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The Cosmic Watermark Hypothesis: Symmetry and Wigner's Ladder


All scientists (orginally known as "natural philosophers") are seeking hidden patterns in presently unclear events. When our investigation discovers simple patterns in things we originally considered random, we begin to suspect that the universe itself is at least partially a rigged game, with powerful developmental patterns, or watermarks, waiting to be discovered by an unreasonably small application of human intellect.

Natural philosophers, such as Plato and Pythagoras, and early scientists, such as Kepler and Newton are united in their expectation that a succession of conceptually emergent simplicities, both analytical and analogical, must exist in the natural world. Such simplicities are both relatively accessible to the human thinker, and are able to explain the complex dynamics of a wide range of heretofore poorly related physical systems. This intuition is core to the concept of general systems theory, and has been proven correct in countless examples over the course of human mental development. Occasionally systems theorists overplay these suspicions, as with mysticism of Pythagoreas, or the alchemy of Newton. But with surprising regularity amazingly powerful, scientifically testable conceptual simplicities do emerge.

In a famous 1960 paper, Eugene Wigner called this simplifying phenomenon the "unreasonable effectiveness of mathematics in the natural sciences," and systems theorists extend this effectiveness to many classes of analogical, as well as analytical thinking. Or as neural network scientist Bart Kosko says, "For some reason, science tracks math [and often, simple math], but logically, it doesn't have to." Why does the wave equation for light pop so easily out of Maxwell's theorems of electromagnetism? Why do such comprehensible and ubiquitous structures as black holes, empirically observed in the 1970's, and gravity waves, widely expected to be discovered in the next decade, lie dormant in Einstein's equations? Why are so many complex and universal phenomena, such as the action-reaction and the interconversion of mass and energy, explainable by such simple equations as F = ma or E = mc^2? And perhaps most importantly, why is our universe apparently structured to allow these emergent simplicities to be discovered by relatively simple and primitive applications of human intellect?

Note that mathematical simplicities are only the beginning of the story of comprehensibility. Conceptual simplicities continuously emerge in the analogical world as well. Our ability to generally use Aristotelian logic, Darwinian evolutionary theory, and less definitively, cellular automata models of unpredictable (e.g., evolutionary) local randomness and predictable (e.g., developmental) systemic emergent constraint are all examples of analogies that have a far wider applicability than their original implementation, though some with broader utility than others, of course.

Stated in its most provocative form, we may call this expectation of an intrinsic simplicity and human comprehensibility of universal dynamics the "Cosmic Watermark Hypothesis." Sentient human beings look at the universe, apply a little intellect, and previously hidden "watermarks," or ordered messages (please bear with me a moment, this is clearly a loaded phrase) seem to appear. Intelligent systems repeat their computational processes recursively, and yet more such watermarks easily appear.

What physical processes encode and enable these watermarks? We can identify a number of candidates, but topping the list must be such processes as symmetry and self-similarity.

Symmetry encodes underlying simplicity, order, and elegance, and is at the root of the beauty mathematicians and theoretical physicists seek to discover in nature. Murray Gell-Mann's use of such elegant mathematical structures as the SU(3) Lie group to construct an early quark model (“the eightfold way”) elegantly accounted for properties of existing baryons and mesons, and predicted the discovery of a particle, the spin 3/2, Omega- baryon, that was subsequently found. One may consider this simply a result of implicit flavor symmetries' between different kinds of quarks.

Self-similarity, the realization that much of the structure of our evolutionary and developmental universe is likely to have been iterated recursively from simpler systems, is a way of understanding the power of both analogy and of general systems theories. Because of the symmetries and self-similarities that may be present at the base of physics, equations, patterns, and models may much simpler than they would be otherwise, making the application of intelligence a strongly nonzero sum game.

Some well-regarded books on these topics (the last technical) are Symmetry and the Beautiful Universe, Lederman and Hill, 2008; The Recursive Universe, Poundstone, 1985; The Force of Symmetry, Icke, 1995; Scaling, Self-Similarity, and Intermediate Asymptotics, Barenblatt, 1996). It seems likely that all the cosmic watermark phenomena will eventually be explained by simple symmetries and self-similarities in a universe that uses both evolution and development to construct complexity.

In such a universe the application of intellligence in our particular universe becomes a sustained positive feedback loop, as the primitive efforts of local intelligences, once they emerge, are rewarded by rapidly scaling the modelling heights of a universally-intrinsic "Wigner's Ladder," wherein the spacing of each new rung gets ever closer together and easier to attain, due to the intrinsic developmental structure of our present universe. Such climbing leads to hyperexponentially more useful local models of universal developmental structure over time, and is another way of understanding our proposed law of Locally Asymptotic Computation, should it eventually be proven to exist. As a result, increasingly inclusive and predictive universal developmental models emerge even as the evolutionary possibities of all real physical systems remain far more difficult (in fact, intrinsically impossible) to reduce to such elegant simplicity.

This hyperacceleration of universal developmental knowledge (Sagan's Cosmic Calendar, in terms of computational tractability of universal structure) has apparently sprung from a universe where the game of computation has been rigged to reward non-zero sum computations, and to differentially promote intelligence development as a general goal of living systems. Intelligence development, in our particular universe, has therefore become a goal that is much more adaptively valuable than, say, destructive, computationally neutral, or random activities. This is the essence of Wigner's Ladder, or the Cosmic Watermark Hypothesis, and it aptly characterizes the record of human mental productivity not only in the age of science, but throughout the history of civilization, indeed, over the entire last six billion years of our universe's present lifespan.

In the context of our developmental singularity hypothesis, we may ask whether our particular universe has been tuned (self-selected, self-organized, self-designed), over many successive cycles, so that its large scale developmental structure (though not its specific evolutionary variations) will be readily comprehensible by the computing systems that emerge developmentally within it. Or is such comprehensibility simply a side benefit of a universe built on symmetry and self-similiarity? To what extent is there parametric freedom in the types of symmetries and self-similarities in our universe, if such freedom exists, can we show that a special subset has been chosen to make universal developmental (not evolutionary) structure easily comprehensible from within?

We may be too early to attempt to answer such questions for the universe as a system, but we may also investigate them in the domain of biological development. What the Cosmic Watermark Hypothesis proposes seems identical, for example to the way that human nervous and immune systems can be shown to developmentally self-organize locally useful, and informationally consistent (though incomplete) models of the structure and function of the 10-100 trillion cells of the human body.

In other words, one genetic teleology, or developmental purpose, of nervous and immune systems is to allow a higher level of processing to occur (e.g., within the cultural and technologic domains of human systems). To do so, they must be able to easily develop a low-level encoding, or "world model," of the larger developmental structure and function of human body, which functions as the neuroimmune system's developmental "universe". Likewise, one of the key purposes of cosmic intelligence, though certainly not its only purpose, appears to be to easily discover a developmental structure, trajectory, and purpose for the universal body (though at the same time knowing little about its future evolutionary dynamics).

This information-processing arrangement apparently allows multi-local universal intelligence to be maximally useful to the long range evolutionary development of each universe unfolding within the multiverse. In this fashion, all local intelligences, including the one that is rapidly developing on our planet Earth, may reasonably be assumed to play a key role in ongoing universal lineages, and in the developmental singularity hypothesis, to encode systems that will further the computational capacity of our present universal system by creating subsequent, more finely tuned and structured evolutionary and developmental universes within the multiverse.

I'll revisit these fascinating, though still quite early and speculative concepts, at greater length in my forthcoming book.