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Complexity levels and what they suggest

Jul 14th, 2016
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  1. Complexity levels and what they suggest.
  2.  
  3. At many complexity levels there seems to be two fundamental classes of
  4. information systems:
  5.  
  6. 1. Elementary particles are first of all either bosons or fermions.
  7. Bosons are generally force carrier particles, whereas fermions
  8. are usually associated with matter.
  9.  
  10. 2. Atomic nucleus and electron cloud.
  11.  
  12. 3. Life molecules including RNA and DNA, versus all other, lifeless molecules.
  13. Living creatures are able to be proactive towards their environment, whereas
  14. lifeless matter is adaptive (reactive) to environment rather than proactive.
  15.  
  16. 4. Starting from the rather simple living creatures, most organisms are either
  17. proactive (animals) or adaptive (plants) to resources of the environment.
  18.  
  19. 5. Living creatures of relatively more advanced species are either proactive (males)
  20. or adaptive (females) with respect to other individuals of their species.
  21.  
  22. 6. Placebo effect suggests that there is a proactive and an adaptive agent in psyche.
  23.  
  24. 7. It's hard to look above and beyond, but it seems likely that individuals
  25. in advanced societies are either mostly creators or mostly consumers
  26. of informational products (decisions, innovations, virtual realities...)
  27. Thus again, mostly either proactive or adaptive, now towards their society.
  28.  
  29. 8. It also seems likely that most societies position themselves first of all as
  30. either proactive or adaptive towards their space-time neighbors.
  31.  
  32. Supposedly this is because information systems evolve better when there are features
  33. enabling bimodal distributions, and seemingly proactive/adaptive is one of such
  34. features.
  35.  
  36. If the Mathematical Universe Hypothesis[1] is true, that is, the hypothesis that
  37. our external physical reality is isomorphic to a huge mathematical structure (HMS),
  38. then it seems possible that the gradual increase of total complexity of HMS is
  39. what we subjectively perceive as time, and increase of complexity in a self-aware
  40. core (perhaps the proactive agent of psyche) could be essential for what we
  41. subjectively perceive as qualia and consciousness.
  42. Note this is descriptive (Kolmogorov) complexity, not computational complexity.
  43. Descriptive complexity of a 10^122 bit long sequence[5] is below 1000 bits
  44. if the sequence is fully describable with a short pattern and a repeat count.
  45.  
  46. We can assume that HMS always contains an infinite amount of "random" data, which
  47. gradually become "non-random". For a finite, binary, one-dimensional illustration
  48. consider a set of 2^Z files such that the first N bits are the same in all files
  49. of the set, while data in the last Z bits are different in each file of the set.
  50. Then at the next (for this reference frame) moment t+tp, where tp is Planck time,
  51. the set contains 2^(Z-x) files such that N+x bits are the same, and Z-x bits are
  52. all different. Or M groups of files (if we assume that M variants of future
  53. may be equally real) such that N+x bits are same within each group.
  54. M <= 2^x, x is negligible compared to N, N is negligible compared to Z: x << N << Z.
  55. Descriptive complexity of HMS is the complexity of only the "non-random" part of it,
  56. because the "random" part is kind of "outside" and invisible.
  57.  
  58. There is no time in the suggested picture in the sense that universe contains
  59. nothing except mathematical structures. However, there is time in the sense that
  60. structures of lower complexity "precede" structures of higher complexity, and
  61. the latter somehow arise from the former.
  62.  
  63. The age of our universe (currently estimated as 13.8 billion years) and the total
  64. complexity of our universe are the two measures of our distance from "the origin":
  65. the area where HMS is so simple that the description could be packed into a few
  66. hundred bits (perhaps representing something like fundamental physical laws and
  67. constants, e.g. space dimensionality equals three, gravitational constant G equals...)
  68.  
  69. Supposedly age of our universe is not as good measure as the total complexity,
  70. because although we discover rather than invent the relatively simple mathematical
  71. structures, it seems possible that we actually invent rather than discover almost
  72. all of laws and constants of our external physical reality.
  73. For example, an HMS from a set of HMS's observationally indistinguishable from our
  74. "year 1800" (according to our point of view in 1800) could possibly evolve into an
  75. HMS corresponding to our "year 2016" but such that the age of the universe is 13.5
  76. billion years according to the best estimate of cosmologists inhabiting it.
  77. And similarly Mp/Me = 1835, instead of 1836, where Mp is mass of proton, and Me
  78. is mass of electron (Mp/Me = 1836 in our universe).
  79.  
  80. A few prominent contemporary physicists share quite similar ideas, for example
  81. Neil Turok, director of Perimeter Institute for Theoretical Physics:
  82. "It is a striking fact that the geometric mean of the Hubble and Planck lengths is
  83. the size of a living cell: the scale on which we live, where nature is at her most
  84. complex.
  85. What is exciting about this picture is that it requires a new kind of theory, one
  86. which is simple at both the smallest and largest scales, and very early and very
  87. late cosmological times so that it is capable of explaining these properties of
  88. our world. In fact, there are more detailed hints from both theory and data that,
  89. at these extremes, the laws of physics should become independent of scale. Such
  90. a theory won't be concerned with kilograms, meters or seconds, only with information
  91. and its relations. It will be a unified theory, not only of all the forces and
  92. particles but of the universe as a whole." [6]
  93.  
  94. Another example is from Lee Smolin:
  95. "But how are we to describe physics, if it is not in terms of things moving in a
  96. fixed spacetime? Einstein struggled with this, and my only answer is the one he
  97. came to near the end of his life: fundamental physics must be discrete, and its
  98. description must be in terms of algebra and combinatorics." [7]
  99. "It is beginning to seem as if nature is just unnaturally fine tuned. In my opinion
  100. we should now be seeking explanations for why this might be. Perhaps the laws of
  101. nature are not static, but have evolved through some dynamical mechanism to have
  102. the unlikely forms they are observed to have." [8]
  103.  
  104. The question of whether space-time can be based on logic and computation has been
  105. discussed, e.g. by Ämin Baumeler and Stefan Wolf [9].
  106.  
  107. Are there testable predictions from the hypothesis that we invent physical laws?
  108. Fine-tuning can give a clue.
  109.  
  110. Let's address an easier question: is there anything that looks like an evidence
  111. supporting the hypotheses "increase of total complexity of HMS is ... time"
  112. and "increase of complexity in a self-aware core ... consciousness" ?
  113. Yes, [2] and [3] respectively.
  114.  
  115. With respect to [2] the falsifiable prediction is that nuclear decay rate will be
  116. significantly lower on the edges of Solar system, and with respect to [3] and [4]
  117. the falsifiable prediction is that hit rates will increase with the number of
  118. starers, supposedly because the subjective increase of complexity runs differently
  119. with starers than without them.
  120.  
  121. [1] Max Tegmark (2014), Our Mathematical Universe: My Quest for the Ultimate Nature of Reality, ISBN 978-0-307-59980-3
  122. and http://en.wikipedia.org/wiki/Mathematical_universe_hypothesis
  123. [2] Jenkins, Fischbach et al., Evidence for Correlations Between Nuclear Decay Rates and Earth-Sun Distance, http://arxiv.org/abs/0808.3283
  124. [3] http://www.theepochtimes.com/n3/917468-ability-to-sense-when-someones-staring-at-you-is-common-studies-show/
  125. [4] Richard Wiseman & Marilyn Schlitz, Experimenter effects and the remote detection of staring, http://www.richardwiseman.com/resources/staring1.pdf
  126. [5] Matt Mahoney, Data Compression Explained, http://mattmahoney.net/dc/dce.html#Section_Conclusion
  127. [6] Neil Turok, Answer to the 2016 question on Edge.org, https://www.edge.org/response-detail/26742
  128. [7] Lee Smolin, Answer to the 2005 question on Edge.org, https://www.edge.org/response-detail/11130
  129. [8] Lee Smolin, Answer to the 2016 question on Edge.org, https://www.edge.org/response-detail/26610
  130. [9] Ämin Baumeler, Stefan Wolf, Causality - Complexity - Consistency: Can Space-Time Be Based on Logic and Computation? http://arxiv.org/abs/1602.06987
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