Loveliness is Rare

by Eric Steinhart

Order, complexity, regularity, patterning, are all examples of features that I’ll just refer to as lovely. It’s a term of art, and it’s a lovely term.

Within many familiar systems, loveliness is very very rare. It’s very rare within the models of simple physical theories and even more rare within the models of complex physical theories (e.g. the solutions to the equations of string theory). This can be illustrated with the cellular automaton known as the game of life. You can read lots about the game of life on the web. I’ll just give a very quick presentation of the relevant points.

The game of life is played on a grid composed of square cells, like a chessboard. A clock is ticking (all cells can hear it). A cell is either ON or OFF (alternatively, LIVE or DEAD, or 1 and 0). Cells blink ON and OFF like lightbulbs, according to a rule each cell computes every time the clock ticks: (1) a cell counts its ON neighbors; (2) if it is ON and has 2 or 3 ON neighbors, then it stays ON, else it turns OFF; if it is OFF and has 3 ON neighbors, then it turns ON, else it stays OFF.

The figure below illustrates how cells change according to the life rule.

The game of life supports regular patterns, such as the glider, which appears to move across the space of the life grid. The glider is shown below.


It’s even possible to construct universal Turing machines and self-reproducing patterns in the game of life. But the game of life is rare within the class of similar cellular automata.

The rule for the game of life can be expressed in a small table. The table is shown in the figure below.

Since there are 16 slots in this table, and each can take the value 0 or 1, there are 2^16 different variants of the game of life. That’s 65536 variants. These are all the possible classes of life-like universes. Some of these variants are shown below.

Out of these, very few support any physical content at all. Perhaps a dozen or so support moving patterns. And only one is known to support patterns that compute and that reproduce (namely, the game of life itself). Within an extremely large number of physical systems, or purely mathematical systems, loveliness is vanishingly rare. Hence, that any actual universe is lovely, when almost all possible universes are not, is extremely surprising.

To say a fact is “surprising’ is far from merely subjective. Surprising facts almost always carry information. That’s because carrying information is itself a lovely feature. And that’s why our brains are highly sensitive to loveliness: when, out of the endless background of noise, you are given a signal carrying information, you’d better pay attention. It’s a good rule to follow in any uncertain environment.

About Daniel Fincke

Dr. Daniel Fincke  has his PhD in philosophy from Fordham University and spent 11 years teaching in college classrooms. He wrote his dissertation on Ethics and the philosophy of Friedrich Nietzsche. On Camels With Hammers, the careful philosophy blog he writes for a popular audience, Dan argues for atheism and develops a humanistic ethical theory he calls “Empowerment Ethics”. Dan also teaches affordable, non-matriculated, video-conferencing philosophy classes on ethics, Nietzsche, historical philosophy, and philosophy for atheists that anyone around the world can sign up for. (You can learn more about Dan’s online classes here.) Dan is an APPA  (American Philosophical Practitioners Association) certified philosophical counselor who offers philosophical advice services to help people work through the philosophical aspects of their practical problems or to work out their views on philosophical issues. (You can read examples of Dan’s advice here.) Through his blogging, his online teaching, and his philosophical advice services each, Dan specializes in helping people who have recently left a religious tradition work out their constructive answers to questions of ethics, metaphysics, the meaning of life, etc. as part of their process of radical worldview change.

  • http://nojesusnopeas.blogspot.com James Sweet

    If by “possible universes” you mean all universes that you can imagine, then I’ll agree with you.

    If by “possible universes” you mean all universes which actually could be in reality, then I think we must be more guarded. You are once again making an argument by analogy, with all the weaknesses that entails — weaknesses that are only intensified when we are discussing a domain (the first instants of our universe and “before”) where the application of human intuition is highly questionable. You still haven’t adequately refuted the Necessity Hypothesis (“I can imagine it!” is not a refutation), so we must leave that open as a possibility — even if, like you, I tend to doubt it.

    • Daniel Fincke

      You still haven’t adequately refuted the Necessity Hypothesis (“I can imagine it!” is not a refutation), so we must leave that open as a possibility — even if, like you, I tend to doubt it.

      The unstated premise seems to be that logical possibility implies ontological possibility.

  • http://nojesusnopeas.blogspot.com James Sweet

    Expertly put. That is indeed the unstated premise that seems to be in dispute. I not only reject the idea that logical possibility does not imply ontological possibility, but I’m not even willing to say without caveat that the set of worlds which are ontologically possible is a strict subset of those worlds which are logically possible. That’s probably the case, but… I don’t feel comfortable asserting that.

    I recall from a previous post that Eric believes in some sort of mathematical object as a “Ground of All-Being”. (I hope I got that more or less right?) I’m still a little vague on what that means, but it certainly would seem to imply that mathematics is so fundamental that it transcends all possible worlds. That may be the case, and in fact I suppose I share Eric’s belief that it is, but I don’t think it necessarily has to be so.

    Who knows if in the next Universe over, inductive reasoning even works at all? I assume it does, but then again I’m using induction to get me there… But of course that’s another discussion (Daniel, you’re still supposed to get back to me with how the problem of induction is a virtuous circle rather than a vicious circle… I don’t mean to be the guy shouting, “Blog for me, monkey!”, but I was really interested in that conversation :) )

    • Daniel Fincke

      But of course that’s another discussion (Daniel, you’re still supposed to get back to me with how the problem of induction is a virtuous circle rather than a vicious circle… I don’t mean to be the guy shouting, “Blog for me, monkey!”, but I was really interested in that conversation )

      I know, I know, I haven’t forgotten…


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