Two-Semester Intermediate Course Sequence in Physics for the Life Sciences

This week I spoke at the American Association of Physics Teachers 2021 Summer Meeting. Getting to the meeting was easy; I just logged onto a website. Because of the Covid-19 pandemic, the entire conference was virtual and all the talks were prerecorded. A video of my talk—“Two-Semester Intermediate Course Sequence in Physics for the Life Sciences”—is posted below. If you want a powerpoint of the slides, you can find it here. As readers of this blog might suspect, the courses I describe are based on the textbook Intermediate Physics for Medicine and Biology. 

“Two-Semester Intermediate Course Sequence in Physics for the Life Sciences,” delivered at the AAPT 2021 Virtual Summer Meeting on August 2, 2021. https://www.youtube.com/watch?v=_1b9OdQktrI

Redish, E. F. (2021)
“Using Math in Physics: Overview,”
The Physics Teacher, 59:314–318.

In my lecture, I emphasize the role of toy models in developing insight, and the importance of connecting math to physics and biology. After the talk, I had a chat with Ed Redish (who I’ve mentioned in this blog before), and he referred me to a series of articles he’s publishing in The Physics Teacher. The first is titled “Using Math in Physics: Overview” (Volume 59, Pages 314–318, 2021). Redish and I seem to be singing the same song, although his lyrics are better. What he says about math in physics describes what Russ Hobbie and I try to do in IPMB. Redish begins

The key difference between math as math and math in science is that in science we blend our physical knowledge with our knowledge of math. This blending changes the way we put meaning to math and even the way we interpret mathematical equations. Learning to think about physics with math instead of just calculating involves a number of general scientific thinking skills that are often taken for granted [my italics] (and rarely taught) in physics classes. In this paper, I give an overview of my analysis of these additional skills. I propose specific tools for helping students develop these skills in subsequent papers.

He makes other good points, such as

• Math in math classes tends to be about numbers. Math in science is not. Math in science blends physics conceptual knowledge with mathematical symbols

and my favorite

• In introductory math, equations are almost always about solving and calculating. In physics [they’re] often about explaining! [his italics, my exclamation point].

The Art of Insight
in Science and Engineering
by Sanjoy Mahajan.

I like to paraphrase Richard Hamming and say “the purpose of equations is insight, not numbers.” Redish’s article reminds me of Sanjoy Mahajan’s book The Art of Insight in Science and Engineering. Both are superb.

In subsequent articles in The Physics Teacher (some already published, some in the works), Redish discusses skills every student needs to master.

• Dimensional Analysis 
• Estimation 
• Anchor Equations 
• Toy Models 
• Functional Dependence 
• Reading the Physics in a Graph 
• Telling the Story
  

I like to think that IPMB reinforces these skills. They certainly are ones that I try to emphasize in my “Biological Physics” and “Medical Physics” classes, and that Russ and I attempt to reinforce in our homework problems.

Screenshot of the
Living Physics Portal.

Finally, a valuable resource for teachers of physics-for-the-life-sciences was noted during the Q&A: the Living Physics Portal.

The Living Physics Portal is an online environment for physics faculty to share and discuss free curricular resources for teaching introductory physics for life sciences (IPLS). The objective of the Portal is to improve the education of the next generation of medical professionals and biologists by making physics classes more relevant for life sciences students. We do this by supporting physics instructors in finding and creating curricular materials and engaging in community discussions with other instructors to improve their courses.

Although IPMB is not intended to be used in an introductory course, I believe many materials on the Living Physics Portal would be useful to instructors teaching from IPMB. Conversely, much of the information you find in IPMB, and on this blog, could be helpful to introductory teachers. 

 

If you’re preparing to teach a class based on Intermediate Physics for Medicine and Biology, I suggest first looking at the materials on the book’s website, then scanning through the book’s blog (especially those posts marked “useful for instructors”), next reading Redish’s The Physics Teacher articles, and finally browsing the Living Physics Portal. Then you’ll be ready to teach physics for the life sciences at any level.

From Vision to Change: Educational Initiatives and Research at the Intersection of Physics and Biology

A few months ago, the journal CBE—Life Sciences Education published a special issue about education at the intersection of physics and biology. This topic is of great interest to readers of the 4th edition of Intermediate Physics for Medicine and Biology. The special issue was motivated by the American Association for the Advancement of Science report Vision and Change in Undergraduate Biology Education. While there were many interesting articles in this issue, my favorite was the essay “Learning Each Other’s Ropes: Negotiating Interdisciplinary Authenticity” (Volume 12, Pages 175–186, 2013), by Edward Redish and Todd Cooke, both from the University of Maryland. They describe their goals in the paper’s abstract.

A common feature of the recent calls for reform of the undergraduate biology curriculum has been for better coordination between biology and the courses from the allied disciplines of mathematics, chemistry, and physics. Physics has lagged behind math and chemistry in creating new, biologically oriented curricula, although much activity is now taking place, and significant progress is being made. In this essay, we consider a case study: a multiyear conversation between a physicist interested in adapting his physics course for biologists (E.F.R.) and a biologist interested in including more physics in his biology course (T.J.C.). These extended discussions have led us both to a deeper understanding of each other’s discipline and to significant changes in the way we each think about and present our classes. We discuss two examples in detail: the creation of a physics problem on fluid flow for a biology class and the creation of a biologically authentic physics problem on scaling and dimensional analysis. In each case, we see differences in how the two disciplines frame and see value in the tasks. We conclude with some generalizations about how biology and physics look at the world differently that help us navigate the minefield of counterproductive stereotypical responses.

I found this paper to be fascinating, and it will be helpful as Russ Hobbie and I prepare the 5th edition of IPMB. It is interesting that the authors use the word “negotiating” in the title, because I felt that Redish and Cooke were involved in an extended negotiation about how much physics to include in an introductory biology class. This process is not restricted to instruction; I go through an often painful negotiation regarding the emphasis of biology versus physics with the reviewers of almost every research article I’ve ever published. I like the conversational tone of Redish and Cooke’s paper, and how it describes the growth of a close collaboration between a biologist and a physicist, each with a different worldview. Probably the most important contribution of the article is the story of how they uncovered and dealt with their hidden biases (they use the term epistemologies, which is one of those words from the science education literature that I dislike). Readers of this blog may remember Redish; one of my blog entries earlier this year discussed his article in Physics Today about “Reinventing Physics for Life Science Majors.” At first, I was annoyed by Redish and Cooke’s habit of referring to themselves collectively in the first person and individually in the third person (as in, “our physicist” and “our biologist”), but as I read on this technique began to grow on me and in the end I found it endearing. I particularly enjoyed their discussion about the role of problem solving in physics and biology, and what makes a good homework problem.

In our interdisciplinary discussions, we also learned that biologists and physicists had dramatically different views of what makes a good biological example in physics… We came to understand that what would be of value in a physics class is biological authenticity—examples in which solving a physics problem in a biological context gives the student a deeper understanding of why the biological system behaves the way it does.

Russ and I strive to achieve authenticity in our end-of-chapter homework problems. Our book is aimed at an intermediate level--we assume the student is comfortable with calculus--so we may have an easier time constructing nontrivial physics exercises applied to biology than an introductory instructor would, but I sometimes wonder if the biologists and medical doctors find them as useful as we think they are.

Redish and Cooke present a list of “cultural components” of both physics and biology that are illuminating.

Physics: Common Cultural Components

• Introductory physics classes often stress reasoning from a few fundamental (usually mathematically formulated) principles. 

• Physicists often stress building a complete understanding of the simplest possible (often highly abstract) examples— “toy models”—and often do not go beyond them at the introductory level.
 
• Physicists quantify their view of the physical world, model with math, and think with equations, qualitatively as well as quantitatively.
 
• Physicists concern themselves with constraints that hold no matter what the internal details (conservation laws, center of mass, etc.).

Biology: Common Cultural Components

• Biology is often incredibly complex. Many biological processes involve the interactions of component parts leading to emergent phenomena, which include the property of life itself. 

• Most introductory biology does not emphasize quantitative reasoning and problem solving to the extent these are emphasized in introductory physics.
 
• Biology contains a critical historical constraint in that natural selection can only act on pre-existing molecules, cells, and organisms for generating new solutions.
 
• Much of introductory biology is descriptive (and introduces a large vocabulary).
 
• However, biology—even at the introductory level—looks for mechanism and often considers micro–macro connections between the molecules involved and the larger phenomenon.
 
• Biologists (both professionals and students) focus on and value real examples and structure–function relationships.

As I read these lists, it is clear to me that I am definitely in the physics camp. It would not be an exaggeration to say that a primary goal of IPMB is to force introduce the physicist’s culture, as described above, to students interested in biology and medicine.

I do have one minor criticism. Initially I was impressed by Redish’s analysis of the relationship of flow to pressure in a blood vessel (Hagen-Poiseuille flow), with the appearance of the fourth power of the radius, using simple arguments involving no calculus. Upon further reflection, however, I’m not totally comfortable with the derivation. Here it is in brief:

F_pressure = ΔP A

F_drag = b L v

Q = A v

where ΔP is the pressure drop, A is the cross-sectional area of the vessel, L is the vessel length, v is the speed (assumed uniform, or plug flow), b is a frictional proportionality constant, and Q is the volume flow. If you set the two forces equal, and eliminate v in favor of Q, you get

ΔP = (b L/A²) Q

The 1/A² dependence implies that the flow increases as the fourth power of the radius. My concern is this: suppose a student approaches Redish and says “I follow your derivation, but shouldn’t the drag force be proportional to the surface area where the flow contacts the vessel wall? In other words, shouldn’t the drag force be given by F_drag = c (2πrL) v?” (I use c for the proportionality constant because it now has different units that b.) Of course, if you do the calculation using this expression for the drag force, you get the wrong answer (a 1/r³ dependence)! I wonder if any of his students ever brought this up, and how he responded? The complete derivation is given in Chapter 1 of IPMB, and the central point is that the frictional force depends on dv/dr rather than v, but the analysis uses some rather advanced calculus that would be inappropriate in the introductory biology class that Redish and Cooke consider. The trade-off between simplifying a concept so it is accessible versus being as accurate as possible is always difficult. I don’t know what the best approach would be in this case. (I can always make one recommendation: buy a copy of IPMB!)

Despite this one reservation, I enjoyed Redish and Cooke’s paper very much. Let me give them the last word.

We conclude that the process [of interdisciplinary collaboration aimed at revising the biology introductory course] is significantly more complex than many reformers working largely within their discipline often assume. But the process of learning each other’s ropes—at least to the extent that we can understand each other’s goals and ask each other challenging questions—can be both enlightening and enjoyable. And much to our surprise, we each feel that we have developed a deeper understanding of our own discipline as a result of our discussions.

Joe Redish (1943–2024)

Edward “Joe” Redish, a University of Maryland physics professor, died August 24 of cancer. Joe has been mentioned many times in this blog (here, here, here, and here). He was deeply interested in how students—and in particular biology students—learn physics, an interest with obvious relevance to Intermediate Physics for Medicine and Biology.

Redish, E. F., 
“Using Math in Physics: 7. Telling the Story,”
Phys. Teach., 62: 5–11, 2024.

I knew Joe, and valued his friendship. Rather than writing about him myself,  I’ll share some of his thoughts in his own words. He had a wonderful series of papers in The Physics Teacher about using math in physics. The last of the series (published this year) was about using math to tell a story (Redish, E. F., “Using Math in Physics: 7. Telling the Story,” Phys. Teach., Volume 62, Pages 5–11, 2024). He wrote

Even if students can make the blend—interpret physics correctly in mathematical symbology and graphs—they still need to be able to apply that knowledge in productive and coherent ways. As instructors, we can show our solutions to complex problems in class. We can give complex problems to students as homework. But our students are likely to still have trouble because they are missing a key element of making sense of how we think about physics: How to tell the story of what’s happening.

We use math in physics differently than it’s used in math classes. In math classes, students manipulate equations with abstract symbols that usually have no physical meaning. In physics, we blend conceptual physics knowledge with mathematical symbology. This changes the way that we use math and what we can do with it.

We use these blended mental structures to create stories about what’s happening (mechanism) and stabilize them with fundamental physical laws (synthesis).

In an oral history interview with the American Institute of Physics, Joe talked about using simple toy models when teaching physics to biology students.

One of the problems that students run into, that teachers of physics run into teaching biology students, is we use all these trivial toy models, right? Frictionless vacuum. Ignore air resistance. Treat it as a point mass. And the biology students come in and they look at this and they say, “These are not relevant. This is not the real world.” And they know in biology, that if you simplify a system, it dies. You can’t do that. In physics we do this all the time. Simple models are kind of a core epistemological resource for us. You find the simplest example you possibly can and you beat it to death. It illustrates the principle. Then you see how the mathematics goes with the physics. The whole issue of finding simple models is where a lot of the creative art is in physics.

Redish and Cooke,
“Learning Each Other’s Ropes:
Negotiating Interdisciplinary Authenticity”
CBE—Life Sciences Education,
12:175–186, 2013.

My favorite of Joe’s papers is “Learning Each Other’s Ropes: Negotiating Interdisciplinary Authenticity” which he coauthored with biologist Todd Cooke (CBE—Life Sciences Education, Volume 12, Pages 175–186, 2013).

From our extended conversations, both with each other and with other biologists, chemists, and physicists, we conclude that, “science is not just science.” Scientists in each discipline employ a tool kit of different types of scientific reasoning. A particular discipline is not characterized by the exclusive use of a set of particular reasoning types, but each discipline is characterized by the tendency to emphasize some types more than others and to value different kinds of knowledge differently. The physicist’s enthusiasm for characterizing an object as a disembodied point mass can make a biologist uncomfortable, because biologists find in biology that function is directly related to structure. Yet similar sorts of simplified structures can be very powerful in some biological analyses. The enthusiasm that some biologists feel toward our students learning physics is based not so much on the potential for students to learn physics knowledge, but rather on the potential for them to learn the types of reasoning more often experienced in physics classes. They do not want their students to think like physicists. They want them to think like biologists who have access to many of the tools and skills physicists introduce in introductory physics classes… We conclude that the process is significantly more complex than many reformers working largely within their discipline often assume. But the process of learning each other’s ropes—at least to the extent that we can understand each other’s goals and ask each other challenging questions—can be both enlightening and enjoyable. And much to our surprise, we each feel that we have developed a deeper understanding of our own discipline as a result of our discussions.

You can listen to Joe talk about physics education research on the Physics Alive podcast.

We’ll miss ya, Joe.

Reinventing Physics For Life-Science Majors

The July issue of Physics Today contained an article by Dawn Meredith and Joe Redish titled “Reinventing Physics for Life-Science Majors.” Much in the article is relevant to the 4th edition of Intermediate Physics for Medicine and Biology. The main difference between the goals of their article and IPMB is that they discuss the introductory physics course, whereas Russ Hobbie and I wrote an intermediate-level text. Nevertheless, many of the aims remain the same. Meredith and Redish begin

Physics departments have long been providing service courses for premedical students and biology majors. But in the past few decades, the life sciences have grown explosively as new techniques, new instruments, and a growing understanding of biological mechanisms have enabled biologists to better understand the physiochemical processes of life at all scales, from the molecular to the ecological. Quantitative measurements and modeling are emerging as key biological tools. As a result, biologists are demanding more effective and relevant undergraduate service classes in math, chemistry, and physics to help prepare students for the new, more quantitative life sciences.

Their section on what skills should students learn reads like a list of goals for IPMB:

• Drawing inferences from equations…. 
• Building simple quantitative models…. 
• Connecting equations to physical meaning…. 
• Integrating multiple representations…. 
• Understanding the implications of scaling and functional dependence…. 
• Estimating….”

Meredith and Redish realize the importance of developing appropriate homework problems for life-science students, which is something Russ and I have spent an enormous amount of time on when revising IPMB. “We have spent a good deal of time in conversation with our biology colleagues and have created problems of relevance to them that are also doable by students in an introductory biology course.” They then offer a delightful problem about calculating how big a worm can grow (see their Box 4). They also include a photo of a “spherical cow”; you need to see it to understand. And they propose the Gauss gun (see a video here) as a model for exothermic reactions. They conclude

Teaching physics to biology students requires far more than watering down a course for engineers and adding in a few superficial biological applications. What is needed is for physicists to work closely with biologists to learn not only what physics topics and habits of mind are useful to biologists but also how the biologist’s work is fundamentally different from ours and how to bridge that gap. The problem is one of pedagogy, not just biology or physics, and solving it is essential to designing an IPLS [Introductory Physics for the Life Sciences] course that satisfies instructors and students in both disciplines.

A Theoretical Physicist’s Journey into Biology

Many physicists have shifted their research to biology, but rarely do we learn how they make this transition or, more importantly, why. But the recent article “A Theoretical Physicist’s Journey into Biology: From Quarks and Strings to Cells and Whales” by Geoffrey West (Physical Biology, Volume 11, Article number 053013, 2014) lets us see what is involved when changing fields and the motivation for doing it. Readers of the 4th edition of Intermediate Physics for Medicine and Biology will remember West from Chapter 2, where Russ Hobbie and I discuss his work on Kleber’s law. West writes

Biology will almost certainly be the predominant science of the twenty-first century but, for it to become successfully so, it will need to embrace some of the quantitative, analytic, predictive culture that has made physics so successful. This includes the search for underlying principles, systemic thinking at all scales, the development of coarse-grained models, and closer ongoing collaboration between theorists and experimentalists. This article presents a personal, slightly provocative, perspective of a theoretical physicist working in close collaboration with biologists at the interface between the physical and biological sciences.

On Growth and Form,
by D'Arcy Thompson.

West describes his own path to biology, which included reading some classic texts such as D’Arcy Thompson’s On Growth and Form. He learned biology during intense free-for-all discussions with his collaborator James Brown and Brown’s student Brian Enquist.

The collaboration, begun in 1995, has been enormously productive, extraordinarily exciting and tremendous fun. But, like all excellent and fulfilling relationships, it has also been a huge challenge, sometimes frustrating and sometimes maddening. Jim, Brian and I met every Friday beginning around 9:00 am and finishing around 3:00 pm with only short breaks for necessities. This was a huge commitment since we both ran large groups elsewhere. Once the ice was broken and some of the cultural barriers crossed, we created a refreshingly open atmosphere where all questions and comments, no matter how “elementary,” speculative or “stupid,” were encouraged, welcomed and treated with respect. There were lots of arguments, speculations and explanations, struggles with big questions and small details, lots of blind alleys and an occasional aha moment, all against a backdrop of a board covered with equations and hand-drawn graphs and illustrations. Jim and Brian generously and patiently acted as my biology tutors, exposing me to the conceptual world of natural selection, evolution and adaptation, fitness, physiology and anatomy, all of which were embarrassingly foreign to me. Like many physicists, however, I was horrified to learn that there were serious scientists who put Darwin on a pedestal above Newton and Einstein.

West’s story reminds me of the collaboration between physicist Joe Redish and biologist Todd Cook that I discussed previously in this blog, or Jane Kondev’s transition from basic physics to biological physics when an assistant professor at Brandeis (an awkward time in your career to make such a dramatic change).

I made my own shift from physics to biology much earlier in my career—in graduate school. Changing fields is not such a big deal when you are young, but I think all of us who make this transition have to cross that cultural barrier and make that huge commitment to learning a new field. I remember spending much of my first summer at Vanderbilt University reading papers by Hodgkin, Huxley, Rushton, and others, slowly learning how nerves work. Certainly my years at the National Institutes of Health provided a liberal education in biology.

I will give West the last word. He concludes by writing

Many of us recognize that there is a cultural divide between biology and physics, sometimes even extending to what constitutes a scientific explanation as encapsulated, for example, in the hegemony of statistical regression analyses in biology versus quantitative mechanistic explanations characteristic of physics. Nevertheless, we are witnessing an enormously exciting period as the two fields become more closely integrated, leading to new inter-disciplinary sub-fields such as biological physics and systems biology. The time seems right for revisiting D’Arcy Thompson’s challenge: “How far even then mathematics will suffice to describe, and physics to explain, the fabric of the body, no man can foresee. It may be that all the laws of energy, and all the properties of matter, all… chemistry… are as powerless to explain the body as they are impotent to comprehend the soul. For my part, I think it is not so.” Many would agree with the spirit of this remark, though new tools and concepts including closer collaboration may well be needed to accomplish his lofty goal.