Forman Acton (1920 – 2014)

Numerical Methods That Work,
by Forman Acton.

The American computer scientist Forman Acton died ten years ago this Sunday. In Intermediate Physics for Medicine and Biology, Russ Hobbie and I cite Acton’s Numerical Methods That Work. For readers interested in using computers to model biological processes, I recommend this well written and engaging book.

Before he died, Acton donated funds to establish the Forman Acton Foundation. Here is how their website describes his life:

Forman Sinnickson Acton was born in Salem City, and he went on to change the world.

Born on August 10, 1920, he began his education in the Salem City school system before attending private boarding school at Phillips Exeter Academy and college at Princeton University. He graduated with two degrees in engineering toward the end of World War II, during which he served in the Army Corps of Engineers and worked on a team involved in the Manhattan Project.

After his service, he earned his doctorate in mathematics from Carnegie Institute of Technology, helped the Army develop the world’s first anti-aircraft missiles and became a pioneer in the evolving field of computer science.

Acton conducted research and taught at Princeton from 1952 to 1990, during which time he wrote textbooks on mathematics at his cabin on Woodmere Lake in Quinton Township, Salem County. When he turned 80, he joined the Lower Alloways Creek pool to stay in shape, swimming six days a week for 14 years.

He died on February 18, 2014, in Woodstown, New Jersey, but not before he anonymously donated thousands of dollars toward scholarships for Salem City School District students, some of whom were just then graduating from college. Before he passed, he made it clear to friends and confidants that he wanted these students to have access to the incredible educational experiences he enjoyed.

Eight months after his passing, the Forman S. Acton Educational Foundation was officially incorporated to ensure that all of Salem’s youth also have a chance to change the world.

Sometimes I will read a passage and say to myself “That’s exactly what students studying from IPMB need to hear.” I feel this way about Acton’s preface to Numerical Methods That Work. Russ and I include many homework problems in IPMB so the student can gain experience with the art of mathematical modeling. Below, in Acton’s words, is why we do that. Just replace phrases like “solving equations numerically” with “building models mathematically” and his words apply equally well to IPMB.

Numerical equation solving is still largely an art, and like most arts it is learned by practice. Principles are there, but even they remain unreal until you actually apply them. To study numerical equation solving by watching someone else do it is rather like studying portrait painting by the same method. It just won’t work. The principle reason lies in the tremendous variety within the subject…

The art of solving problems numerically arises in two places: in choosing the proper method and in circumventing the main road-blocks that always seem to appear. So throughout the book I shall be urging you to go try the problems—mine or yours.

I have tried to make my explanations clear, but sad experience has shown that you will not really understand what I am talking about until you have made some of the same mistakes I have made. I hesitate to close a preface with a ringing exhortation for you to go forth to make fruitful mistakes; somehow it doesn’t seem quite the right note to strike! Yet, the truth it contains is real. Guided, often laborious, experience is the best teacher for an art.

 

Subtracting Large Numbers

One of the most notorious difficulties in numerical computations is the loss of precision when subtracting two similar, large numbers to obtain a smaller one. Russ Hobbie and I illustrate this hazard in Chapter 11 of the 4th edition of Intermediate Physics for Medicine and Biology. We begin this chapter with a discussion of the method of least squares, and we derive the formulas (Eqs. 11.5a and 11.5b) for fitting data to a straight line, y = ax + b. We then add “In doing computations where the range of data is small compared to the mean, better numerical accuracy can be obtained from…” and then present alternative formulas (Eqs. 11.5c, 11.5d, and 11.5e). Homework Problem 7 in Chapter 11 (one of the many new problems in the 4th edition) illustrates the advantage of the second set of equations.

Problem 7 Consider the data

   x       y
100   4004
101   4017
102   4039
103   4063

(a) Fit these data with a straight line y=ax+b using Eqs. 11.5a and 11.5b to find a.

(b) Use Eq. 11.5c to determine a. Your result should be the same as in part (a).

(c) Repeat parts (a) and (b) while rounding all the intermediate numbers to 4 significant figures. Do Eqs. 11.5a and 11.5b give the same result as Eq. 11.5c? If not, which is more accurate?

(Spoiler alert: Don’t continue reading if you want to solve the problem yourself first, as you should.) If you solve this problem, you will find that Eqs. 11.5a and 11.5b do not work very well at all for this problem. Their flaw is that they require you to subtract two really big numbers to get a much smaller one.

Numerical Methods That Work,
by Forman Acton.

A good discussion of this issue can be found in Forman Acton’s book Numerical Methods that Work.

The following problem often appears as a puzzle in Sunday Supplements. The difficulties are numerical rather than formulative and hence it is an especially appropriate challenge to the aspiring numerical analyst. We strongly urge that the reader solve it in his own way before turning to the “official” solution.

A railroad rail 1 mile long is firmly fixed at both ends. During the night some prankster cuts the rail and welds in an additional foot, causing the rail to bow up in the arc of a circle. The classical question concerns the maximum height this rail now achieves over its former position. To put it more precisely: We are faced…with the chord of a circle AB that is exactly 1 mile long and the corresponding arc AB that is 1 mile plus 1 foot and our question concerns the distance d between the chord and the arc at their midpoints. [See Acton’s book for the accompanying figure]

The relationships available are the simple ones from trigonometry involving the subtended half angle, θ, and the Pythagorean relationship. The student at this point should attempt to solve the problem before turning to the solution given in Chapter 2. He should attempt to find the distance d to an accuracy of three significant figures. In his effort he will probably be faced with subtracting two large and nearly equal numbers, which will cause a horrendous loss of significant figures. He can live with this process by shear brute force, but it will involve use eight-significant-figure trigonometric tables to preserve three figures in his answer. The point of the problem here is to find another method of calculating d, one that does not require such extreme measures. The three-figure answer can, indeed, be obtained rather easily using nothing more than pencil, paper, and a slide rule. The student should seek such a method.

If you find numerical methods interesting (as I do), you will love Acton’s delightfully written book. Originally published in 1970, it is all the more charming for its now-quaint references to slide rules and trigonometric tables. Yet, the concepts are not out-of-date. Even with powerful computers, errors can arise from subtracting nearly equal numbers. I’ve run into the issue myself when using the finite difference method and relaxation to solve Laplace’s equation with a fine grid and only single precision arithmetic.

Real Computing Made Real,
by Forman Acton.

Unfortunately, Acton’s book is not cited in the 4th edition of Intermediate Physics for Medicine and Biology (we’ll have to fix that in later editions), although I have mentioned it before in this blog. Acton is an emeritus professor in the Department of Computer Science at Princeton University (a department with an illustrious history). Also interesting is his more recent book Real Computing Made Real: Preventing Errors in Scientific and Engineering Calculations.

Numerical Computing

My research involves computer simulations, so I spend a lot of time implementing numerical algorithms. I view a numerical technique as a tool for solving a problem, not as something intrinsically interesting itself. But as a numerical modeler it pays to become familiar with your tools, so I have.

The first question is which programming language to use? I use FORTRAN, and I’m sure that makes me a dinosaur in the eyes of many. But FORTRAN is still common among physicists, and has served me well since I first learned it as a senior in high school. If you look in the solution manual for the 4th edition of Intermediate Physics for Medicine and Biology, you will find a few programs written in FORTRAN. Russ Hobbie humored me by letting me write these in FORTRAN rather than C, although C appears in the textbook itself.

Numerical Recipes:
The Art of Scientific Computing,
by Press et al.

I tend to avoid software like Matlab, Mathematica, and Maple as being to “black-boxy.” I like to tinker with the guts of my program, and often you can’t do that with high-level software packages. Perhaps younger scientists disagree. I do use Matlab for graphics.

When I face a numerical problem that is new to me, the first place I look is Numerical Recipes: The Art of Scientific Computing, by Press, Teukolsky, Vetterling, and Flannery . The copy on my bookshelf is the 2nd edition of Numerical Recipes in FORTRAN 77: The Art of Scientific Computing. In the preface Press et al. write

We call this book “Numerical Recipes” for several reasons. In one sense, the book is indeed a “cookbook” on numerical computation. However there is an important distinction between a cookbook and a restaurant menu. The latter presents choices among complete dishes in each of which the individual flavors are blended and disguised. The former—and this book—reveals the individual ingredients and explains how they are prepared and combined.

Numerical Methods That Work,
by Forman Acton.

For a guide to some of the lore of numerical computing, I recommend two delightful books by Forman Acton: Numerical Methods that Work, and Real Computing Made Real: Preventing Errors in Scientific and Engineering Calculations. In Real Computing, Acton writes

This book addresses errors of the third kind. You’ve never heard of them? But you've made them; we all make them every time we write a computer program to solve a physical problem.

Errors of the first kind are grammatical—we write things that aren’t in our programming language. The compiler finds them.

Errors of the second kind are our mistakes in programming the algorithms we sought to use. They include n−1 errors, inversions of logical tests, overwriting array limits (in Fortran) and a lot of other little technical mistakes that just don’t happen to be ungrammatical. We have to find them.

Then, Mirabile visu, the program runs—and even gives the correct answers to the two test problems we happen to have already solved.

Errors of the third kind are the ones we haven’t found yet. They show up only for as-yet-untested input values—often for quite limited ranges of these parameters. They include (but are not limited to) loss of significant digits, iterative instabilities, degenerative inefficiences in algorithms and convergence to extraneous roots or previously docile equations. Since some of these errors occur only for limited combinations of parameters inputs they may never disturb our results; more likely some of them will creep into our answers, but so quietly that we don't notice them—until our bridge has collapsed!

Real Computing Made Real,
by Forman Acton.

In the rest of the book, Acton serves up a feast of tricks, tips, and techniques. Even if you don’t particularly like numerical methods, you will enjoy these books. Readers of Intermediate Physics for Medicine and Biology will find them useful when trying to write a computer program to solve the Hodgkin and Huxley equations or implement the Fourier method for computed tomography.

I end with a quote from Acton’s book that he attributes to Richard Hamming. It is one of my favorite quotes, and one I believe is worth repeating:

The purpose of computing is insight, not numbers.

The Mathematics of Diffusion

The Mathematics of Diffusion,
by John Crank.

Diffusion is one of those topics that is rarely covered in an introductory physics class, but is essential for understanding biology. In the 4th edition of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss diffusion and its biomedical applications. One of the books we cite is The Mathematics of Diffusion by John Crank. Hard-core mathematical physicists who are interested in biology and medicine will find Crank’s book to be a good fit. Physiologists who want to avoid as much mathematical analysis as possible may prefer to learn their diffusion from Random Walks in Biology, by Howard Berg.
Crank died five years ago this week. Like Wilson Greatbatch, who I discussed in my last blog entry, Crank was one of those scientists who came of age serving in the military during World War Two (Tom Brokaw would call them members the “Greatest Generation”). Crank’s 2006 obituary in the British newspaper The Telegraph states:

John Crank was born on February 6 1916 at Hindley, Lancashire, the only son of a carpenter’s pattern-maker. He studied at Manchester University, where he gained his BSc and MSc. At Manchester he was a student of the physicist Lawrence Bragg, the youngest-ever winner of a Nobel prize, and of Douglas Hartree, a leading numerical analyst.

Crank was seconded to war work during the Second World War, in his case to work on ballistics. This was followed by employment as a mathematical physicist at Courtaulds Fundamental Research Laboratory from 1945 to 1957. He was then, from 1957 to 1981, professor of mathematics at Brunel University (initially Brunel College in Acton).

Crank published only a few research papers, but they were seminal. Even more influential were his books. His work at Courtaulds led him to write The Mathematics of Diffusion, a much-cited text that is still an inspiration for researchers who strive to understand how heat and mass can be transferred in crystalline and polymeric material. He subsequently produced Free and Moving Boundary Problems, which encompassed the analysis and numerical solution of a class of mathematical models that are fundamental to industrial processes such as crystal growth and food refrigeration.

Crank is best known for a numerical technique to solve equations like the diffusion equation, developed with Phyllis Nicolson and known as the Crank-Nicolson method. The algorithm has the advantage that it is numerically stable, which can be shown using von Neuman stability analysis. They published this method in a 1947 paper in the Proceedings of the Cambridge Philosophical Society

Crank, J., and P. Nicolson (1947) “A Practical Method for Numerical Evaluation of Solutions of Partial Differential Equations of the Heat Conduction Type,” Proc. Camb. Phil. Soc., Volume 43, Pages 50–67.

Rather than describe the Crank-Nicolson method, I will let the reader explore it in a new homework problem.

Section 4.8

Problem 24 ½ The numerical approximation for the diffusion equation, derived as part of Problem 24, has a key limitation: it is unstable if the time step is too large. This problem can be avoided using the Crank-Nicolson method. Replace the first time derivative in the diffusion equation with a finite difference, as was done in Problem 24. Next, replace the second space derivative with the finite difference approximation from Problem 24, but instead of evaluating the second derivative at time t, use the average of the second derivative evaluated at times t and t+Δt.
(a) Write down this numerical approximation to the diffusion equation, analogous to Eq. 4 in Problem 24.
(b) Explain why this expression is more difficult to compute than the expression given in the first two lines of Eq. 4. Hint: consider how you determine C(t+Δt) once you know C(t).
The difficulty you discover in part (b) is offset by the advantage that the Crank-Nicolson method is stable for any time step. For more information about the Crank-Nicolson method, stability, and other numerical issues, see Press et al. (1992).

The citation is to my favorite book on computational methods: Numerical Recipes (of course, the link is to the FORTRAN 77 version, which is the edition that sits on my shelf).

One Hundred Books About Physics for Medicine and Biology

When I was in high school, I became intrigued by St. John’s College and their Great Books program. I had their brochure, which included a list of the books to read each year; the most famous works of western civilization.

In the spirit of St. John’s, below I list one hundred Great Books about physics applied to medicine and biology. Read all these and you will have obtained a liberal education in biological and medical physics. One book you won’t find on this list is Intermediate Physics for Medicine and Biology. I’m going to assume you’ve already read IPMB and my goal is to suggest books to supplement it.

Where to begin? I’ll assume you have taken a year of physics and a year of calculus. Once you have these prerequisites, start reading.

1. Powers of Ten. First an overview that’s easy and fun. It provides an intuitive feel for the relative sizes of things. 
2. The Machinery of Life. Although I’m assuming you’ve studied some physics and math, I’m not assuming you have much background in biology. This book provides a gentle introduction to biochemistry. Plus, it has those wonderful drawings by David Goodsell. 
3. The Art of Insight in Science and Engineering. Remember: We seek insight, not just facts.
4. Physical Models of Living Systems. IPMB is about modeling in medicine and biology. Philip Nelson’s little book gets us started building models. 
5. The Feynman Lectures on Physics. I know, I know...you’ve already studied introductory physics, but The Feynman Lectures are special. You don’t want to miss them, and they contain some biology too.
6. Air and Water. Now we get to our main topic: physics applied to biology. Mark Denny’s book covers many topics found in the first half of IPMB.
7. Physics with Illustrative Examples from Medicine and Biology. This classic three-volume set covers much of the same ground as IPMB.
8. The Double Helix. To further strengthen your background in biology, read James Watson’s first-person account of how he and Francis Crick discovered the structure of DNA. It’s a required text for any student of science, and is an easy read.
9. The Eighth Day of Creation: The Makers of the Revolution in Biology. After warming up with The Double Helix, it’s time to dig deeper into the history and ideas of modern biology. Physicists play a large role in this book, and it’s wonderfully written.
10. Biomechanics of Human Motion. Chapter 1 in IPMB covers statics applied to the bones and muscles of the body. It’s our first book that focuses in detail on a specific topic.
11. Structures, or Why Things Don’t Fall Down. A delightful book about mechanics, including some biomechanical examples. It’s one of the most enjoyable books on this list. Don’t miss the sequel, The New Science of Strong Materials.
12. Biomechanics: Mechanical Properties of Living Tissue. We need a book about biomechanics that treats tissue as a continuous medium. YC Fung’s textbook fills that niche.
13. A Treatise on the Mathematical Theory of Elasticity. This book is long and technical, and may contain more material than you really need to know. Nevertheless, it’s a great place to learn elasticity. I’m sure there are more modern books that you may prefer. Skip if you’re in a hurry.
14. The Physics of Scuba Diving. An easy read about how hydrostatics impacts divers.
15. Life in Moving Fluids. Fluid dynamics is one of those topics that’s critical to life, but is often skipped in introductory physics classes. This book by Steven Vogel provides an excellent introduction to the field of biological fluid dynamics.
16. Vital Circuits. Another book by Vogel, which focuses on the fluid dynamics of the circulatory system. 
17. Boundary Layer Theory. This large tome may be too advanced for the list, but I learned a lot from it. Skip if you need to move along quickly.
18. Textbook of Medical Physiology. We need to get serious about learning physiology. This classic text is by Arthur Guyton, but any good physiology textbook will do. Not much physics here. The book contains more biology than we need, but physiology is too important to skip.
19. e, The Story of a Number. A gentle introduction into calculus and differential equations, and a great history of the exponential function, the topic of IPMB’s second chapter.
20. Quick Calculus. Yes, you already studied calculus. But we are about to get more mathematical, and this book will help you brush up on math you may have forgotten. If you don’t need it, move on. 
21. Used Math. Finish your math review with this outline of mathematics essential for college physics.
22. The Essential Exponential. It’s time to focus specifically on the exponential function and its properties, so important in biology and medicine.
23. A Change of Heart. Chapter 2 of IPMB mentions the Framingham heart study. Read the story behind the project.
24. On Being the Right Size. This is really an essay, but indulge me while I include it here among the books. J. B. S. Haldane is too fascinating of a writer to miss.
25. Scaling: Why is Animal Size so Important? Knut Schmidt-Nielsen’s study of scaling, a key topic in Chapter 2 of IPMB.
26. Lady Luck. Chapter 3 of IPMB requires us to know some probability, and Warren Weaver’s book is an engaging introduction.
27. Statistical Physics. The first few sections of Chapter 3 in IPMB develop the ideas of statistical physics in a way reminiscent of Frederick Reif’s volume in the Berkeley Physics Course.
28. An Introduction to Thermal Physics. For those who want a more traditional approach to thermodynamics, I recommend Daniel Schroeder’s textbook.
29. Lehninger Principles of Biochemistry. Biological thermodynamics overlaps with biochemistry. Any good biochemistry book will do. They all contain more detail than you need, but a biological physicist must know some biochemistry.
30. The Second Law. This delightful book by Peter Atkins will fill a hole in IPMB: a penetrating discussion about the second law of thermodynamics.
31. Div Grad Curl and All That. Chapter 4 of IPMB uses vector calculus, and there is no better introduction to the topic.
32. Random Walks in Biology. Howard Berg’s wonderful little book about diffusion.
33. The Mathematics of Diffusion. John Crank’s intimidating giant tome about diffusion. Mathephobes shouldn’t bother with it; Mathephiles shouldn’t miss it.
34. Conduction of Heat in Solids. Like the book by Crank, this ponderous textbook by Horatio Carslaw and John Jaeger presents all you ever want to know about solving the heat equation (also known as the diffusion equation).
35. How Animals Work. Another delightful book by Schmidt-Nielsen that considers comparative physiology, and topics in Chapter 5 of IPMB such as countercurrent heat exchange.
36. The Nuts and Bolts of Life. A colorful book about the first dialysis machine.
37. The Biomedical Engineering Handbook. Don’t read this encyclopedia-like multi-volume handbook in one sitting. Yet it provides dozens of examples of how physics is applied to medicine. Ask your library to buy this set and the next one.
38. Encyclopedia of Medical Devices and Instrumentation. The title should be Case Studies: How Physics is Applied to Medicine.
39. Plant Physics. IPMB doesn’t say much about plants, but physics impacts botany as well as zoology.
40. Nerve, Muscle, and Synapse. Bernard Katz’s excellent, if somewhat dated, introduction to all the electrophysiology you need for Chapter 6 of IPMB.
41. The Conduction of the Nervous Impulse. Read about the Hodgkin-Huxley model from the pen of Alan Hodgkin himself.
42. From Neuron to Brain. A modern introduction to neuroscience.
43. Electricity and Magnetism. This book by Ed Purcell is part of the Berkeley Physics Course. The first of three physics books about electricity and magnetism.
44. Introduction to Electrodyamics. David Griffiths’s text competes with Purcell’s for my favorite electricity and magnetism book.
45. Classical Electrodynamics. John David Jackson’s famous graduate-level physics text may be more electricity and magnetism than you want, but how could I leave it off the list?
46. Galvani’s Spark. A history of neurophysiology.
47. Shattered Nerves. A fascinating look at using electrical stimulation to compensate for neural injury. A history of neural prostheses.
48. Bioelectricity: A Quantitative Approach. The first, and probably easiest, of three bioelectricity textbooks.
49. Bioelectromagnetism. Jaakko Malmivuo and Robert Plonsey’s big book about bioelectricity.
50. Bioelectricity and Biomagnetism. Another big tome. Ramesh Gulrajani’s alternative to Malmivuo and Plonsey.
51. The Art of Electronics. In order to understand voltage clamping and other electrophysiological methods, you need to know some electronics. This book is my favorite introduction to the topic. 
52. Mathematical Handbook of Formulas and Tables. Chapter 6 contains lots of mathematics, and the next three books are references you may want. This Schaum’s Outline contains most of the math you’ll ever need. It’s cheap, light, and easy to use. Keep it handy.
53. Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. No one would sit down and read this handbook straight through, but “Abramowitz and Stegun” is invaluable as a reference.
54. Table of Integrals, Series, and Products. “Gradshteyn and Ryzhik” is the best integral table ever. Let the library buy it, but have them keep it in the reference section so you can find it quickly. 
55. Numerical Recipes. If you want to solve the equations of the Hodgkin-Huxley model, you need to program a computer. This book is great for finding the needed numerical methods.
56. Numerical Methods that Work. Forman Acton’s book is more chatty than Numerical Recipes, but full of insight.
57. Machines in our Hearts. Chapter 7 of IPMB examines the heart. Read this history of pacemakers and defibrillators to put it all in perspective.
58. Cardiac Electrophysiology: From Cell to Bedside. This multi-author, multi-edition work contains everything you always wanted to know about the electrical properties of the heart, but were afraid to ask.
59. Cardiac Bioelectric Therapy. Another multi-author collection, with several excellent chapters about the bidomain model.
60. When Time Breaks Down. Art Winfree’s unique analysis of the electrical properties of the heart.
61. Electric Fields of the Brain. Paul Nunez’s book about the electroencephalogram from the perspective of a physicist.
62. Iron, Nature’s Universal Element. Why people need iron and animals make magnets.
63. The Spark of Life. An accessible introduction to electrophysiology and ion channel diseases.
64. Ion Channels of Excitable Membranes. The definitive textbook about ion channels, by Bertil Hille.
65. Voodoo Science. Some of the topics in Section 9.10 of IPMB about possible effects of weak electric and magnetic fields make me yearn for this hard-hitting book by Bob Park.
66. Dynamics: The Geometry of Behavior. Chapter 10 of IPMB covers nonlinear dynamics. This beautiful book introduces dynamics using pictures.
67. From Clocks to Chaos. Leon Glass and Michael Mackey introduce the idea of a dynamical disease.
68. Nonlinear Dynamics and Chaos. Steven Strogatz’s classic; my favorite book about nonlinear dynamics.
69. Mathematical Physiology. An award-winning textbook about applying math to biology.
70. Mathematical Biology. Another big fine textbook for the mathematically inclined.
71. The Geometry of Biological Time. A quirky book by Art Winfree, more wide-ranging than When Time Breaks Down.
72. Data Reduction and Error Analysis for the Physical Sciences. Many of the ideas about least squares fitting discussed in Chapter 11 of IPMB are related to analyzing noisy data.
73. The Fourier Transform and its Applications. The Fourier transform is the most important concept in Chapter 11. Ronald Bracewell’s book is a great place to learn about it.
74. Introduction to Membrane Noise. Louis DeFelice’s book explains how to deal with noise.
75. Naked to the Bone. A historical survey of medical imaging.
76. Medical Imaging Physics. A book by William Hendee and E Russell Ritenour, at a level similar to IPMB but dedicated entirely to imaging. Also see its partner, Hendee's Radiation Therapy Physics.
77. Foundations of Medical Imaging. A big, technical book about imaging.
78. Theoretical Acoustics. Not much biology here, but a definitive survey of acoustics to back up Chapter 13 of IPMB.
79. Physics of the Body. This book discusses many topics, including hearing.
80. Musicophilia. An extraordinary book by Oliver Sacks about the neuroscience of hearing.
81. Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles. My choice for a modern physics textbook, with much information about the interaction of light with matter.
82. The First Steps in Seeing. Robert Rodieck’s incredible book about the physics of vision.
83. The Optics of Life. This masterpiece by Sonke Johnsen walks you through optics, examining all the biological applications. A great supplement to Chapter 14 of IPMB.
84. From Photon to Neuron. A study of light, imaging, and vision.
85. Introduction to Physics in Modern Medicine. Suzanne Amador Kane’s nice introduction to physics applied to medicine, covering many topics in the last half of IPMB.
86. Introduction to Radiological Physics and Radiation Dosimetry. Frank Herbert Attix wrote the definitive textbook about how x-rays interact with tissue, a topic covered in Chapter 15 of IPMB.
87. Radiobiology for the Radiologist. The go-to reference for how cells and tissues respond to radiation.
88. Molecular Biology of the Cell. The classic textbook of cell biology.
89. Radiation Oncology: A Physicists Eye View. Explains how to treat cancer using radiation.
90. The Physics of Radiation Therapy. Faiz Khan’s in-depth study of radiation therapy.
91. The Atomic Nucleus. An classic about nuclear physics, providing background for Chapter 17 of IPMB. You could replace it with one of many modern nuclear physics textbooks.
92. The Immortal Life of Henrietta Lacks. A fascinating study of how a women treated for cancer using radioactivity ended up providing science with an immortal cell line.
93. Strange Glow. How radiation impacts society.
94. The Radium Girls. This book is about women poisoned by radium-containing paint (lip, dip, paint). It reminds us why we study medical physics.
95. Magnetic Resonance Imaging: Physical Properties and Sequence Design. All you need to know about MRI.
96. Principles of Nuclear Magnetic Resonance Microscopy. Paul Callaghan’s view of magnetic resonance imaging.
97. Echo Planar Imaging. Advanced MRI techniques.
98. Biological Physics. IPMB is not strong in covering physics applied to cellular and molecular biology. Here are three great books to fill that gap.
99. Cell Biology by the Numbers. I love the quantitative approach to biology.
100. Physical Biology of the Cell. How physicists view biology. 

Don’t see your favorite listed? Here’s my call to action: Add your recommendations to the comments below.

I didn’t end up going to St. John’s College and studying the Great Books. Instead, I attended a more traditional school, the University of Kansas. I loved KU, and I have no regrets. But sometimes I wonder...