Closer to home we have the Drake Equation, which views intelligent life in the universe through a lens of probability theory, combining the probability of earth-like (Goldilocks zone) planets, emergence of life, emergence of intelligence, longevity of technological civilizations, etc., into an overall probability of the existence of smart life such ourselves. Though Drake's interest was in SETI, the same argument can be used to compute a likelihood of our own existence. The books Rare Earths by Ward and Brownlee, as well as Gribbin's Alone in the Universe and Waltham's Lucky Planet all make the case that the probability of intelligent life is so low that it is unlikely to exist elsewhere. If so, what does that say about us? It would imply that we are a highly improbable statistical fluke, i.e., another level of Anthropic selection on universes beyond the constants of Nature..

The uncertainties in the Drake Equation terms are generally still thought to be too large to say whether we should expect intelligent life to be common or rare, though recent results from the Kepler satellite have reduced the uncertainty of some of the terms into a more life-friendly range. The early emergence of life on Earth has been interpreted to mean that the probability of life given an Earth-like planet is high, while the relatively late emergence of intelligence and technology on Earth suggests that the probability of these things given life is low. Life was purely microbial for much of its history; the dinosaurs lasted hundreds of millions of years and might still be dominating the Earth today if a random asteroid hadn't taken them out. Even given chimp-like organisms, the probability of language and technology may not be that high, since these have persisted for millions of years without evincing a tendency to evolve towards language or tool use (except along our lineage).

The question I am pondering is, how far should we take Anthropic reasoning? Physicists seem to want to use it as sparingly as possible. Maybe you need it to explain why space is so flat, or why dark matter or the fine structure constant has just the right value, but then we get back as quickly as possible to explanations that are as far from "unlikely coincidence" as possible: a rational universe governed by mathematical laws, which happens to have a few fortuitously chosen parameters.

What if it is worse than that -- what if we need to invoke improbability over and over again to explain our existence? We already seem to need improbability to explain cosmological fine-tuning, and perhaps our civilization if the Drake Equation settles down to a value of much less than one technical civilization per universe.

What might constitute evidence for our own improbability? The John Gribbin short story "the Doomsday Machine", unfortunately not available on the Internet, has been summarized by Hans Moravec in his book Mind Children. In it, the newest, biggest particle accelerator accidentally destroys the universe whenever it is switched on. The story takes seriously the many worlds interpretation of quantum mechanics, and not all the branching universe are destroyed. Observers remain only in universes where the accelerator is never switched on due to some random-seeming unlikely coincidence.: someone spilled coffee on the power button, or a rat ate through a cable. After a sufficiently long and unlikely series of such coincidences, someone figures out that selection on universes must be occurring. In other words, the evidence of selection on universes for unlikely observers would be a string of random-seeming unlikely coincidences favorable to their own existence. Do we see anything like that in our history? Possible candidates:

- The presence of suitable materials for intelligent life, including metals needed for civilization.
- The presence of a good Jupiter in the solar system
- The presence of Earth's moon
- The presence of Earth's magnetic field
- The oxygenation of Earth's atmosphere by microbes, enabling the evolution of animals, as well as the discovery/possibility of fire, metalworking, technology.
- The land/water ratio on the Earth's surface -- just right (though this argues that perhaps a range of ratios might be tolerable).
- The extinction of the dinosaurs -- very convenient.
- The absence of any planet-sterilizing catastrophes in the 4.5BY Earth history (e.g. catastrophic impacts, nearby supernovae, )
- The absence (to date) of nuclear self-destruction
- ,,,?

(Note that many of these are arguably already captured in the Drake equation, specifically in the probability of life given an Earth-like planet, the probability of technological civilization given life, and the half-life of technological civilizations.)

What is the right balance between causal explanation and Anthropic selection? The Anthropic Principle seems to open the door to any amount of improbability. And maybe that is right -- maybe our existence is, in a very literal, technical sense, miraculous!

Max Tegmark's highly recommended Our Mathematical Universe embeds the various physical versions of the multiverse in an ultimate mathematical multiverse. (Brag: I had this idea independently many years ago and pitched it to Marvin Minsky, whom I knew slightly. His reaction was an immediate "Obviously!".) The idea is that if we had a theory of everything, possibly with some added initial conditions, that completely "explained" our universe, this would be a mathematical structure with the same sort of mathematical "existence" as pi, the Euclidean plane, or prime numbers. (Such mathematical objects "exist", in some sense, independently of us, in that we can infer, but not decide, their properties. We don't get to decide whether the 15'th digit of pi is a 1, or whether 17 is prime. Mathematics is discovered, not invented.) Of all the mathematically possible universes, this particular mathematical Theory of Everything would describe ours, i.e., it is real. But is it somehow more real than all the others -- does it have physical existence while the others only have mathematical existence? Is ours the one that has been uniquely "realized" (pun intended)? In the catalog of mathematically possible universes does this one have a * next to it, saying "this one is real"? This is the same as saying that there is some extra property of "reality" that this possible universe has, but which the other ones lack. However we started out by assuming a Theory of Everything. If that theory does not include this "reality" property, then it is incomplete, and so not a Theory of Everything; if it does include it, then "reality" (the *) is a mathematical property like all the others captured by the theory. If physical existence is a type of mathematical existence, there is really no need for a designing God to somehow search the space of possible universes to compassionately bring into existence just the one (or ones) suitable for creatures like ourselves. Divine selection is no more necessary than the "reality" property. Occam's Razor rejects both.

One way out for theists is to put God in charge of mathematics rather than being subordinate to it. In Carl Sagan's "Contact" (the quite good book, not the travesty of a movie!), the heroine finds a message embedded in the digits of pi, raising the prospect of beings so powerful that mathematics is their creative medium.

What is the right balance between causal explanation and Anthropic selection? The Anthropic Principle seems to open the door to any amount of improbability. And maybe that is right -- maybe our existence is, in a very literal, technical sense, miraculous!

## Theological Epilog

Many people have followed similar lines of reasoning and concluded that these cosmic coincidences constitute proof of the existence of their preferred flavor of deity: effectively, an Anthropic Argument for the Existence of God to add to all the other arguments.Max Tegmark's highly recommended Our Mathematical Universe embeds the various physical versions of the multiverse in an ultimate mathematical multiverse. (Brag: I had this idea independently many years ago and pitched it to Marvin Minsky, whom I knew slightly. His reaction was an immediate "Obviously!".) The idea is that if we had a theory of everything, possibly with some added initial conditions, that completely "explained" our universe, this would be a mathematical structure with the same sort of mathematical "existence" as pi, the Euclidean plane, or prime numbers. (Such mathematical objects "exist", in some sense, independently of us, in that we can infer, but not decide, their properties. We don't get to decide whether the 15'th digit of pi is a 1, or whether 17 is prime. Mathematics is discovered, not invented.) Of all the mathematically possible universes, this particular mathematical Theory of Everything would describe ours, i.e., it is real. But is it somehow more real than all the others -- does it have physical existence while the others only have mathematical existence? Is ours the one that has been uniquely "realized" (pun intended)? In the catalog of mathematically possible universes does this one have a * next to it, saying "this one is real"? This is the same as saying that there is some extra property of "reality" that this possible universe has, but which the other ones lack. However we started out by assuming a Theory of Everything. If that theory does not include this "reality" property, then it is incomplete, and so not a Theory of Everything; if it does include it, then "reality" (the *) is a mathematical property like all the others captured by the theory. If physical existence is a type of mathematical existence, there is really no need for a designing God to somehow search the space of possible universes to compassionately bring into existence just the one (or ones) suitable for creatures like ourselves. Divine selection is no more necessary than the "reality" property. Occam's Razor rejects both.

One way out for theists is to put God in charge of mathematics rather than being subordinate to it. In Carl Sagan's "Contact" (the quite good book, not the travesty of a movie!), the heroine finds a message embedded in the digits of pi, raising the prospect of beings so powerful that mathematics is their creative medium.

*We*may not get to decide if 17 is prime, but God does! On the other hand, if all mathematics is grounded in a few simple principles of correct reasoning it is hard to see how much creative freedom God(s) can have, even if nonobvious conclusions often follow from that reasoning.
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