Karsten Pultz outlined his approach here: Why randomness depends on order: Comparing to evolution, the randomness produced by the orderly dice, would be the same randomness having produced the dice itself, because that’s how evolution works, slowly building order by random events from the bottom up. Applying the same hypothetical process to bicycles the random event that I get a puncture when riding my bike would be the same type of event which initially created the bike.
Experimental physicist Rob Sheldon responds:
A couple of comments on your excellent post:
a) in computer science, it is very difficult to make a random number generator. Successive runs of the code should not produce the same numbers. But most generators do. Likewise, if the numbers are grouped in triplets, and plotted in a cube, do they fill the cube smoothly, or is it clumpy? Again, most random number generators are clumpy. That’s because a program with information is attempting to act like randomness. There are even companies that use a radioactive material whose decays are turned into numbers to get a random number generator! In this case, attempting to throw away all the information in a computer program.
So I do understand your claim that disorder is only in reference to order. Because our tools are all about order. Nevertheless, there can be randomness without tools, without programs, without persons. Such randomness, however, isn’t recognized. It is only when we apply a tool to it, like the decays of radioisotopes, that we find it is random. Ontologically, neither the randomness or the order is first, but it takes order to recognize disorder.
b) Second, randomness, like the computer that uses a radioisotope to make random numbers, can be a orderly process. There is no reason that disorder cannot be the product of an ordered system. Purpose includes both order and disorder. On the other hand, disorder cannot include order at all. So in one sense, order is the greater of the two, and swallows up, or incorporates randomness. This can be seen, for example, in “intrinsically disordered proteins”, that by design, do not settle down in a specific shape. Clearly, it takes effort to find a protein that is so unstable, and the cell makes use of such proteins.
Likewise, in the dice example, there is a careful preparation of a perfect cube with a centered center-of-gravity. In college I had a shop class, and tried to make a die on the end-mill. I could not get a perfect cube, as I watched my project shrinking to a smaller and smaller piece of metal. It takes skill to make a die random, and disordered end-mill cuts only made things worse. Randomness does not arise by accident.
c) Finally, let me say something about physics. In the 1800’s we described the motion of an object as subject the forces acting on it. The theoretical equations of motion were described by the “Lagrangian”. The solutions to the Lagrangian determined the motion of the particle. So powerful was this paradigm that a philosophical position was called “Lagrangian Determinism”, that we were all made of atoms, and the atoms all behaved as point particles with forces, and therefore given the initial conditions, we could integrate the Lagrangian and determine the future.
Common wisdom is that QM destroyed this possibility, but actually even before the advent of QM, at the turn of the century, Henri Poincare showed that there were numerical solutions to Lagrangians that were “chaotic”, indescribable by any regular function. Russian mathematicians around the time of the Communist revolution, showed that there were entire classes of functions that had no derivative or continuity—that knowing the value of a function at time t, told you nothing about later times t+dt. Determinism was impossible. (These mathematicians were Russian Orthodox, and felt that their math would prove the Communist programme to be a failure.)
No one knew what to do with these discoveries at the time. We invented computers and in the 1960’s rediscovered chaos. It turns out, that if you make a “Poincare plot” by say, plotting the position versus velocity of a pendulum at t, t+dt, t+2dt, t+3dt etc, the points sometimes retrace a figure showing a “closed solution” and sometimes scatter all over the place filling the area densely, “chaotic solution”. So if you compare the area of chaotic orbits to the area of closed, deterministic orbits, you find that chaos is by far the most common behavior. We just had never seen it because we didn’t have computers, and the tools to find it.
What this says is that far from “Lagrangian determinism”, we are far more likely to have “Lagrangian chaos” for physical systems. It takes planning to make a system deterministic, closed orbits.
But does this mean the system is most likely random? By no means. These chaotic orbits have special properties. For one thing, they obey the Lagrangian equations. They have little islands and inclusions that represent closed solutions. And often they present “strange attractors” or basins where all the solutions end up. So just as mathematicians find that true randomness is very hard to produce in a program, so physicists have come to realize that we live on the edge between chaos and order, where the chaos is just order on a higher plane. Chaos is a global solution, not just a local one. The equations or area described by the chaotic orbits is not defined by the current values of x,v_x, but rather by the global properties and boundaries of the system.
Why is this significant? Because in the 1800’s physics believed that diffusion, heat, transport were local, random, processes defined by a Maxwell-Boltzmann distribution. That randomness was inherent in Nature, and that global order was a difficult, information-rich process that rapidly degenerated (entropized) on its own. Darwinism was a direct result of applying that local physics to biology. Now the very same systems are seen to be part of a global chaotic system with its own set of rules. Diffusion is no longer random, but a process by which the global system approaches its lowest energy state. When magnet domains are involved, that minimum energy state can be “frustrated”, leading to many “non-equilibrium” long-lasting states. In other words, we have learned to make global “smart materials” that do not behave like the 19th century “dumb” materials subject to local diffusion and entropy.
It is not that our materials are different, it is because physics is no longer assuming that “randomness” is a natural or inevitable state of matter, or that all forces are local. Locality and randomness isn’t as basic as we thought. It is actually a subset of all states that are available, being unable to account for global states. Darwin is just so 19th century, but we are now in the 21st.
I hope this gives a flavor of what I enjoyed about your post. – Rob