Friday, July 31, 2020

Free Convection and the Origin of Life

Free convection is an important process in fluid dynamics. Yet Russ Hobbie and I rarely discuss it in Intermediate Physics for Medicine and Biology. It appears only once, in a homework problem analyzing Rayleigh-Benard convection cells.

How does free convection work? If water is heated from below, it expands as it becomes hotter, reducing its density. Less dense water is buoyant and rises. As the water moves away from the source of heat, it cools, becomes denser, and sinks. The process then repeats. The fluid flow caused by all this rising, sinking, heating, and cooling is what’s known as free convection. One reason Russ and I don’t dwell on this topic is that our body is isothermal. You need a temperature gradient to drive convection.

“Thermal Habitat for RNA Amplification and Accumulation,”  by Salditt et al. (Phys. Rev. Lett., 125:048104, 2020), superimposed on Intermeidate Physics for Medicine and Biology.
Thermal Habitat for RNA Amplification and Accumulation,”
by Salditt et al. (Phys. Rev. Lett., 125:048104, 2020).
Is free convection ever important in biology? According to a recent article in Physical Review Letters (Volume 125, Article Number 048104) by Annalena Salditt and her coworkers (“Thermal Habitat for RNA Amplification and Accumulation”), free convection may be responsible for the origin of life!

Many scientists believe early life was based on ribonucleic acid, or RNA, rather than DNA and proteins. RNA replication is aided by temperature oscillations, which allow the double-stranded RNA to separate and make complementary copies (hot), and then accumulate without being immediately degraded (cold). Molecules moving with water during free convection undergo such a periodic heating and cooling. One more process is needed, called thermophoresis, which causes long strands of RNA to move from hot to cold regions preferentially compared to short strands. Salditt et al. write
The interplay of convective and thermophoretic transport resulted in a length-dependent net transport of molecules away from the warm temperature spot. The efficiency of this transport increased for longer RNAs, stabilizing them against cleavage that would occur at higher temperatures.
Where does free convection happen? Around hydrothermal vents at the bottom of the ocean.
A natural setting for such a heat flow could be the dissipation of heat across volcanic or hydrothermal rocks. This leads to temperature differences over porous structures of various shapes and lengths.
The authors conclude
The search for the origin of life implies finding a location for informational molecules to replicate and undergo Darwinian evolution against entropic obstacles such as dilution and spontaneous degradation. The experiments described here demonstrate how a heat flow across a millimeter-sized, water-filled porous rock can lead to spatial separation of molecular species resulting in different reaction conditions for different species. The conditions inside such a compartment can be tuned according to the requirements of the partaking molecules due to the scalable nature of this setting. A similar setting could have driven both the accumulation and RNA-based replication in the emergence of life, relying only on thermal energy, a plausible geological energy source on the early Earth. Current forms of RNA polymerase ribozymes can only replicate very short RNA strands. However, the observed thermal selection bias toward long RNA strands in this system could guide molecular evolution toward longer strands and higher complexity.
You can learn more about this research from a focus article in Physics, an online magazine published by the American Physical Society.

Salditt et al.’s article provides yet another example of why I find the interface of physics and biology is so fascinating.

Friday, July 24, 2020

Tests for Human Perception of 60 Hz Moderate Strength Magnetic Fields

The first page of “Tests for Human Perception of 60 Hz Moderate Strength Magnetic Fields,” by Tucker and Schmitt (IEEE Trans. Biomed. Eng. 25:509-518, 1978), superimposed on Intermediate Physics for Medicine and Biology.
The first page of “Tests for Human Perception
of 60 Hz Moderate Strength Magnetic Fields,”
by Tucker and Schmitt (IEEE Trans. Biomed. Eng.
25:509-518, 1978).
In Chapter 9 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss possible effects of weak external electric and magnetic fields on the body. In a footnote, we write
Foster (1996) reviewed many of the laboratory studies and described cases where subtle cues meant the observers were not making truly “blind” observations. Though not directly relevant to the issue under discussion here, a classic study by Tucker and Schmitt (1978) at the University of Minnesota is worth noting. They were seeking to detect possible human perception of 60-Hz magnetic fields. There appeared to be an effect. For 5 years they kept providing better and better isolation of the subject from subtle auditory clues. With their final isolation chamber, none of the 200 subjects could reliably perceive whether the field was on or off. Had they been less thorough and persistent, they would have reported a positive effect that does not exist.
In this blog, I like to revisit articles that we cite in IPMB.
Robert Tucker and Otto Schmitt (1978) “Tests for Human Perception of 60 Hz Moderate Strength Magnetic Fields.” IEEE Transactions on Biomedical Engineering, Volume 25, Pages 509-518.
The abstract of their paper states
After preliminary experiments that pointed out the extreme cleverness with which perceptive individuals unintentionally used subtle auxiliary clues to develop impressive records of apparent magnetic field detection, we developed a heavy, tightly sealed subject chamber to provide extreme isolation against such false detection. A large number of individuals were tested in this isolation system with computer randomized sequences of 150 trials to determine whether they could detect when they were, and when they were not, in a moderate (7.5-15 gauss rms) alternating magnetic field, or could learn to detect such fields by biofeedback training. In a total of over 30,000 trials on more than 200 persons, no significantly perceptive individuals were found, and the group performance was compatible, at the 0.5 probability level, with the hypothesis that no real perception occurred.
The Tucker-Schmitt study illustrates how observing small effects can be a challenge. Their lesson is valuable, because many weak-field experiments are subject to systematic errors that provide an illusion of a positive result. Near the start of their article, Tucker and Schmitt write
We quickly learned that some individuals are incredibly skillful at sensing auxiliary non-magnetic clues, such as coil hum associated with field, so that some “super perceivers” were found who seemed to sense the fields with a statistical probability as much as 10–30 against happening by chance. A vigorous campaign had then to be launched technically to prevent the subject from sensing “false” clues while leaving him completely free to exert any real magnetic perceptiveness he might have.
Few authors are as forthright as Tucker and Schmitt when recounting early, unsuccessful experiments. Yet, their tale shows how experimental scientists work.
Early experiments, in which an operator visible to the test subject controlled manually, according to a random number table, whether a field was to be applied or not, alerted us to the necessity for careful isolation of the test subject from unintentional clues from which he could consciously, or subconsciously, deduce the state of coil excitation. No poker face is good enough to hide, statistically, knowledge of a true answer, and even such feeble clues as changes in building light, hums, vibrations and relay clatter are converted into low but significant statistical biases.
IPMB doesn’t teach experimental methods, but all scientists must understand the difference between systematic and random errors. Uncertainty from random errors is suppressed by taking additional data, but eliminating systematic errors may require you to redesign your experiment.
In a first round of efforts to prevent utilization of such clues, the control was moved to a remote room and soon given over to a small computer. A “fake” air-core coil system, remotely located but matched in current drain and phase angle to the real large coil system was introduced as a load in the no-field cases. An acoustically padded cabinet was introduced to house the experimental subject, to isolate him from sound and vibration. Efforts were also made to silence the coils by clamping them every few centimeters with plastic ties and by supporting them on air pocket packing material. We tried using masking sound and vibrations, but soon realized that this might also mask real perception of magnetic fields.
Designing experiments is fun; you get to build stuff in a machine shop! I imagine Tucker and Schmitt didn’t expect they would have this much fun. Their initial efforts being insufficient, they constructed an elaborate cabinet to perform their experiments in.
This cabinet was fabricated with four layers of 2 in plywood, full contact epoxy glued and surface coated into a monolithic structure with interleaved corners and fillet corner reinforcement to make a very rigid heavy structure weighing, in total, about 300 kg. The structure was made without ferrous metal fastening and only a few slender brass screws were used. The door was of similar epoxyed 4-ply construction but faced with a thin bonded melamine plastic sheet. The door was hung on two multi-tongue bakelite hinges with thin brass pins. The door seals against a thin, closed-cell foam-rubber gasket, and is pressure sealed with over a metric ton of force by pumping a mild vacuum inside the chamber of means of a remote acoustically silenced hose-connected large vacuum-cleaner blower. The subject received fresh air through a small acoustic filter inlet leak that also assures sufficient air flow to cool the blower. The chosen “cabin altitude” at about 2500 ft above ambient presented no serious health hazard and was fail-safe protected.
An experimental scientist must be persistent. I remember learning that lesson as a graduate student when I tried for weeks to measure the magnetic field of a single nerve axon. I scrutinized every part of the experiment and fixed every problem I could find, but I still couldn’t measure an action current. Finally, I realized the coaxial cable connecting the nerve to the stimulator was defective. It was a rookie mistake, but I was tenacious and ultimately figured it out. Tucker and Schmitt personify tenacity.
As still more isolation seemed necessary to guarantee practically complete exclusion of auxiliary acoustic and mechanical clues, an extreme effort was made to improve, even further, the already good isolation. The cabinet was now hung by aircraft “Bungee” shock cord running through the ceiling to roof timbers. The cabinet was prevented from swinging as a pendulum by four small non-load-bearing lightly inflated automotive type inner tubes placed between the floor and the cabinet base. Coils already compliantly mounted to isolate intercoil force vibration were very firmly reclamped to discourage intracoil “buzzing.” The cabinet was draped inside with sound absorbing material and the chair for the subject shock-mounted with respect to the cabinet floor. The final experiments, in which minimal perception was found, were done with this system.
Once Tucker and Schmitt heroically eliminated even the most subtle cues about the presence of a magnetic field, subjects could no longer detect whether or not a magnetic field was present. People can’t perceive 60-Hz, 0.0015-T magnetic fields.

Russ and I relegate this tale to a footnote, but it’s an important lesson when analyzing the effects of weak electric and magnetic fields. Small systematic errors abound in these experiments, both when studying humans and when recording from cells in a dish. Experimentalists must ruthlessly design controls that can compensate for or eliminate confounding effects. The better the experimentalist, the more doggedly they root out systematic errors. One reason the literature on the biological effects of weak fields is so mixed may be that few experimentalists take the time to eradicate all sources of error.

Tucker and Schmitt’s experiment is a lesson for us all.

Friday, July 17, 2020

Physics World: Medical Physics

I subscribe to a weekly newsletter from Physics World about medical physics. This newsletter and its associated website ( replace what used to be Like medicalphysicsweb, the newsletter is edited by Tami Freeman, which means the quality remains high. It’s one of the best ways to learn what’s new in medical physics.

On the website you find videos, podcasts, research updates, webinars, interviews, career advice, and job ads related to medical physics. You may find it almost as useful as! Seriously, it has more and better content than this blog, but I suspect it has more resources behind it. In any event, both cost you the same: nothing. Sign up for an account at Physics World, then subscribe to the medical physics weekly newsletter. You won’t regret it.

Below is a sampler; some videos from Physics World that readers of Intermediate Physics for Medicine and Biology might find useful or interesting. Enjoy!

What are the benefits of proton therapy.

Reality check: Covid-19 and UV disinfection.

How neutrons can help in the Covid-19 pandemic.

The curious case of the porpoises and the wind farm.

Faces of physics: human organs on a chip.

Friday, July 10, 2020

An S1 Gradient of Refractoriness is Not Essential for Reentry Induction by an S2 Stimulus

Sometimes the shortest papers are my favorites. Take, for example, an article that I published twenty years ago last month: a two-page communication in the IEEE Transactions on Biomedical Engineering titled “An S1 Gradient of Refractoriness is Not Essential for Reentry Induction by an S2 Stimulus” (Volume 47, Pages 820–821, 2000). It analyzes the electrical stimulation of cardiac tissue, and focuses on the mechanism for inducing an arrhythmia.

The introduction is two short paragraphs (a mere hundred words). The first puts the work in context.
Successive stimulation (S1, then S2) of cardiac tissue can induce reentry. In many cases, an S1 stimulus triggers a propagating action potential that creates a gradient of refractoriness. The S2 stimulus then interacts with this S1 refractory gradient, causing reentry. Many theoretical and experimental studies of reentry induction are variations on this theme [1]–[9].
When I wrote this communication, the critical point hypothesis was a popular explanation for how to induce reentry in cardiac tissue. I cited nine papers discussing this hypothesis, but I associate it primarily with the books of Art Winfree and the experiments of Ray Ideker.
A schematic illustration of the critical point hypothesis. The top panel shows the S1 wave front just before the S2 stimulus. The bottom panel shows the tissue just after the S2 stimulus, and the resulting reentry.
The critical point hypothesis.
The figure above illustrates the critical point hypothesis. A first (S1) stimulus is applied to the right edge of the tissue, launching a planar wavefront that propagates to the left (arrow). By the time of the upper snapshot, the tissue on the right (purple) has returned to rest and recovered excitability, while the tissue on the left (red) remains refractory. The green line represents the boundary between refractory and excitable regions: the line of critical refractoriness.

The lower snapshot is immediately after a second (S2) stimulus is applied through a central cathode (black dot). The tissue near the cathode experiences a strong stimulus above threshold (yellow), while the remaining tissue experiences a weak stimulus below threshold. The green curve represents the boundary between the above-threshold and below-threshold regions: the circle of critical stimulus. S2 only excites tissue that is excitable and has a stimulus above threshold (inside the circle on the right). It launches a wave front that propagates to the right, but cannot propagate to the left because of refractoriness. Only when the refractory tissue recovers excitability will the wave front begin to propagate leftward (curved arrow). Critical points (blue dots) are located where the line of critical refractoriness intersects the circle of critical stimulus. Two spiral waves—a type of cardiac arrhythmia where a wave front circles around a critical point, chasing its tail—rotate clockwise on the bottom and counterclockwise on the top.

A beautiful paper from Ideker’s lab provides evidence supporting the critical point hypothesis: N. Shibata, P.-S. Chen, E. G. Dixon, P. D. Wolf, N. D. Danieley, W. M. Smith, and R. E. Ideker (1988) “Influence of Shock Strength and Timing on Induction of Ventricular Arrhythmias in Dogs,” American Journal of Physiology, Volume 255, Pages H891–H901.

The second paragraph of my communication begins with a question.
Is the S1 gradient of refractoriness essential for the induction of reentry? In this communication, my goal is to show by counterexample that the answer is no. In my numerical simulation, the transmembrane potential is uniform in space before the S2 stimulus. Nevertheless, the stimulus induces reentry.
The critical point hypothesis implies the answer is yes; without a refractory gradient there is no line of critical refractoriness, no critical point, no spiral wave, no reentry. Yet I claimed that the gradient of refractoriness is not essential. To explain why, we must consider what happens following the second stimulus.
An illustration of cathode break excitation, and the resulting quatrefoil reentry.
Cathode break excitation.
The tissue is depolarized (D, yellow) under the cathode but is hyperpolarized (H, purple) in adjacent regions along the fiber direction on each side of the cathode, often called virtual anodes. Hyperpolarization lowers the membrane potential toward rest, shortening the refractory period (deexcitation) and carving out an excitable path. When S2 ends, the depolarization under the cathode diffuses into the newly excitable tissue (dashed arrows), launching a wave front that propagates initially in the fiber direction (solid arrows): break excitation. Only after the surrounding tissue recovers excitability does the wave front begin to rotate back, as if there were four critical points: quatrefoil reentry.

Russ Hobbie and I discuss break excitation in a homework problem in Chapter 7 of Intermediate Physics for Medicine and Biology.
Problem 48. During stimulation of cardiac tissue through a small anode, the tissue under the electrode and in the direction perpendicular to the myocardial fibers is hyperpolarized, and adjacent tissue on each side of the anode parallel to the fiber direction is depolarized. Imagine that just before this stimulus pulse is turned on the tissue is refractory. The hyperpolarization during the stimulus causes the tissue to become excitable. Following the end of the stimulus pulse, the depolarization along the fiber direction interacts electrotonically with the excitable tissue, initiating an action potential (break excitation). (This type of break excitation is very different than the break excitation analyzed on page 181.)
(a) Sketch pictures of the transmembrane potential distribution during the stimulus. Be sure to indicate the fiber direction, the location of the anode, the regions that are depolarized and hyperpolarized by the stimulus, and the direction of propagation of the resulting action potential.
(b) Repeat the analysis for break excitation caused by a cathode instead of an anode. For a hint, see Wikswo and Roth (2009).
Now we come to the main point of the communication; the reason I wrote it. Look at the first snapshot in the illustration above, the one labeled S1 that occurs just before the S2 stimulus. The tissue is all red. It is uniformly refractory. The S1 action potential has no gradient of refractoriness, yet reentry occurs. This is the counterexample that proves the point: a gradient of refractoriness is not essential.

The communication contains one figure, showing the results of a calculation based on the bidomain model. The time in milliseconds after S1 is in the upper right corner of each panel. S1 was applied uniformly to the entire tissue, so at 70 ms the refractoriness is uniform. The 80 ms frame is during S2. Subsequent frames show break excitation the development of reentry.

A figure based on Fig. 1 in “An S1 Gradient of Refractoriness is Not Essential for Reentry Induction by an S2 Stimulus” (IEEE Trans. Biomed. Eng., Volume 47, Pages 820–821, 2000). It is the same as the figure in the communication, except the color and quality are improved.
An illustration based on Fig. 1 in “An S1 Gradient of Refractoriness is Not Essential for Reentry Induction by an S2 Stimulus” (IEEE TBME, 47:820–821, 2000). It is the same as the figure in the communication, except the color and quality are improved.
The communication concludes:
My results support the growing realization that virtual electrodes, hyperpolarization, deexcitation, and break stimulation may be important during reentry induction [8], [9], [14], [15], [21]–[24]. An S1 gradient of refractoriness may underlie reentry induction in many cases [1]–[6], but this communication provides a counterexample demonstrating that an S1 gradient of refractoriness is not necessary in every case.
This is a nice calculation, but is it consistent with experiment? Look at Y. Cheng, V. Nikolski, and I. R. Efimov (2000) “Reversal of Repolarization Gradient Does Not Reverse the Chirality of Shock-Induced Reentry in the Rabbit Heart,” Journal of Cardiovascular Electrophysiology, Volume 11, Pages 998–1007. These researchers couldn’t produce uniform refractoriness, so they did the next best thing: repeated the experiment using S1 wave fronts propagating in different directions. They always obtained the same result, independent of the location and timing of the critical line of refractoriness.

Does this calculation mean the critical point hypothesis is wrong? No. See my paper with Natalia Trayanova and her student Annette Lindblom (“The Role of Virtual Electrodes in Arrhythmogenesis: Pinwheel Experiment Revisited,” Journal of Cardiovascular Electrophysiology, Volume 11, Pages 274-285, 2000) to examine how this view of reentry can be reconciled with the critical point hypothesis.

One of the best things about this calculation is that you don’t need a fancy computer to demonstrate that the S1 gradient of refracoriness is not essential; A simple cellular automata will do. The figure below sums it up (look here if you don’t understand).

A cellular automata demonstrating that an S1 gradient of refractoriness is not essential for reentry induction by an S2 stimulus.
A cellular automata demonstrating that an S1 gradient of refractoriness is not essential for reentry induction by an S2 stimulus.

Friday, July 3, 2020

Dreyer’s English

Dreyer’s English, by Benjamin Dreyer, superimposed on Intermediate Physics for Medicine and Biology.
Dreyer’s English,
by Benjamin Dreyer.
In this blog I’ve reviewed several books about writing (On Writing Well, Plain Words, Do I Make Myself Clear?). I do this because many readers of Intermediate Physics for Medicine and Biology will become writers of scientific articles, grant proposals, or textbooks. Today, I review the funniest of these books: Dreyer’s English: An Utterly Correct Guide to Clarity and Style. If you believe a book about writing must be dull, read Dreyer’s English; you’ll change your mind.

At the start of his book, Benjamin Dreyer writes
Here’s your first challenge: Go a week without writing
• Very
• Rather
• Really
• Quite
• In fact
And you can toss in—or, that is, toss out—“just” (not in the sense of “righteous” but in the sense of “merely”) and “so” (in the “extremely” sense, through as conjunctions go it’s pretty disposable too).

Oh yes: “pretty.” As in “pretty tedious.” Or “pretty pedantic.” Go ahead and kill that particular darling.

And “of course.” That’s right out. And “surely.” And “that said.”

And “actually”? Feel free to go the rest of your life without another “actually.”

If you can last a week without writing any of what I’ve come to think of as the Wan Intensifiers and Throat Clearers—I wouldn’t ask you to go a week without saying them; that would render most people, especially British people, mute—you will at the end of that week be a considerably better writer than your were at the beginning.
Let’s go through Intermediate Physics for Medicine and Biology and see how often Russ Hobbie and I use these empty words.


I tried to count how many times Russ and I use “very” in IPMB. I thought using the pdf file and search bar would make this simple. However, when I reached page 63 (a tenth of the way through the book) with 30 “very”s I quit counting, exhausted. Apparently “very” appears about 300 times.

Sometimes our use of “very” is unnecessary. For instance, “Biophysics is a very broad subject” would sound better as “Biophysics is a broad subject,” and “the use of a cane can be very effective” would be more succinct as “the use of a cane can be effective.” In some cases, we want to stress that something is extremely small, such as “the nuclei of atoms (Chap. 17) are very small, and their sizes are measured in femtometers (1 fm = 10−15 m).” If I were writing the book again, I would consider replacing “very small” by “tiny.” In other cases, a “very” seems justified to me, as in “the resting concentration of calcium ions, [Ca++], is about 1 mmol l−1 in the extracellular space but is very low (10−4 mmol l−1) inside muscle cells,” because inside the cell the calcium concentration is surprisingly low (maybe we should have replaced “very” by “surprisingly”). Finally, sometimes we use “very” in the sense of finding the limit of a function as a variable goes to zero or infinity, as in “for very long pulses there is a minimum current required to stimulate that is called rheobase.” To my ear, this is a legitimate “very” (if infinity isn’t very big, then nothing is). Nevertheless, I concede that we could delete most “very”s and the book would be improved.


I counted 33 “rather”s in IPMB. Usually Russ and I use “rather” in the sense of “instead” (“this rather than that”), as in “the discussion associated with Fig. 1.5 suggests that torque is taken about an axis, rather than a point.” I’m assuming Dreyer won’t object to this usage (but you know what happens when you assume...). Only occasionally do we use “rather” in its rather annoying sense: “the definition of a microstate of a system has so far been rather vague,” and “this gives a rather crude image, but we will see how to refine it.”


Russ and I do really well, with only seven “really”s. Dreyer or no Dreyer, I’m not getting rid of the first one: “Finally, thanks to our long-suffering families. We never understood what these common words really mean, nor the depth of our indebtedness, until we wrote the book.”


I quit counting “quite” part way through IPMB. The first half contains 33, so we probably have sixty to seventy in the whole book. Usually we use “quite” in the sense of “very”: “in the next few sections we will develop some quite remarkable results from statistical mechanics,” or “there is, of course, something quite unreal about a sheet of charge extending to infinity.” These could be deleted with little loss. I would keep this one: “while no perfectly selective channel is known, most channels are quite selective,” because, in fact, I’m really quite amazed how so very selective these channels are. I would also keep “the lifetime in the trapped state can be quite long—up to hundreds of years,” because hundreds of years for a trapped state! Finally, I’m certain our students would object if we deleted the “quite” in “This chapter is quite mathematical.”

In Fact

I found only 24 “in fact”s, which isn’t too bad. One’s in a quote, so it’s not our fault. All the rest could go. The worst one is “This fact is not obvious, and in fact is true only if…”. Way too much “fact.”


Russ and I use “just” a lot. I found 39 “just”s in the first half of the book, so we probably have close to eighty in all. Often we use “just” in a way that is neither “righteous” nor “merely,” but closer to “barely.” For instance, “the field just outside the cell is roughly the same as the field far away.” I don’t know what Dreyer would say, but this usage is just alright with me.


Searching the pdf for “so” was difficult; I found every “also,” “some,” “absorb,” “solute,” “solution,” “sodium,” “source,” and a dozen other words. I’m okay (and so is Dreyer) with “so” being used as a conjunction to mean “therefore,” as in “only a small number of pores are required to keep up with the rate of diffusion toward or away from the cell, so there is plenty of room on the cell surface for many different kinds of pores and receptor sites.” I also don’t mind the “so much…that” construction, such as “the distance 0.1 nm (100 pm) is used so much at atomic length scales that it has earned a nickname: the angstrom.” I doubt Russ and I ever use “so” in the sense of “dude, you are so cool,” but I got tired of searching so I’m not sure.


Only one “pretty”: “It is interesting to compare the spectral efficiency function with the transmission of light through 2 cm of water (Fig. 14.36). The eye’s response is pretty well centered in this absorption window.” We did a pretty good job with this one.

Of Course

I didn’t expect to find many “of course”s in our book, but there are fourteen of them. For example, “both assumptions are wrong, of course, and later we will improve upon them.” I hope, of course, that readers are not offended by this. We could do without most or all of them.


None. Fussy Mr. Dreyer surely can’t complain.

That Said



I thought Russ and I would do okay with “actually,” but no; we have 38 of them. Dreyer says that “actually…serves no purpose I can think of except to irritate.” I’m not so sure. We sometimes use it in the sense of “you expect this, but actually get that.” For example, “the total number of different ways to arrange the particles is N! But if the particles are identical, these states cannot be distinguished, and there is actually only one microstate,” and “we will assume that there is no buildup of concentration in the dialysis fluid… (Actually, proteins cause some osmotic pressure difference, which we will ignore.)” Dreyer may not see its purpose, but I actually think this usage is justified. I admit, however, that it’s a close call, and most “actually”s could go.

Books I keep on my desk
(except for Dreyer’s English, which is a
library copy; I need to buy my own).
I was disappointed to find so many appearances of “very,” “rather,” “really,” “quite,” “in fact,” “just,” “so,” “pretty,” “of course,” “surely,” “that said,” and “actually” in Intermediate Physics for Medicine and Biology. We must do better.

Dreyer concludes
For your own part, if you can abstain from these twelve terms for a week, and if you read not a single additional word of this book—if you don’t so much as peek at the next page—I’ll be content.
 The next page says
Well, no.

But it sounded good.