I became enthused about using mathematical models to understand the natural world as an undergraduate, got trained to do so, and spent my career working on a wide variety of applications. Most recently, I translated ideas from disease modeling to understand cyber variability and security.
To maximize success when applying mathematics to the natural or (for cyber) operational world, one needs to master the appropriate mathematical tools and have a deep knowledge of the subject matter. My recommendations are three really great books that will help you gain proficiency in the needed mathematical tools and how to apply them, and two equally great books on cyber systems.
There is no better starting point for preparing yourself to work on disease biology as it applies to cybersecurity than The Feynman Lectures on Physics, which are incredible and I have read (as have some Nobel prize-winning physicists) multiple times over my career.
Most recently, I read the chapters on optics and vision in the first part of 2025 because of research I am now doing on octopuses.
Richard Feynman has been a well-deserved hero in science for at least 65 years. He became a broader cultural hero in the mid 1980s with the publication of Surely You’re Joking Mr. Feynman and then in the 2000s when Alan Alda starred in essentially a one-person play about Feynman.
These lectures were originally given to first-year physics students at the California Institute of Technology, and you might think that they are not appropriate for most people. Well, yes and no. It is certain that the more mathematics you know, the more you will enjoy Feynman’s teaching, but everyone can appreciate his easy style, his honesty about how hard the work is (and how even he makes mistakes). And everyone can appreciate the way that he explains science and helps develop intuition about the natural world.
I used Feynman’s lectures as a model for my own writing about applying mathematics in biology, and one of the greatest compliments that I ever received was a review of one of my books that complained “too many words about mathematics”!
Feynman’s lectures are brilliant and will give you a sense of how to think about using mathematics to understand cyber variability.
The whole thing was basically an experiment," Richard Feynman said late in his career, looking back on the origins of his lectures. The experiment turned out to be hugely successful, spawning publications that have remained definitive and introductory to physics for decades. Ranging from the basic principles of Newtonian physics through such formidable theories as general relativity and quantum mechanics, Feynman's lectures stand as a monument of clear exposition and deep insight. Timeless and collectible, the lectures are essential reading, not just for students of physics but for anyone seeking an introduction to the field from the inimitable Feynman.
This is one of two books (the other is Cyberspace in Peace and War) that I think anybody seriously interested in cyber security (which should be everybody) should have on their shelf.
It is filled with insights on a wide range of topics. I refer to it many times in my book, including why biology is a better metaphor for cyber defense than war, how people new to analytical thinking about cyber systems should approach the topic, the general meaning of cyber security, what it means for a cyber system to be resilient, and the need for operational cyber drills (analogous to experiments in biology).
The writing in this book is accessible, and it is both fun to read and really informative.
Dependence on computers has had a transformative effect on human society. Cybernetics is now woven into the core functions of virtually every basic institution, including our oldest ones. War is one such institution, and the digital revolution's impact on it has been profound. The American military, which has no peer, is almost completely reliant on high-tech computer systems. Given the Internet's potential for full-spectrum surveillance and information disruption, the marshaling of computer networks represents the next stage of cyberwar. Indeed, it is upon us already. The recent Stuxnet episode, in which Israel fed a malignant computer virus into Iran's nuclear…
It is April 1st, 2038. Day 60 of China's blockade of the rebel island of Taiwan.
The US government has agreed to provide Taiwan with a weapons system so advanced that it can disrupt the balance of power in the region. But what pilot would be crazy enough to run…
This is a wonderfully informative introduction to cyber system variability, and is something to both read from cover to cover and have on your shelf (physical or electronic) to dip into from time to time, as I do.
Libicki’s ideas appear throughout my book, including the advice he gives on page 1 that "…when facing a problem such as the threat from cyberspace it pays to be serious but not desperate."
If you seriously want to understand how to use disease models to understand cybersecurity and variability, the books by Libicki and Singer and Friedman provide a fantastic background in the subject matter.
This updated and expanded edition of Cyberspace in Peace and War by Martin C. Libicki presents a comprehensive understanding of cybersecurity, cyberwar, and cyber-terrorism. From basic concepts to advanced principles, Libicki examines the sources and consequences of system compromises, addresses strategic aspects of cyberwar, and defines cybersecurity in the context of military operations while highlighting unique aspects of the digital battleground and strategic uses of cyberwar.
This new edition provides updated analysis on cyberespionage, including the enigmatic behavior of Russian actors, making this volume a timely and necessary addition to the cyber-practitioner's library.
This is a classic! I have had (and worn through copies) since 1969.
There is no explicit mention of disease in Maynard Smith’s book, but the two chapters on population regulation will give you all the tools you need to start applying ideas from disease biology.
As with the Feynman lectures, there is mathematics in this book – but it begins with arithmetic. I recommend it for much the same reason that I recommend Feynman because it will show you how mathematical reasoning can illuminate biology and was written by one the great mathematical biologists of the 20th century.
The book is written for biologists and has the same quality as Feynman’s lectures of having plenty of words that bring the mathematics to life.
This is a lucid introduction to some of the mathematical ideas which are useful to biologists. Professor Maynard Smith introduces the reader to the ways in which biological problems can be expressed mathematically, and shows how the mathematical equations which arise in biological work can be solved. Each chapter has a number of examples which present further points of biological and mathematical interest. interest. Professor Maynard Smith's book is written for all biologists, from undergraduate level upwards, who need mathematical tools. Only an elementary knowledge of mathematics is assumed. Since there are already a number of books dealing with statistics…
It is April 1st, 2038. Day 60 of China's blockade of the rebel island of Taiwan.
The US government has agreed to provide Taiwan with a weapons system so advanced that it can disrupt the balance of power in the region. But what pilot would be crazy enough to run…
This is a short (about 100 pages) and relatively new (2020) book showing how mathematical modeling of the dynamics of populations can be used to give new insights to the classic experiments by the scientist Georgy Gause on predation by one kind of single-celled organism called Didinium on another single celled organism Paramecium (which may sound familiar from high school biology), where the populations are the numbers of the two species and to the outcomes of classical military battles like Trafalgar, where the populations are the sizes of the forces of each side.
McCue’s book is very well written and most of it is accessible with relatively simple mathematics. It will also show you how we can include the randomness that is inherent to nature (and to all operational situations) in models.
McCue is a top flight operations analyst; as with Feynman and Maynard Smith, reading this book – even if you skip all the mathematics – will give you an understanding about how we can bring scientific ideas to the study of operational problems.
F.W. Lanchester famously reduced the mutual erosion of attrition warfare to simple mathematical form, resulting in his famous "Square Law," and also the "Linear Law." Followers have sought to fit real-world data to Lanchester's equations, and/or to elaborate them in order to capture more aspects of reality.In Beyond Lanchester, Brian McCue--author of the similarly quantitative U-Boats In The Bay Of Biscay--focusses on a neglected shortcoming of Lanchester's work: its determinism. He shows that the mathematics of the Square Law contain instability, so that the end-state it predictes is actually one of the least likely outcomes.This mathematical truth is connected to…
Many of the words used to describe disease ('infection', 'transmission', 'virus') are also used to characterize cyber security (for example: a computer is infected by a virus that can be transmitted to other currently uninfected computers). Using models from the population biology of disease shows this correspondence much deeper than a convenient metaphor.
The aim of my book is to show how the models developed to understand the dynamics of infection, recovery, and possible re-infection in disease can be generalized to understand attack, compromise, and recovery of components of a cyber system and how such attacks affect performance of the cyber system or the physical system, depending on the cyber system. The mathematics is relatively simple, and I stress intuitive understanding of the analysis.
