Marvellous Merchiston

James Joseph Sylvester: Mathematitian and "poet".

noreply@blogger.com (Math Wizard) — Wed, 11 Nov 2009 15:03:00 +0000

There is a rather interesting transcribed speech here which discusses the poetical efforts of J. J. Sylvester, who was the first Jew to hold a professorship at Oxford. In particular, as mentioned by Bell, he wrote a poem called, "To a missing member of a family of terms in an algebraical formula" which starts as such:

Lone and discarded one! divorced by fate,
From thy wished-for fellows--whither art flown?
Where lingerest thou in thy bereaved estate,
Like some lost star or buried meteor stone?

So yeah, his math was better than his poetry.

What I'm Reading: Men of Mathematics

noreply@blogger.com (Math Wizard) — Sun, 08 Nov 2009 01:26:00 +0000

Men of Mathematics by Eric Temple Bell is a collection of personal and professional biographies of thirty great mathematicians. The first three are from ancient Greece: Zeno, Eudoxus, and Archimedes. The others are from the seventeenth to nineteenth centuries, from Descartes to Cantor.

It was written in 1937, which shows. Not just when the author refers to Bertrand Russell in the present tense, but also, for example, when he mentions in the introduction that certain "writers and artists (some from Hollywood)" have been interested in "how many of the great mathematicians have been perverts." ("None.")

The great thing about this book is the richness of detail Bell gives in the details of the subjects' personal lives. One gets the sense that Bell cares for the mathematicians personally, and also that there is a distinct lack of objectivity here. Gauss in particular is the recipient of torrents of praise. Anyone who opposed or insulted him, or who he disliked, is savaged, usually hilariously.

For example, Napoleon apparently once told Laplace that he would read his book "the first free month he could find." Bell, after relating this, proceeds to write that "Newton and Gauss might have been equal to the task; Napoleon no doubt could have turned the pages in his month without greatly tiring himself."

Later in the chapter, Bell mentions that Gauss didn't like Lord Byron, then goes on to describe the poet in terms of "posturing", "reiterated world-weariness", "affected misanthropy", and "histrionics". He then points out that "no man who guzzled good brandy and pretty women as assiduously as Byron did could be so very weary of the world as the naughty young poet with the flashing eye and the shaking hand pretended to be."

Right now, I'm on the chapter about William Hamilton. It starts with relating that when Hamilton was thirteen he knew a language for every year of his life. Bell does not approve. ("Good God! What was the sense of it all?") At fourteen he wrote a letter of welcome to the Persian Ambassador, in Persian, which Bell imagines may have been responsible for the Ambassador giving an excuse to avoid meeting him. According to an article of Nature (from 1883!) I found on Google Books, it read like this:

As the heart of the worshiper is turned towards the altar of his sacred vision, and as the sunflower to the rays of the sun, so to thy polished radiance turns expanding itself the yet unblossomed rosebud of my mind, desiring warmer climates whose fragrancy and glorious splendor appear to warm and embalm the orbit about thee, the Star of the State, of brilliant lustre.

The article says it was received warmly.

So all in all, this book is amusing and a good read for those interested in the personalities behind the major mathematical discoveries of the seventeenth to nineteenth centuries. But while Bell was an accomplished mathematician in his own right, Men of Mathematics is in large part a work of opinion, and does not in all cases possess the rigor that history is capable of having.

An issue of terminology.

noreply@blogger.com (Math Wizard) — Thu, 21 May 2009 20:34:00 +0000

Wheel in the Sky

noreply@blogger.com (Math Wizard) — Sat, 09 May 2009 18:58:00 +0000

The Analytical Language of John Wilkins

noreply@blogger.com (Math Wizard) — Thu, 30 Apr 2009 01:08:00 +0000

The article can be found here. The main idea can be summed up as

...it is clear that there is no classification of the Universe not being arbitrary and full of conjectures. The reason for this is very simple: we do not know what the universe is.

I can think of four systems of elements that supposedly categorize all things. Two are from history, the Western classical elements and the Chinese version. One is from a game, and one is something else entirely. There are surely more, as many as imagination allows, and that is the key.

At the end of Maybe Logic, there are exercises. One of them is to gather a bunch of arbitrary objects and divide them into two categories in as many different ways as possible. This is a concrete demonstration of the principle that categories are a mental phenomenon and not a property of the universe-as-such. Thus philosophical attempts to discover the "true nature" of the "real categories" of the objects in the universe are misguided.

Spring Break: Alchemical Texts and Darwin Art

noreply@blogger.com (Math Wizard) — Wed, 22 Apr 2009 20:37:00 +0000

I went to new Haven for spring break.

The Beinecke Rare book and Manuscript Library has several interesting past, current, and future exhibitions dealing with the history of math and science. For example, "Trees in Fact and Fable" examines its subject from several disciplines, including botany. There is one about mathematics in early modern England, an International Year of Astronomy exhibition called "Starry Messenger", and some works on alchemy in the European imagination. (I got to see that one.)

Also at Yale, the Yale Center for British Art is hosting an exhibition called "Endless Forms": Charles Darwin, Natural Science, and the Visual Arts (site here). It deals with the effect the publication of Origin of Species had on the arts world. It includes scientific diagrams, paintings depicting prehistoric humans and other creatures, fanciful illustrations of past humanity, Romantic depictions of "the struggle for existence", and photographs of non-European people meant for the scientific study of race. Or I might say pseudo-scientific.

Science and Math Tattoos

noreply@blogger.com (Math Wizard) — Sat, 18 Apr 2009 18:45:00 +0000

Check out the Science Tattoo Emporium. One interesting thing is that many people who get tattoos involving the DNA molecule use it for its heavy symbolic content. For example, here, here, here, and my favorite here.

noreply@blogger.com (Math Wizard) — Tue, 17 Mar 2009 00:24:00 +0000

A long, detailed, and nuanced discussion of the affair between Galileo and the Church may be found here. Part of the interest is in the exposure of some of the "mythology" that surround this issue. Such as this:

According to one of these readings, Galileo knew the Earth to go round the Sun, as Copernicus had written, rather than the converse as implied in several Biblical passages. The Church would not allow science to disprove the revealed truth of Scripture, however, and hence threw Galileo to the Inquisition where he was forced under threat of torture to disclaim this opinion and never speak of it again. He was then imprisoned under house arrest for the remainder of his life, a clear example of the conflict between scientific investigation of the world around us and the presumed infallible authority of the Bible.

Which is a story often cited as the truth of history.

noreply@blogger.com (Math Wizard) — Mon, 16 Mar 2009 23:46:00 +0000

A comic.

Double comic after a long break!

noreply@blogger.com (Math Wizard) — Thu, 05 Feb 2009 01:36:00 +0000

Double comic. There are two.

10 Remarkable Female Mathematicians

noreply@blogger.com (Math Wizard) — Mon, 17 Nov 2008 21:46:00 +0000

I wrote a post much like this one, a while back.
The post is here.

Mathy comics

noreply@blogger.com (Math Wizard) — Fri, 07 Nov 2008 23:48:00 +0000

In Questionable Content, Hannelore reveals one of her hobbies: theoretical knitting. If you've ever wondered why bubble-form tests ask you to use a #2 pencil, XKCD reveals the awful truth. And Saturday Morning Breakfast Cereal pits A 17th Century Explorer vs. Calculus.

Science, meet Politics. Charmed, I'm sure

noreply@blogger.com (Math Wizard) — Sat, 25 Oct 2008 17:11:00 +0000

This was never meant to be a political blog, but what happens now will become history. And in this day and age, scientific research is intertwined with politics. So yeah. I can't think of anything witty to say.

A 29th twofer.

noreply@blogger.com (Math Wizard) — Mon, 29 Sep 2008 23:23:00 +0000

First, an interesting little article on a very strange research project that, strangely, seems to have produced some results. Strange ones. Basically, they are trying to map personality traits according to geography in the US.

Second, an article about the mistakes made by Einstein. This, in my opinion, is an important thing to write and read about, because it defuses the idea that science is ideology. If a physicist whose name and countenance are symbols of intelligence itself can be shown to have been wrong - well, that's only to be expected really.

All the other great scientists of the past were wrong about things, because advancing the state of the art in knowledge is like that - better theories, better data, better models - but never The Truth. Just a useful approximation. This is the power and glory of science: to recognize and correct its errors.

This is why I dislike terms such as "Darwinism" and "evolutionism" so intensely. They attempt to crystallize the ever changing ideas of how species originate into an ideology that, if somehow shown to be false, can then be defeated. It surely must be comforting for opponents of science and knowledge to think that this could possibly work. However, they are just as wrong about this as they are about so many other things.

Beauty's Truth

noreply@blogger.com (Math Wizard) — Sun, 28 Sep 2008 19:52:00 +0000

Find here an old but very interesting essay about what makes a scientific theory beautiful. Essentially, the author argues that the beauty of a theory comes from its truth, and not the other way around. That is, having preconceived notions of what a beautiful theory is can prevent scientists from accepting one that may describe reality better.

Especially interesting given the recent news about the Large Hadron Supercollider. Let's see what happens - maybe we will live to see new theories emerge. This is a historic time.

The Innumeracy of Intellectuals

noreply@blogger.com (Math Wizard) — Tue, 12 Aug 2008 22:51:00 +0000

Magnolia Sitter has linked to this very interesting article. The double standard of engineering students who don't like humanities versus humanities students who don't like math or science is especially interesting.

Also interesting to me is that in medieval education, the trivium and quadrivium consisted of grammar, logic, and rhetoric; and arithmetic, geometry, music, and astronomy, respectively. Of the seven courses in the original liberal arts curriculum, two were explicitly mathematical and three were closely related to mathematics.

To paraphrase Robert Anton Wilson, "Some people at the university specialized in manipulating mathematical symbols, others in verbal ones. Because the people who manipulated verbal symbols were better with language, they got to define themselves as the intellectuals."

The Most Important Image Ever Taken

noreply@blogger.com (Math Wizard) — Tue, 12 Aug 2008 21:54:00 +0000

According to this video, it is the Hubble Deep Field, and I'm inclined to agree. Whenever I look at it, I feel chills. This image, and the even higher resolution Ultra Deep Field, contain hundreds and hundreds of points, blobs, and smears of light. Each one is not a star, but an entire galaxy.

On the less inspired side of things, if you want to see something that manifests such intense stupidity and willful, possibly malevolent ignorance that it is capable of causing physical pain in those who watch it, go here.

The basic "idea", for those unwilling or unable to subject themselves to such gibbering imbecility, is staggeringly nonsensical, and incandescently moronic; a train wreck of epic cognitive ineptitude: Rainbows are a government conspiracy.

Or as the video says: "Everywhere we look, the visible spectrum, is rainbows. This cannot be natural." This is why we need math and science education with tough, rigorous, and reality-based curricula.

The Quest to Solve the Hardest Math Problem

noreply@blogger.com (Math Wizard) — Fri, 08 Aug 2008 13:22:00 +0000

A recent article (which appears not to be available online) in Mental Floss talked some about the quest to prove the Poincaré conjecture. It's the sort of thing that, at some level, seems to be true intuitively but is a nightmare to prove. One of the people who attempted to do so eventually quit math and took up poetry, another swore he would not marry until he proved it - and died a bachelor.

Between 2002 and 2003, a reclusive mathematician named Perelman posted online an outline of a proof, which was then filled out and verified by others. He refused the Fields Medal which the ICM offered him for this feat. Given that the conjecture was proposed in 1904, and this only after Poincaré himself found a flaw in his own proof, the problem went unsolved for over a hundred years.

As for Mental Floss, it is awesome. And they have a couple of articles in the "More" section that are math related: 5 Rap Songs That don't Make the Grade and a proof that Vampires are Mathematically Impossible. Which is flawed because the quoted author assumes that vampires turn everyone they feed on instead of killing most of them. To use Anne Rice's terminology, not everyone deserves the Dark Gift.

“I don’t imitate nature. I try and understand her operating principles.”

noreply@blogger.com (Math Wizard) — Fri, 08 Aug 2008 12:53:00 +0000

As John Todd quotes Bucky Fuller in this interview. This is a vision of ecology, industry, and design that uses natural processes as inspiration. It will take me a while to absorb so much exciting thought. There is an example of this sort of design at the NC Estuarium, which is next to a wetlands that was built to clean the runoff from the town of Washington before releasing it into the Pamlico Sound. It is home to muskrats, dragonflies, turtles, birds, fish, lily pads, and algae.

univers revolved

noreply@blogger.com (Math Wizard) — Fri, 25 Jul 2008 18:23:00 +0000

Check out this font based on taking letter forms and revolving them though the third dimension. The infinitely symmetrical forms allow the letters to be placed into three dimensional and nonlinear arrangements. Very cool, mind bending stuff.

Steampunk Star Wars

noreply@blogger.com (Math Wizard) — Tue, 15 Jul 2008 01:40:00 +0000

While not technically the sort of thing this blog is supposed to be for, this is far too cool to leave alone. My favorite part is the steampunk name for a light saber.

Three Amazing Women

noreply@blogger.com (Math Wizard) — Wed, 09 Jul 2008 19:59:00 +0000

In chronological order.

1. Hypatia of Alexandria is the first known female mathematician. She lived during the fourth and fifth centuries in Roman Egypt, which was long enough ago that her life has had time to become legendary, as well as fodder for propaganda. Her father was Theon, the last mathematician to work at the Library of Alexandria before it was shut down by the Patriarch (which is what we now call the Pope, more or less) in 391. Having a distinguished father, she also had considerable mathematical and philosophical gifts. She edited her father's commentaries on the Almagest and the Elements, among other things.

Clearly a woman who went far beyond the sort of roles that women were expected to fill in the ancient world, she was a follower of Plotinus and taught the works of Plato and Aristotle. To men, in public. (shocking!) Despite this, and her paganism, there were Christians who respected her and attended her lectures. Being a Neoplatonist, she was not so much into "the delights of the flesh", "carnal desires", or that sort of thing, and this earned her a reputation for virtue among Christians and pretty much everybody else. Socrates Scholasticus describes her thus:

"There was a woman at Alexandria named Hypatia, daughter of the philosopher Theon, who made such attainments in literature and science, as to far surpass all the philosophers of her own time. Having succeeded to the school of Plato and Plotinus, she explained the principles of philosophy to her auditors, many of whom came from a distance to receive her instructions. On account of the self-possession and ease of manner, which she had acquired in consequence of the cultivation of her mind, she not unfrequently appeared in public in presence of the magistrates. Neither did she feel abashed in going to an assembly of men. For all men on account of her extraordinary dignity and virtue admired her the more."

In one story she gets rid of a man who is interested in her by showing him one of her used pads (so to speak, women used cloth rags at the time) and telling him that such things were not beautiful. It's really the ultimate rebuttal, in a way. I can just imagine:

Suitor: Pleased would I be, Hypatia, if you would allow me to recieve your favors.
Hypatia: And what would those be?
Suitor: The favors of marriage, Hypatia.
Hypatia: And why do you want such favors from me? Please tell me, because I do not know why it is that you would desire such fleshy congress.
Suitor: For you are beautiful, O Hypatia, and it is in the nature of Man to desire and pursue beauty.
Hypatia, getting out rags and waving them around: Even now do you think carnal desires are a source of beauty? Is this a beautiful sight to you?
Suitor, runnng away: GAAAAHHHHHH!
Hypatia: Right then, time for some Ptolemy.

(Props to Plato, these things are hard to write.)

Eventually, a rumor got around that Hypatia, by talking to a man named Orestes, was preventing him from coming to terms with the Archbishop. So a mob of Christians led by someone calling himself "Peter" tracked her down and murdered her.

Later writers would claim that she was somehow doing magic on people using music or astronomy or something. Even later than that, it would be suggested that the story of St. Catherine (whose symbol is the wheel) was a Christianized version of Hypatia's life. Since then, her story has been used to illustrate the brutality of mob violence, to show the irrationality of religious fervor, and as an archetype of a powerfully intellectual woman, which she surely was.

2. As far as I know, Ada Lovelace is the only woman to ever have a programming language named after her. She, along with Charles Babbage, did work that helped inspire a whole subgenre of speculative fiction - steampunk. Babbage designed a mechanical computer called the Analytical Engine. Lovelace translated an Italian article about the machine and then described how to use it to do mathematical calculations like finding the Bernoulli numbers. For a number of reasons, Babbage was not able to build the machine, which is the might-have-been that inspired the literary genre. So Lovelace wrote a program for the computer before it existed, which was also before any computers existed. Not only that, she had foresight about the not-really-scientific roles computers might someday play:

"the Engine might compose elaborate and scientific pieces of music of any degree of complexity or extent."

So there she is anticipating experimental computer music in a time before the Rite of Spring caused riots and a sudden demand for smelling salts at the apothecary. As QC points out, steampunk music would be awesome.

I don't want to neglect some other things that only make the story more amazing. Her maiden name was Byron, because she was the daughter of Lord Byron. The name Lovelace is from having married the Earl of Lovelace. So basically the noble daughter of a famous poet was an accomplished mathematician and, using the overwhelming force of her intellect, wrote programs for doing advanced mathematical calculations on a nonexistent computer. She then predicted correctly that computers would be useful in the arts.

Babbage wrote about her:

Forget this world and all its troubles and if
possible its multitudinous Charlatans - every thing
in short but the Enchantress of Numbers.

So we can add "inspired an engineer to write poetry" to the list.
All this before dying from cancer at the age of 36.

3. Hedy Lamarr was a Hollywood actress born in Austria. She starred in films from the thirties through the fifties and during the war, helped invent a technology to control missiles. It was too advanced to be used effectively.

Lamarr became notorious first in 1933 for starring in a movie made in Czechoslovakia with overt nudity and sexuality. Later she married a fascist who attempted to buy all the copies of the film. He didn't let her act, instead bringing her to military and business meetings. Being talented mathematically, she became knowledgeable about technical matters. When not using her as eye candy for other fascists, he kept her in his castle. But her husband didn't exactly have supervillain effectiveness, and Lamarr escaped in 1937.

During the war, she and her neighbor George Antheil worked on and invented the first spread spectrum communications technique. It used the roll from a player piano to "hop" the frequency of a radio signal between eighty-eight different values (the number of keys on a piano.) Unfortunately, the technology of the time wasn't up to the task of actually using it to control a torpedo as it was intended to do. Lamarr and Antheil were granted a patent in 1942, but the technology was not actually used until 1962, when the patent had already expired. They made no money from it.

Lamarr made films during the forties, and the government considered her celebrity endorsement of War Bonds to be more important to the war effort than her inventing. Her output declined in the fifties, and in the sixties she was involved in a shoplifting scandal and left public life.

In 1997 the EFF gave Lamarr special recognition for her invention:

"Actress Hedy Lamarr and composer George Antheil are being honored by the EFF this year with a special award for their trail-blazing development of a technology that has become a key component of wireless data systems. In 1942 Lamarr, once named the "most beautiful woman in the world" and Antheil, dubbed "the bad boy of music" patented the concept of "frequency-hopping" that is now the basis for the spread spectrum radio systems used in the products of over 40 companies manufacturing items ranging from cell phones to wireless networking systems."

After that, she was recognized in various ways. Corel used her image to market CorelDRAW 8 (she sued them and reached a settlement), Elyse Singer wrote a play about the invention, and the Inventor's Day in German speaking countries is celebrated on her birthday, November 9.

Lamarr died in 2000, at the age of 86.

Getting some eats.

noreply@blogger.com (Math Wizard) — Tue, 08 Jul 2008 02:24:00 +0000

At long last a comic!

Some thoughts about psychology.

noreply@blogger.com (Math Wizard) — Wed, 28 May 2008 21:00:00 +0000

Cracked.com recently had an article about "Psychological experiments that prove humanity is doomed." It's one of those cases where the humor comes mainly from the sensation of truth attempting to flank the rational mind. In this case, uncomfortable truth.
Psychology doesn't always get a lot of respect, which is a shame, because we tend to discover interesting things about whatever we study with the scientific method. Human personality and behavior is no different. Science can shatter the myths we hold about ourselves and our own mental independence just as well as it can demolish literal interpretations of mythology.
I have even heard people go so far as to say that psychology isn't a science. This attitude is usually based on a definition of science that focuses on the subject matter instead of the method. There is no reason for such a distinction when it is easier to say that science is when people study something scientifically.

It's like a graphic novel.

noreply@blogger.com (Math Wizard) — Fri, 23 May 2008 23:02:00 +0000

It's a comic on 5/23, appropriately irregular. I think this would make a great movie.