Turtles Much of the Way Down

Paul Davies has published an Op-Ed in the New York Times, about science and faith. Edge has put together a set of responses — by Jerry Coyne, Nathan Myhrvold, Lawrence Krauss, Scott Atran, Jeremy Bernstein, and me, so that’s some pretty lofty company I’m hob-nobbing with. Astonishingly, bloggers have also weighed in: among my regular reads, we find responses from Dr. Free-Ride, PZ, and The Quantum Pontiff. (Bloggers have much more colorful monikers than respectable folk.) Peter Woit blames string theory.

I post about this only with some reluctance, as I fear the resulting conversation is very likely to lower the average wisdom of the human race. Davies manages to hit a number of hot buttons right up front — claiming that both science and religion rely on faith (I don’t think there is any useful definition of the word “faith” in which that is true), and mentioning in passing something vague about the multiverse. All of which obscures what I think is his real point, which only pokes through clearly at the end — a claim to the effect that the laws of nature themselves require an explanation, and that explanation can’t come from the outside.

Personally I find this claim either vacuous or incorrect. Does it mean that the laws of physics are somehow inevitable? I don’t think that they are, and if they were I don’t think it would count as much of an “explanation,” but your mileage may vary. More importantly, we just don’t have the right to make deep proclamations about the laws of nature ahead of time — it’s our job to figure out what they are, and then deal with it. Maybe they come along with some self-justifying “explanation,” maybe they don’t. Maybe they’re totally random. We will hopefully discover the answer by doing science, but we won’t make progress by setting down demands ahead of time.

So I don’t know what it could possibly mean, and that’s what I argued in my response. Paul very kindly emailed me after reading my piece, and — not to be too ungenerous about it, I hope — suggested that I would have to read his book.

My piece is below the fold. The Edge discussion is interesting, too. But if you feel your IQ being lowered by long paragraphs on the nature of “faith” that don’t ever quite bother to give precise definitions and stick to them, don’t blame me.

***

Why do the laws of physics take the form they do? It sounds like a reasonable question, if you don’t think about it very hard. After all, we ask similar-sounding questions all the time. Why is the sky blue? Why won’t my car start? Why won’t Cindy answer my emails?

And these questions have sensible answers—the sky is blue because short wavelengths are Rayleigh-scattered by the atmosphere, your car won’t start because the battery is dead, and Cindy won’t answer your emails because she told you a dozen times already that it’s over but you just won’t listen. So, at first glance, it seems plausible that there could be a similar answer to the question of why the laws of physics take the form they do.

But there isn’t. At least, there isn’t any as far as we know, and there’s certainly no reason why there must be. The more mundane “why” questions make sense because they refer to objects and processes that are embedded in larger systems of cause and effect. The atmosphere is made of atoms, light is made of photons, and they obey the rules of atomic physics. The battery of the car provides electricity, which the engine needs to start. You and Cindy relate to each other within a structure of social interactions. In every case, our questions are being asked in the context of an explanatory framework in which it’s perfectly clear what form a sensible answer might take.

The universe (in the sense of “the entire natural world,” not only the physical region observable to us) isn’t like that. It’s not embedded in a bigger structure; it’s all there is. We are lulled into asking “why” questions about the universe by sloppily extending the way we think about local phenomena to the whole shebang. What kind of answers could we possibly be expecting?

I can think of a few possibilities. One is logical necessity: the laws of physics take the form they do because no other form is possible. But that can’t be right; it’s easy to think of other possible forms. The universe could be a gas of hard spheres interacting under the rules of Newtonian mechanics, or it could be a cellular automaton, or it could be a single point. Another possibility is external influence: the universe is not all there is, but instead is the product of some higher (supernatural?) power. That is a conceivable answer, but not a very good one, as there is neither evidence for such a power nor any need to invoke it.

The final possibility, which seems to be the right one, is: that’s just how things are. There is a chain of explanations concerning things that happen in the universe, which ultimately reaches to the fundamental laws of nature and stops. This is a simple hypothesis that fits all the data; until it stops being consistent with what we know about the universe, the burden of proof is on any alternative idea for why the laws take the form they do.

But there is a deep-seated human urge to think otherwise. We want to believe that the universe has a purpose, just as we want to believe that our next lottery ticket will hit. Ever since ancient philosophers contemplated the cosmos, humans have sought teleological explanations for the apparently random activities all around them. There is a strong temptation to approach the universe with a demand that it make sense of itself and of our lives, rather than simply accepting it for what it is.

Part of the job of being a good scientist is to overcome that temptation. “The idea that the laws exist reasonlessly is deeply anti-rational” is a deeply anti-rational statement. The laws exist however they exist, and it’s our job to figure that out, not to insist ahead of time that nature’s innermost workings conform to our predilections, or provide us with succor in the face of an unfeeling cosmos.

Paul Davies argues that “the laws should have an explanation from within the universe,” but admits that “the specifics of that explanation are a matter for future research.” This is reminiscent of Wolfgang Pauli’s postcard to George Gamow, featuring an empty rectangle: “This is to show I can paint like Titian. Only technical details are missing.” The reason why it’s hard to find an explanation for the laws of physics within the universe is that the concept makes no sense. If we were to understand the ultimate laws of nature, that particular ambitious intellectual project would be finished, and we could move on to other things. It might be amusing to contemplate how things would be different with another set of laws, but at the end of the day the laws are what they are.

Human beings have a natural tendency to look for meaning and purpose out there in the universe, but we shouldn’t elevate that tendency to a cosmic principle. Meaning and purpose are created by us, not lurking somewhere within the ultimate architecture of reality. And that’s okay. I’m happy to take the universe just as we find it; it’s the only one we have.

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110 Responses to Turtles Much of the Way Down

  1. Count Iblis says:

    First, folks, if Tegmark were right, there’d be no reliable continuity (lawful patterns continuing into the future) because of all the “universes” where attractive forces change into being some other rule than 1/r^2 (or r^(N-1) if N is large space dimensions) and etc. After all, they are describable – I just did. Our chance of being in a description that really simulated lawfulness long-term would be negligible, even if we were in such a model up to this point.

    Such universes require more information to describe. One has to assume that universes that can be described with less bits are more likely. Note that an observer is itself a mathematical model that is simulated by a brain which in turn is described by the laws of physics.

    You can think of an observer as living in the simulation that the brain is computing. But the effective laws of physics of this virtual world are extremely complicated. In this virtual world the qualia we can experience are fundamental physical objects.

    This world exists as a universe in its own right, but because you need an enormous amount of information to describe it, we don’t find ourselves there, rather we see ourselves being simulated in this universe.

  2. Not Required says:

    Sean C said: “The final possibility, which seems to be the right one, is: that’s just how things are. ”

    I guess SC is aware that many philosophers respond in just this way when talking about the low-entropy conditions at the beginning of the universe. I’m sure that SC would dismiss that. But why? That’s just how things were at the beginning of time.

    In fact, “that’s just how things are” is not so far from “It’s God’s Will”. Both of them are cop-outs.

  3. Elliot says:

    the haiku master
    is embedded silently
    within the haiku

    e.

  4. Cynthia says:

    In one sense, Paul Davies leans towards the proponents of ID, meaning the non-secular anthropists. In another sense, though, he leans towards the ID opponents, meaning the secular anthropists.

    But because some IDers appear rather pleased with Davies’ message (at least see his message in a positive light), this may serve as evidence that Davies’ anthropic leanings are slightly non-secular in origins.

    http://www.uncommondescent.com/intelligent-design/taking-science-on-faith/

    In the meantime, though, I’ll reserve judgement as to which way Davies leans till I hear what secular anthropists (namely the theorists studying the stringy Landscape) have to say about his message. But as long as the non-secular anthropists see ID as reality while the secular anthropists see ID as an illusion, the secular ones (Raphael Bousso, Joseph Polchinski, and Lenny Susskind, to name a few) won’t be too pleased to hear that Davies’ message pleases some IDers…

    Be mindful, though, despite the recent slew of media attacks on strings, I’m still of the strong opinion that the stringy Landscape offers, far and away, the best approach to the cosmological constant problem, not to mention the best approach to the origins of our pocket Universe!

  5. John Merryman says:

    Three dimensions of space are simply the coordinate system of the point these three lines cross and the same space could be described by any number of such coordinate systems/frames. Therefore the motion of any particular coordinate system, relative to the other systems, isn’t an additional dimension, but a process of interaction, where any action is matched by an equal and opposite reaction, so that to the hands of the clock, it is the face going counterclockwise. There is no dimension of time, as one direction is balanced by the other. Motion in space creates a series of events, so that as one is replaced by the next, the previous recedes into the past. The physical reality isn’t moving along this narrative, it is creating it.

    If no one is willing to stand up and defend four dimensional spacetime, how much of the rest of what is being discussed is the modern equivalent of arguing how many angels can dance on the head of a pin?

  6. bob says:

    why is so much time spent here talking about gods? It may be arrogant to say so but really, the subject borders on the infantile.

  7. bob says:

    okay, that came out sounding like a criticism of Cosmic Variance but my point is actually just the opposite — I love this blog for its science and just don’t see any point discussing gods.

  8. graviton383 says:

    Do you think we’ll STILL be having these arguments in 300 years??

  9. Alejandro says:

    Cynthia: According to Davies’s book (which I reviewed and criticized a while ago) he disagrees with both secular anthropicists (which put the “ultimate turtle” on a random selection from a multiverse) and IDers (which put it on the will of a transcendental deity). His preferred explanation for why the universe is what it is, and friendly for life, is some sort of teleological principle inherent in the laws of nature, instead of transcendent to it. He offers little articulation on how this principle would work, and even less arguments in support of it.

  10. Cynthia says:

    Alejandro: Thanks so much for clearing up some of my misconceptions regarding Davies’ views on the Cosmos! And I must commend you on putting together an excellent review of “Cosmic Jackpot.” Even if Davies isn’t very good at creating his own philosophy, I think I’ll still read this book of his just because he’s good at explaining philosophies of others.

    BTW, I stumbled upon this talk of his at Fermilab 10/05 which seems to serve as a rough draft for “Cosmic Jackpot”:

    http://vmsstreamer1.fnal.gov/VMS_Site_03/Lectures/Colloquium/051005Davies/index.htm

  11. Ivan says:

    Math or Magic/miracle ?
    Some people (e.g. physicists) prefer Math, because Math gives
    predictions (right or wrong, it depends; Magic can produce only
    illusions (of hope)).

    It is far not right that any math is suitable for our reality.

    (1) It seems we need a Field Theory — otherwise there will
    be some form of action at a distance, which is a kind of magic
    (hard spheres with Newton gravitation, this description was not
    appropriate for Newton himself); such a magic can look pretty
    well only in computer games, or in sci-fi books and movies.

    (2) That fundamental (or low-level) field theory should be
    NON-LINEAR — otherwise Achilles would not fill/see his turtle-pet
    (moreover, both would not exist) — and hyperbolic (and well-posed,
    with D>=4; and, advisably, should provide solutions with digital
    information, say, topological charges and quasi-charges,
    leading to quantum-like phenomenological (upper-level) models).

    (3) Last but not least: solutions of general positions (to this theory) should be eternal (like that sin(wt) for pendulum, where all time moments are of equal rights); and this requirement is very-very difficult (gradient catastrophe and singularities); today i know only one theory that meets all these demands.

    Assume we have a very perfect computer (not even without intellect and some sense of humor, although a bit artificial). That computer is not interested how we call our fields (amplitude of probability, metric field, or something else) — “no metaphysics, please”.
    He/she/it only asks:
    -“Please give me your equations. Pragmatism, yeah? “.
    – Oh, you know, we still should quantize that gravity, so at the moment we do not have a closed and self-consistent theory..
    -“Well, if you so convinced that you should do this, nothing can be done about (nichego ne popishesh’)”.

  12. Michael T says:

    What strikes me as interesting in the discussion of Davies article and indeed “The Cosmic Jackpot”, is that it is firmly based in the Christian narrative (actually one can include all of the Abrahamic religions in this context). I think that it is important to recognize the boundaries and constraints it necessarily imposes upon the dialog. That said, if you were a Taoists you wouldn’t be having this discussion, as a matter of fact, Davies wold not have even written such a piece. But I digress.

    I hate to do this but to quote scripture Paul defined faith (in one of many translations) as “the assured expectations of realities not beheld”. Is it then fair to say that a scientific assertion unable to be tested falls within the founder of Christianities very definition of faith?

  13. Harvey says:

    Bad

    Thanks for taking the time out to answer my question.

    many thanks

    Harvey

  14. Thomas Larsson says:

    When I was in grad school, I heard a talk by Davies. I definitely got the impression from senior people that Davies was somebody that one should laugh at, like Fritjof Capra. But maybe they were just envious that he had made a bundle on his books. This was around or before the first string theory revolution, so string theory had nothing to do with it.

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  16. Jason Dick says:

    First, folks, if Tegmark were right, there’d be no reliable continuity (lawful patterns continuing into the future) because of all the “universes” where attractive forces change into being some other rule than 1/r^2 (or r^(N-1) if N is large space dimensions) and etc. After all, they are describable – I just did. Our chance of being in a description that really simulated lawfulness long-term would be negligible, even if we were in such a model up to this point.

    This is completely false, in a number of regards:
    1. Mathematical structures don’t change. They are a particular way because of the axioms used to generate them, and cannot change. Therefore any complex substructure that is capable of understanding the universe it is in will necessarily see a universe that has understandable, mathematical laws, and there would be a most fundamental representation of those laws that was completely invariant.
    2. Just because you can describe something doesn’t mean that that something is a mathematical structure. In order for it to be so, it must be free from contradiction, not just something that can be imagined.

  17. tyler says:

    Oooh, a Tegmark paper brawl! I have *so* been waiting for this. Go!

  18. Greg Egan says:

    1. Mathematical structures don’t change. They are a particular way because of the axioms used to generate them, and cannot change. Therefore any complex substructure that is capable of understanding the universe it is in will necessarily see a universe that has understandable, mathematical laws, and there would be a most fundamental representation of those laws that was completely invariant.

    That’s the simplest possibility, but I’m not sure that other possibilities are entirely ruled out. For example, suppose that a Turing machine, or any other system with computational universality, is taken to be the true underlying mathematical system. (For those who don’t believe a Turing machine can support consciousness, feel free to augment it with whatever extra structure is needed.)

    It’s not hard to imagine a Turing machine running a simulation of a world with, simultaneously, conscious beings with consistent memories, but variable and/or inconsistent “laws of physics”. Computer games do the latter all the time: there is usually no underlying set of universal rules, just a patchwork of ad hoc approaches to different phenomena. The conscious participants would then have to be supported by separate algorithms, rather than being supported by what they perceived as the laws governing the world around them.

    Now this is obviously a very ugly and inelegant class of mathematical structures, but if all mathematical structures exist, these ones certainly include conscious inhabitants, and would have to be counted.

    That said, though Tegmark talks about measures on the space of all mathematical structures, I don’t think he’s ever proposed an actual candidate for such a measure. Personally, I’m of the opinion that the measure is irrelevant! If all structures get to exist, then even if Turing machines with patchwork physics vastly “outnumbered” structures with uniform laws of physics, then I think it’s committing the selection fallacy to say that we learn anything by noticing that we’re not in the majority class. When the hypothesis says the minority class must exist along with the majority, P(at least one observer finds themself in the minority class | hypothesis) = 1, so the probability of the hypothesis is unaltered by the observation. IMO, Tegmark’s hypothesis is aesthetically appealing but completely untestable.

  19. This is what happens when you go all squishy and start accepting statements like “religious people are just as intelligent as atheists, and deserve the same level of respect”.
    Dawkins and Hitchens have the right idea.

  20. Peter Shor says:

    graviton says

    Do you think we’ll STILL be having these arguments in 300 years??

    I think this is the question which distinguishes philosophy from science, and I would bet that this is philosophy.

  21. Count Iblis says:

    I don’t think the argument will go on for 300 years. In a century from now we’ll have intelligent machines that more powerful than the human brain. Humans will then be replaced by machines. From the perspective of intelligent machines, the Tegmarkian way of looking at things is more natural than it is for us…

  22. Jason Dick says:

    It’s not hard to imagine a Turing machine running a simulation of a world with, simultaneously, conscious beings with consistent memories, but variable and/or inconsistent “laws of physics”. Computer games do the latter all the time: there is usually no underlying set of universal rules, just a patchwork of ad hoc approaches to different phenomena. The conscious participants would then have to be supported by separate algorithms, rather than being supported by what they perceived as the laws governing the world around them.

    Then the invariant laws would be those that determine how the “laws of physics” change with time. Heck, you might even have something as complex as a self-referencing algorithm for the change of the laws, such that the laws can, in effect, modify themselves. But there would still be an invariant algorithm somewhere.

    That said, though Tegmark talks about measures on the space of all mathematical structures, I don’t think he’s ever proposed an actual candidate for such a measure. Personally, I’m of the opinion that the measure is irrelevant! If all structures get to exist, then even if Turing machines with patchwork physics vastly “outnumbered” structures with uniform laws of physics, then I think it’s committing the selection fallacy to say that we learn anything by noticing that we’re not in the majority class. When the hypothesis says the minority class must exist along with the majority, P(at least one observer finds themself in the minority class | hypothesis) = 1, so the probability of the hypothesis is unaltered by the observation. IMO, Tegmark’s hypothesis is aesthetically appealing but completely untestable.

    Whenever we deal with whether or not a theory is correct, we must necessarily deal with probabilities. This means, yes, that it is possible we are incorrect. Therefore it only makes sense to rule out a theory when the probabilities are so astronomical that we might as well consider it impossible.

    For example, if you found that there were two types of mathematical structure in which intelligent life could potentially evolve (structure A and structure B), and 10^10 more intelligent observers would evolve in A than in B, but we observe that we live inB, then we expect that there’s something wrong with our theory. A theory which instead predicts that there will be as many observers in structure A as in B, or more observers in B, is vastly more likely to be correct.

  23. Coin says:

    Do you think we’ll STILL be having these arguments in 300 years??

    Of course we will. We were having them in 1707! Why wouldn’t one expect to be having them in 2307 as well?

  24. Neil B. says:

    About faith in science: “Faith”, like lots of conceptual things, isn’t well defined. I prefer as a general definition, something you believe because of some attraction but in the *absence* of positive evidence (N.E.T. presence of negative evidence.) Remember that added traits can be assigned to a subcategory, so what you would still believe even in the face of contrary evidence could be called “blind faith” etc. The faith that *everything* about the universe can be discovered scientifically is “faith” because that degree of scope *is not* evidenced, despite all the things we have gotten such a handle on already (fallacy of presuming a trend *must* continue? Uh, some don’t.) In fact, it looks more like “blind faith” to me, since e.g. we already know that the specific time when a Co-60 nucleus will decay is not discoverable or explainable. Calling it “probability” doesn’t keep that from having those implications. Every method, every tool, has its pros and cons, its capabilities and its limitations. There was no reason to assume that the process used for discovering “laws” would lend itself to answering why they are like that to start with. It is an act of faith, of assuming apples from oranges, to think it will, regardless of how many particular processes have been explained *in terms of* the laws of nature.

    I can accept that many of you are suspicious of “metaphysics”, and I have no problem with someone believing or not in whatever is yet undecided or undecidable. But can’t you see the hypocrisy of blithely throwing around “other universes” and variable or other laws of physics if you say you don’t accept what isn’t scientifically accessible? Those things are just not accessible to current or maybe any level of science. Why aren’t you demanding laboratory proof of other universes, “the landscape”, other laws of physics in action, etc? I say – you don’t because of the common vulgar practice of letting “your own” get away with whatever they need to, and only complaining when the other side does it (like in political partisanship, which this argument parallels too much.) Some have accused philosophical theologians (PTers) like me of being “dishonest” – well, I have described real dishonesty. (But it’s OK for someone who admits to doing philosophy to use such ideas, since there’s no self-contradiction. Tough.)

    As for whether we should be able to describe “God” etc., no, the best argument is that the universe is not existentially self-sufficient and therefore “something else” is responsible. Such negative arguments are valid avenues of reasoning – we do not, again, have to get any precise handle on what is left if a given postulate (the universe *is* self-sufficient) is rejected. Those who are throwing around clearly uninformed and naïve pretensions of what you think the best arguments in theological philosophy are like, I can only say, you just don’t know how it’s done. Finally, don’t refer to PT as like “ID” – AFAICT, the IDers think of intervention in nature, even I suppose of creatures being made whole like Venus on the half-shell or Adam from dust. PTers consider the issues of existential dependency, why laws are what they are, etc: it has nothing to do with altering what’s here. (Sure, “if God existed maybe He could do that, right?”; and if nature wasn’t orderly, maybe it could act like that anyway too, doh – I am working off the apparent lack of *evidence* that it does, just like you are – only the interpretation of the “Why” is different.) Comparing PT to ID is like comparing liberals to communists. (BTW, many of the militant atheist/anti-metaphysicians remind me so of harsh talk-radio bullies like Rush Limbaugh and even Ann Coulter – it’s the same tough guy/gal, anti-sentimentalist (the other side are soft-hearted sissies and we are cold-hearted and red-blooded real men, etc.) bullying instinct at work. I don’t mean that is evidenced by failure to accept a given theological argument, but it’s out there.

  25. I like Greg Egan’s comment! Of course, there may be a way to locally test Tegmark’s theory, by probing whether or not our universe is logically consistent. Which calls to mind a story called “Luminous” … by Greg Egan.

    Davies opens a can of multidimensional worms with inter-relating Theology, Math, and Physics. This he does without axiomatizing his Theophysics and Theomathematics.

    Here’s my first cut at classifying, enumerating, and unifying some of the arguments made in this thread.

    Let G = “God exists.”
    Let M = “Math works (is consistent, etc.).”
    Let P = “The physical universe exists.”

    Not sure how to draw the symbol on HTML, so let’s use the word
    “proves” instead the symbol from Proof Theory.

    We have 6 metaphysical stances related to these 6 statements, for each
    of which I make a brief comment:

    P proves M (and Applied Math is more “real” than nonphysical abstract Math).

    P proves G (Deist and Creationist argument that the beauty and harmony
    of the cosmos prove the glory of the creator).

    G proves P (Spinoza’s theory that the universe exists “in the mind of God”).

    G proves M (God is the ultimate mathematician, Blak’s etching of God
    as Geometer).

    M proves G (specious Mathematical “proofs” of the existence of God).

    M proves P (Tegmark’s theory that we live inside a mathematical object).

    Pairs of these can give isomorphisms related to Medieval and Galileo’s
    claim that the Book of Nature and the Bible are two different views of
    the same thing.

    We can also provide 6 Unifications of Theomathematics and Theophysics:

    P proves M proves G
    P proves G proves M
    G proves P proves M
    G proves M proves P
    M proves G proves P
    M proves P proves G

    which can, if a loop is valid (such as M proves P proves G proves M),
    collapse God, Math, and Physics to equivalence.

    Many open questions remain. For eample: does “The Unreasonable
    Effectiveness of Mathematics in the Natural Sciences” by Eugene Wigner
    suggest that M proves P or P proves M?

    I don’t think there is any new content here; just an original
    notational way to classify a large body of writings from disparate
    authors.

    Of course, some of the arguments that I classify have intrinsic
    historical importance, or literary merit.

    For example:

    “The famous beginning of Psalm 19 announces that the heavens declare
    the glory of God and the sky declares his handiwork.”

    When I classify that as “P proves G” something has clearly been lost
    in translation.

    Books
    Desert Storm Understanding the capricious God of the Psalms.
    by James Wood October 1, 2007
    The New Yorker

    “What is God like? Is he merciful, just, loving, vengeful, jealous? Is
    he a bodiless force, a cool watchmaker, or a hot interventionist, a
    doer with big opinions, a busy chap up in Heaven? Does he, for
    instance, approve of charity and disapprove of adultery? Or are these
    attributes instead like glass baubles that we throw against the statue
    of his invisibility, inevitably shattering into mere words? The
    medieval Jewish thinker Maimonides thought that it was futile to
    belittle God by giving him human attributes; to do so was to commit
    what later philosophers would call a category mistake. We cannot
    describe his essence; better to worship in reverent silence. ‘Silence
    is praise to thee,’ Maimonides wrote, quoting from the second verse of
    Psalm 65….” [truncated]

    Needless to say, many of the “complaints, fears, hopes…prayers,
    songs, incantations…soliloquies” are mutually inconsistent, and much
    writing on these subjects is internally contradictory.

    And so, I think, is the Davies argument. Of course, he’s made over a megabuck from such arguments, so avoiding contradiction may not be his goal.