Razib has a little post on cultural cladism, but I think he gets it quite wrong.
He repeats the usual trope canard that culture isn't like biology in terms of its evolution. I think it is exactly like it, and that the "analogy" between cultural traditions and species is quite exact. All that differs is the frequency of the various kinds of evolution.
For instance, take Razib's example. He says that because Judaism is very unlike Christianity in some respects, and much more strictly like Islam in its monotheism, it should be seen as a sister taxon to Islam and not Christianity, and the term "Judeo-Christian" should be dismissed. I have my own objections to "Judeo-Christian", which I'll get to in a minute, but let's consider the philosophies of classification used here.
The historical tree might seem to be this (figure, A). Judaism coalesced with the "reforms" of Hezekiah, and most historical scholars think that was the foundation of that religion. It was when the Torah began to be formed and the rituals were established, although something akin to modern Judaism didn't develop until the end of the 7th century BCE with the reign of Josiah after the return from exile.
Christianity developed, as is well known, out of the messianic cult that had strong connections with the P'rushim (pharisees) in Judaism of the first century CE, and which was eventually melded with classical culture of the Roman era. Islam was a reaction to the polytheistic folk religions of the Arabian peninsula, and to the Jewish and Christian communities in that region. Mohammed was something of an eclectic, in that he adopted the Jewish form of monotheism, but he also adopted the universalism of Christianity. Islam was for all people, as was Christianity, not merely a given ethnic group. Depending on what you choose to measure each religion against, you get differing historical connections.
Now with three "taxa" there are three different cladograms. Note that a cladogram is not the same as an evolutionary tree - it is a classification. It roughly says that "A is more closely related to B than either is to C", but "closely related" can mean "more recently descended from a common ancestor" or "more similar" or a bunch of other things. If you have n taxa, there are (2n-3)!/[2n-2(n-2)!] possible trees, so with 3 taxa you get 3 trees. I give them here as B - (Judaism, (Christianity, Islam)), C - (Christianity, (Judaism, Islam)), and D - (Islam, (Christianity, Judaism)). What these man in terms of evolutionary history is another matter.
If we classify according to the overall totality of characters - monotheism, ritual, law, doctrine, and so forth, based on modern religions, then we might think that Razib is right - Judaism and Islam are both strongly monotheistic, while Christianity, with its Trinitarian doctrine, is compromised, and both Judaism and Islam have strict ritual requirements of their adherents, while Christianity doesn't, such as ritual washing and the like. But this would overlook the fact that initially Christian traditions fought violently, literally and metaphorically, over their monotheisms, and what we have under the so-called Nicene version of Christianity is actually a much derived form of religious belief compared to earlier schools of thought (the Trinitarian doctrine is late - 3rd century). Moreover it will overlook that there are many kinds of rituals, and no Christian tradition has been free of rituals until fairly recently. It is very much a matter of what you choose to call a "ritual". So if you drew a tree in the 2nd century, catholic Christianity and Judaism might pair up against a third alternative (say, the Paulicians, a form of gnosticism) or even against the much later Islam.
Moreover, we can usefully see the rigid monotheism of Islam as inheriting a "plesiomorphy", which is to say an underived or ancestral state, from its Jewish heritage, rather than seeing the evolution of these religions as irrelevant to their classification. Plesiomorphies in cladistics are uninformative - having four limbs is not informative about the evolution of tetrapods. Not having limbs is informative about the snake clade. To find tree C intuitive, as Razib does, you have to focus on those character states that are more similar, but I wonder if the history of those religions really does support C rather than B. I take it that nobody (but extremist Muslims, perhaps) thinks that tree D has any cogency.
Classification of this kind is intended to use the totality of evidence to group historical groups. There is, as Razib noted, another kind of classification - phenetics. Phenetic comparisons are useful, in a way, because they make explicit the similarities used, and they are able to mark the degree of difference, but they are arbitrary in their divisions, and worse, they are highly sensitive to the characters used. If you use one set of components in your analysis, you get one grouping, but the very same taxa or specimens can be regrouped in a radically different manner by choosing other characters.
The difference between phenetic and cladistic classification can be summarised thus: a cladistic classification allows you to identify groups within which you can predict that many characters will be shared, compared to the outgroup, even if those characters were not used in the initial classification; while phenetic classifications are only good for the characters used in the analysis. You can inductively generalise a cladogram, but you can only deductively infer from a phenogram.
On the other hand, a cladogram is only good when you actually have independently evolving lineages. Cultural evolution is thought by many to be constantly recombining, and this would swamp a phylogenetic signal. If Islam is a "hybrid", then the historical tree would look like this (E):
Which side of the hybrid lines one makes dotted will depend on which side contributes the most. I think that the Jewish element is influential but less so than the Christian. Mileage may vary. If the matter is not decideable, or is arbitrarily reliant upon choices of characters, then we have an unresolved tree, in this case a trichotomy.
The point of all this is to show that intuitions here are not reliable when it comes to classifying in either biology or culture. There are issues that need to be resolved in a fair bit of detail. I haven't even begun here to discuss the varieties of sects in each religion - the CHristian and post-Christian sects number around 1500 in the US alone, and the number is probably much higher. There is a kind of cladogram of Christian religious denominations, the main ones, here. Islam has its own separate traditions, at least five. And Judaism has numerous diverging traditions, usually grouped into the Orthodox, Conservative and Reform, but also including such things as the Kabbalist traditions, and Karaites, and so on.
Two final points: The "Judeo-Christian tradition" is a construct in itself. It doesn't really give much in the way of characters, nor is it a coherent tradition. On cladistic grounds, it would be a paraphyletic group, formed by excising the Islamic lineages arbitrarily. If we adopt the less offensive "Abrahamic religions" (since they all claim Abraham as their founder in one way or another) we lose what the Judeo-Christian term is supposed to capture. If we adopt a crown clade definition, then you might have the Christian-Islamic tradition, which makes more sense of a lot of the interactions between the West and Arabian East. Sibling fight more than cousins...
Finally, we should note that we can identify these traditions, irrespective of occasional cross-lineage borrowings, just as we can for languages, styles of art, and so on. There are "species", or at any rate, taxa, in culture as in biology, and they are tolerably salient. Given the complexity of biological taxa once you stop obsessing on things with fur and feathers, it should come as no surprise that culture has taxa too, and that we can use cladistic methods to analyse it. As a postscript, let me direct readers to
Mace, Ruth, Clare J. Holden, and Stephen Shennan. 2005. The evolution of cultural diversity: a phylogenetic approach. London: UCL Press.
as an example of how this can be done formally (in this case on a variety of case studies).
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I'm by no means hostile to the application of evolutionary ideas to history, though, as my earlier comments in other threads attest, I'm skeptical that very much has been accomplished so far. The notion that a cladistic analysis of the relationships among Judaism, Christianity, and Islam means very much of anything strikes me as a huge stretch, however. What is supposed to be filiated here? Not populations of actual, breathing human beings, I assume, since it is not the case that the bulk of Christians were once Jews and it is certainly not true that the bulk of Muslims were once either Jews or Muslims. Relgious traditions may seem to be real individual things in retrospect, once orthodoxy has been constructed and a sacred history has been retroactively invented; but what is the real substance of these faiths? What is supposed to have evolved? Ideal types?
In this case what has evolved are religious ideas and practices. Cultural evolution is roughly decoupled from the evolution of organic beings. Instead, what evolves here are the agents of culture and their characters.
Moreover, the evolution of one kind of cultural tradition, say religious beliefs, is not going to be ipso facto mappable in a simple amnner onto another, say language. Even among religions like Islam or Judaism that make a particular language de rigeur for adherents, languages evolve to the point that Indonesian Arabic and Yemeni Arabic are distinct dialects, while the religious traditions may cut across those boundaries.
If you broke things down into lower level practics and ideas, I might be more convinced. For example, I can imagine writing an evolutionary history of such things as religious marketing techniques such as the sermon, devotional practices such as the personal worship of saints or gods (bhakti), theological themes such as negative theology, mythic themes like the apocalypse, literary mechanisms like the canon of scriptures, or even the notion of doctrinal orthodoxy itself. All these things developed in the centuries in question, but they also developed across denominational lines (however you draw 'em) with lots of borrowing and imitation between traditions--orthodox Christianity apparently defined its canon in response to Marcion the Gnostic, for example, who apparently did it first, perhaps inspired by some of the efforts of the Rabbis to decide what was and what wasn't scripture. I assume both the Jews and Christians got the notion of the ressurection of the dead from some common source. Everybody seems to have fallen in love with the program of negative theology--it was virutally a pan-Eurasian fad, etc. The point is, the mix of features that came to be associated with the major religions once they had defined their own boundaries was pretty much a set of frozen accidents.
By the way, any attempt to figure out the relationship between the religions needs to decide whether to take the point of view of the religions themselves or to look at things from the outside. Since the historical religions all defined themselves against other religions--you might call 'em metareligions--any theory of how they relate to one another has to compete with the theories inside the faiths themselves. The Christians developed an elaborate body of ideas about Judaism, Muhammad (or the Angel Gabriel) claimed that both Judaism and Christianity were earlier dispensations of the true faith, and in the Talmud the Jews developed a theory of what to make of Christianity. Of course you could simply extend one of the cladagrams and make the evolutionary theory of religion branch off from Islam. Failing that, I think it's important to distinguish the ideas that believers had about their beliefs and practices, which at a minimum includes the convinction that the religions have a core or essence, from the view from outside.
1. 'Cultural evolution does not work like biological evolution,' could be called a commonplace, a canard, a platitude, or a bromide, but it is not a trope.
I don't say this to be a pedantic jerk; I fear that my use of word over and over in negative settings in discusion threads has conveyed a false meaning.
A trope traditionally means a figure of speech, such as a simile, but 'metaphor' has broadened to serve the same purpose, so writers (borrowing perhaps from musical composers) sometimes use 'trope' to refer to larger units of sustained, developed comparison, since the old word for these--'allegory'--has come to connotate fable. If I call Hobbes' State of Nature an allegory it implies that he doesn't believe it; so I call it a trope to imply nothing about its truth, utility, sincerity, or seriousness.
2. The more common canard, if so one wishes to call it, is not that cultural evolution doesn't work like biological evolution, but that one cannot assume a priori that it does, or know a priori how much it does, or know a priori in what way it does. I intutitively feel that it somehow does. I know that smarter people than me think it does. And I intend to find and read the book(s) you recommend. Unfortunately, I also know that smarter people than me have also thought culture changed by Hegelian Dialectics, Marxist Dialectics, Whig Progress, and so on. One can hope that the discipline of biological science will keep a cultural evolution based on it from drifting into metaphysics, but I haven't such a sanguine view of human nature.
3. If you and the blogger you link too, both intelligent and reasonable people, cannot agree on the correct Cladistic taxonomy of subjects as historically attested and thoroughly analyzed as Islam, Christianity and Judaism, do you see how some of us might have reasonable doubts about the efficacy of this approach? Won't this just mean endless battles (claddles?) over the taxonomy itself?
languages evolve to the point that Indonesian Arabic and Yemeni Arabic are distinct dialects
john, do you mean 'indonesian arabic' in a figurative sense? :) seeing as how arabic is not spoken in indonesia unless you are talking about in a religious context, which would usually imply recitation of classical arabic (which is quite distinct from spoken dialects, and from what i gather even from the egyptian influenced written arabic in literature).
good post. i'll link/comment after work if i have time.
Even among religions like Islam or Judaism that make a particular language de rigeur for adherents,
also, to be precise, neither hebrew or arabic were required as spoken languages for these cultures. only religious professionals need have any understanding. e.g., hebrew was a dead language for nearly 2,000 years, and fewer than 1 out of 5 muslims speak any form of arabic.
I mean the sort of Arabic that those who read and speak Arabic in Indonesia speak. Of course, Bahasa Indonesia is a creole of Malay and Arabic (or rather, it has a lot of loan words), but even when they speak Arabic to other speakers elsewhere, they are recogniseably Indonesian.
And of course nobody needs to speak Hebrew to be Jewish or Arabic to be Islamic, but it is taught to those who grow upin that language (for bar and bat Mitzvah, say), as, say, Koine Greek or post-classical Latin is not in the Christian tradition.
I mean the sort of Arabic that those who read and speak Arabic in Indonesia speak. Of course, Bahasa Indonesia is a creole of Malay and Arabic (or rather, it has a lot of loan words), but even when they speak Arabic to other speakers elsewhere, they are recogniseably Indonesian.
i'm curious about this. i'm not really getting what you mean. i have, for example, actually spent time in a madrassa. many of the kids were close to memorizing the koran, but they didn't "know arabic." no one spoke arabic since no one in that madrass were arabs, and i am curious as to your suggestion that in religious institutions in southeast asia people actually speak (as opposed to ritually recite) arabic. is this what you're talking about? btw, my understanding is that the arabic in the koran is pretty much unintelligible in relation to modern colloquial arabic dialects. so the appropriate analog is church latin, but unlike christian intellectuals until a few hundred years ago i don't believe that classical arabic has the same status as a medium of intercultural discourse. anyway, my curiosity has been piqued.
btw, my own impression is that prior to the rebirth of hebrew in the 20th century, that language's existence was very similar to latin in pre-vatican ii catholicism.
p.s. and john, as an australian, i am aware you might have an understanding of indonesia that i, as an american do not. so that's why i'm pushing that point, i'm curious as to what i might not know.
John
It's a fascinating blog entry and has led to some interesting discussion. It's a side issue to the discussion, but there's no way Indonesian can be described as a creole of Malay and Arabic. Indonesian is one of the vast Austronesian language family, stretching from Madagascar to Easter Island. The official Indonesian language Bahasa Indonesia, and traditional Malay on which it is based, could both be described as dialects of the same language these days (as close to each other as American English and Australian English). Indonesian has many loan words from Arabic for historical and religious reasons (and from Sanskrit, Dutch and even Portuguese), but it would have just as many from English by now. Razib was being very polite in deferring to you on this point!
Anyway, as I said, it's a side issue to the main discussion, which intriguingly blends science and history/religion.
John Monfries
I concede. I heard from a a linguist that Arabic has local dialects, including Indonesia, but I really don't know shit for sure...
While I'm backpedalling, I also accept that I meant canard rather than trope...
I concede. I heard from a a linguist that Arabic has local dialects, including Indonesia, but I really don't know shit for sure...
if you heard this from a linguist than you have good reason to pass the buck! of course, the linguist might have been meaning that the dialect of recited arabic in the pesantrans (southeast asian madrassas) has a particular lilt.
i'll prolly post a 'response' to this post tonight, time permitting, FYI.
Now, now, that makes you a social Darwinist and therefore responsible for the Nazi atrocities 1933-1945.
But, using cladistics is deceiving. Cladistics is based on bifurcation at some characteristic shared by all members on one of the branches. That's a chosen methodological scheme.
On its own this doesn't make biology and culture one and the same, only analogous in some respects.
Some care should be exercised when dealing with analogies - just think about the watchmaker argument.
Um, yes, I said that in the post. But it's not one characteristic, but a number of synapomorphies, and it is that colligation that licenses inductions about the shared properties beyond the data set used in analysis.
And, to be controversial, there never was a social Darwinism.
True; but it's still simply a methodology, and depending on your weighting of synapomorphies you may end up with different results.
Could that be true? If so, then how can Richard Weikart in his book From Darwin to Hitler claim that Hitler was a social Darwinist. Are you really saying that Weikart is inventing things?
Seriously though, to revert to the above quote, what was new in Darwin's theory of evolution was the dissolution of the species concept. Therefore any X Darwinist should also have that characteristic, and that doesn't appear to be the case for Hitler.
A comparison between Hitler and Darwin depends on, what characteristic you choose, and how much weight you attribute to it.
In Descent of Man Darwin writes some things that may be interpreted as racist; but he also suggests that there is really only one human species, indeed only one human race. Using cladistics in for cultural analysis has exactly this problem that you can pick and choose and come up with whatever you want. Darwin was picking up some racist ideas that were common in his social environment, though using them for his own purposes; but really his won idea was that 'race' as well as 'species' were simply conventions.
Physical characteristics of organisms do not possess the same flexibility. I live close to an airport; but believe me, i haven't grown wings just from that!
No, Darwin did not think race (as a subspecific category) and species were simply conventions. He didn't think there was aspecific or racial rank. Species (and races) were real enough, but it was convention when to recognise a variety as one or the other.
And it is not the case that, in cladistics, you can simply choose whatever you like (this is more true of phenetics). If you add more characters and they fail to support the cladogram, then you have a falsified cladogram. If you try to pick and choose, the technique will, under the right conditions, bite you in the bum. You don't weight synapomorphies in cladistics. You weight characters in phenetics.
And I can't parse your last sentence.
This PDF file has a cladistic analysis of the |xanadu| meme based on some empirical evidence. As you may know, "Xanadu" was the Mongolian capital established by Kubla Khan. The term made it's way to Europe in a 16th century travel book, which was subsequently read by S. T. Coleridge, the English poet, who put it into his most famous poem, "Xanadu." Orson Welles quoted the poem at the opening of Citizen Kane, Ted Nelson named his hypertext project Xanadu, and Olivia-Newton John starred in a movie and sang popular song of that name. Those events are the branch points in the cladogram. The PDF document spells that out in some detail while discussing this that and the other. That document is derived from this discussion.
No, Darwin did not think race (as a subspecific category) and species were simply conventions. He didn't think there was aspecific or racial rank. Species (and races) were real enough, but it was convention when to recognise a variety as one or the other.
Umm, that would be against the principle of nominalism and make Darwin yet another Platonist, wouldn't it?
And it is not the case that, in cladistics, you can simply choose whatever you like (this is more true of phenetics). If you add more characters and they fail to support the cladogram, then you have a falsified cladogram. If you try to pick and choose, the technique will, under the right conditions, bite you in the bum. You don't weight synapomorphies in cladistics. You weight characters in phenetics.
Ok, I'll take your word for it :-) But by 'weighting' I meant ordering, you select the order of synapomorphies, don't you?
According to the Wikipedia article about Cladistics:
When equivalent possibilities turn up, one is usually chosen based on the principle of parsimony: the most compact arrangement is likely the best hypothesis of relationship (a variation of Occam's razor). Another approach, particularly useful in molecular evolution, is maximum likelihood, which selects the optimal cladogram that has the highest likelihood based on a specific probability model of changes.
This does sound to me as if some choosing is done.
And I can't parse your last sentence.
What I meant is that environmental influences come in different varieties. Even if your parents are Jewish, you may become more-or-less-Christian if you live among Christians - religion isn't built in. But even if I went out into the woods to live with the wolves, I wouldn't become a wolf, would I?
that would be against the principle of nominalism and make Darwin yet another Platonist, wouldn't it?
No, of course not. One can think that something is real without having to think there is an eternal form for that thing. And anyway, Darwin need not have been a nominalist on any topic; arguably one can be a transmutationist on Aristotelian grounds (not that Darwin was, although he expressed great admiration for Aristotle late in life).
Darwin thought species were (temporarily) real things. He just didn't think there was an absolute rank or category of things that included all and only species, or that there was a qualitative difference between species and varieties. The "conventionalism" here is that Darwin thought (I believe wrongly) that where we drew the line was a matter of choice by specialists - he was one of those who drew up the 1840 Strickland Rules that defined species as, effectively, whatever a specialist chose to call one. In the sixth edition of the Origin he writes
In cladistics you do not choose the ordering of synapomorphies; at best you exclude homoplasious characters (since they are uninformative about phylogeny). Maximum likelihood and parsimony are choices of the resulting trees, not of the characters used to determine that trees. This is because the number of trees are very large for any appreciable set of characters, and one needs to find ways to reduce that set. Another more recent method is the supertree analysis, which effectively overlays all the trees and takes a consensus topology.
As to your final point, all I can say is that you are confusing the cultural adaptations with the biological. It may pay a biological organism to act like one's neighbours (and so-called "feral children" show that this happens if you are raised by wolves too). What is happening here, though, is that the cultural items are gaining a greater frequency in the population of social agents, the way that genes do. Don't confuse the biological level with the cultural - what evolves in culture are the cultural items, not the organisms.
John, thanks for your comments.
I'll take the last one first:
As to your final point, all I can say is that you are confusing the cultural adaptations with the biological. It may pay a biological organism to act like one's neighbours (and so-called "feral children" show that this happens if you are raised by wolves too). What is happening here, though, is that the cultural items are gaining a greater frequency in the population of social agents, the way that genes do. Don't confuse the biological level with the cultural - what evolves in culture are the cultural items, not the organisms.
I agree, and that was exactly my point: there may be analogy between biological evolution and cultural evolution, but they are not the same. In biological evolution hereditary characteristics are fixed at conception, but not so with cultural characteristics. It's through social interaction you became, say, a Jew, not by having Jewish parents - although, to count as a Jew for immigration to Israel you are required to be born by a Jewish mother.
This is a point, where I am sure that sociobiologists go wrong. They forget that no matter our genes, we are born into an already existing society, that imposes its rules upon us.
As for cladistics, you write:
In cladistics you do not choose the ordering of synapomorphies; at best you exclude homoplasious characters (since they are uninformative about phylogeny). Maximum likelihood and parsimony are choices of the resulting trees, not of the characters used to determine that trees.
But trees have branches. And branches have twigs. Somehow it must be decided have to order the branching points before you have much of a tree.
Maybe I have misunderstood it all. Is there an online text on cladistics, you'd recommend?
As for Darwin: if you turn a species into a convention, it's still a very different thing than having them exist in the sense Agassiz did (and that modern day baraminologists do with their kinds.
In "Descent of Man", chapter 7, "On the Races of Man", Darwin writes:
It is not my intention here to describe the several so-called races of men; but I am about to enquire what is the value of the differences between them under a classificatory point of view, and how they have originated. In determining whether two or more allied forms ought to be ranked as species or varieties, naturalists are practically guided by the following considerations; namely, the amount of difference between them, and whether such differences relate to few or many points of structure, and whether they are of physiological importance; but more especially whether they are constant.
All here is relative - a species cannot be defined independently, only by its differences from other species, and of course that cannot lead to any absolutism.
Darwin ends Origin of Species with the words:
In short, we shall have to treat species in the same manner as those naturalists treat genera, who admit that genera are merely artificial combinations made for convenience. This may not be a cheering prospect; but we shall at least be freed from the vain search for the undiscovered and undiscoverable essence of the term species.
I cannot read this as anything else than saying that species do not exist outside our systematics. Of course, one given guidelines about how to do systematics, species are granted some meaning, but its not an inherent (essential) meaning, only a nominal meaning.
That's how I read it :-)
...what evolves in culture are the cultural items, not the organisms.
This is very important. And this is what Dawkins got right when he talked about memes. It's the cultural items that evolve and, in some extreme cases (e.g. suicidal religious fundamentalism), they may do so at the expense of the organisms that are their necessary substrate. And the "fitness" that's of concern, is the fitness of cultural items to propagate through a population.
Of course these cultural items, though quite real, are no more autonomous agents than are Dawkinsian selfish genes. We know how to explicate the actions of those genes in the terms of genetics, thereby removing all mystery from their apparent selfish agency. We don't yet know how to do that for cultural items.
pwe: I still don't think you get it. Yes, biological characteristics are (sort of) fixed at birth. So too, are the cultural items at their conception. They don't change just because the "host" changes which ones they bear. The process of cultural evolution, strictly conceived, is as "Darwinian"as that of genes. It's only a "different"process if you confuse the two levels, and take changes in what cultural items the host carries as a change in the cultural items themselves.
I don't know how to make this clearer. Consider the hosts, the biological individuals like your Jewish example, as the region or ecology, and the cultural items (I'm going to abbreviate these as culits) as the genes that exist in that ecosystem. When culits migrate in or out of the region (the "host"), the region changes, but not the culits themselves. So if a Jewish person (host) adopts Christian ideas, what this is strictly analogous to is the immigration of new alleles into a population that is adapting to its ecosystem.
Of course, culits also (in mine and Bill's view) include external objects, like pottery, hunting techniques and tools, and inherited infrastructure like roads. So it is here the use of these objects that has the cultural fitness.
As to cladistics, I really do think you have the wrong idea, fundamentally. A good undergraduate level intro is by this, by Diane Lipscomb at GWU. In particular read the section on optimality criteria. You should work through all the examples here on paper to get an idea of what the technique is about.
To understand Darwin on species, you need to read more widely than the Origin or Descent. In particular you need to know what he did as well as what he said. The point he is making is that that "species" is practically applied to groups that have constant shared characters. But he is not saying that the groups are purely conventional, only their diagnosis. Recall that Darwin describes a lot of species in his barnacle books, and also used specific designations throughout his work. He was not a pure conventionalist, but rather denied that species had any platonic essence as Agassiz thought they did (and Agassiz was very much in the minority among taxonomists of the day - his Essay on Classification was archaic before he published it).
In my review of Darwin's thinking on species in my (perhaps never to be published) book, I conclude that he thought the groups were real, but that the ranking was conventional and arbitrary.