Figure It Out

Does mathematics have the solution – or perhaps the problem? Carl Sagan’s novel, published by Arrow in 1986.

Does mathematics have the solution – or perhaps the problem? Carl Sagan’s novel, published by Arrow in 1986.

Ancient Greece was an amazing place for developing many of the ideas that are still relevant in science today.  Undoubtedly, research since the scientific revolution of the seventeenth century has overtaken much of what the ancient Greeks proposed, but many of the concepts, and certainly the approach to investigating the universe, are still influential after over two thousand years.

In his highly readable book Eureka! The Birth of Science, Andrew Gregory gives an account of the origins of the scientific endeavours that we see all around us.  One of the more unusual aspects which he describes, though, is the approach towards mathematics and science originating with the followers of the philosopher Pythagoras.

Nowadays, we almost take it for granted that mathematical structure underlies the world, and that we can express findings in physics through mathematical laws, but the Pythagoreans were the first to consider that there could be a relationship between mathematics and nature.  The trouble is that they took it a bit too far, and thought they saw numbers and mathematics in absolutely everything.

The philosopher Plato developed the idea.  He saw the universe as being created using geometry and mathematics, which meant that humans should be able to understand the structure of the cosmos.  It’s a concept which we still have – in a deep sense, the universe is mathematical.

So perhaps we shouldn’t be too surprised that, earlier this year, Max Tegmark, physics professor at MIT, argued in his book Our Mathematical Universe: My Quest for the Ultimate Nature of Reality that not only is the universe excellently described by mathematics, but it actually is mathematics.

On the face of it, that sounds decidedly odd, but Professor Tegmark provides a well-reasoned and plausible argument.  He sees several levels of the multiverse, working up (if the word “up” has meaning in this context) through parallel worlds to the “highest”, and simplest, level of the realm of mathematical structure.  In effect, physical existence is mathematical existence.

Science fiction?  No, Professor Tegmark knows what he’s talking about, and it certainly explains why mathematics is so powerful in describing everything around us.  But it’s a little un-nerving to think that, at a fundamental level, we are all based on mathematics.

We’ve occasionally seen science fiction focusing on an underlying mathematical basis for the universe, as when imagining what might happen in the depths of infinite number sequences such as the non-recurring decimal places of the mathematical constant pi.  In his novel Contact, Carl Sagan envisaged that, deep in the expansion, the randomness stops and there’s a pattern which reveals the existence of an intelligence which pre-dates the universe.

But possibly one of the most intriguing creatures based on mathematics appears briefly in Out of the Dead City, the first novel in Samuel R Delany’s The Fall of the Towers trilogy.  At one stage, our heroes appear to be fighting battles by proxy through various intelligent alien species throughout the galaxy.  The weirdest are beings which seem to be mathematical oscillations inside a star where, if the correct sequences combine, a frequency can simply be made to contract and disappear.

Needless to say, this is nothing like the higher-level mathematical structures which Professor Tegmark describes.  There would be no possibility of our existence being wiped out through unfortunate combinations of the wrong structures at the wrong time.  At least, let’s hope not.

Richard Hayes, Assistant Editor (Odyssey)

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