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The Sign Laws of Multiplication Book 3
The Sign Laws of Multiplication Book 3
The Sign Laws of Multiplication Book 3
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The Sign Laws of Multiplication Book 3

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In this book we look at many of the demonstrations and proofs of the sign laws of multiplication, highlighting errors in the logic within them. They all contain errors. The only exception is one based on a circular theory of number, emphasizing the need to switch to such a theory for teaching children these fundamental laws of arithmetic.

LanguageEnglish
PublisherRobert Taylor
Release dateFeb 11, 2023
ISBN9780908681389
The Sign Laws of Multiplication Book 3
Author

Robert Taylor

Following active duty as a commissioned officer in the U.S. Army, Robert Taylor served as an intelligence officer in the Defense Intelligence Agency, Middle East Division. He subsequently served as policy advisor in the Office of the Secretary of Defense, Office of International Security Affairs, Near East South Asia Division, and on Capitol Hill for several U.S. Senators. He currently resides in Virginia with his family, just outside of Washington D.C.

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    The Sign Laws of Multiplication Book 3 - Robert Taylor

    The Sign Laws of Multiplication

    book 3

    The Sign Laws of Multiplication Book 3

    Published by Robert Taylor at Smashwords

    Copyright 2023 Robert Michael Taylor

    ISBN: 978-0-908681-38-9

    This e-book is licensed for your personal enjoyment only. This e-book may not be re-sold or given away to other people. If you would like to share this book with another person, please purchase an additional copy for each recipient. If you're reading this book and did not purchase it, or it was not purchased for your use only, then please return it to your favourite e-book retailer and purchase your own copy. Thank you for respecting the hard work of this author.

    The Sign Laws of Multiplication

    The sign laws are notoriously difficult to teach to a child.

    The inability to produce a purely mathematical, simple, clear cut

    demonstration and proof of these laws

    points to the need to adopt a circular theory of number.

    This then changes everything.

    It changes how we interpret mathematical equations.

    It changes how we interpret the laws of physics.

    It changes how we look at our world and our own minds.

    Being pivotal, three books are devoted to it.

    The Sign Laws of Multiplication

    book 1

    In Book 1 we will show:

    – How in fact to successfully demonstrate the sign laws to a child –

    – How to use a calculator to extend the demonstration to bigger numbers –

    Perfect for mothers teaching their children.

    The Sign Laws of Multiplication

    book 2

    In Book 2 we will:

    – Give a gentle introduction to algebra –

    – Show how to prove the sign laws –

    – Introduce the other three fundamental laws of algebra –

    – Use these to do trick magic multiplications –

    Perfect for parents/teachers helping an older child.

    The Sign Laws of Multiplication

    book 3

    In this book we will critically examine:

    – Examples of most categories of existing proofs and demonstrations

    of the sign laws on the straight line as found today on the internet –

    and find:

    – That Imaginary Numbers, so vital to physics, can be given a rational basis –

    Perfect for anyone prepared to question the conclusions of today’s

    science and mathematics.

    *Make sure you’ve read the other two books in the trilogy first!*

    CONTENTS

    Introduction

    Chapter 1

    The Bird's Eye View

    Chapter 2

    The Spinning Wheel of Illusion

    Chapter 3

    The Demonstrations that use Analogy

    Chapter 4

    The Red Block Demo

    Chapter 5

    What Does the Red Block Demo Actually Demonstrate?

    Chapter 6

    The Confusing (((Brackets))) Demo

    Chapter 7

    The CAD Laws

    Chapter 8

    The Walker Demo

    Chapter 9

    The Pop-Up Opposites Demonstration

    Chapter 10

    The Proof by Definition Method

    Chapter 11

    The We-Can-Come-Back-to-it-Later Approach

    Chapter 12

    The Elegant Proof

    Chapter 13

    Proof by Symmetry

    Chapter 14

    The Vector Demo

    Chapter 15

    The Over-the-Top Demo

    Chapter 16

    Imaginary Numbers

    Chapter 17

    Circlemaths is NOT Modulo Arithmetic

    Conclusion

    Introduction

    What is it that holds science together?

    It is mathematics.

    Mathematics is the logical framework supporting science.

    It is the backbone of science.

    Without it science as we know it

    would fall apart.

    Today’s cosmologists and quantum physicists

    will always put the interpretation

    of the mathematical equations of physics

    above what we call common sense.

    If you look at a physics textbook

    you will find maths formulae.

    The higher up you go the more maths formulae you will see.

    Pages and pages of them.

    Our ideas of the universe, how it began,

    whether there is a God or not, what is life, and so on

    no longer come from religion.

    They come from science.

    From the mathematical interpretations

    of the scientific equations.

    What if we haven’t got our maths right?

    Then, yes, our understanding of the equations

    will be inaccurate or incomplete,

    and so will our understanding

    of the universe.

    We Haven’t Got Our Maths Right

    This book is written precisely because

    we haven’t got our maths right!

    The world is round, space-time is curved,

    every heavenly body is a sphere, an oval or an ellipse,

    but our arithmetic

    - which so accurately reflects and predicts reality -

    counts out upon an infinite straight line.

    Wait a moment... does that really sound sensible?

    Right at the very start we begin our mathematical lives

    with an anachronism inherited from the dark ages.

    The straight counting line to infinity

    which rightfully belongs to a flat Earth.

    The task of this book is to examine

    in intricate detail

    the existing demonstrations and proofs

    of the sign laws

    and to show

    that none of them

    are mathematically sound.

    None of them are suitable to act

    as the foundation of our children’s

    developing mathematical understanding.

    The destruction of these outmoded ideas

    opens the door to the creation of other exciting possibilities.

    Suppose out of all the various

    demonstrations and proofs

    available

    we were able to show

    one or two of them

    had errors.

    That would mean nothing.

    But suppose it turned out

    that

    EVERY SINGLE ONE OF THEM

    contained errors?

    That there was

    no clear cut, correct

    demonstration nor proof

    of the sign laws

    suitable to teach children?

    With one exception.

    Suppose there was

    only one

    which fitted the bill exactly.

    Did everything we wanted.

    Gave a clear mathematically correct

    demonstration and proof

    even children could follow.

    But

    it required a complete re-think

    of our fundamental conception of number

    right at ground level.

    Then the implications

    are profound.

    And that is indeed the case.

    The circular demonstrations

    work and work well.

    All others can be shown to fall over.

    The implications are indeed profound!

    The Black Box Radiator

    The older classical physics

    could do most things.

    But it failed to explain one tiny problem.

    It couldn't correctly predict

    the colour of light

    which comes out of a black hollow ball

    which had been heated in a furnace.

    Many physicists said So what?

    Unimportant.

    But hiding behind this tiny blemish

    was a new theory of physics (quantum mechanics)

    which jumped us into the modern world of electronics.

    The ‘error’ in predicting the exact color of emitted light

    acted as a pointer to its existence.

    The claim of this book

    is that none of the existing

    demonstrations or proofs

    of the sign laws of multiplication

    available to educators today

    are good enough

    to lay the foundations

    for mathematics.

    There is an old Chinese proverb

    that says:

    "the disease of one-thousand cures

    has no cure".

    When we wish to demonstrate

    2 x 3 = 6

    there is only one demonstration.

    It is explicit

    crystal clear

    fully up to the task.

    There is no need to give any other.

    But when we wish to demonstrate

    -2 x -3 = +6

    suddenly we find 20 or 30 different approaches.

    One talks about balloons,

    another people walking,

    another deals with opposites along a line

    another has no line,

    just a bucket that negative numbers are dropped into,

    and another is written in incomprehensible technical jargon.

    What is missing

    is a single comprehensive demonstration

    that is so indisputable

    that no other is required.

    The plethora of different arguments

    should tip

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