So my name is Cohl Furey and I'm a
postdoctoral
fellow in theoretical physics at Trinity
Hall University of Cambridge.
So the short answer is that the octonions are this special number system in
pure mathematics and the octonions
could be important for particle physics
because they seem to mirror the behavior
of certain elementary particles under
the strong and electro weak forces. So
the real numbers are the numbers that
you're used to using in everyday life.
They span from minus infinity to plus
infinity and they include numbers such
as 0 1 2 3 4 and they also include other
numbers like irrational numbers like the
number of pi. So we say that the real
numbers are one-dimensional because we
can lay out all the real numbers on an
infinitely long line. Now the octonions
are not one-dimensional it turns out
that they of twenty ones are eight
dimensional and they also have some
curious properties. So for example the
real numbers are commutative so that
means that that a times B is always
equal to B times A but this isn't always
true for the octonions. Also the real
numbers are associative and what that
means is that it's a A B and C like this
where you multiply the a and the B first
is always equal to a B C like this where
you multiply the B and the C first but
this isn't true all the time in the Octonions. Now it turns out that thanks to
these unusual properties of the octonions
you can show that the octonions are
able to describe the behavior of certain
elementary particles under the strong
and electroweak forces.
