Science and Faith: Discovery or Invention?

(If it is not already apparent from the short history of posts here, I expect to be content to alternate with little gear-shifting between probing philosophical questions and recreational mathematics.  I hope your reading mood is fickle.)

Are science and faith compatible?  Can a scientist pursue truth, be comfortable with doubt, and at the same time believe in God?  I think these are interesting, important, and personal questions.  Because they are personal, I don’t think my answers to them should be particularly important to you.  But hopefully the discussion will at least be interesting.

Before discussing these questions directly, though, I want to take what may at first seem like a rather abrupt detour.  Please be patient: this detour is at least mildly interesting in its own right, but does also have direct bearing on the main question.

Is mathematics discovered or invented?  (Remember, be patient.)  That is, when a mathematician describes some new theorem, or new algorithm, or new connection between previously unrelated areas of mathematics, has he or she invented something new “out of thin air,” or discovered something that was “there” all along and simply had yet to be found?

I tend toward the Platonist idea of discovery.  This seems particularly apparent when considering the many historical examples of two or more people, often greatly separated geographically, arriving nearly simultaneously at the same or similar results.

(I focus on mathematics here only briefly, mainly because I am a mathematician, and I think in that particular field the question is actually a bit more interesting, since mathematical truth is frequently so abstract.  But I think the discussion follows through at least as well in other scientific fields, particularly physics.)

To provide a visual analogy to this idea of discovery of pre-existing truths and connections between them, imagine that our world, be it mathematical, physical, or whatever, is one large, very dark room.  In that room is a great engine, consisting of countless parts, gears, rods, etc., all of which move together with humming smoothness.  Each part of the engine corresponds to some mathematical truth or physical law governing how our universe works, and those parts are connected and interact with each other in fascinating ways.

It is a wonderful machine… but the room is completely dark, and we can’t see how it works.  However, each of us is equipped with a flashlight.  Most of those flashlights, mine included, are relatively dim, and a very few others are extremely bright.  Sometimes we know where to shine our lights from what others have learned, and other times we simply get lucky and look in the right place.

(I do not recall when or how this particular description of this idea occurred to me.  But I certainly see in it at least hints of Plato’s Allegory of the Cave, and Newton’s “smoother pebbles” and “shinier shells” on the shore of the “undiscovered great ocean of truth,” images that I remember being fascinated with when I first read them.)

So, to work my way back to my main point… my motivation for this whole discussion is to relate the “exploring a dark room” analogy to the issue of compatibility between science and faith.  As I see it, science is our ongoing attempt to understand how that great engine works.  We currently have a very limited view; some parts of the engine seem relatively easy to see, other parts we have pretty good ideas about how they work and how they are connected… and other parts are in near total darkness.

To me, faith is an expression of belief about that part of the world that we cannot yet see or understand clearly.  Faith is to science what conjecture is to theorems.  More precisely, faith deals with those ideas about which we cannot yet make useful testable predictions.  In this respect, I see science and faith as perfectly compatible… but somewhat vacuously so, since their domains are mutually exclusive.  And as long as those domains remain disjoint, I think we are free to believe whatever we like.

But every once in a while, someone shines a light so bright that we are able to significantly expand the frontier between what is lit and what is dark.  Or perhaps someone illuminates an area that we thought we understood pretty well, but by viewing it from a direction not previously considered, we see it more clearly for what it is.  Historical examples abound, from Ptolemy to Galileo to Newton to Einstein.

This latter situation is critical, since to me it lies at the heart of a scientific view of the world.  We can today make statements of varying degrees of confidence about how the world works… but about none of those statements can we be 100% certain.  We must always qualify our understanding as being possibly wrong (!), and be prepared to revise that understanding should someone shine a brighter light from a more illuminating direction.

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16 Responses to Science and Faith: Discovery or Invention?

  1. nomasir says:

    I, of course, agree with the notion of science and faith being compatible. But, this should no doubt not surprise you as I am a person of faith working in a scientific field … how confused would I be if I didn’t see them as compatible.

    I’ve always liked the Galileo reference – it points to the very serious error of theocracy. Nothing that I can find in my Bible describes the church’s view (at the time) on geocentrism as correct; and therefore I cannot find a piece of the Bible to refute as errant owing to Galileo’s support of Copernicanism. But, as is the case with theocracies, authority over all portions of life had been committed to the church. There was no feedback, no challenging of ideas, no growth of ideas. We just make some conclusions based on what we think we read in scripture and denounce those as heretical who dare challenge us.

    We (I’m speaking of me now) find this troubling, and from a Biblical standpoint. First, from Proverbs 27:17 – “As iron sharpens iron, so one man sharpens another.” We needn’t be afraid of challenging new ideas that break our old modes of thinking. Second, is from Jesus’ interaction with “doubting Thomas” in John 20:27 – “Then he said to Thomas, ‘Put your finger here, and see my hands; and put out your hand, and place it in my side. Do not disbelieve, but believe.'” Here we see Jesus answering a doubter with “try me out and see – I’m not afraid of your questions and I won’t condemn you for having them.”

    I, as you may well imagine, fall squarely in the discovery rather than invention camp, by the way.

    • Thanks for the references– I really like the one from Proverbs. I have lately said on more than one occasion that it is good for us to “rub against” the different ideas of others to “polish the rough edges” of our own. As usual, my turn of phrase is less than eloquent… and also as usual, it is not new.

      I admit that I find science and faith compatible only in the limited– and thus mostly non-useful– sense described in the post. As you point out, I see little in the Bible to contradict our current understanding of our position in the universe. However, I think other contradictions do exist, at least assuming a literal interpretation of the text. The account of creation of both the (young) earth as well as of man in Genesis are two commonly discussed examples.

      • BeverlyLynn says:

        It seems to me that often people approach a problem or a discovery with a preconceived notion of what they are expecting. Now this is obviously not wrong, considering how everyone is taught the “scientific method” and how to form hypothesis in elementary school, however, I think that it often colors our results. Just like statistics can almost be twisted in any direction to say whatever the researchers (yesterday I read an article about face recognition with the line “the correct match rate was as low as 90%”), people, even scientists, find ways to support their view. The most famous example of this is Einstein’s cosmological constant because he refused to believe that the universe was dynamic. (I know that this is now being deemed useful again because of acceleration, but that is not why Einstein put it in there).

        Much of the evidence for an old earth has alternate explanations as does much of the evidence for a young earth. The old earth assumption, however, is necessary for current theories of evolution, and thus is the accepted theory.

        Evolution, by the way, does not have a mechanism for “testable predictions.” Microevolution, yes, but macroeevolution, i.e. species differentiation, origin of life, etc. cannot be tested, so by your definition, this too requires some measures of faith.

  2. I am not sure that I agree with the suggestion that “twisting” either theory or data to support a prior view is either common, standard, or accepted scientific practice. A good scientist must not be married, or even betrothed, to a “preconceived notion” of how the world works. And although such things do happen, I would come to Einstein’s defense on this one. I don’t think he “refused to believe,” but rather I think he was simply uncomfortable with the funky implications of a theory that allowed the universe to expand or contract. The addition of a cosmological constant, or more precisely the assumption of a static universe that required its addition, was arguably not in keeping with the “keep it simple” mindset… but I think that is largely hindsight on our part. The important point is that Einstein acknowledged the problem once evidence was available that suggested problems with the theory (namely, Hubble’s observations).

    (In a very similar vein, Ptolemy is frequently criticized for his “epicycles” describing the motion of the planets in an attempt to maintain the Earth’s position at the center of the universe, as was assumed at the time. This is sometimes used as an example of religion’s bad influence on science, which I think is unfair for the same reason as above; just because it wasn’t the *right* refinement doesn’t make it a *bad* refinement– it’s actually pretty ingenious– as long as subsequent contradictory evidence is sufficient to acknowledge the error and discard the incorrect theory.)

    Regarding the age of the earth, I think you are correct that the theory of evolution would suffer greatly if the earth were as young as creationists suggest; there simply isn’t enough time for everything to happen :). Note, however, that the converse is also true: the Christian account of creation would also be difficult to accept if the earth is as *old* as current scientific theory suggests.

    We can discuss the actual technical arguments for these two viewpoints in a separate post, but consider the following: which camp has the most vested interest in the outcome being one way or the other? I would argue that a good scientist enjoys a freedom that Christians do not, namely to acknowledge the possibility of being wrong. I want the *truth*, whatever it may be; my current view of the world is not one of attacking religion, but is simply the maximum likelihood view, the simplest view that is consistent with the current observations.

    I am prepared to discard that view, should contradictory evidence be available tomorrow… are Christians prepared to do the same?

    • beverlylynn says:

      “A good scientist must not be married, or even betrothed, to a “preconceived notion” of how the world works. ”

      I agree with you that most scientists don’t intentionally twist findings or views (with the exception, perhaps of those global warming experts), but often our world view, whatever it may be, colors our findings. I believe that for most people, it is nearly impossible to completely divorce yourself from your preconceived notions, and approaching anything 100% objectively.

      Also, to be honest I am not 100% on the young earth/old earth debate, (for I have not studied it enough) the old earth theory does not harm Creationism as much as you might think:
      Genesis 1:2 Now the earth was formless and empty, darkness was over the surface of the deep, and the Spirit of God was hovering over the waters. Light and Day was created on the first day, but something “formless and empty” was created before the light and there is no time line there, so no contradiction even when taking a complete literal translation of Genesis.

      • At risk of being more instead of less confusing, I should point out that I am not an atheist, which might be the impression from this and earlier posts and comments. I think that atheism, at least when defined as the position that there is no God, is no less dogmatic and thus unscientific than Christianity. I suppose I would call myself an extremely doubtful agnostic :).

        Along those lines, I also think that the notion of a creator need not be at odds with an old universe and old earth. Indeed, if I have to imagine the finger of God pressing things into motion, what better time and place (to the extent that either of those notions makes sense) than the Big Bang?

        Having said all that, my objection is to the precision with which some Christians attempt to specify the means of that creation, because it just doesn’t fit the data. Your suggested relaxation of interpretation seems to me to be insufficient; the real challenge is not in the first day, but in everything that must happen between the fourth and fifth. There is an observable history of animal life with measurable locations on our timeline that make it tough to get everything done, so to speak.

        The response to this argument is typically that that “observable timeline” is not as readily measurable as we think. I admit to being very curious about this; what is it, exactly, that Christians struggle with when it comes to techniques for age estimation?

        (This question isn’t rhetorical, but I must warn readers, the resulting discussion must necessarily be mathematical. The math isn’t hard, but we can’t talk about exponential decay, absolute vs. relative error, etc., in a hand-waving way and expect to convince anyone of anything.)

  3. Pingback: Re-Measuring Morton | Possibly Wrong

  4. Tthree says:

    First off I believe the Bible to be symbolic truth not literal. While the history in it may have happened in most cases what it symbolized is the real lesson.

    One of the problems with science is they base most of their extrapolations on assumptions. These assumptions are the best assumptions they can make given the current data. They lead to the most likely conclusion they can make but the thing they fail to acknowledge is it is far more likely that they are wrong. The only given is that their primary assumption that everything continued the same into the past is definitely wrong but without evidence as to how things were different they have to make that assumption. Nobody seems to want to address this fact.

    Now let us discuss the true missing link in the theory of evolution. Perhaps from your comments you are smart enough to realize this as basic biology class gives you the information necessary to figure it out. I majored in Mathematics but minored in Anthropology and Archaeology so I have asked for an explanation at every level of teaching and only received the same response every time I asked. That response was, that is the best question I have ever heard anyone ask. I never got even an attempt to answer the question.

    The theory of evolution through changes to genes on chromosomes has no problem making any species change to anything over time. It only requires the changing of the right parts of chromosomes. The problem arises when you consider the difference between species is not the information on the chromosomes but the number of chromosome pairs each possess. For asexual reproduction this does not present much of a problem. A chromosomal mutation (having a different number of chromosome pairs than the parent) would only need to make new copies of itself and a new species is born. Having a different number of chromosome pairs would make you another species by definition. The problem arises when you have only sexual reproduction. The chromosomal mutant that is a new species would have no others of its species to reproduce with so the species would die out with the individual. This is the missing link. We don’t have a mechanism that allows chromosomal mutation to form a new species once there is sexual reproduction particularly among higher mammals that typically produce one offspring. The fossil record tells us that for some reason periodic chromosomal mutation must happen across all species on a massive scale creating the same mutation in offspring often enough to allow for mating of the new species’ to produce fertile offspring. The fossil record shows little change or stasis for long periods of time followed by lots and lots of new species arriving in geologic time is overnight. This overnight in geologic terms is where chromosomal mutation must happen on a massive scale across all species. We don’t ever see this chromosomal mutation today so if it exists what is the cause? If it doesn’t exist the tree theory of Macroevolution fails to explain the forking once sexual reproduction is the only form of reproduction

    I first asked about this in 9th grade in 1976. I have periodically checked to see if an answer has been found. On my last check last year I was pleased to see they are at least teaching of the problems existence if you get to graduate level Biology classes. Now that they teach the problem exists maybe next time I check they will have a theory.

    • There are several interesting points here, I’ll try to touch on them all:

      “… [Scientists] fail to acknowledge is it is far more likely that they are wrong.” I don’t see how this follows. It is far more likely that what, exactly, is wrong? And if so, what is the more likely correct alternative?

      “The problem arises when you consider the difference between species is not the information on the chromosomes but the number of chromosome pairs each possess.” This is not true. Two organisms being different species does not imply that they must have different numbers of chromosomes. Put another way, not all speciation must occur by a mutation involving a changing number of chromosomes.

      But this is still an excellent question: how can speciation involving a changing number of chromosomes ever occur? This is a great question… but not because it doesn’t have an answer. The problem, I think, is the same as that with most creationist arguments against evolution, or for intelligent design: namely, a lack of appreciation for the scale of times involved, and for the lack of an “invisible hand”, i.e., that evolution is *random*, not necessarily *optimizing*.

      First, organisms can and *do* survive with mutations involving changing numbers of chromosomes. Also, the process of sexual reproduction in diploid organisms is not the “clean,” mathematical process that we might like to think of it as. The bad news is that it’s complicated; the good news is that part of this complication means that it is by no means impossible for reproduction to take place between organisms with different numbers of chromosomes. Witness Down Syndrome, for example.

      One final thought: I think it is interesting to turn the “assumptions about the past” argument on its head. That is, creationists often argue, “we can’t know for sure what happened in the past, so it isn’t certain that we evolved from common ancestors with other species.” But suppose that we turn the clock *forward*: if life on Earth manages to survive for, say, just the next million years, does anyone believe that we would observe *no* evolution, *no* speciation, of exactly the type that would explain in such a simple manner the history and diversity of *past* life that we know of?

  5. Tthree says:

    Did I lose any hope of a scientific discussion by my lead off paragraph? I don’t mix my faith with scientific discussion and I think those that try to mix the two are foolish.

    As for you confusion about the more likely wrong comment that has to do with huge extrapolation from assumptions made about the unknown. This is common in Anthropology and Astronomy. The assumption is made that all processes remain the same throughout history at the same rate as today unless they have evidence to the contrary. They come up with the most likely conclusion given the tiny bit of data at hand. Their degree of certainty is lucky to be as high as 5% but is higher than any other conclusion. What they fail to recognize is while that is the most likely conclusion it has a very small probability of being right. It is about 20 times more likely to be wrong. In analyzing a data field you can extrapolate out about 30% with a high degree of certainty. After 30% the degree of certainty falls off to essentially 0 pretty quickly. They routinely extrapolate millions and even billions of percent and act like there conclusions have relevance. All the dating methods can’t be considered accurate but are quite useful for comparative dating. Carbon-14 is only used for written history dating because it doesn’t behave the way it should so it needs to be calibrated by a known calender. Potassium argon behaves well over the short time of written history but since it is also radioactive dating there is no guarantee that the good behavior seen over 5000 years continues into the past. We can assume accuracy for another 30% which gets you to 6500 years ago. Beyond that your degree of certainty for the date quickly falls off. The object dated at 200,000 years old could easily be much older or younger. Typically they run the dating three times and get three very different results and choose the one that fits their preconceived ideas the best. They don’t average or throw the oddball out. Most not learned in Anthropology or related sciences don’t know this and assume very accurate dates are produced. For the Biblical literalists out there rarely is a date so out of whack with the others that it fits your model. Sorry.

    As for your comment on births with different number chromosomes you are right (trisomy). It is a different number of chromosome PAIRS that create the problem. For you to have a common ancestor with other primates this problem must be solved. My last contact had a confirmation from a genetic scientist that having a chromosomal mutation defined as a different number of chromosome pairs, not trisomy which has a chromosome tripling, would be a different species and not be able to produce fertile offspring with the parent species. Without fertile offspring the next generation can’t reproduce. It also had a graduate level Biology professor confirm they teach this problem in their graduate level classes only as most people just can’t understand it (i spotted it about 40 years ago in my first biology class in 9th grade). His comment was he didn’t see it as a problem to long term evolution only if you look at short term evolution. I said, So you are saying if we ignore the forks in the branches this presents no problem to evolution as we explain it today. He somewhat embarrassingly admitted I understood him correctly. I am not saying an explanation doesn’t exist as I am sure it does simply that the main force in evolution in our history, the very quick changes across all species in geologic time (Punctuated Equilibrium), are not explained without explaining the mechanism for chromosomal mutation and how it solves the problem of sexual reproduction. Since this problem of changing the number of chromosome pairs while producing fertile offspring must have a solution for us to have a common ancestor with any other species and since it is never observed in our short history of observation as scientists the mechanism must be in those rare points of punctuation of the stasis in equilibrium of species . In other words those points where the little change in any species over a long period of time is replaced by vast changes to all species in a short period of time. I believe in evolution. I just argue that the mechanism that Darwin came up with is the lazy sister to the main driving force in changes to species and that force is totally unknown and unexplained. Whatever that force is it will explain the chromosomal mutations as the main mover in evolution and solve the sexual reproduction problem. We will probably have to wait for the next extinction event to actually witness it. Hopefully someone will figure it out by then but the problem is few are taught that the problem exists so not many are thinking about a solution.

    • “In analyzing a data field you can extrapolate out about 30% with a high degree of certainty. After 30% the degree of certainty falls off to essentially 0 pretty quickly.”

      I confess I am not sure where to begin. So I won’t :). It is unclear to me what the above quoted comment means, either exactly or even generally. What does “analyzing a data field” mean, and where does the 30% figure come from?

  6. Tthree says:

    If you have a set of data the conclusions drawn from the data can be expected to be highly accurate to 30% beyond the data sampling and after that it quickly becomes almost totally uncertain pretty quickly. I used to work analyzing environmental impact studies and that is what is the accepted range for reasonable extrapolation for data is in science. Many of what I call the psuedo-sciences take a set of data that shows a constant well behaved over a short observation period. Then they make unbelievable extrapolations out from the well behaved data set. Radioactive dating is one such tool. Cabrbon 14 dating didn’t behave well over the short period of written history. It came up with very wrong ages for objects whose age was known from the written record. For that reason it is only used for objects that are younger than the written record so the levels used in dating are not from a decay formula but from a calibration of radioactive isotope levels to known dates established by the written record and other already dated samples of the decay levels. Potassium-Argon dating is used for older samples it behaves pretty much as predicted through the written record but how far back in time can that assumption be assumed to be reasonably accurate. The 30% rule should be applied. If our written record was 100,000 years we could assume it was very accurate to 130,000 years. Unfortunately our written record tis short so certainty of any date older than about 10,000 years is low. When you consider dating an object at 120,000 years old could produced 3 dates ranging from 80,000 years to 150,0000 years this lack of certainty is not surprising. The best use is as a relative dating tool rather than an exact one.

    • “When you consider dating an object at 120,000 years old could produced 3 dates ranging from 80,000 years to 150,0000 years this lack of certainty is not surprising.”

      This clarifies things at least a little bit, but unfortunately this is simply false. I don’t know where you got “the 30% rule” from– I can only guess this probably came from someone’s misguided interpretation of the normal distribution that they read about in an undergraduate statistics text. If you have any references that refer to this “30% rule,” particularly in the context of radiometric dating, I would like to read more.

  7. Tthree says:

    Here is a quote from a textbook circa 1995. The accuracy has improved since then but this gives you an idea of how large the range is in dating a sample 3 times.

    “As simulation of the processing of potassium-argon samples show, the standard deviations for K-Ar dates are so large that resolution higher than a million years is almost impossible to achieve.”

    The quote comes in the paragraph before the conclusion part of the link below.

    Note that this standard deviation that is “so large” is considered very accurate. And laypeople believe the dates produced by these techniques are fact. Usually the three dates are very different because of the large standard deviation in the process.

    Sorry about the 30% rule but we proved it to be the breaking point of accuracy in environmental studies. Assumptions of stasis or no bias to the sample become more and more uncertain in an exponential pattern of increasing uncertainty. Once uncertainty started to become a factor it quickly became the dominant factor. We had to play it safe as lives and ecosystems depended on our work being accurate. Industries hated us because we made them be clean industries which cost them money. It was determined that 30% was the safe end that all samples would fall on the safe side. Obviously some things would fall well outside this but if certainty is what you are looking for 30% was the established rule. that all things fall on the safe side. In my opinion it is scientifically irresponsible to assume high accuracy after that point. You may very well have high accuracy well beyond that point but to assume it is bad science. We couldn’t afford to be wrong.

    • I should give up at this point, but here I go again. I still don’t understand– or see– the mathematics behind the “30% rule,” and from your description this sounds more like engineering judgment than mathematically justifiable criteria.

      But perhaps we are arguing about different things. I got the impression that you were arguing that the *whole approach* of radiometric dating was hopelessly inaccurate and thus useless for understanding the age, absolute or relative, of stuff around us. If that’s the case, then I’m not sure how to help. If not, then perhaps we are in violent agreement about the basic concept of measurement uncertainty.

      You are exactly correct that any single measurement of age based on K-Ar decay has a large variance. And to make only three measurements and try to report an accurate result is necessarily difficult/impossible. But that’s why we put confidence intervals on such results. (Is this what you mean by the “30% rule”?) I don’t know of anyone, “layperson” or otherwise, that does not acknowledge the uncertainty in scientific measurements. When we say that the Earth is 4.5 billion years old, for example, that doesn’t mean that we know it is 4,500,000,000 years old, and not 4,500,123,456 years.

      In short, I am not sure who is unjustifiably “assuming high accuracy.”

  8. Tthree says:

    I said it is useful for relative measurements of age. Most of the laypeople I talk to believe these dates are very accurate. In Astronomy and Anthropology they tell you the new theory and it becomes accepted as right. Twenty years later it is proven absolutely wrong and then the next theory takes its place. This is a cycle that has been repeated many times. It is due to the fact that the best assumptions that get extrapolated back in time or out into the universe both give the best conclusion possible compared to the certainty of other conclusions however at the same time it is almost certainly wrong. Then they get a tiny bit more data and disprove the old theory and rally behind a new one with the same problem.

    An example I like to use is dating through sediment depths. It is easy to understand. They know how quick sediment accumulates and assume a constant rate of accumulation throughout the ages. A simple measurement of how much sediment there is gives the age of a layer. The problem is the main assumption is almost certainly wrong. Look at the sediment accumulations after Mount Saint Helens exploded. You have hundreds of thousands of years accumulation of sediment in less than a couple months. All these pseudo-sciences do the same kind of extreme extrapolations of assumptions through time or space. The one given is the assumptions or that they are unchanging conditions are almost certainly wrong. If your assumptions are wrong your conclusions are at best shaky.

    I love to keep up with the latest scientific understanding but I don’t have a problem spotting the shaky assumptions that lead to bad conclusions. They abound in the pseudo-sciences. I am lucky enough to be able to correspond with genius level experts in most disciplines and rarely do they say my points are invalid. Many times they are in total agreement but some scientist earns his respect from the rest by having his new theory’s short life as the next thing. I just thought with your websites title of Possibly Wrong you had tread some of the same ground. In a couple hundred years they will look at what we believe today in the same way we look at what was believed 200 years ago.

    Sorry if you think this was a waste of time.

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