Yester-day, I got hit with a significant wave of depression. I'd been trying to dodge it, but it got me.

My parents are expecting a visit from me; in fact, they expected me to have driven there by sometime yester-day. But I've not got my ducks in-a-row to travel, and right now I'd rather just curl-up in a ball for a while.

One of the things that really upsets me in such a context is when people throw-away my maybe. I tell them that I plan to do something or hope to do something or some-such, and some people act as if I've said that I will or even shall do it. I generally choose my words, even in extemporaneous conversation, fairly carefully, and I resent people ignoring what I've said with the result of a spuriously implied commitment, even if they don't themselves recognize the implication.

I've been taking another run at Subjective Probability: The Real Thing (2004) by Richard C. Jeffrey. I'd started reading it a while back, but got distracted. Anyway, Jeffrey was an important subjectivist — someone who argued that probability is a measure of belief, and that any degree of belief that does not violate certain rationality constraints is permitted. (As I have noted earlier, the subjectivism here is in the assignment of quantities not specifically required by objective criteria. The subjectivists believe either that quantity by reason must be assigned, albeït often arbitrarily, or that Ockham's Razor is not a binding constraint.) And the posthumous Subjective Probability was his final statement.

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At some point, I encountered the following entry in the index:

Nozick, Robert, 119, 123

which entry was almost immediately annoying. Page 119 is in the References section, and indeed has the references for Nozick, but that's a pretty punk thing to drop in an index. Even more punk would be an index entry that refers to itself; and, indeed, page 123 is in the index, and it is on that page that one finds Nozick, Robert, 119, 123.

Well, actually, I'd forgot something about this book, which is probably an artefact of its being posthumous: Most or all of the index entries are off by ten pages, such that one ought to translate Nozick, Robert, 119, 123 to Nozick, Robert, 109, 113. And, yes, there are references to Nozick on those pages (which are part of a discussion of Newcomb's Problem and of related puzzles). It was just chance-coïncidence that ten pages later one found the listings in the references and in the index.

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In decision theory, there are propositions call independence axiomata. The first such proposition to be explicitly advanced for discussion (in an article by Paul Anthony Samuelson) is the Strong Independence Axiom, the gist of which is that the value of a reälized outcome is independent of the probability that it had before it was reälized. Say that we had a lottery of possible outcomes X₁, X₂,… X_n, each X_i having associated probability p_i. If we assert that the expected value of this lottery were

Σ[p_i · u(X_i)]

where u( ) is some utility function, then (amongst other things) we've accepted an independence proposition. Otherwise, we may have to assert something such as that the expect value were

Σ[p_i · u(X_i,p_i)]

to account for such things as people taking an unlikely million dollars to be somehow better than a likely million dollars.

Anyway, there's another proposition which to most of us doesn't look like the Strong Independence Axiom, and yet is pretty much the same thing, the Sure Thing Principle, which is associated with Leonard Jimmie Savage (an important subjectivist, whom I much admire, and with whom I markèdly disagree). Formally, it's thus:

{[(A ∧ B) pref C] ∧ [(A ∧ ¬B) pref C]} ⇒ (A pref C)

Less formally,

If the combination of A and B is preferred to C, and the combination of A without B is preferred to C, then A is just plain preferred to C, regardless of B.

Savage gives us the example of a businessman trying to decide whether to buy a piece of property with an election coming-up. He thinks-through whether he would be better off with the property if a Democrat is elected, and decides that he would prefer that he had bought the property in that case. He thinks-through whether he would be better off with the property if a Republican is elected, and decides that he would prefer that he had bought the property in that case. So he buys the property. This seems very reasonable.

But there is a famous class of counter-examples, presented by Jeffrey in the form of the case of the Marlboro Man. The hypothetical Marlboro Man is trying to decide whether to smoke. He considers that, if he should live a long life, he would wish at its end that he had enjoyed the pleasure of smoking. He considers that, if he should live a short life, he would wish at its end that he had enjoyed the pleasure of smoking. So he smokes. That doesn't seem nearly so reasonable.

There is an underlying difference between our two examples. The businessman would not normally expect his choice to affect the outcome of the election; the Marlboro Man ought to expect his choice to affect the length of his life. Jeffrey asserts that Savage only meant the Sure Thing Principle to hold in cases where the probability of B were independent of A.

But what makes the discussion poignant is this: Jeffrey, dying of surfeit of Pall Malls, wrote this book as his last, and passed-away from lung cancer on 9 November 2002.

All these experiments, however, are thrown completely into the shade by the enormously extensive investigations of the Swiss astronomer Wolf, the earliest of which were published in 1850 and the latest in 1893. In his first set of experiments Wolf completed 1000 sets of tosses with two dice, each set continuing until every one of the 21 possible combinations had occurred at least once. This involved altogether 97,899 tosses, and he then completed a total of 100,000. These data enabled him to work out a great number of calculations, of which Czuber quotes the following, namely a proportion of .83533 of unlike pairs, as against the theoretical value .83333, i.e. 5/6. In his second set of experiments Wolf used two dice, one white and one red (in the first set the dice were indistinguishable), and complete 20,000 tosses, the details of each result being recorded in the Vierteljahrsschrift der Naturforschenden Gesellschaft in Zürich. He studied particularly the number of sequences with each die, and the relative frequency of each of the 36 possible combinations of the two dice. The sequences were somewhat fewer than they ought to have been, and the relative frequency of the different combinations very different indeed from what theory would predict. The explanation is easily found; for the records of the relative frequency of each face show that the dice must have been very irregular, the six face of the white die, for example, falling 38 percent more often than the four face of the same die. This, then, is the sole conclusion of these immensely laborious experiments,—that Wolf's dice were very ill made. Indeed the experiments could have had no bearing except upon the accuracy of his dice. But ten years later Wolf embarked upon one more series of experiments, using four distinguishable dice,—white, yellow, red, and blue,—and tossing this set of four 10,000 times. Wolf recorded altogether, therefore, in the course of his life 280,000 results of tossing individual dice. It is not clear that Wolf had any well-defined object in view in making these records, which are published in curious conjunction with various astronomical results, and they afford a wonderful example of the pure love of experiment and observation.

Previously, I wrote of how a Jack Black® Pure Performance Shave Brush, with synthetic bristles, proved to be far better than the Burma Shave™ boar-bristle brush that I had been using.

I said that I would probably try, for the sake of comparison, an Art of Shaving® badger-bristle brush that I had, and there was some interest in my doing so.

That badger-bristle brush is not of the highest grade. Above it would be the best badger, and better than the best would be the silvertip badger. I'm not going to be trying a best brush or a silvertip brush, because I'm not going to contribute to the the deaths of more badgers. (Again, I got my boar-bristle brush in a state of ignorance, and my badger bristle brush was likewise got by someone who didn't know that badgers were killed for the bristles.) FWIW, I've read that there isn't much difference between an ordinary badger-bristle shave brush and a best badger-bristle shave brush, but that there is a remarkable difference between a silvertip brush and a best badger-bristle shave brush.

In any event, I found the Art of Shaving® badger-bristle brush much better than the Burma Shave™ boar-bristle brush, but the Jack Black® synthetic-bristle brush significantly better than the Art of Shaving® brush.

The Art of Shaving® brush still irritated my skin somewhat. I don't know to what extent that was a result of the overt texture of the bristles and to what extent it was an allergic reäction or something like an allergic reäction. The Black brush has no such effect.

Both the badger brush and the the Black brush have a much greater tendency to hold water than does the boar brush.

I've only tried the badger brush and the Black brush with a hard cake shaving soap. (I once tried the boar brush with a thick shaving cream from Lush, but that the experiment suggested that that stuff shouldn't be applied with a brush at all.) I have other shaving soaps with which I can experiment later, but I don't mean to conductive extensive further comparisons of these brushes.

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For those who are interested, here is a list of the synthetic shave brushes of which I am aware:

• Jack Black Pure Performance Shave Brush
• Body Shop
• Culmak
• Delong (see also Delong brush heads)
• Gentleman's Shop
• Edwin Jagger
• Men-Ü (in America) (outside of America)
• Mühle: classic & modern
• L'Occitane
• Omega
• R.A. Rooney
• Cyril R. Salter (apparently same product as Rooney)
• Taylor of Old Bond Street (NB: Brushes simply marked imitation may contain some natural hair.)

Many of them have been reviewed at Badger & Blade.

A pH change of .24 of the oceans is definitely cause for concern. However, the natural pH of seawater is 8.2, well into the alkaline range, and reducing that by something between .24 and .45 would mean that the ocean were still in the alkaline range (though quite worryingly less). So the headline here

and much of the rhetoric within the body of the article is just rot.

As to the suggestion that the pH will be lowered by as much as .35, it comes from the IPCC, so caveat lector.

In conversation to-day with the Woman of Interest, I said something that I have often said jocularly

I'm not so much a fool as you think.

It's actually a line in translation from a play, Policja, by Sławomir Mrożek. The line is spoken by the character of the General, after his paranoiac nature has kept him from being killed in an explosion.

I only saw that play once, back in late '71 when it was broadcast on WNET, with John McGiver in the rôle of the General. But that one line has very much stuck with me, and repeatedly been used by me, ever since.

A minor prediction: Over the next few weeks, news stories about the economy are going to make increasing reference to Joseph Alois Schumpeter.

Schumpeter was an economist from the Austrian School. His theory of the business cycle was, however, distinct from that which has come to be seen as the Austrian School theory of business cycles (which theory I will not labor here). Schumpeter believed that economic crises were processes of creative destruction, whereby economies restructured in consequences of accepting pent-up innovations (typically technological) incompatible with the existing order, but ultimately beneficial.

Unless this theory is in some way trivialized, it does not explain the present crisis; but I none-the-less expect various journalists and alleged economists to pitch exactly the idea that it does. And I would actually not be surprised for the economy to emerge significantly restructured, but that would be more a matter of a sort of economic gerrymandering by the Democratic Party, taking advantage of the crisis.

I had an odd dream this morning. The Woman of Interest was in Mexico, for some sort of anthropological or archæological project. This was at-or-near a city named Juarez, but it was not the well-known Juarez; rather, it was at a lake in the center of the state of Chihuahua (about where, in real life, the city of Chihuahua is located). Anyway she was taken captive by rebels or by criminals of some sort.

I was in Texas (G_d knows why) when she was kidnapped. So I began trying to make arrangements to get to this dream-world Juarez, the nearest airport to which was a dreadfully named Hitler - Little Hitler International. The next and perhaps only flight to HLH Int from the (unnamed) airport nearest to me would be that of the Smithsonian Institution's airline. (No, the Smithsonian does not have an airline in real life.) I was scrambling to get my passport, and would then try to persuade the SI airline to sell passage to me. I wasn't sure what I was going to do about a visa, but I figured that I'd have to deal with that at HLH.