Bionumbers

One feature of the 4th edition of Intermediate Physics for Medicine and Biology that distinguishes it from many other medical or biological textbooks is its focus on analyzing biomedical topics quantitatively. This point of view is also promoted at the BIONUMB3R5 (bionumbers) website, established by researchers in the systems biology department at Harvard. There is also a BIONUMB3R5 wiki where many researchers are coming together to provide new insights into key numbers in biology.

I particularly like the “Bionumber of the Month” feature. The March 2010 entry (“What are the Time Scales for Diffusion in Cells”) could easily be made into a homework problem for Chapter 4 of Intermediate Physics for Medicine and Biology. The January 2010 entry (“What is Faster, Transcription or Translation?”) is fascinating.

Transcription, the synthesis of mRNA from DNA, and translation, the synthesis of protein from mRNA, are the main pillars of the central dogma of molecular biology. How do the speeds of these two processes compare? …

Transcription of RNA by RNA polymerase in E. coli cells proceeds at a maximal speed of about 40–80 bp/sec… Translation by the ribosome in E. coli proceeds at a maximal speed of about 20 aa/sec… Interestingly, since every 3 base pairs code for one amino acid, the rates of the two processes are quite similar…

The “collection of fundamental numbers in molecular biology” found at the bionumbers website has the same tone as the first section of Chapter 1 in Intermediate Physics for Medicine and Biology, in which Russ Hobbie and I look at the relative size of biological objects. The collection contains this gem: “concentration of 1 nM in a cell the volume of E. coli is ~ 1 molecule/cell.”

The bionumbers website arose from an article by Rob Phillips and Ron Milo in the Proceedings of the National Academy of Sciences (Volume 106, pages 21465–21471, 2009), “A Feeling for the Numbers in Biology.” The abstract of their paper is given below:

Although the quantitative description of biological systems has been going on for centuries, recent advances in the measurement of phenomena ranging from metabolism to gene expression to signal transduction have resulted in a new emphasis on biological numeracy. This article describes the confluence of two different approaches to biological numbers. First, an impressive array of quantitative measurements make it possible to develop intuition about biological numbers ranging from how many gigatons of atmospheric carbon are fixed every year in the process of photosynthesis to the number of membrane transporters needed to provide sugars to rapidly dividing Escherichia coli cells. As a result of the vast array of such quantitative data, the BioNumbers web site has recently been developed as a repository for biology by the numbers. Second, a complementary and powerful tradition of numerical estimates familiar from the physical sciences and canonized in the so-called “Fermi problems” calls for efforts to estimate key biological quantities on the basis of a few foundational facts and simple ideas from physics and chemistry. In this article, we describe these two approaches and illustrate their synergism in several particularly appealing case studies. These case studies reveal the impact that an emphasis on numbers can have on important biological questions.

Russ and I introduce similar order-of-magnitude estimates (Fermi problems) in Chapter 1 of our book (for example, see homework problems 1–4, which are new in the 4th edition). One of my favorite Fermi problems, which I first encountered in the book Air and Water by Mark Denny, is to calculate the concentration of oxygen molecules in blood and in air, and compare them. Not too surprisingly, they are nearly the same (about 8 mM). I suspect the bionumbers folks would enjoy Air and Water. (I hope they would enjoy Intermediate Physics for Medicine and Biology, too.)

For those of you who find all of this interesting but prefer video over text, see the bionumbers video on YouTube.

Bionumbers: The data base of useful biological numbers. 

https://www.youtube.com/embed/psE0H1ejxKE

Seeing the Natural World with a Physicist’s Lens

One theme of this blog—and indeed, one theme of the 4^th edition of Intermediate Physics for Medicine and Biology—is the role of physics in the biological sciences. So imagine my delight when Russ Hobbie sent me a similarly themed article from the November 1 issue of the New York Times (a publication that, alas, has more readers than does my blog). Natalie Angier, who studied for two years at that little college down the road in Ann Arbor, wrote an article titled “Seeing the Natural World With a Physicist’s Lens.” Its thesis is that many biological systems have evolved to perfection, in the sense that physical laws don’t let them get any better. Angier writes

Yet for all these apparent flaws, the basic building blocks of human eyesight turn out to be practically perfect. Scientists have learned that the fundamental units of vision, the photoreceptor cells that carpet the retinal tissue of the eye and respond to light, are not just good or great or phabulous at their job. They are not merely exceptionally impressive by the standards of biology, with whatever slop and wiggle room the animate category implies. Photoreceptors operate at the outermost boundary allowed by the laws of physics, which means they are as good as they can be, period. Each one is designed to detect and respond to single photons of light—the smallest possible packages in which light comes wrapped…

Photoreceptors exemplify the principle of optimization, an idea, gaining ever wider traction among researchers, that certain key features of the natural world have been honed by evolution to the highest possible peaks of performance, the legal limits of what Newton, Maxwell, Pauli, Planck et Albert will allow. Scientists have identified and mathematically anatomized an array of cases where optimization has left its fastidious mark… In each instance, biophysicists have calculated, the system couldn’t get faster, more sensitive or more efficient without first relocating to an alternate universe with alternate physical constants.

Angier has written a lot of articles for the NYT, and has published several books, that will be of interest to readers of Intermediate Physics for Medicine and Biology. Enjoy!

Iatrogenic Problems in End-Stage Renal Failure

In Section 5.7 of the 4th edition of Intermediate Physics for Medicine and Biology, where Russ Hobbie and I discuss the artificial kidney, we say

The artificial kidney provides an example of the use of the transport equations to solve an engineering problem… The reader should also be aware that this “high-technology” solution to the problem of chronic renal disease is not an entirely satisfactory one. It is expensive and uncomfortable and leads to degenerative changes in the skeleton and severe atherosclerosis…

The alternative treatment, a transplant, has it own problems, related primarily to the immunosuppressive therapy. Anyone who is going to be involved in biomedical engineering or in the treatment of patients with chronic disease should read the account by Calland (1972), a physician with chronic renal failure who had both chronic dialysis and several transplants.

The paper by Chad Calland, in the New England Journal of Medicine (“Iatrogenic Problems in End-Stage Renal Failure,” Volume 287, Pages 334–336, 1972), was published on the same day that Calland took his own life. Wikipedia defines “iatrogenic” as “inadvertent adverse effects or complications caused by or resulting from medical treatment or advice.” It is a problem we must constantly be aware of as we seek to improve medical care through technology. Calland wrote

The physician is more often a voyeur than a partaker in human suffering. I am a physician who has undergone chronic renal failure, dialysis and multiple transplants. As a physician-partaker, I am distressed by the controversial dialogue that separates the nephrologist from the transplant surgeon, so that, in the end, it is the patient who is given short shrift. I have observed that both nephrologist and transplant surgeon work alone in their own separate fields, and that the patient becomes lost in a morass of professional role playing and physician self-justification. As legitimate as their altruistic but differing opinions may be, the nephrologist and the transplant surgeon must work together for the patient, so that therapy is tailored to suit the individual patient, his circumstances, his needs and the quality of his life.

Glimpses of Creatures in Their Physical Worlds

Glimpses of Creatures
in their Physical Worlds,
by Steven Vogel.

I am a loyal member of Sigma Xi, the Scientific Research Society, and am a regular reader of its marvelous magazine American Scientist. One of the best parts of this bimonthly periodical is its book reviews. In the November-December 2010 issue of American Scientist, Mark Denny (author of Air and Water) reviews the new book by Steven Vogel: Glimpses of Creatures in Their Physical Worlds (Princeton University Press, 2009). Both Denny and Vogel appear in the 4th edition of Intermediate Physics for Medicine and Biology. Denny writes

Vogel’s contributions to biomechanics have had two admirable objectives. In Life in Moving Fluids (1981), Life’s Devices (1988), Vital Circuits (1992), Prime Mover (2001) and Comparative Biomechanics (2003), his goal is to explain the mechanics of biology to a general audience. If you want to know how fish swim, fleas jump and bats fly, or why hardening of your arteries is a bad thing, them dip into these sources; you will come away both informed and amused…

All too often, biologists observe only what they are prepared to see. Vogel’s second objective is therefore to expand their perspectives by conjuring up and carefully analyzing systems that might be… For example, dogs don’t sweat as humans do. Instead, they pant, evaporating water from their respirator tracts and expelling the resulting warm, moist air with each breath. But panting requires the repeated contraction of chest muscles, which adds to the heat the animal desires to loss. Could there be a better way?...

To find out, read Glimpses of Creatures in Their Physical Worlds. Here, as in Cats’ Paws and Catapults (1998), Vogel takes a decidedly nontraditional look at biology, unleashing his talent for unbridled speculation. The 12 chapters of Glimpses, which began as a series of essays in the Journal of Biosciences, have been revised and updated. They cover topics that range from the ballistics of seeds (plants use both catapults and cannons to launch their propagules) to the breathing apparatus of diving spiders (tiny hairs on the body take advantage of surface tension to maintain an airspace into which oxygen can flow), with stops along the way to explore the efficiency of man-made and natural pumps, the twist-to-bend ratios of daffodils in the breeze, and the physics of cow tipping…

If what you desire in a readable science book is food for thought, Glimpses of Creatures in Their Physical Worlds provides a feast. Biologists, engineers and physicists—indeed, anyone with curiosity about the natural world—will revel in this smorgasbord of biomechanical ideas.

I’ll put reading Glimpses on my to do list, maybe during the semester break.

If you get a copy of American Scientist so you can read Denny’s entire review, don’t miss another review in the same issue about a new edition (with notes and commentary) of the classic Flatland by Edwin Abbott. Flatland is a favorite of mine, and I agree with Colin Adams who says in his review: “In the pantheon of popular books about mathematics, one would be hard-pressed to name another that has lasted so long in popularity or had such a dramatic impact.”

Michael Faraday, Biological Physicist?

Last week in this blog I discussed the greatest physicist of all time, Isaac Newton. However, if we narrow consideration to only experimental physicists, I would argue that the greatest is Michael Faraday (with apologies to Ernest Rutherford, who is a close second). In Section 8.6 of the 4th edition of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss Faraday’s greatest discovery: electromagnetic induction.

In 1831 Faraday discovered that a changing magnetic field causes an electric current to flow in a circuit. It does not matter whether the magnetic field is from a permanent magnet moving with respect to the circuit or from the changing current in another circuit. The results of many experiments can be summarized in the Faraday induction law.

I have always admired the 19th century Victorian physicists, such as Faraday, Maxwell and Kelvin. Michael Faraday, in particular, is a hero of mine (it is good to have heroes; they help you stay inspired when the mundane chores of life distract you). I had the pleasure of quoting from Faraday’s Experimental Researches in Electricity in an editorial I wrote in 2005 for the journal Heart Rhythm:  “Michael Faraday and Painless Defibrillation.” I tried to get a picture of Faraday included as part of the editorial, but alas the journal editor removed it. The article described a heart defibrillator having a design that included a type of Faraday cage.

Michael Faraday, arguably the greatest experimental physicist who ever lived, first demonstrated the shielding effect of a hollow conductor in 1836 by building a 12 ft × 12 ft × 12 ft cubic chamber out of metal. We would now call it a “Faraday cage.”

“I went into the cube and lived in it, and using lighted candles, electrometers, and all other tests of electrical states, I could not find the least influence upon them, or indication of anything particular given by them, though all the time the outside of the cube was powerfully charged, and large sparks and brushes were darting off from every part of its outer surface.” [Faraday M. Experimental Researches in Electricity. Paragraph 1174. Reprinted in: Hutchins RM, editor. Great Books of the Western World, Volume 45. Encyclopedia Britannica, Chicago, 1952.]

Faraday cages are used to shield sensitive electronic equipment. The metal skin of an airplane, acting as a Faraday cage, protects passengers from injury by lightning. Researchers perform electrophysiology experiments inside a Faraday cage to prevent external noise from contaminating the data. A rather spectacular example of shielding can be seen in the Boston Museum of Science, where a van de Graaff generator of over one million volts produces a dramatic display of lightning, while the operator stands nearby—safe inside a Faraday cage.

Why this little physics lesson? In this issue of Heart Rhythm, Jayam et al. [Jayam V, Zviman M, Jayanti V, Roguin A, Halperin H, Berger RD. “Internal Defibrillation with Minimal Skeletal Muscle Activation: A New Paradigm Toward Painless Defibrillation,” Heart Rhythm, Volume 2, Pages 1108–1113, 2005] describe a new electrode system for internal defibrillation that eliminates the skeletal muscle activation and pain associated with a shock. The central feature of their design is a Faraday cage: a conducting sock fitted over the epicardial surface of the heart…

In Section 8.7, Russ and I describe what may be the most important biomedical application of Faraday’s work: magnetic stimulation.

Since a changing magnetic field generates an induced electric field, it is possible to stimulate nerve or muscle cells without using electrodes. The advantage is that for a given induced current deep within the brain, the currents in the scalp that are induced by the magnetic field are far less than the currents that would be required for electrical stimulation. Therefore transcranial magnetic stimulation (TMS) is relatively painless. Magnetic stimulation can be used to diagnose central nervous system diseases that slow the conduction velocity in motor nerves without changing the conduction velocity in sensory nerves [Hallett and Cohen (1989)]. It could be used to monitor motor nerves during spinal cord surgery, and to map motor brain function. Because TMS is noninvasive and nearly painless, it can be used to study learning and plasticity (changes in brain organization over time). Recently, researchers have suggested that repetitive TMS might be useful for treating depression and other mood disorders.

I worked on magnetic stimulation for many years while at the National Institutes of Health in the 1990s. It was a pleasure to explore an application of Faraday induction; it is my kind of biological physics.

Faraday’s name can be found in a few other places in our book. It first appears in Chapter 3, when the Faraday constant is defined: F = 96,485 Coulombs per mole. It also appears in an abbreviated form in the unit of capacitance: a farad (F).

I suppose by now the reader realizes that I like Mike. But is he a biological physicist? Doubters might want to look at another physics blog: http://skullsinthestars.com/2010/05/15/shocking-michael-faraday-does-biology-1839. Faraday apparently did studies on the electrodynamics of electric fish. So, yes, I claim him as a biological physicist, and the question mark in the title of this blog post is unnecessary.

Isaac Newton, Biological Physicist?

Arguably the greatest physicist of all time (and probably the greatest scientist of all time) is Isaac Newton (1643–1727). Newton is so famous that the English put him on their one pound note (although I gather nowadays they use a coin instead of paper currency for one pound). Given Newton’s influence, it is fair to ask what his role is in the 4th edition of Intermediate Physics for Medicine and Biology. One way Newton (along with Leibniz) contributes to nearly every page of our book is through the invention of calculus (or, as I prefer, “the calculus”). Russ Hobbie states in the preface of our book that “calculus is used without apology.”

When I search the book for Newton’s name, I find quite a few references to Newton’s laws of motion, and in particular the second law, F = ma. Newton presented his three laws in his masterpiece, the Principia (1687). (Few people have read the Principia, including me, but a good place to learn about it is the book Newton’s Principia for the Common Reader by Subrahmanyan Chandrasekhar) Of course, the unit of force is the newton, so his name pops up often in that context. The only place where we talk about Newton the man is very briefly in the context of light.

A controversy over the nature of light existed for centuries. In the seventeenth century, Sir Isaac Newton explained many properties of light with a particle model. In the early nineteenth century, Thomas Young performed some interference experiments that could be explained only by assuming that light is a wave. By the end of the nineteenth century, nearly all known properties of light, including many of its interactions with matter, could be explained by assuming that light consists of an electromagnetic wave.

Newton’s name also arises when talking about Newtonian fluids (Chapter 1): a fluid in which the shear stress is proportional to the velocity gradient. Not all fluids are Newtonian, with blood being one example. Newton appears again when discussing Newton’s law of cooling (Chapter 3, Problem 45).

Some of Newton’s greatest discoveries are not addressed in our book. For instance, Newton’s universal law of gravity is never mentioned. Except for a few intrepid astronauts, animals live at the surface of the earth where gravity is simply a constant downward force and Newton’s inverse square law is not relevant. I suppose tides influence animals and plants that live near the ocean shore, and the behavior of tides is a classic application of Newtonian gravity, but we never discuss tides in our book. (By the way, harkening back to my vacation in France last summer, the tides at Mont Saint Michel are fascinating to watch. I really must plan a trip to the Bay of Fundy next.) Newton, in his book Optiks, made important contributions to our understanding of color, but Russ and I introduce that subject without referring to him. We don’t discuss telescopes in our book, and thus miss a chance to honor Newton for his invention of the reflecting telescope.

Never at Rest:
A Biography of Isaac Newton,
by Richard Westfall.

A wonderful biography of Newton is Never at Rest, by Richard Westfall. I must admit, Newton is a strange man. His argument with Leibniz about the invention of calculus is perhaps the classic example of an ugly priority dispute. He does not seem to be particularly kind or generous, despite his undeniable genius.

Was Newton a biological physicist? Well, that may be a stretch, but Colin Pennycuick has written a book titled Newton Rules Biology, so we cannot deny his influence. I would say that Newton’s contributions are so widespread and fundamental that they play an important role in all subfields of physics.

Ultraviolet Light Causes Skin Cancer

The New England Journal of Medicine is arguably the premier medical journal in the world. Russ Hobbie is a regular reader, and he sometimes calls my attention to articles that are closely related to topics in the 4th edition of Intermediate Physics for Medicine and Biology. The September 2, 2010 issue of the NEJM contains the article “Indoor Tanning—Science, Behavior, and Policy” (Volume 363, Pages 901–903), by David Fisher and William James. The article begins

The concern arises from increases in the incidence of melanoma and its related mortality. In the United States, the incidence of melanoma is increasing more rapidly than that of any other cancer. From 1992 through 2004, there was a particularly alarming trend in new melanoma diagnoses among girls and women between the ages of 15 and 39. Data from the National Cancer Institute’s Surveillance, Epidemiology, and End Results Registry show an estimated annual increase of 2.7% in this group. Researchers suspect that the increase results at least partially from the expanded use of tanning beds.

Russ and I discuss ultraviolet light in Section 14.9 of Intermediate Physics for Medicine and Biology. In particular, Section 14.9.4 is titled Ultraviolet Light Causes Skin Cancer.

Chronic exposure to ultraviolet radiation causes premature aging of the skin. The skin becomes leathery and wrinkled and loses elasticity. The characteristics of photoaged skin are quite different from skin with normal aging [Kligman (1989)]. UVA radiation was once thought to be harmless. We now understand that UVA radiation contributes substantially to premature skin aging because it penetrates into the dermis. There has been at least one report of skin cancer associated with purely UVA radiation from a cosmetic tanning bed [Lever and Lawrence (1995)]. This can be understood in the context of studies showing that both UVA and UVB suppress the body’s immune system, and that this immunosuppression plays a major role in cancer caused by ultraviolet light [Kripke (2003); Moyal and Fourtanier (2002)]. There are three types of skin cancer. Basal-cell carcinoma (BCC) is most common, followed by squamous cell carcinoma (SCC). These are together called nonmelanoma or nonmelanocytic skin cancer (NMSC). Basal-cell carcinomas can be quite invasive (Fig. 16.44) but rarely metastasize or spread to distant organs. Squamous-cell carcinomas are more prone to metastasis. Melanomas are much more aggressive and frequently metastasize.

The Skin Cancer Foundation advocates vigorously for the reduction of indoor tanning, and the American Association for Cancer Research has also spoken out against tanning beds. The problem seems to be growing.

Fisher and James conclude their article

An estimated six of every seven melanomas are now being cured, thanks to early detection, but the U.S. Preventive Services Task Force does not recommend skin-cancer screening, since the evidence for its benefit has not been validated in large, prospective, randomized trials. Meanwhile, a number of promising new drugs for metastatic melanoma are progressing slowly through clinical trials to satisfy the FDA’s stringent safety and efficacy criteria—requirements that, remarkably, have not been applied to indoor tanning devices. Relatively few human cancers are tightly linked to a known environmental carcinogen. Given the mechanistic and epidemiologic data, we believe that regulation of this industry may offer one of the most profound cancer-prevention opportunities of our time.

Adrien-Marie Legendre

On page 181 of the 4th edition of Intermediate Physics for Medicine and Biology, Russ Hobbie and I introduce Legendre polynomials. The Legendre polynomial P₂(cos(θ)) arises naturally when calculating the extracellular potential in a volume conductor at a position far from an active nerve axon. We include the footnote “You can learn more about Legendre polynomials in texts on differential equations or, for example, in Harris and Stocker (1998).” On page 184, we list the first four Legendre polynomials (and have another footnote referring to Harris and Stocker). Any physics student should memorize at least the first three of these polynomials:

P₀(x) = 1

P₁(x) = x

P₂(x) = (3 x² – 1)/2 .

Legendre polynomials have many interesting properties. They are a solution of Legendre’s differential equation

(1–x²) d²P_n/dx² – 2 x dP_n/dx + n(n+1) P_n = 0 .

You can calculate any Legendre polynomial using Rodrigues formula

P_n(x) = 1/(2ⁿ n!) dⁿ((x²–1)ⁿ)/dxⁿ .

They form an orthogonal set of functions for x over the range from −1 to 1, which is rather too technical of a property to explain in this blog entry, but is very important.

The astute reader might note that Legendre’s differential equation is second order, so there should be two solutions. That is right, but the other solution—called a Legendre function of the second kind, Q_n—is rarely used, and tends to be poorly behaved at x = 1 and x = –1. For instance

Q₀(x) = ½ ln((1+x)/(1–x)) .

A definitive source for information about Legendre polynomials is the Handbook of Mathematical Functions, by Milton Abramowitz and Irene Stegun.

When do Legendre’s polynomials appear in physics? You often find them when working in spherical coordinates, especially when (to use an analogy with the earth) a function depends on latitude but not longitude (axisymmetry). For instance, the general axisymmetric solution to Laplace’s equation in spherical coordinates is a series of powers of the radius r multiplied by Legendre polynomials with x = cos(θ), where θ is measured from the z-axis (or, to use the earth analogy again, from the north pole). Take an introductory class in electricity and magnetism (from, say, the book by Griffiths), and you will use Legendre polynomials all the time.

Why do I bring up Legendre polynomials today? Regular readers of this blog may recall my recent obsession with all things French. Adrien-Marie Legendre (1752–1833) was a French mathematician. Details of his life are given in A Short Account of the History of Mathematics, by Rouse Ball.

Adrian Marie Legendre was born at Toulouse on September 18, 1752, and died at Paris on January 10, 1833. The leading events of his life are very simple and may be summed up briefly. He was educated at the Mazarin College in Paris, appointed professor at the military school in Paris in 1777, was a member of the Anglo-French commission of 1787 to connect Greenwich and Paris geodetically; served on several of the public commissions from 1792 to 1810; was made a professor at the Normal school in 1795; and subsequently held a few minor government appointments. The influence of Laplace was steadily exerted against his obtaining office or public recognition, and Legendre, who was a timid student, accepted the obscurity to which the hostility of his colleague condemned him.

Legendre’s analysis is of a high order of excellence, and is second only to that produced by Lagrange and Laplace, though it is not so original. His chief works are his Géométrie, his Théorie des nombres, his Exercices de calcul intégral, and his Fonctions elliptiques. These include the results of his various papers on these subjects. Besides these he wrote a treatise which gave the rule for the method of least squares, and two groups of memoirs, one on the theory of attractions, and the other on geodetical operations.

Augustin-Jean Fresnel

Apparently, dear reader, I am still obsessed by my trip to Paris last summer, because this will be the third week in a row that this blog has been about a famous French scientist. I hope you enjoy it.

Diffraction is a fundamental topic in physical optics that receives scant attention in the 4th edition of Intermediate Physics for Medicine and Biology. The index contains no entry for diffraction. (By the way, Russ Hobbie and I worked hard to make the index as complete and useful as possible.) However, a search for the term "diffraction" yields many appearances. Often it shows up as part of the term “x-ray diffraction,” but I have already addressed that technique in this blog a few weeks ago. A footnote on page 327, in Chapter 12 about images, mentions interference and diffraction in the context of coherence, and diffraction appears several times when discussing point-spread functions in that chapter. In Chapter 13 on ultrasound, diffraction is mentioned again as representing a limit to our ability to obtain an image. In Chapter 14, diffraction is discussed as a factor limiting our visual acuity.

The study of diffraction has a fascinating history, going back to the fundamental work of the French physicist Augustin-Jean Fresnel (1788-1827). Fresnel makes only one brief appearance in Intermediate Physics for Medicine and Biology, when discussing diffraction effects and the “Fresnel Zone” produced by an ultrasound transducer. To try and make up for Fresnel’s absence from our book, I will provide here some of the highlights of his short life (he died at age 39). Incidentally, I’m not the only blogger interested in Fresnel.

Waves and Grains:
Reflections on Light and Learning,
by Mark Silverman.

I first came to appreciate Fresnel’s contributions when reading the books of physicist Mark Silverman. In particular, I enjoyed Silverman’s Waves and Grains: Reflections on Light and Learning. He writes

Fresnel, as the reader will discover (if it is not already obvious), is a central figure and something of a hero in this book. Pathetically all too human in his desperate desire to distinguish himself in the world of science, his ambitions are the ambitions of all of us who do research, write papers, and seek recognition. As a young man trained in engineering, he first turned his attention to industrial chemistry but learned to his chagrin that what he thought was original work was anticipated by others. Disappointed, he later immersed himself in the wave theory of light, guided and encouraged by Francois Arago—one of very few wave enthusiasts in the Paris Academy—who helped publicize his work both in France and abroad…

In 1817 the Paris Academy launched a competition for the essay best accounting for the diffraction of light. With the exception of Arago, the committee responsible for the event consisted exclusively of partisans, like Laplace and Biot, of the particle hypothesis [of light…] Fresnel, as one might imagine, was not initially enthusiastic about entering—his whole direction of research having apparently already been ruled out by the wording. Nevertheless, urged on again by Arago, he composed a lengthy paper summarizing his philosophical approach, his methods, and his results. It is an amusing irony of history that Simeon-Denis Poisson—another graduate of the Polytechnique noted for his broad theoretical contributions to physics and mathematics, and a staunch advocate of the corpuscular theory—noted a glaring inconsistency in Fresnel’s theory. Applying this theory to an opaque circular screen, Poisson deduced the (to him) ludicrous result that the center of the shadow (doit) etre aussi eclaire que si l’ecran n’existait pas (must be as brightly illuminated as if the screen did not exist). Arago performed the experiment in advance of the committee’s decision, and the bright center—which history records as Poisson’s spot—showed up as predicted.

Fresnel, his relentless efforts finally recognized, received the prize—but Biot, Poisson, and other remained unshaken in their particle convictions.

If you get a copy of Silverman’s book, don’t miss the last chapters on Science and Learning.

Living here in Michigan, surrounded by the Great Lakes, I’ve become fond of lighthouses, and particularly with the spectacular Fresnel lenses that you can find in many of them. Click here to see pictures of some, and here to see information about Fresnel lenses found in Michigan. It is another of Fresnel’s many contributions to science.

Joseph Fourier

The August 2010 issue of Physics Today, published by the American Institute of Physics, contains an article by T. N. Narasimhan about “Thermal Conductivity Through the 19th Century.” A large part of the article deals with Joseph Fourier (17687–1830), the French physicist and mathematician. Russ Hobbie and I discuss Fourier’s mathematical technique of representing a periodic function as a sum of sines and cosines of different frequencies in Chapter 11 of the 4th edition of Intermediate Physics for Medicine and Biology. Interestingly, this far-reaching mathematical idea grew out of Fourier’s study of heat conduction and thermal conductivity. Russ and I introduce thermal conductivity in Homework Problem 15 of Chapter 4 about diffusion. This is not as odd as it sounds because, as shown in the problem, heat conduction and diffusion are both governed by the same partial differential equation, typically called the diffusion equation (Eq. 4.24). The concept of heat conduction is crucial when developing the bioheat equation (Chapter 14), which has important medical applications in tissue heating and ablation.

Narasimhan’s article provides some interesting insights into Fourier and his times.

In 1802, upon his return to France from Napoleon’s Egyptian campaign, Fourier was appointed perfect of the department of Isere. Despite heavy administrative responsibilities, Fourier found time to study heat diffusion. He was inspired by deep curiosity about Earth and such phenomena as the attenuation of seasonal temperature variations in Earth’s subsurface, oceanic and atmospheric variations in Earth’s subsurface, oceanic and atmospheric circulation driven by solar heat, and the background temperature of deep space…

Thermal conductivity, appropriate for characterizing the internal conduction, was defined by Fourier as the quantity of heat per unit time passing through a unit cross-section divided by the temperature difference of two constant-temperature surfaces separated by unit distance… Fourier presented his ideas in an unpublished 1807 paper submitted to the Institut de France.

Fourier was not satisfied with the 1807 work. It took him an additional three years to go beyond the discrete finite-difference description of flow between constant-temperature surfaces and to express heat flow across an infinitesimally thin surface segment in terms of the temperature gradient.

When Fourier presented his mathematical theory, the nature of heat was unknown… Fourier considered mathematical laws governing the effects of heat to be independent of all hypotheses about the nature of heat… No method was available to measure flowing heat. Consequently, in order to demonstrate that his mathematical theory was physically credible, Fourier had to devise suitable experiments and methods to measure thermal conductivity.

It is not widely recognized that in his unpublished 1807 manuscript and in the prize essay he submitted to the Institut de France in 1811, Fourier provided results from transient and steady-state experiments and outlined methods to invert exponential data to estimate thermal conductivity. For some reason, he decided to restrict his 1822 masterpiece, The Analytical Theory of Heat, to mathematics and omit experimental results.

For more insight on Fourier’s life and times, see Keston’s article “Jospeh Fourier: Policitian and Scientist.” It begins

The life of Baron Jean Baptiste Joseph Fourier (1768–1830) the mathematical physicist has to be seen in the context of the French Revolution and its reverberations. One might say his career followed the peaks and troughs of the political wave. He was in turns: a teacher; a secret policeman; a political prisoner; governor of Egypt; prefect of Isère and Rhône; friend of Napoleon; and secretary of the Académie des Sciences. His major work, The Analytic Theory of Heat, (Théorie analytique de la chaleur) changed the way scientists think about functions and successfully stated the equations governing heat transfer in solids. His life spanned the eruption and aftermath of the Revolution; Napoleon's rise to power, defeat and brief return (the so-called Hundred Days); and the Restoration of the Bourbon Kings.