Knife Edge Diffraction

Intermediate Physics for Medicine and Biology doesn’t analyze diffraction. It’s mentioned a few times—in the chapters about images (Chap. 12), sound (Chap. 13), and light (Chap. 14)—but it’s never investigated in detail. In this post, I want to take a deeper dive into diffraction. In particular, we will examine a specific example that highlights many features of this effect: diffraction from a knife edge.

Assume a plane wave of light, with intensity I₀ and wavelength λ, is incident on a half-infinite opaque screen (the knife edge, shown below with the incident light coming from the bottom upwards). If optics were entirely geometrical (light traveling in straight lines with no effect of its wavelength) the screen would cast a sharp shadow. All the light for x < 0 would continue propagating upward (in the y direction) while all the light for x > 0 would be blocked. But that’s not what really happens. Instead, light diffracts off the screen, causing fringes to appear in the region x < 0, and some light entering the shadow region of x > 0.

Optics,
by Hecht and Zajac.

Knife-edge diffraction is one of the few diffraction problems that we can solve analytically. I’ll follow the solution given in Hecht and Zajac’s textbook Optics (1979), which I used in my optics class when I was an undergraduate physics major at the University of Kansas. The solution to the knife-edge problem involves Fresnel sine and cosine integrals

I’ve plotted C and S in the top panel of the figure below. Both are odd functions that approach one half as ξ approaches infinity, albeit with many oscillations along the way. There’s lots of interesting mathematics behind these integrals, like the Cornu spiral, but this post is long enough that we don’t have time for that digression. 

If we solve for the intensity distribution beyond the screen (y > 0), we get 

This is an interesting function. When I first saw this solution plotted, I noticed oscillations on the left (x < 0) but none in the shadow region on the right (x > 0). But C and S are both odd, so they oscillate on the right and left. The middle two panels in the figure above show how this happens. Taking one half minus C and one half minus S just flips the two functions and adds a constant, so the functions vary from roughly zero to one instead of minus a half to plus a half. When you square these functions, the oscillations that are nearly equal to zero get really small (a small number like one tenth, when squared, gets very small) while the oscillations that are nearly equal to one are preserved (one squared is just one). There are still some small oscillations in the shadow region (x > 0), but somehow when you add the cosine and sine parts even they go away, and you end up with the classic solution in the bottom panel, which you see in all the textbooks.

I was curious to know is how this function behaves for different wavelengths. Diffraction effects are most important for long wavelengths, but for short wavelengths you expect to recover plain old geometrical optics. Interestingly, the wavelength λ only appears as a scaling factor for x in our solution. So changing λ merely stretches or contracts the function along the x axis. The figure below shows the solution for three different wavelengths. Note that the argument of the Fresnel sine and cosine functions is dimensionless: x has units of distance, but so do the wavelength λ and the distance past the opaque screen y, and they appear as a product under a square root. Therefore, we don’t need to worry about the units of x, y, and λ. As long as we use consistent units we are fine. As the wavelength gets small, the distribution gets crowded together close to x = 0. The red curve is the geometrical optics limit (λ = 0). The case of λ = 0.1 approaches this limit in a funny way. The amplitude of the oscillations does not change, but they fall off more quickly, so they basically only exist very near the knife edge. You wouldn’t notice them unless you looked with very fine spatial resolution. The intensity does seep into the shadow regions, and this is more pronounced at large wavelengths than at small. 

The picture above was plotted for one distance, y = 1. It’s what you would get if you put a projector screen just behind the knife edge so you could observe the intensity pattern there. What happens if you move the screen farther back (increase y). Since y and λ enter our solution only as their product, changing y is much like changing λ. Below is a plot of intensity versus x at three different values of y, for a single wavelength. Making this plot was simple: I just changed the labels on the previous plot from λ to y, and from y to λ. As you get farther way (y gets larger), the distribution spreads out. But the spreading is not linear. Because of that square root, the spreading slows down (but never stops) at large y.

You can see the full pattern of intensity in the color plots below. Remember, x is horizontal and the opaque screen is on the right, y is vertical and opaque screen is at the bottom, and color indicates intensity. Yellow is the incident intensity I₀, and blue is zero intensity (darkness). The geometrical limit would be a strip of blue on the right (the shadow) and yellow on the left (the unobstructed incident wave). The case for λ = 0.01 closely approximates this. The case of a really long wavelength (λ = 100) is interesting. The light spreads out all over, giving more of a uniform distribution. For long wavelengths, the light “bends” around the opaque screen. This is why you can still hear music even if there is an obstacle between you and the band. The sound wave diffracts because of its long wavelength (especially the low pitched notes).

Diffraction is fascinating, but it’s a bit too complicated to be included in IPMB. Nevertheless, it’s a part of the physics behind visual acuity, microscope resolution, ultrasound transducers, and many other applications.

The Age of Reason Begins

The Age of Reason Begins,
by Will and Ariel Durant.

The title of this week’s post is ironic, because with all the events of the last few months I often suspect that the Age of Reason is coming to a close. The title comes from volume seven of Will and Ariel Durant’s The Story of Civilization. After I retired from Oakland University, I set about reading the entire eleven-volume series. The subtitle of The Age of Reason Begins is: A History of European Civilization in the Period of Shakespeare, Bacon, Montaigne, Rembrandt, Galileo, and Descartes: 1558–1648.

Today I want to focus on Francis Bacon, who is probably the central figure in the Durants’ book (his picture was their choice for gracing the book’s cover). They introduce him this way.

Francis Bacon, who was destined to have more influence on European thought than any other Elizabethan, had been born (1561) in the very aura of the court, at York House, official residence of the Lord Keeper of the Great Seal, who was his father, Sir Nicholas; Elizabeth called the boy ‘the young Lord Keeper.’ His frail constitution drove him from sports to studies; his agile intellect grasped knowledge hungrily; soon his erudition was among the wonders of those ‘spacious times.’

Why bring up Bacon now? Well, the last few months have seen unprecedented attacks on science and scientists: Budget cuts to the National Institutes of Health and the National Science Foundation, climate change denial and vaccine hesitancy, conspiracy theories, political requirements for government funding, the demonization of scientists such an Anthony Fauci, and more. It seems like something horrible happens every day. This makes me wonder: what is the key feature of science that must be preserved above all else? What one thing must we save? I can think of many possibilities. Science drives our economy and prosperity. Scientific discoveries have led to amazing advances in human health. Educating and providing opportunities for our young scientists is a critical investment in our future. Yet, as important as these things are, they aren’t the central issue. They aren’t what we must save lest all be lost. It’s this key element of science, its essence, that brings me to Francis Bacon.

Bacon was an early promoter of the scientific method. The Durants write

Bacon felt that the old Organon [of Aristotle] had kept science stagnant by its stress on theoretical thought rather than practical observation. His Novum Organum proposed a new organ and system of thought—the inductive study of nature itself through experience and experiment. Though this book too was left incomplete, it is, with all its imperfections, the most brilliant production in English philosophy, the first clear call for an Age of Reason.

Let me explain (and perhaps expand on) Bacon’s idea in my own words. How do we know what is true and what is not? By evidence. By experiment. By data. By comparing our ideas to what we can measure happening in the world. By accepting as true only those hypotheses that survive our best efforts to disprove them. By submitting our conclusions to rigorous peer review from our fellow scientists. Yet the current Republican administration seems to have its own ideas of what is true, regardless of the evidence. This is the very opposite of science. It is anti-science.

For example, the reality of climate change and humanity’s impact on global warming is backed by an enormous body of data. We have records of temperature, carbon dioxide concentration, and increasingly violent storms. We have sophisticated mathematical models with which we can conduct numerical experiments to predict what will happen in the future. The evidence is truly overwhelming. Yet, many—including President Trump—don’t care about the evidence. They claim climate change is a “hoax.” They don’t back these claims with facts. They don’t approach the topic as an inductive study based on experience and experiment. They believe things for their own reasons that have nothing to do with evidence or science.

Another example is vaccines. There are so many clinical studies showing that vaccines don’t cause autism. Again, the evidence is overwhelming. Yet people like Health and Human Services Secretary Robert F. Kennedy, Jr. believe just the opposite: that autism is caused by vaccines. They don’t support such claims by presenting new evidence. While they occasionally drag up discredited studies or cherry-pick data, they don’t systematically examine all the evidence and weigh both sides. They don’t try to falsify their hypotheses. They don’t subject their ideas to peer-review. 

Still another example is the source of covid. The evidence is uncertain enough that we cannot say definitively how the covid pandemic arose. Yet, the data points strongly in one direction: Spillover from an animal to a human. Nevertheless, the government’s covid.gov website now claims that the “lab leak” hypothesis has been proven, and asserts that covid arose from sinister events in a lab in China. No, we don’t know that. While we can’t yet be certain, the evidence suggests that the cause was not a lab leak. Just because some politicians want the source of covid to be a lab leak doesn’t make it so.

One more example, of particular relevance to Intermediate Physics for Medicine and Biology, is cell phone safety. Although again there are uncertainties in the data (especially in laboratory experiments), the evidence suggests that radiofrequency electromagnetic radiation from cell phones does not cause cancer. I think that to say “suggests” is an understatement. The evidence is compelling that cell phones are safe. Yet RFK Jr. and others continue to argue otherwise, as if evidence doesn’t matter.

I would love to be proved wrong, and shown that, say, climate change is actually not happening. That would truly be wonderful, and millions of lives would be saved. But you have to prove that using evidence. You can’t just declare it. My dad was born in Kansas City and he used to say “I’m from Missouri and you have to show me!” That’s the gist of what it means to be a scientist. You have to show me, not tell me. Convince me with the data.

So, what is the feature of science that is essential? What aspect, if we lose it, means we no longer have science at all. I would say the belief that evidence matters. That experiments are how we determine what is true and what is not. If we give that up, all is lost and we’re back to the age of faith. Not religious faith necessarily, but an age where truth is determined not by evidence but by what is consistent with your personal beliefs, your friends and family, your wishful thinking, your fears, or your politics. The supremacy of evidence is where we must focus our resistance. That must be our line in the sand that we will not cross. That must be the hill from which we defend against the onslaught of the Republican War on Science, so that the Age of Reason can resume.

Francis Bacon,
From the cover of
The Age of Reason Begins.

The Durants conclude

Because he [Bacon] expressed the noblest passion of his age—for the betterment of life through the extension of knowledge—posterity raised to his memory a living monument of influence. Scientists were stirred and invigorated not by his method but by his spirit. How refreshing, after centuries of minds imprisoned in their roots or caught in webs of their own wistful weaving, to come upon a man who loved the sharp tang of fact, the vitalizing air of seeking and finding, the zest of casting lines of doubt into the deepest pools of ignorance, superstition, and fear!...

…[Bacon] repudiated the reliance upon traditions and authorities; he required rational and natural explanations instead of emotional presumptions, supernatural interventions, and popular mythology. He raised a banner for all the sciences, and drew to it the most eager minds of the succeeding centuries.

The Philosophy of Sir Francis Bacon, from Let’s Talk Philosophy.

https://www.youtube.com/watch?v=Mj4N0O7QnPY

Women in the IPMB100

Intermediate Physics for
Medicine and Biology.

Last week I presented the IPMB100, a list of the one hundred people who most influenced Intermediate Physics for Medicine and Biology. In that post, I noted that my list contained few women. Because I support diversity, equity, and inclusion—and because students reading IPMB may be wondering where all the women in biological and medical physics are—this week I’d like to explore the contributions of women to IPMB in more detail. My list last week included Marie Curie, Eugenie Mielczarek, Eleanor Adair, and Irene Stegun. What other females might I have added? 

One would be my friend Natalia Trayanova (born 1960?). I collaborated with Trayanova back in the 1990s, when I was at the National Institutes of Health and she was at Duke University. She is cited in IPMB when Russ Hobbie and I discuss the bidomain model of cardiac tissue. She’s been inducted into the Women of Technology International Hall of Fame and has received the Distinguished Scientist Award from the Heart Rhythm Society. She’s now on the faculty of Johns Hopkins University. 

Another candidate is Rita Hari (born 1948). Russ and I included the biomagnetism researcher Matti Hämäläinen in the IPMB100 list, and Hari is from the same Finnish research group and has made similar contributions as Hämäläinen. She was in fact second author after Hämäläinen on the definitive review article that Russ and I cite about magnetoencephalography (MEG). We cite another paper by Hari when discussing the clinical applications of the MEG.

Bettyann Kevles (1938–2023) was an award-winning author in the Department of History at Yale. Russ and I cite her book Naked to the Bone: Medical Imaging in the Twentieth Century when we discuss the history of imaging.

Frances Ashcroft (born 1952) is an Oxford physiologist known for her work on ion channels. Her popular science book The Spark of Life: Electricity and the Human Body is cited in IPMB when Russ and I discuss channelopathies.

I knew Carri Glide-Hurst (born 1979) when she was at Wayne State University here in southeast Michigan. She’s currently associated with the famous University of Wisconsin medical physics program. In IPMB Russ and I cite her Point/Counterpoint article in the journal Medical Physics, which examines the use of ultrasound for breast cancer screening.

Elizabeth Cherry (born 1975?) at Georgia Tech is a biomedical engineer who works on modeling cardiac electrophysiology. She is a co-author on a landmark paper looking at ways to perform low-energy defibrillation.

The contributions of three of my graduate students—Marcella Woods, Debbie Janks, and Debbie Langrill Beaudoin—are honored in IPMB by having their research turned into homework problems. And Russ’s daughter Sarah is cited for her studies on fitting ecological data using exponentials.

Several other women scientists have influenced IPMB but are not explicitly mentioned or cited in the textbook. These include Lisa Meitner (who worked on Auger electrons simultaneously with but independently of Auger); Rosalind Franklin (whose x-ray diffraction data was critical in Watson and Crick’s model of the structure of DNA); Dorothy Crowfoot Hodgkin (another x-ray crystallographer who discovered the structure of penicillin and insulin); Irene Joliot-Curie (a daughter of Marie Curie who, together with her husband Frédéric Joliot-Curie, discovered induced radioactivity); Rosalyn Yalow (invented the radioimmunoassay); Marie Goeppert Mayer (helped develop the nuclear shell model), Wanda Krassowska (a friend of mine and a colleague of Trayanova’s at Duke University in the 1990s, and who made fundamental contributions to the bidomain model of cardiac tissue); Maria Stuchly (a Polish/Canadian electrical engineer who studied the effect of microwaves on the body); and Marcela Panizza (an Italian clinical neurophysiologist who I collaborated with at NIH when working on magnetic stimulation).

So yes, many females have contributed to IPMB, and could easily have been included in the IPMB100. You could probably name even more. I suspect that future editions of IPMB will feature many more women.

IPMB100

I’m a regular reader of TIME magazine. Every year they publish an issue devoted to the TIME100: the hundred most influential people of that year. I thought I would do the same, except I’d focus on Intermediate Physics for Medicine and Biology. So, below is a list of the one hundred scientists, physicians, engineers, and mathematicians who most influenced IPMB. I list them by impact, with the most influential first.

Like for the TIME100, selecting the list is not an exact science. It’s based on mentions in IPMB, numbers of citations, and my own personal opinions. I’m sure your list would be different, and that’s okay.

There are many brilliant scientists who didn’t make the list (for example: Newton, Faraday, Maxwell, Rutherford, and Einstein). I tried to focus on people who had a direct impact on IPMB, rather than fundamental but not biomedical contributions to physics, so these and other luminaries were left off. 

The oldest scientists are Brown (born 1773) and Poiseuille (1797). The youngest are Basser, Goodsell, Hämäläinen, LeBihon, MacKinnon, Mattiello, Strogatz, and Xia (all more or less my age). I’m embarrassed to say there are only three women (Curie, Eleanor Adair, and Mielczarek; four if you count Abramowitz’s coauthor Stegun). Thirty three are alive today. Twenty are Nobel Prize winners (marked with an asterisk). I know ten personally (marked with a §). When I wasn’t sure about the year a scientist was born or died, I guessed and marked it with a question mark. There are many more I would like to honor, but I decided to—like TIME—stop at 100.

Enjoy!

1. Alan Hodgkin* (1914–1998) English physiologist who discovered how nerve action potentials work and developed the Hodgkin-Huxley model. 
2. Andrew Huxley* (1917–2012) English physiologist and computational biologist who discovered how nerve action potentials work and developed the Hodgkin-Huxley model. 
3. Godfrey Hounsfield* (1919–2004) British electrical engineer who invented the first clinical computed tomography scanner. 
4. Paul Lauterbur* (1929–2007) American chemist who developed a method to do magnetic resonance imaging using magnetic field gradients. 
5. Edward Purcell* (1912–1997) American physicist who co-discovered nuclear magnetic resonance, was author of the article “Life at Low Reynolds Number,” and wrote volume 2 of the Berkeley Physics Course titled Electricity and Magnetism. 
6. Allan Cormack* (1924–1998) South African physicist who developed much of the mathematical theory behind computed tomography. 
7. Hermann von Helmholtz (1821–1894) German physicist and physician; First to measure the propagation velocity of a nerve action potential. 
8. Adolf Fick (1829–1901) German physician and physiologist who derived the laws of diffusion (Fick’s laws). 
9. Willem Einthoven* (1860–1927) Dutch medical doctor and physiologist who was the first to accurately measure the electrocardiogram. 
10. Marie Curie** (1867-1934) Polish-French physicist and chemist who discovered the elements radium and polonium; The unit of the curie is named after her. 
11. Jean Léonard Marie Poiseuille (1797–1869) French physicist and physiologist who determined the law governing the flow of blood in small vessels. 
12. Max Kleiber (1893–1976) Swiss biologist who established a ¾ power law relating metabolic rate to mass. 
13. Felix Bloch* (1905–1983) Swiss-American physicist who co-discovered nuclear magnetic resonance and derived the Bloch equations. 
14. Peter Mansfield* (1933–2017) English physicist who developed techniques used in magnetic resonance imaging, including echo planar imaging. 
15. Roderick MacKinnon* (1956) American biophysicist who determined the structure of the potassium ion channel. 
16. Erwin Neher* (1944) German biophysicist who co-invented the patch clamp method to record from single ion channels. 
17. Bert Sakmann* (1942) German physiologist who co-invented the patch clamp method to record from single ion channels. 
18. Tony Barker (1950) English engineer who invented transcranial magnetic stimulation. 
19. Robert Plonsey§ (1924–2015) American engineer who contributed to theoretical bioelectricity and wrote Bioelectric Phenomena and other books. 
20. Peter Basser§ (1959?) American engineer who invented the magnetic resonance imaging technique of diffusion tensor imaging. 
21. William Oldendorf (1925-1992) American medical doctor who first designed a computed tomography device. 
22. J. B. S. Haldane (1892–1964) British evolutionary biologist who published “On Being the Right Size,” an essay about scaling. 
23. Geoffrey West (1940) British theoretical physicist who derived a model to explain the ¾ power law of metabolism. 
24. George Ralph Mines (1886–1914) English cardiac electrophysiologist who demonstrated reentry in cardiac tissue. 
25. Bernard Cohen (1924–2012) American physicist who opposed the linear no-threshold model of radiation risk. 
26. John Wikswo§ (1949) American physicist who measured the magnetic field of a nerve. 
27. Arthur Winfree§ (1942–2002) American mathematical biologist who studied cardiac arrhythmias and wrote When Time Breaks Down: The Three Dimensional Dynamics of Electrochemical Waves and Cardiac Arrhythmias. 
28. Richard Blakemore (1950?) Researcher who discovered magnetotactic bacteria. 
29. John Moulder (1945–2022) Radiation biologist who debunked suggestions that radiofrequency electromagnetic fields are dangerous. 
30. Kenneth Foster§ (1945) American bioengineer and expert on the biological effects of electromagnetic fields. 
31. Paul Callaghan (1947–2012) New Zealand physicist who wrote Principles of Nuclear Magnetic Resonance Microscopy. 
32. Paul Nunez (1950?) Analyzed electroencephalography using mathematics, and author of Electric Fields of the Brain. 
33. Charles Bean (1923–1996) American physicist who studied porous membranes and reverse osmosis. 
34. John Hubbell (1925–2007) American radiation physicist who measured and tabulated x-ray cross sections. 
35. Arthur Compton* (1892–1962) American physicist who analyzed Compton scattering of x-rays. 
36. William Bragg* (1862–1942) English physicist who discovered the Bragg peak of energy deposition from charged particles in tissue. 
37. Mark Hallett§ (1943) National Institutes of Health neurophysiologist who helped develop transcranial magnetic stimulation and wrote, with Leo Cohen, the article “Magnetism: A New Method for Stimulation of Nerve and Brain.” 
38. Selig Hecht (1892–1947) American physiologist who performed a classic experiment on scotopic vision. 
39. Milton Abramowitz (1915–1958) American mathematician who, with Irene Stegun, coauthored the Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. 
40. Knut Schmidt-Nielsen (1915–2007) Norwegian-American comparative physiologist and author of How Animals Work and Scaling: Why Is Animal Size So Important? 
41. Steven Vogel (1940–2015) American biomechanics researcher and author of Life in Moving Fluids: The Physical Biology of Flow and other books. 
42. Mark Denny (1951) American physiologist and author of Air and Water: The Biology and Physics of Life’s Media. 
43. Howard Berg (1934–2021) American biophysicist who studied the motility of E. coli and wrote Random Walks in Biology. 
44. Frank Herbert Attix (1925) Radiologist who is the author of Introduction to Radiological Physics and Radiation Dosimetry. 
45. Steven Strogatz (1959) American mathematician and author of Nonlinear Dynamics and Chaos and other books. 
46. Frederick Donnan (1870–1956) British chemist who analyzed Donnan equilibrium. 
47. Gustav Bucky (1880–1963) German-American radiologist who invented the Bucky grid used in x-ray imaging. 
48. Gopalasamudram Narayanan Ramachandran (1922–2001) Indian physicist who, with A. V. Lakshminarayanan, developed mathematical methods used in computed tomography. 
49. Peter Agre* (1949) American molecular biologist who discovered membrane water channels called aquaporins. 
50. Eleanor Adair (1926–2013) American physiologist who studied the health risks of microwave radiation. 
51. Robert Adair (1924–2020) American physicist who studied the biological effects of weak, extremely-low-frequency electromagnetic fields. 
52. Yuan-Cheng Fung (1919–2019) Chinese-American biomedical engineer, and author of Biomechanics. 
53. Herman Carr (1924–2008) American physicist and pioneer in magnetic resonance imaging. 
54. Matti Hämäläinen (1958) Finnish physicist who was lead author on the article “Magnetoencephalography—theory, instrumentation, and applications to noninvasive studies of the working human brain”. 
55. Saul Meiboom (1916–1998) Israeli researcher who, with David Gill, co-invented of the Carr-Purcell-Meiboom-Gill pulse sequence used in magnetic resonance imaging. 
56. Oskar Klein (1894–1977) Swedish physicist who, with Japanese physicist Yoshio Nishina, developed the Klein-Nishina formula for Compton scattering of x-rays. 
57. Chad Calland (1934–1972) Medical doctor, kidney transplant patient, and author of the paper “Iatrogenic Problems in End-Stage Renal Failure.” 
58. Walter Blount (1900–1992) American orthopedic surgeon who advocated for the use of a cane. 
59. Albert Bartlett (1923–2013) American physicist and author of The Essential Exponential! For the Future of Our Planet. 
60. Pierre Auger (1899–1993) French physicist who studied the emission of Auger electrons. 
61. Rolf Sievert (1896–1966) Swedish medical physicist who studied the biological effects of ionizing radiation; The unit of the sievert is named after him. 
62. Louis Gray (1905–1965) English physicist who worked on the effects of radiation on biological systems. The unit of the gray is named after him.
63. Richard Frankel (1943?) American researcher who studied magnetotactic bacteria. 
64. Frederick Reif (1927–2019) Austrian-American physicist who wrote volume 5 of the Berkeley Physics Course, titled Statistical Physics. 
65. Richard FitzHugh (1922–2007) Co-inventor, with Jinichi Nagumo, of the FitzHugh-Nagumo model of a neuron. 
66. Arthur Guyton (1919–2003) American physiologist and author of the Textbook of Medical Physiology. 
67. Leon Glass (1943) American researcher and co-author, with Michael Mackey, of From Clocks to Chaos: The Rhythms of Life. 
68. Ken Kwong (1948) Chinese-American nuclear physicist who studied functional magnetic resonance imaging. 
69. Seiji Ogawa (1934) Japanese biophysicist who studied functional magnetic resonance imaging. 
70. Jay Lubin (1947) National Cancer Institute epidemiologist who battled with Bernard Cohen over the linear no-threshold model and the risk of radon. 
71. Eugenie Mielczarek (1931-2017) American physicist and author of Iron: Nature’s Universal Element: Why People Need Iron and Animals Make Magnets. 
72. David Goodsell (1960?) American structural biologist and science illustrator who wrote the book The Machinery of Life. 
73. Philip Morrison (1915–2005) American physicist who was lead author on Powers of Ten. 
74. Henri Becquerel* (1852–1908) French physicist who discovered radioactivity; the unit of the becquerel is named after him. 
75. Wilhem Roentgen* (1845–1923) German physicist who discovered x rays; The unit of the roentgen is named after him. 
76. Bertil Hille (1940) American biologist and author of Ion Channels of Excitable Membranes. 
77. George Benedek (1928) American physicist who co-authored, with Felix Villars, the three-volume Physics with Illustrative Examples from Medicine and Biology. 
78. William Hendee (1938) Coauthor, with E. Russell Ritenour, of Medical Imaging Physics. 
79. John Cameron (1922–2005) Medical physicist and coauthor of Physics of the Body. 
80. Lawrence Stark (1926–2004) American neurologist and expert on the feedback system controlling the size of the pupil in the eye. 
81. Ernst Ruska* (1906–1988) German physicist who invented the electron microscope. 
82. Britton Chance (1913–2010) American physicist who developed biomedical photonics. 
83. Johann Radon (1887–1956) Austrian mathematician who developed the radon transform used in computed tomography. 
84. Alan Garfinkel (1944?) American researcher who analyzed cardiac restitution for controlling heart arrhythmias. 
85. Eric Hall (1950?) Author of Radiobiology for the Radiologist. 
86. Osborne Reynolds (1842–1912) British engineer who studied fluid mechanics; the Reynolds number is named after him. 
87. Bernard Katz* (1911–2003) German-British biophysicist and author of Nerve, Muscle, and Synapse. 
88. William Rushton (1901–1980) British physiologist who worked with Alan Hodgkin studying nerve conduction. 
89. Robert Eisberg (1928) Coauthor with Robert Resnick of Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles. 
90. John Clark (1936–2017) American bioengineer who worked with Robert Plonsey. 
91. Raymond Ideker§ (1942) American physiologist and medical doctor who studied the electrical activity of the heart. 
92. Denis LeBihan§ (1957) French physicist and medical doctor who developed diffusion magnetic resonance imaging, and worked with Peter Basser on diffusion tensor imaging. 
93. Ronald Bracewell (1921–2007) Author of Fourier Transforms and Their Applications. 
94. Robert Brown (1773–1858) Scottish botanist who discovered Brownian motion. 
95. Louis DeFelice (1940?–2016) Wrote Introduction to Membrane Noise. 
96. H. M. Schey (1930?) Author of Div, Grad, Curl, and All That. 
97. Warren Weaver (1894–1978) American mathematician and science administrator who wrote Lady Luck: The Theory of Probability. 
98. Peter Atkins (1940) English chemist and author of The Second Law. 
99. Yang Xia§ (1955) Oakland University physicist who studied the magic angle in magnetic resonance imaging. 
100. James Mattiello§ (1958-2017) Oakland University alumnus and American physicist who worked with Peter Basser and Denis LeBihan to developed diffusion tensor imaging.

Where Have You Gone, Physicist Bob Park? Our Nation Turns Its Lonely Eyes to You. Woo, Woo, Woo.

Voodoo Science, by Bob Park, superimposed on
Intermediate Physics for Medicine and Biology.

Bob Park died five years ago this week. He had been in poor health since suffering a stroke in 2013. Park was a physicist and the director of public information at the Washington office of the American Physical Society. He was a leading voice against pseudoscience, both in his weekly column What’s New (which, when in graduate school, I used to look forward to seeing in my email every Friday) and in his books such as Voodoo Science.

I wonder what Park would say if he were alive today? I suspect he would be horrified. But I doubt he would have said that. He was not a whine-and-fuss sort of guy. His tools were humor, irony, and sarcasm. Here is what I imagine What’s New would have looked like this week.

What’s New, by Bob Park

Friday, April 25, 2025

1. VITAMIN A FOR THE MEASLES

The Texas measles outbreak continues. Over 600 cases have now been reported, which is more than for the entire year in 2024. Health and Human Services Secretary Robert F. Kennedy, Jr. encouraged parents to treat their children suffering from measles with vitamin A, and now children are suffering from liver disease because of vitamin A overdosing. Why don’t parents simply ask their pediatrician what to do? Because pediatricians are part of the conspiracy, of course!

2. IF WE IGNORE IT, IT WILL GO AWAY

The Trump administration is trying to undo all the progress fighting climate change that has accumulated over the last few decades. His thinking is: if you ignore climate change, the problem goes away. Besides, it’s all a HOAX! King Canute tried this. He commanded the tide to stop coming in. How do you think that turned out? Physics has a way of winning in the end, whether or not it’s politically popular.  

3. LAB LEAK

The Trump administration has rewritten the covid.gov website to advocate for the lab leak hypothesis for the source of covid-19. Don't worry that the evidence is flimsy! If covid resulted from a lab leak, then it’s the scientists fault. Blame those arrogant liberal elitists like Fauci. But watch out for the next spillover event! (Can I interest anyone in some bird flu?)

4. LYSENKO

Back in the USSR, when Stalin was in charge, a crackpot named Lysenko took control of Russian science. He didn’t believe in modern genetics, regardless of the evidence. Russian agriculture collapsed and millions died. Here in the United States, we have our own version of the Lysenko affair. Trump is Stalin, RFK Jr is Lysenko, and vaccine hesitancy and climate change are genetics. I fear the outcome will be the same, which is bad for science and worse for humanity.

5. HOORAY FOR HARVARD

The NIH (remember that place that used to be the greatest biomedical research institution anywhere, ever?) has stopped funding grants to several universities, including Harvard. HARVARD! Apparently these universities will not cave in to Trump's ideological agenda. What will happen next? Who knows. Maybe Trump will be stopped by the Supreme Court. Maybe the House and Senate will decide they’ve had enough. And maybe, just maybe, it will be the end of American science.

Asimov’s Corollary

Regular readers of this blog know that I am a huge fan of Isaac Asimov. I decided on a career in science in large part from reading Asimov’s books. As a teenager I particularly enjoyed his collections of essays from The Magazine of Fantasy and Science Fiction. He wrote an essay there each month about science: astronomy, physics, chemistry, biology, geology, medicine, and even mathematics. Every time he collected seventeen essays, he would publish them in a book. It would not be an exaggeration to say that I came to be a coauthor on Intermediate Physics for Medicine and Biology largely because of the influence those essay collections had on me when I was young.

Quasar, Quasar, Burning Bright,
by Isaac Asimov.

This week I want to look at one of those essays that is especially germane today. It appears as the final chapter in the book Quasar, Quasar, Burning Bright. The essay is titled “Asimov’s Corollary,” and was first published in the February, 1977 issue of The Magazine of Fantasy and Science Fiction. Now, almost fifty years later, it seems more relevant than ever.  I urge you to get a copy and read it in its entirety. I will quote parts that I think are especially important. 

To help set the stage, let me note a few things.

• When Asimov mentions “Arthur” he is talking about Arthur C. Clarke, his fellow science fiction writer and good buddy. Along with Robert Heinlein, Asimov and Clarke are considered the “Big Three” in science fiction.
• Asimov loved to talk about himself. You might at first think he’s egotistical, but once you’ve read enough of his works you will realize it’s all a big act…sort of. It is one of the reasons I loved to read his essays.
• By today’s standards Asimov and Clarke sound a bit sexist, assuming all scientists are men. This is, in part, a sign of the times when they lived. I won’t defend their sexism, but I’ll forgive them because of all the good they did and all they taught me.

Asimov writes:

In Arthur’s book Profiles of the Future (Harper & Row, 1962) he advances what he himself calls “Clarke’s Law.” It goes as follows:

When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is very probably wrong…

…Naturally when I read a paragraph like that, knowing Arthur as I do, I begin to wonder if, among all the others, he is thinking of me…

Asimov was an elderly scientist at that time, and was fond of making all sorts of predictions, many of which claimed something was impossible.

Doesn’t Clarke’s Law make me uneasy, then? Don’t I feel as though I am sure to be quoted extensively, and with derision, in some book written a century hence by some successor to Arthur?

No, I don’t. Although I accept Clarke’s Law and think Arthur is right in his suspicion that the forward-looking pioneers of today are the backward-yearning conservatives of tomorrow, I have no worries about myself. I am very selective about the scientific heresies I denounce, for I am guided by what I call Asimov’s Corollary to Clarke’s Law. Here is Asimov’s Corollary:

When, however, the lay public rallies around an idea that is denounced by elderly but distinguished scientists and supports that idea with great fervor and emotion—the distinguished but elderly scientists are then, after all, probably right.

But why should this be?… Human beings have the habit (a bad one, perhaps, but an unavoidable one) of being human; which is to say that they believe in that which comforts them…

Asimov then examines a few cases of people believing things without evidence. He concludes

Then why do people believe? Because they want to. Because the mass desire to believe creates a social pressure that is difficult (and, in most times and places, dangerous) to face down. Because few people have had the chance of being educated into the understanding of what is meant by evidence or into the techniques of arguing rationally.

But mostly because they want to...

When I read this, I think of people claiming (falsely, we know from the evidence) that vaccines cause autism; I think of people claiming (again, falsely) that cell phone radiation causes cancer; and I think of people claiming (still again, falsely) that climate change is a hoax. When I hear these assertions, made passionately and vehemently but with no evidence provided, I think that the elderly scientists (what I would call “the scientific consensus”) is right after all. And while Asimov writes “probably,” I would write “almost certainly.”

I miss you, Isaac Asimov. We need you now more than ever.

 

There is a cult of ignorance. 

https://www.youtube.com/watch?v=oTV1iQyjFFU

 

 Isaac Asimov predicts the future.

https://www.youtube.com/watch?v=cIB1b_8hqB0

Oops!

Finding a mistake in something you wrote is always annoying. When revising the chapter on Atoms and Light for the sixth edition of Intermediate Physics for Medicine and Biology, I found a whopper. It’s on page 402 of the 5th edition, in the section on Blue and Ultraviolet Radiation. Here is the offending sentence:

The minimum erythemal dose at 254 nm is about 6 × 10⁷ J m^-2.

I was trying to add a homework problem to the sixth edition in which I would ask the student to calculate how long it would take to get sunburn for some typical ultraviolet light intensity and I kept getting a ridiculously long time (years) because our value of 6 × 10⁷ is way, way too big. The error goes back to the 3rd edition of IPMB, where you find a reference for that value:

Diffey, B. L. and Farr, P. M. (1991) Quantitative aspects of ultraviolet erythema. Clin Phys Physiol Meas 12:311-325.

The 3rd edition is even more specific, saying the value is in Table 2 in that paper. So, I obtained the article interlibrary loan (kudos to the Oakland University interlibrary loan office, who got the paper for me in about an hour on a Sunday evening). Here is Diffey and Farr’s Table 2. 

The value for minimal erythema at 254 nm is 6 mJ cm^-2, which is equivalent to 60 J m^-2. I think the incorrect value in IPMB arose because of a unit conversion error. There are 1000 millijoules in a joule, not 1000 joules in a millijoule. Such a mistake would cause a factor of one million error, which would result in an erroneous value of 60 × 10⁶ J m^-2, or 6 × 10⁷.

You may have some questions.

• Who did it? Although Russ Hobbie made the initial mistake (he was sole author on the 3rd edition), I read this number when teaching from our book, and when preparing the 4th edition and then again when preparing the 5th edition and never batted an eye. Apparently 60 MJ of UV light causing a person to have only a mild reddening of the skin didn’t bother me at all. I always tell my students to “THINK BEFORE YOU CALCULATE!” but I didn’t. 
• If it was in the book, how could it be wrong? Don’t believe everything you read. Just because something is written in a textbook doesn’t make it true. Authors try their best to get everything right, but sometimes they make mistakes. Read critically and thoughtfully. (I’m giving this advice to myself here, more than to you, dear reader). 
• What’s erythema? Erythema is redness of the skin. In our context, it is a the initial stages of a sunburn.
  
• What is the “minimum erythemal dose”? Here’s what Diffey and Farr say: “The erythemal response of the skin to ultraviolet radiation is usually inferred from the minimal erythemal dose (MED). This value is determined by exposing adjacent areas of skin to increasing doses of radiation (usually employing a geometrical series of dose increments) and recording the lowest dose of radiation to achieve erythema at a specified time, usually 24 hours, after irradiation. The visual detection of erythema is subjective and is affected by unrelated factors such as viewing geometry, intensity and spectral composition of ambient illumination, colour of unexposed surrounding skin… and the experience and visual acuity of the observer.” So, it’s the dose where you say “Gosh, my skin is slightly red, I must have gotten a little too much sun today,” and then go about your business with hardly another thought. 
• Why did Russ and I give the value for 254 nm? We mean that the ultraviolet radiation has a wavelength of 254 nm, which puts it in the UVC range (100–280 nm). UVC light can certainly cause damage and sunburn, but almost no UVC gets through the earth’s atmosphere to reach our bodies. Most sun tans and sunburns are caused by UVB, which is in a narrow band of wavelengths from 280–315 nm. Wavelengths much shorter are removed by the atmosphere, and the photons for wavelengths much longer do not have enough energy to do significant damage. The wavelength in the above Table 2 that’s most appropriate for this discussion is 300 nm. So, looking at Table 2, perhaps a better value for the minimum erythemal dose would be 24 mJ cm^-2 or 240 J m^-2. In the sixth edition of IPMB, we will use 200 J m^-2 as our typical value (unless we change our minds…when it comes to revising a textbook, it ain’t over till it’s over). Warning: this value depends on factors such as your complexion, so don’t take it too seriously. It’s a ballpark estimate. Everyone is a bit different. 
• Well, just how much UVB are we exposed to? We can estimate that from Figure 14.28 in IPMB. In the range from about 295 to 315 nm, the average value of the spectral dose is about 10 mW m^-2 nm^-1. If we multiply by a 20 nm range, we get 200 mW m^-2, or about 0.2 W m^-2. That value is for the sun straight overhead (noon near the equator with a clear sky). It’s consistent with other values I have found. 
• How is all this related to the “UV index” that the weather forecaster talks about? The UV index is a linear scale (not logarithmic like the decibel scale for hearing), and to calculate it you multiply the intensity in W m^-2 by 40. So, the value of 0.2 W m^-2 that I quoted earlier corresponds to a UV index of 8. Here in southeast Michigan we can reach a UV index of 8 at noon on a cloudless summer day. In January we are at a UV index of about 2. Latitude and time of the year make a big difference, as does time of the day (in the morning and evening, sunlight comes in at an angle and must therefore pass through more atmosphere than at noon). 
• So, how long can I stay in the sun before getting sunburn? On the beach in Hawaii during the summer at noon you can reach a UV index of about 12, so the intensity is 0.3 W m^-2, which means 0.3 joules per second per square meter. If your minimum erythemal dose is 200 J m^-2, then (0.3 J m^-2 s^-1) t = 200 J m^-2, so t = 667 seconds or 11 minutes. That’s the minimum dose. I bet you could go a half hour before suffering from something you would call a serious sunburn. But if you stay out all afternoon surfing at Waikiki, it could be a problem. 
• Can’t I protect myself with sunscreen? Yes, the sun protection factor (SPF) is the factor by which the intensity actually reaching your skin is reduced by the sunscreen. If you put on SPF 30 sunscreen there in Hawaii, your time for a minimum erythemal dose goes up from 11 minutes to five and a half hours. Maybe you can get away with all day, since the UV index will be lower in the morning and evening, extending your time. Just make sure it doesn’t get washed off in the water. You may have to reapply it often.
  

Let me apologize one more time for the bogus value of minimal erythemal dose in the 5th edition of IPMB. I feel bad about it. I sure hope no one used it to justify spending lots of time in a tanning booth. I call those things “cancer booths.” Stay away from them. 

I'll be proofreading the 6th edition of IPMB extra carefully. My motto will be: THINK BEFORE YOU WRITE!