# The Universe of Discourse

Sun, 07 Feb 2016

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.

Mon, 21 Dec 2015

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. ]

Fri, 18 Dec 2015

I only posted three answers in August, but two of them were interesting.

• In why this !!\sigma\pi\sigma^{-1}!! keeps apearing in my group theory book? (cycle decomposition) the querent asked about the “conjugation” operation that keeps cropping up in group theory. Why is it important? I sympathize with this; it wasn't adequately explained when I took group theory, and I had to figure it out a long time later. Unfortunately I don't think I picked the right example to explain it, so I am going to try again now.

Consider the eight symmetries of the square. They are of five types:

1. Rotation clockwise or counterclockwise by 90°.
2. Rotation by 180°.
3. Horizontal or vertical reflection
4. Diagonal reflection
5. The trivial (identity) symmetry

What is meant when I say that a horizontal and a vertical reflection are of the same ‘type’? Informally, it is that the horizontal reflection looks just like the vertical reflection, if you turn your head ninety degrees. We can formalize this by observing that if we rotate the square 90°, then give it a horizontal flip, then rotate it back, the effect is exactly to give it a vertical flip. In notation, we might represent the horizontal flip by !!H!!, the vertical flip by !!V!!, the clockwise rotation by !!\rho!!, and the counterclockwise rotation by !!\rho^{-1}!!; then we have

$$\rho H \rho^{-1} = V$$

and similarly

$$\rho V \rho^{-1} = H.$$

Vertical flips do not look like diagonal flips—the diagonal flip leaves two of the corners in the same place, and the vertical flip does not—and indeed there is no analogous formula with !!H!! replaced with one of the diagonal flips. However, if !!D_1!! and !!D_2!! are the two diagonal flips, then we do have

$$\rho D_1 \rho^{-1} = D_2.$$

In general, When !!a!! and !!b!! are two symmetries, and there is some symmetry !!x!! for which

$$xax^{-1} = b$$

we say that !!a!! is conjugate to !!b!!. One can show that conjugacy is an equivalence relation, which means that the symmetries of any object can be divided into separate “conjugacy classes” such that two symmetries are conjugate if and only if they are in the same class. For the square, the conjugacy classes are the five I listed earlier.

This conjugacy thing is important for telling when two symmetries are group-theoretically “the same”, and have the same group-theoretic properties. For example, the fact that the horizontal and vertical flips move all four vertices, while the diagonal flips do not. Another example is that a horizontal flip is self-inverse (if you do it again, it cancels itself out), but a 90° rotation is not (you have to do it four times before it cancels out.) But the horizontal flip shares all its properties with the vertical flip, because it is the same if you just turn your head.

Identifying this sameness makes certain kinds of arguments much simpler. For example, in counting squares, I wanted to count the number of ways of coloring the faces of a cube, and instead of dealing with the 24 symmetries of the cube, I only needed to deal with their 5 conjugacy classes.

The example I gave in my math.se answer was maybe less perspicuous. I considered the symmetries of a sphere, and talked about how two rotations of the sphere by 17° are conjugate, regardless of what axis one rotates around. I thought of the square at the end, and threw it in, but I wish I had started with it.

• How to convert a decimal to a fraction easily? was the month's big winner. OP wanted to know how to take a decimal like !!0.3760683761!! and discover that it can be written as !!\frac{44}{117}!!. The right answer to this is of course to use continued fraction theory, but I did not want to write a long treatise on continued fractions, so I stripped down the theory to obtain an algorithm that is slower, but much easier to understand.

The algorithm is just binary search, but with a twist. If you are looking for a fraction for !!x!!, and you know !!\frac ab < x < \frac cd!!, then you construct the mediant !!\frac{a+c}{b+d}!! and compare it with !!x!!. This gives you a smaller interval in which to search for !!x!!, and the reason you use the mediant instead of using !!\frac12\left(\frac ab + \frac cd\right)!! as usual is that if you use the mediant you are guaranteed to exactly nail all the best rational approximations of !!x!!. This is the algorithm I described a few years ago in your age as a fraction, again; there the binary search proceeds down the branches of the Stern-Brocot tree to find a fraction close to !!0.368!!.

I did ask a question this month: I was looking for a simpler version of the dogbone space construction. The dogbone space is a very peculiar counterexample of general topology, originally constructed by R.H. Bing. I mentioned it here in 2007, and said, at the time:

[The paper] is on my desk, but I have not read this yet, and I may never.

I did try to read it, but I did not try very hard, and I did not understand it. So my question this month was if there was a simpler example of the same type. I did not receive an answer, just a followup comment that no, there is no such example.

Sat, 12 Dec 2015

This is page 22 of the Cosmic Call message. An explanation follows.

The 10 digits are:

 0 1 2 3 4 5 6 7 8 9

This page discusses properties of the entire universe. It is labeled with a new glyph, , which denotes the universe or the cosmos. On this page I am on uncertain ground, because I know very little about cosmology. My explanation here could be completely wrong without my realizing it.

The page contains only five lines of text. In order, they state:

1. The Friedmann equation which is the current model for the expansion of the universe. This expansion is believed to be uniform everywhere, but even if it isn't, the recipients are so close by that they will see exactly the same expansion we do. If they have noticed the expansion, they may well have come to the same theoretical conclusions about it. The equation is:

$$H^2 = \frac{8\pi G}3\rho + \frac{\Lambda c^2 }3$$

where !!H!! is the Hubble parameter (which describes how quickly the universe is expanding), !!G!! is the universal gravitation constant (introduced on page 9, !!\rho!! is the density of the universe (given on the next line), and !!\Lambda c^2!! () is one of the forms of the cosmological constant (given on the following line).

2. The average density of the universe , given as !!2.76\times 10^{-27} \mathrm{kg} ~\mathrm{m}^3!!. The “density” glyph would have been more at home with the other physics definitions of page 9, but it wasn't needed until now, and that page was full.

3. The cosmological constant !!\Lambda!! is about !!10^{-52} \mathrm{m}^{-2}!!. The related value given here, !!\Lambda c^2!!, is !!1.08\cdot 10^{-35} \mathrm{s}^{-2}!!.

4. The calculated value of the Hubble parameter !!H!! is given here in the rather strange form !!\frac1{14000000000}\mathrm{year}^{-1}!!. The reason it is phrased this way is that (assuming that !!H!! were constant) !!\frac1H!! would be the age of the universe, approximately 14,000,000,000 years. So this line not only communicates our estimate for the current value of the Hubble parameter, it expresses it in units that may make clear our beliefs about the age of the universe. It is regrettable that this wasn't stated more explicitly, using the glyph that was already used for the age of the Earth on page 13. There was plenty of extra space, so perhaps the senders didn't think of it.

5. The average temperature of the universe, about 2.736 kelvins. This is based on measurements of the cosmic microwave background radiation, which is the same in every direction, so if the recipients have noticed it at all, they have seen the same CMB that we have.

The next article will discuss the final page, shown at right. (Click to enlarge.) Try to figure it out before then.

Sun, 06 Dec 2015

This is page 21 of the Cosmic Call message. An explanation follows.

The 10 digits are:

 0 1 2 3 4 5 6 7 8 9

This page discusses the message itself. It is headed with the glyph for “physics” .

The leftmost part of the page has a cartoon of the Yevpatoria RT-70 radio telescope that was used to send the message, labeled “Earth” . Coming out the the telescope is a stylized depiction of a radio wave. Two rulers measure the radio wave. The smaller one measures a single wavelength, and is labeled “frequency = 5,010,240,000 Hz ” and “wavelength = 0.059836 meters ”; these are the frequency and the wavelength of the radio waves used to send the message. The longer ruler has the notation “127×127×23”, describing the format of the message itself, 23 pages of 127×127 bitmaps, and also “43000 people ”, which I do not understand at all. Were 43,000 people somehow involved with sending the message? That seems far too many. Were there 43,000 people in Yevpatoria in 1999? That seems far too few; the current population is over 100,000. I am mystified.

At the other end of the radio wave is the glyph , which is hard to decipher, because it appears only on this page and on the unhelpful page 23. I guess it is intended to refer to the recipients of the message.

[ Addendum 20151219: Having reviewed page 23, I am still in the dark. References to the mass and radius of suggest that it refers to the recipients’ planet, but references to the mathematics, physics, and biology of suggests that it refers to the recipients themselves. ]

In the lower-right corner of the page is another cartoon of the RT-70, this time with a ruler underneath showing its diameter, 70 meters. Above the cartoon is the power output of the telescope, 150 kilowatts.

The next article will discuss page 22, shown at right. (Click to enlarge.) Try to figure it out before then.

Sat, 28 Nov 2015

These are pages 19–20 of the Cosmic Call message. An explanation follows.

These two pages are a map of the surface of the Earth. Every other page in the document is surrounded by a one-pixel-wide frame, to separate the page from its neighbors, but the two pages that comprise the map are missing part of their borders to show that the the two pages are part of a whole. Assembled correctly, the two pages are surrounded by a single border. The matching sides of the map pages have diamond-shaped registration marks to show how to align the two pages.

The map projection used here is R. Buckminster Fuller's Dymaxion projection, in which the spherical surface of the Earth is first projected onto a regular icosahedron, which is then unfolded into a flat net. This offers a good compromise between directional distortion and size distortion. Each twentieth of the map is distorted only enough to turn it into a triangle, and the interruptions between the triangles can be arranged to occur at uninteresting parts of the map.

Both pages are labeled with the glyph for “Earth”. On each page, the land parts of the map are labeled with and the water parts with , as on page 14, since the recipients wouldn't otherwise be able to tell which was which.

The next article will discuss page 21, shown at right. (Click to enlarge.) Try to figure it out before then.

Mon, 02 Nov 2015

This is page 18 of the Cosmic Call message. An explanation follows.

The 10 digits are:

 0 1 2 3 4 5 6 7 8 9

This page depicts the best way to fry eggs. The optimal fried egg is shown at left. Ha ha, just kidding. The left half of the page explains cellular respiration. The fried egg is actually a cell, with a DNA molecule in its nucleus. Will the aliens be familiar enough with the structure of DNA to recognize that the highly abbreviated picture of the DNA molecule is related to the nucleobases on the previous page? Perhaps, if their genetic biochemistry is similar to ours, but we really have no reason to think that it is.

The illustration of the DNA molecule is subtly wrong. It shows a symmetric molecule. In reality, one of the two grooves between the strands is about twice as big as the other, as shown at right.

The top formula says that C6H12O6 and O2 go into the cell; the bottom formula says that CO2 comes out. (Energy comes out also; I wonder why this wasn't mentioned.) The notation for chemical compounds here is different from that used on page 14: there, O2 was written as ; here it is written as (“2×O”).

The glyph near the left margin does not appear elsewhere, but I think it is supposed to mean “cell”. Supposing that is correct, the text at the bottom says that the number of cells in a man or woman is !!10^{13}!!. The number of cells in a human is not known, except very approximately, but !!10^{13}!! is probably the right order of magnitude. (A 2013 paper from Annals of Human Biology estimates !!3.72\cdot 10^{13}!!.)

Next to the cell is a ruler labeled !!10^{-5}!! meters, which is a typical size for a eukaryotic cell.

The illustration on the right of the page, annotated with the glyphs for the four nucleobases from the previous page , depicts the duplication of genetic material during cellular division. The DNA molecule splits down the middle like a zipper. The cell then constructs a new mate for each half of the zipper, and when it divides, each daughter cell gets one complete zipper.

The next article will discuss pages 19 and 20, shown at right. (Click to enlarge.) Try to figure it out before then.

Fri, 02 Oct 2015

This is page 17 of the Cosmic Call message. An explanation follows.

The 10 digits are:

 0 1 2 3 4 5 6 7 8 9

This page depicts the chemical structures of the four nucleobases that make up the information-carrying part of the DNA molecule. Clockwise from top left, they are thymine , adenine , guanine , and cytosine .

The deoxyribose and phosphate components of the nucleotides, shown at right, are not depicted. These form the spiral backbone of the DNA and are crucial to its structure. Will the recipients understand why the nucleobases are important enough for us to have mentioned them?

The next article will discuss page 18, shown at right. (Click to enlarge.) Try to figure it out before then.

Wed, 30 Sep 2015

This is page 16 of the Cosmic Call message. An explanation follows.

The 10 digits are:

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This page, about human vital statistics and senses, is in three sections. The text in the top left explains the population of the Earth: around 6,000,000,000 people at the time the message was sent. The three following lines give the life expectancy (70 years), mass (80 kg), and body temperature (311K) of humans. In each case it is stated explicitly that the value for men and for women is the same, which is not really true.
The glyph used for life expectancy is the same one used to denote the age of the Earth back on page 13 even though the the two notions are not really the same. And why 311K when the commonly-accepted value is 310K?

The diagram at right attempts to explain the human sense of hearing, showing a high-frequency wave at top and a low frequency one at bottom, annotated with the glyph for frequency and the upper and lower frequency limits of human hearing, 20,000 Hz and 20 Hz respectively. I found this extremely puzzling the first time I deciphered the message, so much so that it was one of the few parts of the document that left me completely mystified, even with the advantage of knowing already what humans are like. A significant part of the problem here is that the illustration is just flat out wrong. It depicts transverse waves:

but sound waves are not transverse, they are compression waves. The aliens are going to think we don't understand compression waves. (To see the difference, think of water waves, which are transverse: the water molecules move up and down—think of a bobbing cork—but the wave itself travels in a perpendicular direction, not vertically but toward the shore, where it eventually crashes on the beach. Sound waves are not like this. The air molecules move back and forth, parallel to the direction the sound is moving.)

I'm not sure what would be better; I tried generating some random compression waves to fit in the same space. (I also tried doing a cartoon of a non-random, neatly periodic compression wave, but I couldn't get anything I thought looked good.) I think the compression waves are better in some ways, but perhaps very confusing:

On the one hand, I think they express the intended meaning more clearly; on the other hand, I think they're too easy to confuse with glyphs, since they happen to be on almost the same scale. I think the message might be clearer if a little more space were allotted for them. Also, they could be annotated with the glyph for pressure , maybe something like this:

This also gets rid of the meaningless double-headed arrow. I'm not sure I buy the argument that the aliens won't know about arrows; they may not have arrows but it's hard to imagine they don't know about any sort of pointy projectile, and of course the whole purpose of a pointy projectile (the whole point, one might say) is that the point is on the front end. But the arrows here don't communicate motion or direction or anything like that; even as a human I'm not sure what they are supposed to communicate.

The bottom third of the diagram is more sensible. It is a diagram showing the wavelengths of light to which the human visual system is most sensitive. The x-axis is labeled with “wavelength” and the y-axis with a range from 0 to 1. The three peaks have their centers at 295 nm (blue), 535 nm (green), and 565 nm (often called “red”, but actually yellow). These correspond to the three types of cone cells in the retina, and the existence of three different types is why we perceive the color space as being three-dimensional. (I discussed this at greater length a few years ago.) Isn't it interesting that the “red” and green sensitivities are so close together? This is why we have red-green color blindness.

The next article will discuss page 17, shown at right. (Click to enlarge.) Try to figure it out before then.

Mon, 28 Sep 2015

This is page 15 of the Cosmic Call message. An explanation follows.

The 10 digits are:

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This page starts a new section of the document, each page headed with the glyph for “biology” . The illustration is adapted from the Pioneer plaque; the relevant portion is shown below.

Copies of the plaque were placed on the 1972 and 1973 Pioneer spacecraft. The Pioneer image has been widely discussed and criticized; see the Wikipedia article for some of the history here. The illustration suffers considerably from its translation to a low-resolution bitmap. The original picture omits the woman's vulva; the senders have not seen fit to correct this bit of prudery.

The man and the woman are labeled with the glyphs and , respectively. The glyph for “people” , which identified the stick figures on the previous page, is inexplicably omitted here.

The ruler on the right somewhat puzzlingly goes from a bit above the man's toe to a bit below the top of the woman's head; it does not measure either of the two figures. It is labeled 1.8 meters, a typical height for men. The original Pioneer plaque spanned the woman exactly and gave her height as 168 cm, which is conveniently an integer multiple of the basic measuring unit (21 cm) defined on the plaque.

To prevent the recipients from getting confused about which end of the body is the top, a parabolic figure (shown here at left), annotated with the glyph for “acceleration”, shows the direction of gravitational acceleration as on the previous page.

The next article will discuss page 16, shown at right. (Click to enlarge.) Try to figure it out before then.

Fri, 25 Sep 2015

This is page 14 of the Cosmic Call message. An explanation follows.

The 10 digits are:

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This is my favorite page: there is a lot of varied information and the illustration is ingenious. The page heading says to match up with the corresponding labels on the previous three pages. The page depicts the overall terrain of the Earth. The main feature is a large illustration of some mountains (yellow in my highlighted illustration below) plunging into the sea (blue).

The land part is labeled , the air part , and the water part . Over on the left of the land part are little stick figures, labeled people . This is to show that people live on the land part of the Earth, not under water or in the air. The stick figures may not be clear to the recipients, but they are explained in more detail on the next page.

Each of the three main divisions is annotated with its general chemical composition, with compounds listed in order of prevalence., All the chemical element symbols were introduced earlier, on pages 6 and 7:

The lithosphere : silicon dioxide (SiO2) ; aluminium oxide (Al2O3) ; iron(III) oxide (Fe2O3) ; iron(II) oxide (FeO) . Wikipedia and other sources dispute this listing, giving instead: SiO2, MgO, FeO, Al2O3, CaO, Na2O, Fe2O3 in that order.

The atmosphere : nitrogen gas (N2) ; oxygen gas (O2) ; argon (Ar) ; carbon dioxide (CO2) .

The hydrosphere : water (H2O) ; sodium (Na) ; chlorine (Cl) .

There are rulers extending upward from the surface of the water to the height of top of the mountain and downward to the bottom of the ocean. The height ruler is labeled 8838 meters, which is the height the peak of Mount Everest, the point highest above sea level. The depth ruler is labeled 11000 meters, which is the depth of the Challenger Deep in the Mariana Trench, the deepest part of the ocean. The two rulers have the correct sizes relative to one another. The human figures at left are not to scale (they would be about 1.7 miles high), but the next page will explain how big they really are.

I don't think the message contains anything to tell the recipients the temperature of the Earth, so it may not be clear that the hydrosphere is liquid water. But perhaps the wavy line here will suggest that. The practice of measuring the height of the mountains and depth of the ocean from the surface may also be suggestive of a liquid ocean, since it would not otherwise have a flat surface to provide a global standard.

There is a potential problem with this picture: how will the recipients know which edge is the top? What if they hold it upside-down, and think the human figures are pointing down into the earth, heads downwards?

This problem is solved in a clever way: the dots at the right of the page depict an object accelerating under the influence of gravity, falling in a characteristic parabolic path. To make the point clear, the dots are labeled with the glyph for acceleration.

Finally, the lower left of the page states the acceleration due to gravity at the Earth's surface, 9.7978 m/s2. The recipients can calculate this value from the mass and radius of the Earth given earlier. Linked with the other appearance of acceleration on the page, this should suggest that the dots depict an object falling under the influence of gravity toward the bottom of the page.

The next article will discuss page 15, shown at right. (Click to enlarge.) Try to figure it out before then.

Wed, 23 Sep 2015

This is page 13 of the Cosmic Call message. An explanation follows.

The 10 digits are:

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There are three diagrams on this page, each depicting something going around. Although the direction is ambiguous (unless you understand arrows) it should at least should be clear that all three rotations are in the same direction. This is all you can reasonably say anyhow, because the rotations would all appear to be going the other way if you looked at them from the other side.

The upper left diagram depicts the Earth going around the Sun and underneath is a note that says that the time is equal to 315569268 seconds, and is also equal to one year . This defines the year.

The upper-right diagram depicts the Moon going around the Earth ; the notation says that this takes 2360591 seconds, or around 27⅓ days. This is not the 29½ days that one might naïvely expect, because it is the sidereal month rather than the synodic month. Suppose the phase of the Moon is new, so that the Moon lies exactly between the Earth and the Sun. 27⅓ days later the Moon has made a complete trip around the Earth, but because the Earth has moved, the Moon is not yet again on the line between the Earth and the Sun; the line is in a different direction. The Earth has moved about !!\frac1{13}!! of the way around the sun, so it takes about another !!\frac1{12}\cdot 27\frac13!! days before the moon is again between Earth and Sun and so a total of about 29½ days between new moons.

The lower-right diagram depicts the rotation of the Earth, giving a time of 86163 seconds for the day. Again, this is not the 86400 seconds one would expect, because it is the sidereal day rather than the solar day; the issue is the same as in the previous paragraph.

None of the three circles appears to be circular. The first one is nearly circular, but it looks worse than it is because the Sun has been placed off-center. The curve representing the Moon's orbit is decidedly noncircular. This is reasonable, because the Moon's orbit is elliptical to approximately the same degree. In the third diagram, the the curve is intended to represent the surface of the Earth, so its eccentricity is indefensible. The ellipse is not the same as the one used for the Moon's orbit, so it wasn't just a copying mistake.

The last two lines state that the ages of the Sun and the Earth are each 4550000000 years. This is the first appearance of the glyph for “age”.

The next article will discuss page 14, shown at right. (Click to enlarge.) Try to figure it out before then.