In recognition of this 50th blog post, I wanted to zoom out and think about one of the big picture themes of this blog. To wit: “how knowable is the universe?” For a physicist, usually this boils down ultimately to grappling with the related question, “how far can be push reductionism?” Modern science has enjoyed tremendous successes using as a unifying rallying cry the conviction that complicated phenomena can be explained via simpler fundamental rules. Physicists have become so accustomed working this way that we generally expect toy models and back-of-the-envelope estimates we think up on the spot to be at least approximately right. As noted in Physics Today, scientists in other disciplines, especially biologists, are right when they murmur about “spherical cow” models. They know that life has emergent properties (like being alive), and strongly resists our best effects to reduce it to a list of equations. The development of quantum mechanics, and later, chaos and complexity theory, show that even in the realm of physics, there are hard limits on how much we can know. Some pro-science proponents look at technology and say things like “Airplanes fly, don’t they? How wrong can we be?.” While true to some extent, this does not insure that our textbook explanation of flight is not horribly wrong. Seemingly accurate explanations might only be “brain puns,” as coined by Ian Stewart in Collapse of Chaos. In this book, he also examines the power and limits of reductionism.
It may turn out the real difference between phenomena that we think we understand very well (Newton’s laws or Quantum Field Theory) and things we suspect may be too complicated to EVER be able to make reliable predictions about (the weather a month from now, psychohistory ) is that in the first category, errors and imprecision in knowledge become less and less important and our best guesses can converge to towards the right answer. In the second category, however, small changes in initial conditions (or knowledge of the laws of nature) lead to hugely different outcomes.
The duality between the “convergent” and the “divergent” can be seen in this picture of smoke, making the transition from laminar to turbulent flow.