The case is still not watertight however. Cellular automata, and indeed any computation proceeding within a computer, move in discrete steps. If the Universe is an on-going computation, then, strictly speaking, it ought to proceed in discrete state transitions, frame by frame as it were. Mathematician Martin Gardiner who originally introduced the Game of Life to readers of the Scientific American, was one of the first to speculate upon this. He wrote:
“There is even the possibility that space-time itself is granular, composed of discrete units, and that the Universe....is a cellular automaton run by an enormous computer.”
In other words, if the Universe is a computation, there is likely to be a smallest unit of time (time is granular) which cannot be broken down further. Such a hypothetical smallest unit of time is known as a chronon. A chronon is an absolute moment in which the Universe is in a particular state. This state will then proceed by a discrete ‘jump’ to form the next chronon according to whatever laws are operating on that state, much like the movement of electrons which are supposed to discretely jump from one orbit to another. There are believed to be no intermediary states between successive ‘jumps’.
One might now be tempted to ask why we experience time as flowing. There is no surprise here, for to talk of discrete time is like talking of the successive frames of a film. If the frames are presented quickly enough the illusion of continuity becomes apparent. Such an illusion of continuity is also manifest in the Game of Life. The state transitions of Life automata can be processed by a computer so quickly as to give rise to patterns which, on the computer monitor, appear to flow across the 2-dimensional playing field. In fact, all computer displays move in discrete stages, even in the most advanced programs. For instance, computer games might look as if they are flowing smoothly, yet in actuality they are proceeding in rapid state transitional jumps (at the current time this fact of computational ‘jumpiness’ is a problem being tackled by virtual reality engineers who are striving to speed up their computerised VR graphic displays in order to make their necessary complex virtual worlds flow smoothly like the real world).
The ‘illusion’ of flowing forms which seem to constitute the Universe must therefore be due to the presence of stable patterns within the computation, patterns which endure from one moment to the next. If one were to take one snapshot slice of reality, one chronon as it were, then one would not be able to properly discern any patterns, rather the patterns we observe, like planets and people, are patterned structures which emerge over a multiple succession of such slices. Likewise, I would assume that consciousness seems to flow precisely because it is an informational pattern which endures across successive frames of granular time.
There have been attempts to quantify the hypothetical chronon. For what its worth, it is assumed to be the shortest conceivable length divided by the velocity of light. For obvious reasons, I’ll take this definition on trust. Anyhow, this yields what is sometimes called the ‘Planck time’, and this may represent the elusive chronon. Intuitively it seems there must be discrete time, for otherwise a second could be divided into an infinity of moments. If so, then it is hard to see how time appears to flow at all. An echo of this ‘timely dilemma’ is found in particle physics. Are there any smallest bits, or does scale and size continue indefinitely? As with time, it makes more sense to think of a smallest unit of matter/information and a smallest unit of time. The case remains open however, though it is doubtful that any measuring instrument could be built to observe the discrete moves in time. Alternatively, it may still be possible to hold the computational view of the Universe with non-discrete time. This is a task someone else can tackle.
I’ve seen mention to N.A. Kozyrev on your website. I quote his work extensively in the above link. If it’s true his experiments have been confirmed then time is actually something you can measure outside of our own subjective experience. Too bad the guy is pretty much ignored amongst the science guild.
I think if you want to see the reality “film projector” just keep a steady dream journal each night.
Gardiner sez: “...and that the Universe....is a cellular automaton run by an enormous computer.â€
I’m seeing fractal iterations of simulations and so forth : Turtles all the way down
thirtyseven - do you know who wrote the psilocybin article at v72.org?
Man, I’ve been trying to source that one, too! I’m suspicious because it seems like parts of it are from McKenna talks I remember hearing—as in, verbatim—and yet there’s no authorship...it’s a weird document. It’s also huge and very interesting, and I’d think whoever made that would want to...well, yeah.
I’ve been very interested in the debate over “continuous vs. discrete physics” that the “God is the Machine” article kicked off. I’m struck by the fact I find myself overwhelmingly on the site of the discrete physics weirdos—I think that the “continous” geometric curvature that classical physics sees is a trick of perspective. Similar to how a photomosiac becomes a coherent image from far enough away, or how the discrete samples of an audio .wav file look like a smooth sine wave when you zoom out enough. It’s a matter of scale, from far enough out, the discrete values begin to resemble geometric, continuous curves.
I’m also struck by the fact “continuous” physics is still insanely useful—after all, it’s often far more valuable to compute the general trend of complex events than to calculate precise values for every tiny element.
Even continuous physical models are still evaluated discretely, the formal language is always discrete.
The continuum and the discrete line seem to me to be mutually constitutive, if you can define one, you can always define the other. Think about harmonic waves, there are often places in physics where we see discrete phenomena arise, but often that’s just because the (discrete) natural numbers will naturally arise as co-efficients in continuous equations.
The way I see it: Physics equations are always discretely interpreted, so computational interpretations of physical formulas are always valid. At the same time, I find nowhere in my life experience any discontinuity, I can always look closer at any apparent discontinuity in my sensible field and find more detail, but never an abrupt break.
So the computationalists feel that physics equations (which indicate discrete) accurately reflect what’s “really” going on, whereas I feel it is more sober to say that discrete models are always applicable, without making the metaphysical leap of “the universe is discrete”.
The ‘digital philosophy’ point of view is quite relevant to this quote from Harman:
Well, according to science, about 15 billion years or so ago, there was a big bang and the universe began to evolve and this was an evolution of stars and the planets and then elementary life forms on at least one of those planets. This all happened accidentally; that is, things were behaving according to scientific laws and coincidentally, certain chemical elements came together in such a way as to create the first elementary life forms.
We know the authority of modern science, especially now with quantum physics and chaos theory, and it looks as though it’s on the edge of really explaining everything. This dominant myth infuses our education system, it infuses our health care system, it infuses our legal justice system-every institution in society.
So, what if it were wrong? It would affect everything. Now that’s a pretty bold statement-and remember that I was trained as a scientist too and I have a lot of respect for science in terms of what it does. But what we’ve done, in modern society, is to take this scientific world view which was really aimed at prediction, and control, and creating technologies, and we’ve given it so much prestige and power that we put it in the position of a world view to try to live our lives by, and guide our societies by, and shape our powerful institutions by, and that’s where it gets to be misleading. I could quibble and make it sound a little bit better if I just said “incomplete” or a “little bit off” but I don’t want to say that. I want us to think seriously about the possibility that there is a fundamental error in there and that it’s important for ordinary citizens to recognize that.
Now, whether or not ‘reality’ is discrete or continuous, all computable theories are discretely embodied in formal systems.
Every physical theory requires a set of axioms to actually evaluate it formally and reach conclusions. What Chaitin showed is that the amount of predictive power measured in bits of any formal system cannot exceed the number of bits required to define the axioms for that system.
This means that we do not gain any fundamentally new knowledge except for when (perhaps implicitly) we redefine our axioms, all we’re doing when we compute is shuffle around the information we already have.
Algorithmic information theory is sort of a quantitative realization of Goedel’s insights.
The data processing theorem states that data processing destroys information.
(or at best, in the case of reversible computing, data is not destroyed, but no new bits of information can be got.)
no new bits of information can ever be learned except by observing, not by computing.
I believe this also implies that certain ‘truths’ or facts are fundamentally unlearnable by humans, but there are lots of smarter people than me who don’t agree.
Sorry to go OT again, but I remembered a couple papers very relevant to Harman’s contention that science fundamentally cannot cover all experience, in contrast to what many people assume:
These are interesting in that they show specific, concrete problems of practical value that simply cannot be solved (barring the unlikely possibility of hypercomputation.)
My friend, I don’t think “off topic” exists and I love seeing the associations people bring to the table. I’m 1/2 way through the Svozil and loving it, thanks for these links.
i think they may also have encoded a methodology and course of movements/contemplative practice that would align the ‘energies’ of the human body with the ‘energies’ of the created universe in a fractal pattern (as above, so below/man created in god’s image, etc.).
It was inevitable that the “timeless” conception of classical physics would clash with the metaphysical conceptions of the Western world. It is not by accident that the entire history of philosophy from Kant through Whitehead was either an attempt to eliminate this difficulty through the introduction of another reality (e.g. the noumenal world of Kant) or a new mode of description in which time and freedom, rather than determinism would play a fundamental role. Be that as it may, time and change are essential in problems of biology and in sociocultural evolution. In fact, a fascinating aspect of cultural and social changes, in contrast with biological evolution, is the relatively short time in which they take place. Therefore, in a sense, anyone interested in cultural and social matters must consider, in one way or another, the problem of time and the laws of change: perhaps inversely, anyone interested in the problem of time cannot avoid taking an interest in the cultural and social changes of our time as well.
Classical physics, even extended in quantum mechanics and relativity, gave us relatively poor models of time evolution. The deterministic laws of physics, which were at one point the only acceptable laws, today seem like gross simplifications, nearly a caricature of evolution. Both in classical and in quantum mechanics, it seemed that, if the state of a system at a given time were “known” with sufficient accuracy, the future (as well as the past) could be at least predicted in principle. Of course this is a purely conceptual problem; in fact, we know that we cannot even predict whether it will rain in, say, one month from now. Yet, this theoretical framework seems to indicate that in some sense the present already “contains” the past and future. We shall see that this is not so. The future is not included in the past. Even in physics, as in sociology, only various possible “scenarios” can be predicted. But it is for this very reason that we are participating in a fascinating adventure in which, in the words of Niels Bohr, we are “both spectators and actors.”
—Ilya Prigogine, From Being to Becoming: Time and Complexity in the Physical Sciences
