# All is Number

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Major funding for this project, has been provided by the Peter Moores trust
and additional funding from the University of the West Indies
To see a world
in a grain of sand and heaven in a wild flower
hold infinity in the palm of your hand
and eternity in an hour
William Blake could have been writing about the myriad of things in the
universe, that at its heart and soul
are described by mathematics.
It was well over 2000 years ago that the
Greek mathematician Pythagoras showed
that in any right angle triangle
the square of this side plus
the square of this side, gives you the square of the hypotenuse.
Indeed we could not get through school without
having been taught that.
Pythagoras is known as the father of numbers
he lead a school of thought that believed
that all things around us could be explained
and understood by mathematics.
Or as he so elegantly put it,
"All is Number."
Join me on a journey,
as we discover that mathematics is the
heart and soul of all things around us,
even when we least suspect it.
All science depends very heavily
on mathematics, which is the
language of science.
Now you may think that as a biologist
you do not need that much mathematics,
but when you think of the sophisticated statistics,
which are used by biologists as they
examine the natural world
then you will see that
you perhaps have a quality
of mathematics which is
beyond many other people.
Even in social sciences where
they tend to think of themselves as
somehow different,
they depend very heavily on
graphs and analysis of graphs
which is of course mathematics.
Everywhere we go,
there is mathematics.
Clouds are not spheres,
mountains are not cones,
coastlines are not circles,
and bark is not smooth.
Nor does lightning travel in a straight line.
These are the words of Mandelbrot,
the man who discovered the geometry to describe such complex
patterns, known as fractals.
And first I should try and explain
in very superficial fashion
exactly what a fractal is.
Everyone knows that a line is one dimensional
and that a plane is two dimensional
a sphere three dimensional and so on.
What many people do not realise is that there are objects that
which have a dimensionality between one and two.
and between two and three.
They have what is called a fractal dimension
which may be 1.6, 1.4,
2.3 or anything like that.
A prime simple example of that is a coastline.
The fundamental question is,
how long is a coastline?
Well, the answer depends on the measurement stick used.
If we look at the coastline of Barbados,
a meter stick will give you a shorter length than if you use a string that will allow you to go around every stone and peeble.
The more you increase the accuracy of your measurement,
the longer your distance becomes.
This is a property of fractals.
Fractals are figures with an infinite amount of detail.
The more detailed you measure, the
more its size increases.
There is structure at all scales.