Oops!

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

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

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

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

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

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

You may have some questions.

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

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

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

Tomie De Paola

Sound,
written by Lisa Miller,
illustrated by Tomie De Paola

Children’s book author Tomie De Paola died five years ago last Sunday. I fondly recall reading De Paola’s books to my daughters Stephanie and Kathy when they were growing up. But how could Tomie De Paola possibly intersect with Intermediate Physics for Medicine and Biology? Well, you might be surprised! The first book that De Paola illustrated was Sound, written by Lisa Miller. It was part of the “Science is What and Why” series published by Coward–McCann, Inc.

Each book in the Science is What and Why series introduces fundamentals of physical science using a simple, attractive approach specifically designed for young boys and girls. Straightforward, lively language and distinguished illustrations which are a practical extension of the text present scientific facts as fascinating and exciting as the realm of the imagination.

As Gene Surdutovich and I work on the 6th edition of IPMB, I think we should strive for “straightforward, lively language and distinguished illustrations.”

De Paola’s drawings in Sound have much more charm than the figures in Chapter 13 of IPMB, which is about Sound and Ultrasound. Yet, his book covers topics that Russ Hobbie and I also discuss, such as the wavelength, frequency, and amplitude of a sound wave, and echos. I can’t help but think of De Paola as a kindred soul.

Sound appeared early in De Paola’s career; it was published in 1965. He continued illustrating books about science (I need to read The Popcorn Book), but he is best known for his children’s stories. Many of his books were autobiographical. I loved reading The Art Lesson and Tom with my girls. Although I’m not particularly religious, I thought his best work was The Clown of God.

Now, with my first grandchild due this summer, I’m looking forward to rereading many of De Paola’s books. I can’t wait.

 

Meet Tomie dePaola

https://www.youtube.com/watch?v=3_XINGTzl5U

Tomie De Paola on the television show Barney, another favorite of my daughters. 

https://www.youtube.com/watch?v=s01_ikK_SrQ

 


Tomie De Paola: Why Reading is Important 

https://www.youtube.com/watch?v=7epT0qUaaX4&t=16s

 

 

The Art Lesson 

https://www.youtube.com/watch?v=9TUQ4F27HMo 

 

Tom by Tomie de Paola 

https://www.youtube.com/watch?v=doFJAxHX5yw

 

The Clown Of God by Tomie De Paola 

https://www.youtube.com/watch?v=Gnwlzj1xdmM

The Rest of the Story 5

Bill grew up in Schenectady, New York, the youngest of four children. While a child he became interested in science because of his fascination with telescopes. He was smart; he graduated from high school at the age of 15, and then attended Schenectady’s Union College, finishing in just three years. By the age of 22 he had graduated with an M.D. from the Albany Medical College. Many of his friends didn’t realize how bright Bill was, because he was so modest and friendly, and had such a wonderful sense of humor.

Bill became an active duty medical officer posted at the U.S. Naval Hospital in Newport, Rhode Island. After a fellowship in neurology at the University of Minnesota, he joined the new medical school at UCLA. He was much loved as a medical doctor and a mentor, but he disliked many of the invasive procedures that he had to perform as a clinical neurologist.

In 1959, Bill had an idea how to noninvasively image the brain using multiple x-ray beams in different directions. After two years of effort he had a working prototype, applied for a patent, and published an article about this work. But when he approached a leading x-ray manufacturer, the company president couldn’t image there would ever be a market for such a device. Frustrated, Bill turned his attention to other things.

Page 2

Bill’s idea for how to image the brain did not go away. Other scientists took up the challenge. Physicist Allan Cormack and engineer Ronald Bracewell each developed detailed mathematical techniques for obtaining an image from beams in different directions. Engineer Godfrey Hounsfield built the first brain scanner in 1971. And the rest is history. Bill’s invention is now known as Computed Tomography (originally called a CAT scan and now referred to as CT for short). It has revolutionized medicine. In 1979, Cormack and Hounsfield won the Nobel Prize in Physiology or Medicine for their contributions to CT. William (“Bill”) Oldendorf did not share the prize, but he shared in the discovery.

William Oldendorf.

And now you know the rest of the story.

Good day! 

_________________________________________________

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

You can learn more about Computed Tomography in Chapter 16 of Intermediate Physics for Medicine and Biology.

William Oldendorf was born March 27, 1925, one hundred years ago yesterday. Happy birthday Bill!

Dipole-Dipole Interaction

One strength of Intermediate Physics for Medicine and Biology is its many homework problems. The problems stress (but perhaps not enough) the ability to make general arguments about how some quantity will depend on a variable. Often getting a calculation exactly right is not as important as just knowing how something varies with something else. For instance, you could spend all day learning how to compute the volume and surface area of complicated objects, but it’s still useful simply to know that volume goes as size cubed and surface area as size squared. Below is a new homework problem that emphasizes the ability to determine a functional form.

Section 6.7

Problem 20½. Consider an electric dipole p a distance r from a small dielectric object. Calculate how the energy of interaction between the dipole and the induced dipole in the dielectric varies with r. Will the dipole be attracted to or repelled from the dielectric? Use the following facts:

1. The energy U of a dipole in an electric field E is U = – p · E,

2. The net dipole induced in a dielectric, p', is proportional to the electric field the dielectric experiences,

3. The electric potential produced by a dipole is given by Eq. 7.30.

Let’s take a closer look at these three facts.

1. When discussing magnetic resonance imaging in Chapter 18 of IPMB, we give the energy U of a magnetic dipole μ in a magnetic field B as U = – μ · B (Eq. 18.3). An analogous relationship holds for an electric dipole in an electric field. The energy is lowest when the dipole and the electric field are in the same direction, and varies as the cosine of the angle between them. I suggest treating the original dipole p as producing the electric field E, and the induced dipole p' as interacting it. 

2. Section 6.7 of IPMB discusses how an electric field polarizes a dielectric. The net dipole p' induced in the dielectric object will depend on the electric field and the objects shape and volume. I don’t want you to have to worry about the details, so the problem simply says that the net dipole is proportional to the electric field. You might get worried and say “wait, the electric field in the dielectric is not uniform!” That’s why I said the dielectric object is small. Assume that it’s small enough compared to the distance to the dipole that the electric field is approximately uniform over the volume of the dielectric. 

3. What is the electric field produced by a dipole? Russ Hobbie and I don’t actually calculate that, but we do give an equation for a dipole’s electrical potential, which falls off as one over the square of the distance. (It may look like the cube of the distance in Eq. 7.13, but there’s a factor of distance in the numerator that cancels one factor of distance cubed in the denominator, so it’s an inverse square falloff.) The electric field is the negative gradient of the potential. Calculating the electric field can be complicated in the general case. I suggest you assume the dipole p points toward the dielectric. Fortunately, the functional dependence of the energy on the distance r does not depend on the dipole direction.

I won’t work out all theentire solution here. When all is said and done, the energy falls off as 1/r⁶, and the dipole is attracted to the dielectric. It doesn’t matter if the dipole originally pointed toward the dielectric or away from it, the force is always attractive.

This result is significant for a couple reasons. First, van der Waals interactions are important in biology. Two dielectrics attract each other with an energy that falls as 1/r⁶. Why is there any interaction at all between two dielectrics? Because random thermal motion can create a fluctuating dipole in one dielectric, which then induces a dipole in a nearby dielectric, causing them to be attracted. These van der Waals forces play a role in how biomolecules interact, such as during protein folding.

From Photon to Neuron:
Light, Imaging, Vision.

Second, there is a technique to determine the separation between two molecules called fluorescence resonance energy transfer (FRET). The fluorescence of two molecules, the donor and the acceptor, is affected by their dipole-dipole interaction. Because this energy falls off as the sixth power of the distance between them, FRET is very sensitive to distance. You can use this technique as a spectroscopic ruler. It’s not exactly the same as in the problem above, because both the donor and acceptor have permanent dipole moments, instead of one being a dielectric in which a dipole moment is induced. But nevertheless, the 1/r⁶ argument still holds, as long as the dipoles aren’t too close together. You can learn more about FRET in Philip Nelson’s book From Photon to Neuron: Light, Imaging, Vision.

The First Measurement of the Magnetocardiogram

Biomagnetism: The First Sixty Years.

A couple years ago, I published a review article titled “Biomagnetism: The First Sixty Years.” I wrote about that article before in this blog, but I thought it was time for an update. The paper is popular: according to Google Scholar it has been cited 28 times in two years, which is more citations than any other of my publications in the last decade. I remember working on this paper because it was my Covid project. That year I got Covid for the first—and, so far, only—time. I quarantined myself in our upstairs bedroom, wore a mask, and somehow avoided infecting my wife. I remember having little to do except work on my biomagnetism review.

As a treat, I thought I would reproduce one of the initial sections of the article (references removed) about the first measurement of the magnetocardiogram. Russ Hobbie and I talk about the MCG in Chapter 8 of Intermediate Physics for Medicine and Biology. This excerpt goes into more detail about how MCG measurements began. Enjoy!

2.1. The First Measurement of the Magnetocardiogram

In 1963, Gerhard Baule and Richard McFee first measured the magnetic field generated by the human body. Working in a field in Syracuse, New York, they recorded the magnetic field of the heart: the magnetocardiogram (MCG). To sense the signal, they wound two million turns of wire around a dumbbell-shaped ferrite core that responded to the changing magnetic field by electromagnetic induction. The induced voltage in the pickup coil was detected with a low-noise amplifier.

The ferrite core was about one-third of a meter long, so the magnetic field was not measured at a single point above the chest, but instead was averaged over the entire coil. One question repeatedly examined in this review is spatial resolution. Small detectors are often noisy and large detectors integrate over the area, creating a trade-off between spatial resolution and the signal-to-noise ratio.

The heart’s magnetic field is tiny, on the order of 50–100 pT (Figure 1). A picotesla (pT) is less than a millionth of a millionth as strong as the magnetic field in a magnetic resonance imaging machine. The magnetic field of the earth is about 30,000,000 pT (Figure 1), and the only reason it does not obscure the heart’s field is that the earth’s field is static. That is not strictly true. The earth’s field varies slightly over time, which causes geomagnetic noise that tends to mask the magnetocardiogram (Figure 1). Moreover, even a perfectly static geomagnetic field would influence the MCG if the pickup coil slightly vibrated. A key challenge in biomagnetic recordings, and a major theme in this review, is the battle to lower the noise enough so the signal is detectable

Figure 1. Noise sources in biomagnetism.

Most laboratories contain stray magnetic fields from sources such as electronic equipment, elevators, or passing cars (Figure 1). Baule and McFee avoided much of this noise by performing their experiments at a remote location. Even so, they had to filter out the ubiquitous 60 Hz magnetic field arising from electrical power distribution. A magnetic field changing at 60 Hz is a particular nuisance for biomagnetism because the magnetic field typically exists in a frequency band extending from 1 Hz (1 s between heartbeats) to 1000 Hz (1 ms rise time of a nerve or muscle action potential).

One limitation of a metal pickup coil is the thermal currents in the winding due to the random motion of electrons, creating extraneous magnetic fields caused by the measuring device itself. The ultimate source of noise is thermal currents in the body, but fortunately, their magnetic field is minuscule (Figure 1).

Baule and McFee suppressed background noise by subtracting the output of two pickup coils. A distant source of noise gave the same signal in both coils and did not contribute to their difference. One coil was placed over the heart, and the magnetocardiogram was larger there and did not cancel out. The two coils formed a rudimentary type of gradiometer (Figure 2).

The magnetocardiogram resembled the electrocardiogram (ECG) sensed by electrodes attached to the skin. Baule and McFee speculated that the MCG might contain different information than the ECG, another idea that reappears throughout this review. In a followup article, they theoretically calculated the magnetic field produced by the heart. The interplay between theory and experiments is yet one more subject that frequently arises in this article.

Figure 2. Types of gradiometers.

Einstein and Smoluchowski

In Chapter 4 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss the Einstein relationship between diffusion and viscosity. We wrote

The diffusion constant…is closely related to the viscosity, as was first pointed out by Albert Einstein. This is not surprising, since diffusion is caused by the random motion of particles under the bombardment of neighboring atoms, and viscous drag is also caused by the bombardment of neighboring atoms.

All this random bombardment is also related to Brownian motion: the random movement of small particles when they collide with many water molecules.

What is typically referred to as the Einstein relationship is given by our Eq. 4.22,

      D = kT/β,       (4.22)

where D is the diffusion constant, k is Boltzman’s constant, T is the absolute temperature, and β is a factor relating the viscous force to the drift velocity, sometimes called the frictional drag coefficient. Essentially, β is like the reciprocal of the mobility. This equation doesn’t contain the viscosity, but if you use Stokes’ law for β you get

      D = kT/6πηa,     (4.23)

where a is the radius of the particle being considered and η is the coefficient of viscosity.

Russ and I refer to Eq. 4.22 as the Einstein relationship. However, if you look in Howard Berg’s marvelous book Random Walks in Biology, you find this expression is called the Einstein-Smoluchowski relationship. So the natural question is: just who is this Smoluchowski?

To answer that question, I consulted my favorite biography of Einstein, Abraham Pais’s Subtle is the Lord. Pais writes

If Marian Ritter von Smolan-Smoluchowski had been only an outstanding theoretical physicist and not a fine experimentalist as well, he would probably have been the first to publish a quantitative theory of Brownian motion.

Smoluchowski, born to a Polish family, spent his early years in Vienna, where he also received a university education. After finishing his studies in 1894, he worked in several laboratories abroad, and then returned to Vienna, where he became Privatdozent. In 1900 he became professor of theoretical physics in Lemberg (now Lvov), where he stayed until 1913. In that period he did his major work. In 1913 he took over the directorship of the Institute for Experimental Physics at the Jagiellonian University in Cracow. There he died in 1917, victim of a dysentery epidemic.

It is quite remarkable how often Smoluchowski and Einstein simultaneously and independently pursued similar if not identical problems. In 1904 Einstein worked on energy fluctuations, Smoluchowski on particle number fluctuations of an ideal gas. Einstein completed his first paper on Brownian motion in May 1905; Smoluchowski his in July 1906.

So even the great Einstein had competition for many of his ideas. In fact, Smoluchowski nearly derived the relationship first. Pais continues

Smoluchowski began his 1906 paper by referring to Einstein’s two articles of 1905: “The findings [of those papers] agree completely with some results which I had… obtained several years ago and which I consider since then as an important argument for the kinetic nature of this phenomenon.” Then why had he not published earlier? “Although it has not been possible for me till now to undertake an experimental test of the consequences of this point of view, something I originally intended to do, I have decided to publish these considerations…”

Apparently he wanted to get experimental support for his ideas, and by waiting he got scooped.

Both Einstein and Smoluchowski went on to independently study critical opalescence: how the scattering of light passing through a gas increases in the neighborhood of a critical point. Pais concludes

Smoluchowski’s last contribution to this problem [of critical opalescence] was experimental: he wanted to reproduce the blue of the sky in a terrestrial experiment. Preliminary results looked promising, and he announced that more detailed experiments were in progress. He did not live to complete them.

After Smoluchowski’s death, Sommerfeld and Einstein wrote obituaries in praise of a good man and a great scientist. Einstein called him an ingenious man of research and a noble and subtle human being.

My Final Question

Suppose I died tomorrow. When my soul came before that great scientist in the sky, she might say “because of your contributions to Intermediate Physics for Medicine and Biology, I’ll answer one question for you. What is your question?” I can think of many things I would like to know, but the question I’d ask is: “is the linear no-threshold model appropriate at low doses?”

What’s the linear no-threshold model, and why’s it so important? Russ Hobbie and I explain it in Chapter 16 of IPMB.

In dealing with radiation to the population at large, or to populations of radiation workers, the policy of the various regulatory agencies has been to adopt the linear no-threshold (LNT) model to extrapolate from what is known about the excess risk of cancer at moderately high doses and high dose rates to low doses, including those below natural background.

If the excess probability of acquiring a particular disease is αH in a population N [where H is the equivalent dose per person in sieverts and α is a proportionality constant], the average number of extra persons with the disease is

                 m = α N H.         (16.42)

The product NH, expressed in person Sv, is called the collective dose. It is widely used in radiation protection, but it is meaningful only if the LNT assumption is correct. Small doses to very large populations can give fairly large values of m, assuming that the value of α determined at large doses is valid at small doses.”

Let me give you an example of why this question is so consequential. Should our society spend its time and money trying to reduce radon exposure in people’s homes? Radon is a radioactive gas that is produced in the decay chain of uranium. This noble gas can seep into basements, where it may be breathed into the lungs. The decay of radon and its progeny can cause lung cancer. However, the typical yearly dose from radon is very low, about 2 mSv. For an individual the resulting cancer risk is tiny, but if the linear no-threshold model is correct then when multiplied by the population of the United States (over 300,000,000) there can be tens of thousands of cancer deaths each year caused by radon. On the other hand, if a threshold exists below which there is no risk of cancer, then radon probably causes few if any cancer deaths. So, from a public health perspective, the answer to my question about the validity of the linear no-threshold model is crucial.

Other examples are

• The severity of low-dose, widespread exposure to radiation caused by a terrorist attack, such as a small amount of radioactivity dissolved in the water supply of a major city, 
• The hazard caused by low-dose x-ray backscatter scanners used at airports for security, 
• The danger from the release into the Pacific Ocean of minuscule amounts of radioactivity in water leftover from the Fukushima nuclear accident, or 
• The risks associated with storing radioactive waste from nuclear power plants in underground storage facilities.

All these situations have one thing in common: small individual doses to a large number of people. Public health officials need to know whether or not the collective dose is significant, and is it something we should spend our scarce resources trying to minimize.

On that fateful day I fear that even if she answers my last question, I won’t be able share it with you, dear readers (I don’t think they allow blogging down there). We’ll just have to examine the evidence available today.

Quackwatch

One goal of Intermediate Physics for Medicine and Biology is to provide readers with an understanding of the physics underlying biomedicine, so they can recognize and refute pseudoscientific ideas. For instance, in Chapter 9 of IPMB Russ Hobbie and I discuss the physics behind the discredited claim that weak, low frequency electromagnetic fields (ranging in frequency from 60 Hz powerline fields to cell phone radiowaves) are dangerous.

These days, with so much pseudoscience parading as fact, and with the United State’s Secretary of the Department of Health and Human Services being a leading proponent of anti-science nonsense, what we need is something to point out and refute all this quackery. What we need is Quackwatch.org. According Quackwatch’s mission statement, 

Quackwatch is a network of Web sites and mailing lists developed by Stephen Barrett, M.D. and maintained by the Center for Inquiry (CFI). Their primary focus is on quackery-related information that is difficult or impossible to get elsewhere. Dr. Barrett’s activities include:

• Investigating questionable claims

• Answering inquiries about products and services

• Advising quackery victims

• Distributing reliable publications

• Debunking pseudoscientific claims

• Reporting illegal marketing

• Improving the quality of health information on the Internet

• Attacking misleading advertising on the Internet 

For those of you who prefer social media, you can follow Quackwatch on Facebook and Twitter.

Quackwatch was established by Stephen Barrett, a retired medical doctor. These days he’s in his 90’s and deserves a rest after a lifetime of defending science. Unfortunately, there’s no rest for the weary; we need him now more than ever.

Five years ago, Quackwatch become part of the Center for Inquiry, another group that opposes pseudoscience malarkey and that publishes the Skeptical Inquirer magazine. I mention both Quackwatch and the Center for Inquiry in my book Are Electromagnetic Fields Making Me Ill?

Thank you Stephen Barrett for giving the world your wonderful website Quackwatch.org. I wish we all deserved it. 

 

Quackery: A History of Fake Medicine and Cure-alls. CBS Sunday Morning.

https://www.youtube.com/watch?v=G_3K0lFuvHQ

My 50+ Years of Antiquackery Activity with Stephen Barrett and William M. London. Center for Inquiry.

https://www.youtube.com/watch?v=EjYIjBae0wM

Sine and Cosine Integrals and the Delta Function

Trigger warning: This post is for mature audiences only; it may contain Fourier transforms and Dirac delta functions. 

In Chapter 11 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I examine some properties of Fourier transforms. In particular, we consider three integrals of sines and cosines. After some analysis, we conclude that these integrals are related to the Dirac delta function, δ(ω – ω’), equal to infinity at ω = ω’ and zero everywhere else (it’s a strange function consisting of one really tall, thin spike).

Are these equations correct? I now believe that they’re almost right, but not entirely. I propose that instead they should be 

You’re probably thinking “what a pity, the second three equations looks more complicated than the first three.” I agree. But let me explain why I think they’re better. Hang on, it’s a long story.

Let’s go back to our definition of the Fourier transform in Eq. 11.57 of IPMB

The first thing to note is that y(t) consists of two parts. The first depends on cos(ωt), which is an even function, meaning cos(–ωt) = cos(ωt). There’s an integral over ω, implying that many different frequencies contribute to y(t), weighted by the function C(ω). But one thing we know for sure is that when you add up the contributions from all these many frequencies, the result must be an even function (the sum of even functions is an even function). The second part depends on sin(ωt), which is an odd function, sin(–ωt) = – sin(ωt). Again, when you add up all the contributions from these many frequencies weighted by S(ω), you must get an odd function. So, we can say that we’re writing y(t) as the sum of an even part, y_even(t), and an odd part, y_odd(t). In that case, we can rewrite our Fourier transform expressions as

We should be able to take our expression for y_even(t), put our expression for C(ω) into it, and then—if all works as it should—get back y_even(t). Let’s try it and see if it works. To start I’ll just rewrite the first of the four equations listed above

Now for C(ω) I’ll use the third of the four equations listed above. In that expression, there is an integral over t, but t is a dummy variable (it’s an “internal” variable; after you do the integral, the result does not depend on t), so to keep things from getting confusing we’ll call the dummy variable by another name, t'

Next switch the order of the integrals, so the integral over t' is on the outside and the integral over ω is on the inside

Ha! There, inside the bracket, is one of those integrals were’re talking about. Okay, the variables ω and t are swapped, but otherwise it’s the same. So, let’s put in our new expression for the integral

The 2π’s cancel, and a factor of one half comes out. An integral containing a delta function just picks out the value where the argument of the delta function is zero. We get

But, we know that y_even(t) is an even function, meaning y_even(–t) equals y_even(t). So finally

It works! We go “around the loop” and get back our original function.

You could perform another calculation just like this one but for y_odd(t). Stop reading and do it, to convince yourself that again you get back to where you started from, y_odd(t) = y_odd(t).

Now, you folks who are really on the ball might realize that if you had used the old delta function relationships given in IPMB (the first three equations in this post), they would also work. (Again, try it and see.) So why use my fancy new formulas? Well, if you have an integral that adds up a bunch of cos(ωt), you know you’re gonna get an even function. There’s no way it can be equal to δ(ω – ω’), because that function is neither even nor odd. So, it just doesn’t make sense to say that summing up a bunch of even functions gives you something that isn’t even. In my new formula, that sum of two delta functions is an even function. The same argument holds for the integral with sin(ωt), which must be odd.

Finally (and this is what got me started down this rabbit hole), you often see the delta function written as

Jackson even gives this equation, so it MUST be correct. (For those of who aren’t physicists, John David Jackson wrote the highly regarded graduate textbook Classical Electrodynamics, known by physics graduate students simply as “Jackson.”)

In Jackson’s equation, i is the square root of minus one. So, this representation of the delta function uses complex numbers. You won’t see it in IPMB because Russ and I avoid complex numbers (I hate them).

Let’s use the Euler formula e^iθ = cosθ + i sinθ to change the integral in Jackson’s delta function expression to

Now use a couple trig identities, cos(A–B) = cosA cosB + sinA sinB and sin(A–B) = sinA cosB –cosA sinB, to get

This is really four integrals,

Then, using the relations between these integrals and the delta function given in IPMB (the first three equations at the top of this post), you get that the sum of these integrals is equal to

which is obviously wrong; we started with 2πδ and ended up with 4πδ. Even worse, do the same calculation for δ(ω + ω') with a plus instead of a minus in front of the ω'. I’ll leave it to you to work out the details, but you’ll get zero! Again, nonsense. However, if you use the integral relations I propose above (second set of three integrals at the top of this blog), everything works just fine (try it).

Gene Surdutovich, my new coauthor for the sixth edition of IPMB, and I are still deciding how to discuss this issue in the new edition (which we are hard at work on but I doubt will be out within the next year). I don’t want to get bogged down in mathematical minutia that isn’t essential to our book’s goals, but I want our discussion to be correct. Once the sixth edition is published, you can see how we handle it.

I haven’t seen my new delta function/Fourier integral relationships in any other textbook or math handbook. This makes me nervous. Are they correct? Moreover, Intermediate Physics for Medicine and Biology does not typically contain new mathematical results. Maybe I haven’t looked hard enough to see if someone else published these equations (if you’ve seen them before, let me know where…please!). Maybe I’ll find these results in Morse and Feshbach (another one of those textbooks known to all physics graduate students) or some other mathematical tome. I need to make a trip to the Oakland University library to look through their book collection, but right now its too cold and snowy (we got about four to five inches of the white stuff in the last 48 hours).

The Air They Breathe

I’m used to thinking about climate change from a physics perspective: what technologies can we use to reduce the amount of carbon dioxide and methane going into the atmosphere. Even when I consider the health effects of climate change, I tend to focus on the technical aspects (as you might expect from an author of a book titled Intermediate Physics for Medicine and Biology). Moreover, I often consider the long-term risks of climate change, and how it will harm future generations.

The Air They Breathe,
by Debra Hendrickson.

In her wonderful new book The Air They Breathe: A Pediatrician on the Front Lines of Climate Change, Debra Hendrickson has a different perspective. She explains how climate change is harming her young patients today. Specifically, she highlights four ways they are in danger.

1. Bad air from burning fossil fuels and from forest fires caused by climate change hurts children, particularly those with breathing problems like asthma. Here in Michigan, sometimes climate change seems a distant threat. But I remember the summer of 2023, when the air in the Detroit area was filled with smoke from fires in Canada. Hendrickson often makes her points by examples of specific children, such as a young girl named Anna, whose asthma was worsened by a forest fire burning near her home in Reno, Nevada in 2013. In The Air They Breathe, Hendrickson writes

Since Anna’s visit to my clinic that afternoon, thousands of other wildfires have raged through California, just a few miles to our west. They have grown bigger and more explosive, devouring not just forests, but towns. Every summer and fall now, waves of smoke pass through my city, and more of my young patients cough and wheeze. In 2018, the Mendocino Complex wildfire would become the largest California had ever seen, darkening the skies for weeks. Only two years later, in 2020, the August Complex fire would shatter that record, becoming the first to burn more than a million acres. And in 2021 we spent not just days breathing smoke, as we did in 2013, but months, as both the Dixie and Caldor fires raged a few miles away.

When I look back today, I see that the Rim Fire was not an isolated event, as it seemed to us then; it was the beginning of a trend. It was a sample of the world we are creating for our children.

2. Excessive heat can cause heatstroke in children, particularly in infants left in hot cars and high school football players who practice in the extreme heat. Children are especially sensitive to overheating. Heat waves can kill. Hendrickson tells the story of Joey Azuela, a child who almost died when hiking on a hot summer day near Phoenix, Arizona, saved only after being rushed to a hospital where he was covered with ice and injected with cold saline. She writes

Heatstroke is treated with extreme urgency; minutes make the difference between life and death. Joey Azuela is alive because he was cooled so quickly. Yet as the world watches temperatures climb, we drift, and delay; we risk pushing the planet to tipping points of rapid and uncontrollable changes, from which we cannot recover. The speed of our response is everything. It will determine not just the type of future our children have, but whether they have a future, at all.

3. Trauma and post traumatic stress disorder can occur in children who experience disasters caused by climate change, such as a hurricane, flood, or forest fire. Hendrickson examines in particular how in 2017 hurricane Harvey dumped as much as 40 inches of rain on Houston, Texas. One boy, Lucus, had to escape the rising water with his mother and siblings from their neighbor’s roof, saved by a passing boat. She writes

Natural disasters have always plagued us; the events themselves are nothing new. But a warming world is turning up their dial, and with it, the potential for trauma. Though some years are better than others, weather-related catastrophes are clearly trending worse over time: becoming more frequent, more powerful, and more destructive. Globally, natural disasters have increased fivefold over the last half century. Extreme weather events—the worst examples of these disasters, like 100-year floods and Category 4 hurricanes—are growing steadily more severe, and more common.

4. Infectious diseases, such as an increase in malaria caused by a greater range for mosquitoes, are becoming more common with global warming. Hendrickson tells us about Darah, an infant born in New Jersey who got the Zika virus from her mother while in the womb, and who suffered from microcephaly: an underdeveloped brain. She explains

To understand the connection between climate change and Darah’s case, we have to zoom out from her small New Jersey apartment and see that she shares this planet with trillions of other living things. That her body is linked to the Earth not just by water and air, but by a rich sea of organisms, friend and foe, living within and around her. Many of them are being affected by rising temperatures and shifting rains; by changes in habitats and seasons.

One point this book makes clear is the health care and climate change are not separate issues. The two are intertwined. Another point is that this is not merely a problem that we will all face in the coming decades. It’s happening now, as described by the horrific stories of these children. I found this book to be a call to action. It motivates me to make an even greater effort to address global warming, because—as Hendrickson warns us—“The only heroes our children have are us.”

Vaccines Did Not Cause Rachel's Autism

Vaccines Did Not
Cause Rachel’s Autism,
by Peter Hotez.

I recently listened to an audio recording of Peter Hotez’s book Vaccines Did Not Cause Rachel’s Autism: My Journey as a Vaccine Scientist, Pediatrician, and Autism Dad. Hotez is the same author who wrote The Deadly Rise of Anti-Science, which I reviewed previously in this blog. I’m troubled by the current anti-vaccine sentiment, which is foolish and dangerous. Along with climate change denial, vaccine hesitancy is a worrisome example of an alarming anti-science movement in the United States.

Hotez’s book provides insight into the challenges faced by parents with autistic children (by the way, Peter Hotez is not the hero of this book; the hero is his wife Ann). Moreover, the book makes a compelling argument that vaccines do not cause autism. Hotez reviews much of the scientific literature relevant to the relationship of vaccines to autism. In particular, he mentions a meta-analysis of clinical studies published by a group from Australia. As much as I enjoyed and admired Hotez’s book, I probably would have led off by discussing that publication, rather than waiting until late in the book to bring it up.

“Vaccines are Not Associated With Autism:
An Evidence-Based Meta-Analysis of
Case-Control and Cohort Studies”
by Taylor, Swerdfeger, and Eslick,
Vaccine, 32:3623–3629, 2014.

Today I’ll discuss that article, titled “Vaccines are Not Associated With Autism: An Evidence-Based Meta-Analysis of Case-Control and Cohort Studies” by Luke Taylor, Amy Swerdfeger, and Guy Eslick. This paper appeared in 2014 in the journal Vaccine (Volume 32, Pages 3623–3629). The abstract appears below.

There has been enormous debate regarding the possibility of a link between childhood vaccinations and the subsequent development of autism. This has in recent times become a major public health issue with vaccine preventable diseases increasing in the community due to the fear of a ‘link’ between vaccinations and autism. We performed a meta-analysis to summarise available evidence from case-control and cohort studies on this topic (MEDLINE, PubMed, EMBASE, Google Scholar up to April, 2014). Eligible studies assessed the relationship between vaccine administration and the subsequent development of autism or autism spectrum disorders (ASD). Two reviewers extracted data on study characteristics, methods, and outcomes. Disagreement was resolved by consensus with another author. Five cohort studies involving 1,256,407 children, and five case-control studies involving 9,920 children were included in this analysis. The cohort data revealed no relationship between vaccination and autism (OR: 0.99; 95% CI: 0.92 to 1.06) or ASD (OR: 0.91; 95% CI: 0.68 to 1.20), nor was there a relationship between autism and MMR (OR: 0.84; 95% CI: 0.70 to 1.01), or thimerosal (OR: 1.00; 95% CI: 0.77 to 1.31), or mercury (Hg) (OR: 1.00; 95% CI: 0.93 to 1.07). Similarly the case-control data found no evidence for increased risk of developing autism or ASD following MMR, Hg, or thimersal exposure when grouped by condition (OR: 0.90, 95% CI: 0.83 to 0.98; p = 0.02) or grouped by exposure type (OR: 0.85, 95% CI: 0.76 to 0.95; p = 0.01). Findings of this meta-analysis suggest that vaccinations are not associated with the development of autism or autism spectrum disorder. Furthermore, the components of the vaccines (thimersal or mercury) or multiple vaccines (MMR) are not associated with the development of autism or autism spectrum disorder.

Some of the terms and concepts mentioned in the abstract may be unfamiliar, so let me explain them.

• Autism and Autism Spectrum Disorders. Autism is a disorder of the nervous system that begins during the development of a fetus. An autistic person may engage in repetitive, inflexible behaviors or have problems interacting with people. The disorder can vary in its severity and symptoms, so people with different degrees of severity are said to be on the autism spectrum.
• Vaccine. A vaccine is a biological agent that stimulates a person’s immune system to recognize and destroy a microorganism causing an infectious disease. Vaccines are often made from a weakened form of the microbe.
• The MMR Vaccine. The MMR vaccine protects children against three diseases: measles, mumps, and rubella (German measles). An initial dose of the MMR vaccine is typically given around a child’s first birthday and a second dose before entering school. It’s usually given by injection.
• Thimersal-Containing Vaccine. Thimersal is a molecule containing mercury. The element mercury, whose chemical symbol is Hg, is a known toxin. However, not all molecules containing mercury are as toxic as is mercury metal itself. Mercury compounds like thimersal are used in low doses as a preservative in some vaccines. Before 1991, thimersal was included in the childhood vaccine DPT which protects against diphtheria, tetanus (lockjaw), and pertussis (whopping cough). Now no childhood vaccines contain thimersal, although it’s still used in some flu vaccines.
• Meta-Analysis. Meta-analysis is a statistical method of analyzing and summarizing several clinical trials. A meta-analysis can increase the number of patients being analyzed, resulting a more statistical power. It can also help in resolving studies with inconsistent results.
• Case-Control Study. A case-control study is a clinical study that compares two groups: one having a disease and one not (the control). It is often retrospective, meaning it uses existing data from people known to have a disease, and therefore can be conducted quickly.
• Cohort Study. A cohort study is a clinical trial that takes a group of people and follows them through time to determine what fraction develop some disease. It is prospective, collecting data on exposure to some suspected cause. A cohort study can take a long time to complete and, for a rare disease, requires studying a large population, but it’s less susceptible to bias than a case-control study.
• Odds Ratio. The odds ratio (OR) is a statistical measure to determine if some factor has an effect. For example, suppose in a case-control study you examined the medical records of 600 people who had the MMR vaccine; 570 were healthy but 30 had autism (the odds of being healthy are 570:30, or 19:1). As a control, you examined the medical records of 400 people who did not have the MMR vaccine; 380 were healthy but 20 had autism (the odds of being healthy are 380:20, or 19:1). In that case, the odds ratio would be
  
  When the odds ratio is one, you conclude the MMR vaccine had no effect (the odds of having autism are the same whether or not you had the vaccine). If, however, among the 600 people who had the MMR vaccine 510 were healthy and 90 had autism (with the control group being unchanged from that given above) then the odds ratio would be
  
  In this case, the MMR vaccine would have a clear effect. For smoking and lung cancer, the odds ratio is quite large, about 10.
• 95% Confidence Interval. How large must the odds ratio be in order to conclude there is some effect? That depends on how much uncertainty there is. For instance, if you flip a coin four times, the most likely result is two heads and two tails. However, there is still one chance out of sixteen, about 6%, that you’ll get four heads. If you want to be more certain that a coin is fair and not biased, you would need to flip the coin more than four times. In the same spirit, to completely characterize how much confidence you have in the result of a clinical trial, you must indicate how large the uncertainty is in the result. Most clinical studies will give the odds ratio and a range of values for which—based on a statistical analysis—there is a 95% chance that the odds ratio is within that interval. The convention is that if the 95% confidence interval does not contain the value of one, then there is a statistically significant effect. If it does contain one, any effect is not statistically significant. Using a value of 95%, rather than say 98%, is arbitrary, but you have to draw the line somewhere, and 95% confidence is the usual medical criteria for significance. For example, if in one of these autism studies the odds ratio was 1.05 and the 95% confidence interval was 0.8 to 1.3, you would conclude that there is not a statistically significant effect of the vaccine. If, on the other hand, the odds ratio were 1.05 and the 95% confidence interval was 1.02 to 1.08, you would conclude there is a small but statistically significant effect of the vaccine on autism. Note that in statistics the word “significance” does not mean “important.” It means “unlikely to be due to chance.” One virtue of a meta-analysis is that by combining several studies the number of people analyzed increases, which can shrink the 95% confidence range, which provides better statistical power to say if the odds ratio is significantly different than one. 
• p-value. Whenever you have an arbitrary threshold, like saying a result is or is not statistically significant, you worry about cases that are near the threshold. To provide additional information, researchers sometimes give the p-value. It is the probability that a result at least this extreme could happen by chance. In medicine, usually p = 0.05 is the cutoff between a result being considered significant or not significant. But if the result has p = 0.03, you might say it is significant (less than 0.05) but you might think that it is still questionable and maybe you should repeat that study with a larger number of people. On the other hand, if p = 0.0002 you would say that the result almost certainly didn’t happen by chance and you would therefore have a lot of confidence in it. In this meta-analysis, the p-value is sometimes given, especially for borderline cases, to help the reader estimate the true significance of the result.
• MEDLINE, PubMed, EMBASE, Google Scholar. These databases contain information about scientific publications, including articles describing clinical trials. They can be searched using various keywords to find publications about a particular subject. MEDLINE is a database compiled by the National Library of Medicine, and covers all biomedical research. It can be searched online using a tool called PubMed, which includes MEDLINE plus a few other databases. EMBASE is an international database that focuses on the pharmaceutical industry. Google Scholar is a free web search engine that covers all scholarly publications.

Now that we understand the vocabulary, what does this meta-analysis show? It indicates that there is no evidence supporting a connection between vaccines and the development of autism. It also shows there is no risk that thimersal or mercury causes autism. In fact, some of the results suggest a weak protective effect caused by thimersal. For example, an odds ratio of 0.85 with a 95% confidence interval of 0.76 to 0.95 suggests that the odds ratio may be slightly less than one, which means the vaccine prevents people from getting autism. However, the p-value for this result was 0.01 which is small but not that small, and I wouldn’t put too much confidence in the claim that the vaccine is protective. But the results sure don’t suggest there is a health risk.

What I’ve analyzed today is one paper, albeit a meta-analysis. It’s over ten years old. There are lots of other data out there now, and Hotez describes some of it in Vaccines Did Not Cause Rachel’s Autism. He also emphasizes that autism is thought to arise from problems during the development of a fetus, long before the child receives any vaccines, so there’s no reason to suspect vaccines as a cause of autism. All this evidence, taken together, implies the probability of vaccines causing autism is extremely low.

Why do people still claim vaccines cause autism? There will certainly be cases where a child will receive a vaccine and then start showing symptoms of being on the autism spectrum. Some might point to such cases and say “see, I told you so!” The question is, how many of those children would have started showing symptoms of autism even if they didn’t get the vaccine? Homework problem 9 in Chapter 3 of Intermediate Physics for Medicine and Biology explores this type of question quantitatively. The reason you need a large, controlled statistical study is so you’re not fooled by a few such coincidences.

One thing clinical studies, such as the one that I discussed today, cannot give you is certainty. You can’t say with absolute certainty (p = 0) that vaccines don’t cause autism. Science doesn’t deal in certainties, just probabilities. All you can say is that the evidence suggests there is no connection between vaccines and autism. The best you can do is to collect enough evidence so that the probability of a relationship is very small. That is where we are today. The probability of vaccines causing autism is extremely low. That’s the best conclusion science can offer. And when the probability is vanishingly small, we often feel confident in summarizing the situation with a simple (if somewhat too simple) declarative sentence, such as Vaccines Did Not Cause Rachel’s Autism.

Outbreak News TV: Vaccines Did Not Cause Rachel's Autism.

https://www.youtube.com/watch?v=xDh3QZPx2ns&t=461s

Peter Hotez wins award for Scientific Freedom and Responsibility.

https://www.youtube.com/watch?v=WHtWmSz4cXE

Dr. Peter Hotez's mission to make a difference.

https://www.youtube.com/watch?v=xC-3ofA1hIE