Page 28-29: The physical origin of information:
During the twentieth century our understanding of the arrow of time and the physical origin of information became reconciled with the physical nature of reality. New theories were able to show that information was not an anomaly but something to be expected. These theories did not contradict the dynamics of Einstein and Newton or the statistical mechanics of Boltzmann, since they showed that the origin of information and the arrow of time hinged on additional physical principles and conciderations. The key thinker was the Russian-born and Belgian-raised statistical physicist Ilya Prigogine. Prigogine was awarded the 1977 Nobel Prize in Chemistry "for his contribution to non-equilibrium thermodynamics, particularly the theory of dissipative structures." Prigogine produced many important insights, but the one that is of concern hereis the idea that information emerges naturally in the states of physical systems that are out of equilibrium. This statement, which summarizes the physical origins of information, sounds awfully complicated. Yet if we go carefully through a series of examples, we will realize that it is not. So in the next paragraphs I will unpack the meaning of Prigogine's statementa point at which its meaning will become obvious.
To understand the physical origins of information we need to understand a few things fuirst. One is the idea of a steady state. The second is the difference between a dynamic steady state and a static steady state. A very simple case of a static steady state is a marble dropped into a bowl. We all know what happens here. after a short period of time the marble sits quietly at the bottom of the bowl. this represents a static steady state.
A more interesting case is a box filled with gas. If we put gas inside a box and wait for a bit, the amount of gas in the right side of the box will be equal to the amount in the left side of the box. The steady state of a box filled with gas, however, is not analogous to that of a marble sitting in the bottom of a bowl. In a box filled with gas, the molecules are not at all resting in a fixed position. they are moving constantly, and the steady state is reached when the number of gas molecules moving from left to right is equal to the number of molecules moving from right to left. the box with gas (like the example of a drop of ink fully diffused within a glass of water) represents a case of dynamic steady state.
Now let's consider the state of a non-equilibrium system. The classic example in this case is the whirlpool that forms when you empty a bathtub. As soon as you remove the stopper and water starts racing down the drain, the water above the drain begins to organize into a whirlpool. The whirlpool is a steady state, since it is steady as long as there is water flowing in the system. It is also an information-rich state, since whirlpools are rare configurations of water molecules that do not appear spontaneously in still water. Unlike still water, whirlpools are organized structures in which water molecules are not going in random directions, but have a speed and trajectory that is correlated with that of the water molecules traveling next to them. the information-rich state of a whirlpool emerges naturally—it is something that we get for free in an out-of-equilibrium system. Going back to our original sentence, we can see that the whirlpool is an example of information that emerges naturally in the steady state of a system that is out of equilibrium.
Information
We are still left with the question: What is information?
Each molecule in the whirlpool has a state (position, speed) and behaviour (driven by relations to other molecules and to the earths gravity and rotation).
Hence information is an emergent property of interacting objects?
Page 36-40: information, computation and matter:
While a tree is technically a computer, its power source is not an electrical outlet but the sun. A tree is a computer that, just like we cannot run MATLAB, but unlike computers and us, it has the knowhow to run photosynthesis. Trees process information, and they are able to do so because they are steady state out-of-equilibrium systems. Trees embody knowhow, which they use to survive.
But since a tree is alive I cannot use it to argue that computation precedes life (although it is a convincing example of computation predating humans). To illustrate the probiotic nature of the ability of matter to process information, we need to consider a more fundamental system. Here is where the chemical systems that fascinated Prigogine come in handy.
Consider a set of chemical reactions that takes a set of compunds {I} and transforms them into a set of outputs {O} via a set of intermediate compounds {M}. Now consider feeding this system with a steady state flow of {I}. If the flow of {I} is small, then the system will settle into a steady state where the intermediate inputs {M} will be produced and consumed in such way that their numbers do not fluctuate much. The system reach a state of equilibrium. In most chemical systems, however, once we crank up the flow of {I} this equilibrium will become unstable, meaning that the steady state of the system will be replaced by two or more stable steady states that are different from the original state of equilibrium. When these new steady states emerge, the system will need to "choose" among them, meaning that it will have to move to one or the other, breaking the symmetry of the system and developing a history that is marked by those choices. If we crank up the input compounds {I} even further, these new steady states willbecome unstable and additional new steady states will emerge. This multiplication of states can lead chemical reactions to highly organized states, such as exhibited by molecular clocks, which are chemical oscillators, comunds that change periodically from one type to another. But does such a simple chemical system have the ability to process information?
Now consider that we can push the system from one of these steady states by changing the concentration of inputs {I}. Such a system will be "computing" since it will generate outputs that are conditional on the inputs it is ingesting. It would be a chemical transistor. In an awfully crude way this chemical system models a primitive metabolism. In an even cruder way, it is a model of a cell differentiating from one cell to another—the cell types can be viewed abstractly as the dynamic steady states of these systems, as the complex systems biologist Stuart Kauffman suggested decades ago.
Highly interacting out-of-equilibrium systems, whether they are trees reacting to the change of seasons or chemical systems processing information about the inputs they receive, teach us that matter can compute. These systems tell us that computation presedes the origin of life just as much as information does. The chemical changes encoded by these systems are modifying the information encoded in these chemical compounds, and therefore they represent a fundamental form of computation. Life is a consequence of the ability of matter to compute.
Finally, we need to explain how all of this relates to the irreverability of time. After all, this is where the chapter started. To explain this, I will use once again the work of Prigogine, and as an example, I will invite you to imagine a box filled with trillions of ping-pong balls.
Imagine tat the ping-pong balls collide with each other without lsing energy, so these interactions never cease. Next, assume that you started observing the system when all of the ping-pong were located neatly in one quadrant of the box, but also were endowed with enough kinetic energy—or speed—to eventually scatter all around the box. This is similar to the drop-of-ink example we used before.
In this simple statistical system, the question of reversibility of time is the question of whether it is possible, at any given point in time, to reverse the motion of the ping-pong balls such that time is seen to run backward. That is, is it possible to put the ping-pong balls on a trajectory where the final state is the neat configuration we defined as the initial configuration?
Thinking of what happens when we runthis "movie" forward is easy. Ping-pong balls fill up the box with their incessant motion, ending up in what we now know as a dynamic steady state. But let's give the time-reversal experiment a shot. To make things easy I will assume that we have two machines. One of the machines is able to take a number of balls and modify their velocities instantly if we provide the machine with with an input file containing the desired velocities for each ball. The machine has infinite precision, but it executes instructions only with the precision of the information it is fed. that is, if positions and velocities are provided with a precision of two digits (i.e. speed in centimeters per second), then the machine will assign velocities of the balls with only that precision, making all unspecified decimals (i.e. millimeters per second and beyond) random. The second machine we have measure the position and velocity of each ball with a finite but arbitrary large precision. So the question is, can we use these two imaginary machines to reverse the velocities of the balls such that the "movie" plays backward?
Let us irst try the experiment by reversing velocities of each ball with a very coarse precision. For instance, if the velocity of a given ball in the x direction is vx = 0.2342562356237128... [mts/sec], we simply reverse it by taking the first two digits i.e., we make a new vx = -0.23). Will this simple reversal be enough to make the movie play backward? The answer is certainly not. A system of trillions of ping-pong balls that never lose energy, like the one I am describing here, id by definition chaotic, meaning that small differences in initial conditions grow exponentially over time. The chaotic nature of the system implies that the precision of two digits is not enough to put the balls on a trajectory that will naturally evolve back to its original configuration. But is this just a matter of precision or is there a fundamental constraint at play? Given enough precision in our measurements and actions, can we reverse time?
Armed with our imaginary machines, we can rerun this thought experiment with greater precision, but as long as that precision is finite, we will not reverse time. Instead of using a couple of digits, we could specify velocity with ten, twenty or a hundred digits. But the reversal of time will still not be achieved because in a chaotic system, the imprecisions of our measurements will grow to dominate the system. In mathematical language, we can say this is a case where the importance of digits is inverted.Normally when we have a number with many digits, the digits to the left are more important than those to the right (especially in your bank account). But in a chaotic system this is not the case, since such a system it is the last digit of measurement, not the first one that grows to become dominant. Yet no matter how precise our measurement, there is always a digit to the right of the number. So even without bringing in Heisenberg's uncertainty principle (which will limit our precision to a few tens of digits), we can conclude that the movie will always look as it is playing forward, except for the brief period of time in which we are injecting energy into the system by changing the velocities of the particles with our machines.
So time is irreversible in a statistical system because the chaotic nature of systems with many particles implies that an infinite amount of information would be needed to reverse the evolution of the system. This also means that statistical systems cannot go backward as there are an infinite number of paths that are compatible with any present. As statistical systems move forward they quickly forget how to get back. This infiniteness is what Prigogine calls the entropy barrier, and is what provides a perspective of time that is not spatialized like the theories of time advanced by Newton and Einstein. For Prigogine, the past is not just unreachable, it simply does not exist. There is no past, although there was a past. In our universe there is no past, and no future, but only a present that is being calculated in every instant. This instantaneous nature of reality is deep because it helps us connect statistical physics with computation. The instantaneous universe of Prigogineimplies that the past is unreachable becauseit is incomputable at the micro level. Prigogine's entropy barrier forbids the present to evolve into the past, except in idealized systems, like a pendulum or planetary orbits, which look the same going forward and backward (when there is no dissipation involved).
Photosynthesis
The photosynthesis is actually conducted by the chloroplasts where the photosynhetic chlorophyll captures energy from sunlight, splitting water into oxygen and hydrogen, and employing carbondioxid to produce hydrocarbons given as energy to the tree.
Trees get energy in the form of hydrocarbons from the chloroplasts which in return get convenient access to sunlight and water.
Tree and chroroplast live in a tight symbiosis.
Neither tree nor chroroplast process information,even if they process matter and energy?
Precision and units
The talk about precision is merely bringing confusion as it depends on units (btw. the unit mts is an unknown novelty), and is of no significance for the phenomenon.
The initial state may be reached in principle, but the probability is diminishing with increasing number of interacting components (molecules or balls do not matter).