Skip to content

Turtles all the way down

Last updated on 22 Jun 2018

There is a story, often told about the philosopher William James:

One day when the philosopher William James, who had a liking for scientific popularization, had just finished explaining in a small American town how the earth revolved around the sun, he saw, according to the anecdote, an elderly lady approaching with a determined look. Apparently, she strongly disagree, expressing herself in the following terms: no, the earth does not move, because, as is well known, it sits on the back of a turtle. James decided to be polite and asked what, according to the hypothesis, the turtle rested on. The old lady replied without hesitating” But on another turtle, of course.” And James persisted: “But what does the second turtle rest on?” Then, so the story goes, the old lady triumphantly exclaimed: “It’s no use, Mr James, it’s turtles all the way down.” [From Isabelle Stenger’s book, Power and Invention. However, in similar form, the story is widely found ascribed to James.]

So the story goes. The same event is also ascribed to Bertrand Russell or an unnamed scientist. I amuse myself from time to time, now I have access to archive.org and Google Books trying to find the source of these phrases. I may not have found the oldest of all, but the oldest accessible one is dated 1905 in a sermon (a “testimonial”) by Oliver Corwin Sabin, a bishop of the Reformed Christian Science church, in his Washington News Letter:

The old original idea which was enunciated first in India, that the world was flat and stood on the back of an elephant, and the elephant did not have anything to stand on. was the world’s thought for centuries. That story is not as good as the Richmond negro preacher’s who said the world was flat and stood on a turtle. They asked him what the turtle stood on and he said another turtle, and they asked what that turtle stood on and he said another turtle, and finally they got him in a hole and he said. “I tell you there are turtles all the way down.”

Of course, somebody found it before me in Wikipedia (what is the reason people belittle Wikipedia? There are pedants and curmudgeons aplenty contributing to it enough to make it pretty accurate). What’s interesting is that it is not ascribed to an old lady, but to a “Negro preacher”. In both versions of the story (also told by Stephen Hawking, whose literary and historical skills are not so good as one might think, given how often he is quoted authoritatively on this subject), the flat earther is a member of a despised and ridiculed group – blacks and old ladies – and in both they stand in for the stupidity of the folk belief and believer, overcome by the truths of science.

But the fact is, flat earth views (unlike geocentric views) were never the default view (“the old original idea”). Here is a picture I took in Exeter Cathedral, of a clock that dated to the 14th century:

exeter_clock

It shows the “two sphere” universe, with a globe earth at the centre. Spherical earth representations also appear in images of European rulers. Here’s Charlemagne in the 9th century holding the orb that represents secular power over the earth:

charlemagne.jpg

and Harold II from the Bayeaux Tapestry:

31-01-01/21

These anecdotes serve to legitimate the narrative of the teller of tales, to show they are on the right side of history, and to lessen our appreciation for the ordinary person. And they are pernicious. The weak minded have failed and we strong minded have succeeded, and history was always moving towards this point. This is the positivistic narrative of Comte: society has shrugged off the superstitious and theological and achieved enlightenment. Except that it is a lie.

While folk science is often wrong, it is also often right, and we find evidence of clever people making good inferences any time, culture or region you care to investigate. In my species book I state that people were not stupid and bad observers before Darwin, and that Darwin did not make us clever and good observers. It turns out that humans all have pretty much the same neural material between their ears, and achieve much the same cleverness no matter what they are placed into. This means that we should not expect that having the historical accident of science and technology makes us better than the poor beknighted religious, natives, or old wives. We should not expect that we will behave any better, nor should we think that our scientific thinking is going to make our societies somehow free of the errors humans have always fallen into. Or else, how to explain the antiscience movements that run our attitude engineering technologies (mass medias)?

Recently, an article claimed that religion is becoming extinct in some countries. This is because the trends to date have been the decline of religious adherence there. But trends in social structure are not like the movements of continents or large weights on ice. They have no momentum. They change because conditions are such that individuals may choose not to put resources into religion, or because religion no longer serves a particular need, or simply because it hasn’t yet adapted to new technologies and economic conditions.

All religions have a social ecology to which they must adapt. And they do adapt, just like a species of plant or animal that must adapt to an invader or new disease. Some fail to do this, of course, and they become extinct. We do not hear very much about the Moravian Brethren or the Shakers these days. Others find a way to circumvent or even exploit the new conditions. Hence televangelists. But if we think that because we in these nine enlightened countries happen to have the conditions under which around 20% of people lack religious beliefs, that no more means that religion will fail ultimately than the fact some people have a resistance to AIDS means AIDS will eventually disappear. And no amount of Turtle Anecdotes will make it so.

We misunderstand the nature of history and science if we think that we make ourselves better through an act of will that the misled simply lacked the strength to choose. It is a bit like blaming the poor for being poor, as Reaganesque conservatives do. Things are more complex and more egalitarian than that. There, but for the grace of the right narrative, go we ourselves.

Late Note: Nick Matzke has found one, also in a sermon, from 1854. See the comments.

85 Comments

  1. Do I get a prize? Here’s one from 1854

    [at the end of night #2 of a public debate between a Christian and a skeptic of some sort in 1854]

    It is singular, that what I said about the ever-present agency of Providence in the affairs of this world, should have driven my opponent into the dreary regions of atheism. He discards a particular superintending Providence, and represents this world as governed by laws that change not. But did these laws make themselves? Did they make the world? Are they entirely independent of God? Do they need no one to superintend their operations? Will he pretend that God lives insulated from the creatures of this hands, from the world he made? What abominable folly of atheism. (General applause.) In what he said of plagues, did he not avow his unblushing atheism? (Enthusiatic applause.) And the marshes? (Renewed applause.) Agues come from marches, do they? But who fixed the law which makes auges come from marshes? (Applause.) My opponent’s reasoning reminds me of the heathen, who, being asked on what the world stood, replied, “On a tortoise.” But on what does the tortoise stand? “On another tortoise.” With Mr. Barker, too, there are tortoises all the way down. (Vehement and vociferous applause.)

    p. 48, Great Discussion on the Origin, Authority, and Tendency of the Bible, between Rev. J. F. Berg, D.D., of Philadelphia, and Joseph Barker, of Ohio. Boston, J.B. Yerrington & Son, printers, 1854.

    Barker & Berg discussion & Four sermons by T. Parker: A collection of 12 pieces
    By Joseph Barker, Joseph Frederick Berg, Theodore Parker

    Given that all the early references seem to be in sermons, that’s probably the ancestral state. Which is ironic, considering that the dominant usage is probably now amongst skeptics…

    • John S. Wilkins John S. Wilkins

      I will of course give you a firm and respectful handshake in recognition of your superior skillz…

    • TomS TomS

      May I suggest that you modify the Wikipedia article “Turtles all the way down” to include this reference?

  2. Nick Matzke Nick Matzke

    Other early versions (although after 1854) seemed to have the joke as the tortoise in on an elephant, and the elephant’s legs go “all the way down”.

  3. Matthew Edney Matthew Edney

    (1) minor point (in terms of your argument): The use of the 14c clock is a red herring. Medieval scholars well knew the sphericity of the earth (the orb in royal iconography) and indeed the entire cosmos. The problem came in artistic conventions that did not represent 3D figures (such as spheres) in perspective … to modern eyes, medieval diagrams look like proof of a flat cosmology. For example, manuscripts of the Etymologiae of Isidore of Seville, early medieval bishop and encyclopedist, include a diagram of five interlocking circles, that in turn comprise a circle (sort of like an Olympic logo turned in on itself), to represent the five climatic zones of the spherical earth (polar frigid zones, the equatorial torrid zone, and the temperate zones in between).

    (2) bigger question: The interesting thing in these incredible stories that you’ve unearthed is that the idea of the flat earth resting on the back of elephants, and them on the turtle, was popularized in the 19c by British and other Europeans mocking Hindu belief systems as part of their assertion of an ideology supportive of British domination of South Asia. (We’re rational, they’re not; think Thomas Macauley and his ilk.) I know of no actual folk or religious tradition outside of South Asia that is supposed to have held such a belief, not even at the folk level. The attribution of them by modern commentators to the marginalized intellect within Christian societies, the black and the woman/witch, is truly an act of derision!

    • John S. Wilkins John S. Wilkins

      So we might expect that in 500 years people will think we 21st centurians thought the world looked like a peeled orange, because of the Mercator projection? I can see that happening.

  4. Brian Brian

    An infinite set of space fairing Turtles. That was what I took out of this. 🙂

    • Bob O'H Bob O'H

      Ah, but a countably infinite set. Be thankful for small mercies.

  5. Ian H Spedding FCD Ian H Spedding FCD

    The load-bearing requirements of a geomechanical column probably mandate elephants or even mammoths forming the lower strata but at the higher levels we would expect to see them mutating into teenage Ninja turtles.

  6. Reminds me of your Synthese paper.

    I love this stuff. We are ALL fallible, and the people who disagree with you are often just as smart/honest/competent/etc as you. IMO this principle is the heart of fruitful dialogue, and of fruitful skepticism (which is why there is some irony in lumping in the New Atheists with skeptics).

    • Brian Brian

      Which New Atheists? The famous ones? The punters in blog comments? All of them?

  7. You write “trends in social structure are not like the movements of continents or large weights on ice. They have no momentum. ” Do you really believe that? Models of the growth of religious groups are often based on the premise that the number of new members in a given time frame is a function of the number of current members because religious conversion usually occurs by social contact and the more missionaries the more converts. That may or may not be valid, but it isn’t obviously silly either. After all, many population processes have momentum–kids have kids–and social structures surely involve populations. Of course it is also true that fitting a curve with a plausible function doesn’t justify thoughtless extrapolation; but it may identify a real mechanism, albeit one that may be counteracted by other mechanisms and factors as, for example, exponential growth is always limited by the availability of resources.

    For the record, I don’t think religion is going away, but my read on the situation is that it has actually lost more ground than appears from purely quantitative surveys. Much of the decline is qualitative. That the numbers don’t necessarily catch the difference between belief and mere cultural identification has been pointed out by many people lately. I’d add that for millions religion has gone from being the template of daily life to a mere hobby; but that fact, if it is a fact, isn’t easy to validate through survey sampling.

    By the way, the logo I’ve acquired would be more apropos if the eyes were crossed.

    • John S. Wilkins John S. Wilkins

      Social changes are in effect momentary rates of change. Whether or not a trend continues depends on whether the conditions for the rate of change persists. In effect, the social physics is Aristotelian. Now religion might continue to recede in these 9 countries, but equally it might simply stop at some equilibrium or even stage a comeback. And what causes that will depend solely on the social ecology.

      • I’m not sure where your certainty about the nature of social change comes from or why what amounts to a reverse bandwagon effect strikes you as obviously impossible. The argument in the paper about the decline of religions is a reprise of an argument developed to model the decline of minority languages and simply argues that the decline in church affiliation in several countries can be explained or at least modeled by assuming that belonging to a group, like speaking a particular language, becomes less valuable as the group shrinks. There’s a feedback loop. The authors are well aware that they are leaving out all sorts of complexities, and they don’t appear to be driven by some ideological desire to gloat over the possible demise of the Episcopalians. In fact, they sound like a couple of physicists who hope that a very simple mechanism explains most of the observed change.

        I’m not really interested, or competent, to argue in favor or against this specific hypothesis. I just find it curious that it strikes you as implausible on its face. It is no doubt true, as you say, that “Whether or not a trend continues depends on whether the conditions for the rate of change persists.” I doubt if the authors of the study or anybody else would deny that. It’s just that unless we’re going to give up on trying to explain social change, aren’t we going to continue to look for explanations of why things are changing now and, absent some alteration in the situation, can be expected to go on changing?

  8. Richard Aubrey Richard Aubrey

    I am not in the name-recalling mode this morning. So I can’t recall the name of the Greek–probably Hellenistic period–who calculated the circumference of the world.

    • Eratosthenes of Cyrene (c. 276 – c. 195 BCE) is the name you are failing to recall however he is only one of many Hellenic mathematicians, cartographers and geographers who calculated the circumference of the earth.

      • Gorillas are notoriously slow off the mark it’s all that leaf chewing!

  9. Really great post. It is tragic when some exhibit a attitude that we are somehow wise and our predecessors were not.

  10. Some things are difficult to reverse, although I concede that it’s not impossible. It’s hard to imagine that when people abandon religion they’ll ever get it back.

    • I think they’ll abandon some forms of religion – history is replete with cases of that. I think that there is a way to go of a lack of traditional religions. But I also think that what will replace that will not be a lack of religion but new forms of it. However, not to overstate it – there will be a considerable and persistant portion of lack of religion: real Nones. Eventually that might also be forced out by religious control at some point in the future. In the short to medium term, though, I expect that in my country and the other eight listed, religion will continue to decline some more.

  11. @Jim H.,

    I think the point about momentum is that it’s a metaphor all too easy to take literally, or uncritically. Social movements may have momentum in the sense that we can see them trend toward some target. But it would be teleological to imagine that we know what they’ll look like in 10, 25 or 100 years, based on these trends alone. Not taking to account the “social ecology,” as John calls it, is sort of like predicting the motion of a billiard ball right after the break, without factoring in the other balls on the table. It’s going over there–no, wait, it’s headed for this point here–no, sorry, recalculating…

    Nothing *prohibits* a “reverse bandwagon” effect–but until we are able to tease out the social laws that generate such an effect (or its opposite), it’s too soon to predict one. The appeal to momentum does nothing to explain social change, it just consigns it to a facile analogy to physics. If momentum alone was a predictor of social behavior, we’d all still be doing the Macarena.

    I don’t see John arguing against the possibility of the extinction of religion, just against premature rumors of its demise based on a tiny and rather fragile data set, peppered with the teleological “escalator fallacy.” There is more than a little wishful thinking in the conclusion that religion is headed for the dustbin of history, which I take to be John’s main point. When you come to a flattering conclusion based on little evidence and overly simplistic modeling, there is usually significant ideological influence on your thinking.

    • The newspaper accounts that John references demonstrate the sensationalism and exaggeration typical of science journalism. I read the actual paper, which you can download at http://arxiv.org/abs/1012.1375, and came away with a very different impression of what it’s authors were trying to accomplish. They were acting like physicists, trying to come up with the simplest mechanism to explain a set of data. I don’t know whether one can speak of teleology in such explanatory schemes. It’s more like what thermodynamics folks do when they explain macroscopic tendencies by invoking microscopic processes. It may be that social physics is impossible, but trying to be Hari Seldon is not the same thing as rooting for the demise of religion. The gnu atheists will seize on anything that suggests that belief in God is on the way out, just as religious individuals jump all over every ambiguous scientific finding as vestiges of the logos. Ruling an exercise in model building out of court may also have its ideological motivations. What I don’t know is that Abrams, Yaple, and Wiener are emotionally invested in a particular result.

      • Jim,

        I read the original paper too. I agree the authors’ language is more careful than the journalistic treatments of it, which is always the way.

        Yet they clearly invoke a trend to extinction:

        “The model predicts that for societies in which the perceived
        utility of not adhering is greater than the utility of adhering, religion will be driven toward extinction.”

        It’s a tautology to say that if people find reasons not to adhere to a religion, they will tend not to adhere to religion, and vice versa. But these reasons don’t necessarily have any special impetus to them. Union membership has been in steady decline in the US for decades, but it would be fatalism to declare trade unionism moribund based on that trend. We can make arguments for collective bargaining, in the wake of the Scott Walker regime in Wisconsin, and the brothers Koch can make arguments for “right to work” laws and the tightening of the collective belt. The overall persuasiveness of all that rhetoric falls under the rubric of social ecology. We don’t know what the the level of support for trade unions will be in 10 or 100 years. We can make educated guesses, but I doubt they will be much more accurate than the average NCAA playoff bracket.

        The real question is what influences the “perceived utility” of adhering or not adhering to a religion (or to trade unionism). That’s fungible, making it something very unlike the momentum of a tectonic plate or a weight sliding on ice.

        • I should not have used tectonics as a disanalogy either. Continents do not have in internal impetus to move – they are moved by (I gather) isostasy and convection, and if either stops or changes direction, so too will the movement of the tectonic plates. In fact, it is a very good analog to social change.

        • Which is just to say that “momentum” is in part a folk-empirical concept.

        • To be precise, the authors predict a trend towards the extinction of religions. They don’t invoke, posit, celebrate, or even insist upon such a trend–the main thing they seem to be happy about is that their rather simple model yields a testable hypothesis. I made an error above when I wrote that these guys were acting like physicists when they were actually acting as physicists. Once again, I have no skin in this game. I don’t dream of the day when religion disappears and I wouldn’t miss it evaporated tomorrow. I continue to be puzzled by the rather dogmatic assertions about social process that are made apropos of these issues. I must have slept through the lecture where the causes of social change were explained once and for all. I thought that was still up in the air.

          By the way, complaining that momentum is a folk metaphor is, if you pardon me, a bit of red herring here. The authors of the paper never talk about momentum, doubtlessly because as engineers and physicists they think of momentum as the product of mass and velocity and that’s not involved in their calculations. What is momentum like about some social and demographic processes is simply that they continue for some time after their original causes diminish or disappear. Thus the human population will continue to increase for some considerable time even though the birthrate in many countries is at or below replacement. In the case of religious affiliation, the changes that made church membership less attractive may have mostly taken place in the past and yet the effects of the lessened attraction may work out as a further decline in membership by the mass action mechanisms suggested in the paper. (Once again, I don’t know if the argument holds water. I’m just making the meta point that it isn’t obviously absurd to talk about the social equivalent of chemical kinetics where the speed and direction of a reaction often depends upon the relative size of the products and reactants.)

          I wonder if you are as automatically critical of mathematical models of the growth of Christianity in the first couple of centuries of the common era. I don’t have a reference to hand, but I’ve seen estimates of the minimum time it required for conversion to reach a critical mass granted the (to me, anyhow) reasonable assumption that conversion in antiquity was largely a person-to-person phenomenon. These estimates essentially treat religion the way that epidemiologists study infectious diseases, but you don’t have to think that religions are diseases to find the methodology useful. Or is that too metaphorical as well?

        • I was objecting to the linked blog post, not the paper, but it occurs to me that they are describing not a trend but a distribution of social mix, roughly an exponential curve. If so (and I am famously ignorant of mathematics), why think it is a trend? Why not think of it as a surface on which social structures tend to move? A society may regress back along the curve described as easily as moving “up” it. The overall mix will be along the surface, but which way it will move depends on local conditions.

        • Oh, and of course social causes are still disputed. My view is that societies have no general dynamic, but are in effect the aggregate of all the psychological and economic choices and behaviours of the agents of that society (a kind of methodological individualism so long as you include somewhat broader agency than individual adult males; I include small scale institutions like clubs and groups, and nonhuman agents like communication networks. But that’s a discussion for another time).

          So since I am employing my own views here, I get to express them forcefully from time to time. As Putnam once said, “I should use somebody else’s beliefs?”

        • “I continue to be puzzled by the rather dogmatic assertions about social process that are made apropos of these issues. I must have slept through the lecture where the causes of social change were explained once and for all.”

          What dogmatic assertions? Who has asserted that religion cannot go extinct? (My own take is that it’s too imprecise a statement to be true or false, but that hardly seems dogmatic.)

          “To be precise, the authors predict a trend towards the extinction of religions. They don’t invoke, posit, celebrate, or even insist upon such a trend–the main thing they seem to be happy about is that their rather simple model yields a testable hypothesis.”

          There is a great deal of fallacious reasoning in this paper. (See below). Fallacies are often an indicator of implicit biases, which is why I suggested there was an ideological influence at play, but that’s not as important one way or the other as the fact that the reasoning is fallacious. That’s my skin in the game, anyway.

          “The authors of the paper never talk about momentum, doubtlessly because as engineers and physicists they think of momentum as the product of mass and velocity and that’s not involved in their calculations.”

          You’re right that it’s not explicit, but that doesn’t mean it doesn’t inform their modeling. The very concept of a trend presumes a kind of Newtonian inertia. I can’t find any explanation in the paper for the fact that historical trends will continue along the same mathematical curve they’ve historically observed; it’s just taken for granted.

          “What is momentum-like about some social and demographic processes is simply that they continue for some time after their original causes diminish or disappear.”

          Sure, there can be latency. But this needs to be distinguished from the assumption that things will continue on the same course they’ve historically followed. Waves on the ocean continue long after the forces that initiated them, but ultimately they come to the shore and are broken back. Latency itself is totally insufficient to explain the projection of a current trend.

          “I wonder if you are as automatically critical of mathematical models of the growth of Christianity in the first couple of centuries of the common era.”

          The important difference here is that these patterns being in the past, we have the whole growth curve to analyze. No projection is necessary. We know how it all played out.

          My main point is just that the authors presume, without apparent justification, that historical religious affiliation will meet its final end in given regions, once people in those regions embrace non-affiliation. This, to me, smacks of the escalator fallacy, where it’s just assumed that secular society is destined to supersede religious society. There is no analog to it in either of the main metaphors being used here–language and disease. If Quechua dies out, it’s the end of Quechua, not of language. Not to mention that if Quechua died out in Ecuador, but was still widely spoken by billions of, let’s say, East Asians, we’d have no reason to imagine it couldn’t be re-imported to Ecuador in time. Likewise, though malaria has been all but eradicated in the industrialized world, we can easily imagine the conditions that might induce its return. Even smallpox, which has been essentially eradicated globally, will remain a potential contagion as long as it is preserved for experimental use.

          The implicit bias in the study is that non-affiliation has a *self-evident* advantage in perceived utility over religious affiliation. This is its greatest methodological weakness, and the best reason why the authors are quite probably wrong.

        • I resorted to the low expedient of researching the background of the authors of this paper and discovered that their activities are relentlessly, nerdishly technical. They haven’t published anything remotely hostile to religion. A lot of their work involves applying the mathematical techniques used in the religion paper to a wide range of other issues including the decline of languages, membership in competitive but secular groups, and oil depletion. I just don’t think it’s fair to accuse them of parti pris. It’s like accusing somebody of being part of the war on Christmas because they wish you Happy Holidays.

          Let me suggest an alternate frame for considering the ideas in the paper. Church membership and attendance has declined markedly in Europe and more recently in the U.S. One explanation, which, oddly enough, is favored both by Fundamentalists and atheists, is that the advance of science accounts for the decline: Evolution = disbelief. The sociologists of religion mostly demur, looking for other explanations that involve trends such as urbanization, increasing wealth, and the availability of alternate social support systems. In the context of researching these kinds of explanations, it is perfectly reasonable to use mathematical modeling to find out if changes in the utility of religious affiliation suffice to account for observed rates of change. The strategy is not really that different from what population geneticists do when they calculate the probable fates of more or less favorable traits. And just as the early pages of Crow and Kimura feature radically simple cases involving single alleles in unchanging environments, the authors of the despised paper make the most drastically simplifying assumptions they can. I don’t know if they make a good run at accomplishing what they set out to do, but I don’t see their efforts as ideological unless merely thinking about the obvious decline of religious participation is automatically suspect.

        • “It is perfectly reasonable to use mathematical modeling to find out if changes in the utility of religious affiliation suffice to account for observed rates of change.”

          This might be true. But utility is exactly what is not being measured in this study. Rather utility is, in the authors’ own words, “assumed” to track to religious participation. They present no data that claims to quantify utility except in the tautological sense that social change is presumed a priori to be a function of utilitarian calculus.

          Other than that, your comment is largely non-responsive to what I’ve argued the last couple times around. You don’t have to agree with my analysis, of course, but just ignoring my arguments inspires me to question the utility of continuing this conversation. My calling the authors “ideological” isn’t meant to be some terrible slander; it’s just another way of saying that they haven’t shown all their work. If you want to take issue with that you can start by addressing some of my criticisms in the comments above.

        • Everybody always thinks that the other guy isn’t addressing their concerns. Part of my problem is that I just don’t think you understand the paper. For example you don’t like me pointing out that somewhat similar methods have been used to model the growth of Christianity on the grounds that unlike retrospective studies, the paper makes predictions and doesn’t just fit a curve. But that’s not a bug, it’s a feature. One defines a hypothesis and makes predictions. If the predictions fail, you learn something. It’s the hypothetical-deductive method, isn’t it? Asserting that religion has to disappear in the real world because of a mathematical exercise would be a fallacy, but I don’t think it’s a fallacy these authors are guilty of.

          As I understand their approach, the authors look at the declining rates of church participation in several countries and come up with a utility value that would explain the trend so far, granted the assumptions they make. Then they propose a test of their estimate. They don’t even predict the end of religion. They predict a trend in that direction, which is not the same thing unless you project on them ulterior motives.

          You write: “My main point is just that the authors presume, without apparent justification, that historical religious affiliation will meet its final end in given regions, once people in those regions embrace non-affiliation.” I doubt very much if that’s what the authors presume at all. As I’ve tried to point out, though you think it’s off the subject, I guess, the aims of the paper are very limited and its authors are obviously aware of how tentative their conclusions are. They write “We believe that, with the application of techniques from the mathematics of dynamical systems and perturbation theory, we have gained a deeper understanding of how various assumptions about human behavior will play out in the real world.” In other words, if you change the assumptions, for example if the utility of religious membership changes, which obviously could happen, the predictions would change.

          The authors suggest that their method may applied to competitive social systems such as smoker vs. non-smoker, vegetarian vs. meat-eater, obese vs. non-obese, and Mac use vs. PC user. Since, as you say, you have no skin in this issue, I assume you’d be just as unhappy if a future paper predicted that there was a trend towards the end of cigarette smoking because even if smoking went extinct there would be other bad habits to take its place…

        • “You don’t like me pointing out that somewhat similar methods have been used to model the growth of Christianity on the grounds that unlike retrospective studies, the paper makes predictions and doesn’t just fit a curve. But that’s not a bug, it’s a feature. One defines a hypothesis and makes predictions. If the predictions fail, you learn something. It’s the hypothetical-deductive method, isn’t it?”

          It sounds like just guessing to me. If you don’t isolate your variables (which the authors don’t), then what have you learned? What will we know if non-affiliation reaches 70 percent by midcentury in the Netherlands, as the model predicts? The authors say that it will be due to perceived utility, but as far as I can see we only have their word for it, since they haven’t taken any trouble to anticipate other causes. (They even concede that “Logistic growth [which they predict] would be a reasonable null hypothesis for the observed data.”)

          “Asserting that religion has to disappear in the real world because of a mathematical exercise would be a fallacy, but I don’t think it’s a fallacy these authors are guilty of.”

          I don’t think I accused them of this.

          “You write: “My main point is just that the authors presume, without apparent justification, that historical religious affiliation will meet its final end in given regions, once people in those regions embrace non-affiliation.” I doubt very much if that’s what the authors presume at all.”

          Why do you doubt what they explicitly state? I don’t see much room for ambiguity in the phrase “religion will be driven to extinction.”

          “In other words, if you change the assumptions, for example if the utility of religious membership changes, which obviously could happen, the predictions would change.”

          So why not structure the study to account for this variable? By declaring it a constant by fiat, all the authors are really saying is “things will stay the same unless they change.” I could have told you that.

          Where is the external data measuring degrees of perceived utility? In each case they illustrate, u sub x is defined as a function of the curve portraying rates of change in affiliation. To turn around and use that variable as an *explanation* for that change is utterly tautological.

          If all this paper amounts to is that current declines in religious affiliation will continue unless some new influences arise to change the trajectory, then frankly I don’t see its superiority over common sense.

          “The authors suggest that their method may applied to competitive social systems such as smoker vs. non-smoker, vegetarian vs. meat-eater, obese vs. non-obese, and Mac use vs. PC user. Since, as you say, you have no skin in this issue, I assume you’d be just as unhappy if a future paper predicted that there was a trend towards the end of cigarette smoking because even if smoking went extinct there would be other bad habits to take its place…”

          That’s their analogy, not mine, and I don’t buy it. To say that one’s metaphysical disposition can be modeled along the same lines as ones diet or what computer one uses takes far more for granted than I’m willing to allow.

  12. @Larry,

    Feeling especially empirical today? 😉

    • Chris, I don’t have any interest in plaguing you; but you’re the only one who is talking about metaphysical dispositions. The authors appear to be talking about something much crasser and sociological, i.e. affiliation with a church. Why that can’t be approached via mathematical modeling is obscure to me, though I guess the impasse in our conversation does reflect metaphysical dispositions in one way because mutual incomprehension is perhaps inevitable between a votary of philosophical idealism and somebody with a more Democritean outlook. So we’ll have to leave it at that until the next round of this interminable boxing match in which it is not absolutely obvious that the two combatants are in the same ring.

      • Jim, I never argued that church affiliation can’t be measured or mathematically modeled. I fact I agreed with you that historical affiliation, as with the early Christian church, can and has been measured and modeled. I don’t even argue that social trends can’t be projected. I have specific concerns about this particular study, which I have mentioned.

        As for metaphysical disposition, it’s true the authors don’t set out to measure it, but it’s hardly incidental to the phenomenon of religious affiliation. Changing one’s affiliation often–not always–indicates a change to one’s most deeply held beliefs, which is not something we could say for quitting smoking (though perhaps it applies to using a Mac instead of a PC ;)).

        • Maybe a meeting of the minds. I have never been particularly interested in defending this particular exercise in modeling/projection. As advertised, my interests in this business are rather meta. I decided to write a comment in the first place because John’s original post, as he later agreed, addressed the journalism about the study much more than the study itself. I also thought some of your comments were unfair to the authors, who may be wrong, but aren’t obviously combatants in the current Internet religious wars. I also wanted to speak up for the general project of trying to explain the decline in church affiliation over the last 100+ sociologically because I just don’t believe that changes in the scientific and philosophical opinions of elites explains very much of the observed trend. I find it implausible that the theory of evolution is what emptied the church parking lots, though I do think that the fact that the evidence didn’t turn out to support a theistic view of the world had a modest indirect effect by denying the churches the support of the scientific community.

  13. Jeb Jeb

    E.B Tylor took a comparative look at the world- tortoise myth in Asia and North America.

    Researches into the early history of mankind and the development of civilization, 1865 pp. 332-336

  14. Allen Hazen Allen Hazen

    The wording in the sermon Nick matzke quotes sounds to me as if the preacher assumed the idea was already familiar to the listeners. So, traceable or not, there were probably earlier occurrences. (William james, b.t.w., was 12 years old in 1854: he may at some point have told this story, but if so it was probably the retelling of an old joke for him.)

  15. garymar garymar

    The East India Trading Company (according to Wikipedia) was chartered in 1600, and actually began to rule parts of India in 1757. So we have a couple hundred years in which Western scholars would have begun exploring Indian culture and reporting back to Europe. Somewhere in there someone heard a narrative about turtles and elephants and wrote it up. Of course we don’t know if this was a highly developed theological belief or just something parents told their children before bedtime.

  16. Great article, except for the rather weird crack about conservatives at the end. Was that a joke? Reaganesque conservatives are a lot more likely to believe the poor are poor because of stupid/evil liberal policies, than blaming the poor themselves.

    • Here’s Reagan himself:

      I asked, “What about the homeless? Do you think you could have done anything for them?”

      Reagan said, “Well, it’s been so exaggerated. Millions, there aren’t millions. Real research reveals probably 300,000 or less, nationwide. And a lot of those are the type of people that have made that choice. For example, more than 40% of them are retarded, mentally deficient people, that is the result of the ACLU. Look at the girl in NY who went to court after Koch had ordered her to get off the street and be put in a shelter. She went to court and actually fought, under her Constitutional rights, to go on living in that cardboard box on the street.“

      Source: Dutch, by Edmund Morris, p.645-646 Jan 9, 1988

      A certain kind of conservative (i.e., the revisionist kind, not the traditional kind, who I respect) holds that poverty is due to a personality defect or poor moral choice, like Reagan did. For example, the Personal Responsibility and Work Opportunity Act institutionalised this extreme Calvinist view into American law.

      • ad*m ad*m

        Excellent post.

        Don’t mix ‘poor’ and ‘homeless’. Many people that are ‘homeless’ are not primarily ‘poor’, they have a psychiatric disorder that makes them want not to have a permanent abode. Remember anti-psychiatry in the 60’s: that is where the idea originated to let psychiatric patients roam the streets, leading to the large increase in the number of homeless we see now.
        Poor and homeless are two different problems, with different causes, and Reagan was referring to homeless people.

        And that brings me to a second point: it is interesting that you start your argument with the flat earth hypothesis. But there is a lot of ‘folk wisdom’ out there that has been scientifically confirmed, but that continues to be vigorously denied by liberals. I do not want to be banned, so will go no farther than this except to remark that one such wisdom relates to ‘ICE’ as ‘IBM’ does to ‘HAL’.

  17. Mark Hadfield Mark Hadfield

    It’s funny, but I’ve always considered “turtles all the way down” to be a sophisticated metaphor, indicating a grasp of the infinite. So the idea that it was invented to mock the intellectually marginal–though it may well be true–had not occurred to me before now.

    • This may have something to do with the long standing objection to infinite series that dates back at least to Aristotle, who objected to an infinite chain of causes to argue that there must, logically, be a first cause. This would have been widely understood by the relatively educated in that period. In fact, Russell, James and others would have had no problem at all with an infinite series. A foundationalist ontology might have been problematic.

      • It has been pointed out by numerous historians of mathematics that the dislike of infinity is a product of Greek philosophy, Indian philosophy however had no fear or dislike of the infinite a fact that is used to explain the greater facility of Indian mathematicians with number systems.

    • Jeb Jeb

      I don’t see any reason to assume one single, straight line repetition when it comes to origin and meaning with these kind of things.

      I made sense of it in the same way as you, when I first read it.

  18. Steve Schaffner Steve Schaffner

    The eight hundred thousand or so Moravian Brethren in the world will be surprised to learn that they’re extinct.

  19. I wonder if Hawking played with the story of the infinite number of turtles compared to his view of an infinite number of past verses in a multiverse. I suppose he was having fun with the irony.

  20. Certainly some number of people are poor because of poor moral choices. I think we all know intelligent people who ruined themselves in one way or another. But conservatives constantly harp on the ill effects of government programs which either harm the economy, make it hard for people of modest intelligence to start businesses, or encourage people on the margins to stay poor. To emphasize the one view and ignore the other to pure partisanship. Cherry-picking quotes is fun, but pretty weak.

  21. Roberto Gonzalez-Plaza Roberto Gonzalez-Plaza

    are you aware that some “Native American” “tribes” call what is today North america, turtle island?

    • John Harshman John Harshman

      I’ve heard that, but I’ve always found it difficult to believe that any of those tribes had a real concept of North America as a continent, or in fact a concept of “continent” at all.

      Can anyone provide documentation for this (I suspect) urban legend?

      • I don’t know about the ‘turtle island’ thing but I can tell you that Hopi legend had an idea of North and South America as continents because according to their tradition groups of them traveled to the northern, southern, eastern and western most regions of the new land after they emerged (according to their legend) from the underground.

  22. Roberto Gonzalez-Plaza Roberto Gonzalez-Plaza

    You suspect wrong. Concept of a ‘continent’? It doesnt matter really what anyone calls “continent”, but anyone can distinguish another “island”. Why do you need documentation? ask the Indians.

    • John Harshman John Harshman

      Well, I am properly chastened. Thanks for the documentation.

  23. I wonder if the notion of the turtle holding everything up owes anything to the iconography of Kurma, Vishnu’s turtle avatar. In Hindu mythology Kurma saved the day when the Gods and Asuras were churning the sea of milk to produce the elixir of immorality. The deities tried to use Mount Mandara as the churn, but the mountain was so heavy that it threatened to break through the bottom of the ocean. That’s when Kurma arrived to serve as the base of the pillar. There are lots of pictures of this famous episode.

    • My favourite story of Vishnu as a turtle is as follows. Vishnu and Brahma were walking through heaven one day arguing as to which of them was the greatest god when they came across a mysterious pillar of fire. Neither of them could explain what it was and so they decided to investigate. Brahma turned into a swan and flew up the pillar and Vishnu turned into a turtle and swam down it. Both of them travelled for a thousand years but saw no end in sight. Returning to their starting point they shared their puzzlement. Suddenly Shiva appeared and said the pillar is my lingam and I’m the greatest of the gods.

      • You left out the rest of the poem:

        But Kali arrived and called Shiva a phony.
        An infinite prick needs a bottomless Yoni.

        • Was that before or after she borrowed his arms?

  24. According to Wikipedia Turtle Island is a concept created by the Beat poet Gary Snyder. Turtle Island is also an excellent jazz string quartet!

  25. Roberto Gonzalez-Plaza Roberto Gonzalez-Plaza

    This is what actually Wikipedia shows. It is wrong regarding historical evidence. Ask the Indians.

    “Turtle Island is an English language translation ostensibly of many Native American tribes’ terms for the continent of North America. There is little if any historical evidence that any tribes had such a term in their language or used it in this manner, although it is used today by many Native tribes and Native rights activists. The newly coined term is proposed as a substitute for or synonym for North America. The term was brought into popular usage by Gary Snyder through his book Turtle Island [1] in 1974. In a later essay, published in At Home on the Earth,[1] Snyder claimed this title as a term referring to North America which synthesizes both indigenous and colonizer cultures by translating the indigenous name into the colonizer’s languages (the Spanish “Isla Tortuga” being proposed as a name as well). Snyder argues that understanding North America under the name of Turtle Island will help shift conceptions of the continent.”

  26. Anthony McCarthy Anthony McCarthy

    I’d love to have an etymological dictionary of common blog buzzwords and phrases. Or one that tracked their devolution into invariably meaning either “I like that” or, more often ” I don’t like that” and most often “I don’t like that but can’t think of anything to refute it with”.

  27. Roberto Gonzalez-Plaza Roberto Gonzalez-Plaza

    What a good idea!! I would like a buzzword for “i dont know what you taking about”

  28. Roberto Gonzalez-Plaza Roberto Gonzalez-Plaza

    That was totally great! It is “talking about” not” taking about”. Beautiful

  29. I always assumed that the phrase gained its popularity from a reference to the turtle-support theory in Bertrand Russell’s “Why I am Not a Christian,” whom in turn I assumed got it from either Hume (DcNR, IV) or Locke (EcHU, II:xxiii).

    • Well spotted, although in Hume it is an elephant:

      “Let us remember the story of the Indian philosopher and his elephant. It was never more applicable than to the present subject. If the material world rests upon a similar ideal world, this ideal world must rest upon some other; and so on, without end. It were better, therefore, never to look beyond the present material world.”

      Philo is speaking.

      In Russell, page 7, he writes:

      “If everything must have a cause, then God must have a cause. If there can be anything without a cause, it may just as well be the world as God, so that there cannot be any validity in that argument. It is exactly of the same nature as the Hindu’s view, that the world rested upon an elephant and the elephant rested upon a tortoise; and when they said, “How about the tortoise?” the Indian said, “Suppose we change the subject.” ”

      which is as you say the same argument, but not the quote. I suspect Russell is half remembering both Hume and the saying/joke.

      This is getting interesting. Now we know why Russell is often cited here.

      Locke’s passage is more closely related to the saying:

      “If any one should be asked, what is the subject wherein colour or weight inheres, he would have nothing to say, but the solid extended parts; and if he were demanded, what is it that solidity and extension adhere in, he would not be in a much better case than the Indian before mentioned who, saying that the world was supported by a great elephant, was asked what the elephant rested on; to which his answer was — a great tortoise: but being again pressed to know what gave support to the broad-backed tortoise, replied — something, he knew not what. “

      • TomS TomS

        By a remarkable coincidence, the Wikipedia article has been edited to include a citation to Hume.

      • “If there can be anything without a cause, it may just as well be the world as God, so that there cannot be any validity in that argument.”

        A causeless cosmology would exclude multiverse inflation hypotheses because all such hypotheses propose that each verse was caused by gravity in a previous verse. I also suppose that it would be pushing it to say that 21st century cyclic cosmology models are causeless because a big rip might be a prerequisite for the beginning of a new cycle. Additionally, the entire idea of an infinitely regressing cycle suggests an infinitely regressing cause. However, the good old fashioned big bang with no cause would best fit this bill, but science apparently rejects this as impossible.

  30. Leo inspired me and now I have found one from 1711:

    “We ought not to laugh so much at the Indian Philosophers, who to satisfy their People how this huge Frame of the World is supported, tell ’em ’tis by an Elephant. And the Elephant how? A shrewd Question! but which by no means shou’d be answer’d. ‘Tis here only that our Indian Philosophers are to blame. They shou’d be contented with the Elephant, and go no further. But they have a Tortoise in reserve; whose Back, they think, is broad enough. So the Tortoise must bear the new Load: And thus the matter stands worse than before.”

    From Anthony Ashley Cooper, Earl of Shaftesbury, Characteristicks of men, manners, opinions and times, vol 2, p202.

    Locke beats it by 21 years, though.

  31. Roberto Gonzalez-Plaza Roberto Gonzalez-Plaza

    Are you aware that “Native Americans” are Indians?
    So much for Russell, and quote a racist on Turtle island issues?)

  32. Ian H Spedding FCD Ian H Spedding FCD

    For some reason, all this talk of turtles suddenly reminded me of a short-lived British TV show called Turtle’s Progress. It was a sort of Minder style Cockney comedy, if I remember. I used to love it, never missed an episode. I doubt anyone remembers it now, though. I think my age is showing.

  33. Allen Hazen Allen Hazen

    Aristotle may not have liked the infinite, but at least one earlier Greek philosopher would have regarded “turtles all the way down” as at least coherent. Some of the early Ionians worried about what kept the Earth from falling. Xenophanes had an answer: the ground we walk on is supported by the subsoil beneath it, which is supported by what is beneath it, and so on down forever. (He was also a flat-earther, who thought — minor irregularities of hills and valleys aside — that we lived on an infinite plane. Since this didn’t have edges for the sun to rise over or set beyond, he also thought there were an infinite series of suns, following each other ever westward. Since it shows up in several places in his cosmology, I think it is clear that he had — and LIKED — a conception of the infinite.)

    • John Wilkins John Wilkins

      For every Greek philosopher there is an equal and opposite Greek philosopher.

      • Can I steal that please?

        • John Wilkins John Wilkins

          Not original to me. Knock yourself out.

  34. Jim Arnold Jim Arnold

    Stephen Hawkins “Information lost in black holes is recovered in the multiverse ”
    TURTLES ALL THE WAY DOWN

Comments are closed.

Optimized by Optimole