Would you buy a car that only works some of the time? Would you
accept a theory of gravity that only works some of the time? Why
accept a theory of zero that only works some of the time?
This is a book about zero. This is not about the zero you learnt
about in school. This is a tale of three different types of zeros, a
misunderstanding and the impact it has had on Western mathematics and
physics. It is one of the strangest tales in the history of
mathematics and science.
It is no coincidence that the most controversial areas of
mathematics are also involved in many of the unexplained problems in
physics. After thousands of years of research, you would think that we
would know all there is to know about basic algebra. However, as our
understanding of mathematics and physics has advanced, it has exposed
deficiencies in our theories about numbers and basic mathematics.
These deficiencies show up as strange or undefined results in the
mathematics of physics. Our misunderstandings lead to strange
conclusions, such as that the laws of physics must break down
sometimes or that the mathematics of the Universe does impossible
things.
It is generally assumed that this is "just the way things
are" and that the Universe has some strange behaviour. The actual
truth is much simpler: human error. A few bad assumptions made
centuries ago still colour our views and lead us to the wrong
conclusions.
Much of what we learn about zero in school is wrong. It is based on
opinion and philosophy dating back many centuries, rather than being
based on the way that the Universe actually does things.
There are several different types of zero in common use. Each of
these uses started at a different time and for different reasons.
Confusion about these different types of zeros is at the heart of many
controversies involving zero.
In this book we will examine the properties of three types of zeros
as well as where and how this confusion arises and the effect it has
on mathematics, geometry and physics.