Time is measured by sequences of changes. Classic examples of sequences that have been used are beats of the heart, apparent positions of the sun and of the moon, and the solstices. In theory, any sequence might be used.

When one measure of time is gauged against another, it is ultimately a matter of counting how many changes of each sort occur. When the rate of some different changes seems to be constant relative to those by which time has been measured, if these different changes occur in greater number then it may be decided to substitute these changes as the primary measure of time, and thus have a finer-grained measure.

Speeds and frequencies are not normally recognized as conversion factors for measures of time against each other, but that is exactly what they are. In the case of speeds generally, the changes are quantifications (of physical position, perhaps). In the more specific case of frequencies, one has a sequence of changes that are attainment of — or departure from — what is regarded as a recurring state; a count of these attainments or departures might be quantified as a pure number.

To say that some changes take place at a constant rate over time is simply to say that there is an invariant correspondence between the number of the changes by which we measure time and the number of the changes whose rate is being measured.

Such constancy occurs trivially when the changes that are used to measure time are measured against time — they're just being measured against themselves. If time is measured by appearances of the sun above the horizon, then the conversion factor for the frequency with which the sun appears above the horizon is necessarily 1. If we use these appearances to meaure the frequency with which the heart beats, that frequency will almost certainly be inconstant; but if we use heart-beats as our measure of time, then their frequency will necessarily be 1 (and the frequency with which the sun appears will almost certainly be inconstant).

If someone should ask about using the average rate at which the heart beats as the measure of time, then he or she is implicitly presuming something other than heart-beats in measuring them, or their average frequency will necessarily be 1. Any comfort in imagining that the reference changes are being averaged is a comfort in confusion.

Someone else will insist that it is obvious that the rate at which any reference-heart beats is objectively inconstant, but it is no such thing. Rather, the convenience for the formulation of descriptions of the world around us of some measures is so limited, and that of others so pronounced as to make it seem that some are closer to objective constancy than are others.

If the measure of time were in terms of Scott's heart-beats, then his mood would figure into descriptions of the universe (the rest of the world would be slower when Scott were excited), and we'd need his pulse whenever we timed things (in particular, all other changes would happen infinitely fast after Scott died). These characteristics make Scott's heart-beats grossly inconvenient for everyone excepting, perhaps, Scott.

What one wants of measures of time are accessibility, for them to result in manageable descriptions of rest of the world, and for them to not to deviate intolerably from our subjective experiences of time. There is a certain amount of rivalry at least between the first two desiderata. Those measurements that are most easily made don't correspond to the simplest descriptions of the rest of the world. But some measurements of time result in many fairly simple descriptions (some of those descriptions are even of other rates as constants) that appear perfectly accurate. It is the latter sort of measurement that is mostly likely to be taken as objective, but if the measurements that supported the simplest statements of physical laws made a very poor fit for subjective experiences of time, then these measurements would not widely be accepted (even by scientists) as measurements of time at all, objective or otherwise!

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We're often told that the speed of light (in vacuo) is constant. Many people wonder why this constancy is so; others whether it is so. But what is actually meant by the assertion itself that the speed of light be constant is that the changes in the position of light maintain a fixed ratio with the changes by which we have chosen to measure time. In effect, those (such as Einstein) who said that this speed were constant were declaring that we ought to measure time in a manner that made the speed of light constant. And the reason that we ought to measure it thus was because accurate descriptions of the behavior of things of interest would be as simple as possible (or, at the least, as simple as possible without resulting in a measure unrecognizable as time).

The real question is not of why or whether the speed of light is constant; the real question is of why treating it thus simplifies accurate descriptions. And the basic answer is because light and stuff very much like it do a lot. One whoozit affects another by way of that stuff.

Of course, that basic answer shouldn't satisfy anyone with more than passing curiosity. My point is just that the idea that the speed of light is constant doesn't represent a mystery of the sort that many people take it to be.

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This entry was primarily motivated by my desire to get the point about the constancy of the speed of light off my chest, but the more general part of it actually has application to questions of method in economics.

When I was in the graduate programme at UCSD, there was a student who wanted to do some sort of econometric work where the changes by which time were measured would be transactions, rather than ticks of an ordinary clock — he called this alternate measure market time. (I don't know whether he arrived at the concept or at this term on his own, but he didn't cite a prior source.) Sadly, his initial presentation was a disaster; when he attempted to explain this idea to the professors who were to judge his work, he came across to them and to most of the rest of the audience as incoherent. I might well have been the only other person in the room who really understood what he was trying to say. (I had for some while been thinking skeptically about the propensity of economists to use the physicists' t.)

Afterwards, I sat down with him and tried to explain to him what he had to communicate; but he seemed not to listen to me as he insisted that the response of the professors were unfair. And, the next time that he gave a presentation on the idea, he essentially repeated his previous performance.

It is at least plausible to me that a major part of the reason that he could not communicate what he was proposing to do was that he had only a vague intuïtion about the nature of measures of time and about distinctions amongst them.

I would note that the particular measure of time that he suggested is certainly not the one for economists to use in all or even most cases, and that it has never been one that had distinctively useful application to a problem that I've investigated.

Occasionally, I am confronted with the question of the nature of economics.

A great many people believe that they know what economics is. Many of these people have inferred a definition for economics from references in the popular media and from politicians to the economy, and from popular media presentations of or about various people labelled economist. Some people have taken one or two courses in high school or in college about something called economics, and have presumed that whatever definitions were given in their textbooks were uncontroversial.

Well, the fact is that the popular media do no better job in representing economics than they do in representing those subjects with which you (my reader) have a real familiarity. High school economics textbooks are often disasters written by people who aren't economists. First-year college textbooks often over-simplify things. And when a respected economist attempts to define economics, while his definition may be embraced by a great many other respected economists, it will be challenged by still other respected economists! (I'll define what I here mean by economist below. If you must have a definition right now, then take it to mean one who has received a degree or appointment by which he or she has been so labelled!)

Tromping where angels fear to tread, I am going to tell you how I define economics.

Economics is a cluster of studies. The studies that I have in mind concern these questions:

They are clustered because significant theories (propositional structures) hold that these studies have important inter-relationships.

(And now I'll define economist to mean someone who engages in more than casual study of any one or more of these areas.)

Someone may come along and show some serious flaw in my definition. But, on the expectation that it works, I'm going to discuss it.

There's a whole bunch of things not explicitly mentioned in my definition that lay-people associate with economics. That's because those things are particular cases of more general concepts. For example, households, firms, industries, bourses, and nations are each sorts of communities. There are economists whose studies concern social orders in which all of these communities exist, but the presumption of such a social order is not intrinsic to economics. Business administrators may find economics useful, but they also may find mathematics useful. Neither is simply a hand-maiden of business studies.

Not everyone who has attempted or attempts scientific or scholarly consideration of these questions accepts the existence of the inter-relationships described by the aforementioned theories. In some cases, they may subscribe to theories which accept significant inter-relationship, but on some very different theoretical basis. In some cases, researchers may claim that, where other theories see a bilateral causality, there is just a one-way causality. For example, these economists may insist that, while prices inform individual decisions, those prices are formed without regard to individual decisions.

Further, even economists who accept that these studies are all importantly inter-related don't necessarily spend much-if-any effort studying in all areas. Indeed, some may confine themselves to just one area. For example, every one of the living economists who is widely known to lay-people is a macroeconomist, which is to say that he or she is concerned with the behavior of aggregates such as prices levels, employment rates, and GDP. But, as a share of economists more generally, macroeconomists are a tiny minority. Most economists don't like macroeconomics. It is signally ignorant to ask a typical economist what the stock-market is going to do most days, because that's outside of his or her area of concern.

You surely noticed that the first row of question were non-normative, while the second row were corresponding normative questions. Some economists would insist that there is very little to be said normatively. On the other hand, often of normative theory of a sort is used to approximate non-normative theory, as when it is assumed that individuals have complete, transitive, and acyclical preferences.

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For what it's worth, the words economy and economics comes to us from the Greek stems ὀικ-, referring to the household, and νομ-, referring to the law or to custom (with the -ic- from the adjectival suffix -ικ-). Greek ὀικονομ[ικ]- referred to management of the household and of its resources.

Transliterated into Latin, ὀικονομ[ικ]- became oeconom[ic]- and entered English thus. Somewhere along the line, the initial o fell silent.

In English, œconomy referred to resource management, typically at the the level of the household, that was wise, frugal, or perhaps tight-fisted, or to a savings realized by such management (a definition that still has some currency to-day); and œconomist to a manager who was wise, frugal, or tight-fisted. Conceptualizing a political community as household, the term political œconomy began to be used in reference to the sorts of management in which political authorities might engage. (German has a very similar term, Nationalökonomie.)

The initial o began to fall away from œconom-; and, in part because of the currency of political [o]economy, [o]economist became increasingly dissociated from thoughts of households or of other work-a-day management, and more concerned with a sort of philosophical or scientific study (though not, as it happens, before The Economist got its name).

Eventually, peculiar association of economics with the literal household was so forgotten that, when a term was wanted with the original sense, the philologically redundant home economics was adopted, with only quiet laughter off in the distance.

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A few people now-a-days call themselves oeconomist, spelled in that archaic manner, as a way of asserting that they are or seek to be wise practical managers of resources. That's not, however, why I label myself thus.

Although my published work doesn't look simply modernistic but in fact hyper-modernistic, I'm sympathetic to much of the criticism of modernism in economics; I think that we need to reconsider some of the work done before the era of modernism. My œ is a way of saying that there's something deliberately old-fashioned to my thinking.

Yester-day, I finished reading the 1969 version of Choice without Preference: A Study of the History and of the Logic of the Problem of Buridan's Ass by Nicholas Rescher, which version appears in his Essays in Philosophical Analysis. An earlier version appeared in Kantstudien volume 51 (1959/60), and some version has or versions have appeared in later collections. I have only read the 1969 version, and some of the objections that I raise here may have been addressed by a revision.

The problem of Buridan's ass may not be familiar by name to all of my readers, but I imagine that all of them have encountered some form of it. A creature is given a choice between two options neither of which seems more desirable than the other. The question then is of how, if at all, the creature can make a choice. In the classical presentation, the creature is a donkey or some other member of the sub-genus Asinus of Equus, the choice is between food sources, and a failure to make a choice will result in death by starvation. The problem was not first presented by the Fourteenth-Century cleric and philosopher Jean Buridan, but it has come to be associated with his name. (Unsurprisingly, my paper on indifference and indecision makes mention of Buridan's ass.)

Rescher explores the history of the problem, in terms of the forms that it took, the ultimate purposes for which a principle were sought from its consideration, and the principles that were claimed to be found. Then he presents his own ostensible resolution, and examines how that might be applied to those ultimate purposes.

One of the immediate problems that I have with the essay is that nowhere does Rescher actually define what he means by preference. I feel this absence most keenly when Rescher objects that there is no preference where some author and I think there to be a preference.

As it happens, in my paper on indifference and indecision, I actually gave a definition of strict preference: which is to say that X₁ is strictly preferred to X₂ if X₂ is not in the choice made from the two of them.[1] So, in that paper, strict preference really just refers to a pattern of choice. I didn't in fact define choice, and I'll return to that issue later.

The Merriam-Webster Dictionary essentially identifies preference as a gerund of prefer, and offers two potentially relevant definitions of prefer:

1. to promote or advance to a rank or position
2. to like better or best

The first seems to be a description of selection as such. The second might be taken to mean something more. But when I look at the definition of like, I'm still wondering what sense I might make of it other than an inclination to choose.

I'm not claiming that Rescher is necessarily caught-up in an illusion. Rather, I'm claiming, first, that he hasn't explained something that is both essential to his position and far from evident; and, second, that his criticism of some authors is based upon confusing their definitions with his own.

When I used the notion of a choice function C( ) in my paper, my conception of choice was no more than one of selection, and that's what I was unconsciously taking Rescher to mean until, towards the end of his essay, speaking of decisions made by flips of coins (and the like), he writes

In either event, we can be said to have "made a choice" purely by courtesty. It would be more rigorously correct to say that we have effected a selection.

Well, no. This isn't a matter of rigor, whatever it might be. The word choice can rigorously refer to selection of any sort. It can also refer to selection with care of some sort, which seems to be what he had in mind.

Some of the authors whom Rescher cites, and Rescher himself, assert that when a choice is to be made in the face of indifference, it may be done by random means. Indeed, Rescher argues that it must be done by such means. But he waits rather a long time before he provides any explicit definition of what he means by random, and he involves two notions without explaining why one must invoke the other, and indeed seemingly without seeing that he would involve two distinct notions. When he finally gives an explicit notion, it to characterize a choice to be made as random when there is equal weight of evidence in favor of each option. However, when earlier writing of the device by which the selection is to be made, he insists

The randomness of any selection process is a matter which in cases of importance, shall be checked by empirical means.

Now, one does not test the previously mentioned equal weight of the evidence by empirical means. An empirical test, instead, adds to the fund of evidence. We can judge the weight of the present evidence about the selection device by examining just that present evidence. The options are characterized by equal plausibility, yet Rescher has insisted that the selection device must instead be characterized by equal propensity. It isn't clear why the device can't simply also be characterized by equal plausibility.[2]

Rescher makes a somewhat naïve claim just before that insistence on empirical testing. For less critical choices, he declares

This randomizing instrument may, however, be the human mind, since men are capable of making arbitrary selections, with respect to which they can be adequately certain in their own mind that the choice was made haphazardly, and without any reasons whatsoever. This process is, it is true, open to possible intrusions of unrecognized biases, but then so are physical randomizers such as coins.

Actually, empirical testing of attempts by people to generate random numbers internally show very marked biases, such that it's fairly easy to find much less predictable physical selectors.

Rescher's confusion of notions of randomness is entangled with a confounding taxonomy of choice which is perhaps the biggest problem with Rescher's analysis. The options that he allows are

1. decision paralysis
2. selection favoring the first option
3. selection favoring the second option
4. random selection, in which random entails a lack of bias

And, proceeding thence, he seems to confuse utterly the notion that choice without some preference somewhere is impossible with the notion that choice without some preference somewhere is unreasonable. In any case, Rescher insists that only the last of these modes of selection is reasonable, and this insistence would tell Buridan's ass that it must starve unless it can find a perfectly unbiased coin![3] Reason would be a harsher mistress than I take her to be!

Another term that Rescher uses without definition is fair and its coördinates, as when he writes

Random selection, it is clear, constitutes the sole wholly satisfactory manner of resolving exclusive choice between equivalent claims in a wholly fair and unobjectionable manner.

I certainly don't see that random selection should be seen as wholly satisfactory (though I believe it to often be the least unsatisfying manner), and I don't know what Rescher imagines by fair. My experience is that when the word fair is used, it is typically for something more appealing than justice to those inclined to envy. In the case of allotments by coin-flip, there may be no motivation for envy ex ante, but things will be different ex post. People do a great deal of railing against the ostensible unfairness of their luck or of that of another.

I recall one final objection, which moves us quite out of the realm of economics, but which I have none-the-less. One of the applications of these questions of choice without preference (or, at least, without preference except stemming from meta-preference) has been to choices made by G_d. In looking at these problems, Rescher insists that G_d's knowledge must be timeless; I think that he ought to allow for the possibility that it were not.

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[1] That might seem an awkward way of saying that X₁ is strictly preferred to X₂ if only X₁ is in the choice from the two of them, but it actually made the proofs less awkward to define strict preference in this odd manner.

[2] Even if one insists that the selection device must be characterized by equal propensity, there is in fact little need for empirical testing, if one accepts the presumptions that a coin may be considered to have unchanging bias and that flips of a coin may be independent one from another. Implicitly making these assumptions, my father proposes a method for the construction of a coin where the chances of heads and of tails would be exactly equal. One starts with an ordinary coin; it comes-up heads sometimes, and tails others. Its bias is unknown; at best approximated. But, whatever the bias may be, says my father, in any pair of flips, the chances of heads-followed-by-tails are exactly equal to the chances of tails-followed-by-heads. So a pair of flips of the ordinary coin that comes-up heads-tails is heads for the constructed coin; a pair of flips of the ordinary coin that comes-up tails-heads is tails for the constructed coin; any other pair for the ordinary coin (heads-heads, tails-tails, or one or both flips on edge) is discarded.

[3] I don't know that my father could explain his solution to a donkey. I've had trouble explaining it to human beings.

I am making freely available a PDF file of Zahl und Mass in der Ökonomik: Eine kritische Untersuchung der mathematischen Methode und der mathematischen Preistheorie (1893), by Andreas Heinrich Voigt, which is encoded as text rather than as graphics.

I wanted a transcription for my own purposes — a resource that might be used for a paper on which I am working — and decided that I should make it available to other researchers, and do a proper job of its assembly.

Up-Date (2020:04/09): I have made the first-pass of an English-language translation as Number and Measure in Economics: A Critical Examination of Mathematical Method and of Mathematical Price Theory.

Perhaps I'm a Constitutional hipster, in-so-far as I was talking about section 4 of the Fourteenth Amendment before it was cool to do so. After it had become cool, I felt moved to explain

[The Fourteenth Amendment] is indeed [the law that empowers the President to increase the ceiling] — where the only way not otherwise in violation of the Constitution to pay debt that has come due is to borrow beyond the existing limit. If the debt can be paid in some other way, then no special authority can be found for the President in section 4.

[…] The President doesn't get to say that he or she must raise the limit to continue funding institutions to which he or she can apply profound and moving terms, unless those institutions are indeed Constitutionally mandated.

With talk of the President raising the borrowing limit by decree again heating-up, I feel moved to labor aspects of what I'd earlier explained.

As debt comes due, for which sufficient funding has not been allocated, the Federal government can do one or more of five things:

• Default.
• Increase tax collections.
• Decrease other expenditures to allocate more revenue for debt service.
• Liquidate assets.
• Engage in new borrowing to service the debts from previous borrowing.

Advocates of the President raising the ceiling by decree want to pretend that the Constitutional prohibition of the first of these five options empowers the President to effect the last of these options by decree. But there would be three other options; it is appropriate to ask why the President wouldn't instead be required to choose one or more of the other three.

And, if a decision must be made amongst some or all of the four options not prohibitted by section 4 of the Fourteenth Amendment, it is not evident that it is the President's decision to make, even if the Congress will not. In the absence of Constitutional guidance, there is no apparent reason that abdicated legislative responsibility should go to the executive branch as opposed to the judicial branch.

Years ago, when I was in graduate school, I got into an argument, about a real-world crime statistic, with another student who didn't have much math-sense. The mathematics itself is very simple, and yet at least one implication of it seems to run counter to the intuïtions of many people.

Let's say that a population p is divided into groups, each i-th group with population p_i p = ∑(p_i) And let's say that the i-th group has a propensity c_i to commit crimes, such that c_i · p_i gives the sum of the crimes committed (however measured) by members of that population.

If criminals from within each group draw their victims with each person having an equal chance of victimization regardless of his or her own group, then the proportionate share of victims that they draw from the j-th group will be p_j / p The total number of crimes then committed against the j-th group by members of the i-th group will then be (p_j / p) · (c_i · p_i) and the ratio of i-on-j crime to j-on-i crime will be [(p_j / p) · (c_i · p_i)] / [(p_i / p) · (c_j · p_j)] = c_i / c_j So, if c_i = c_j, then the ratio of i-on-j crime to j-on-i crime will simply be 1:1.

The other graduate student had been sure that, if group i were the smaller group, then the ratio should be larger than 1:1, because group j furnished more potential victims. The proper intuïtion here is that, if one group is larger than another, then it furnishes proportionally both more potential victims and more potential victimizers; or, to say the same thing differently, if one group is smaller than another, then it furnishes proportionally both fewer potential victims and fewer potential victimizers.

If we see a very different ratio, then the difference implies that one group has a greater propensity to criminality than the other, or that one group is seeking (or avoiding) the other in its acts of criminality, or both.

It should be noted that members of the j-th group may be sought or avoided for reasons other than their being members of that group as such. For example, members of the j-th group may happen to have more portable wealth. Still, if one sees a ratio of, say, about 50:1, then it's hard to explain this lop-sided ratio in terms simply of the j-th group having more wealth, or of the i-th group simply having a greater propensity to criminality. With a ratio like that, one should expect that members of the j-th group are indeed being targetted for being in that group, by members of the i-th group.

And the truth is, it will take more than a few years for us to solve challenges that have built up over decades.

A decade is of course a period of ten years, so that decades would refer to twenty or more years. Now, perhaps President Obama was allowing that problems had continued to build-up during his term, though it would seem more likely that he meant to refer to twenty or more years before he took office; but, in any case, he must have been referring to a period that began no later than 1992.

I'm not seen the main-stream of the media nor the right-wing alternative take note of the implication here. President Obama has once again given part of the blame for the present economic situation to the 1993–2001 Administration of President Clinton.

During the 2008 campaign, I noted

There had been a sort of forced nostalgia for Bill Clinton, but once Obama came over the horizon, Democrats became more willing to look critically at Clinton and at his Presidency;

The base of the Democratic Party were imagining Barack Obama as a leader who would show, after all, that Clinton had been mistaken to declare The era of big government is over, that instead a considerably more humane nation and world could be shaped by extending still further the sort of management by the state of economic resources which had characterized the New Deal and the Great Society. As a candidate, Mr Obama had even at one point gone so far as to assert that some of the foundations of economic problems in 2008 had been laid by the Clinton Administration (though Mr Obama quickly retreated from that claim in the face of outrage from the Clinton camp).

But as the economic crisis continued through the Administration of President Obama, there has been a return to that forced nostalgia, noting of course that President Clinton were a Democrat, and not paying a great deal of attention to what had determined his policies.

(Mr Clinton ran as a New Democrat — one with a more skeptical eye towards state intervention. But, once elected, he tacked to the left. One of the political results was that the Democratic Party lost control of Congress in the next mid-term elections. It was after these losses that President Clinton gave the speech in which he declared the death of big government. For the most part, he thereäfter chose his policies by discerning where things were going, and running out in front, pretending thus to lead. One notable exception to this approach was in his support for adjustive discrimination (affirmative action), which appears to be something to which he had a genuine commitment.)

For his part, Former President Clinton has been glad to be called for help. William Jefferson Clinton enjoys the game of politics. He enjoys playing the game. He enjoys demonstrating, to those who can see what he does for what it is, how good he is at it. He very much enjoys coming to the rescue of Barack Obama, as proof that Mr Clinton is better at this game than is Mr Obama. Mr Clinton has not forgot that the Obama campaign and its allies treated the Clintons as, well, Republicans during the 2008 race; that Mr Obama took the nomination from Hillary Clinton; nor that episode of laying some of the blame for the economic crisis on Mr Clinton's door-step.

Mr Obama recognizes this motivation, and would resent his dependence upon Mr Clinton's greater present popularity even were Mr Clinton not seeking to rub Mr Obama's nose in it. And, while part of his reference to challenges that have built up over decades was simply because challenges that have built up over the previous eight years doesn't sound nearly so persuasive, there was a deliberate slap at Mr Clinton there. Mr Obama had already got a speech out of Mr Clinton, who would be unlikely to try, somehow, to take it back. And it wasn't Mr Clinton's best effort anyway.

On the other hand, as the Woman of Interest noted when I was talking about this slap, Mr Clinton may be many things, but he is not too stupid to see that what Mr Obama did. So it's not likely that there will be much more help from Mr Clinton, without some sort of profound obeisance from Mr Obama. Barack Hussein Obama may come to regret his act of petulence.

Yester-day or this morning, I encountered yet another instance of argumentation over what Keynes really meant in The General Theory of Employment, Interest and Money. I don't plan to labor here what I believe that Keynes intended to say; rather I want to draw attention to something about many of these arguments over the meaning or intention of some works.

When I consider the meaning or intention of the works of people who in turn attempt to interpret something else, I regard my interpretation of their interpretation as concerned with thought as such; I am thinking about how someone is or was thinking; my interpretation might be informed by my own understanding of the subject about which they thought, but the interpretation is of their thought.

It's good to know what any one of these people intended to say; it's good to know what they actually did say (whether intended or not); but it's almost always more desirable to have best approximations of the truth about which they ostensibly spoke than to have best approximations of the claims that they intended to make. It is a fortunate error when someone gets closer to the truth about the underlying subject by misinterpretting the work of someone who was mistaken about that subject. And, if one simply doesn't know which interpretation to make, but finds the truth amongst the possibilities, then there isn't even a positive misinterpretation.

It's different when one is attempting to interpret words which themselves impose rules, as in the cases of legislation, of formalized games, or of works of fiction. In those cases, the words creäte the relevant reälity.

Some people believe in prophets. By prophet I do not mean simply a forecaster, but a person through whom G_d (or something like G_d) speaks (perhaps about the future, but perhaps not). Amongst ostensible prophets I would count those believed to have a direct knowledge of external reälity, unmediated by the senses. Unsurprisingly, I do not believe in prophecy.

But, if one does believe in prophecy, then it makes sense to concern oneself with its meaning as-if resolving its meaning were the same thing as getting a best approximation of the underlying subject — because, indeed, prophecy would be just that best approximation. Of course, I take exception to the presumption that this-or-that work were holy scripture; but I take rather greater exception to an unacknowledged presumption to such effect.

And that brings me to what is so wrong with so many of the arguments about what Keynes really meant: Too many of the participants are perfectly sure that, whatever he really intended, it must have been right, and that it is for this reason that we must discover what he intended. One sees even more of this sort of thinking in debates about what Marx really meant. And I've seen basically the same thing in discussions about what Ayn Rand really meant. These three (and various others) are unacknowledgedly being treated as prophets. As far as I'm concerned, in such cases discussion has run off the rails.

Now, there are those who would insist that Marx, by way of dialectical reasoning, or Rand, by way of thorough-going objectivist epistemology, could apprehend things so very clearly that we should just take for granted that, indeed, whatever they said must be right. But those propositions each would strike me as highly dubious even if I didn't already possess what I regard as counter-proofs. (Certainly there would seem to be a claim of personal infallibility or a fallible claim on the part of whomever were testifying to the infallibility of Marx or of Rand.) And I've not encountered even that much of an argument for treating Keynes as if he were a prophet. (I have seen his economic intuïtion championed by reference to his having made a fortune investing in stocks, but I wasn't much persuaded by this argument even before I learned that, earlier, he had faced financial ruin through such investments, and been rescued by his father.)

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.)

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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.

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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.

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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.

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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.)

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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.

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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.

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

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.

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[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.