© David Staume 2006

Is hope a mathematical certainty?

Hope may come from an intuitive feeling of purpose; hope may come from the feeling that things can’t get any worse; hope may come from seeing our children grow up and the realisation that they are better than we are, or hope may be the naive product of a deluded mind, one that refuses to see the world as it really is.

I'd like to think that optimists will always be right given enough time, and while this could just be wishful thinking, there is a line of reasoning that gives hope to the question of hope. Well, reasoning may be too strong a word, let's call it conjecture, but the conjecture is that hope could be a mathematical certainty.

From 0º Celsius the temperature can rise and get hotter and hotter to infinity, but in the downward direction the temperature can only go as low as the point of absolute zero – minus 273º Celsius, or 0º Kelvin – the point at which matter and energy slow to a complete stop.

For most people this is a scientific fact of no great importance, something that you might have learnt in school and had to remember for an exam, but to imaginative philosophers it’s a potentially extraordinary concept, because it suggests that infinity only goes in one direction.

The ‘infinity only goes in one direction’ theory, postulates a positive infinity, but no negative infinity. If this is true, and it applies universally – two rather large assumptions I know – it would be one of the most heartening and beautiful concepts imaginable.

When we extrapolate from this concept, the first things that come to mind are a limit to contraction but no limit to expansion, a limit to darkness but no limit to brightness, a limit to chaos but no limit to order. It’s interesting, but not sensational. But look at what happens when we take it a step further.

Imagine that there are no limits to the heights we can go to, but a definite limit to the depths we can descend. Now imagine that there’s a limit to misery, but no limit to joy; a limit to narrow-mindedness, but no limit to broadmindedness; a limit to foolishness, but no limit to wisdom; a limit to unattractiveness, but no limit to beauty; a limit to evil, but no limit to good.

Granted it's extrapolation gone slightly mad, but it's not nonsense. And if it’s true, it could explain why so many great intellects are optimists, or it could explain why good will triumph over evil – as a matter of reason, not just faith – because the infinite must prevail over the finite.

There are many heroes that we can respect and admire, but I would like to nominate William Thomson, who was knighted as Lord Kelvin. Born in Scotland in 1824, William Thomson was a physicist, mathematician, and engineer. He made an outstanding contribution to the physical sciences in the 19th century, making discoveries in the fields of electricity, thermodynamics, and atomic physics. He is credited with the discovery of the atom and the concept of absolute zero. He took out a number of electrical and marine patents, and was a primary figure in the laying of the transatlantic telegraph cable.

Lord Kelvin might be turning in his grave at the thought that someone had latched onto his discovery of absolute zero and twisted his careful mathematics into an emotional crutch. He might be immensely pleased, or highly amused, I'm not sure. So is it true? Is hope a mathematical certainty? Well I'm not sure of that either. What fascinates me though is the possibility of an emotional concept being able to be expressed in mathematical terms.

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