Authors at Oakland: A Celebration of the Book

Are Electromagnetic Fields Making Me Ill?,
by Brad Roth

Every year the Kresge Library at Oakland University hosts an event called “Authors at Oakland” where they honor publications by Oakland University faculty. This year was “a celebration of the book.” Intermediate Physics for Medicine and Biology was featured at a previous Authors at Oakland event, and this year I submitted Are Electromagnetic Fields Making Me Ill? Two authors were selected to give a short talk about their book, and I was one of them. So on Wednesday, March 20 I spoke to an audience of OU librarians, members of the faculty senate library committee, and other interested professors and students.

The talk was not recorded but below is a transcript, as best as I can remember it.

Thank you for selecting my book Are Electromagnetic Fields Making Me Ill? to be featured here at Authors at Oakland. My friend David Garfinkle once told me that any time a book has a title in the form of a question, the answer’s always “no.” That’s true for my book, and sums it up in a nutshell.

How did I come to write this book? In November of 2019, just before Covid arrived, I was asked to participate in a town hall meeting in Rochester, Michigan about the then-new 5G cell phones. I was to be the health effects expert. I thought I was going to give a short talk to a quiet and respectful audience. Little did I know what was in store. [At this point I showed about the first one and a half minutes of the video below.]

I discussed the hazards of 5G cell phone radiation at a town hall meeting in Rochester, Michigan in 2019. The audience was not convinced by my claim that the risks are small. https://www.youtube.com/watch?v=smQ0Nnz7lLk

This experience got me to wondering why people believe things that aren’t supported by the evidence and what could I do about it? In response to the second question, I wrote this book.

The book covers several topics, but today I’ll focus on the issue that started it all: cell phones and cancer.

Not everyone agrees with me that 5G cell phone radiation is harmless. Devra Davis has written a book titled Disconnect, in which she claims to tell “the TRUTH about cell phone RADIATION, what the INDUSTRY has done to HIDE it, and how to PROTECT your FAMILY.” I disagree with her conclusions, but the issue shouldn’t be viewed as my word against hers. Let’s look at the evidence. That’s how science works.

The electromagnetic spectrum.
(From: https://www.niehs.nih.gov/health/topics/agents/
emf/index.cfm)

To start we need to discuss a little physics. Electromagnetic waves come in many frequencies, from extremely low frequencies like those produced by 60 Hz power lines, to intermediate frequencies such as from cell phones, to very high frequencies such as x-rays.

Quantum mechanics tells us that electromagnetic radiation is not continuous but comes in lumps called photons. The energy of a photon is proportional to its frequency. Very high frequency photons like for x-rays have enough energy that they can disrupt DNA, causing mutations leading to cancer. However, cell phones operate at a much lower frequency, on the order of a gigahertz (one billion oscillations per second), in the realm of microwaves. These photons have an energy of about 0.000004 eV (an eV or “electron volt” is a unit of energy appropriate when discussing single atoms or molecules). What should we compare that energy to? All molecules are bouncing around randomly, called thermal motion. The thermal energy at our body temperature is about 0.02 eV. A cell phone photon would be swamped by the thermal noise. Chemical bonds have strengths of several electron volts. A cell phone photon is far too weak to break bonds, so they can’t directly disrupt DNA and cause cancer like x-ray photons can. If they have any effect it must be an indirect one, such as affecting our immune system or suppressing our body’s ability to repair DNA damage.

A microwave oven.
(Consumer Reports, CC BY-SA 4.0,
https://creativecommons.org/
licenses/by-sa/4.0, via Wikimedia Commons)

Even though one photon can’t damage our tissue, you might be wondering what would happen if we deposited many, many photons into our body? Physicists have a word for that: “heat.” We know microwaves can heat tissue. You prove that every time you warm up your leftovers in your microwave oven. However, physicists understand how microwaves heat tissue very well, and can predict how hot tissue will get when exposed to microwaves. Cell phones don’t emit enough microwave radiation to significantly heat tissue. The Federal Communications Commission limits the amount of radiation a cell phone can emit to levels that don’t cause significant heating. Your cell phone doesn’t cook your brain. If microwave radiation represents a hazard to our tissue, it’s not only through an indirect effect but also a nonthermal effect.

Let’s now look at four types of evidence about the risk of cell phone radiation: 1) theoretical analysis, 2) cancer rates, 3) epidemiological evidence, and 4) laboratory experiments.

Asher Sheppard and his colleagues have analyzed every theoretical mechanism they could think of to determine if microwaves have a significant affect on our tissue. After an exhaustive search, they concluded that

In the frequency range from several megahertz to a few hundred gigahertz, the focus of this paper, the principal mechanism for biological effects, and the only well-established mechanism, is the heating of tissues.

I can imagine that you’re thinking “well, maybe those armchair theorists just weren’t smart enough to dream up the correct mechanism.” Perhaps, but the point I want to make is that the concern about cell phone radiation isn’t being driven by a theoretical prediction. Theory does not predict there should be an effect.

Cell phone use and brain cancer trends between 1976 and 2006.
(Data from Inskip et al.)

Now look at this plot of brain cancer trends. Back in the 1980s, when I was a graduate student, no one had cell phones. The use of cell phones has exploded since then. The data shown only goes out to about 2010, but if you extend the data to today essentially everyone has a cell phone. However, the cancer rate has been flat over those decades. And the brain cancer rate, in particular, has been nearly flat. If cell phones are causing brain cancer, it’s not a strong enough signal to show up in the cancer rate data.

Epidemiology studies examine large groups of people, some exposed to a hazard and some not, to compare their health. One of the first epidemiological studies is called the INTERPHONE study, and it did suggest a weak association of heavy cell phone use with cancer. INTERPHONE was a case control study; the researchers interviewed many people with brain cancer to determine their prior cell phone use, and compared these people to a control group without cancer. These studies are useful for getting data on rare hazards quickly, but they’re susceptible to biases, such as “recall bias” where a person with cancer who used their cell phone a lot will remember that clearly and perhaps regretfully while a member of the control group might not remember whether or not they even used a cell phone at all. A cohort study is a better type of epidemiological analysis. A large number of people, some cell phone users and some not, are followed for many years to see who gets cancer. Two large cohort studies—the Million Women Study in Europe and another study that involved essentially the entire population of Denmark—didn’t indicate a signal for an increased rate of cancer caused by cell phone use. A meta-analysis of many epidemiological studies by Martin Röösli and his coworkers concluded that

Epidemiological studies do not suggest increased brain or salivary gland tumor risk with [mobile phone] use, although some uncertainty remains regarding long latency periods (>15 years), rare brain tumor subtypes, and [mobile phone] usage during childhood.

Another large cohort study, called COSMOS, is now being carried out in Europe. When I was preparing this Powerpoint presentation, I thought I’d have to tell you that we’ll need to wait a few years until the results are published. Then, just this week, a preliminary report found that there’s no evidence that cell phone use is associated with higher rates of brain cancer. Some people might claim that there’s a long latency period between the exposure to cell phone radiation and the occurrence of cancer, and that a large uptick in the cancer rate will happen soon. Maybe, but as each year goes by that scenario becomes less and less likely.

The final type of evidence is laboratory experiments, such as studies using rats, mice, or cells in a dish. The evidence here is mixed; many experiments see effects and many do not. In fact, you could make a compelling case for or against cell phone health effects, depending on which articles you read. Unfortunately, the quality of these studies is also mixed.

Often scientists sometimes conduct a systematic review, weighing the pros and cons of the many experiments. For example, Anne Perrin and her collaborators reviewed the effects of radiofrequency electromagnetic fields on the blood brain barrier, and found that

recent studies provide no convincing proof of deleterious effects of [radiofrequency radiation] on the integrity of the [blood brain barrier].

But other systematic reviews have come to different conclusions, and I fear it’s difficult to draw definite conclusions from the experimental investigations.

Federal agencies—such as the Food and Drug Administration, the Center for Disease Control, and the National Cancer Institute (part of the National Institutes of Health)—often conduct their own reviews of the evidence. My favorite is the National Cancer Institute, which was the agency that got the round of boos during that 5G town hall meeting I participated in. These aren’t bureaucrats conducting the review, but instead are our nation’s top cancer scientists. They concluded that

The human body does absorb energy from devices that emit radiofrequency radiation. The only consistently recognized biological effect of radiofrequency radiation absorption in humans that the general public might encounter is heating to the area of the body where a cell phone is held (e.g., the ear and head). However, that heating is not sufficient to measurably increase core body temperature. There are no other clearly established dangerous health effects on the human body from radiofrequency radiation.

So, the evidence from theoretical analysis, cancer trends, epidemiology, and experiments makes a strong case that there are no health risks from cell phone radiation. Impossibility proofs are difficult in biology and medicine, but to me the evidence is compelling that the electromagnetic waves emitted by cell phones are safe.

A final question is if we should believe the scientists. Should we trust the National Cancer Institute to provide a unbiased review, or are they trying to hide hazardous effects. I believe a conspiracy secretly carried out by hundreds if not thousands of scientists and medical doctors is absurd. In my book I wrote

Dangers arising from cell phone radiation strike me as unlikely, but not inconceivable. However, the claims that there exists a vast plot, with scientists colluding to conceal the facts, are ridiculous.

My book covers other topics besides just cell phone radiation. There’s a chapter on power line electric and magnetic fields causing leukemia, another on the Havana Syndrome, and others. My conclusion is that all these potential affects of electromagnetic fields are overblown.

Finally, in the acknowledgments section of my book I thank the Kresge Library for “assisting me with obtaining books and articles related to this research.” In particular, the interlibrary loan office here at Kresge Library has been essential to my research. I worked them pretty hard. You can’t write a book like this without a good interlibrary loan department.

Thank you. Does anyone have questions?

I must admit the biggest applause arose from my comment about the interlibrary loan office, but then the crowd was largely librarians. Overall Authors at Oakland was a wonderful event, and I deeply appreciate being invited to speak at it.

Oh, Myyy!

Recently I was reading an article by Ramsay Lewis and Yuhong Dong in The Epoch Times titled Invisible Electromagnetic Fields: Do They Harm Your Health? My friend and colleague David Garfinkle once told me that whenever you see a book or article whose title is in the form of a question, the answer is always “no.” I assumed that would be the case for this article, and I began reading.

The article describes how citizens of Virginia Beach opposed an offshore renewable energy project, justifying their opposition in part because of possible health hazards from electric and magnetic fields produced by transmission cables.

The article started off well and discussed many of the issues described in Chapter 9 of Intermediate Physics for Medicine and Biology and in my book Are Electromagnetic Fields Making Me Ill? (which, by the way, does follow Garfinkle’s rule of the title question having “no” for an answer). Then, suddenly, Lewis and Dong took a bizarre turn. They wrote

In repeated experiments, Nobel Prize laureate Professor Luc Montagnier amazingly demonstrated that a low intensity electromagnetic field (EMF) of 7 HZ (similar to Schumann resonances), could produce DNA in a tube of pure water, simply by being adjacent to another tube containing DNA. In other words, he created something—DNA—out of nothing, simply by being close to DNA and adding low frequency EMFs.

Wait... What?! This sounded serious enough that I decided to look into it. After all, the idea was championed by one of the discovers of HIV, the virus responsible for AIDS.

Luc Montagnier in 2008
Prolineserver, GFDL 1.2, via Wikimedia Commons

I found a paper published by Montagnier and his coworkers (Montagnier et al., 2009, “Electromagnetic signals are produced by aqueous nanostructures derived from bacterial DNA sequences,” Interdisciplinary Sciences: Computational Life Sciences, Volume 1, Pages 81–90). Below I reproduce their abstract.

A novel property of DNA is described: the capacity of some bacterial DNA sequences to induce electromagnetic waves at high aqueous dilutions. It appears to be a resonance phenomenon triggered by the ambient electromagnetic background of very low frequency waves. The genomic DNA of most pathogenic bacteria contains sequences which are able to generate such signals. This opens the way to the development of highly sensitive detection system for chronic bacterial infections in human and animal diseases.

The key phrase in the abstract is “at high aqueous dilutions.” The authors repeatedly made 10:1 dilutions of the DNA solution. After 18 dilutions, the concentration of DNA should be 0.000000000000000001 times what it was originally. The purported electromagnetic wave effect persisted, even though there was no DNA left in the sample. The water “remembered” the DNA. It’s homeopathy all over again.

Oh, Myyy! This is the worst sort of pseudoscience.

A 2010 interview in Science politely hinted that this idea is absurd.

Virologist and Nobel laureate Luc Montagnier announced earlier this month that, at age 78, he will take on the leadership of a new research institute at Jiaotong University in Shanghai. What has shocked many scientists, however, isn’t Montagnier’s departure from France but what he plans to study in China: electromagnetic waves that Montagnier says emanate from the highly diluted DNA of various pathogens…

But Montagnier’s new direction evokes one of the most notorious affairs in French science: the “water memory” study by immunologist Jacques Benveniste. Benveniste, who died in 2004, claimed in a 1988 Nature paper that IgE antibodies have an effect on a certain cell type even after being diluted by a factor of 10¹²⁰. His claim was interpreted by many as evidence for homeopathy, which uses extreme dilutions that most scientists say can’t possibly have a biological effect. After a weeklong investigation at Benveniste’s lab, Nature called the paper a “delusion.”

Here’s part of the interview with Montagnier.

Q: You have called Benveniste a modern Galileo. Why? 

L.M.: Benveniste was rejected by everybody, because he was too far ahead. He lost everything, his lab, his money. … I think he was mostly right, but the problem was that his results weren’t 100% reproducible. 

Q: Do you think there’s something to homeopathy as well? 

L.M.: I can’t say that homeopathy is right in everything. What I can say now is that the high dilutions are right. High dilutions of something are not nothing. They are water structures which mimic the original molecules. We find that with DNA, we cannot work at the extremely high dilutions used in homeopathy; we cannot go further than a 10⁻¹⁸ dilution, or we lose the signal. But even at 10⁻¹⁸, you can calculate that there is not a single molecule of DNA left. And yet we detect a signal.

Why should we care about all this silliness? Wouldn’t it be better to just ignore it? Here’s the problem: Climate change is real. There’s a consensus among scientists that it’s a serious, man-made crisis that must be addressed. One way to fight climate change it is to build alternative sources of energy, such as offshore wind farms. Yet citizens and journalists are citing ridiculous nonsense like Montagnier’s water memory hypothesis to oppose wind farms. Quackery and voodoo science are being used to impede solutions to what may be the most dire challenge mankind has ever faced.

To quote Charles Dickens, “I’ll retire to bedlam.”

Co-discoverer of HIV Luc Montagnier dies aged 89. BBC News

https://www.youtube.com/watch?v=Iat2FncJ1to

 

What is Homeopathy, by Science Saves.

https://www.youtube.com/watch?v=Rw766-Z97BI

 

Bill Catterall (1946–2024)

William Catterall, known as “the father of ion channels,” died on February 28 at the age of 77. Russ Hobbie and I cite Catterall’s article on the structure of sodium ion channels in Chapter 9 of Intermediate Physics for Medicine and Biology.

Payandeh J, Scheuer T, Zheng N, Catterall WA (2011) The crystal structure of a voltage-gated sodium channel. Nature 475:353–358.

Catterall worked in the intramural program at the National Institutes of Health in the laboratory of Marshall Nirenberg. He then moved to the University of Washington, where he was a professor of Pharmacology for over 40 years. There he was a collaborator with Bertil Hille, the author of the landmark textbook Ion Channels of Excitable Membranes. An obituary published by the University of Washington website states

First and foremost, Bill was an exceptional scientist. He pioneered the biochemical investigation of calcium and sodium ion channels; molecular portals that allow the controlled passage of ions across cell membranes. The proper passage of ions into the cell is essential for healthy brain, heart, and muscle function. Early work from Catterall elucidated the molecular basis of ion channel gating whereas later studies with UW Pharmacology colleague Dr. Ning Zheng revealed details of how these clinically relevant macromolecular machines operate at the atomic level. With this latter information, Catterall was able to ascertain how a variety of toxins as well as local anesthetics and antiarrhythmic drugs act to “lock the gate” on these ion channels. Bill was recognized for these pivotal discoveries by election to the National Academy of Sciences USA and the Royal Society London. He also received prestigious awards including the Gairdner Award from Canada, the Robert R. Ruffolo Career Achievement Award in Pharmacology from the American Society of Pharmacology and Therapeutics, and a Lifetime Achievement Award from the International Union of Pharmacologists.

To learn more, listen to Catterall discuss his work in a three-part series of lectures for iBiology. 

William Catterall (U. Washington) Part 1: Electrical Signaling: Life in the Fast Lane  

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

 

William Catterall (U. Washington) Part 2: Voltage-gated Na+ Channels at Atomic Resolution

 https://www.youtube.com/watch?v=hfXGsJCOC9A

 

William Catterall (U. Washington) Part 3: Voltage-gated Calcium Channels

https://www.youtube.com/watch?v=bUE8gzMqqb8

Happy Birthday, Erwin Neher!

German biophysicist Erwin Neher turned 80 last week. Neher and Bert Sakmann received the 1991 Nobel Prize in Physiology or Medicine for their development of patch clamping: a method to record the current through individual ion channels. Russ Hobbie and I discuss Neher and Sakmann’s work in Chapter 9 of Intermediate Physics for Medicine and Biology.

I will turn over the rest of this post to Neher. In the two-minute video below, he offers advice to young scientists.

 

Erwin Neher's Advice to Young People: From a Nobel Prize Winner 

https://www.youtube.com/watch?v=vB3MNPuMFCI

 

In a ten-minute video, listen to Erwin Neher discuss advances in modern medicine.

Erwin Neher, Nobel Laureate for Medicine | Journal Interview 

https://www.youtube.com/watch?v=Rm3gHuxouZo

Finally, in this longer lecture, Neher describes the development of patch clamping. 

Lecture by Erwin Neher at the University of Hyderabad. The talk begins at approximately minute 18, after a rather long introduction.

https://www.youtube.com/watch?v=okB2coPEJJk

Happy Birthday, Erwin Neher!

A New Version of Figure 10.13 in the Sixth Edition of IPMB

Gene Surdotovich and I are hard at work preparing the 6^th edition of Intermediate Physics for Medicine and Biology. One change compared to the 5^th edition is that we are redrawing most of the figures using Mathematica. It’s a lot of work, but the revised figures look great and many are in color.

One advantage of redrawing the figures is that it forces us to rethink what the figure is all about and if it makes sense. This brings me to Figure 10.13 in the chapter about feedback. Specifically, it is from Section 10.6 about a negative feedback loop with two time constants. Without going into detail, let me outline what this figure is describing.

Chapter 10 centers around one particular feedback loop, relating the amount of carbon dioxide in your lungs (which we call x) to your breathing rate (y). The faster you breath, the more CO₂ you blow out of your lungs, so an increase in y causes a decrease in x. But your body detects when CO₂ is building up and reacts by increasing your breathing rate, so an increase in x causes an increase in y. There is one additional parameter, your metabolic rate, p. If your metabolic rate increases, so does the amount of CO₂ in your lungs.

Our book emphasizes mathematical modeling, so we develop a toy model of how x and y behave. We assume that initially x and y are in steady state for some p, and call these values x₀, y₀, and p₀. At time t = 0, p increases from  p₀ to p₀ + Δp, which could represent you starting to exercise. How do x and y change with time? We define two new variables, ξ and η, that represent the deviation of x and y from their steady state values, so x = x₀ + ξ and y = y₀ + η. We then develop two differential equations for ξ and η,

The variables ξ and η have different time constants, τ₁ and τ₂. The parameters G₁ and G₂ are the “gains” of the system, determining how much ξ changes in response to η, and how much η changes in response to ξ. In our model, G₁ is negative (an increase in breathing rate causes the amount of CO₂ in the lungs to decrease) and G₂ is positive (an increase in CO₂ causes the rate of breathing to increase). The “open loop gain” of the feedback loop is the product G₁G₂. Finally, the constant a is simply a factor to get the units right.

All is good so far. But now let’s look at the 5^th edition’s version of Fig. 10.13. 

What’s wrong with it? First, the calculation uses a positive value of G₁ and a negative value of G₂, so it doesn’t correspond correctly to our model, which has negative G₁ and positive G₂. Second, the calculation uses Δp = 0, so the steady state values of x and y don’t change and ξ and η both approach zero. That’s odd. I thought the whole point of the model was to look at how the system responds to changes in p. Finally, the initial values of ξ and η are not zero. What’s up with that? We know their values are zero for t < 0, when x = x₀ and y = y₀. How could they suddenly change at t = 0?

In the 6^th edition, the new version of Figure 10.13 is going to look something like this: 

The figure has color and switches from landscape to portrait orientation. Those changes are trivial. Here are the important differences:

1. I made G₁ negative and G₂ positive, like in our breathing model. Now an increase in CO₂ causes the body to increase the breathing rate, rather than decrease it as in the 5^th edition figure.
2. The parameter Δp is no longer zero. To be simple, I set aΔp = 1. The person starts exercising at t = 0.
3. Because there is a change in metabolic rate, the new steady state values of ξ and η are not zero. In fact, they are equal to ξ = aΔp/(1-G₁G₂) and η = G₂aΔp/(1-G₁G₂). Notice how the factor of 1-G₁G₂ plays a big role. Since the product G₁G₂ is negative, this means that 1-G₁G₂ is a positive number greater than one. It’s in the denominator, so it makes ξ smaller. That’s the whole point. The feedback loop is designed to keep ξ from changing much. It’s a control system to suppress changes in ξ. To make life simple, I set G₁ = −5 and G₂ = 5 (the same values from the 5^th edition except for the signs), so the open loop gain is 25 and the steady state value of ξ is only 1/26 of what it would be if no feedback were present (in which case, ξ would rise monotonically to one while η would remain zero).
4. The initial values of ξ and η are now zero, so there is no instantaneous jump of these variables at t = 0.

When revising the 5^th edition of IPMB, I began wondering why Russ Hobbie and I never worried about the units for the time constants, the gains, a, or Δp. This motivated me to write a new homework problem for the 6^th edition, in which the student is asked to rewrite the model equations in nondimensional variables Ξ, Η, and T instead of ξ, η, and t. Interestingly, such a switch results in a pair of differential equations for Ξ and Η that depend on only two nondimensional parameters: the ratio of time constants and the open loop gain. So, our plot in the 5^th edition has the qualitative behavior correct (except for the signs of G₁ and G₂). The system oscillates because the open loop gain is so high. The correct units for the various parameters would only rescale the horizontal and vertical axes. 

Is the new version of Figure 10.13 in this blog post what you’ll see in the 6^th edition of IPMB? I don’t know. I haven’t passed the figure by Gene yet, and he’s my Mathematica guru. He might make it even better.

What’s the moral of this story? THINK BEFORE YOU CALCULATE! That’s the motto I often would tell my students, but it applies just as well to textbook authors. The plot should not only be correct but also make physical sense. You should be able to explain what’s happening in words as well as pictures. If you can’t tell the story of what’s taking place by looking at the figure, something’s wrong.

Finally, is there really no physical problem that the original version of Fig. 10.13 describes? Actually, there is. Imagine you are resting throughout this “event”; you sit in your chair and don’t change your metabolic rate, so Δp = 0 meaning p is the same before and after t = 0. However, at time t = 0, your “friend” sneaks up on you, shoves a fire extinguisher in front of your face, and gives you a quick, powerful blast of CO₂. Except for the sign issue on G₁ and G₂, the original figure shows how your body would respond.

Stirling's Approximation

I've always been fascinated by Stirling’s approximation,

ln(n!) = n ln(n) − n,

where n! is the factorial. Russ Hobbie and I mention Stirling’s approximation in Appendix I of Intermediate Physics for Medicine and Biology. In the homework problems for that appendix (yes, IPMB does has homework problems in its appendices), a more accurate version of Stirling’s approximation is given as

ln(n!) = n ln(n) − n + ½ ln(2π n) .

There is one thing that’s always bothered me about Stirling’s approximation: it’s for the logarithm of the factorial, not the factorial itself. So today, I’ll derive an approximation for the factorial. 

The first step is easy; just apply the exponential function to the entire expression. Because the exponential is the inverse of the natural logarithm, you get

n! = e^{n ln(n) − n + ½ ln(2π n)}

Now, we just use some properties of exponents

n! = e^{n ln(n)} e⁻ⁿ e^{½ln(2π n)}

n! = (e^ln(n))ⁿ e⁻ⁿ √(e^{ln(2π n)})

n! = nⁿ e⁻ⁿ √(2π n) 

And there we have it. It’s a strange formula, with a really huge factor (nⁿ) multiplied by a tiny factor (e⁻ⁿ) times a plain old modestly sized factor (√(2π n)). It contains both e = 2.7183 and π = 3.1416.

Let's see how it works.

n	n!	nn e−n √(2π n)	fractional error (%)
1	1	0.92214	7.8
2	2	1.9190	4.1
5	120	118.02	1.7
10	3.6288 × 106	3.5987 × 106	0.83
20	2.4329 × 1018	2.4228 × 1018	0.42
50	3.0414 × 1064	3.0363 × 1064	0.17
100	9.3326 × 10157	9.3249 × 10157	0.083

For the last entry (n = 100), my calculator couldn’t calculate 100¹⁰⁰ or 100!. To get the first one I wrote

100¹⁰⁰ = (10²)¹⁰⁰ = 10^{2 × 100} = 10²⁰⁰.

The calculator was able to compute e⁻¹⁰⁰ = 3.7201 × 10⁻⁴⁴, and of course the square root of 200π was not a problem. To obtain the actual value of 100!, I just asked Google.

Why in the world does anyone need a way to calculate such big factorials? Russ and I use them in Chapter 3 about statistical dynamics. There you have to count the number of states, which often requires using factorials. The beauty of statistical mechanics is that you usually apply it to macroscopic systems with a large number of particles. And by large, I mean something like Avogadro’s number of particles (6 × 10²³). The interesting thing is that in statistical mechanics you often need not the factorial, but the logarithm of the factorial, so Stirling's approximation is exactly what you want. But it’s good to know that you can also approximate the factorial itself. 

Finally, one last fact from Mr. Google. 1,000,000! = 8.2639 × 10^5,565,708. Wow!

Stirling’s Approximation

https://www.youtube.com/watch?v=IJ5N28-Ujno

A Text-Book on Medical Physics

Intermediate Physics for Medicine and Biology provides, for the first time, a textbook about the role that physics plays in medicine.

Well… no.

I recently found a textbook that preceded IPMB by over a century. Below is its preface.

The fact that a knowledge of Physics is indispensable to a thorough understanding of Medicine has not yet been as fully realized in this country as in Europe, where the admirable works of Desplats and Gariel, of Robertson, and of numerous German writers, constitute a branch of educational literature to which we can show no parallel. A full appreciation of this, the author trusts, will be sufficient justification for placing in book form the substance of his lectures on this department of science, delivered during many years at the University of the City of New York.

Broadly speaking, this work aims to impart a knowledge of the relations existing between Physics and Medicine in their latest state of development, and to embody in the pursuit of this object whatever experience the author has gained during a long period of teaching this special branch of applied science. In certain cases topics not strictly embraced in the title have been included in the text—for example, the directions for section-cutting and staining; and in other instances exceptionally full descriptions of apparatus have been given, notably of the microscope; but in view of the importance of these subjects, the course pursued will doubtless be approved. Attention may be called to the paragraph headings and italicized words, which suggest a system of questions facilitating a review of the text.

In conclusion, the author will feel that his labor has not been in vain if the work should serve to call deserved attention to a subject hitherto slighted in the curriculum of medical education.

Readers of IPMB might be interested in a brief table of contents for this earlier book.

I. Matter

      1. Properties of matter

      2. Solid matter

      3. Liquid matter

      4. Gaseous matter

      5. Ultragaseous and radiant matter

II. Energy

               1. Potential energy 

               2. Kinetic energy 

               3. Machines and instruments 

               4. Translatory molecular motion 

               5. Acoustics 

               6. Optics 

               7. Heat 

               8. Electricity 

               9. Dynamic electricity 

             10. Magnetism 

             11. Electrobiology

Many of these topics are familiar to readers of IPMB. Yet, the list and the language seem quaint and just a little old-fashioned.

A Text-Book on Medical Physics,
by John C. Draper.

This should not be surprising. The book was titled A Text-Book on Medical Physics, written by John C. Draper, and published in 1885. Russ Hobbie and I are following a long tradition of applying physics to medicine and biology. In nearly 140 years much has changed, but also much has stayed the same. The last sentence of the preface could serve as our call to arms, and the subtitle of Draper’s book could be our own: “For the Use of Students and Practitioners of Medicine.” 

Below I post the definition of medical physics in the Text-Book. I love it. Draper should have written a blog!

 

The Rest of the Story 4

Allan was born in Johannesburg, the youngest of three children. He spent his teenage years in Cape Town, and was interested in debating, tennis, and acting. He also loved astronomy, which triggered an interest in physics and mathematics.

At the University of Cape Town he studied electrical engineering, following in the footsteps of his father and brother. But he soon abandoned engineering to learn physics and to engage in mountaineering. After he obtained his undergraduate degree, he went to England and studied physics at the Cavendish Laboratory in Cambridge. 

He didn’t finish his PhD, however, because in Paul Dirac’s quantum mechanics class he fell in love with one of his classmates, an American physics student named Barbara Seavey. He wanted to marry her but he had no money. As fortune would have it, there was a teaching position available back in Cape Town. He married Barbara and returned home to South Africa. There he was happy, but isolated from cutting edge research. He didn’t seem posed for success in the high-power and competitive world of physics.

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At Cape Town Allan eventually qualified for a sabbatical, which Barbara wanted to spend in the United States. So they traveled to the Harvard cyclotron, where he worked on nucleon-nucleon scattering with Norman Ramsey and Richard Wilson. While on sabbatical leave, he was offered a position at Tufts University.

Allan became interested in a computer imaging problem: how to make a 2-d image of the inside of an object based on projections taken at different angles. He published the results of this work, but it didn’t make a splash. No one seemed to care about his algorithm. So he went back to his research on high energy physics.

Several years latter, researchers suddenly began to pay attention to Allan’s imaging work. Medical doctors were interested in forming two- or even three-dimensional images of the body using X-rays applied from different directions. Allan’s algorithm was exactly what they needed.

These studies became fundamental to the emerging field of medical imaging. It was so important, that in 1979 he—Allan MacLeod Cormack—and Godfrey Hounsfield shared the Nobel Prize in Physiology or Medicine for the invention of computed tomography.

And now you know the rest of the story.

Good day!

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

Imagining the Elephant:
A Biography of Allan MacLeod Cormack.
by Christopher Vaughan.

This blog post was written in the style of Paul Harvey’s “The Rest of the Story” radio program. You can find three other of my “The Rest of the Story” blog posts here, here, and here.

The content is based on Cormack’s biography on the Nobel Prize website. You can read about tomographic reconstruction techniques in Chapter 12 of Intermediate Physics for Medicine and Biology.

Allan MacLeod Cormack was born on February 23, 1924, exactly 100 years ago today. 

Happy birthday Allan!

Forman Acton (1920 – 2014)

Numerical Methods That Work,
by Forman Acton.

The American computer scientist Forman Acton died ten years ago this Sunday. In Intermediate Physics for Medicine and Biology, Russ Hobbie and I cite Acton’s Numerical Methods That Work. For readers interested in using computers to model biological processes, I recommend this well written and engaging book.

Before he died, Acton donated funds to establish the Forman Acton Foundation. Here is how their website describes his life:

Forman Sinnickson Acton was born in Salem City, and he went on to change the world.

Born on August 10, 1920, he began his education in the Salem City school system before attending private boarding school at Phillips Exeter Academy and college at Princeton University. He graduated with two degrees in engineering toward the end of World War II, during which he served in the Army Corps of Engineers and worked on a team involved in the Manhattan Project.

After his service, he earned his doctorate in mathematics from Carnegie Institute of Technology, helped the Army develop the world’s first anti-aircraft missiles and became a pioneer in the evolving field of computer science.

Acton conducted research and taught at Princeton from 1952 to 1990, during which time he wrote textbooks on mathematics at his cabin on Woodmere Lake in Quinton Township, Salem County. When he turned 80, he joined the Lower Alloways Creek pool to stay in shape, swimming six days a week for 14 years.

He died on February 18, 2014, in Woodstown, New Jersey, but not before he anonymously donated thousands of dollars toward scholarships for Salem City School District students, some of whom were just then graduating from college. Before he passed, he made it clear to friends and confidants that he wanted these students to have access to the incredible educational experiences he enjoyed.

Eight months after his passing, the Forman S. Acton Educational Foundation was officially incorporated to ensure that all of Salem’s youth also have a chance to change the world.

Sometimes I will read a passage and say to myself “That’s exactly what students studying from IPMB need to hear.” I feel this way about Acton’s preface to Numerical Methods That Work. Russ and I include many homework problems in IPMB so the student can gain experience with the art of mathematical modeling. Below, in Acton’s words, is why we do that. Just replace phrases like “solving equations numerically” with “building models mathematically” and his words apply equally well to IPMB.

Numerical equation solving is still largely an art, and like most arts it is learned by practice. Principles are there, but even they remain unreal until you actually apply them. To study numerical equation solving by watching someone else do it is rather like studying portrait painting by the same method. It just won’t work. The principle reason lies in the tremendous variety within the subject…

The art of solving problems numerically arises in two places: in choosing the proper method and in circumventing the main road-blocks that always seem to appear. So throughout the book I shall be urging you to go try the problems—mine or yours.

I have tried to make my explanations clear, but sad experience has shown that you will not really understand what I am talking about until you have made some of the same mistakes I have made. I hesitate to close a preface with a ringing exhortation for you to go forth to make fruitful mistakes; somehow it doesn’t seem quite the right note to strike! Yet, the truth it contains is real. Guided, often laborious, experience is the best teacher for an art.

 

Robert Kemp Adair (1924–2020)—Notes on a Friendship

Robert Adair.
Photo credit: Michael Marsland/Yale University.

I try to write obituaries of scientists who appear in Intermediate Physics for Medicine and Biology, but for some reason I didn’t write about Robert Adair’s death in 2020. Perhaps the covid pandemic over-shadowed his demise. In Chapter 9 of IPMB, Russ Hobbie and I cite seven of his publications. He was a leader in studying the health effects (or, lack of heath effects) from electric and magnetic fields.

Recently, I read a charming article subtitled “Notes on a Friendship” about Adair, written by Geoffrey Kabat, the author of Getting Risk Right: Understanding the Science of Elusive Health Risks. I have Getting Risk Right on my to-read list. It sounds like my kind of book.

I admire Adair’s service in an infantry rifle platoon during World War II. I loved his book about baseball. I respect his independent assessment of the seriousness of climate change, although I don’t agree with all his conclusions. He certainly was a voice of reason in the debate about health risks of electric and magnetic fields. He led a long and useful life. We need more like him.

I will give Kabat the final word, quoting the last paragraph of his article.

In early October 2020, Bob’s daughter Margaret called me to tell me that Bob had died. I looked for an obituary in the New York Times, and was shocked when none appeared, likely due to the increased deaths from the pandemic. I wrote to an epidemiologist colleague and friend, who knew Bob’s work on ELF-EMF [extremely low frequency electromagnetic fields] and microwave energy, and who had served on a committee to assess possible health effects of the Pave Paws radar array on Cape Cod. My friend Bob Tarone wrote back, “Very sad to hear that. Adair was not directly involved in the Pave Paws study, but we relied heavily on his superb published papers on the biological effects of radio-frequency energy in our report. He and his wife were superb scientists. Losing too many who don’t seem to have competent replacements. Too bad honesty and truth are in such short supply in science today.” He concurred that there should have been an obituary in the Times.