The Gaussian-School of Higher-Arithmetic (1831, updated 2022) ; tutorial #7.
Making sense of all ratio-metric magnitudes within our Natural World.
So far, you will have only been taught what can be described as the neo-Pythagorean school of "flat-earth-arithmetic", last erroneously updated by Euler in about 1730. Quite how anybody ever coped with that deranged and archaic claptrap is quite hard for me to imagine, but nevertheless, most people did sort of cope.
MIIS stands for Machine (electronic calculator) Induced Innumeracy Syndrome.
My own exquisite 34 cm Faber Castell NOVO-DUPLEX is double sided and has 23 scales in all. Even though it is no longer actually used by myself, it sits on my desk as a constant reminder of the beautiful curves of the natural numbers.
Author's comment:
Exponential or Logarithmic?
The confusion between the words "exponential" and "logarithmic" (which mean the same thing) arises from John Napier's 16th century name for his new technique. Had he instead called his transform "the exponential transform", then no confusion would ever have arisen. The function e^x is "the reverse-exponential transform", the exponential number is x and taking e to the power of that exponential number decrypts x into the equivalent flat (finger counting) number y. Where one might be obliged to start with a flat (finger counting) number y, then x is determined as ln(y).
In other words; within my diagram below I use the language "anti-logarithm" but I should really be using the term "reverse exponential transform". However, that language has never been introduced and mainly out of great respect for John Napier, I really don't think that I need to make any changes here.
Author's notes:
Albert Einstein had nothing but justifiable contempt for the absurd neo-Pythagorean School of so-called "mathematics"; and yet still their puerile claptrap had the poor young lad confused.
Einstein is quoted as sating; "As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality". Unfortunately, Einstein was not informed about mathematics at all, he just knew that the neo-Pythagorean doctrine that they had attempted to indoctrinate him into did not make sense and did not refer to reality. Einstein believed (in the religious sense of the word "belief") that "reality" actually existed. Unfortunately, he spent almost his entire life on a wild goose chase, reality only seems to exist, but as any quantum physicist can confirm, no such "reality" actually exists.
Having said that, Einstein failed to notice that his excellent General Theory of Relativity utterly contradicted his pathetic earlier failed attempt to define and understand special relativity. He should have gone back and corrected his own special theory (to make it General Theory coherent), but as at that time (in say 1918) the special theory of relativity was his only solid relativity "success story", he presumably felt constrained not to go back and tear his own special theory success story into pieces. Anyone who thinks that Einstein actually understood the implications of his own General Theory is clearly delusional, that would have required a man like Newton, but unfortunately our only real "Newton" was already 191 years in his grave by that time.
Einstein's Special Theory of Relativity conceals an energy inversion error behind a hidden double-inversion, thus giving merely an hypnotic mirage of being helpful. Albert Einstein was no respecter of orthodox mathematical theory, but he nevertheless applied the neo-Pythagorean (flat-earth-arithmetic) School of accounting for space-time separation and this yielded him a Special Theory of Relativity which is not only comically misleading in respect of the fundamental nature of matter and the role of gravity in primordial matter formation, but also utterly contradicts his own completely correct General Theory of Relativity. The simple Newtonian projection of gravity, and the more exacting General Theory, both show that matter must consist of inverse energy with respect to an absolute gravitational free-space reference platform. Therefore; the c^2 term (in E0 = mc^2) must evaluate to an inverse number.
1) Keep the inertial mass in energy units (mE);
2) c = (1.i0/-1.i1) ie. one unit of space per unit of inverted (imaginary) historic depth;
3) c^2 = 1.i2 (i.e. -1) ;
4) E0 = -mE.
5) Therefore; the nuclear forces must be gravitational (i.e. the so-called "graviton" has a zero working radius).
Proof; light appears to slow and be bent by any transparent matter field.
In other words; your own eye lenses work for exactly the same reason that light is lensed by a star's gravity. What we call light experiences within our eye lenses more space so close to the matter fields and seems to us to slow. I can quote up to six more proofs, but that is the best and the simplest to follow. Of course, for a person who cannot integrate the General Theory field equations at all, let alone to infinite limits, there is no proof that they could ever be convinced by. If souls could laugh from the grave, then just trust me here, Newton would be laughing now, Einstein; not so much. It is not that Einstein's work was unhelpful in any way, quite to the contrary, but Einstein missed an opportunity to nail it. He fluffed that opportunity by chasing tail, boys will be boys I suppose and I should know. Newton left boyhood behind him at age 13, but he fluffed it too by chasing alchemy. That left the field open for Maxwell and his later student (Bieżanek, 2022) to actually nail it.
Maybe you think that I am in jest? Well, try proof number two then. The strong nuclear force is just our old friend gravity acting within fantastic space-time scale compression ratios that are far too tiny for ordinary minds to contemplate. The tyranny of Occam's razor dictates that if there is one explanation that there is gravity and two extra mysterious forces, the strong nuclear force and the weak force and the other explanation is that all three force fields are all one and the same thing, we are obliged to elect the later explanation; we are obliged adopt the simpler explanation.
If you feel that you are a master of two-axis exponential numeracy (that is ratio-metric magnitude and rotational polarity) and that you understand Maxwell, Einstein (GR) and the Copenhagen Interpretation of Bohr, then my entire thesis can be followed just by scrolling down this page. If on the other hand you are less confident about all that, then please just click on the diagram shown above.
The Grand Unified Theory; GUT
The special theory of relativity becomes upgraded within the Quantum-Relativity reinterpretation into a correct understanding of time that solves all of the problems with existing false misconceptions of it. At its tiny beating heart, qr is so simple that one could cry. The proper units of space are of course time (the light time of flight) and this understanding of the true nature of space as being actually time, became embedded within all theoretical physics by about 1980. Since then, that understanding has formed our very definition of the metre; 3.335... nanoseconds (rather absurdly quoted by the CIPM in the numerical reciprocal as 1/c seconds).
The Newtonian gravitational mechanics consistent solution; Quantum-Relativity
The proper relativistic unit for what we presently call time is the imaginary historic depth in i-seconds. The apparent wave-velocity in Quantum-Relativity is shown to be 1.i0/-1.i1. The square of the "apparent-wave-velocity", (1.i0/-1.i1)^2 , being quite naturally inverse one (-1) or 1.i2. This is a Newtonian gravitational mechanics consistent velocity and of course, there were only two choices for the nature of time.
Therefore; the
Quantum-Relativity
interpretation of time is self-evidently correct and Einstein's 1905 interpretation of time must become rejected as being no more than an inexperienced and poorly educated young man's hopeless little day-dream over a matter that, as gifted, as well-intentioned and as hard-working as he obviously was, in fact lay vastly beyond his intellectual capability.
Alternatively, simply continue scrolling down this page.
Unified FNN is suitable for all work, but is more advanced than is strictly essential for simpler work fields than Quantum-Physics and electro-magnetic wave theory.
Abstract-Set is utter and archaic nonsense and will cause great confusion with any work in Quantum-Physics and electromagnetic wave theory. For many simpler work fields, one can "get away with it".
click on the cartoon to understand the origins of the new arithmetic required for understanding Quantum-Relativity or scroll.
The Unified theory of Exponential Natural Numbers (ENN-theory);
ENN-theory successfully enumerates the master-clock of the Universe, the Arithmetic of Time itself.
Click me to read more or just scroll on downwards.
How many know that Maxwell died of TB before his field equations were even published?
With the exponential solution to Maxwell's field equations, the term e^(0 + iωt) does not actually require the antilogarithmic transform there because the evaluation of e^(0 + iωt) is in fact just 1.iωt (see my footnote). Within Quantum Relativity, we must realize that the observer is always positioned at ωt = 0, he can only record the history of his observation. Only the observation history forms, there was no wave within finite space-time. As Maxwell himself put it, we must think of the wave as occurring within the 377-ohm superconductive waveguide of free-space, but that exists beyond the quantum-observation-horizon (beyond time-now) and so outside of (or private to and hidden from) the observer's finite space-time.
The fabulous Katherine Mary Dewar Maxwell together with her very poorly looking husband, the founding father of all post-1890 electrical engineering. Click on the photo to read my footnote.
Footnote: With Maxwell's term e^(iωt), Maxwell merely repeats Euler's misunderstanding in omitting the magnitude of the exponential rotating quantity, e^(iωt) written like that is algebraic gibberish. In my opinion, Euler's understanding of the logic of this rotation was almost non-existent. The exponential magnitude is zero and so the illegitimate term e^(iωt) should be written as the legitimate term e^(0 + iωt), which evaluates to 1.iωt. We need to understand that "1.iωt" and "e^(0 + iωt)" are identical terms and both refer to the same value upon what one should call the "flat-rotational-plane". The exponential value of e^(0 + iωt) is simply (0 + iωt). It took me 57-years to cotton on to the fact that nobody else understood the expression e^(iωt). To me, for 57-years what I have just explained seemed to me to be too obvious to even mention or make a great fuss about.
Shortly after this photo was taken, Maxwell died of TB at age 48. I was 9 years older than Maxwell was at his death, when I finally took up from where he had left off. The full-time work at 80 hours per week took me another 17 years, and I had known the basic answer for the 43 years before I even started out on this great scientific Odyssey for
mathematical completion.
Where does my material originate from?
Not from studying more maths' and physics, that's for sure. I am no longer even interested in those two subjects. Since 2007, my only remaining scientific interest has been in studying deeply into how my own mind works. Yours will work the same as mine too, so just relax and follow me and my very own (and your very own)
"Mr Tambourine Man".
Most of the words of the Byrd's 1965 song "Turn Turn Turn" were taken in 1959 by Pete Seeger from Ecclesiastes Ch 3, v1-9 (KJV). However, in Ecclesiastes Ch 3 verses 1 through 9 we do not read the vital words "Turn Turn Turn", therefore my inspiration that time and rotation are mathematically identical probably came to me in 1965 through the genius folk song writer Pete Seeger (1919 - 2014).
However, the logical decryption of that deep subliminal mind message required a second and vastly deeper subliminal hint, as follows:
Background photo; an hypnotically distorted view of "the Great Jewels of the Pleiades".
(At this trivial magnification, all distant stars should actually be represented by single pixels of light.)
