TIBERIUS CLAUDIUS schreef: ↑02 mei 2021 10:13
Ze zijn slechts wiskundige abstracties, geen fysische entiteiten als bijvoorbeeld: Goud , Waterstof , Planeet.
Aangezien dit deel van de discussie is voortgekomen uit mijn opmerking over de geclaimde ontologie van getallen (imaginair en negatief), en die opmerking terug te voeren is tot de veel uitgebreidere uitwerking van dit onderwerp door Mike Hockney (ik ben in veel opzichten een leek), lijkt het me goed om erbij te vermelden wat
hij er specifiek mee bedoelt.
The Power of the Flowing Point
All power is concentrated at the flowing point. This is the ontological carrier of mathematical functionality. There can be no other. The flowing point is, of course, inherently in motion, which means that it contradicts the abstract notion of anything approaching a fixed, static point, which is essentially the concept lying behind the traditional “calculus of limits”. Mathematics is a holistic, holographic system. The whole is in every part. Every part necessitates every other part. Limits have to be considered in that context, not in relation to fixed, static points, which don’t exist. Calculus, as part of mathematics, must reflect these considerations. A radically new mindset is required to see calculus for what it really is. It’s a property of numbers, and numbers are ontological sinusoids. How can you define calculus if you can’t define, in complete and consistent terms, what a number is, and what mathematics itself is? If you fail to do so, you are simply making up a definition of calculus to suit your own ideology and philosophy, your own Mythos. Calculus must not be linked to empiricism, materialism, set theory, formalism, axioms, mathematical meta logic, logicism, or anything else. Calculus must be grounded in mathematical ontology.
Numbers
The Cartesian coordinate grid was one of the greatest innovations in mathematics. Unfortunately, it supports the fallacy that numbers are abstract rather than ontological.
There are three related categories of ontological numbers: frequencies, distances (periods and wavelengths) and scalars (amplitudes). Frequencies are the most fundamental numbers and these are dimensionless. Frequencies do not exist in space and time. Amplitudes are also dimensionless and do not exist in space and time. The numbers that do exist in space and time are distances.
Distances always involve at least two numbers (with the distance obviously measuring the gap between them). Frequencies and scalars, on the other hand, are single, self-standing numbers. You can have a frequency (mental), dimensionless domain without distances, but you cannot have a dimensional domain unless it’s underpinned by a dimensionless domain. Dimensional distances arise from dimensionless numbers.
The whole of scientific materialism is predicated on the existence of dimensional numbers only. Dimensionless numbers are entirely denied. Moreover, science says that only “real” dimensional numbers exist, while imaginary dimensional numbers are also denied.
The greatest problem in science is what happens when the distance between two numbers reduces to zero. In science, if a force is being calculated and is dependent on division by the distance between two particles, the calculation, according to scientists, becomes impossible when the distance is zero (since infinity results). This is exactly what happens in black hole singularities and the Big Bang singularity – where scientists say that the laws of physics break down.
Of course, the laws don’t break down at all. What breaks down is the materialist ideology.
In terms of ontological mathematics, when a distance is reduced to zero it in fact means that the dimensional domain has been left behind and the dimensionless domain entered. Black hole singularities and the Big Bang singularity do not belong to the dimensional, material world but to the dimensionless, mental world.
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When matter is crushed into a black hole singularity, it leaves the spacetime world and enters the frequency domain. It’s converted into dimensionless energy.
Note that negative numbers cannot be considered “less” than zero. Negative numbers are simply positive numbers viewed from a different symmetry perspective. Only zero is dimensionless. Everything dimensional is larger than the dimensionless.
As Pythagoras said, “All things are numbers; number rules all.” People such as Tegmark are slowly catching on, but they still have such a long way to go.
A number is both a form and a deliverer of content. Imagine a number as being akin to a piano note. Each number delivers an exact content, as part of an organised series. All the numbers together constitute the ontological piano of the cosmos. On it, any tune can be played. Infinite tunes are possible. The piano notes never alter, but the music they play is always changing.
So it is with numbers. All of the numbers are rationally fixed, but they can generate infinite combinations, corresponding to a myriad of empirical content.
Numbers provide us with two views of reality. We can study the numbers themselves and their rational relations (this is mathematics, the subject of the eternal and necessary), or we can study the empirical content produced by the temporal, contingent of numbers (this is science, art, Mythos, language, religion, philosophy, etc.).
You cannot understand reality by listening to the music and ignoring the piano. Science is effectively a system which claims that all that exists are the different types of music, and nothing is playing the music. Our senses detect the perceivable music, but not the unseen, unobservable, mathematical piano. Given that science subscribes to the irrational doctrine that absence of evidence is evidence of absence, science doesn’t even contemplate any hidden piano. Instead, it says that there’s some unreal, abstract potentiality piano, which mysteriously and probabilistically plays a note whenever anyone puts their hand to their ear. You have no idea what note you are going to get, but you will probably get this note rather than that one. There is no real, eternal, necessary, immutable, Platonic piano out there.
Well, do numbers actually exist, or don’t they?
In fact, numbers, not logic, are the ontological foundations of reality. Numbers are the products of the principle of sufficient reason, and nothing else.
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Both Wittgenstein and the mathematical logicians are wrong. It’s not mathematical logic that is ontological, it’s mathematics itself. Numbers are the ultimate reality, the foundations of existence. This is a numerical universe.
Not all waves are perfect sinusoids, but they are all derived from perfect sinusoids. That was Fourier’s dazzling insight, one of the most important since Pythagoras said that all things are numbers. In fact, sinusoids are numbers, and numbers are energy. This is a universe of energetic vibrations, perfectly describable via math.
Waves, remember, are what numbers are ontologically. Forget Buddhism and meditation. Get a good book on Fourier math and study as hard as you can. But that’s not as “sexy” as meditation, is it? And it’s infinitely harder. You don’t like difficulty, do you? Much easier to sit down under a tree, cross your legs, close your eyes, fold your arms, and try to abandon your mind and your reason... just like the Buddha, one of the worst anti-intellectuals in history, right up there with Jesus Christ, Mohammed and Martin Luther.
Numbers, ontologically, must have a precise terminus determined by the mathematical causality dictated by the God Equation [Euler's Formula]. Nothing can vanish into an indefinite haze.
Numbers are not bottomless. They have an ontological limit, meaning that they have a definite terminus. It’s because mathematics is holographic – the whole is in every part – that we can reach any terminus. All infinities are resolved within the whole. As Hegel said, “The true is the whole.” Nothing is undefined with regard to the whole system. Everything has its allotted, reachable place.
Think of an analogue clock with hands. If there are infinite points between 12 and 6, how does the clock ever get from 12 to 6? In fact, how does the clock tick to any destination at all? Why isn’t its progress simply swallowed up by infinity?
The answer, of course, is that time consists of dimensional flowing points, not static dimensionless points. Although time seems to be forever poised on the razor’s edge of “now”, it is in fact always flowing into the next “now”, hence has a tiny but definite size. This definite size, combined with the fact of constant motion, means that there’s no infinite barrier to progress. To say that there are infinite points between two numbers such as 12 and 6 is to refer to an abstraction, not an ontological reality. Only something with zero speed and size (a static point) would be confronted by infinite points that it could never traverse. To be a flowing point is to be able to traverse any gap in due course. The infinite abstract points are swallowed up in the ontological finitary motion.
