Russ Hobbie wrote a review of a revised edition of Physics with Illustrative Examples from Medicine and Biology for the magazine Physics Today (July, 2001). Here are some excerpts.
The Physics Department of the Massachusetts Institute of Technology began about 30 years ago to offer a special calculus-based introductory course for freshmen and sophomores interested in biology. This led to the first edition of George B. Benedek and Felix M. H. Villars’s Physics with Illustrative Examples from Medicine and Biology. The book was issued by Addison-Wesley in 1979 as three paperback typescript volumes. The book fascinated many physicists with the applications of physics in biochemistry and physiology, but they have been out of print since 1990. Now that the AIP Press and Springer-Verlag have issued a second edition, as printed volumes, a new generation of physicists can learn from them…
These are classic books, and anyone planning to include biophysical examples in a calculus-level course should study them carefully. The authors are to be congratulated for their work, and I commend AIP Press and Springer-Verlag for making the books available again.
In his review, Russ lists the book as published in 1979, but I think there must have been earlier editions, because the first edition of Intermediate Physics for Medicine and Biology, published in 1978, cites Physics with Illustrative Examples from Medicine and Biology several times, and lists the publication date as 1973 (Volume 1) and 1974 (Volume 2). Clearly Benedek and Villars influenced the first edition of IPMB and all subsequent editions. You can learn more about Physics with Illustrative Examples from Medicine and Biologyhere, here, and here.
Benedek wasn’t just a textbook author. He invented quasi-elastic light scattering spectroscopy and became a fellow of the American Physical Society in 1962. He received the Association for Research in Vision and Ophthalmology’s Proctor Medal in 1997 for “outstanding research in basic or clinical sciences as applied to ophthalmology.” He was a true biological physicist. He’ll be missed.
MKUltra (pronouced M-K-ultra) was a covert Central Intelligence Agency research program carried out between 1953 and 1973 to investigate mind control. It used techniques such as high doses of the psychedelic drug LSD, hypnosis, sensory isolation, and electroshock therapy to influence a subject’s brain, and in particular to obtain secrets from unwilling people. This program is notorious for torturing studying subjects without their consent, which is considered a grave sin in research today.
One subproject of MKUltra (#119) was to use very low frequencyelectromagnetic fields to influence the brain. This project comes disturbingly close to techniques I’ve worked on over the years, such as transcranial magnetic stimulation. It got me to wondering: is mind control using electromagnetic fields possible?
I guess I have thought about this before, because in the August 14, 2015 post in this blog I suggested that the “psychic probe” described in Isaac Asimov’s famous Foundation Trilogy might be made by combining transcranial magnetic stimulation (TMS) and magnetoencephalography (MEG), which are both described in Chapter 8 of Intermediate Physics for Medicine and Biology. In that post I wrote “a combo TMS/MEG unit could therefore both detect and alter brain function.” Of course, I was writing tongue-in-cheek, joking about how a science fiction device might have worked within the constraints of real science. On the other hand, perhaps I was actually an MKUltra agent sending a secret message to my underground accomplices?
That last sentence mocks the recent conspiracy theories surrounding MKUltra. Last week the House Task Force on the Declassification of Federal Secrets held a hearing about the research program. It didn’t focus on the historical record (which is sparse because most of the MKUltra documents were destroyed) but instead went off on weird tangents, talking about things like mind control related to the assassination of President Kennedy. The purpose of this hearing seemed to be aimed primarily at blaming science in general for past errors. Some issues that were brought up, like MKUltra itself, were serious mistakes that should be, and have been, investigated. Others, like bogus lab leak theories related to the origin of Covid, were just crazy talk with no scientific justification. One researcher, Elizabeth Ginexi, a respected former program official at the National Institutes of Health, was invited by the Democrats to talk about the horrendous anti-science policies currently imposed on NIH by anti-vax zealot Robert F. Kennedy, Jr. Ginexi (a hero in my view) tried to discuss these vital issues, but was constantly cut off by Republican members of the committee who were focused on the bizarre and engaged in an attempt to demonize scientists and public health workers.
But back to my question: could electromagnetic fields be used for brain control? Well, transcranial magnetic stimulation is currently used to treat depression, so you can’t rule out the possibility. However, the technique is very nonspecific. I spent seven years at NIH trying to improve the focality and spatial resolution of transcranial magnetic stimulation. Generating a localized stimulus is extraordinarily difficult, especially for activating deep brain structures. You can use transcranial magnetic stimulation to make individual fingers move, but only because the hand has a widespread representation in the motor cortex. The idea that transcranial magnetic stimulation could control individual thoughts or suggest specific actions seems like science fiction to me. Other techniques that have been suggested as potentially useful for mind control are brain-computer interfaces and deep brain stimulation. Both of these have important medical uses. For example, deep brain stimulation can help reduce or control tremors caused by Parkinson’s disease. Perhaps these techniques could potentially be used for controlling behavior, but they are highly invasive (requiring surgery to implant electrodes in the brain).
Are Electromagnetic Fields Making Me Ill?
What about techniques growing out of subproject 119? That work was led by W. Ross Adey and Mary (“Mollie”) Brazier, two leading scientists studying how electromagnetic fields interact with, and are produced by, the brain. I mentioned Adey in my book Are Electromagnetic Fields Making Me Ill?. He claimed to find “window” effects, for which one particular applied field strength resulted in an observable effect, but stronger or weaker fields did not. Similarly, he found that certain frequencies had marked responses (“resonances”) but both higher and lower frequencies did not. These window effects are not very reproducible and are not widely accepted today. Generally, resonant effects are claimed at very low frequencies (say, 20 Hz). Ultimately subproject 119 ended in failure because no mind control methods were found. Some say that a modern offshoot of this research is microwave weapons responsible for the Havana syndrome. Again, in Are Electromagnetic Fields Making Me Ill? I discuss why electromagnetic fields are almost certainly not responsible for the Havana syndrome. My opinion is that this is another anti-science conspiracy theory.
The final question I address is: could something like MKUltra happen today? The ethics rules governing research are far more stringent now than several decades ago. About 15 years ago, I served for one year in an interim role as Oakland University’s Vice Provost for Research, which is the chief research officer at the institution. Among other things, I was in charge of overseeing research misconduct issues at OU. Any human subjects research had to go through our Institutional Review Board. If a faculty member merely wanted to give a simple survey to students, that survey had to be assessed by this board and a detailed consent form was required. Any potentially dangerous human studies were monitored particularly closely, and informed consent was essential. It’s the same at all academic institutions. MKUltra would be virtually impossible in today’s academic research environment. Could it happen in the CIA or another research center associated with the military? I don’t know. Perhaps. But the CIA and other intelligence agencies can’t compete with academia and scientific institutions like the NIH and NSF when it comes to scientific advances. (Take, for example, the recent brouhaha over the military’s claims about “ghost murmur” which are almost certainly bogus.) I don’t believe MKUltra or anything related to it is going on today, especially involving electromagnetic fields to control the brain. I believe that such a suggestion is a conspiracy theory, advanced to discredit scientists and scientific institutions. It’s part of the Republican War on Science. Please, don’t believe the anti-science crackpots. At the very least, insist that they support their claims with evidence. They rarely can.
Angela Rasmussen and Liz Ginexi discuss MKUltra and What Really Happened in the Wuhan Lab
I’m old enough to remember the bicentennial. In 1976 the USA reached the age of 200. I was 15 years old, about to start my junior year in high school, and living in Ashland, Ohio. I recall the bicentennial being a much bigger event than what we are experiencing this year. Perhaps I was simply younger and more easily impressed. Or, perhaps, Chuck Todd’s explanation is correct; I’ve always liked Chuck. Or, perhaps, the problem is that semiquincentennial is so @#%& hard to pronounce!
What was the status of Intermediate Physics for Medicine and Biology back in the summer of 1976? Russ Hobbie, then the sole author, was 43 years old. Just three years before he finished auditing all the courses medical students take in the first two years at the University of Minnesota and must have been hard at work on the first edition of IPMB, published two years later, in 1978, the year I graduated from high school. I didn’t become aware of the book until I reached graduate school at Vanderbilt University. I probably saw it first in 1982 or 1983.
Move forward 50 years and the 6th edition of IPMB should appear (assuming all goes well) just a couple months after the semiquincentennial celebration. Russ Hobbie passed away in 2021, but Gene Surdutovich will join as an author of this new edition.
I expect that during the tricentennial celebration in 2076 people will look back at 2026 as a dark and dangerous time for science, when anti-science forces came to dominate the federal government, promoting vaccine hesitancy, climate change denial, and other nonsense. I hope that by 2076 this era will have passed, and science will have become respectable again, but I’m not certain that will be the case. Will IPMB still be read and used in college courses? Who knows? I’ll be gone by then, and most likely Gene will too. But perhaps new coauthors will come along, and the tricentennial will coincide with the 11th edition of Intermediate Physics for Medicine and Biology!
For you scientists and science-lovers celebrating the 4th of July, I recommend a series of events sponsored by the American Philosophical Society about science during the founding of the United States, called America’s Scientific Revolutionaries. I particularly like the lecture in the video below, about Benjamin Rush—an American Founding Father who was also a medical doctor—and his role in early American medicine. The video is also about the war on vaccines today, and features vaccine scientist Paul Offit. It’s an interesting analysis of how much progress medicine has been made in the last 250 years, how much ground we have lost recently, and the work ahead of us during the next half century.
Communicating Disease: Assessing Benjamin Rush's Public Health Legacies at America's 250th.
“Methodological Guidelines for Circadian Modeling of Daylight Saving Time: Application to the United States”
Most mornings I get an email from arXiv, an archive of preprints in the sciences, especially physics. (Here at the start of this post I should warn you: Preprints on arXiv are not peer reviewed. They are preliminary, and are meant to get results out quickly, avoiding the delays associated with publishing in a scientific journal. But peer review is not just slow, it is also valuable. Almost all preprints contain some mistakes and some are garbage. So, reader beware!)
In my daily email from arXiv, I get a list of new preprint titles and abstracts submitted under the category of biological physics. Most days, I scan the titles and don’t find anything that interests me. But last week (Thursday, June 18), I saw this:
arXiv:2606.19541 (*cross-listing*)
Date: Wed, 17 Jun 2026 19:33:48 GMT (587kb)
Title: Methodological guidelines for circadian modeling of Daylight Saving Time: application to the United States
Modeling the circadian impact of seasonal clock changing requires precise
synchronization between solar and social time. This report critiques a recent
study that associated disease prevalence in the United States with seasonal
clock exposure. We identify a fundamental computational error in which a sign
reversal of the longitudinal offset effectively inverted the US East-West axis,
cross-correlating local health data with the circadian burden of hypothetical
locations on the opposite side of a time zone. We outline the methodology for a
correct modelization [note: I hate the word “modelization”] of the circadian process in the context of US geography.
This preprint, which I downloaded and read as a pdf, illustrates science in action. It critiques a previously published paper and claims to show there is a fundamental flaw in its analysis. (Another disclaimer: I am not an expert in circadian rhythms, and I cannot say from my own research who is right: the original authors Lara Weed and Jamie Zeitzer from Stanford University, or the Spanish physicists Jose Martin-Olalla and Jorge Mirab.)
Weed and Zeitzer’s original paper looked at the health hazards caused by daylight saving time. It’s fairly well known that changing the clocks twice a year at the beginning and end of daylight saving time can be associated with health problems. But how significant are those problems? And, more specifically, if we eliminate the time change, should we replace it with permanent standard time or permanent daylight saving time? Weed and Zeitzer used mathematical modeling to analyze the degree of “circadian burden” on health. Circadian burden is the physiological strain on your body’s biological clock when your daily schedule in not in sync with the sun’s natural rhythms. Weed and Zeitzer concluded that
As compared to current time policy [switching back and forth between standard time and daylight saving time], permanent SDT [standard time] and [permanent] DST [daylight saving time] reduce circadian burden and are anticipated to reduce the prevalence of obesity and stroke with SDT having a more positive impact than DST.
The preprint by Martin-Olalla and Mirab claims to have found a bug in Weed and Zeitzer’s computer program.
We identify a fundamental computational error in which a sign reversal of the longitudinal offset effectively inverted the US East-West axis, cross-correlating local health data with the
circadian burden of hypothetical locations on the opposite side of a time zone.
They conclude that
Consequently, the original study’s conclusions currently lack empirical support.
Who’s right? I can’t say for sure, and I would like to read Weed and Zeitzer’s response to this preprint before I draw any definite conclusion. But the physicists make a convincing case for a fundamental flaw. They quote Weed and Zeitzer’s computer code line by line, highlighting where the bug occurs. It seems to be a sign error in how the burden shifts with position in the time zone, inverting east and west.
Martin-Olalla and Mirab include a “manuscript timeline” in their preprint that may not survive peer review and journal policy, but is interesting nonetheless.
The curiosity bug bit us. We decided to pull down and run the original code ourselves to compute and observe the yearly burden… all of a sudden, we uncovered the inversion error. It... was sitting right there in plain sight, but we had initially trusted the comments embedded within the script rather than checking the raw mechanics. We checked that the light diets were inverted: Western locations had brighter mornings and darker evenings in their clock time analysis.
Before I go on, I should confess to you some of my biases. First, I’m a physicist, so I naturally suspect that the physicists will be more skilled at mathematical and computer modeling. Second, I live in Michigan, just north of Detroit, which is pretty far north and is near the western edge of the Eastern Time Zone. In the winter, it doesn’t get light until about 8 am. If we were on permanent daylight time, it wouldn’t get light until 9. I’m a morning person, and this would annoy me. My circadian clock would suffer from a whole lotta burden. So I’m passionately against the idea of permanent daylight time, and would rather keep switching twice a year if we can’t get permanent standard time.
And now back to the story. What lessons can be learned from this scientific debate?
Science is difficult. Sometimes you’re wrong. Wrong doesn’t mean evil, and wrong doesn’t mean stupid. Although I don’t know who is wrong in this case, I’m pretty sure one pair of authors is right and one is wrong (I don’t see how both pairs could each be a little right and a little wrong). That’s why science has peer review. In this case, peer review by the journal doesn’t seem to have spotted the problem. But peer review also occurs when other scientists get bit by the curiosity bug. It may take a long time, but the truth is usually uncovered by the peer review process. It can be painful on a personal level, but is vital for science as a whole.
Mathematical modeling is difficult. I should know, because I did mathematical modeling and computer simulation for a living for nearly 40 years. It’s easy for a bug to creep into a computer program. That’s why you have to test, test, test each part of the code. Toy models with analytical solutions of special cases can help verify your program. They can’t prove the code is correct, but they can uncover flaws. In general, I always tried to analyze special cases and examine intermediate results “by hand” to make sure they make sense. It’s slow, painstaking work, but minimizes the chances of being wrong.
Sharing computer code is good. I rarely shared my code early in my career; it just wasn’t a thing people did back then (and was difficult to do before the internet). But the trend now is to share code openly. Some journals insist on it. This can be embarrassing if your program is wrong, and even if it’s right but written in an ugly, complicated way. But sharing is essential. Share you code, and write your code in a way so you aren’t embarrassed to share it.
Sign up for arXiv. It’s one of the best ways I know of to keep up with the current literature. Nowadays the scientific literature sprays out like from a fire hose, so we need all the help we can get.
This is a story about science, not antiscience. Over the last couple years, the forces of antiscience are everywhere (consider vaccine hesitancy and climate change denial for starters). Antiscience advocates demonize scientists and ignore evidence. The authors I’m talking about today—Weed, Martin-Olalla, Mirab, and Zeitzer—have nothing to do with antiscience. They are merely engaged in a scientific debate. They are showing us how science should be done. Compared to advocates of antiscience, both pairs of authors in this debate are heroes. I love them all, no matter who turns out to be right in the end.
If the Week and Zeitzer article is flawed, then is permanent standard time really better than permanent daylight time? Frustratingly, Martin-Olalla and Mirab don’t say. They don’t reproduce Week and Zeitzer’s analysis using a corrected program. So, after all this debate, we still don’t know what is best. I’ll hope for permanent standard time, but policy should depend on scientifically-established, country-wide analysis and not on Brad Roth’s personal preferences. I’m not convinced we have the answer to this issue right now. Stay tuned.
Ed was born in Taylorville, a small town in central Illinois, in 1912. Some of his earliest memories were of scavenging electronic equipment like transformers, capacitors, and generators from old telephones.
He went to college at Purdue University and graduated in 1933 with a degree in electrical engineering. These were the years of the Great Depression, and many of his classmates, who had trouble affording college, would live in the basement of one of the research labs. After graduation, Ed obtained an exchange fellowship to spend a year in Germany. On the ship traveling across the Atlantic, he met Beth Busser, another exchange student from Bryn Mawr College who was studying German literature. Ed eventually attended Harvard University for graduate school. In 1937 he married Beth, and in 1938 he earned a PhD in Physics.
When World War II ended, Ed returned to Harvard on the faculty, and had to figure out what his research topic would be. Rabi had been studying nuclear magnetic moments in molecular beams, and Ed wondered if similar effects could be observed in a solid. By Christmas 1945, Ed and his coworkers had measured resonance absorption of an oscillating magnetic field by nuclear magnetic moments in paraffin wax.
Russ Hobbie and I like to use the homework problems in Intermediate Physics for Medicine and Biology to illustrate modeling. But rarely does a problem encompass the entire process of constructing and analyzing a mathematical model. Gene Surdutovich and I try to do better in the 6th edition of IPMB (due out in a few months). Here is a homework problem that is not in any edition of IPMB, but that requires the student to analyze a model in its entirety. At least, that’s the goal.
Section 11.1
Problem 4½. Consider a variable that changes discretely (in steps, not continuously). You measure it in consecutive steps and get
step
data
1
3.2184
2
4.0680
3
2.2896
4
4.6490
5
0.3875
6
1.3951
Your hypothesis is that this data can be obtained from a logistic map. Develop a mathematical model. Quantify it, analyze it, determine any unknown parameters, and decide if the data support your hypothesis.
The central question to be answered by this problem is: can this data be explained by a logistic map? You can’t definitively answer this question, but you can assess if the data support this hypothesis.
First you have to quantify what a logistic map is. The first equation in Section 10.9 of IPMB states that the logistic map is represented by the equation
The counter j indicates which data point is which, and yj is the value of the jth data point. There are two parameters: a and y∞.
We will want to use least squares to determine these parameters. Least squares is simpler if the parameters enter the model linearly. Ours don’t, but we can define b = a/y∞ and then write the logistic map as
Now we are in a position to apply the method of linear least squares, as described in Section 11.1 of IPMB. Define the quantity Q as
Q represents the average of the squares of the differences between the data and the model. (Although we have six data points, the sum goes from one to five. We can’t use j = 6 because then we would need a seventh point for yj+1). Our goal is to minimize Q, thereby obtaining the best fit to the data. The variables we can vary to minimize Q are a and b. To find the minimum, we set ∂Q/∂a = ∂Q/∂b = 0. Setting ∂Q/∂a = 0 gives
which reduces to
Similarly, setting ∂Q/∂b = 0 reduces to
Next, you need to calculate all these sums. I find it easiest to construct a table like that below
j
yj
yj2
yj3
yj4
yjyj+1
yjyj+12
1
3.2184
10.3581
33.3365
107.2902
13.0925
42.1367
2
4.0680
16.5486
67.3198
273.8570
9.3141
37.8897
3
2.2896
5.2423
12.0027
27.4814
10.6444
24.3713
4
4.6490
21.6132
100.4798
467.1305
1.8015
8.3751
5
0.3875
0.1502
0.0582
0.0226
0.5406
0.2095
6
1.3951
sum
53.9124
213.1970
875.7817
35.3931
112.9823
The two equations for a and b become
53.9124 a – 213.1970 b = 35.3931
213.1970 a – 875.7817 b = 112.9823
You can solve these two linear equations for the two unknowns. You will find
a = 3.920 and b = 0.8253
which means that
a = 3.92 and y∞ = 4.75
These are exactly the parameters I used to construct the original data. If you calculate Q, you will get zero (expect, perhaps, for some round-off error) because I didn’t add any noise to the data. The model explains the data well.
The two parameters have different interpretations. The parameter y∞ merely scales the size of the data. Dividing yj by y∞ transforms the data so it lies in the range between zero and one. The parameter a, however, cannot be scaled away. It’s a fundamental parameter characteristic of the logistic map (Eq. 10.39 in IPMB). Moreover, a = 3.92 is well into the range for which the logistic map results are chaotic.
Other than for practice, why create this new problem? It requires the student to go through the entire modeling procedure. Translating the hypothesis (the logistic map) into quantitative form, identifying the unknown parameters (a and y∞), using least squares to evaluate the parameters from the data, and examining the quality of the fit to determine if the calculation supports the hypothesis. You are getting about as close to modeling as you can hope for with a simple homework problem.
The Five Step Method: Math Modelling, with Jason Bramburger
For the last six months, I’ve been the Michigan Representative of the volunteer group Grandparents For Vaccines. Our group’s mission is to ensure America’s grandchildren have their best start in life without the threat of vaccine-preventable diseases. We do this by sharing the stories of people who have lived during the time before vaccines were common.
There’s a link between being a coauthor of the textbook Intermediate Physics for Medicine and Biology and volunteering for Grandparents For Vaccines. In IPMB, Russ Hobbie and I discuss the misconceptions associated with electromagnetic fields, such as the debunked claims that 60-Hz powerline fields cause leukemia and radiofrequency fields emitted by cell phones cause brain cancer. I explored these topics further in my popular science book Are Electromagnetic Fields Making Me Ill? A tremendous amount of misinformation and many conspiracy theories are associated with these issues. After the rise of the Make America Healthy Again movement, I noticed similar misinformation and conspiracy theories associated with the opposition to vaccines. Naturally I was attracted to groups advocating for vaccines, especially vaccines for children. In addition, last August I became a first-time grandfather. So Grandparents For Vaccines seemed like a perfect fit for me.
Want to learn more about Grandparents For Vaccines? This week I had an essay published by Your Neighborhood Scientist. This nonprofit organization works to make science accessible, understandable, and human-centered. It strives to explain why science is important to communities and why we should support science. Boy, do we need more of that. I thank the founder and executive director of Your Neighborhood Scientist, Audrey Drotos, for publishing my essay and am grateful to the two editors who helped me write it: Trinity Pirrone and Kate Giffin. You can read the essay here.
In this age, in this country, public sentiment is everything. With it, nothing can fail; against it, nothing can succeed. Whoever molds public sentiment goes deeper than he who enacts statutes, or pronounces judicial decisions.
I believe this holds true for the role of science in America today. We cannot defeat the forces of antiscience by legislation or lawsuits. Our only hope is to convince the public of the value of science.
The main thing Grandparents For Vaccines does is collect videos of people (mostly, but not exclusively, grandparents) telling stories about their experiences with vaccine-preventable illnesses. If you want to hear some of these inspiring stories, you can find them on the Grandparents For Vaccines YouTube channel. I link to several of these stories below, and others can be found in my Your Neighborhood Scientist essay. If you have such a story of your own, please consider sharing it with us.
Christine from North Carolina talks about getting the polio vaccine as a child.
Teri from Oregon tells her story about vaccines. The irrepressible Teri Mills, a retired nurse, recruited and trained me as the Michigan Rep for Grandparents For Vaccines.
DeeDee from Colorado is another nurse who understands the importance of vaccines.
Renowned vaccine scientist Paul Offit describes a polio unit in the 1950s.
Arthur Lavin is the founder of Grandparents For Vaccines.
This is the worst of this bunch of videos, recorded by an odd guy with poor public speaking skills. I include it to show that even if your story isn’t the most inspiring or articulate one, it’s still worth telling.
I’ve been following Keener’s work since I was a graduate student. His study of reentry induction in a sheet of anisotropic cardiac tissue influenced my own work significantly (J. Math. Biol., Volume 26, Pages 41–56, 1988). He and I were both were interested in the bidomain model of the heart, a mathematical description of the electrical properties of cardiac tissue. I mentioned him in my brief history of the bidomain model because of his article in a special issue of the journal Chaos.
The next publication is an exception to my rule of not citing reviews. It appears in a 1998 focus issue of the journal Chaos edited by Art Winfree and dedicated to describing fibrillation in normal ventricular myocardium. It included a review by Brad Roth and Wanda Krassowska (Roth and Krassowska 1998), an analysis of an improved algorithm to solve the bidomain equations by mathematician Jim Keener of the University of Utah and his student Kristina Bogar (Keener and Bogar 1998), and the paper we examine in this section, a review by Natalia Trayanova and her graduate students Kirill Skouibine and Felipe Aguel (Trayanova, Skouibine, and Aguel 1998).
I could discuss many of Keener’s other articles. He wrote an excellent review about modeling traveling waves with singular perturbation theory (Physica D: Nonlinear Phenomena, Volume 32, Pages 326–361, 1988) and did some research on ephaptic coupling in cardiac tissue that I wasn’t so keen on (Proc. Natl. Acad. Sci., Volume 107, Pages 20935–20940, 2010). But overall I found his research to be uniformly excellent. I would rank him just behind the late Art Winfree as the best mathematical biologist I have ever known.
Using Math in Physics: 4. Toy Models, by Joe Redish.
In Intermediate Physics for Medicine and Biology, Russ Hobbie and I introduce many “toy models.” These are simplified models that strip away detail to expose fundamental processes. Why use toy models in biology, which is notoriously complex? To explore this question, I want to focus on an article by the late Joe Redish published in The Physics Teacher: “Using Math in Physics: 4. Toy Models” (Volume 59, Pages 683–688, 2021). The paper is one in a series of articles that Redish wrote about using math in physics, several of which will be cited in the 6th edition of IPMB.
As physicists, we consider our highly simplified models an obvious and natural way to approach physics. Mathematical models of complicated systems can be tricky, so the best way to understand the math is to take the simplest possible example that illustrates a phenomenon, then take it apart and put it back together again, matching the math with physical intuitions and building a mental blend of what the math means physically.
He goes on to say
Simple systems help build understanding: Learning to use this resource effectively to build new understanding
is an important step in learning to be an effective scientist.
Toy models help students to learn
to blend physical concepts, knowledge, and intuition with mathematical symbols and processing.
I couldn’t agree more.
One important skill when using a toy model is deciding what to include and what to ignore. Redish addresses this issue:
In choosing a model, we have to decide what phenomena we are trying to describe, how to quantify the quantities involved, and, perhaps most important, what matters and what doesn’t. The world is too complex for us to include everything that’s going on. Deciding what matters and what can be ignored (at least at first) is an essential scientific skill, one that is, unfortunately, rarely taught explicitly even to our physics majors.
Toy models are useful for teaching students how to go back and forth from physics (and biology and medicine) to mathematics. When I was teaching, I noticed that many students understood the physics qualitatively and had good math skills, but had trouble translating between the two. They tend to think of these skill as being separate. Redish says
Once we’ve mapped our physical quantities onto math, we inherit processing tools from mathematics that let us solve problems that we might have difficulty solving. But once we have completed our calculation, we have to interpret the result back in the physics. What did the solution tell us about the physical world? Finally, we have to evaluate that interpretation. Is our model good enough for what we needed to do? Or are there refinements that we have to make, additional factors or effects that we really need to include?
Redish is explicit about why toy models are useful and important.
We use toy models widely in introductory physics because they support multiple pedagogically valuable developments.
Toy models help students build the blend by focusing on the math-physics connection.
Toy models are built into most of our problems and can help build physical intuition.
Some toy models work way better than we might expect.
I consider the second bullet point to be particularly critical. Students need to gain intuition into how systems behave. They need insight. If they use no math, any insight is totally qualitative. If they use math, they risk missing the insight because they are focused entirely on manipulating the mathematical symbols. In graduate school, I took a course on general relativity. I learned how to do the math well enough to get an A, but I never felt I understood what was happening physically. I would have benefited from some toy models.
Some biologists and medical doctors like to put all possible details into a complicated “black box” computer model. While such an approach has its uses, such as for making numerical predictions to compare to experiments, it provides no insight. (Perhaps the researcher who writes the computer program gains some insight, but the user does not.) Redish says
Many real-world phenomena include lots of competing effects. Making sense of them, figuring out what matters most, and how to approach them can be challenging. Toy models are not just a way of learning to build the blend; they are an analytical tool for approaching a complicated system.
The sixth edition of Intermediate Physics for Medicine and Biology relies even more heavily on toy models than previous editions. If students can gain the intuition from these toy models and can practice building models and analyzing them mathematically, they will be ready to examine even more complicated and diverse biological and medical systems quantitatively.
Elective MRI Screening of the General Public—Buyer Beware.
I saw an article by Matthew Davenport and Scott Reeder published recently in JAMA(TheJournal of the American Medical Association) titled “Elective MRI Screening of the General Public—Buyer Beware.” My initial reaction was “oh no, not more nonsense about the health risks of static magnetic fields!” Fortunately, that’s not what the article is about. No risks from exposure to magnetic fields are mentioned. So, what’s the problem?
Apparently many people are paying for elective whole bodymagnetic resonance imaging scans, even when not recommended by standard medical practice. In these images, benign growths can look just like small, early-stage tumors; you can’t distinguish them. This leads to additional procedures—such as biopsies, endoscopies, or surgeries—which each carry their own risk. Also, a false positive result can cause anxiety, sleeplessness, and financial strain. When you put all these issues together, elective whole body MRI scans may cause more harm than good, even if the direct risks of having a MRI are nonexistent (take “direct risk” here to mean the risk you are exposed to if you have an MRI scan for free but then the image is accidentally deleted before anyone can look at it).
This may seem an odd topic for a blog about Intermediate Physics for Medicine and Biology. But it reminds us that while physics is important in medicine, other non-technical issues are also critical. You might think that having an image of the inside of the body is always better than not having an image. But apparently it’s not.
Does this mean we should stop striving to develop even better MRI scanners? No! Better scanners should lead to better images and therefore better diagnoses. But we must be careful when interpreting the images (even improved images) especially when screening, where false positives will always be a challenge. As Russ Hobbie and I say in Chapter 5 of IPMB when analyzing the artificial kidney, we must recognize “the distinction between a high-technology treatment [or, in this case, image] and a real conquest [or identification] of a disease.”
I am an emeritus professor of physics at Oakland University, and coauthor of the textbook Intermediate Physics for Medicine and Biology. The purpose of this blog is specifically to support and promote my textbook, and in general to illustrate applications of physics to medicine and biology.
