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December 30, 2010


David Clark

Sorry, I got to this point and stopped reading:

Imagine a physicist or mathematician putting down her tools and saying, "Fuck it. It's a mystery. We'll leave it at that." Those fields require that the practitioner continue to try to solve the mystery as new information, data, statistics, etc., become available.

Having studied physics in college I can assure you that not only do physicists say "Fuck it, it's a mystery" they go one further and say, "Fuck it, it's a mystery, and I know it is with mathematical precision and certainty." And then just to drive the point home, when the sorry little undergraduate carps that that can't be the case, they are also taught the how's, the when's, and the why's of saying, "Fuck it, it's a mystery."

The most obvious case in point is the Heisenberg Uncertainty principle, which is popularized in the layman's version of it called "Schroedinger's Cat." The idea is you shoot a particle at a sensor, if it's spin up, the cat dies, if it's spin down, the cat lives. The question is you shoot a particle at the sensor and ask, "Before you take a look at the cat (this is the important part that always trips people up), Is the cat alive or dead?" The only answer is either, "We can't tell" or "Both." However, either of those answers is functionally equivalent to "it's a mystery." The only way to give a coherent and consistent answer is to posit things even more bizarre than "It's a mystery" such as parallel universes created with each quantum measurement (see the Star Trek TNG episode called "Parallels" to see a layman's explanation of this explanation).

Most people who don't have the mathematical training to see this worked out in rigorous detail think there is some trick going on, that there is some way to know, or that physicists are missing something that they need to look harder for. But, the uncertainty principle has been worked out in amazing mathematical detail and has passed every experimental verification ever tried with it. In fact, it's probably one of the most secure pieces of knowledge that humans have ever discovered. But at it's core is a strict and precise limitation to knowledge, anything behind it is strictly and mathematically a mystery. Any physicist who tries to sneak a peak behind it learns very quickly to say, "Fuck It" and move on to something else.

Greg Horton

I'm sure Leighton will have a more coherent response, but here's what I'll say. Heisenberg is not a mystery in the sense of "why is there evil in the world created by a good god?" It's a mystery because it defied expectations, yet we've come to believe it's true. It simply pointed to a way things worked than was different than we expected. It's not like we're waiting for a solution to why it can't be right or why we can understand the mechanism. The point remains that scientists and mathematicians try with rigor to sort out whether or not their results are accurate. If they are, then "it's a mystery" would seem to be more of a euphemism than an ontological statement.

Greg Horton

Oh, and unless I'm mistaken, there is an irony in arguing a point about measurable phenomena to contrast a point about non-measurable phenomena. That the Heisenberg uncertainty principle came about as a result of controlled experiments is without contradiction. That seems an important point.

David Clark

Of course I mis-spoke. Schrodinger's Cat has nothing to do with the Heisenberg Uncertainty principle. It has to do with the inherent un-predictability of the quantum wave function collapse when a measurement is made. My apologies for the confusion.

David Clark
It's not like we're waiting for a solution to why it can't be right or why we can understand the mechanism.

Actually, that's precisely the problem. Physicists have no real understanding of the quantum wave function at a physical level. That's why Schrodinger's cat is a mystery (again my apologies for putting Heisenberg in there, I was typing too fast and switched thoughts mid-stream). Physicists can paper over this by looking at probabilities associated with aggregating multiple instances wave-function collapse, by watching it happen a lot and then taking an average, but the mechanism and the ability to predict what is going on at the particle level is an utter mystery.

And when I mean "no real understanding" I don't mean that they are waiting for more data on the phenomenon, or that they lack precision or something like that. They are faced with the paradox of 1) Being pretty certain that they have accounted for all of the data, 2) Being pretty certain that there is no more data forthcoming on this particular phenomenon, and 3) Still being left with no understanding of and no way to predict what is happening at the particle level. In short, it's a mystery.

David Clark
Most people who don't have the mathematical training to see this worked out in rigorous detail think there is some trick going on, that there is some way to know, or that physicists are missing something that they need to look harder for.
The point remains that scientists and mathematicians try with rigor to sort out whether or not their results are accurate. If they are, then "it's a mystery" would seem to be more of a euphemism than an ontological statement.

No, I can assure you it's a fundamental ontological fact of reality. It's a mathematically precise and experimentally verified mystery, as in "We don't know what the hell is going on there."

I'll go away now.


Yeah, I do think there are a couple different definitions of mystery going on here - maybe not semantically, but pragmatically.

Pick two examples: one one hand, there is quantum mechanics' "Why do really little things not behave like bigger things," which really ought to be rephrased "Why do everyday objects made up of particles behave so differently than the particles on their own?" And on the other is theology's "How can Jesus be both completely human and completely divine?" Both are really counterintuitive (at least, the first is until you get used to the math).

It's true that one is inescapable if you pay any kind of attention to physical evidence, and the other is a nonsensical political consensus that didn't even arise until the fourth century. But that's not the real difference.

When mathematicians talk about mystery (that's where my training is), it's always in the context of figuring out how to get an answer, or proving that you can't get an answer (and developing a new, far more interesting theory than the original mystery in the process). And my understanding from talking to physics students in grad school is that the mysteries of quantum mechanics only give rise to more clever ways of formulating experiments. (I did hang out disproportionately with theorists; it may be different for the experimentalists who actually have to worry about funding their equipment.)

For theologians, though, using "mystery" isn't a starting point for discovery or a workaround, or a motivation to keep working on other things that might be more immediately explicable instead. It's a stopping point. Not for writing, of course; theologians make their livings like any academics. But what have we had in the past sixteen hundred years that's an elaboration on the dual nature of Christ? What have we learned using that assumption as a starting point, that we couldn't have gotten more parsimoniously some other way?

Polemic aside, if you get really comfortable with thinking about quantum mechanics in terms of function spaces and their dual spaces (rather than the classical model of objects in space), it makes intuitive sense that particles can behave the way they do. It's true that experimentalists don't like expressing what ought to be physical objects in those terms, and they actually have to talk about it for a living, so I will gladly defer to them as to whether it is not a legitimate mystery. But from my biased theorist-sympathetic position, I don't really have a problem thinking that there are things in the universe that are more like the functions I modeled in school than anything like what I can pick up or touch or taste. Why they should be this way is still an open question, of course (and one of the most wonderful and interesting ones in my opinion), but it's not intuitively shocking anymore.

By contrast, from what perspective can it ever make sense that someone could be both perfectly human (which by any coherent definition entails not having godlike powers) and perfectly divine? It's not as though physicists say that photons are fully waves and fully particles; they have the freedom to be honest and say that they're more properly neither wave nor particle, but will behave as one or the other depending on what experiment they're using to examine them. One camp says that our everyday intuition is not adequate for understanding the universe, so let's improve it. The other camp says that our everyday intuition is inadequate for understanding the universe, and let's rejoice in it! The difference is that with physics, we will eventually find an even cooler mystery than wave-particle duality. Dual nature theologians are stuck with a seventeen-century-old assertion.

Greg Horton

David, meet Leighton, if you haven't before. I remember you from the LDS thing a while back, but Leighton may not have been part of that. I'll defer to you two for now; I have a wine dinner tonight. I've told Leighton I'll revise if necessary. I do think we're working from different definitions, but this is an ongoing conversation and I'm happy to tweak my definition for the sake of clarity and accuracy. I learn much from Leighton, and I appreciate the insight you're providing as well.



First, Jesus appears to be a human being who was brutally murdered on a cross.

However, his followers founded a movement offering a creed based on love and redemption.

He created a Western movement similar to an earlier movement in India.

In contemporary history, we should recognize the evolution of thought Jesus and Buddha brought to us.

We cannot always see these men literally, but their mythologies still help me move mountains.

They resonate as archetypes but are not gods. The mysterious still resides in me as I continue to interpret their Incarnate meaning in me.


David Clark


From a mathematical standpoint you are completely correct. The mathematics of quantum mechanics is well understood and to understand it just takes a bit of getting used to. When working with the equations it helps to let go of trying to figure out how it relates to physical reality and just be content with the formalisms. Apart from the fact that most QM systems have no analytical solutions, there isn't much that's mysterious about the math of AM (and as you are well aware, not having an analytical solution to a PDE system is the rule, not the exception, so it's not that mysterious at all).

That works fine for theoretical physicists, but the experimental physicists have to match that up with reality, and that's where the mystery comes in. You are correct that physicists have become adept at creative experiments to coax the theory and the experiment to match up. Indeed, QM is probably the best tested and most accurate scientific theory ever devised.

The mystery comes in how the experimentalists get creative. It's not a matter of them coming up with elegant solutions to get the data they want, it's a matter of them coming up with set ups that give them data at all. It's a matter of them working around mysteries, not in elucidating them.

Just take a simple example, the time independent Schrodinger wave equation. It's the first equation you see in the intro to QM class that all physics majors take. The first thing most people notice is that it's got an imaginary quantity in it. Mathematicians shrug their shoulders and just start manipulating the equation. The problem for experimentalists is that no one has a ruler with a spot marked i on it. So, the experimentalists get rid of the i by calculating expectation values, which of course gives the correct experimental results, and now the experimentalists are happy. However, that shift is where part of the mystery lies. The Schrodinger equation perfectly and completely describes the behavior of a quantum particle, but at the same time you can't actually use it to look at the behavior of any quantum particle.

I'll be the first to admit that most physicists just ignore this problem and go on being theorists or experimentalists. However, they haven't elucidated the mystery, they have worked around it. Depending on your philosophy of science, that may be good enough. However, it takes a pretty bare-boned philosophy of science to do that, in my opinion a fatally weak philosophy of science, to ignore it.

That was my main point in the original comment I made. Physicists are taught to simply ignore this, perhaps not explicitly, but through learning the art of being a practicing physicist. Most of the ones who do try and think about it end up saying, "Fuck it, it's a mystery" and get back to their jobs.

It's hard to give non-technical examples with QM, but perhaps this will point at the mysterious aspects of QM (that get ignored by physicists). There are multiple interpretations of what QM means in a physical sense. That is utterly baffling. The math is well known and understood. The experiments predict the right results. But, the interpretations are many and they are in conflict. What makes it rise to the level of mystery to me is that physicists are pretty sure that the data is all in on this particular phenomenon (low-energy, classical, QM). One can of course hold as an article of faith that more data will solve the problem, but very few physicists would put much stock in that.

Back to the original post. I actually don't have much of a beef with getting on theologian's cases for invoking mystery too often. It's especially egregious when theologians invoke mystery just in time to salvage their preferred theological, political, and ethical notions. Mysteries should generally be forced upon you and you probably won't like them. Everyone prefers classical physics to QM, it's just an unfortunate fact of reality that QM is right, and classical mechanics is not. So, physicists learn to work with, avoid, and work around the mysteries. Perhaps that's a good model for theologians.

My main beef is that I get sick of the polemic by both sides that pits science against religion, that one side is the guardian of all that is good, while the other side is the receptacle of all that is crap. I saw science being held up as some "mystery free zone" where there are no mysteries, and if there are mysteries they are obliterated by conscientious and intelligent scientists. I hope the above shows why I don't think that's a fair description of physics and by implication science in general.



Thanks for your response. I definitely agree that there are a lot of unknowns in science, and that some may well be structural rather than temporary accidents of the order in which we happened to have discovered things. My beef is probably close to yours; in my opinion, the mystery of science is the whole reason for doing it (well, once you're done using it for basic survival anyway), and calling the scientific process primarily about eliminating questions is both shortsighted and contrary to how actual research operates. The questions are the whole point. As a corollary of this, I am really not a fan of using "mystery" as a final answer as theologians tend to. I do agree that we can't solve everything (maybe not right now, maybe not ever). But if we did magically (heh) come across some new evidence for an interpretation of QM, it would be fantastic and exciting. Nothing could happen that would lead dual nature theologians to revise* the Nicean consensus. I think Greg's comment could probably be rephrased to this effect and still illustrate his point, which I read as saying primarily "Don't say something is an explanation when it's actually just a mechanism of social control and power consolidation."

* Footnote - maybe I should say "rephrase" instead. There has been plenty of redefining of "human" and "divine" until they no longer mean anything like what native speakers of the language mean by "human" and "divine," but this doesn't seem like a useful exercise to me.

I'm picking specifically on theologians and church leaders, though. I'm sympathetic to the right kind of mystery expressed in non-scientific terms; I would most likely be pushing Jungian concepts like what Jon articulated above, were it not for the fact that I would be helping prop up what I think are destructive and abusive societal power structures. I like reading the writings of mystics, but I'd make a crappy one, because they use their imagery in subsersive ways, which entails being part of the community (however broadly defined) whose language they're subverting. I don't have the stomach to associate that closely with churches.

That tangent aside, I'll move on to the fun stuff. It's absolutely my theorist's bias, but I'm not as bothered by the apparent disconnect between mathematical models and physical reality. I don't agree with Feynman's principle that we don't really understand something we couldn't explain to a bright college freshman. (How do you explain the Faraday tensor simply? Maxwell's Rules, sure, but I've never had any luck with tensors.) i in particular doesn't bother me any more than the counting numbers. What is "5" but an adjective that we pretend is a noun because it's useful for counting? It's just that fewer people happen to do things where i turns out to be useful. And sure, calculating the properties of particles takes more complicated conceptual tools than calculating the measurements of everyday objects. Probably because I have never had to write a grant application to buy research equipment, this is interesting to me but not an existential concern. For now (and this is certainly subject to revision), I'm comfortable saying the confusion is a consequence of human minds and language being optimized to talk about and think about everyday objects rather than the really hard-to-spot quantum effects that took us millennia to come across. (I tend to think of mathematics and its use in scientific models as a language game a la Wittgenstein.) I don't see any reason why the universe should behave in ways that are explicable in everyday terms, so when it doesn't, it's fascinating to me but not disturbing.

I do think you're right about the creative aspect of experiment design, which seems to be a lot more like what painters do than what people imagine logicians do. I'm not sure how much of a mystery that is to psychologists who study artists, musicians and creative writers. Not that we have anywhere near an ideal understanding of inspiration by any means, but there are a lot of interesting things we can find out about it.

Mathematical logic (which is where I did most of my grad school coursework) also talks about things called models, though they're very different creatures than scientific models. In model theory, when you have a basic model M, you can build any arbitrary number of larger models M1, M2, ... etc. that contain M, and each is structurally compatible with M (I'm handwaving a lot here), but they are all incompatible with each other. There's absolutely no reason to prefer, say, M502 above M795, unless you add additional concerns that would make you prefer one model extension above another. Although this is very different than processing scientific models, thinking along these lines is how I've come to terms with being agnostic about the interpretation of quantum mechanics. It's understandable that people whose living it is to try to answer those questions are rightly more concerned about it, though. I guess it depends on what you look for in a philosophy of science. I'm happy investigating the relationships between evidence and models, and studying how models become more and less accepted over time. Trying to decide between competing explanations of QM is more metaphysics than I'm comfortable with; I'm not convinced some of those questions have answers. But that says more about me than it does the practice of QM.

Greg Horton

David, I'll happily agree with most of your last paragraph. I'm not as anti-religion as you suppose, but that's not really an issue I need or want to defend. I'm as skeptical of science as I can be, I think. I know about the politics, the laziness, the fudged numbers--basically, it's as prone to human error and corruption as any other field of endeavor. I think I have more confidence in it, and I'll accept Leighton's restatement of my point almost in its entirety here, because it actually has tools that at least show me why I can or can't know the answer. Which is to say, when they say, "it's a mystery," I think I heard both of you say that it's because they've actually tried to solve it and there is data to support it. Yes? Anyway, Leigton's example of Jesus' dual nature is excellent because it's the kind of mystery that simply can't ever be solved, but it can never be solved because it's a metaphysical claim that can never be verified or negated. We might just as well say he had three natures (trinitarially lovely): divine, human, plant. How can we begin to demonstrate it's true or not? I like the idea of mystery as starting point, not end point. I think Leighton gets that right, and I do agree that we were functioning with two definitions. My issue with contrasting science and religion or math and religion is that religion relies on faith which can never be a mode of knowledge. Ever. It's like comparing apples to Volkswagens. My issue isn't that science is the arbiter of all that's good; it's that religion can't be.

David Clark

Greg and Leighton,

I think we've had a meeting of the minds, at least as much as one can tell such things when communicating solely via the interwebs.


One of the reasons that I started following your blog is because it appears that you have left faith after some kind of crisis of faith. Having been through my own crisis of faith, the way that plays out in different faith traditions and with different people is fascinating to me. Do you have a/some post(s) which you would categorize as your "exit narrative"? If so, could you please post the link(s).

Greg Horton

David, sure. If you use the search function on the top right of the blog, you can find a few. Just use post-Christian as the search term. The first two or three are perfect, but you have to read An Explanation of Sorts after Post-Christian Parish or it won't make any sense.

Also, I don't think I suffered a crisis of faith; perhaps I did. Mine was like a slow whittling away of belief though rather than a moment of existential angst. Eventually, I wasn't satisfied with any of the answers because they were often used on questions that were only asked from within a certain set of metaphysical assumptions. This seemed both unfair and dishonest, as no one had bothered to verify if the assumptions even made sense. I hope that's clear, but if not, the posts might help.

David Clark

Thanks. BTW, I wasn't being lazy, I tried searching for stuff, but didn't have much luck. I didn't try post-Christian, hence the failure.


I tried t_ link s_me things earlier, but I am having keyb_ard issues due t_ an incident inv_lving a cat and a half-full glass of beer. I'll be useless until my replacement arrives later this week.


I think you guys are mainly done with this conversation by now, but I want to say my piece anyway: having been subjected to a required theology class last semester with a bunch of would-be Aquinas scholars, I had ample time to contemplate what would make theology a useful endeavor. Although I probably have no room to speak on this, not being a person with a "horse in the race" anymore, I did come to a place of real appreciation for theologians who took it upon themselves not to solve mysteries but those who actually made the mysteries more mysterious and more beautiful - like leading into a cave with a small candle. In that way, I guess, I differ from you Greg, because not only do I see mystery as a plus, but I also think that the kind of mysteries that theologians attempt to explore are best explored via poetry, art, music -- or at least well-written, poetic prose. It's when theology becomes a "science" (in our 21st c. understanding of the term) and sees itself as an explainer-away of mysteries (or succumbing to them when reason breaks down) that it starts to... suck.

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