Published June 2008,February 2011.
poet and philosopher Lucretius wrote On the Nature of Things (c. 60 CE)
where he described the motion of dust particles dancing in the
light of a sunbeam, and attributed their motion to the invisible
blows of atoms. Nowadays we might explain this by the small
currents of air moving the dust, but there are other situations
where we can see this happening. For example, in the school
laboratory, it is possible to see this kind of motion with
Lycopodium Powder [see note 1] floating on water and viewed under a
the botanist Robert Brown noticed that if you looked at pollen
grains in water through a microscope, the pollen jiggles about. He
called this jiggling 'Brownian motion', but Brown couldn't
understand what was causing it. He thought at first the pollen must
be alive, but after testing the phenomenon with fine dust
particles, he confirmed that the movement was not due to any living
John Dalton (1766-1844), a Quaker from Cumbria became the Secretary
of the Manchester Literary and
Philosophical Society [see note 2]. Dalton became one of the
most important chemists of his time and through his experimental
work promoted the first systematic ideas of an atomic theory. As
with all scientific theories, there were many people who
contributed their views, and Dalton's achievements rested on those
of a number of scientists from France and England [see note 3].
Einstein became interested in the phenomenon of Brownian Motion,
and in the same year he published three papers which finally came
up with an explanation.
Einstein realised that the jiggling of the pollen grains seen in
Brownian motion was due to molecules of water hitting the tiny
pollen grains, like children randomly kicking a ball in a
playground. The pollen grains were visible but the water molecules
were not, which was why it looked like the pollen was bouncing
around on its own.
Einstein also showed that it was possible to work out how many
molecules were hitting a single pollen grain and how fast the water
molecules were moving - all by looking at the pollen grains.
papers together with the independent work of the Polish scientist
Marian Smoluchowski (1872-1917) in 1906 brought the solution of the
problem to the attention of physicists, and presented it as a way
to indirectly confirm the existence of atoms and molecules.
At last scientists had made predictions about the properties of
atoms that could actually be tested. The French physicist Jean
Perrin (1870-1942) then used Einstein's predictions to work out the
size of atoms and remove any remaining doubts about their
The Mathematics of
Randomness now applies to many aspects of our everyday life,
though we may not be aware of it. Not only to the movement of
atoms, but also to anything that has irregular movement or
irregular appearance like the stock market, the identification of
images, analysis of fingerprints, testing forgery of paintings and
other art objects, tracking animals, gambling, gene mutation,
signal communication, computer simulations, the list goes on. It is
one of the exciting things about being a mathematician that the
same piece of mathematics can get modified and applied to some of
the most unexpected aspects of our lives.
Lycopodium powder is a fine yellow powder derived from the
spores of Lycopodium clavatum (stag's horn club moss, running
In the later 18th Century, a number of 'Literary and
Philosophical' societies existed in England to promote literacy and
technical education for working people, and to develop new
In particular, Joseph Priestly (1733-1804) in England, and
Antoine Lavoisier (1743-2794), and Joseph Luis Gay-Lusac
(1778-1850) in France.
CoLoS Virtual Physics Laboratory This
site shows a Java Applet where you can alter the number of
particles, their speed and mass ratio, and get a trace of a random