With It

28 July 2016

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 [image combining modified Hillary Clinton logo with Borg announcement] 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 lesser of the n evils.)

Strong Independence in Decision Theory

21 July 2016

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 Ross 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(x1m(x1) + prob(x2m(x2) + … + prob(xnm(xn) where xi is the i-th possible outcome, prob(xi) is the probability of that i-th possible outcome, and m(xi) is some measure (mass, temperature, dollar-value, or whatever) of that outcome. In our coin-flipping examples, each expectation is of form prob(headspayout(heads) + prob(tailspayout(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(x1u(x1) + prob(x2u(x2) + … + prob(xnu(xn) 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 aj, associates it with a set of probabilities {prob(x1|aj),prob(x2|aj),…,prob(xn|aj)} (the probabilities now explicitly noted as conditioned upon the choice of action) and asserts that we should chose an action ak which gives us an expected utility prob(x1|aku(x1) + prob(x2|aku(x2) + … + prob(xn|aku(xn) 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.

Passcodes Redux

1 July 2016

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 p1p2p148675309p22p23 where each pi were an unknown character, and the new password would be p1p2p14p22p23 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.)

Toxic Taxonomy

17 June 2016

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.

It's the Water

5 June 2016

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?) 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.

Annvs Horribilis

31 May 2016

A thousand miles is a measure of special symbolism in the poetry of hearts longing or wounded. A more accurate figure in my case might be 1061 miles. Or, if one reckoned driving distance, something like 1254 miles. But exactitude does me little good; were she hundreds of miles closer, she still might as well be a thousand miles away.

Behind the Veil

28 May 2016

Yester-day, I made the unhappy discovery that seven entries to this 'blog that were intended to be publicly accessible have instead been restricted. Apparently the restriction was caused by a bug in a WordPress plugin or in WordPress itself. The bug doesn’t seem to have bitten since 2010, so I believe that it were resolved by some software up-date.

I used a little MySQL to set things straight, then went over a back-up copy of the dB to identify all the affected entries, so that I could list them here.

Three of the affected entries are simply trivial. One is about poor performance by my previous site host 'Blog Bog [16 March 2008] and two are about entries to a contest to create types of jelly beans. and why it should win [16 March 2008]
Full of Beans [19 March 2008]

Two of the entries are on IT A Useful Bit o' PHP Code, Set Right [16 June 2008]
Installing Firefox 3.0 under Red Hat Enterprise Linux 5.x [17 June 2008]
and that second IT entry now has very little marginal value except to someone making odd software choices.

The remaining two entries are also the most recent. A Big Ol' Entry on Patents and Copyrights [20 June 2008]
Thoughts on Boolean Laws of Thought [13 February 2010]
I very much regret that the entry on intellectual property has apparently been hidden from most visitors for more almost eight years!

Hard Case

28 May 2016

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.

Looked and Felt

26 May 2016

Some days ago, people who consume this 'blog by an ordinary visit with a graphics-enabled browser were confronted with different graphics within the header. The prior and present graphics look like this [image of archaic header lettering, white] but, for a while, the graphics looked like this [image of art-deco header lettering, metallic with grey borders] and then like this [image of art-deco header lettering, the larger being metallic with grey borders and the smaller being white with grey borders]

I had been in the mood to try a change. I constructed some new letters of a general form that I like, which used to be popular for the cover titles of pulps and of comic books. I decided to give them a metallic look (which was done by layering gradient fills of blue-grey).

But my big problem with the results was readability, especially of the subtitle. Changing the subtitle fill from a metallic texture to a solid white helped somewhat, but readability still wasn’t what I wanted. The problem was even worse when displayed on my tablet, which resizes images to suit itself and can thereby further blur graphics.

Additionally, though I don’t worry a great deal about the æsthetic opinions of others when it comes to my 'blog, both of the people who expressed a preference expressed it for the prior lettering. (One of them declared the newer graphics to be faux-cool.)

I may not be done with these experiments though. I’ve been thinking of converting the visual theme of this 'blog into a meta-theme, whose graphic components vary, perhaps as a function of time or perhaps randomly or pseudo-randomly.

I have played-around with elements for a distinct presentation to mobile devices, but I note that the screens of typical mobile devices are now fairly large and of high resolution. Meanwhile, the current presentation actually seems pretty good on my agèd cellular phone, which has a screen with a 3.1-inch diagonal, with 480×640 pixels.

On the Concept of Ownership

23 May 2016

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 some sort of ownership 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 to some sort of limits of 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 subobject 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.