Young (1773–1829) went to medical school and was a practicing physician. How did he learn enough math and physics to become a biological physicist? In Young’s case, it was easy. He was a child prodigy and a polymath who learned more through private study than in a classroom. As an adolescent he was studying optics and building telescopes and microscopes. As a teenager he taught himself calculus. By the age of 17 was reading Newton’s Principia. By 21 he was a Fellow of the Royal Society.
Some of his most significant contributions to biological physics were his investigations into physiological optics, including accommodation and astigmatism. In Intermediate Physics for Medicine and Biology, Russ Hobbie and I state that the “ability of the lens to change shape and provide additional converging power is called accommodation.” Robinson describes Young’s experiments that proved the changing shape of the lens of the eye is the mechanism for accommodation. For instance, he was able to rule out a mechanism based on changes in the length of the eyeball by making careful and somewhat gruesome measurements on his own eye as he changed his focus. He showed that patients whose lens had been removed, perhaps because of a cataract, could no longer adjust their focus. He also was one of the first to identify astigmatism, which Russ and I describe as “images of objects oriented at different angles… form at different distances from the lens.”
Young’s name is mentioned in IPMB once, when analyzing the wave nature of light: “Thomas Young performed some interference experiments that could be explained only by assuming that light is a wave.” The Last Man Who Knew Everything describes Young’s initial experiment, where he split a beam of light by letting it pass on each side of a thin card, with the beams recombining to form an interference pattern on a screen. Young presents his famous double-slit experiment in his book A Course of Lectures on Natural Philosophy and the Mechanical Arts. Robinson debates if Young actually performed the double-slit experiment or if for him it was just a thought experiment. In any case, Young’s hypothesis about interference fringes was correct. I’ve performed Young’s double-slit experiment many times in front of introductory physics classes. It establishes that light is a wave and allows students to measure its wavelength. Interference underlies an important technique in medical and biological physics described in IPMB: Optical Coherence Tomography.
A green laser passing through two slits 0.1 mm apart produces an interference pattern. Photo by Graham Beards, published in Wikipedia.
Was Young a better biological physicist than Helmholtz? Probably not. Was Young a better scientist? It’s a close call, but I would say yes (Helmholtz had nothing as influential as the double slit experiment). Was Young a better scholar? Almost certainly. In addition to his scientific contributions, he had an extensive knowledge of languages and helped decipher the Rosetta Stone that allowed us to understand Egyptian hieroglyphics. He really was a man who knew everything.
Importance Concerns over radiofrequency radiation (RFR) and carcinogenesis have long existed, and the advent of 5G mobile technology has seen a deluge of claims asserting that the new standard and RFR in general may be carcinogenic. For clinicians and researchers in the field, it is critical to address patient concerns on the topic and to be familiar with the existent evidence base.
Observations This review considers potential biophysical mechanisms of cancer induction, elucidating mechanisms of electromagnetically induced DNA damage and placing RFR in appropriate context on the electromagnetic spectrum. The existent epidemiological evidence in humans and laboratory animals to date on the topic is also reviewed and discussed.
Conclusions and Relevance The evidence from these combined strands strongly indicates that claims of an RFR–cancer link are not supported by the current evidence base. Much of the research to date, however, has been undermined by methodological shortcomings, and there is a need for higher-quality future research endeavors. Finally, the role of fringe science and unsubstantiated claims in patient and public perception on this topic is highly relevant and must be carefully considered.
Public perception is also an important consideration, especially
in the context of addressing patient fears. Given the combined
biophysical and epidemiological evidence base to date against
the proposition that RFR is carcinogenic, it might seem surprising
that this belief is so widely evangelized and propagated relentlessly.
A major and unedifying part of the reason for this is the noxious
influence of fringe science on confounding public understanding; the
BioInitiative Report, a nonscholarly [non-peer reviewed] work that insists that RFR causes
many harms from cancer to autism, has been widely circulated since
2007. Despite its popularity, it has been repeatedly debunked by
health bodies worldwide, and the attempts to treat its unsubstantiated
assertions as equivalent to the weight of peer-reviewed weight
of scientific evidence are archetypical false balance.
Tellingly perhaps, the recent misinformation propagated around
5G is not even new—the same grave claims were made about prior
mobile technologies for decades and were equally unsupported.
Their renaissance now is underpinned by disinformation perpetuated
across social media and a microcosm of a greater problem with
online disinformation. There is, for example, a thriving online market
for dubious devices that promise to protect consumers from RFR,
furthering a likely misguided perception of harm. Cancer is an emotive
topic, which undoubtedly increases the virulence of misguided
assertions. It is accordingly important to be cognizant of the fact that
while the issue may be strictly academic to researchers, it is a source
of anxiety and apprehension to patients and the general public, and
there is an onus on scientists to both convey the scientific consensus
and to ensure that future work is conducted to a high standard.
The International Agency for Research on Cancer designation of RFR as a group 2B agent (a possible carcinogen) in 2011 is also frequently
misunderstood as implying evidence of harm. However, such
an interpretation is incorrect, as reiterated in the most recent International
Agency for Research on Cancer communication in 2020,
which stated that “despite considerable research efforts, no mechanism
relevant for carcinogenesis has been consistently identified to
date. In the past 5 years, epidemiological research on mobile phone
use and tumours occurring in the head has slowed down compared
with the previous decade. Most new and previous case-control studies
do not indicate an association between mobile phone use and
risk of glioma, meningioma, acoustic neuroma, pituitary tumours,
or salivary gland tumours.”
It is worthwhile too to acknowledge a potentially political dimension
to the propagation of falsehoods on 5G in particular; a New
York Times investigation found that Russian state forces were complicit
in spreading falsehoods, with the European Commission finding
the fingerprints of both Russian and Chinese health disinformation
rising with the advent of COVID-19, including false claims
linking cancer to RFR. All of this undermines collective understanding and makesit imperative that scientists be at the vanguard of communicating the evidence to prevent detrimental misconceptions [my italics].
Grimes has taken much criticism for his article, all of which, in my opinion, is undeserved. See, for example, this website containing an attack titled “Why did JAMA Oncology publish a paper written by a Telecom industry spokesperson?” by Joel Moskowitz (JAMAOncology did no such thing). Several groups called for JAMA Oncology to retract Grimes’s article, but the journal refused (I’m proud of them). My advice for Grimes is to just be happy that people are paying attention to his work. Are Electromagnetic Fields Making Me Ill?, which covers much of the same ground and comes to similar conclusions, has not been similarly criticized, apparently because the critics are either unaware of it or don’t think it’s important enough to bother with.
Problem 24. The differential form of Ampere’s law,
Eq. 8.24, provides a relationship between the current density
j and the magnetic field B that allows you to measure
biological current with magnetic resonance imaging (see, for
example, Scott et al. (1991)). Suppose you use MRI and find
the distribution of magnetic field to be
Bx = C(yz2 − yx2)
By = C(xz2 − xy2)
Bz = C4xyz
where C is a constant with the units of T m−3. Determine
the current density. Assume the current varies slowly enough
that the displacement current can be neglected.
To solve this homework problem, calculate the curl of the magnetic field to get, within a proportionality constant, the current density.
By the way, the problem doesn’t ask you to do this, but you might want to verify that the divergence of B is zero as it must be according to Maxwell’s equations, and that the divergence of j is zero (conservation of current).
Using MRI to measure current density was one of those ideas I wish I’d thought of, but I didn’t. When Peter Basser and I wrote a paper analyzing an alternative (and less successful) method to detect action currents using MRI, we cited four of Joy’s articles in our very first sentence! I first met Joy when we co-chaired a session at the 2009 IEEE Engineering in Medicine and Biology Society Conference in Minneapolis. I had the honor of being the external examiner for one of Joy’s graduate students, Nahla Elsaid, at her 2016 dissertation defense. Joy was a delightful guy, and a joy to work with.
I’ll miss him.
MICHAEL LAWRENCE GRAHAME JOY (July 31, 1940–July 5, 2020) was born in Toronto and died at Drynoch Farm in Caledon, on his own terms, in his own time. He was predeceased by his wife Jane (née Andras) and will be dearly missed by his wife Carol Fanning, his son Rob, his daughters Gwen and Ellen, their partners, his grandchildren (Asha, Nel, Tallulah, Freya, Kelvin, and Skyler) and generations of nieces, nephews, cousins, former students, friends and colleagues.
Mike was professor emeritus at the University of Toronto; Institute of Biomaterials & Biomedical Engineering; Department of Electrical & Computer Engineering. He was a pioneer in the development of Magnetic Resonance and Electric Current Density Imaging and earned numerous significant grants, awards and citations.
Mike, (Muncle Ike, Zeepa) was truly a unique individual. He was a man of many interests who always had time for the numerous children who would follow him like shadows as he puttered on his latest amazing project. He could turn the most mundane chore into both an adventure and a learning experience. He imparted his love of nature, enquiry and adventure on his young assistants, whether tinkering on his jet boat Feeble, constructing a zip line, building model rockets, fishing, or going on long walks where “getting lost” was all part of the fun.
Mike enjoyed being surrounded by those he loved. His birthday parties at the Bay were the highlight of the summer while the Christmas tree parties at the Farm kicked off the festive season. Whether at summer picnics, Church, dinners, gatherings, bridge games, visiting family at Nares Inlet or summer afternoons on the side porch, he was always at the center of things with his distinctive laugh and quick sense of humour.
Mike left his imprint on so many. His was a life well lived and well loved. In lieu of flowers, please consider a donation to the Georgian Bay Land Trust, one of the many conservation projects Mike supported.
This blog is about physics applied to medicine and biology, but if we don’t solve the climate crisis there’s no use developing fancier ways to do medical imaging or radiation therapy; we’ll all be dead. So today I’m going to tell you about a book I just read, titled Drawdown: The Most Comprehensive Plan Ever Proposed to Reverse Global Warming. It’s the book I’ve been looking for. It analyzes all the different ways we can address global warming, and ranks them by impact and importance. Here’s how the editor Paul Hawken begins Drawdown.
The genesis of Project Drawdown was curiosity, not fear. In 2001 I began asking experts in climate and environmental fields a question: Do we know what we need to do in order to arrest and reverse global warming? I thought they could provide a shopping list. I wanted to know the most effective solutions that were already in place, and the impact they could have if scaled. I also wanted to know the price tag. My contacts replied that such an inventory did not exist, but all agreed it would be a great checklist to have, though creating one was not within their individual expertise. After several years, I stopped asking because it was not within my expertise either.
Then came 2013. Several articles were published that were so alarming that one began to hear whispers of the unthinkable: It was game over. But was that true, or might it possibly be game on? Where did we actually stand? It was then that I decided to create Project Drawdown. In atmospheric terms drawdown is that point in time at which greenhouse gases peak and begin to decline on a year-to-year basis. I decided that the goal of the project would be to identify, measure, and model one hundred substantive solutions to determine how much we could accomplish within three decades towards that end.
Many solutions are presented in Drawdown, but here I count down the top ten, ranked according to their total atmospheric carbon dioxide reduction, with a brief quote from Drawdown accompanying each.
10. Rooftop Solar
As households adopt rooftop solar… they transform generation [of electricity] and its ownership, shifting away from utility monopolies and making power production their own.
9. Silvopasture
Silvopasture is… the integration of trees and pasture or forage into a single system for raising livestock… Trees create cooler microclimates and more protective environments, and can moderate water availability. Therein lies the climatic win-win of silvopasture: As it averts further greenhouse emissions from one of the world’s most polluting sectors, it also protects against changes that are now inevitable.
8. Solar Farms
Any scenario for reversing global warming includes a massive ramp-up of solar power by mid-century. It simply makes sense: the sun shines every day, providing a virtually unlimited, clean, and free fuel at a price that never changes. Small, distributed clusters of rooftop panels are the most conspicuous evidence of the renewables revolution powered by solar photovoltaics (PV). The other, less obvious iteration of the PV phenomenon is large-scale arrays of hundreds, thousands, or in some cases millions of panels [solar farms] that achieve generating capacity in the tens or hundreds of megawatts.
7. Family Planning
Increased adoption of reproductive healthcare and family planning is an essential component to achieve the United Nations’ 2015 medium global population projection of 9.7 billion people by 2050. If investment in family planning, particularly in low-income countries, does not materialize, the world’s population could come closer to the high projection, adding another 1 billion people to the planet.
6. Educating Girls
Girls education, it turns out, has a dramatic bearing on global warming. Women with more years of education have fewer, healthier children and actively manage their reproductive health… Synchronizing investments in girls’ education with those in family planning would be complementary and mutually reinforcing. Education is grounded in the belief that every life bubbles with innate potential. When it comes to climate change, nurturing the promise of each girl can shape the future for all.
5. Tropical Forests
In recent decades, tropical forests... have suffered extensive clearing, fragmentation, degradation, and depletion of flora and fauna… One of the dominant storylines of the nineteenth and twentieth centuries was the vast loss of forestland. Its restoration and re-wilding could be the twenty-first-century story.
Whether on the farm, near the fork, or somewhere in between, efforts to reduce food waste can address emissions and ease pressure on resources of all kinds, while enabling society more effectively to supply future food demand.
2. Wind Turbines
Ongoing cost reduction will soon make wind energy the least expensive source of installed electricity capacity, perhaps within a decade.
1. Refrigerant Management
As temperatures rise, so does reliance on air conditioners. The use of refrigerators, in kitchens of all sizes and throughout “cold chains” of food production and supply, is seeing similar expansion. As technologies for cooling proliferate, evolution in refrigerants and their management is imperative.
While reading Intermediate Physics for Medicine and Biology, let’s turn up the thermostat a bit during warm days. Between chapters, let’s ditch the hamburger and eat a salad instead (and if you can’t finish it, save the rest for leftovers). Let’s make sure girls in particular are encouraged to read IPMB (or whatever else that will help with their education). And let’s write our congressional representatives and encourage them to support solar and wind energy sources.
If you don’t have the time to read Drawdown, or don’t have easy access to it, then visit the website drawdown.org or watch the videos below, which summarize the plan to reverse global warming.
“Earth teems with sights and textures, sounds and vibrations, smells and tastes, electric and magnetic fields. But every animal can only tap into a small fraction of reality’s fullness. Each is enclosed within its own unique sensory bubble, perceiving but a tiny sliver of our immense world.”
An Immense World sometimes overlaps with Intermediate Physics for Medicine and Biology. For example, both books discuss vision. Yong points out the human eye has better visual acuity than most other animals. He writes “we assume that if we can see it, they [other animals] can, and that if it’s eye-catching to us, it’s grabbing their attention… That’s not the case.” Throughout his book, Yong returns to this idea of how sensory perception differs among animals, and how misleading it can be for us to interpret animal perceptions from our own point of view.
Like IPMB, An Immense World examines color vision. Yong speculates about what a bee would think of the color red, if bees could think like humans.
Imagine what a bee might say. They are trichromats, with opsins that are most sensitive to green, blue, and ultraviolet. If bees were scientists, they might marvel at the color we know as red, which they cannot see and which they might call “ultrayellow” [I would have thought “infrayellow”]. They might assert at first that other creatures can’t see ultrayellow, and then later wonder why so many do. They might ask if it is special. They might photograph roses through ultrayellow cameras and rhapsodize about how different they look. They might wonder whether the large bipedal animals that see this color exchange secret messages through their flushed cheeks. They might eventually realize that it is just another color, special mainly in its absence from their vision.
Both An Immense World and IPMB also analyze hearing. Yong says
Human hearing typically bottoms out at around 20 Hz. Below those frequencies, sounds are known as infrasound, and they’re mostly inaudible to us unless they’re very loud. Infrasounds can travel over incredibly long distances, especially in water. Knowing that fin whales also produce infrasound, [scientist Roger] Payne calculated, to his shock, that their calls could conceivably travel for 13,000 miles. No ocean is that wide.…
Like infrasound, the term ultrasound… refers to sound waves with frequencies higher than 20 kHz, which marks the upper limit of the average human ear. It seems special—ultra, even—because we can’t hear it. But the vast majority of mammals actually hear very well into that range, and it’s likely that the ancestors of our group did, too. Even our closest relatives, chimpanzees, can hear close to 30 kHz. A dog can hear 45 kHz; a cat, 85 kHz; a mouse, 100 kHz; and a bottlenose dolphin, 150 kHz. For all of these creatures, ultrasound is just sound.
In IPMB, Russ Hobbie and I introduce the decibel scale for measuring sound intensity, or how loud a sound is. Yong uses this concept when discussing bats.
The sonar call of the big brown bat can leave its mouth at 138 decibels—roughly as loud as a siren or jet engine. Even the so-called whispering bats, which are meant to be quiet, will emit 110-decibel shrieks, comparable to chainsaws and leaf blowers. These are among the loudest sounds of any land animal, and it’s a huge mercy that they’re too high-pitched for us to hear.
Yong examines senses that Russ and I never consider, such as smell, taste, surface vibrations, contact, and flow. He wonders about the relative value of nociception [a reflex action to avoid a noxious stimulus] and the sensation of pain [a subjective feeling created by the brain].
The evolutionary benefit of nociception is abundantly clear. It’s an alarm system that allows animals to detect things that might harm or kill them, and take steps to protect themselves. But the origin of pain, on top of that, is less obvious. What is the adaptive value of suffering?
On the continuum ranging from life’s unity to diversity, Yong excels at celebrating the diverse, while Russ and I focus on how physics reveals unifying principles. I’m sometimes frustrated that Yong doesn’t delve into the physics of these topics more, but I am in awe of how he highlights so many strange and wonderful animals. There’s a saying that “nothing in biology makes sense except in light of evolution.” That’s true for An Immense World, which is a survey of how the evolution of sensory perception shapes they way animals interact, mate, hunt their prey, and avoid their predators.
Two chapters of An Immense World I found especially interesting were about sensing electric and magnetic fields. When discussing the black ghost knifefish’s ability to sense electric fields, Yong writes
Just as sighted people create images of the world from patterns of light shining onto their retinas, an electric fish creates electric images of its surroundings from patterns of voltage dancing across its skin. Conductors shine brightly upon it. Insulators cast electric shadows.
Then he notes that
Fish use electric fields not just to sense their environment but also to communicate. They court mates, claim territory, and settle fights with electric signals in the same way other animals might use colors or songs.
Although flowers are negatively charged, they grow into the positively charged air. Their very presence greatly strengthens the electric fields around them, and this effect is especially pronounced at points and edges, like leaf tips, petal rims, stigmas, and anthers. Based on its shape and size, every flower is surrounded by its own distinctive electric field. As [scientist Daniel] Robert pondered these fields, “suddenly the question came: Do bees know about this?” he recalls. “And the answer was yes.”
The chapter on sensing magnetic fields is different from the others, because we don’t yet know how animals sense these fields.
Magnetoreception research has been polluted by fierce rivalries and confusing errors, and the sense itself is famously difficult both to study and to comprehend. There are open questions about all the senses, but at least with vision, smell, or even electroreception, researchers know roughly how they work and which sense organs are involved. Neither is true for magnetoreception. It remains the sense that we know least about, even though its existence was confirmed decades ago.
If you want to read a beautifully written book that explores how much of the physics in Intermediate Physics for Medicine and Biology can be used by species throughout the animal kingdom to sense their environment, I recommend An Immense World. You’ll love it.
Umwelt: The hidden sensory world of animals. By Ed Yong.
Suppose Russ Hobbie and I had not given you that integral. What would you do? Previously in this blog I explained how the integral can be evaluated analytically and perhaps you’re skilled enough to perform that analysis yourself. But it’s complicated, and I doubt most scientists could do it. If you couldn’t, what then?
You could integrate numerically. Your goal is to find the area under the curve shown below.
Unfortunately x ranges from zero to infinity (the plot shows the function up to only x = 10). You can’t extend x all the way to infinity in a numerical calculation, so you must either truncate the definite integral at some large value of x or use a trick.
A good trick is to make a change of variable, such as
When x equals zero, t is also zero; when x equals infinity, t is one. The integral becomes
Although this integral looks messier than the original one, it’s actually easier to evaluate because the range of t is finite: zero to one. The integrand now looks like this:
The colored stars in these two plots are to guide the reader’s eye to corresponding points. The blue star at t = 1 is not shown in the first plot because it corresponds to x = ∞.
We can evaluate this integral using the trapezoid rule. We divide the range of t into N subregions, each extending over a length of Δt = 1/N. Ordinarily, we have to be careful dealing with the two endpoints at t = 0 and 1, but in this case the function we are integrating goes to zero at the endpoints and therefore contributes nothing to the sum. The approximation is shown below for N = 4, 8, and 16.
The area of the purple rectangles approximates the area under the red curve This approximation gets better as N gets bigger. In the limit as N goes to ∞, you get the integral.
I performed the calculation using the software Octave (a free version of Matlab). The program is:
N=8;
dt=1/N;
s=0;
for i=1:N-1
t=i*dt;
s=s+dt*t^3/((exp(t/(1-t))-1)*(1-t)^5);
endfor
I found the results shown below. The error is the difference between the numerical integration and the exact result (π4/15 = 6.4939…), divided by the exact result, and expressed as a percent difference.
N
I
% error
2
1.1640
–82
4
6.2823
–3.26
8
6.6911
3.04
16
6.5055
0.178
32
6.4940
0.000282
64
6.4939
0.00000235
128
6.4939
0.00000000174
These results show that you can evaluate the integral accurately without too much effort. You could even imagine doing this by hand if you didn’t have access to a computer—using, say, N = 16—and getting an answer accurate to better than two parts per thousand.
For many purposes, a numerical solution such as this one is adequate. However, 6.4939… doesn’t look as pretty as π4/15. I wonder how many people could calculate 6.4939 and then say “Hey, I know that number; It’s π4/15”!
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...
One of the earliest investigations was reported by Barker, Jalinous and Freeston (1985). They used a solenoid in which
the magnetic field changed by 2 T in 110 μs to apply a stimulus
to different points on a subject’s arm and skull. The
stimulus made a subject’s finger twitch after the delay required
for the nerve impulse to travel to the muscle.
The story of how Tony Barker invented transcranial magnetic stimulation is fascinating. You can hear about it in the video below, where John Rothwell—another early magnetic stimulation researcher—reminisces with Barker about his invention. The most interesting part of the video is when Barker describes a crucial trip he made from Sheffield (he worked at the Royal Hallamshire Hospital in Sheffield, England) to London (The National Hospital, Queen’s Square), so he could demonstrate his device to leading neurophysiologist Pat Merton. Rothwell, also at Queen’s Square, had his brain stimulated that day, and the next day he wrote Barker asking to get a stimulator of his own. Barker’s 1985 paper in The Lancet (cited in IPMB) was the first publication about magnetic stimulation of the brain. As Barker says, “like all the best papers it was one page long.”
The 15-minute video is well worth your time. I’ll stop writing so you can listen. Enjoy!
Anthony Barker reminiscing with John Rothwell about the invention of transcranial magnetic stimulation.
In Table 13.1 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I list the approximate intensity levels of various sounds, in decibels. The minimum perceptible sound is 0 dB, a typical office has a sound level of 50 dB, a jack hammer is 100 dB, and the loudest sound listed is a rocket launch pad at 170 dB.
Can there be even louder sounds? Yes, there can! This new homework problem lets you calculate the loudest possible sound.
Section 13.4
Problem 17 ½. Let us calculate the loudest possible sound in air.
(a) Use Eq. 13.29 to calculate the intensity of a sound in Wm−2, using 428 Pa s m−1 for the acoustic impedance of air and one atmosphere (1.01 × 105 Pa) for the pressure. This pressure is the largest that can exist for a sinusoidally varying sound wave, as an even louder sound would create a minimum pressure below zero (less than a vacuum).
(b) Use the result from part (a) to calculate the intensity in decibels using Eq. 13.34.
For those of you who don’t have a copy of IPMB at your side, here are the two equations you need
I = ½ p2/Z(13.29)
Intensity level = 10 log10(I/I0)
(13.34)
where I is the intensity, Z is the acoustic impedance, p is the pressure, I0 is the minimum perceptible intensity (10−12 W m−2), and log10 is the common logarithm.
I’ll let you do the calculation, but you should find that the loudest sound is about 191 dB. Is this really an upper limit? No, you could have a peak pressure larger than one atmosphere, but in that case you wouldn’t be dealing with a traditional sound wave (with pressure ranging symmetrically above and below the ambient pressure) but more of a nonlinear acoustic shock wave.
Krakatoa, by Simon Winchester.
Has there ever been a sound that loud? Or, more interestingly, what is the loudest sound ever heard on earth? That’s hard to say for sure, but one possibility is the 1883 eruption of the Krakatoa volcano. We know this sound was loud, because people heard it so far from where the eruption occurred.
In August 1883 the chief of police on Rodriguez was a man named James Wallis, and in his official report… for the month he noted:
On Sunday the 26th the weather was stormy, with heavy rain and squalls; the wind was from SE, blowing with a force of 7 to 10, Beaufort scale. Several times during the night (26th–27th) reports were heard coming from the eastward, like the distant roar of heavy guns. These reports continued at intervals of between three and four hours, until 3 pm on the 27th, and the last two were heard in the directions of Oyster Bay and Port Mathurie [sic].
This was not the roar of heavy guns, however. It was the sound of Krakatoa—busily destroying itself fully 2,968 miles away to the east. By hearing it that night and day, and by noting it down as any good public servant should, Chief Wallis was unknowingly making for himself two quite separate entries in the record books of the future. For Rodriguez Island was the place furthest from Krakatoa where its eruptions could be clearly heard. And the 2,968-mile span that separates Krakatoa and Rodriguez remains to this day the most prodigious distance recorded between the place where unamplified and electrically unenhanced natural sound was heard and the place where that same sound originated.
Winchester concludes
The sound that was generated by the explosion of Krakatoa was enormous, almost certainly the greatest sound ever experienced by man on the face of the earth. No manmade explosion, certainly, can begin to rival the sound of Krakatoa—not even those made at the height of the Cold War’s atomic testing years.
No one knows how many decibels Krakatoa’s eruption caused on the island itself. The sound was almost certainly in the nonlinear regime, and probably had an intensity of over 200 dB.
I was particularly fascinated by Rhodes’s tale of Wilson and James Watson as competing assistant professors at Harvard in the late 1950s. Watson advocated for molecular biology, while Wilson favored evolutionary biology. It was a battle between the unity and diversity of life. Wilson, with a job offer from Stanford in hand, was offered tenure if he would remain at Harvard. Watson—already famous for discovering the structure of DNA with Francis Crick—was livid that Wilson was to be tenured before he was. In the end, Harvard gave them both tenure (a wise decision). Decades later Wilson and Watson become friends. Listen to them discuss their rivalry in the video at the end of this post.
Readers of Intermediate Physics for Medicine and Biology will be interested in Wilson’s online high-school biology textbook Life on Earth. Physicists, mathematicians, and engineers who want to apply their field to biology or medicine always face the obstacle of learning biology. Sometimes they don’t need a deep knowledge of biology, but merely must know enough to collaborate with a biologist. Life on Earth is an excellent introduction to the field. It is free, available online, is written by a giant in the field of biology, and contains beautiful photographs and engaging videos. The only problem: it was written to be used on a Mac. I am a Mac guy, so this is not a problem for me. I don’t know if it works on a PC. Life on Earth should provide you with enough biology to understand IPMB.
Problem 37. The consumption of a finite resource is
often modeled using the logistic equation. Let y(t) be the
cumulative amount of a resource consumed and y∞ be
the total amount that was initially available at t = −∞.
Model the rate of consumption [I wish Russ and I had written “amount consumed” instead of “rate of consumption”] using Eq. 2.29 over the range
−∞ < t < ∞.
(a) Set y0 = y∞/2, so that the zero of the time axis
corresponds to when half the resource has been used.
Show that this simplifies Eq. 2.29.
(b) Differentiatey(t) to find an expression for the rate
of consumption. Sketch plots of dy/dt versus t on linear
and semilog graph paper. When does the peak rate of
consumption occur?
The answer to this exercise can be found in the IPMB solution manual. (The solution manual is available free of charge to instructors. If you need a copy, email me at roth@oakland.edu.) All exercises in the solution manual have a brief preamble, explaining the goal of the exercise and why it’s important.
2.37¶ This is not a biological example, except in the sense that if we ignore this example we humans may all end up dead. Students use a variation of the logistic equation to analyze the consumption of a finite resource (e.g., oil).
I won’t solve the entire problem in this blog post, but I will show the semilog plot from the solution manual.
A semilog plot of amount consumed (solid) and the rate of consumption (dashed) for a finite resource modeled using the logistic equation. This plot is part of the solution to Problem 37b.
The rate of consumption of the resource (dy/dt) first rises exponentially, reaches a peak, and then falls exponentially. (Remember, a straight line on a semilog plot corresponds to exponential growth or decay.) For the mathematically inclined, the dy/dt curve corresponds to a hyperbolic secant squared.
Why do I bring up this topic? Recently I read Energy: A Human History, by Richard Rhodes, a sweeping account of energy transitions that changed our world. Rhodes includes a figure that looks a little bit like this:
My rendition of a figure from the final chapter of Energy: A Human History showing the historical evolution of the world energy mix.
What a wonderful plot! It both summarizes Rhodes’s book and illustrates the power and ubiquity of Hubbert’s peak. That semilog plot from Homework Problem 37 appears over and over as one finite resource replaces another.
I should add a few qualifiers.
Historical data is noisy and the curves pictured above merely approximate a complicated behavior.
The plot begins at about the time of the industrial revolution. The population of humans was probably too small, and our technology too primitive, to apply this model before that time.
All future data (say, after 2016, the year Energy was published) is extrapolation or prediction.
Let’s hope that the Renewables curve corresponds to an infinite resource, not a finite one, so it will never reach a peak and then fall. Is that wishful thinking? I don’t know, but the figure encourages us to ask such questions.
Nuclear energy shot up much faster than would be expected right after World War II, but then the curve flattened prematurely because of fears about radiation.
Natural gas appears to be with us for the foreseeable future, unless we can wean ourselves off of it to address global warming. The use of coal is almost done (regardless of what a certain senator from West Virginia thinks), and the use of oil has reached its peak and is on its way down (now might be a good time to buy an electric car).
Climate change is the critical issue looming over the right side of the plot. We must leave many of those fossil fuels (coal, oil, gas) in the ground to prevent an environmental disaster.
Perhaps I need to add extra parts to that homework problem.
(c) Suppose at time t you discover that pollution from this finite resource is killing people, and you stop consuming it immediately. How would that change the plots you made in part (b)?
(d) What would happen if the resource is killing people but people continue to consume it nevertheless?
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.
