Complexity levels and what they suggest

Complexity levels and what they suggest.

At many complexity levels there seems to be two fundamental classes of
information systems:

1. Elementary particles are first of all either bosons or fermions.
   Bosons are generally force carrier particles, whereas fermions
   are usually associated with matter.

2. Atomic nucleus and electron cloud.

3. Life molecules including RNA and DNA, versus all other, lifeless molecules.
   Living creatures are able to be proactive towards their environment, whereas
   lifeless matter is adaptive (reactive) to environment rather than proactive.

4. Starting from the rather simple living creatures, most organisms are either
   proactive (animals) or adaptive (plants) to resources of the environment.

5. Living creatures of relatively more advanced species are either proactive (males)
   or adaptive (females) with respect to other individuals of their species.

6. Placebo effect suggests that there is a proactive and an adaptive agent in psyche.

7. It's hard to look above and beyond, but it seems likely that individuals
   in advanced societies are either mostly creators or mostly consumers
   of informational products (decisions, innovations, virtual realities...)
   Thus again, mostly either proactive or adaptive, now towards their society.

8. It also seems likely that most societies position themselves first of all as
   either proactive or adaptive towards their space-time neighbors.

Supposedly this is because information systems evolve better when there are features
enabling bimodal distributions, and seemingly proactive/adaptive is one of such
features.

If the Mathematical Universe Hypothesis[1] is true, that is, the hypothesis that
our external physical reality is isomorphic to a huge mathematical structure (HMS),
then it seems possible that the gradual increase of total complexity of HMS is
what we subjectively perceive as time, and increase of complexity in a self-aware
core (perhaps the proactive agent of psyche) could be essential for what we
subjectively perceive as qualia and consciousness.
Note this is descriptive (Kolmogorov) complexity, not computational complexity.
Descriptive complexity of a 10^122 bit long sequence[5] is below 1000 bits
if the sequence is fully describable with a short pattern and a repeat count.

We can assume that HMS always contains an infinite amount of "random" data, which
gradually become "non-random". For a finite, binary, one-dimensional illustration
consider a set of 2^Z files such that the first N bits are the same in all files
of the set, while data in the last Z bits are different in each file of the set.
Then at the next (for this reference frame) moment t+tp, where tp is Planck time,
the set contains 2^(Z-x) files such that N+x bits are the same, and Z-x bits are
all different. Or M groups of files (if we assume that M variants of future
may be equally real) such that N+x bits are same within each group.
M <= 2^x, x is negligible compared to N, N is negligible compared to Z: x << N << Z.
Descriptive complexity of HMS is the complexity of only the "non-random" part of it,
because the "random" part is kind of "outside" and invisible.

There is no time in the suggested picture in the sense that universe contains
nothing except mathematical structures. However, there is time in the sense that
structures of lower complexity "precede" structures of higher complexity, and
the latter somehow arise from the former.

The age of our universe (currently estimated as 13.8 billion years) and the total
complexity of our universe are the two measures of our distance from "the origin":
the area where HMS is so simple that the description could be packed into a few
hundred bits (perhaps representing something like fundamental physical laws and
constants, e.g. space dimensionality equals three, gravitational constant G equals...)

Supposedly age of our universe is not as good measure as the total complexity,
because although we discover rather than invent the relatively simple mathematical
structures, it seems possible that we actually invent rather than discover almost
all of laws and constants of our external physical reality.
For example, an HMS from a set of HMS's observationally indistinguishable from our
"year 1800" (according to our point of view in 1800) could possibly evolve into an
HMS corresponding to our "year 2016" but such that the age of the universe is 13.5
billion years according to the best estimate of cosmologists inhabiting it.
And similarly Mp/Me = 1835, instead of 1836, where Mp is mass of proton, and Me
is mass of electron (Mp/Me = 1836 in our universe).

A few prominent contemporary physicists share quite similar ideas, for example
Neil Turok, director of Perimeter Institute for Theoretical Physics:
"It is a striking fact that the geometric mean of the Hubble and Planck lengths is
the size of a living cell: the scale on which we live, where nature is at her most
complex.
What is exciting about this picture is that it requires a new kind of theory, one
which is simple at both the smallest and largest scales, and very early and very
late cosmological times so that it is capable of explaining these properties of
our world. In fact, there are more detailed hints from both theory and data that,
at these extremes, the laws of physics should become independent of scale.  Such
a theory won't be concerned with kilograms, meters or seconds, only with information
and its relations. It will be a unified theory, not only of all the forces and
particles but of the universe as a whole." [6]

Another example is from Lee Smolin:
"But how are we to describe physics, if it is not in terms of things moving in a
fixed spacetime? Einstein struggled with this, and my only answer is the one he
came to near the end of his life: fundamental physics must be discrete, and its
description must be in terms of algebra and combinatorics." [7]
"It is beginning to seem as if nature is just unnaturally fine tuned. In my opinion
we should now be seeking explanations for why this might be. Perhaps the laws of
nature are not static, but have evolved through some dynamical mechanism to have
the unlikely forms they are observed to have." [8]

The question of whether space-time can be based on logic and computation has been
discussed, e.g. by Ämin Baumeler and Stefan Wolf [9].

Are there testable predictions from the hypothesis that we invent physical laws?
Fine-tuning can give a clue.

Let's address an easier question: is there anything that looks like an evidence
supporting the hypotheses "increase of total complexity of HMS is ... time"
and "increase of complexity in a self-aware core ... consciousness" ?
Yes, [2] and [3] respectively.

With respect to [2] the falsifiable prediction is that nuclear decay rate will be
significantly lower on the edges of Solar system, and with respect to [3] and [4]
the falsifiable prediction is that hit rates will increase with the number of
starers, supposedly because the subjective increase of complexity runs differently
with starers than without them.

[1] Max Tegmark (2014), Our Mathematical Universe: My Quest for the Ultimate Nature of Reality, ISBN 978-0-307-59980-3
    and http://en.wikipedia.org/wiki/Mathematical_universe_hypothesis
[2] Jenkins, Fischbach et al., Evidence for Correlations Between Nuclear Decay Rates and Earth-Sun Distance, http://arxiv.org/abs/0808.3283
[3] http://www.theepochtimes.com/n3/917468-ability-to-sense-when-someones-staring-at-you-is-common-studies-show/
[4] Richard Wiseman & Marilyn Schlitz, Experimenter effects and the remote detection of staring, http://www.richardwiseman.com/resources/staring1.pdf
[5] Matt Mahoney, Data Compression Explained, http://mattmahoney.net/dc/dce.html#Section_Conclusion
[6] Neil Turok, Answer to the 2016 question on Edge.org, https://www.edge.org/response-detail/26742
[7] Lee Smolin, Answer to the 2005 question on Edge.org, https://www.edge.org/response-detail/11130
[8] Lee Smolin, Answer to the 2016 question on Edge.org, https://www.edge.org/response-detail/26610
[9] Ämin Baumeler, Stefan Wolf, Causality - Complexity - Consistency: Can Space-Time Be Based on Logic and Computation? http://arxiv.org/abs/1602.06987