William Kunstler's "terrible myth"

"And that's the terrible myth of organized society. That everything that's done through the establishe­d system is legal. And that word has a powerful psychologi­cal impact. It makes people believe that there is an order to life and an order to a system and that a person that goes through this order and is convicted has gotten all that is due him. And therefore society can turn its conscience off and look to other things and other times.

And that's the terrible thing about these past trials is that they have this aura of legitimacy­, this aura of legality. I suspect that better men than the world has known and more of them have gone to their death through a legal system than through all the illegaliti­es in the history of man. Six million people in Europe during the Third Reich? Legal. Sacco/Vanz­etti? Quite legal. The Haymarket defendant? Legal. The hundreds of rape trials throughout the South where black men were condemned to death? All legal. Jesus? Legal. Socrates? Legal. And that is the kaleidosco­pic nature of what we live through here and in other places. Because all tyrants learn that it is far better to do this thing through some semblance of legality than to do it without that pretence."

William Kunstler

Zurek's improvement of the definition of entropy

"A potentially important application of algorithmic complexity to physics was proposed by Wojtek Żurek of the Los Alamos National Laboratory in New Mexico. In order to rid Boltzmann's definition of entropy of its troublesome element of subjectivity, Żurek suggested an almost imperceptible modification of it. Recall that entropy is a measure of missing information about a system. It therefore depends on what an observer happens to know: a smarter being has more information, is missing less, and thus assigns a lower entropy to a system than a more limited creature. To render entropy more objective, Żurek recommended adding a measure of recorded information to that of missing information. The sum of the two remains constant --if you remove data from one column, it reappears in the other. The observant creature thus becomes redundant; only the entries in its notebook or computer memory matter.

But how to access the amount of recorded information? Żurek chose algorithmic complexity as the most natural measure. Accordingly, his new, improved entropy consists of two portions: the conventional entropy as measured by the formula on Boltzmann's tomb, plus a piece that is normally inconceivably tiny, and accounts for the algorithmic complexity of the listing of recorded knowledge about the system. A mathematical description of the size and shape of a vessel containing a gas might be a typical item in the list, while missing information includes the coordinates of a vast number of atoms. Notice that in the hypothetical case that every position and every velocity of every atom is known, the Boltzmann entropy of the system is zero, but the added term --the length of the description of what's known, in binary code-- will be huge, bringing the total entropy back to its previous value. After a hundred years the reek of subjectivity has finally been lifted from the Second Law of Thermodynamics.

In spite of its cogency, Żurek's improved entropy has not gained much support.

Hans Christian von Baeyer, Information, the new language of science, Chapter 12

Simple. It reminds me of the kinetic and potential energy in adiabatic mechanical system, in which the sum of the two stays constant at all times. I also remember vaguely that the history of the total energy followed the same trajectory than that of entropy; only one portion of the energy was first defined and only when the second portion was defined, the energy became a constant of the system and starting to be accepted with its components, as valid quantities.

Has the Universe finite or infinite complexity?

"[L]et's now finally discuss whether the physical universe is like π=3.1415926... which only has a finite complexity, namely the size of the smallest program to generate π, or like Ω, which has unadulterared infinite complexity.
Well, if you believe in quantum physics, then Nature plays dice, and that generates complexity, an infinite amount of it, for example, as frozen accidents, mutations that are preserved in our DNA. So at this time most scientists would bet that the universe has infinite complexity, like Ω does. But then the world is incomprehensible, or at least a large part of it will always remain so, the accidental part, all those frozen accidents, the contingent part.
But some people still hope that the world has finite complexity like π it just looks like it has high complexity. If so, then we might eventually be able to comprehend everything, and there is an ultimate TOE [Theory of Everything]! But then you have to believe that quantum mechanics is wrong, as currently practiced, and that all quantum randomness is really only pseudo-randomness, like what you find in the digits of π. You have to believe that the world is actually deterministic, even though our current scientific theories say that it isn't!
[...]Wolfram believes that very simple deterministic algorithms ultimately account for all the apparent complexity we see around us, just like they do in π. He believes that the world looks very complicated, but is actually very simple. There's no randomness, there's only pseudo-randomness. Then nothing is contingent, everything is necessary, everything happens for a reason. [Leibniz!]
[...]
Or perhaps from inside this world we will never be able to tell the difference, only an outside observer could do that."

Gregory Chaitin, Metamath!, Appendix II.

Notice that the last argument has also been mentioned by Karl Popper in his Open Universe (see my review of his book).