The Well-Tempered Clavichord

“Prelude No. 1,” from the Well-Tempered Clavichord, by Johann Sebastian Bach.
I played it (or tried to play it) back when I was 15 years old.

Most of my blog posts are about physics applied to medicine and biology, but today I want to talk about music. This topic may not seem relevant to Intermediate Physics for Medicine and Biology, but I would argue that it is. Music is, after all, as much about the human perception of sound as about sound itself. So, let’s talk about how we sort the different frequencies into notes.

Below I show a musical keyboard, like you would find on a piano.

Each key corresponds to a different pitch, or note. I want to discuss the relationships between the different notes. We have to start somewhere, so let’s take the lowest note on the keyboard and call it C. It will have some frequency, which we’ll call our base frequency. On the piano, this frequency is about 33 Hz, but for our purposes that doesn’t matter. We will consider all frequencies as being multiples of this base frequency, and take our C as having a frequency of 1.
 

When you double the frequency, our ear perceives that change as going up an octave. So, one octave above the first C is another C, with frequency 2.
 

Of course, that means there’s another C with frequency 4, and another with frequency 8, and so on. We get a whole series of C’s.
 

Now, if you pluck a string held down at both ends, it can produce many frequencies. In general, it produces frequencies that are multiples of a fundamental frequency f, so you get frequency f plus “overtone” frequencies 2f, 3f, 4f, 5f, etc. As we noted earlier, we don’t care about the frequency itself but only how different frequencies are related. If the fundamental frequency is a C with frequency 1, the first overtone is one octave up (with a frequency 2), another C. The second overtone has a frequency 3. That corresponds to a different note on our keyboard, which we’ll call G.

You could raise or lower G by octaves and still have the same note (like we did with C), so you have a whole series of G’s, including 3/2 which is between C’s corresponding to frequencies 1 and 2. When two notes have frequencies such that the upper frequency is 3/2 times the lower frequency (a 3:2 ratio), musicians call that a “fifth,” so G is a fifth above C.
 

Let’s keep going. The next overtone is 4, which is two octaves above the fundamental, so it’s one of the C’s. But the following overtone, 5, gives us a new note, E. 

 

As always, you can go up or down by octaves, so we get a whole series of E’s.

 

C and E are related by a ratio of 5:4 (that is, E has a frequency 5/4 times the C below it), which musicians call a “third.” The notes C, E, and G make up the “C major chord.”

The next overtone would be 6, but we already know 6 is a G. The overtone 7 doesn’t work. Apparently a frequency ratio of 7 is not one that we find pleasant (at least, not to those of us who have been trained on western music), so we’ll skip it. Overtone 8 is another C, but we get a new note with overtone 9 (and all its octaves up and down, which I’ll stop repeating again and again). We’ll call this note D, because it seems to fit nicely between C and E. The D right next to our base note C has a frequency of 9/8.

Next is overtone 10 (an E), then 11 (like 7, it doesn’t work), 12 (a G), 13 (nope), 14 (no because it’s an octave up from 7), and finally 15, a new note we’ll call B. 

We could go on, but we don’t perceive many of the higher overtones as harmonious, so let’s change track. There’s nothing special about our base note, the C on the far left of our keyboard. Suppose we wanted to use a different base note. What note would we use if we wanted it to be a fifth below C? If we started with a frequency of 2/3, then a fifth above that frequency would be 2/3 times 3/2 or 1, giving us C. We’ll call that new base frequency F. It’s off our keyboard to the left, but its octaves appear, including 4/3, 8/3, etc.  

What if we want to build a major chord based on F. We already have C as a fifth above F. What note is a third above F? In other words, start at 2/3 and multiply by 5/4 (a third), to get 10/12 which simplifies to 5/6. That’s off the keyboard too, but its octaves 5/3, 10/3, 20/3, etc. appear. Let’s call it A. So a major chord in the key of F is F, A, and C.

Does this work for other base frequencies? Try G (3/2). Go up a fifth from G and you get 9/4, which is a D. Go up a third from G and you get 15/8, which is a B. So G, B, and D make up a major chord in the key of G. It works again!

So now it looks like we’re done. We’ve given names and frequencies to all the notes: C (1), D (9/8), E (5/4), F (4/3), G (3/2), A (5/3), and B (15/8). This collection of frequencies is called “just intonation,” with “just” used in the sense of fair and honest. If you play a song in the key of C, you use only those notes and frequencies and it sounds just right.

What about those strange block notes between some, but not all, of the white notes? How do we determine their frequencies? For example, start at D (9/8) for your base note and build a major chord. First you and go up a third and get 9/8 times 5/4, or 45/32. That note, corresponding to the black key just to the right of F, is F-sharp (or F^♯). To express the frequency as a decimal, 45/32 = 1.406, which is midway between F (4/3 = 1.333) and G (3/2 = 1.500). We could continue working out all the frequencies for the various sharps and flats, but we won’t. It gets tedious, and there is an even more interesting and surprising feature to study.

To complete our D major chord, we need to to determine what note is a fifth above D. You get D (9/8) times a fifth (3/2), or 27/16 = 1.688. That is almost the same as A (5/3 = 1.667), but not quite. It’s too close to A to correspond to A-sharp. It’s simply an out-of-tune A. In other words, using the frequencies we have worked out above, if you start with C as your base (that is, you play in the key of C) your G (a fifth) corresponds to a frequency ratio of 5/3 = 1.667. If you play, however, using D as your base (you play in the key of D), your A (what should be a fifth above D) has a frequency ratio of 27/16 = 1.688. Different keys have different intonations. Yikes! This is not a problem with only the key of D. It happens again and again for other keys. The intonation is all messed up. You either play in the key of C, or you play out of tune.

To avoid this problem, nowadays instruments are tuned so that there are 12 steps between octaves (the steps includes both the white and black keys), where each step corresponds to a frequency ratio of 2^1/12 = 1.0595. A fifth (seven steps) is then 2^7/12 = 1.498, which is not exactly 3/2 = 1.500 but is pretty close and—importantly—is the same for all keys. A third is 2^4/12 = 1.260, which is not 5/4 = 1.250 but is not too bad. A keyboard with frequencies adjusted in this way is called “well-tempered.” It means that all the keys sound the same, although each is slightly out of tune compared to just intonation. You don’t have to have your piano tuned every time you change keys.

Johann Sebastian Bach wrote a lovely set of piano pieces called The Well-Tempered Clavichord that showed off the power of well-tempered tuning. My copy of the most famous of these pieces is shown in the photo at the top of this post. Listen to it and other glorious music by Bach below.

 

Bach’s “Prelude No. 1” from The Well-Tempered Clavichord, played by Alexandre Tharaud.

https://www.youtube.com/watch?v=iWoI8vmE8bI

Bach’s “Cello Suite No. 1,” played by Yo Yo Ma.

https://www.youtube.com/watch?v=Rx_IibJH4rA

Bach’s “Toccata and Fugue in D minor.”

https://www.youtube.com/watch?v=erXG9vnN-GI

Bach’s “Jesu, Joy of Man’s Desiring,” performed by Daniil Trifonov.

https://www.youtube.com/watch?v=wEJruV9SPao

Bach’s “Air on the G String.”

https://www.youtube.com/watch?v=pzlw6fUux4o

Bach and Gounod’s “Ave Maria,” sung by Andrea Bocelli.

https://www.youtube.com/watch?v=YR_bGloUJNo

An IPMB Episode of Meeting of Minds

A few weeks ago, I published a blog post about the television show Meeting of Minds. That show from the late 1970s was created and hosted by Steve Allen and featured historical figures as guests in a talk show format. In my earlier post, I wrote that if I were going to have an episode of Meeting of Minds based on Intermediate Physics for Medicine and Biology, it would include guests Alan Hodgkin, Willem Einthoven, Paul Lauterbur, and Marie Curie.

As your Christmas present, I offer you a script for the IPMB episode of Meeting of Minds.

Enjoy!

***********************************************************

Meeting of Minds, IPMB episode.

Allen: Good evening. I’m Steve Allen and I’d like to welcome you to this week’s episode of Meeting of Minds. Our guests will all be drawn from the field of physics applied to medicine and biology. We have the French physicist Marie Curie, the English physiologist Alan Hodgkin, the Dutch medical doctor Willem Einthoven, and the American chemist Paul Lauterbur. I’d first like to introduce Alan Hodgkin. [applause]

Hodgkin: [Hodgkin enters from stage right, and sits at the table.] Thank you, thank you. It’s such a pleasure to be here, Mr. Allen.

Allen: The pleasure’s all mine, Dr. Hodgkin. Tell me, I understand you were born in the market town of Banbury, England in 1914, the son of Quakers. How did a Quaker upbringing influence your early life?

Hodgkin: It had a huge influence. As you know, Quakers are pacifists, and I was born just as World War I began. When I was only two, my father, George Hodgkin, traveled to Armenia to try to help the many refuges trying to escape genocide committed by the Ottoman Empire. He tried to return to to Armenia two years later, but ended up dying of dysentery in Baghdad. This was just a few weeks after my brother Keith was born. I was only four when dad died.

Allen: But your Quaker roots didn’t stop you from participating in World War II?

Hodgkin: No, not at all. In fact, I was eager to do my part against the Nazis. I had visited Germany in 1932 and that experience destroyed any pacifist beliefs I might’ve held. During World War II, I worked on radar. In fact, I was on one of the first test flights of a Bristol Blenheim light bomber when it was fitted with our airborne centimetric radar system.

Allen: Going back to your childhood, were there any influences that led you to a scientific career?

Hodgkin: Oh yes. My mother encouraged my scientific interests and so did my Aunt Katie, who used to take me bird watching. In high school, I even got a job surveying rookeries and heronries. I spent many hours wading around in the salt marshes watching birds. This experience kindled my love for science.

Allen: I see you started your career in the biological sciences. Where did you gain the knowledge of the physical sciences that allowed you to work on radar?

Hodgkin: When at college at Cambridge, one of my zoology professors gave me some good advice: study as much math and physics as you can! I also picked up a lot doing student research. And of course, during the war I learned on the job. I’m very interested in learning how my esteemed colleague Willem Einthoven made a similar transition from biology to physics.

Allen: In that case, let’s welcome the father of clinical electrocardiography, Willem Einthoven. [applause]

Einthoven: [Einthoven enters from stage left and sits at the table across from Hodgkin] So good to meet you Mr. Allen. And it is truly a delight to meet the famous Alan Hodgkin, of Hodgkin and Huxley fame. Dr. Hodgkin, I see we have something in common.

Hodgkin: Oh, what’s that?

Einthoven: We both lost our fathers early in our life. My father, Jacob Einthoven, was a doctor, and died when I was only six. I was not born in the Netherlands, but in Java, which at that time was part of the Dutch East Indies. After dad died, we returned to the Netherlands and settled in Utrecht.

Allen: I understand you studied medicine.

Einthoven: Yes, Mr. Allen. When I was 25 I received my medical degree from the University of Utrecht. Then I became a professor at the University of Leiden, where I spent my career. At that time, I married my first cousin Frédérique Jeanne Louise de Vogel.

Hodgkin: First cousin! [giggles from the audience]

Einthoven: Yes, a wonderful woman. [frowning]

Allen: Like Dr. Hodgkin, your biological and medical research required knowledge of physics and math. How did you learn these subjects?

Einthoven: Through self study, Mr. Allen.

Hodgkin: The best type of learning.

Einthoven: I obtained a textbook by the Dutch physicist Hendrik Lorentz and taught myself differential and integral calculus. Thirty years later, I gave a copy of that book to the American cardiologist Frank Wilson (of the Wilson central terminal) with the inscription “May I send you the excellent book of Lorentz’ Differential- und Integralrechnung? I have learned my mathematics from it after my nomination as a professor in this University and I hope you will have as much pleasure and profit by it as I have had myself.” I also benefited from talks with my brother-in-law Julius, a physics professor at Utrecht. My training and degree was in medicine, but in my heart of hearts I was a physicist.

Hodgkin: Fascinating.

Einthoven: What is truly fascinating is how all the guests tonight contributed to the study of bioelectricity and biomagnetism. I developed the electrocardiogram, and you Dr. Hodgkin figured out how nerves work. I am anxious to meet Dr. Lauterbur, who invented magnetic resonance imaging.

Allen: Then without further ado, let me invite Dr. Paul Lauterbur to join our stimulating discussion. [applause]

Lauterbur: [Lauterbur enters from stage right, and sits next to Hodgkin.] Steve Allen [shakes hand]. Drs. Hodgkin and Einthoven [nods]. So happy to be here. Willem, my ancestors came from over in your neck of the woods. They’re from Luxembourg.

Einthoven: Interesting. Luxembourg is more closely related to France and Germany than the Netherlands, but….

Hodgkin: Ha!

Lauterbur: Yeah, we Americans are a little weak on our geography. I was born and raised in the small town of Sidney, Ohio, just north of Dayton.

Einthoven: And how did you become interested in science, Dr. Lauterbur?

Lauterbur: As a teenager I built my own chemistry laboratory in the basement of our house.

Hodgkin: Nice.

Lauterbur: My high school chemistry teacher realized that I liked experimenting, so he let me do my own chemistry experiments in the back of the room during class.

Einthoven: Such a wise teacher.

Lauterbur: I got my bachelor’s degree in industrial chemistry form Case Institute of Technology in Cleveland, which is now part of Case Western Reserve University. Like Dr. Hodgkin, I served in the army. In the early 1950s I was assigned to the army chemical center in Edgewood, Maryland. They let me spend part of my time using an early nuclear magnetic resonance machine. It didn’t do imaging…

Allen: Of course not! You invented imaging.

Lauterbur: …but NMR machines are important for chemical identification. I actually published four papers by the time I was discharged.

Hodgkin: And where did you do your famous work on imaging?

Lauterbur: I was at Stony Brook University for 22 years.

Einthoven: On Long Island?

Lauterbur: Yes, Willem, your geography’s better than mine [quiet laughter from the audience].

Allen: I look forward to hearing about your development of MRI later in our discussion, but now I would like to introduce our last guest, Marie Curie [enthusiastic applause, louder than for any of the other scientists].

Curie: [Curie enters from stage left and sits next to Einthoven] Thank you. Thank you so very much.

Einthoven: The honor is ours, Dr. Curie. Why, you are the only one of us who has an element named for them.

Curie: Yes, element 96 is named curium.

Lauterbur: While on the topic of geography, I seem to associate you with two countries, Marie: France and Poland. Which is your home?

Curie: Well, I was born and raised in Warsaw, which at that time was part of the Russian Empire. It was only when I was 24 that I went to Paris, and I spent the rest of my life in France. But I never lost my Polish heritage. I made sure my daughters learned the Polish language, and we went on trips to Poland. And Dr. Einthoven, you will be interested to know that I managed to get an element, polonium, named after my beloved homeland [scattered applause from the audience].

Einthoven: Nicely done.

Hodgkin: And how did you get started in science, Dr. Curie?

Curie: “Dr. Curie.” That still seems strange to hear. You see, it wasn’t as easy for a young lady to start a career in science as it was for you men.

Allen: I’m sure it wasn’t.

Curie: Also, my education was difficult because my parents were involved in uprisings to gain Polish independence. We lost much of the family fortune. My father was a physics teacher. When Russia eliminated laboratory instruction from Polish schools, dad brought all the lab equipment home for us kids to use. The Russians finally fired my father. Like Drs. Hodgkin and Einthoven, I lost a parent when I was young. For me, it was my mother, who died of tuberculosis when I was ten. I couldn’t pursue higher education then, because I was a woman…

Einthoven: So unfair.

Curie: I did become involved with the clandestine Flying University, a Polish patriotic institution that admitted women. Eventually my sister Bronislawa and I made a deal. I stayed in Poland and made money to pay for her medical studies in Paris. In exchange, she agreed to help me pay for my education two years later.

I got a job tutoring for some wealthy relations of my father. I fell in love with one of the sons, Kazimierz, but his family wouldn’t allow a marriage to a poor tutor. Kazimierz later became a famous mathematician. When he was an old man and I had died, he would come sit and stare at my statue at the Radium Institute.

I eventually was able to go to Paris and join my sister. Still, life was hard. I studied so hard I often forgot to eat! I hit the books all day and tutored in the evenings to pay the bills.

Hodgkin: How did you meet your husband Pierre Curie?

Curie: We met through our mutual love of science. When Pierre proposed, I was reluctant to accept because I planned to return to Poland. Pierre said he would give up his distinguished physics career to join me! [applause from the audience]. We eventually were married. One smart aleck called me “Pierre’s greatest discovery” but his work in magnetism was very important in its own right.

Allen: Now I would like to switch the conversation to the science that made each of you famous. Dr. Hodgkin, you first. Tell us a little about your work with the squid nerve axon.

Hodgkin: I’d love to. Yes, Dr. Curie, some people think they’re so witty. In my case, one wise guy said that “it’s the squid who really deserved the Nobel Prize” [polite laughter from the audience]. I must admit he had a point. We conducted our experiments using the giant axon of the squid, which is up to one millimeter in diameter.

Einthoven: One millimeter!? For a nerve axon, that is huge!

Hodgkin: Yes, that’s the point. It was big enough that we could stick electrodes down its length.

Curie: Who is “we,” Dr. Hodgkin?

Hodgkin: I worked mainly with my collaborator, Andrew Huxley. He was a little younger than me and started as my student, but eventually became a true collaborator. He was an excellent experimentalist, but one of his greatest strengths was his skill in mathematics.

Lauterbur: Do go on, Alan. What did ya do with those axons?

Hodgkin: We developed a technique called the “voltage clamp” in which we used two electrodes, one to measure the voltage across the axon membrane and the other to pass current across the membrane. The electrodes were attached to a feedback circuit, which applied whatever current was necessary to keep the voltage constant. With this device, we could monitor both the current and voltage, and thus determine the membrane conductance.

Allen: But Dr. Hodgkin, wasn’t the voltage clamp originally invented by Kenneth Cole at Woods Hole in the United States?

Hodgkin: Yes, he did some of the early work. And it’s true I visited Woods Hole and learned the technique from Cole. But some of his measurements were questionable. He reported action potentials that went positive by over 100 millivolts!

Einthoven: Oh my.

Hodgkin: An action potential that positive would have invalidated the idea that the membrane depolarized until it reached the sodium equilibrium voltage, which was the basis for the Hodgkin and Huxley model. In any case, we were able to calculate the membrane conductance and could determine how the membrane changed its conductance for both sodium and potassium individually.

Lauterbur: Because the sodium and potassium ions passed through selective ion channels?

Hodgkin: Yes, but we didn’t know it at the time. We just knew that two ions were involved: sodium and potassium. At rest the axon was primarily permeable to potassium and during the action potential it became permeable to sodium. We imagined that “gates” allowed the current to pass through the membrane: the m and h gates for sodium, and the n gate for potassium. It may sound a bit ad hoc, but our Hodgkin and Huxley model was really a gigantic curve-fitting exercise.

When the membrane was slightly depolarized—that is, when the membrane voltage was made slightly positive compared to its resting value—the m gate began to open, letting in sodium. The positive charge of the sodium ions raised the membrane voltage further, resulting in the m gate opening more, allowing more sodium to enter…

Einthoven: Positive feedback!

Hodgkin: Yes, the upstroke of the action potential is a positive feedback loop.

Lauterbur: But Alan, positive feedback can be explosive. What stopped the rise in membrane voltage?

Hodgkin: When the membrane voltage reached the sodium equilibrium voltage, there was no longer a tendency for sodium to enter the nerve. Even though there was more sodium outside the axon than inside, the high positive voltage in the axoplasm prevented any more positive sodium ions from diffusing in. That’s why Cole’s huge action potentials didn’t make any sense. Their reported action potentials went above the sodium equilibrium voltage.

Curie: But Dr. Hodgkin, what then caused the voltage to return to rest?

Hodgkin: Well, the n gate slowly opened, allowing potassium to leave the axon (carrying positive charge with it). But more importantly, the h gate slowly closed, preventing any further sodium current.

Einthoven: But if the h gate closes, would not that destroy the positive feedback loop of the action potential?

Hodgkin: Yes indeed. The closing of h made the axon “refractory.” It couldn’t fire another action potential until the h gate finally opened again and the membrane returned to its resting state.

Allen: Interesting, Dr. Hodgkin. And you made a mathematical model of this?

Hodgkin: Yes. Much of that was Andrew’s work.

Lauterbur: Don’t some people call Huxley the “greatest mathematical biologist ever”?

Hodgkin: They do. Our model required solving a set of nonlinear differential equations. This was back in the days before digital computers were available. You should’ve seen Andrew working that hand-held mechanical calculating machine to solve those equations numerically. Boy, did his fingers fly!

Allen: Dr. Einthoven, you also worked in bioelectricity. Perhaps you could tell us about your discoveries?

Einthoven: Well, I was the first to record the electrocardiogram, which is the electrical signal produced by the heart.

Lauterbur: I often had an ECG taken during my yearly physical.

Einthoven: Yes, it has become one of the most important diagnostic tools of modern medicine. But unlike Dr. Hodgkin, I didn’t have fancy voltmeters and oscilloscopes that I could use to measure electrical current. I had to invent an improved “string galvanometer.”

Hodgkin: Yes, yes. You passed a current through a wire in a magnetic field, causing a force on the wire proportional to the current.

Enithoven: Indeed, Dr. Hodgkin. We could not measure currents that changed too rapidly or that were too weak, but the device was sufficient to record the electrocardiogram. Unlike Hodgkin and Huxley, I could not insert an electrode into a heart cell, so I had to be content with measuring the voltage produced on the body surface by the electrical activity of the distant heart.

Curie: And wasn’t it you, Dr. Einthoven, who assigned the names P-wave, QRS-complex, and T-wave to the various electrocardiogram deflections?

Enithoven: Yes it was. The P-wave corresponded to the atria depolarizing, the QRS-complex to the ventricles depolarizing, and the T-wave to the ventricles repolarizing.

Allen: And what about the atria repolarizing?

Einthoven: That tiny signal was buried in the QRS-complex.

Lauterbur: And how did ya interpret your data?

Einthoven: I imagined that the heart produced a dipole, which just means current passed out of the heart cells at one point and reentered the cells at another, like an electric dipole made from two charges separated by a distance. Really, the ECG is produced by tiny dipoles associated with each cardiac cell, but there are billions of cells so I simplified the situation by representing the current source as a single dipole.

Hodgkin: A “toy model”!

Einthoven: Yes, sometimes we must make approximations to simplify a complicated situation so we can understand it better. A dipole is a vector, meaning it has a magnitude and a direction. To determine its direction, I placed electrodes on the left arm, right arm, and left leg. These three electrodes roughly form an equilateral triangle…

Lauterbur: Einthoven’s triangle!

Einthoven: Some people started calling it that, which was quite an honor. The signal from the three electrodes forming “Einthoven’s” triangle, if you will, determine the dipole direction.

Curie: Can’t the electrocardiogram be used to treat diseases?

Einthoven: Not really treat, but diagnose. The details of the electrical signal provide information about heart arrhythmias. Once you know the type of arrhythmia, then you can treat it properly.

Allen: I believe that our modern artificial pacemakers and defibrillators are what you are referring to.

Einthoven: Yes. These miraculous devices can use ECG recordings to determine the correct place and time to stimulate the heart to overcome the arrhythmia. It is all quite wonderful, but those devices were invented long after I had left the scene.

Curie: But they’re based on your work, Dr. Einthoven. We all owe you a great debt of gratitude.

Einthoven: And to you, Dr. Curie, for your work on…

Allen: Before we discuss Dr. Curie’s research, I would like to hear from Dr. Lauterbur about his studies that led to magnetic resonance imaging.

Lauterbur: Steve, I’d love to talk about it. Some nuclei have a property called “spin.” A nucleus with spin, such as that of the hydrogen atom, precesses, or rotates, about a magnetic field, with its precession frequency proportional to the magnetic field strength. This precession is the basis for nuclear magnetic resonance.

Now, the secret to magnetic resonance imaging is to apply a large, static magnetic field that causes the spins to precess, plus a magnetic field gradient that you can turn on and off. The gradient makes the magnetic field larger in one location than another; it maps magnetic field strength to position. This causes the precession frequency to also vary with position. It’s the frequency that we measure during MRI. Therefore, the gradient maps frequency to position, allowing you to determine a nucleus’s location from its frequency.

Hodgkin: Wonderful! Why didn’t they call the method “nuclear magnetic resonance imaging”?

Lauterbur: Ha! People are so afraid of the word “nuclear” that they dropped it and renamed the technique “magnetic resonance imaging,” or MRI. Some people have such irrational fears of anything having to do with the nucleus or radiation.

Curie: I know what you mean, I remember when…

Allen: Yes, but let Dr. Lauterbur finish his story.

Lauterbur: I remember the day I came up with the idea of using gradient fields to do MRI. I was sitting in a Big Boy restaurant and it just came to me: Eureka! I immediately scribbled the thought down on the only thing I had available: a paper napkin.

Hodgkin: I’m glad they didn’t use cloth napkins.

Lauterbur: Ha. Not likely at a Big Boy. I would’ve walked out with it if they had. So I built the first simple MRI machine and started creating images. I tried to publish my initial results in the journal Nature…

Einthoven: Ah, that English journal is one of the finest in all of science.

Lauterbur: Perhaps, but they initially rejected my manuscript.

Curie: Goodness!

Lauterbur: They thought my images were too fuzzy. But they were the very first magnetic resonance images, for crying out loud. I persisted and asked them to review it again. It was finally published in Nature, and the article became a classic. I believe you could write the entire history of science in the last 50 years in terms of papers rejected by Science or Nature.

Allen: Really?

Lauterbur: Yes. I tried to patent my ideas, but Stony Brook decided not to pursue it. Patents are expensive, and they didn’t expect the potential earnings justified the cost of the lawyers and filing fees.

Curie: What a mistake.

Allen: Can you tell us a little about your controversy with Raymond Damadian regarding the invention of MRI.

Lauterbur: Steve, I thought ya might bring that up [audience laughs awkwardly]. Yes, Damadian also was working on imaging using MRI. He was particularly interested in finding if signals from a tumor were different from normal tissue. It was nice work, but it didn’t contain the idea of using a magnetic field gradient to map frequency to position, which is the essence of my method. When Peter Mansfield and I each received the Nobel Prize for developing MRI, Damadian took out a full-page ad in the New York Times claiming the prize should have gone to him too! He was bitter about it all his life. But I think history is on my side.

Einthoven: What about Herman Carr?

Lauterbur: Carr’s work was a precursor to mine and he probably had a better claim to the Nobel Prize than Damadian did. I should’ve cited Carrr’s work. And Mansfield thought Erwin Hahn deserved a piece of the prize for his discovery of spin echo. Scientific discoveries and inventions are complex processes, and the credit must often be shared among many researchers.

Hodgkin: Yes, I know. Besides Huxley, my work was assisted by Bernard Katz and William Rushton among others.

Allen: Including Kenneth Cole.

Hodgkin: [Sighs] And Cole.

Allen: Now, Dr. Curie, could you tell us a little of your important work.

Curie: Yes. I’ve been waiting patiently for my turn [quiet laughter]. First a little background. I lived in an exciting time for science…

Einthoven: I believe all times are exciting for science.

Curie: I agree, but the end of the 19th century was a particularly exciting time for physics. In 1895 Wilhelm Rontgen discovered x-rays (a type of very high frequency electromagnetic radiation) and then in 1896 Henri Becquerel discovered radiation from uranium. I decided to examine uranium in more detail.

Lauterbur: Didn’t you find three types of radiation: alpha, beta, and gamma?

Curie: No, Dr. Lauterbur, that was found by my good friend Ernest Rutherford. But back to my work. I started with a ton of pitchblende (an ore containing uranium) and analyzed it chemically, separating the radioactive and nonradioactive parts. My husband Pierre was so interested in this work that he abandoned his own research to help me. After years of analysis, we finally ended up with less than a gram of a new element we named radium. It was highly radioactive. Along the way, we also discovered another element, polonium, which I mentioned previously.

Hodgkin: Those discoveries must’ve made you very famous.

Curie: Well, it did allow me to finally obtain my doctorate from the University of Paris. I was then invited to the Royal Institution in London to lecture about radioactivity. But since I was a woman, I was not allowed to speak, and Pierre alone gave the presentation [indignant murmur from the audience]. The committee that decides the Nobel Prize was going to award it to only Pierre and Henri Becquerel, but Pierre put a stop to that. I miss Pierre so much. In 1906, he was killed in a road accident. It was devastating…

Allen: I’m so sorry, Dr. Curie [Allen pats Curie on the shoulder].

Curie: But I soldiered on. Almost immediately x-rays and radium began to be used in medicine, creating the new discipline of medical physics. During the First World War, my daughter Irene and I developed x-ray imaging equipment mounted on trucks that could be used as mobile radiography units at the front. They were known as “petites Curies,” or “Little Curies.” [Curie smiles.]

Einthoven: Was not Irene herself a famous scientist?

Curie: Yes, Irene and her husband won their own Nobel Prize for discovering artificial radioisotopes.

Allen: I know this may be a delicate subject, but could you tell us about your relationship with physicist Paul Langevin?

Curie: Mr. Allen, I’m surprised you have so little tact [audience laughs nervously]. But I suppose if you must know, Paul was a former student of Pierre’s. He was married, but was estranged from his wife. After Pierre died, Paul and I were lovers. The press got a hold of the news (by that time I was quite famous) and started calling it the “Langevin affair.” They tortured me about that relationship.

Allen: Thank you, Dr. Curie, for sharing that difficult part of your past. [Looking up at the entire group] There is one thing all four of you have in common. You all won a Nobel Prize.

Lauterbur: Yes, you’ve already heard my embarrassing story about the prize. I received mine, jointly with Mansfield, for Physiology and Medicine.

Hodgkin: I also received mine in Physiology or Medicine, along with Huxley and neurophysiologist John Eccles.

Einthoven: Mine was for Physiology or Medicine too, but it was a solo award.

Curie: I’m so proud of you all. But gentlemen, do any of you have two Nobel Prizes [all laugh]?

Hodgkin: Yes, Dr. Curie, you were the first woman to receive a Nobel Prize, and you ended up with two: one in physics and one in chemistry [several young female members of the audience start stomping their feet and cheering for Curie; one yells “girl power!”].

Allen: [Laughing] With that thought, my friends, I fear we have run out of time. I hope you will join us again next week for another episode of Meeting of Minds.

One Hot Summer: Dickens, Darwin, Disraeli, and the Great Stink of 1858

One Hot Summer,
by Rosemary Ashton.

I recently finished Rosemary Ashton’s book One Hot Summer: Dickens, Darwin, Disraeli, and the Great Stink of 1858. Her prologue begins

What was it like to live in London through one of the hottest summers on record, with the Thames emitting a sickening smell as a result of the sewage of over two million inhabitants being discharged into the river? How did people cope with the extraordinary heat leading up to the hottest recorded day, Wednesday, 16 June 1858? What did those living or working near the Thames—including at the Houses of Parliament and the law courts in Westminster Hall—do when they found their circumstances intolerable? What did the newspapers say?

Ashton proposes to examine London for just a few months in the summer of 1858, providing a snapshot of one moment in Victorian England. Such a microhistory provides insight into the life of mid-19th century Britain.

Microhistory, the study in depth and detail of historical phenomena, can uncover hitherto hidden connections, patterns, and structures. Some events and incidents are revealed over time to have been life changing or nation building. Examples from 1858 are the tackling of London’s sewage and the resultant improvement of public health, Brunel’s engineering feats, the initial laying of the Atlantic telegraph cable, the beginnings of a long process of attaining justice and equality in the matter of marriage and divorce, and the transformation of the miscellaneous medical practice into a proper profession.

She focuses on the novelist Charles Dickens, biologist Charles Darwin, and politician Benjamin Disraeli.

A comparatively neglected time in Disraeli’s career can be shown to have been remarkably important in bringing him to prominence. The attention of historians and biographers has focused hitherto on his reckless youth, his racy novels, his controversial journalism, and his late-won success from 1868, when he finally became prime minister. His hard work in the parliamentary session of 1858, particularly in the hectic weeks before the summer break beginning on 2 August, and his success in turning round a hostile press and distrustful colleagues by his efforts, deserve to be acknowledged. In Dickens’s case his painful and self-exposing actions in connection with his failed marriage have been fully discussed, but no detailed account exists of the day-to-day struggles he faced in the long summer which followed his catastrophic error of judgment in advertising his separation from his wife in the early days of June. As for Darwin, though much has been written about his abrupt shock and change of plans on receiving in mid-June Wallace’s letter outlining natural selection, little attention has been paid to the interaction between his family life and scientific work in summer 1858.

This idea of a microhistory sounds fun, and I thought readers of Intermediate Physics for Medicine and Biology might be interested in learning about events in the summer of 1858 that influenced physics, biology, and medicine. So, in this blog post I augment Ashton’s analysis by adding incidents from the world of science.

Charles Darwin (age 48, all ages are as of summer 1858) had been developing his theory of evolution by natural selection for twenty years, since returning to England in 1836 after his famous voyage on the HMS Beagle. Over the years he had told his friends Joseph Hooker (age 41) and Charles Lyell (age 61) about his ideas, but had never published them. Ashton describes how on June 18, 1858 Darwin received a letter from Alfred Russel Wallace (age 35), containing a draft of a paper describing the same idea of natural selection as the mechanism of biological evolution, written while Wallace was collecting biological specimens in the Malay Archipelago. Hooker and Lyell arranged to have some early private writings of Darwin’s, along with the paper by Wallace, published on July 1 at a meeting of the Linnean Society of London. 

On the Origin of Species,
by Charles Darwin.

The following year, Darwin published his much more detailed book On the Origin of Species, changing biology forever. One of the most pugnacious of the advocates for natural selection was his young friend Thomas Henry Huxley (age 33), known as “Darwin’s Bulldog.” In 1858 Huxley was the Fullerian Professor of Physiology at London's Royal Institution, and on June 17, 1858 he gave the Royal Society’s annual Croonian Lecture. Darwin’s friend Charles Lyell—winner of the Royal Society’s prestigious Copley Medal in 1858 for his contributions to geology—never completely embraced natural selection.

On June 10, 1858 the botanist Robert Brown died in London, at age 84. In Chapter 4 of IPMB, Russ Hobbie and I write

This movement of microscopic-sized particles, resulting from bombardment by much smaller invisible atoms, was first observed by the English botanist Robert Brown in 1827 and is called Brownian motion.

Brown’s death had an interesting impact on the Darwin/Wallace publications. Ashton writes

By a stroke of luck the death of the former president Robert Brown had induced the [Linnean] society to postpone its summer meeting from 17 June, the day before Darwin received Wallace’s letter, to Thursday, 1 July. This meant that Darwin (and Wallace) would not have to wait until September to have their papers made public.

One of the most famous scientists in England during 1858 was Michael Faraday (age 65). In Chapter 8 of IPMB, Russ and I discuss electromagnetic induction, which underlies transcranial magnetic stimulation of the brain.

In 1831 Michael Faraday discovered that a changing magnetic field causes an electric current to flow in a circuit.

Faraday, Maxwell, and the
Electromagnetic Field,
by Forbes and Mahon.

After a long career at the Royal Institution, Faraday moved from his home at the RI to a house at Hampton Court in 1858. In their book Faraday, Maxwell, and the Electromagnetic Field, Nancy Forbes and Basil Mahon write

As Faraday’s health and mental faculties declined, he began to relinquish his various responsibilities at the Royal Institution, finally handing over the directorship to John Tyndall in 1865. The consequent loss of income, and of his flat, would have been a worry, but in 1858 Prince Albert, a great admirer, had asked the queen to put a house at Hampton Court at his disposal. Faraday had refused at first, fearing the high cost of repairs, but the queen said she would pay. He and Sarah [his wife] moved in, and the new house became his last home.

Although his research career was winding down, Faraday was still a great science communicator. On June 12, 1858 he gave a RI lecture “On the relation of gold to light,” about light scattering from gold colloids (nowadays we would call them gold nanoparticles). He was also famous for his Christmas lectures, which he gave annually throughout the 1850s.

Faraday’s work in electricity and magnetism was carried on by the young James Maxwell (age 27), who was married on June 2, 1858 in Aberdeen, Scotland. That year, Maxwell published his paper “On Faraday’s Lines of Force” (although it had been read before the Cambridge Philosophical Society in late 1855 and early 1856). Forbes and Mahon write

In February 1857, [Maxwell] decided to send a copy of his paper “On Faraday’s Lines of Force” to the great man [Faraday]. No doubt, he did so with some trepidation… He needn’t have worried. As we’ve seen, Faraday’s response was grateful, gracious, and charming. The two had at once formed a rare bond.

In the 1860s Maxwell continued his research on electromagnetism, and eventually developed the four Maxwell’s equations that rival Darwin’s theory of evolution as the most significant scientific contribution of the 19th century.

A Thread Across the Ocean,
by John Steele Gordon.

Besides Faraday and Maxwell, a third great Victorian physicist was William Thomson (age 34), who was one of the main scientists involved in developing the transatlantic telegraph. As part of that effort, in February of 1858 Thomson patented the mirror galvanometer, which is an instrument to measure electrical current. In his book A Thread Across the Ocean, John Steele Gordon describes this device.

In a long submarine cable, immersed in a conducting medium—saltwater—the current if often very low, sometimes no more than ten mircoamperes. (The current in a standard incandescent lightbulb is about 100,000 times as great.) The standard galvanometers then available were often inadequate to detect a signal coming through a cable that would be two thousand miles long. So Thomson—half Einstein, half Edison—developed a much better one. He took a very small magnet and attached a tiny mirror to it. Both together weighed no more than a grain. He suspended the magnet from a silk thread and set it in the middle of the coil of very thin insulated copper wire.

When the faint current flowing through the cable was allowed to flow through the copper coil, it created a magnetic field. This caused the magnet, with its attached mirror, to deflect. Thomson simply directed a beam of light from a shaded lamp onto the mirror and allowed it reflection to hit a graduated scale.

In June of 1858 two ships—the Agamemnon and the Niagara—attempted to meet in the middle of the Atlantic Ocean, splice together the two halves of the cable, and then each pay out the cable as they sailed toward shore: the Niagara toward Newfoundland and the Agamemnon toward Ireland. However, a terrible storm struck the North Atlantic that month, nearly capsizing the Agamemnon with Thomson on board and aborting the mission.

On Sunday, June 20, the storm unleashed a fury such as few sailors ever see and even fewer live to tell about. The caption feared that the coil on the deck, working against its restraints, might break lose and smash through the side, undoubtedly causing the ship to founder.

A second try several weeks later proved more successful. On August 16, the first transatlantic telegraph message was sent between Queen Victoria in England and President James Buchanan in the United States. Unfortunately, the cable soon failed, and it was not until some years later that reliable telegraph service was established across the Atlantic.

Based on his basic research discoveries and his contributions to the telegraph, Thomson became a scientific hero. Gordon writes

In 1892, William Thomson became the first British scientist to be raised to the peerage, when Queen Victoria created him Lord Kelvin of Largs. He has been known ever since as Lord Kelvin. In 1908, the year after he died, the Kelvin temperature scale, devised by him in the 1850s, was named in his honor.

The absolute temperature scale, with Kelvin’s name attached to the unit of temperature, appears throughout IPMB.

Still another notable Victorian physicist was George Stokes (age 36), who at that time was the Lucasian Professor at Cambridge University (a position held earlier by Isaac Newton and later by Stephen Hawking). IPMB often uses Stokes’ law for the viscous force of a small sphere in a fluid. Stokes and Thomson were close friends, and their many letters are preserved. I provide a few excerpts from these letters during late 1857 and 1858.

2 College, Glasgow

Dec. 23, 1857

My Dear Stokes

That principle, in the hydrodynamics of a “perfect liquid”, which I first learned from you, is something that I have always valued as one of the great things of science, simple as it is, and I now see more than ever its importance. One conclusion from it is that instability, or a tendency to run to eddies, or any kind of dissipation of energy, is impossible in a perfect liquid (a fluid with neither viscosity nor compressibility)... [several pages follow with many equations]...Some of the simplest applications of the theory are very interesting: for instance the... case of a circular disc or oblate spheroid, moving... in a perfect [liquid]...

As to Faraday’s magneto-optic experiment, I think my argument that it must depend on a peculiar state of motion induced by magnetic influence (Proceedings R. S. June or July 1856) is unanswerable. Have you considered it?...

It seems like old times for me to be writing you so long a letter, and I am afraid you will be less disposed to be so bored. Your redress simply be not to read it.

With best wishes for a “Merry Christmas” of which there can be no doubt now, I remain

Yours always truly

William Thomson

Stokes responded,

69 Albert Street Regent's Park London N.W.

Feb. 12, 1858

My Dear Thomson,

I have been so very busy of late that your letter has remained for a long time unanswered. I now set to answer it, though I have still got plenty of work before me...

Without having a decided opinion either way I have always inclined to the belief that the motion of a perfect incompressible liquid, primitively at rest, about a solid which continually progressed, was unstable... [pages of math...]

In speculating a good while ago (in fact no great time after Faraday’s discovery) as to the cause of magnetic rotation I naturally tried rotations of the luminiferous ether as suggested by Ampere’s theory...

Yours very truly

G. G. Stokes

Finally, late in 1858, Stokes wrote

The Athenaeum

Oct 5/58

My Dear Thomson,

... It is a great pity to see the [transatlantic] cable in its present state after apparently so successful a laying down. Still the thing has been done and even if this should be utterly lost the matter will not I presume rest there.

I did not go to Leeds this meeting [The British Science Association met in Leeds in 1858]. On the morning of the 27th my wife was safely delivered of a fine boy. She is going on very well but I am afraid her complete recovery will be slow.

Yours very truly

G. G. Stokes

James Joule (age 39) was yet another English physicist of the Victorian era. His name appears repeatedly in IPMB because the unit of energy is named after him. In the 1840s Joule had done pioneering work on the mechanical equivalent of heat and the conservation of energy, and in the 1850s had collaborated to explain the Joule-Thomson effect. In 1858 he was in a train wreck while traveling home from London. Although unhurt, the accident made him reluctant to travel, somewhat isolating him from the scientific community.

Gray’s Anatomy.

 A major event in medicine occurred during the summer of 1858: the publication of the first edition of Gray’s Anatomy. In his article “Happy Birthday, Gray’s Anatomy,” Adrian Flatt (Proc. Bayl. Med. Cent., 22:342–345, 2009) writes

Anatomy Descriptive and Applied was first published in London in the summer of 1858 by two young demonstrators of anatomy in St. George’s Hospital at Hyde Park Corner… These two young men were very different. Henry Gray [age 31] wrote the text; he was 4 years older than Henry Vandyke Carter [age 27], who drew all the illustrations…

The print number of 2000 books had been decided, page size was fixed, and all the paper purchased. Considerable adjustments were successfully made and by mid May 1857, the work was going well but was to be interrupted by the absence of Gray. He had received an invitation to “attend” the Duke of Sutherland on his private yacht sailing around England and Scotland and at the estate at Dunrobin Castle for the next 6 months, from June to November 1857. This was manna from heaven for Gray; service for such an aristocrat would be of enormous help to his practice. Carter continued work on the book, of which the final proof corrections were done in late June or early July 1858, in time for the book to be available for students arriving in September.

Gray died at age 34, just three years after publication of his textbook, of smallpox. Apparently the relationship between Gray and Carter was strained. Flatt states that

Gray never gave Carter one penny from all the royalties the early editions of the book earned.

Diagram of the causes of mortality
in the army in the East (1858).

Another leading figure of Victorian health care was Florence Nightingale (age 38), the founder of modern nursing. In 1858 Nightingale published Notes on Matters Affecting the Health, Efficiency, and Hospital Administration of the British Army. Founded Chiefly on the Experience of the Late War. Presented by Request to the Secretary of State for War. This work contained a color statistical illustration called “Diagram of the Causes of Mortality in the Army of the East” that showed that epidemic disease—which caused more British deaths during the Crimean War than battlefield wounds—could be controlled by nutrition, ventilation, and shelter. The infographic became known as Nightingale’s “coxcomb.” Her achievements in statistics were so remarkable that in 1858 she was selected as the first woman fellow of the Royal Statistical Society. Two years later she established her nursing school at Saint Thomas’ Hospital in London.

Another noteworthy happening in medicine was the death of John Snow (age 45) on June 16, 1858 (London’s hottest day of that steamy summer). Snow was best known for figuring out the source of the Broad Street cholera outbreak in 1854, when he demonstrated that cholera was being spread through contaminated water from one specific pump. He also studied using ether as an anesthesia during surgery. 

The Ghost Map,
by Steven Johnson.

In his fascinating book The Ghost Map, Steven Johnson writes about the prevailing belief that miasma (bad air) caused disease.

In June 1858, a relentless early-summer heat wave produced a stench of epic proportions along the banks of the polluted Thames. The press quickly dubbed it the “Great Stink”... [Yet] the rates of death from epidemic disease proved to be entirely normal. Somehow the most notorious cloud of miasmatic air in the history of London had failed to produce even the slightest uptick in disease mortality... It's easy to imagine John Snow taking great delight in [this] puzzling data... But he never got the opportunity. He had suffered a stroke in his office on June 10... and died six days later, just as the Great Stink was reaching its peak above the foul waters of the Thames.

Joseph Lister (age 31) was in Edinburgh in 1858, studying the coagulation of blood and inflammation. In the 1860s he developed antiseptic surgery, and later relocated to London. In their article “Joseph Lister: Father of Modern Surgery” (Can. J. Surg., 55:E8–E9, 2012), Dennis Pitt and Jean-Michel Aubin claim that 

it was Lister’s application of germ theory to the care of surgical patients that laid the foundation for what surgeons do now. He directed the minds of physicians and surgeons to the vital necessity of keeping wounds clean and free of contamination.

Finally, in 1858 Elizabeth Garrett Anderson (age 22) was a young woman dreaming of making a career in medicine. She eventually became the first female doctor in the United Kingdom.

Ashton believes that microhistory provides valuable insight into Victorian England. Near the end of her Prologue she concludes

Intense scrutiny of the lives of these men [Dickens, Darwin, and Disraeli, plus Brown, Faraday, Maxwell, Thomson, Stokes, Joule, Gray, Nightingale, Snow, and others] over a short period of a few months allows us to make fresh threads of connection between each of them and the larger society in which they lived, all at a time of public events which provided to be of lasting national importance.