dynamic, has motion, and is always changing. However, we only have a static definition of ‘0’ and its encoded patterns that net zero. Analytical motion is a sequential relationship between values encoded in the ‘0’ circle. A point can travel the values at a certain speed with should be defined in purely mathematical terms. Let us now define speed.
Rule 12: A point MUST explore the circle in an analytical sense at some mathmatical speed.
c = λf
1 = λf
λ = 1 / f
f = 1 / λ‘λ’ is called lambda and is used to denote wavelength, wavelength is the ‘length’ of one oscillation measured according to angle in natural revolutions. ‘f’ is the frequency.
‘c’ is the speed of the frequency. The speed of frequency is equal to wavelength (λ) times frequency (f), which is equal to 1.
Given this, we can state that `λ * f = 1`
This means that even though c is always equal to 1, this 1 can be realized through every possible frequency and wavelength combination as long as unity is maintained. Hence a point is always moving at speed c = 1.
Rule 13: The speed of a point traveling in mathematical motion is always 1. This is formulated by `c = λf = (1/f)f = 1`.
Rule 14: It follows that the constant unity speed (c) can be realized through every possible frequency (f) and wavelength (λ) combination as long as unity is maintained, and therefore they MUST exist.
In next chapter this speed is linked to the constant light speed factor which we are familiar of.
13. Conclusive
Base rule: There is no sufficient reason to prevent nothingness from existing, and therefore it MUST exist
Rule 1: ‘0’ is nothingness, self-contained, self-grounded, non-dependent, and therefore MUST exist.
Rule 2: Anything that is not equal to ‘0’, nothingness, is something thus for something to exist, it MUST be equal to ‘0’.
Rule 3: Any unions of opposites that sums to ‘0’ MUST exist. Formulated by `-n + n = n + (-n) = 0`
Rule 4: The sum of any complex circle nets to ‘0’, and therefore MUST exist.
Rule 6: By Euler’s formula, any wave pattern that is an integer multiple of the unit wave, is a ‘stable’ pattern that nets to ‘0’, and therefore MUST exist.
Rule 7: By Euler’s Formula any complex circle introduces a combination of stable sinusoidal waves (rule 6) and therefore both the complex circle and stable sinusoidal waves MUST exist.
Rule 8: By the Fourier series any complex wave can be created by summing stable frequency patterns generated by rule 6, which adheres to rule 7.
Rule 9: Whenever Rule 8 produces a complex wave that does not net to zero, a complementary wave is also produced that, when combined with the first wave, reduces it to zero ensuring that the total system nets to zero, which MUST exist.
Rule 10: A monad is a collection of all possible wave patterns generated by rule 9, and therefore sums to ‘0', and therefore MUST exist.
Rule 11: Since one monad is possible a multitude of monads are possible since the sum of them is equal to 0, and therefore MUST exist.
Rule 12: A point MUST explore the circle in an analytical sense.
Rule 13: The speed of a point traveling in mathematical motion is always 1. This is formulated by `c = λf = (1/f)f = 1`.
Rule 14: It follows that the constant unity speed (c) can be realized through every possible frequency (f) and wavelength (λ) combination as long as unity is maintained, and therefore they MUST exist.
14. Conclusion
From absolute nothingness, to ‘0’, to a complex circle encoded in ‘0’, to eulers formula, to all possible stable wave frequencies by Fourier series, to a monad, to a mathematical point in motion at speed 1. All encoded in 0.
In the next article, we will use this theoretical foundation and deduce reality as we know it. It will elaborate on how space-time is introduced and how existence came into being. The speed, frequencies, and wave orthogonality are important factors in this.
15. Debatable
Debatable 1
Is ‘nothingness’ equatable to the number ‘0’? If it isn't the leap from nothingness to 0 is rendered false and therefore this whole ontological mathematics theory is false. Please comment why you think it is or is not. I challenge you to think about arguments on both sides.
Debatable 2
Does a necessary self-grounding ground exclude infinite regress? Why wouldn't infinite regress be a possibility?
Debatable 3
Real numbers exist, which in itself cannot be proven due to Godel’s incompleteness theorem. Morque instead uses the principle of sufficient reason, if something exists, there is a reason for it. With this rule, he escapes the need to define real numbers. He is falling back on reason being the fundamental truth of existence. Disagreeing that reason is not fundamental automatically implies reason to be necessarily true. If you disagree you must have a reason. Since we experience the world as it is there must be a sufficient reason for its existence. Something caused it whether it was God, maths, or something else. Hence, the best thing is to use deductive truths only in reasoning about existence and build up to the existence we experience.
