Registered: Oct 2003
Towards the fundamental process
Seven years on from NKS, my current experiment has allowed me to tick off one more important prerequisite for it to be believable that the fundamental process is discrete. Before now, this prerequistite has at best been a reasonable assumption, but I'm always happier when I've seen solid evidence.
Tony Smith has attached this image:
Before getting on with the details, I need to record an uncomfortably long list of disclaimers so nobody has any excuse for presuming I'm making a step too far:
The world we find ourselves in
- The experiment is a simple enough cellular automata which provides the basis for a conclusion via a "weak" understanding of the principle of computational equivalence and does not in any way suggest that any CA, let alone this one, is a candidate for the fundmental process.
- I don't have any expectation of ever being able to say definitively that the fundamental process is discrete.
- My hypthesised fundamental discrete process is basically a rule (Wolfram would say "program") for determining the next local state from the previous local state, for some suitable definition of "local". Wolfram and others have shown how spatial distance might emerge from an evolving graph-theoretic network, but I see experiential/relativistic time needing to similarly emerge and don't (yet?) have any conception of the form of a discrete system that would meet that requirement.
- All my experiments are with strictly deterministic systems made interesting by being computationally irreducible. I have no opinion as to whether the fundmental discrete process can be strictly deterministic, in part because I'm not sure that local states will be able to be strictly enumerated.
- While I've never been convinced by 19th century arguments that Planck units are necessarily fundamental, I do indulge the term as shorthand for "sufficiently small enough". Based on every other interesting level of emergence, the Planck scale would appear to be at least three levels removed from photon-mediated observables.
- Everything I see is through the lens of more than 20 years using and developing emergence/systems/complexity as my core theoretical framework, integrating its many dialects/perspectives including NKS. Initially rare/chance synergies between widely divergent forms are an important contributor to emergence in sufficiently large domains/experiments.
- My experiments all begin with simple starting conditions which I consider as philosophically important as simple rules. The longest iteration runs I have made with my current rule started with the only viable asymmetric head on collision between two common orthogonal spaceships, a seed which is regenerated with statistical frequency. This is typical. Complicated engineering is for others.
Before getting back to the actual result I want to talk about here, it is useful to think about the wonderful world we find ourselves in because, at least to me, the whole point of these explorations is to make progress towards a naturalistic account for our very existence.
I see the stable existence of numerous atomic elements beyond helium as the first essential step in making our world truly interesting. Those elements, "metals" to astrophysicists, are quantitatively negligible but collectively the source of almost all long term persistence and structure below the galactic scale.
Yet there is nothing of principle in the underlying physics which brings us hydrogen, helium, fusion, stars, photons, neutrinos, galaxies and (presumably) dark matter which makes those heavier nuclei necessary, let alone the complex quantum rules for neutralising electron orbitals that facilitate their binding in a limitless variety of more and more complex molecules. To me, the synergy between protons and electrons remains remarkable while to generations of reductionist physicists it just is.
Following the over-celebrated overthrow of aether, there has been little to encourage physicists to develop their understanding of the nowadays inescapable fact that empty space is very definitely something rather than nothing. I have long been convinced that the substance of empty space is not somehow getting thinner at anything like the rate that standard interpretations of Hubble expansion demand. This led to my sympathetic interest in Mark Suppes's Mechanical Gravity Theory and, from there, in Reg Cahill's Process Physics.
Seeing the multiverse as always in the process of creating its next (local) state makes more sense to me than trying to shoehorn three spatial dimensions into imaginary time.
Is Generations 345/3/6 deeper in Class 4 than the fundamental rule needs to be?
The end of July marked eight months study of iteration from simple seeds under the Generations 345/3/6 cellular automata rule, aka LivingOnTheEdge (LOTE). For more than half that time a new 24 inch iMac has been dedicated to long iteration runs. And new discoveries keep coming. But as with my earlier discrete systems experiments it is the revelation of underlying principles which motivates me more than the presentation of detailed results.
A couple of months back I was more concerned with discussing the creative synergy between deterministic chaos and emergent order in what turns out to be more of a boundary zone than a narrow edge. Class 4 is best seen as a region where both Class 2 and Class 3 operate interchangeably. But that is only one of LOTE's lessons.
Even earlier LOTE had revealed that a cellular automata could exhibit strong resilience and even limited self-repair, the previous lack of which had been one more argument against CAs being more than toys. It had also provided evidence I did not want in favour of a growth imperative right at the time when presumptions about a growth imperative are the last things we need to leave unchallenged on a finite planet operating under conservative physics. There is no doubt that the slow but statistically consistent growth of viable patterns in LOTE is essential to its continuing innovation. (LOTE's fractal population growth curves are far too reminiscent of financial market graphs, but that is another story.)
I should minimally recap the fact that any viable LOTE seed produces a chaotic core in which locally stable high density patterns (58% live) with never settled edges are embedded in a sea of common small patterns. (Average core density is 12% live, 6.5% dying.) A typically circular tending square core forms the base of narrow triangles of (orthogonal space)ships heading NSEW (0.016% live, 0.017% dying).
It is essential to the rest of this story that LOTE forms four common enough classes of what are strictly all puffer trails and which are generally produced by different tail mechanisms which move along with engines formed by a pair of ships with a gap of two cells which is bridged by a new rung every four iterations. In decreasing order of occurence frequency, those four classes are:
As the most aggresive mechanism for accelerating the spread of chaotic core, it is important that naked Delta is correspondingly rare, as are the "Rugby" mechanisms that "deltify" p.192 puffers. They and the viable ship collision products which tend to smooth and then square core boundaries generally fail to dominate the growing list of distinct mechanisms which ignite new seeds of active chaos far from the original core, but only under Generations 345/3/6. Under other rules, deltified or even faster mechanisms spread (near) contiguous chaotic core too fast or too often for other mechanisms to proliferate. Even in the uniquely closest other rule, generations 3458/3/6, the common p.192 puffer takes on the Delta form, upsetting the balance between core-spreading mechanisms.
- track laying with a continuous line of live cells flanked on either side by alternate live cells and gaps. Such track can be easily held stable by an end block but otherwise erodes slightly faster than it is created until it reaches the engine and reblocks, or changes form in a phase dependent reaction for shorter engines.
- p.192 puffer leaves a cluster of settled debris every 96 cells and a pair of rakes, the cycle being dictated by an eroding track phase which always fails to reblock.
- block trail laying in which a symmetric and a less common off-centre tail mechanism each leave a new (2x2) block every eight iterations
- "Delta" in which an initial p.56 tail reaction produces either of two very different modes further back depending on the presence of absence of a second period doubling mechanism. The "naked" mode keeps doubling along a narrow wedge of LOTE's familar chaotic core with many rakes forming a delta wing-like pattern. The rakeless mode leaves a debris trail repeated every 56 cells. Any disturbance to a large area behind the engine is likely to flip the trail between modes.
Reminiscent of the chemical elements that enrich our world, an ever longer list of distinct mechansims run along LOTE's tracks and trails spreading new seeds of active chaos. Engines in an outbound ship stream are protected from disturbance by their emergent dynamics, especially their common 1/2 speed of movement. But tracks erode faster and they readily acquire attached second tracks (tagalongs) which travel faster still. Block trails also commonly acquire a couple of faster and one slightly slower moving mechansims, all of which can interact in multiple ways far from the core from which the tracks and trails originally emerged.
While the underlying process of our multiverse needs, across several levels of emergence, to support far more wonders than LOTE is ever likely to, I'm no longer confident I can tell which process will show stronger first level emergence. And that may well mean that the real fundamental rule will not be any more complicated, though we will be left with a chellenge of a different order to validate it across those extra levels.
I've attached a short animation which is intended to be a pivotal close up within a much longer sequence. It is from iterations 426250-426350 of the Whoa (Wild head on asym) seed centred at (34325, 115230). It starts with a new gap producing "tagalong" approaching a single cell discontinuity in a gapless tagalonged track, the discontinuity being left over from an earlier head on collision between two gapless tagalongs had left them (almost) cleanly joined. The new passing taglong disturbs the previously stable discontinuity, the disturbance soon settling leaving a larger disturbed but again stable section to the left and a periodic gap closing process moving right at 2 cells per 11 iterations, 2/11 being the slowest speed yet seen of any moving pattern in LOTE where (lateral space)ships and track-laying engines move at 1/2 with only a few attached structures moving faster such as taglongs at 2/3. (Green cells are live, the four shades of red are the four stages of dying.)
Complex Systems Analyst
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