Dictionaries and thesauri often treat accuracy and precision as synonymous, or as nearly so. But the words accuracy and precision and their coördinates[1] are each most strongly associated with a distinct and important notion. The word exactitude (often treated as synonymous with the previous two) and coördinates are most strongly associated with something rather like the combined sense of those other two, but with a notable difference.

When we say that a specification is precise, we do not necessarily mean that it were correct when judged against the underlying objectives. We may merely mean that it were given with considerable explicit or implicit detail. If I tell you that a musical show will begin at 8:15:03 PM, then I am being precise (indeed, surprisingly so). But the show may begin at some other time; in fact, it may never have been planned to begin at that stated time; I can be both precise and wrong.

If your friend tells you that the show will begin shortly after 9 PM, then she may be accurate, though she was far less precise than I.[2] The word accuracy and coördinates are associated with closeness to the truth; and, in everyday discourse, she might be said to be more accurate were she to be more precise while remaining within the range implied by shortly after 9 PM. But the word is also associated with encompassing the truth; if the precision seemed to narrow the range of possibilities in a way that excluded what proved to be the truth, then she might be regarded a having become less accurate. (If one is told that the show is to begin at 9:15 PM, but it begins at 9:05 PM, then one might feel more misled than had one been less precisely told shortly after 9 PM.)

(Note that it would be seen as self-contradiction to say that someone were accurately wrong, though we sometimes encounter the phrase precisely wrong. The latter carries with it the sense — usually hyperbolic — that the someone had managed to be so wrong that even the slightest deviation from what he or she had said or done would be an improvement.)

Although some people might jocularly, eristically, or sophistically pretend that one truth were somehow truer than another, any meaningful proposition is either simply true or simply false (though which may be unknown and there are degrees of plausibility). If Tom and Dick each go to the store, then it is true that one of them has gone to the store. It is not closer to the truth that two of them have gone to the store. It might be said that it were more accurate that two of them have gone to the store, but this seems to imply that it is truer that two went than that one went, and this implication is false. Fortunately, we have a word and coördinates that can carry with them a particular sense of accuracy and precision, with exclusion. These words are exact, exactly, and exactitude.[3] It is true that one person has gone to the store, but it is not true that exactly one person has gone to the store.[4]

(The expression exactly wrong is usually in hyperbolic contrast with exactly right, but is sometimes applied elliptically, when there is believed to be exactly one way in which to have been wrong.)

Even if one is not greatly concerned with rigor, these distinctions can be important. Asking members of an audience to be more accurate when one wants them to be more precise may inadvertently suggest to the audience that one thinks them to have been untruthful! Typically, risking that inference brings no benefit. It would then be better to ask them to be more precise or more exact.[5] The latter may work best with the passive-aggressive or with the autistic, who might otherwise be more precise while less accurate.

[1] The coördinates of a word are simply the other parts of speech built of the same root and carrying the same general sense adapted to a different grammatical rôle. For example, the adjective accurate and the adverb accurately are coördinate with the abstract noun accuracy.

[2] In discussions of computer science, the everyday distinction between accuracy and precision is made more emphatic, because the mathematics of computing is discrete, and limitations in detail have important implications. For example, ordinary floating-point encoding imperfectly represents numbers such as 1/10. That's why calculators and computers so often seem to add or to subtract tiny fractions to or from the ends of numbers. Number-crunching scientist who do not themselves recognize this issue have generated spurious results by proceeding as if computers have unlimited precision, and thus by mistaking artefacts of limited precision for something meaningful within the data. I strongly suspect that a major reason that so many reported econometric results were not subsequently found by other researchers poring over the very same data was that the original researchers (or, sometimes, the later researchers!) were not taking into account the implications of limited precision.

[3] The words just and only can carry the same meaning, but often bring normative implications.

[4] In mathematics, ∃x translates to for some x, while ∃!x translates to for exactly one x.

[5] Asking a person to be more just or more only would almost surely provoke bafflement.

Just as in a natural language there are issues of style on top of those of grammar, of orthography, and of syntax, there are issues of style in computer languages.

For example, in some languages, var = 3 sets var to 3, while var == 3 tests whether var is (already) equal to 3. Omit an = in a test, and the test accidentally becomes an assignment; many programs silently fail as a result of such an omission. But adopt the style of always putting any constant on the left side of the test (eg, 3 == var) and the error (eg, 3 = var, which attempts to set 3 to something) is noticed as soon as the compiler or interpetter reaches it. (There are compilers, interpretters, and separate utilities that will spot possible instances of errors of this sort. It's good to use tools with these features, but best not to be dependent upon them; and one doesn't want the notice of a genuine error to be lost in a sea of largely spurious warnings.)

The specifications of some computer languages, especially of those that are older, significantly limit the lengths of names and of labels; but it's otherwise stylistically best to chose names and labels that clearly identify the nature of whatever is named or labelled. Transparent names and labels then function as integrated documentation. One identifies a lazy or thoughtless programmer by the needless use of opaque names and labels. In Java, the stylistic convention is to name things in ways that clearly identify them; and the convention is to camel-case the names of variables, methods, and classes (eg, countOfBadBits); other languages also allow names to be clearly identifying, but the convention is to separate naming words with underscores (eg, count_of_bad_bits). One uses the naming convention that prevails amongst programmers of that language, so as not to throw-off other programmers who have to deal with the code; it is literally uncivil[1] to use the convention prevailing amongst programmers of one language when writing code in a language where a different convention prevails. (Had it been up to me, then we'd use a different naming style in Java; but it wasn't up to me and I abide by the prevailing convention.)

Many languages end statements with ;. When I helped other students debug SAS programs, I found that the error that they most often made was to omit that semicolon. Sometimes the program wouldn't compile, but sometimes it would compile and silently do something unintended. So I told them to put a space just before the semicolon. The program would still compile just fine if otherwise properly done; but, with all the semicolons visually floating instead of being up against something else, an omission would more easily be spotted. I don't myself use this style for every language in which it would work, but I adopt it for languages in which I notice myself or others omitting the semicolon.

(I was reminded of the general issue of coding style when working on some code written in Python, and wondering whether to put a space before each semicolon.)

[1] Civility is not conterminous with pleasantry; but, rather, a matter of behaving to avoid and to resolve conflict in interaction with other persons.

Most or all of us have heard or read of the question of how many angels can dance on the head of a pin. This question was introduced to satirize and to dismiss a problem that challenged scholastic philosophers, namely Given that there are things that do not have body but do have location, can two or more of these things occupy the same location at the same time? Now, we might labor the idea of body; but suffice it to say that it were presumed that things with body could not simultaneously occupy the exact same location, but that there were things of another class that could occupy the exact same location as could a thing with body. The question then was whether they could occupy the same location as other things of their own class.

One of the ways in which this puzzle had bearing was on attempts to understand the nature of devils (fallen angels) and how they might interact with ordinary people. The question thus actually had bearing on the witchcraft mania.

But another way in which this question had bearing was in consideration of how we distinguish one thing from another, perceptually and conceptually. In theory, two things might be identical except for location, but the distinct locations perhaps permit us to discern that there are two things, rather than one. And, if the location of an object at any one time is unique to that object, one can combine a description that might fit many other things with that location to identify a singular object, and thus to have an intrinsically singular corresponding concept, as opposed to a concept that might fit more than one thing.

That perhaps seems perfectly sound, but I don't understand space as other than a structure of relationships. For example, when a physicist asserts that objects of mass warp space increasingly with that mass, I take this to be no more or less than a claim that objects of larger or smaller mass have different spatial relationships with things, and cause other things to have different spatial relationships each with others. (The latter implies that a spatial relationship involving the object of mass underlies the spatial relationships amongst the things other than that object.) When we attempt to distinguish objects based upon location, which is a matter of relationships amongst objects, remarkable considerations arise.

First imagine a very small universe, having just one body in it. A universe is not small by virtue of one hitting a wall after travelling some distance; it is small by virtue of having a non-Euclidean geometry, such that after a relatively short amount of travel one finds oneself back where one started. As light travelled from the object, it would eventually find its way back to the object. If one could somehow see, as if within this universe, and looked in various directions, with sufficiently strong vision, one might see the object, seemingly off in the distance, even if the view began as if one were standing right at or on the object. Seemingly beyond the object, one might see the object yet again, and so forth. That's the experience in one sort of universe. Now imagine an infinitely large universe, as if built by tiling duplicate sectors, in which there were infinitely many objects, positioned to given the same experience as in the first universe.

I declared that a universe had just one object; I declared that a universe had infinitely many objects. I don't actually believe that the apparently second universe is intrinsically distinct from the first. I think that we may conceptualize the first universe as the second, and vice versa, and that the count of objects is an artefact of our conceptualization. Of course, if there were no more than indiscernible differences amongst what seemed to be infinitely many objects, then I might claim that there were no practical differences from a universe of one object; but I here make the stronger claim that, if there are no differences beyond perhaps whatever is captured by the two given descriptions of location, then these descriptions are each of the same universe. It would simply beg the question to insist that one universe is different from the other in that one were finite but configured so that it seemed infinitely repeating, while the other truly were infinite and repeating. Granted that viewing as if within the universe seems to locate a means of viewing close to one object. (One might even imagine oneself invisibly located as an additional object in the universe.) But how is the location of that means near one object distinct from its location near all of them? (How is oneself's being located in the universe near one object distinct from the location of a perfect duplicate of oneself being near each of them?)

In a universe more like our own, if we had what seemed to be two otherwise indistinguishable objects at different locations, there would be other discernible objects that seemed to support a distinction. What we might regard as one object would be near to various other objects, and far from still others. Likewise for what we might regard as a different object, with a distinct set of things.

Let's mentally step away from that scenario for a bit, and return to the scholastic problem of things that do not have body but do have location. If two of these things are otherwise indistinguishable, and if they can occupy the same location at the same time, then ex hypothesi there is no way to distinguish one from another when they do occupy the same location. (The space occupied might be different when both moved into it — for example, it might become less translucent — but that doesn't mean that we can distinguish one of two things from another. And if the properties of these things are not in some sense additive or subtractive, but combine according to inclusive disjunction — that is to say that the attribute is either there or not, but has no further possible ordering to it — then we cannot tell how just many of these things are there by discernment of these properties.)

But, when they occupy the same location, I ask whether there are in fact two things. What would be the difference of two such things coming to occupy one location from two otherwise identical things coming to be one thing at one location? Perhaps what seemed one thing might again become two, but that wouldn't prove that they had remained distinct at the one location. Perhaps one thing might have become three, each just like the two from which the one had been formed. My experience (and, as I believe, yours) is that this has never happened. But I know of no logic that prevents it from happening; it merely violates my present best guess of the physical laws (which entail principles of conservation). If what seemd to be two things came together and seemed to be one, and then that one thing seemed to become three, some person might guess that what had earlier seemed to be two things were atually three things, two already in combination. But if all the attributes combined in conformance with inclusive disjunction, then in what sense would that be different from just what had seemed to happen?

If we accept that two otherwise indistinguishable things become one thing when they occupy one location, does that thing continue to exist should it become two things? Is it one of the two things? both of the two things? each of the two things? Is the proper answer different when the two things are indistinguishable except for location from what was one thing?

(If we are transporting some very great criminal by paddy wagon and, upon arrival, find three persons, each indistiguishable from the person whom we tossed into the wagon, and each insisting that he is just that person, do we treat each of them as that person, or charge each with no more than abetting an escape, on the theory that it is most likely of any given one of them that he is not that person? This problem might be primarily epistemological — so that one of the three suspects is our original perpetrator even if we shall never know whom — but that's bad enough; and we can make it still more fundamental if we allow for teleportation and for matter duplication.)

Let's mentally step back to the scenario of two otherwise indistinguishable objects at different locations in a universe rather like our own. Are these actually two objects, or one object that is bi-located, or one object in one location that appears as two locations because of a strangeness of space? Do these three descriptions actually distinguish different realities? If we mark one of these apparently two objects and see an identical mark appear on the other, do we regard it as the same object, or as two objects such that one is some sort of sympathy with the other? If we mark what seems one object and a mark does not appear on the other, do we regard this as proof that there were never one bilocated object nor a weirdness of space, or do we interpret this case as of one object becoming two distinct objects (with an end to the bilocation or with an adjustment of space), perhaps exactly as a a result of our action? (The classic formulation of Ockham's Razor is entia non sunt multiplicanda præter necessitatem. If we posit that there were always two objects, are we conforming to that prescription?)

Because space need not be as Euclid had insightfully assumed and as Platon and Kant had thoughtlessly presumed, we can interpret any case where we have what otherwise must be a single thing simulatenously occupying multiple locations as in fact that single thing in one location. The practical cost, however, is that we are compelled to identify locations by the things occupying them (and not merely by the things about them); but we had set-out to identify things by the locations that they occupied!

Let's say that we have an object in a strange space, so that it is effectively bilocated, and we point to it and say this. Assuming that we don't also say not that, pointing to the other apparent location, is there any problem? It is one thing to incorporate mistaking of one thing for two into an assertion; another simply not to recognize some of the characteristics of that one thing. (There is a problem if Selina Kyle cries I am in love with Bruce Wayne, not with the Batman! but there would have been no such problem had she simply declared I am in love with Bruce Wayne!)

But if the case of two otherwise identical but differently located objects (perhaps each in perfect sympathy with the other) and the case of one apparently bilocated object are really just different descriptions of the same situation, then the applicability of not that — and number more generally — seems in some cases to be an artefact of the descriptive framework. Especially in the context of such implications, some people will insist that one of these descriptions must surely be mistaken, even if as a practical matter we cannot tell which. (Some people will further insist that the description that conforms to simpler spatial relations (that of two objects in perfect sympathy) is the one that is more likely correct; other people will insist that the description that requires fewer objects (that of a bilocated object) is more likely correct.) However, the apparent contradiction isn't internal to either description, and each description may be translated into the other. That one of them is right doesn't make the other wrong.

If I cannot point to something and say this and thereby distinguish it not merely from everything not there but from everything not it, then how can I have an intrinsically singular concept? To baldly incorporate singularity into a concept is just question-begging. (One ought not to say that two spheres are exactly alike except just in-so-far as one is unique, or is uniquely unique.)

Where, then, is singularity to be found? I think that it is to be found in experience, literally. The raw stuff of experience is sensation and sense-perception, not conception. (We may have concepts of sensations, but sensations are not themselves concepts; we may have concepts of sense-perceptions, but sense-perceptions are not themselves concepts.) Percepts and concepts are constructed to explain sensation and sense-perception. Those percepts and concepts may be perfectly accurate, but they are not intrinsically singular except to the extent that we associate them with sensation or with sense-perception. That is to say, for example, that we have a cluster of sensation or of sense-perception, and we have or build a concept of something by which to explain it, which concept is not singular except in-so-far as we implicitly or explicitly add to it the attribute of causing that particular cluster. And, if we do that, then we must in such case commit to a concept that does not allow co-location of otherwise identical things. That is not to say that we forbid co-location in general; but that singular concepts cannot be fitted to such co-located things. (It is probably a very bad idea to construct an explanatory model that employs co-location of otherwise identical things all of whose attributes combine in accordance with inclusive disjunction.)

In any case, the alternatives to exploring such considerations are dogmatism and nihilism. There is nothing intrinsically practical about dogmatism nor about nihilism, which stand in the way of our understanding the universe as deeply as we might and of our helping those who lose (or never find) their ways in their own attempts to understand the world. The scholastics who worried about the relationship of location to identity during what have come to be dismissed as the Dark Ages were concerned with foundational questions of what we ought to practice. It is fine to jest about their efforts only if the joke does not hide the truth.

I'm not a great fan of Star Trek, for reasons that I won't labor here; but at times it provides useful cultural references.

Various people have drawn a comparison between the Clinton campaign and the Borg, prompting me to put together this logo And then to make stickers and magnets with it available at CafePress. Presumably anyone voluntarily displaying one of these magnets or stickers would be doing so ironically.

(For what little it's worth, I endorse no candidate, and still will not be voting for the least of the n evils.)

Up-Date (2016:07/29): Resistance is difficult. Yester-day after-noon, I received notice from CafePress that my graphic was being investigated as a possible violation of intellectual property. This charge is absurd, in that the Clinton logo and slogan are too simple to be copyrighted and no trademark protection has been attempted; likewise for the Borg reference. And, even if the Clinton logo and slogan were intellectual property, none-the-less my use of these elements would constitute fair use. (Though it must be admitted that, since I am not satirizing the Borg, if there were intellectual property there then my use would be more questionable.)

While the image is under investigation, the items on which it was to be placed are unavailable. A decision is supposed to come within 48 hours of the announcement. Of course, someone at CafePress may make a partisan call; such actions have become commonplace. In that case, I will look for a different service through which to get things produced.

Up-Date (2016:07/29): Resistance continues. CafePress simply chose to misrepresent the design as in violation of their stated content policy. So, as I said that I would, I've begun migrating to alternative vendors. I will also be billing CafePress for my labor.

In the course of some remarks on Subjective Probability by Richard C. Jeffrey, and later in defending a claim by Gary Stanley Becker, I have previously given some explanation of the model of expected-utility maximization and of axiomata of independence.

Models of expected-utility maximization are so intuïtively appealing to some people that they take one of these models to be peculiarly rational, and deviations from any such model thus to be irrational. I note that the author of a popular 'blog seems to have done just that, yester-day.[0]

My own work shows that quantities cannot be fitted to preferences, which pulls the rug from under expected-utility maximization, but there are other problems as well. The paradox that the 'blogger explores represents a violation of the strong independence axiom. What I want to do here is first to explain again expected-utility maximization, and then to show that the strong independence axiom violates rationality.

A mathematical expectation is what people often mean when they say average — a probability-weighted sum of measures of possible outcomes. For example, when a meteorologist gives an expected rainfall or an expected temperature for to-morrow, she isn't actually telling you to anticipate exactly that rainfall or exactly that temperature; she's telling you that, given observed conditions to-day, the probability distribution for to-morrow has a particular mean quantity of rain or a particular mean temperature.

The actual mathematics of expectation is easiest to explain in simple cases of gambling (which is just whence the modern, main-stream theories of probability itself arose). For example, let's say that we have a fair coin (with a 50% chance of heads and a 50% chance of tails); and that if it comes-up heads then you get $100, while if it comes-up tails then you get $1. The expected pay-out is .5 × $100 + .5 × $1 = $50.50 Now, let's say that another coin has a 25% chance of coming-up heads and a 75% chance of coming-up tails, and you'd get $150 for heads and $10 for tails. Its expected pay-out is .25 × $150 + .75 × $10 = $45 More complicated cases arise when there are more than two possible outcomes, but the basic formula is just prob(x₁)·m(x₁) + prob(x₂)·m(x₂) + … + prob(x_n)·m(x_n) where x_i is the i-th possible outcome, prob(x_i) is the probability of that i-th possible outcome, and m(x_i) is some measure (mass, temperature, dollar-value, or whatever) of that outcome. In our coin-flipping examples, each expectation is of form prob(heads)·payout(heads) + prob(tails)·payout(tails)

One of the numerical examples of coin-flips offered both a higher maximum pay-out ($150 v $100) and a higher minimum pay-out ($10 v $1) yet a lower expected pay-out ($45 v $50.50). Most people will look at this, and decide that the expected pay-out should be the determining factor, though it's harder than many people reälize to make the case.

With monetary pay-outs, there is a temptation to use the monetary unit as the measure in computing the expectation by which we choose. But the actual usefulness of money isn't constant. We have various priorities; and, when possible, we take care of the things of greatest priority before we take care of things of lower priority. So, typically, if we get more money, it goes to things of lower priority than did the money that we already had. The next dollar isn't usually as valuable to us as any one of the dollars that we already had. Thus, a pay-out of $1 million shouldn't be a thousand times as valuable as a pay-out of $1000, especially if we keep in-mind a context in which a pay-out will be on top of whatever we already have in life. So, if we're making our decisions based upon some sort of mathematical expectation then, instead of computing an expected monetary value, we really want an expected usefulness value, prob(x₁)·u(x₁) + prob(x₂)·u(x₂) + … + prob(x_n)·u(x_n) where u() is a function giving a measure of usefulness. This u is the main-stream notion of utility, though sadly it should be noted that most main-stream economists have quite lost sight of the point that utility as they imagine it is just a special case of usefulness.

A model of expected-utility maximization is one that takes each possible action a_j, associates it with a set of probabilities {prob(x₁|a_j),prob(x₂|a_j),…,prob(x_n|a_j)} (the probabilities now explicitly noted as conditioned upon the choice of action) and asserts that we should chose an action a_k which gives us an expected utility prob(x₁|a_k)·u(x₁) + prob(x₂|a_k)·u(x₂) + … + prob(x_n|a_k)·u(x_n) as high or higher than that of any other action.

If there is a non-monetary measure of usefulness in the case of monetary pay-outs, then there is no evident reason that there should not be such a measure in the case of non-monetary pay-outs. (And, likewise, if there is no such measure in the case of non-monetary pay-outs, there is no reason to suppose one in the case of monetary pay-outs, where we have seen that the monetary pay-out isn't really a proper measure.) The main-stream of economic theory runs with that; its model of decision-making is expected-utility maximization.

The model does not require that people have a conscious measure of usefulness, and certainly does not require that they have a conscious process for arriving at such a measure; it can be taken as a model of the gut. And employment of the model doesn't mean that the economist believes that it is literally true; economists across many schools-of-thought regard idealizations of various sorts as approximations sufficient for their purposes. It is only lesser economists who do so incautiously and without regard to problems of scale.

But, while expected-utility maximization may certainly be regarded as an idealization, it should not be mistaken for an idealization of peculiar rationality nor even for an idealization of rationality of just one variety amongst many. Expected-utility maximization is not rational even if we grant — as I would not — that there is some quantification that can be fitted to our priorities.

Expected-utility maximization entails a proposition that the relevant expectation is of potential outcomes which are taken themselves to be no better or worse for being more or less probable. That is to say that what would be the reälized value of an outcome is the measure of the outcome to be used in the computation of the expectation; the expectation is simply lineär in the probabilities. This feature of the model follows from what is known as the strong independence axiom (underscore mine) because Paul Anthony Samuelson, having noticed it, conceptualized it as an axiom. It and propositions suggested to serve in its stead as an axiom (thus rendering it a theorem) have been challenged in various ways. I will not here survey the challenges.

However, the first problem that I saw with expected-utility maximization was with that lineärity, in-so-far as it implies that people do not benefit from the experience of selecting amongst discernible non-trivial lotteries as such.[1]

Good comes from engaging in some gambles as such, exactly because gambling more generally is unavoidable. We need practice to gamble properly, and practice to stay in cognitive shape for gambling. Even if we get that practice without seeking it, in the course of engaging in our everyday gambles, there is still value to that practice as such. A gamble may become more valuable as a result of the probability of the best outcome being made less probable, and less valuable as a result of the best outcome becoming more certain. The value of lotteries is not lineär in their probabilities!

It might be objected that this value is only associated with our cognitive limitations, which limitations it might be argued represented a sort of irrationality. But we only compound the irrationality if we avoid remedial activity because under other circumstance it would not have done us good. Nor do I see that we should any more accept that a person who needs cognitive exercise to stay in cognitive shape is thus out of cognitive shape than we would say that someone who needs physical exercise to stay in physical shape is thus out of physical shape.

[0 (2016:07/22)] Very quickly, in a brief exchange, he saw the error, and he's corrected his entry; so I've removed the link and identification here.

[1] When I speak or write of lotteries or of gambling, I'm not confining myself to those cases for which lay-people normally use those terms, but applying to situations in which one is confronted by a choice of actions, and various outcomes (albeït some perhaps quite impossible) may be imagined; things to which the term lottery or gamble are more usually applied are simply special cases of this general idea. A trivial lottery is one that most people would especially not think to be a lottery or gamble at all, because the only probabilities are either 0 or 1; a non-trivial lottery involves outcomes with probabilities in between those two. Of course, in real life there are few if any perfectly trivial lotteries, but a lot of things are close enough that people imagine them as having no risk or uncertainty; that's why I refer to discernible non-trivial lotteries, which people see as involving risk or uncertainty.

To-day, I found myself unable to log-in to this 'blog. I got a diagnostic that I were entering the wrong password. I don't want to burden my readers with a detailed retelling, but what had actually happened was that an up-date of WordPress rejected my password — it wasn't that I were entering the wrong password; it was that the password that I was entering was now prohibitted.

On top of the login code misreporting the problem, the code for resetting the password wouldn't tell me why my password was being rejected. But it was rejected for containing a particular sub-string; and when I removed that sub-string, the password was then accepted.

If you understand passcodes (perhaps in part from reading my previous entry in which they were discussed), then you should see that there is something literally stupid in the WordPress software. Let's say that the forbidden sub-string were 8675309 and that my password were X.52341-hunao-8675309.Y. If I drop the 8675309, the password becomes X.52341-hunao-.Y. That is now accepted, though it is less secure!

If a would-be intruder knew where in the original password 8675309 appeared, and knew the length of the password, then the password would effectively be p₁p₂…p₁₄8675309p₂₂p₂₃ where each p_i were an unknown character, and the new password would be p₁p₂…p₁₄p₂₂p₂₃ so that the two passwords would be equally secure! (Either way, an intruder must find a sequence of sixteen unknown characters.) But, as it is, would-be intruders wouldn't be sure that the sub-string appeared, let alone where in the code it would appear, nor how long the password were. One could, in fact, conceptualize the sub-string 8675309 as if it were a single character of extraordinary length (a macro-character) and of great popularity which character might appear within a string of equal or greater length, in which case prohibiting the sub-string would be rather like prohibiting the use of E.

That's not to say that common sub-strings should simply be accepted as passwords or within passwords. A great many systems have been hacked because someone foolishly used passwords such as password, root, or batman. But, instead of rejecting a password because it contained a popular sub-string, the software could, for example, test to see whether the password would be secure if the sub-string were excised, in which case it should be at least slightly more secure if the sub-string were retained.

(Note that this approach works with popular sub-strings of any length, including those of just one character! In fact, when there is no upper-limit on the length of passcodes, they may be securely constructed of nothing but popular sub-strings each of which has multiple characters; a secure password could be made by concatenating ten or more of the one hundred most popular passcodes. Mathematically, the problem of using just one popular passcode is fundamentally the same as that of using a short passcode!)

Sometimes, it's smart programming to write stupid programs, because the costs of designing, implementing, and maintaining more sophisticated software out-weigh the benefits. But, here, the WordPress programmers have opted for cheapness in a way that needlessly thwarts and insults some users, and can actually make systems less secure in those cases. (And the poor diagnostics are simply inexcusable.)

Most of the time, the inability or unwillingness of people to understand the difference between sex and gender is simply a low-level annoyance for me.[1] But, over the past few days, I have been increasingly irritated by the bigotry that this confusion is facilitating.

Unfortunately, many cultures, including our own, put pressure on people of a particular sex to adopt a particular gender; this is bigotry of one sort. Unfortunately, people of a sex who don't want to be of the socially prescribed gender often develop an active hostility towards those of that sex-gender combination; that is bigotry of another sort.

People who want to be of a given gender but who are not do not represent a toxic expression of that gender, because they are not of that gender. Claiming that a non-masculine person were toxically masculine or that a non-feminine person were toxically feminine entails a logical contradiction, regardless of whether the person were a male wanting to be masculine or a female wanting to be feminine.[2] And when toxicity results exactly from the fact that a person is not of a gender that the person feels that he or she ought to be, the illogic is especially acute.

Omar Mir Seddique Mateen was certainly toxic, but he lacked at least one of the core attributes of masculinity. His desire as a non-masculine male to be masculine contributed greatly to his toxicity.

Whether intentionally or merely thoughtlessly, to use toxic masculinity in describing Mateen is a slur against masculinity.[3] And that slur will come most naturally to those who are implicitly or explicitly hostile to masculinity.

He simply wasn't of my gender; no one should speak or write as if he were.

[1] Sex is a condition of the structures of the body, and associated with reproductive function. The term gender is sometimes used as a foolish mincing term for sex, but I mean here to refer to the set of behavioral characteristics (including rôles) that are associated with sex by expectations at the social, familial, and personal level. The term gender is taken by analogy from grammar, as are the terms masculine and feminine.

[2] There are sexes other than male and female and genders other than masculine and feminine, but traditional social expectations have included correspondences amongst such sexes and such genders. Instead, people who do not fit neatly as male or as female have been expected either to seek some sort of treatment to become one of those two sexes (with a masculine gender for males and a feminine gender for females) or to withdraw from society.

[3] It would be accurate, but misleading, to instead describe his condition as one of toxic non-masculinity.

In the '70s or earlier, it was noticed that, in America, academic departments of economics that were located at or near the Atlantic or Pacific Ocean tended to have one set of attitudes about macrœconomics, while those away from the oceans and in particular near the Great Lakes tended to have another. From this, they were grouped as saltwater and as freshwater (or as sweetwater), respectively.

The distinction was most widely recognized in macrœconomics, with the freshwater departments arguing for founding macrœconomics in micrœconomics considerations (especially in the theory of individual decision-making under uncertainty), for using dynamic models, and for quantification. However, though (or perhaps because) they emphasized the importance of micrœconomic considerations for the development of macrœconomic theory, the freshwater schools seemed more content with standard micrœconomic theory than were the saltwater schools, where non-standard decision-theory was more investigated (while being regarded as less important to macrœconomics).

It has been claimed that the distinction between these groups has faded to irrelevancy, with younger economists having adopted insights from both, and with older disputants having departed. However, since the on-set of the most recent financial crisis, old-fashioned Keynesians have become more vociferous, if not actually much more numerous. (Paul Krugman no longer takes any water with his salt.)

It occurs to me that, for one group of heterodox economists, we might refer to the Wien, or … to the Danube. So … blue-water? (Blauewasser?[1]) Indeed, as one branch of that school-of-thought tends to represent itself as definitive for the whole school, perhaps blue-water could be the more inclusive term.

Meanwhile, through Cambridge runs the River Cam. There's something in that water. Something bad.

[1 (2022:04/02)] [ˈblaʊeˌvasa].

I have lots of keys. Most of those that are not on the key-ring that I routinely carry with me are tagged, so that I know to what they go. But, as I was going through the drawer in which those keys are kept, I found one that was labelled HARD KEY. I confess that this label was not and is not now very helpful.

There is such a thing as is called a soft key; it's a passcode of some sort. What would one call a hard key? A key that is not a soft key? That would make every key in that drawer a hard key; there'd be no use in labelling a key of that sort simply as a key of that sort.

My best guess is that this key were a key that were badly cut or worn, so that it were hard to use. But to use where?

Well, I couldn't and cannot remember; but that's okay, because I found that it matches another key that I have on a ring labelled Orphans, and nothing goes on that ring unless I know that it's no longer possible or no longer permissible for me to use the key in its lock. (There is separate ring for keys that are merely probable orphans.) Some of the orphans also have further tags; some, as in the case of the brother of the HARD KEY do not; but when that brother was put on the ring, I knew to what it went, and knew that I couldn't or shouldn't access that lock.

I didn't save the orphans thinking that I might someday match one with an unidentified key. A few of them I saved for their sentimental values. Most I saved simply to have keys with which to do other things; for example, they could be filed into bump keys or given to children or used as props; the intention in identifying them as orphans was that most of these keys be distinguished as expendible. Of course now, in the case of a key with no twin on that ring, I will be a bit more reluctant to alter or part with it, as it might someday be matched with another mysterious key. I am enslaved by my keys.

I have long and often encountered discussion that implicitly or explicitly involves notions of property or of ownership, which discussion is rendered incoherent from a failure to consider what it means for something to be property, what it means to own something.

Some confusion arises because we have come often to use the word property casually to mean an object (physical or more abstract) to which ownership of some sort may apply, without our considering whether the object is well conceptualized for purposes of considering property rights,[1] and without considering that actual ownership associated with that object might be distributed in some complicated ways amongst multiple parties.

One might, for some reason, associate a plot of land with an object imagined as beginning at the center of the Earth and extending into the atmosphere (or beyond); from such an association, and then from a presumption that the whole object were property, farmers were once known to shoot at airplanes as trespassing vehicles. Yet other folk would assert that owning a plot of land as such only entitled one to control things to lesser depths and heights, in which case the rights could be associated with a smaller object, representing a sub-object as it were. One person might be thought to have the right to farm the aforementioned land, and another to extract its mineral resources so long as he didn't thereby interfere with the farming. Possibly others would claim peculiar easements, allowing them to travel through some or all of the object without thereby trespassing. There might be purported rights entitling still others to flows of resources such water, air, and electromagnetic radiation travelling through the object. In the case of sunlight (an electromagnetic radiation), the rights would typically be presumed to involve only some space above the soil, and the farmer might both have claims against her neighbors doing things that reduced her sunlight and be constrained by similar claims for her neighbors.

If we are thinking in terms of one object, and then change to thinking of an object within it, previously relevant rights of ownership may become irrelevant. If we instead think in terms of an object of which our original object is but a part, then new claims may become relevant. Two objects, neither of which is completely contained in the other, may share some third object as a part; so that any thorough consideration of ownership involving these two objects containing the third may involve rights that are literally identical and rights that are different. The minimal object relevant to describe some asserted set of property rights might not be sufficient to describe other rights none-the-less associated with that object. The minimal object in each of the previously mentioned cases (of farming, of easement, of mineral extraction, and of unobstructed resource flow) is somewhat different from the minimal object in the other cases.

A farmer who somehow forfeits her right not to have sunlight artificially obstructed may still be imagined to own the plot of land on which she grew her crops, yet she doesn't own what once she owned. Likewise, a house-holder who somehow surrenders his right to come and go from the plot on which the house sits doesn't own what once he owned. And, though it would perhaps seem very unsual, one might imagine these rights not transformed into claims for those who have prior rights to surrounding spaces, but instead coming into possession of third parties. For example, perhaps I speculate that I can buy whatever rights I need to build a skyscraper, on the assumption that I can buy a right to block the sunlight to a neighboring farm; I could purchase that latter right first, then discover that I am thwarted as to other purchases. This might work nicely for the farmer, but she no longer has a right that she once had; she no longer owns something that she once owned.

We can still express what things are owned as if they are objects, but we must then select our objects to match our rights of use. And our discourse can become strained and unnatural if we insist on always treating the thing owned as a distinct object rather than as a right of use. For example, if Timo is exclusively entitled to inhabit a cabin in the Winter and James is likewise entitled to inhabit it in the Summer, and we must express them as owning distinct objects, then we must treat the cabin in Winter as one object and the cabin in Summer as another. Indeed, we will surely have to be far more contrived in our construction of objects to account for what the two jointly do not own of the cabin! On the other hand, we can say that each has a right to use the cabin in some way without necessarily specifying how other rights of use are distributed; the concept of the cabin is available without first settling questions of ownership.

I don't propose that we generally stop using the word property as in the ordinary sense of a piece of property, merely that we understand that this everyday use may be misleading. Nor would I suggest that we should somehow stop thinking in terms of objects when we carefully consider ownership. But we must be alert to the fact that our choice of objects with which to think is largely taxonomic and to some degree arbitrary, and we should not take results that are no more than artefacts of that taxonomy as anything more profound.

In fact, the right of use may be recognized as itself an object of an abstract sort, but the right to use a right of use is not distinct from simply that right of use, and thus cannot be dissociated from it.[1.5]

My laboring of the relationship of ownership to objects and their uses isn't quibbling nor pirouetting. People who imagine an object as such to be owned tend all too often to imagine it somehow being owned beyond any of its various possible uses. They thus imagine that it can remain the property of one person or group even as another party — most often those in control of the state — appropriate its use, and even as this second party seizes every right of use. It then also becomes absurdly thinkable that one person might retain every right of use that she had, associated with an object, yet transfer ownership to some other party. Ownership would be reduced to absolutely nothing more than something such as a formal title.

When the state regulates property, it is taking rights of use and hence ownership. This transfer is relevant to questions of compensation (as in the case of the guarantees of the Fifth Amendment to the US Constitution[2]), and of whether state regulation of the means of production is a form of socialism.

[1] The word object comes from the Latin ob-iacere, meaning throw-before, and referred originally to that thrown before the mind. What we now call objects are, however, mental organizations of what is thrown before us. Thus, to use a classic example, we can talk about my hand as an object, and my fist as an object; they seem to be the same object, yet only sometimes. (We may still, in good conscience, use the word objective for perceptible external reality. And extending it to include unperceived and imperceptible external reality shouldn't cause more than mild discomfort; the rightful demands of etymology are not unlimited.)

[1.5] This paragraph was added on 24 May.

[2] That Amendment (with an underscore by me) reads

No person shall be held to answer for a capital, or otherwise infamous crime, unless on a presentment or indictment of a grand jury, except in cases arising in the land or naval forces, or in the militia, when in actual service in time of war or public danger; nor shall any person be subject for the same offense to be twice put in jeopardy of life or limb; nor shall be compelled in any criminal case to be a witness against himself, nor be deprived of life, liberty, or property, without due process of law; nor shall private property be taken for public use, without just compensation.