## Ask a Scientist: Is infinity something real?

*Otago Daily Times, 6 September 2002*

Jamie Hunt, of Cashmere Primary School, asks:-
*Is infinity something real?*

**David Wiltshire**, *a cosmologist at the University of
Canterbury responds:*
If we definitely knew that the Universe went on forever, or that it would
last forever, we could say that infinity is real. We might be able to
answer those questions some day but we cannot do so yet.

There is another way of looking at the question though, by asking what do
we mean by "real"? Computers contain both hardware - the stuff inside the
boxes - and software - the programs that run on them. Most people would say
that software is real even though it is not stuff you can touch, because
computers would not work without programs. The laws of physics that describe
the way the Universe works are real in a very similar sense to computer
programs being real. The mathematical idea of infinity is very important for
the laws of physics, so in that sense infinity is real.

Actually there are many different sorts of infinity. Think of counting by
ones - 1,2,3,4,5,... - and then think of counting by twos - 2,4,6,8,10,...
Both ways of counting get to infinity but if you are counting in ones and
a friend is counting in twos, your friend's numbers will get infinitely
large twice as quickly. Mathematicians deal with this by calling the first
infinity "omega", and the second infinity two times omega.

Not only is it possible to multiply omega by an ordinary number, but one
can even multiply infinities together, and divide infinities. For example,
imagine cutting a pie into infinitely many small pieces, and then cutting
each infinitely small piece into infinitely many pieces again, and again
and again... Of course, that is not something you can do with a real pie
but it is something that you can do mathematically. By imagining such things
mathematicians have discovered numbers which include all possible sorts
of infinities, both large and small, and which are very different to
ordinary numbers. These numbers are called "surreal numbers" because
they are very strange, even for mathematicians. Physicists who think
about the laws of the Universe have not yet had to use surreal numbers,
but we do know of parts of physics where they might be useful. If that
turns out to be true then not only is infinity real, but different sorts
of infinity are real too.

Dr David Wiltshire

Department of Physics and Astronomy

University of Canterbury

Homepage:
http://www2.phys.canterbury.ac.nz/~dlw24/