Registered: Dec 2009
Posts: 22

Distler, Shah & Sorge 2011 (Table 3.)

MikkH has attached this image:

Last edited by MikkH on 02-11-2012 at 02:21 PM

Report this post to a moderator | IP: Logged

Registered: Dec 2009
Posts: 22

If numbers express size and the groups symmetries, then it is perhaps fair to say that even less constrained creatures like CA (of the classes 3 and 4) can express all this but in addition also nonanticipativeness of their time evolution that in general can not be fully anticipated from outside by any formal or natural system. However, even if using irreversible NKS models, there will always be certain time lag between the outputs of a system and models of it.

From irreducibly complex fabrics (e.g., in Fig), produced by some short asymmetrical CA rules & initial conditions we commonly used to extract out certain explainables, i.e. regular (symmetrical) patterns, like the repetitive or nested (relying on our reducibility constrained anticipation paradigm) and imagined that nothing essential remains uncovered by such operational short-cut paths (resulted by various symmetries). This has perhaps resulted also in some well known suggestions like treating time as subjective illusion, or just as some simple parameter, the complexity of which can be freely ignored without any serious consequences.

However, this will change with evolving notions of complexity, incompleteness, computation, irreversibility, and irreducibility due to gigants like Leibniz, Gödel, Turing, Prigogine, Chaitin, Wolfram, and many others. Of course, time complexity is ignored in simple formal symmetry biased descriptions of reality relying on anticipativeness, but we know now that such path is not without serious obstacles. In simple finite comprehensible explanations of reality one is just ignoring the time complexity and irreversibility, but this will inevitably leave outside the scope complex emergent phenomena like life, consciousness, and free will.

Only in simple enough (e.g., repetitive and self-similar), strictly symmetry constained (reducible) systems the expressibles (everything which the systems can express) are equal to explainables (which they can explain). The complex irreducible systems can always express vastly more than they are able to explain. This is a fundamental asymmetry characteristic to complex irreducible systems which cannot be reduced to any combination of symmetries (whatsoever monstrous) to outrun their time evolution. Thus, still pretty widespread opinion that our obsession with symmetries can provide us with power to outrun even time evolution of complex systems, has to be regarded as an illusory dream.

[Nonetheless, people's faith in ultimate power of symmetries seems to be common between science and religion, and must never be underestimated. Many such people (at least in Estonia) are going to spend the precious time around 21.XII 2012 inside their own built wooden (not Woodin's!) pyramids, wearing folium made pyramid-shaped hats, hoping to be among 10%... of the ACTA survivors :)
Eventually, dictators in the world are also blinded by symmetry, worshiping and utilizing always its decisive power.]

What else might NKS tell about the nature of Time?
Only if causality breaks down Time irreversibly steps forward?

Can Wolfram's PCE and the speed of light in fact be two sides of the same coin?

Would it make sense to formulate the Principle of Computational Inequivalence? (e.g.
"All computations which are not obviously simple (reducible due to symmetries) or equal are of inequivalent sofistication")

Happy Anniversary to all NKS fans!

---
Évariste Galois (1811–1832):
«Je n'ai pas le tems» [I do not have the time; the gut-wrenching line
from his last letter.]

"For those of us who believe in physics, the distinction between past,
present, and future is only a stubbornly persistent illusion."
Albert Einstein (1879-1955) in a letter of condolence to the Besso family,
March 21, 1955, less than a month before his own death (Einstein Archives 7-245).

MikkH has attached this image:

Last edited by MikkH on 07-07-2012 at 07:10 AM

Report this post to a moderator | IP: Logged

Registered: Dec 2009
Posts: 22

1. NKS may give us a clue for answering the following fundamental question, namely, why is the Universe 3-dimensional? Three is just the minimal number of components the interactions of which can lead to computational irreducibility and the arrow of time.

2. It would be interesting to study savants' responses to certain CA images (static and dynamic). Perhaps they can visualize computational landscapes in a similar way?

3. Maximal predictive power of a finite scientific theory (mathematical ones included) is limited to symmetries of the Monster group (the largest sporadic group, the Fischer-Griess group). The group operations might correspond to computational shortcuts.

---
Unlike the explanatory and predictive power of science, Nature is not constrained to symmetries.

Last edited by MikkH on 12-26-2012 at 01:55 PM

Report this post to a moderator | IP: Logged