The reported status of my probability paper has remained Editor Assigned for more that eleven weeks now. I have sent a message to the Journals Editorial Office, requesting precise information on the actual status of the paper.

The reply that I received from the Journals Editorial Office was that the editor had my manuscript and I would be informed of a decision after it had been reviewed. I responded that this were not a proper answer, and explained that I would not be so patient as I had been when a Springer journal had been slow and uncommunicative about a previous paper.

If I do not receive a proper answer by Tuesday morning and the reported status remains unchanged, then I will attempt to write directly to the editor. Right now, there seems a substantially greater probability that I will soon inform the journal that my paper is no longer available for their consideration.

I received a more informative answer from the Journals Editorial Office early this morning. They reported that the paper were still being evaluated by the editor, and that the search for reviewers had not been begun.

It is disgraceful if the editor truly hasn't completed his own evaluation after the passage of so much time. Editors have many papers at which to look, but still it is the norm for them to have evaluated any given paper within one month. My paper is challenging, but not so challenging as to justify taking more than twice the standard amount of time.

I am trying to decided when to withdraw the paper from their consideration if I have not been told that reviewers are assigned or at least that a search for reviewers is underway. I do not think that there is any constructive use in issuing an ultimatum; that would almost surely result in a quick rejection. So I think that I need simply to decide for myself at what point to contact them and tell them that the paper is no longer available to them.

It has famously been argued that the word game cannot be defined in a way that adequately captures the various senses in which it is used. I believe that, in everyday use, the term game most often means a system of contrived challenges properly imposed or undertaken for purposes of amusement. Hence, someone might assert something such as Love is not a game! But, even in lay-use, game can have other meanings. For example, when a person proceeds deceitfully or insincerely, he or she may be said to be making a game of things, without necessarily seeking amusement in proceeding in this way.

Economists and mathematicians applying themselves to problems of economics or proximate to those of economics can use the term so very broadly as to refer to any problem of optimization. But, most often, they mean a system in which multiple parties interact with the potential for one or more parties to advance an interest or something that is treated as an interest (such as reproduction). It is in this sense that I here use the term game.

The rules of games are often subject to to change, and those changes may be affected or effected by players of the governed game. There is thus a meta-game — a system in which multiple parties interact with the potential for one or more of them to advance an interest by changing the rules of the game; or, in the context of others trying to changing the rules, by preserving the rules. The concept of meta-games is hugely important for understanding social processes.

Of course, a meta-game might have its own meta-game — a meta-meta-game. For example, the determination of a legal frame-work might be the meta-game of the social processes that the frame-work governs, and a struggle over social values might be the meta-game of the determination of the frame-work and thus the meta-meta-game of those social processes. But it can be difficult — without necessarily being useful — to work-out an actual hierarchy.

Sometimes, all that we really need to recognize is that some activity is a meta-game of some other game, without concerning ourselves as to whether the other game is itself a meta-game. People might readily recognize meta-gaming in activities such as political lobbying, but they generally don't recognize it when it's effected by psychologists, by teachers, or by screen-writers.

I want to draw upon this notion of meta-games for at least one 'blog entry, but I will probably want to draw upon it for multiple entries, so I will leave this entry as infrastructure. And I may later and without notice rework it, in an attempt to improve it as infrastructure.

Many animals, across different classes, have two distinct sounds that may be classified as growls or as whines, respectively. The growls signal threat; the whines signal friendship or appeasement.

The bark of a dog is actually a combination of a growl with a whine; it is thus not a pure signal of aggression, as many take it to be; it is literally a mixed signal, perhaps indicating confusion on the part of the dog, perhaps signalling both that the dog is prepared to fight and that the dog would consider a peaceful interaction.

When women talk with men whom they find attractive, women tend to raise the pitches of their voices. Men tend to do something different when talking with women whom they find attractive; they mix deeper tones than they would normally use with higher tones than they would normally use. The deep tones are signals of masculinity, of being able to do what men are expected to do. The higher tones of men carry much the same significance as do the higher tones of women — with the additional point in contrast to the deep tones that the man does not mean to threaten the woman.

It amused me to reälize consciously that this behavior by men is at least something like barking. Then I grimly considered that some men are actually barking, telling the woman that he can be nice to her if she is nice to him, but will actively make things unpleasant if she is not. But at least it should typically be possible to disambiguate the threatening behavior, based upon where the low notes are used, and of course the choice of words.

In a previous entry, I noted that the original definition of racism was a theory or an adherence to a theory that merit is in part intrinsically a function of race. It was exactly by analogy with the word racism that the word sexism was introduced in 1968, thus referring to a theory or an adherence to a theory that merit is in part intrinsically a function of sex.

Now, here is where matters get tricky. In any case in which one rejects sexism, it is regarded as an inappropriate response to the sex of people; and, in particular, the treatment is likely to be seen as unethical. A very great many folk employ the concept of unethical response to the sex of people as if that were the very definition of sexism. That notion is going to operationalize very much like the actual definition whenever and wherever the issue at hand is one of ethics and ethics actually call for neutrality — for a rejection of the relevance of sex to the issue. But nearly all of us regard people of one sex as better suited to some rôles that are of importance. For example, if I presume that sexism must refer to something unethical, then I am compelled either to associate sexism with something other than neutrality of a sort, or as a matter of justice to try to entertain thoughts of accepting a man as a potential spouse for myself. (People are led astray by the analogy with racism; the cases in which sex is relevant to selection loom larger because of the importance of reproduction.) And the substituted notion is not going to operationalize at all like the original definition exactly when someone believes that merit is a function of sex in a far wider range of cases than do folk such as I; then the substitution is going to get things almost perfectly twisted around. He or she will label anti-sexism as sexism and will label some sort of sexism — perhaps quite an intense sexism — as anti-sexism.

The spurning of a claim of relevance is the maintenance or adoption of indifference. This indifference is an equality of one sort — and we often see the words equal and equality used in antonymy to sexism — but it is not an equality of various other sorts. Advancement of a conflicting equality would itself be sexist. Such conflicting equalities can arise when the equality sought is equality of outcome. If people, regardless of sex, may be presumed to respond to a framework in essentially identical ways, and we observe markèdly different outcomes for one sex compared to those for another, then this difference is prima facie evidence that the framework is sexist. But if it is recognized that people of one sex behave differently in that framework, then the presumption that the framework is sexist does not follow from the mere presence of a difference. If we say that the different behaviors must be treated as of equal merit because otherwise a difference in outcomes emerges, then the merit that is ascribed to the behavior is treated as a function of the sex of the people who engage in that behavior; that prescription is itself intrinsically sexist.

For example, the rates at which men are arrested for, charged with, and convicted of criminal behavior of various sorts are much higher than the corresponding rates at which women are arrested, charged, and convicted. We cannot conclude simply from these differences that the system of criminal law is sexist, because it may be that men simply engage in that behavior more often; indeed, most of us are fairly sure that this latter case holds. If we insist that the behaviors themselves must be decriminalized in order to reduce the rates at which men are arrested, charged, and convicted, then we are inferring the relative merit of the behavior from the sexes of those who engage in it. The very same sort of analysis would apply to hiring practices and to the wages or salaries paid to those in various occupations.[1]

(Many people, including certainly me, would argue that an unfortunate sexism prior to whatever exists in the legal system is one factor contributing to greater criminality by men, but few-if-any people propose that part of an appropriate response would be an adjustive sexism, giving more tolerance to male criminalized behavior than to female criminalized behavior. Likewise, some of us assert that an unfortunate sexism prior to whatever exists in the jobs market is one factor leading to different career outcomes for women, but we don't propose an adjustive sexism attempting to compel employers to pay women more than the expected values of their marginal products.)

The confused presumptions that only an unethical discrimination can count as sexism and that sexism is found where there is some sort of inequality other than non-neutrality — an attention to sex — causes people in all sincerity to misapply the word sexism and to fail to see legitimate application of the word, perhaps to their own attitudes and actions. If substitutions of these sorts are not recognized by those who use the word sexism in accordance with its definition, then interactions will be characterized by mutual incomprehension, quite possibly enraged. Attempts to employ logic and facts won't be persuasive because one of the two groups will actively misunderstand a word central to any communication. Additionally, there are people who implicitly believe that ethical significance clings to symbols, such that by changing labels what was wrong may be made to be right and vice versa. In dealing with them, the principal point that ought to be made is not that words cannot be redefined, but that, if we should for any reason redefine sexism, then whatever case was made against what was originally called sexism isn't thereby logomantically transformed into a case against whatever is now to be called sexism, nor is a case against something that was originally called sexism somehow invalidated by ceasing to call it by that name.[2] Of course, there are also those who effect the substitution as a device of unconscious projection, and others who opportunistically seek to sow further confusion.

[1] In the absence of a coherent explanation otherwise, if any population really could be hired at bargain rates, then not only should we expect all members of that population to be hired before any members of any other population; we should expect employers to bid-up the wages and salaries of this less expensive population to the point that they matched those of other populations, before hiring any members of those other populations. If there is some occupation such that the cost of hiring workers for it is notably less than the expected values of their marginal products, then we should expect employers to increase their hirings for those occupations, and in doing so (each in competition with the others and in the face of otherwise ever more reluctant workers) to bid-up the wages or salaries of those workers until the difference disappears.

[2] The same principle of course applies to efforts to redefine racism.

Elsewhere, Pierre Lemieux asked In two sentences, what do you think of the Monty Hall paradox? Unless I construct sentences loaded with conjunctions (which would seem to violate the spirit of the request), an answer in just two sentences will be unsatisfactory (though I provided one). Here in my 'blog, I'll write at greater length.

The first appearance in print of what's called the Monty Hall Problem seems to have been in a letter by Steve Selvin to The American Statistician v29 (1975) #1. The problem resembles those with which Monty Hall used to present contestants on Let's Make a Deal, though Hall has asserted that no problem quite like it were presented on that show. The most popular statement of the Monty Hall Problem came in a letter by Craig Whitaker to the Ask Marilyn column of Parade:

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, Do you want to pick door No. 2? Is it to your advantage to switch your choice?

(Before we continue, take car and goat to stand, respectively, for something that you want and something that you don't want, regardless of your actual feelings about cars and about goats.)

There has been considerable controversy about the proper answer, but the text-book answer is that, indeed, one should switch choices. The argument is that, initially, one has a 1/3 probability that the chosen Door has the car, and a 2/3 probability that the car is behind one of the other two Doors. When the host opens one of the other two Doors, the probability remains that the car is behind one of the unchosen Doors, but has gone to 0 for the opened Door, which is to say that the probability is now 2/3 that the car is behind the unchosen, unopened Door.

My first issue with the text-book answer is with its assignment of initial, quantified probabilities. I cannot even see a basis for qualitative probabilities here; which is to say that I don't see a proper reason for thinking either that the probability of the car being behind a given Door is equal to that for any other Door or that the probability of the car being behind some one Door is greater than that of any other Door. As far as I'm concerned, there is no ordering at all.

The belief that there must be an ordering usually follows upon the even bolder presumption that there must be a quantification. Because quantification has proven to be extremely successful in a great many applications, some people make the inference that it can be successfully applied to any and every question. Others, a bit less rash, take the position that it can be applied everywhere except where it is clearly shown not to be applicable. But even the less rash dogma violates Ockham's razor. Some believe that they have a direct apprehension of such quantification. However, for most of human history, if people thought that they had such literal intuitions then they were silent about it; a quantified notion of probability did not begin to take hold until the second half of the Seventeenth Century. And appeals to the authority of one's intuition should carry little if any weight.

Various thinkers have adopted what is sometimes called the principle of indifference or the principle of insufficient reason to argue that, in the absence of any evidence to the contrary, each of n collectively exhaustive and mutually exclusive possibilities must be assigned equal likelihood. But our division of possibilities into n cases, rather than some other number of cases, is an artefact of taxonomy. Perhaps one or more of the Doors is red and the remainder blue; our first division could then be between two possibilities, so that (under the principle of indifference) one Door would have an initial probability of 1/2 and each of the other two would have a probability of 1/4.

Other persons will propose that we have watched the game played many times, and observed that a car has with very nearly equal frequency appeared behind each of the three Doors. But, while that information might be helpful were we to play many times, I'm not aware of any real justification for treating frequencies as decision-theoretic weights in application to isolated events. You won't be on Monty's show to-morrow.

Indeed, if a guest player truly thought that the Doors initially represented equal expectations, then that player would be unable to choose amongst them, or even to delegate the choice (as the delegation has an expectation equal to that of each Door); indifference is a strange, limiting case. However, indecision — the aforementioned lack of ordering — allows the guest player to delegate the decision. So, either the Door was picked for the guest player (rather than by the guest player), or the guest player associated the chosen Door with a greater probability than either unchosen Door. That point might seem a mere quibble, but declaring that the guest player picked the Door is part of a rhetorical structure that surreptitiously and fallaciously commits the guest player to a positive judgment of prior probability. If there is no case for such commitment, then the paradox collapses.

Well, okay now, let's just beg the question, and say not only that you were assigned Door Number 1, but that for some mysterious reason you know that there is an equal probability of the car being behind each of the Doors. The host then opens Door Number 3, and there's a goat. The problem as stated does not explain why the host opened Door Number 3. The classical statement of the problem does not tell the reader what rule is being used by the host; the presentation tells us that the host knows what's behind the doors, but says nothing about whether or how he uses that knowledge. Hypothetically, he might always open a Door with a goat, or he might use some other rule, so that there were a possibility that he would open the Door with a car, leaving the guest player to select between two concealed goats.

Nowhere in the statement of the problem are we told that you are the sole guest player. Something seems to go very wrong with the text-book answer if you are not. Imagine that there are many guest players, and that outcomes are duplicated in cases in which more than one guest player selects or is otherwise assigned the same Door. The host opens Door Number 3, and each of the guest players who were assigned that Door trudges away with a goat. As with the scenario in which only one guest player is imagined, more than one rule may govern this choice made by the host. Now, each guest player who was assigned Door Number 1 is permitted to change his or her assignment to Door Number 2, and each guest player who was assigned Door Number 2 is allowed to change his or her assignment to Door Number 1. (Some of you might recall that I proposed a scenario essentially of this sort in a 'blog entry for 1 April 2009.) Their situations appear to be symmetric, such that if one set of guest players should switch then so should the other; yet if one Door is the better choice for one group then it seems that it ought also to be the better for the other group.

The resolution is in understanding that the text-book solution silently assumed that the host were following a particular rule of selection, and that this rule were known to the guest player, whose up-dating of probabilities thus could be informed by that knowledge. But, in order for the text-book solution to be correct, all players must be targeted in the same manner by the response of the host. When there is only one guest player, it is possible for the host to observe rules that respond to all guest players in ways that are not not possible when there are multiple guest players, unless they are somehow all assigned the same Door. It isn't even possible to do this for two sets of players each assigned different Doors.

Given the typical presentation of the problem, the typical statement of ostensible solution is wrong; it doesn't solve the problem that was given, and doesn't identify the problem that was actually solved.

[No goats were harmed in the writing of this entry.]

Ordinary language typically uses rent to mean a recurring payment for the use of some good or service, especially for the use of land. The word has various other meanings in ordinary language; but, in economics, rent is used to mean something given in exchange, above and beyond what would have been the minimum necessary to effect the exchange in the absence of some restraint of trade. Usually, this concept is applied to pecuniary payment for a good or service above and beyond the minimum necessary to get that good or service, but one should see that exchanges without money might still involve such increased payment of one good or service for another, and that the same basic idea could be applied to cases in which someone were compelled to deliver more of a good or service than the minimum otherwise necessary to secure some amount of money.

It's mostly because of David Ricardo (18 April 1772 – 11 September 1823), an influential economist, that rent has this meaning. Ricardo used the word rent to refer to payment for the indestructible powers of land. That is to say that rent meant payment for the use of those properties of land that were not diminished by use; payment for harvesting things such as preëxisting plants and minerals would not, strictly speaking, be rent. Perhaps the only thing that could literally meet this criterion would be specific area, but Ricardo favored simplified models, so one might consider highly durable or naturally renewed properties as indestructible.

In Ricardo's mind, if someone renting land were given a right to cut down trees already on the land, or to quarry marble from it, then this right were essentially of the same sort as the right of someone buying lumber or stone at a mill; we certainly don't label the prices of such commodities as rent. Ricardo wanted to identify what were distinctive and essential in what we called rent, and to reserve the word rent just for those components of payments.

Ricardo imagined land as of different qualities, even when viewed only in terms of indestructible properties, but imagined the existing quantities of lands of each quality as not something ever increased by human action. And, in the context of his models, he concluded that rent were not determined by its cost of manufacture nor otherwise by some minimum below which the land-owner could not afford to produce it; rent, according to Ricardo, were purely an artefact of monopoly in the provision of land.

So long as this belief prevailed, it was natural for economists to extend the use of the word rent to other payments which they regarded as perfectly analogous. The word rent came to stand for any payment above and beyond the minimum necessary to effect an exchange were there a non-monopolistic market. And, even when most economists moved away from Ricardo's theory, as classical economics yielded to more thorough-going marginalism, they held onto this extended use of the term rent.

Because this use of rent can certainly be confusing, both when economists are interacting with lay-persons and when economists are attempting to discuss markets in which commodities are leased, sometimes instead of the bald word rent, they use the term economic rent. (This solution is imperfect, as that term can in ordinary language refer to a leasing payment which is in some sense reasonable for a lessee or potential lessee to bear.)

Economic rent, and the pursuit of rent — called rent-seeking — are considered quite important by most economists.

Rent-seeking, perhaps often unconscious but certainly almost never acknowledged, is wide-spread, and explains a very great deal of the political process.

Rents cannot be paid unless they are paid by someone; often, those paying them do not even realize that they are bearing these costs, or mistake their sources. Worse, rents typically transfer wealth inefficiently, with more lost by whoever is made to pay the rent than would be lost by some other transfer mechanism. Still worse, rent-seeking imposes costs even when it is unsuccessful.

Within a neo-classical framework, rent (or economic rent) might be alternately be defined as something given in exchange, above and beyond the opportunity cost of producing that for which it is exchanged. When the frequent assumptions of complete preferences, continuous divisibility of goods and of services, and ignorability of small costs hold, this new definition is equivalent to the original definition. But, exactly because one ought not to over-commit to those assumptions, it is best not to adopt the alternate definition as such.

I have encountered professors of economics asserting things to be rents that certainly were not. For example, one simply declared that the salary of a specific basketball player were a rent, but the professor had lost himself in a taxonomy which imagined the player simply as playing basketball or as idling. In fact, the player could have played for teams other than the one that hired him, and could have applied his abilities to something other than playing in professional basketball. If there were a rent in his salary, it may not even have been the major portion.

* This entry is primarily infrastructural. I want to be able to refer to rent and to rent-seeking in later entries, without there defining the associated terms.

In Chapter 6 of Through the Looking Glass by Charles Lutwidge Dodgson (writing as Lewis Carroll), a famous and rather popular position on language is taken:

When I use a word, Humpty Dumpty said, in rather a scornful tone, it means just what I choose it to mean — neither more nor less.

If Mr Dumpty's words simply mean whatever he intends them to mean, then the rest of us are not in a position to understand them. If he provides us with verbal definitions, we must know what the defining words mean. He could not even declare in a manner intelligible to us that he meant most words in the same sense as do you or I. We might attempt to tease-out meanings by looking for correlations, but then we would be finding meanings as correlations, which assumes properties (such as stability) that represent more than pure choice on the part of Mr Dumpty. Having been made perfectly private, his vocabulary as such would have no practical value except for internal dialogue. There is a paradox here, which Dodgson surely saw, yet which so very many people don't: If Mr Dumpty's apparent declaration were true, then it could not be understood by us. He might actually just be making some claim about breakfast. We might take (or mistake) his claim for a true proposition (that his vocabulary were purely idiosyncratic), but any co-incidence between his intention and our interpretation would be a result of chance. We could not actually recognize it for whatever proposition it actually expressed.

In order to communicate thoughts with language to other persons, we must have shared presumptions not only about definitions of individual words, but also about grammar. The more that such presumptions are shared, the more that we may communicate; the more fine-grained the presumptions, the more precise the communication possible. In the context of such presumptions, there are right ways of using language in attempt to communicate — though any one of these ways may not be uniquely right or even uniquely best — and there are ways that are wrong.

Those who believe that there are right ways and wrong ways to use language are often called prescriptivist, and generally by those who wish to treat prescriptism as wrong-headed or as simply a position in no way superior to the alternatives. Yet, while one could find or imagine specific cases where the beliefs concerning what is right or wrong in language-use were indeed wrong-headed, forms of prescriptivism follows logically from a belief that it is desirable for people to communicate, and especially from a belief that communication is, typically speaking, something rather a lot of which is desirable. As a practical matter, altogether rejecting prescriptivism is thoughtless.

To the extent that the same presumptions of meaning are shared across persons, the meanings of words are independent of the intentions of any one person. Meanings may be treated as adhering to the words themselves. Should Mr Dumpty take a great fall, from which recovery were not possible, still his words would mean exactly what they meant when he uttered them. A very weak prescriptivism would settle there, with the meaning of expressions simply being whatever were common intention in the relevant population. This prescriptivism is so weak as not often to be recognized as prescriptivism at all; but even it says that there is a right and wrong within the use of language.

Those more widely recognized as prescriptivists want something rather different from rude democracy. In the eyes of their detractors, these prescriptivists are dogmatic traditionalists or seeking to creäte or to maintain artificial elites; such prescriptivists have existed and do exist. But, more typically, prescriptivism is founded on the belief that language should be a powerful tool for communication as such. When a typical prescriptivist encounters and considers a linguistic pattern, his or her response is conditioned by concern for how it may be expected to affect the ability to communicate, and not merely in the moment, but how its acceptance or rejection will affect our ability to understand what has been said in the past and what will be said in the future. (Such effects are not confined to the repetition of specific pattern; other specific patterns may arise from analogy; which is to say that general patterns may be repeated.) Being understood is not considered as licensing patterns that will cause future misunderstandings.

In opposing the replacement of can with the negative can't in can hardly, the typical prescriptivist isn't fighting dogmatically nor to oppress the downtrodden, nor merely concerned to protect our ability to refer to the odd-ball cases to which can't hardly with its original sense applies; rather, the prescriptivist is trying to ward-off a more general chaos in which we can hardly distinguish negation from affirmation. (Likewise for the positive could care less standing where the negative couldn't care less would be proper.) When the prescriptivist objects to using podium to refer to a lectern, it's so that we continue to understand prior use and so that we don't lose a word for the exact meaning that podium has had. We already have a word for lecterns, and we can coin new words if there is a felt need for more.

The usual attempt to rebut prescriptivism of all sorts notes that language evolves. Indeed it does, but prescriptivisms themselves — of all sorts — play rôles in that evolution. When a prescriptivist objects to can't hardly being used where can hardly would be proper, he or she isn't fighting evolution itself but participating in an evolutionary struggle. Sometimes traditional forms are successfully defended; sometimes old forms are resurrected; sometimes deliberate innovations (as opposed to spontaneous innovations) are widely adopted. Sometimes the results have benefitted our ability to communicate; sometimes they have not; but all these cases are part of the dynamic of real-world linguistic evolution.

The Evolution Card is not a good one to play in any event. Linguistic evolution may be inevitable, but it doesn't always represent progress. It will not even tend to progress without an appropriate context. Indeed, sometimes linguistic evolution reverses course. For example: English arose from Germanic languages, in which some words were formed by compounding. But English largely abandoned this characteristic for a time, only to have it reïntroduced by scholarly contact with Classical Greek and Latin. (That's largely why our compounds are so often built of Greek or Latin roots, whereäs those of Modern German are more likely to be constructed with Germanic roots.) It was evolution when compounding was abandoned, and evolution when it was reädopted. If compounding were good, then evolution were wrong to abandon it; if compounding were bad, then evolution were wrong to reëstablish it. And one cannot logically leap from the insight that evolution is both inevitable and neither necessarily good nor necessarily bad to the conclusion that any aspect of linguistic practice is a matter of indifference, that nothing of linguistic practice is good or bad. One should especially not attempt to apply such an inference peculiarly to views on practice that one dislikes.

Sometimes, I don't know how to write about important matters. Please bear with me, because this subject is far more important than it might initially seem.

When most people encounter the word species, it is either in the context of a biological discussion, or the word is used as a metaphorical borrowing from discussion of that sort. It actually has more general meanings, the broadest simply being class of things of shared characteristics. But what concerns me here is indeed its biological sense.

Most people who have any notion at all of the word derive their understanding of the biological signification from a combination of observed use and whatever was told to them by middle- and high-school texts of alleged science. Many of them know that organisms are categorized hierarchically, and that species is a finer category than genus. But, if asked to describe the classification of animals as different, say, as are cats and dogs, far more people would descibe them as of different species than as of different family or as of different genus. There is an inferred sense that difference in species is rather fundamental.

The Shorter Oxford English Dictionary gives the biological sense thus:

A taxonomic grouping ranking next below genus and subgenus, which contains organisms that are uniquely distinguished from others by certain shared characteristics and usu. by an inability to interbreed with members of other such groupings; such a grouping as denoted by a Latin binomial, and freq. subdivided into subspecies, races, varieties, etc.; the organisms of such a grouping.

That bit about inability to interbreed is a bit loose; for example, most biologists would classify horses and donkeys as of different species, though they can produce offspring. However, a striking characteristic of those offspring is that they cannot themselves produce further offspring. The infertility of those offspring is usually cited towards explaining the speciation.

In any case, The SOED hedged with that usu. because some biologists categorize animals as of different species though they can interbreed down through indefinitely many generations, as in the case of coyotes (C. latrans) with wolves (C. lupus).

Over some decades, anthropologists disagreed over whether to classify Neanderthalers as a distinct species, H. neanderthalensis, or as a sub-species of H. sapiens. As there was no way to observe potential interbreeding, early disagreement turned on issues of overt morphology — the shapes of skulls, dentition, &c. But then interbreeding became, in a sense, potentially observable as it became possible to extract and analyze DNA from remains of Neanderthalers. Initial results (quite surprising to me) suggested no interbreeding, and it became more commonly accepted that they should be considered a distinct species. However, when later genetic evidence began to show the presence of Neanderthaler genes in some modern populations of H. sapiens, the practice of treating them as a distinct species was not universally abandoned. It is still common to classify Neanderthalers as a distinct species, though this implicitly means that species is not being used with the usu. signification. And when, far more recently, a similar archaïc population, the Denisovans, were distinguished, it became fairly common also to categorize them as a distinct species, though their genes are likewise found in some modern populations of H. sapiens.

But, again, when most lay-people hear or read the word species, they are imagining a quite significant distinction. And when they hear and read of Neanderthalers or of Denisovans as distinct species, they infer that these people were not human. Here are three example articles that I quickly found of journalists doing just that in the case of Neanderthalers or in that of Denisovans:

• Neanderthals: Facts About Our Extinct Human Relatives by Jessie Szalay on 19 March 2013 at LiveScience (The title refers to the Neanderthalers as human relatives, but the body of the article treats them as distinct from human.)
• Study confirms that Neanderthals and humans got it on by Arielle Duhaime-Ross on 8 April 2014 at the Verge
• Early man's love triangle with neighbors helped us survive by Traci Watson on 10 November 2016 at USA Today (This article describes the Neanderthalers and Denisovans as not-quite-human creatures.)

As these archaïc populations are extinct, there may not seem to be any more of a social issue here than there typically is with misunderstood science. But a problem is coming right at us. And it's associated with the point that the genes of archaïc populations are found in modern populations — in different distributions. Take, for example, this article:

• Aboriginal Australians, Pacific Islanders carry DNA of unknown human species, research analysis suggests on 26 October 2016 from ABC

The author or authors blithely refer to the Neanderthalers, to the Denisovans, and to an additional, hypothesized archaïc population as distinct species without explaining whatever is there meant by the term. A large share of readers will regard the archaïc populations as not fully human, and infer that different ethnic groups have more or less genetic material that is not fully human. It will be inappropriately inferred that some ethnic groups are thus less human or more human than are others.

Anthropologists and biologists who talk with lay-persons, and especially with journalists and with other informal educators, need to emphasize the arbitrariness in use of the word species, and these scientists need to impress upon their audiences that the word should be avoided or explained in all popular-science journalism that touches upon our relationships with archaïc populations.