Friday, March 28, 2014

The Correspondence Between Sir George Gabriel Stokes and Sir William Thomson, Baron Kelvin of Largs

I recently obtained through interlibrary loan a copy of The Correspondence Between Sir George Gabriel Stokes and Sir William Thomson, Baron Kelvin of Largs, edited by David Wilson. This wonderful collection of over 650 letters spans the years 1846 to 1901. Robert Purrington, in his book Physics in the Nineteenth Century, claims that “the Thomson-Stokes correspondence is one of the treasures of nineteenth-century scientific communication.” I thought I would share a few excerpts from these letters with the readers of this blog.

Stokes (1819-1903) was the older of the two men. For years he served as the Lucasian Professor of Mathematics at the University of Cambridge. I have discussed him in this blog before. In the 4th edition of Intermediate Physics for Medicine and Biology, Russ Hobbie and I mention Stokes in connection to Stokes’ law for the drag force of a sphere moving in a viscous fluid, and the Navier-Stokes equations of fluid dynamics.

Kelvin (1824-1907) was five years younger than Stokes. He was born with the name William Thomson, but was made a Lord in 1892 and was thereafter referred to as Lord Kelvin. Russ and I don’t mention Kelvin in IPMB, but we do mention the unit of absolute temperature named after him. He spent his career at the University of Glasgow in Scotland, and is remembered for many accomplishments, but primarily for his contributions to thermodynamics.

Stokes’ and Kelvin’s letters were full of mathematics (Stokes was primarily a mathematical physicist) and critiques of the many famous physicists of their era. They spent a lot of time trying to obtain copies of papers. In the days before the internet, or even the Xerox machine, making a copy of a scientific paper was not easy, and they were constantly lending out the few copies they possessed. In some years, their letters were primarily about reviewing manuscripts, as both men served as editors of journals at one time and as reviewers for journals at another. Most commonly Stokes, as editor, was trying to coax Kelvin to complete his reviews on time.

A letter of April 7, 1847—between two relatively young and up-and-coming physicists—highlights the different areas of interest of the two men.
My Dear Stokes,
Many thanks for your letters…..I have been for a long time thinking on subjects such as those you write about, and helping myself to understand them by illustrations from the theories of heat, electricity, magnetism, and especially galvanism; sometimes also water. I can strongly recommend heat for clearing the head on all such considerations, but I suppose you prefer cold water….
Yours very truly, William Thomson
In this letter from Oct 25, 1849, Kelvin congratulates Stokes on becoming the Lucasian Professor.
My Dear Professor
I have been daily expecting to hear of the election of a Lucasian Professor and whenever the Times has been in my hands I have looked for such a proceeding in the University Intelligence, and now I am glad to be able to congratulate you on the result…
Yours sincerely, William Thomson
Sometimes the two engaged in a bit of trash-talking about other scientists. In a Jan 6, 1851 letter, Stokes adds a pugnacious postscript.
My Dear Thomson,
Yours very truly, G. G. Stokes.
P.S. Have you seen Prof Challis’s awful heterodoxy in the present no. of the Phil. Mag. I am half inclined to take up arms, but I fear the controversy would be endless.
Readers of IPMB will recall the cable equation in Chapter 6 that describes the electrical properties of a nerve axon. This equation was not originally derived to model an axon, but instead was proposed by Kelvin to describe a submarine telegraph cable. Kelvin was deeply involved with the trans-Atlantic cable, and in this Oct 30, 1854 letter he described this work to Stokes.
My Dear Stokes,
An application of the theory of the transmission of electricity along a submarine telegraph wire, which I omitted to mention in the haste of finishing my letter on Saturday, shows how the question raised by Faraday as to the practicability of sending distinct signals along such a length as the 2000 or 3000 miles of wire that would be required for America, may be answered. The general investigations will show exactly how much the sharpness of the signals will be worn down, and will show what the maximum strength of current through the apparatus in America, would be produced by a specified battery action on the end in England, with wire of given dimensions etc.
The following form of solution of the general equation
σ2kc dv/dt = d2v/dx2 - hv
which is the first given by Fourier, enables us to compare the times until a given strength of current shall be obtained, with different dimensions etc of wire….
Yours always truly, William Thomson
Neither scientist could properly be called a biological physicist. Medicine and biology almost never appear in their letters (unless one of them is sick). Kelvin once brought up a biological topic in his Jan 28, 1856 letter.
My Dear Stokes,
…Have you seen Clerk Maxwell’s paper in the Trans R S E [Transactions of the Royal Society of Edinburgh] on colour as seen by the eye? you believe that the whites produced by various combinations, such as two homogenous colours, three homogeneous colours, etc. are absolutely indistinguishable from one another and from solar white by the best eye?...Are you at all satisfied with Young’s idea of triplicity in the perceptive organ?
Yours very truly, William Thomson
Stokes’ curt reply on Feb 4 indicated he could not have been less interested in the topic.
My Dear Thomson,
….I have not made any experiments on the mixture of colours, nor attended particularly to the subject….
Yours very truly, G. G. Stokes
Once Kelvin was late getting some page proofs sent to Stokes, and in a Jan 20, 1857 letter he received a stern tongue lashing (one suspects, tongue-in-cheek).
My Dear Thomson,
You are a terrible fellow and I must write you a scolding…Hoping you will be more punctual for the future I remain
Yours most sincerely, G. G. Stokes
This was not the last time Kelvin was slow in responding to Stokes, and he often apologized for being late. He was tardy once when reviewing one of Maxwell’s papers for a journal. To me, Maxwell is a giant of physics, to be spoken of in the same category as Newton and Einstein. But for Kelvin, reviewing one of Maxwell’s papers was just another chore he needed to find time to do.

Although most of the letters were about science, personal matters were sometimes mentioned. Kelvin wrote a Dec 27, 1863 letter of consolation after scarlet fever took the life of Stokes’ infant child. Stokes himself was also ill with the disease.
My Dear Stokes,
I am very sorry to hear of the loss you have had and I feel much concerned about the danger you have yourself suffered. I hope you are still improving steadily, and that you will soon be quite strong again….
Yours always truly, W. Thomson
I hope the others of your family have perfectly recovered, if not escaped the scarlet fever.
When Kelvin became a Lord, Stokes’ Jan 2, 1892 letter had a bit of fun with the event. But afterwards, his letters were always addressed to Kelvin rather than Thomson.
My Dear Lord (What?)
I write to congratulate you on the great honour Her Majesty has bestowed on you, and through you on science, by creating you a Peer. At the same time I may add my congratulations to those of my wife to The Lady Thomson, or whatever she is to be called. I was speculating whether you would be Lord Thomson, or Lord Netherhall, or Lord Largs, or what. Time will tell….
Yours sincerely, G. G. Stokes
They didn’t always agree on scientific issues. In an Oct 27, 1894 letter, the 75-year-old Stokes’ humerously addresseed a disagreement about the behavior of a fluid in some container.
My Dear Lord Kelvin,
…..perhaps you think to demolish me by saying, Let the vessel be rigid but massless. Well. There is life in the old dog yet….
Yours sincerely, G. G. Stokes
I found it fascinating to listen as they corresponded about the important physics of their era. For instance, they discussed Rontgen’s discovery of X-rays extensively in 1896, and considered writing a joint note about their electromagnetic nature. They debated Becquerel’s discovery of radioactivity from uranium in 1897. Their last letter, in 1901, analyzed a problem from fluid dynamics and contained mathematical equations.

I didn’t have time to read all the letters, but I did spend most of a Saturday sampling many of them. The letters provide a valuable glimpse into the relationship between two intelligent yet human scientists. Wilson lists a few quotes at the start of his book, with the last one by Arthur Schuster (1932) stating
I shall always remember Lord Kelvin, as he stood at the open grave, almost overcome by his emotion, saying in a low voice: “Stokes is gone and I shall never return to Cambridge again.”

Friday, March 21, 2014

A Dozen New Homework Problems

Russ Hobbie and I are hard at work on the 5th edition of Intermediate Physics for Medicine and Biology. Sometimes we consider adding new material, try things out, debate its merits, but in the end it doesn’t make the cut. For instance, we thought about adding a section on elasticity theory to Chapter 1, but that was going to be too long (we are constantly battling between adding important topics and keeping the book from getting too fat), so we tried writing some new homework problems to teach the material that way. But it was also too much, and eventually we gave up on the idea. For those wanting to learn more about the biological applications of elasticity theory, I recommend Y. C. Fung’s book Biomechanics: Mechanical Properties of Living Tissue (cited in IPMB), or his more general textbook First Course in Continuum Mechanics.

I don't want to see good homework problems go to waste, so I offer them here in this blog. Twelve new homework problems. Free. They offer a way to learn a bit of elasticity theory. Enjoy.
Problem 1 Consider the rod in Fig. 1.20; the x-axis is along the rod’s length and x=0 is where the rod meets the wall. Let the displacement u(x,y) be the change in position of each point in the material in response to the force F. Express the displacement as ux=Ax, uy=0, and uz=0, where A is a constant.
(a) Calculate the normal strain εn using Eq. 1.24 and Fig. 1.20.
(b) Calculate εn using the definition εn=∂ux/∂x . Is it the same as in (a)?

Problem 2 Consider the rod in Fig. 1.23; x is horizontal, y is vertical, and y=0 is where the rod meets the floor. Express the displacement as ux=By, uy=0, and uz=0, where B is a constant.
(a) Calculate the shear strain εs using Eq. 1.27 and Fig. 1.23 (assume B « 1)
(b) Calculate εs using the definition εs=∂ux/∂y+∂uy/∂x. Is it the same as in (a)?
Problem 3 The normal and shear strains can be combined into a strain tensor, which a 3 x 3 matrix. Define the diagonal components of this tensorxx, εyy, εzz) as the normal strain in each direction, and the off-diagonal components (εxy, εyz, εzx) as one half of the shear strain in each direction. For example, εxy=(∂ux/∂y+∂uy/∂x)/2.
(a) Derive expressions relating each component of the strain tensor to the displacement.
(b) Show that the strain tensor is symmetric (e.g., εxy=εyx).
Note: This expression for the strain tensor is correct for small strains. For large strains it is a more complicated nonlinear function of the displacement (Fung, 1993).

Problem 4 The dilatation is defined as the change in volume over the original volume, ΔV/V. For small strains, the dilatation is εxxyyzz .
(a) Calculate the dilatation for the displacement in Problem 1. Does the volume change?
(b) Calculate the dilatation for the displacement in Problem 2. Does the volume change?
(c) Calculate the dilatation for the displacement ux=Cx, uy=Cy, uz=Cz, where C is a constant. Does the volume change?
(d) Show that the dilatation is equal to the trace of the strain tensor (the trace of a matrix is the sum of the diagonal components) and also is equal to the divergence of the displacement (the divergence is defined in Chapter 4).

Problem 5 Consider the displacement ux=Dx, uy=-Dy, uz=0, where D is a constant.
(a) Sketch a plot of the displacement distribution by drawing the displacement vectors over a 5 x 5 grid centered at the origin.
(b) Sketch how a small square in the x-y plane centered at the origin is deformed.
(c) Calculate the strain tensor (defined in Problem 3) for this displacement.
(d) Calculate the dilatation (defined in Problem 4) for this displacement.

Problem 6 Repeat the analysis of Problem 5 for the displacement ux=Fy, uy=Fx, uz=0, where F is a constant.

Problem 7 Repeat the analysis of Problem 5 for the displacement ux=Hy, uy=-Hx, uz=0, where H is a constant. This is a special case of rigid body motion. Interpret this displacement physically.

Problem 8 Like the strain, the stress can be written as a 3 x 3 symmetric tensor. For an isotropic material, the relationship between the components of the stress tensor, sij, and the strain tensor, εij, is sij=λδijxxyyzz)+2μεij, where λ and μ are the Lame parameters, and δij is the Kronecker delta (1 if i=j, and 0 otherwise).
(a) Show that for the case in Problem 1, this relationship reduces to Eq. 1.25 where s
n=sxx and εnxx. Express the Young’s modulus E in terms of the Lame parameters.
(b) Show that for the case in Problem 2, this relationship reduces to Eq. 1.28 where s
s=sxy and εs=2εxy. Express the shear modulus G in terms of the Lame parameters.
(c) Show that for the case in Problem 4c, this relationship reduces to Eq. 1.32 where the diagonal components of the stress tensor are given in terms of the pressure p as s
xx=syy=szz=-p. Express the compressibility κ in terms of the Lame parameters.

Problem 9 Figure 1.25 shows that pressure p will exert a net force on an element of fluid only if p is not uniform. Similarly, a stress will exert a net force on an element of tissue only if the stress is not uniform. The equations of mechanical equilibrium (zero net force) are ∂six/∂x+∂siy/∂y+∂siz/∂z=0, where i is either x, y, or z.
(a) Substitute the relationship from Problem 8 into these equations, and derive three equations of mechanical equilibrium written in terms of the strain tensor.
(b) Substitute the relationships between the components of the strain tensor and the displacement found in Problem 3 and derive the equations of mechanical equilibrium in terms of the displacement.

Problem 10 Figure 1.20, showing a rod subject to a force along its length, is a simplification. Actually, the cross-sectional area of the rod shrinks as the rod lengthens. A better representation of the displacement than that given in Problem 1 would be ux=Ax, uy=-Aνy, and uz=-Aνz, where A is a constant and ν is the Poisson’s ratio.
(a) Use the results of Problem 4 to calculate the dilatation.
(b) What value of Poisson’s ratio corresponds to an incompressible material (zero dilatation)?
(c) For an isotropic material, -1 « ν « 0.5. How would a material with negative ν behave?
Elliott et al. (2002) measured Poisson’s ratio for articular (joint) cartilage under tension and found 1 « ν « 2. This large value is possible because cartilage is anisotropic: its properties depend on direction.

Problem 11 Many biological tissues are composed mainly of water and are therefore nearly incompressible. To analyze such a tissue, start with the stress-strain relationship in Problem 8. (Assume uz=0 and all derivatives in the z direction are zero; the case of “plane strain”.)
(a) For an incompressible tissue, εxxyy goes to zero and λ goes to infinity such that λ(εxxyy) is finite. Set it equal to –p, where p is the pressure.
(b) The displacement can be found from a stream function φ(x,y), where ux=∂φ/∂y and uy=-∂φ/∂x. Show that these definitions ensure that the dilatation is zero. Express the strain tensor in terms of φ.
(c) Write the components of the stress tensor (sxx, syy, sxy) in terms of p and φ.
(d) Use the analysis of Problem 9 to derive the equations of mechanical equilibrium in terms of p and φ.
(e) Manipulate these equations to find two new equations, one for p only and one for φ only. (Hint: try taking derivatives of the equations).

Problem 12 Start with the stress-strain relationship in Problem 8 and modify it to describe a two-dimensional sheet of cardiac muscle (Ohayon and Chadwick 1988). (Assume uz=0 and all derivatives in the z direction are zero; the case of “plane strain”.)
(a) Cardiac tissue is nearly incompressible. For an incompressible tissue, εxxyy goes to zero and λ goes to infinity such that λ(εxxyy) is finite. Set it equal to –p, where p is the pressure.
(b) Cardiac muscle can develop an active tension T along the myocardial fibers caused by the interaction of actin and myosin molecules. Assume the fibers lie along the x direction, and add the term T to the expression for sxx.
(c) The extracellular space consists of collagen fibers that can exert a shear force. Assume the collagen is isotropic, and interpret μ in Problem 8 as the collagen’s shear modulus.
(d) Derive expressions for sxx, syy, and sxy in terms of p, μ, T, and the strain tensor.
(e) Assume a solution ux=-Ax, uy=Ay, and p=P, where A and P are constants. If the tissue is free at its edges, then it must have zero stress throughout. Use this condition to derive expressions for A and P in terms of T and μ.
(f) Let T=3 x 104 Pa and μ=104 Pa (typical for cardiac tissue). Calculate values for A and P. Are the strains small? Sketch qualitatively the displacement distribution.

Ohayon, J. and R. S. Chadwick (1988) “Effects of Collagen Microstructure on the Mechanics of the Left Ventricle, Biophys. J., Volume 54, Pages 1077–1088.

Friday, March 14, 2014

Light Scattering

In the 4th edition of Intermediate Physics for Medicine and Biology, Russ Hobbie and I often discuss the scattering of light. We mention four types of scattering, each differentiated by the name of the brilliant scientist who first studied it: Compton scattering, Thomson scattering, Rayleigh scattering, and Raman scattering. Let’s see if we can get these all straight.

Compton Scattering

In Chapter 15 (Interaction of Photons and Charged Particles with Matter) of IPMB, Russ and I analyze Compton scattering. This is a particularly simple case: a photon interacts with a free electron, resulting in a scattered photon of lower energy and a recoiling electron. This type of scattering is particularly important for x-rays. You might be wondering how often do we encounter a free electron? Aren’t most electrons bound to atoms? If the incident photon has an energy much greater than the binding energy, then the electron is to a first approximation free and Compton scattering occurs. In the interaction of x-rays with biological tissue, Compton scattering is the dominant mechanism contributing to the interaction cross-section at intermediate energies; say, one tenth to a few MeV. Since the electrons act almost as if they were free, the atomic number of the target atom is unimportant and scattering depends only on how many electrons are present (meaning the mass attenuation coefficient is nearly independent of atomic number). You don’t really want to do imaging of tissue when Compton scattering is the dominate interaction because you don’t get much discrimination between different tissues (the weak dependence on atomic number) and, well, you get a lot of scattering that blurs the image.

Compton scattering is named after Arthur Holly Compton (1892–1962), an American physicist who played a key role in the Manhattan Project. Compton scattering was important in the development of quantum mechanics. The light quanta hypothesis had been developed by Planck and Einstein, but was not widely embraced until 1923, when Compton analyzed his x-ray scattering data by treating the x-ray photon as a particle with energy and momentum, interacting with another particle, the electron. Compton won the 1927 Nobel Prize in Physics for his discovery.

Thomson Scattering

When Compton scattering occurs at such a low energy that we can ignore the difference in energy between the incident and scattered photons, the process is called Thomson scattering. We can analyze Thomson scattering by treating the incident light as an electromagnetic wave rather than a photon. The electric field accelerates the electron, causing it to radiate an electromagnetic wave at the same frequency. The direction of the electric field is important for determining the distribution of the outgoing dipole radiation, so Thomson scattering depends on the polarization of the incident light. This type of scattering is particularly important in plasma physics, where many free charged particles are present. It is not too important in biology and medicine, because usually either the photon energy is so high that Compton scattering occurs, or else the photon energy is so low that one cannot treat the electron as being free. Because the frequency of the light (and therefore the energy of the photons) does not change, Thomson scattering is a type of elastic scattering.

Thomson scattering was first analyzed by, and was named after, J. J. Thomson (1856–1940), the British physicist who discovered the electron, for which he received the Nobel Prize in Physics in 1906. I have my own connection to Thomson: academically speaking, he is my great-great-great-great-great-grandfather.

Rayleigh Scattering

Rather than scattering from a single electron, light can also scatter from an entire atom or molecule, and even larger particles. When the wavelength of the light is much larger than the size of the particle, we get Rayleigh scattering. Like for Thomson scattering, in Rayleigh scattering the light is treated as an electromagnetic wave. However, unlike Thomson scattering, in Rayleigh scattering the scatterer is not a single particle, but instead can be represented by a continuous, polarizable medium. The electric field of the light causes the induced charge distribution to oscillate at the same frequency as the incident light, resulting in the scattered light having the same frequency as the incident light. In IPMB, Russ and I refer to Rayleigh scattering as coherent scattering, because the atom responds coherently as a whole, rather than as individual charged particles. In tissue, coherent scattering dominates Compton scattering at low energies (say, below 1 keV), but such low energy photons also interact by the more important photoelectric effect, so Rayleigh scattering is often not very important. It is crucial for understanding how sunlight scatters off the molecules of the air, causing the blue color of the sky.

When I was an undergraduate at the University of Kansas, I had my first research experience in Professor Wes Unruh’s laboratory studying light scattering off of colloidal impurities in crystals. We were able to determine the size of the impurities by measuring the scattered light as a function of angle. However, these colloids tended to be large, so that you could not ignore interference between light scattered from different parts of the particle. In that case, you must use a more advanced theory, called Mie theory, to calculate the distribution of scattered light. I recall struggling to learn Mie theory from Milton Kerker’s book The Scattering of Light and Other Electromagnetic Radiation. I didn’t work much with Unruh himself, but rather was mentored by then-graduate student Robert Bunch. The first item in my CV is an abstract resulting from that research (Bunch, Roth, and Unruh, 1983, “Size Distributions of Ni and Co Colloids Within MgO,” March Meeting of the American Physical Society).

Rayleigh scattering is named after English physicist John William Strutt (1842-1919), also known as Lord Rayleigh. He was awarded the Nobel Prize for Physics in 1904 for the discovery of argon. Because one of Rayleigh’s students was J. J. Thomson, Rayleigh is my academic great-great-great-great-great-great-grandfather. Rayleigh was the second Cavendish Professor of Physics at the University of Cambridge, following Maxwell and succeeded by J. J. Thomson, Ernest Rutherford, and William Bragg; quite an impressive bunch.

Raman Scattering

In IPMB, Russ and I discuss Raman scattering in Chapter 14 (Atoms and Light). The mechanism of Raman scattering is similar to Rayleigh scattering, in that the scattering occurs off an entire molecule. However, it is unlike Rayleigh scattering in that the scattered light does not have the same frequency as the incident light (inelastic scattering). Instead, some of the energy induces transitions between different vibrational energy levels. These transitions result in the scattered light having a lower energy (Stokes) or a higher energy (Anti-Stokes). Also, because the vibrational energy levels are quantized, the spectrum of Raman scattered light consists of a series of discrete lines. This spectrum contains information about the vibrations within the molecule, and therefore about the chemical bonds.

The description of Raman scattering given above (and in IPMB) is a quantum view that depends on the presence of discrete energy levels. However, one can also develop a classical model of Raman scattering. For instance, treat a simple diatomic molecule as two atoms attached by a spring, so that the molecule has its own natural frequency of oscillation, fo. If an electric field of frequency f is incident on the atom, it will respond by not only oscillating both at frequency f (Rayleigh scattering) but also at frequencies f+fo and f-fo (Raman scattering). The frequency difference between adjacent lines is fo, which is the same frequency as one would expect in the infrared absorption spectrum. (For those who have read Appendix F of IPMB and are wondering why the the scattered light oscillates with a component at the natural frequency, realize that the charge induced by polarization depends on the electric field, so the force on the charge--charge times electric field--depends on the square of the electric field and the problem is nonlinear.)

Raman scattering was named after Indian physicist C. V. Raman (1888–1970), whose discovery led to the 1930 Nobel Prize for Physics.

Four types of scattering, named after four Nobel Prize winners. Here are some ways to keep them straight: Compton and Thomson scattering is off a single charged particle (usually an electron), whereas Rayleigh and Raman scattering is off an entire atom or molecule or particle. Thomson and Rayleigh scattering are elastic, whereas Compton and Raman scattering are inelastic. Thomson and Rayleigh scattering are most commonly described using the classical wave theory of light, whereas Compton and Raman scattering are typically analyzed using quantum mechanics (although Raman scattering is sometimes analyzed with classical theory).

I admire all four scientists: Compton, Thomson, Rayleigh, and Raman. Who is my favorite? I like Rayleigh best. Love those Victorians.

Friday, March 7, 2014

Letters to a Young Scientist

Letters to a Young Scientist, by Edward Wilson, superimposed on Intermediate Physics for Medicine and Biology.
Letters to a Young Scientist,
by Edward Wilson.
I just finished reading Edward Wilson’s book Letters to a Young Scientist. (I know, I know….I don’t qualify as a young scientist anymore, but I can still enjoy the book.) Wilson is a leading biologist who established two fields of study: island biogeography and sociobiology. He is one of the world’s experts on the taxonomy of ants. Last week’s blog post about the binomial nomenclature for naming animal species was motivated in part from reading this book. You can hardly get further from physics than the taxonomy of ants, so this may seem like an odd topic to discuss in a blog about physics applied to medicine and biology. But the book considers universal themes common to all scientists.

What is Wilson’s main message for young scientists? He writes
First and foremost, I urge you to stay on the path you’ve chosen, and to travel on it as far as you can. The world needs you—badly.
How true. My favorite of Wilson’s letters was number seven, “Most Likely to Succeed.”
Conventional wisdom holds that science of the future will be more and more the product of “teamthink,” multiple minds put in close contact…But is groupthink the best way to create really new science? Risking heresy, I hereby dissent. I believe the creative process usually unfolds in a very different way. It arises and for a while germinates in a solitary brain. It commences as an idea and, equally important, the ambition of a single person who is prepared and strongly motivated to make discoveries in one domain of science or another. The successful innovator is favored by a fortunate combination of talent and circumstance… When prepared by education to conduct research, the most innovative scientists of my experience do so eagerly and with no prompting. The prefer to take first steps alone. They seek a problem to be solved, an important phenomenon previously overlooked, a cause-and-effect connection never imagined. An opportunity to be the first is their smell of blood.
I also liked the point Wilson made in letter three, “The Path to Follow.”
If a subject is already receiving a great deal of attention, if it has a glamorous aura, if its practitioners are prizewinners who receive large grants, stay away from that subject. Listen to the news coming from the current hubbub, learn how and why the subject became prominent, but in making your own long-term plans be aware it is already crowded with talented people… Take a subject instead that interests you and looks promising, and where established experts are not yet conspicuously competing with one another…You may feel lonely and insecure in your first endeavors, but all other things being equal, your best chance to make your mark and to experience the thrill of discovery will be there.
He then states a general principle using a military metaphor.
March away from the sound of the guns. Observe the fray from a distance, and while you are at it, consider making your own fray.
He continues with an observation about big science.
The sequencing of the human genome, the search for life on Mars, and the finding of the Higgs boson were each of profound importance for medicine, biology, and physics, respectively. Each required the work of thousands and cost billions. Each was worth all the trouble and expense. But on a far smaller scale, in fields and subjects less advanced, a small squad of researchers, even a single individual, can with effort devise an important experiment at relatively low cost.
I agree with Wilson on all these points. I think there is a lot to be said for small groups. And I think that too often researchers chase the latest fad. I second Wilson’s advice to march away from the sound of the guns, and to make your own fray instead.

Often those applying physics to biology and medicine are skirmishers whose goal is to probe the unknown searching for vulnerabilities, rather than to join the mass attack. My suggestion is to first get a broad education in both physics and biology, perhaps using a book like the 4th edition of Intermediate Physics for Medicine and Biology (you knew I would get the plug in somewhere), and then find some interesting but little-studied topic, and see where it leads you. And above all, have fun while you are doing it.

But don’t take my word for it. Read the book, or listen to Wilson give his advice to young scientists in his TED talk.

Edward Wilson giving a TED talk about Advice to Young Scientists.