A list of discovered and derived constant-relationals of Physics and Mathematics// math-physics by Archimedes Plutonium This is AP's 260th published book of science published on Internet, Plutonium-Atom-Universe, PAU newsgroup is this.
Archimedes Plutonium
A list of discovered and derived constant-relationals of Physics and Mathematics// math-physics
by Archimedes Plutonium
This is AP's 260th published book of science published on Internet, Plutonium-Atom-Universe,
PAU newsgroup is this.
https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe
Preface: The word "constant" is not enough to describe these numbers, for all numbers are important in science and math. Some numbers though, come up often because of their relationship to other numbers, and so I want to describe them not as "constants" but as constant-relationals as they relate to other numbers. It is abhorrent to think some numbers are more important than other numbers. What is true, though, is that some numbers come up more often than other numbers. That they are used more often than other numbers. This book follows my 257th book of science where I derive the gravitational constant from numbers out of electromagnetism. And whilst doing that 257th book, I had trouble remembering how I derived the elementary Coulomb constant, the force strength of the magnetic monopole of 1.618*10^-19 C. Realizing that I will be often going back to my derived and discovered constants, I decided to list them in this book and so in the future, when I have trouble remembering, I will look for this reference manual. I just go to this reference book if I need refreshing of facts and data. I should include how I discovered them in this reference book. And I often go to the Internet for lists of physics constants and a list of math constants. Some decades back the Internet had web sites of special characteristics of individual numbers, but I no longer see any of those websites. Maybe they were taken down, such a pity and shame.
Cover Picture: Planck constant of doubling of atoms in geological time.
-------------------------------
Table of Contents
-------------------------------
1) My history of this book.
2) The Atom Totality theory and its primal axiom-postulate.
3) Decimal Grid System of Numbers, true numbers of mathematics.
4) 1, one as unit constant.
5) 0, zero, the alien imported quasi number into mathematics.
6) Scale Numbers ...0.0001, 0.001, 0.01, 0.1, 0, 1, 10, 100, 1000, 10000,...
7) 94 and 231 constants in Atom Totality.
8) 22/7 and 19/7.
9) The 840 constant for proton, as compared to 105 for muon.
10) Rectangle of Whirling Squares Fibonacci Sequence as calculus in action in 2D.
11) 1.618.... phi or golden mean constant; pi = 3.14159... and e = 2.71828... and 5.859.
12) The number 0.5 or 1/2.
13) Speed of Light.
14) Permeability and Permittivity.
15) Fine Structure constant.
16) Coulomb constant.
17) Gravitational constant.
18) Boltzmann's constant.
19) Planck's constant.
20) Biology time constant.
21) Theory of Nines.
22) 0.256 constant.
23) Infinity borderline and algebraic completeness of borderline.
24) Psi^2 as a constant method.
-------------
Text
-------------
1) My history of this book.
This book started on 29 September 2023, as a need for a collected reference book on constants of both physics and math. I was tired of having to hunt down in several hundreds of my books what I wrote on constants of physics and mathematics. So now I have all those constants consolidated into this one book.
Archimedes Plutonium
Sep 29, 2023, 3:29:27 PM
to Plutonium Atom Universe
AP's 260th book of science-- List of Derived Physics & Math constants, by Archimedes Plutonium
Given my overwhelming success in my 257th book of science where I derive the Newton's Gravitational Constant of 6.70*10^-39 GeV/c^2 as that coming from elementary-Coulomb unit- squared times a pretty constant of math 0.256.
(1.618*10^-19)^2 x (0.256)
Heady with success, I decided to write a book on the constants of science, physics, math which I have derived or discovered. For I am tending to forget how I derived some of these constants and is quite embarrassing for me, but I am 73 years old as an excuse.
I especially want to make explicit how I derived Fine Structure Constant. But make a whole list of constants that I tackled. I am sure I will tackle more constants in the future.
Now one must not get the silly notion that one number is more important than another number. For this is philosophy and not science itself. All numbers are important as they are a network, a web of Space, and no number is more important than another number.
However, some numbers are used more often, way way more often than other numbers, and that is what a constant of physics or math-- not more important, but used so often. As in mathematics, we use pi very much, the 3.1415.... that relates the diameter of every circle to the circumference of that circle. In physics we use the speed of light as a constant so much often that it seems to be more important than other constants or numbers of physics. But that is not true. All numbers are equally important, it is just that some are used more often than others.
The opposite of "constant" is "variable" and it is here that numbers like pi a constant are important, but unimportant when we speak of variables. So we have a list of constants such as 3.1415...., and 2.71828..... and 1.618...... and my newly discovered constant for gravitational constant to work is 0.2560000..... Those are four important constants, but when we talk of variables, say we talk of 11, 12, 13, 14, 15, 881.3, 9201.5 as variables, could we ever have the case that those seven variables be important or more important than the four constants listed?
Yes, yes of course we can have the situation where variables are more important than constants. For consider, the calculus of mathematics is the pinnacle peak of mathematics and the math used most often in physics. Calculus of first order derivative and integral is the use of variables such as speed, and if we go higher in calculus to 2nd order derivative we have acceleration, more variables. Constants in calculus are not interesting. Variables make calculus interesting.
What I am trying to convey to readers is that this list of constants are the best numbers in all the world. No, they are a list of the __most often used numbers in physics and science__. For all numbers are important.
2) The Atom Totality theory and its primal axiom-postulate.
I suppose an argument or discussion can be focused on whether axioms and postulates are constants of physics and mathematics. Can we say an axiom of math is a constant? Can we say a postulate or principle of physics is a constant of physics? This is an interesting question. Of course principles and postulates and axioms usually do not speak directly of numbers or number quantities. And I am not sure if it is all that important on whether an axiom of math is a constant or a principle of physics is a physical constant.
I am sure that all sciences including math starts with the Atom Totality theory that the entire universe is one big gigantic atom of 231Plutonium, which contains inside itself smaller atoms.
And a first and primal axiom-postulate of the Atom Totality theory is --- All is Atom, and Atoms are nothing but electricity and magnetism.
3) Decimal Grid System of Numbers.
Here we come to the backbone of mathematics number systems. One of the reasons Old Math made so so many ignorant mistakes is that they used the Reals and Complex numbers for their striving of continuous and continuity, yet Quantum Mechanics as early as 1900 with Planck was discovering the world was discrete not continuous and yet the ignorant fools of mathematics kept on with their continuum and continuity program.
The true numbers of mathematics are Decimal Grid Systems, starting with the 10 Grid, then 100, then 1000 etc. Each Grid system ends in a decimal scale number, 10, 100, 1000, 10000, etc. Each has the number 0 appended onto it. Math is all about how precise you want to be in choosing what grid system you work in, for many of us 10 Grid is not enough, even 100, so we often go to the 1000 or 10,000 Grid system for more accuracy.
The Scale Numbers makes mathematics number systems obey and follow Mathematical Induction Principle itself. So that if you find truths in 10 Grid, then a higher Grid and its successor Grid, you found a truth in all of mathematics. The silly Reals and Complex never had such a property.
This is the 10 Grid.
9.0, 9.1, 9.2, 9.3, 9.4, 9.5 9.6, 9.7, 9.8, 9.9, 10.0
8.0, 8.1, 8.2, 8.3, 8.4, 8.5, 8.6, 8.7, 8.8, 8.9,
7.0, 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8, 7.9,
6.0, 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.8, 6.9,
5.0, 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 5.9,
4.0, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9,
3.0, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9,
2.0, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9,
1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9,
0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9,
Notice it is manufactured by adding 0.1 from 0 and then continually adding 0.1 until you reach 10.
It has exactly 100 numbers if we do not count 0.
The 100 Grid looks similar only it starts with 0, 0.01, 0.02, etc etc.
These decimal grid systems are the true numbers of mathematics for they allow for a geometry proof of the Fundamental Theorem of Calculus. The reason they do that is because they are discrete numbers, for between one number and the next number is a hole, a gap, an empty space.
In Old Math, they strived from continuity where there was no empty space between one number and the next. They never payed any attention to physics from 1900 onwards with Quantum Mechanics for this physics is discrete Space, discrete quantities, no continuum.
The pinnacle peak of mathematics is the calculus, and since calculus only works in discrete space, means the true numbers of mathematics are Decimal Grid System numbers.
The true numbers of mathematics are the Decimal Grid System of Numbers. Old Math was bogged down in pitiful and pathetic quest of continuous and continuity and so their numbers involved Reals and Complex for that pitiful striving of continuity when math and geometry are discrete. Starting in 1900 with Planck doing quantum mechanics physics, which is a math of discrete-- quantum means discrete. And sadly no mathematician starting 1900 was pursuing discrete rather than continuous. Not until AP discovers by 2013 with his "True Calculus" books, that you cannot have a fundamental theorem of calculus unless the numbers of mathematics are discrete. And that is what Decimal Grid Number systems are -- discrete.
4) 1, one as unit constant.
One is likely to be the most used number in all of mathematics and science. For it is a one Atom Totality with smaller atoms inside itself. When each of us is borne, it is one that we look out for, for we know our survival is dependent on looking out for ourself.
The number 1 is unique in all of mathematics as units. The unit for mathematical induction as the other counting numbers are built by adding 1 to 1 and continuing to add 1 to build more new numbers. And that 1 as units is the multiplicative identity for 1x1 = 1. Not true of zero, although one mistakenly can argue that 0x0 = 0, yet 1/1 x 1/1 = 1/1 but not true for 0/0 x 0/0 is not equal to 0/0 but undefined. I discuss more of 0 in the next chapter.
The number 1 in geometry is unique in that it contains all the fractions smaller than 1 that lie between 0 and 1. Give me any counting number above 1 and divide it into 1 is a fraction that lies between 0 and 1. For example 8 inverse is 1/8, is a fraction of 0.125 between 0 and 1. And all fractions larger than 1 for example 11.3333 has an inverse that lies between 0 and 1, for it is 1/11.3333 = 0.0882355..
1 is units in math, but physics has no concept of units, a concept like that of units for math. And one can say then that Mathematics for its 1 as unit concept is a __deductive science__. While physics having no 1 as unit concept is a __experimental science__ where we have to go out and test and measure. While in math we set out axioms and postulates and deduce via logic the truths of mathematics. And so physics uses mathematics as a tool.
5) 0, zero, the alien imported quasi-number into mathematics.
0, zero as a number is essential as the measure of distance length for unit 1. What is the number 1? You need zero to measure 1. Without the existence of 0, you do not have a accurate measure of length that is 1. We could start with a small fraction such as 1/9 and its distance length to 1, but that is only a estimate. So zero is essential in mathematics as the starting point to measure the distance length of unit 1.
If you use and employ mathematics long enough in your studies you slowly begin to realize that zero is unlike any other number, and rightly you be. It is a alien number but needed. What zero does is a place marker. You can say zero is the infinity border for the smallest possible number. And we need infinity of the small, the micro-infinity to be zero so we can measure a distance that is a 1 unit distance. The distance between 0 and 1 having all those fractions like 1/4, 1/2, 2/3, etc between 0 and 1, that distance can only exist *accurately* with the existence of the number 0.
Some have said that 0 is not even a number. I would not go that far. I would say it is so much different from all the other numbers of the Decimal Grid System of numbers, that zero is a alien imported quasi-number. We attach 0 to the Decimal Grid System of numbers.
1 as unit constant and 0 as measure of nothing-- it comes from temperature absolute zero and not from empty space, for we must consider Space as being Lines of EM force and to say nothing-space or no-space is contradictory. A void of space approaches 0 but then there is still space there and is not 0. 0 is a tricky one and needed to bound in 1. From 0 to 1 carries all the small numbers and 0 is needed to make the unit measure of 1.
6) Scale Numbers ...0.0001, 0.001, 0.01, 0.1, 0, 1, 10, 100, 1000, 10000,...
The following are quotes from my textbook TEACHING TRUE MATHEMATICS.
--- quoting TEACHING TRUE MATHEMATICS: Volume 2 for ages 5 to 18, math textbook series, book 2
by Archimedes Plutonium 2019 ---
43) Lesson 4-4 Grade Schoolers first proof in math, why decimals are special// What is the Binary number system and other number systems, compared to Decimal Number System.
Alright we need at least one lesson in teaching what other Number System bases there are.
Ask the 13-14 year olds if they have a computer. Ask them if they know what the underlying electronics is for a Computer. I doubt you will get a correct answer. For the underlying idea of a computer in electronics is gate open or gate closed. Either a 1 or a 0. And for this reason alone we need to teach the Binary Number System based on the number 2, not 10 but 2. So the only digits we have in binary are 0 and 1.
So we count in Binary as 0, then 1, then 10, for we use the 1 and 0 to form 2, now we go to 3 and that is 11, then 4 is 100, then 5 is 101, then 6 is 110, etc.
So pause and tell the students, that in Binary, you have just two digits and you have to use just those two digits to count.
Here is Decimal counting to 12
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
Here are those same numbers in Binary System
0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100
Now here is the base 3, called Ternary System, where you have just three digits, 0, 1, 2 and let us count to 12 in ternary
0, 1, 2, 10, 11, 12, 20, 21, 22, 100, 101, 102, 110
So, teacher, see if the students catch on to counting these different base number system.
We just want the students to recognize there are other number base systems and the binary is used extensively in computer technology. And this lesson is really to prepare for the remarkable next lesson, which claims that the Decimal Number System base 10 is superior to all other number system bases. And this is the first proof in mathematics in this textbook, to be taught at age 13 or 14, or both.
Teacher, consult the Common Core and see what is offered there for teaching binary and ternary and some exercises or homework.
44) Lesson 4-5 discovering why the Decimal Number System is superior over all other number base systems.
Proof at last, why Decimals are the superior base Re: discovering why the Decimal Number System is superior over all other number base systems
Let me go to bed with perhaps the best answer for why Decimals are superior and the only valid Number System for all of math. And binary and other base systems are just mediocre local use systems, not general for all of mathematics.
I am so glad I am the first mathematician to discover the Array Proof of mathematics, where we simply get right to the "heart of the matter" and shuck aside all the teasing and leading up to what makes a proof work. We waste no time in building up the answer, we go directly to the heart.
Scale Numbers
Scale Numbers are those which have only 1s and 0s, and only one 1 is allowed.
.
.
.
10000
1000
100
10
1
.1
.01
.001
.0001
.00001
.
.
.
0
Alright, only the Decimal Base Number system is built from a "natural in house scale number" There is no number system built on 0 or 1, they are lacking substance. So, the first number in all the Counting Numbers that is a scale number for a number system is 10. And once you have 10 as a number system, then you no longer need say a base 100 system or a 1000 base system because base 10 absorbs all other scale numbers.
Now in Old Math, they spent gobs and gobs of time on what they called Prime numbers, but this is New Math and we learn that no prime numbers exist in Grid Number Systems. So in New Math we throw out all prime numbers as a folly waste of time of math.
All other number systems are artificial and have just a local use, not general enough. For example, base 2, we call 2 = 10 and 2 is not a scale number, only 10 = 10 is a scale number to allow for accurate representation of fractions and calculations on fractions.
In ternary base, we call 3=10 only artificially for 10 = 3 is not a scale number.
Same goes for every other base except 10 (and its derivatives-- 100, 1000 etc)
Only in base 10, in decimals compose all Scale numbers appear naturally. And this allows for accurate precise fractions.
So, that is the proof that Decimals are the Superior base, because Decimals are a Scale-Numbers base, allowing for accurate precise fraction operations.
Well, now I can go to bed and sleep sound, and that was not hard after all. Just a little recognition of basic facts.
Alright, let me write out that proof for 13 year olds. Since this is the first proof in this textbook. And what is a proof in Math? Well, a proof is simply a fancy well thought out argument that shows the truth of a beginning statement.
Statement: Decimal Number System is special and the only number system good enough to handle all of mathematics, and other number systems are not good enough, not general enough.
Proof:: Every Number System Base has a 10 number in it. For binary it is 2, where 2 = 10, for ternary it is 3 where 3 = 10, etc etc. But one Number System has it where 10 actually equals 10, and is the decimal system, because in decimals the first Scale-Number after 1 which is 10, allows for operations of fractions. Where fractions look mirror image to the whole numbers. The large Scale Numbers are 10, 100, 1000, 10000, etc etc. So, why are Decimals the only good enough Number System to do all fractions with precision and the other systems fail? Because every Number System has a "10" number, and only Decimals have it where 10 actually equals 10 = 10 to handle fractions. QED
Now the symbol "QED" simply means end of proof, and is a Latin abbreviation for quod erat demonstrandum, meaning-- what was to be demonstrated.
So the above is the very first proof the Grade School math takes up.
Why does all of Mathematics have to be based on Decimals and any other number system is just a fly by local use? Because only in Decimals can you do fractions precisely.
Alright, here, teacher, not much exercise or homework, just a study of many terms and what they mean--
1) proof
2) statement
3) QED
4) scale-number
5) decimal number system
6) binary number system
7) ternary number system
--- end quoting from one of my TEACHING TRUE MATHEMATICS textbooks ---
7) 94 and 231 constants in Atom Totality.
The chemical element 94 is plutonium. When I discovered the Plutonium Atom Totality theory on 7 November 1990, I made a rush to the library at the college to see what chemical element fits the best of the common math constants of pi and logarithmic spiral equiangular number 2.71828.... And I wanted a physics constant of note, which is the Fine Structure Constant, the inverse is 137. So in the chemistry & physics library, I poured over the tables and charts and found that plutonium had 22 subshells of S,P,D,F inside of 7 shells, and only 19 of those occupied at any instant of time. There, on 7Nov1990, I discovered the Atom Totality had to be plutonium, a Plutonium Atom Totality for in one stroke, it elucidated the fact that pi and 2.71828.... were 22/7 and 19/7 tied together. So now, I needed to know which isotope of plutonium was the Atom Totality. Since the inverse Fine Structure Constant was 137, meant it had 137 neutrons to its 94 protons so the Atom Totality was 231Pu. Now small and weak minds outside of science would call this numerology, and with their small and weak minds, they should never be in science in the first place.
Small and weak minds would quickly complain that 231Pu is highly radioactive and comes apart. To a real scientist, this is good news for a Atom Totality needs **time** and time is provided to the cosmos by a radioactive Atom Totality, for a stable Atom Totality has little time and things do not move along in a stable Atom Totality.
8) 22/7 and 19/7.
Alright, I need the pair of fractions representing Shells and Subshells of Plutonium of 22/7 and 19/7. Plutonium has when fully occupied 22 subshells in 7 shells and as a fraction that is pi within sigma error.
Normally plutonium has only 19 subshells occupied in 7 shells and that is the log spiral number or equiangular number of 2.71828..... 19/7 within sigma error.
Alright time to write up this book and publish it before end of week.
Now to the untrained eye or untrained scientist, 22/7 and 19/7 may appear as coincidence and a little mind would then invoke numerology. However, because they come in a connected pair, with 7 the same denominator, related to the same concepts of shells and subshells means they are significant, for they tie both constants together in a single physical reality-- plutonium atom structure.
22/7 is 3.14285.... while pi is 3.14159.... Comparing those two for sigma error is 3.14285/3.14159 is 0.04% sigma error. In science we say one is equal to the other if within 0.7% or less. So here we can safely say that Plutonium 231 isotope derives pi.
19/7 is 2.71428.... while the equiangular log spiral number is 2.71828. What sigma error do we have here? 2.71828/2.71428 = 0.1% which is way smaller than 0.7% and we accept that as two equal numbers.
No other chemical element delivers a tied together connected 3.14... with a 2.71....
1s
2s....2p
3s....3p....3d
4s....4p....4d....4f
5s....5p....5d....5f
6s....6p....6d....6f
7s....7p....7d....7f
9) The 840 constant for proton, as compared to 105 for muon.
--- quoting from my 205th book of science ---
Faraday Law is inverse projective-geometry of Coulomb-gravity Law//Physics-Math
by Archimedes Plutonium
Preface: This book discusses the symmetry of the 4 differential laws of Electromagnetic theory, the Faraday law, Ampere-Maxwell law, Coulomb-gravity law and the Transformer law. This book also dives into the numbers of importance of physics and math, the 1/137, the pi, the pi subtract 2.71... and much more.
Cover Picture: Is my iphone photograph of 840 windings of slinky toy to form a torus that is the proton torus of physics of its 840MeV with a muon stuck inside at 105MeV doing the Faraday law.
--------
If true, my conjecture then places the meaning of the Fine Structure Constant, -- its meaning is geometrical, in that the fine-structure-constant is a measure of how many windings you need to make a torus, that allows the Faraday law to be carried out as freely in a torus, as the Faraday law is carried out in a cylinder.
The 840 windings is the minimum number of windings that creates a angle so that the band that represents the muon thrusting through the torus, that the muon band is still almost touching the torus walls but moves freely inside the torus to travel round and round in the Faraday law.
So now, what sort of angle are we talking about in this Conjecture? Well a circle or torus has 360 degrees and thus we have 360/840 = about 0.428 degrees. We are talking about a small angle of 0.428 degrees that gives a torus the ability to move a band-width-muon through the torus, as freely as if it moves through a cylinder.
The angle of 0.428 degrees in radian measure is 0.0072, the Fine Structure Constant of physics.
So, this is an exquisite idea of the physics Fine Structure Constant. We knew its algebraic numeric value for a long time. Just today, we are learning its Geometry meaning.
Its geometry meaning is that give me a circle, any size of circle you want. Call it the unit circle. Then take 840 of those unit circles and make a slinky toy torus out of those 840 circles as 840 windings. It is the Minimum torus for that given size circle for which the muon electron as bar magnet, fits inside that slinky toy torus and does the Faraday Law producing Maximum Electricity.
As Wikipedia defined the Fine Structure Constant -- "fundamental physical constant which quantifies the strength of the electromagnetic interaction between.." elementary Dirac magnetic monopoles. AP is adverse to "charge" in physics for that is a fake concept and the true concept is magnetic monopoles.
Yes, the Maxwell Equation of Gauss that says no magnetic monopole exists is a false law. Magnetic monopoles exist every time one finds a 0.5MeV particle.
Of course, we never see the 1/137 or the 137, but we do see the square root of 1/137 as that of 0.084 which is the prefix of the rest-mass of true proton 840MeV, and the true electron is the muon at 105MeV, stuck inside the proton torus doing the Faraday law with the proton.
--- end quoting from my 205th book ---
Only the number of windings of 840 in a Faraday coil combined with 360 degrees gives the Fine Structure Constant of physics.
10) Rectangle of Whirling Squares Fibonacci Sequence as calculus in action in 2D.
Archimedes Plutonium
Sep 30, 2023, 11:22:15 PM
to Plutonium Atom Universe
Alright, I have taken the Fibonacci sequence out to 2584.
1,1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, ....
Now I divide every fourth number into that number, such as 610/2584 = 0.2360.... And apparently, at infinity it converges to this number 0.2360....
But the number I am interested in is the number 0.256000..... For if the Rectangle of Whirling Squares of Fibonacci Sequence were such that every fourth number divided into this number then the log spiral would close and not be a open spiral. So, 5/21 and 8/34. If that had been 5/20 instead of 5/21, then the squares would close the curve, same goes for 8/32, in fact we can drop to 8/31 and it would close.
I see the Rectangle in Whirling Squares as a calculus on 2D, and perhaps the most elementary calculus of curved figures. Of course the straight line geometry Y --> mx + b is elementary calculus on straightline figures.
Alright, now I am playing tricks on the Fibonacci sequence to see how I can get the numbers 94, 231, possibly 840 or 945.
So I make a slight modification by subtracting 1 in each turn. This sequence then becomes 2,2,3,4,6,9,14,22,35,56,90,145, 234,.... and what is the rate of curvature? It is not 0.2560000 but rather 56/234 = 0.2393.... Is it still an open curve or is it closed???
11) 1.618.... phi or golden mean constant; pi = 3.14159... and e = 2.71828...
Archimedes Plutonium
Oct 9, 2023, 5:25:40 PM
to Plutonium Atom Universe
On the chapter of the constant of exponential constant 2.71828..... I need to do better job than all of modern literature, modern day math education on this number.
What I mean is this. If we learn pi 3.14159... for the first time in a classroom as an integral dx/(sqrt(1-x^2)) from interval -1 to 1 as Weierstrass did, then we are being kookish.
If we learn pi for the first time as "twice the smallest positive number at which the cosine function equal 0" according to Landau is again being kookish in math.
And there are scores of other kookish formulations of pi.
In education, there is the most simple, most direct, most intuitive formulation of a constant.
For pi, this is the formulation of a ratio, a ratio of any circle circumference divided by diameter. It takes 3.14159... diameters of any given circle to go around the circumference of that circle.
That should and must be our first education of what pi is. Unfortunately for mathematics, the exponential constant that I like calling the equiangular constant of the logarithmic spiral 2.71828... unfortunately has never been found its formulation that is the most simple, most direct formulation that is worth teaching in classrooms in schools.
Our teaching of 2.71828.... in schools is the same as if the Weierstrass or Landau pi teaching of pi in school.
Years back I stumbled on the very best teaching of 2.71828.... as the ratio of the circumference to a diameter in one of the squares of the log spiral set up in the Fibonacci Sequence 1,1,2,3,5,8,13,21, 34, ...... For circles that ratio is 3.14159.... but for log spirals that ratio is 2.71828....
All other definitions of 2.71828... are ancillary to the most simple and basic definition.
Pi is geometry foremost, Phi is geometry foremost, would indicate to us with a logical brain, that 2.71828... is geometry and must have the root explanation and education in that root primitive definition.
World's finest explanation of the number "e".
Newsgroups: sci.math
Date: Sun, 8 Feb 2015 02:11:23 -0800 (PST)
Subject: discovery of "e" is the pi of log spirals Re: Geometry meaning of "e"
and how we get pi+e as upper bound barrier
From: Archimedes Plutonium
Discovery of "e" is the pi of log spirals Re: Geometry meaning of "e" and how we get pi+e as upper bound barrier.
Now when I went to college in 1968-1972 was the first time I learned of "e" and its special significance for rate of change. I learned it in Calculus class. But I never really felt fully comfortable with that understanding. Perhaps because it was not geometrical enough for me. So that whenever I needed to explain "e", I had to go through all those hurdles of a algebra explanation. When explaining pi to a new student, the explanation is so super easy and the student immediately sees the connections of circumference and diameter that it satisfies 100%, both student and teacher. But never the case with "e" with its long drawn out explaining and having to use silly things like bank account money.
So, why has no-one ever tried explaining "e" purely geometrical? Perhaps because no-one before was smart enough in math. Because I have done a search and found no-one has ever taught "e" as the "pi of the golden mean log spiral". If you take the Rectangles of whirling squares of the Fibonacci sequence 1,1, 2, 3, 5, 8, 13, 21, 34, 55, etc and take a fixed amount of squares as a turn, we easily can get "e" to be the "pi" of a diameter.
So, why in the history of mathematics was no-one ever able to see that before I discovered it some years past? Why? It is not difficult. The reason I believe, is that no-one ever asked if "e" was more geometrical than actually algebraic? If you never ask yourself the question-- where does "e" appear in pure geometry, then you never will discover that "e" is the pi of log spirals.
Newsgroups: sci.math
Date: Sun, 8 Feb 2015 04:30:06 -0800 (PST)
Subject: "e" is to the golden mean log-spiral what pi is to a circle
From: Archimedes Plutonium
The number "e" is to the golden mean log-spiral what pi is to a circle.
Looking through a Google search it appears.
Years 2010-2013 and on July15, 2013, I wrote this about "e":
Only it does not show the Fibonacci sequence of squares as shown in this picture from "Mathematics: A Human Endeavor" by Harold Jacobs, 1970.
Now in that Jacobs text on page 291 is a picture of a logarithmic spiral inside a rectangle of whirling squares. It is probably on the Internet somewhere, but I want the student or reader to photocopy that page of Jacobs and then get a piece of flexible wire, and cut the wire of a length that matches the radius as shown on that page of length 55. Now, three and a tiny bit more of those 55 lengths should be as long as two of those arcs in the 55 square shown, (that is a semicircle). Now, however, using that same wire track down the length of the wire that it takes to cover the 55 square and the 34 square and finally the 8 square, note that the 8 square has to be extended over to the right inside the 21 square.
What the student or reader should find is that it takes roughly 2.71 of the wire to cover that arc.
So here we learn the best meaning of the number "e". The number "e" is pi in hyperbolic geometry where circles are not closed but are open and spiraling outwards.
--- end quoting old post of mine ---
Back in 2013, I did not need precision and used a stiff wire to measure. But now I need more precision.
If we look at the squares of 8, 5, and 3:
For 8 square 1/4 x 3.1 x 16 = 12.4 arclength
For 5 square 1/4 x 3.1 x 10 = 7.75 arclength
For 3 square 1/4 x 3.1 x 6 = 4.65 arclength
Summing those arclengths gives 24.8.
Taking the radius of the log-spiral in squares 8, 5, 3 as that of 8+1 for the center square gives a radius of 9. And 9 x 2.7 = 24.3. Not bad. So let us try larger squares of 55, 34, 21
For 55 square 1/4 x 3.1 x 110 = 85.25 arclength
For 34 square 1/4 x 3.1 x 68 = 52.7 arclength
For 21 square 1/4 x 3.1 x 42 = 32.5 arclength
Summing those results gives 170.5 and the radius for these three squares is 55+8 = 63.
Now 63x 2.7 = 170.1. So we see a convergence of three squares involving a center of the log-spiral.
So the idea here is that "e" is to the golden mean log spiral that pi is to a circle.
Newsgroups: sci.math
Date: Sun, 8 Feb 2015 14:27:34 -0800 (PST)
Subject: world's finest explanation of number "e"; chat on numbers in New Math
From: Archimedes Plutonium
World's finest explanation of number "e"; chat on numbers in New Math.
The number "e" is to the golden mean log-spiral what pi is to a circle.
Looking at the picture on page 291 from "Mathematics: A Human Endeavor" by Harold Jacobs, 1970.
Now in that Jacobs text on page 291 is a picture of a logarithmic spiral inside a rectangle of whirling squares.
Back in 2013, I did not need precision and used a stiff wire to measure arclength with to find out that "e" is to pi, only instead of circles, it is log-spirals. But now I need more precision.
If we look at the squares of 55, 34, and 21:
For 55 square 1/4 x 3.1 x 110 = 85.25 arclength
For 34 square 1/4 x 3.1 x 68 = 52.7 arclength
For 21 square 1/4 x 3.1 x 42 = 32.5 arclength
Summing those results gives 170.5 and the radius for these three successive squares is 55+8 = 63.
Now 63x 2.7 = 170.1. So we begin to see a convergence of three squares involving a center of the log-spiral.
Now we look at the next three successor squares of 13, 8, 5:
For 13 square 1/4 x 3.1 x 26 = 20.1 arclength
For 8 square 1/4 x 3.1 x 16 = 12.4 arclength
For 5 square 1/4 x 3.1 x 10 = 7.75 arclength
Summing those results we have 40.2 and we see the radius of those three successive squares is 13+2 =15 and we have 15x 2.7 = 40.5 which is very close to 40.2.
Now we have one last three successive squares whose radius is independent of previous squares.
If we look at the squares of 3, 2, and 1:
For 3 square 1/4 x 3.1 x 6 = 4.65 arclength
For 2 square 1/4 x 3.1 x 4 = 3.1 arclength
For 1 square 1/4 x 3.1 x 2 = 1.55 arclength
Summing those arclengths gives 9.3. Now all we need is the radius and that is 3+.5 since the center is in the middle of the 1 square. Finally we have 3.5 x 2.7 = 9.45 which is rather close to 9.3.
So, what I have found here is that the world's finest and best explanation of the number "e" comes from geometry and not algebra. The number "e" acts as pi for open spirals, specifically the Fibonacci or golden mean log-spiral. The number "e" is to the log spiral in the formula 1/2Circumference = e*radius as what pi is in the formula 1/2 Circumference = pi*radius.
This makes sense in the fact that "e" represents equiangular for the log spiral, and "e" represents self-similar for the log-spiral.
The concepts of self-similar and equiangular were rather tough concepts to explain in algebra.
Newsgroups: sci.math
Date: Sun, 8 Feb 2015 17:23:04 -0800 (PST)
Subject: why this discovery now, instead of past Re: world's finest
explanation of number "e"; chat on numbers in New Math
From: Archimedes Plutonium
Why this discovery now, instead of past Re: world's finest explanation of number "e"; chat on numbers in New Math.
So, why is this important discovery take until 2010-2015 to be discovered, rather than before Gauss and Riemann or why not the 1800s or 1900s rather than 2010?
Is it that no-one was smart enough to ask, what is the pure geometry explanation of "e"?
Surely there must have been some past mathematician who was unhappy with "e" explained by algebra or even calculus. Surely there must have been one mathematician that wanted a explanation for "e" as easy as it is to explain pi to a circle.
But no, there was no-one bright enough in the past history of math to push the envelope of explaining "e" as a different version of pi.
Could it be that most mathematicians are rather dull and dumb and that they should be told they are dull and dumb because why does it take so long to explain "e" properly?
Newsgroups: sci.math
Date: Sun, 8 Feb 2015 23:30:48 -0800 (PST)
Subject: geometrical meaning of pi+e = 5.85.... as a pi of a larger expanse of
the golden mean log spiral
From: Archimedes Plutonium
Geometrical meaning of pi+e = 5.85.... as a pi of a larger expanse of the golden mean log spiral.
So, what is the meaning of pi+e in mathematics, both algebra and geometry? It involves golden mean log spiral again, and this pattern emerges:
Alright to get the geometrical meaning of pi+e=5.85... we group these arclengths as to groups of four:
For 55 square 1/4 x 3.1 x 110 = 85.25 arclength
For 34 square 1/4 x 3.1 x 68 = 52.7 arclength
For 21 square 1/4 x 3.1 x 42 = 32.5 arclength
For 13 square 1/4 x 3.1 x 26 = 20.1 arclength
For 8 square 1/4 x 3.1 x 16 = 12.4 arclength
For 5 square 1/4 x 3.1 x 10 = 7.75 arclength
For 3 square 1/4 x 3.1 x 6 = 4.65 arclength
For 2 square 1/4 x 3.1 x 4 = 3.1 arclength
For 1 square 1/4 x 3.1 x 2 = 1.55 arclength
First 4 Group:
For 55 square 1/4 x 3.1 x 110 = 85.25 arclength
For 34 square 1/4 x 3.1 x 68 = 52.7 arclength
For 21 square 1/4 x 3.1 x 42 = 32.5 arclength
For 13 square 1/4 x 3.1 x 26 = 20.1 arclength
Sum of arclength is 190.6 divided by 5.85 = 32.5 which is the arclength of 21 square acting as the diameter for this stretch of the log spiral
Second 4 Group:
For 34 square 1/4 x 3.1 x 68 = 52.7 arclength
For 21 square 1/4 x 3.1 x 42 = 32.5 arclength
For 13 square 1/4 x 3.1 x 26 = 20.1 arclength
For 8 square 1/4 x 3.1 x 16 = 12.4 arclength
Sum of arclength is 117.7 divided by 5.85 = 20.1 which is the arclength of 13 square acting as the diameter for this stretch of the log spiral
Third 4 Group:
For 21 square 1/4 x 3.1 x 42 = 32.5 arclength
For 13 square 1/4 x 3.1 x 26 = 20.1 arclength
For 8 square 1/4 x 3.1 x 16 = 12.4 arclength
For 5 square 1/4 x 3.1 x 10 = 7.75 arclength
Sum of arclength is 72.75 divided by 5.85 = 12.4 which is the arclength of 8 square acting as the diameter for this stretch of the log spiral
Fourth 4 Group:
For 13 square 1/4 x 3.1 x 26 = 20.1 arclength
For 8 square 1/4 x 3.1 x 16 = 12.4 arclength
For 5 square 1/4 x 3.1 x 10 = 7.75 arclength
For 3 square 1/4 x 3.1 x 6 = 4.65 arclength
Sum of arclength is 44.9 divided by 5.85 = 7,67 which is the arclength of 5 square acting as the diameter for this stretch of the log spiral
And finally Fifth 4 Group:
For 8 square 1/4 x 3.1 x 16 = 12.4 arclength
For 5 square 1/4 x 3.1 x 10 = 7.75 arclength
For 3 square 1/4 x 3.1 x 6 = 4.65 arclength
For 2 square 1/4 x 3.1 x 4 = 3.1 arclength
Sum of arclength is 27.9 divided by 5.85 = 4.7 which is the arclength of 3 square acting as the diameter for this stretch of the log spiral
So, we see an obvious pattern, but how to interpret the arclengh of one of the squares behaving as the diameter that when multiplied by pi+e=5.85 gives the total arclength.
Let me think about that.
Newsgroups: sci.math
Date: Thu, 12 Feb 2015 00:44:22 -0800 (PST)
Subject: More details on what numbers exist in New Math (32) Uni-text 9th
ed.:True Calculus #113 Correcting Math 4th ed
From: Archimedes Plutonium
More details on what numbers exist in New Math (32) Uni-text 9th ed.:True Calculus #113 Correcting Math 4th ed.
I need some more information to give on special numbers of Old Math which are not that special in New Math and how they differ from what Old Math thought of these numbers to how New Math views these numbers.
There are three very special numbers in Old Math, and many more, but the three that usually get spoken about are pi, e and i.
Now in New Math there are only two types of numbers whereas in Old Math there are half a dozen or more. In New Math, there are the Rationals which mathematics works on and then there are the irrationals which so to speak exist and surround the Rationals, but which mathematics does not work on them for they end up with imprecise answers. A close analogy would be the Uncertainty Principle in physics that we are allowed only definite answers of position versus momentum even though both exist alongside one another.
In Old Math, the numbers of pi and e were considered Reals and their Reals could be any of these four types: rational, irrational, transcendental, algebraic. In Old Math, pi and e were considered irrational and transcendental. In New Math we totally eliminate transcendental and algebraic because when you precisely define an infinity borderline, you get rid of fakery classes of transcendental and algebraic.
In New Math, both pi and "e" are rational numbers for they are 3.14..... and 2.71..... to the 603rd digit rightwards of the decimal point as rational and finite numbers. They both still are special in New Math because they both perform in the formulas of Circumference of Circle = pi * diameter and Circumference of Log Spiral in turns = e* turn diameter.
In New Math there are no curves at all, but rather, whenever you think you see a curve, you actually are seeing tiny straightline segments so small and when compiled has a appearance of a smooth curve when in fact it is a compilation of straightlines. So in New Math, pi is not the number that gives a length of the curve of circumference, but gives instead, the length of tiny straightline segments adjoined. So that pi is a measure of the circumference of a polygon that looks like a smooth curve of a circle, sometimes regular-polygon. And so, pi in New Math is still a constant and relates perimeter of polygon to diameter, but is not the hullaballoo that Old Math makes out.
In New Math, "e" is a rational number which relates to the open log spiral of its circumference of a turn with diameter. It is smaller than pi because a full circle is larger circumference than a log spiral of turn.
And "e" is also rational. And "e" relates to a regular-polygon as equiangular and self-similar.
Now in New Math, the imaginary number "i" as sqrt-1, is also a rational number and nothing special over sqrt2 or sqrt5. The irrational numbers that are square roots are not just one number but are in fact two rational numbers acting as though they were one number. In physics, we have the analogy of the scalar and vector. The scalar is one number acting as one number, and the vector is at least two numbers acting as though it were one number entity.
In New Math, sqrt2 is not 1.4142.... but is actually two different rational numbers of 1.4142*1.4143 in 10^3 Grid where in Old Math you would get 1.999.... when multiplying root while in New Math, we actually get 2.000....
So "i" in New Math is the conjugate pair of two different rationals of -1 and +1. Now early in the text, I often wrote that a line in mathematics cannot have length yet no width and no depth. It cannot have that if it is composed of just points with no length, no width, no depth. But a line can exist in New Math because a line contains many more irrational numbers than rational. Some line segments contain just two rational numbers as the endpoints of a line segment. So what gives lines length are the irrationals that the lines contain, because the length of the irrational number sqrt-1 is a length from -1 to +1 which is a length of 2 units. The length that sqrt2 gives to a line segment is 1.4143-1.4142 = 0.0001 in 10^3 Grid.
So in New Math, we see numbers classified altogether far different, far better, and far easier than in Old Math with their cobbled together garbage.
--
Recently I re-opened the old newsgroup PAU of 1990s and there one can read my recent posts without the hassle of spammers, off-topic-misfits, front-page-hogs, stalking mockers, suppression-bullies, and demonizers.
https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe
Archimedes Plutonium
Newsgroups: sci.math
Date: Thu, 12 Feb 2015 23:47:18 -0800 (PST)
Subject: best explanation of the number "e" in New Math (33) Uni-text 9th
ed.:True Calculus #114 Correcting Math 4th ed
From: Archimedes Plutonium
Best explanation of the number "e" in New Math (33) Uni-text 9th ed.:True Calculus #114 Correcting Math 4th ed.
Geometry meaning of "e" and how we get pi+e as upper bound barrier.
Alright, I wrote a long time ago that the best way to teach "e" since it is so complicated to new learners is via geometry. And to show how "e" is to an open circle-- the logarithmic spiral, as pi is to a closed circle, the fact that 3.14.... diameters equals the circumference.
To show the meaning of "e" as another form of pi, only the circles are open.
If you look at the Golden Mean Log Spiral, the Rectangles of Whirling Squares of Fibonacci number sequence as shown on page 291 of Jacobs, Mathematics, A Human Endeavor 1970 and make photocopies of page 291 and then use those photocopies to get our tools to measure arclength what we find is not only a "pi" as in the quarter circles but an "e" as in several quartercircles, and finally we find a pi+e = 5.85... on several quartercircles as a upper barrier of those turns.
I am looking at the quartercircles of 55, 34, 21, 13
And using a approx to pi as 3 and 2.7 for "e".
I have this data
1/4 * 3 * 26 = 19.5
1/4 * 3 * 42 = 31.5
1/4 * 3 * 68 = 51
1/4 * 3 * 110 = 82.5
______________________ summation
184.5 is the sum
divide by 5.85 gives me approx 31.5
So, in effect, if I used the arclength of the 21 by 21 square as the "diameter of the open spiral from 13 through 21 through 34 through 55" and using pi+e = 5.85, I get 184.5 total arclength.
What I am pursuing here is the idea that the best way to teach what "e" is, is a pi that handles log spirals. And in that teaching we can have a upper bound of pi+e=5.85...
Discovery of "e" is the pi of log spirals.
Now when I went to college in 1968-1972 was the first time I learned of "e" and its special significance for rate of change. I learned it in Calculus class. But I never really felt fully comfortable with that teaching of "e" as a interest from banks or finance. Perhaps because it was not geometrical for me, because most people have a higher power of insight with geometry, rather than with algebra and quantities. It is just the way human minds are wired to see geometry truths far better than algebra truths. So that whenever I needed to explain "e", I had to go through all those hurdles of a algebra explanation. When explaining pi to a new student, the explanation is so super easy and the student immediately sees the connections of circumference and diameter that it satisfies 100%, both student and teacher. But never the case with "e" with its long drawn out explaining and having to use silly things like bank account money.
So, why has no-one ever tried explaining "e" purely geometrical? Perhaps because no-one before was smart enough in math. Because I have done a search and found no-one has ever taught "e" as the "pi of the golden mean log spiral". If you take the Rectangles of whirling squares of the Fibonacci sequence 1,1, 2, 3, 5, 8, 13, 21, 34, 55, etc and take a fixed amount of squares as a turn, we easily can get "e" to be the "pi" of a diameter.
So, why in the history of mathematics was no-one ever able to see that before I discovered it some years past? Why? It is not difficult. The reason I believe, is that no-one ever asked if "e" was more geometrical than actually algebraic? If you never ask yourself the question-- where does "e" appear in pure geometry, then you never will discover that "e" is the pi of log spirals.
The number "e" is to the golden mean log-spiral what pi is to a circle.
Looking through a Google search for my history on this discovery, it appears in the years 2010-2013 and on July15, 2013, I wrote this about "e":
Only it does not show the Fibonacci sequence of squares as shown in this picture from "Mathematics: A Human Endeavor" by Harold Jacobs, 1970.
Now in that Jacobs text on page 291 is a picture of a logarithmic spiral inside a rectangle of whirling squares. It is probably on the Internet somewhere, but I want the student or reader to photocopy that page of Jacobs and then get a piece of flexible wire, and cut the wire of a length that matches the radius as shown on that page of length 55. Now, three and a tiny bit more of those 55 lengths should be as long as two of those arcs in the 55 square shown, (that is a semicircle). Now, however, using that same wire track down the length of the wire that it takes to cover the 55 square and the 34 square and finally the 8 square, note that the 8 square has to be extended over to the right inside the 21 square.
What the student or reader should find is that it takes roughly 2.71 of the wire to cover that arc.
So here we learn the best meaning of the number "e". The number "e" is pi in geometry where circles are not closed but are open and spiraling outwards.
--- end quoting old 2013 post of mine ---
Archimedes Plutonium
Oct 9, 2023, 9:22:50 PM
to Plutonium Atom Universe
Now the summation of pi and 2.71828.... is 5.859..... And looking to see if there are any math or physics constants with prefix digits of 5.859...
In physics there is what is called the Wien frequency displacement law constant of 5.878...*10^10 Hz*K^-1. That would be a sigma error of 5.878/5.859 = 0.3% highly acceptable. But before we can accept it, we have to give some physical explanation why a logarithmic spiral relates to a physics frequency displacement.
Archimedes Plutonium
Oct 10, 2023, 12:03:04 AM
to Plutonium Atom Universe
On Monday, October 9, 2023 at 9:19:46 PM UTC-5, Archimedes Plutonium wrote:
> Now the summation of pi and 2.71828.... is 5.859..... And looking to see if there are any math or physics constants with prefix digits of 5.859...
>
> In physics there is what is called the Wien frequency displacement law constant of 5.878...*10^10 Hz*K^-1. That would be a sigma error of 5.878/5.859 = 0.3% highly acceptable. But before we can accept it, we have to give some physical explanation why a logarithmic spiral relates to a physics frequency displacement.
>
Now if the 5.859 of sum of pi and 2.71828... applies to Wien law, then the Wien law should have a constant for wavelength with prefix that comes close to 2.71828....
And looking up the constants, sure enough we have a Wien wavelength displacement law constant, 2.897*10^-3 m*K, with a prefix of 2.887...
Now admittedly the sigma error is in excess of that for the Wien frequency law constant. For we have 2.887/2.718 = 6% sigma error while the frequency error was a meagre 0.3%. But for me, the fact that frequency and wavelength in blackbody radiation come so close to pi+2.71 and 2.71, indicates to me there is a connection.
Now there is another Wien law constant of Wien entropy displacement law constant 3.00*10^-3 m*K with its prefix digits of 3.00, so close to either speed of light prefix 3 or to prefix of pi at 3.14.....
Since we have a string of 3 math constants close to a string of quantum mechanics constants of their prefix digits is a warning sign that they are fundamentally connected. Although at this moment I am not able to give that connection.
12) The number 0.5 or 1/2.
The number 0.5 stands out in importance as being 1/2 way between 1 and 10 in the 10 Grid. It is also a midpoint number between two successive integers. It is essential in Calculus Fundamental Theorem of Calculus proof as we lift up a right triangle hinged at the midpoint of two successive numbers in that Grid system. We need 1/2 or 0.5 as midpoints between successive whole numbers such as 1.5 is between 1 and 2, or 3.5 is between 3 and 4 for the calculus proof of Fundamental Theorem of Calculus seeks the midpoint of intervals, not just 0.5 of whole numbers but for example 8.985 between 8.980 and 8.990.
The number 0.5 is crucial in Wave Mechanics of Physics as 1/2 of a closed loop wave. When we have the proton as 840 full windings of closed loops, that 1/2 of a closed loop is a photon of energy, a magnetic monopole at 0.5MeV. So it is natural that in physics laboratories they would find the rest mass of the magnetic monopole (JJ Thomson discovery of 1897) find the rest mass to be 0.5MeV.
The number 0.5 for 0.5MeV magnetic monopole.
And in comparing binary, ternary, base 4, base 5, base 6, base whatever, except base 10, we need the number 5 halfway in between 1 and 10 and we need the true base of mathematics have 2x5 = 10.
13) Speed of Light.
I wrote a whole book on the speed of light.
--- quoting my 122nd published book of science---
Confirming true speed of light is 3.16*10^8 m/s, not 2.99; review of past results// Physics focus series, book 9
by Archimedes Plutonium (Author) (Amazon's Kindle)
Preface: So much of physics is squaring, x^2 or a^2 and inverse squaring 1/x^2. And of course there is Psi^2, the Psi squared probability function of quantum mechanics. The number 2.99 from experimental results as the coefficient of light speed, that light speed is close to 3.14 of pi and is off in sigma error by 5%. As for square root of 10 being 3.16, then 3.16/2.99 is a sigma error of 5.6%. What this book argues is that in several incidents in physics involving the speed of light, in those instances, the speed of light should be a coefficient of square root of 10. Now, many illogical minds will cast doubt on this idea of coefficient being 3.16, for merely the reason that if in a different derived unit rather than the meter per second unit system changes, and thus the coefficient changes. But here I back up the claim by saying "logically" if we had a different unit system, than the meter per second. That in that other system, there is a fundamental constant whose coefficient is again 3.16, and it may not be the speed of light, so that in that "other system" some constant again needs the 3.16 coefficient.
In the system of SI derived units, the meter per second, the constant that happens to be 3.16 coefficient is the speed of light. For many equations in physics need for a speed of light squared be that of value 1 and the square root being the prefix numbers 3.16.
Cover Picture: Is my iphone photograph of a Google search for "1849 Hippolyte Fizeau, toothed wheel 315000 +5.1% error. Where Fizeau almost hit the true value of speed of light at 316,000 km/sec with a sigma error of only 0.3%. Why did Fizeau come so close to the true speed of light while the others mostly hovered around 2.99 coefficient? I suspect the reason is that the others were more into "reflection" and that is causing such a huge huge error. Fizeau is a mechanical means. And anything dealing with the speed of light, you have to find a method that is not of light itself, such as a mechanical spinning wheel.
--- end quoting my 122nd book of science ---
To derive the speed of light, well, Maxwell did that in the 1860s with his Speed^2 = 1/(permeability*permittivity). End of story on deriving speed of light.
However, there is one problem in the prefix number. Some experiments come up with 2.99 for prefix number, and some just say 3.00 for prefix number.
I argue that the speed of light needs to be the prefix number 3.16 the square root of 10 exactly. I argue this because so so many constants have a speed of light component especially speed of light squared. If you square 3.16 you end up with 10 prefix which is 1 in Scientific Notation.
Out of pristine beauty of coherence and symmetry, the speed of light prefix number must be 3.16*10^8 meters/second.
14) Permeability and Permittivity.
Archimedes Plutonium
Aug 5, 2020, 12:31 AM
to Plutonium Atom Universe
Alright, I solved it.
And what Old Physics called electric charge becomes 1*10^-19 Coulomb Re: AP fixing Old Physics electric constant number of 1.602*10^-19 Coulomb
In Old Physics they just defined permeability, not measure it from any experiment. They defined it as 1.256*10^-6 N*A^-2, where they simply said it is a coefficient of 4pi = 12.56 then 1.256 *10. That is rather hypocritical of scientists to grasp out of thin air 4pi. They did measure permittivity at 8.854*10^-12 F*m^-1.
In Old Physics they did this.
So if we plug into this formula
c = 1/sqrt(permittivity*permeability)
c = 1/sqrt(8.854*10^-12 * 1.256*10^-6)
c = 1/sqrt(11.12*10^-18)
c = 1/ 3.334*10^-18 s/m
c = 0.299*10^9 m/s
c = 2.99*10^8 m/s
In New Physics we take a different approach of defining permeability by a probability Fibonacci sequence where we can have north pole then south pole arbitrarily picked. This leads to a special math constant of 1.131...
New Physics
c = 1/sqrt(permittivity*permeability)
c = 1/sqrt(8.85*10^-12 * 1.13*10^-6)
c = 1/sqrt(10.000*10^-18)
c = 1/ 3.16*10^-18 s/m
c = 0.316*10^9 m/s
c = 3.16*10^8 m/s
Well, I am happy with the above, although a half hour late after midnight.
In physics with the Primal Axiom-- All is Atom and atoms are nothing but electricity and magnetism, means that the basic units of physics are many of them are going to be 1, 10, 100 etc coefficients.
15) Fine Structure constant.
In 1990-1991 after discovery of the Plutonium Atom Totality-- I did not derive Fine Structure but rather assumed it to be 137 inverse in order to obtain the isotope of the Atom Totality 231Pu.
On Friday, April 10, 2020 at 4:28:59 AM UTC-5, Archimedes Plutonium wrote:
> 109th book of AP// The ultimate meaning of Planck’s constant and Fine-Structure-Constant
>
> Quoting Feynman:
> There is a most profound and beautiful question associated with the observed coupling constant, e – the amplitude for a real electron to emit or absorb a real photon. It is a simple number that has been experimentally determined to be close to 0.08542455. (My physicist friends won't recognize this number, because they like to remember it as the inverse of its square: about 137.03597 with about an uncertainty of about 2 in the last decimal place. It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.) Immediately you would like to know where this number for a coupling comes from: is it related to pi or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the "hand of God" wrote that number, and "we don't know how He pushed his pencil." We know what kind of a dance to do experimentally to measure this number very accurately, but we don't know what kind of dance to do on the computer to make this number come out, without putting it in secretly!
>
> — Richard P. Feynman (1985). QED: The Strange Theory of Light and Matter
>
On Friday, April 10, 2020 at 4:28:59 AM UTC-5, Archimedes Plutonium wrote:
> 109th book of AP// The ultimate meaning of Planck’s constant and Fine-Structure-Constant
>
> Quoting Feynman:
> There is a most profound and beautiful question associated with the observed coupling constant, e – the amplitude for a real electron to emit or absorb a real photon. It is a simple number that has been experimentally determined to be close to 0.08542455. (My physicist friends won't recognize this number, because they like to remember it as the inverse of its square: about 137.03597 with about an uncertainty of about 2 in the last decimal place. It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.) Immediately you would like to know where this number for a coupling comes from: is it related to pi or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the "hand of God" wrote that number, and "we don't know how He pushed his pencil." We know what kind of a dance to do experimentally to measure this number very accurately, but we don't know what kind of dance to do on the computer to make this number come out, without putting it in secretly!
>
> — Richard P. Feynman (1985). QED: The Strange Theory of Light and Matter
>
--- quoting from my 205th book of science ---
Faraday Law is inverse projective-geometry of Coulomb-gravity Law//Physics-Math
by Archimedes Plutonium
Preface: This book discusses the symmetry of the 4 differential laws of Electromagnetic theory, the Faraday law, Ampere-Maxwell law, Coulomb-gravity law and the Transformer law. This book also dives into the numbers of importance of physics and math, the 1/137, the pi, the pi subtract 2.71... and much more.
Cover Picture: Is my iphone photograph of 840 windings of slinky toy to form a torus that is the proton torus of physics of its 840MeV with a muon stuck inside at 105MeV doing the Faraday law.
--------
If true, my conjecture then places the meaning of the Fine Structure Constant, -- its meaning is geometrical, in that the fine-structure-constant is a measure of how many windings you need to make a torus, that allows the Faraday law to be carried out as freely in a torus, as the Faraday law is carried out in a cylinder.
The 840 windings is the minimum number of windings that creates a angle so that the band that represents the muon thrusting through the torus, that the muon band is still almost touching the torus walls but moves freely inside the torus to travel round and round in the Faraday law.
So now, what sort of angle are we talking about in this Conjecture? Well a circle or torus has 360 degrees and thus we have 360/840 = about 0.428 degrees. We are talking about a small angle of 0.428 degrees that gives a torus the ability to move a band-width-muon through the torus, as freely as if it moves through a cylinder. When we convert 0.428 degrees to radians we have 0.0072, the physics Fine Structure Constant. Who would have thought that the Fine Structure Constant was a angle?
Exquisite relationships-- the proton has to be 840 windings arranged as a torus, that leaves a spacing angle of 0.428 degrees from one winding to the next, and this 0.428 degrees is 0.0072 radians. And 0.0072 is the Fine Structure Constant.
So, this is an exquisite idea of the physics Fine Structure Constant. We knew its algebraic numeric value for a long time. Just today, we are learning its Geometry meaning.
Its geometry meaning is that give me a circle, any size of circle you want. Call it the unit circle. Then take 840 of those unit circles and make a slinky toy torus out of those 840 circles as 840 windings. It is the Minimum torus for that given size circle for which the muon electron as bar magnet, fits inside that slinky toy torus and does the Faraday Law producing Maximum Electricity.
As Wikipedia defined the Fine Structure Constant -- "fundamental physical constant which quantifies the strength of the electromagnetic interaction between.." elementary Dirac magnetic monopoles. AP is adverse to "charge" in physics for that is a fake concept and the true concept is magnetic monopoles.
Yes, the Maxwell Equation of Gauss that says no magnetic monopole exists is a false law. Magnetic monopoles exist every time one finds a 0.5MeV particle.
Of course, we never see the 1/137 or the 137, but we do see the square root of 1/137 as that of 0.084 which is the prefix of the rest-mass of true proton 840MeV, and the true electron is the muon at 105MeV, stuck inside the proton torus doing the Faraday law with the proton.
In my 205th book of science I discover a way of producing four important constants of physics and math-- pi, Fine Structure, 840, and 360. One of those is a angle measure-- the 360 for a full revolution.
In an experiment described in that 205th book, I took 840 identical circles and crafted them into a perfect torus. To find the angle of separation I did a 360/840 and found an angle of 0.428 degrees. Look up what 0.428 degrees is in radians-- for it is the Fine Structure constant of physics 0.0072. Then in that experiment I measured the diameter and radius of the torus I constructed from 840 identical circles placed with a angle 0.428 degree separation. Measuring the diameters of circles and of the donut hole, the diameter of the donut hole of 840 circles forming a ratio which is pi = 3.14159....., specifically, in my experiment --
--- quoting my book ---
Alright, time for some calculations, and I harken back to a experiment I did in 2022, where I bought enough slinky toys to sort of guide me in what a 840 windings of a torus geometry produces in numbers. Here is a view of that experiment. What I want to do is given a sphere of radius 10, diameter 20 compute the radius and diameter of a torus composed of 840 windings inside the sphere and tangent at the equator line. Compute the r radius, not the big R radius, and diameter of this smaller circle that composes the torus of 840 windings, being sure the ratio of donut hole diameter is that of 3.14159....
On September 17, 2022 in sci.math,sci.physics, plutonium-atom-universe, I wrote a corrected copy:
A fabulous discovery of science physics.
Alright, curiosity in my lifetime has been indefatigable. I wanted to get a rough estimate of the donut hole of 840 windings so I bought 9 more slinky toys to combine with my 2 already owned ones. And I measured what a 840 winding torus donut hole was. My torus of 840 windings has a donut hole diameter of 205 mm and has a slinky toy diameter of 65mm. That would be a total diameter of torus as 65 + 205 +65 = 335mm with the donut hole diameter 205mm.
Now I play with those numbers and see what becomes of them for the Conjectures I placed so far. The most important being the idea that 840 windings is the physical geometry of the Fine Structure Constant as a torus the produces Maximum Electricity in the Faraday law.
Alright, well it is easy to see that 205/65 is 3.15... And I went back to the lab and measured again and it was actually 205mm to 65mm. That gives me 205/65 = 3.15 and compared to pi 3.15/3.14 is a 0.3% sigma error, so close that it is automatic we announce that given any circle, and if you have 840 of those circles wound around into a torus, that the donut hole diameter divided by given circle diameter is pi number.
Now also, looking at the angle which 840 circles create in a torus is 360/840 = 0.428 degree.
Amazingly a angle of 0.428 degree is in radians that of 0.0072 or the physics Fine Structure Constant. Here I have an angle for a torus which allows for a free thrusting of a muon inside the torus, as if the muon is in a cylinder in the Faraday law. And this angle of 0.428 allows the muon to freely thrust without bumping into the torus walls.
But the amazement does not stop there, for where is the number 0.42 degree angle come up in Physics constants? Well if you take pi 3.14 and subtract from "e" 2.71 you get 0.42.
AP
16) Coulomb constant.
Archimedes Plutonium
Sep 26, 2023, 6:45:58 PM
to Plutonium Atom Universe
On Tuesday, September 26, 2023 at 5:14:45 PM UTC-5 Archimedes Plutonium wrote:
I only vaguely recall deriving the Coulomb electric magnetic monopole of 1.618*10^-19 C. And I need to check what that was, because here I use this constant to derive the Gravitational constant.
My memory is vague on this issue, and about the only thing I remember is I used both permittivity in conjunction with permeability to get Coulomb monopole.
quoting from --- My 151st published book of science.
TEACHING TRUE PHYSICS// 1st year College// Physics textbook series, book 4
Kindle Edition
by Archimedes Plutonium (Author)
Preface: This is AP's 151st book of science published. It is one of my most important books of science because 1st year college physics is so impressionable on students, if they should continue with physics, or look elsewhere for a career. And also, physics is a crossroad to all the other hard core sciences, where physics course is mandatory such as in chemistry or even biology. I have endeavored to make physics 1st year college to be as easy and simple to learn. In this endeavor to make physics super easy, I have made the writing such that you will see core ideas in all capital letters as single sentences as a educational tool. And I have made this textbook chapter writing follow a logical pattern of both algebra and geometry concepts, throughout. The utmost importance of logic in physics needs to be seen and understood. For I have never seen a physics book, prior to this one that is logical. Every Old Physics textbook I have seen is scatter-brained in topics and in writing. I use as template book of Halliday & Resnick because a edition of H&R was one I was taught physics at University of Cincinnati in 1969. And in 1969, I had a choice of majors, do I major in geology, or mathematics, or in physics, for I will graduate from UC in 1972. For me, geology was too easy, but physics was too tough, so I ended up majoring in mathematics. If I had been taught in 1969 using this textbook that I have written, I would have ended up majoring in physics, my first love. For physics is not hard, not hard at all, once you clear out the mistakes and the obnoxious worthless mathematics that clutters up Old Physics, and the illogic that smothers much of Old Physics.
Maybe it was good that I had those impressions of physics education of poor education, which still exists throughout physics today. Because maybe I am forced to write this book, because of that awful experience of learning physics in 1969. Without that awful experience, maybe this textbook would have never been written by me.
Cover picture is the template book of Halliday & Resnick, 1988, 3rd edition Fundamentals of Physics and sitting on top are cut outs of "half bent circles, bent at 90 degrees" to imitate magnetic monopoles. Magnetic Monopoles revolutionizes physics education, and separates-out, what is Old Physics from what is New Physics.
--- end quoting from --- My 151st published book of science---
What I am going to do is review what that teaching of Avogadro's number because it is a similar idea to the "Elementary Coulomb".
So what was Avogadro's Number in most simple teaching? Avogadro's number, or mole, was taking a "elementary mass" and knowing that in every 1 gram of mass, there is a specific number of these elementary mass units. So if I have a 1 gram of iron or a 1 gram of silver, or a 1 gram of oxygen gas or a 1 gram of sodium or a 1 gram of hydrogen or a 1 gram of H2O or a 1 gram of CO2. If I have 1 gram of anything of matter, it has a number of particles that is the same number in all 1 gram of matter. What is that elementary particle of mass? It is called nucleon in Old Physics and is either the neutron at 945MeV or the proton 840MeV + muon 105MeV = 945MeV.
So we need to measure the mass of the neutron or the proton+muon and both come close to 1.618*10^-24 grams. And if I divide that mass unit, call it the "Elementary Mass Unit", if I divide it into 1 as in 1 gram, what I procure is the Avogadro number, or the mole. So, 1/ 1.618*10^-24 = 6.18*10^23 elementary mass particles that compose every 1 gram of mass.
So in summary, every atomic or molecular material that has a mass of 1 gram, has 6.18*10^23 nucleons. It does not matter if it is a element or a molecule, so long as its mass is 1 gram.
Now we are going to do the same sort of thing with "Elementary Coulomb" where coulomb means quantity of electricity. So we do not have mass, we have electricity, and we need a Elementary Coulomb, just as the neutron or proton+muon was the elementary mass.
So, how do we get this elementary coulomb? It is going to be similar to the number 1.618*10^-24 grams mass. Only it is coulombs electricity. Remember, electricity is a wave energy, a hoola hoop wave. And the number is 1.618^10^-19 coulomb. So how do we get that number 1.618^10^-19 ?
And the answer is by Experiments. And the best experiments to get 1.618*10^-19 is from Faraday's Experiment into finding the Faraday constant and dividing it by Avogadro's number 6.18*10^23.
--- end quoting from my 151st book ---
Archimedes Plutonium
Sep 26, 2023, 8:41:45 PM
to Plutonium Atom Universe
So the Faraday constant F is 96485 Amperes/mole
The Avogadro constant, N_A is 6.*10^23 per mole
If we divide F/N_A
9.6*10^4 / 6*10^23
We end up with 1.6*10^-19 Coulomb electrical force.
I do not know how easy or difficult it is to repeat Faraday's Experiment. But it is the superior teaching experiment.
Setting up the Faraday Constant Experiment in class.
--- further quoting from my 1st year college Teaching True Physics textbook ---
Archimedes Plutonium
Sep 26, 2023, 9:56:36 PM
to Plutonium Atom Universe
So, this is a beautiful, beautiful ending here.
We experimentally measure Faraday constant and Avogadro constant and then by theory are able to step and tiptoe our way into what the Gravitational constant is as a Psi-squared upon 1.6*10^-19 C times a constant.
We never really had to perform any experiment to find out Gravity constant save for Faraday constant and Avogadro constant.
Looking in Wikipedia at the ease of experimentally producing Faraday constant and Avogadro constant.
--- quoting Wikipedia ---
The value of F was first determined by weighing the amount of silver deposited in an electrochemical reaction in which a measured current was passed for a measured time, and using Faraday's law of electrolysis.
--- end quote ---
Much much easier than the Cavendish set-up to measure gravitational constant.
And how easy was it to measure Avogadro's number?? Well, this is the measuring of the mass of the proton+muon or the neutron in grams and you instantly have Avogadro's number.
So the chain link between finding gravity constant starts with Avogadro number and Faraday constant and ends with Coulomb monopole constant of 1.618*10^-19 C.
However there is that pesky constant at the end, of 0.256000... the Psi-squared constant. And I am still working on it. In the derivation of Fine Structure constant we find that it is an angle in a torus of 840 rings or windings. The angle of separation of the windings in a torus of 840 windings is a angle in radians of 0.0072.
So is the AP Psi-squared constant some sort of angle?? Must most laws of physics have a angle input?
So far I have 0.256000... as a pure number constructed from perfect-squares. It is similar to the Meissel-Mertens constant of 0.261 which is related to a Log of Log function. It may relate to the Feigenbaum constant 2.50 as a electromagnetic quantum field bifurcation.
Or it simply is a constant needed when working with Psi-squared, and perhaps other topics in Psi-squared make use of a constant 0.2560000. At this moment in time, I think this constant is a mixture of Feigenbaum and of Meissel-Merten constant, both contributing to some geometry of a Electromagnetic Field that composes the weakest EM force-- gravity.
17) Gravitational constant.
In my 257th book of science ---
On Wednesday, September 27, 2023 at 12:29:10 AM UTC-5, Archimedes Plutonium wrote:
> Alright, I am going to completely drop this further quest of making a physical meaning of the brand new constant in math and physics of AP's Psi-squared constant 0.2560000. It is used to find the Gravitational constant using Psi-squared upon the elementary Coulomb monopole 1.618*10^-19 C. and when that is squared and multiplied by 0.256, we end up with the exact Gravitational Constant 6.70*10^-39.
>
On second thought, I found what I was looking for.
I remembered that the Fibonacci Sequence of a Rectangle in Whirling Squares is Calculus in 2D for squares on rectangles. For I reduced 0.256 to its 32/125 and remembered that in the Fibonacci sequence I had a 34 then four squares later a 144 for 34/144 = 0.2361 whereas 32/125 = 0.256. Fourth square later is important as the full rotation. The meaning is clear. The Open log spiral is governed by a constant close to 0.2360000 while to close the spiral, the minimum to close the curve to be a oval, ellipse, circle is 0.256.
In Harold Jacobs book Mathematics a Human Endeavor, page 291 we see the Rectangle in Whirling Squares calculus and that focusing upon the 8 square and the larger 34 square above it. Where 8/34 = 0.2352 and 8/32 = 0.25. If we had a square 32 instead of 34, would cause the curve to form a circle that would enclose the first 32 square as it swung back around and no longer be an open curve.
The constant 0.256 is the smallest number to create a closed curve in gravitational bound masses. In addition to the fact that the constant 0.256 is formed from perfect square numbers in Psi-squared.
I knew I could not leave this alone until solved.
18) Boltzmann's constant.
Archimedes Plutonium
Oct 7, 2023, 12:41:23 AM
to Plutonium Atom Universe
One of the reasons I wanted to do this book, other than my forgetfulness on how I derived these constants, was because I suspected my Boltzmann constant derivation of a few years back was wrong and in error. There I thought it was a derivation from Conductance Quantum and with the sigma error adjustment of speed of light as 3.16*10^8 m/s rather than 2.99*10^8 m/s.
And so I was anxious to get back in touch.
And this time around I take a new tactic altogether. For I employ the formula c^2 = 1/(permeability* permittivity) and I replace permeability with Boltzmann constant, asking for research to find the permittivity replacement. We already see glimmers of this replacement in what is called --- Thermal conductance quantum 9.46*10^-13 W/K^2.
And I am far more happy and satisfied with this derivation. For it directly puts Boltzmann constant into the EM Spectrum, and up and down that Spectrum we can find dual pairs of constants such as Boltzmann's for infrared radiation. And I suspect one for radio waves and another for Pair Production in X-rays and gamma rays.
When the primal axiom of physics is --- All is Atom and Atoms are nothing but electricity and magnetism, we need not have to look far to make Thermodynamics an integral part of EM Spectrum and thereby, easily explaining the constant of Boltzmann.
--- quoting in parts from my 121st published book of science ---
Unification of Thermodynamics with Electromagnetism// Physics focus series, book 8
by Archimedes Plutonium
Preface: For years now, I have been saying a short statement that summarizes all of physics. That statement is-- "All is Atoms, and atoms are nothing but electricity and magnetism". And abiding under that statement would be a unification of thermodynamics and all its laws as a form of electricity and magnetism. So, how can we unify thermodynamics as being electricity and magnetism? We do this taking all the 4 laws of thermodynamics plus add on the Ideal Gas Law of PV = nRT and match them with the 6 laws of electricity and magnetism. In this revised edition, while doing TEACHING TRUE PHYSICS, 2nd year College, I came upon a mistake I had made in previous years. That it is Volume in the Ideal Gas Law which matches Voltage in New Ohm's law of Voltage = Current x Magnetic field x Electric field V= CBE. Previously I thought the "pressure" in Ideal Gas law was voltage. For in school, I heard many times from professors that voltage was a "pressure phenomenon" but now I realize that was a mistake. For it is Volume that matches Voltage, and the pressure in 1/P once you flip-up the terms meters^-1 seconds^-2 flip those up in 1/P becomes a current, matching electric current and Electric field.
Cover Picture: The Right-Hand Rule in which the direction of current in green wire, represented by my thumb, causes the direction of curl of the magnetic field be that of how my four fingers curl wrap-around the wire. Remember, this is Ampere's law of EM theory. The Right-Hand Rule so easily matches the 2nd law of thermodynamics.
------------
Newsgroups: sci.physics
Date: Thu, 30 Apr 2020
Subject: But what can prove the thermodynamics is the same as Capacitor law of
EM theory is a constant I seldom if ever use. The Conductance Quantum, and
here this constant is related to Capacitors
From: Archimedes Plutonium
Conductance Quantum and Boltzmann's constant compared.
What can prove the thermodynamics is the same as Capacitor law of EM theory is a constant I seldom if ever use. The Conductance Quantum, and here this constant is related to Capacitors.
Conductance Quantum is G_0 = 2e^2/h = 7.74*10^-5 S
Boltzmann's constant is 8.617*10^-5 eV/K
Of course, I would have to relate units of S with eV/K, but first, let me see if the numbers equilibrate.
This would give me a Sigma error of 8.61/7.74 = 1.112 for a 11% error, unacceptable. But when I was doing this in April of 2020, I was thinking the sigma error could be drawn down to near zero if I factored in the idea that speed of light was really 3.16*10^8 meter/second and that is a sigma error of 3.16/2.99 = 5.6%. And if I say that both Conductance Quantum and Boltzmann constant were each effected by a 5.6 and another 5.6 would sum to a 11.2% sigma error which takes into account the prefix numbers 8.61 and 7.74. But this is messy physics as I look back from the viewpoint of October 2023.
Derivations of physics constants should be much more clean and cleaner than this.
It would be nice to say of the Conductance constant, that Conductance constant and Boltzmann constant are one and the same. Thus we can safely say all of thermodynamics is now a subset of Electromagnetic theory and in particular all under the Capacitor Law of EM. But we cannot from the above analysis, for it is not a derivation of Boltzmann's constant from Conductance constant.
More work has to be done to derive Boltzmann's constant.
We need a true derivation of Boltzmann's constant for in Old Physics they missed in their thermodynamics is the accounting of radiation wave energy as heat, for all they had was average kinetic energy of particles, and no waves. I suppose they dismissed their error and gaping hole of theory by thinking particle and wave duality allows them to dismiss waves as heat, but not so.
Magnetic Permeability is a wave structure and its constant is close and nearby to Boltzmann's constant, only its prefix number is off and its exponent is off by 1.
Magnetic Permeability constant is 1.256*10^-6 H/m
Boltzmann's constant is 8.617*10^-5 ev/K
If I take the inverse of Magnetic Permeability I end up with 0.79*10^6 m/H which is 7.9*10^5 m/H and here I can say that Magnetic Permeability inverse is within sigma error of Conductance constant 7.74*10^-5 S, provided S relates to m/H.
And perhaps that is true, for perhaps I derived Magnetic Permeability from Conductance Constant, which is another chapter in this book of list-of-constants.
On Thursday, April 30, 2020, Archimedes Plutonium wrote:
All I need to do to prove that thermodynamics, the complete entire thermodynamics is the Capacitor Law of EM equations, by showing that the Boltzmann's constant 8.617*10^-5 ev/K is the same constant as Magnetic Permeability 1.256*10^-6 H/m. But that did not happen, instead I probably derived the Magnetic Permeability constant from that of the Conductance constant.
Showing the Conductance Quantum is G_0 = 2e^2/h = 7.74*10^-5 S is the same constant as Magnetic Permeability 1.256*10^-6 H/m.
--- end quoting in parts from my 121st published book of science ---
--- quoting in parts from my 174th published book of science ---
TEACHING TRUE PHYSICS, 2nd year College
by Archimedes Plutonium
Preface: At the moment this is a physics book for 2nd year College. But as the months and years go by, I intend to convert it into a textbook of about 200 to 300 pages. It is mostly about thermodynamics for in my own college education 1968-1972 at University of Cincinnati, I took physics thermodynamics in the 2nd year (according to memory).
Cover-Picture: Is a iphone photograph of the Chemistry textbook I used at UC 1968-1972 with my own paper cut-outs of magnetic monopoles. Pictured are 4 bent circles, bent at 90degrees from diameter and each bent circle is a individual magnetic monopole.
--------
Conductance Quantum is G_0 = 2e^2/h = 7.74*10^-5 S
Boltzmann's constant is 8.617*10^-5 eV/K
Magnetic Permeability in vacuum constant is 1.256*10^-6 H/m
--- end quoting my 174th published book of science ---
When I wrote my 174th book of science on thermodynamics I was rather struck with and fascinated that the speed of light comes from the Maxwell Equations in the formula of c^2 = 1/(permeability* permittivity). Using Old Physics value for light speed "c" as 3*10^8 meters/second. Carefully as we plug into that formula, sure enough it works out equal on both sides of the equation.
And I wrote the 174th book in February 2022, and only now by October 2023, am I fully in appreciation of that formula c^2 = 1/(permeability*permittivity). As I write my 260th book of science as this List-of-Physics-and-Math-constants.
I was really not happy and satisfied with my so called derivation of Boltzmann's constant in my 121st book, citing the sigma error as a missing factor of 5.6% plus another 5.6% by using speed of light as 3.16 rather than 2.99*10^8 meters/second.
So let me derive what I feel is the correct and true Boltzmann constant.
What if we take c^2 = 1/(Boltzmann * unknown) considering heat is merely photonic energy infrared.
Here I am saying that Boltzmann constant is the analog of permeability constant, and all I need is to look for a analog of a permittivity type of constant.
(3*10^8)^2 = 1/ (8.6*10^-5)(unknown)
9*10^16 (unknown) = 1/(8.6*10^-5)
unknown = 0.11*10^5 / 9*10^16
unknown = 11*10^3 / 9* 10^16
unknown = 1.22 * 10^-13
There is a constant in connection to Boltzmann's constant called the Thermal conductance quantum.
Thermal conductance quantum 9.46*10^-13 W/K^2. It has the correct exponent value of -13. However its prefix number value of 9.46 is not near 1.22. Even the inverse of 9.46 of 1/9.46 is not close enough at 0.105 which would also throw the exponent off.
Now Electric Permittivity in vacuum is 8.85*10^-12 F*m^-1.
And based upon c^2 = 1/(permeability*permittivity).
Archimedes Plutonium
Oct 5, 2023, 3:38:09 PM
to Plutonium Atom Universe
I am in the process of revising and correcting the Boltzmann constant.
I can see better now on this derivation. The key is that Thermodynamics and Heat are part of EM theory as specialized part of EM theory.
There is another constant that is analog to Boltzmann, just as permeability is analog to permittivity. Those two are seen in the equation c^2 = 1/(permittivity*permeability)
Likewise we should see a similar equation for Boltzmann constant in the form of
c^2 = 1/(Boltzmann constant*another constant)
At the moment I am playing around with this constant-- Thermal conductance quantum 9.46*10^-13 W/K^2
Thermodynamics, is after-all a specialized portion of the EM spectrum.
Archimedes Plutonium
Oct 5, 2023, 3:55:22 PM
to Plutonium Atom Universe
To prove me correct on this derivation of Boltzmann's constant that there is another set of constants further up in the EM Spectrum scale.
So that the equation c^2 = 1/(permeability*permittivity) has a thermodynamic equation for the Infrared region of the Spectrum as c^2 = 1/(Boltzmann constant * another constant). And this other constant may not yet be discovered. Although the Thermal conductance quantum 9.46*10^-13 W/K^2 is very much close in value to this other constant that is the analog-- or should I say dual, quantum dual to Boltzmann constant.
Now to check on whether I am on the correct way of derivation, this dual analog should be repeated in the EM Spectrum near the X-ray or Gamma ray region of the Spectrum.
Where we should have a similar situation of c^2 = 1/(something * another thing). Perhaps near the phenomenon of Pair Production.
So we would end up with three phenomenon in 3 different regions of the EM Spectrum. We would have c^2 = 1/(permittivity*permeability) and I view that as the Visible Region. Then the Infrared Region is taken up with thermodynamics and Boltzmann's constant the analog of permeability. Finally we have a new third region as yet discovered by modern day physics. A region I suspect is in the X-ray to gamma ray region. Or, well, it could be in the Radio wave region, or both.
So this would be fantastic new discoveries in EM theory.
Now, I really have not derived Boltzmann's constant but only hypothesized that there is another constant dual to Boltzmann with number values near 1.22 * 10^-13. I await research news to prove me correct.
19) Planck's constant.
I count my derivation of the Planck's constant as the most beautiful derivation in this entire book. How angular momentum units in Planck's constant derives from the passage of time and the increase in atoms created from Faraday law. And the cover picture of this book is a picture of passage of geological time of 140,000,000 years.
The Planck constant is in angular momentum units of ML^2T^-1, the quantum of action. It is one of the most important constants in physics.
And my purpose of deriving it, is to see if I can bring clarity to its meaning.
Newsgroups: sci.math
Date: Fri, 10 Apr 2020 11:47:40 -0700 (PDT)
Subject: 109th book of AP// The ultimate meaning of Planck’s constant and Fine-Structure-Constant
From: Archimedes Plutonium
> Alright on 9APR2020, AP discovered the New Physics Planck’s constant from the math technique of Divisional Inverse.
The Divisional Inverse Technique is what one can think of as being-- a Physics Constant in the large scale as in astronomy or physics at large, has the same physics constant on the microscope scale. For example, the time it takes for a hydrogen atom to reproduce itself by its muon thrusting through its proton of 840 windings (proton is 840MeV) as a torus coil in Faraday law is 132,000,000 years which in seconds is 1.32*10^8 * (3.1*10^7) = 4.1*10^15 seconds. And thus, the discreteness of the Atom in Planck's constant is 4.1*10^-15 eV*seconds. Special note:: AP gets 3.1*10^7 as the amount of seconds in a single year.
Deriving Planck's constant from the mere idea of the doubling of hydrogen atom systems.
Planck's constant is 4.1*10^-15 eV*seconds.
The Divisional Inverse of Planck's constant is 4.1*10^15, numerically. And when you multiply 1.32 *10^8 years by 3.1*10^7 seconds in a year you get 4.1*10^15.
April 2024 add-on detail of Planck's constant being 4.135*10^-15 eV*second. For in the course of writing my 294th book of science on the existence of a 6th Regular Polyhedron-- which in fact is the sphere itself for in Quantum Mechanics Physics, geometry is discrete, not a continuum. I wrote this in my 294th book but the facts of Planck's constant from this book is used.
What is the smallest quantity of microscopic regular hexagons to craft a sphere = 6th regular polyhedron?
Archimedes Plutonium
Apr 30, 2024, 1:31 AM
to Plutonium Atom Universe newsgroup
Re: AP proudly announcing his 294th published book of science-- My 294th published book of science. The sphere in geometry is actually the 6th Regular Polyhedron-- hexagonal faces at infinity // Math proof by Archimedes Plutonium
Now Planck's constant is this-- 4.135*10^-15 eV*second. Most scientists are not accustomed to seeing Planck's constant in EM form, and it is h= 4.135*10^-15 eV*second.
Now the surface of a sphere follows the formula of 4 pi r^2 while volume follows the formula 4/3 pi r^3.
Now what is (4/3)pi equal to?? It is (1.3333...)(3.1415....) = 4.188....
Now let us take the Sigma Error of 4.135 and 4.188 and we have 4.188/4.135 and we have a sigma error of 1.2%. Now take the Sigma Error of surface area of 4 versus 4.188 and we have 4.188/4 = 4.7%.
Actually both are acceptable as saying the prefix of Planck's constant equals the prefix numbers of surface area of sphere and volume of sphere prefix numbers.
Being acceptable simply means I do not have to go out to the Infinity Borderline of 1*10^-604 in order to determine how many regular hexagons in quantity and in size. I do not have to use exponents of 603 or 604 but can use exponents of Planck's constant of 15 and 16.
So, say I wanted to tile the sphere to be a Regular Polyhedron all faces as regular hexagons. Then I can use the regular hexagon size to be that of 10^-15, and I will need 4*(3.1415) = 12.56*10^15 such regular hexagons to completely tile a sphere of radius 1. Please check these figures for mistakes.
I need to include this also in my book on constants, my 260th book of science, as to keep that book updated. List this under Planck's constant. "A list of discovered and derived constant-relationals of Physics and Mathematics// math-physics"
by Archimedes Plutonium, my 260th book of science.
y z
| /
| /
|/______ x
Most scientists are not accustomed to seeing Planck's constant in EM form, and it is h= 4.135*10^-15 eV*second, or, h-bar = 6.58*10^-16 eV*second. In my above analysis, what I have derived is Planck's constant from the mere idea of the doubling of hydrogen atom systems, every 132,000,000 years via the Faraday law of a muon thrusting through its proton coil torus producing electricity which after 132 million years duplicate that hydrogen atom. The Planck constant is a rate of duplication of hydrogen atoms in the universe.
So where do I get 132,000,000 years? I get it from biology and geology.
The Faraday Law inside of each atom is a doubling over time of that same atom of hydrogen. So at t_0 we have one atom of hydrogen and at t_1 we have 2 atoms of hydrogen, and at the same interval of time t_2 we doubled the 2 to be 4 now. So a doubling in physics. So we write out a chart.
Number of Hydrogen atoms Doubling time interval Math form
1 t_0 2^0
2 t_1 2^1
4 t_2 2^2
8 t_3 2^3
16 t_4 2^4
32 t_5 2^5
. . .
. . .
1,073,741,824 t_30 2^30
2,147,483,648 t_31 2^31
4,294,967,296 t_32 2^32
Now I stop there because it is nearby to the total time covered of 4,500,000,000, the 4.5 billion years.
And here is where I divide that time of Earth existence by the number 32 in order to get what the doubling time interval is all about.
4,500,000,000/ 32 = approximately 140,000,000, the 140 million years.
So my time interval in Nature for a hydrogen atom to double itself by Faraday law electricity going on inside the hydrogen atom is approximately 140 million years of a time interval. Every hydrogen atom in Nature, in the Universe doubles itself in 140 million years.
Later, I would see that the number is closer to 132,000,000. And that 140,000,000 was a crude first estimate.
Newsgroups: sci.physics,sci.math,plutonium-atom-universe
Date: Thu, 9 Apr 2020 13:59:54 -0700 (PDT)
Subject: So, what Bohr missed in his model, is the true electron is the muon
and stuck inside a proton which is a torus coil doing the Faraday Law. That
produces electricity, quantized electricity, and in that production, every
132,000,000 years
From: Archimedes Plutonium
So, what Bohr missed in his model, is the true electron is the muon and stuck inside a proton which is a torus coil doing the Faraday Law. That produces electricity, quantized electricity, and in that production, every 132,000,000 years
On Thursday, April 9, 2020 at 2:14:16 PM UTC-5, Archimedes Plutonium wrote:
>
> Newsgroups: sci.math, sci.physics, plutonium-atom-universe
> Date: Thu, 9 Apr 2020 12:03:58 -0700 (PDT)
> Subject: Yes, today, AP finds a second Planck's constant that is far more
> meaningful than Max Planck's constant of year 1900. A 120 years after Max
> Planck, does AP find a better constant, because its meaning is completely
> visible to the mind
> From: Archimedes Plutonium <plutonium...@gmail.com>
> Injection-Date: Thu, 09 Apr 2020 19:03:58 +0000
>
> Yes, today, AP finds a second Planck's constant that is far more meaningful than Max Planck's constant of year 1900. A 120 years after Max Planck, does AP find a better constant, because its meaning is completely visible to the mind
>
Yes, a new first in math and science, for we are all familiar with a multiplicative inverse, but no-one ever paid attention to a Divisional Inverse. That is what AP was faced with on 8APR2020. For seeing that Planck's constant was 4.1*10^-15 eV*seconds. Then AP converting the duplication of Faraday Law inside of atoms, is 140,000,000 years, converting that to seconds is 4.3*10^15 seconds.
So, a first in all of science, math and physics. What is the divisional inverse of 4.3*10^15? And the answer is 4.3*10^-15.
This is the first time in the history of science that the Divisional Inverse is so super important.
For it is plain to see that this Faraday Law Production of Electricity is the Planck's constant of Old Physics.
Now the interpretation of Planck's Constant, of course, well Max Planck interpreted as a Quantization of the World at the atomic level there is no continuum but a Discrete world. And Max Planck has a correct interpretation, even today with AP resolving it further. But a another interpretation of Planck's constant that became more famous than Planck's interpretation is the Bohr model of the inside of atoms, where Bohr interpreted the constant as meaning that electrons as little balls change orbits and emit energy as they change **only specific orbits** giving a discrete quantized energy. Unfortunately Bohr's model is all wrong, but still Planck's discrete interpretation is correct but not fulfilling of an explanation. If Bohr had said the true electron was the muon thrusting inside its proton coil of torus, producing magnetic monopoles and electricity. And it is these magnetic monopoles and electricity that is quantized.
My number of 140,000,000 years is the time that each and every atom in the entire Universe takes to create a new atom identical to itself via Faraday Law. It is the Planck constant. The Planck Constant is the time it takes for a given atom to reproduce itself via the Faraday Law, only the inverse.
> On Thursday, April 9, 2020 at 3:16:50 AM UTC-5, Archimedes Plutonium wrote:
> > H-bar is 6.5*10^-16 eV*sec
> >
> > Terribly close to that of 2*10^-16 inverse time to duplicate a arbitrary atom via Faraday law. Let us say they are the very same number for it is easy to tweak the number 140,000,000 years to make equality. What extraordinary deduction can be made if equal? What it would mean is that the ultimate meaning of Planck’s constant is it is the “cosmic rate of production of new mass and energy via Faraday’s law of muon thrusting through proton inside each and every atom.” It would take the vagueness out of Old Physics understanding of Planck’s constant.
>
>
> A day ago I wrote this:
>
> So, I am looking for connections, connections to 140,000,000 years as the time for any arbitrary given atom to double in size, and thus double in number, from Faraday Law going on inside them of muon thrusting through proton torus coil. To 10^40/ 10^32 as the number of planets with intelligent life. Both are a form of 10^8. Where 10^40 is the gravity force strength compared to EM. And, 10^32 is either Planck's constant 4.1*10^-15 eV*sec squared or is the total quantity of cells+viruses on Earth.
>
> Now in that 1.4*10^8 years let me reduce that to seconds by multiply 60*60*24*365 = 3.1*10^7. So that is 1.4*10^8 (3.1*10^7) = 4.3 *10^15 seconds and the inverse would be 2*10^-16 inverse seconds which one can say is physically a frequency. And that number is smack in the middle of first radiation constant and first radiation constant for spectral radiance.
>
> Planck's Constant is 4.1*10^-15 eV*second commonly called H
>
> Now up until today I had thought that mathematically speaking given any number there is one and only one inverse. A multiplicative inverse is what I had always known. But today I realize the world has a divisional inverse. I am probably the first person in math and science to note that there are two different types of inverses. There is the multiplicative inverse such as 137 versus 1/137, but, there is a division inverse so that for 137, the division inverse is just 137.
>
> Now, most would say, why even bother, for any number is its divisional inverse.
>
> And this is probably why the world never saw a divisional inverse.
>
> Some months back I resolved the fact that the Faraday Law inside of atoms of its muon thrusting through its proton yields electricity that when this activity goes on for 140,000,000 years, that the atom in question doubles itself from that electricity produced. And, further, if I multiply those years by a conversion to seconds, the number I achieve is 4.3*10^15 seconds.
>
> See any resemblance between 4.3*10^15 sec and Planck's constant at 4.1*10^-15 eV*sec. They are virtually the same numbers if I did a Divisional Inverse on 4.3*10^15, for a divisional inverse is 4.3*10^-15.
>
> Now, what is the Sigma Error of 4.3 versus 4.1? That would be 4.3/4.1 = 4.8%
>
> In science, is a Sigma Error of less than 5% acceptable as being equal?
>
> Well, what if I said the true years is not 140,000,000 but rather is 135,000,000, then my seconds for a atom to reproduce and double itself is 1.35*10^8 (3.1*10^7) = approx 4.2. What I am saying here, is that it is reasonable to think that the 140,000,000 years figure is not as well tuned as the Planck's constant is well tuned experimental number.
>
> So, given the above analysis, AP declares he has found a second Planck's Constant. A more meaningful Planck's constant than even what Max Planck found in the year 1900. For the AP Planck constant ties directly into the Cosmic Faraday Law that the inside of atoms are a Faraday law going on, of its muons and protons producing electricity that will double the number of atoms given 135,000,000 years.
>
> Yes, today, AP finds a second Planck's constant that is far more meaningful than Max Planck's constant of year 1900. A 120 years after Max Planck, does AP find a better constant, because its meaning is completely visible to the mind.
>
So, let us assume that Planck's constant is the most accurate number, derived from experiment as 4.1*10^-15 eV*second. And we want the time of atom-self reproduction to be as accurate. Simple. What we do is set up a proportionality equation and have
Y x 3.1*10^7 =4.1*10^15 and solve for Y
So we have 4.1*10^15 / 3.1*10^7
And I get 1.32*10^8 years instead of my 1.4*10^8 years.
This is fun and pretty and beautiful, that quantum physics has now ventured into explaining why dragonflies of the Devonian geological time period could grow so large in size, because Earth doubles its mass every 132,000,000 years. And the Earth at the time of the Devonian was 1/2x1/2x1/2 = 1/8 the mass Earth is today and with such weak gravity, dragonflies could grow huge in size.
So, what Bohr missed in his model, is the true electron is the muon and stuck inside a proton which is a torus coil doing the Faraday Law. That produces electricity, quantized electricity, and in that production, every 132,000,000 years every atom reproduces itself completely.
But, does this new discovery help in my quest of Reincarnation science? Well, it surely does not hurt for you cannot discover a higher science if you do not have a "lower science" straightened out.
The method of DIVISIONAL INVERSE is key here. For now I look for the divisional-inverse of 10^32 and 10^40 and 10^8 in other physics constants.
AP
20) Biology time constant, 1.4*10^8.
The Faraday Law inside of each atom is a doubling over time of that same atom of hydrogen. So at t_0 we have one atom of hydrogen and at t_1 we have 2 atoms of hydrogen, and at the same interval of time t_2 we doubled the 2 to be 4 now. So a doubling in physics. So we write out a chart.
Number of Hydrogen atoms Doubling time interval Math form
1 t_0 2^0
2 t_1 2^1
4 t_2 2^2
8 t_3 2^3
16 t_4 2^4
32 t_5 2^5
. . .
. . .
1,073,741,824 t_30 2^30
2,147,483,648 t_31 2^31
4,294,967,296 t_32 2^32
Now I stop there because it is nearby to the total time covered of 4,500,000,000
And here is where I divide that time of Earth existence by the number 32 in order to get what the doubling time interval is all about.
4,500,000,000/ 32 = approximately 140,000,000
So my time interval in Nature for a hydrogen atom to double itself by Faraday law electricity going on inside the hydrogen atom is approximately 140 million years of a time interval. Every hydrogen atom in Nature, in the Universe doubles itself in 140 million years.
21) Theory of Nines.
I need also to include the theory of nines into this list. The idea that the summation of digits of a number when a factor of 9 is special. I still do not fully understand this phenomenon. I do understand that a string of 9s greets a new scale number of 1 followed by zeros such as 999 before 1000. And it appears to have something to do with angles as 90, 180, 270, 360, 450, 540, 630, 720, 810, 900, 990, 1080, etc etc.
Archimedes Plutonium
Oct 11, 2023, 3:07:35 PM
to Plutonium Atom Universe
The theory of nines is very amazing and dazzling. I have yet to fully understand it.
It is of course the adding of the digits of a number to see if the sum adds up to a factor of 9.
And then the amazing aspect is that any such number, for example the Fibonacci sequence number 144, is divisible by 9.
So now I play around with this idea experimenting to see if all such numbers are divisible by 9.
801 is
8001 is
1233 is
3213 is
3312 is
3321 is
Yet any other such sum of digits if not a sum of 9 or a factor of 9 no longer has that ability of division.
For example try sum of 6
231 is not factored by 6
132 is factored by 6
312 is factored by 6
So, maybe there are counterexamples to Nines theory, for which I have just not yet found.
Archimedes Plutonium
Oct 11, 2023, 11:37:08 PM
to Plutonium Atom Universe
Let me try combinations, see if I can pull up a counterexample.
417582 is a factor of 9 46,398
So, time for a conjecture here.
Conjecture: given any whole number if its digits add up to a factor of 9, then the entire number is evenly divisible by 9 and it is only the 9 number that has that ability, characteristic, not 2, 3, 4, 5, 6, 7, 8 in Decimal Number System.
If true may also lead to another proof that Decimal System is superior to any other base system.
And if true leads me closer to an idea of why Theory of Nines, Theory of 9s is important to math and physics.
The idea is that 9 is just before we reach the last whole number in a Decimal Grid System. The 9 or 9.9 for 10 Grid, the 99, or 99.99 for 100 Grid etc etc. And so 9s serves as a Borderline for number systems. As if the last number of a system is the infinity border between the last 9s number in that system. So for example, 9.9 is the finite borderline and then 10 is infinity in 10 Grid. And 99.99 is the finite borderline in 100 Grid before reaching infinity number 100 in 100 Grid.
As for physics, the 9.9,99.99, 999.999, 9999.9999, sequence is a curvature angle, a bending around of a circle or ellipse. So in 10 grid, 10 is 0 and 9.9 is like -1. In 100 grid, 100 is like 0, and 99.99 is a bending around into a circle where 99.99 is like -1 ready to jump off onto 0 as 100. This is commonly known as p-adic theory in mathematics. And so theory of 9s appears to take parts of p-adic theory.
Archimedes Plutonium
2:20 PM, 12Oct2023
to Plutonium Atom Universe
Let me try 11,111,111 is not evenly divisible by 9
Trying 111,111,111 is evenly divisible by 9
What about 1111111101 is evenly divisible by 9
What about 11111111001 is evenly divisible by 9
In the entire history of mathematics, this is likely the strangest theory of all, yet so simple in explanation-- if the digits add up to a factor of 9, then the division is evenly divided by 9.
We easily learn of angles 90, 180, 270, 360 are theory of nines. And as we divide by 2 or multiply by 2, we retain the theory of nines.
And I am going to conjecture that the theory of nines is a specific proof that decimals are the unique number system for all of mathematics, binary, base 2 or ternary base 3, or any other base cannot do mathematics, only decimal system can do mathematics.
This is a far far cry from Old Math with their Reals, their continuity and continuum, and their belief that decimals are nothing special.
Archimedes Plutonium
Oct 13, 2023, 2:57:45 AM
to Plutonium Atom Universe
Unfortunately this has become my 260th book of science, for I am stalled by entrees into this book. It has taken me far longer to complete this book than first expected, and the book looks as though it may reach 100 pages. So I published my solution on the Israeli-Palestinian Conflict tonight and have pushed this book up in the queue-line to be 260th.
Talking more about the mysteries of the 9 number. There is another number in mathematics that has this property of addition similar to multiplication. And perhaps this other number can shed light on theory of Nines.
This number is of course the number 2 in connection to 4. 2 is the only number where 2x2 equals 2+2. So in a sense 9s is addition of digits of a number and is connected with division by 9. 2 is addition and connected with multiplication. And 2 is just 1 above 1, while 9 is 1 below 10.
So can this help ease the mysteries of Nines?
Archimedes Plutonium
Oct 13, 2023, 3:21:17 PM
to Plutonium Atom Universe
Yes indeed this is my 260th book for I was not aware that it would be a 100 pages or more. And with new discoveries.
The theory of Nines is a neglected topic in Old Math for they saw it as numerology and not even math. So much of the theory of Nines is brand new to mathematics and I am going to be a pioneer of this new topic.
And the Fibonacci Sequence was not seen as a major math topic by Old Math. It is massive and hugely important, for it is calculus in 2D geometry. The Fibonacci Sequence brings together the three important numbers of 1.618... 2.71828.... and 3.14159..... along with 3.162277.... and probably more important numbers once the wind and rain settles down.
As to Theory of Nines I want to see the sequence with starting with 9.
9, 9, 18, 27, 45, 72, 117, 189, 306, 495, 801, 1296, . . .
And yes, all the members are Nines summed digits.
Now I need to know how many members of the 100 Grid are covered by the 10 Grid?
1,1,2,3,5,8,13,21,34,55,89
2,2,4,6,10,16,26,42,68
3,3, ...
4,4, ...
5,5, ...
6,6, ...
7,7, ...
8,8, ...
9,9, 18,27,45,72,
10,10, 20,30,50,80
So I am going to see what numbers in 100 Grid are produced by 10 Grid and see if that ratio is a important number also. For 1 yields 10 members, while 10 yields only 4 new members. I am betting it yields 27 or 31.
Archimedes Plutonium
Oct 13, 2023, 10:08:22 PM
to Plutonium Atom Universe
1,1,2,3,5,8,13,21,34,55,89
2,2,4,6,10,16,26,42,68
3,3, 6,9,15,24,39,63
4,4, 8,12,20,32,52,84
5,5, 10,15,25,40,65
6,6, 12,18,30,48,78
7,7, 14,21,35,56,91
8,8, 16,24,40,64
9,9, 18,27,45,72
10,10, 20,30,50,80
So, the 10 Grid in Fibonacci sequence gives me 1,2,3,4,5,6,7,8,9,10, no 11, 12,13,14,15,16, no 17, 18, no 19, 20
21, no 22, no 23, 24, 25, 26, 27, no 28, no 29, 30, no 31, 32, no 33, 34,35, 39,40, 42, 45, 50, 52, 55, 56,63,64,65,68,
72,78,80,84,89,91
I count 44 generated numbers.
Numbers 0,1,2,3,4,5,9,10 to uniquely form a Decimal number representation system.
Archimedes Plutonium
4:16 PM, 14Oct2023
to Plutonium Atom Universe
Alright that was yesterday, and today is 14Oct2023.
There is a smaller grid system than the 10 Grid but it is rather a useless system of the 1 Grid. Useless until moments like this.
The 1 Grid system accounting of the 10 Grid in Fibonacci sequence would be this.
1,1,2,3,5,8
And so we see that a 1Grid accounting of a 10 Grid is 1,2,3,5,8
Above we saw that a 10 Grid accounting of 100 Grid yielded a 44% coverage.
We see that a 1 Grid accounting of 10 Grid is 50%.
And here is where I make use of that, to find a convergence point of the Sequence of Grids accounted for by a N/10 lower Grid. So far this sequence goes like this.
Sequence on Grids:: 50%, 44%, ......
What is the percentage of coverage of the 1000 Grid by the 100 Grid??
Now AP is starved of time and is unwilling to take all 100 counting numbers plugged into the Fibonacci sequence to find out that next percentage.
So here I ask computers to solve the first four percentages after my above 44%.
I am going to guess that the sequence converges closer to 44% than to 50%. And I may even have made a mistake in the 10 measuring 100 Grid. It maybe I missed a count and is actually 45%, not 44%?
Archimedes Plutonium
9:42 PM, 14Oct2023
to Plutonium Atom Universe
On Saturday, October 14, 2023 at 1:41:37 AM UTC-5, Archimedes Plutonium wrote:
> On Saturday, October 14, 2023 at 1:09:57 AM UTC-5, xxxxx wrote:
> > On 10/12/2023 12:36 AM, Archimedes Plutonium wrote:
> >
> > > Conjecture: given any whole number if its digits add up to a factor of 9, then the entire number is evenly divisible by 9 and it is only the 9 number that has that ability, characteristic, not 2, 3, 4, 5, 6, 7, 8 in Decimal Number System.
> > This has been known pretty much since the adoption of the decimal system.
> > >
> > > If true may also lead to another proof that Decimal System is superior to any other base system.
> > No, not unique to the decimal system. For any base N, the digits of a
> > number expressed in Base N will (recursively) add up to N-1 if it is
> > divisible by N-1. For example, in Base 16, if all the digits of a number
> > expressed in Base 16 are divisible by 15 (F in Base 16, if using the
> > usual convention of digits 0-9A-F). For example, 45 is 2D in Base 16.
> > 2+D=F (15), so 2D (45) is evenly divisible by 15.
> >
> > It also works for factors of N-1. If adding the digits in Base 16 add up
> > to 5, A or F, it is a multiple of 5, and 5 is a factor of 15 (F). Also
> > if the digits add to 3, 6, 9, C or F it is a multiple of 3, a factor of
> > 15 (F).
> >
> > This also works for the decimal system (N=9), if the digits add up to 3,
> > 6 or 9, it is a multiple of 3, since 3 is a factor of N-1 which is 9.
> >
> The screwball math written above has no merit.
>
> The best proof that decimal system is unique to true numbers, and no other system can cope, is the fractions.
>
> Only fractions such as 0.5 in decimals which is 1/2, or 1/3 as 0.333... can negotiate arithmetic of math. A binary or ternary or base 4, base 5 etc cannot handle fractions without gaps in arithmetic.
>
> What the theory of Nines does for that proof of fractions is bolster it even higher. For example 81.7245 or 81.2457 is superfluous where the decimal point is located. But in base 2, base 3, base 4, whatever, except base 10, is halted and thwarted in this systems.
>
> AP
The theory of Nines highlights the fact that Decimals are the only legitimate representation of numbers of mathematics.
Archimedes Plutonium
9:45 PM, 14Oct2023
to Plutonium Atom Universe
In AP's 260th book// Only the Decimals form a valid Arithmetic & Math Number System-- Binary, Ternary, base 4, base 5, etc all fail except Decimals
Now my proof many many years back, perhaps decades ago, that the Decimal System is the only number system that is legitimate is a proof based on the fact that only Decimals can deliver representation of Fractions along side the inverse counterpart. For example, only Decimals can represent fully every fraction along with its inverse counterpart-- 1/3 as compared to 3, or 1/2 as compared to 2, or 1/11 as compared to 11.
It is easy to see that other base systems can yield the Counting Numbers, that is easy to recognize. But the troubles start when these other systems try to represent Fractions, with their pock mark holes inability to represent all fractions.
Essentially that was the proof that Decimals are the only unique representation of numbers while other bases fail. For they find it impossible to represent all the fractions. Decimals are unique in that accord and it has to do also with that Decimals are unique to Scientific Notation.
Now in this post I want to discuss more about why 10 base is so unique and why all other bases fail.
To form a base, a number base has to be able to handle all Fractions and to handle numbers like pi = 3.14159.... or phi = 1.618..... or exponent base 2.71828....
The reason only Decimals is that it is a system constructed of 1 and zeros such as 1, 10, 100, 1000, etc
And from 1 to 10, it has composition of 2x5 =10 so that 1/2 is 0.5 and composed of 1+9 = 10 where 9 is 3*3. Also it has 4 the product and sum of 2, 2+2, 2*2 = 4.
In biology, humanity has 10 fingers, each hand has 5 fingers on 2 hands, 2*5= 10. It takes 10 fingers for the dexterity in experimentation and building electrical machines that can harness electricity, fly to the Moon and build Atomic bombs. You need a opposable thumb to the other 4 digits on the hand.
If humanity were binary or ternary or base 4 or base 5 or base 6 etc etc, we would not have built the bomb, flown to the Moon or have electric power stations.
Base 10 is the only base that has no holes to represent every number below 1 with every counting number C such that 1/C is represented.
22) 0.256 constant.
Archimedes Plutonium
Sep 30, 2023, 11:22:15 PM
to Plutonium Atom Universe
Alright, I have taken the Fibonacci sequence out to 2584.
1,1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711....
Now I divide every fourth number into that number, such as 610/2584 = 0.2360.... And apparently, at infinity it converges to this number 0.2360....
But the number I am interested in is the number 0.256000..... For if the Rectangle of Whirling Squares of Fibonacci Sequence were such that every fourth number divided into this number then the log spiral would close and not be a open spiral. So, 5/21 and 8/34. If that had been 5/20 instead of 5/21, then the squares would close the curve, same goes for 8/32, in fact we can drop to 8/31 and it would close.
I see the Rectangle in Whirling Squares as a calculus on 2D, and perhaps the most elementary calculus of curved figures. Of course the straight line geometry Y --> mx + b is elementary calculus on straightline figures.
Archimedes Plutonium
Oct 1, 2023, 12:53:17 AM
to Plutonium Atom Universe
Alright, now I am playing tricks on the Fibonacci sequence to see how I can get the numbers 94, 231, possibly 840 or 945.
So I make a slight modification by subtracting 1 in each turn. This sequence then becomes 2,2,3,4,6,9,14,22,35,56,90,145, 234,.... and what is the rate of curvature? It is not 0.2560000 but rather 56/234 = 0.2393.... Is it still an open curve or is it closed???
23) Infinity borderline and algebraic completeness of borderline.
I was challenged in year 2009 by someone in sci.math to make a borderline for finite numbers and above would be infinite numbers. I gladly accepted the challenge. And so I utilized Huygens's tractrix to fetch out this borderline. It is where pi digits have 3 zero digits in a row that the area under the tractrix graph equals for the first time the area of the associated circle. This equalization of area is the infinity borderline.
But I took that borderline to be a scale number 1*10^604 with its algebraic completeness at 1*10^1208. But to this day, I sometimes think I should have taken all the pi digits also, rather than a scale number of pure 1 and all the rest zeroes.
Maybe in the end, it is both, and use both depending on what applications are needed.
Concept that Infinity = a borderline between finite and infinite was discovered by AP 2009. Simple beautiful idea-- there must be a borderline between finite and infinite, otherwise, all is just one and the same, and not two different concepts. And so I defined the concept of infinity itself as this border crossing.
Borderline between finite and infinity
Now this mistake in not having a correct Infinity in math, affects the Calculus by a large measure, a large degree. It is impossible to have a correct calculus, when you have a bozo-kook understanding of what is infinity.
This is probably the biggest mistake in all of pure mathematics for it
affects all other mathematics. Of course the other sciences, especially physics rarely needs to know what the correct proper infinity is. However, it does show up frequently in the best physics-- quantum electrodynamics, in which it is
often used to eliminate infinities that crop up in calculations. This physics math procedure is called Renormalization-- getting rid of the infinities.
The trouble with Old Math, is, well, they were terribly shoddy in logic, in thinking straight and clear. For a logical person, knows, that if you have a concept of finite versus infinite, the only way to handle those two concepts is to realize a border must go between them so that you can tell if any given number is finite or infinite. Otherwise, there is no infinity, if there is no borderline.
There is only one way you can have a concept of finite, by having a
concept of infinity, and the only way you can have both, is that a
borderline exists between them.
I have pinpointed that borderline from tractrix-circle analysis, from
algebraic analysis of algebraic completeness, and from angles of
regular polyhedra. The borderline in micro-infinity is 1*10^-604 and in
macro-infinity is 1*10^604.
The easiest way to see the borderline is to see where pi digits ends in a three zero digits in a row.
Applied to 1*10^1208, the Algebraic Completeness of the infinity borderline of 1*10^604.
50 per line.
3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510
58209 74944 59230 78164 06286 20899 86280 34825 34211 70679
82148 08651 32823 06647 09384 46095 50582 23172 53594 08128
48111 74502 84102 70193 85211 05559 64462 29489 54930 38196
44288 10975 66593 34461 28475 64823 37867 83165 27120 19091
45648 56692 34603 48610 45432 66482 13393 60726 02491 41273
72458 70066 06315 58817 48815 20920 96282 92540 91715 36436
78925 90360 01133 05305 48820 46652 13841 46951 94151 16094
33057 27036 57595 91953 09218 61173 81932 61179 31051 18548
07446 23799 62749 56735 18857 52724 89122 79381 83011 94912
98336 73362 44065 66430 86021 39494 63952 24737 19070 21798
60943 70277 05392 17176 29317 67523 84674 81846 76694 05132
00056 81271 45263 56082 77857 71342 75778 96091 73637 17872
Notice the 3 zeros in a row at 601,602,603 place value-- this is the infinity borderline.
14684 40901 22495 34301 46549 58537 10507 92279 68925 89235
42019 95611 21290 21960 86403 44181 59813 62977 47713 09960
51870 72113 49999 99837 29780 49951 05973 17328 16096 31859
50244 59455 34690 83026 42522 30825 33446 85035 26193 11881
71010 00313 78387 52886 58753 32083 81420 61717 76691 47303
59825 34904 28755 46873 11595 62863 88235 37875 93751 95778
18577 80532 17122 68066 13001 92787 66111 95909 21642 01989
38095 25720 10654 85863 27886 59361 53381 82796 82303 01952
03530 18529 68995 77362 25994 13891 24972 17752 83479 13151
55748 57242 45415 06959 50829 53311 68617 27855 88907 50983
81754 63746 49393 19255 06040 09277 01671 13900 98488 24012
85836 160
Notice the single zero in the 1208 place value which is the algebraic completeness of infinity borderlines. It is also where geometry figures are evenly divisible by 6 factorial = 720.
Compare that with the digits of square root of 10.
50 per line.
3.16227 76601 68379 33199 88935 44432 71853 37195 55139 32521
68268 57504 85279 25944 38639 23822 13442 48108 37930 02951
87347 28415 28400 55148 54885 60304 53880 01469 05195 96700
15390 33449 21657 17925 99406 59150 15347 41133 39484 12408
53169 29577 09047 15764 61044 36925 78790 62037 80860 99418
28371 71154 84063 28552 99911 85968 24564 20332 69616 04691
31433 61289 49791 89026 65295 43612 67617 87813 50061 38818
62785 80463 68313 49524 78031 14376 93346 71973 81951 31856
78403 23124 17954 02218 30804 58728 44614 60025 35775 79702
82864 40290 24407 97789 60345 43989 16334 92226 52612 06779
26516 76031 04843 66977 93756 92615 57205 00369 89490 94694
21850 00735 83488 44643 88273 11092 89109 04234 80542 35653
40390 72740 19786 54372 59396 41726 00130 69900 00955 78446
31096 26790 69441 83361 30181 30289 45417 03315 80773 16263
86395 19379 37046 54765 22063 20636 86587 19782 20493 12426
05345 41116 09356 97982 81324 52297 00079 88835 23759 58532
85792 51362 96468 65114 97675 21712 34595 59238 03937 56251
25369 85519 49553 25099 94703 88439 90336 46616 54706 47234
99979 61323 43403 02185 70521 87836 67634 57895 10732 98287
51579 45215 77165 21396 26324 43839 90184 84560 93576 26020
31676 80424 07958 94693 42478 14145 80651 43045 33258 89714
46769 31113 75924 04705 07701 85460 43927 21283 58941 92143
79843 26343 22941 00698 41773 83356 07269 11107 12554 92745
61841 70775 86544 42076 02567 83418 20374 14829 45546 15347
20993 41059
Now this book is mostly a listing of previous work I have done. A listing of constants and not much new, except for the idea of the question which is the infinity borderline?? Is it 3.14...*10^604 or is it 1*10^604 the perfect scale number?? Is it the pi digits in the Huygens tractrix that found the infinity borderline or is it the perfect scale number at that place value??
When I discovered the infinity borderline in 2009, I made it easy on myself and chose the perfect scale number the 1 followed by zero digits.
But here, in a book of constants, I want to explore that question in detail. Perhaps it is the pi digits rather than the perfect scale number.
But there is also more to it. In the idea that pi is really square root of 10, and see if and how that entangles with pi as 3.14...
I like for something new in each and every book I write. For this book is mostly a reminder of how I derived some constants, rather than go searching through 250 books published, searching, when all I need to do is look in this book.
24) Psi^2 as a constant method.
Archimedes Plutonium
Oct 23, 2023, 12:51:16 PM
to Plutonium Atom Universe
On Sunday, October 22, 2023 at 11:23:27 PM UTC-5, Archimedes Plutonium wrote:
> Now I need to add the constant of Physics of Psi^2 in Shrodinger wavefunction. It is a strange constant for it is a constant-of-format, not of a particular number value. A constant of a technique. And I want to make it as simple as possible so that High School students can understand it. The mark and quality of a science as to its understanding, in my opinion, rests upon whether High School students can understand the subject. As of today, few college students can understand what Psi^2 is or means, even in the best of classrooms.
>
> And do it in a fashion and style that is super easy. I intend to do it as a extended chapter of Jacobs book "Mathematics A Human Endeavor, 1970, Chapter 8 The Mathematics of Chance (1) Probability-- The Measure of Chance (2) Some Dice Probabilities (3) Binomial Probability (4) Pascal's Triangle (5) Independent and Dependent Events (6) Complementary Probabilities.
>
> I have already written a book on Psi^2 and intend on including some of this work into that book also.
>
> My 112th published book of science.
>
> New Perspective on Psi^2 in the Schrodinger Equation in a Atom Totality Universe// Atom Totality series, book 5
>
> by Archimedes Plutonium (Author) (Amazon's Kindle)
>
> I first heard of the Schrodinger equation in college chemistry class. We never actually did any problem solving with the equation, and we were only told about it. Then taking physics my next year in college and after I bought the Feynman Lectures on Physics, just for fun for side reading, three volume set did I learn what this Schrodinger equation and the Psi^2 wavefunction was about. I am not going to teach the mathematics of the Schrodinger equation and the math calculations of the Psi or Psi^2 in this book, but leave that up to the reader or student to do that from Feynman's Lectures on Physics. The purpose of this book is to give a new and different interpretation of what Psi^2 is, what Psi^2 means. Correct interpretation of physics experiments and observations turns out to be one of the most difficult tasks in all of physics.
>
> Cover Picture: a photograph taken of me in 1993, after the discovery of Plutonium Atom Totality, and I was 43 years old then, on a wintery hill of New Hampshire. It is nice that Feynman wrote a physics textbook series, for I am very much benefitting from his wisdom. If he had not done that, getting organized in physics by writing textbooks, I would not be writing this book. And I would not have discovered the true meaning of the Fine Structure Constant, for it was Feynman who showed us that FSC is really 0.0854, not that of 0.0072. All because 0.0854 is Psi, and Psi^2 is 0.0072.
So now, let me get going on this project and looking to Feynman Lectures on Physics.
In his Volume 3 of Lectures on Physics, 1965, page 21-6 he talks about "The meaning of the wave function"
--- quoting ---
When Schrodinger first discovered his equation he discovered the conservation law of Eq.(21.9) as a consequence of his equation. But he imagined incorrectly that P was the electric charge density of the electron and that J was the electric current density, so he thought that the electrons interacted with the electromagnetic field through these charges and currents. When he solved his equations for the hydrogen atom and calculated Psi, he was not calculating the probability of anything --- there were no amplitudes at that time -- the interpretation was completely different. The atomic nucleus was stationary but there were currents moving around; would radiate light. He soon found on doing a number of problems that it did not work out quite right. It was at this point that Born made an essential contribution to our ideas regarding quantum mechanics. It was Born who correctly (as far as we know) interpreted the Psi of the Schrodinger equation in terms of a probability amplitude-- that very difficult idea that the square of the amplitude is not the charge density but is only the probability per unit volume of finding an electron there, and that when you do find the electron some place the entire charge is there. That whole idea is due to Born.
--- end quoting ---
Now Feynman in his Volume 1, to his credit, does discuss Probability theory, to sort of lead a student to quantum mechanics probability. But in my opinion, his probability is far too abstract.
I want probability teaching so that High School students can breeze through it.
So I intend to write this on Psi^2 so that High School students follow it easily.
And what I propose to make Psi^2 probability easy, is to link it to the two sides of a right-triangle, so that the right triangle not only delivers trigonometry of sine and cosine, but delivers probability of either the dual one side or the other side of the right triangle.
Going back to page 21-4 in Feynman Lectures on Physics.
(21.9) delP/del(t) = Psi"(delPsi/del(t)) + Psi (delPsi"/del(t))
And the reason I focus upon that equation is because it is the Pythagorean theorem of A^2 + B^2 = C^2.
Quantum Mechanics is duality and the Wave is a duality of electricity to magnetism. The Circle formed from right-triangles in sine and cosine. Where one side of right triangle not hypotenuse is electricity, other side not hypotenuse is magnetism, or, where the hypotenuse is current or magnetic monopole.
When we form the trigonometry half circle of sine or cosine, they are formed by the motion of right triangles where the Pythagorean right triangles A^2 + B^2 = C^2.
AP
zzzzzzzzzz
plutonium dot archimedes at gmail dot com. Looking for a College or University press to hardcover publish all 260+ AP books of science, likely to become 500-600 maybe even 700 books by the time I die. E-books are too prone to unbalanced-unhinged censor-editors, who can easily make your books vanish by pulling a switch. Science should never have gatekeepers, who thwart access to true science.
| /
| /
|/______ hardcover or paperback
PAU newsgroup is this.
https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe
Archimedes Plutonium
Archimedes Plutonium
In my 205th book of science I discover a way of producing four important constants of physics and math-- pi, Fine Structure, 840, and 360. One of those is a angle measure-- the 360 for a full revolution.
In an experiment described in that 205th book, I took 840 identical circles and crafted them into a perfect torus. To find the angle of separation I did a 360/840 and found an angle of 0.428 degrees. Look up what 0.428 degrees is in radians-- for it is the Fine Structure constant of physics 0.0072. Then in that experiment I measured the diameter and radius of the torus I constructed from 840 identical circles placed with a angle 0.428 degree separation. Measuring the diameters of circles and of the donut hole, the diameter of the donut hole of 840 circles forming a ratio which is pi = 3.14159....., specifically, in my experiment --
--- quoting my book ---
Note, that the circle is picked at random size but the 840 circles all have to be identical