Now one of the major reasons writing a textbook is painful for me, as I have found, that I finish many chapters and then discover new ideas that alters the previous chapters. Now this probably does not occur to the dull author of textbooks, for they seldom discover new science, and so there is nothing to change. But for me, it is a major ongoing hazard, and one of the major reasons I have so many editions. For I have so many new discoveries. It is too late in the year for me to start over with this book, so I decided to just finish the chapters as I go, noting that pages may have been better positioned earlier on in the textbook.
This page is a highly crucial critical page. It is dazzling beautiful in LOGIC, and it is a foundation of how to teach all the sciences-- where to start, both physics, math, and even logic.
Let me call this page the FOUNDATION OF SCIENCE-- where to start
And, this page belongs as the starting page of chapter 2. At present I have this as starting page of chapter 2
Page15, 2-1, EM theory becomes the axioms over all of physics/ Atom-Totality-Universe / textbook 8th ed 2017
But I need this Foundation page/s come before I revamp the Maxwell Equations.
FOUNDATION OF SCIENCE
Now, every major science can start with this page, especially mathematics, geometry, algebra, physics, chemistry, and especially logic.
Let us say the reader is a student with a mind that is "blank slate" a slate ready to be filled with the best of knowledge of science.
Where does he/she start?
Surprisingly, the start is a remarkable understanding of the world, the cosmos we live in. The start of all science is an equation, and it is a equation that is simple, pure, and unquestionable. It is logically pristine. Written in just symbol form is this
A = L*W*H
Now the reader is asked a question here. And do not think too hard, too long.
Question, given a equation A = b x c x d, or written as L x W x H, does it remind you of something?
I do not know what Grade in Grade School that the volume of something is taught? At what age? Does a typical average student of 10 years old recognize volume as being Length x Width x Height ( or depth).
Or is the formula L*W*D taught in High School and students younger are unaware of it?
Anyway, many sharp and many dumb intellects want a formula or equation that describes the whole universe. These dumb ones cite things like Schrodinger and Dirac equations, and even dumber ones cite E= mc^2.
And all will agree that no-one has ever given the equation that "tells all and spells all" about science. And that the idea that there is such an equation is really fruitcake nonsense. To think one equation is going to encapsulate such a complex reality as the world, is fruitcake.
But, we can say, that one equation is special over all other equations in describing the world at large and small. That is reasonable and not fruitcake.
Science has just that one equation that is more special than all other equations, for it reaches into not only physics, but mathematics, logic, and all other sciences.
We know it from Geometry as a rectangular solid volume is Length * Width * Depth
But now, notice that it describes, not just a object as a rectangle solid, but all the space of that solid and the size of it can be the Universe itself.
So, in a sense we can say
Universe = Length * Width * Depth
Now, let us be more specific of a volume, that of a single atom of hydrogen
Hydrogen Atom = L*W*D
Now, with the hydrogen atom let us alter the symbols to be P*E*N
Where P = proton, E = electron, N = either neutrino or photon.
Now we stop there and pause for a moment and reflect. If given any Object in the world it is
L*W*H. Even an atom is a Object that has a volume and is L*W*H
But, an atom can replace the length width depth by say proton, electron, photon (or neutrino).
A neutron is the addition of proton + electron+ photon
Now here we contend that a photon and neutrino are one and the same
So a neutron is not a fundamental particle but a composite of fundamental particles.
So another way of writing Hydrogen Atom = L*W*H is to write proton + electron + photon
But now, we proceed to electricity and magnetism-- EM
And so we have EM = L*W*H and we replace Length with current, Width with Magnetic Field, Height with Angular Momentum.
So, we have EM = an Object and all objects are L*W*H
And for EM, we end up with i *B*L, in other words we end up with Voltage as New Ohm's Law.
You see the power that Object = L*W*H has? It is an enormously powerful equation.
Basically, what it is saying is the World always has objects and all objects have at least three things involved forming a fourth thing. If the three things are length width depth, the fourth is volume.
If the three things are proton, electron, photon the fourth is an atom.
If the three things are current, Magnetic Field, Angular Momentum, the fourth is Voltage.
Now, all of mathematics comes from such a beginning of Object = L*W*H and it is geometry made plain and simple. But how about Logic and Algebra?
Do they fit into Object = L*W*H
Ever notice that Logic has 4 and only 4 connectors (the true logic not the error filled Boole logic).
Here is a short synopsis of Logic is 4 things, just like the Object = LWH
Correction of Logic errors by Archimedes Plutonium 3. Logic errors:: otherwise we cannot think clearly and think straight and true History of those pathetic errors::
by Archimedes Plutonium
The 4 connectors of Logic are:
1) Equal (equivalence) plus Not (negation) where the two are combined as one 2) And (conjunction) 3) Or (exclusive or) (disjunction) 4) Implication
EQUAL/NOT table: T = T = T T = not F = T F = not T = T F = F = T
Equality must start or begin logic because in the other connectors, we cannot say a result equals something if we do not have equality built already. Now to build equality, it is unary in that T=T and F =F. So we need another unary connector to make equality a binary. Negation is that other connector and when we combine the two we have the above table.
Equality combined with Negation allows us to proceed to build the other three logic connectors.
Now, unfortunately, Logic must start with equality allied with negation and in math what this connector as binary connector ends up being-- is multiplication for math. One would think that the first connector of Logic that must be covered is the connector that ends up being addition of math, not multiplication. But maybe we can find a philosophy-logic answer as to why Logic starts with equal/not and is multiplication rather than addition.
Here you we have one truth table equal/not whose endresult is 4 trues.
New Logic AND T & T = T T & F = T F & T = T F & F = F
AND is ADD in New Logic, and that makes a whole lot of common sense. AND feels like addition, the joining of parts. And the truth table for AND should be such that if given one true statement in a series of statements then the entire string of statements is true. So if I had P and Q and S and R, I need only one of those to be true to make the string true P & Q & S & R = True if just one statement is true.
The truth table of AND results in 3 trues and 1 false.
New Logic OR(exclusive) T or T = F T or F = T F or T = T F or F = F
OR is seen as a choice, a pick and choose. So if I had T or T, there is no choice and so it is False. If I had T or F there is a choice and so it is true. Again the same for F or T, but when I have F or F, there is no choice and so it is false. OR in mathematics, because we pick and discard what is not chosen, that OR is seen as subtraction.
OR is a truth table whose endresult is 2 trues, 2 falses.
New Logic IMPLIES (Material Conditional) IF/THEN MOVES INTO T -> T = T T -> F = F F -> T = U probability outcome F -> F = U probability outcome
A truth table that has a variable which is neither T or F, but U for unknown or a probability outcome. We need this U so that we can do math where 0 divided into something is not defined.
Now notice there are four truth tables where the endresult is 4 trues, 3 trues with 1 false, 2 trues with 2 falses and finally a truth table with a different variable other than T or F, with variable U. This is important in New Logic that the four primitive connectors, by primitive I mean they are independent of one another so that one cannot be derived by the other three. The four are axioms, independent. And the way you can spot that they are independent is that if you reverse their values so that 4 trues become 4 falses. For AND, reversal would be FFFT instead of TTTF. For OR, a reversal would be TFFT instead of FTTF.
To be independent and not derivable by the other three axioms you need a condition of this:
One Table be 4 of the same One Table be 3 of the same One Table be 2 of the same And to get division by 0 in mathematics, one table with a unknown variable.
So, how did Old Logic get it all so wrong so bad? I think the problem was that in the 1800s when Logic was being discovered, is that the best minds of the time were involved in physics, chemistry, biology and looked upon philosophy and logic as second rate and that second rate minds would propose Old Logic. This history would be from Boole 1854 The Laws of Thought, and Jevons textbook of Elementary Lessons on Logic, 1870. Boole started the Old Logic with the help of Jevons and fostered the wrong muddleheaded idea that OR was ADD, when it truly is AND.
Now the way people actually live, is an indicator of how well they thought and how well any of their ideas should be taken seriously. In the case of Boole, he went to class in a downpour rain, why without a raincoat? And reaching class, instead of changing into dry warm clothes, stood for hours in front of students, sopping wet and shivering. Of course he caught pneumonia, but instead of being sensible, common sense that even a fly would have, he insisted his wife give him cold showers and make the bed all wet and freezing. Of course, he would die from this. Now, does anyone today, think that a mind like that has anything to offer Logic or mathematics, is as crazy as what Boole was.
But once you have textbooks about Logic, it is difficult to correct a mistake because of the money making social network wants to make more money, not go around fixing mistakes. So this nightmarish mistakes of the truth tables was not seen by Frege, by Russell, by Whitehead, by Carnap, by Godel, and by 1908 the symbols and terminology of the Old Logic truth tables were so deeply rooted into Logic, that only a Logical minded person could ever rescue Logic.