As I mentioned the other day, I’ve recently (at the direction of my old friend Deirdre McCloskey) been reading some of the work of John Polkinghorne, the physicist-turned-theologian who seems to write about a book a week attempting to reconcile his twin faiths in orthodox science and orthodox Christianity.
Although Belief in God in an Age of Science is a very short book, it is too long to review in a single blog post. Fortunately, though, much of the non-lunatic content is concentrated in roughly the first ten pages, so I’ll comment here only on those.
Polkinghorne begins in awe. He is awestruck by the extent to which our Universe seems to have been fine-tuned to support life; this is the subject matter of the much-discussed anthropic cosmological principle. To take just one example (which Polkinghorne does not mention): The very existence of elements other than hydrogen and helium depends on the fact that it’s possible, in the interior of a star, to smoosh three helum atoms together and make a carbon atom; everything else is built from there. But it’s not enough to make that carbon atom; you’ve also got to make it stick together long enough for a series of other complicated reactions to occur. Ordinarily, that doesn’t happen, but now and then it does. And the reason it happens even occasionally is that the carbon atom happens to have an energy level of exactly 7.82 million electron volts. In fact, this energy level was predicted (by Fred Hoyle and Edwin Salpeter) before it was observed, precisely on the basis that without this energy level, there could be no stable carbon, no higher elements, and no you or me.
That energy level is only one of many (apparent) cosmic coincidences that make us possible; change any of the fundamental physical constants (like, say, the strength of gravity) by a little bit in either direction, and the Universe would, as far as we can tell, become completely inhospitable to life. So one does tend to feel that there’s something here that needs explaining.
Some have attempted to dismiss the issue by turning the direction of causality on its head: Here we are, so of course the laws of physics must allow for our existence. Case closed. Douglas Adams, for example, offers this brief and brilliant parable:
Imagine a puddle waking up one morning and thinking, ‘This is an interesting world I find myself in, an interesting hole I find myself in, fits me rather neatly, doesn’t it? In fact it fits me staggeringly well, must have been made to have me in it!’
But I have some sympathy for Professor Polkinghorne’s refusal to accept this dismissal. Instead, he takes his stand with the philosopher John Leslie:
The fine tuning is evidence, genuine evidence, of the following fact: that God is real, and/or there are many and varied universes.
I agree with that (with the proviso that evidence is not proof). I agree with it to exactly the same extent that I agree with this:
The fine tuning is evidence, genuine evidence of the following fact: Either invisible pink bunny rabbits, created at the time of the Big Bang, fine tuned the physical constants in order to make the Universe hospitable to lettuce, and/or there are many and varied universes.
Or, more succinctly:
The fine tuning is evidence, genuine evidence of the following fact: There are many and varied universes.
Polkinghorne wants to reject this second horn of Leslie’s dilemma, but he manages to do so, I think, only by taking too crabbed a view of what those many and varied Universes might be. First, we have the parallel worlds promised to us by the many-worlds interpretation of quantum theory; Polkinghorne is absolutely right to say these can’t be the worlds we’re looking for, because they all obey the same basic laws of nature. Higher on what Polkinghorne calls the “scale of bold speculation” we have suggestions from quantum cosmology that Universes are bubbling up all the time as quantum fluctuations in some universal substrate. But again, Polkinghorne is right to say that this only pushes the mystery back a bit—why do those fluctuations obey laws that have even a chance of producing a habitable Universe? Where do the laws come from?
This is the point where Polkinghorne gives up and falls back on God. But it seems to me that he has given up just one level of abstraction too soon. A Universe is fundamentally a mathematical object—it’s an abstract pattern that might or might not contain subpatterns that might or might not be sufficiently complex in just the right away to achieve an awareness of their surroundings, and might or might perceive those surroundings as physical objects. And of course there are many Universes, because there are many mathematical patterns, including, as just one of a dazzling infinity of examples, the Universe in which we live.
That, in any event, is the best explanation I can come up with, and it’s an explanation that feels completely right to me (which admittedly proves nothing). In The Big Questions, I’ve elaborated on what I mean by all this, how it can be true, and why it is entirely consistent with mainstream physics and the stated views of many mainstream physicists.
Now, Professor Polkinghorne might or might not buy this vision, but my point is that he never even contemplates it. He makes the leap to theism by considering and rejecting all of the weakest alternatives, but ignoring the only one that makes sense. This oversight is all the more remarkable because Polkinghorne devotes his closing pages to a rousing defense of the independent reality of mathematical objects, in clear and convincing language that had me wishing I’d written these pages myself.
The rest of the book is far worse. I might come back to that in a later post.
“First, we have the parallel worlds promised to us by the many-worlds interpretation of quantum theory; Polkinghorne is absolutely right to say these can’t be the worlds we’re looking for, because they all obey the same basic laws of nature”
I think you are much too quick to dismiss this. There is no reason that these worlds should have the same energy levels for Carbon, nor the same number of quarks, or (famously) cosmological constant. Have you read Leonard Susskind’s articles / book? Surely you have…
A Universe is fundamentally a mathematical object—it’s an abstract pattern that might or might not contain subpatterns that might or might not be sufficiently complex in just the right away to achieve an awareness of their surroundings, and might or might perceive those surroundings as physical objects. And of course there are many Universes, because there are many mathematical patterns, including, as just one of a dazzling infinity of examples, the Universe in which we live.
This sounds very much like the ideas discussed in these papers. Do you reference them in your book?
Andy Wood: Yes, I talk about these papers at some length in the book.
You’ve already heard this since I told you this while reviewing a draft of the book :) but —
Even though there’s nothing internally contradictory about the hypothesis that (roughly speaking) all conceivable universes can and do already exist since they exist as a mathematical pattern, consider the moral implications of this statement. Should you help a stranger who needs a sandwich to eat? Under the all-universes hypothesis, it makes no difference what you do, because either way, there continues to exist a universe in which you helped him, and there continues to exist a universe in which you didn’t. The total amount of suffering by conscious beings is the same.
It only makes a difference in the narrow solipsistic sense that if you help the person, *you’ll* get to feel better by seeing them become happier. And in the case of indirectly helping someone on the other side of the world that you’ll never ever meet, not even that counts for anything.
Bennett: Your argument makes absolutely no sense to me whatsoever. I have to take what’s going on in the other Universes as outside my influence. If I can do good here in this Universe, that good is not diminished by the fact that others elsewhere are suffering. Just as there is great moral value in feeding a starving child, even in a world where millions of other children starve to death.
I tread lightly here because a) I have nowhere near the mathematical chops to run with the big dogs and b) I haven’t read your book (although I’ve read Polkinghorne’s).
But I wonder if you could explain to a layman why your claim that “A Universe is fundamentally a mathematical object” escapes the objections, to which you seem sympathetic, that greet the quantum fluctuation argument: Where do the laws come from? Whatever you mean by a “mathematical object”, you surely mean that a universe is a thing of mathematical coherence, right? But where does the coherence come from?
As I understand Polkinghorne, I think he might address your “mathematical patterns” argument, but he dismisses it pretty summarily. Am I wrong to substitute “mathematical patterns” for “laws of nature” in this passage?
“Maybe the laws of nature themselves fluctuate, so that a vast portfolio of conceivable or (to us) inconceivable, worlds rise and fall in the relentless exploration of random possibility – occasional patches of transient and varied order in a sea of seething chaos. We have moved far beyond anything that could be called scientific in this exercise of prodigal conjecture.” (p.9)
It seems to me the question “why is there something rather than nothing?” can’t be answered. But thinking deeply about the question can be a very powerful yet calming experience. What’s fascinating though is that there IS an answer to this question…there is a reason why there is something rather than nothing and for some reason this it’s fascinating to know there is an answer to this question – regardless of whether we will ever know
Peter: The vision I’ve tried to sketch is that mathematical objects exist by necessity, and that their properties are what their properties have to be.
A euclidean plane, for example, is a mathematical object. It contains lines and points, and these lines and points obey certain laws, such as “through any two points there is exactly one line”. The laws come from the nature of the object.
Physicists routinely model the universe as a substantially more complicated mathematical object. For exampe, they might start not with a 2-dimensional plane, but with its 4-dimensional analogue. Then they suppose that instead of being flat, this object is curved in ways that represent the influence of gravity, and that it has attached to it some more complicated geometric objects that represent the effects of electricity and magnetism, etc.
There is no doubt that this mathematical object exists; one can study it as a purely mathematical construction in its own right. It’s also supposed to be some sort of approximation to what the universe looks like.
My suggestion is that the actual universe—the one that this object is supposed to approximate—is not an entirely different kind of animal; instead it’s a far *more* complicated mathematical object, endowed with additional geometric curlicues whose significance we haven’t yet recognized. And the properties of that object are determined internally, just as the properties of a plane are determined internally.
So to summarize: 1) The properties of mathematical objects are what they are because they couldn’t be otherwise. The properties of a plane are what the are because if they were different, we wouldn’t be talking about a plane—we’d be talking about some other mathematical object. 2) Physical theories routinely approximate the universe we live in by pretending that it is a mathematical object. 3) I suggest that the universe we live in *is* a mathematical object, which is approximated by the objects in the physicists’ theories. 4) There are many many mathematical objects, some of which are complicated enough in the right sorts of ways to be called universes. All of those universes exist, because mathematical objects can’t help but exist.
There is of course more in the book!
Is God a mathematician?
http://plus.maths.org/issue49/reviews/book5/index.html
In my comment above I realize I (not surprisingly) could be wrong. There may not be an answer to the question “why is there something rather than nothing?” true or false: there has always been something. If you believe this statement is true, then I don’t think an answer exists. If you think it’s false then there Is an answer but you have to believe somethig came from nothing …is my thinking flawed?? Or just elemntary?
Steve,
Many thanks for your accessible explanation. I think I may have to read the book, though, to try to follow the argument more carefully. I’m with you up to point 4) of your summary, but at that point, it seems to me that whether I zig with Polkinghorne toward God or zag with you toward eternal mathematics is a question that gets decided with an equal mix of faith and evidence when it comes to describing other possible universes. It seems like the choice would have to be made on other grounds (like, say, “what feels completely right to me.”)
As far as I can see, it all boils down to the issue of independent evidence. That the Universe exists because it is a self-consistent mathematical pattern, or that it exists because it was sneezed out of the nose of the Great Green Arkleseizure (as suggested by Douglas Adams), look to me like equally valid hypotheses, as long as neither of them can find support in independent evidence; that is, evidence independent from the existence of the Universe. (I am stinking my neck out by writing this before reading the book; my excuse is that I am addressing the argument presented in this post, and nothing more.)
Also, I note that the existence of all mathematical patterns is not an argument against the existence of God: it could be that mathematical patterns exist only in the mind of God. (Though this post does not seem to argue against the existence of God, only against the Polkinghorne argument.)
OK, I came late to this party, but, being here, I should clarify the intuition behind my comment from yesterday.
The intuition is that the “Platonist hypothesis”, that all internally consistent mathematical patterns exist, reminds me of the ontological argument for the existence of God. The ontological argument says that God exists because a perfect entity must necessarily exist, otherwise He would not be perfect. The Platonist hypothesis says that self-consistent mathematical patterns must exist, otherwise they would not be true. The problem that I see in both cases is that we are trying to argue about existence from pure reason, without any reference to empirical facts.
Snorri: Do you doubt that arithmetic is consistent? I claim a) that we know this with as much certainty as we know anything, and b) that this knowledge does not derive primarily from empirical facts.
I’d like to explore why Polkinghorne might find the idea of God a good solution to the question in the first place.
What is he actually envisioning when he imagines a God as solving the problem of fine tuning? I haven’t read his particular book, by in my experience, theologians (and especially many scientists trying to do theology) rarely explain just what they imagine a God actually does to tackle this problem: they just assume that God is really really powerful and smart, and thus somehow, it makes things happen the way it wants (which of course, raises the deeper question of why, if a God is all-powerful, there even NEEDS to be a logic or underlying “way” in which things work: what Mill called ‘resorting to mere artifice’).
But people do often seem to have, and assume we all have, some vague model of “how” God helps explain things. I mean, how do intelligent beings in general tackle engineering problems? They think about them. And what does that really entail? Well, as far as we know, it means envisioning things as they might be: modeling them out, or even testing them out via trial and error. Seeing what’s needed, making adjustments, figuring out what’s the best way to make what you want happen the WAY you want it.
And I mean, it’s all well and good to say that a God might be omniscient and omnipotent and just wills things to BE, but SOME sub-routine of omnipotence must at some point have to be tasked with figuring out the exact right energy state for certain atoms if they are going to form heavier elements. _Something_ has to work out the details, and there has to be some sort of process to get there. Otherwise, the universal constants would just BE inexplicably correct in God’s mind, in which case, why not simply assume that they are inexplicably correct period, and do away with the extraneous concept of needing a “mind” to figure out what they need to be.
Of course, once we’ve imagined all that, we’re basically talking about God having a mental reproduction of not only the entire universe, but all possible universes: isn’t that what “omniscience” implies? And doesn’t that put us right back to the concept of multiverses, meaning that “God” is no escape from that possibility?
Of course. someone might, at this point, conclude that where I’ve been going with this is to say that reality is all simply the mind of God. Oooo, ahhhh, how poetic. Except that idea seems sort of silly to me. If these things are/need to be all modeled out in some extremely detailed way in order to imagine a MIND being behind setting them up, then why do we need to assume any sort of MIND at all? Minds cost extra, in terms of explanatory necessity. Just have the multiverse, and we happen to be in one of them, noticing all this. Why? I dunno. No one can say why there should just randomly be an omniscient mind either.
Of course, as I’ve tried to discuss elsewhere, I’m not even sure fine-tuning is actually as interesting a philosophical issue as it is a physics issue. By that, I mean that the particular values of the constants being such that they produce a universe that has (some) complexity and (some) intelligence is “interesting” (i.e. a serious problem demanding an answer) only in the context of physics and assumptions physicists make. It’s interesting only if we imagine that the constants are randomly determined in some _specific_ game of cosmic dice and we got an amazingly improbable roll on the first roll.
But, of course, go beyond physics, ask why the game of dice is even set up that way, why it couldn’t have been set up differently: open up the larger world of philosophical possibility, and we no longer have any reason to assume that our universe is especially unlikely at all.
That’s what always irritates me about theologians: they wish to go beyond the constraints of physical necessity, of laws and puzzles and even explanations… but they then refuse to see just HOW MUCH that opens up: their God hypothesis is certainly one possibility, but it’s one amongst zillions. You can’t just declare all the rules broken, and then try to use the path the rules carved out to head to a very narrow destination. Once you simply do away with physics, you also do away with all the constraints that made the problem a problem in the first place.
Ahh, the universe is a mathematical object. This makes the same mistake as anthromorphic claims. Math has evolved for thousands of years specifically to explain and predict natural phenomenon; and now you mistake the model for the reality; like mistaking a photograph for the landscape.
The problem with the mathematical approach is that it fails to explain anything except fundamental phenomena, and these are insufficient to explain things such as consciousness, free will, and emotions without hand-wavy allusions and metaphorical hocus-pocus.
Mind, I am 100% atheist and non-supernaturalist; but I regard free will as an observable fact: People agonize over decisions, make decisions and I believe these decisions change their future. I am also a mathematician, and any “mathematical” treatment of the universe must claim that all of this mental cogitation, emotion and worry is mere facade, an electro-chemical reaction that by the immutable laws of mathematics has a pre-determined outcome, just like adding up a list of millions of numbers has one and only one correct answer.
Quantum physics does not rescue this dilemma; if our decisions are founded upon completely random decays and paths of electrons we also have no free will or true ability to decide.
In short, the mathematical view leaves us with pre-determined fate. Nothing we do or think can change the future, it is fixed. Or if you subscribe to quantum effects, it is not fixed but we have no say in how it turns out, either, not in the short run and not in the long run.
I reject that outcome. Instead, I’d generalize the lesson I take from that great philosopher, Douglas Adams. The puddle mentioned fails to understand why its little universe fits it, like the anthropomorphists fail to understand why their universe fits them. In both cases, the proper lesson to be drawn is simply that there are things we do not understand. My philosophy does not demand I have an answer to how, physically, free will is possible, but certainly my own observations strongly suggest that free will exists.
Likewise, we simply do not need to leap to an answer on why the universe supports life, and we certainly don’t need unprovable non-answers like God or that the universe is a “mathematical object.”
As a scientist, I claim such “explanations” do more harm than good. They may make one feel content and secure (a benefit) but may also make one complacent (a detriment) that they have “solved” the riddle and “got the answer,” when in fact they are simply delusional. There are people like me that regard being delusional as a sorrier state than simply being ignorant. Delusion is harder to correct than ignorant, because the first step in throwing off delusion is the difficult step of attaining and accepting a state of ignorance.
And finally, the biggest problem with delusion is the problem with believing any lie: beliefs at odds with reality can bite very hard, because the inanimate universe just does not care what we believe, no matter how hard we believe it does.
“…insufficient to explain things such as consciousness, free will, and emotions without hand-wavy allusions and metaphorical hocus-pocus.”
Until someone can explain what SORT of thing WOULD BE sufficient to explain these things, and roughly how it would go about doing so, I think declaring anything “insufficient” is premature. In fact, there is every reason to believe that we have not even defined these concepts very clearly in the first place, so it’s really no wonder that we don’t have good explanations for them.
I don’t disagree with you that much is uncertain and unknown. But you have to understand that agnosticism is often it’s own worst enemy. If you don’t know something, then you probably ALSO can’t go on to claim that it’s _impossible_ to know it. After all, knowing THAT would require knowing far more about the unknown thing than you claim to know already. :)
“Mind, I am 100% atheist and non-supernaturalist; but I regard free will as an observable fact: People agonize over decisions, make decisions and I believe these decisions change their future.”
Believing that their decisions change their future from what it might otherwise have been is not an “observable fact” because the very facts you would need to observe never came into being.
I’m not sure why my choices being predetermined would make them a facade anyway (not that I believe that they are: I honestly have no idea). If there is any such thing as “me” then it is a PARTICULAR me that reacts to certain things in certain ways. So they are my decisions, in the sense that a given choice is offered to ME and I react to it in MY characteristic way, feeling my characteristic emotions, and so on. So what’s the problem, whether or not all of that is predictable? It’s still me.