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Nature by Numbers March 31, 2010

Posted by isotopeeffect in Biology, Math.
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Nature by Numbers from Cristóbal Vila on Vimeo.

The math behind the movie – the Fibonacci sequence, the Golden Ratio, Voronoi tilings, Delaunay triangulation.

For about 1100 pages on similar topics, see On Growth and Form, written in 1945 (2nd edition) by D’Arcy Wentworth Thompson, a pioneering work in mathematical biology. The color PDF is a (free) 75 MB download.

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This Will Change Everything March 4, 2010

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This Will Change Everything is the title of a book (subtitle: Ideas That Will Shape The Future) edited, or perhaps assembled would be a better word, by John Brockman of the Edge Foundation. Brockman posed the question “What game-changing scientific ideas and developments do you expect to live to see?” to over 100 high-profile individuals drawn from fields including physics, biology, psychology, philosophy, information science, writing, and music. The book is a compilation of their responses, ranging from the gnomic (“Discovering that someone from the future has already come to visit us,” is the complete response of Stefano Boeri) to the fairly short (three pages being about the longest entry). It’s a perfect book to take along on spring break. But is it any good?

Two of the pieces (The Use of Nuclear Weapons against a Civilian Population by Lawrence Krauss and Adopting Rationality and Sustainability by Patrick Bateson) open with the same quotation, by Albert Einstein: “The release of atom power has changed everything except our way of thinking.” This proves, perhaps, that that both authors are fans of Einstein for whom the phrase “change everything” rang a bell, or perhaps that both are adept at Googling. It also serves as evidence that Einstein was good not only for explanations of relativity, the photoelectric effect, Brownian motion, and mass-energy equivalence (all of this in 1905, his annus mirabilis), but could also come up with witty epigrams to rival Woody Allen’s “My one regret in life is that I am not someone else.”

The titles of the pieces could be the names of short stories by J. G. Ballard. Examples:

The Robotic Moment

Breaking the Species Barrier

Avoiding Doomsday

The Ebb of Memory

Wisdom Reborn

The Reality of Time

The Slow-Motion Revolution

Perhaps unsurprisingly given the premise, many of the pieces do indeed read a little bit like outlines for science fiction stories.

There is some rough grouping based on content: sudden climate change, new energy sources, nuclear accidents, the interface between man and computer, synthetic life, the future of reading and learning. Some of the pieces are plausible, some less so. Some are startlingly insightful and intellectually stimulating; some, not so much.

The topic I found most interesting, curiously enough, is a biological one, represented in two pieces, one by Robert Shapiro (a chemist) and one by Paul Davies (a physicist). Davies’ piece (Shadow Biosphere) is the more striking. The “tree of life” present on Earth today is understood to consist of a single set of interrelated species all sharing a single genetic code and having a common origin. BUT… at the same time, almost all living things on Earth are microbes, and only a tiny fraction of microbial life has been studied to date. It is possible that there was a second, or even a third, origin of life, and that we share the planet with the products of this other genesis, a “shadow biosphere”. These micro-organisms would be extremely hard to detect, because detection and identification methods have been developed to study life “as we know it”. Wild speculation, perhaps, but thought-provoking, and experimentally-testable (if you can get the grant funding).

Supermassive Black Hole March 3, 2010

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Not the track by Muse, but the object at the center of our galaxy, in the region known as Sgr A* (pronounced “Sagittarius A-star”).

Here it is in action:

What you see in this video clip are the trajectories of stars in the vicinity of Sgr A*, plotted from observations over a period of about 15 years. (You can see the date updating in the top left-hand corner.) This is very close to the orbital period of the star S0-2, which can be seen describing an almost complete ellipse during the period of the observations. At its closest approach, S0-2 is 17 light hours from the black hole itself, and reaches a velocity of about four percent of the speed of light. (Fast!)

Sgr A* (and therefore the galactic center) is about 25,000 light years away from us. The mass of the black hole is estimated to be about 4 million solar masses.

The observations were made by a team led by Andrea Ghez at UCLA, primarily using the Keck telescopes, situated near the summit of Mauna Kea in Hawai’i. The telescopes are not “just” telescopes, but are equipped with a suite of instruments including cameras and spectrometers sensitive to different regions of the electromagnetic spectrum. These particular measurements use NIRC, the Near InfraRed Camera, which is “so sensitive it could detect the equivalent of a single candle flame on the moon” (according to Wikipedia), using a wavelength of 2.2 μm. Specialized adaptive optics ensure that the measurements are made with the highest resolution possible (the so-called diffraction limit). The measurements are made in this spectral region rather than the visible region because visible light is strongly attenuated by interstellar dust.

If our galaxy, which is rather inactive (fortunately for us), has a black hole at its center, goes the reasoning, so do almost all galaxies. (Here’s what the Goddard Space Flight Center has to say about active galaxies.)

Links to PDF preprints of several papers are given on Prof. Ghez’s web site.

Maxwell on Molecules February 22, 2010

Posted by isotopeeffect in Chemistry, Physics.
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This post continues the art theme, at least momentarily.

While refreshing my memory about the works of the Pre-Raphaelite Brotherhood I stumbled upon the rather excellent Victorian Web, a web site gathering links on areas of interest from that era ranging from fine art through science, from religion through economics, a veritable liberal arts goldmine.

There is plenty of material on the site to recommend itself under the heading of science, but I was particularly struck by an essay by James Clerk Maxwell entitled “Molecules”, first published in Nature in 1873.

Maxwell opens with a reference to the ancient Greeks, by distinguishing the philosophy of the atomists, represented by Democritus, from that of Socrates’ teacher Anaxagoras (a somewhat less well-known – because “wrong” – philosophy called Homoiomereia). Neither philosophical stance counts as what we would now call science; both are essentially entirely speculative in nature. Anaxagoras’ perspective was that substances are homogeneous and thus can be subdivided indefinitely without losing their character, while that of the atomists was that a limit would be reached where matter can no longer be so subdivided, but has been reduced to its fundamental units, atoms, objects which (literally) cannot be cut.

Of course, for all the ingenuity of the ancient Greeks they had no concept of molecules (their idea of “elements” more closely resembling our modern idea of “states of matter”), so jumping to a more modern concept, Maxwell quickly defines the molecule as the simplest unit of a particular substance that retains the composition of the whole before moving on to his main arguments.

Maxwell’s overall goal in this essay is to introduce the public to recent research in the field of molecular science, areas of study that we would nowadays call statistical thermodynamics and the kinetic-molecular theory of gases.

The first part of Maxwell’s argument is the modern counterpart to the opinion of Lucretius that bodies are in ceaseless motion (on what we would now call the atomic scale), even when they appear to be at rest. Tracing a historical thread that runs through the “usual suspects” Boyle and Charles to Bernoulli, Clausius, Joule, and Boltzmann, not to mention Maxwell himself, Maxwell shows how once gas pressure is recognized as a product of atomic motion and collisions a theory can be built that allows us to calculate the speeds at which molecules move (“about seventeen miles per minute”), the average distance between molecules (“about the tenth part of the length of a wave of light”), and the number of collisions undergone per second (“hundreds of millions”).

The next section of the essay contrasts the “historical method”, in which the history of an individual is followed through time, with the “statistical method”, in which general results relating to groups or populations are obtained. This section is remarkable enough to quote at length:

“The equations of dynamics completely express the laws of the historical method as applied to matter, but the application of these equations implies a perfect knowledge of all the data. But the smallest portion of matter which we can subject to experiment consists of millions of molecules, not one of which ever becomes individually sensible to us. We cannot, therefore, ascertain the actual motion of any one of these molecules, so that we are obliged to abandon the strict historical method, and to adopt the statistical method of dealing with large groups of molecules.

“The data of the statistical method as applied to molecular science are the sums of large numbers of molecular quantities. In studying the relations between quantities of this kind, we meet with a new kind of regularity, the regularity of averages, which we can depend upon quite sufficiently for all practical purposes, but which can make no claim to that character of absolute precision which belongs to the laws of abstract dynamics.

“Thus molecular science teaches us that our experiments can never give us anything more than statistical information, and that no law deduced from them can pretend to absolute precision. But when we pass from the contemplation of our experiments to that of the molecules themselves, we leave the world of chance and change, and enter a region where everything is certain and immutable.

“The molecules are conformed to a constant type with a precision which is not to be found in the sensible properties of the bodies which they constitute. In the first place the mass of each individual molecule, and all its other properties, are absolutely unalterable. In the second place the properties of all molecules of the same kind are absolutely identical.”

Maxwell here points out the astonishing fact that molecules resemble one another in a manner very different from that in which, for example, apples or golf balls do; while the latter may be similar but for a nick or blemish, the former are (up to the point of being in different quantum states) completely identical in every respect.

The indistinguishability of atomic or molecular states has ramifications even Maxwell did not think of. In the world of quantum mechanics, the wavefunction of a system of particles must show a distinct symmetry with respect to the pairwise interchange of particle labels. For particles like electrons, for example, the requirement that the wavefunction be antisymmetric is known as the Pauli principle, which every chemistry student knows as the principle determining that an orbital can contain only two electrons. A slightly more elusive implication of the antisymmetry principle, however, is that if a helium atom is in the 1s2s state, we cannot say which of the two electrons is the 1s electron. In statistical thermodynamics, symmetry requirements impact which combinations of states can exist and lead to phenomena such as Bose-Einstein condensation (see here for NIST’s BEC site) and degeneracy pressure (the phenomenon that keeps white dwarf stars from collapsing).

Maxwell goes on to show that the identical nature of all molecules (or atoms) of a particular type is precisely that which allows us to use the methods of spectroscopy to make discoveries not only about samples in front of us in the laboratory but about any object in the universe from which light can be detected. Here’s Maxwell again:

“But in the heavens we discover by their light, and by their light alone, stars so distant from each other that no material thing can ever have passed from one to another, and yet this light, which is to us the sole evidence of the existence of these distant worlds, tells us also that each of them is built up of molecules of the same kinds as those which we find on earth. A molecule of hydrogen, for example, whether in Sirius or in Arcturus, executes its vibrations in precisely the same time.”

In this latter point, Maxwell is not quite right. Light from distant objects beyond our galaxy exhibits a redshift due to the velocity at which these objects are receding from us. (In their own reference frame, as Maxwell states, they emit radiation of the same frequency as molecules on Earth. ) There is an approximately linear correlation between recession velocity and distance which led Georges Lemaître to his theory that the universe that we now know evolved from a “primeval atom” (his term) in which all the mass-energy now present was compressed into a tiny volume, via a cosmic explosion now universally known as the Big Bang.

Quoting Maxwell again:

“Natural causes, as we know, are at work, which tend to modify, if they do not at length destroy, all the arrangements and dimensions of the earth and the whole solar system. But though in the course of ages catastrophes have occurred and may yet occur in the heavens, though ancient systems may be dissolved and new systems evolved out of their ruins, the molecules out of which these systems are built — the foundation stones of the material universe — remain unbroken and unworn.”

To revise Maxwell, our current understanding is that atoms (specifically, hydrogen atoms) did not exist until about 400,000 years after the Big Bang. Before that, there was too much energy present in the compact early universe for atoms to be stable, so any atoms formed would instantly ionize. Traveling further back in time, a few minutes after the Big Bang energy was so concentrated that protons and neutrons themselves could not exist; the tiny universe was an extremely hot “quark soup”. In the first microsecond after the Big Bang quarks themselves were not stable. An enhanced understanding of what happened in those first few instants after the Big Bang is a research goal of the Large Hadron Collider.

It is an interesting irony that in this essay Maxwell seems to so strongly espouse a “particulate” picture of the universe. Most physics students first meet Maxwell through his famous equations describing the behavior of electromagnetic fields. The modern descendents of Maxwell’s work are the various forms of quantum field theory that describe the universe in a manner in which “particles” are viewed as excited states of a quantum field, an entity that spreads throughout space. Perhaps the followers of Anaxagoras were not entirely wrong.

Photosynthesis and Quantum Coherence February 9, 2010

Posted by isotopeeffect in Biology, Chemistry, Physics.
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A recent paper in Nature by Gregory Engel and co-workers presents direct evidence from two-dimensional Fourier Transform electronic spectroscopy that quantum coherence plays a role in energy transport within the Fenna-Matthews-Olson bacteriochlorophyll complex. Popular accounts of the research appear in various venues such as Wired magazine and The Scientist.

So what does that mean?

Photosynthetic light-harvesting is an incredibly efficient process, which seems at odds with the great complexity of the chain of molecules involved. The “wire” along which the excitation energy signal travels is sensitive to the precise geometric relationship between orbitals on all the molecules in the chain between the light-harvesting antenna protein and the reaction center, which in turn is sensitive to thermal agitations at the operating temperature of the photosynthetic system.

Past work on attempting to understand these processes has focused on semiclassical models involving (classical) “hopping” of energy between individual excited (quantum) states. The new experiment is a laser “pump-probe” measurement using ultrafast (sub-picosecond) laser pulses to excite one part of the system and detect changes remote from the original excitation. The key finding is the existence of “quantum beats”, correlations in phase between the wavefunction on one part of the system and another separated from it by a distance of thousands of atoms. These are illustrated below.

So, what’s the significance of all this?

The “beats” imply that the energy transport is wavelike, in other words truly quantum-mechanical (or “coherent”). The quantum state enveloping the whole photosynthetic system allows energy transport to occur along a superposition of multiple pathways, ensuring that the energy reaches its destination efficiently, with some degree of protection from the randomizing effects of thermal jostling. The energy travels along all possible pathways, so whatever the circumstances it travels along the “best” pathway (as well as all the others).

This is a remarkable result given the large size of the photosynthetic system. Such quantum effects are not observed in the macroscopic world, where “decoherence” scrambles the phase of the wavefunction, considerably impairing our ability to be in two places at once.

Full disclosure: I was first alerted to this paper via the blog Cosmic Variance (direct link via image above), where you can also see video of Drew Brees throwing a football at an archery target with rather disturbing accuracy.

Early computers February 8, 2010

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What did early computers look like?

Well, they looked a bit like this.

From around the beginning of the eighteenth century, when laborious numerical calculations began to be a regular part of scientific activity particularly in fields such as navigation and astronomy, the need arose for a person or group of persons to carry out these calculations carefully and as far as possible without error. Over time, this became a respected and important job.

A recent book by David Alan Grier – whose grandmother was one of these “human computers” – documents this history.

Brute-force numerical solution of equations is required when an analytical solution is not possible. An example of such a case is the “three-body problem” in mechanics, in which the trajectories of a group of objects (such as planets interacting through gravitational forces) cannot be solved analytically if the number of objects is greater than two. Although Edmund Halley had already predicted (in 1705, using Newtonian calculus) the return of the comet named after him, a much more accurate calculation was carried out in 1757 by Clairaut, Lalande, and Lepaute, who broke the orbit down into a series of small steps and incorporated the comet’s gravitational interactions with the orbits of the then-known major planets Jupiter and Saturn. (The primary source of error in their calculations would have been the neglect of the gravitational effects of Uranus and Neptune, which were unknown at the time.) This is one of the earliest known examples of parallel computing, still used today to make large numerically complex problems tractable in a reasonable amount of time by distributing the effort over multiple “computational nodes”.

Initially the profession of “computer” was mainly the province of men, and largely closed to women (although Lepaute was female), but over time this situation gradually changed. The Harvard astronomer Edward Charles Pickering (known, for example, for the “Pickering series” due to ionized helium, first observed in the spectrum of the hot O-type star ζ Puppis) employed a group of computers known as “Pickering’s Harem”, one of whom, Henrietta Swan Leavitt, went on to discover the relationship between the period and luminosity of Cepheid variables, without which work Edwin Hubble would not have been able to find the linear relationship between galactic redshift and distance that led to the understanding that we live in an expanding universe.

The prevalence of women in Pickering’s group was most likely a consequence of Harvard’s pay scale at the time, in which women were remunerated at half the standard rate for men.

The last days of the human computer came at the time of the Manhattan Project, where the complex calculations involved in the design of the atomic bomb were mostly accomplished by hand (carried out by the scientists’ wives, an interesting window into the gender hierarchy of intellectual work at the time). The ever-puckish Richard Feynman, who was responsible for overseeing the laboratory of human computers and who with Nicholas Metropolis was charged with installation of the first electronic computers using IBM punch cards, staged a showdown between human computers and punchcard-programmed machines. For two days the humans held their own; on the third day, the humans began to slow down, and the tireless machines pulled ahead.

There is an intriguing postscript to the era of human computers. The first six people charged with setting up programs on the ENIAC, one of the world’s first general-purpose computers (that is, not set up to solve a single, specific problem), were drawn from the job marketplace of human computers, and thus the world’s first professional computer programmers were women, specifically Kay McNulty, Betty Snyder, Marlyn Wescoff, Ruth Lichterman, Betty Jean Jennings, and Fran Bilas.

There’s a review of the Grier book here, and a very nice Scientific American article on the subject of the origins of computing here.

Martian wallpaper January 22, 2010

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Linear dune fields on the floor of crater Noachis Terra, in the Hellas impact basin.

(From the HIgh Resolution Imaging Science Experiment, Lunar and Planetary Laboratory, University of Arizona.)

RMM

Critical Point of Water January 22, 2010

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For those who missed it in CHE 305, here’s the critical point of water again:

The “DECLIC high temperature insert” mentioned at the beginning of the video is a DEvice for the study of Critical LIquids and Crystallization designed for use in the study of phase transitions in microgravity aboard the ISS.

More here, here, and here.

RMM