On Sunday, 27 May, I received a pair of e.mail messages announcing formal acceptance for publication of my paper on indecision, and I ceased being braced for rejection. From 15 June, Elsevier had a version for sale on-line (first the uncorrected proof, then the corrected proof, now the version found in the journal). The issue itself (J Math Econ v48 #4) was made available on-line on 3 August. (I assume that the print copies will be received by subscribers soon.)

---

Reader may recall that, not very long ago, I was reading A Budget of Paradoxes by Augustus de Morgan, and that when de Morgan used the term paradox he did not use in in the sense of an apparent truth which seems to fly in the face of reason, but in the older sense of a tenet opposed to received opinion. De Morgan was especially concerned with cases of heterodoxy to which no credibility would be ascribed by the established mainstream.

Some paradoxes would later move from heterodoxy to orthodoxy, as when the Earth came to be viewed as closely approximated by a sphere, and with no particular claim to being the center of the universe. But most paradoxes are unreasonable, and have little chance of ever becoming orthodoxy.

I began reading de Morgan's Budget largely because I have at least a passing interest in cranky ideas. But reading it at the time that I did was not conducive to my mental health.

---

Under ideal circumstances, one would not use a weight of opinion — whether the opinion were popular or that of experts — to approximate most sorts of truth. But circumstances are seldom ideal, and social norms are often less than optimal whatever the circumstances. When confronted with work that is heterodox about foundational matters, the vast majority of people judge work to be crackpot if it is not treated with respect by some ostensibly relevant population.

In cases where respect is used as the measure of authority, there can be a problem of whose respect is itself taken to have some authority; often a layering obtains. The topology of that layering can be conceptualized in at least three ways, but the point is that the layers run from those considered to have little authority beyond that to declare who has more authority, to those who are considered to actually do the most respected research, with respected popularizers usually in one of the layers in-between. In such structures, absurdities can obtain, such as presumptions that popularizers have themselves done important research, or that the more famous authorities are the better authorities.

---

As I was reading de Morgan's book, my paper was waiting for a response from the seventh journal to which it had been offered. The first rejection had been preëmptory; no reason was given for it, though there was some assurance that this need not be taken as indicating that the paper were incompetent or unimportant. The next three rejections (2nd, 3rd, 4th) were less worrisome, as they seemed to be about the paper being too specialized, and two of them made a point of suggesting what the editor or reviewer thought to be more suitable journals. But then came the awful experience of my paper being held by Theory and Decision for more than a year-and-a half, with editor Mohammed Abdellaoui refusing to communicate with me about what the Hell were happening. And this was followed by a perverse rejection at the next journal from a reviewer with a conflict of interest. Six rejections[1] might not seem like a lot, but there really aren't that many academically respected journals which might have published my paper (especially as I vowed never again to submit anything to a Springer journal); I was running-out of possibilities.

I didn't produce my work with my reputation in mind, and I wouldn't see damage to my reputation as the worst consequence of my work being rejected; but de Morgan's book drew my attention to the grim fact that my work, which is heterodox and foundational, was in danger of being classified as crackpot, and I along with it.

---

Crackpots, finding their work dismissed, often vent about the injustice of that rejection. That venting is taken by some as confirmation that the crackpots are crackpots. It's not; it's a natural reäction to a rejection that is perceived to be unjust, whether the perception is correct or not. The psychological effect can be profoundly injurious; crackpots may collapse or snap, but so may people who were perfectly reasonable in their heterodoxy. (Society will be inclined to see a collapse or break as confirmation that the person were a crackpot, until and unless the ostensible authorities reverse themselves, at which point the person may be seen as a martyr.)

---

As things went from bad to worse for my paper, I dealt with how I felt by compartmentalization and dissociation. When the paper was first given conditional acceptance, my reäction was not one of happiness nor of relief; rather, with some greater prospect that the paper would be published, the structure of compartmentalization came largely undone, and I felt traumatized.

---

Meanwhile, some other things in my life were going or just-plain went wrong, at least one of which I'll note in some later entry. In any case, the recent quietude of this 'blog hasn't been because I'd lost interest in it, but because properly to continue the 'blog this entry was needed, and I've not been in a good frame-of-mind to write it.

---

[1] Actually five rejections joined with the behavior of Abdellaoui, which was something far worse than a rejection.

More than a year after finding that I could no longer log into LiveJournal with my OpenID, I am now again able to do so.

The server software that I had been using has long been orphaned. But, with some assistance from Kelvin Mo, I was able to get his SimpleID functioning properly for the most part. I worked around a final glitch yester-day. (I still have a problem with Blogspot/Blogger; but, for practical reasons, that is of less concern than was the problem with LJ.)

I am still trying to figure-out how to get the original OpenID for the Woman of Interest again working. She uses a different sort of directory structure and WordPress configuration than do I, and this is breaking something.

The conditions for the acceptance of my paper on indecision were revealed to me in early April. Apparently the intention had been to provide them in mid-March, when I was informed of the conditional acceptance, but there'd been a bit of confusion.

Some of the conditions imposed were pretty strong. With the exception of one change,[1] I actively disliked every one of them. I thought that some of them sought reasonable objectives but would bring more cost than benefit; I thought that others were simply wrong-headed.

However, I made or attempted to make all of the changes except for three sorts. I figured that the editor would support me when it came to two of those remaining three sorts, as one would have formatted the references very differently from the journal's own standard (with which the reviewer was apparently unfamiliar) and the other would have dropped-in a proposition that would in fact have been perfectly superfluous in my paper (though an important axiom in most theories of probability).

I was, however, very concerned about the effect of my refusing to make one of the changes against which I dug-in. That change was suggested or demanded (it was not clear which) by the reviewer in order to simplify the presentation by simplifying the structure. Unfortunately, it would also have torn the work from part of its empirical foundations. I genuinely felt that it would be better not to have the paper published than to make the change, yet I was not sure that my intransigence would be properly understood. But I was afforded an opportunity to explain myself on this point (and on every other), and apparently my explanation was accepted.

Yester-day, I was told that the changes that I made had sufficiently addressed the reviewer's original concerns, and that the paper would be accepted conditional upon my modifying the acknowledgments (to be less specific as to what the acknowledged parties had done) and upon my removing the dedication (which the editor or reviewer suggested replacing with an acknowledgment of support). I have made those changes.

I also fixed a broken cross-reference that I had spotted. And I replaced one symbol with another. In order to effect one sort of change that the reviewer had wanted, I had introduced an explicit symbol for binary paralysis. [Erratum (2013:04/25): (Well, actually, for the union of binary paralysis with identity.)] Specifically, I used U+224e (≎) I had adopted this particular character because nothing better occurred to me quickly, and I didn't want to grind to a halt over a d_mn'd symbol. (How dreadful to be paralyzed in the choice of a symbol for paralysis!) But I wasn't comfortable with it. I felt that the reader would have trouble remembering what it meant as it occurred here-and-there, that it was too suggestive of an equality, and that it would be awkward to write by hand. I eventually decided that what I wanted was a π (for παράλυσις)[2] centrally superscripted over a dash.

Anyway, there is some small chance that my effecting this change of symbols will cause me difficulty with the editor, but I believe that the paper is effectively accepted now. I don't know how long it might be before the paper is actually published.

---

[1] I had inserted a foot-note specifically to preëmpt a repeat of an inappropriate criticism delivered by the reviewer at the previous journal. I was planning to request, upon acceptance of the paper, that the foot-note be removed. In the event, the latest reviewer insisted that the foot-note be removed.

[2] The Latin p is too readily associated with preference, and indeed P was once very common for the binary relation of strict preference or that of weak preference.

On 16 March, I queried the journal to which I most recently submitted my paper on operationalizing the difference between indifference and indecision. To-day, I received informal e.mail from the editor letting me know

The paper is accepted, pending some (substantial) revisions. You’ll be getting the formal material from the journal soon.

I dread the thought of subtantial revisions, but it's to be presumed that I can live with the changes demanded. The state of things appears to be excellent.

Those who attempted to visit this 'blog yester-day met with this proclamation that it were suspended by its author in protest against SOPA and against PIPA. None-the-less, when the Woman of Interest asked me whether I thought that the black-out protests would be effective, my answer in the late morning was negative.

First, I was inclined in advance to believe that deciding positions had already been taken (albeït not announced) some days ago by a majority in Congress and by the President, and that final outcomes would not be actually swung by the sort of protest that could plausibly be expected.

Additionally, by late morning, I felt that a rather poor protest had been mounted. Wikipedia, most famous of the protestors, ostensibly blacked-out its pages, but had left them so that hitting Esc as they loaded caused the ordinary content to be delivered. Google merely changed its home-page graphic, partially (but, tellingly, not fully) covering-over their name with a cocked black rectangle; never mind that those who invoke searches with a browser text-field don't see that graphic anyway! Many sites did no more than change their color-schemes.

I think that least effective were those who expressed their ostensible support for the black-out by posting those expressions, through-out the day, on the WWWeb, while withdrawing nothing. Now, let me make it plain that I have no quarrel with those who simply didn't participate in the black-out, or those who shut-down only some of their sites; the former may be perfectly consistent, the latter perhaps efficient. But those who weren't blacked-out in the least and discoursed upon their support for the black-out on the WWWeb as that black-out were in-progress seem not to understand that they were providing content in attempted support of an effort to provide a sense of the loss of content that would follow upon the passage of something such as SOPA or as PIPA. And if the only content that one normally provide were tweets and such, then exactly that were what one needed to halt to actually support a black-out.

Those in that last group ought to understand that SOPA or PIPA wouldn't simply mean that the WWWeb no longer offered them so much information and passive amusement; such an act would limit their ability to express themselves as freely as they do now. Along with Google and YouTube and Tumblr would go Facebook and Twitter and Blogger and all the other centralized social-networking sites. (Which is not to say that more autonomous sites, such as mine, would be spared.) People who won't g_dd_mn'd shut-up would be quite hard hit — which might be an amusing thought, but freedom of expression is essential, and not to be reduced to quiet chatter-boxes and pontificators.

My participation in the protest, however, wasn't conditioned on a presupposition that it would sway the body politic. My actions were essentially symbolic, and it wasn't necessary for me to believe that I would sway anyone, though I would hope at least that there'd be one or two sympathetic readers.

And my negativity about the black-out doesn't mean that I expected or expect one of these bills to pass, nor for it to avoid a Presidential veto, nor for the Supreme Court to rule in its favor. I don't know about the first two. (The President will certainly require cover if he is not to veto a bill of this sort, but perhaps he will think that he can get that cover from a signing statement.) I would be unpleasantly surprised by the last; the Supreme Court seems more genuinely alert to concerns about freedom of expression in recent years.

Of course, I may be wrong about the effect of the black-out, however feeble it may look to me. Representatives and Senators have been spooked by scarecrows in the past. But, if the bills failed, that failure wouldn't itself demonstrate that the black-out had a deciding effect.

I would definitely caution at this point that what appears to be strategic retreat may be merely tactical. The interests behind these bills are not going to go away, and features of these bills may be withdrawn at one stage only to be reïntroduced at another (such as reconciliation).

---

The principal recommendation of many of those participating (however convincingly or pathetically) in the protest was that people should contact their Senators and Representatives. Well, the Senators from California are a knavish fool and a foolish knave, and the Representative for my district is at best a twit. I've tried moving those three in the past, and been met by silence or with inane boiler-plate. If they voted against these bills, it wouldn't be because of anything that I said to them. There's not even a sympathetic reader to be found amongst them. But I do know that other districts are not so grim.

For dinner last night, I went to a local restaurant that is part of a larger chain. I was given a number to place on my table, and a cup to fill with tea or with soda at a dispenser.

I placed the number on a table, filled the cup, and returned to the table to look through an art-supply catalogue that I had brought with me.

The catalogue is about 8 in × 10 in × ½ in (20.3 cm × 24.5 cm × 1.3 cm) — roughly the size of a residential telephone directory for a medium-sized American city — and illustrated with pictures of, well, art supplies.

At about the time that I'd got to the mannikins, I had emptied my cup, so I went back to get more tea. As I was taking care of that, I noticed that my food was delivered to my table.

When I returned, I discovered that some fellow had happily sat himself down before the plate, his smart phone to one side, and was looking at the pictures of mannikins in the catalogue.

So, suddenly, he hears a deep, very angry voice, asking You're going to take my food? and he looks up to see me. I'm not sure just how I looked to him, but probably like someone on the edge of violence. After a momentary pause, his mind apparently now wonderfully concentrated, he got-up quickly, explaining that he was at the next table, and thought that they'd brought his food while he was away.

Let's back-up a sec: This fellow hadn't merely mistaken one table for another — something that I suspect most of us, and certainly I, would be capable of doing — he was looking at the pictures in the rather large art-supply catalogue. One doubts that he actively imagined that a restaurant were in the habit of presenting such a catalogue along with one's meal. Rather, his mind was simply disengaged. Here's the food! And, what's this? Oo! Shiny!

I have such low expectations of the mindfulness of other people that I believed his claim immediately, and indeed his order was brought to that next table not long afterwards. But I didn't much enjoy my meal nor the rest of the catalogue; my body was still geared-up for a fight.

I collided yester-day with Brouwer's Fixed-Point Theorem while writing a program that aids artists in creating on-line web galleries.

There's a notion in art of complementary color. The lighter a color is, the darker is its complement, and v.v.. And, if one locates a color on a color wheel, this complement is its diametrical opposite on the wheel. Complementary colors are used, well, to complement things. So, for example, a dark red object is thought to look best against a light green background (if one uses the classic red-yellow-blue color system) or against a light turquoise background (if one uses the red-green-blue system).

I thought (and think) that it would be a fine thing if an image should be automatically displayed on a page whose background color were the complement of the average color of the image. In keeping with this complementarity, it might seem to be a good idea for the page text to be the complement of the background, which is to say that original average color. Well, here is where Brouwer pokes his head in the room and suggests a problem.

Brouwer's Fixed-Point Theorem tells us that every continuous function f from a closed ball onto itself has a point x such that f(x) = x. A color wheel is a closed ball in two dimensions. Grey-scale is a closed ball in one dimension. Half-way between black and white is a shade of grey which is its own complement. The color dead-center on a color wheel is its own complement. So the center of the cylinder formed by the Cartesian product of light-and-dark with the color wheel is its own complement. And any colors near this center have their complements also near this center, which means that there isn't enough contrast for real usability. Color schemes such as medium grey text on a medium grey background just don't cut it.

I don't know what the best adjustment is; I'm not even sure that there is a unique best to be found. But I believe that the proper adjustment would be to alter the lightness — and only the lightness — of the foreground text, making sure that it were different from that of the background by increasing any existing relative difference. (In cases were the brightness is dead-center, a movement in either direction should be fine.)

As previously noted, I submitted my paper on indecision to yet another journal on 28 July. On 11 August, the reported status of the paper was changed to With Editor. Yester-day, 12 December, that was changed to Under Review, which indicates that the paper has been sent onward to one or more reviewers.

Editors generally have the authority to reject papers on their own authority. If they think that a paper might be appropriate to the journal, then they send the paper on to one or two reviewers, with ostensible expertise in the specific area of the paper. These reviewers judge the paper to be suitable as it stands, or suggest revisions that would make it suitable, or decide that it is unlikely to become suitable even after revision. At some journals, editors have the authority to over-rule reviewers, but such is rarely done.

Most submitted papers are rejected by editors before they reach reviewers. Most papers that reach reviewers are rejected by those reviewers. Most that are not rejected are required to be revised in some way, small or large.

I don't know why the paper was listed as With Editor for almost exactly four months. The editor may have been too busy to evaluate the paper at all, or may have spent a fair amount of time in his-or-her own evaluation of it, or may have had trouble finding a reviewer for it.

I recently acquired a copy of this image as a page removed from an issue of Theater Magazine. I'm not sure that I would have got it had I known that it came thence; I'm not comfortable the practice of dismembering old books and magazines for their images, except in cases where there is truly negligible interest in the volume or issue in question being held together.

In any case, I think it a very nice picture.

A recent comment by Zenicurean notes, implicitly, that economic pædagogy often uses a widget as a hypothetical economic good.

I most frequently use the veeblefetzer (borrowed from Harvey Kurtzman) when I want a good about which the audience will know little or nothing, and the hot dog when I want a good that will seem familiar.

I like the hot dog as an example in part because it has a long tradition in economic education while being fairly absurd as an artifact.

I also like it because it is easy to explain the idea of a shift in the demand curve using the hot dog. First, I present my students with a set of prices, polling them as to how many hot dogs they would buy at each of these prices; that gives us an initial demand curve. Then I discuss some of the things that are permitted to go into hot dogs, and we repeat the process for the prices. (So far, the demand curve has always shifted inwards.)

But the main reason that I like to use hypothetical hot dogs is because I think back to a question on the economics GRE when I took it.[1] In the set-up for the question, a family was working-out its annual budget, and decided that they would spend $800 per year on hot dogs, regardless of the price of hot dogs.[2]

The question was of what sort of demand elasticity were here displayed. Elasticity is a measure of sensitivity or responsiveness, with a general form of

or of (Whether there's a negative sign and whether an instantaneous form is used is based on what's convenient and practicable.) In the case of demand elasticity, the y is quantity demanded, and the x is unit price. One might think that demand responsiveness could be measured more simply by slope (Δy/Δx or dy/dx), but elasticity has a useful property. When elasticity is less than 1 in absolute value, responsiveness is sufficiently weak that expenditures (the product of quantity demanded and unit price) increase as price is increased; whereäs if elasticity is greater than 1, responsiveness is sufficiently strong that expenditures shrink as price is increased. The seller gets less revenue by increasing prices in the second case, where the curve is said to be elastic (sensitive); the seller gets more revenue by increasing prices in the first case, where the curve is said to be inelastic (insensitive).

If the elasticity is exactly 1 (in absolute value) then quantity demanded drops or rises to exactly off-set any price change; expenditures are constant as price changes. This is called unit elasticity. (BTW, a demand curve that is everywhere unit elastic will be a hyperbola.)

On the GRE, I was supposed to identify the demand curve of the family in the question as unit elastic, and so I did. But, because I'm not autistic, I was also greatly amused by this example. Imagine a family that is conscientious enough to budget, but they eat hot dogs. Imagine a family that budgets, but budgets such that if a hot dog costs $1600 then they will try to buy half a hot dog, and if a hot dog costs a penny then they will buy eighty thousand g_dd_mn'd hot dogs!

I laughed when I read this question. And, because I made multiple passes through the test, I glanced at that question repeatedly, laughing each time. I was the only person in room laughing. (The room had people taking different subject GREs, and I may have been the only one taking the economics test.)

When I use hot dogs as an example, it's mostly just in fond memory of that hypothetical family, crazy for hot dogs.

---

[1] This tale may seem somewhat familiar to those who read my now long-since-purged LJ.

[2] The amount may have been $600 per year, or perhaps $400 per year; it has been quite some time since I took that test, and I don't remember. But, mutatis mutandis, my remarks hold.