A Return to Empiricism

Over the last four centuries the Newtonian description of the physical world in terms of differential equations has been brilliantly successful. It began with precise and accurate descriptions of the motion of the planets and their satellites and found further application in the design of the machinery which was the basis of industrial civilisation.

But it does not apply to fluids. This is the “Fluid Catastrophe”. In effect the Quantum Revolution bypassed Fluid Dynamics, whose practitioners still cling to the 19th century idea of the continuum. The belief that any real fluid may be regarded as a deterministic, Newtonian continuum has had a stifling effect on development. Fluid Dynamics has become the province of Applied Mathematicians who are skilled in the manipulation of partial differential equations but in little else. They are not trained to perform experiments. They do not have an empirical, “Popperian” outlook. They are mathematical rationalists who only pay lip service to the scientific method. It is time for Fluid Dynamics to recognise its “catastrophe” and become an empirical science once again. Until that happens, its predictions of future states of the Earth’s atmosphere must be taken with a large grain of salt.

This book has challenges contemporary Fluid Dynamics. It examines the myth on which it is based: that a fluid is a continuum which can be fully described by the deterministic equations of differential calculus. This idea is at odds with the stochastic assumption underlying statistical inference and with the post-quantum conception of entropy. It is a relic of a bygone era when the natural world was regarded as a perfect machine. Once the world was Paley’s timepiece, created and wound up by God at the Creation and left ticking steadily for us to examine and to marvel at. Perhaps this was appropriate in the early 19th Century but there has since been a vast increase in the range of phenomena accessible to science. Wherever we look we see a Universe that is chaotic and unpredictable; more like stock market than timepiece.

Furthermore it is not the pristine perfection of a Laplacian universe that matters, but rather its imperfections. Without occasional, random imperfections in nucleic acids, life could never have become more complex than the virus. Turbulence is everywhere, in cumulus clouds, in breaking waves, in the sound of a clarinet and yet it is inaccessible to the elegant equations of 19th century physics. By presupposing an underlying Newtonian, perfection, we blind ourselves to the amazing realities of the world around us. Only by experiment and observation can we truly see.



Chapter 16 of The Fluid Catastrophe by John Reid