Mathematical Physics - Quantum-Relativity (qr)
The Gaussian-School of Higher-Arithmetic; published in 1831 by JCF Gauss, as updated in 2022 by this author. Introduction (tutorial #0).
Gaussian scientific unified number theory.
Way back in 1972, my mathematics teachers admitted that the theories that they taught us were not very good, but that those theories were all that we had. Well, not quite all that we had, but for some reason that I still fail to understand, the truth about this was always beyond them. For the next 50-years I gave up on attempting to help them. The only problem being that now that I have found the time to be more explicit for them; they have all died on me.
Forget all about that deranged and impossible so-called "complex numerical plane"; we first need to consider the top down view of the three-dimensional exponential-polar-manifold.
Language notice: The ambiguous and absurdly highfalutin terms logarithmic and exponential both refer to the same pathetically simple concept of ratio-metric proportionality, that is the ratio-metric proportionality of numerical scale in the so-called logarithmic (but also so-called exponential) counting domain. As our so-called mathematicians have spent the last 400 years failing to notice that logarithmic and exponential mean the same thing, we must discard the teaching of such innumerate and illiterate numerical zombies and instead start actually thinking for ourselves.
Caution Notice: The exponential polar manifold is merely a useful transitional device empowering the partial interpretation of the mind-numbing natural exponential number plane into flat (finger-counting) numbers. The mathematic of nature is exponential and is not the happy over simplistic bean-counting neo-Pythagorean claptrap taught in our so-called "mathematics" schools.
Author's notes:
Only bother to read my author's notes later when you might return here again for a more detailed reading. For now, please just follow my simple graphical flow by clicking on the above sketch of the general ratios manifold.
The reason that people (including Einstein himself) have found Einstein's General Theory of Relativity hard to visualise is because they do not understand the infinite relative gravitational scalability of everything in the universe. This failing is aggravated by being taught about numbers by "enchanted gnomes" of no philosophical flexibility (our so-called "mathematicians") who insist upon a doctrine that one can take a real number (of things) away from nothing and that nothing (zero) is a finite number. Both those elements of that absurdly religious numerical doctrine, a doctrine that there exists a real number continuum that can pass smoothly through the black hole ratio (zero), are catastrophically deranged.
In other words, in Nature there is no such thing as a one dimensional ratio. All ratios in Nature must have two properties, the property of relative magnitude and the property of relative polarity (or direction) about the circles of constant numerical magnitude. We must express the relative ratio-metric magnitude property in the exponential form as a power of the natural base ratio e. Think of the manifold depth (normal to my top view sketch) as being stated from plus infinity to minus infinity with zero being an arbitrary base declaration which could be, but does not need to be, nominally in the finite visible chart range. People are not generally very good with double ended infinite ranges, well if you can't handle that, either stay out of this real mathematics kitchen all together or just read on and see how much of this new mathematical understanding it is that you can understand.
The nomenclatures "+1" and "-1" are merely two shorthand forms for just two complimentary anti-phase points upon the infinite extent of possible polarising lines crossing the circle of unity at zero (a ratio or number with zero exponent; i.e. e^0 = 1). One might well ask which of my many circles is the circle of unity? Well, you can arbitrarily fix on any circle of constant exponential ratio-metric magnitude because the above diagram bears the property of infinite relative scalability. One might also ask which of my radial phase lines is the base for +1, well, once again, you can arbitrarily fix that on any radial because the relative numerical polarity (phase) rotation is in fact infinitely endless in both rotational directions.
For example: one could say that one metre is the same as 3.335.. x 10^-9 seconds (i.e. 1/c seconds), but Nature never heard about any such thing as a metre or use deranged mixed log and flat arithmetic (3.335.. flat and -9 log). Given the arbitrary human-defined second in the first place, she counts that as -19.518.. natural log seconds (i.e. -19.518.. exponential seconds), that is her projection of that spatial displacement (or historic offset) in her natural exponential numerical environment of space-time. Just ditch the two identical and absurdly ambiguous terms "exponential" and "logarithmic" and replace them both with the new language; ratio-metric, i.e. proportional. Everything in the universe, including time itself, must be in ratio-metric proportion to everything else in the universe. For any of this to work out properly, we require an understanding of the universal property of reciprocal supersymmetry. Everything must work out equally well in the reciprocal ratio-metric form. Just think of every physical parameter as a ratio which has no particular relativistic perspective. For example; one could say that the apparent phase velocity in vacuum is c metres per second or that is 1/c seconds per metre; it makes no difference to any answers that we are seeking. In just the same way, who cares if my car returns 62 mpg (22 km/litre) or consumes 4.5 l/100km? The two specific fuel flow ratios are identical but stated in mutually reciprocal forms.
Hint: e^-19.518.. seconds is the same as -19.518.. natural-log-seconds = ln(3.335.. nanoseconds). Anyway, that was the case when I aged 13, last thought about the subject in 1964. In 1980, the CIPM changed their formal definition of the metre to 1/c seconds which means the same as 3.335.. nanoseconds. When they did that, I breathed a sigh of relief because it meant that maybe at least some other people understood the General Theory. In other words, I might not be on my own after all. I waited for the next 27-years for the penny to drop, but it never did. But why did the penny never drop because none of this is exactly "rocket science"? That was my only real puzzle; why does the penny never drop? This is clearly a psychological puzzle and not really number theory at all. Hence my brand new topic of meta-cybernetics, but first we should clear up some obvious misconceptions about the rather trivial subject of whether or not there can be any such thing as a negative-rotten-lemon. Can we take away one rotten lemon where no rotten lemons exist? Absolutely not; there could never be fewer rotten lemons than no rotten lemons at all.
Footnote 1:
What we are taught wrongly, at about age 7, is that taking one away from nothing to get minus-one is an invalid mathematical operation. We can still teach negative numbers to very young children as a useful dodge operation but we need to remind them that negative numbers are mathematically invalid and we will later learn about inverse numbers as a mathematically valid replacement for negative numbers.
Footnote 2:
Cantor's and Dedekind's set theory of numbers is a religious belief system, there is nothing scientific about it. This absurd religion was completely debunked by Kurt Gödel in 1931 (a genuine logician and a friend of Albert Einstein). For the last 94 years, young mathematicians have been forcibly indoctrinated into loving an absurd piece of human hubris and calling that "mathematics". It is a joke, there is nothing mathematically valid in it, as proven by Kurt Gödel about a year after our so-called "mathematicians" formally adopted a policy of going stark raving bonkers. In my work, I need to refer to this so-called "mathematical" community. I refer to those people as members of the neo-Pythagorean School; well, "School" is rather too polite of me, but just for now I'll call that silly "mathematical " cult a School.
Meta-Cybernetics.
Introduction.
If you are more intrigued by psychology than the underlying mathematics of relativity, then first read about the meta-cybernetic model of the generic human mind. If you want to beat the AI robots, then you need to know this neural network based model of all of us humans. Absent the remaining perhaps 100,000 bushmen of the Kalahari, without this powerful model working in our favour, we modern humans are "toast". The discovery of quantum-relativity is not so much just the theoretical nicety of completeness for our mathematical and scientific understanding of the Universe; due to the rapid roll out of AI, it has now become an existential threat to the very survival of our species. So, while we might not like finding out that our so-called "mathematicians" have been making fools of themselves and all of the rest us for the last 300 years, ignoring this thorny issue has become something that we no longer have the luxury of doing. Death is a certainty for everybody. Who cares how much longer I live for? At age 74, I no longer even care for my own account, but while I can still breath, think and publish here, I must do my best to at least try and ensure the survival of my species.
BMJC Bieżanek, 10th July 2024; Shropshire, England.
PS: The meta-cybernetic model explains for instance that if a person confirms his dysfunctional set theory of numbers by taking the action of teaching that silly claptrap (action confirmation bias) then he renders himself clinically blind to any functional Unified Number Theory. We need to turn our backs upon the absurd abstract set theory of numbers and adopt Unified Number Theory, only then will the penny drop and everything in the Universe and Nature make perfect scientific sense.
