The Sign Laws of Multiplication Book 3
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About this ebook
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.
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