Author Archives: Massimo

About Massimo

Massimo is the K.D. Irani Professor of Philosophy at the City College of New York. He blogs at platofootnote.org and howtobeastoic.org. He is the author of How to Be a Stoic: Using Ancient Philosophy to Live a Modern Life.

Plato’s reading suggestions, episode 137

Here it is, our regular Friday diet of suggested readings for the weekend:

Benjamin Libet and the denial of free will. Again.

Why we don’t read. More data.

The pseudoscience of college admission.

What kept me from killing myself (books).

When scientists use philosophical jargon without knowing what they are talking about. And when corrected they dig their heels in.

Is Gauguin’s unethical behavior toward his family and the subjects of his paintings somehow countered by the greatness of his art?

Could “it” happen here? Three analyses.

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Please notice that the duration of the comments window is three days (including publication day), and that comments are moderated for relevance (to the post one is allegedly commenting on), redundancy (not good), and tone (constructive is what we aim for). This applies to both the suggested readings and the regular posts. Also, keep ‘em short, this is a comments section, not your own blog. Thanks!

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Once more: is there such a thing as metaphysical necessity?

Some philosophers distinguish among three classes of necessary (or, conversely, impossible) things: (i) physical necessities (and impossibilities), meaning things that are going to happen (or can never happen) because of the ways the laws of physics are; (ii) logical necessities (and impossibilities), that is things that are true (or impossible) because of the laws of logic; and (iii) metaphysical necessities (and impossibilities), meaning things that are the case (or can never be the case) because of…? Yeah, the latter is the problematic one. Nobody doubts the existence of the laws of physics (though some philosophers reject that kind of talk and prefer to think in terms of causal regularities). Some people think that logical necessity / impossibility is actually the result of human constructs, since one can adopt different kinds of logic, but this is controversial. And then there is a small number of philosophers, the metaphysicians (sometimes they call themselves metaphysicists) who insist on a separate existence of the third category. And this is very controversial.

I wrote about metaphysical necessity / impossibility back in 2014, and then again (on the specific issue of “grounding”) in 2015. In both cases, I was rather skeptical of distinguishing metaphysical anything from either the physical or the logical realm. The way I saw it was this: logical necessity / impossibility > physical necessity / impossibility > contingency. That is, if something is, say, logically impossible, it is a fortiori physically impossible, and it can’t happen no matter what the specific circumstances. However, if something is happening, then it must be both physically and logically possible. And so forth. My argument in the past is that whatever examples of alleged metaphysical necessity / impossibility one would come up with it would either turn out to belong to the physical class or to the logical one, with nothing either in between or, somehow, above logic.

(For the rest of this discussion I will bracket two obvious questions: (a) where do the laws of physics come from? And (b) if logic is a human construct, then in what sense can we talk about logical necessity / impossibility? The only hint that I will give here is that I think the laws of physics themselves are a human construct, but they reflect a fundamental structure of reality. Something similar may be going on with logic. So there…)

Recently, a friend of mine and former student at CUNY’s Graduate Center (she has just successfully defended her thesis!) Antonella Mallozzi, has put out a very conveniently and nicely put together diagram to explore (and defend, in her case) the idea of metaphysical necessity as distinct from both the physical and the logical varieties. With permission from Antonella, I reproduce the diagram below, as it will guide us through the rest of the discussion. (Antonella has also guest edited a special issue on this topic for the journal Synthese, entitled “New directions in the epistemology of modality.” You can see her leading article here. I hear that my colleague Graham Priest, one of the best logicians out there, is also skeptical of the notion of metaphysical necessity, but I have purposely not read his paper, currently in print, so to be able to develop my own ideas.)

So what I’d like to do now is to go through each of Antonella’s possibilities for metaphysical necessity, briefly look at the examples that she presents, and see what happens. We will start with the right-center portion of her large circle (labelled “general metaphysical necessities”) and proceed counter-clockwise, one category and set of examples at a time.

(I) Logical, mathematical, and geometrical necessity (middle right of the large circle). Her examples here include “necessarily, everything is self-identical,” and: “necessarily, two plus two equals four.” As she points out, some philosophers are skeptical that these are examples of necessity, or that these statements are true, pointing to the existence of non-classical logics, non-euclidean geometries, etc. But I’m going to accept these examples as valid given certain axioms (classical logic, euclidean geometry, and so forth). You may disagree, of course, but as I mentioned above, I’m going to bracket any further discussion of this particular issue. Even if we do accept the examples, however, they fall squarely into the logical end of my continuum above, they are not distinctly metaphysical.

(II) Conceptual necessity (upper right of the large circle). Antonella here distinguishes between things that are epistemically necessary, but not metaphysically so (the part of the small conceptual circle that lies outside the largest one), and things that are both epistemically and metaphysically necessary (the little bit of the small conceptual circle that lies inside the largest one). An example of alleged epistemic (but not metaphysical) necessity is the following: “Julius” designates the inventor of the zip. It then is a priori (epistemically) necessary that if anyone invented the zip, Julius did. This seems to me a very weak sense of epistemically necessary, since it simply states that given that X is true, you better take X to be true. I think the use of the word “a priori” is misleading here, as it is obviously a contingent fact that Julius, and not someone else, invented the zip. More importantly, because of the latter possibility, even Antonella agrees that this is a case of metaphysical contingency.

What about metaphysical conceptual necessities? Antonella gives two examples: “necessarily, anything colored is extensive,” and “necessarily, there is a valley in between two mountains.” She also adds, however, that some people think these are logical, not distinctly metaphysical necessities. The case seems particularly clear for the second example: once one defines mountains as things that have peaks and are surrounded by valleys, then it is obviously logically necessary that if there are two mountains next to each other they will be separated by a valley. As far as the color example is concerned, it sounds to me like a case of contingency due to biology: colors are not “out there,” but rather the result of the interaction between physico-chemical properties of materials and the specific physiological and perceptual apparatus of a given organism. Perhaps one could say that more obviously intrinsic physical properties necessitate extension (meaning, something more than a geometrical point), but now that begins to look like a physical necessity, and even that is doubtful, if one accepts certain radical views of what actually constitutes the physical world.

(III) Grounding and mereology (top of the large circle). Antonella’s examples are “necessarily [P&Q] is grounded in [P], [Q],” and “necessarily, everything is a part of itself.” I have expressed my skepticism about the concept of grounding in metaphysics elsewhere (it’s pretty vague and slippery, and doesn’t seem to add anything), but Antonella herself comments that some people would consider these examples of logical necessity, not a distinctive metaphysical class.

(IV) Ethical-deontological necessities (upper left of the large circle). “Necessarily, violence is wrong.” Well, no. My ethics is a naturalistic one, so I don’t think there is anything that is necessary in that realm, at all. Ethics is very clearly, to me, a human construction, constrained by our biology as social animals capable of language, which means it isn’t entirely arbitrary, but also that there is nothing necessary about it. I am, most definitely, not a deontologist.

The last two classes of metaphysical necessities proposed by Antonella are important, because they fall into the circle labelled “distinctively metaphysical” (or Kripkean, in honor of the highly influential philosopher Saul Kripke, currently at CUNY’s Graduate Center). That is, in her mind these are the ones that cannot be reduced in any way to logical or physical necessities, so let’s pay particular attention.

(V) Causally-nomic (lower left of the large circle). Even Antonella readily admits that it is controversial whether anything at all falls into this group! Her examples include the laws of physics and chemistry, but it is an open question to say the least why the fundamental laws of physics are the way they are (those of chemistry, presumably, can be reduced to physics). It may be that they could not possibly have been different, because of the way the causal world is structured; or perhaps they could have been different, and the ones we observe are that way because of contingency. The first scenario would seem to be a case of physical necessity, while in the second scenario the only constraints would be imposed by logical impossibility and necessity. Again, no distinctive metaphysical criterion appears to be required.

(VI) Finally, we get to the most promising class, that of “de re,” a posteriori things that have their source in the fundamental nature, or essence, of things (lower part of the large circle). The pertinent examples are classics of the metaphysical literature: “necessarily, water is H2O,” or “necessarily, I could not have had different parents then the ones I actually have.” I am, however, utterly unconvinced. Water is H2O either as a matter of physical necessity (if the laws of physics could not have been otherwise) or it is a contingent fact about our universe (if the laws of physics could have been different). As for my parents, that seems an entirely contingent fact of our biology. For instance, if humans were a clonal species that reproduced by budding, “I” could have had a lot of different specific parents and still be “me” (not to mention that this example depends on one’s conception of personal identity, a controversial issue in its own right).

I guess this third look at metaphysical necessity / impossibility, despite Antonella’s brave and very clever attempt, still leaves me unmoved. I keep thinking that the logic > physics > contingency conceptual scheme is sufficient to account for all examples that have been presented, and that metaphysics is an artificial category situated between logic and physics: each alleged example of metaphysical necessity turns out, upon closer inspection, to be either a case of logical necessity, or one of physical necessity. But I remain open to be convinced otherwise. Stay tuned for a fourth possible look at the issue, a few years down the road!

Plato’s reading suggestions, episode 136

Here it is, our regular Friday diet of suggested readings for the weekend:

Another psychological classic bites the dust: the marshmallow study doesn’t say what you think it says.

Sometimes you just have to know when to quit.

Ladies and gentlemen, once again, the meaning of life.

The illiberal philosophers and our fractured politics.

The pseudoscience of things (not) to put into your vagina.

The Stanford Prison Experiment was a fraud. And even more adventures in the ongoing replication crisis in psychology.

Neuronal activity sheds light on the origin of consciousness.

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Please notice that the duration of the comments window is three days (including publication day), and that comments are moderated for relevance (to the post one is allegedly commenting on), redundancy (not good), and tone (constructive is what we aim for). This applies to both the suggested readings and the regular posts. Also, keep ‘em short, this is a comments section, not your own blog. Thanks!

Book Club: Early Socratic Dialogues, 4, the Lysis and the nature of friendship

Achilles and Patroclus: philia, eros, or both?

The ancient Greeks had a number of words that translate to the modern English “love,” and rightly so, since there are different manifestations and nuances of the concept. The Lysis deals with one particular kind, rendered in the original as “philia,” which refers to fond affection, as distinct, for instance, from the kind of passionate love that goes under the term “eros” (the latter is the subject of one of the best Platonic dialogues, the Symposium, which I will not cover in this series).

Interestingly, the main characters in the dialogue are related by a complex web of philia and eros: the young Hippothales is in love with the title character, Lysis, and that love is definitely (homo) erotic (if, at the moment of the action, unreciprocated by Lysis). Indeed, Hippothales is explicitly referred to as the (would be) eron, or sexually active partner, because he is older, while Lysis would be the eromenos, or sexually passive one, since he is younger. Lysis, meanwhile feels philia toward another boy, Menexenus, and Socrates is also in a relationship of philia, toward all three boys.

Moreover, the dialogue connects philia and paideia, or education, because philia means you want to make someone happy, and education makes people happy — in the Socratic scheme of things — because it allows people to choose and then pursue what they want. This may sound strange, but remember that knowledge, for Socrates, is always knowledge of the good, even outside the strictly moral context. So a condition for happiness is to know what is good for you (as well as what is bed, and therefore to be avoided). As a generalization of this, then, everyone will feel philia for the wise person, and vice versa, a conclusion that later led the Stoics to imagine that in their ideal Republic (inhabited by wise people) everyone would naturally love everyone else, the perfection of the notion of cosmopolitanism.

Unfortunately, the dialogue is rather confusing, because of “Plato’s failure to distinguish between philia as a loving human relationship and philia as the pursuit of a loved object [in the abstract]. These are essentially separate questions, but Plato treats them as if they were the same [for a reason, as we shall see]. He starts off by investigating the former, moves without warning to considering the second, and then abruptly embraces the first again.” (p. 115)

It’s also noteworthy, in this dialogue, that although Menexenus is supposed to represent the sophists (and he is characterized as a “formidable opponent in debate”) we actually see Socrates himself engage in a bit of sophistry, as when he argues for one answer to the question at hand (what is friendship?), and then for its opposite. Despite its limitations, the scene setting and characters are captivating, and the eristics throughout the dialogue are dazzling, so the Lysis is certainly worth reading in its entirety.

The dialogue begins by setting the scene and then introducing the distinction between unreciprocated eros (between Hipothales and Lysis) and reciprocated philia (between Lysis and Menexenus). Just to give you a flavor, here is how Hippothales answers Socrates when the latter asks him what he and his friends are doing:

‘We spend our time there,’ he went on, ‘and we’re not the only ones. Lots and lots of other young men do too, handsome young men.’ ‘What is this place? What do you do here?’ ‘It’s a wrestling-school,’ he said, ‘built not long ago. We spend most of our time there having discussions. We’d be glad to have you join us in them.’

That’s no gym I’ve ever gone too… A little later, Socrates says to Hippothales:

‘I may not know much else, I may be useless at other things, but somehow God’s given me the power to recognize in an instant a man in love and the boy he’s in love with.’

So much for the notion of the philosopher lost in the clouds! Socrates goes on giving a veritable lesson on love to Hippothales, putting forth philia as a superior kind of love (and friendship), because one is concerned with the happiness of the other person, and wish to educate him in order to help him (remember that Hippothales is older than Lysis, and of course Socrates is older than both). Indeed, we even get some idea of how to conduct good parenting, also based on philia: we want to educate our children (in the broad sense of making them wise, not just giving them formal schooling) so that they will have the opportunity to pursue what they want, thus achieving happiness (eudaimonia). Moreover, knowledge in this broad sense makes one both useful and good, and therefore universally sought after as a philos, a friend.

Socrates is pretty pleased with his demonstration to Hyppothales of how to talk to the young Lysis, but he refrains from embarrassing his interlocutor:

“I looked at Hippothales and almost put my foot in it. It was on the tip of my tongue to say, ‘There, Hippothales, that’s how one ought to talk to one’s boy, making him humble and unaffected, not, as you do, making him conceited and spoiled.’ Well, I noticed he was squirming with embarrassment at what we’d been saying and I remembered that, though he was standing near by, he wanted to avoid being seen by Lysis, so I checked myself and said nothing.”

The next section in the Lysis is where the confusion begins, because Plato alternates between the masculine (philos) and the neutral (philon) versions of the central term. Moreover, Socrates begins by asking “how does a person become a friend of another?” but then immediately switches to “when someone loves someone else, which is the friend of which?” After a complex series of steps, some leading to paradoxical answers that are rightly rejected (e.g., (i) I love wine; (ii) wine cannot love me in return; (iii) therefore, wine is not dear to me), Socrates gets to the important point: philia does not need to be reciprocated, which means that one can love one’s enemy, as counterintuitive as that may sound. Notice that this cannot be the case for eros, which cannot be fulfilled if not reciprocated.

‘Then, Menexenus, it would appear that what is loved is dear to what loves it whether it loves what loves it or whether it actually hates it. For example, some newly born children do not yet love, while others actually hate their mother or father when they are punished by them. None the less they are most dear to their parents at the time they actually hate them.’

Socrates then engages in a convoluted discussion aimed at determining whether friendship is something that happens between people that are “like” or “unlike” (meaning similar or opposites), and concludes by rejecting both possibilities (though not exactly in an airtight fashion). Where is he going? We get the answer when he concludes what a friend is by way of an analogy with philosophy (of course), i.e., with love of wisdom:

“The example of philosophy, the love of wisdom, is used to illustrate and summarize the results: (i) those who are already wise no longer love wisdom: like (good) is not friend to like (good); there is no presence of bad. (ii) those who are so ignorant that they are bad do not love wisdom: opposite (bad) is not friend to opposite (good); (iii) those who possess ignorance (a bad thing), but have not yet been rendered stupid (bad) by it (i.e. those who are neither good nor bad), do love wisdom: what is neither good nor bad is the friend of the good because of the presence of bad. Socrates concludes that (iii) gives the answer to the question of what a friend is.” (p. 142)

If you find yourself perplexed and unconvinced by this, you are not alone. I mean, I can sort of see the reasoning as far as love of wisdom is concerned (though even there, why wouldn’t the wise person keep loving wisdom even after she has achieved it?), but I doubt anything of substance follows about the nature of friendship. Again, this is because Plato confuses different questions and distinct possible objects of philia.

It doesn’t help that Plato, near the end of the dialogue, uses yet another analogy, this time with medicine: “what is neither good nor bad (the body) is the friend of the good (medicine) because of the bad (disease) for the sake of (another) good (health).” (p. 144) Sure, but the sort of “love” we may feel for abstract concepts (like philosophy, health) is not the same sort of love we feel for our friends, or our children. Yet, there is a reason why Plato is going about it this way: he is presumably beginning to explore notions that will be fully developed in the Republic, and particularly the notion of the Forms, where he explicitly does connect the ideal world outside the cave with its pale reflection that we perceive while stuck inside. In that sense, then, it is understandable why he is ambiguous about his objective throughout the Lysis. Remember, this is one of the early dialogues, in which Socratic philosophy is dominant, and yet in which Plato is beginning to articulate his own ideas, ideas that will become fully formed and better laid out in the middle and later dialogues.

What are we to make of all this? I think the best parts of the dialogue are the early ones, before Plato begins to equivocate in a more or less conscious pursuit of his own agendas. There is, indeed, more than one kind of love, and even the same kind (e.g., philia) can manifest itself in different ways (e.g., between parents and offspring, or friends of different ages, or mentor and student). Our modern vocabulary is poorer for not making those distinctions, which may even constrain people’s thoughts and limiting their imagination and understanding of that broad phenomenon we call “love.”

(next: the Charmides, on the nature of self-knowledge)

Plato’s reading suggestions, episode 135

Here it is, our regular Friday diet of suggested readings for the weekend:

Why some scientists say physics has gone off the rails.

Sources of error: the illusory illusions of reductionism.

Does honor matter? A critique.

Why professors distrust beauty.

The defeat of reason. Two new books on physics and philosophy of science during the 20th century.

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Please notice that the duration of the comments window is three days (including publication day), and that comments are moderated for relevance (to the post one is allegedly commenting on), redundancy (not good), and tone (constructive is what we aim for). This applies to both the suggested readings and the regular posts. Also, keep ‘em short, this is a comments section, not your own blog. Thanks!

Biological landscapes, surfaces, and morphospaces: what are they good for?

ammonite

Metaphors are rampant in both everyday language and in science, and while they are inevitable, readers of this blog also know by now that I’m rather skeptical of their widespread use, both in professional publications and, especially, when addressing the general public. (See here, here, here, and here.) One such problematic metaphor is that of so-called adaptive landscapes, or surfaces, in evolutionary biology, something on which I did a fair amount of research when I was running a laboratory of ecology and evolutionary biology.

My detailed criticism of the way the landscape metaphor has sometimes warped biologists’ thinking is detailed in a chapter that was published back in 2012 as part of a very interesting collection entitled The Adaptive Landscape in Evolutionary Biology, edited by Erik Svensson and Ryan Calsbeek for Oxford University Press. As it often happens, mine was the lone contribution from the token skeptic…

Few metaphors in biology are more enduring than the idea of adaptive landscapes, originally proposed by Sewall Wright in 1932 as a way to visually present to an audience of typically non-mathematically savvy biologists his ideas about the relative role of natural selection and genetic drift in the course of evolution. The metaphor was born troubled, not the least reason for which is the fact that Wright presented different diagrams in his original paper that simply cannot refer to the same concept and are therefore hard to reconcile with each other. For instance, in some usages, the landscape’s non-fitness axes represent combinations of individual genotypes, while in other usages the points on the diagram represent gene or genotypic frequencies, and so are actually populations, not individuals.

typical (hypothetical) fitness landscape

Things got even more confusing after the landscape metaphor began to play an extended role within the Modern Synthesis in evolutionary biology and was appropriated by G.G. Simpson to further his project of reconciling macro- and micro-evolution, i.e. to reduce paleontology to population genetics. This time the non-fitness axes of the landscape were phenotypic traits, not genetic measures at all. How one would then translate from one landscape to another (i.e., genes to morphologies) is entirely unaddressed in the literature, except for vague motions to an ill-defined and very rarely calculated “genotype-phenotype mapping function.”

These are serious issues, if we wish to use the landscape metaphor as a unified key to an integrated treatment of genotypic and phenotypic evolution (as well as of micro- and macro-evolution). Without such unification evolutionary biology would be left in the awkward position of having two separate theories, one about genetic change, the other about phenotypic change, and no conceptual bridge to connect them.

To try to clarify things a bit, I went through the available literature and arrived at a typology of four different kinds of “landscapes” routinely used by biologists:

Fitness landscapes. These are the sort of entities originally introduced by Wright. The non-fitness dimensions are measures of genotypic diversity. The points on the landscape are typically population means, and the mathematical approach is rooted in population genetics. (see figure above)

Adaptive Landscapes. These are the non straightforward “generalizations” of fitness landscapes introduced by Simpson, where the non-fitness dimensions now are phenotypic traits. The points on the landscape are populations speciating in response to ecological pressures or even above-species level lineages (i.e., this is about macro-evolution). There is — with very special exceptions discussed in my paper — no known way to move from fitness to adaptive landscapes or vice versa, even though this is usually assumed by authors.

Fitness surfaces.These were introduced by Russell Lande and Steve Arnold back in the ‘80s to quantify the study of natural selection. Here phenotypic traits are plotted against a surrogate measure of fitness, and the landscapes are statistical estimates used in quantitative genetic modeling. The points on the landscape can be either individuals within a population or population means, in both cases belonging to a single species (i.e. this is about micro-evolution).

Morphospaces. These were first articulated by paleontologist David Raup in the mid-’60s, and differ dramatically from the other types for two reasons: (a) they do not have a fitness axis; and (b) their dimensions, while representing phenotypic (“morphological”) traits, are generated via a priori geometrical or mathematical models, i.e. they are not the result of observational measurements. They typically refer to across species (macro-evolutionary) differences, though they can be used for within-species work as well.

The first thing to note is that there are few actual biological examples of fitness landscapes (Wright-style) or Adaptive Landscapes (Simpson-style) available, while there is a good number of well understood examples of morphospaces (Raup-style) and particularly of adaptive surfaces (Lande–Arnold style). These differences are highly significant for my discussion of the metaphor. The paper summarizes examples — both conceptual and empirical — of each type of landscape and the complex, often barely sketched out, relationships among the different types.

When it comes to asking what the metaphor of landscapes in biology is for, we need to distinguish between the visual metaphor, which is necessarily low-dimensional, and the general idea that evolution takes place in some sort of hyper-dimensional space. Remember that Wright introduced the metaphor because his advisor suggested that a biological audience at a conference would be more receptive toward diagrams than toward a series of equations. But of course the diagrams are simply not necessary for the equations to do their work. More to the point, subsequent research by my former University of Tennessee colleague Sergey Gavrilets and his collaborators has shown in a rather dramatic fashion that the original (mathematical) models were far too simple and that the accompanying visual metaphor is therefore not just incomplete, but highly misleading. It turns out that hyper-dimensional dynamics are very much qualitatively different from the low-dimensional ones originally considered by Wright.

In a very important sense Wright’s metaphor of fitness landscapes was meant to have purely heuristic value, to aid biologists to think in general terms about how evolution takes place, not to actually provide a rigorous analysis of, or predictions about, the evolutionary process (it was left to the math to do that work). Seen from this perspective, fitness landscapes have been problematic for decades, generating research aimed at solving problems — like the so-called peak shift one (how do populations stuck on a local fitness peak “shift” to a higher one?) that do not actually exist as formulated, since high-dimensional landscapes don’t have “peaks” at all, as their topology is radically different.

There are problems also with the Lande-Arnold type landscapes (discussed in the paper), but here I want to shift to some good news: the actual usefulness of the fourth type of landscape: Raup-style morphospaces. One of the best examples was produced by Raup himself, with crucial follow-up by one of his graduate students, John Chamberlain. It is a study of potential ammonoid forms that puts the actual (i.e., not just heuristic) usefulness of morphospaces in stark contrast with the cases of fitness and adaptive landscapes. Ammonoids, of course, were beautiful shelled marine invertebrates that existed in a bewildering variety of forms for a good chunk of Earth’s biological history, and eventually went extinct 65 million years ago, together with the dinosaurs. This is going to be a bit technical, but stick with me, it will be worth it.

Raup explored a mathematical-geometrical space of ammonoid forms defined by two variables: W, the rate of expansion of the whorl of the shell; and D, the distance between the aperture of the shell and the coiling axis. Raup arrived at two simple equations that can be used to generate pretty much any shell morphology that could potentially count as “ammonoid-like,” including shells that — as far as we know — have never actually evolved in any ammonoid lineage. Raup then moved from theory to empirical data by plotting the frequency distribution of 405 actual ammonoid species in W/D space and immediately discovered two interesting things: first, the distribution had an obvious peak around 0.3 <D <0.4 and W near 2. Remember that this kind of peak is not a direct measure of fitness or adaptation, it is simply a reflection of the frequency of occurrence of certain forms rather than others. Second, the entire distribution of ammonoid forms was bounded by the W = 1/D hyperbola, meaning that few if any species crossed that boundary on the morphospace. The reason for this was immediately obvious: the 1/D line represents the limit in morphospace where whorls still overlap with one another. This means that for some reason very few ammonites ever evolved shells in which the whorls did not touch or overlap.

one-peak ammonoid morphospace

Raup’s initial findings were intriguing, but they were lacking a sustained functional analysis that would account for the actual distribution of forms in W/D space. Why one peak, and why located around those particular coordinates? Here is where things become interesting and the morphospace metaphor delivers much more than just heuristic value. John Chamberlain, a student of Raup, carried out experimental work to estimate the drag coefficient of the different types of ammonoid shells. His first result clarified why most actual species of ammonoids are found below the W=1/D hyperbola: shells with whorl overlap have a significantly lower drag coefficient, resulting in more efficiently swimming animals.

However, Chamberlain also found something more intriguing: the experimental data suggested that there should be two regions of the W/D morphospace corresponding to shells with maximum swimming efficiency, while Raup’s original frequency morphospace detected only one peak. It seemed that for some reason natural selection found one peak, but not the other. Four decades had to pass from Raup’s paper for the mystery of the second peak to be cleared up: the addition of 597 new species of ammonoids to the original database showed that indeed the second peak had also been occupied!, a rather spectacular case of confirmed prediction in evolutionary biology, not exactly a common occurrence, particularly in paleontology.

two-peak ammonoid morphospace, with representative shell forms

So, is the landscape metaphor in biology useful? It depends. The original versions, those introduced by Sewall Wright to make his math accessible to his colleagues, have been highly influential for decades, and yet have arguably channeled both empirical and theoretical research in unproductive directions, inventing problems (like the peak shift one) that arguably do not exist, at least not as formulated. The Lande-Arnold landscapes, which I have not discussed in this post, but do treat in the paper, have a mixed record. They have been heuristically useful for biologists interesting in quantifying natural selection in the field, but have also arguably brought about a degree of tunnel vision in both the theoretical and empirical study of that most important concept in modern evolutionary theory. Morphospaces, by contrast, have a very good record of being useful in terms of generating insight into the evolution of animal (and plant) form, and yet, they are actually the least commonly deployed version of the landscape idea in the technical literature. And because population genetics, with its mathematical approach, is considered more sophisticated than paleontology, things are unlikely to change in the near future. Unfortunately.

Plato’s reading suggestions, episode 134

Here it is, our regular Friday diet of suggested readings for the weekend:

Barbara Ehrenreich’s radical critique of wellness and self-improvement.

What makes people distrust science? Surprisingly, not (only) politics.

Bullshit jobs and the myth of capitalist efficiency.

Sex, sport, and Track and Field’s new rules on intersex athletes: two contrasting views (here and here).

What can Aristotle teach us about the routes to happiness? (A lot, but the author needlessly gets the Stoics wrong.)

What’s the best way to avoid regrets?

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Please notice that the duration of the comments window is three days (including publication day), and that comments are moderated for relevance (to the post one is allegedly commenting on), redundancy (not good), and tone (constructive is what we aim for). This applies to both the suggested readings and the regular posts. Also, keep ‘em short, this is a comments section, not your own blog. Thanks!