Wednesday, January 21, 2015

Making Invisible Fields Visible

Illustration showing movement of air through various rooms,
from Lectures on Ventilation (1869) by Lewis W. Leeds.
Image via Wikimedia Commons.
I used to teach physics to arts students and geophysics to environment science students. One of the mathematical concepts which was a challenge to convey was that of the field. In broad terms, it's rather simple really. A field is simply something which is defined at all points in space. A temperature field in a room is a scalar field; that means there is simply a value for temperature, a number you could measure, at any point (distance north from the corner, distance east from the corner and height off the floor) in the room. A vector field is the same thing, but at every point there is an amplitude and a direction. Add a fan or simply ventilation to the room and you can measure airflow at any point; this is a vector field. The illustration gives you an immediate sense of both the temperature and air flow field in a room - illustration as early data visualization.

Berenice Abbott (1898 - 1991) created brilliant
black and white science photographic illustrations like this one

Scifi loves the idea of a force field; this is a vector field descripting a force, like for instance, gravity, at all points in space. You can't see these fields; they are invisible - but they are (hopefully) easy to imagine. You may remember seeing a simple demonstration of magnetic field lines: iron fillings around a bar magnet, tracing out loops from pole to pole. Such a simple experiment is shown - complete with extra electrically conductive metal key - in Berenice Abbott's photo.

Our own Earth has a magnetic field of course, and it is really not that different from that of a bar magnet. Certainly, to first order as physicists say, you can imagine our earth with magnetic field lines from pole to pole tracing loops similar to those in the photo in a full three dimensions. The main complication to this picture is the sun, and way the solar wind intereacts with the Earth's magnetic field.

"Lines of Force and Equipotential Surfaces in a diametral section of a spherical Surface in which the superficial density is a harmonic of the first degree" from A Treatise on Electricity an Magnetism, James Clerk Maxwell, 1873

Schematic diagram of how the Sun interacts with the Earth's magnetic
field (curtesy of the USGS). The solar wind distorts the field basically
compacting the field in on the sunward side creating a bowshock and 
blowing a long 'magnetotail' outward on the night side of the Earth.
Geophysicists use the way these fields interact to probe our planet. We
can all enjoy the beauty of the auroras caused by this interaction. Solar 
storms can also interfer with radio communications, damage GPS and 
other satellites, and even cause electrical blackouts. 

I love the creative, eerie and entrancing take of Semiconductor (the duo of Ruth Jarman and Joe Gerhardt) take in their short film 'Magnetic Movie'. They let NASA space scientists talk about magnetic field lines, and then animate the Space Science Laboratories at UC Berkeley employing very low frequency radio audio recordings (3 Hz to 30 kHz) as an input for their animated embellishments. They are taking poetic license with reality, but somehow expressing more than we might, if we could literally reveal these invisible fields.

Magnetic Movie from Semiconductor on Vimeo.

They write,
The secret lives of invisible magnetic fields are revealed as chaotic ever-changing geometries . All action takes place around NASA's Space Sciences Laboratories, UC Berkeley, to recordings of space scientists describing their discoveries. Actual VLF audio recordings control the evolution of the fields as they delve into our inaudible surroundings, revealing recurrent ‘whistlers' produced by fleeting electrons . Are we observing a series of scientific experiments, the universe in flux, or a documentary of a fictional world?

Perhaps a little more literal, is another artistic work by Semiconductor, which strives to make the invisible geomagnetic field visible. In '20 Hz' they employ data gathered by CARISMA (the Canadian Array for Realtime Investigations of Magnetic Activity, the magnetometer element of the Geospace Observatory Canada project, operated by U of Alberta) of a geomagnetic storm in the Earth's upper atmosphere - data recorded at the frequency of 20 Hertz (of course). They 'play' the data as the audio track and use the data to generate the visuals.

20 Hz from Semiconductor on Vimeo.

They write,

20 Hz observes a geo-magnetic storm occurring in the Earth's upper atmosphere. Working with data collected from the CARISMA radio array and interpreted as audio, we hear tweeting and rumbles caused by incoming solar wind, captured at the frequency of 20 Hertz. Generated directly by the sound, tangible and sculptural forms emerge suggestive of scientific visualisations. As different frequencies interact both visually and aurally, complex patterns emerge to create interference phenomena that probe the limits of our perception.

Thursday, January 15, 2015

Nihilist Girl: Great Russian Mathematician Sofia Kovalevski

Sofia Kovalevski linocut
'Sofia Kovalevski', linocut 9.25" by 12.5" (23.5 cm by 32 cm), 2014 by Ele Willoughby
Today is the birthday of the great Russian mathematician and writer, Sofia Vasilyevna Kovalevski (1850-1891), in honour of which, I'm going to make the first of a series of posts about scientists I've portrayed.

Also known as Sofie or Sonya, her last name has been transliterated from the Cyrillic Со́фья Васи́льевна Ковале́вска in a variety of ways, including Kovalevskaya and Kowalevski. Sofia's contributions to analysis, differential equations and mechanics include the Cauchy-Kovalevski theorem and the famed Kovalevski top (well, famed in certain circles, no pun intended). She was the first woman appointed to a full professorship in Northern Europe or to serve as editor of a major scientific journal. She is also remembered for her contributions to Russian literature. All of this despite living when women were still barred from attending university. Her accomplishments were tremendous in her short but astonishing life.

Born Sofia Korvin-Krukovskaya, in Moscow, the second of three children, she attributed her early aptitude for calculus to a shortage of wallpaper, which lead her father to have the nursery papered with his old differential and integral analysis notes. Her parents nurtured her early interest in math, and hired her a tutor. The local priest's son introduced her to nihilism. So both her bent for revolutionary politics and passion for math were established early.

Unable to continue her education in Russia, like many of her fellow modern, young women including her sister, she sought a marriage of convenience. Women were both unable to study at university or leave the country without permission of their father or husband. Men sympathetic to their plight would participate in "fictitious marriages" to allow them an opportunity to seek further education abroad. She married the young paleontology student, Vladimir Kovalevsky, later famous for his collaboration with Charles Darwin. They emigrated in 1867, and by 1869 she enrolled in the German University of Heidelburg, where she could at least audit classes with the professors' permission. She studied with such luminaries as Helmholtz, Kirchhoff and Bunsen. She moved to Berlin and studied privately with Weierstrass, as women could not even audit classes there. In 1874, she present three papers, on partial differential equations, on the dynamics of Saturn's rings (as illustrated in my linocut) and on elliptic integrals as a doctoral dissertation at the University of of Göttingen. Weierstrass campaigned to allow her to defend her doctorate without usual required lectures and examinations, arguing that each of these papers warranted a doctorate, and she graduated summa cum laude - the first woman in Germany to do so.

She and her husband counted amongst their friends the great intellectuals of the day including Fyodor Dosteyevsky (who had been engaged to her sister Ann), Thomas Huxley, Charles Darwin, Herbert Spencer, and George Elliot. The sentence "In short, woman was a problem which, since Mr. Brooke's mind felt blank before it, could hardly be less complicated than the revolutions of an irregular solid." from Elliot's Middlemarch, is undoubtedly due to her friendship with Kovaleski. Sofia and Vladimir believed in ideas of utopian socialism and traveled to Paris to help those the injured from the Paris Commune and help rescue Sofia's brother-in-law, Ann's husband Victor Jaclard.

In the 1880s, Sofia and her husband had financial difficulties and a complex relationship. As a woman Sofia was prevented from lecturing in mathematics, even as a volunteer. Vladimir tried working in business and then house building, with Sofia's assistance, to remain solvent. They were unsuccessful and went bankrupt. They reestablished themselves when Vladimir secured a job. Sofia occupied herself helping her neighbours to electrify street lamps. They tried returning to Russia, where their political beliefs interfered with any chance to obtain professorships. They moved on to Germany, where Vladimir's mental health suffered and they were often separated. Then, for several years, they lived a real marriage, rather than one of convenience, and they conceived their daughter Sofia, called Fufa. When Fufa turned one, Sofia entrusted her to her sister so she could return to mathematics, leaving Vladimir behind. By 1883, he faced increasing mood swings and the threat of prosecution for his role in a stock swindle. He took his own life.

Mathematician Gösta Mittag-Leffler, a fellow student of Weierstrass, helped Sofia secure a position as a privat-docent at Stockholm University in Sweden. She developed an intimate "romantic friendship" with his sister, actress, novelist, and playwright Duchess Anne-Charlotte Edgren-Leffler, with whom she collaborated in works of literature, for the remainder of her too short life. In 1884 she was appointed "Professor Extraordinarius" (Professor without Chair) and became the editor of the journal Acta Mathematica. She won the Prix Bordin of the French Academy of Science, for her work on the rotation of irregular solids about a fixed point (as illustrated by the diagram in my linocut) including the discovery of the celebrated "Kovalevsky top". We now know there are only three fully integrable cases of rigid body motion and her solution ranks with those of mathematical luminaries Euler and Lagrange. In 1889, she was promoted to Professor Ordinarius (Professorial Chair holder) becoming the first woman to hold such a position at a northern European university. Though she never secured a Russian professorship, the Russian Academy of Sciences granted her a Chair, after much lobbying and rule-changing on her behalf.

Her writings include the memoir A Russian Childhood, plays written in collaboration with Edgren-Leffler, and the semi-autobiographical novel Nihilist Girl (1890).

Tragically, she died at 41, of influenza during the pandemic. Prizes, lectures and a moon crater have been named in her honour. She appears in film and fiction, including Nobel laureate Alice Munro's beautiful novella 'Too Much Happiness', a title taken from Sofia's own writing about her life.

Wednesday, January 14, 2015

Exoplanet Travel Posters

I've written previously about retro travel posters for otherwhere - different places in spacetime, different planets within our solar system, and previous geological eras. NASA has recently released a delightful collection of retro travel posters for the growing collection of exoplanets. With ongoing planetary science research into planets outside our own solar system (beyond Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Nepture and the larger planetessimals like the ever-popular Pluto and lesser-known Sedna and so forth), there is now a immense database of planets orbitting other stars. Further, astronomers and planetary scientists are able to deduce not only the existence of these planets (by, for instance, the way their home stars' light dims when planets pass between us and the stars), but often their scale, mass and other physical properties. These retro-style travel posters are a fabulous art/science collaboration, means of communicating science and plain old beautiful graphic design. They are also inspiring of humanity's dreams of space exploration. I approve wholeheartedly.

Courtesy NASA/JPL-Caltech.
The planet Kepler-16b orbits a binary star. It may be a rocky terrestrial planet, like our Earth, or a gassy giant like Jupiter, though they've selected to show a more familiar terrestrial planet but point out that one of unfamiliar (and perhaps unexpected) consequences of having two suns.

Courtesy NASA/JPL-Caltech.
Planet HD 40307g has twice the volume and eight times the mass of Earth! It may be rocky or an icy gas giant ...but it most certainly has one heck of a gravitational pull.

Courtesy NASA/JPL-Caltech.

Kepler-186f is an exciting find; it was the first Earth sized planet detected believed to be in the habitable zone around a star, where temperature conditions could allow liquid water. Unlike our sun, Kepler-186f orbits a much colder, redder star. So, if it were to have plant life using photosynthesis, they infer that, "ts photosynthesis could have been influenced by the star's red-wavelength photons, making for a color palette that's very different than the greens on Earth".

You can find and download the exoplanet posters here.

In other news, in 2015, I hope to bring you more magpie&whiskeyjack posts. I haven't disappeared, or retired, but 2014 posts were few and far between, because baby, as they say. I'm working on balancing my various artistic, scientific and other endeavours with being a new parent. I'll get there, and eventually manage to share all that I would like to!

Tuesday, October 14, 2014

Ada Lovelace Day 2014: The hard-earned fame of Marie Skłodowska-Curie

Today is the 6th annual international day of blogging to celebrate the achievements of women in technology, science and math, Ada Lovelace Day 2014 (ALD14). I'm sure you'll all recall, Ada, brilliant proto-software engineer, daughter of absentee father, the mad, bad, and dangerous to know, Lord Byron, she was able to describe and conceptualize software for Charles Babbage's computing engine, before the concepts of software, hardware, or even Babbage's own machine existed! She foresaw that computers would be useful for more than mere number-crunching. For this she is rightly recognized as visionary - at least by those of us who know who she was. She figured out how to compute Bernouilli numbers with a Babbage analytical engine. Tragically, she died at only 36. Today, in Ada's name, people around the world are blogging.

(Cross-posted to the minouette blog)

This year I'm participating in an entire group art show celebrating Ada Lovelace Day. The Art.Science.Gallery show Go Ahead and Do It: Portraits of Women in STEM culminates today! I will share all of my portraits of women in science (and links to where I tell their stories) below.

Marie Curie linocut glows in the dark
Marie Skłodowska-Curie, linocut with glow-in-the-dark ink by Ele Willoughby, 2014

In previous years, I've specifically avoided writing about Marie Curie because she is often the one historical figure people can name. I don't like to do the obvious thing and particularly want to highlight the under appreciated heroines of science. However the result is that her truly remarkable achievements haven't been celebrated here, just because of her fame. So, with a collection of portraits and stories written on the less well known, today I'll write about the well-known and why she in fact deserves her fame.

Marie Skłodowska-Curie (7 November 1867 – 4 July 1934), Polish-born, naturalized-French physicist and chemist, as the first woman to win a Nobel prize, the only woman to ever win TWO Nobel prizes, and the only person ever to win in two different sciences: physics and chemistry! She was also the first female professor at the University of Paris, and in 1995 became the first woman to be entombed on her own merits in the Panthéon in Paris. Born Maria Salomea Skłodowska in Warsaw, she studied secretly at the Floating University there before moving to Paris where she earned higher scientific degrees, met her PhD supervisor and future husband Pierre.

She was one of the pioneers who helped explain radioactivity, a term she coined. She was the one who first developed a means of isolating radioacitve isotopes and discovered not one, but two new elements: polonium (named for her native country) and radium. She also pioneered radioactive medicine, proposing the treatment of tumors with radioactivity. She founded medical research centres, the Curie Institutes in Paris and Warsaw which are still active today. She created the first field radiology centres during World War I. Each one of these achievements alone would warrant being memorialized in the annals of science and medicine; she did all of these things. She died in 1934 from aplastic anemia brought on by exposure to radiation, including carrying test tubes of radium in her pockets during research and her World War I service in her mobile X-ray units.

Her pioneering work explaining radioactivity earned her the 1903 Nobel Prize in Physics with her husband Pierre Curie and with physicist Henri Becquerel. At first, the Committee intended to honour only Pierre and Becquerel, but Swedish mathematician Magnus Gösta Mittag-Leffler, an advocate of women in science, alerted Pierre to the situation. (You may recall that it was the same man who helped Sofia Kovalevski secure a University position in Stockholm and that she collaborated on works of literature and had what was called a "romantic friendship" with his sister Duchess Anne-Charlotte Edgren-Leffler).  After Pierre's complaint, Marie's name was added to the nomination. The 1911 Nobel Prize in Chemistry was awarded to her "in recognition of her services to the advancement of chemistry by the discovery of the elements radium and polonium, by the isolation of radium and the study of the nature and compounds of this remarkable element."

Her life and legacy are truly extraordinary!

Marie Skłodowska-Curie, linocut with glow-in-the-dark ink show in the light and dark by Ele Willoughby, 2014

Not only was her work original and providing revolutionary insight on the theoretical side at the time, but the sheer heroic dedication and labour involved in her experimental work cannot be overstated. Having recognized that pitchblende ore must contain multiple elements which were giving off radiation, she and Pierre were able to show in 1898 that two new elements Polonium and Radium were needed to explain their observations. They then sought to actually isolate these elements. From a ton of pitchblende, she separated one-tenth of a gram of radium chloride in 1902. In 1910 Marie Curie isolated pure radium metal - a full 12 years after she and Pierre published their preliminary evidence for its existence. This involved working in a shed, meticulously separating the radioactive material from the inert and then dividing the radioactive material into its various sources for many years - all the while raising their young daughter when not at the lab.

Both of the elements she discovered are radioactive, meaning that they spontaneously give off radiation. All of the isotopes of polonium emit alpha particles, but Polonium-210 will emit a blue glow which is caused by excitation of surrounding air. Radium emits alpha, beta and gamma particles - that is 2 protons and 2 neutrons, electrons as well as x-rays. Thus, I've shown her sample surrounded by the symbols of these particles: the straight and wiggly lined arrows for the massive particles and high-energy light photons or gamma rays respectively, and made the sample with glow-in-the-dark ink. While the materials she discovered and worked with would have glowed due to radioactivity, never fear... these prints glow due to phosphorescence - a different process which is not dangerous. The ink will absorb UV light (for instance, from sunlight) and re-emit it in the dark.

The linocut is printed on Japanese kozo paper 9.25" by 12.5" (23.5 cm by 32 cm) in an edition of eight.

You can also find my complete set of women in STEM portraits here.

Monday, October 13, 2014

Music about Data

Gafurius's Practica musice, 1496 showing Apollo,
the Muses, the planetary spheres and musical ratios.
Science and music, like other arts, have a longstanding, close connection. Music can be described in terms of physics; notes translate to waveforms at a certain frequency, or equivalently certain pitch. Acoustics, tempo, rhythm, tones and overtones, harmonies and more can be explained in terms of physics. We can likewise discuss our physical world in terms of music.

In ancient Greece, Pythagoras and his followers placed a mystical meaning on his discovery of the mathematical underpinnings of music; he found that the length of a plucked string determined its pitch and that   simple (rational) ratios of a given length produced harmonies. They turned this idea on its head and apparently concluded that other fundamental patterns in nature were due not so much to mathematics, but that there was a musical underpinning to the known universe. Hence, the idea of the 'music of the spheres' and the hypothesis that planetary motions obeyed mathematical equations corresponding to musical notes and that the whole solar system together played its own symphony.

Kepler's musical notation for planetary motion and the range of sound
he ascribed to Saturn, Jupiter, Mars, Earth, Venus and Mercury
The idea was so persistent that when Johannes Kepler (1571- 1630) was developing the best model of our solar system to fit the beautiful dataset gathered by his mentor Tycho Brahe (1546-1601), one of the first notations he used was not mathematical, but musical. In fact, the idea was pervalent, and Kepler ended up embroiled in a priority dispute with Robert Fludd (1574-1637), whose own harmonic theory had been recently published in De Musica Mundana. While we tend to think of Kepler with his rational, more precise elliptical version of a Copernican heliocentric solar system as one of the first, modern scientists, he progressed from his musical notation, to a model based on a rather mystical appreciation for the Platonic Solids. That is, rather than explaning planetary motion in terms of his laws, as we know then today, he tried to make a model spacing of the planets from the sun based on the relative size of a nested spheres just large enough to coat a  series of special shapes called the Platonic Solids: the tetrahedron, the cube, the octahedron, the dodecahedron and icosahedron. He progressed from there, in his Harmonices Mundi (literally, harmonies of the worlds) to describe planetary motions in musical terms. He found that the difference between the maximum and minimum angular speeds of a planet in its orbit was very close to a harmonic proportion. For instance Earth's maximal angular speed relative to the sun varies by about a semitone (a ratio of 16:15), from mi to fa, between aphelion (the furthest point from the sun on its elliptical orbit) and perihelion (its closest point to the sun). In his words, "The Earth sings Mi, Fa, Mi", and he built up a choir of similarly singing planets. He found that all but one of the ratios of the maximum and minimum speeds of planets on neighboring orbits approximate musical harmonies within a margin of error of less than a diesis (a 25:24 interval) - to use a musical term.

Today we would attribute these patterns to the underlying mathematics of planetary motion, or the physics of music, rather than a music of the spheres underlying everything. Nonetheless this trick of Kepler's, of mapping observed patterns onto music, or of writing data as music still has its place. I recall a professor extolling the virtues of plotting data as it was collected, because we are wired to see patterns and would for instance, recognize a friend's face in a crowd with much greater ease than their phone number from a list of 7-digit numbers. The same can be said of sound; we are wired to recognize musical patterns. We can both appreciate the beauty of regular data mapped onto sounds we can hear, or use what we hear to recognize patterns.

Galileo Galilei (1564-1642) was the son of a famous lutenist, composer, and music theorist, which may have primed him to be observant of the measure of time, rhythm and periodic patterns. In Galileo's Daughter, author Dava Sobel argues that in the absence of accurate time pieces, music likely played an important role in his experiments. Many experiments involved timing repeated observations as precisely as possible and it is likely that he may have used song as his yardstick of time.

A couple of contemporary examples of expressing experimental data musically have been in the news of late.

The European CERN particle physics lab in Switzerland celebrated its 60th birthday with this delightful composition by physicist and musician Domenico Vicinanza, which turns data from four detectors at the Large Hadron Collider into LHChamber Music. Performed by CERN scientists and engineers, the result is surprisingly musical, like Baroque chamber music. Vicinanza has 'sonified' data before (including the satelitte Voyager I's magnetometer data), employing an algorithm to assign a musical note to each measurement created by experiments, so that the same data is presented as a musical score, much like Kepler did.

Sonifying data also allows scientists to hear patterns, to cope with massive datasets and find complexity which may otherwise have escaped them. Above, cicada calls are replaced with notes. The University of Uppsala team explains their sonification and visualization of the data:
The circles represent recording stations in the Australian bush that pick up the calls of cicadas. The intensity of the circle’s colour and its size is proportional to volume of sound in that area of the forest at that time (the videos is 15 x real time).
They could also add the sound of the cicadas themselves (speed up 15 times), but in the words of researcher James Herbert-Read, "that would be horrific". Instead they decided to translate cicada calls into music.
Each one of the four different coloured block of recorders also plays a different chord (we chose the standard I–V–vi–IV progression in the key of C major). By doing this, you can now not only see, but hear when cicadas in different areas of the forest start to sing, when other cease singing, and listen to the additive effect of all individuals singing together across large swathes of the forest.
The video is the cicada 'morning chorus' beginning at 5:30 am when light strikes the right hand side of the area shown, where the  first cicadas call. You see and hear other cicadas join, the early oscillations in volume and then the crescendo to full volume for the remainder of the chorus.

Locals had noted waves of cicada song moving through the forest and the researchers wanted whether they could prove the cicadas were in fact synchronized. They found quantifiable waves did in fact move through the forest. Though, they theorize that this is an emergent pattern, where each cicada follows his own rules and does not consciously try to synchronize with his neighbours.

Wednesday, August 6, 2014

Earth Sci Animation

This is a very simple post, but I really must share this great little animation. I am after all, a geophysicist by training, and this elegant animation “Everything You Need to Know About Planet Earth” by Munich-based Kurzgesagt, covers much of a first year physics of the Earth course in a lucid, fun, succinct way, with a great minimalist aesthetic, and a few extra dinosaurs.

Their rapid summary of plate tectonics does leave out mid-ocean ridges, transform faults, collision zones and more... but in fairness, an entire plate tectonics future video is promised. Way to go Kurzgesagt!

(via Laughing Squid)

Monday, August 4, 2014

Illustration/Math Venn Diagram

Even those who do not happen to revel in mathematics, know a little set theory - or least one of its useful visual tools: the Venn diagram. Today would be the 180th birthday of English philosopher and logician John Venn (4 August 1834 – 4 April 1923) remembered for the eponymous diagrams. Somehow by making a way to visualize sets and their intersections, he created a mathematical tool beloved of illustrators and graphic designers. (It's the subject of today's Google doodle). This sort of math one can "see" has made it into - dare I say - a large set of fun and fabulous illustrations. I thought I'd gather some for his birthday.

I love this hilarious example by Tenso Graphics:  

'Math' by Tenso Graphics available here

The diagrams are so recognizable, people even take liberties with the concept and we still understand, say that moustaches are the intersection of shaved areas with facial hair:

Venn diagram of facial hair by Tim Easley
 Or this interesting one:
one of a series of Venn diagrams by Satchel And Sage
Though sometimes they are quite literal, as in these Venn diagrams in the 'light theory' pillow:

Light theory pillow by dirtsastudio
But, I think this one is my all time favorite,

by Elise Towle Snow of Argyle Whale


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