My expected 241st book of science// Practice in turning statements of language into formulas and equations of math and logic

241st book of science for AP

My expected 240th book is how Parametric Equations are thrown out of math, because simply the only valid function is a polynomial function, so there is no need for parametric equations. In the course of that conversation in sci.math, a Hugh popped up to put a hate-filled stalker in place. And looking at Hugh's put down of Jan Burse, I was wondering of a correct translation into a math formula of the language statement. I had done this type of work in logic classes when I attended college in early 1970s and found it fun to do these translations. So I think the subject of Logic is deserving of having a book, workbook that translates ordinary language statements into quantified logic or math formulas or equations.

Really, a scientist can never really get enough logic and logic practice in their lifetime career in science.

Practice on how to turn statements of language into formulas and equations of math and logic.

by Archimedes Plutonium

Archimedes Plutonium

Apr 28, 2022, 1:01:01 AM

to sci.math

On Wednesday, April 27, 2022 at 3:01:04 PM UTC-5, Hugh Itoh wrote:

> Mostowski Collapse wrote:

> AP forget twice as much mathematics you think you can do.

>

In my college training of Logic, formal logic, two years of logic. We had lessons in which we take sentences and transcribe them into mathematical logical quantity formulas.

So let me see if I can transcribe Hugh's sentence which was meant to be:

AP forgot twice as much mathematics, that Jan Burse will ever do in his entire lifetime.

So if I can remember back to 1970, over 50 years ago. Interesting and let us give it a try. And by the way, the DC Dan Christensen poop crap certainly cannot do anything remotely like this-- quantify a sentence of a language into math.

Let me denote these:

AP_t.k. = AP's total knowledge

AP_f.k. = forgotten AP knowledge

JB_t.k. = Jan Burse's total knowledge

Do I need a forgotten knowledge of Jan Burse? I do not think so, at this moment anyway.

So we have AP_t.k. = Summation of every piece of knowledge for 72 years subtract AP_f.k.

For Jan Burse we have JB_t.k. = 1/2 (AP_f.k.)

Now I should be able to make this more detailed.

So in every year that AP gains knowledge we have 72(AP_t.k.)

And let us say that AP forgot in those 72 years, let us say he forgot 2 years worth of logic.

So we have 72(AP_t.k.) - (2)

That would leave the total knowledge accessible for the brain of Jan Burse would be 1/2(-2).

In other words, the brains of Jan Burse, Swiss Zurich ETH, are brains that can accummulate in his lifetime of the knowledge that AP picked up in 1 year time.

So the brains of AP would be a graph of Y = 72x while the brains of Jan Burse would be a graph of Y= 1

AP brains graphed would look like this:

knowledge gained

| /

|/

|/__________

While Jan Burse brains graphed for 72 years would look like this:

|

|

|--------------------_________________knowledge gained

No, definitely the DC Dan Christensen nutjob proof machine could never give pictures or formulas

Archimedes Plutonium

Apr 28, 2022, 10:30:25 AM

to sci.math

Calling on failure of Logic Dan Christensen with his failed machine of DC proof. Yoo, Dan, you logic failure, how do you translate the below, with or without your failed DC proof. I am sure I made errors, for the below was my first take on "AP forgot more math than twice the amount of math Jan Burse will ever learn in his entire lifetime".

DC how do you quantify that into logic, you ignorant waif with your AND truth table of TFFF when it is actually TTTF.

I tease Dan because he believes Boole is correct with AND truth table being TFFF which leads to the absurdity of 2 OR 1 = 3 with AND as subtraction. Of course the real truth table of AND connector is TTTF, for we never want to throw out the baby in the bathwater. All it takes for AND to be true is for one of many statements to be true, hence all of them together must be true, even if all the rest of the collective statements is false.

AP

This is going to be one of my most important books of science. And it is a nexus of Logic and Mathematics. Not only practice in turning sentences of language into logic and math formulas or equations but in a units calibration of all of physical science.

Calculus involves Functions and functions are all polynomials. Functions are a subset of Equations. For equations embody far more than just polynomials.

Formulas are incomplete equations. We can look at formulas the same way we look at Rational numbers are fractions. The only true numbers that exist are Decimal Grid Numbers, so a number such as 1.3 exists, 1.33 exists, 1.333 exists etc. But 4/3 is a rational number which is an incomplete division. It is "not a number at all". For 4/3 is not divided out to be a specific 1.3, 1.33, 1.333, 1.3333, 1.33333, .... in this sequence of Decimal Grid numbers. So a representation of a number is 4/3 but not a true number as is, until divided out and given a assigned Decimal Grid Number. In the same scheme, a formula is a equation but not specific enough.

For example, Y = x^2 is a polynomial and also a equation and also a function. And AP_t.k. = x^2 is a formula and is a equation but it is not a polynomial for we do not know what AP_t.k. represents for it certainly does not represent the graphing coordinate system of x and y axes.

Now, I need to get to a Units Calibration of all Physical Sciences.

Since the only true functions are polynomials and all the rest need to be transformed over an interval if not a polynomial and thus converted into a polynomial to be used in calculus. We need a Units Calibration.

The Power Rules are two of them. For derivative of polynomial x^2 it is 2x^1 where the rule is --- throw the exponent to be a coefficient and subtract 1 from existing exponent. That language translation becomes -- take the 2 and place in front of x, now subtract 1 from 2 leaving us 1, so our final answer is 2x. Reader, try it out on x^3 and x^4. For x^3 we throw 3 in front of the x to be 3x, and for the final exponent we subtract 1 from 3 to give us 2, leaving us with 3x^2 for derivative of x^3.

The Power Rule for Integral is easy as well, and a reversal. So for example x^2 we take the exponent and add 1 and divide it into 1, thus we have 1/3 and for the final exponent we add 1 to given exponent, leaving us with 1/3x^3.

Now notice, that the Integral is the reverse of derivative for if we take the derivative of 1/3x^3 we end up with our original polynomial function of x^2.

In fact, we can say that the proof of the Fundamental Theorem of Calculus is as simple as the explanation of the two Power Rules, one for derivative and one for integral. That one is the reverse of the other.

But let me get down to business of this post. I want Units Calibration for All Physical Sciences.

So, if I start with the polynomial of straight line as I worked out in the Sentence: The total brains of Jan Burse is 1/2 the brains of all that AP has forgotten knowledge. Where my first attempt of translating that language statement into math or logic formula was a straight line formula of 72AP_t.k. - 2.

One can easily see that if all of science were confined to Area as x^2, and function as Y= mx+b, then the derivative is a constant function Y = k.

This limits me too much. This limits and bounds all science too narrowly and too strictly.

So what I need to do is expand the boundary of All Physical Science so that the Integral is at least x^3, making the function be x^2 and thus the derivative be a straight line of Y = mx+b.

Before, in Old Math, they limited themselves to integral being x^2, then function was x and finally their derivative was a constant k. That is far far too narrow minded and restrictive.

And so, we need to up the ante in all of physical science. We need for the Calculus integral to be volume of Y= x^3 at a minimum. That gives us the function as x^2 and the derivative as Y = mx+b, a straightline function.

This calibration upwards of at least Y = x^3 for science is necessary.

And we can easily see that Geometry requires this Upward Calibration for we have a square x^2 as starting polynomial function. Say our square is of side 2, then area is 4, the integral would be x^3 be 8, the derivative would be x or 1, (note: I ignore coefficients in power rules). Say our starting square is 3, then area is 9, the integral is volume and is 27, the derivative is x or 3.

If I did what Old Math does as that of integral as area, then the function is a straightline Y = mx+b, and the derivative is always a constant. This is too impoverished of math for physical science, and what it requires is a recalibration upwards so as to include "volume in geometry" not just area.. This allows for the derivative to be more than a constant k, for every function. It allows the derivative to be one of the infinite choices of Y = mx+b.

So the mistake made in Old Math and Old Logic is a mistake of not calibrating upwards, so that the derivative is not some impoverished useless function. It is a mistake that would have all addition and subtraction end up being a zero in physics. (I think this is the cause of QED quantum mechanics ending up with bizarre infinites that need to be as Feynman describes it-- renormalized out). Here I am Recalibrating Upwards, whereas QED renormalized.

AP, King of Science, especially physics-chemistry

This is now my 188th book of science. It is important for logic and gives a new concept of math Calculus as the Default Units of Calculus.

This reminds me of default units for computers. Such as font, time, settings.

The default of Calculus must be that the derivative must be at least Y = mx+b. So that the function must at least be area Y = x^2 and integral be volume Y= x^3.

The default of Calculus must be derivative is mx+b, starting function x^2 and integral x^3. Default cannot be starting function Y= mx+b for that leaves the derivative as a constant k. And leaves the integral as an area x^2.

AP

So call it the Default Units of Calculus, that the derivative must be no lower than Y= mx + b function, a polynomial, then the starting function can be no lower than Y = x^2. And thus the integral function can be no lower than Y = x^3 a volume.

If the derivative is lower than Y = mx+b such as a constant function of say Y = k, then the integral ends up being a area, such as Y = x^2.

And the reason for why mathematics never saw this pitfall this error is that we were lulled to sleep with the idea of integral being area under the curve of a function graph. We were not trained to think outside the box.

And the only reason I discovered this important idea of a Primal Default Units of Calculus, is my attempt to quantize the statement made in sci.math by a poster saying "AP forgot twice as much mathematics, that Jan Burse will ever do in his entire lifetime."

By trying to express that statement in Symbolic Logic or in mathematics, I need to involve Calculus. And after giving a error filled first attempt, I realize that Calculus needs a default Units where the derivative cannot go lower than the straightline function Y = mx+b. It cannot go to being a Y = constant. The derivative must be at least as rich as Y = mx+b.

And that makes the default of integral in calculus must be at least a volume, Y = x^3 at minimum.

So in all of mathematics we have a new idea in Calculus-- a default zone. I liken this idea to modern day computers with their "default settings" so that if you have your computer totally completely "reset", then the settings will come on line as the default settings.

And the default setting of all of Calculus is the derivative is no lower than Y = mx+b and the starting function no lower than Y= x^2 and the integral no lower than Y= x^3.

So this is a brand new idea in all of calculus mathematics. Does it have any wider implications? I do not know.

But I do know it is important in translating Language statements into quantification symbolic logic or math functions, formulas or equations.

A language statement of "AP forgot twice as much mathematics, that Jan Burse will ever do in his entire lifetime." When correctly translated must have the starting function be as rich as Y= x^2 at a bare minimum. And I made the mistake of thinking the starting statement could be Y = mx+b.

AP

So where could this idea of a Default Units Calculus apply in physics.

Well, my TEACHING TRUE MATHEMATICS textbook series for sophomore year college teaches the 3D calculus. Calculus in 3rd dimension, and the conclusion I drew from that, was that 3D calculus was the Faraday law. And I wrote that idea in several of my books on Angular Momentum.

So if Calculus has a Default Units of derivative no lower than Y = mx+b, starting function no lower than Y= x^2, and integral no lower than Y= x^3, suggests that the integral of calculus is the laws of physics, the Electromagnetic laws. If true means the "starting function as Y=x^2" represents something of physics and finally the derivative as Y=mx+b represents something of physics.

So if integral represents Faraday law, then starting function must represent something like electric or magnetic field. And then derivative representing current or Coulombs.

72nd published book

TEACHING TRUE MATHEMATICS: Volume 4 for age 19-20 Sophomore-year College, math textbook series, book 5 Kindle Edition
by Archimedes Plutonium (Author)

Preface: This is volume 4, book 5 of Teaching True Mathematics, designed for College Sophomore-year students, students of age 19-20. It is the continuation of volume 3 in the end-goal of learning how to do the mathematics of electricity and magnetism, because everything in physics is nothing but atoms and atoms are nothing but electricity and magnetism. To know math, you have to know physics. We learned the Calculus of 2nd dimension and applied it to the equations of physics for electricity and magnetism. But we did not learn the calculus of those equations for 3rd dimension. So, you can say that Sophomore year College math is devoted to 3D Calculus. This sophomore year college we fill in all the calculus, and we start over on all of Geometry, for geometry needs a modern day revision. And pardon me for this book is mostly reading, and the students doing less calculations. The classroom of this textbook has the teacher go through page by page to get the students comprehending and understanding of what is being taught. There are many hands on experiments also.

Cover Picture shows some toruses, some round some square, torus of rings, thin strips of rings or squares and shows them laid flat. That is Calculus of 3rd dimension that lays a ring in a torus to be flat in 2nd dimension.
Length: 105 pages

Product details
• ASIN ‏ : ‎ B0828M34VL
• Publication date ‏ : ‎ December 2, 2019
• Language ‏ : ‎ English
• File size ‏ : ‎ 952 KB
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• Print length ‏ : ‎ 105 pages
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• Best Sellers Rank: #242,037 in Kindle Store (See Top 100 in Kindle Store)
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