…”We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.” says Laplace in his Essai. Between 1771 and 1787 he produced much of his original work in astronomy. This commenced with a memoir, read before the French Academy in 1773, in which he showed that the planetary motions were stable, and carried the proof as far as the cubes of the eccentricities and inclinations. This was followed by several papers on points in the integral calculus, finite differences, differential equations, and astronomy.
During the years 1784-1787 he produced some memoirs of exceptional power. Prominent among these is one read in 1784, and reprinted in the third volume of the Méchanique céleste, in which he completely determined the attraction of a spheroid on a particle outside it. This is memorable for the introduction into analysis of spherical harmonics or Laplace’s coefficients, as also for the development of the use of the potential – a name first given by Green in 1828.
“Je me dois de vous fournir des travaux permettant des prédictions” said Laplace to Napoleon and formulated science as a predictive discipline. Yet Heisenberg’s uncertainty principle tells us that those predictions are probabilities as it is impossible to know all the initial conditions on which they are based. A problem may be solvable computationally in principle, but in actual practice it may not be that simple. It might require large amounts of time or an inordinate amount of space. So computing the causality of infinity would require infinite time and space as well as an infinite calculator, who could evaluate the result. But as the variables are infinite it would take for ever to do the calculation. Now those who know already that the answer is 42 will remember the total perspective vortex. Spinoza was a lens grinder and I wonder whether his profession gave him some special insight into the all seeing eye, if such an entity exists. Deus sive natura so nature knows itself and for me there is the rub of the whole dilemma. If we are prisoners in Plato’s cave then our prisoner’s dilemma is that we know it would be better to pool our resources to solve our problems yet the math tells us that in the short run we are better off being selfish. As Henry Ford pointed out in the long run we are dead.
Now those with a good heart will accept their limitations and try to be compassionate. Those who believe in karma will accept their fate. Given that we have an urgent need as a species to adopt an environmental ethic that is acceptable to us all we do face a dilemma. We have neither infinite time nor infinite knowledge. In Spinoza’s home city of Amsterdam we are having a January of record warm temperatures with a daily average of 8.8 degrees Celsius. All the evidence we have tells us that the planet is getting warmer yet this knowledge is not absolute and Laplace’s demon has not yet made any public announcement. We have discovered perhaps no more than 10% of all the species on earth and have very little idea of how ecosystems work. I would plead for a cautionary principle and a minimalist approach to our use of the earth’s resources. Future generations have enough time to find out if the answer really is 42 if we leave them a viable planet to live on.
Neither Nostradamus nor the Mayan calendar has all the answers. There is a simplicity of desperation in much of current thinking. Reading the runes or the tea leaves is fine as a party piece and I myself am a lover of the tarot. Yet determinist thinking should not blind us to the simple fact that we do have choices. Heisenberg has shown us our limitations. Within them there is still much to enjoy and wonder at. Just to be part of infinity is marvellous.
Copyright Leighton Cooke 2007