One book that had a big impact on me when I was young is Jacob Bronowski’s The Ascent of Man. The book is based on a television series by the same name, broadcast by the British Broadcasting Corporation. You could call The Ascent of Man a history of science, but it is a rich and philosophical history, covering all the sciences. The book was published in 1973, so I probably first read it in high school.
Bronowski is an example of a type of physicist who we encounter often in Intermediate Physics for Medicine and Biology: one who made the transition to biology. He writes in the book’s foreword:
There has been a deep change in the temper of science in the last twenty years: the focus of attention has shifted from the physical to the life sciences. As a result, science is drawn more and more to the study of individuality. But the interested spectator is hardly aware yet how far-reaching the effect is in changing the image of man that science moulds.
As a mathematician trained in physics, I too would have been unaware, had not a series of lucky chances taken me into the life sciences in middle age. I owe a debt for the the good fortune that carried me into two seminal fields of science in one lifetime; and though I do not know to whom the debt is due, I conceived The Ascent of Man in gratitude to repay it.
The book is well written and beautifully illustrated. I highly recommend it.
To view The Ascent of Man TV series, Part 1 click on the link below.
I recently finished Bill McKibben’s excellent book Here Comes The Sun (McKibben and I are about the same age, so we both like the Beetles reference. The page just before the Table of Contents has a single line of text: “And I say, it’s all right.”). The subtitle is “A Last Chance for the Climate and a Fresh Change for Civilization.” It’s one of the most optimistic climate change books I have read. After summarizing his past angst-ridden pronouncements on global warming, McKibben writes in the introduction to Here Comes The Sun“And yet, right now, really for the first time, I can see a path forward. A path lit by the sun.”
The heart of his argument is that now, finally, wind power and especially solar power have gotten so cheap that the change to green energy will be not only virtuous but also economically advantageous. In his book, McKibben addresses four questions that are often asked by green energy skeptics. I’ll look at them one by one.
Can We Afford it?
McKibben writes
Sometime in those 10 years [between 2014 and 2024] we passed some invisible line where producing energy pointing a sheet of glass at the sun became the cheapest way to produce power, and catching the breeze the second cheapest... As the energy investor Rob Carlson put it recently, continuing to burn fossil fuel is a “self-imposed financial penalty” that will “ultimately degrade America's long-term global competitiveness.”
The gist of his argument is that with fossil fuels, you have to pay for the fuel each and every time you use it to get energy. Year after year you keep paying for coal or oil or gas. With solar and wind energy, you pay once to set up the technology and then the fuel (the sun and wind) is free. FREE! FOREVER! (Or at least for the lifetime of the solar panel or wind turbine.) I’m an cheapskate and I love free stuff. And you save the planet as a bonus. As McKibben points out, one problem is that energy becomes so cheap that energy companies can’t make money supplying it. What a wonderful problem to have.
But Can the Poor World Afford It?
It turns out that the developing world is leapfrogging straight to solar power, skipping the centralized fossil fuel phase. Why?
The switch is being driven by the desire for reliable and affordable power.
McKibben compares it to how cell phones allowed poor countries to skip the expensive land line infrastructure and go straight to mobile communication. Countries in Africa and the Middle East are right now putting up solar panels, with the process starting at the grass roots rather than from the top down. Who do they buy their solar panels from? China.
But Is There Enough Stuff?
McKibben thinks the concerns about having enough raw materials such as lithium to build the solar panels, wind turbines, and batteries is a legitimate problem, but probably not an insurmountable one.
Yes, you have to mine lithium to build a battery. But once you've mined it, that lithium sits patiently in the battery doing its job for a decade or two (after which, as we will see, it can be recycled). If you mine coal, on the other hand, you immediately set it on fire—that's the point of coal. And then it’s gone. And then you have to go mine some more.
He says we should compare the risks and cost of mining and recycling green energy materials to the much greater risks of mining and dealing with the left over from fossil fuels, such as coal ash.
Do We Have Enough Land?
The land needed for solar and wind is surprisingly small, especially compared to that taken up by fossil fuels. McKibben quotes an estimate that oil and gas wells, coal mines, pipelines, power plants, and the like take up about 1.3% of America’s land. Green energy will require far less. McKibben compares a solar array to a corn field.
Converting some of these [corn] fields to solar panels makes enormous ecological sense. That's because one way to look at a field of corn (or any other crop) is that it’s already an array of solar panels. A plant is a way to convert sunshine into energy through photosynthesis... Somewhere between 1 and 3 percent of the sunlight falling on a leaf actually becomes energy. The photovoltaic panel works considerably better [20, and possibly some day up to 40, percent]...
You could supply all the energy the US currently uses by covering 30 million acres with solar panels. How much land do we currently devote to growing corn ethanol [not the corn we eat, but the corn we use to help fuel our cars]? About 30 million acres.
The biggest threat is not a lack of land, but the not-in-my-backyard attitude so common in the USA.
Because this is a blog about my textbook Intermediate Physics for Medicine and Biology, let’s do one of those estimation problems that Russ Hobbie and I encourage. The solar constant is 1390 W/m2. That’s how much light energy from the sun per square meter that reaches the earth (or, at least, the top of our atmosphere). The cross-sectional area of our planet that intercepts this light is πR2, where R is the earth’s radius (6.4 × 106 m2). That gives 1.8 × 1017 W, or 180,000 TW (the “T” is for tera, or 1012). Humanity’s worldwide average power consumption is about 18 TW. So, we only need 0.01% of the solar energy available. Granted, some of that sunlight is reflected or absorbed by the atmosphere, some is incident on the ocean, and no solar panel is 100% efficient. Still, the land area needed for solar and wind farms, while not small, is reasonable.
The Final Word
When I can, I like to give authors the final word in my blog posts. So, here is how McKibben ends Here Comes The Sun
I end this book saddened, too, of course—saddened by all that happened in the last 40 years, and by all that we haven’t done. But I also end it exhilarated. Convinced that we’ve been given one last chance. Not to stop global warming (too late for that) but perhaps to stop it short of the place where it makes civilization impossible. And a chance to restart that civilization on saner ground, once we’ve extinguished the fires that now both power and threaten it.
I’ve changed my mind. I’m gonna give George Harrison the final word.
Since a changing magnetic field generates an induced electric
field, it is possible to stimulate nerve or muscle cells
without using electrodes. The advantage is that for a given
induced current deep within the brain, the currents in the
scalp that are induced by the magnetic field are far less than
the currents that would be required for electrical stimulation.
Therefore transcranial magnetic stimulation (TMS) is
relatively painless. It is also safe (Rossi et al. 2009).
Magnetic stimulation can be used to diagnose central nervous
system diseases that slow the conduction velocity in
motor nerves without changing the conduction velocity in
sensory nerves (Hallett and Cohen 1989). It could be used
to monitor motor nerves during spinal cord surgery, and to
map motor brain function. Because TMS is noninvasive and
nearly painless, it can be used to study learning and plasticity
(changes in brain organization over time; Wassermann
et al. 2008). Recently, researchers have suggested that repetitive
TMS might be useful for treating disorders such as
depression (O’Reardon et al. 2007) and Alzheimer’s disease
(Freitas et al. 2011).
One of my first tasks at NIH was to meet with two
medical doctors in the National Institute of Neurological Disorders and Stroke—Mark Hallett and Leo Cohen—who
had recently begun using magnetic stimulation. Hallett
obtained his medical degree from Harvard and was chief
of the Human Motor Control Section, housed in NIH’s
famous clinical center. He is a leading figure in neurophysiology,
specifically in magnetic stimulation research, and is
often asked to publish tutorials about magnetic stimulation
in leading journals. Hallett once told me that he
began college as a physics major but switched to a pre-med
program after a year or two. Cohen earned his MD from the
University of Buenos Aires in Argentina. In the late 1980s,
he worked in Hallett’s section, but eventually became the
head of his own Human Cortical Physiology Section at
NIH. Together Hallett and Cohen were doing groundbreaking
research in magnetic stimulation but lacked the
technical expertise in physics required to do things like
calculate the electric fields produced by different coils…
Hallett and Cohen obtained a magnetic stimulator at
NIH in the late 1980s. They described magnetic stimulation
and its potential uses in the Journal of the American Medical
Association [Magnetism: A new method forstimulation of nerve and brain. JAMA, 262, 538–541, 1989.], where they highlighted how assessment
of central conduction times using magnetic stimulation
could be useful for diagnosing diseases, such as multiple sclerosis, and also how the method could be suitable for
monitoring the integrity of the spinal cord during surgery.
They emphasized that although methods existed to measure
the conduction time in the brain for sensory fibers,
stimulation of the brain was needed to measure conduction
times in central motor fibers.
Not entirely realizing the explosion of research I was
lucky enough to be wading into, I started collaborating
with Hallett and Cohen to calculate the electric fields
produced during magnetic stimulation... Our first
work together was a technical paper comparing the electric
and magnetic fields produced by a variety of coils with
different shapes… Hallett and Cohen were most interested in the electric
field induced during transcranial magnetic stimulation,
so my next task was to use a three-sphere model to
calculate the electric field in the brain...
Hallett was one of my most important collaborators throughout my career. In fact, if you look at Google Scholar to examine my most influential articles (those with over 100 citations each), Hallett was my most common coauthor (13), followed closely by Leo Cohen (11), then my PhD advisor John Wikswo (8), and finally my good friend from NIH Peter Basser (6), who also collaborated with Hallett. One could argue that no other scientist except Wikswo had such an impact on my career.
Hallett was a giant in his field of neurology. He will be missed by many, including me.
Oral History 2013: Stanley Fahn Interviews Mark Hallett
Today I want to discuss an experiment that led to the discovery of messenger RNA (mRNA). Why did I choose to focus on one specific experiment? First, because of its importance in the history of molecular biology. Second, the experiment highlights the use of radioisotopes like those Russ Hobbie and I describe in Chapter 17 of Intermediate Physics for Medicine and Biology. Third, the recent development and of mRNA vaccines for Covid and other diseases makes this a good time to review how our knowledge of mRNA was established.
A crucial experiment was performed by Arthur Pardee and Monica Riley at the University of California, Berkeley, and published in 1960. Let me provide some context and set the stage. The structure of DNA had been discovered by Watson and Crick in 1953. By 1960, scientists knew that individual genes in DNA coded for individual proteins. The question was how the genetic information got from DNA to the protein. RNA was suspected to be involved, in part because ribosomes—the stable cellular macromolecules where DNA was produced—are made from RNA. Were the ribosomes the messenger, or was there something else? Many key experiments in biology, like the one by Pardee and Riley, are performed using a simple model system: E coli bacteria. Another important tool of early modern biology was radioisotopes, a product of modern physics from the first half of the twentieth century that was essential for biology during the second half of the century.
The experiment Pardee and Riley had done in Berkeley was new, technically amusing, and persuasive. It amounted to removal of the gene from the cell after it had begun to function. They had grown… bacteria… carrying [a specific gene to produce the protein enzyme beta-galactosidase]… in a broth where the available phosphorus [an important element in DNA] was the radioactive isotope 32P. The bacteria, with their DNA heavily labeled, were then centrifuged out... [and] resuspended in a nonradioactive broth… [Next] they added glycerol [a type of antifreeze]. Then they took one sample to test for enzyme activity [to check if beta-galactosidase was produced]. They put other samples into small glass ampules, sealed the ampules by fusing the glass at the neck, and lowered them into a vacuum-insulated flask of liquid nitrogen. The bacteria were frozen almost instantly at 196 degrees below zero centigrade. Protected from bursting by the glycerol, the bacteria were not killed, but their vital processes were arrested while the radiophosphorus in the DNA… continued to decay… From day to day, Riley raised ampules of the frozen bacterial suspension from the liquid nitrogen and thawed them… For comparison, they ran the whole [experiment] in parallel without the radioactivity [this was their control].
Before telling you the result, let me digress a bit about phosphorus-32. It’s an unstable isotope that undergoes beta decay to stable sulfur-32. This means the 32P ejects an electron (and an antineutrino) and transforms to 32S. In many cases (such as in sodium-24 examined in Fig. 17.9 of IPMB), beta decay occurs to an excited state that then emits gamma rays. But 32P is “pure” meaning there are no gamma rays, or even different competing beta decay paths. The book MIRD: Radionuclide Data and Decay Schemes by Eckerman and Endo, often cited in IPMB, shows this simple process with this figure and table.
Note the half-life of 32P is two weeks, and the average energy of the ejected electron is 695 keV.
What happens when 32P decays? First, the electron can damage the cells. An electron of this energy has a range of about a millimeter, so that damage would not be localized to an individual bacterium (with a size on the order of 0.001 mm). However, when the 32P isotope decays, it will recoil, which could eject it from the DNA molecule, causing a strand break. Even if the recoil is not strong enough remove the atom from DNA, there would now be a sulfur atom where a phosphorus atom should be, and these two atoms, being in different columns of the periodic table, will have different chemical properties which surely would disrupt the DNA structure and function. As Judson says
An atom of 32P decays by emitting a beta particle, which is a high-speed electron, whereupon it is transformed into an atom of sulphur. The transformation, and the recoil of the atom as the electron leaves, breaks the bonds of the backbone of the DNA at that point… Half of those decayed in fourteen days. The [beta-galactosidase] genes were being killed.
So, what was the result? Judson summarizes,
The nonradioactive bacteria sampled before freezing were synthesizing enzyme copiously. So were the radioactive ones before freezing… Thawed after ten days, samples of nonradioactive bacteria synthesized beta-galactosidase just as vigorously as those never frozen. But the bacteria whose [beta-galactosidase] genes had suffered ten days of radioactive decay made the enzyme at less than half the rate they had before. Inactivation of the gene… abolished protein synthesis without delay. Stable intermediates between the gene and its protein—in other words, ribosomes whose RNA carried information to specify the sequence of amino acids—were ruled out. Continual action of the gene was necessary, either directly or by way of an intermediate that was unstable and so had to be steadily renewed.
When Francis Crick and Sydney Breener learned of Pardee and Riley’s results, they combined their knowledge of this experiment with a previous one by Elliot Volkin and Lazarus Astrachan using bacteriophages [a virus that infects bacteria] to hypothesize that a new type of RNA, called messenger RNA, was the unstable intermediary connecting DNA and protein. And the rest is history.
The Pardee and Riley experiment (which made up Monica Riley’s PhD dissertation… wow, what a dissertation topic!) is beautiful and important. It is also relevant today. Why do mRNA vaccines (like the Pfizer and Moderna Covid vaccines) have to be kept so cold when being transported and stored before use? As Pardee and Riley showed, the mRNA is unstable. It will decay quickly if not kept ultra-cold. Can mRNA change the DNA in your cells? No, the mRNA is simply a messenger that transfers the stored genetic information in DNA to the proteins formed on ribosomes. Moreover, one difference between E coli bacteria and human cells is that in humans the DNA is located inside the cell nucleus (bacteria don’t have nuclei) and the ribosomes are in the cytoplasm outside the nucleus. DNA can’t leave the nucleus, and mRNA can only go out of, not into, the nucleus. So an mRNA vaccine will cause human cells to make virus proteins (for the covid vaccine, it will produce the spike protein) that will be detected by your immune system, but the mRNA will only be present a short time before it decays and will not affect your DNA. Finally, the vaccine contains mRNA for only the spike protein, not for the entire virus. So, no actual intact viruses are produced by the vaccine. The spike protein simply activates your immune system, without exposing you to an infection.
Madison Stockton Spach died recently. An Instagram post by the account for the Duke Pediatric Cardiology Fellowship stated
Very sad to report the passing of Dr. Madison Spach. Dr. Spach was the first Division Chief of Pediatric Cardiology at Duke and the founder of our program. He was a legend in the field and mentored others who also went on to become preeminent in the field. His impact through innovations, the patients he cared for, those he mentored, and the program he built is immeasurable.
I have not been able to find an obituary about Spach (I hope one is published eventually). However, here’s a picture and bio published in the IEEE Transactions of Biomedical Engineering in 1971.
His wife Cecilia passed away seven years ago. Her obituary said
Cecilia Goodson Spach, 92, died peacefully in her sleep on Oct 20, 2018, after a short illness. Madison Spach, her loving husband of nearly 70 years, was with her when she passed away…
Cecilia Goodson was born and raised in Winston-Salem. She was a star athlete at Reynolds High School, where she met her perfect match in Madison Spach. Cecilia earned a nursing degree from Presbyterian Hospital School of Nursing in Charlotte. When Madison returned from the service, they married and moved to Durham, where Madison attended Duke University.
Madison Spach was born in 1926. This would mean if he entered the service right out of high school, he may have fought in the last year of World War II. He was 98 when he died this year. It’s sad that we are losing so many of our veterans of the greatest generation these days, when we need them most.
In the 1980s, Duke was the center for research about the electrical behavior of the heart. Not only was Plonsey there, along with his collaborator Barr and his student Henriquez, but also it hosted several other leading scientists. Barr was a long-time collaborator with Madison Spach, a Duke medical doctor known for his electrophysiological experiments on cardiac tissue. Some of their analyses foreshadowed key features of the bidomain model (Spach et al. 1978).
The citation was to Spach’s paper with long-time collaborator Roger Barr and others published in the journal Circulation Research.
In addition, when reviewing Craig Henriquez and Robert Plonsey’s work on cardiac wave fronts propagating through cardiac tissue surrounded by a perfusing bath, I wrote
The bidomain model represents cardiac tissue as a continuous syncytium, so Henriquez and Plonsey’s mathematical simulations provided a new interpretation of earlier experimental data that had been used to argue that cardiac tissue acted like a discrete collection of cells (Spach et al. 1981).
This citation was to Spach’s hugely influential article
It’s no secret that, like Henriquez and Plonsey, I disagreed with Spach’s interpretation of his data as implying discontinuous propagation in cardiac tissue. But I’ve told that story before and this isn’t the time or place to rehash it. Suffice to say, according to Google Scholar Spach’s paper has been cited about 950 times. Another paper on the same topic (Spach’s most highly cited article) with Paul Dolber has over a thousand citations.
Duke now has a scholarship named jointly for Roger Barr and Madison Spach. Here’s what the Duke scholarship website says about Spach’s contributions.
Madison S. Spach is a James B. Duke Professor Emeritus of medicine and Professor Emeritus of pediatrics in the School of Medicine. A renowned pediatric cardiologist and scientist, his research examined electrophysiology and the mechanisms behind cardiac dysrhythmias. On the faculty from 1960–1996, Spach developed Duke's training program in pediatric cardiology.
As I said in last week’s post, one goal I have for this blog is to support scientists, and that includes retired ones who’ve made important contributions. Madison Spach helped us advance our knowledge of cardiac electrophysiology. His was a life worth living.
In Science Under Siege we seek to provide a succinct yet detailed delineation of the five forces behind the modern-day antiscience movement (the five p’s, as we call them—the plutocrats, the petrostates, the pros, the propagandists, and our press). We draw upon our respective experiences on two different fronts of the war on science to identify and delineate the drivers and their financial backers. We provide a road map for dismantling the antiscience machine, through stories that at times are quite personal but speak to challenges and threats that are broad and sweeping. This book is a warning. But it is also a call to arms. While there is urgency—unlike any we’ve ever known—there is still agency. We can still avert disaster if we can understand the nature of the mounting antiscience threat and formulate a strategy to counter it.
In their first chapter they write
We find ourselves facing not just a one-two punch of pandemics and the climate crisis, but a one-two-three punch, with that third punch, antiscience, obstructing the needed response from governments and civil society. The future of humankind and the health of our planet now depend on surmounting the dark forces of antiscience.
My favorite chapter was their last one, titled “The Path Forward.” They present a Venn diagram for winning the war against antiscience.
About it they write
One circle describes ways to expand the visibility of scientists, while providing the tools for scientists to better engage with the public. Another characterizes efforts to protect scientists. And the remaining circle emphasizes the battle against the intensifying flow of antiscience disinformation. We propose a framework for accomplishing this tripartite mission.
I’m going to adopt this Venn diagram as a guide for my future posts. 1) I will continue to communicate constructively about Intermediate Physics for Medicine and Biology, but in addition I’ll stress how important science is in our society and oppose the forces of antiscience. I also will try to fulfill this role in my “Bob Park’s What’s New” series that I also publish weekly here. 2) I will search out and attempt to debunk and defeat disinformation. I’ve been trying to do this all along, but this goal is more urgent now. 3) I’ll support scientists. I can’t do much to support them financially or materially, but in this blog I can take on the role of cheerleader-in-chief and provide moral support, especially to those who are attacked by the forces of antiscience.
Mann and Hotez adopt a strident and pugnacious tone in Science Under Siege. Is it justified? It is. I truly believe that there is a Republican War on Science. I believe the forces of antiscience are currently winning this war. And I am certain we must oppose antiscience with all our resources. Particularly as a retired scientist, I have an obligation to fight antiscience for the sake of the next generation of scientists. And as a new grandfather, I must oppose antiscience for the sake of my grandson and all the others of his generation.
Science is humanity’s best insurance against threats from nature, but it is a fragile enterprise that must be nourished and protected. What is now happening to virology is a stark demonstration of what is happening to all of science. It will come to affect every aspect of science in a negative and possibly dangerous way, as has already happened with climate science. It is the responsibility of scientists, research institutions, and scientific organizations to push back against the anti-virology attacks, because what we are seeing now may be the tip of the proverbial iceberg.
Book Talk: Michael E. Mann and Peter J. Hotez — Science Under Siege
Sensitive detectors are constructed from superconducting materials. Some compounds, when cooled below a certain critical temperature, undergo a sudden transition and their electrical resistance falls to zero. A current in a loop of superconducting wire persists for as long as the wire is maintained in the superconducting state. The reason there is a superconducting state is a well-understood quantum-mechanical effect that we cannot go into here. It is due to the cooperative motion of many electrons in the superconductor (Eisberg and Resnick 1985, Sect. 14.1; Clarke 1994). The [line integral of the electric field] around a superconducting ring is zero, which means that [the change in magnetic flux] is zero, and the magnetic flux through a superconducting loop cannot change. If one tries to change the magnetic field with some external source, the current in the superconducting circuit changes so that the flux remains the same.
This was not the first Nobel Prize related to the SQUID. In 1973 Brian Josephson shared the Nobel Prize “for his theoretical predictions of the properties of a supercurrent through a tunnel barrier, in particular those phenomena which are generally known as the Josephson effects.” Now, over fifty years later, it’s Clarke’s turn.
Clarke joined Berkeley Lab in 1969 and retired as a faculty senior scientist in the Materials Sciences Division in 2010. At the time of their prize-winning research, Martinis worked as a graduate student researcher, and Devoret as a postdoctoral scholar, in the Clarke group at Berkeley Lab and UC Berkeley….
[Clarke’s circuit using a tunnel barrier] is the foundation for an ultrasensitive detector called a SQUID or a superconducting quantum interference device. Clarke has pioneered and used SQUIDs in many applications, including detection of nuclear magnetic resonance (NMR) signals at ultralow frequencies; geophysics; nondestructive evaluation of materials; biosensors; detection of dark matter; and observing qubits, the fundamental unit of information in a quantum computer.
In my early days as a research student at Cambridge, my supervisor, Brian Pippard, proposed that I use a SQUID to make a highly sensitive voltmeter. In those days, procedures for making Josephson junctions were in their infancy and not practicable for manufacturing instruments. One day early in 1965, over the traditional afternoon tea at the Cavendish Laboratory, I was discussing this problem with Paul C. Wraight, a fellow student. He suggested that a molten blob of solder (an alloy of lead and tin that becomes superconducting in liquid helium) deposited onto a niobium wire might just conceivably make a Josephson junction. His rationale was that niobium has a native oxide layer that might behave as a suitable tunnel barrier.
We rushed back to the laboratory, begged a few inches of niobium wire from a colleague, melted a blob of solder onto it, attached some leads and lowered it into liquid helium. As we hoped, Josephson tunneling! The fact that Wraight’s idea worked the first time was important. If it had not, we would never have bothered to try again. Because of its appearance, we christened the device the SLUG. Later I was able to make a voltmeter that could measure 10 femtovolts (10-14 volt), an improvement over conventional semiconductor voltmeters by a factor of 100,000.
Clarke’s article goes on to describe many of the biological applications of SQUIDs, including for measuring the magnetocardiogram (magnetic field of the heart) and the magnetoencephalogram (magnetic field of the brain).
Congratulations to John Clarke and this colleagues on their Nobel Prize. It’s another wonderful example of physics applied to biology and medicine.
UC Berkeley press conference 10/7/2025: Professor Emeritus John Clarke 2025 Nobel Prize in Physics
My hearing is not what it used to be. It’s not terrible now; I still get along okay. But I find myself asking my wife “what?” a lot. So, I borrowed a copy of Physics of the Body—by John Cameron, James Skofronick, and Roderick Grant (1999)— and read Section 11.9: Deafness and Hearing Aids. It covers much of the information that Russ Hobbie and I discuss in Chapter 13 of Intermediate Physics for Medicine and Biology, and more. Below I quote a paragraph from Physics of the Body, with references removed and my comments in brackets.
In 1985 it was estimated that 21 million persons in the United States were either deaf or hard of hearing. The frequency range most important for understanding conversational speech is from about 250 to 3000 Hz. [The figure below shows the hearing response curve for a young adult from IPMB, with the range from 0.25 to 3 kHz shaded.] A person who is “deaf” above 4000 Hz but who has normal hearing in the speech frequencies is not considered deaf or even hard of hearing. [I was taking a walk with my daughter Kathy a few months ago. As we passed one house she grimaced said “what is that terrible high-pitched noise?” I said “what noise?”] However, that person should not spend a lot of money on good stereo equipment. [Music sounds the same now as I remember it back when I was a teenager. Nevertheless, I need no additional encouragement to not spend money; I’m a cheapskate.] Hearing handicaps are classified according to the average hearing threshold at 500, 1000, and 2000 Hz in the better ear [I haven’t noticed any difference between my left and right ears]. A person with a hearing threshold 30 dB above normal would probably not have a hearing problem. People with hearing thresholds of 90 dB are considered deaf or stone deaf. [According to Table 13.1 in IPMB, 30 dB is the “maximum background sound level tolerable in a broadcast studio” and 90 dB is the sound “inside a motor bus.” I am definitely not stone deaf. Is my threshold below 30 dB? I don’t know.] About 1% of the population have thresholds for speech frequencies greater than 55 dB [IPMB says 55 dB is between “office” sounds and “speech at 1 m.” I definitely can hear speech at 1 m. It’s speech from my wife calling from another room that I have trouble with.] and should use hearing aids [Both my mom and dad used hearing aids when they got older. My health has generally parallels my father’s. I fear it is just a matter of time]. About 1.7% have a slight hearing handicap; they have problems with normal speech but have no difficulty with loud speech [I think I am better than that]. Hearing problems increase with age [Yes, that’s the problem. I’m getting old.]
The average sound level of speech is about 60 dB. We adjust the sound level of our speech unconsciously according to the noise level of our surroundings. Speech sound levels in a quiet room may be as low as 45 dB; at a noisy party they may be 90 dB. A person with a hearing loss of 45 dB in the 500 to 2000 Hz range may do all right (hearing-wise) at a cocktail party but hear very little of speech in a quiet room. [I don’t know. It seems to me that I have more of a problem distinguishing speech from background sounds than just hearing speech. I suspect I would do worse at the cocktail party even with people speaking at 90 dB than chatting at 45 dB in the quiet room.]
Now that I’m on Medicare, my wife is encouraging me to have my hearing checked. I suppose I should.
The book is fascinating. It was published in 1959, the year before I was born. All three coauthors are British, and are famous enough to have Wikipedia pages. Cecil Frank Powell was a particle physicist who received the Nobel Prize in 1950 for developing the photographic method for studying nuclear processes, and for using this method to discover the pion. He was trained at the Cavendish Laboratory working with Rutherford. He died in 1969. Peter Howard Fowler was a student of Powell’s who worked on cosmic radiation. He was a radar officer with the Royal Air Force during World War II, and was able to detect German radar jamming and identify its source, leading to a destruction of the responsible German radar station. He was married to physicist Rosemary Fowler, who discovered the kaon. His grandfather was Ernest Rutherford. Fowler died in 1996. Donald Hill Perkins discovered the negative pion. He studied proton decay, and found early evidence of neutrino oscillations. Perkins and Fowler were the first to suggest using pion beams as therapy for cancer in 1961 (The use of pions in medicine hasn't panned out). Perkins died at the ripe old age of 97 in 2022.
When skimming through the book, I noticed an interesting illustration of a trident track produced by high energy electrons. It looks something like this:
A trident arises from the process of bremsstrahlung followed by pair production; both of which are described in IPMB. A fast electron interacts with an atomic nucleus, decelerating the electron and emitting a bremsstrahlung photon. This photon, if it has high enough energy, can then interact with an atomic nucleus to create an electron-positron pair. The intermediate photon can be “virtual,” existing only fleetingly. The end result is three particles: the original electron plus the pair. I gather that this requires a very high energy electron, and its cross-section is small, so it seems to contribute little to the dose in medical physics. The authors talk about the production of tridents for energies of more than a BeV, which is an old-fashioned way of saying a GeV, equivalent to 1000 MeV.
I’m glad Russ and I included figures from The Study of Elementary Particles by the Photographic Method. I hope I can figure out the permissions situation (the authors are all dead, and the publisher was sold to another company) and we can continue to include the figures in the 6th edition.
Most mornings I take a walk to keep myself in shape. Usually I listen to an audiobook while walking, but for some reason my earbuds didn’t recharge properly overnight and this morning they didn’t work right. So, I had to take my constitutional in silence.
It so happens that yesterday I was revising Appendix H (The Binomial Probability Distribution) for the 6th edition of Intermediate Physics for Medicine and Biology. (Yes, you’re right, Gene Surdutovich and I are getting close to being done if we’re already up to the appendices.) As I was reviewing the material, I thought “it sure would be nice to have some more nontrivial but not too complicated word problems for this appendix.” So, as I hiked I came up with this:
Appendix H
Problem 6. You are a young college student who wants to make a little extra cash for living expenses. You also are an occasional Dungeons and Dragons player, so you have a twenty-sided die in the top drawer of your desk. You decide to set up what you call the “Dollar and Dime” game. Any student in your dormitory can come to you and pay you a dollar and a dime, and you will take out your twenty-sided die and roll it once. If it gives a one, you hand the student a crisp, new twenty dollar bill. If it it rolls a two through twenty, the student walks away empty handed. You’re pretty happy with the game. On average, the dollars earned cover the required payouts, and the dimes are all profit. The game becomes popular among your dormmates, and people stop by to play dozens of times each day.
A page from the Rodgers and Hammerstein Song Book.
John comes to you late one Friday afternoon. He has invited Jane to attend the school musical Oklahoma! with him that evening (Jame loves musicals, especially those by Rodgers and Hammerstein), but two tickets will cost him $40, and all he has is $11. It’s too late to find a part-time job or to beg funds from his parents. His only chance to avoid reneging on the theater date is to get the needed cash by playing the Dollar and Dime game. John slaps the eleven bucks down on your desk and says “I wanna play ten times.”
Your first thought is to tell John to go to the bank and exchange the ten dollar bill for ten ones and the one dollar bill for ten dimes, so he can play the game properly. But John is on the school wrestling team, is six foot three, and weighs 270 pounds, so you decide to waive this technicality. You accept his $11, get out the twenty-sided die, and start rolling.
Ordinarily when playing this game you relax, knowing that in the long run you will make a profit. However, today you’re a bit nervous because you only have three portraits on Andrew Jackson in the envelope where you store the cash for your game. Earlier in the day, you told your wealthy roommate Peter about your situation, hoping he could cover you if needed (he declined). Now, if John wins the game four or more times, he’s gonna to be upset that you can’t pay him what you owe him, and John is not the kind of guy you want to make mad.
(a) What is the probability that John wins enough money to take Jane to Oklahoma!?
(b) What is the probability that you get clobbered by John?
(c) How do all these results change if Peter (who is annoyed that you converted your dorm room to a casino with people coming and going and noisily rolling that silly icosahedron at all hours of the night) loans John an extra $22, interest free?
Consider an experiment with two mutually exclusive outcomes, which is repeated N times, with each repetition being independent of every other one. One of the outcomes is labeled “success”, the other is called “failure.”
The binomial distribution is given by Eq. H.2,
where N is the number of tries (John has $11 so he can play the game ten times, N = 10), p is the probability of success for each try (it is a twenty sided die, so p = 0.05), and n is the number of successes (rolling a one). John will make 20n dollars by playing the Dollar and Dime game. The key question is, what’s the probability P that John gets n wins.
The odds of John never rolling a one and leaving broke is
Yikes! He has 3:2 odds of losing everything. Next, the probability that John wins only once are
Only one win will make John twenty bucks, so after paying $11 to play he’ll be nine dollars ahead, but that still isn’t enough to take Jane to see Curly give Laurey that ride in his surrey which, as you will recall, costs $40. He needs at least two wins for that. We now have enough information to answer part (a). The probability that John takes Jane to the show is one minus the probability that he doesn’t earn at least $40. So, John can avoid an unpleasant call to Jane (or, worse, escape being a no show) with a probability of 1 – 0.599 – 0.315 = 0.086. That means the odds are about 11:1 against making Jane happy. Looks like John’s in trouble.
John’s best chance is to win the Dollar and Dime game twice and earn the $40 needed for tickets. The odds are
Boy, that would be great. But if John is really lucky, he’ll win enough for the tickets plus some extra cash for a large popcorn and two medium soft drinks (which costs $18.49).
There’s only a one percent chance of Jane getting her popcorn.
But wait. If John wins four or more times, you won’t have the cash to cover his winnings. Either he’ll thrash you, or (more likely) you’ll be forced to make a deal where you pay John all that you have, $60, and promise to return his original investment of $11, and grovel before him begging for mercy. That would be good news for John. He would walk away with at least $71, and perhaps more if he knows how to drive a hard bargain (after all, you don’t want to end up daid, like poor Jud). What are the odds he’ll bust the bank?
We should also add in the chance that John will win five times, or six, or more, but those will be very small (calculate them yourself if you don’t believe me). So, the probability of a disaster (for you, not for John) is about one part per thousand, or a tenth of a percent. The odds are small, but the consequences would be dire (with you possibly ending up in the hospital), so you’re still nervous until John finishes all ten of his rolls.
Now, consider the final twist to the story. Imagine that when your so-called “friend” Peter sees John arrive, he pulls him aside, gives him a wink, and loans him another $22. (Pete could have easily just lent $29 so John would have enough to cover the cost of his date with Jane, but that would defeat his purpose, wouldn’t it?). Now John has $33 to spend on the Dollar and Dime game. The only thing that changes is N increases from ten to thirty. How does that change the probabilities? You can work out the details. I’ll just state the results.
nP
0 0.215
1 0.339
2 0.259
3 0.127
4 0.045
The chances of John taking Jane to the musical is now 0.446, so the odds are approaching 50-50. Still not great odds, but much better than before. John’s starting to dream that after he takes Jane to Oklahoma! “people will say we’re in love.” More importantly for you (and for that evil Peter), the odds of busting the bank are now 6%. So, at no cost to himself, Peter just increased the odds of shutting down the hated casino by a factor of sixty. Win or lose, you vow to start looking for another roommate; one who doesn’t know as much math.
By the time I came up with this homework problem, I had just about finished my walk. The problem has no biology or medicine in it, so it probably won’t make it into the revised sixth edition. With any luck, tomorrow I’ll be back to the audio book (and, oh, what a beautiful morning that will be). By the way, our goal is to submit the 6th edition of IPMB to our publisher, Springer, before the end of the year. It’s gonna be close, but we just might make it.
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.
