Stephen Wolfram has posted a long article “A 50-Year Quest: My Personal Journey with the Second Law of Thermodynamics”, chronicling his efforts, from age 12 to the present, to truly understand the second law of thermodynamics, the meaning of entropy, emergence of a perceived arrow of time in systems in which the fundamental laws are time-symmetric, and how all of this relates to computation and the information embodied in a physical system.

It is an enlightening journey, where one sees ideas such as computational irreducibility and computational equivalence peek out from the empirical data and gradually take form as general principles.

Looking at the cover of the Berkeley Physics CourseStatistical Physics book and realising the filmstrip of a handful of elastic scattering particles in a box taxed the computational capabilities of a weapons lab computer in the mid-1960s can’t help but make one wonder how different our view of mathematics and physics might have been if we’d had the tools to experimentally explore these fields computationally instead of spending centuries seeking closed form solutions to problems where nature seems to feel no requirement to make them comprehensible that way, and considering “numerical methods” somewhat disreputable compared to timeless, eternal solutions to simplified models of real physical systems.

Great read which took the better part of a sunny afternoon here at grid EN90dx.
Big takeaways:
-Wolfram was a PhD at 19!
-started doing serious thinking at age 12!
-He and Feynman both exhibited the very human tendency of clinging to their theories in the face of contrary evidence.
-all the Greats write it down! They document everything.

Great recommendation there Mr. Walker!

PS: somewhere in the recesses of my brain I keep thinking I read Hawking connected the 2nd Law to Black Holes (??)

In 1981Jacob Bekenstein showed on theoretical grounds that the maximum entropy that could be contained in a volume of space was finite and equal to what came to be called the “Bekenstein bound”. This was later shown to be equal to the area of a black hole event horizon enclosing the volume expressed in Planck units.

This meant that black holes had entropy, and led to the formulation of black hole thermodynamics by Bekenstein, Hawking, and others. There are a set of laws governing black holes that are a direct analogy to those of thermodynamics, which suggests they may be the same thing and deeply related to the role of information in fundamental physics.

One of the many interesting features of Dr. Wolfram’s account is his admission that he was puzzled by the Second Law of Thermodynamics – he who was a pimply 19 year old English boy at MIT defending his PhD thesis against Richard Feynman! It makes those of us in the Great Unwashed who were also confused feel a little less bad about it.

Well, I read Dr. Wolfram’s extended discussion of the Second Law. It is very interesting, worth while, and thought provoking. Sadly, while the good doctor clearly believes he has cracked the puzzle, I still have to count myself among the unilluminated – or at least the unconvinced. Humility demands that I accept that Dr. Wolfram is at such an elevated intellectual level that the comprehension problem is all on my side.

At one point, Dr. Wolfram sounds slightly dismissive of the old days when physicists practiced “Natural Philosophy” – but how can we talk about the Second Law without straying into philosophical issues? Dr. Wolfram may have found a better mathematical representation of a weird physical phenomenon and the arrow of time, but does that tell us anything about the underlying physical reality?

The good doctor strives mightily to find a “proof” for the Second Law, which is commendable. But think about the First Law for a moment – the Energy of the Universe is Constant. How could one mathematically “prove” the First Law? Even Euclid had to start with a set of postulates which were assumed to be true rather than proved to be true. Perhaps the Laws of Thermodynamics are analogous? But that gets us perilously close to philosophy.