# a blog about things that I've been thinking hard about

# Response to "Possible" Proof of "God's" Existence

23 August, 2008
A response to Mark Chu-Carroll's response to my previous article A Possible Proof of God's Existence from Multiversity Assumptions.
by Philip Dorrell

After I added a link to my A Possible Proof of God's Existence from Multiversity Assumptions as a comment to Mark Chu-Carroll's blog article Numeric Pareidolia and God in Π, Mark wrote a response claiming to refute my proof.

## A Summary of the Original Argument

I called my proof a "possible" proof, and I did so because it depends on various assumptions. None of these assumptions can be proven to be true, at least not given the current state of scientific knowledge, but I do consider them to be plausible.

If we can show that even one of my "plausible" assumptions is not at all plausible, then the overall proof ceases to be even "possible", and that would be the end of it.

The proof's argument depends on two lists of assumptions. The assumptions in the first list hold true whether or not "God" exists. The assumptions in the second list are consistent with the non-existence of "God", and my aim is to show how these assumptions give rise to a prediction which can, in principle, be falsified.

### First List of Assumptions (with or without God)

1. The probability of the origin of life is very, very low. (To give a couple of ball-park estimates, maybe 10-10000, or maybe 10-1000000.)
2. We live in a multiverse of universes, each of which has this same probability of the origin of life. The multiverse contains so many universes that life will almost certainly originate in at least one of those universes.
3. Within this multiverse, the laws of physics depend on a finite set of N numerical parameters which are fixed for that multiverse, but which are not a priori constrained to have any particular set of values.
4. The probability of the origin of life is very sensitive to these N parameters in the neighbourhood of its maximum value (i.e. it falls off very quickly as you move away from the maximum value).
5. Within the same (very small) neighbourhood, the probability of the evolution of intelligent life from more primitive life forms is not so sensitive to variations in the N free parameters.

### Second List of Assumptions (consistent with non-existence of God)

6. We live in a multi-multiverse of multiverses where the N free parameters take on all possible values.
7. Any a priori probability distribution of the N free parameters is sufficiently smooth, that, within the above-mentioned small neighbourhood of the maximum value of the probability of the origin of life, it is approximately uniform.

### The Anthropic Principle + Multiplicity

For the purpose of my argument, the Anthropic Principle can be regarded as a method of "scientifically" explaining an apparent miracle.

A "miracle" is an observation which appears to involve a highly improbable event. An apparent "miracle" can be considered to be "explained" when it can be shown to be not so improbable when conditioned on the requirement that we as an intelligent life form are able to make the observation and think about its improbability.

By itself the Anthropic Principle is a principle of "necessity", i.e. we have to exist in order to exist. To truly turn an improbable observation into a probable observation, we have to additionally assume a sufficient multiplicity of opportunities for the observed event to occur.

For the purposes of my argument, "God" can be defined as the cause of any "miracle" which cannot be explained by the application of the Anthropic Principle combined with a multiplicity assumption.

### Two Different Miracles

In the above lists of assumptions there appear two different miracles, each separately explained by a separate application of the Anthropic Principle and a related multiplicity assumption.

The first miracle is the origin of life, and this is explained by the multiplicity of universes in the multiverse.

The second miracle is the choice of values for the N free parameters which allow life to originate and to evolve into intelligent life such as ourselves. This is explained by the multiplicity of multiverses in the multi-multiverse where the N free parameters range over all possible values.

Both of these miracles can be "explained", because in each case we cannot disprove the existence of the relevant multiplicity of universes or multiverses.

However, and this is the crux of my argument, the second list of assumptions given above implies a prediction, which is in principle falsifiable, and this prediction is that:

> The observed values of the N free parameters must be very close to the unique point in the N-dimensional parameter space which maximises the probability of the origin of life.

If we succeed in making an observation which conflicts with this prediction, then we have succeeded in observing an unexplained "miracle", one which cannot be explained by the application of the Anthropic Principle combined with multiplicity assumptions.

To be precise, the observed "miracle" would be the observation of a "choice" of a point in the N-dimensional free parameter space which does not correspond to the maximum possible probability of the origin of life, and which indeed corresponds to a much (much) lower value of the probability.

Because this observed choice could not have been made "anthropically", we can do some hand-waving, and conclude that it was made by "God". At this point one is free to speculate as to how much this tells us about who or what God is.

### Does the Current Author Believe in "God"?

If you read some of my other blog articles, you might conclude that I am not a religious person. Applying this non-religiosity to the current argument, it follows that I must predict that if all the assumptions I make here do turn out to be true, and we do manage to observe the N free parameters, and calculate the probability of the origin of life as a function of those N parameters, then I am expecting that they will correspond to the maximum possible value of the probability of the origin of life, or something very close to it.

## Plausibility Analysis

### 1. The probability of the origin of life is very, very low

This is plausible for two main reasons.

The first reason is that, so far, science has failed to reconstruct a history of the origin of life which does not involve some highly improbable event. This doesn't prove that life originated by means of a highly improbable event (or sequence of events), but at the same time we cannot yet prove that it didn't.

The second reason is that we have no evidence that life has ever appeared more than once. The lack of evidence comes from three major sources:

- All life on planet Earth appears to have descended from a common ancestor.
- There is no evidence of any kind of life on any other planet.
- There is no evidence of life anywhere outside of the Solar System.

It might seem unreasonable to expect any evidence of life from outside the Solar System, because other stars are so far away that any signs of life would be too difficult to detect. However, it seems reasonably likely that at least some technological civilisations would advance to the point where they could exploit energy and matter resources in their own stellar neighbourhood on a scale that would (after at least a few million years) be visible even from thousands of light years away. Indeed many people consider that our own civilisation is only a few decades away from an expected explosion of self-accelerating technological development, the so-called Technological Singularity.

The idea that there is an unexplained shortage of visible alien life in the Universe is not a new one. For further details, see Fermi paradox, Where are they? Why I hope the search for extraterrestrial life finds nothing and The Great Filter.

The only hard lower bound on our current knowledge of the probability of life originating is the probability of a minimal viable independent organism, i.e. a bacterium, forming by a fortuitious arrangement of precursor molecules. This is a very pessimistic bound, and there are some good reasons to presume it is too pessimistic:

- Even current life forms show evidence of previous simpler states, especially there is reason to believe in the existence of a precursor RNA-based life form.
- The earliest life-form did not have to compete against any other life form, so some of the machinery that current life forms have would not be necessary just to reproduce and survive.

Nevertheless, the actual known bounds on the probability of the origin of life, measured for example on a per-star basis, remains uncertain over a very wide range values, anywhere from perhaps 10-1 to 10-1000000.

### 2. We live in a multiverse of universes

There are actually two reasons this is plausible (and one should be sufficient). The first is that there is simply no way to rule out the possibility of multiple universes. Just because we live in one universe doesn't mean that other universes don't exist. The second reason is that our current understanding of quantum mechanics pretty much requires a multiverse. One can argue about whether a wave-function of the Universe is exactly the same thing as a multiverse, but as far as the Anthropic Principle is concerned, when requiring a multiplicity to explain the occurrence of improbable events, it works just as well. Certainly it gets us well past the 10-1000000 "universes" that are needed to cancel out the worst possible value we can have for the probability of the origin of life.

### 3. The laws of physics depend on N free parameters

As it happens, the standard model has (give or take) 18 free parameters. Of course it might turn out these can all be explained and constrained by some deeper and more complete theory of physics. But until we find that deeper theory, we won't know one way or the other. It is also possible that a deeper theory might force the existence of multiple multiverses with the multiverses ranging over some set of possible values for the N free parameters. Such a theory would be equivalent in its effect to assumption 6 (and it might give us assumption 7 for free), and it would be similarly falsifiable.

### 4. The probability of the origin of life would be very sensitive to any free parameters

This is perhaps the most "hand-wavy" of my assumptions. What matters the most, for the sake of my "proof", is that the origin of life be more sensitive than the evolution of intelligent life from more primitive life forms (which is what the next assumption is about).

The following is an attempted analysis of this issue.

#### Enzymes

Inside the cells of living organisms, various chemical reactions occur. These reactions are controlled by enzymes. If the enzymes were not there, the "correct" reactions would not be the most probable, and, they would not occur at a useful rate. The job of enzymes is to make the correct reactions both most probable and reasonably fast.

#### Origin of Life: No Enzymes

If we consider a particular pathway to the origin of life, then a particular sequence of chemical reactions is required to occur within a given mixture of pre-cursor chemicals. Unfortunately, there are no enzymes to select which reactions will occur. Possibly heat can have the effect of speeding up reactions in general, but heat will speed up the wrong reactions just as much (or more so) than the correct reactions.

For each "correct" reaction required to occur in the sequence of reactions leading up to the origin of self-sustaining life, there is a set of competing "incorrect" reactions involving the same participants.

#### Anthropic Principle via Free Parameter Choice as a Pseudo-Enzyme

If it were possible to subtly alter the laws of physics, for example by selecting different values for N free parameters, one could manipulate the relative probabilities of correct versus incorrect reactions within each step of the required sequence, to maximise the relative likelihood of the correct reactions compared to the incorrect reactions.

These same alterations would not interfere so much with the occurrence of normal biological chemical reactions, because those reactions are "protected" by enzymes against competition from alternative incorrect reactions. That is, the enzymes make the "correct" reactions strongly favoured over all alternatives. This preference will be relatively robust against incremental changes to the laws of physics, and even if the laws of physics are changed to the point where an enzyme ceases to perform its function, there would probably be some other enzyme able to perform the same catalysis function under the altered physical laws. Especially given that there are plenty of degrees of freedom available to choose the structure of an enzyme.

#### Limited Dimensionality

Unfortunately the number of available free parameters is very limited. The standard model has just 18, and not all of these are necessarily useful for altering the relative probabilities of different chemical reactions. Compared to the information required to specify the structure of even one enzyme, we don't have much to work with.

If the set of competing reactions with similar probabilities to one of the "correct" reactions is very large, then any small deviation from the maximum relative probability of each reaction will cause it to "lose place" to a relatively large number of competitors.

However, although manipulation of free parameters will not be enough to make the improbable probable, it would succeed in making the improbable somewhat less improbable, and there will be some point in the N-dimensional free parameter space which maximises the probabilities of the required sequence of chemical reactions occurring.

#### Summary

I'll admit that assumption 4 is more a matter of guesswork than rigorous analysis, and perhaps requires more investigation. However it should also be noted that all assumptions about the dependence of probabilities as functions of free parameters are in principle decidable. That is, once we know the required physics, we can specify an algorithm for calculating the values of the probabilities. Of course the required calculation might require an impossibly large number of steps to complete.

But even if the mathematics to actually calculate the probabilities is too hard, it might still be possible to discover mathematical methods which allow us to deduce something about the sensitivities of probabilities of different kinds of events as functions of free parameters in the laws of physics. (A bit like doing topological dynamics, which can tell you something about a system, even though solving the dynamics of the system exactly might be impossibly hard.)

### 5. The probability of the evolution of intelligent life is insensitive to free parameters in the region "close" to the maximum probability of the origin of life.

The probability of the origin of life is more sensitive than the probability of the evolution of intelligent life, because it depends on a specific sequence of most probable but still very improbable chemical reactions. The evolution of intelligent life, presumably, is not restricted to one specific sequence of events, and even if it does involve uncommon events, the processes involved are generally a function of enzymatic catalysis, and therefore, as explained above, relatively insensitive to those minor changes in the laws of physics which do affect the probability of the origin of life.

### 6. We are in a multi-multiverse where N free parameters take on all possible values

Similarly as argued for assumption 2, we cannot rule out the possibility of multiple multiverses, unless (as mentioned earlier), we discover "deep" physics that tells us what the N parameters have to be, in which case, of course, they are not "free" any more.

### 7. Any a priori probability distribution of the free parameters is uniform in the "possible life" region

Of course who knows what an a priori distribution of free physical parameters might be, but it is at least plausible that it is relatively smooth, in which case, by a continuity argument, it will be approximately uniform over a very small region.

We can also appeal to Occam's razor: that out of all possible distributions that we could assume, a uniform distribution is the simplest possible hypothesis.

## Mark Chu-Carroll's Refutation

Here I will answer some of the specific issues that Mark raised.

Why arbitrarily restrict variation in the laws of physics to a finite set of free parameters?

It is exactly the state of physics now that we have a theory which contains a finite set of free parameters. Of course that physics is incomplete. But when we do find what looks like a complete theory of physics, which subsumes QFT and general relativity, then we might still find that it has N free parameters. Or, we might find a theory which predicts the existence of a multiverse with different parameter values for each universe in the multiverse (there are already speculative theories of physics and cosmology which do this). Either way, we are then left with the need to "explain" the particular values of the free parameters that we observe in our "own" universe.

It's wrong that quantum mechanics "requires" a multiverse.

I actually said "virtually requires", but the difference may not matter. As I understand it, there is no mathematically consistent interpretation of quantum mechanics other than the Many-Worlds interpretation, so although other "interpretations" of quantum mechanics may exist (including of course the tradition Copenhagen interpretation), those interpretations are all wrong. Or, if one of them is correct, then quantum mechanics is wrong, because if you take the equations of quantum mechanics completely at face value as a description of reality, then what you get is the Many-Worlds interpretation.

Occurrence of evolution versus occurrence of origination of life

Mark rejects my empirical comparison of evolution and survival of life, against the origin of life. To make the point again, as I see it:

- The origination of life has only been observed once, ever, anywhere.
- The survival, reproduction and evolution of life forms has happened many, many times.

I am not the only person ever to propose that the sheer lack of evidence of alien technology is evidence that aliens actually don't exist at all, or, they are so utterly far away from us that we will never meet them (see my references above). In either case, one plausible explanation for the non-existence of aliens in the visible universe is the extreme improbability of the origin of life. This argument depends substantially on the idea of the Singularity, i.e. that technology accelerates the development of technology, so that if a technological civilisation does not self-destruct (which may happen sometimes, but it seems unlikely to always happen), then it will rapidly "explode" into nearby space, consuming natural resources in a manner likely to be obvious even to someone looking through a telescope from a distant star. And if the aliens are anywhere near us, they (or their technologically constructed successors) would already have got here by space travel, and they would have consumed the Earth and all its resources, killing our ancestors off before we even got a chance to evolve.

Mark also distinguishes the evolution of life and the evolution of intelligent life, an issue that admittedly I did not discuss in any detail in my article. However, intelligence has increased separately in the evolution of different animal groups, suggesting that the evolution of intelligence is not so unlikely.

It is possible that some of these steps leading up to the evolution of human intelligence were unique, and may have been highly improbable. Because much of the evolutionary history of life is recorded indirectly in the genomes of living organisms, we may one day be able to reconstruct how most of these steps occurred.

In the mean time, I would point out that intelligence is something that exists on a continuum, ranging from the very simplest of responses to environment, and the very simplest "learning" mechanisms, up to the complexities of the human brain. Therefore intelligence can evolve incrementally. By contrast, there is no continuum between life and non-life, and incremental evolution is something that can only start after life has developed.

In practice, I suspect that the tendency of life to evolve in to large numbers of different species vastly increases the probability of any of the required unique steps happening (i.e. to at least one of those species). Whereas the origin of life depends on the existence of a non-living precursor, and such a pre-cursor does not have any intrinsic mechanism for proliferating itself into a large variety of different states.

The existence of a multiverse is not observable from within our universe.

Here Mark is being a bit pedantic about the meaning of "universe". What he seems to mean by "universe" is "all of reality", whereas what I mean is "planets, stars, galaxies and everything else in space" which is the normal useage of the word "universe". So if our "universe" turns out to be only a small part of "total reality", then we give that "total reality" some other name, like "multiverse".

In practice, we "observe" other universes in the quantum multiverse when we do experiments like the double-slit experiment. In the Many-Worlds interpretation, when the electron goes through slit 1 or slit 2, and then these two possibilities interfere with each other on the target screen, this is interpreted as the universe splitting into two universes, one for each slit that the electron could have gone through, and then joining up together again. So we "observe" other universes when they interfere with our own by virtue of being in substantially the same state. And in the case of those universes which are in a state further removed from our own, such that we are unlikely to interfere with them any time in the near future, we observe them more indirectly, by a process of extrapolation, i.e. assuming that quantum mechanics holds true even on a classical scale.

## General Points

### The Proof is a "Possible" Proof

I presented my proof (or at least I intended to present it) as a proof which would be valid, if certain assumptions held true, where those assumptions were at least plausible.

To some extent Mark appears to be reading the proof as if I am declaring those assumptions to be certainly true.

Which is far from the case. For example, I don't even have a strong opinion on whether there are any free parameters in an ultimate theory of physics. I just allow for the possibility that there might be, and that if there are, then one could make the type of argument that I am making here.

### The Nature of "God"

I invoke the concept of "God" in my proof somewhat tongue-in-cheek, as a presumed explanation of some observation that cannot be explained "scientifically".

If you want to be really precise, you could replace the term "God" with "some agent so far not accounted for, which is required to explain the observed values of certain quantities, given that the observed values are otherwise unexplained".

Obviously this "God" doesn't correspond to any specific God as described by any particular religion, and cannot be attributed all the various qualities that "He" (or "She") is attributed by any such religion.

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