Assume that you have a perfect twelve-hour clock, with an hour hand and minute hand, each of which moves continuously.

At certain times of day, the minute hand and hour hand will be pointed in exactly opposite directions. The obvious case is that of six o'clock. What are the other times? (Specify your answers precisely, rather than rounding to the nearest minute or second.)

At certain times of day, the minute hand and hour hand will be pointed in exactly the same direction. The obvious case is that of twelve o'clock. What are the other times? (Again, specify your answers precisely.)

(The actual mathematics here is very simple. And the insight that would allow one to answer the first question should apply with very minor modification to the second one.)

Sometimes ethics stick one in odd corners.

A while back, I queried an artist about commissioning a sketch to be given to my sister-in-law. He turned-down the commission as such, but offered to send to her a drawing containing the major element, without charge, if I provided a SASE. I accepted the offer, and he sent her the drawing. By reports, my sister-in-law was thrilled. (I have insisted to all parties that the principal thanks are owed to the artist.)

I'd like to be able to thank him here by name for his generosity, but won't do so without his permission, as it might cause him to be beseiged by similar requests. And he just passes in silence over my request for that permission.

So, well, he did something really sweet. I'm sorry that I cannot tell you who he is.

In 1988, George Herbert Walker Bush ran for President, and expressed his central campaign promise

Read my lips: No New Taxes.

After he took office, a repeated, emphatic message from the main-stream media was that he was stupid for holding to this promise and resisting any increase in taxes. Ultimately, he folded, and supported a tax increase, at which point, the main-stream media turned on a dime, and one of its repeated, emphatic messages was that he had dishonorably broken his promise.

Back in May of 2010, I posted an entry about the Fourteenth Amendment to the US Constitution and the national debt. I'm not sure that readers found that entry particularly interesting at the time, but it gets an ever-increasing number of hits, as the United States approaches default, and as parts of the political left have begun drawing attention to the Amendment. More specifically, parts of the political left have claimed that the Amendment actively requires Congress to increase the debt ceiling, and other parts have claimed that the Amendment empowers the President to increase the debt limit without consent of Congress. It's that latter claim that I will now examine.

Let's return to the actual language of section 4:

The validity of the public debt of the United States, authorized by law, including debts incurred for payment of pensions and bounties for services in suppressing insurrection or rebellion, shall not be questioned. But neither the United States nor any State shall assume or pay any debt or obligation incurred in aid of insurrection or rebellion against the United States, or any claim for the loss or emancipation of any slave; but all such debts, obligations and claims shall be held illegal and void.

(Underscores mine.) Now, an important phrase here is authorized by law; the question is of how a debt as such comes to be authorized by law.

The Constitution itself is law, superior to any-and-all further legislation. It is the Constitution that creätes the Presidency. Before and after the Fourteenth Amendment, the Constitution does not invest any law-making authority in the Presidency beyond what can be said to exist in ability to negotiate treaties with foreign powers (and these treaties must be ratified by a two-thirds majority of the Senate), and Congress has not delegated to the Presidency the authority to increase the debt ceiling.

So the question truly is of whether and when the Fourteenth Amendment might, as parts of the political left claim, be itself exactly the law that empowers the President to increase the ceiling. And the answer is that it is indeed that law — 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.

And there is the rub. 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. The political left will find none of its distinguishing programmes amongst these institutions. (And, should they bother to read what's actually there, the political right would find that many things that it regards as essential are not actually required by the Constitution.)

Some weeks ago, the Woman of Interest spotted an interesting deck of cards on eBay. The deck was miniature, Disney-themed (Mickey Mouse on the backs and on the box), and dated from the late '30s or perhaps 1940. I later found a similar or identical sort of deck listed.

These decks are very appealing, but there's something disturbing about them as well. Here are the joker cards shown in the listings: The two designs, of course, are basically identical except for coloration and for the presence of a background cloud in one and not in the other. I don't yet know whether these cards represent two designs found in each deck, or distinguish one sort of deck from another, but I believe that the latter is the case.

In any event, each pictures Goofy's head and neck sticking-up from within or from behind a woodpile.

There's an expression

a n_gg_r in the woodpile

It refers to a condition where something significant, typically undesirable, is believed to be concealed. This unpleasant metaphor is no longer current in America;[1] in fact, I had to relate and to explain it to the Woman of Interest, who had never encountered it, and I had to double-check on its exact meaning. But it used to be quite current here, and certainly would have been when those cards were designed and when they were released. I cannot help but think that in the mind of the designer, these graphics are meant to be an allusion to that expression, with the underlying notion being that Goofy is an analogue, within the Disney universe, of the stereotypical black character from that era.

I draw attention to the point that one cannot infer that this is how Disney or the rest of the firm conceptualized Goofy; an alien analogy would not be recognized as such, and the image could have been seen as simply silly.

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[1] It evidently retains some currency in Britain, where state and corporate officials continue to let it slip in public!

Having retrieved a previous month's USPS mail, I was flipping through the July-August issue of American Scientist (v99 #4), and found a picture captioned thus:

Middle-aged and elderly people exercising during Respect for the Aged Day in Tokyo in 2005. Japan's population is aging particularly quickly. The ratio of people younger than 20 compared to those older than 65 is shifting, from 9.3 in 1950 to a predicted 0.59 in 2025. If scientists succeed at slowing aging, this trend may well accelerate.

(Underscores mine.) So the caption is claiming that the population is aging quickly and may age even more quickly if aging is slowed.

Now, what's really happening in that caption is that the verb age is being used in two related but very different senses. In aging particularly quickly, the sense is one of increase in average chronological age; in slowing aging, the sense is one of become decrepit. The underlying thought is entirely reasonable; the expression is inept, because it moves from one meaning to the other (and then implicitly back to the first) without signally that it is doing so except in the sense that the passage is otherwise absurd; best not to make the reader sort-out such things.

I don't know who wrote that caption. The author of the piece in which it is embedded actually notes

the word aging refers to different things

exactly to explain how confusions of these meanings results in practice in logically invalid arguments.

Since some time in April, a bug in the software at LiveJournal.com has kept me from logging into it, and from logging into other sites using that same software, with my OpenID. To-day I received an admission that the problem hasn't been worked and is not likely to be worked any time soon. If you're an LJ friend who posts nothing but Friends-only or otherwise filtered entries, then you might as well write me off.

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More generally, my experience filing bug reports has not been very happy. I've recently reported my problems with the formula editor of OpenOffice.

Rather longer ago than that, I noted how WordPress, after letting two dead-lines slip, had just un-scheduled a bug-fix by setting a milestone of Future Release. This morning, I discovered that a spurious claim that the bug was not manifest had caused the report to be closed about three weeks ago. After I was compelled to jump through some otherwise superfluous hoops, it was plainly established that WordPress indeed had exactly the bug that I'd reported (on 29 April 2008), and that, from my initial description, the point of failure could have been quickly found and fixed. A patch was filed, and I thought that the fix would be scheduled for the next bug-fixing release (3.1.4 or 3.2.0, whichever came first), but then the milestone was instead re-set for Future Release. It might still be fixed in the next release, but there is simply no assurance of that. (I can hack my own installation, of course.)

Greek seems to be in-fashion these days. First, last night, a friend called me to ask how to say man who touches elephants in Classical Greek. Then, to-day, as I was attempting to comment to a 'blog earlier to-day, I was presented with the following 'bot challenge: That's right, the string was unadresG ψ1,, and that's a psi, not a w nor a u with a slash through it. Entering a ψ worked just fine. (Not that I actually have my keyboard configured to deliver psi, but I keep Greek characters about, for copying-and-pasting.)

I was sufficiently perturbed by the typographical error in the version that I most recently submitted of my paper on indecision that I decided that, were it not bounced back to me before the first mensiversary of its submission, I would offer a correction. (My thought in waiting a month was that I should limit the frequency with which I pestered them.) I did so, and the journal accepted that with perfect helpfulness.

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I am still wrestling with Sprint over charges to my account for mobile broadband service.

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On 11 May, I opted to switch my principal operating system to Fedora. (I had been considering Scientific Linux as well.) I've since had some problems with installing fonts for all users, and the system has been a little bit flakier, but on the whole the new operating system has been a satisfying choice.

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I am scheduled for some non-trivial dental work on the mornings of 26 and 27 May. Two fillings that I have had since childhood have eroded to the point that they should be replaced, and there is to be a deep cleaning below my gum-line.

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The Woman of Interest and I will be visiting my parents for a few days at the end of the month. (I plan to stay-on for some time after she has flown away.)