Jared and Todd discuss the stories and worldbuilding of J.R.R. Tolkien as found in The Hobbit, The Lord of the Rings, The Silmarillion, and others. We discuss the Tolkien cosmogony and pantheon, Eru Ilúvatar, the Music of the Ainur, the Valar and the Maiar, the importance of myth for Tolkien, and the possibility of Tolkien’s world as viable myth for the modern age. We discuss the books and films and their cultural impact, the importance of song, the desire for power (even for ostensibly good purposes), the surrender of control to fate or grace, Christ figures, creation and sub-creation, industry and nature, the scars of war, our Baggins and Took natures, hope in hopelessness, infinite resignation and faith, hastiness, and the gift of death.
This is the first in a series of episodes exploring a philosophy of structure. To introduce the concept and to start thinking about structure I make use of ideas from thermodynamics, phase spaces, information theory, The Three-Body Problem, the Hebrew Bible, the Book of Mormon, Daniel Dennett, and Jorge Luis Borges. Drawing from a variety of sources the objective is to find patterns in structures across multiple fields, to understand a general structure of structure.
The Hebrew Bible describes the condition of the earth before creation as תֹהוּ וָבֹהוּ (tohu va-bohu), “formless and void”. Both terms, tohu and bohu, convey formlessness and emptiness. It’s an interesting pair of ideas. And carrying these ideas beyond their original narrative setting, I’m intrigued by the thought that lack of form, or structure, could be understood also as a kind of emptiness, or nothingness.
With this episode I’d like to start what I intend to be a series of episodes about structure, looking at a philosophy of structure. Today I just want to introduce some general ideas and then explore particular examples of structure in more detail in later episodes, looking at structure in music, chemistry, biology, and other fields.
To introduce the subject I’d like to pull together some ideas from different subjects that range from highly technical and quantitatively rigorous to conceptual and qualitative. There are tools in physics and in information theory that can give very specific measures of certain kinds of structures. And those tools are also conceptually instructive. But I don’t think those measures exhaust or cover everything that we mean by or understand structure to be. So all of this will fall into a diverse toolbox of ways to think about structure and to approach the topic.
Going back to the Hebrew Bible and the primordial condition of tohu va-bohu, if we think of this condition as a lack of structure, the kind of emptiness or nothingness I imagine in the lack of structure is not absolute nothingness, whatever that might be. But it’s nothingness of the sort of there not being anything very interesting. Even if there’s “stuff” there there’s not really anything going on. Or even if there’s stuff going on, like as a whirling, chaotic mass, it still amounts to uniformity with all the pieces just canceling each other out, adding up to not very much.
Part of the lack is an aesthetic lack. An absence of engaging content. There’s a great literary illustration of this idea in Cixin Liu’s novel The Three Body Problem. This is from a scene where one of the characters, who is suffering from a mental illness, is meditating and trying to heal his troubled mind:
“In my mind, the first ‘emptiness’ I created was the infinity of space. There was nothing in it, not even light. But soon I knew that this empty universe could not make me feel peace. Instead, it filled me with a nameless anxiety, like a drowning man wanting to grab on to anything at hand. So I created a sphere in this infinite space for myself: not too big, though possessing mass. My mental state didn’t improve, however. The sphere floated in the middle of ‘emptiness’—in infinite space, anywhere could be the middle. The universe had nothing that could act on it, and it could act on nothing. It hung there, never moving, never changing, like a perfect interpretation for death. I created a second sphere whose mass was equal to the first one’s. Both had perfectly reflective surfaces. They reflected each other’s images, displaying the only existence in the universe other than itself. But the situation didn’t improve much. If the spheres had no initial movement—that is, if I didn’t push them at first—they would be quickly pulled together by their own gravitational attraction. Then the two spheres would stay together and hang there without moving, a symbol for death. If they did have initial movement and didn’t collide, then they would revolve around each other under the influence of gravity. No matter what the initial conditions, the revolutions would eventually stabilize and become unchanging: the dance of death. I then introduced a third sphere, and to my astonishment, the situation changed completely… This third sphere gave ‘emptiness’ life. The three spheres, given initial movements, went through complex, seemingly never-repeating movements. The descriptive equations rained down in a thunderstorm without end. Just like that, I fell asleep. The three spheres continued to dance in my dream, a patternless, never-repeating dance. Yet, in the depths of my mind, the dance did possess a rhythm; it was just that its period of repetition was infinitely long. This mesmerized me. I wanted to describe the whole period, or at least a part of it. The next day I kept on thinking about the three spheres dancing in ‘emptiness.’ My attention had never been so completely engaged.”
And that’s a very imaginative description of what’s known in physics and mathematics as the three-body problem, which unlike a two-body problem has no closed-form solution, which is the reason for the unending, non-repeating motion. What I like about this story is the way the character responds to the increasing structure in his mental space. As structure increases he becomes increasingly engaged. I think this subjective response to structure will have to be an indispensable aspect of any philosophy of structure.
Another literary, or scriptural example, of this idea is in Latter-day Saint scripture in the Book of Mormon. A prophet named Lehi talks about how existence itself depends on the tension between opposites: “For it must needs be, that there is an opposition in all things. If not so… righteousness could not be brought to pass, neither wickedness, neither holiness nor misery, neither good nor bad. Wherefore, all things must needs be a compound in one; wherefore, if it should be one body it must needs remain as dead, having no life neither death, nor corruption nor incorruption, happiness nor misery, neither sense nor insensibility.” (2 Nephi 2:11)
There’s a similar idea here of “death” as with Cixin Liu’s character who finds only death in his static or repetitive mental structures.
Another idea that comes up in both the aesthetic and technical instances of structure is that of distinction. Lehi talks about opposition, setting one thing against another. We could say that the opposing entities endow each other with definition and identity. The Hebrew Bible also contrasts the formlessness and emptiness, the תֹהוּ וָבֹהוּ (tohu va-bohu), with separation. Elohim brings order the earth by separating things, the verb in the Bible of separation is בָּדל (badal). וַיַּבְדֵּ֣ל אֱלֹהִ֔ים בֵּ֥ין הָאֹ֖ור וּבֵ֥ין הַחֹֽשֶׁךְ (va-yavdel elohim ben ha-or u-ben ha-choshek); “and God separated the light from the darkness” (Genesis 1:4). God separated the sky from the sea, the day from the night. Through separation what was a formless void came to have structure.
What are some examples of structure from a more technical side, scientifically and philosophically? Interestingly enough there are actually some concepts that overlap with these literary and scriptural ones, sharing notions of both distinction and form.
One way to think about a system is by using a phase space. A phase space is an abstract space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space. This is also called a state space. To get the general concept of an abstract space you can think of a graph with a horizontal axis and a vertical axis, each axis representing some property. The points on the graph represent different combinations of the two properties. That’s a kind of phase space.
To give a very simple example, consider a system of 2 particles in 1-dimensional space, which is just a line. The state space containing all possible arrangements of a system of n particles in 1-dimensional space will have 1n dimensions. Such a space dealing strictly with positions is also called a configuration space. So for our 2 particle system the configuration space will have 2 dimensions. We can represent this on a graph using a horizontal axis for one particle and a vertical axis for the second particle. Any point on the graph represents a single combination of positions for particles 1 and 2. That example is nice because it’s visualizable. When we expand to more than 3 dimensions we lose that visualizability but the basic principles still apply.
A classic example of a phase space is for a system of gas particles. Say we have a gas with n particles. These particles can have several arrangements. That’s putting it mildly. The collection of all possible arrangements makes up a configuration space of 3n dimensions, 3 dimensions for every particle. Such a space could have billions upon billions of dimensions. This is not even remotely visualizable but the principles are the same as in our 2 dimensional configuration space above. A single point in this configuration space is one possible arrangement of all n particles. It’s like a snapshot of the system at a single instant in time. All the points in the configuration space comprise all possible arrangements of these n particles.
To get a more complete picture of the system a phase space will have 3 additional dimensions for the momentum of each particle in the 3 spatial directions. So the phase space will have 6n dimensions. A snapshot of the system, with the positions and momenta of every particle at one instant, will occupy a single point on the 6n dimensional phase space and the entire 6n dimensional phase space will contain all possible combinations of position and momenta for the system. The evolution of a system through successive states will trace out a path in its phase space. It’s just a mind-bogglingly enormous space. There’s no way we can actually imagine this in any sort of detail. But just the concept is useful.
The sum total of all possible states that a system can take constitutes a tremendous amount of information, but most states in a phase space aren’t especially interesting and I’d suggest that this is because they aren’t very structured. One useful affordance of phase spaces is that we can collect groups of states and categorize them according to criteria of interest to us. The complete information about a single state is called a microstate. A microstate is complete and has all the information about that system’s state. So for example, in the case of a system of gas particles the microstate gives the position and momentum of every particle in the system. But for practical purposes that’s too much information. To see if there’s anything interesting going on we need to look at the state of a system at a lower resolution, at its macrostate. The procedure of moving from the maximal information of microstates to the lower resolution of macrostates is called coarse graining. In coarse graining we divide the phase space up into large regions that contain groups of microstates that are macroscopically indistinguishable. We can represent this pictorially as a surface divided up into regions of different sizes. The states in a shared region are not microscopically identical. In the case of a system of particles, the states have different configurations of positions and momenta for the particles composing them. But the states in the shared region are macroscopically indistinguishable, meaning that they share some macroscopic property. Examples of such macroscopic properties for a gas are temperature, pressure, volume, and density.
The size of a macrostate is given by the number of microstates included in it. Macrostates of phase spaces can have very different sizes. Some states are very unique and occupy tiny regions of the phase space. Other states are very generic and occupy enormous regions. A smaller macrostate would be one where there are fewer microstates that could produce it. It’s more unique. Larger phase spaces are more generic. An example of an enormous macrostate region is thermodynamic equilibrium. Thermodynamic equilibrium is a condition in which the macroscopic properties of a system do not change with time. So, for example, macroscopic properties like temperature, pressure, volume, and density would not change in thermodynamic equilibrium. The reason the space of thermodynamic equilibrium is huge is because it contains a huge number of macroscopically indistinguishable microstates. What this means is that a condition of thermodynamic equilibrium can be realized in an enormous number of ways. In a gas for instance, the particle can have an enormous number of different configurations of positions and momenta that make no difference to the macroscopic properties and that all manifest as a condition of thermodynamic equilibrium. The system will continue to move through different microstates with time, tracing out a curve in phase space. But because the macrostate of thermodynamic equilibrium is so huge the curve will remain in that region. The system is not going to naturally evolve from thermodynamic equilibrium to some more unique state. It is so statistically unlikely to be, for our practical considerations, a non-possibility.
I think of the Biblical תֹהוּ וָבֹהוּ (tohu va-bohu) as a kind of thermodynamic equilibrium. It’s not necessarily that there’s nothing there. But in a sense, nothing is happening. Sure, individual particles may be moving around, but not in any concerted way that will produce anything macroscopically interesting.
This thermodynamic equilibrium is the state toward which systems naturally tend. The number of indistinguishable microstates in a macrostate, the size of a macrostate, is quantified as the property called entropy. Sometimes we talk about entropy informally as a measure of disorder. And that’s well enough. It also corresponds nicely, albeit inversely, to the notion of structure. More formally, the entropy of a macrostate is correlated (logarithmically) to the number of microstates corresponding to that macrostate. Using the intuition of the informal notion of disorder you might see how a highly structured macrostate would have fewer microstates corresponding to it. There aren’t as many ways to put the pieces together into a highly structured state as there are to put them into a disordered state.
Some notions related to structure, like meaning or function, are fairly informal. But in the case of entropy it’s actually perfectly quantifiable. And there are equations for it in physics. If the number of microstates for a given macrostate is W, then the entropy of that macrostate is proportional to the logarithm of W, the logarithm of the number of microstates. This is Boltzmann’s equation for entropy:
S = k log W
in which the constant k is the Boltzmann constant, 1.381 × 10−23 J/K and entropy has units of J/K. This equation for entropy holds when all microstates of a given macrostate are equally probable. But if this is not the case then we need another equation to account for the different probabilities. That equation is:
S = -k ∑ pi log pi
or equivalently,
S = k ∑ pi log (1/pi)
Where pi is the probability of each microstate. This reduces to the first equation if the probabilities of all the microstates are equal and pi = 1/W.
How might W look differently for different macrostates? It’s fairly easy to imagine that a state of thermodynamic equilibrium would have a huge number of indistinguishable microstates. But what if the system has some very unusual macrostate? For example, say all the gas particles in a container were compressed into a tiny region of the available volume. This could still be configured in multiple ways, with many microstates, but far fewer than if they were distributed evenly throughout the entire volume. Under such constraints the particles have far fewer degrees of freedom and the entropy of that unusual configuration would be much lower.
Let’s think about the different sizes of macrostates and the significance of those different sizes in another way, using an informal, less technical, literary example. One of my favorite short stories is La biblioteca de Babel, “The Library of Babel”, by Argentine author Jorge Luis Borges. Borges was a literary genius and philosophers love his stories. This is probably the story referred to most, and for good reason. In La biblioteca de Babel Borges portrays a universe composed of “an indefinite and perhaps infinite number of hexagonal galleries”. This universe is one vast library of cosmic extension. And the library contains all possible books. “Each book is of four hundred and ten pages; each page, of forty lines, each line, of some eighty letters… All the books, no matter how diverse they might be, are made up of the same elements: the space, the period, the comma, the twenty-two letters of the alphabet.” So there are bounds set to the states this library or any of its books can take. But this still permits tremendous variability. As an analogy with statistical mechanics we can think of the Library of Babel as a phase space and of each book as a microstate.
Daniel Dennett has referred to the Library of Babel in his philosophy and proposed some of the books that, under the conditions set by Borges, must be understood to exist in this library: “Somewhere in the Library of Babel is volume consisting entirely of blank pages, and another volume is all question marks, but the vast majority consist of typographical gibberish; no rules of spelling or grammar, to say nothing of sense, prohibit the inclusion of a volume… It is amusing to think about some of the volumes that must be in the Library of Babel somewhere. One of them is the best, most accurate 500-page biography of you, from the moment of your birth until the moment of your death. Locating it, however, would be all but impossible (that slippery word), since the Library also contains kazillions of volumes that are magnificently accurate biographies of you up till your tenth, twentieth, thirtieth, fortieth… birthday, and completely false about subsequent events… Moby Dick is in the Library of Babel, of course, but so are 100,000,000 mutant impostors that differ from the canonical Moby Dick by a single typographical error. That’s not yet a Vast number, but the total rises swiftly when we add the variants that differ by 2 or 10 or 1,000 typos.” (Darwin’s Dangerous Idea)
A key takeaway from this fantastical story is that only an infinitesimal portion of its volumes are even remotely meaningful to readers. The vast majority of the books are complete nonsense. The Library of Babel is a little easier for me to think about in certain ways than phase space. For many things I’m not sure how to generate a phase space by picking out specific properties and assigning them axes onto which individual states would project with numerical coordinates. A lot of things don’t easily lend themselves to that kind of technical breakdown. But thinking of microstates and macrostates more informally, let’s just take the macrostate of all the books in the Library of Babel that are completely meaningless. This would be a huge macrostate comprising the vast majority of the library, the vast majority of its books, i.e. microstates. As with thermodynamic equilibrium this is the most likely macrostate to be in. And the evolution system, moving from one book to the next, will more than likely never leave it, i.e. will never find a book with any meaningful text.
But the Library of Babel does contain meaningful texts. And we could coarse grain in such a way to assign books to different macrostates based on the amount of meaningful text they contain. After the macrostate containing books of complete nonsense the next largest macrostate will contain books with a few meaningful words. The macrostates for books with more and more meaningful words get successively smaller. And even smaller macrostates when those words are put into meaningful sentences and then paragraphs. The smallest macrostates will have entire books of completely meaningful text. But as any book browser knows, books vary in quality. Even among books of completely meaningful text some will be about as interesting as an online political flame war. The macrostates of literary classics and of interesting nonfiction will be comparatively miniscule indeed.
We can think of a book in the Library of Babel as a kind of message. And this is to start thinking about in terms of another technical field that I think is relevant to a philosophy of structure. And that is information theory. Information theory has some interesting parallels to statistical mechanics. And it even makes use of a concept of entropy that is very similar to the thermodynamic concept of entropy. In information theory this is sometimes called Shannon entropy, named after the great mathematician Claude Shannon. The Shannon entropy of a random variable is the average level of “information”, “surprise”, or “uncertainty” inherent in the variable’s possible outcomes. It’s calculated in a very similar way to thermodynamic entropy. If Shannon entropy is H and a discrete random variable X has possible outcomes x1,…,xn, with probabilities P(x1),…,P(xn), then the entropy is calculated by the equation:
H(X) = – ∑ P(xi) logb (xi)
That equation should look very familiar because it’s identical in form to the equation for thermodynamic entropy, in the case where the microstates have different probabilities. The base of the logarithm is b, often base 2, with the resulting entropy being given in units of bits. A bit is a basic unit of data that represents a logical state with one of two possible values. So for example, whether a value is 0 or 1 is a single bit of information. Another example is whether a coin toss result is heads or tails.
An equation of this form gives an average quantity. The value -log pi, or equivalently log (1/pi), is the “surprise” for a single outcome and so has a higher value when its probability is lower, which makes sense. More improbable outcomes should be more surprising. When the surprise values for all the outcomes, multiplied by their respective probabilities are summed together, i.e. the average surprise, the total is the Shannon entropy. This average quantity can also be used to calculate the total information the message contains. It’s equal to the entropy of the message per bit, multiplied by the length of the message. That gives the total information content of the message.
This is an extremely useful way to quantify information and this is just a taste of the power of information theory. Even so I don’t think it exhausts our notions of what information is, or can be. Daniel Dennett makes a distinction between Shannon information and semantic information (From Bacteria to Bach and Back). Shannon information is the kind of information studied in information theory. To explore this distinction let’s return to Borges’s library.
One thing I like about La biblioteca de Babel is the way it conveys the intense human reaction to semantic meaning, or the incredible lack of it in the case of the library’s inhabitants. The poor souls of the Library of Babel are starving for meaning and tortured by the utter senselessness of their universe, the meaningless strings of letters and symbols they find in book after book, shelf after shelf, floor after floor. There’s a brilliant literary expansion of Borges’s library in the novella A Short Stay in Hell by Steven L. Peck, in which one version of Hell itself actually is the Library of Babel, with the single horrific difference that its inhabitants can never die.
In terms of Shannon information most books on the shelves of the Library of Babel contain a lot of information. But almost all the books contain no semantic information whatsoever. This is an evaluation we are only able to make as meaning-seeking creatures. Information theory doesn’t need to make distinctions about semantic meaning. It doesn’t need to and is able to accomplish its scope of work without it. But when we’re thinking about structures, with meaning and functions, in the way I’m trying to, we need that extra level of evaluation that is, at least for now, only available to humans.
That’s not to say there’s an absolute, rigid split between the objective and subjective. Information theory makes use of the subjective phenomena of human perceptions like sight and sound. This is critical to perceptual coding. We’re all beneficiaries of perceptual coding when we use jpeg images, mp3 audio files, and mp4 video files. These are all file types that compress data, with loss, by disposing of information that is determined to be imperceptible to human senses.
That’s getting a little closer to semantic information. Semantic information doesn’t have to be transmitted word for word. Someone can get the “gist” of a message and convey it with quite high fidelity, in a certain sense anyway. The game of telephone notwithstanding, we can share stories with each other without recording and replaying precise scripts of characters or sound wave patterns. We can recreate the stories in our own words at the moment of the telling.
That’s not to say that structure has to be about perception. Something like a musical composition or narrative has a lot to do with perception and aesthetic receptivity. But even compositions and narratives can contain structure that few people or even no people pick up on. And there are also structures in nature and in mathematics that remain hidden from human knowledge until they are discovered.
I think there are some affinities between what I will informally call the degree of structure in the hidden and discovered structures in nature and mathematics and the degree to which the outputs of those structures can be compressed. Data compression is the process of encoding information using fewer bits than the original representation. How is that possible? Data compression programs exploit regularities and patterns in the data and produce code to represent the data more efficiently. Such a program creates a new file using a new, shorter code, along with a dictionary for the code so that the original data can be restored. It’s these regularities and patterns that I see being characteristic of structure. This can be quantified in terms of Kolmogorov complexity.
The Kolmogorov complexity of an object is the length of the shortest computer program that produces the object as output. For an object with no structure that is completely random the only way for a computer program to produce the object as an output is just to reproduce it in its entirety. Because there are no regularities or patterns to exploit. But for a highly structured object the computer program to produce it can be much shorter. This is especially true if the output is the product of some equation or algorithm.
For example an image of part of the Mandelbrot set fractal might take 1.61 million bytes to store the 24-bit color of each pixel. But the Mandelbrot set is also the output of a simple function that is actually fairly easy to program. It’s not necessary to reproduce the 24-bit color of each pixel. Instead you can just encode the function and the program will produce the exact output. The Mandelbrot set is a good example for illustration because the fractal it produces is very elegant. But the same kind of process will work with any kind of function. Usually the program for a function will be much shorter than the data set of its output.
Often scientific discovery is a matter of finding natural structures by working backward from the outputs to infer the functions that produce them. This is the project of trying to discover the laws of nature. Laws are the regularities and patterns at work in nature. The process can be tricky because there are often many confounding factors and variables are rarely isolated. But sorting through all that is part of the scientific process. As a historical example, Johannes Kepler had in his possession a huge collection of astronomical data that had been compiled over decades. Much of it he had even inherited from his mentor Tycho Brahe. What Kepler was ultimately able to do was figure out that the paths traced out by the recorded positions of the planets in space were ellipses. The equation for an ellipse is fairly simple. Now knowing that underlying regularity makes it possible not only for us to reproduce Brahe and Kepler’s original data sets. But we can retrodict and predict the positions of planets outside those data sets, because we have the governing equations.
That kind of pattern-finding often works well in discerning natural structures. It’s less relevant to human structures where creativity, novelty, and unpredictability can actually be features of greater aesthetic structure. It’s for reasons like this that my approach to a philosophy of structure is highly varied and somewhat unsystematic, pulling pieces together from several places.
Structure seems especially important in the arts and a philosophy of structure in the arts will necessarily overlap with the study of aesthetics. It’s really creative, artistic structures that I find most interesting of all.
Dieter F. Uchtdorf talked about human creativity in a way that I think touches on the key aesthetic features of structure. He said: “The desire to create is one of the deepest yearnings of the human soul… We each have an inherent wish to create something that did not exist before… Creation brings deep satisfaction and fulfillment. We develop ourselves and others when we take unorganized matter into our hands and mold it into something of beauty.” (italics added) A number of important ideas here. I’ll focus on two: (1) that creation is bringing into existence something that did not exist before and (2) that creation is a process of taking unorganized matter and molding it into something of beauty. This coheres with the idea I proposed earlier of the Hebrew creation story, that the lack of form, or structure, in the primordial chaos could be understood also as a kind of emptiness, or nothingness. By imposing a new structure onto raw, unorganized materials it’s possible to bring into existence something that did not exist before.
This is similar to Aristotle’s idea of a formal cause. In Aristotle’s metaphysics he identified four kinds of causes: material, formal, efficient, and final. We’ll just look at the first two here. The material cause is the raw material that composes whatever is being brought about. If we want to understand how a wooden table is created the material cause is the wood used to make it. That’s the unorganized matter. The formal cause is the form, arrangement, shape, or structure, into which this material is fashioned. Clearly the formal cause is just as important to bringing the object about.
The ways we evaluate structure and its aesthetic virtues, its beauty, is a complex subject. Are aesthetic criteria objective or subjective? The aesthetic response is certainly a subjective process. But is the subjective response a consistent and law-like process that correlates to objective features? It’s difficult to say.
David Bentley Hart said of aesthetics: “The very nature of aesthetic enjoyment resists conversion into any kind of calculable economy of personal or special benefits. We cannot even isolate beauty as an object among other objects, or even as a clearly definable property; it transcends every finite description. There have, admittedly, been attempts in various times and places to establish the ‘rules’ that determine whether something is beautiful, but never with very respectable results… Yes, we take pleasure in color, integrity, harmony, radiance, and so on; and yet, as anyone who troubles to consult his or her experience of the world knows, we also frequently find ourselves stirred and moved and delighted by objects whose visible appearances or tones or other qualities violate all of these canons of aesthetic value, and that somehow ‘shine’ with a fuller beauty as a result. Conversely, many objects that possess all these ideal features often bore us, or even appall us, with their banality. At times, the obscure enchants us and the lucid leaves us untouched; plangent dissonances can awaken our imaginations far more delightfully than simple harmonies that quickly become insipid; a face almost wholly devoid of conventionally pleasing features can seem unutterably beautiful to us in its very disproportion, while the most exquisite profile can do no more than charm us… Whatever the beautiful is, it is not simply harmony or symmetry, or consonance or ordonnance or brightness, all of which can become anodyne or vacuous of themselves; the beautiful can be encountered—sometimes shatteringly—precisely where all of these things are deficient or largely absent. Beauty is something other than the visible or audible or conceptual agreement of parts, and the experience of beauty can never be wholly reduced to any set of material constituents. It is something mysterious, prodigal, often unanticipated, even capricious.” (The Experience of God)
These are good points. Aesthetic judgment is difficult to systematize. And I can’t say I know of any theory that successfully defines precise evaluative procedures from objective criteria. But neither is that to say that aesthetic judgment is arbitrary. There are easy cases where there is near universal agreement that artistic creations are of high or low quality. And there are also harder cases where appreciation for high quality art requires refined tastes, refined through training and initiation into an artistic practice. Even the best critics are not able to fully articulate their reasons for making the judgments they do. And they may have imprecise vocabulary that is incomprehensible to those outside the practice. Sommeliers and wine tasters, for example, have a vocabulary for their craft that goes completely over my head (and taste buds). But I don’t doubt that the vocabulary is meaningful to them. I believe all these artforms have structures to which we can refer, if only imprecisely.
Having looked briefly in this episode at some general ideas pertaining to structure, what I want to do in following episodes for the series is look closely at examples of structure in more detail, focusing on individual fields, one at a time. Like music, chemistry, biology, language, social and political organizations, and mathematics. I expect that the characteristics of structure in these different cases will be varied. But I hope that as the coverage gets more comprehensive it will give more opportunity for insight into the general nature of structure. I hope through some inductive and abductive reasoning to infer general patterns of structure across these various domains, to understand a general structure of structure.
In two competing accounts the origin of human rights has been framed as a product of Christian moral teachings or as a process of rejecting and overcoming oppressive religious superstitions. Where do human rights come from? The Christian origins are significant but a more complete account should also address additional historical factors that helped to activate and further shape our conception of human rights in modern times.
In a previous episode on the Nature of Divine Law I talked about Christine Hayes’s historical study of the biblical tradition and Greek thought and her comparison of their conceptions of the nature of divine law, along with some comments on my own perspective in response to both of these conceptions. As a recap, the difference as she framed it, was that in Greek thought “divine law is divine ‘because it expresses the profound structures of a permanent natural order’… Divine law is an element operating within the physical world and our natures, rather than something imposed upon the world by a god from without.” Whereas in the biblical tradition “the law is divine ‘because it emanates from a god who is master of history’… It is the expression of a personal divine being’s will, which can take the form of detailed written instruction and legislation.” Another way of saying this is that in the Greek conception divine law is internally justified. It is self-contained and right in virtue of itself, much like a logical or mathematical proof. Whereas in the biblical tradition divine law is justified because it is declared from the mouth of God. It is right because God says it is right. Personally I’ve found a synthesis of these two positions most tenable, as I talked about in that earlier episode. But I’d like to pick up on these ideas and look at them with another set of questions.
One of the issues I’ve been considering a lot recently is the problem of fitting together two highly contestable ideas that both seem right to me but that don’t fit very well with each other. The first idea is that the biblical tradition forms the basis of the liberal values of Western culture and our modern ideas of human rights. The second idea is that the our modern ideas of human rights only really took off after seventeen hundred years of Christian history. So what took so long? That’s the big question for me. If Christianity is foundational to human rights why didn’t the Universal Declaration of Human Rights emerge in the first century rather than in the twentieth century?
I mentioned that both of these ideas are highly contestable. So it’s worth addressing the matter of whether they’re even true in the first place. First then, does the biblical tradition actually form the basis of the liberal values of Western culture and our modern ideas of human rights?
There was a debate over this question between Tom Holland and A.C. Grayling in 2019, with Holland arguing that Christianity historically gave us our human values and Grayling arguing that it did not. Tom Holland actually wrote a book on the subject called Dominion: How the Christian Revolution Remade the World, in which he made a detailed case for this. Steven Pinker by contrast, in his 2011 book The Better Angels of Our Nature: Why Violence Has Declined, is very dismissive of religion as a force for peace and human rights. In his view the decline in violence and rise of respect for human rights has occurred apart from and even in spite of religion and in spite of Christianity in particular. In fact he argues that it’s often been a process of overcoming and rejecting Christianity’s illiberal tendencies. I’ve read both Holland’s and Pinker’s books and recently watched the Holland-Grayling debate. I actually think both sides make some good points. Neither side is completely wrong. But neither side is completely right either. So I think the fuller picture is more complex.
What about the second idea, that the liberal values of Western culture and our modern ideas of human rights only really took off after seventeen hundred years of Christian history? This idea is also contested by defenders of Christianity. And much of this may be as a reaction to the excesses of anti-religious and anti-Christian polemics that have distorted the historical narrative, particularly in popular consciousness. The historical distortion is not new. Even going back to Petrarch, who lived from 1304 to 1374, Renaissance figures tried to contrast what they considered their enlightened and open perspective to what they portrayed as the medieval “Dark Ages”. And this narrative has persisted and been repurposed through the Enlightenment and into the present day. And a counter-reaction has been warranted. The negative portrayal of the middle ages isn’t fair. They weren’t the bleak dystopian nightmares they’ve been made out to be. Many of the purported anti-intellectual offenses of Christianity, destroying libraries and burning classical texts, are either distortions or fictions. Tom Holland as well as David Bentley Hart, in his contentiously titled book Atheist Delusions, address many of these popular misunderstandings.
Something both Holland and Hart address as well is that it’s really just not the case that no change in values took place in the first century. One of the important features of the preceding classical moral outlook is the different value it placed on the lives of different classes of people, ranging from nobles to slaves. It wasn’t the case that all human lives were of the same value or equal dignity. The highest value was for “the best”, the ἄριστος (áristos) in Greek, from which we get the word “aristocracy”. That was just natural. But then Jesus came along and taught, in quite a revolution of values, that what matters is how we treat “the least”, the ἐλάχιστος (eláchistos). A complete reversal and a conceptual revolution. So that was a big change that indeed started in the first century. So it’s not like nothing happened for the first seventeen hundred years.
Still, I think the biggest changes have come about in the last two or three hundred years. What’s interesting to me as a Christian is that I think we’re closer now to living consistently with the teachings of Jesus than at any other time in history. We still have a long way to go. But we’re closer. Closer than at any other time in the centuries leading up to modern times, at least at the scale of large states. I think modern critics of Christianity like Grayling and Pinker have a point when they say that Christianity has indeed coexisted with and even encouraged a lot of cultural values and practices that have been illiberal and offensive to our modern ideas of human rights. But when I look at the ideas of Jesus, at just a conceptual level, as in the Sermon on the Mount, they seem not only consistent with human rights but even surpass our modern notions of human rights. So what might that imply?
In general, what are a few ways we could say that one thing has caused another, like Christianity leading to human rights? Say A causes B. Just as abstract variables for a moment. Say we have B. B occurs. Consider three ways of looking at the relationship of A to B, given that B occurs:
1. B would not have occurred if A had not occurred. 2. B would not have occurred if either A or C had not occurred. 3. B would not have occurred if both A and D had not occurred.
Those are abstract so let’s apply it to the issue at hand. What does it mean to say that Christianity led to the development of the liberal values of Western culture and our modern ideas of human rights?
Let’s take case 1, where B would not have occurred if A had not occured. The application here would be that without Christianity human rights would not have developed; we wouldn’t believe in human rights and there would be no such thing. I think we really need to entertain that possibility. One of the things Tom Holland said a few times in his debate with A.C. Grayling is that it’s important to recognize that our values of human rights are contingent. We could easily not believe in human rights in the way we do. And I think that’s true. We might imagine that we would just inevitably deduce human rights naturally through reason, but I find that highly unlikely. Moral philosophy through the Enlightenment has basically been a process of trying to back-calculate and rationally justify the values that we had already inherited through tradition. And even having a cheat sheet, knowing the “right answer” that we were supposed to arrive at, none of these efforts has been especially convincing. Some of them have been internally consistent and viable by their own standards. But they fail to conclusively ground the human rights we want them to ground. In other words, these rational systems don’t exclude the kinds of actions we would want to consider unjustifiable, to be violations of human rights. Utilitarianism, for example, can rationally justify many violations of human rights of individuals for the benefit of a larger number of people. Which is fine if you don’t care about human rights. But it’s a problem if you do. Alasdair MacIntyre gives an extensive overview of this in his book After Virtue in his chapters on “The Enlightenment Project of Justifying Morality” and “Why the Enlightenment Project of Justifying Morality Had to Fail”. This is one reason I think we wouldn’t just rationally deduce our notions of human rights if we didn’t already have them.
Another reason I think we would not, out of necessity, just arrive at human rights without some kind of traditional basis for them is that many cultures in the past and even today just don’t believe in human rights in the way we do. So it’s definitely a human possibility. Not only a possibility but a human reality. It might be hard for us to imagine our own culture not believing in human rights because we are so embedded in it as a culture that it just seems normal. Everything that shapes our imagination, including our ability to imagine our culture being other than it is, is also influenced by the culture itself. That’s not to say that it’s impossible to think outside our cultural horizon. But it’s a challenge. So I think Holland is right to say that human rights are contingent. And maybe without the historical heritage of Christianity we wouldn’t believe in them.
Let’s take case 2, where B would not have occurred if either A or C had not occurred. In other words, if A does not occur B might still occur, but for some other reason, such as if C occurs. The application here would be that even without Christianity, something else might have inspired our belief in human rights. Maybe some other tradition. A.C. Grayling noted that Christian ideas like the Golden Rule have been expressed in other traditions and that many religions of the Axial Age (8th to 3rd century B.C.) had ideas that could lead to human rights. I think that’s a fair point. I’m a Christian but I know that many of the same insights of Christianity are found in other traditions. And I think that’s a good thing. And I certainly think it’s possible for human rights to be grounded in other cultures through these traditions. That’s actually important to think about as we try to generalize human rights worldwide. Still, I think it is the case that in the West it was Christianity that was the traditional vehicle for these ideas, even if it might have been otherwise.
And now, let’s take case 3, where B would not have occurred if both A and D had not occurred. The application here would be that Christianity is one factor that leads to the development of human rights, but it’s not the only one and it’s not enough by itself. Other factors are needed to contribute to this development. I want to focus on this case from here on out because it’s the one I find most convincing. Recall my two ideas that are in tension with each other: that Christianity forms the basis for human rights in the West and that human rights only really took off after seventeen hundred years of Christian history. Why? This third case gives a possible explanation. Christianity was one vital component, but the human rights revolution, in which societies made dramatic shifts toward actually putting the ideals of Jesus’s teachings into practice, required additional circumstances that did not come about before the eighteenth century.
This is basically the position of German sociologist Hans Joas in his book The Sacredness of Persons: A New Genealogy of Human Rights. Joas gives a historical account and philosophical explanation of the “genealogy” or historical origin of human rights by way of a process he calls the “sacralization of the person”, a process in which every human being comes to be viewed as sacred. In his book Joas sets up the same problem I’ve proposed for understanding the Christian foundations of human rights:
“Traditions do not perpetuate themselves but are sustained through the actions of individuals. Even if we concede, at least retrospectively, that human rights may to some extent be considered a modern rearticulation of the Christian ethos, we must be able to explain why it took seventeen hundred years for the Gospel to be translated into legally codified form in this regard.”
For Joas a proper historical explanation must refer to changes in values, institutions, and practices, as well as their historical precursors such as demographic changes, movements of populations, economic and political developments, etc. It’s not that human rights aren’t a modern rearticulation of the Christian ethos. He believes they are. But it’s a question of what caused this modern rearticulation when it happened.
Joas sets up a contrast between two perspectives on human rights that I find similar to the two perspectives on divine law that Christine Hayes identifies in the biblical tradition and in Greek thought. For Joas the two perspectives on human rights are those typified by two great German philosophers: Immanuel Kant and Friedrich Nietzsche. For the Greeks, according to Hayes, divine law is rational and beyond historical contingencies. Whereas in the biblical tradition divine law is given by God acting in history, to particular groups of people, at particular times and places. Joas similarly contrasts rational and historical bases for human rights in the Kantian and Nietzschean schools of thought. By pursuing a “new genealogy” Joas is following the Nietzschean school of thought. But unlike Nietzsche his genealogical project is affirmative rather than destructive. He doesn’t wish to undermine human rights, but rather to show how they have emerged historically, so that we can better understand them.
In contrast to the Kantian position Joas says he does “not believe in the possibility of a purely rational justification for ultimate values.” But he also says that “unlike Nietzsche, [he does] not assume that discovering the genesis of values removes the scales from our eyes to reveal the false gods and idols we have believed in.” That’s why his genealogy of human rights is affirmative. He says: “As a narrative, such an account makes us aware that our commitment to values and our notion of what is valuable emerge from experiences and our processing of them; this shows them to be contingent rather than necessary. Values no longer appear as something pregiven that we merely have to discover or perhaps reestablish.”
This kind of contingency of morality and rights, that they might have been otherwise or might not have been at all, is another thing I’ve thought a lot about recently both in philosophy and in theology. Philosophically my primary resource on the subject of contingency is Richard Rorty. And theologically my resource on contingency is James K.A. Smith. Smith is quite interesting because he also gives insightful commentary on Rorty. And I think both have ideas that cohere well with Joas’s points about the contingent, but still valid nature of human rights.
Rorty addresses contingency and its implications for liberalism quite directly in his book Contingency, Irony, and Solidarity. In spite of the contingent, non-essential nature of human rights we are not prevented from standing in solidarity with each other and affirming those ideas anyway. We can still make that choice. James K.A. Smith, in his book Who’s Afraid of Relativism? Community, Contingency, and Creaturehood takes this idea of contingency, appropriating many ideas from Rorty directly, and applies them to Christian ideas of creaturehood and community. Smith affirms the theological notion of our contingent existence, as opposed to God’s necessity. God exists of necessity. He cannot not be, by his very nature as the one who is: אֶֽהְיֶ֖ה אֲשֶׁ֣ר אֶֽהְיֶ֑ה (ehyeh asher ehyeh), “I AM THAT I AM” (Exodus 3:14). We however, do not exist necessarily. We are created. And so we are contingent. We could not exist. But we do exist because God created us. Much like human rights, I think. Human rights could not exist. They don’t exist out of necessity. Even morality, or “The Law”, as in certain expressions of the biblical tradition, is created. But from this we don’t need to despair that morality and human rights are merely arbitrary. In the biblical tradition The Law is covenantal, but it is not lesser for that fact. From a certain perspective that gives us the benefit of being invested in it by taking the direct action to enter into that covenant. Whether by covenant, in the biblical view, or by solidarity, in Rorty’s secular view, the contingency of morality and human rights can be just as compelling as ever.
So if human rights are contingent and have historical origins what are those historical factors that have contributed to their development into the form we hold them today? I’m more convinced of the idea that there are such historical factors than I am about any particular set of factors. But I have some ideas. And I’ll share the ones put forward by Hans Joas in his book that I find most convincing. I’ll mention four: the Protestant Reformation, the American Revolution, American slavery, and the two World Wars.
I’ll start with the American Revolution and work my way back chronologically to the Reformation because the two are closely connected in Joas’s account. And actually Joas is basing his ideas off the work of another German scholar, Georg Jellinek (1851-1911). In his book The Declaration of the Rights of Man and of Citizens: A Contribution to Modern Constitutional History, Jellinek had argued that the French Declaration of the Rights of Man, was significantly influenced by and modeled on the American Revolution and the American Declaration of Independence and American Bill of Rights. This is interesting, not just as a matter of patriotism (yeah, I’m a proud American but Joas and Jellinek are German), but it’s interesting as it relates to the question of why certain ideas of human rights took off as they did in Europe after the French Revolution at the end of the eighteenth century rather than, say, five hundred years earlier, or one thousand years earlier. France and the Ancien Régime, the “Old Regime”, had, as the name implies, been around for a long time. But the situation in America was comparatively novel. Obviously the continent itself wasn’t new. It had very ancient peoples and civilizations. But there was a radically different and new demographic situation on the ground in which large populations from Europe were colonizing the continent, bringing ideas and beliefs from Europe into these regions that were geographically separated from Europe. There were just a lot of new factors at play.
Jellinek’s thesis was that one important feature that characterized the American colonies was how highly they valued being able to practice their own religious denominations. Some communities had been organized specifically for that purpose. And this related to an idea that carried over from the Protestant Reformation. The Reformation was many things. It involved several issues of doctrine that are very interesting and important. But for the purposes of the issue at hand the most significant is the issue of authority. All these denominations continued to have ideas of ecclesiology, the theological study of a church organization. But the critical move was separating the authority of God from the authority of Rome. It wasn’t the eradication of authority. But by separating from Rome the Reformation passed over earthly authorities and looked to transcendent authority in God. And once you have that you’re moving toward something that looks like human rights.
For example, Martin Luther is reported to have said at the Imperial Diet of Worms in 1521: “Unless I am convinced by Scripture and plain reason – I do not accept the authority of the popes and councils, for they have contradicted each other – my conscience is captive to the Word of God. I cannot and I will not recant anything, for to go against conscience is neither right nor safe.” Note his appeal to reason. That almost sounds like the Enlightenment. Luther is claiming a freedom of conscience above and beyond anything codified by earthly authorities. And that is a challenge not only to the proper exercise of authority but also to the legitimate extent of authority itself, at least apart from God. That’s starting to look a lot like human rights that neither illegal nor legal authority can violate.
Here’s a passage from Joas on this point: “[Jellinek] was also correct to point out that there is a difference between theories of natural law and the legal codification of specific individual rights intended to hold for all people and removed from legislative authority. ‘The assertion of objective moral and legal limits to all worldly powers,’ writes Hasso Hofmann, agreeing with Jellinek, does not itself equate with ‘a theory of subjective rights. The idea of constitutional freedom and security against illegal tyranny is not equivalent to the human rights idea of basic, individual freedoms and protection against legal tyranny.’”
Once you bypass that earthly seat of authority, as in Rome, you place your source of authority above earthly powers, not only in theory, as it always had been, but also in practice. After the Reformation we’re in an era where people can actually disobey the papacy and its authority, get away with it, and truly believe that they’re authorized in doing so. That’s a new experience. And of course that all started and happened in Europe but in America it gets intensified. People are not only living under cuius regio, eius religio, the system in which you could have different religions in different kingdoms, depending on the religion of the ruler: “whose realm, their religion”. In America we get smaller, purposefully created communities with localized religious authority.
On this point Joas also refers to the work of German theologian Ernst Troeltsch (1865-1923) who “recognized the transformative effects that Enlightenment thought exerted on Protestant Christianity in North America.” This unique situation in the American colonies also produced a curious synergy with religious thought and Enlightenment thought. I can see from Luther’s appeal to reason how this would come about. In the Protestant doctrine of sola scriptura, the doctrine that Christian scriptures are the sole infallible source of authority for Christian faith and practice, the new necessity was for individual Christians to read the Bible and to understand it for themselves. And it is in this reading and interpretation of the Bible that we find the ultimate source of authority, rather than in Popes and priests. That is substantial breakthrough for independent thinking. And this is how the American colonists learn to think, as independent readers and thinkers. “In a well-known phrase, Americans in the eighteenth century learned their Enlightenment from the pulpit.”
So we could point out two things here. One, and this was more the point that Jellinek was making, is that the Enlightenment in America was highly religious in nature. But another point that I think addresses my question, is that religion in America was also highly Enlightened, it had a strong Enlightenment flavor that was new in Christian history. Christianity in America was wrapped up in supporting notions of independence from earthly authorities and independent, rational verification of the meaning of Christian doctrines through the actual reading and study of scripture. Something that literacy and the availability of printed Bibles no doubt also enabled. So you’ve got a whole set of new historical developments: technological developments, movements of large populations, major shifts in the balance of political powers. And these things are producing novel situations that influence the way Christianity is practiced and thought about. And that feeds back into the way Christianity influences the culture, so that Christian ideas that had been dormant before will start to exercise more live influence.
So we have the Reformation and the American Revolution, which influences the French Revolution, which shakes up all of Europe. Another factor Joas touches on is American slavery. He talks about this in a chapter titled “Violence and Human Dignity: How Experiences Become Rights”. This is the same chapter in which he address the two World Wars and the Shoah (or Holocaust), which we’ll get to next. The idea he proposes in the chapter is that our conception of human rights is also contingent on particular historical experiences of atrocity, or trauma. We respond to these atrocities in the way we develop our ideas about human rights. And the implication of this contingency is that if certain atrocities that happened in history and that appalled people in certain ways had not occurred or if different atrocities had occurred, that our conceptions of human rights would be different than they are. So what are some of the great atrocities that had these significant effects? American slavery is an important one.
Joas lists three components for his explanation as to why conceptions of human rights moved decisively against the institution of slavery in the nineteenth century. It might seem obvious that any notion of human rights should oppose slavery. But this was clearly not the case since, significantly, slavery was countenanced and even defended in America, in many cases by the same people who so forcefully defended what they understood to be the rights of men. The French Revolutionaries went a little further, at least in theory, in their pronouncements against slavery. But when it came to actually ceasing to think of human beings as property, as in the French slave colony of Saint-Domingue, today Haiti, they fell far short. So what set this particular advance of the “sacralization of the person” in motion? The three components Joas lists are:
1. “Intensification of the motivation to put into practice a universalist morality that already exists in principle.” 2. “A sociostructurally induced expansion in the cognitive attribution of moral responsibility.” 3. “The practical transnational organization of moral universalism.”
As in the case with the Reformation, trans-Atlantic colonization, etc., we’re looking for factors that make something happen that didn’t happen before. In this case an expansion of conceptions of human rights against slavery. And these three factors are the ones Joas identifies as the novel circumstances that produced that new development.
Joas acknowledges that a universalist morality already existed in principle in Christianity. For example, we see a universalist message in Acts 10 with Peter’s vision of a sheet with unclean animals on it, descending from heaven. Peter is told to eat the unclean animals and he resists because it goes against his traditional dietary laws. But he is told: “What God has cleansed, do not call common” (Acts 10:15). There is no longer to be that kind of separation. Peter was instructed to open the ministry to all people, regardless of ethnicity, to Jew and Gentile alike. We also see a strong universalism in Paul, the Apostle to the Gentiles. For Paul the Gospel was for παντὶ τῷ πιστεύοντι (pantí to pisteúonti), “everyone who believes”, he says to the Jew and to the Greek, i.e. everyone (Romans 1:16). In the Epistle to the Ephesians it is said: “You are no longer strangers and foreigners, [ξένοι καὶ πάροικοι (ksénoi kai pároikoi)] but fellow citizens with the saints and members of the household of God” (Ephesians 2:19). Such distinctions are being broken down. So the universalist ideas are there. That morality already exists in principle. But Joas claims there’s an intensification of the motivation to put this into practice.
He attributes this intensification in the nineteenth century United States to the particular revivalist form of religious practice taking place there:
“Slavery was declared a sin, while resistance to it signaled that individuals meant to live a life that truly reflected Christ’s moral demands. They tended to be particularly outraged when slaveholders and their supporters opposed the evangelization of the slaves and thus Christ’s Great Commission. The antislavery movement became part of the intermittent revivalist movements. These movements cannot be described simply in terms of their religious content; above all we must consider their specific dynamics. Here prophetic speakers castigated misdeeds as sinful and interpreted them as an occasion for repentance. Such discourse may set in motion major collective processes of moral reorientation that we cannot trace back to the interests of those involved. Indeed, through such processes they learn to completely redefine their interests. Here the adoption of religiously practiced forms of the public confession of sins and assurances of a moral rebirth helped politicize moral objectives.”
Joas sees this revivalist form of religious practice working hand in hand along with the second factor, the sociostructurally induced expansion in the cognitive attribution of moral responsibility, i.e. awareness of increased global interconnectedness. With slavery being part of the domestic and global economy it was impossible not to be a participant in it.
“Our conception of our own moral responsibility depends on cognitive preconditions. If we are to feel responsible, we must make empirical assumptions about the connection between our actions and misdeeds elsewhere. Does what we consume really come from a country in which slaves or forced laborers are involved in production? Also lying on the cognitive level is how we assess our possible intervention… All of our moral positions are embedded in a context of empirical and thus fallible assumptions about the conditions, means, and consequences of our action and that of others and about causal connections between our action and that of others. On the basis of these insights, American historian Thomas Haskell has ingeniously connected the rise of industrial capitalism and the concurrent advance of a ‘humanitarian sensibility’… From this perspective, increasing global interlinkage of social relations, on economic grounds, is a precondition for a movement such as abolitionism. The same process that, for example, allows businesspeople to expand their utility-oriented action across the world, in the slave trade itself but also other activities, enables others to relate a formerly consequence-free moral repudiation of abuses in other places causally to their own conduct. They thus experience a sense of responsibility for putting a stop to these abuses–as a realistic option for action and de facto moral obligation. So with the expansion of market relations, the space for moral responsibility becomes larger, and this is relevant to our actions.”
So here’s another novel situation. The economies of the world are becoming more complex and interconnected. That’s a new material situation on the ground that has implications for the ways that people live and think about their actions. So you can take the same Christian preconditions that were always there and by putting them in this new situation certain issues become much more salient and live issues.
Joas’s third factor for why conceptions of human rights moved against slavery is the practical transnational organization of moral universalism. This is related to the economic factor but there’s also feedback. Once these antislavery ideas start to intensify other nations start looking at each other. Britain ends its slave trade but still depends on it economically through U.S. cotton imports. Then during the Civil War Britain has to decide if it will give military aid to the Confederacy. Well, the whole world is watching now. So they end up rejecting that idea. Slavery is becoming more internationally unacceptable and that accelerates the development of public opinion in other individual nations.
When I think about the historical contingency of slavery and the abolitionist movement one of the things that stands out to me is the Fourteenth Amendment to the United States Constitution, passed in 1868, shortly after the Civil War and the end of American slavery. The Equal Protection Clause of this Amendment has been one of the most significant Constitutional passages in the history of U.S. Supreme Court cases and the American history of civil rights:
“All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside. No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.”
This text is part of our identity as a people now and it’s been a model around the world. And it was created in response to the atrocity of American slavery and subsequent, often successful efforts to curtail the rights of former slaves. Certainly it would have been better for slavery never to have happened. But just as a way of looking at the history of the way human rights developed, it’s noteworthy that it had a major impact on the kinds of things we consider central to the nature of human rights today.
This kind of historical memory embedded into our morality reminds me of the refrain in the Torah, כִּֽי־גֵרִ֥ים הֱיִיתֶ֖ם בְּאֶ֥רֶץ מִצְרָֽיִם (ki gerim hayitem be-aretz mitzraim), “for you were strangers in the Land of Egypt”.
“You shall neither mistreat a stranger nor oppress him, for you were strangers in the land of Egypt.” (Exodus 22:21)
“The stranger who dwells among you shall be to you as one born among you, and you shall love him as yourself; for you were strangers in the land of Egypt: I am the Lord your God.” (Leviticus 19:34)
“Therefore love the stranger, for you were strangers in the land of Egypt.” (Deuteronomy 10:19)
The memory of Egypt and their slavery in it is ever present in the Torah. The Lord repeatedly reminds the people of it. Far from something ahistorical, the Law given by the Lord is given explicit rationale in the events of history. Certain commandments are given in the form that they are, explicitly and self-consciously because of certain events in the past, even great catastrophes, like intergenerational slavery. In this respect I think many of the forms our modern values of human rights take are not so different.
The last events and atrocities of historical significance that I’ll mention in the development of our modern notions of human rights are the two World Wars of the twentieth century. Memory of these events was also explicitly mentioned in the drafting of the Universal Declaration of Human Rights, another canonical text today in our modern understanding of human rights and what we consider to be rights. The Shoah, also known as the Holocaust, certainly stands out as especially significant in our memory and conscience. And that’s definitely a major influence. But there were also many other atrocities even prior to that during these decades that got people thinking about what kinds of rights human beings should have, extending all the way from the rude awakening of World War I to the horrendous events of the Shoah. The influence is mentioned explicitly in the preamble of the Declaration:
“Whereas disregard and contempt for human rights have resulted in barbarous acts which have outraged the conscience of mankind…”
The articles of the declaration are clear responses to these outrages. Here’s an overview of antecedents to various articles in the declaration from Joas:
“The emphasis on the unity of the human race in Article 1 is consciously intended to counter the destruction of universalism in racial theories. The emphasis on the ‘right to life’ in Article 3 was just as consciously inspired by the Nazi ‘euthanasia’ of the disabled. Article 4 opposes slavery and ‘servitude’ in part as a means of denouncing the forced labor among citizens of conquered countries of the kind that occurred during the Second World War in Germany. Article 5 not only declares a ban on torture, but also ‘cruel, inhuman, or degrading treatment or punishment’ in order to preclude crimes such as the medical experiments carried out by National Socialist doctors on death-camp inmates and disabled people. The declaration of the right to asylum in Article 14 (‘Everyone has the right to seek and to enjoy in other countries asylum from persecution’) can be traced back directly to the mass expatriations of the Third Reich… Article 21 declares the right to political participation. This was aimed directly at the fascist doctrine that the true will of the people should be embodied in a leader with unchecked power… Article 30 provides the beginnings of an ‘internationalist’ interpretation of human rights that makes the international community collectively responsible for policies and envisages a legal system consonant with human rights in individual states. This is bound up with the fact that the struggle against National Socialism in Germany before the war was by no means regarded as the responsibility of other states.”
Again we might ask, how would we think about human rights today if history had been different? If the World Wars and the mass scale of carnage had not taken place? Certainly it would have been better if these things had never happened. But it’s another case where we can consider the way particular historical events have shaped our values and how they might have been otherwise. It’s interesting how the ideas of racial sciences and eugenics, which had been very intellectually fashionable in the early decades of the twentieth century, dramatically fell out of fashion to become not only unfashionable but even reprehensible. And we have these strong, visceral reactions to euthanasia of the disabled, medical experiments, and any kind of compulsory “camp” because of the experience and memory of seeing these things being done. For instance, I imagine the internment camps of Japanese and Japanese-American persons during World War II, look a lot different after Auschwitz than before Auschwitz. And we probably react more strongly to the re-education camps of the Uyghurs currently operating in China because of association with the camps of Nazi Germany, though I’d say our reaction is still not strong enough in that particular and ongoing case. We can’t really know these kinds of counterfactuals. But it’s instructive and useful to understand these historical antecedents to our modern ideas of human rights.
So getting back to the issues at the beginning of all this – that the biblical tradition forms the basis of the liberal values of Western culture and our modern ideas of human rights and that these ideas of human rights only really took off in their present form after seventeen hundred years of Christian history – I still think both are true and that there are historical reasons for the delay and eventual emergence. Like I said, I’m more convinced that there are historical reasons for the delay and eventual realization of human rights from their latent form in Christianity than I am about the particular historical accounts I’ve shared here, borrowing from Hans Joas. But I do find his ideas plausible. I still think Christianity is conceptually foundational to the emergence of human rights, even if a number of features were dormant for a very long time. So I don’t think the accounts of human rights that attribute their origin to exclusively Christian or secular ideas are going to be accurate. I find a more complex story more convincing. And as a Christian I appreciate the genius of Christianity in both its realized and its potential forms. And I believe many aspects of Christianity have yet to be realized still. In fact that’s pretty much an assumption of eschatology, the theological study of future and end times. I also appreciate, as a Christian, that God acts in history. Christian morality doesn’t have to be ahistorical. Much as the Universal Declaration of Human Rights refers to particular “barbarous acts which have outraged the conscience of mankind” I can appreciate how the Torah hearkens back to when “you were strangers in the Land of Egypt”. That’s the nature of all this. And I believe thinking about the history of our values can enrich our commitment to them.
Models are critical tools that enable us to think about, qualify, and quantify features of many processes. And as with any kind of tool, different kinds of models are better suited to different circumstances. Here we look at two kinds of models for understanding transport phenomena: causal and emergent models. In a causal process there is some kind of distinct, sequential, goal-oriented event with an observable beginning and end. In an emergent process there are uniform, parallel, independent events with no beginning or end but in which observable patterns eventually emerge.
For the video version of this episode, which includes some visual aids, see on YouTube.
Since my university studies I’ve been fascinated by the ways we use models to understand and even make quantitative descriptions and predictions about the world. I don’t remember when exactly, but at some point I really began to appreciate how the pictures of chemical and physical processes I had in my head were not the way things “really” were (exactly) but were useful models for thinking about things and solving problems.
Conceptual models in science, engineering, economics, etc. are similar to toy models like model cars or model airplanes in that they aren’t the things themselves but have enough in common with the things they are modeling to still perform in similar ways. As long as a model enables you to get the information and understanding you need it is useful, at least for the scale and circumstances you’re interested in. Models are ubiquitous in the sciences and one of the major activities in the sciences is to improve models, generate new models, and create more models to apply to more conditions.
Something to bear in mind when working with a model is the set of conditions in which it works well. That’s important because a model may work very well under a certain set of conditions but then break down outside those conditions. Outside those conditions it may give less accurate results or just not describe well qualitatively what’s going on in the system we’re trying to understand. This could be something like being outside a temperature or pressure range, extremes in velocity or gravitational field strength, etc. And often it’s a matter of geometric scale, like whether we’re dealing in meters or nanometers. The world looks different at the microscopic and molecular scale than at the macroscopic scale of daily life.
I’m really a pluralist when it comes to models. I’m in favor of several types to meet the tasks at hand. Is a classical, Newtonian model for gravity superior to a relativistic model for gravity? I don’t think so. Yeah, a Newtonian model breaks down under certain conditions. But it’s much easier and intuitive to work with under most conditions. It doesn’t make sense to just throw away a Newtonian model after relativity. And we don’t. We can’t. It would be absurdly impractical. And practicality is a major virtue of models. That’s not to say there’s no such thing as better or worse models. A Newtonian model of planetary motion is better than a Ptolemaic one because it’s both more accurate and simpler to understand. So I don’t embrace pluralism without standards of evaluation. I suppose there’d be an infinite number of really bad models in the set of all possible models. Even so, there are still multiple that do work well, that overlap and cover similar systems.
I studied chemical engineering in the university and one of my textbooks was Transport Phenomena by Bird, Stewart, and Lightfoot, sort of a holy trinity of the discipline. Transport phenomena covers fluids, heat, and diffusion, which all share many features and whose models share a very similar structure. One of the ideas I liked in that book is its systematic study of processes at three scales: macroscopic, microscopic, and molecular. I’ll quote from the book for their explanations of these different scales.
“At the macroscopic level we write down a set of equations called the ‘macroscopic balances,’ which describe how the mass, momentum, energy, and angular momentum in the system change because of the introduction and removal of these entities via the entering and leaving streams, and because of various other inputs to the system from the surroundings. No attempt is made to understand all the details of the system.”
“At the microscopic level we examine what is happening to the fluid mixture in a small region within the equipment. We write down a set of equations called the ‘equations of change,’ which describe how the mass, momentum, energy, and angular moment change within this small region. The aim here is to get information about velocity, temperature, pressure, and concentration profiles within the system. This more detailed information may be required for the understanding of some processes.”
“At the molecular level we seek a fundamental understanding of the mechanisms of mass, momentum, energy, and angular momentum transport in terms of molecular structure and intermolecular forces. Generally this is the realm of the theoretical physicist or physical chemist, but occasionally engineers and applied scientists have to get involved at this level.”
I came across an interesting paper recently from a 2002 engineering education conference titledHow Chemical Engineering Seniors Think about Mechanisms of Momentum Transport by Ronald L. Miller, Ruth A. Streveler, and Barbara M. Olds. It caught my attention since I’ve been a chemical engineering senior so I wanted to see how it compared to my experience. And it tracked it pretty well actually. Their idea is that one of the things that starts to click for seniors in their studies, something that often hadn’t clicked before, is a conceptual understanding of many fundamental molecular-level and atomic-level phenomena including heat, light, diffusion, chemical reactions, and electricity. I’ll refer mostly to the examples from this paper by Miller, Streveler, and Olds but I’ll mention that they base much of their presentation on the work of Michelene Chi, who is a cognitive and learning scientist. In particular they refer to her work on causal versus emergent conceptual models for these physical processes. Her paper on this is titledMisconceived Causal Explanations for Emergent Processes. Miller, Streveler, and Olds propose that chemical engineering students start out using causal models to understand many of these processes but then move to more advanced, emergent models later in their studies.
In a causal process there is some kind of distinct, sequential, goal-oriented event with an observable beginning and end. In an elastic collision for instance, a moving object collides with a previously stationary object and transfers its momentum to it. In an emergent process there are uniform, parallel, independent events with no beginning or end but in which observable patterns eventually emerge. Electricity, fluid flow, heat transfer and molecular equilibrium are examples of emergent processes. Miller, Streveler, and Olds correlate causal and emergent explanations with macroscopic and molecular models respectively. As Bird, Stewart, and Lightfoot had said in their descriptions of their three scales, it’s at the molecular level that “we seek a fundamental understanding of the mechanisms.” But at the macroscopic scales we aren’t looking at so fundamental an explanation.
Miller, Streveler, and Olds use diffusion, i.e. mass transport, as an example to show the difference between causal and emergent explanations. Say we have a glass of water and we add a drop of color dye to it. The water is a solvent and the color dye is a solute. This color dye solute starts to diffuse, or spread, into the water solvent and we can explain this diffusion process in both causal and emergent ways; or we could also say in macroscopic and molecular ways.
First, a quick overview of diffusion. The mathematical model for diffusion is Fick’s Law of Diffusion. The equation for this is:
J = -D(dC/dx)
Where, J is the diffusion flux C is concentration x is position D is diffusivity, the applicable constant of proportionality in this case
The basic logic of this equation is that the diffusion of a solute is proportional to the gradient of the concentration of that solute in a solvent. If the solute is evenly distributed in the solution the concentration is the same everywhere in the solution, so there is no concentration gradient and no diffusion. But there is a gradient if the solute concentration is different at different positions in the space, for example, if it is highly concentrated at one point and less concentrated as you move away from that point. The diffusion flux is proportional to the steepness of that decrease, that gradient. If a drop of dye has just been placed in a glass of water the flux of diffusion is going to be very high at the boundary between that drop and the surrounding water because there is a huge difference in the concentration of the dye there.
So that’s the logic of Fick’s Law of Diffusion. But why does this happen? And here we can look at the two different kinds of explanations, causal and emergent explanations.
Here are a few examples of both:
Causal Explanation: “Dye molecules move towards water molecules.” Emergent Explanation: “All molecules exercise Brownian motion.”
Causal Explanation: “Dye molecules flow from areas of high concentration to areas of low concentration.” Emergent Explanation: “All molecules move at the same time.”
Causal Explanation: “Dye molecules are ‘pushed’ into the water by other dye molecules.” Emergent Explanation: “Molecules collide independently of prior collisions. What happens to one molecule doesn’t affect interactions with other molecules.”
Causal Explanation: “Dye molecules want to mix with water molecules.” Emergent Explanation: “The local conditions around each molecule affect where it moves and at what velocity.”
Causal Explanation: “Dye molecules stop moving when dye and water become mixed.” Emergent Explanation: “Molecular interactions continue when equilibrium is reached.”
This is gives something of a flavor of the two different kinds of explanations. Causal explanations have more of a top-down approach, looking for the big forces that make things happen, and may even speak in metaphorical terms of volition, like what a molecule “wants” to do. Emergent explanations have more of a bottom-up approach, looking at all the things going on independently in a system and how that results in the patterns we observe.
I remember Brownian motion being something that really started pushing me to think of diffusion in a more emergent way. Brownian motion is the random motion of particles suspended in a medium, like a liquid or a gas. If you just set a glass of water on a table it may look stationary, but at the molecular scale there’s still a lot of movement. The water molecules are moving around in random directions. If you add a drop of color dye to the water the molecules in the dye also have Brownian motion, with all those molecules moving in random directions. So what’s going to happen in this situation? Well, things aren’t just going to stay put. The water molecules are going to keep moving around in random directions and the dye molecules are going to keep moving around in random directions. What kind of patter should we expect to see emerge from this?
Let’s imagine imposing a three-dimensional grid onto this space, dividing the glass up into cube volumes or voxels. Far away from the drop of dye, water molecules will still be moving around randomly between voxels but those voxels will continue to look about the same. Looking at the space around the dye, voxels in the middle of the drop will be all dye. Voxels on the boundary will have some dye molecules and some water molecules. And voxels with a lot of dye molecules will be next to voxels with few dye molecules. As water molecules and dye molecules continue their random motion we’re going to see the most state changes in the voxels that are different from each other. Dye molecules near a voxel with mostly water molecules can very likely move into one of those voxels and change its state from one with few or no dye molecules to one with some or more dye molecules. And the biggest state changes will occur in regions where voxels near to each other are most different, just because they can be so easily (albeit randomly) changed.
This is a very different way of looking at the process of diffusion. Rather than there being some rule imposed from above, telling dye molecules that they should move to areas of high concentration to low concentration, all these molecules are moving around randomly. And over time areas with sharp differences tend to even out, just by random motion. From above and from a distance this even looks well-ordered and like it could be directed. The random motion of all the components results in an emergent macro-level pattern that can be modeled and predicted by a fairly simple mathematical expression. The movement of each individual molecule is random and unpredictable, but the resulting behavior of the system, the aggregate of all those random motions, is ordered and highly predictable. I just think that’s quite elegant!
Miller, Streveler, and Olds give another example that neatly illustrates different ways of understanding a physical process at the three different scales: macroscopic, microscopic, and molecular. Their second example is of momentum transport. An example of momentum transport is pumping a fluid through a pipe. As a brief overview, when a fluid like water is moved through a pipe under pressure the velocity of the fluid is highest at the center of the pipe and lowest near the walls. This is a velocity gradient, often called a “velocity profile”, where you have this cross-sectional view of a pipe showing the velocity vectors of different magnitudes at different positions along the radius of the pipe. When you have this velocity gradient there is also a transfer of momentum to areas of high momentum to areas of low momentum. So in this case momentum will transfer from the center of the pipe toward the walls of the pipe.
The model for momentum transport has a similar structure to the model for mass transport. Recall that in Fick’s Law of Diffusion, mass transport, i.e. diffusion, was proportional to the concentration gradient and the constant of proportionality was this property called diffusivity. The equation was:
J = -D(dC/dx)
The corresponding model for momentum transport is Newton’s law of viscosity (Newton had a lot of laws). The equation for that is:
τ = -μ(dv/dx)
Where
τ is shear stress, the flux of momentum transport v is velocity x is position μ is viscosity, the applicable constant of proportionality in this case
So in Newton’s law of viscosity the momentum transport, i.e. shear stress, is proportional to the velocity gradient and the constant of proportionality is viscosity. You have higher momentum transport with a higher gradient, i.e. change, in velocity along the radius of the pipe. Why does that happen?
So they actually asked some students to explain this in their own words to see on what geometric scales they would make their descriptions. The prompt was: “Explain in your own words (no equations) how momentum is transferred through a fluid via viscous action.” And they evaluated the descriptions as one being of the three scales (or a mixture of them) using this rubric. So here are examples from the rubric of explanations at each of those scales:
Macroscopic explanation: The pressure at the pipe inlet is increased (usually by pumping) which causes the fluid to move through the pipe. Friction between fluid and pipe wall results in a pressure drop in the direction of flow along the pipe length. The fluid at the wall does not move (no-slip condition) while fluid furthest away from the wall (at the pipe centerline) flows the fastest, so momentum is transferred from the center (high velocity and high momentum) to the wall (no velocity and no momentum).
Microscopic explanation: Fluid in laminar flow moves as a result of an overall pressure drop causing a velocity profile to develop (no velocity at the wall, maximum velocity at the pipe centerline). Therefore, at each pipe radius, layers of fluid flow past each other at different velocities. Faster flowing layers tend to speed up [and move] slower layers along resulting in momentum transfer from faster layers in the middle of the pipe to slower layers closer to the pipe walls.
Molecular explanation: Fluid molecules are moving in random Brownian motion until a pressure is applied at the pipe inlet causing the formation of a velocity gradient from centerline to pipe wall. Once the gradient is established, molecules that randomly migrate from an area of high momentum to low momentum will take along the momentum they possess and will transfer some of it to other molecules as they collide (increasing the momentum of the slower molecules). Molecules that randomly migrate from low to high momentum will absorb some momentum during collisions. As long as the overall velocity gradient is maintained, the net result is that momentum is transferred by molecular motion from areas of high momentum to areas of low momentum and ultimately to thermal dissipation at the pipe wall.
With these different descriptions as we move from larger to smaller scales we also move from causal to emergent explanations. At the macroscopic level we’re looking at bulk motion of fluid. At the microscopic scale it’s getting a little more refined. We’re thinking in terms of multiple layers of fluid flow. We’re seeing the gradient at a higher resolution. And we can think of these layers of fluid rubbing past each other, with faster layers dragging slower layers along, and slower layers slowing faster layers down. It’s spreading out a deck of cards. In these explanations momentum moves along the velocity gradient because of a kind of drag along the radial direction.
But with the molecular description we leave behind that causal explanation of things being dragged along. There’s only one major top-down, causal force in this system and that’s the pressure or force that’s being applied in the direction of the length of the pipe. With a horizontal pipe we can think of this force being applied along its horizontal axis. But there’s not a top-down, external force being applied along the vertical or radial axis of the pipe. So why does momentum move from the high-momentum region in the center of the pipe to the low-momentum region near the pipe wall? It’s because there’s still random motion along the radial or vertical axis, which is perpendicular to the direction of the applied pressure. So molecules are still moving randomly between regions with different momentum. So if we think of these layers, these cylindrical sheets that are dividing up the sections of the pipe at different radii, these correspond to our cube voxels in the diffusion example. Molecules are moving randomly between these sheets. The state of each layer is characterized by the momentum of the molecules in it. As molecules move between layers and collide with other molecules they transfer momentum. As in the diffusion example the overall pattern that emerges here is the result of random motion of the individual molecular components.
So, does this matter? My answer to that question is usually that “it”, whatever it may be, matters when and where it matters. Miller, Streveler, and Olds say: “If the macroscopic and microscopic models are successful in describing the global behavior of simple systems, why should we care if students persist in incorrectly applying causal models to processes such as dye diffusion into water? The answer is simple – the causal models can predict some but not all important behavioral characteristics of molecular diffusional processes.” And I think that’s a good criterion for evaluation. I actually wouldn’t say, as they do, that the application of causal models is strictly “incorrect”. But I take their broader point. Certainly macroscopic and causal models have their utility. For one thing, I think they’re easier to understand starting off. But as with all models, you have to keep in mind their conditions of applicability. Some apply more broadly then others.
One thing to notice about these transport models is that they have proportionality constants. And whenever you see a constant like that in a model it’s important to consider what all might be wrapped up into it because it may involve a lot of complexity. And that is the case with both the diffusion coefficient and viscosity. Both are heavily dependent on specific properties of the system. For the value of viscosity you have to look it up for a specific substance and then also for the right temperature range. Viscosity varies widely between different substances. And even for a single substance it can still vary widely with temperature. For diffusivity you have to consider not only one substance but two, at least. If you look up a coefficient of diffusivity in a table it’s going to be for a pair of substances. And that will also depend on temperature.
At a macroscopic scale it’s not clear why the rates mass transport and momentum transport would depend on temperature or the type of substances involved. But at a microscopic scale you can appreciate how different types of molecules would have different sizes and would move around at different velocities at different temperatures and how that would all play into the random movements of particles and the interactions between particles that produce, from that molecular scale, the emergent processes of diffusion and momentum transport that we observe at the macroscopic scale.
Once you open up that box, to see what is going on behind these proportionality constants, it opens up a whole new field of scientific work to develop – you guessed it – more and better models to qualify and quantify these phenomena.
Todd Decker 