Don Page is one of the world’s leading experts on theoretical gravitational physics and cosmology, as well as a previous guest-blogger around these parts. (There are more world experts in theoretical physics than there are people who have guest-blogged for me, so the latter category is arguably a greater honor.) He is also, somewhat unusually among cosmologists, an Evangelical Christian, and interested in the relationship between cosmology and religious belief.
Longtime readers may have noticed that I’m not very religious myself. But I’m always willing to engage with people with whom I disagree, if the conversation is substantive and proceeds in good faith. I may disagree with Don, but I’m always interested in what he has to say.
Recently Don watched the debate I had with William Lane Craig on “God and Cosmology.” I think these remarks from a devoted Christian who understands the cosmology very well will be of interest to people on either side of the debate.
Open letter to Sean Carroll and William Lane Craig:
I just ran across your debate at the 2014 Greer-Heard Forum, and greatly enjoyed listening to it. Since my own views are often a combination of one or the others of yours (though they also often differ from both of yours), I thought I would give some comments.
I tend to be skeptical of philosophical arguments for the existence of God, since I do not believe there are any that start with assumptions universally accepted. My own attempt at what I call the Optimal Argument for God (one, two, three, four), certainly makes assumptions that only a small fraction of people, and perhaps even only a small fraction of theists, believe in, such as my assumption that the world is the best possible. You know that well, Sean, from my provocative seminar at Caltech in November on “Cosmological Ontology and Epistemology” that included this argument at the end.
I mainly think philosophical arguments might be useful for motivating someone to think about theism in a new way and perhaps raise the prior probability someone might assign to theism. I do think that if one assigns theism not too low a prior probability, the historical evidence for the life, teachings, death, and resurrection of Jesus can lead to a posterior probability for theism (and for Jesus being the Son of God) being quite high. But if one thinks a priori that theism is extremely improbable, then the historical evidence for the Resurrection would be discounted and not lead to a high posterior probability for theism.
I tend to favor a Bayesian approach in which one assigns prior probabilities based on simplicity and then weights these by the likelihoods (the probabilities that different theories assign to our observations) to get, when the product is normalized by dividing by the sum of the products for all theories, the posterior probabilities for the theories. Of course, this is an idealized approach, since we don’t yet have _any_ plausible complete theory for the universe to calculate the conditional probability, given the theory, of any realistic observation.
For me, when I consider evidence from cosmology and physics, I find it remarkable that it seems consistent with all we know that the ultimate theory might be extremely simple and yet lead to sentient experiences such as ours. A Bayesian analysis with Occam’s razor to assign simpler theories higher prior probabilities would favor simpler theories, but the observations we do make preclude the simplest possible theories (such as the theory that nothing concrete exists, or the theory that all logically possible sentient experiences occur with equal probability, which would presumably make ours have zero probability in this theory if there are indeed an infinite number of logically possible sentient experiences). So it seems mysterious why the best theory of the universe (which we don’t have yet) may be extremely simple but yet not maximally simple. I don’t see that naturalism would explain this, though it could well accept it as a brute fact.
One might think that adding the hypothesis that the world (all that exists) includes God would make the theory for the entire world more complex, but it is not obvious that is the case, since it might be that God is even simpler than the universe, so that one would get a simpler explanation starting with God than starting with just the universe. But I agree with your point, Sean, that theism is not very well defined, since for a complete theory of a world that includes God, one would need to specify the nature of God.
For example, I have postulated that God loves mathematical elegance, as well as loving to create sentient beings, so something like this might explain both why the laws of physics, and the quantum state of the universe, and the rules for getting from those to the probabilities of observations, seem much simpler than they might have been, and why there are sentient experiences with a rather high degree of order. However, I admit there is a lot of logically possible variation on what God’s nature could be, so that it seems to me that at least we humans have to take that nature as a brute fact, analogous to the way naturalists would have to take the laws of physics and other aspects of the natural universe as brute facts. I don’t think either theism or naturalism solves this problem, so it seems to me rather a matter of faith which makes more progress toward solving it. That is, theism per se cannot deduce from purely a priori reasoning the full nature of God (e.g., when would He prefer to maintain elegant laws of physics, and when would He prefer to cure someone from cancer in a truly miraculous way that changes the laws of physics), and naturalism per se cannot deduce from purely a priori reasoning the full nature of the universe (e.g., what are the dynamical laws of physics, what are the boundary conditions, what are the rules for getting probabilities, etc.).
In view of these beliefs of mine, I am not convinced that most philosophical arguments for the existence of God are very persuasive. In particular, I am highly skeptical of the Kalam Cosmological Argument, which I shall quote here from one of your slides, Bill:
- If the universe began to exist, then there is a transcendent cause
which brought the universe into existence. - The universe began to exist.
- Therefore, there is a transcendent cause which brought the
universe into existence.
I do not believe that the first premise is metaphysically necessary, and I am also not at all sure that our universe had a beginning. (I do believe that the first premise is true in the actual world, since I do believe that God exists as a transcendent cause which brought the universe into existence, but I do not see that this premise is true in all logically possible worlds.)
I agree with you, Sean, that we learn our ideas of causation from the lawfulness of nature and from the directionality of the second law of thermodynamics that lead to the commonsense view that causes precede their effects (or occur at the same time, if Bill insists). But then we have learned that the laws of physics are CPT invariant (essentially the same in each direction of time), so in a fundamental sense the future determines the past just as much as the past determines the future. I agree that just from our experience of the one-way causation we observe within the universe, which is just a merely effective description and not fundamental, we cannot logically derive the conclusion that the entire universe has a cause, since the effective unidirectional causation we commonly experience is something just within the universe and need not be extrapolated to a putative cause for the universe as a whole.
However, since to me the totality of data, including the historical evidence for the Resurrection of Jesus, is most simply explained by postulating that there is a God who is the Creator of the universe, I do believe by faith that God is indeed the cause of the universe (and indeed the ultimate Cause and Determiner of everything concrete, that is, everything not logically necessary, other than Himself—and I do believe, like Richard Swinburne, that God is concrete and not logically necessary, the ultimate brute fact). I have a hunch that God created a universe with apparent unidirectional causation in order to give His creatures some dim picture of the true causation that He has in relation to the universe He has created. But I do not see any metaphysical necessity in this.
(I have a similar hunch that God created us with the illusion of libertarian free will as a picture of the true freedom that He has, though it might be that if God does only what is best and if there is a unique best, one could object that even God does not have libertarian free will, but in any case I would believe that it would be better for God to do what is best than to have any putative libertarian free will, for which I see little value. Yet another hunch I have is that it is actually sentient experiences rather than created individual `persons’ that are fundamental, but God created our experiences to include beliefs that we are individual persons to give us a dim image of Him as the one true Person, or Persons in the Trinitarian perspective. However, this would take us too far afield from my points here.)
On the issue of whether our universe had a beginning, besides not believing that this is at all relevant to the issue of whether or not God exists, I agreed almost entirely with Sean’s points rather than yours, Bill, on this issue. We simply do not know whether or not our universe had a beginning, but there are certainly models, such as Sean’s with Jennifer Chen (hep-th/0410270 and gr-qc/0505037), that do not have a beginning. I myself have also favored a bounce model in which there is something like a quantum superposition of semiclassical spacetimes (though I don’t really think quantum theory gives probabilities for histories, just for sentient experiences), in most of which the universe contracts from past infinite time and then has a bounce to expand forever. In as much as these spacetimes are approximately classical throughout, there is a time in each that goes from minus infinity to plus infinity.
In this model, as in Sean’s, the coarse-grained entropy has a minimum at or near the time when the spatial volume is minimized (at the bounce), so that entropy increases in both directions away from the bounce. At times well away from the bounce, there is a strong arrow of time, so that in those regions if one defines the direction of time as the direction in which entropy increases, it is rather as if there are two expanding universes both coming out from the bounce. But it is erroneous to say that the bounce is a true beginning of time, since the structure of spacetime there (at least if there is an approximately classical spacetime there) has timelike curves going from a proper time of minus infinity through the bounce (say at proper time zero) and then to proper time of plus infinity. That is, there are worldlines that go through the bounce and have no beginning there, so it seems rather artificial to say the universe began at the bounce that is in the middle just because it happens to be when the entropy is minimized. I think Sean made this point very well in the debate.
In other words, in this model there is a time coordinate t on the spacetime (say the proper time t of a suitable collection of worldlines, such as timelike geodesics that are orthogonal to the extremal hypersurface of minimal spatial volume at the bounce, where one sets 
) that goes from minus infinity to plus infinity with no beginning (and no end). Well away from the bounce, there is a different thermodynamic time 
(increasing with increasing entropy) that for 
increases with 
but for 
decreases with (so there becomes more positive as becomes more negative). For example, if one said that is only defined for 
, say, one might have something like
the positive square root of one less than the square of . This thermodynamic time only has real values when the absolute value of the coordinate time , that is, 
, is no smaller than 1, and then increases with .
One might say that begins (at 
) at 
(for one universe that has growing as decreases from -1 to minus infinity) and at 
(for another universe that has growing as increases from +1 to plus infinity). But since the spacetime exists for all real , with respect to that time arising from general relativity there is no beginning and no end of this universe.
Bill, I think you also objected to a model like this by saying that it violates the second law (presumably in the sense that the coarse-grained entropy does not increase monotonically with for all real ). But if we exist for 
(or for 
; there would be no change to the overall behavior if were replaced with 
, since the laws are CPT invariant), then we would be in a region where the second law is observed to hold, with coarse-grained entropy increasing with 
(or with 
if ). A viable bounce model would have it so that it would be very difficult or impossible for us directly to observe the bounce region where the second law does not apply, so our observations would be in accord with the second law even though it does not apply for the entire universe. I think I objected to both of your probability estimates for various things regarding fine tuning. Probabilities depend on the theory or model, so without a definite model, one cannot claim that the probability for some feature like fine tuning is small. It was correct to list me among the people believing in fine tuning in the sense that I do believe that there are parameters that naively are far different from what one might expect (such as the cosmological constant), but I agreed with the sentiment of the woman questioner that there are not really probabilities in the absence of a model. Bill, you referred to using some “non-standard” probabilities, as if there is just one standard. But there isn’t. As Sean noted, there are models giving high probabilities for Boltzmann brain observations (which I think count strongly against such models) and other models giving low probabilities for them (which on this regard fits our ordered observations statistically). We don’t yet know the best model for avoiding Boltzmann brain domination (and, Sean, you know that I am skeptical of your recent ingenious model), though just because I am skeptical of this particular model does not imply that I believe that the problem is insoluble or gives evidence against a multiverse; in any case it seems also to be a problem that needs to be dealt with even in just single-universe models.
Sean, at one point your referred to some naive estimate of the very low probability of the flatness of the universe, but then you said that we now know the probability of flatness is very near unity. This is indeed true, as Stephen Hawking and I showed long ago (“How Probable Is Inflation?” Nuclear Physics B298, 789-809, 1988) when we used the canonical measure for classical universes, but one could get other probabilities by using other measures from other models.
In summary, I think the evidence from fine tuning is ambiguous, since the probabilities depend on the models. Whether or not the universe had a beginning also is ambiguous, and furthermore I don’t see that it has any relevance to the question of whether or not God exists, since the first premise of the Kalam cosmological argument is highly dubious metaphysically, depending on contingent intuitions we have developed from living in a universe with relatively simple laws of physics and with a strong thermodynamic arrow of time.
Nevertheless, in view of all the evidence, including both the elegance of the laws of physics, the existence of orderly sentient experiences, and the historical evidence, I do believe that God exists and think the world is actually simpler if it contains God than it would have been without God. So I do not agree with you, Sean, that naturalism is simpler than theism, though I can appreciate how you might view it that way.
Best wishes,
Don
Bill,
I agree with you, and I see what you mean, but you are asking for the assumption of something you are not going to get from theists, as their starting point is admitted to be that “physics is all there is” is not true. This is why I made effort to treat their reasoning from their own assumptions, and still show that (via bayesian reasoning) they make an error when considering the evidence at hand.
I appreciate your insightful comment Bill.
Don, can I address you on your own terms for a bit and see if I can get a better understanding? Let me momentarily cede the possibility of adding god and thereby making the universe simpler. If so, I would be pressed with some troubling concerns.
You mention:
“Also, the theism that I am assuming includes the hypothesis that god does what is best…”
Wouldn’t you then need to define “best?” I feel this is not trivial since, with god being the progenitor of all antecedent natural laws, what is “best” is in a sense a part of your ontology. Furthermore, I personally feel like it would need to be defined it such a way that it was not dependent upon its antecedents (something which I think would be impossible).
You also say:
“I am assuming that God’s nature constrains Him to maximize the good.”
Again, what does this mean? I don’t see how this could be constrained to a unitary concept. For instance, even by translating this as the well-being of sentient creatures, how are the competing interests and diverse possibilities judged? We can not simply allow the black box to contain that god determines this or we are left with a tautology (a sort of “God does good which is defined by God”).
If we say to these that we simply do not know the answer to these questions yet (as we might with the answers to various other questions in science), then I would go back to wondering why god is a better model if it, as it would seem, be less explanatory and also with enough free variables to potentially (whether it is in truth or not) be more complex.
Don noted:
“However, one could consider a different fudged Newtonian model in which the parameter a in arcseconds per century has a single value, the same as The Answer to the Ultimate Question of Life, The Universe, and Everything in The Hitchhiker’s Guide to the Galaxy. Then the likelihoods of both the Einstein model and this Hitchhiker’s Newtonian model would be essentially the same with the original data, basically determined by the experimental uncertainty that was large in comparison with the difference between 42 and the modern value you gave of 42.98. Of course, I think most of us would say the Einstein model is simpler than the Hitchhiker Newtonian model, so we would assign it a higher prior probability, thus getting a higher posterior probability for the Einstein model.”
Sure, but the reason not to propose a model with exactly (or nearly) the right value of the parameter has nothing to do with simplicity, and it has nothing to do with prior probability.
We know that the number 42.98″/century just “falls out” of the physics of general relativity.
I think you would be hard pressed to propose this number unless Newtonian theory predicted it because of planetary perturbations (which it does not).
That’s not “simplicity”, it’s “don’t beg the question,” where I am using that term in its original meaning, “don’t assume your conclusion”. There is no way to get a number near 42″/century naturally out of Newtonian theory. Everyone who has studied this problem knows that the number was put in by hand because we knew what it had to be (pre-Einstein).
https://en.wikipedia.org/wiki/Begging_the_question
You’ll have to do better than this, Don!
Don wrote,
“Other examples can be even more extreme. The maximum likelihood model for my present sentient experience would be that only it exists, since then its probability would be unity.”
Huh? This doesn’t even make sense. Do you understand what a likelihood is?
Likelihoods are an equivalence class. They are the probability that a particular piece of evidence would be observed, given some set of conditions. The fact of a piece of evidence (e.g., “your present sentient experience exists”) doesn’t tell you what the likelihood is, since you haven’t specified the conditions. Under what prior conditions (hypotheses) would it ever be that the probability of “your present sentient experience existing” would be 1??? What if you had never been born???
What you have computed is P(A|A)=1 where
A=”your present sentient experience exists”.
That’s a trivial tautology. It’s not meaningful.
Let me give you an example, illustrating this equivalence class.
Let’s imagine that an experiment has been conducted, and (as I recall how it goes, details may be wrong but the idea is correct) 9 out of 12 outcomes of what was purported to be a fair coin toss are heads. If you calculate the probability that 9 or more heads would be observed in a predetermined experiment of 12 coin tosses you get a number less than 0.05 (p-value<0.05), so a frequentist statistician u would be justified in "rejecting" the hypothesis that the coin was fair.
But then, suppose that the experimenter informed the statistician that in fact, although the data (9 out of 12) were correct, the experiment wasn't as the statistician thought. The statistician thought that the experimenter would take 12 data points and report the number of heads (and incidentally tails=12-heads). However, what the experimenter planned to do was to take data until 9 heads were observed and report the number of heads and tails (where it happened that heads + tails = 12 in this experiment). In this experiment, there could have been only 9 tosses, there could have been 15, and the experimenter would have reported (9 out of 12) just because the experiment happened to end at 12 tosses. The statistician does the calculation, and reports that the probability in this experiment (p-value) would have been greater than 0.05, and therefore not rejectable.
The numbers reported (the probabilities) are different, but if you now evaluate the whole experiment in terms of likelihood ratios, everything cancels out. That's what a Bayesian or likelihood calculation would do.
So the likelihoods are an equivalence class of numbers that are proportional. It’s not exactly wrong to think of them as probabilities, but it’s not right either.
In any case, it is definitely wrong to think that the likelihood of an event that is known to have happened (“your present sentient experience existing”) is 1 just because it has happened. That likelihood is only 1 if it would have been inevitable, given the hypotheses. And I don’t think you can make that claim.
Let me add to my comment on likelihoods:
You cannot think about likelihoods as simply probabilities, since they do not add over the hypotheses to 1 (or to any other particular number).
Yes, we calculate the probability of observed data D, given a hypothesis H1, as the likelihood of D under H1, e.g, we write L(H1;D) ∝ P(D|H1).
Under hypothesis H2, we would write L(H2;D) ∝ P(D|H2)
But, P(D|H1)+P(D|H2)≠1 in general (and in particular in my example of the coin toss where H1 might by “the coin is fair” and H2 might mean “the coin is biased 2/3 for heads against tails). That’s because probabilities only sum to 1 over the arguments to the left of the conditioning bar ‘|’; they do not sum to anything particular over the arguments to the right of the conditioning bar. That is because, as likelihoods, they are just an equivalence class of functions, with the same data, but conditioned on different hypotheses, that may differ by an arbitrary factor. That factor automatically cancels out when doing a likelihood ratio or Bayesian analysis.
This is the fundamental reason why the numerical value of a likelihood under a particular hypothesis is not meaningful, except as it relates to the numerical value under another hypothesis. It is not a “probability” in the usual meaning of the word.
Ray commented that my theodicy (which admittedly is highly speculative and is not a traditional Christian theodicy, though it is of the common type of a `greater good’ theodicy) has the consequence of “God as a utility monster. It is very clever, but it is 100% backwards from how Christianity typically conceives of things. In your scenario, humans suffer so that God can experience Plato’s heaven made real in our mathematically elegant universe. However in traditional Christianity, it is God who suffers so that humans may experience heaven.”
I don’t believe that God is a utility monster in the sense that His utility always overrides that of His creatures. However, I do believe that it is at least somewhat true that “humans suffer so that God can experience Plato’s heaven made real in our mathematically elegant universe,” though God may have other reasons as well. But I also agree that “in traditional Christianity, it is God who suffers so that humans may experience heaven.” I believe that God did suffer an enormous sacrifice, partly suffering in creating a universe that is not maximally mathematically elegant but which also has sentient experiences that do have on the whole positive value, and particularly suffering in the Incarnation, thereby making both sacrifices to increase human utility (our happiness). I think the Incarnation and Crucifixion symbolize (among other things) that God not only experienced the sufferings of the particular human Jesus, but actually all of our sufferings, so I do believe that God has been willing to undergo Himself all the suffering that is the foreseen but unintended inevitable consequence of His maximizing total value.
If God does what maximizes total happiness, including huge sacrifices on His part, I don’t see that it would be fair for us to demand that He totally sacrifice His own happiness to make it so that just our happiness is maximized.
There’s a bug in the voting software I think. I just voted against my own hidden comment by mistake.
There is no single route or algorithm to happiness however. It is dependent on various complicating factors–three simple examples being cultural values, competing happiness of individuals, and also whether we value acute happiness (if sharp) or long-term happiness (if dull) more favorably. These things did not exist before we did, so either two scenarios are true:
A) God already held these considerations in himself before the universe was created.
B) God acquired the capacity to judge and maximize happiness as the context was created.
If A is true, then God must be at least as complex as these many complicating factors. If B is true, then how did this happen and why should god evolve in this manner? Why not be ambivalent to this, or even maximize misery? And if god did not preclude such things in his nature originally, how did he differ from the original laws of nature (he would seem neutered to the point of barely being god-like)?
Perhaps you find these trivial, but again, by positing god you are establishing a claim about reality. If this theory about reality is to support or supplant naturalism it must do better and predict more while constraining its free parameters as much as possible.
Bill Jefferys, let me explain what I meant by the following paragraph you quoted, since I see that I wrote it too tersely to be understood:
“Other examples can be even more extreme. The maximum likelihood model for my present sentient experience would be that only it exists, since then its probability would be unity.”
I am assuming that the world has a set of sentient experiences, each with a measure that can be normalized to sum to one over all experiences. I am assuming that these normalized measures can be interpreted in a Bayesian analysis as if they were probabilities (even if the world is completely deterministic, with all of these measures giving in a sense how much the various experiences occur). (One might dispute these assumptions, but I am just asking that you consider them as part of the framework that I am using for a Bayesian analysis, so that in terms of this framework I can make my point.)
Now let us consider three hypotheses or theories for the world. Just to keep things finite and not too large, I shall assume here that that there are only one million possible sentient experiences E_i in each of the hypotheses, so i ranges from 1 to one million. Let E_1 be my present sentient experience, the one I am using to test the hypotheses. I assume that E_1 includes all that I know now, including reports from others, so I have no direct access to any other sentient experiences that may or may not exist in the world.
H_1: Each of the one million possible sentient experiences has the same measure, 0.000001.
H_2: Each of the first thousand possible sentient experiences has the same positive measure, 0.001, and the remaining ones each have zero measure.
H_3: The first sentient experience (my actual one) has measure 1, and all the remaining ones have zero measure.
H_3 corresponds to the model I mentioned in the quoted paragraph above, that only my present sentient experience exists. This gives P(E_1|H_3) = 1, whereas P(E_1|H_1) = 0.000001 and P(E_1|H_2) = 0.001. H_1 is a crude analogy for cosmological theories in which Boltzmann brain observations dominate, and H_2 is a crude analogy for theories in which the observations of ordinary evolved observers dominate.
I went on to write, “However, I would suspect that the complexity of my present sentient experience would make this extreme solipsistic model (not even having any of my memories corresponding to real experiences at any previous time) sufficiently complex that its prior probability would be much less than the product of the prior and the (admittedly extremely low) likelihood for a simpler theory giving my sentient experience as just one out of an enormous number of other sentient experiences.” As an example of this, in the present example, I might assign prior probabilities P(H_1) = 0.9, P(H_2) = 0.099999999, and P(H_3) = 0.000000001, since I would regard H_1 is the simplest, H_2 is somewhat more complex, and H_3 is far more complex in view of the complexity of my present sentient experience.
Then one gets the following products of the priors and the likelihoods:
P(H_1)P(E_1|H_1) = 0.0000009,
P(H_2)P(E_1|H_2) = 0.000099999999,
P(H_3)P(E_1|H_3) = 0.000000001.
When I normalize by dividing by the sum of these products, which is 0.000100900999, I get the following posterior probabilities (rounded to five places after the decimal point):
P(H_1|E_1) = 0.00892,
P(H_2|E_1) = 0.99107,
p(H_3|E_1) = 0.00001.
Therefore, even though the extreme solipsistic model H_3 has the highest possible likelihood (1), with the choice of priors above it has the smallest posterior probability. On the other hand, for the comparison of H_1 and H_2, the priors differed less than the likelihoods, so H_2 was favored, the model that I chose to be analogous to domination by sentient experiences of `ordinary observers’ rather than by either Boltzmann brains as in H_1 or by my own present sentient experience as in H_3.
In further thinking, I wonder that we’ve gotten lost in the details of this conversation. Don, is it possible that your position can be summed up as so?:
“We observe a universe derived from consistently simpler laws, therefore in lack of absolute determining evidence, we should bias ourselves towards simpler theories. Since we also observe miracles (such as the resurrection) that would coincide with the existence of a god, we note that god is has more explanatory power than naturalism which would require undue complexity (more free parameters) to explain true miracles. Meanwhile, god may conceivably remain quite simple while still explaining these miracles.”
If that’s close to a decent summary, I think we might should move the conversation past claims of simplicity and more to the existence of miracles such as the resurrection. That would seem more to the point. After all, if they did exist, I do think god would be the theory that explains all the parameters better.
I’m sorry, Don, but what you wrote makes no sense to me. I have no idea what you mean by “Let E_1 be my present sentient experience, the one I am using to test the hypotheses.”
In particular, this statement is wrong:
“H_3 corresponds to the model I mentioned in the quoted paragraph above, that only my present sentient experience exists. This gives P(E_1|H_3) = 1, whereas P(E_1|H_1) = 0.000001 and P(E_1|H_2) = 0.001.”
What you should have written is P(E_1|H_3,E_1)=1. Basically, you’ve written what amounts to a tautology…what I’ve observed, given that I’ve observed it.
But that’s not how likelihood inference works. You can’t assume your observation a priori which is what you’ve essentially done here. The observation has to be something unknown a priori that you then find out has been observed.
Don, not to beat a dead horse here, but H_3 isn’t a hypothesis. You couldn’t come up with any functional form that represented it. It doesn’t assign any one measure to your probability space in the absence of data. It only specifies a class of hypotheses, namely the set H_3_i where i ranges 1 to a 1,000,000. It doesn’t predict which of the one million sentient experiences is your “present” one.
In this light, the probability of any one sentient experience in this hypothesis class H_3 is basically equivalent to H_1 as you can’t assign anything but uniform weight to each of the hypotheses H_3_i.
So physics is all there is?
If physics as we know it, or even some more accurate, consistent and fundamental physics going beyond what we have now, then we are some sort of Boltzmann brains or similar random entity.
All the apparent sophistication of our artistic, emotional, analytic, sensory life is just an elaborate entropy anomaly, yet the rationalist ‘feels’ a need to reduce it all back to the physics from which it arose.
There is then no reality to your consciousness, no meaningful ability to evaluate or believe anything. Your own reductionism has taken you to a place where you can know for sure that it is unreliable.
Unless the higher level descriptors of the experience of consciousness (choice, desire, conviction, analysis, elegance etc etc) have some absolute, and physics-independent meaning.
Josh
‘We can not simply allow the black box to contain that god determines this or we are left with a tautology (a sort of “God does good which is defined by God”).’
Not if we need to understand everything. Which if a sensible presupposition, means we believe we can understand everything. For which we have no rational basis.
Seems to me that is all God is going to give you. He called himself ‘I am that I am’.
Josh said, “If that’s close to a decent summary, I think we might should move the conversation past claims of simplicity and more to the existence of miracles such as the resurrection. That would seem more to the point. After all, if they did exist, I do think god would be the theory that explains all the parameters better.”
This is why I was bringing up the issue of a metric for simplicity. Our choices of information encoding language/processing may not correspond to that the universe has. The universe may have another form of processing inherently different from that of a Turing machine, so our concept of information would not directly translate into the universe’s “concept of information.” From our evaluations it would seem simpler but there’d be no guarantee it would be “simpler” in any cosmological sense.
His argument is not a cosmological argument for God, just a practical one. I think all Don can effectively argue from this paradigm is that it’s better to operate as if God existed, not that God actually existed. Hence why I urged him to address this simplicity issue. He’s right that this extends to naturalism in general, but I don’t think physicists care one way or the other if the standard model is “cosmologically real” since all we care about is the assumptions we should operate under for experiments/engineering. The model that makes the best predictions is after all better than a model that may be more “true” but more vague. Don cares about truth though, so the metrics used are held to a different standard. I don’t think the simplicity issue can be dropped.
First, I appreciate the civility of this discussion, that is rare in this subject.
On the Bayesian approach, I don’t think it is appropriate to use it quantitatively in this context. It’s fine to use it as a qualitative model, but since we can’t even define the prior hypotheses (never mind their a priori probabilities), attempts to quantify posterior probabilities provide only false confidence. Even if one could, it wouldn’t be definitive.
On Occam’s razor, some people seem to use it as a form of evidence. That is also not appropriate. Two theories that have the same predictive power and supporting evidence can be tie broken by adopting the simpler, but if one theory has objective evidence and is more complicated, it should be preferred over another theory that is simple with no evidence (e.g. the Hopi cosmological creation story).
Daniel,
I don’t think discussion of simplicity can be dropped, but I also don’t think Don is making his assertions of what is truth from this. For instance, Don previously said in a comment that:
[Don] “Now I will admit that this reasoning alone (e.g., leaving aside evidence for the miracle of the Resurrection) would leave me highly agnostic about the existence of God. I am mainly presenting it here as an argument that just from the evidence of our sentient experiences that lead to the postulate of fairly simple laws of nature for our Universe, one should be at least open to the possibility of the existence of God. Then one can approach historical evidence for the Resurrection without having a huge bias against the hypothesis of theism.”
It seems to me Don is just arguing simplicity to make room for god. On this I agree. It is certainly possible there exists some external “something” to the universe which is both simpler and its progenitor. How this something would then translate to a specific religion or how one could ascribe any properties to it is beyond me. That’s why I think his argument hinges on the resurrection, and only contingent upon that is he/can he make truth claims beyond just possibilities.
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Simon,
The issue is more about which is a better model not necessarily which allows us to know everything. If you can’t get past good as synonymous with god, then I find it difficult to make predictions on what the universe would look like (a la, it would be a poor model in this regard). Moreover, if you are trying to explain the “good” in the universe, you must explain it with something different from itself.
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bonstontola,
What you said about Occam’s is spot on and why I think Don must really be saying his theory (god) could be simpler, but that doesn’t make it true. I think what he thinks makes it true must be the resurrection (and similar miracles). Perhaps he can clear this up however.
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Simon:
Would you believe a new medical treatment (or an old one, like homeopathy, say) was efficacious on the basis of the sort of evidence you are advancing for faith healings? Would you accept a miracle report of a resurrection credited to a non-Christian religion/diety on the basis that the person telling you it thought that the person who told them it seemed trustworthy?
A while back, you wrote:
I’m not sure what your argument is here. “Faith” appears to mean “pretending you know things you don’t”. This is a bad thing, both epistemically and in its moral consequences. (“moral consequences” because, as C.S. Lewis wrote, witch burnings happened because people didn’t realise there are no such things as witches, so I take it there is a moral duty not to pretend to know such things and then act on it).
So, why think that removing the need for “faith” is the bad thing? Pretending to know things you don’t is not a virtue.
Joz seems to think that, if God’s existence were more obvious, this would remove free will. But in fact, even if it were completely obvious that God exists (I take it that both Joz and you accept that it isn’t obvious), it would still be open to people to choose what they did about that.
You write that: “If you dislike the idea of God you have in your head, you will be disposed against any rational argument for him.” Do you believe you have made any rational arguments? Why do you think your hidden comment collected so many downvotes? I’m interested in how much insight you have into how you appear here, I guess.
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Bill Jefferys and Daniel Kerr, let me try to explain more carefully what I meant. I was taking the different sentient experiences E_i to be distinguished by their content, so in my example I was assuming that there are one million different possible observations, taking an sentient experience to be an observation. If you like, you could say E_i represented different possible sets of observed data. For example, it could be the one million different possible 6-digit nonnegative decimal integers, including leading zeros to make number smaller than 100,000 into 6-digit numbers, so that the numbers range from 000000 to 999999. I might then represent E_1 by the number 000000.
Now I am taking P(E_i|H_j) to be the probability of observing the data E_i given the hypothesis H_j. In my model hypotheses the following statement was not wrong:
“H_3 corresponds to the model I mentioned in the quoted paragraph above, that only my present sentient experience exists. This gives P(E_1|H_3) = 1, whereas P(E_1|H_1) = 0.000001 and P(E_1|H_2) = 0.001.”
By P(E_1|H_3) I did not mean P(E_1|H_3,E_1), just as by P(E_1|H_1) I did not mean P(E_1|H_1,E_1), and by P(E_1|H_2) I did not mean P(E_1|H_2,E_1). The numerical values for P(E_1|H_1) = 0.000001 and for P(E_1|H_1,E_1) = 1 are not equal, and the numerical values for P(E_1|H_2) = 0.001 and for P(E_1|H_2,E_1) = 1 are also not equal, though I did choose H_3 so that P(E_1|H_3) = 1 and P(E_1|H_3,E_1) = 1 happened to be equal.
Daniel, I don’t understand why you say that H_3 is not a hypothesis. It is the hypothesis that the probability of the observation E_1 (or of the number 000000) is unity and the probability of all other observations is zero. For example, IF one postulated that the probability of each of the observations were equal to the expectation value of a corresponding set of orthogonal rank-one projection operators, then H_3 would be the hypothesis that the quantum state is, as a density operator, the projection operator corresponding to the observation E_1, the pure state that gives 000000 with unit probability and all other 6-digit numbers with zero probability.
Josh, I agree with your summary (though I might have capitalized a few words you didn’t):
“We observe a universe derived from consistently simpler laws, therefore in lack of absolute determining evidence, we should bias ourselves towards simpler theories. Since we also observe miracles (such as the resurrection) that would coincide with the existence of a god, we note that god is has more explanatory power than naturalism which would require undue complexity (more free parameters) to explain true miracles. Meanwhile, god may conceivably remain quite simple while still explaining these miracles.”
I am at the airport about to board a flight to London to participate in a workshop with Stephen Hawking, so I may be delayed in future comments.
I agree with Dr. Page (for what little that is worth), that his argument is an argument about Boltzmann Brains (BB), and H_3 is the hypothesis that he is a BB and he is the only BB that exists. H_1 is a truncated form of the hypothesis that all possible different BB’s exist, and H_2 is the hypothesis that a number of BB’s exist but not all possible ones. I think it is a bit easier to follow put that way, because Dr. Carroll had a previous post on BB’s back on Cosmic Variance which prepared me for the concept. Interestingly, I think Dr. Carroll’s argument, based on entropy, concluded that it was more likely than not that we are in fact BB’s – that is, that I came into existence a nanosecond ago with a complete set of memories due to the configuration of particles and energies that happened to spontaneously form in a vacuum at that time. At least, some commenters, myself included, understood it that way, and argued against it on the basis of the conditional probability of our memories being so self-consistent, but this argument was dismissed by Dr. Carroll, no doubt with good reason (the most likely one being that I have mis-remembered his argument).
So I prefer the result of Dr. Page’s calculation (under the restriction that only BB’s exist) since it caters somewhat to my feeling about not being alone in the universe, although it depends on assuming prior probabilities which I can’t prove are correct. Anyway, perhaps the main point is that almost any conclusion can be swayed by the prior probabilities one assumes.
My own prior is that the person who invents and makes and programs a new machine (or universe) understands both the machine and how to make it, and must be more complex than the machine itself – unless it was a trial-and-error process, like the evolution of biological creatures and human designs.
Don, I just don’t see how H_3 can be formulated as you state then, as it depends on the measurement E1 to know you should assign 000000 a probability of unity. It seems you’re setting up an iterative process to calculate a final posterior probability, so H_3 _000000 is assigned a nonzero probability as the result of a posterior probability given by the data E1. You know all other H_3_i have posterior probabilities of zero. You can’t use E1 again to calculate the next iterative posterior, but the very nature of the experiment does not allow you to sample any other Ei. Nonetheless, you didn’t know before measuring E1 that 000000 was the correct sentient state.
Don, I’m sorry, but this is just a mistake.
The same mistake has been made before by others, and it is an easy one to fall into. I’ve addressed it here:
http://bayesrules.net/papers/OldData.pdf
It is simply not the case that you can write P(E1|H1)=1 on the grounds that E is what you have observed. This is what you have done.
BTW I agree with Daniel. His recent comment is spot on.
This is an interesting discussion, which I’ve learned a lot from. Thanks to all. I freely admit that I’m in way over my head here.
If I could ask a question from the left field bleachers:
If Einstein says (proved?) that we live in a universe where everything is relative to its own system, and if the statements everything is relative and nothing is absolute have the same effective meaning (which I believe they do), than what are we doing searching for or positing Absolutes, except for reasons of ego?