# The Universe of Discourse

Tue, 07 Jul 2020

Michael Lugo recently considered a problem involving the allocation of swimmers to swim lanes at random, ending with:

If we compute this for large !!n!! we get !!f(n) \sim 0.4323n!!, which agrees with the Monte Carlo simulations… The constant !!0.4323!! is $$\frac1{2(1-e^{-2})}.$$

I love when stuff like this happens. The computer is great at doing a quick random simulation and getting you some weird number, and you have no idea what it really means. But mathematical technique can unmask the weird number and learn its true identity. (“It was Old Man Haskins all along!”)

A couple of years back Math Stack Exchange had Expected Number and Size of Contiguously Filled Bins, and although it wasn't exactly what was asked, I ended up looking into this question: We take !!n!! balls and throw them at random into !!n!! bins that are lined up in a row. A maximal contiguous sequence of all-empty or all-nonempty bins is called a “cluster”. For example, here we have 13 balls that I placed randomly into 13 bins:

In this example, there are 8 clusters, of sizes 1, 1, 1, 1, 4, 1, 3, 1. Is this typical? What's the expected cluster size?

It's easy to use Monte Carlo methods and find that when !!n!! is large, the average cluster size is approximately !!2.15013!!. Do you recognize this number? I didn't.

But it's not hard to do the calculation analytically and discover that that the reason it's approximately !!2.15013!! is that the actual answer is $$\frac1{2(e^{-1} - e^{-2})}$$ which is approximately !!2.15013!!.

Math is awesome and wonderful.

(Incidentally, I tried the Inverse Symbolic Calculator just now, but it was no help. It's also not in Plouffe's Miscellaneous Mathematical Constants)

(The expressions in the solutions of M. Lugo's problem and this one are very similar, and the two questions do seem related, but looking at his analysis and at mine I see no reason why the answers should have similar forms. I need to think about this more.)

Mon, 06 Jul 2020

The Philadelphia Inquirer's daily email newsletter referred me to this excellent article, by Jeremy Schwartz and Perla Trevizo.

Wow!” I said. “This is way better than the Inquirer's usual reporting. I wonder what that means?” Turns out it meant that the Inquirer was not responsible for the article. But thanks for the pointer, Inquirer folks!

The article is full of legal, political, and engineering details about why it's harder to build a border wall than I would have expected. I learned a lot! I had known about the issue that most of the land is privately owned. But I hadn't considered that there are international water-use treaties that come into play if the wall is built too close to the Rio Grande, or that the wall would be on the river's floodplain. (Or that the Rio Grande even had a floodplain.)

Wed, 24 Jun 2020

Reddit today had this delightful map, drawn by Peter Klumpenhower, of “the largest city in each 10-by-10 degree area of latitude-longitude in the world”:

(Click to enlarge.)

Almost every square is a kind of puzzle! Perhaps it is surprising that Philadelphia is there? Clearly New York dominates its square, but Philadelphia is just barely across the border in the next square south: the 40th parallel runs right through North Philadelphia. (See map at right.) Philadelphia City Hall (the black dot on the map) is at 39.9524 north latitude.

This reminds me of the time I was visiting Tom Christiansen in Boulder, Colorado. We were driving on Baseline Road and he remarked that it was so named because it runs exactly along the 40th parallel. Then he said “that's rather farther south than where you live”. And I said no, the 40th parallel also runs through Philadelphia! Other noteworthy cities at this latitude include Madrid, Ankara, Yerevan, and Beijing.

Anyway speaking of Boulder, the appearance of Fort Collins was the first puzzle I noticed. If you look at the U.S. cities that appear on the map, you see most of the Usual Suspects: New York, Philadelphia, Chicago, Los Angeles, Seattle, Dallas, Houston. And then you have Fort Collins.

“Fort Collins?” I said. “Why not Denver? Or even Boulder?”

Boulder, it turns out, is smaller than Fort Collins. (I did not know this.) And Denver, being on the other side of Baseline Road, doesn't compete with Fort Collins. Everything south of Baseline Road, including Denver, is shut out by Ciudad Juárez, México (population 1.5 million).

There is a Chinese version of this. The Chinese cities on the map include the big Chinese cities: Shanghai, Beijing, Chongqing, Shenzhen, Chengdu. Shenyang. A couple of cities in Inner Mongolia, analogous to the appearance of Boise on the U.S. map. And…

Wenchang. What the heck is Wenchang?

It's the county seat of Wenchang County, in Hainan, not even as important as Fort Collins. China has 352 cities with populations over 125,000. Wenchang isn't one of them. According to the list I found, Wenchang is the 379th-largest city in China. (Fort Collins, by the way, is 159th-largest in the United States. For the 379th, think of Sugar Land, Texas or Cicero, Illinois.)

Since we're in China, please notice how close Beijing is to the 40th parallel. Ten kilometers farther north and it would have displaced Boise — sorry, I meant Hohhot — and ceded its box to Tianjin (pop. 15.6 million). Similarly (but in reverse), had Philadelphia been a bit farther north, it would have disappeared into New York's box, and yielded its own box to Baltimore or Washington or some other hamlet.)

Opposite to the “what the heck is?" puzzles are there “what the heck happened to?” puzzles. Some are easier than others. It's obvious what happened to Seoul: it's in the same box as Shanghai. The largest missing U.S. city is Phoenix, which you can probably guess is in the same box as Los Angeles.

But what the heck happened to Nairobi? (Nairobi is the ninth-largest city in Africa. Dar Es Salaam is the sixth-largest and is in the same box.)

What the heck happened to St. Petersburg? (at 59.938N, 30.309E, it is just barely inside the same box as Moscow. The map is quite distorted in this region.)

What the heck happened to Tashkent? (It's right where it should be. I just missed it somehow.)

There are some boxes where there just isn't much space for cities. Some of these are obvious: most of Micronesia; notoriously isolated places like Easter Island, Tristan Da Cunha, and St. Helena; other islands like Ni‘ihau, Saipan, and Bermuda. But some are less obvious. We saw Wenchang already. Most of West Falkland Island is in the same box as Río Gallegos, Argentina (pop. 98,000). But the capital, Stanley, (pop. 2,460) is on the East Island, in the next box over.

Okay, enough islands. Some of those little towns, alone in their boxes, are on the mainland and (unlike, say, Ittoqqortoormiit) in places where people actually live. But they just happened to get lucky and be the only town in their box. Gabon isn't a big part of Africa. Port-Gentil (pop. 136,462) isn't the largest city in Gabon. But it's on the mainland of Africa and it's the largest city in its box.
I think my favorite oddity so far is that Maputo (population 2.7 million) would have won in its box, if Durban (population 3.7 million) were 13 kilometers farther south. But Durban is at 29.9°S, and that means that the largest settlement in Africa east of 30°E that is also south of 30°S is Port Shepstone (pop. 35,633).

[ Addendum: Reddit discussion has pointed out that Clifden (pop. 1,597) , in western Ireland, is not the largest settlement in its box. There are two slivers of Ireland in that box, and Dingle, four hours away in County Kerry, has a population of 2,050. The Reddit discussion has a few other corrections. The most important is probably that Caracas should beat out Santo Domingo. M. Klumpenhower says that they will send me a revised version of the map. ]

[ Thanks to Hacker News user oefrha for pointing out that Hohhot and Baotou are in China, not Mongolia as I originally said. ]

[ Addendum 20200627: M. Klumpenhower has sent me a revised map, which now appears in place of the old one. It corrects the errors mentioned above. Here's a graphic that shows the differences. But Walt Mankowski pointed out another possible error: The box with Kochi (southern India) should probably be owned by Colombo. ]

Fri, 12 Jun 2020

This article isn't going to be fun to write but I'm going to push through it because I think it's genuinely important. How often have you heard me say that?

A couple of weeks ago the Insurrection Act of 1807 was in the news. I noticed that the Wikipedia article about it contained this very strange-seeming claim:

A secret amendment was made to the Insurrection Act by an unknown Congressional sponsor, allowing such intervention against the will of state governors.

“What the heck is a ‘secret amendment’?” I asked myself. “Secret from whom? Sounds like Wikipedia crackpottery.” But there was a citation, so I could look to see what it said.

The citation is Hoffmeister, Thaddeus (2010). "An Insurrection Act for the Twenty-First Century". Stetson Law Review. 39: 898.

Sometimes Wikipedia claims will be accompanied by an authoritative-seeming citation — often lacking a page number, as this one did at the time — that doesn't actually support the claim. So I checked. But Hoffmeister did indeed make that disturbing claim:

Once finalized, the Enforcement Act was quietly tucked into a large defense authorization bill: the John Warner Defense Authorization Act of 2007. Very few people, including many members of Congress who voted on the larger defense bill, actually knew they were also voting to modify the Insurrection Act. The secrecy surrounding the Enforcement Act was so pervasive that the actual sponsor of the new legislation remains unknown to this day.

I had sometimes wondered if large, complex acts such as HIPAA or the omnibus budget acts sometimes contained provisions that were smuggled into law without anyone noticing. I hoped that someone somewhere was paying attention, so that it couldn't happen.

But apparently the answer is that it does.

Thu, 11 Jun 2020

In case you're interested, here's what the Caxton “eggys” anecdote looked like originally:

1
2
3
4
5
6
7
8
9
10
11
12

In my dayes happened that
certain marchaȗtes were in a ship in tamyse for to haue
sayled ouer the see into zelande / and for lacke of wynde thei
taryed atte forlond. and wente to lande for to refreshe them
And one of theym named Sheffelde a mercer cam in to an
hows and axed for mete. and specyally he axyd after eggys
And the goode wyf answerde.that she coude speke no fren-
she. And the marchaȗt was angry. For he also coude speke
no frenshe. But wolde haue hadde egges / and she understode
hym not/ And thenne at laste a nother sayd he wolde
haue eyren/ then the good wyf sayd that she understod hym
wel/

It takes a while to get used to the dense black-letter font, and I think it will help to know the following:

• Except at the end of a word, the letter ‘s’ is always written as the “long s” , ‘ſ’, which is easy to confuse with ‘f’ .

Compare the ‘f’ and ‘s’ in “frenshe” (line 9) or “wyf sayd” (line 11).

• Some of the ‘r’s are the “rounded r”, ‘ꝛ’, . which looks like a ‘2’. But it is not a ‘2’, it is an ‘r’.

Examples include “for” (line 2) and “after” (line 6).

• In “marchaȗtes” (line 2), the mark above the ‘ȗ’ is an abbreviation for letter ‘n’ (it's actually a tiny ‘n’), so this word is actually “marchauntes”. Similarly “marchaȗt” in line 8 is an abbreviation for “marchaunt”. I have written about this kind of abbreviation before: Abbreviations in medieval manuscripts.

Wed, 10 Jun 2020

The eighth story on the seventh day of the Decameron concerns a Monna Sismonda, a young gentlewoman who is married to a merchant. She contrives to cheat on him, and then when her husband Arriguccio catches her, she manages to deflect the blame through a cunning series of lies. Arriguccio summons Sismonda's mother and brothers to witness her misbehavior, but when Sismonda seems to refute his claims, they heap abuse on him. Sismonda's mother rants about merchants with noble pretensions who marry above their station. My English translation (by G.H. McWilliam, 1972) included this striking phrase:

‘Have you heard how your poor sister is treated by this precious brother-in-law of yours? He’s a tuppenny-ha’penny pedlar, that's what he is!’

“Tuppeny-ha’penny” seemed rather odd in the context of medieval Florentines. It put me in mind of Douglas Hofstadter's complaint about an English translation of Crime and Punishment that rendered “S[toliarny] Pereulok” as “Carpenter’s Lane”:

So now we might imagine ourselves in London, … and in the midst of a situation invented by Dickens… . Is that what we want?

Intrigued by McWilliam's choice, I went to look at the other translation I had handy, John Payne's of 1886, as adapted by Cormac Ó Cuilleanáin in 2004:

‘Have you heard how your fine brother-in-law here, this two-bit huckster, is treating your sister?’

This seemed even more jarring, because Payne was English and Ó Cuilleanáin is Irish, but “two-bit” is 100% American. I wondered what the original had said.

Brown University has the Italian text online, so I didn't even have to go into the house to find out the answer:

‘Avete voi udito come il buono vostro cognato tratta la sirocchia vostra, mercatantuolo di quattro denari che egli è?’

In the coinage of the time, the denier or denarius was the penny, equal in value (at least notionally) to !!\frac1{240}!! of a pound (lira) of silver. It is the reason that pre-decimal British currency wrote fourpence as “4d.”. I think ‘-uolo’ is a diminutive suffix, so that Sismonda's mother is calling Arriguccio a fourpenny merchantling.

McWilliam’s and Ó Cuilleanáin’s translations are looking pretty good! I judged them too hastily.

While writing this up I was bothered by something else. I decided it was impossible that John Payne, in England in 1886, had ever written the words “two-bit huckster”. So I hunted up the original Payne translation from which Ó Cuilleanáin had adapted his version. I was only half right:

‘Have you heard how your fine brother-in-law here entreateth your sister? Four-farthing huckster that he is!’

“Four-farthing” is a quite literal translation of the original Italian, a farthing being an old-style English coin worth one-fourth of a penny. I was surprised to see “huckster”, which I would have guessed was 19th-century American slang. But my guess was completely wrong: “Huckster” is Middle English, going back at least to the 14th century.

In the Payne edition, there's a footnote attached to “four-farthing” that explains:

Or, in modern parlance, ‘twopenny-halfpenny.’

which is what McWilliam had. I don't know if the footnote is Payne's or belongs to the 1925 editor.

The Internet Archive's copy of the Payne translation was published in 1925, with naughty illustrations by Clara Tice. Wikipedia says “According to herself and the New York Times, in 1908 Tice was the first woman in Greenwich Village to bob her hair.”

Mon, 08 Jun 2020

Quite a few people wrote me delightful letters about my recent article about how to read Middle English.

### Corrections

• Paul Bolle pointed out that in my map, I had put the “Zeeland” label in Belgium. Here's the corrected map:

I was so glad I had done the map in SVG! Moving the label was trivial.

The printing press was introduced in the late 15th century, and at that point, because most books were published in or around London, the Midlands dialect used there became the standard, and the other dialects started to disappear.

But Derek Cotter pointed out the obvious fact that London is not in the Midlands; it is in the south. Whoooops. M. Cotter elaborates:

You rightly say modern English comes largely from the Midlands dialect, but London isn't in the Midlands, as your map shows; it's in the South. And the South dialects were among the losers in the standardisation of English, as your Caxton story shows: we now say Northern "eggs", not Southern "eyren". William Tyndale from Gloucestershire, Shakespeare from Warwickshire, and Dr Johnson from Staffordshire were influential in the development of modern English, along with hundreds of aristocrats, thousands of prosperous middle class, and millions of migrating workers.

“Schuleth” goes with ‘ye’ so it ought to be ‘schulest’. I don't know what's up with that.

Derek Cotter explained my mistake: the -st suffix is only for singular thou, but ye here is plural. For comparison, consider the analogous -t in “Thou shalt not kill”. I knew this, and felt a little silly that I did not remember it.

### Regarding Dutch

• brian d foy pointed me to this video of a person trying to buy a cow from a Frisian farmer, by speaking in Old English. Friesland is up the coast from Zeeland, and approximately the original home of the Anglo-Saxon language. The attempt was successful! And the person is Eddie Izzard, who pops up in the oddest places.

• I had mentioned a couple of common Middle English words that are no longer in use, and M. Bolle informed me that several are current in Modern Dutch:

• Middle English eke (“almost”) is spelled ook and pronounced /oke/ in Dutch.

• Wyf (“woman”) persists in Dutch as wijf, pronounced like Modern English “wife”. In Dutch this term is insulting, approximately “bitch”. (German cognates are weib (“woman”) and weibliche (“female”).)

• Eyren (“eggs”). In Dutch this is eieren. (In German, one egg is ei and several is eier.) We aren't sure what the -en suffix is doing there but I speculated that it's the same plural suffix you still see only in “oxen”. (And, as Tony Finch pointed out to me, in “brethren” and “children”.) M. Bolle informs me that it is still common in Dutch.

### Regarding German

• My original article was about schuleþ, an old form of “shall, should”. Aristotle Pagaltzis informed me that in Modern German the word is spelled schulden, but the /d/ is very reduced, “merely hinted at in the transition between syllables”.

One trick I didn't mention in the article was that if a Middle English word doesn't seem to make sense as English, try reading it as German instead and see if that works better. I didn't bring it up because it didn't seem as helpful as the other tricks, partly because it doesn't come up that often, and mainly because you actually have to know something. I didn't want to be saying “look how easy it is to read Middle English, you just have to know German”.

• Tobias Boege and I had a long discussion about the intermutations of ‘ȝ’, ‘y’, ‘g’, and ‘gh’ in English and German. M. Boege tells me:

I would just like to mention, although I suppose unrelated to the development in England, that in the Berlin/Brandenburg region close to where I live, the dialect often turns "g" into "y" sounds, for example "gestern" into "yestern".

This somewhat spreads into Saxony-Anhalt, too. While first letter "g"s turn into "y"/"j", internal ones tend to become a soft "ch". The local pronunciation of my hometown Magdeburg is close to "Mach-tte-burch".

and also brought to my attention this amusing remark about the pronounciation of ‘G’ in Magdeburg:

Man sagt, die Magdeburger sprechen das G auf fünf verschiedene Arten, aber G ist nicht dabei!

(“It is said, that the Magdeburgers pronounce the ‘G’ in five different ways, but none of them is /g/!”)

The Wikipedia article provides more details, so check it out if you read German.

It occurs to me now that the ‘G’ in Dutch is pronounced in many cases not at all as /g/, but as /ɣ/. We don't really have this sound in English, but if we did we might write it as ‘gh’, so it is yet another example of this intermutation. Dutch words with this ‘g’ include gouda and the first ‘G’ in Van Gogh.

• Aristotle Pagaltzis pointed out that the singular / plural thou / ye distinction persists in Modern German. The German second person singular du is cognate with the Middle English singular thou, but the German plural is ihr.

### Final note

The previous article about weirdos during the Depression hit #1 on Hacker News and was viewed 60,000 times. But I consider the Middle English article much more successful, because I very much prefer receiving interesting and thoughtful messages from six Gentle Readers to any amount of attention from Hacker News. Thanks to everyone who wrote, and also to everyone who read without writing.

Fri, 05 Jun 2020

In a recent article I quoted this bit of Middle English:

Ȝelde ȝe to alle men ȝoure dettes: to hym þat ȝe schuleþ trybut, trybut.

and I said:

As often with Middle English, this is easier than it looks at first. In fact this one is so much easier than it looks that it might become my go-to example. The only strange word is schuleþ itself…

Yup! If you can read English, you can learn to read Middle English. It looks like a foreign language, but it's not. Not entirely foreign, anyway. There are tricks you can pick up. The tricks get you maybe 90 or 95% of the way there, at least for later texts, say after 1350 or so.

Disclaimer: I have never studied Middle English. This is just stuff I've picked up on my own. Any factual claims in this article might be 100% wrong. Nevertheless I have pretty good success reading Middle English, and this is how I do it.

### Some quick historical notes

It helps to understand why Middle English is the way it is.

English started out as German. Old English, also called Anglo-Saxon, really is a foreign language, and requires serious study. I don't think an anglophone can learn to read it with mere tricks.

Over the centuries Old English diverged from German. In 1066 the Normans invaded England and the English language got a thick layer of French applied on top. Middle English is that mashup of English and French. It's still German underneath, but a lot of the spelling and vocabulary is Frenchified. This is good, because a lot of that Frenchification is still in Modern English, so it will be familiar.

For a long time each little bit of England had its own little dialect. The printing press was introduced in the late 15th century, and at that point, because most books were published in or around London, the Midlands dialect used there became the standard, and the other dialects started to disappear.

[ Addendum 20200606: The part about Midlands dialect is right. The part about London is wrong. London is not in the Midlands. ]

With the introduction of printing, the spelling, which had been fluid and do-as-you-please, became frozen. Unfortunately, during the 15th century, the Midlands dialect had been undergoing a change in pronunciation now called the Great Vowel Shift and many words froze with spelling and pronunciations that didn't match. This is why English vowel spellings are such a mess. For example, why are “meat” and “meet” spelled differently but pronounced the same? Why are “read” (present tense) and “read” (past tense) pronounced differently but spelled the same? In Old English, it made more sense. Modern English is a snapshot of the moment in the middle of a move when half your stuff is sitting in boxes on the sidewalk.

By the end of the 17th century things had settled down to the spelling mess that is Modern English.

### The letters are a little funny

Depending on when it was written and by whom, you might see some of these obsolete letters:

• Ȝ — This letter is called yogh. It's usually a ‘y’ sound, but if the word it's in doesn't make sense with a ‘y’ try pretending that it's a ‘g’ or ‘gh’ instead and see if the meaning becomes clearer. (It was originally more like a “gh-” sound. German words like gestern and garden change to yesterday and yard when they turn into English. This is also why we have words like ‘night’ that are still spelled with a ‘gh’ but is now pronounced with a ‘y’.)

• þ — This is a thorn. It represents the sound we now write as th.

• ð — This is an edh. This is usually also a th, but it might be a d. Originally þ and ð represented different sounds (“thin” and “this” respectively) but in Middle English they're kinda interchangeable. The uppercase version looks like Đ.

Some familiar letters behave a little differently:

• u, v — Letters ‘u’ and ‘v’ are sometimes interchangeable. If there's a ‘u’ in a funny place, try reading it as a ‘v’ instead and see if it makes more sense. For example, what's the exotic-looking "haue”? When you know the trick, you see it's just the totally ordinary word “have”, wearing a funny hat.

• w — When w is used as a vowel, Middle English just uses a ‘u’. For example, the word for “law” is often spelled “laue”.

• y — Where Middle English uses ‘y’, we often use ‘i’. Also sometimes vice-versa.

The quotation I discussed in the earlier article looks like this:

Ȝelde ȝe to alle men ȝoure dettes: to hym þat ȝe schuleþ trybut, trybut.

Daunting, right? But it's not as bad as it looks. Let's get rid of the yoghs and thorns:

Yelde ye to alle men youre dettes: to hym that ye schuleth trybut, trybut.

### The spelling is a little funny

Here's the big secret of reading Middle English: it sounds better than it looks. If you're not sure what a word is, try reading it aloud. For example, what's “alle men”? Oh, it's just “all men”, that was easy. What's “youre dettes”? It turns out it's “your debts”. That's not much of a disguise! It would be a stretch to call this “translation”.

Yelde ye to all men your debts: to him that ye schuleth trybut, trybut.

“Yelde” and “trybut” are a little trickier. As languages change, vowels nearly always change faster than consonants. Vowels in Middle English can be rather different from their modern counterparts; consonants less so. So if you can't figure out a word, try mashing on the vowels a little. For example, “much” is usually spelled “moche”.

With a little squinting you might be able to turn “trybut” into “tribute”, which is what it is. The first “tribute” is a noun, the second a verb. The construction is analogous to “if you have a drink, drink!”

I had to look up “yelde”, but after I had I felt a little silly, because it's “yield”.

Yield ye to all men your debts: to him that ye schuleth tribute, tribute.

We'll deal with “schuleth” a little later.

### The word order is pretty much the same

That's because the basic grammar of English is still mostly the same as German. One thing English now does differently from German is that we no longer put the main verb at the end of the sentence. If a Middle English sentence has a verb hanging at the end, it's probably the main verb. Just interpret it as if you had heard it from Yoda.

### The words are a little bit old-fashioned

… but many of them are old-fashioned in a way you might be familiar with. For example, you probably know what “ye” means: it's “you”, like in “hear ye, hear ye!” or “o ye of little faith!”.

Verbs in second person singular end in ‘-st’; in third person singular, ‘-th’. So for example:

• I drink
• Thou drinkst
• She drinketh

In particular, the forms of “do” are: I do, thou dost, he doth.

Some words that were common in Middle English are just gone. You'll probably need to consult a dictionary at some point. The Oxford English Dictionary is great if you have a subscription. The University of Michigan has a dictionary of Middle English that you can use for free.

Here are a couple of common words that come to mind:

• eke — “also”
• wyf — “woman”

### Verbs change form to indicate tense

In German (and the proto-language from which German descended), verb tense is indicated by a change in the vowel. Sometimes this persists in modern English. For example, it's why we have “drink, drank, drunk” and “sleep, slept”. In Modern German this is more common than in Modern English, and in Middle English it's also more common than it is now.

Past tense usually gets an ‘-ed’ on the end, like in Modern English.

The last mystery word here is “schuleth”:

Yield ye to all men your debts: to him that ye schuleth tribute, tribute.

This is the hard word here.

The first thing to know is that “sch-” is always pronounced “sh-” as it still is in German, never with a hard sound like “school” or “schedule”.

What's “schuleth” then? Maybe something do to with schools? It turns out not. This is a form of “shall, should” but in this context it has its old meaning, now lost, of “owe”. If I hadn't run across this while researching the history of the word “should”, I wouldn't have known what it was, and would have had to look it up.

But notice that it does follow a typical Middle English pattern: the consonants ‘sh-’ and ‘-l-’ stayed the same, while the vowels changed. In the modern word “should” we have a version of “schulen” with the past tense indicated by ‘-d’ just like usual.

“Schuleth” goes with ‘ye’ so it ought to be ‘schulest’. I don't know what's up with that.

[ Addendum 20200608: “ye” is plural, and ‘-st’ only goes on singular verbs. ]

### Prose example

Let's try Wycliffe's Bible, which was written around 1380ish. This is Matthew 6:1:

Takith hede, that ye do not youre riytwisnesse bifor men, to be seyn of hem, ellis ye schulen haue no meede at youre fadir that is in heuenes.

Most of this reads right off:

Take heed, that you do not your riytwisnesse before men, to be seen of them, else you shall have no meede at your father that is in heaven.

“Take heed” is a bit archaic but still good English; it means “Be careful”.

Reading “riytwisnesse” aloud we can guess that it is actually “righteousness”. (Remember that that ‘y’ started out as a ‘gh’.)

“Schulen“ we've already seen; here it just means “shall”.

I had to look up “meede”, which seems to have disappeared since 1380. It meant “reward”, and that's exactly how the NIV translates it:

Be careful not to practice your righteousness in front of others to be seen by them. If you do, you will have no reward from your Father in heaven.

That was fun, let's do another:

Therfore whanne thou doist almes, nyle thou trumpe tofore thee, as ypocritis doon in synagogis and stretis, that thei be worschipid of men; sotheli Y seie to you, they han resseyued her meede.

The same tricks work for most of this. “Whanne” is “when”. We still have the word “almes”, now spelled “alms”: it's the handout you give to beggars. The “sch” in “worschipid” is pronounced like ‘sh’ so it's “worshipped”.

“Resseyued” looks hard, but if you remember to try reading the ‘u’ as a ‘v’ and the ‘y’ as an ‘i’, you get “resseived” which is just one letter off of “received”. “Meede” we just learned. So this is:

Therefore when you do alms, nyle thou trumpe before you, as hypocrites do in synagogues and streets, that they be worshipped by men; sotheli I say to you, they have received their reward.

Now we have the general meaning and some of the other words become clearer. What's “trumpe”? It's “trumpeting”. When you give to the needy, don't you trumpet before you, as the hypocrites do. So even though I don't know what “nyle” is exactly, the context makes it clear that it's something like “do not”. Negative words often began with ‘n’ just as they do now (no, nor, not, never, neither, nothing, etc.). Looking it up, I find that it's more usually spelled “nill”. This word is no longer used; it means the opposite of “will”. (It still appears in the phrase “willy-nilly”, which means “whether you want to or not”.)

“Sothely” means “truly”. “Soth” or “sooth” is an archaic word for truth, like in “soothsayer”, a truth-speaker.

Here's the NIV translation:

So when you give to the needy, do not announce it with trumpets, as the hypocrites do in the synagogues and on the streets, to be honored by others. Truly I tell you, they have received their reward in full.

### Poetic example

Let's try something a little harder, a random sentence from The Canterbury Tales, written around 1390. Wish me luck!

We olde men, I drede, so fare we:
Til we be roten, kan we nat be rype;
We hoppen alwey whil that the world wol pype.

The main difficulty is that it's poetic language, which might be a bit obscure even in Modern English. But first let's fix the spelling of the obvious parts:

We old men, I dread, so fare we:
Til we be rotten, can we not be ripe?
We hoppen alwey whil that the world will pipe.

The University of Michigan dictionary can be a bit tricky to use. For example, if you look up “meede” it won't find it; it's listed under “mede”. If you don't find the word you want as a headword, try doing full-text search.

Anyway, hoppen is in there. It can mean “hopping”, but in this poetic context it means dancing.

We old men, I dread, so fare we:
Til we be rotten, can we not be ripe?
We dance always while the world will pipe.

“Pipe” is a verb here, it means (even now) to play the pipes.

### You try!

William Caxton is thought to have been the first person to print and sell books in England. This anecdote of his is one of my favorites. He wrote it the late 1490s, at the very tail end of Middle English:

In my dayes happened that certayn marchauntes were in a shippe in Tamyse, for to haue sayled ouer the see into zelande, and for lacke of wynde thei taryed atte Forlond, and wente to lande for to refreshe them; And one of theym named Sheffelde, a mercer, cam in-to an hows and axed for mete; and specyally he axyed after eggys; and the goode wyf answerde, that she coude speke no frenshe, And the marchaunt was angry, for he also coude speke no frenshe, but wolde haue hadde ‘egges’ and she understode hym not. And theene at laste another sayd that he wolde haue ‘eyren’ then the good wyf sayd that she vnderstod hym wel.

A “mercer” is a merchant, and “taryed“ is now spelled “tarried”, which is now uncommon and means to stay somewhere temporarily.

Caxton is bemoaning the difficulties of translating into “English” in 1490, at a time when English was still a collection of local dialects. He ends the anecdote by asking:

Loo, what sholde a man in thyse dayes now wryte, ‘egges’ or ‘eyren’?

Thanks to Caxton and those that followed him, we can answer: definitely “egges”.

Wed, 03 Jun 2020
 Order To Kill a Mockingbird from Powell's

Lately I've been rereading To Kill a Mockingbird. There's an episode in which the kids meet Mr. Dolphus Raymond, who is drunk all the time, and who lives with his black spouse and their mixed-race kids. The ⸢respectable⸣ white folks won't associate with him. Scout and Jem see him ride into town so drunk he can barely sit on his horse. He is noted for always carrying around a paper bag with a coke bottle filled with moonshine.

At one point Mr. Dolphus Raymond offers Dill a drink out of his coke bottle, and Dill is surprised to discover that it actually contains Coke.

Mr. Raymond explains he is not actually a drunk, he only pretends to be one so that the ⸢respectable⸣ people will write him off, stay off his back about his black spouse and kids, and leave him alone. If they think it's because he's an alcoholic they can fit it into their worldview and let it go, which they wouldn't do if they suspected the truth, which is that it's his choice.

 Order Cannery Row from Powell's

There's a whole chapter in Cannery Row on the same theme! Doc has a beard, and people are always asking him why he has a beard. Doc learned a long time ago that it makes people angry and suspicious if he tells the truth, which is he has a beard because he likes having a beard. So he's in the habit of explaining that the beard covers up an ugly scar. Then people are okay with it and even sympathetic. (There is no scar.)

Doc has a whim to try drinking a beer milkshake, and when he orders one the waitress is suspicious and wary until he explains to her that he has a stomach ulcer, and his doctor has ordered him to drink beer milkshakes daily. Then she is sympathetic. She says it's a shame about the ulcer, and gets him the milkshake, instead of kicking him out for being a weirdo.

Both books are set at the same time. Cannery Row was published in 1945 but is set during the Depression; To Kill a Mockingbird was published in 1960, and its main events take place in 1935.

I think it must be a lot easier to be a weird misfit now than it was in 1935.

[ Sort of related. ]

Sun, 31 May 2020

This is the third article in a series. ([1] [2]) You may want to reread the earlier ones, which were in 2015. I'll try to summarize.

The original issue considered the implementation of some program feature X. In commit A, the feature had not yet been implemented. In the next commit C it had been implemented, and was enabled. Then there was a third commit, B, that left feature X implemented but disabled it:

  no X     X on     X off

A ------ C ------ B


but what I wanted was to have the commits in this order:

  no X     X off     X on

A ------ B ------ C


so that when X first appeared in the history, it was disabled, and then a following commit enabled it.

I know, you want to say “Why didn't you just use git-rebase?” Because git-rebase wouldn't work here, that's why.

Using interactive rebase here “to reorder B and C” will not work because git-rebase reorders patches, not commits. It will attempt to apply the BC diff as a patch to A, and will fail, because the patch is attempting to disable a feature that isn't implemented in commit A.

My original articles described a way around this, using the plumbing command git-commit-tree to construct the desired commits with the desired parents. I also proposed that one could write a git-reorder-commits command to automate the process, but my proposal gave it a clumsy and bizarre argument convention.

Recently, Curtis Dunham wrote to me with a much better idea that uses the interactive rebase UI to accomplish the same thing much more cleanly. If we had B checked out and we tried git rebase -i A, we would get a little menu like this:

    pick ccccccc implement feature X
pick bbbbbbb disable feature X


As I said before, just switching the order of these two pick commands doesn't work, because the bbbbbbb diff can't be applied on the base commit A.

M. Dunham's suggestion is to use git-rebase -i as usual, but instead of simply reversing the order of the two pick commands, which doesn't work, also change them to exec git snap:

    exec git snap bbbbbbb disable feature X
exec git snap ccccccc implement feature X


But what's git snap? Whereas pick means

run git show to construct a patch from the next commit,
then apply that patch to the current tree

git snap means:

get the complete tree from the next commit,
and commit it unchanged

That is, “take a snapshot of that commit”.

It's simple to implement:

    # read the tree from the some commit and store it in the index
git read-tree $SHA^{tree} # then commit the index, re-using the old commit message git commit -C$SHA


There needs to be a bit of cleanup to get the working tree back into sync with the new index. M. Dunham's actual implementation does this with git-reset (which I'm not sure is quite sufficient), and has some argument checking, but that's the main idea.

I hadn't know about the exec command in a git-rebase script, but it seems like it could do all sorts of useful things. The git-rebase man page suggests inserting exec make at points in your script, to check that your reordering hasn't broken the build along the way.

Thank you again, M. Dunham!

Sat, 30 May 2020

Rob Hoelz mentioned that (one of?) the Nenets languages has different verb moods for concepts that in English are both indicated by “should” and “ought”:

"this is the state of the world as I assume it" vs "this is the state of the world as it currently isn't, but it would be ideal"

Examples of the former being:

• That pie should be ready to come out of the oven
• If you leave now, you should be able to catch the 8:15 to Casablanca

and of the latter:

• People should be kinder to one another
• They should manufacture these bags with stronger handles

I have often wished that English were clearer about distinguishing these. For example, someone will say to me

Using git splurch should fix that

and it is not always clear whether they are advising me how to fix the problem, or lamenting that it won't.

A similar issue applies to the phrase “ought to”. As far as I can tell the two phrases are completely interchangeable, and both share the same ambiguities. I want to suggest that everyone start using “should” for the deontic version (“you should go now”) and “ought to” for the predictive verion (“you ought to be able to see the lighthouse from here”) and never vice versa, but that's obviously a lost cause.

I think the original meaning of both forms is more deontic. Both words originally meant monetary debts or obligations. With ought this is obvious, at least once it's pointed out, because it's so similar in spelling and pronunciation to owed. (Compare pass, passed, past with owe, owed, ought.)

For shall, the Big Dictionary has several citations, none later than 1425 CE. One is a Middle English version of Romans 13:7:

Ȝelde ȝe to alle men ȝoure dettes: to hym þat ȝe schuleþ trybut, trybut.

As often with Middle English, this is easier than it looks at first. In fact this one is so much easier than it looks that it might become my go-to example. The only strange word is schuleþ itself. Here's my almost word-for-word translation:

Yield ye to all men your debts: to him that ye oweth tribute, pay tribute.

The NIV translates it like this:

Give to everyone what you owe them: If you owe taxes, pay taxes

Anyway, this is a digression. I wanted to talk about different kinds of should. The Big Dictionary distinguishes two types but mixes them together in its listing, saying:

In statements of duty, obligation, or propriety. Also, in statements of expectation, likelihood, prediction, etc.

The first of these seems to correspond to what I was calling the deontic form (“people should be kinder”) and the second (“you should be able to catch that train”.) But their quotations reveal several other shades of meaning that don't seem exactly like either of these:

Some men should have been women

This is not any of duty, obligation, propriety, expectation, likelihood, or prediction. But it is exactly M. Hoelz’ “state of the world as it currently isn't”.

Similarly:

I should have gotten out while I had the chance

Again, this isn't (necessarily) duty, obligation, or propriety. It's just a wish contrary to fact.

The OED does give several other related shades of “should” which are not always easy to distinguish. For example, its definition 18b says

ought according to appearances to be, presumably is

and gives as an example

That should be Barbados..unless my reckoning is far out.

Compare “We should be able to see Barbados from here”.

Its 18c is “you should have seen that fight!” which again is of the wish-contrary-to-fact type; they even gloss it as “I wish you could have…”.

Another distinction I would like to have in English is between “should” used for mere suggestion in contrast with the deontic use. For example

It's sunny out, we should go swimming!

(suggestion) versus

You should finish your homework before you play ball.

(obligation).

Say this distinction was marked in English. Then your mom might say to you in the morning

You should¹ wash the dishes now, before they get crusty

and later, when you still haven't washed the dishes:

You should² wash the dishes before you go out

meaning that you'll be in trouble if you fail in your dish washing duties.

When my kids were small I started to notice how poorly this sort of thing was communicated by many parents. They would regularly say things like

• You should be quiet now
• I need you to be quiet now
• You need to be quiet now
• You want to be quiet now

(the second one in particular) when what they really meant, it seemed to me, was “I want you to be quiet now”.

[ I didn't mean to end the article there, but after accidentally publishing it I decided it was as good a place as any to stop. ]

John Gleeson points out that my optical illusion (below left) appears to be a variation on the classic Poggendorff illusion (below right):

Fri, 29 May 2020

I recently complained about people who claim:

you can't have a 1 after an infinite sequence of zeroes, because an infinite sequence of zeroes goes on forever.

When I read something like this, the first thing that usually comes to mind is the ordinal number !!\omega+1!!, which is a canonical representative of this type of ordering. But I think in the future I'll bring up this much more elementary example:

$$S = \biggl\{-1, -\frac12, -\frac13, -\frac14, \ldots, 0\biggr\}$$

Even a middle school student can understand this, and I doubt they'd be able to argue seriously that it doesn't have an infinite sequence of elements that is followed by yet another final element.

Then we could define the supposedly problematic !!0, 0, 0, \ldots, 1!! thingy as a map from !!S!!, just as an ordinary sequence is defined as a map from !!\Bbb N!!.

[ Related: A familiar set with an unexpected order type. ]

A couple of years ago I wrote an article about a topological counterexample, which included this illustration:

Since then, every time I have looked at this illustration, I have noticed that the blue segment is drawn wrong. It is intended to be a portion of a radius, so if I extend it toward the center of the circle it ought to intersect the center point. But clearly, the slope is too high and the extension passes significantly below the center.

Or so it appears. I have checked the original SVG, using Inkscape to extend the blue segment: the extension passes through the center of the circle. I have also checked the rendered version of the illustration, by holding a straightedge up to the screen. The segment is pointing in the correct direction.

So I know it's right, but still I'm jarred every time I see it, because to me it looks so clearly wrong.

[ Addendum 20200530: John Gleeson has pointed out the similarity to the Poggendorff illusion. ]

Fri, 22 May 2020

There have been several reports of the theft of catalytic converters in our neighborhood, the thieves going under the car and cutting the whole thing out. The catalytic converter contains a few grams of some precious metal, typically platinum, and this can be recycled by a sufficiently crooked junk dealer.

Why weren't these being stolen before? I have a theory. The catalytic converter contains only a few grams of platinum, worth around $30. Crawling under a car to cut one out is a lot of trouble and risk to go to for$30. I think the the stay-at-home order has put a lot of burglars and housebreakers out of work. People aren't leaving their houses and in particular they aren't going on vacations. So thieves have to steal what they can get.

[ Addendum 20200522: An initial glance at the official crime statistics suggests that my theory is wrong. I'll try to make a report over the weekend. ]

Thu, 07 May 2020

Yesterday I went through the last few months of web server logs, used them to correct some bad links in my blog articles.

Today I checked the logs again and all the "page not found" errors are caused by people attacking my WordPress and PHP installations. So, um, yay, I guess?

Tue, 05 May 2020

I wrote a really great blog post over the last couple of days. Last year I posted about the difference between !!\frac10!! and !!\frac00!! and this was going to be a followup. I had a great example from linear regression, where the answer comes out as !!\frac10!! in situations where the slope of computed line is infinite (and you can fix it, by going into projective space and doing everything in homogeneous coordinates), and as !!\frac00!! in situations where the line is completely indeterminite, and you can't fix it, but instead you can just pick any slope you want and proceed from there.

Except no, it never does come out !!\frac10!!. It always comes out !!\frac00!!, even in the situations I said were !!\frac10!!.

I think maybe I can fix it though, I hope, maybe. If so, then I will be able to write a third article.

Maybe.

It could have been worse. I almost published the thing, and only noticed my huge mistake because I was going to tack on an extra section at the end that it didn't really need. When I ran into difficulties with the extra section, I was tempted to go ahead and publish without it.

Fri, 01 May 2020

(Previously)

I don't have much to add at this point, but when I looked into Sir Thomas Urquhart a bit more, I found this amazing article by Denton Fox in London Review of Books. It's a review of a new edition of Urquhart's 1652 book The Jewel (Ekskybalauron), published in 1984. The whole article is worth reading. It begins:

Sir Thomas Urquhart … must have been a most peculiar man.

The little we know about Urquhart’s early life comes mostly from his own pen, and is therefore not likely to be true.

Some excerpts will follow. You may enjoy reading the whole thing.

### Trissotetras

I spent much way more time on this than I expected. Fox says:

In 1645 he brought out the Trissotetras … . Urquhart’s biographer, Willcock, says that ‘no one is known to have read it or to have been able to read it,’ …

Thanks to the Wonders of the Internet, a copy is available, and I have been able to glance at it. Urquhart has invented a microlanguage along the lines of Wilkins’ philosophical language, in which the words are constructed systematically. But the language of Trissotetras has a very limited focus: it is intended only for expressing statements of trigonometry. Urquhart says:

The novelty of these words I know will seeme strange to some, and to the eares of illiterate hearers sound like termes of Conjuration: yet seeing that since the very infancie of learning, such inventions have beene made use of, and new words coyned, …

The sentence continues for another 118 words but I think the point is made: the idea is not obviously terrible.

Here is an example of Urquhart's trigonometric language in action:

The second axiom is Eproso, that is, the sides are proportionall to one another as the sines of their opposite angles…

A person skilled in the art might be able to infer the meaning of this axiom from its name:

• E — a side
• Pro – proportional
• S – the sine
• O – the opposite angle

That is, a side (of a triangle) is proportional to the sine of the opposite angle. This principle is currently known as the law of sines.

Urquhart's idea of constructing mnemonic nonsense words for basic laws was not a new one. There was a long-established tradition of referring to forms of syllogistic reasoning with constructed mnemonics. For example a syllogism in “Darii” is a deduction of this form:

• All mammals have hair
• Some animals are mammals
• Therefore some animals have hair.

The ‘A’ in “Darii” is a mnemonic for the “all” clause and the ‘I’s for the “some” clauses. By memorizing a list of 24 names, one could remember which of the 256 possible deductions were valid.

Urquhart is following this well-trodden path and borrows some of its terminology. But the way he develops it is rather daunting:

The Directory of this second Axiome is Pubkegdaxesh, which declareth that there are seven Enodandas grounded on it, to wit, foure Rectangular, Upalem, Ubeman, Ekarul, Egalem, and three Obliquangular, Danarele, Xemenoro, and Shenerolem.

I think that ‘Pubkegdaxesh’ is compounded from the initial syllables of the seven enodandas, with p from upalem, ub from ubamen, k from ekarul, eg from egalem, and so on. I haven't been able to decipher any of these, although I didn't try very hard. There are many difficulties. Sometimes the language is obscure because it's obsolete and sometimes because Urquhart makes up his own words. (What does “enodandas” mean?)

Let's just take “Upalem”. Here are Urquhart's glosses:

• U – the Subtendent side
• P – Opposite, whether Angle or side
• A — an angle
• L — the secant
• E — a side
• M — A tangent complement

I believe “a tangent complement” is exactly what we would now call a cotangent; that is, the tangent of the complementary angle. But how these six items relate to one another, I do not know.

Here's another difficulty: I'm not sure that ‘al’ is one component or two. It might be one:

• U – the Subtendent side
• P – Opposite, whether Angle or side
• Al — half
• E — a side
• M — A tangent complement

Either way I'm not sure what is meant. Wait, there is a helpful diagram, and an explanation of it:

The first figure, Vale, hath but one mood, and therefore of as great extent as it selfe, which is Upalem; whose nature is to let us know, when a plane right angled triangle is given us to resolve, who subtendent and one of the obliques is proposed, and one of the ambients required, that we must have recourse unto its resolver, which being Rad—U—Sapy ☞ Yr sheweth, that if we joyne the artificiall sine of the angle opposite to the side demanded with the Logarithm of the subtendent, the summe searched in the canon of absolute numbers will afford us the Logarithm of the side required.

This is unclear but tantalizing. Urquhart is solving a problem of elementary plane trigonometry. Some of the sides and angles are known, and we are to find one of the unknown ones. I think if if I read the book from the beginning I think I might be able to make out better what Urquhart was getting at. Tempting as it is I am going to abandon it here.

Trissotetras is dedicated to Urquhart's mother. In the introduction, he laments that

Trigonometry … hath beene hitherto exposed to the world in a method whose intricacy deterreth many from adventuring on it…

He must have been an admirer of Alexander Rosse, because the front matter ends with a little poem attributed to Rosse.

### Pantochronachanon

Fox again:

Urquhart, with many others, was taken to London as a prisoner, where, apparently, he determined to recover his freedom and his estates by using his pen. His first effort was a genealogy in which he names and describes his ancestors, going back to Adam. … A modern reader might think this Urquhart’s clever trick to prove that he was not guilty by reason of insanity …

This is Pantochronachanon, which Wikipedia says “has been the subject of ridicule since the time of its first publication, though it was likely an elaborate joke”, with no citation given.

Fox mentions that Urquhart claims Alcibiades as one of his ancestors. He also claims the Queen of Sheba.

According to Pantochronachanon the world was created in 3948 BC (Ussher puts it in 4004), and Sir Thomas belonged to the 153rd generation of mankind.

### The Jewel

Denton Fox:

Urquhart found it necessary to try again with the Jewel, or, to to give it its full title, which in some sense describes it accurately…

EKSKUBALAURON [Εκσκυβαλαυρον]: OR, The Discovery of A most exquisite Jewel, more precious then Diamonds inchased in Gold, the like whereof was never seen in any age; found in the kennel [gutter] of Worcester-streets, the day after the Fight, and six before the Autumnal Aequinox, anno 1651. Serving in this place, To frontal a Vindication of the honour of SCOTLAND, from that Infamy, whereinto the Rigid Presbyterian party of that Nation, out of their Covetousness and ambition, most dissembledly hath involved it.

Wowzers.

Fox claims that the title Εκσκυβαλαυρον means “from dung, gold” but I do not understand why he says this. λαύρα might be a sewer or privy, and I think the word σκυβα means garden herbs. (Addendum: the explanation.)

[The book] relates how… Urquhart’s lodgings were plundered, and over 3200 sheets of his writings, in three portmanteaux, were taken.… One should remember that there is not likely to be the slightest bit of truth in this story: it speaks well for the morality of modern scholars that so many of them should have speculated why Urquhart took all his manuscripts to war with him.

Fox says that in spite of the general interest in universal languages, “parts of his prospectus must have seemed absurd even then”, quoting this item:

Three and twentiethly, every word in this language signifieth as well backward as forward; and how ever you invert the letters, still shall you fall upon significant words, whereby a wonderful facility is obtained in making of anagrams.

Urquhart boasts that where other, presumably inferior languages have only five or six cases, his language has ten “besides the nominative”. I think Finnish has fourteen but I am not sure even the Finns would be so sure that more was better. Verbs in Urquhart's language have one of ten tenses, seven moods, and four voices. In addition to singular and plural, his language has dual (like Ancient Greek) and also ‘redual’ numbers. Nouns may have one of eleven genders. It's like a language designed by the Oglaf Dwarves.

A later item states:

This language affordeth so concise words for numbering, that the number for setting down, whereof would require in vulgar arithmetick more figures in a row then there might be grains of sand containable from the center of the earth to the highest heavens, is in it expressed by two letters.

and another item claims that a word of one syllable is capable of expressing an exact date and time down to the “half quarter of the hour”. Sir Thomas, I believe that Entropia, the goddess of Information Theory, would like a word with you about that.

### Wrapping up

One final quote from Fox:

In 1658, when he must have been in his late forties, he sent a long and ornately abusive letter to his cousin, challenging him to a duel at a place Urquhart would later name,

quhich shall not be aboue ane hunderethe – fourtie leagues distant from Scotland.

If the cousin would neither make amends or accept the challenge, Urquhart proposed to disperse copies of his letter

over all whole the kingdome off Scotland with ane incitment to Scullions, hogge rubbers [sheep-stealers], kenell rakers [gutter-scavengers] – all others off the meanist sorte of rascallitie, to spit in yor face, kicke yow in the breach to tred on yor mushtashes ...

Fox says “Nothing much came of this, either.”.

[ Addendum 20200502: Brent Yorgey has explained Εκσκυβαλαυρον for me. Σκύβαλα (‘skubala’) is dung, garbage, or refuse; it appears in the original Greek text of Philippians 3:8:

What is more, I consider everything a loss because of the surpassing worth of knowing Christ Jesus my Lord, for whose sake I have lost all things. I consider them garbage, that I may gain Christ…

And while the usual Greek word for gold is χρῡσός (‘chrysos’), the word αύρον (‘auron’, probably akin to Latin aurum) is also gold. The screenshot at right is from the 8th edition of Liddell and Scott. Thank you, M. Yorgey! ]

Thu, 30 Apr 2020

Yesterday Katara and I were talking about words for ‘song’. Where did ‘song’ come from? Obviously from German, because sing, song, sang, sung is maybe the perfect example of ablaut in Germanic languages. (In fact, I looked it up in Wikipedia just now and that's the example they actually used in the lede.)

But the German word I'm familiar with is Lied. So what happened there? Do they still have something like Song? I checked the Oxford English Dictionary but it was typically unhelpful. “It just says it's from Old German Sang, meaning ‘song’. To find out what happened, we'd need to look in the Oxford German Dictionary.”

Katara considered. “Is that really a thing?”

“I think so, except it's written in German, and obviously not published by Oxford.”

“What's it called?”

I paused and frowned, then said “Deutsches Wörterbuch.”

“Did you just happen to know that?”

“Well, I might be totally wrong, but yeah.” But I looked. Yeah, it's called Deutsches Wörterbuch:

The Deutsches Wörterbuch … is the largest and most comprehensive dictionary of the German language in existence. … The dictionary's historical linguistics approach … makes it to German what the Oxford English Dictionary is to English.

So, yes, I just happened to know that. Yay me!

Deutsches Wörterbuch was begun by Wilhelm and Jakob Grimm (yes, those Brothers Grimm) although the project was much too big to be finished in their lifetimes. Wilhelm did the letter ‘D’. Jakob lived longer, and was able to finish ‘A’, ‘B’, ‘C’, and ‘E’. Wikipedia mentions the detail that he died “while working on the entry for ‘Frucht’ (fruit)”.

Wikipedia says “the work … proceeded very slowly”:

Hermann Wunderlich, Hildebrand's successor, only finished Gestüme to Gezwang after 20 years of work …

(This isn't as ridiculous as it seems; German has a lot of words that begin with ‘ge-’.)

The project came to an end in 2016, after 178 years of effort. The revision of the Grimms’ original work on A–F, planned since the 1950s, is complete, and there are no current plans to revise the other letters.

Tue, 28 Apr 2020

Urquhart, Rosse, and Browne
[ Warning: I abandoned this article in 2008 and forgot that it existed. I ran across it today and decided that what I did write was worth publishing, although it breaks off suddenly. ]

A couple of years ago, not long before I started this blog, I read some of the works of Sir Thomas Browne. I forget exactly why: there was some footnote I read somewhere that said that something in one of Jorge Luis Borges' stories had been inspired by something he read in Browne's book The Urn Burial, which was a favorite of Borges'. I wish I could remember the details! I don't think I even remembered them at the time. But Thomas Browne turned out to be wonderful. He is witty, and learned, and wise, and humane, and to read his books is to feel that you are in the company of this witty, learned, wise, humane man, one of the best men that the English Renaissance has to offer, and that you are profiting thereby.

The book of Browne's that made the biggest impression on me was Pseudodoxia Epidemica (1646), which is a compendium of erroneous beliefs that people held at the time, with discussion. For example, is it true that chameleons eat nothing but air? ("Thus much is in plain terms affirmed by Solinus, Pliny, and others...") Browne thinks not. He cites various evidence against this hypothesis: contemporary reports of the consumption of various insects by chameleons; the presence of teeth, tongues, stomachs and guts in dissected chameleons; the presence of semi-digested insects in the stomachs of dissected chameleons. There's more; he attacks the whole idea that an animal could be nourished by air. Maybe all this seems obvious, but in 1672 it was still a matter for discussion. And Browne's discussion is so insightful, so pithy, so clear, that it is a delight to read.

Browne's list of topics is fascinating in itself. Some of the many issues he deals with are:

• That Crystall is nothing else but Ice strongly congealed;
• That a Diamond is made soft, or broke by the blood of a Goate;
• That Misseltoe is bred upon trees, from seeds which birds let fall thereon;
• That an Elephant hath no joints;
• That Snayles have two eyes, and at the end of their hornes;
• That men weigh heavier dead then alive;
• Of the pictures of Adam and Eve With Navels [a classic question, that; Saint Augustine took it up in City of God];
• Of the pictures of our Saviour with long haire;
• Of the falling of salt;
• That Children would naturally speak Hebrew [another question of perennial interest. I have heard that Frederick the Great actually made the experiment and raised children in isolation to see if they would learn Hebrew];
• Of the blacknesse of Negroes;
• That a man hath one Rib lesse then a woman;
• Of Crassus that never laughed but once;
• Of the wandring Jew;
• Of Milo, who by daylie lifting a Calfe, attained an ability to carry it being a Bull.
There are many reasons why I enjoy reading books from this period, and that list makes me realize one of them. It was a time when science was new, and there were huge tracts of unexplored territory. Every question was open for investigation, including whether storks will live only in republics. A quick perusal of the table of contents from Richard Waller's Posthumous Works of Robert Hooke will give a similar impression, although with a somewhat different flavor to it. And nobody knew what was going to work and what wasn't. Can you make gold by subliming away all the impurities from iron? (No.) Hey, can you learn anything about vision by sticking a metal spike in your eye socket? (Yes.) I have written before about how the Baroque philosophers often chased ideas that seem crackpot to us now—but we can see these ideas as crackpot only because they were tried by the Baroque guys three hundred years ago, and didn't work.

Well, I digress. To return to that list of topics I quoted, you might see "of the blacknesse of Negroes", and feel your heart sink a little. What racist jackass thing is the 1646 Englishman going to say about the blackness of negroes?

Actually, though, Browne comes out of it extremely well, not only much better than one would fear, but quite well even by modern standards. It is one of the more extensive discourses in Pseudodoxia Epidemica, occupying several chapters. He starts by rebutting two popular explanations: that they are burnt black by the heat of the sun, and that they are marked black because of the curse of Ham as described in Genesis 9:20–26.

Regarding the latter, Browne begins by addressing the Biblical issue directly, and on its own terms, and finds against it. But then he takes up the larger question of whether black skin can be considered to be a curse at all. Browne thinks not. He spends some time rejecting this notion: "to inferr this as a curse, or to reason it as a deformity, is no way reasonable". He points out that the people who have it don't seem to mind, and that "Beauty is determined by opinion, and seems to have no essence that holds one notion with all; that seeming beauteous unto one, which hath no favour with another; and that unto every one, according as custome hath made it natural, or sympathy and conformity of minds shall make it seem agreeable."

Finally, he ends by complaining that "It is a very injurious method unto Philosophy, and a perpetual promotion of Ignorance, in points of obscurity, ... to fall upon a present refuge unto Miracles; or recurr unto immediate contrivance, from the insearchable hands of God." I wish more of my contemporaries agreed.

Another reason I love this book is that Browne is nearly always right. If you were having doubts that one could arrive at correct notions by thoughtful examination of theory and evidence, Pseudodoxia Epidemica might help dispel them, because Browne's record of coming to the correct conclusions is marvelous.

Some time afterward, I learned that there was a rebuttal to Pseudodoxia Epidemica, written by a Dr. Alexander Rosse. (Arcana Microcosmi, ... with A Refutation of Doctor Brown's VULGAR ERRORS... (1652).) And holy cow, Rosse is an incredible knucklehead. Watching him try to argue with Browne reminded me of watching an argument on Usenet (a sort of pre-Internet distributed BBS) where one person is right about everything, and is being flamed point by point by some jackass who is wrong about everything, and everyone but the jackass knows it. I have seen this many, many times on Usenet, but never as far back as 1652.

This is the point at which I stopped writing the article in 2008. I had mentioned the blockheaded Mr. Rosse in an earlier article. But I have no idea what else I had planned to say about him here.

2. I no longer have any idea who Urquhart was, or what I had planned to say about him. Searching for him in conjunction with Browne I find he was Sir Thomas Urquhart, a contemporary of Browne's. There is a Wikipedia article about Urquhart. Like his better-known contemporary John Wilkins, he tried to design a universal language in which the meaning of a word could be inferred from its spelling.

3. I learned that Rosse was the target of sarcastic mockery in Samuel Butler's Hudibras:
There was an ancient sage philosopher
It seems that Rosse was a noted dumbass even in his own lifetime.

4. John Willcock's biography of Urquhart says “Ross himself is now only known to most of us from the mention made of him in Hudibras”, and that was in 1899.

5. Thomas Browne is the source of the often-quoted suggestion that:

What song the Sirens sang, or what name Achilles assumed when he hid himself among women, though puzzling questions, are not beyond all conjecture.
(It appears in his book Hydrotaphia, or Urn Buriall.) This hopeful talisman has inspired many people over the centuries to continue their pursuit of such puzzling questions, sometimes when faced with what seems like a featureless wall of lost history.

6. A few years later I revisited Milo, who by daylie lifting a Calfe, attained an ability to carry it being a Bull.

[ Addendum 20200501: Uquhart was a very peculiar man. ]

Sun, 26 Apr 2020

I ran into this album by Jools Holland:

What do you see when you look at this? If you're me, you spend a few minutes wondering why there is a map of Delaware.

Fri, 24 Apr 2020

There's this thing that happens on Stack Exchange sometimes. A somewhat-clueless person will show up and ask a half-baked question about something they are thinking about. Their question is groping toward something sensible but won't be all the way there, and then several people will reply saying no, that is not sensible, your idea is silly, without ever admitting that there is anything to the idea at all.

I have three examples of this handy, and I'm sure I could find many more.

1. One recent one concerns chirality (handedness) in topology. OP showed up to ask why a donut seems to be achiral while a coffee cup is chiral (because the handle is on one side and not the other). Some people told them that the coffee cup is actually achiral and some others people told them that topology doesn't distinguish between left- and right-handed objects, because reflection is a continuous transformation. (“From a topological point of view, no object is distinguishable from its mirror image”.) I've seen many similar discussions play out the same way in the past.

But nobody (other than me) told them that there is a whole branch of topology, knot theory, where the difference between left- and right-handed objects is a major concern. Everyone else was just acting like this was a nonissue.

2. This category theory example is somewhat more obscure.

In category theory one can always turn any construction backward to make a “dual” construction, and the “dual” construction is different but usually no less interesting than the original. For example, there is a category-theoretic construction of “product objects”, which generalizes cartesian products of sets, topological product spaces, the direct product of groups, and so on. The dual construction is “coproduct objects” which corresponds to the disjoint union of sets and topological spaces, and to the free product of groups.

There is a standard notion of an “exponential object” and OP wanted to know about the dual notion of a “co-exponential object”. They gave a proposed definition of such an object, but got their proposal a little bit wrong, so that what they had defined was not the actual co-exponential object but instead was trivial. Two other users pointed out in detail why their proposed construction was uninteresting. Neither one pointed out that there is a co-exponential object, and that it is interesting, if you perform the dualization correctly.

(The exponential object concerns a certain property of a mapping !!f :A×B\to C!!. OP asked insead about !!f : C\to A× B!!. Such a mapping can always be factored into a product !!(f_1: C\to A)×(f_2: C\to B)!! and then the two factors can be treated independently. The correct dual construction concerns a property of a mapping !!f : C\to A\sqcup B!!, where !!\sqcup!! is the coproduct. This admits no corresponding simplification.)

3. A frequently-asked question is (some half-baked variation on) whether there is a smallest positive real number. Often this is motivated by the surprising fact that !!0.9999\ldots = 1!!, and in an effort to capture their intuitive notion of the difference, sometimes OP will suggest that there should be a number !!0.000\ldots 1!!, with “an infinite number of zeroes before the 1”.

There is no such real number, but the question is a reasonable one to ask and to investigate. Often people will dismiss the question claiming that it does not make any sense at all, using some formula like “you can't have a 1 after an infinite sequence of zeroes, because an infinite sequence of zeroes goes on forever.”. Mathematically, this response is complete bullshit because mathematicians are perfectly confortable with the idea of an infinite sequence that has one item (or more) appended after the others. (Such an object is said to “have order type !!\omega + 1!!”, and is completely legitimate.) The problem isn't with the proposed object itself, but with the results of the attempt to incorporate it into the arithmetic of real numbers: what would you get, for example, if you tried to multiply it by !!10!!?

Or sometimes one sees answers that go no further than “no, because the definition of a real number is…”. But a better engagement with the question would recognize that OP is probably interested in alternative definitions of real numbers.

In a recent blog article I proposed a classification of answers to certain half-baked software questions (“Is it possible to do X?”):

1. It surely could, but nobody has done it yet
2. It perhaps could, but nobody is quite sure how
3. It maybe could, but what you want is not as clear as you think
4. It can't, because that is impossible
5. I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question

and I said:

Often, engineers will go straight to #5, when actually the answer is in a higher tier. Or they go to #4 without asking if maybe, once the desiderata are clarified a bit, it will move from “impossible” to merely “difficult”. These are bad habits.

These mathematically half-baked questions also deserve better answers. A similar classification of answers to “can we do this” might look like this:

1. Yes, that is exactly what we do, only more formally. You can find out more about the details in this source…
2. Yes, we do something very much like that, but there are some significant differences to address points you have not considered…
3. Yes, we might like to do something along those lines, but to make it work we need to make some major changes…
4. That seems at first like a reasonable thing to try, but if you look more deeply you find that it can't be made to work, because…
5. I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question

The category theory answer was from tier 4, but should have been from tier 2. People asking about !!0.0000…1!! often receive answers from tier 5, but ought to get answers from tier 4, or even tier 3, if you wanted to get into nonstandard analysis à la Robinson.

There is a similar hierarchy for questions of the type “can we model this concept mathematically”, ranging from “yes, all the time” through “nobody has figured that out yet” and “it seems unlikely, because”, to “what would that even mean?”. The topological chirality question was of this type and the answers given were from the “no we can't and we don't” tiers, when they could have been from a much higher tier: “yes, it's more complicated than that but there is an entire subfield devoted to dealing with it.”

This is a sort of refinement of the opposition of “yes, and…” versus “no, but…”, with the tiers something like:

1. Yes, and…
2. Yes, but…
3. Perhaps, if…
4. No, but…
5. No, because…
6. I am embarrassed for you

When formulating the answer to a question, aiming for the upper tiers usually produces more helpful, more useful, and more interesting results.

[ Addendum 20200525: Here's a typical dismissal of the !!0.\bar01!! suggestion: “This is confusing because !!0.\bar01!! seems to indicate a decimal with ‘infinite zeros and then a one at the end.’ Which, of course, is absurd.” ]

Wed, 22 Apr 2020

This morning I got spam with this subject:

Subject: yaxşı xəbər

Now what language is that? The ‘şı’ looks Turkish, but I don't think Turkish has a letter ‘ə’. It took me a little while to find out the answer.

It's Azerbaijani. Azerbaijani has an Arabic script and a Latin script; this is the Latin script. Azerbaijani is very similar to Turkish and I suppose they use the ‘ş’ and ‘ı’ for the same things. I speculated that the ‘x’ was analogous to Turkish ‘ğ’, but it appears not; Azerbaijani also has ‘ğ’ and in former times they used ‘ƣ’ for this.

Bonus trivia: The official Unicode name of ‘ƣ’ is LATIN SMALL LETTER OI. Unicode Technical Note #27 says:

These should have been called letter GHA. They are neither pronounced 'oi' nor based on the letters 'o' and 'i'.

Dave Turner pointed me to the 1939 Russian-language retelling of The Wizard of Oz, titled The Wizard of the Emerald City. In Russian the original title was Волшебник Изумрудного Города. It's fun to try to figure these things out. Often Russian words are borrowed from English or are at least related to things I know but this one was tricky. I didn't recognize any of the words. But from the word order I'd expect that Волшебник was the wizard. -ого is a possessive ending so maybe Изумрудного is “of emeralds”? But Изумрудного didn't look anything like emeralds… until it did.

Изумрудного is pronounced (approximately) “izumrudnogo”. But “emerald” used to have an ‘s’ in it, “esmerald”. (That's where we get the name “Esmeralda”.) So the “izumrud” is not that far off from “esmerad” and there they are!

Fri, 17 Apr 2020

In my previous article I claimed

the oldest known metaphorical use of “dumpster fire” is in reference to the movie Shrek the Third.

However, this is mistaken. Eric Harley has brought to my attention that the phrase was used as early as 2003 to describe The Texas Chainsaw Massacre. According to this Salt Lake Tribune article:

One early use found by Oxford Dictionaries' Jeff Sherwood was a 2003 movie review by the Arizona Republic's Bill Muller that referred to that year's remake of "The Texas Chainsaw Massacre" as "the cinematic equivalent of a dumpster fire — stinky but insignificant."

If Sherwood is affiliated with Oxford Dictionaries, I wonder why this citation hasn't gotten into the Big Dictionary. The Tribune also pointed me to Claire Fallon's 2016 discussion of the phrase.

Thank you, M. Harley.

Thu, 16 Apr 2020

Today I learned that the oldest known metaphorical use of “dumpster fire” (to mean “a chaotic or disastrously mishandled situation”) is in reference to the movie Shrek the Third.

The OED's earliest citation is from a 2008 Usenet post, oddly in rec.sport.pro-wrestling. I looked in Google Book search for an earlier one, but everything I found was about literal dumpster fires.

I missed the movie, and now that I know it was the original Dumpster Fire, I feel lucky.

Tue, 07 Apr 2020

I live near Woodlands Cemetery and by far the largest monument there, a thirty-foot obelisk, belongs to Thomas W. Evans, who is an interesting person. In his life he was a world-famous dentist, whose clients included many crowned heads of Europe. He was born in Philadelphia, and land to the University of Pennsylvania to found a dental school, which to this day is located at the site of Evans’ former family home at 40th and Spruce Street.

A few days ago my family went to visit the cemetery and I insisted on visting the Evans memorial.

The obelisk has this interesting ornament:

The thing around the middle is evidently a wreath of pine branches, but what is the thing in the middle? Some sort of leaf, or frond perhaps? Or is it a feather? If Evans had been a writer I would have assumed it was a quill pen, but he was a dentist. Thanks to the Wonders of the Internet, I was able to find out.

First I took the question to Reddit's /r/whatisthisthing forum. Reddit didn't have the answer, but Reddit user @hangeryyy had something better: they observed that there was a fad for fern decorations, called pteridomania, in the second half of the 19th century. Maybe the thing was a fern.

 Order Fern Fever: The Story of Pteridomania from Powell's

I was nerdsniped by pteridomania and found out that a book on pteridomania had been written by Dr. Sarah Whittingham, who goes by the encouraging Twitter name of @DrFrond.

Dr. Whittingham's opinion is that this is not a fern frond, but a palm frond. The question has been answered to my full and complete satisfaction.

My thanks to Dr. Whittingham, @hangeryyy, and the /r/whatisthisthing community.

Mon, 06 Apr 2020

Yesterday browsing the list of Wikipedias I learned there is an Anglo-Saxon Wikipedia. This seems really strange to me for several reasons: Who is writing it? And why?

And there is a vocabulary problem. Not just because Anglo-Saxon is dead, and one wouldn't expect it to have any words for anything not invented in the last 900 years or so. But also, there are very few extant Anglo-Saxon manuscripts, so we don't have a lot of vocabulary, even for things that had been invented beore the language died.

Helene Hanff said:

I have these guilts about never having read Chaucer but I was talked out of learning Early Anglo-Saxon / Middle English by a friend who had to take it for her Ph.D. They told her to write an essay in Early Anglo-Saxon on any-subject-of-her-own-choosing. “Which is all very well,” she said bitterly, “but the only essay subject you can find enough Early Anglo-Saxon words for is ‘How to Slaughter a Thousand Men in a Mead Hall’.”

I don't read Anglo-Saxon but if you want to investigate, you might look at the Anglo-Saxon article about the Maybach Exelero (a hēahfremmende sportƿægn), Barack Obama, or taekwondo. I am pre-committing to not getting sucked into this, but sportƿægn is evidently intended to mean “sportscar” (the ƿ is an obsolete letter called wynn and is approximately a W, so that ƿægn is “wagon”) and I think that fremmende is “foreign” and hēah is something like "high" or "very". But I'm really not sure.

Anyway Wikipedia reports that the Anglo-Saxon Wikipedia has 3,197 articles (although most are very short) and around 30 active users. In contrast, the Hawai‘ian Wikipedia has 3,919 articles and only around 14 active users, and that is a language that people actually speak.

I was looking at this awesome poster of D. Moor (Д. Моор), one of Russia's most famous political poster artists:

This is interesting for a couple of reasons. First, in Russian, “Himmler”, “Göring”, “Hitler”, and “Goebbels” all begin with the same letter, ‘Г’, which is homologous to ‘G’. (Similarly, Harry Potter in Russian is Га́рри, ‘Garri’.)

I also love the pictures, and especially Goebbels. These four men were so ugly, each in his own distinctively loathsome way. The artist has done such a marvelous job of depicting them, highlighting their various hideousness. It's exaggerated, and yet not unfair, these are really good likenesses! It's as if D. Moor had drawn a map of all the ways in which these men were ugly.

My all-time favorite depiction of Goebbels is this one, by Boris Yefimov (Бори́с Ефи́мов):

For comparison, here's the actual Goebbels:

Looking at pictures of Goebbels, I had often thought “That is one ugly guy,” but never been able to put my finger on what specifically was wrong with his face. But since seeing the Efimov picture, I have never been able to look at a picture of Goebbels without thinking of a rat. D. Moor has also drawn Goebbels as a tiny rat, scurrying around the baseboards of his poster.

Anyway, that was not what I had planned to write about. The right-hand side of D. Moor's poster imagines the initial ‘Г’ of the four Nazis’ names as the four bent arms of the swastika. The captions underneath mean “first Г”, “second Г” and so on.

[ Addendum: Darrin Edwards explains the meaning here that had escaped me:

One of the Russian words for shit is "govno" (говно). A euphemism for this is to just use the initial g; so "something na g" is roughly equivalent to saying "a crappy something". So the title "vse na g" (all on g) is literally "they all start with g" but pretty blatantly means "they're all crap" or "what a bunch of crap". I believe the trick of constructing the swastika out of four g's is meant to extend this association from the four men to the entire movement…

Thank you, M. Edwards! ]

Looking at the fourth one, четвертое /chetvyertoye/, I had a sudden brainwave. “Aha,” I thought, “I bet this is akin to Greek “tetra”, and the /t/ turned into /ch/ in Russian.”

Well, now that I'm writing it down it doesn't seem that exciting. I now remember that all the other Russian number words are clearly derived from PIE just as Greek, Latin, and German are:

English German Latin Greek Russian
one ein unum εἷς (eis) оди́н (odeen)
two zwei duo δύο (dyo) два (dva)
three drei trēs τρεῖς (treis) три (tri)
four vier quattuor τέτταρες (tettares) четы́ре (chyetirye)
five fünf quinque πέντε (pente) пять (pyat’)

In Latin that /t/ turned into a /k/ and we get /quadra/ instead of /tetra/. The Russian Ч /ch/ is more like a /t/ than it is like a /k/.

The change from /t/ to /f/ in English and /v/ in German is a bit weird. (The Big Dictionary says it “presents anomalies of which the explanation is still disputed”.) The change from the /p/ of ‘pente’ to the /f/ of ‘five’ is much more typical. (Consider Latin ‘pater’, ‘piscum’, ‘ped’ and the corresponding English ‘father’, ‘fish’, ‘foot’.) This is called Grimm's Law, yeah, after that Grimm.

The change from /q/ in quinque to /p/ in pente is also not unusual. (The ancestral form in PIE is believed to have been more like the /q/.) There's a classification of Celtic lanugages into P-Celtic and Q-Celtic that's similar, exemplified by the change from the Irish patronymic prefix Mac- into the Welsh patronymic map or ap.

I could probably write a whole article comparing the numbers from one to ten in these languages. (And Sanskrit. Wouldn't want to leave out Sanskrit.) The line for ‘two’ would be a great place to begin because all those words are basically the same, with only minor and typical variations in the spelling and pronunciation. Maybe someday.

Sun, 05 Apr 2020

Back when the Web was much newer, and people hadn't really figured it out yet, there was an attempt to bring a dictionary to the web. Like a paper dictionary, its text was set in a barely-readable tiny font, and there were page breaks in arbitrary places. That is a skeuomorph: it's an incidental feature of an object that persists even in a new medium where the incidental feature no longer makes sense.

Anyway, I was scheduled to give a talk to the local Linux user group last week, and because of current conditions we tried doing it as a videoconference. I thought this went well!

We used Jitsi Meet, which I thought worked quite well, and which I recommend.

The usual procedure is for the speaker to have some sort of presentation materials, anachronistically called “slides”, which they display one at a time to the audience. In the Victorian age these were glass plates, and the image was projected on a screen with a slide projector. Later developments replaced the glass with celluloid or other transparent plastic, and then with digital projectors. In videoconferences, the slides are presented by displaying them on the speaker's screen, and then sharing the screen image to the audience.

This last development is skeuomorphic. When the audience is together in a big room, it might make sense to project the slide images on a shared screen. But when everyone is looking at the talk on their own separate screen anyway, why make them all use the exact same copy?

1. Each audience person can adjust the monitor size, font size, colors to suit their own viewing preferences.

With the screenshare, everyone is stuck with whatever I have chosen. If my font is too small for one person to read, they are out of luck.

2. The audience can see the speaker. Instead of using my outgoing video feed to share the slides, I could share my face as I spoke. I'm not sure how common this is, but I hate attending lectures given by disembodied voices. And I hate even more being the disembodied voice. Giving a talk to people I can't see is creepy. My one condition to the Linux people was that I had to be able to see at least part of the audience.

3. With the slides under their control, audience members can go back to refer to earlier material, or skip ahead if they want. Haven't you had the experience of having the presenter skip ahead to the next slide before you had finished reading the one you were looking at? With this technique, that can't happen.

Some co-workers suggested the drawback that it might be annoying to try to stay synchronized with the speaker. It didn't take me long to get in the habit of saying “Next slide, #18” or whatever as I moved through the talk. If you try this, be sure to put numbers on the slides! (This is a good practice anyway, I have found.) I don't know if my audience found it annoying.

The whole idea only works if you can be sure that everyone will have suitable display software for your presentation materials. If you require WalSoft AwesomePresent version 18.3, it will be a problem. But for the past 25 years I have made my presentation materials in HTML, so this wasn't an issue.

If you're giving a talk over videoconference, consider trying this technique.

[ Addendum: I should write an article about all the many ways in which the HTML has been a good choice. ]

Fri, 27 Mar 2020

Last week Pierre-Françoys Brousseau and I invented a nice chess variant that I've never seen before. The main idea is: two pieces can be on the same square. Sometimes when you try to make a drasatic change to the rules, what you get fails completely. This one seemed to work okay. We played a game and it was fun.

Specfically, our rules say:

1. All pieces move and capture the same as in standard chess, except:

2. Up to two pieces may occupy the same square.

3. A piece may move into an occupied square, but not through it.

4. A piece moving into a square occupied by a piece of the opposite color has the option to capture it or to share the square.

5. Pieces of opposite colors sharing a square do not threaten one another.

6. A piece moving into a square occupied by two pieces of the opposite color may capture either, but not both.

7. Castling is permitted, but only under the same circumstances as standard chess. Pieces moved during castling must move to empty squares.

### Miscellaneous notes

Pierre-Françoys says he wishes that more than two pieces could share a square. I think it could be confusing. (Also, with the chess set we had, more than two did not really fit within the physical confines of the squares.)

Similarly, I proposed the castling rule because I thought it would be less confusing. And I did not like the idea that you could castle on the first move of the game.

The role of pawns is very different than in standard chess. In this variant, you cannot stop a pawn from advancing by blocking it with another pawn.

Usually when you have the chance to capture an enemy piece that is alone on its square you will want to do that, rather than move your own piece into its square to share space. But it is not hard to imagine that in rare circumstances you might want to pick a nonviolent approach, perhaps to avoid a stalemate.

The name “Pauli Chess”, is inspired by the Pauli exclusion principle, which says that no more than two electrons can occupy the same atomic orbital.

Tue, 24 Mar 2020

Today I was looking for recent commits by co worker Fred Flooney, address fflooney@example.com, so I did

    git log --author=ffloo


but nothing came up. I couldn't remember if --author would do a substring search, so I tried

    git log --author=fflooney
git log --author=fflooney@example.com


and still nothing came up. “Okay,” I said, “probably I have Fred's address wrong.” Then I did

    git log --format=%ae | grep ffloo


The --format=%ae means to just print out commit author email addresses, instead of the usual information. This command did produce many commits with the author address fflooney@example.com.

I changed this to

    git log --format='%H %ae' | grep ffloo


which also prints out the full hash of the matching commits. The first one was 542ab72c92c2692d223bfca4470cf2c0f2339441.

Then I had a perplexity. When I did

    git log -1 --format='%H %ae' 542ab72c92c2692d223bfca4470cf2c0f2339441


it told me the author email address was fflooney@example.com. But when I did

    git show 542ab72c92c2692d223bfca4470cf2c0f2339441


the address displayed was fredf@example.com.

The answer is, the repository might have a file in its root named .mailmap that says “If you see this name and address, pretend you saw this other name and address instead.” Some of the commits really had been created with the address I was looking for, fflooney. But the .mailmap said that the canonical version of that address was fredf@. Nearly all Git operations use the canonical address. The git-log --author option searches the canonical address, and git-show and git-log, by default, display the canonical address.

But my --format=%ae overrides the default behavior; %ae explicitly requests the actual address. To display the canonical address, I should have used --format=%aE instead.

Also, I learned that --author= does not only a substring search but a regex search. I asked it for --author=d* and was puzzled when it produced commits written by people with no d. This is a beginner mistake: d* matches zero or more instances of d, and every name contains zero or more instances of d. (I had thought that the * would be like a shell glob.)

Also, I learned that --author=d+ matches only authors that contain the literal characters d+. If you want the + to mean “one or more” you need --author=d\+.

Thanks to Cees Hek, Gerald Burns, and Val Kalesnik for helping me get to the bottom of this.

The .mailmap thing is documented in git-check-mailmap.

[ Addendum: I could also have used git-log --no-use-mailmap ..., had I known about this beforehand. ]

Sun, 16 Feb 2020

Over on the other blog I said “Midichlorians predated The Phantom Menace.” No, the bacterium was named years after the movie was released.

Thanks to Eyal Joseph Minsky-Fenick and Shreevatsa R. for (almost simultaneously) pointing out this mistake.

Thu, 13 Feb 2020

Here is Gerhard Gentzen's original statement of the rules of Natural Deduction (“ein Kalkül für ‘natürliche’, intuitionistische Herleitungen”):

Natural deduction looks pretty much exactly the same as it does today, although the symbols are a little different. But only a little! Gentzen has not yet invented !!\land!! for logical and, and is still using !!\&!!. But he has invented !!\forall!!. The style of the !!\lnot!! symbol is a little different from what we use now, and he has that tent thingy !!⋏!! where we would now use !!\bot!!. I suppose !!⋏!! didn't catch on because it looks too much like !!\land!!. (He similarly used !!⋎!! to mean !!\top!!, but as usual, that doesn't appear in the deduction rules.)

We still use Gentzen's system for naming the rules. The notations “UE” and “OB” for example, stand for “und-Einführung” and “oder-Beseitigung”, which mean “and-introduction” and “or-elimination”.

Gentzen says (footnote 4, page 178) that he got the !!\lor, \supset, \exists!! signs from Russell, but he didn't want to use Russell's signs !!\cdot, \equiv, \sim, ()!! because they already had other meanings in mathematics. He took the !!\&!! from Hilbert, but Gentzen disliked his other symbols. Gentzen objected especially to the “uncomfortable” overbar that Hilbert used to indicate negation (“[Es] stellt eine Abweichung von der linearen Anordnung der Zeichen dar”). He attributes his symbols for logical equivalence (!!\supset\subset!!) and negation to Heyting, and explains that his new !!\forall!! symbol is analogous to !!\exists!!. I find it remarkable how quickly this caught on. Gentzen also later replaced !!\&!! with !!\land!!. Of the rest, the only one that didn't stick was !!\supset\subset!! in place of !!\equiv!!. But !!\equiv!! is much less important than the others, being merely an abbreviation.

Gentzen died at age 35, a casualty of the World War.

Source: Gerhard Gentzen, “Untersuchungen über das logische Schließen I”, pp. 176–210 Mathematische Zeitschrift v. 39, Springer, 1935. The display above appears on page 186.

[ Addendum 20200214: Thanks to Andreas Fuchs for correcting my German grammar. ]

Thu, 06 Feb 2020

[ Previously: “Cases in which some statement S was considered to be proved, and later turned out to be false”. ]

In 1905, Henri Lebesgue claimed to have proved that if !!B!! is a subset of !!\Bbb R^2!! with the Borel property, then its projection onto a line (the !!x!!-axis, say) is a Borel subset of the line. This is false. The mistake was apparently noticed some years later by Andrei Souslin. In 1912 Souslin and Luzin defined an analytic set as the projection of a Borel set. All Borel sets are analytic, but, contrary to Lebesgue's claim, the converse is false. These sets are counterexamples to the plausible-seeming conjecture that all measurable sets are Borel.

I would like to track down more details about this. This Math Overflow post summarizes Lebesgue's error:

It came down to his claim that if !!{A_n}!! is a decreasing sequence of subsets in the plane with intersection !!A!!, the the projected sets in the line intersect to the projection of !!A!!. Of course this is nonsense. Lebesgue knew projection didn't commute with countable intersections, but apparently thought that by requiring the sets to be decreasing this would work.

Tue, 28 Jan 2020

Today I learned that James Blaine (U.S. Speaker of the House, senator, perennial presidential candidate, and Secretary of State under Presidents Cleveland, Garfield, and Arthur; previously) was the namesake of the notorious “Blaine Amendments”. These are still an ongoing legal issue!

The Blaine Amendment was a proposed U.S. constitutional amendment rooted in anti-Catholic, anti-immigrant sentiment, at a time when the scary immigrant bogeymen were Irish and Italian Catholics.

The amendment would have prevented the U.S. federal government from providing aid to any educational institution with a religious affiliation; the specific intention was to make Catholic parochial schools ineligible for federal education funds. The federal amendment failed, but many states adopted it and still have it in their state constitutions.

Here we are 150 years later and this is still an issue! It was the subject of the 2017 Supreme Court case Trinity Lutheran Church of Columbia, Inc. v. Comer. My quick summary is:

1. The Missouri state Department of Natural Resources had a program offering grants to licensed daycare facilities to resurface their playgrounds with shredded tires.

2. In 2012, a daycare facility operated by Trinity Lutheran church ranked fifth out of 44 applicants according to the department’s criteria.

3. 14 of the 44 applicants received grants, but Trinity Lutheran's daycare was denied, because the Missouri constitution has a Blaine Amendment.

4. The Court found (7–2) that denying the grant to an otherwise qualified daycare just because of its religious affiliation was a violation of the Constitution's promises of free exercise of religion. (Full opinion)

It's interesting to me that now that Blaine is someone I recognize, he keeps turning up. He was really important, a major player in national politics for thirty years. But who remembers him now?

Fri, 17 Jan 2020

As Middle English goes, Pylgremage of the Sowle (unknown author, 1413) is much easier to read than Chaucer:

He hath iourneyed by the perylous pas of Pryde, by the malycious montayne of Wrethe and Enuye, he hath waltred hym self and wesshen in the lothely lake of cursyd Lechery, he hath ben encombred in the golf of Glotony. Also he hath mysgouerned hym in the contre of Couetyse, and often tyme taken his rest whan tyme was best to trauayle, slepyng and slomeryng in the bed of Slouthe.

I initially misread “Enuye” as “ennui”, understanding it as sloth. But when sloth showed up at the end, I realized that it was simpler than I thought, it's just “envy”.

Thu, 16 Jan 2020

In 2007 I described an impractical scheme to turn the U.S. into a dictatorship, or to make any other desired change to the Constitution, by having Congress admit a large number of very small states, which could then ratify any constitutional amendments deemed desirable.

An anonymous writer (probably a third-year law student) has independently discovered my scheme, and has proposed it as a way to “fix” the problems that they perceive with the current political and electoral structure. The proposal has been published in the Harvard Law Review in an article that does not appear to be an April Fools’ prank.

The article points out that admission of new states has sometimes been done as a political hack. It says:

Republicans in Congress were worried about Lincoln’s reelection chances and short the votes necessary to pass the Thirteenth Amendment. So notwithstanding the traditional population requirements for statehood, they turned the territory of Nevada — population 6,857 — into a state, adding Republican votes to Congress and the Electoral College.

Specifically, the proposal is that the new states should be allocated out of territory currently in the District of Columbia (which will help ensure that they are politically aligned in the way the author prefers), and that a suitable number of new states might be one hundred and twenty-seven.

Tue, 14 Jan 2020

A couple of readers wrote to discuss tripoints, which are places where three states or other regions share a common border point.

Doug Orleans told me about the Tri-States Monument near Port Jervis, New York. This marks the approximate location of the Pennsylvania - New Jersey - New York border. (The actual tripoint, as I mentioned, is at the bottom of the river.)

I had independently been thinking about taking a drive around the entire border of Pennsylvania, and this is just one more reason to do that. (Also, I would drive through the Delaware Water Gap, which is lovely.) Looking into this I learned about the small town of North East, so-named because it's in the northeast corner of Erie County. It's also the northernmost point in Pennsylvania.

(I got onto a tangent about whether it was the northeastmost point in Pennsylvania, and I'm really not sure. It is certainly an extreme northeast point in the sense that you can't travel north, east, or northeast from it without leaving the state. But it would be a very strange choice, since Erie County is at the very western end of the state.)

My putative circumnavigation of Pennsylvanias would take me as close as possible to Pennsylvania's only international boundary, with Ontario; there are Pennsylvania - Ontario tripoints with New York and with Ohio. Unfortunately, both of them are in Lake Erie. The only really accessible Pennsylvania tripoints are the one with West Virginia and Maryland (near Morgantown) and Maryland and Delaware (near Newark).

These points do tend to be marked, with surveyors’ markers if nothing else. Loren Spice sent me a picture of themselves standing at the tripoint of Kansas, Missouri, and Oklahoma, not too far from Joplin, Missouri.

While looking into this, I discovered the Kentucky Bend, which is an exclave of Kentucky, embedded between Tennessee and Missouri:

The “bubble” here is part of Fulton County, Kentucky. North, across the river, is New Madrid County, Missouri. The land border of the bubble is with Lake County, Tennessee.

It appears that what happened here is that the border between Kentucky and Missouri is the river, with Kentucky getting the territory on the left bank, here the south side. And the border between Kentucky and Tennessee is a straight line, following roughly the 36.5 parallel, with Kentucky getting the territory north of the line. The bubble is south of the river but north of the line.

So these three states have not one tripoint, but three, all only a few miles apart!

Finally, I must mention the Lakes of Wada, which are not real lakes, but rather are three connected subsets of the unit disc which have the property that every point on their boundaries is a tripoint.

Thu, 09 Jan 2020

I'm a fan of geographic oddities, and a few years back when I took a road trip to circumnavigate Chesapeake Bay, I planned its official start in New Castle, DE, which is noted for being the center of the only circular state boundary in the U.S.:

The red blob is New Castle. Supposedly an early treaty allotted to Delaware all points west of the river that were within twelve miles of the State House in New Castle.

I drove to New Castle, made a short visit to the State House, and then began my road trip in earnest. This is a little bit silly, because the border is completely invisible, whether you are up close or twelve miles away, and the State House is just another building, and would be exactly the same even if the border were actually a semicubic parabola with its focus at the second-tallest building in Wilmington.

Whatever, I like going places, so I went to New Castle to check it out. Perhaps it was silly, but I enjoyed going out of my way to visit a point of purely geometric significance. The continuing popularity of Four Corners as a tourist destination shows that I'm not the only one. I don't have any plans to visit Four Corners, because it's far away, kinda in the middle of nowhere, and seems like rather a tourist trap. (Not that I begrudge the Navajo Nation whatever they can get from it.)

Four Corners is famously the only point in the U.S. where four state borders coincide. But a couple of weeks ago as I was falling asleep, I had the thought that there are many triple-border points, and it might be fun to visit some. In particular, I live in southeastern Pennsylvania, so the Pennsylvania-New Jersey-Delaware triple point must be somewhere nearby. I sat up and got my phone so I could look at the map, and felt foolish:

As you can see, the triple point is in the middle of the Delaware River, as of course it must be; the entire border between Pennsylvania and New Jersey, all the hundreds of miles from its northernmost point (near Port Jervis) to its southernmost (shown above), runs right down the middle of the Delaware.

I briefly considered making a trip to get as close as possible, and photographing the point from land. That would not be too inconvenient. Nearby Marcus Hook is served by commuter rail. But Marcus Hook is not very attractive as a destination. Having been to Marcus Hook, it is hard for me to work up much enthusiasm for a return visit.

But I may look into this further. I usually like going places and being places, and I like being surprised when I get there, so visting arbitrarily-chosen places has often worked out well for me. I see that the Pennsylvania-Delaware-Maryland triple border is near White Clay Creek State Park, outside of Newark, DE. That sounds nice, so perhaps I will stop by and take a look, and see if there really is white clay in the creek.

Who knows, I may even go back to Marcus Hook one day.

Wed, 08 Jan 2020

In a recent article about Unix utilities, I wrote:

We need the -l flag on bc because otherwise it stupidly does integer arithmetic.

This is wrong, as was kindly pointed out to me by Luke Shumaker. The behavior of bc is rather more complicated than I said, and less stupid. In the application I was discussing, the input was a string like 0.25+0.37, and it's easy to verify that bc produces the correct answer even without -l:

   $echo 0.25+0.37 | bc .62  In bc, each number is represented internally as !!m·10^{-s}!!, where !!m!! is in base 10 and !!s!! is called the “scale”, essentially the number of digits after the decimal point. For addition, subtraction, and multiplication, bc produces a result with the correct scale for an exact result. For example, when multiplying two numbers with scales a and b, the result always has scale a + b, so the operation is performed with exact precision. But for division, bc doesn't know what scale it should use for the result. The result of !!23÷7!! can't be represented exactly, regardless of the scale used. So how should bc choose how many digits to retain? It can't retain all of them, and it doesn't know how many you will want. The answer is: you tell it, by setting a special variable, called scale. If you set scale=3 then !!23÷7!! will produce the result !!3.285!!. Unfortunately, if you don't set it — this is the stupid part — scale defaults to zero. Then bc will discard everything after the decimal point, and tell you that !!23÷7 = 3!!. Long, long ago I was in the habit of manually entering scale=20 at the start of every bc session. I eventually learned about -l, which, among other things, sets the default scale to 20 instead of 0. And I have used -l habitually ever since, even in cases like this, where it isn't needed. Many thanks to Luke Shumaker for pointing this out. M. Shumaker adds: I think the mis-recollection/understanding of -l says something about your "memorized trivia" point, but I'm not quite sure what. Yeah, same. Tue, 07 Jan 2020 Looking up the letter E in the Big Dictionary, I learned that British sociologists were dividing social classes into lettered strata long before Aldous Huxley did it in Brave New World (1932). The OED quoted F. G. D’Aeth, “Present Tendencies of Class Differentiation”, The Sociological Review, vol 3 no 4, October, 1910: The present class structure is based upon different standards of life… A. The Loafer B. Low-skilled labour C. Artizan D. Smaller Shopkeeper and clerk E. Smaller Business Class F. Professional and Administrative Class G. The Rich The OED doesn't quote further, but D’Aeth goes on to explain: A. represents the refuse of a race; C. is a solid, independent and valuable class in society. … E. possesses the elements of refinement; provincialisms in speech are avoided, its sons are selected as clerks, etc., in good class businesses, e.g., banking, insurance. Notice that in D’Aeth's classification, the later letters are higher classes. According to the OED this was typical; they also quote a similar classification from 1887 in which A was the lowest class. But the OED labels this sort of classification, with A at the bottom, as “obsolete”. In Brave New World, you will recall, it is the in the other direction, with the Alphas (administrators and specialists), at the top, and the Epsilons (menial workers with artificially-induced fetal alcohol syndrome) at the bottom. The OED's later quotations, from 1950–2014, all follow Huxley in putting class A at the top and E at the bottom. They also follow Huxley in having only five classes instead of seven or eight. (One has six classes, but two of them are C1 and C2.) I wonder how much influence Brave New World had on this sort of classification. Was anyone before Huxley dividing British society into five lettered classes with A at the top? [ By the way, I have been informed that this paper, which I have linked above, is “Copyright © 2020 by The Sociological Review Publication Limited. All rights are reserved.” This is a bald lie. Sociological Review Publication Limited should be ashamed of themselves. ] Fri, 03 Jan 2020 Sometimes I look through the HTTP referrer logs to see if anyone is talking about my blog. I use the f 11 command to extract the referrer field from the log files, count up the number of occurrences of each referring URL, then discard the ones that are internal referrers from elsewhere on my blog. It looks like this:  f 11 access.2020-01-0* | count | grep -v plover  (I've discussed f before. The f 11 just prints the eleventh field of each line. It is essentially shorthand for awk '{print$11}' or perl -lane 'print $F[10]'. The count utility is even simpler; it counts the number of occurrences of each distinct line in its input, and emits a report sorted from least to most frequent, essentially a trivial wrapper around sort | uniq -c | sort -n. Civilization advances by extending the number of important operations which we can perform without thinking about them.) This has obvious defects, but it works well enough. But every time I used it, I wondered: is it faster to do the grep before the count, or after? I didn't ever notice a difference. But I still wanted to know. After years of idly wondering this, I have finally looked into it. The point of this article is that the investigation produced the following pipeline, which I think is a great example of the Unix “tools” philosophy:  for i in$(seq 20); do
TIME="%U+%S" time \
sh -c f 11 access.2020-01-0* | grep -v plover | count > /dev/null' \
2>&1 | bc -l ;


I typed this on the command line, with no backslashes or newlines, so it actually looked like this:

        for i in $(seq 20); do TIME="%U+%S" time sh -c 'f 11 access.2020-01-0* | grep -v plover |count > /dev/null' 2>&1 | bc -l ; done | addup  Okay, what's going on here? The pipeline I actually want to analyze, with f | grep| count, is there in the middle, and I've already explained it, so let's elide it:  for i in$(seq 20); do
TIME="%U+%S" time \
sh -c '¿SOMETHING? > /dev/null' 2>&1 | bc -l ;


Continuing to work from inside to out, we're going to use time to actually do the timings. The time command is standard. It runs a program, asks the kernel how long the program took, then prints a report.

The time command will only time a single process (plus its subprocesses, a crucial fact that is inexplicably omitted from the man page). The ¿SOMETHING? includes a pipeline, which must be set up by the shell, so we're actually timing a shell command sh -c '...' which tells time to run the shell and instruct it to run the pipeline we're interested in. We tell the shell to throw away the output of the pipeline, with > /dev/null, so that the output doesn't get mixed up with time's own report.

The default format for the report printed by time is intended for human consumption. We can supply an alternative format in the $TIME variable. The format I'm using here is %U+%S, which comes out as something like 0.25+0.37, where 0.25 is the user CPU time and 0.37 is the system CPU time. I didn't see a format specifier that would emit the sum of these directly. So instead I had it emit them with a + in between, and then piped the result through the bc command, which performs the requested arithmetic and emits the result. We need the -l flag on bc because otherwise it stupidly does integer arithmetic. The time command emits its report to standard error, so I use 2>&1 to redirect the standard error into the pipe. [ Addendum 20200108: We don't actually need -l here; I was mistaken. ] Collapsing the details I just discussed, we have:  for i in$(seq 20); do
(run once and emit the total CPU time)


seq is a utility I invented no later than 1993 which has since become standard in most Unix systems. (As with netcat, I am not claiming to be the first or only person to have invented this, only to have invented it independently.) There are many variations of seq, but the main use case is that seq 20 prints


1
2
3
…
19
20


Here we don't actually care about the output (we never actually use $i) but it's a convenient way to get the for loop to run twenty times. The output of the for loop is the twenty total CPU times that were emitted by the twenty invocations of bc. (Did you know that you can pipe the output of a loop?) These twenty lines of output are passed into addup, which I wrote no later than 2011. (Why did it take me so long to do this?) It reads a list of numbers and prints the sum. All together, the command runs and prints a single number like 5.17, indicating that the twenty runs of the pipeline took 5.17 CPU-seconds total. I can do this a few times for the original pipeline, with count before grep, get times between 4.77 and 5.78, and then try again with the grep before the count, producing times between 4.32 and 5.14. The difference is large enough to detect but too small to notice. (To do this right we also need to test a null command, say  sh -c 'sleep 0.1 < /dev/null'  because we might learn that 95% of the reported time is spent in running the shell, so the actual difference between the two pipelines is twenty times as large as we thought. I did this; it turns out that the time spent to run the shell is insignificant.) What to learn from all this? On the one hand, Unix wins: it's supposed to be quick and easy to assemble small tools to do whatever it is you're trying to do. When time wouldn't do the arithmetic I needed it to, I sent its output to a generic arithmetic-doing utility. When I needed to count to twenty, I had a utility for doing that; if I hadn't there are any number of easy workarounds. The shell provided the I/O redirection and control flow I needed. On the other hand, gosh, what a weird mishmash of stuff I had to remember or look up. The -l flag for bc. The fact that I needed bc at all because time won't report total CPU time. The $TIME variable that controls its report format. The bizarro 2>&1 syntax for redirecting standard error into a pipe. The sh -c trick to get time to execute a pipeline. The missing documentation of the core functionality of time.

Was it a win overall? What if Unix had less compositionality but I could use it with less memorized trivia? Would that be an improvement?

I don't know. I rather suspect that there's no way to actually reach that hypothetical universe. The bizarre mishmash of weirdness exists because so many different people invented so many tools over such a long period. And they wouldn't have done any of that inventing if the compositionality hadn't been there. I think we don't actually get to make a choice between an incoherent mess of composable paraphernalia and a coherent, well-designed but noncompositional system. Rather, we get a choice between a incoherent but useful mess and an incomplete, limited noncompositional system.

(Notes to self: (1) In connection with Parse::RecDescent, you once wrote about open versus closed systems. This is another point in that discussion. (2) Open systems tend to evolve into messes. But closed systems tend not to evolve at all, and die. (3) Closed systems are centralized and hierarchical; open systems, when they succeed, are decentralized and organic. (4) If you are looking for another example of a successful incoherent mess of composable paraphernalia, consider Git.)

[ Addendum: Add this to the list of “weird mishmash of trivia”: There are two time commands. One, which I discussed above, is a separate executable, usually in /usr/bin/time. The other is built into the shell. They are incompatible. Which was I actually using? I would have been pretty confused if I had accidentally gotten the built-in one, which ignores $TIME and uses a $TIMEFORMAT that is interpreted in a completely different way. I was fortunate, and got the one I intended to get. But it took me quite a while to understand why I had! The appearance of the TIME=… assignment at the start of the shell command disabled the shell's special builtin treatment of the keyword time, so it really did use /usr/bin/time. This computer stuff is amazingly complicated. I don't know how anyone gets anything done. ]

[ Addenda 20200104: (1) Perl's module ecosystem is another example of a successful incoherent mess of composable paraphernalia. (2) Of the seven trivia I included in my “weird mishmash”, five were related to the time command. Is this a reflection on time, or is it just because time was central to this particular example? ]

[ Addendum 20200104: And, of course, this is exactly what Richard Gabriel was thinking about in Worse is Better. Like Gabriel, I'm not sure. ]

Thu, 02 Jan 2020

Back in early 1995, I worked on an incredibly early e-commerce site.
The folks there were used to producing shopping catalogs for distribution in airplane seat-back pockets and such like, and they were going to try bringing a catalog to this World-Wide Web thing that people were all of a sudden talking about.

One of their clients was Eddie Bauer. They wanted to put up a product catalog with a page for each product, say a sweatshirt, and the page should show color swatches for each possible sweatshirt color.

“Sure, I can do that,” I said. “But you have to understand that the user may not see the color swatches exactly as you expect them to.” Nobody would need to have this explained now, but in early 1995 I wasn't sure the catalog folks would understand. When you have a physical catalog you can leaf through a few samples to make sure that the printer didn't mess up the colors.

But what if two months down the line the Eddie Bauer people were shocked by how many complaints customers had about things being not quite the right color, “Hey I ordered mulberry but this is more like maroonish.” Having absolutely no way to solve the problem, I didn't want to to land in my lap, I wanted to be able to say I had warned them ahead of time. So I asked “Will it be okay that there will be variations in how each customer sees the color swatches?”

The catalog people were concerned. Why wouldn't the colors be the same? And I struggled to explain: the customer will see the swatches on their monitor, and we have no idea how old or crappy it might be, we have no idea how the monitor settings are adjusted, the colors could be completely off, it might be a monochrome monitor, or maybe the green part of their RGB video cable is badly seated and the monitor is displaying everything in red, blue, and purple, blah blah blah… I completely failed to get the point across in a way that the catalog people could understand.

They looked more and more puzzled, but then one of them brightened up suddenly and said “Oh, just like on TV!”

“Yes!” I cried in relief. “Just like that!”

“Oh sure, that's no problem.” Clearly, that was what I should have said in the first place, but I hadn't thought of it.

I no longer have any idea who it was that suddenly figured out what Geek Boy's actual point was, but I'm really grateful that they did.