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Archive for the ‘Curious Stuff’ Category


Perpetually Park

Posted by jns on March 5, 2010

Bob Park, in his “What’s New” this week (5 March 2010) had two items on perpetual-motion machines, an idea, like creationism, that seems not to go away but just to get repackaged on a regular basis, said new packaging bagging lots of new, credulous believers–rather like creationism.

I particularly enjoyed ‘it’s not a perpetual motion machine, but it’s “so efficient that it keeps on producing power when it’s unhooked from an outside power source.”‘ Wow.

As for the case law on perpetual motion machines, you’d think that the second law of thermodynamics might be enough but apparently reality is not a form of legal truth.

The town of Odessa, MO, population 4,818, located somewhere east of Kansas City, needs jobs. So when a company, Manna of Utah, said it wanted to build a plant there employing 3000 people, folks cheered. All the town had to do was provide $90 million in revenue bonds and a site. The company even flew local officials to Florida for a demonstration of the “world-changing” technology that would be built there. It’s a home generator developed by Maglev Energy in Largo, Florida, which is leasing the technology to Manna of Utah. State Representative Mike McGhee (R-Odessa) said the product would be the “equivalent of the light bulb.” Steve Everly of the Kansas City Star thought it might be a good idea to check with scientists and engineers, including Bob Park. The mayor of Odessa, Tony Bamvakais, who went on the trip to Florida, says it’s not a perpetual motion machine, but it’s “so efficient that it keeps on producing power when it’s unhooked from an outside power source.”

When Joseph Newman was refused a patent for his Energy Machine he sued the US patent office. Legendary US District Court Judge Robert Penfield Jackson ordered Newman to turn his machine over to the National Bureau of Standards for testing. It was found to be a motor/generator of a design vastly inferior to those on the market. The case, Newman v. Quigg (Quigg was the patent Commissioner) is cited as case-law giving the patent office authority to reject perpetual-motion claims out of hand. The only effect is that they are no longer called “perpetual motion machines.” They are called over-unity devices, or zero-point-energy machines. Coverage of the Joe Newman case in Wikipedia is terrible. It’s a remarkably useful encyclopedia, but you need to verify.


An Early Conservationist

Posted by jns on September 7, 2009

This is Congressman John Fletcher Lacey (1841 – 1913).* Mr. Lacey came to my attention while I was writing a short article on the introduction of starlings to North America (“Starlings Arrive in North America“), of all things. Just how his name came up should become clear shortly.

Here is my abridged version of his official biography (Biographical Directory of the United States Congress):

Representative from Iowa; born in New Martinsville, Va. (now West Virginia), May 30, 1841; moved to Iowa in 1855 with his parents, who settled in Oskaloosa; attended the common schools and pursued classical studies; engaged in agricultural pursuits; learned the trades of bricklaying and plastering; enlisted in Company H, Third Regiment, Iowa Volunteer Infantry, in May 1861[; ...] studied law; was admitted to the bar in 1865 and commenced practice in Oskaloosa, Iowa; [...] elected as a Republican to the Fifty-first Congress (March 4, 1889-March 3, 1891); unsuccessful candidate for reelection; elected to the Fifty-third and to the six succeeding Congresses (March 4, 1893-March 3, 1907); chairman, Committee on Public Lands (Fifty-fourth through Fifty-ninth Congresses); was an unsuccessful candidate for reelection; resumed the practice of law; died in Oskaloosa, Iowa, September 29, 1913….

These days we’d find it exceedingly odd to find the name of someone associated with the Republican party to be a leading conservationist, but times have changed and Lacey is remembered for two important legislative innovations in conservation: “The Lacey Act of 1900″, and “The Antiquities Act of 1906″.

The Lacey Act of 1900“, sponsored by the congressman, was “the first Federal law protecting game, prohibiting the interstate shipment of illegally taken wildlife, as well as the importation of injurious species. Enforcement of this Act became the responsibility of the Division of Biological Survey, U.S. Department of Agriculture.” (source) The ban on the importation of “injurious species” was the connection with starlings and their introduction to North America, although the legislation came 10 years too late to halt that process.

A curious article from the Thoreau Institute (“State Fish & Wildlife Agencies“) gives some background to the Lacey Act:

A legal tradition dating back thousands of years governed wildlife by a “rule of capture”–meaning that they are owned by no one unless killed or captured. Under U.S. common law, wildlife are owned by the people, and the states, rather than federal or local governments, have jurisdiction over their use.

Therefore, regulation of “market hunting” was up to the states. Some few did regulate the practice in the late 1800s, but most did not. This resulted in the common evasive practice of animals being killed illegally in one state and transported into another, where killing them was legal, for sale.

Efforts to ban or regulate commercial hunting accelerated in 1887 when Theodore Roosevelt and George Bird Grinnell started the Boone and Crockett Club, which soon became the most powerful conservation organization in the country. The club is not as well known today, partly because it restricts its membership to 100 people, but those 100 people tend to be highly influential.

Bans on commercial hunting were difficult to enforce when hunters could take their wares across state lines. In 1900, Boone and Crockett Club member and Iowa Congressman John Lacey convinced Congress to pass a federal law prohibiting interstate shipping of wildlife taken in violation of a state game law. This effectively put commercial hunters out of business.

The Lacey Act was signed into law on May 25, 1900 by President William McKinley.

By the time Lacey introduced “The Antiquities Act of 1906“, Congress had already been creating national parks for some 40 years, including Yosemite Valley, Yellowstone National Park, General Grant, Sequoia, Mount Ranier, and Casa Grande and Mesa Verde. (source). It was concern about vandalism and theft of antiquities from the two historic Indian sites that prompted the Antiquities Act. The bill, signed into law by Theodore Roosevelt on June 8, 1906, gave the President authority to restrict the use of particular public land owned by the federal government by using an executive order to designate a “national monument”. The first use of the act: Roosevelt proclaimed Devils Tower National Monument, Wyoming, on September 24, 1906. (source)

While I was researching Congressman Lacey’s contributions I came across one more interesting one worth noting, this having to do with the “Jefferson Bible”. You may recall that this refers to Thomas Jefferson’s highly abridged version of the New Testament in which he cut out all the miraculous and mystical stuff he didn’t care for and kept the better ethical teachings of Jesus, ending up with a slim, svelt 82-page volume. The work has been published on several occasions, notably the Beacon Press, associated with the Unitarian Church.

Here reporter Cathrine Dunn (“Jefferson Bible returns to publication“) takes up the story:

In 1886 Cyrus Adler found the book, which had been passed down through the Jefferson family. He bought the original copy and donated it to the National Museum – now the Smithsonian Institution – where Iowa Congressman John Lacey happened upon it at the turn of the century [i.e., c1900].

It was Lacey who initiated the idea of publishing the book, introducing legislation in Congress that would fund the printing and distribution of the Jefferson Bible to all senators and representatives at the start of their terms.

Lacey saw the book as an important “moral basis for representatives,” said Bellevue University economics professor Judd Patton. “For a good government, we need to have good leaders with moral principles.”

For unknown reasons the Government Printing Office stopped publishing the book in 1957, and its distribution to new congressional members ceased.

* Image source: collection National Conservation Training Center, U.S. Fish & Wildlife Service.


The Atoms in Watermelon

Posted by jns on September 3, 2009

I did not plan to become the expert on such an arcane topic–although I can answer the question as it arises–but once I had written a blog posting called “Atoms Are Not Watermelons“,* my web was spun, my net set, the trap was ready for the unsuspecting googler who should type such an interesting question as

Are the atoms in a watermelon the same as usual atoms?

Perhaps you don’t find this question as surprising as I do. However, since I am the number-one authority on the atoms in watermelons, at least according to the google, I deem the question worth answering and I will answer it.

The answer to the question: yes. The atoms in a watermelon are definitely the same as the usual atoms.

It is, in fact, the central tenet of the atomic theory that everything in the universe is made from the same constituent particles that we know as “elements”, except for those things that are not made of atoms (subatomic particles, for instance, or neutron stars). Even in the most distant galaxies where there are atoms they are known to be the familiar atomic elements.

Watermelon (Citrullus lanatus) is about 92% water, 6% sugar (both by weight). Thus, by number, the vast majority of atoms in a watermelon are hydrogen, oxygen, and carbon. There are also organic molecules as flavors, amino acids and vitamins, plus trace elemental minerals like iron, magnesium, calcium, phosphorus, potassium, and zinc.

The USDA tells us that “Watermelon Packs a Powerful Lycopene Punch“, saying

Lycopene is a red pigment that occurs naturally in certain plant and algal tissues. In addition to giving watermelon and tomatoes their color, it is also thought to act as a powerful antioxidant. Lycopene scavenges reactive oxygen species, which are aggressive chemicals always ready to react with cell components, causing oxidative damage and loss of proper cell function.

I was interested to discover that one can even buy watermelon powder and Lycopene powder, both from the same source, Alibaba.com, which seems to be a diversified asian exporter.

By request from Isaac, here are some recipes for pickled watermelon rind (about which he says “I’ve always wanted to make it.” I never knew — and after 17 years living with someone you’d think I’d have found out):

  • Sweet Pickled Watermelon Rind — most of the recipes that I turned up seemed to be variations on this sweet version, said to be a traditional “Southern” style of some indeterminate age; I’ve not located the ur-recipe yet. Some gussy it up, many vary the amounts of the ingredients while maintaining the same proportions, and one I read added 4 sliced lemons to the pot, which sounded like a nice variation.
  • Watermelon Rind Pickles — this is the not sweet, more pickley version that I think I would find more to my taste. This recipe makes “fresh” pickle, simply stored in the refrigerator, versus processed & canned pickle as in the previous recipe.

* Having just read Richard Rhodes’ How to Write, the subject at hand was bad metaphors in science writing, which he expressed by saying “atoms are not watermelons”.

Oddly, Yahoo! and Bing do not agree, more their loss.


Spock’s Theremin

Posted by jns on December 1, 2008

This beard belongs to Mr. Spock, the venerable half-Vulcan who served as the science officer aboard the Enterprise in “Star Trek”, the original television series. It is thought that he has another name that is unpronounceable by humans. In grade school I identified quite a bit with Mr. Spock. Personally I hoped to develop the cool, rational demeanor and analytical outlook he displayed; outwardly, it was because my ears were too big for my head and looked vaguely pointy.

It seems that this episode in which Spock had this beard (“Mirror, Mirror“), is the only time Spock was ever portrayed with a beard (and, in fact, the bearded version is a mean, anti-Spock in a parallel universe–his beard kept viewers clued in about which universe events were happening). I think that’s too bad because he looks quite dashing in a beard, but apparently NBC already found the Spock character too “sinister” looking to begin with, and everyone knows beards make men look more sinister.

“Spock’s Beard” is also the name of a progressive rock band I’d never heard of until this morning. Isn’t it splendid to learn new things?

Surely, in addition to the main characters, one of the most recognizable things from the “Star Trek” series was the theme song. Last night, for reasons we may or may not get to, the conversation happened to turn on the question whether the familiar and unusual timbre of the melody was 1) a woman singing; or 2) a theremin, which sounded like a woman singing?

Happily, Wikipedia was there with the answer:

Coloratura soprano Loulie Jean Norman imitated the sound and feel of the theremin for the theme for Alexander Courage’s theme for the original Star Trek TV series. Soprano Elin Carlson sang Norman’s part when CBS-Paramount TV remastered the program’s title sequence in 2006.

I was relieved. I had always thought it was a woman singing, but it did sound remarkably like a theremin. And now we’ve arrived at my real object for this piece: Theremin and his theremin. (He never had a beard, it seems, but I would not be thwarted!)

Léon Theremin (1896–1993), born in Russia, started out as Lev Sergeyevich Termen. His name is familiar to many people these days because he invented the “theremin” (here’s an interesting short piece about the theremin; or course there’s Wikipedia on the theremin, not to mention Theremin World). Theremin invented the instrument in 1919 when he was doing research on developing a proximity sensor in Russia. Lenin loved it. Some ten years later Theremin ended up in New York, patented his instrument, and licensed RCA to build them.

The theremin (played by a “thereminist”) is generally deemed to have been the first ever electronic instrument. It also claims the distinction that it is played by the thereminist without being touched. Instead, the thereminist moves her hands near the two antennae of the instrument, one of which controls pitch and the other of which controls volume; capacitive changes between the antennae and the body of the thereminist affect the frequency of oscillators that alter the pitch and volume of the generated tone.

It is a very simple device and the musical sound is not very sophisticated, and yet there’s something beguiling in watching a good thereminist perform, and something haunting about the sound.

Most people have heard a theremin and typically haven’t recognized it. Most popularly, perhaps, is its appearance in the Beach Boys’ “Good Vibrations”, by Brian Wilson (YouTube performance), although this appears to be a modified theremin played by actually touching it!

My favorite theremin parts are in the score Miklós Rózsa wrote for the Hitchcock film “Spellbound“–fabulous film, fabulous music, for which Rózsa won an Academy Award. (In a bit, a link where you can hear the “Spellbound” music, with theremin). This movie was the theremin’s first outing in such a popular venue–”Spellbound” was the mega-hit, big-budget, highly marketed blockbuster of its day. Later on, of course, the theremin was widely used in science-fiction movies, famously The Day the Earth Stood Still and Forbidden Planet. (On the use of the theremin in film scores, here’s a fascinating article by James Wierzbicki: “Weird Vibrations: How the Theremin Gave Musical Voice to Hollywood’s Extraterrestrial ‘Others’ “).

There seems to have been a resurgence of interest in the theremin in the past few years, or else I’ve just noticed other people’s interest more–the internet can make such things much more visible and seemingly more prevalent. One recent development: a solar-powered theremin that fits in an Altoids box. (Heard, by the way, in the radio program mentioned below.)

Some claim that the new interest began following the release of Steven M. Martin’s 1995 documentary, “Theremin: An Electronic Odyssey“. I don’t know about that, but we did watch this film a few weeks ago (we got a copy for rather few dollars–we couldn’t pass it up because of the rather lurid cover art more suitable for something like “Plan Leon from Outer Space” perhaps), and it is an outstanding documentary. It’s about Theremin and the theremin, and the story is very, very engaging. There’s a lot of weird stuff that went on in Theremin’s very long life, like the time in the 1930s (I think) when he was snatched from his office in New York City by Russian agents and spirited away to the Soviet Union. Friends thought he was dead, but he reappeared years later. He’d been forced to work for the KGB developing small listening devices.

A few people of interest also show up in the film: Brian Wilson (enjoy watching him try to finish one thought or get to the end of a sentence), Nicolas Slonimsky, Todd Rundergren, Clara Rockmore, and Robert Moog (of the Moog Synthesize–he started out making theremin kits). Of particular interest, I thought, was Clara Rockmore (1911–1998), thought of as probably the greatest thereminist of all time. Listening to her talk in the film is interesting, but more interesting is watching and listening to her play the theremin. Check out her technique! It’s great stuff.

Now for one last treat. Here is a link to a 90-minute radio program (and information about it), called “Into the Ether“, presented by a British thereminist who performs under the name “Hypnotique”. The program is nicely done and filled with audio samples of theremin performances in a wide variety of genres. If you don’t have the time for the entire thing, I’ll point out that the “Spellbound Concerto”, by Miklós Rózsa, from his music for the film, is excerpted at the very beginning of the program and that’s a must-hear for thereminophiles, whether new or seasoned.


Sing a Song of Science

Posted by jns on January 16, 2008

As so often happens, this began innocently enough.

It all started on Monday, when a friend of mine sent me a YouTube link, claiming that he had found the prefect theme song for Ars Hermeneutica’s Sun Truck project. Indeed he may have done. The song was called “Why the Sun Shines?”. Fans of the group called “They Might Be Giants” will find the song familiar, because TMBG appear to have performed the song frequently, and many versions and performance recordings exist. This one is my favorite so far.

Then, in an amazing bit of thought convergence, on Tuesday night, another friend announced that he had found the perfect theme song for the Sun Truck project!

“Oh?” I asked, innocently enough. “Does it begin with the line ‘The sun is a mass of incandescent gas…’?”

He was a bit deflated, but only a bit. Being a big fan of very alternative music, his version was a mash-up called “Shining Sun Flash”, put together from Moog Machine’s “Jumpin’ Jack Flash,” Tom Glazer’s “Why Does The Sun Shine?,” and Earth Wind & Fire’s “Shining Star”. It comes from an online album of extraterrestrially themed music called “Sounds for the Space Set“.

This did get us some more information about the song, though, the suggestion that it was originally performed by one Tom Glazer. I decided to do a little follow up to verify that and maybe look into getting permission to use the song with the Sun Truck project.

Well, a little follow up turned into the beginning of a whole project about science songs, a worthwhile topic in itself. I’ve only scratched the surface.

The song “Why Does the Sun Shine?” was indeed first performed by folk-singer Tom Glazer. The song first appearance was as part of a six-LP set of recordings known collectively as the “Singing Science Records” — or, “Ballads for the Age of Science” (Wikipedia entries for Glazer or Zaret differ on this fact).

That 6-LP series contained dozens of songs on science written by Hy Zaret* (lyrics) and Lou Singer (music), produced by Zaret in the late 1950s and early 1960s. The albums,

  • Space Songs
  • Energy & Motion Songs
  • Experiment Songs
  • Nature Songs
  • More Nature Songs

were packed with songs that had titles like:

  • Planet Minuet
  • Ultra Violet And Infra Red
  • It’s A Magnet
  • Warm Fronts, Cold Fronts
  • Why Do Leaves Change Their Color
  • How Does A Cow Make Milk

and, of course, “Why Does the Sun Shine?”. Two of the albums were performed by Tom Glazer.

I was delighted to find that all of the songs on all of the (long out of print) albums are preserved and available online, at the “Singing Science Records” page of Jef Poskanzer.

The song “Why Does the Sun Shine?” appears to have a unique cultural status. Before this week I was blissfully ignorant of its existence, but plenty of other people have enjoyed it for years. Not only that, but it has enough status that its lyrics, for reasons that are not entirely clear to me, appear on a web page served by the National Institutes of Health. At least it saves me the trouble of reproducing them here, although they fail to mention that the couplets following the ellipses are done in interrupted voice-over. But you’ll notice that if you listen to one of the recordings available.

Now, that didn’t quite exhaust the subject for me. While I was searching for information about Tom Glazer and the origins of this particular song, I turned up several fascinating articles, web pages, and databases devoted to the topic of science songs. Hey, I have to put the links somewhere!

  • The New York Times article referenced in the note below, is about a young musician named Timothy Sellers who, along with his band Artichoke, had (at that time) been working on a project to record 26 songs he wrote celebrating the lives of historic scientists, one for each letter of the alphabet. At the time of the article they had just released “26 Scientists: Volume 1, Anning to Malthus”. I admit that I haven’t yet heard any of the songs.

Science songwriting is a little-known avocation indulged in by many working scientists; in many cases their results deserve to remain little known. One sees occasional efforts shared, for example, in the pages of Physics Today. Having found several source-pages for these delightful treasures, I didn’t want to lose track of them again.

There, perhaps that will keep us busy for awhile. I fear that I’m not through with this topic.

Oh dear, it seems that I even forgot to mention Tom Lehrer!
* There is an interesting side-controversy here about the true author of the songs, or rather, about the real Hy Zaret. The name Hy Zaret is associated with the song “Unchained Melody“, which he wrote. We’re told may be the most recorded song of the 20th century. No doubt because of its popularity, there is a person named William Stirrat who claims that he wrote the song “Unchained Melody” using the pseudonym Hy Zaret.

Wikipedia assures us that Stirrat is an impostor, but the page for Zaret notes that the false claim has gotten around. In particular, I myself quickly found that the false information had gotten as far as the New York Times, where one finds this mention:

Around the same time [late 1950s], William Stirrat, an electronics engineer, co-produced six albums of science songs for children (“Why Does the Sun Shine?” and “Vibration”). Mr. Stirrat, whose songwriting nom de plume was Hy Zaret, was better known as the person who wrote the lyrics to “Unchained Melody.”

[Michael Erard, "When You Wish Upon an Atom: The Songs of Science", New York Times, 17 May 2005.]


Noctilucent Clouds

Posted by jns on May 10, 2007

For those who fear that there may be nothing left in the world to discover (hardly a chance!), consider this item from Space Weather News for April 25, 2007:

NIGHT-SHINING CLOUDS: NASA’s AIM spacecraft left Earth Wednesday on a two-year mission to study mysterious noctilucent (night-shining) clouds. Hovering at the edge of space, these clouds were first noticed in the 19th century; they are remarkable for their electric-blue color and sharp, wavy ripples. In recent years noctilucent clouds have been growing brighter and spreading. What causes them? Theories range from space dust to global warming. For the next two years, AIM will scrutinize the clouds from Earth orbit to learn what they may be telling us about our planet. Visit http://spaceweather.com for more information about the AIM mission, pictures of noctilucent clouds and observing tips.


Mandelbrot’s Vegetable Stand

Posted by jns on January 18, 2007

I can’t say I expected to see fractals mentioned in an article about cauliflower — or a casual mention of “the Mandelbrot theory” by a cauliflower farmer — but I wasn’t terribly surprised either. I’ve seen these Romanesco cauliflowers and they are visually astonishing, regardless of whether one is a “Caltech guy” or not. I’m not convinced that our author has a deep understanding of fractals, but she manages to capture the spirit and not do much violence to the idea of self-similarity (at all length scales), so Mrs. Scattergood gets the gold star in science communication for today.

But the Romanesco cauliflower is an heirloom and isn’t to be confused with green cauliflower, or broccoflower, which is a cross between a broccoli and a cauliflower. Romanesco is astonishing in appearance, as much for its composition as for its color. Lime-green in hue, a head (or curd) of Romanesco is a near-perfect example of naturally occurring fractal: a fragmented geometric shape composed of smaller parts that are copies of the whole. The cauliflower resembles an M.C. Escher print more than something you’d find naturally occurring in your vegetable garden.

“The guys at Caltech come down and study them,” says Alex Weiser of Weiser Family Farms, in whose farmers market stands you’ll find all three varieties of cauliflower. “Something about the Mandelbrot theory.” But you don’t need a degree in mathematics to cook them. Whether they’re fully grown or beautiful babies, Weiser prefers his cauliflower roasted, with just a little sea salt and olive oil splashed on before they’re put in a hot oven.

[Amy Scattergood, "A Brilliant Comeback", Los Angeles Times via Baltimore Sun, undated, read on 19 January 2006.]


Doilies & Chaos Theory

Posted by jns on March 28, 2005

Kriston, at Grammar.police posted a fantastic picture of a crocheted sculpture in yarn: “Crocheted Model of Hyperbolic Plane” (1970s) by Daina Taimina. (He references this original article: “Crocheting the Hyperbolic Plane: An Interview with David Henderson and Daina Taimina“)
His reaction:

When I saw the images of Taimina’s crocheted hyperbolic figures, I was immediately struck by how instructive it could be as an applied tool to teach non-Euclidean geometry, because–well, I don’t know anything about crochet, but I get the sense that this is true–one could viscerally experience ultraparallel lines or even space curvature. It turns out that Taimina, in fact, invented the first workable model of Lobachevskian, i.e., hyperbolic geometry by abandoning paper and turning to crochet. Certainly makes a great deal of sense after the fact, doesn’t it?

Now, I’m quite serious in what follows, although it may not appear so.
He’s quite right about Taimina’s crocheted geometrics — they are fascinating and instructive as well. They suggest that there indeed could be more mathematical possibilities along the lines he mentions, regardless of whether one knows anything about crochet or not.

People who know me know that I know a bit about crochet, although I prefer working in thread rather than yarn. I crochet doilies. Obsessively. It serves the purpose of keeping my hands busy and productive when I’d otherwise just fidget. These days, since we watch television so rarely, I make most of my pieces in the car, when Isaac is driving. The problem is that, after doing this for some 10 years, one ends up with a lot of doilies — let’s say several hundreds — which is really more than one household can make use of. (Some of my work is displayed, for sale, at The Pansy Forest; there are still lots more for me to put up, however.)
Anyway, I’d never thought about making crocheted hyperbolic figures, although it’s a brilliant idea. I have, however, designed some of my own doily patterns, and the experience gave me the idea for a book about it. (This started several years ago now.)
The tentative title for the book is Doilies, Chaos Theory, and the Origin of the Universe. Seriously.
I don’t want to go into the entire story here, but I discovered what I felt were interesting and illuminating connections between chaos theory (concerning which I did some reasearch in my early graduate-student and post-doctoral days) and creating doily patterns.
Most doilies are chrocheted “in rounds”, worked successsively in thin rings from the center to the outside. Traditional doily patterns, particularly those that make use of a motif called a “pineapple” (sometimes “acorn”), typically develop their patterns over many rounds — that is to say, the patterns emerge one round at a time over the course of completing, say, 10 or 20 rounds.
Now, at the same time the pattern is emerging, it is necessary that the number of stitches in each round increase (relative to the previous round) in fairly strict geometric ratios. There can be a bit of fudging for a round, maybe two further from the center, but one cant’t get away with it for long.
Doily patterns, therefore, are highly constrained systems, and to set out to create a pattern over the course of many rounds requires planning, good luck, and a cooperative pattern. They don’t always go the way one wants.
Another way to put it is to say that doily patterns can show extreme sensitivity to initial conditions: what is allowed to happen on round 25 can depend critically on what happened on round 6. Sensitivity to initial conditions is a defining characteristic of some “chaotic systems” (at least it characterizes the motion of the systems through its phase space, but that’s a longer version of the story.)
Nevertheless, doilies do not look chaotic. Instead, they are amazingly developed mathematical patterns in many cases. How they can look so organized and yet share these characteristics with certain types of chaotic systems interests me. As for the origins of the universe: contemplating the constraints on how doily patterns emerge brings one pretty easily to considering the anthropic cosmological principle (which I tend to think is mostly bunk) and such topics.
I will be the first to admit that there may not be a big cross-over audience for a book that covers antimacassers and modern ideas about dynamical systems and self-organized complexity and such, but that may not stop me. If only I could figure out how to type the manuscript while I crochet the doilies.