The Universe of Discourse

Sun, 01 May 2016


It will suprise nobody to learn that when I was a child, computers were almost unknown, but it may be more surprising that typewriters were unusual.

Probably the first typewriter I was familiar with was my grandmother’s IBM “Executive” model C. At first I was not allowed to touch this fascinating device, because it was very fancy and expensive and my grandmother used it for her work as an editor of medical journals.

The “Executive” was very advanced: it had proportional spacing. It had two space bars, for different widths of spaces. Characters varied between two and five ticks wide, and my grandmother had typed up a little chart giving the width of each character in ticks, which she pasted to the top panel of the typewriter. The font was sans-serif, and I remember being a little puzzled when I first noticed that the lowercase j had no hook: it looked just like the lowercase i, except longer.

The little chart was important, I later learned, when I became old enough to use the typewriter and was taught its mysteries. Press only one key at a time, or the type bars will collide. Don't use the (extremely satisfying) auto-repeat feature on the hyphen or underscore, or the platen might be damaged. Don't touch any of the special controls; Grandma has them adjusted the way she wants. (As a concession, I was allowed to use the “expand” switch, which could be easily switched off again.)

The little chart was part of the procedure for correcting errors. You would backspace over the character you wanted to erase—each press of the backspace key would move the carriage back by one tick, and the chart told you how many times to press—and then place a slip of correction paper between the ribbon and the paper, and retype the character you wanted to erase. The dark ribbon impression would go onto the front of the correction slip, which was always covered with a pleasing jumble of random letters, and the correction slip impression, in white, would exactly overprint the letter you wanted to erase. Except sometimes it didn't quite: the ribbon ink would have spread a bit, and the corrected version would be a ghostly white letter with a hair-thin black outline. Or if you were a small child, as I was, you would sometimes put the correction slip in backwards, and the white ink would be transferred uselessly to the back of the ribbon instead of to the paper. Or you would select a partly-used portion of the slip and the missing bit of white ink would leave a fragment of the corrected letter on the page, like the broken-off leg of a dead bug.

Later I was introduced to the use of Liquid Paper (don't brush on a big glob, dot it on a bit at a time with the tip of the brush) and carbon paper, another thing you had to be careful not to put in backward, although if you did you got a wonderful result: the typewriter printed mirror images.

I quickly moved from typing alphabets, random letters, and my name to little poems, stories, and other miscellanea, and when my family saw that I was using the typewriter for writing, they presented me with one of my own, a Royal manual (model HHE maybe?) with a two-color ribbon, and I was at last free to explore the mysteries of the TAB SET and TAB CLEAR buttons. The front panel had a control for a three-color ribbon, which forever remained an unattainable mystery. Later I graduated to a Smith-Corona electric, on which I wrote my high school term papers. The personal computer arrived while I was in high school, but available printers were either expensive or looked like crap.

When I was in first grade our classroom had acquired a cheap manual typewriter, which as I have said, was an unusual novelty, and I used it whenever I could. I remember my teacher, Ms. Juanita Adams, complaining that I spent too much time on the typewriter. “You should work more on your handwriting, Jason. You might need to write something while you’re out on the street, and you won't just be able to pull a typewriter out of your pocket.”

She was wrong.

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Sun, 24 Apr 2016

Steph Curry: fluke or breakthrough?

[ Disclaimer: I know very little about basketball. I think there's a good chance this article contains at least one basketball-related howler, but I'm too ignorant to know where it is. ]

Randy Olson recently tweeted a link to a New York Times article about Steph Curry's new 3-point record. Here is Olson’s snapshot of a portion of the Times’ clever and attractive interactive chart:

(Skip this paragraph if you know anything about basketball. The object of the sport is to throw a ball through a “basket” suspended ten feet (3 meters) above the court. Normally a player's team is awarded two points for doing this. But if the player is sufficiently far from the basket—the distance varies but is around 23 feet (7 meters)—three points are awarded instead. Carry on!)

Stephen Curry

The chart demonstrates that Curry this year has shattered the single-season record for three-point field goals. The previous record, set last year, is 286, also by Curry; the new record is 406. A comment by the authors of the chart says

The record is an outlier that defies most comparisons, but here is one: It is the equivalent of hitting 103 home runs in a Major League Baseball season.

(The current single-season home run record is 73, and !!\frac{406}{286}·73 \approx 103!!.)

I found this remark striking, because I don't think the record is an outlier that defies most comparisons. In fact, it doesn't even defy the comparison they make, to the baseball single-season home run record.

Babe Ruth

In 1919, the record for home runs in a single season was 29, hit by Babe Ruth. The 1920 record, also by Ruth, was 54. To make the same comparison as the authors of the Times article, that is the equivalent of hitting !!\frac{54}{29}·73 \approx 136!! home runs in a Major League Baseball season.

No, far from being an outlier that defies most comparisons, I think what we're seeing here is something that has happened over and over in sport, a fundamental shift in the way they game is played; in short, a breakthrough. In baseball, Ruth's 1920 season was the end of what is now known as the dead-ball era. The end of the dead-ball era was the caused by the confluence of several trends (shrinking ballparks), rule changes (the spitball), and one-off events (Ray Chapman, the Black Sox). But an important cause was simply that Ruth realized that he could play the game in a better way by hitting a crapload of home runs.

The new record was the end of a sudden and sharp upward trend. Prior to Ruth's 29 home runs in 1919, the record had been 27, a weird fluke set way back in 1887 when the rules were drastically different. Typical single-season home run records in the intervening years were in the 11 to 16 range; the record exceeded 20 in only four of the intervening 25 years.

Ruth's innovation was promptly imitated. In 1920, the #2 hitter hit 19 home runs and the #10 hitter hit 11, typical numbers for the nineteen-teens. By 1929, the #10 hitter hit 31 home runs, which would have been record-setting in 1919. It was a different game.

Takeru Kobayashi

For another example of a breakthrough, let's consider competitive hot dog eating. Between 1980 and 1990, champion hot-dog eaters consumed between 9 and 16 hot dogs in 10 minutes. In 1991 the time was extended to 12 minutes and Frank Dellarosa set a new record, 21½ hot dogs, which was not too far out of line with previous records, and which was repeatedly approached in the following decade: through 1999 five different champions ate between 19 and 24½ hot dogs in 12 minutes, in every year except 1993.

But in 2000 Takeru Kobayashi (小林 尊) changed the sport forever, eating an unbelievably disgusting 50 hot dogs in 12 minutes. (50. Not a misprint. Fifty. Roman numeral Ⅼ.) To make the Times’ comparison again, that is the equivalent of hitting !!\frac{50}{24\frac12}·73 \approx 149!! home runs in a Major League Baseball season.

At that point it was a different game. Did the record represent a fundamental shift in hot dog gobbling technique? Yes. Kobayashi won all five of the next five contests, eating between 44½ and 53¾ each time. By 2005 the second- and third-place finishers were eating 35 or more hot dogs each; had they done this in 1995 they would have demolished the old records. A new generation of champions emerged, following Kobayashi's lead. The current record is 69 hot dogs in 10 minutes. The record-setters of the 1990s would not even be in contention in a modern hot dog eating contest.

Bob Beamon

It is instructive to compare these breakthroughs with a different sort of astonishing sports record, the bizarre fluke. In 1967, the world record distance for the long jump was 8.35 meters. In 1968, Bob Beamon shattered this record, jumping 8.90 meters. To put this in perspective, consider that in one jump, Beamon advanced the record by 55 cm, the same amount that it had advanced (in 13 stages) between 1925 and 1967.

Progression of the world long jump record
The cliff at 1968 is Bob Beamon

Did Beamon's new record represent a fundamental shift in long jump technique? No: Beamon never again jumped more than 8.22m. Did other jumpers promptly imitate it? No, Beamon's record was approached only a few times in the following quarter-century, and surpassed only once. Beamon had the benefit of high altitude, a tail wind, and fabulous luck.

Joe DiMaggio

Another bizarre fluke is Joe DiMaggio's hitting streak: in the 1941 baseball season, DiMaggio achieved hits in 56 consecutive games. For extensive discussion of just how bizarre this is, see The Streak of Streaks by Stephen J. Gould. (“DiMaggio’s streak is the most extraordinary thing that ever happened in American sports.”) Did DiMaggio’s hitting streak represent a fundamental shift in the way the game of baseball was played, toward high-average hitting? Did other players promptly imitate it? No. DiMaggio's streak has never been seriously challenged, and has been approached only a few times. (The modern runner-up is Pete Rose, who hit in 44 consecutive games in 1978.) DiMaggio also had the benefit of fabulous luck.

Is Curry’s new record a fluke or a breakthrough?

I think what we're seeing in basketball is a breakthrough, a shift in the way the game is played analogous to the arrival of baseball’s home run era in the 1920s. Unless the league tinkers with the rules to prevent it, we might expect the next generation of players to regularly lead the league with 300 or 400 three-point shots in a season. Here's why I think so.

  1. Curry's record wasn't unprecedented. He's been setting three-point records for years. (Compare Ruth’s 1920 home run record, foreshadowed in 1919.) He's continuing a trend that he began years ago.

  2. Curry’s record, unlike DiMaggio’s streak, does not appear to depend on fabulous luck. His 402 field goals this year are on 886 attempts, a 45.4% success rate. This is in line with his success rate every year since 2009; last year he had a 44.3% success rate. Curry didn't get lucky this year; he had 40% more field goals because he made almost 40% more attempts. There seems to be no reason to think he couldn't make the same number of attempts next year with equal success, if he wants to.

  3. Does he want to? Probably. Curry’s new three-point strategy seems to be extremely effective. In his previous three seasons he scored 1786, 1873, and 1900 points; this season, he scored 2375, an increase of 475, three-quarters of which is due to his three-point field goals. So we can suppose that he will continue to attempt a large number of three-point shots.

  4. Is this something unique to Curry or is it something that other players might learn to emulate? Curry’s three-point field goal rate is high, but not exceptionally so. He's not the most accurate of all three-point shooters; he holds the 62nd–64th-highest season percentages for three-point success rate. There are at least a few other players in the league who must have seen what Curry did and thought “I could do that”. (Kyle Korver maybe? I'm on very shaky ground; I don't even know how old he is.) Some of those players are going to give it a try, as are some we haven’t seen yet, and there seems to be no reason why some shouldn't succeed.

A number of things could sabotage this analysis. For example, the league might take steps to reduce the number of three-point field goals, specifically in response to Curry’s new record, say by moving the three-point line farther from the basket. But if nothing like that happens, I think it's likely that we'll see basketball enter a new era of higher offense with more three-point shots, and that future sport historians will look back on this season as a watershed.

[ Addendum 20160425: As I feared, my Korver suggestion was ridiculous. Thanks to the folks who explained why. Reason #1: He is 35 years old. ]

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Wed, 20 Apr 2016

The sage and the seven horses

A classic puzzle of mathematics goes like this:

A father dies and his will states that his elder daughter should receive half his horses, the son should receive one-quarter of the horses, and the younger daughter should receive one-eighth of the horses. Unfortunately, there are seven horses. The siblings are arguing about how to divide the seven horses when a passing sage hears them. The siblings beg the sage for help. The sage donates his own horse to the estate, which now has eight. It is now easy to portion out the half, quarter, and eighth shares, and having done so, the sage's horse is unaccounted for. The three heirs return the surplus horse to the sage, who rides off, leaving the matter settled fairly.

(The puzzle is, what just happened?)

It's not hard to come up with variations on this. For example, picking three fractions at random, suppose the will says that the eldest child receives half the horses, the middle child receives one-fifth, and the youngest receives one-seventh. But the estate has only 59 horses and an argument ensues. All that is required for the sage to solve the problem is to lend the estate eleven horses. There are now 70, and after taking out the three bequests, !!70 - 35 - 14 - 10 = 11!! horses remain and the estate settles its debt to the sage.

But here's a variation I've never seen before. This time there are 13 horses and the will says that the three children should receive shares of !!\frac12, \frac13,!! and !!\frac14!!. respectively. Now the problem seems impossible, because !!\frac12 + \frac13 + \frac14 \gt 1!!. But the sage is equal to the challenge! She leaps into the saddle of one of the horses and rides out of sight before the astonished heirs can react. After a day of searching the heirs write off the lost horse and proceed with executing the will. There are now only 12 horses, and the eldest takes half, or six, while the middle sibling takes one-third, or 4. The youngest heir should get three, but only two remain. She has just opened her mouth to complain at her unfair treatment when the sage rides up from nowhere and hands her the reins to her last horse.

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Tue, 19 Apr 2016

Thackeray's illustrations for Vanity Fair

Last month I finished reading Thackeray’s novel Vanity Fair. (Related blog post.) Thackeray originally did illustrations for the novel, but my edition did not have them. When I went to find them online, I was disappointed: they were hard to find and the few I did find were poor quality and low resolution.


(click to enlarge)

The illustrations are narratively important. Jos Osborne dies suspiciously; the text implies that Becky has something to do with it. Thackeray's caption for the accompanying illustration is “Becky’s Second Appearance in the Character of Clytemnestra”. Thackeray’s depiction of Miss Swartz, who is mixed-race, may be of interest to scholars.

I bought a worn-out copy of Vanity Fair that did have the illustrations and scanned them. These illustrations, originally made around 1848 by William Makepeace Thackeray, are in the public domain. In the printing I have (George Routeledge and Sons, New York, 1886) the illustrations were 9½cm × 12½ cm. I have scanned them at 600 dpi.

Large thumbails

(ZIP file .tgz file)

Unfortunately, I was only able to find Thackeray’s full-page illustrations. He also did some spot illustrations, chapter capitals, and so forth, which I have not been able to locate.

Share and enjoy.

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Sat, 16 Apr 2016

How to recover lost files added to Git but not committed

A few days ago, I wrote:

If you lose something [in Git], don't panic. There's a good chance that you can find someone who will be able to hunt it down again.

I was not expecting to have a demonstration ready so soon. But today I finished working on a project, I had all the files staged in the index but not committed, and for some reason I no longer remember I chose that moment to do git reset --hard, which throws away the working tree and the staged files. I may have thought I had committed the changes. I hadn't.

If the files had only been in the working tree, there would have been nothing to do but to start over. Git does not track the working tree. But I had added the files to the index. When a file is added to the Git index, Git stores it in the repository. Later on, when the index is committed, Git creates a commit that refers to the files already stored. If you know how to look, you can find the stored files even before they are part of a commit.

Each file added to the Git index is stored as a “blob object”. Git stores objects in two ways. When it's fetching a lot of objects from a remote repository, it gets a big zip file with an attached table of contents; this is called a pack. Getting objects from a pack can be a pain. Fortunately, not all objects are in packs. When when you just use git-add to add a file to the index, git makes a single object, called a “loose” object. The loose objects is basically the file contents, gzipped, with a header attached. At some point Git will decide there are too many loose objects and assemble them into a pack.

To make a loose object from a file, the contents of the file are checksummed, and the checksum is used as the name of the object file in the repository and as an identifier for the object, exactly the same as the way git uses the checksum of a commit as the commit's identifier. If the checksum is 0123456789abcdef0123456789abcdef01234567, the object is stored in


The pack files are elsewhere, in .git/objects/pack.

So the first thing I did was to get a list of the loose objects in the repository:

    cd .git/objects
    find ?? -type f  | perl -lpe 's#/##' > /tmp/OBJ

This produces a list of the object IDs of all the loose objects in the repository:


There were 500 loose objects in my repository. The goal was to find the eight I wanted.

There are several kinds of objects in a Git repository. In addition to blobs, which represent file contents, there are commit objects, which represent commits, and tree objects, which represent directories. These are usually constructed at the time the commit is done. Since my files hadn't been committed, I knew I wasn't interested in these types of objects. The command git cat-file -t will tell you what type an object is. I made a file that related each object to its type:

    for i in $(cat /tmp/OBJ); do
      echo -n "$i ";
      git type $i;
    done > /tmp/OBJTYPE

The git type command is just an alias for git cat-file -t. (Funny thing about that: I created that alias years ago when I first started using Git, thinking it would be useful, but I never used it, and just last week I was wondering why I still bothered to have it around.) The OBJTYPE file output by this loop looks like this:

    00f1b6cc1dfc1c8872b6d7cd999820d1e922df4a blob
    0093a412d3fe23dd9acb9320156f20195040a063 tree
    01f3a6946197d93f8edba2c49d1bb6fc291797b0 commit
    fed6767ff7fa921601299d9a28545aa69364f87b tree
    ffd505d2da2e4aac813122d8e469312fd03a3669 tree
    fff732422ed8d82ceff4f406cdc2b12b09d81c2e blob

Then I just grepped out the blob objects:

    grep blob /tmp/OBJTYPE | f 1 > /tmp/OBJBLOB

The f 1 command throws away the types and keeps the object IDs. At this point I had filtered the original 500 objects down to just 108 blobs.

Now it was time to grep through the blobs to find the ones I was looking for. Fortunately, I knew that each of my lost files would contain the string org-service-currency, which was my name for the project I was working on. I couldn't grep the object files directly, because they're gzipped, but the command git cat-file disgorges the contents of an object:

    for i in $(cat /tmp/OBJBLOB ) ; do
      git cat-file blob $i |
        grep -q org-service-curr
          && echo $i;
    done > /tmp/MATCHES

The git cat-file blob $i produces the contents of the blob whose ID is in $i. The grep searches the contents for the magic string. Normally grep would print the matching lines, but this behavior is disabled by the -q flag—the q is for “quiet”—and tells grep instead that it is being used only as part of a test: it yields true if it finds the magic string, and false if not. The && is the test; it runs echo $i to print out the object ID $i only if the grep yields true because its input contained the magic string.

So this loop fills the file MATCHES with the list of IDs of the blobs that contain the magic string. This worked, and I found that there were only 18 matching blobs, so I wrote a very similar loop to extract their contents from the repository and save them in a directory:

    for i in $(cat /tmp/OBJBLOB ) ; do
      git cat-file blob $i | 
         grep -q org-service-curr
           && git cat-file blob $i > /tmp/rescue/$i;

Instead of printing out the matching blob ID number, this loop passes it to git cat-file again to extract the contents into a file in /tmp/rescue.

The rest was simple. I made 8 subdirectories under /tmp/rescue representing the 8 different files I was expecting to find. I eyeballed each of the 18 blobs, decided what each one was, and sorted them into the 8 subdirectories. Some of the subdirectories had only 1 blob, some had up to 5. I looked at the blobs in each subdirectory to decide in each case which one I wanted to keep, using diff when it wasn't obvious what the differences were between two versions of the same file. When I found one I liked, I copied it back to its correct place in the working tree.

Finally, I went back to the working tree and added and committed the rescued files.

It seemed longer, but it only took about twenty minutes. To recreate the eight files from scratch might have taken about the same amount of time, or maybe longer (although it never takes as long as I think it will), and would have been tedious.

But let's suppose that it had taken much longer, say forty minutes instead of twenty, to rescue the lost blobs from the repository. Would that extra twenty minutes have been time wasted? No! The twenty minutes spent to recreate the files from scratch is a dead loss. But the forty minutes to rescue the blobs is time spent learning something that might be useful in the future. The Git rescue might have cost twenty extra minutes, but if so it was paid back with forty minutes of additional Git expertise, and time spent to gain expertise is well spent! Spending time to gain expertise is how you become an expert!

Git is a core tool, something I use every day. For a long time I have been prepared for the day when I would try to rescue someone's lost blobs, but until now I had never done it. Now, if that day comes, I will be able to say “Oh, it's no problem, I have done this before!”

So if you lose something in Git, don't panic. There's a good chance that you can find someone who will be able to hunt it down again.

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Wed, 13 Apr 2016

Neckbeards and other notes on “The Magnificent Ambersons”

Last week I read Booth Tarkington’s novel The Magnificent Ambersons, which won the 1919 Pulitzer Prize but today is chiefly remembered for Orson Welles’ 1942 film adaptation.

(It was sitting on the giveaway shelf in the coffee shop, so I grabbed it. It is a 1925 printing, discarded from the Bess Tilson Sprinkle library in Weaverville, North Carolina. The last due date stamped in the back is May 12, 1957.)

The Ambersons are the richest and most important family in an unnamed Midwestern town in 1880. The only grandchild, George, is completely spoiled and grows up to ruin the lives of everyone connected with him with his monstrous selfishness. Meanwhile, as the automobile is invented and the town evolves into a city the Amberson fortune is lost and the family dispersed and forgotten. George is destroyed so thoroughly that I could not even take any pleasure in it.

I made a few marginal notes as I read.


It was a hairier day than this. Beards were to the wearer’s fancy … and it was possible for a Senator of the United States to wear a mist of white whisker upon his throat only, not a newspaper in the land finding the ornament distinguished enough to warrant a lampoon.

I wondered who Tarkington had in mind. My first thought was Horace Greeley:

His neckbeard fits the description, but, although he served as an unelected congressman and ran unsuccessfully for President, he was never a Senator.

Then I thought of Hannibal Hamlin, who was a Senator:

But his neckbeard, although horrifying, doesn't match the description.

Gentle Readers, can you help me? Who did Tarkington have in mind? Or, if we can't figure that out, perhaps we could assemble a list of the Ten Worst Neckbeards of 19th Century Politics.

Other notes

I was startled on Page 288 by a mention of “purple haze”, but a Google Books search reveals that the phrase is not that uncommon. Jimi Hendrix owns it now, but in 1919 it was just purple haze.

George’s Aunt Fanny writes him a letter about his girlfriend Lucy:

Mr. Morgan took your mother and me to see Modjeska in “Twelfth Night” yesterday evening, and Lucy said she thought the Duke looked rather like you, only much more democratic in his manner.

Lucy, as you see, is not entirely sure that she likes George. George, who is not very intelligent, is not aware that Lucy is poking fun at him.

A little later we see George’s letter to Lucy. Here is an excerpt I found striking:

[Yours] is the only girl’s photograph I ever took the trouble to have framed, though as I told you frankly, I have had any number of other girls’ photographs, yet all were passing fancies, and oftentimes I have questioned in years past if I was capable of much friendship toward the feminine sex, which I usually found shallow until our own friendship began. When I look at your photograph, I say to myself “At last, at last here is one that will not prove shallow.”

The arrogance, the rambling, the indecisiveness of tone, and the vacillation reminded me of the speeches of Donald Trump, whom George resembles in several ways. George has an excuse not available to Trump; he is only twenty.

Addendum 20160413: John C. Calhoun seems like a strong possibility:

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Mon, 11 Apr 2016

“…and she hated every stitch”

Recently the following amusing item was going around on Twitter:

needlework proclaiming “Edith-Anne did this in 1848 and hated ev ery Stitch”

I have some bad news and some good news. First the good news: there is an Edith-Anne. Her name is actually Patty Polk, and she lived in Maryland around 1800.

Now the bad news: the image above is almost certainly fake. It may be a purely digital fabrication (from whole cloth, ha ha), or more likely, I think, it is a real physical object, but of recent manufacture.

I wouldn't waste blog space just to crap on this harmless bit of fake history. I want to give credit where it is due, to Patty Polk who really did do this, probably with much greater proficiency.

Why I think it's fake

I have not looked into this closely, because I don't think the question merits a lot of effort. But I have two reasons for thinking so.

The main one is that the complaint “Edith-Anne … hated every Stitch” would have taken at least as much time and effort as the rest of the sampler, probably more. I find it unlikely that Edith-Anne would have put so much work—so many more hated stitches—into her rejection.

Also, the work is implausibly poor. These samplers were stitched by girls typically between the ages of 7 and 14, and their artisanship was much, much better than either section of this example. Here is a sampler made by Lydia Stocker in 1798 at the age of 12:

Stocker’s sampler 1798

Here's one by Louisa Gauffreau, age 8:

Gauffreau’s sampler 1821

Compare these with Edith-Anne's purported cross-stitching. One tries to imagine how old she is, but there seems to be no good answer. The crooked stitching is the work of a very young girl, perhaps five or six. But the determination behind the sentiment, and the perseverance that would have been needed to see it through, belong to a much older girl.

Of course one wouldn't expect Edith-Anne to do good work on her hated sampler. But look at the sampler at right, wrought by a young Emily Dickinson, who is believed to have disliked the work and to have intentionally done it poorly. Even compared with this, Edith-Anne's claimed sampler doesn't look like a real sampler.

Patty Polk

Web search for “hated every stitch” turns up several other versions of Edith-Anne, often named Polly Cook1 or Mary Pitt2 (“This was done by Mary Pitt / Who hated every stitch of it”) but without any reliable source.

However, Patty Polk is reliably sourced. Bolton and Coe's American Samplers3 describes Miss Polk's sampler:

POLK, PATTY. [Cir. 1800. Kent County, Md.] 10 yrs. 16"×16". Stem-stitch. Large garland of pinks, roses, passion flowers, nasturtiums, and green leaves; in center, a white tomb with “G W” on it, surrounded by forget-me-nots. “Patty Polk did this and she hated every stitch she did in it. She loves to read much more.”

The description was provided by Mrs. Frederic Tyson, who presumably owned or had at least seen the sampler. Unfortunately, there is no picture. The “G W” is believed to refer to George Washington, who died in 1799.

There is a lively market in designs for pseudo-vintage samplers that you can embroider yourself and “age”. One that features Patty Polk is produced by Falling Star Primitives:

Thanks to Lee Morrison of Falling Star Primitives for permission to use her “Patty Polk” design.


1. Parker, Rozsika. The Subversive Stitch: Embroidery and the Making of the Feminine. Routledge, 1989. p. 132.

2. Wilson, Erica. Needleplay. Scribner, 1975. p. 67.

3. Bolton, Ethel Stanwood and Eva Johnston Coe. American Samplers. Massachusetts Society of the Colonial Dames of America, 1921. p. 210.

[ Thanks to several Twitter users for suggesting gender-neutral vocabulary. ]

[ Addendum: Twitter user Kathryn Allen observes that Edith-Anne hated cross-stitch so much that she made another sampler to sell on eBay. Case closed. ]

[ Addendum: Ms. Allen further points out that the report by Mrs. Tyson in American Samplers may not be reliable, and directs me to the discussion by J.L. Bell, Clues to a Lost Sampler. ]

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Fri, 08 Apr 2016

Two things about git

I'm becoming one of the people at my company that people come to when they want help with git, so I've been thinking a lot about what to tell people about it. It's always tempting to dive into the technical details, but I think the first and most important things to explain about it are:

  1. Git has a very simple and powerful underlying model. Atop this model is piled an immense trashheap of confusing, overlapping, inconsistent commands. If you try to just learn what commands to run in what order, your life will be miserable, because none of the commands make sense. Learning the underlying model has a much better payoff because it is much easier to understand what is really going on underneath than to try to infer it, Sherlock-Holmes style, from the top.

  2. One of Git's principal design criteria is that it should be very difficult to lose work. Everything is kept, even if it can sometimes be hard to find. If you lose something, don't panic. There's a good chance that you can find someone who will be able to hunt it down again. And if you make a mistake, it is almost always possible to put things back exactly the way they were, and you can find someone who can show you how to do it.

    One exception is changes that haven't been committed. These are not yet under Git's control, so it can't help you with them. Commit early and often.

[ Addendum 20160415: I wrote a detailed account of a time I recovered lost files. ]

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Sun, 20 Mar 2016

Technical jargon failure modes

Technical jargon is its own thing, intended for easy communication between trained practitioners of some art, but not necessarily between anyone else.

Jargon can be somewhat transparent, like the chemical jargon term “alcohol”. “Alcohol” refers to a large class of related chemical compounds, of which the simplest examples are methyl alcohol (traditionally called “wood alcohol”) and ethyl alcohol (the kind that you get in your martini). The extension of “alcohol” to the larger class is suggestive and helpful. Someone who doesn't understand the chemical jargon usage of “alcohol” can pick it up by analogy, and even if they don't they will probably have something like the right idea. A similar example is “aldehyde”. An outsider who hears this for the first time might reasonably ask “does that have something to do with formaldehyde?” and the reasonable answer is “yes indeed, formaldehyde is the simplest example of an aldehyde compound.” Again the common term is adapted to refer to the members of a larger but related class.

An opposite sort of adaptation is found in the term “bug”. The common term is extremely broad, encompassing all sorts of terrestrial arthropods, including mosquitoes, ladybugs, flies, dragonflies, spiders, and even isopods (“pillbugs”) and centipedes and so forth. It should be clear that this category is too large and heterogeneous to be scientifically useful, and the technical use of “bug” is much more restricted. But it does include many creatures commonly referred to as bugs, such as bed bugs, waterbugs, various plant bugs, and many other flat-bodied crawling insects.

Mathematics jargon often wanders in different directions. Some mathematical terms are completely opaque. Nobody hearing the term “cobordism” or “simplicial complex” or “locally compact manifold” for the first time will think for an instant that they have any idea what it means, and this is perfect, because they will be perfectly correct. Other mathematical terms are paradoxically so transparent seeming that they reveal their opacity by being obviously too good to be true. If you hear a mathematician mention a “field” it will take no more than a moment to realize that it can have nothing to do with fields of grain or track-and-field sports. (A field is a collection of things that are number-like, in the sense of having addition, subtraction, multiplication, and division that behave pretty much the way one would expect those operations to behave.) And some mathematical jargon is fairly transparent. The non-mathematician's idea of “line”, “ball”, and “cube” is not in any way inconsistent with what the mathematician has in mind, although the full technical meaning of those terms is pregnant with ramifications and connotations that are invisible to non-mathematicians.

But mathematical jargon sometimes goes to some bad places. The term “group” is so generic that it could mean anything, and outsiders often imagine that it means something like what mathematicians call a “set”. (It actually means a family of objects that behave like the family of symmetries of some other object.)

This last is not too terrible, as jargon failures go. There is a worse kind of jargon failure I would like to contrast with “bug”. There the problem, if there is a problem, is that entomologists use the common term “bug” much more restrictively than one expects. An entomologist will well-actually you to explain that a millipede is not actually a bug, but we are used to technicians using technical terms in more restrictive ways than we expect. At least you can feel fairly confident that if you ask for examples of bugs (“true bugs”, in the jargon) that they will all be what you will consider bugs, and the entomologist will not proceed to rattle off a list that includes bats, lobsters, potatoes, or the Trans-Siberian Railroad. This is an acceptable state of affairs.

Unacceptable, however, is the botanical use of the term “berry”:

It is one thing to adopt a jargon term that is completely orthogonal to common usage, as with “fruit”, where the technical term simply has no relation at all to the common meaning. That is bad enough. But to adopt the term “berry” for a class of fruits that excludes nearly everything that is commonly called a ”berry” is an offense against common sense.

This has been on my mind a long time, but I am writing about it now because I think I have found, at last, an even more offensive example.

  • Stonehenge is so-called because it is a place of hanging stones: “henge” is cognate with “hang”.

  • In 1932 archaeologists adapted the name “Stonehenge” to create the word “henge” as a generic term for a family of ancient monuments that are similar to Stonehenge.

  • Therefore, if there were only one thing in the whole world that ought to be an example of a henge, it should be Stonehenge.

  • However, Stonehenge is not, itself, a henge.

  • Stonehenge is not a henge.


Stonehenge is not a henge. … Technically, [henges] are earthwork enclosures in which a ditch was dug to make a bank, which was thrown up on the outside edge of the ditch.

— Michael Pitts, Hengeworld, pp. 26–28.

“Henge” may just be the most ineptly coined item of technical jargon in history.

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Sat, 19 Mar 2016

Sympathetic magic for four-year-olds

When Katara was about four, she was very distressed by the idea that green bugs were going to invade our house, I think though the mail slot in the front door. The obvious thing to do here was to tell her that there are no green bugs coming through the mail slot and she should shut up and go to sleep, but it seems clear to me that this was never going to work.

(It surprises me how few adults understand that this won't work. When Marcie admits at a cocktail party that she is afraid that people are staring at her in disgust, wondering why her pores are so big, many adults—but by no means all—know that it will not help her to reply “nobody is looking at your pores, you lunatic,” however true that may be. But even most of these enlightened adults will not hesitate to say the equivalent thing to a four-year-old afraid of mysterious green bugs. Adults and children are not so different in their irrational fears; they are just afraid of different kinds of monsters.)

Anyway, I tried to think what to say instead, and I had a happy idea. I told Katara that we would cast a magic spell to keep out the bugs. Red, I observed, was the opposite of green, and the green bugs would be powerfully repelled if we placed a bright red object just inside the front door where they would be sure to see it. Unwilling to pass the red object, they would turn back and leave us alone. Katara found this theory convincing, and so we laid sheets of red construction paper in the entryway under the mail slot.

Every night before bed for several weeks we laid out the red paper, and took it up again in the morning. This was not very troublesome, and certainly it less troublesome than arguing about green bugs every night with a tired four-year-old. For the first few nights, she was still a little worried about the bugs, but I confidently reminded her that the red paper would prevent them from coming in, and she was satisfied. The first few nights we may also have put red paper inside the door of her bedroom, just to be sure. Some nights she would forget and I would remind her that we had to put out the red paper before bedtime; then she would know that I took the threat seriously. Other nights I would forget and I would thank her for reminding me. After a few months of this we both started to forget, and the phase passed. I suppose the green bugs gave up eventually and moved on to a less well-defended house.

Several years later, Katara's younger sister Toph had a similar concern: she was afraid the house would be attacked by zombies. This time I already knew what to do. We discussed zombies, and how zombies are created by voodoo magic; therefore they are susceptible to voodoo, and I told Toph we would use voodoo to repel the zombies. I had her draw a picture of the zombies attacking the house, as detailed and elaborate as possible. Then we took black paper and cut it into black bars, and pasted the bars over Toph's drawing, so that the zombies were in a cage. The cage on the picture would immobilize the real zombies, I explained, just as one can stick pins into a voodoo doll of one's enemy to harm the real enemy. We hung the picture in the entryway, and Toph proudly remarked on how we had stopped the zombies whenever we went in or out.

Rationality has its limits. It avails nothing against green bugs or murderous zombies. Magical enemies must be fought with magic.

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Sun, 07 Feb 2016

Four Victorian novels

I've read a bunch of 19-century English novels lately. I'm not exactly sure why; it just sort of happened. But it's been a lot of fun. When I was small, my mother told me more than once that people often dislike these books because they are made to read them too young; the books were written for adult readers and don't make sense to children. I deliberately waited to read most of these, and I am very pleased now to find that now that I am approaching middle age I enjoy books that were written for people approaching middle age.

Spoilers abound.

Jane Eyre

This is one of my wife's favorite books, or perhaps her very favorite, but I had not read it before. Wow, it's great! Jane is as fully three-dimensional as anyone in fiction.

I had read The Eyre Affair, which unfortunately spoiled a lot of the plot for me, including the Big Shocker; I kept wondering how I would feel if I didn't know what was coming next. Fortunately I didn't remember all the details.

  • From her name, I had expected Blanche Ingram to be pale and limp; I was not expecting a dark, disdainful beauty.

  • When Jane tells Rochester she must leave, he promises to find her another position, and the one he claims to have found is hilariously unattractive: she will be the governess to the five daughters of Mrs. Dionysus O'Gall of Bitternutt Lodge, somewhere in the ass-end of Ireland.

  • What a thrill when Jane proclaims “I am an independent woman now”! But she has achieved this by luck; she inherited a fortune from her long-lost uncle. That was pretty much the only possible path, and it makes an interesting counterpoint to Vanity Fair, which treats some of the same concerns.

  • The thought of dutifully fulfilling the duty of a dutiful married person by having dutiful sex with the dutiful Mr. Rivers makes my skin crawl. I imagine that Jane felt the same way.

  • Mr. Brocklehurst does not get one-tenth of what he deserves.

Jane Eyre set me off on a Victorian novel kick. The preface of Jane Eyre praises William Thackeray and Vanity Fair in particular. So I thought I'd read some Thackeray and see how I liked that. Then for some reason I read Silas Marner instead of Vanity Fair. I'm not sure how that happened.

Silas Marner

Silas Marner was the big surprise of this batch of books. I don't know why I had always imagined Silas Marner would be the very dreariest and most tedious of all Victorian novels. But Silas Marner is quite short, and I found it very sweet and charming.

I do not suppose my Gentle Readers are as likely to be familiar with Silas Marner as with Jane Eyre. As a young man, Silas is a member of a rigid, inward-looking religious sect. His best friend frames him for a crime, and he is cast out. Feeling abandoned by society and by God, he settles in Raveloe and becomes a miser, almost a hermit. Many years pass, and his hoarded gold is stolen, leaving him bereft. But one snowy evening a two-year-old girl stumbles into his house and brings new purpose to his life. I have omitted the subplot here, but it's a good subplot.

One of the scenes I particularly enjoyed concerns Silas’ first (and apparently only) attempt to discipline his adopted two-year-old daughter Eppie, with whom he is utterly besotted. Silas knows that sooner or later he will have to, but he doesn't know how—striking her seems unthinkable—and consults his neighbors. One suggests that he shut her in the dark, dirty coal-hole by the fireplace. When Eppie wanders away one day, Silas tries to be stern.

“Eppie must go into the coal hole for being naughty. Daddy must put her in the coal hole.”

He half expected that this would be shock enough and that Eppie would begin to cry. But instead of that she began to shake herself on his knee as if the proposition opened a pleasing novelty.

As they say, no plan survives contact with the enemy.

Seeing that he must proceed to extremities, he put her into the coal hole, and held the door closed, with a trembling sense that he was using a strong measure. For a moment there was silence but then came a little cry “Opy, opy!” and Silas let her out again…

Silas gets her cleaned up and changes her clothes, and is about to settle back to his work

when she peeped out at him with black face and hands again and said “Eppie in de toal hole!”

Two-year-olds are like that: you would probably strangle them, if they weren't so hilariously cute.

Everyone in this book gets what they deserve, except the hapless Nancy Lammeter, who gets a raw deal. But it's a deal partly of her own making. As Thackeray says of Lady Crawley, in a somewhat similar circumstance, “a title and a coach and four are toys more precious than happiness in Vanity Fair”.

There is a chapter about a local rustics at the pub which may remind you that human intercourse could be plenty tiresome even before the invention of social media. The one guy who makes everything into an argument will be quite familiar to my Gentle Readers.

I have added Silas Marner to the long list of books that I am glad I was not forced to read when I was younger.

The Old Curiosity Shop

Unlike Silas Marner, I know why I read this one. In the park near my house is a statue of Charles Dickens and Little Nell, on which my daughter Toph is accustomed to climb. As she inevitably asked me who it was a statue of, I explained that Dickens was a famous writer, and Nell is a character in a book by Dickens. She then asked me what the book was about, and who Nell was, and I did not know. I said I would read the book and find out, so here we are.

My experience with Dickens is very mixed. Dickens was always my mother's number one example of a writer that people were forced to read when too young. My grandfather had read me A Christmas Carol when I was young, and I think I liked it, but probably a lot of it went over my head. When I was about twenty-two I decided to write a parody of it, which meant I had to read it first, but I found it much better than I expected, and too good to be worth parodying. I have reread it a couple of times since. it is very much worth going back to, and is much better than its many imitators.

I had been required to read Great Expectations in high school, had not cared for it, and had stopped after four or five chapters. But as an adult I kept a copy in my house for many years, waiting for the day when I might try again, and when I was thirty-five I did try again, and I loved it.

Everyone agrees that Great Expectations is one of Dickens’ best, and so it is not too surprising that I was much less impressed with Martin Chuzzlewit when I tried that a couple of years later. I remember liking Mark Tapley, but I fell off the bus shortly after Martin came to America, and I did not get back on.

A few years ago I tried reading The Pickwick Papers, which my mother said should only be read by middle-aged people, and I have not yet finished it. It is supposed to be funny, and I almost never find funny books funny, except when they are read aloud. (When I tell people this, they inevitably name their favorite funny books: “Oh, but you thought The Hitchhiker’s Guide to the Galaxy was funny, didn't you?” or whatever. Sorry, I did not. There are a few exceptions; the only one that comes to mind is Stanisław Lem's The Cyberiad, which splits my sides every time. SEVEN!

Anyway, I digress. The Old Curiosity Shop was extremely popular when it was new. You always hear the same two stories about it: that crowds assembled at the wharves in New York to get spoilers from the seamen who might have read the new installments already, and that Oscar Wilde once said “one must have a heart of stone to read the death of Little Nell without laughing.” So I was not expecting too much, and indeed The Old Curiosity Shop is a book with serious problems.

Chief among them: it was published in installments, and about a third of the way through writing it Dickens seems to have changed his mind about how he wanted it to go, but by then it was too late to go back and change it. There is Nell and her grandfather on the one hand, the protagonists, and the villain is the terrifying Daniel Quilp. It seems at first that Nell's brother Fred is going to be important, but he disappears and does not come back until the last page when we find out he has been dead for some time. It seems that Quilp's relations with his tyrannized wife are going to be important, but Quilp soon moves out of his house and leaves Mrs. Quilp more or less alone. It seems that Quilp is going to pursue the thirteen-year-old Nell sexually, but Nell and Grandpa flee in the night and Quilp never meets them again. They spend the rest of the book traveling from place to place not doing much, while Quilp plots against Nell's friend Kit Nubbles.

Dickens doesn't even bother to invent names for many of the characters. There is Nell’s unnamed grandfather; the old bachelor; the kind schoolmaster; the young student; the guy who talks to the fire in the factory in Birmingham; and the old single gentleman.

The high point of the book for me was the development of Dick Swiveller. When I first met Dick I judged him to be completely worthless; we later learn that Dick keeps a memorandum book with a list of streets he must not go into, lest he bump into one of his legion of creditors. But Dick turns out to have some surprises in him. Quilp's lawyer Sampson Brass is forced to take on Swiveller as a clerk, in furtherment of Quilp's scheme to get Swiveller married to Nell, another subplot that comes to nothing. While there, Swiveller, with nothing to amuse himself, teaches the Brasses’ tiny servant, a slave so starved and downtrodden that she has never been given a name, to play cribbage. She later runs away from the Brasses, and Dick names her Sophronia Sphynx, which he feels is “euphonious and genteel, and furthermore indicative of mystery.” He eventually marries her, “and they played many hundred thousand games of cribbage together.”

I'm not alone in finding Dick and Sophronia to be the most interesting part of The Old Curiosity Shop. The anonymous author of the excellent blog A Reasonable Quantity of Butter agrees with me, and so does G.K. Chesterton:

The real hero and heroine of The Old Curiosity Shop are of course Dick Swiveller and [Sophronia]. It is significant in a sense that these two sane, strong, living, and lovable human beings are the only two, or almost the only two, people in the story who do not run after Little Nell. They have something better to do than to go on that shadowy chase after that cheerless phantom.

Today is Dickens’ 204th birthday. Happy birthday, Charles!

Vanity Fair

I finally did get to Vanity Fair, which I am only a quarter of the way through. It seems that Vanity Fair is going to live or die on the strength of its protagonist Becky Sharp.

When I first met Ms. Sharp, I thought I would love her. She is independent, clever, and sharp-tongued. But she quickly turned out to be scheming, manipulative, and mercenary. She might be hateful if the people she was manipulating were not quite such a flock of nincompoops and poltroons. I do not love her, but I love watching her, and I partly hope that her schemes succeed, although I rather suspect that she will sabotage herself and undo all her own best plans.

Becky, like Jane Eyre, is a penniless orphan. She wants money, and in Victorian England there are only two ways for her to get it: She can marry it or inherit it. Unlike Jane, she does not have a long-lost wealthy uncle (at least, not so far) so she schemes to get it by marriage. It's not very creditable, but one can't feel too righteous about it; she is in the crappy situation of being a woman in Victorian England, and she is working hard to make the best of it. She is extremely cynical, but the disagreeable thing about a cynic is that they refuse to pretend that things are better than they are. I don't think she has done anything actually wrong, and so far her main path to success has been to act so helpful and agreeable that everyone loves her, so I worry that I may come out of this feeling that Thackeray does not give her a fair shake.

In the part of the book I am reading, she has just married the exceptionally stupid Rawdon Crawley. I chuckle to I think of the flattering lies she must tell him when they are in the sack. She has married him because he is the favorite relative of his rich but infirm aunt. I wonder at this, because the plan does not seem up to Becky’s standards: what if the old lady hangs on for another ten years? But perhaps she has a plan B that hasn't yet been explained.

Thackeray says that Becky is very good-looking, but in his illustrations she has a beaky nose and an unpleasant, predatory grin. In a recent film version she was played by Reese Witherspoon, which does not seem to me like a good fit. Although Becky is blonde, I keep picturing Aubrey Plaza, who always seems to me to be saying something intended to distract you from what she is really thinking.

I don't know yet if I will finish Vanity Fair—I never know if I will finish a book until I finish it, and I have at times said “fuck this” and put down a book that I was ninety-five percent of the way through—but right now I am eager to find out what happens next.

Blah blah blah

This post observes the tenth anniversary of this blog, which I started in January 2006, directly inspired by Steve Yegge’s rant on why You Should Write Blogs, which I found extremely persuasive. (Articles that appear to have been posted before that were backdated, for some reason that I no longer remember but would probably find embarrassing.) I hope my Gentle Readers will excuse a bit of navel-gazing and self-congratulation.

When I started the blog I never imagined that I would continue as long as I have. I tend to get tired of projects after about four years and I was not at all sure the blog would last even that long. But to my great surprise it is one of the biggest projects I have ever done. I count 484 published articles totalling about 450,000 words. (Also 203 unpublished articles in every possible state of incompletion.) I drew, found, stole, or otherwise obtained something like 1,045 diagrams and illustrations. There were some long stoppages between articles, but I always came back to it. And I never wrote out of obligation or to meet a deadline, but always because the spirit moved me to write.

Looking back on the old articles, I am quite pleased with the blog and with myself. I find it entertaining and instructive. I like the person who wrote it. When I'm reading articles written by other people it sometimes happens that I smile ruefully and wish that I had been clever enough to write that myself; sometimes that happens to me when I reread my own old blog articles, and then my smile isn't rueful.

The blog paints a good picture, I think, of my personality, and of the kinds of things that make me unusual. I realized long long ago that I was a lot less smart than many people. But the way in which I was smart was very different from the way most smart people are smart. Most of the smart people I meet are specialists, even ultra-specialists. I am someone who is interested in a great many things and who strives for breadth of knowledge rather than depth. I want to be the person who makes connections that the specialists are too nearsighted to see. That is the thing I like most about myself, and that comes through clearly in the blog. I know that if my twenty-five-year-old self were to read it, he would be delighted to discover that he would grow up to be the kind of person that he wanted to be, that he did not let the world squash his individual spark. I have changed, but mostly for the better. I am a much less horrible person than I was then: the good parts of the twenty-five-year-old’s personality have developed, and the bad ones have shrunk a bit. I let my innate sense of fairness and justice overcome my innate indifference to other people’s feelings, and I now treat people less callously than before. I am still very self-absorbed and self-satisfied, still delighted above all by my own mind, but I think I do a better job now of sharing my delight with other people without making them feel less.

My grandparents had Eliot and Thackeray on the shelf, and I was always intrigued by them. I was just a little thing when I learned that George Eliot was a woman. When I asked about these books, my grandparents told me that they were grown-up books and I wouldn't like them until I was older—the implication being that I would like them when I was older. I was never sure that I would actually read them when I was older. Well, now I'm older and hey, look at that: I grew up to be someone who reads Eliot and Thackeray, not out of obligation or to meet a deadline, but because the spirit moves me to read.

Thank you Grandma Libby and Grandpa Dick, for everything. Thank you, Gentle Readers, for your kind attention and your many letters through the years.

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Mon, 21 Dec 2015

A message to the aliens, part 23/23 (wat)

Earlier articles: Introduction Common features Page 1 (numerals) Page 2 (arithmetic) Page 3 (exponents) Page 4 (algebra) Page 5 (geometry) Page 6 (chemistry) Page 7 (mass) Page 8 (time and space) Page 9 (physical units) Page 10 (temperature) Page 11 (solar system) Page 12 (Earth-Moon system) Page 13 (days, months, and years) Page 14 (terrain) Page 15 (human anatomy) Page 16 (vital statistics) Page 17 (DNA chemistry) Page 18 (cell respiration and division) Pages 19-20 (map of the Earth) Page 21 (the message) Page 22 (cosmology)

This is page 23 (the last) of the Cosmic Call message. An explanation follows.

This page is a series of questions for the recipients of the message. It is labeled with the glyph , which heretofore appeared only on page 4 in the context of solving of algebraic equations. So we might interpret it as meaning a solution or a desire to solve or understand. I have chosen to translate it as “wat”.

I find this page irritating in its vagueness and confusion. Its layout is disorganized. Glyphs are used inconsistent with their uses elsewhere on the page and elsewhere in the message. For example, the mysterious glyph , which has something to do with the recipients of the message, and which appeared only on page 21 is used here to ask about both the recipients themselves and also about their planet.

The questions are arranged in groups. For easy identification, I have color-coded the groups.

Starting from the upper-left corner, and proceeding counterclockwise, we have:

Kilograms, meters, and seconds, wat. I would have used the glyphs for abstract mass, distance, and time, and , since that seems to be closer to the intended meaning.

Alien mathematics, physics, and biology, wat. Note that this asks specifically about the recipients’ version of the sciences. None of these three glyphs has been subscripted before. Will the meaning be clear to the recipients? One also wonders why the message doesn't express a desire to understand human science, or science generally. One might argue that it does not make sense to ask the recipients about the human versions of mathematics and physics. But a later group expresses a desire to understand males and females, and the recipients don't know anything about that either.

Aliens wat. Alien [planet] mass, radius, acceleration wat. The meaning of shifts here from meaning the recipients themselves to the recipients’ planet. “Acceleration” is intended to refer to the planet's gravitational acceleration as on page 14. What if the recipients don't live on a planet? I suppose they will be familiar with planets generally and with the fact that we live on a planet, which explained back on pages 11–13, and will get the idea.

Fucking speed of light, how does it work?

Planck's constant, wat. Universal gravitation constant, wat?

Males and females, wat. Alien people, wat. Age of people, wat. This group seems to be about our desire to understand ourselves, except that the third item relates to the aliens. I'm not quite sure what is going on. Perhaps “males and females” is intended to refer to the recipients? But the glyphs are not subscripted, and there is no strong reason to believe that the aliens have the same sexuality.

The glyph , already used both to mean the age of the Earth and the typical human lifespan, is even less clear here. Does it mean we want to understand the reasons for human life expectancy? Or is it intended to continue the inquiry from the previous line and is asking about the recipients’ history or lifespan?

Land, water, and atmosphere of the recipients’ planet, wat.

Energy, force, pressure, power, wat. The usage here is inconsistent from the first group, which asked not about mass, distance, and time but about kilograms, meters, and seconds specifically.

Velocity and acceleration, wat. I wonder why these are in a separate group, instead of being clustered with the previous group or the first group. I also worry about the equivocation in acceleration, which is sometimes used to mean the Earth's gravitational acceleration and sometimes acceleration generally. We already said we want to understand mass , !!G!! , and the size of the Earth. The Earth's surface gravity can be straightforwardly calculated from these, so there's nothing else to understand about that.

Alien planet, wat. The glyph has heretofore been used only to refer to the planet Earth. It does not mean planets generally, because it was not used in connection with Jupiter . Here, however, it seems to refer to the recipients’ planet.

The universe, wat. HUH???

That was the last page. Thanks for your kind attention.

[ Many thanks to Anna Gundlach, without whose timely email I might not have found the motivation to finish this series. ]

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