1.5 The Paradigm Shift to a New Model
No scientific revolution emerges solely from the dictates of logic and reason. Many prefer comfortable preconceptions. Many prefer to share the opinions of our collective and not stand apart as a radical or a wrong-thinker. There exists an element of intellectual bias to overcome, a preference for the familiar paths we’ve taken for granted since the earliest days of our education. For many, a vast barrier of cognitive dissonance must be breached before new and fundamental ideas may be taken seriously. The more skilled, the more talented, and the more competent the thinker, the greater is the barrier. The more work put into constructing an intellectual edifice, and the more experience appears to have validated one’s premises, the harder it is to question them.
What, then, is the solution? Simplify, simplify, simplify.
The experimental physicist Ernest Rutherford (1871–1937) is said to have claimed that an alleged scientific discovery has no merit unless one can explain it to a barmaid [[i]]. Albert Einstein (1879–1955) is alleged to have said, “If you can’t explain it simply, you don’t understand it well enough” [[ii]]. In the version attributed to physicist Richard Feynman (1918–1988), you don’t really understand something unless you can explain it to a sixth grader. If an intriguing idea can be presented in a simple enough fashion, not only does that indicate understanding, but also allows the idea to reach a large audience minimally encumbered by any pre-existing biases. Figure 1.7 shows these scientists.
This book aims to be understood by a lay reader with no more than a basic comprehension of physics. Do you know that energy is the capacity to do work? That work is a force applied over a distance? That charges give rise to electric fields and moving charges or currents give rise to magnetic fields? If you understand these basics, you’re all set. Understanding basic principles like these will help you take full advantage of what this book has to tell you. Even without that background, you should still be able to get a great deal out of it.
With a greater understanding of physics will come a greater appreciation of the concepts, although accompanied by a greater risk of rejection for emotional reasons. Readers may judge for themselves where they fall on this continuum.
If simplification is the goal, what then are the means?
Physics may be understood as a series of stories we tell ourselves about the world around us. These stories, or models, become the tools through which we seek to understand reality. Typically, one may comprehend the model far more easily than one may apply the model in a detailed calculation of physical phenomena. Consider the geocentric model of the solar system: the Earth and all the planets revolve around the sun. That’s easy to understand. Showing how this model follows from a universal law of gravitation by which every mass attracts every other mass with a force inversely proportional to the distance squared between them – that takes a greater degree of sophistication. It took a genius like Isaac Newton to figure that out for the first time. Lesser minds can follow and understand the path Newton broke for us with a rigorous instruction in the science of mechanics. One does not require that higher level of understanding to grasp the fundamental result that the Earth goes around the Sun and not vice versa, however.
If the discussion stays on the level of the fundamental physical model, the basics may be grasped by a wide audience. Planets go around the sun, not the Earth. This fundamental principle of astrophysics may be understood without a background in celestial mechanics and the ability to calculate Hohmann transfer orbits.
All matter is composed of nearly indivisible units called atoms whose properties give rise to the behavior of the materials that make up the world around us. This fundamental principle of chemistry may be readily understood without appreciating why water comprises two atoms of hydrogen and one of oxygen and not some other configuration, for instance.
Diseases may be caused by germs – microscopic pathogens that can grow on and inside us in ways that may be either harmful or beneficial to our health. We don’t even have to understand the difference between a bacterium and a virus, let alone Koch’s Postulates, to appreciate why washing hands frequently and maintaining social distance may be beneficial when infectious diseases are running rampant.
Feynman noted how a model, or mental picture of reality, can distill an enormous amount of detail and staggering implications in an easily expressed concept:
If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generation of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis... that all things are made of atoms — little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. In that one sentence, you will see, there is an enormous amount of information about the world, if just a little imagination and thinking are applied [[vi]].
What exactly is a model? Let’s take a closer look.
“To the man with only a hammer,” goes the old saying, “every problem is a nail.” While a hammer is an excellent tool with broad utility, eventually the wielder will encounter a problem that is a screw rather than a nail. Without the flexibility to switch to an alternate tool, the problem solver will pound away inefficiently, making little progress. These tools of analytic problem solving may be called “models.” A model is a description of a physical system used in analysis of the system. Alternatively, models are the tools of cognition by and through which we organize what we learn and observe so as to understand the world around us [[vii]].
In The Storytelling Animal: How Stories Make us Human, author Jonathan Gottschall (1972– ) marshals evidence from evolutionary biology, psychology, and neuroscience to argue that stories and storytelling are an essential part of cognition [[viii]].
Fiction helps us imagine and practice navigating our way through complex social situations in the same way practicing in a flight simulator helps a pilot fly and land a plane.
Dreams are our storytelling capability running in autopilot mode stringing together random recollections into a more-or-less comprehensible narrative.
Conspiracy theories are these storytelling reflexes run amok, trying to fit disparate facts into a coherent account, or sometimes teasing out hidden narratives and concealed truths from tenuous evidence.
Marveling at the capabilities and limitations of human cognition, mathematician Ronald L. Graham (1935–2020) observed, “Our brains have evolved to get us out of the rain, find where the berries are, and keep us from getting killed. Our brains did not evolve to help us grasp really large numbers or to look at things in a hundred thousand dimensions” [[ix]]. On the contrary, our brains evolved to understand and outwit the most clever and dangerous enemies of all, each other, and the stories we piece together to understand each other and the world at large are a key aspect of human cognition.
Just as science can make sense of storytelling, so also can stories help us make sense of science. “Science,” Gottschall suggests, “is a grand story (albeit with hypothesis testing) that emerges from our need to make sense of the world” [[x]].
As the discoverer of radio waves, Heinrich Hertz (1857–1894), put it, “We form for ourselves images or symbols of external objects; and the form which we give them is such that the necessary consequents of the images in thought are always the images of the necessary consequents in nature of the things pictured” [[xi]]. Chapter 4 has much more to say of his discoveries, but Hertz’s thinking went on to influence philosophers of science like Ernst Mach (1838–1916), Ludwig Wittgenstein (1889–1951), and Karl Popper (1902–1994) [[xii]].
Models guide our thinking and our observations as we study reality. The Greek astronomer Eratosthenes (~276–195/194 BC) noted that on the summer solstice, the sun threw no shadow at Syene (present day Aswan) in southern Egypt, while at Alexandria to the north there was a shadow in the amount of 1/50th of a circle or 7.2 degrees [[xiii]]. He concluded the distance d = 800 km (500 miles) between the two cities was 1/50th of the circumference of the Earth which he correctly predicted was around 40,000 km (24,900 miles). Figure 1.8 shows this result, as well as an alternate flat-Earth interpretation.
Eratosthenes assumed that the earth was spherical and that the sun was so far away that the sun’s rays were parallel. If instead he assumed the earth was flat, then the same result would have told him that the sun was D = d/tan (7.2o) = 800 km/(0.1263) = 6333 km (3935 miles) away.
If instead Eratosthenes had been able to collect more widely spaced measurements of the sun’s elevation at different latitudes, the results would have allowed him to confirm the “spherical-earth-illuminated-by-parallel-rays-from-a-distance-sun” model matched the data better than the “flat-earth-close-sun” model.
Suppose Eratosthenes had been able to collect data on the apparent position of the sun at the time of the equinox, when the noonday sun is directly overhead along the equator (0o latitude). The further away from the equator one collected data, the lower the sun would appear in the sky. At the poles (90o latitude), the sun would be visible just barely at the horizon. Figure 1.9 shows how the result fits the spherical-earth model but appears inconsistent with the simple flat-earth model.
This example illustrates a key aspect of models. There are often multiple models that agree with a particular measurement or observation. Just because some data agree with one model, that does not rule out another model also potentially explaining the same result. And even if we know that a particular model is wrong in a broader context, it may nevertheless have value applied within more limited contexts where it works well.
While the Earth is spheroidal, an architect or engineer designing a building usually employs the simpler flat-earth model, because the effects of the earth’s curvature are so small as to be negligible over the scale of a building’s foundation.
To illustrate the need for using the correct model, consider the 1954 Castle Bravo hydrogen bomb test. Scientists wanted a shielded line of sight to the 15-megaton nuclear fireball, unobstructed by dust and debris. Engineers designed and assembled a pipe from the vicinity of the fireball to the scientists’ instruments 4000 meters (2.5 miles) away from ground zero.
When the pipe was done, the scientists complained that the engineers’ design was flawed. They could not see through the pipe. Rechecking their calculations, the engineers discovered their design was perfectly level with respect to the Earth. However, the Earth’s curvature meant that the level pipe bowed up enough to block the line of sight.
With sufficient precision, there is no such thing as straight AND level. Instead, it’s straight OR level. By tapering the elevation of the pipe to lower it in the center of the span, making the pipe straight instead of level, the engineers achieved a true line of sight [[xv]]. Figure 1.10 shows the Castle Bravo test.
Similar stories abound throughout science and engineering. Having multiple models makes one more flexible and able to understand real-world complexities by applying the correct model for the particular circumstances.
In his essay, “A Different Box of Tools,” collected in Surely You’re Joking Mr. Feynman, Richard Feynman explains how he came to acquire a great reputation for performing integrations. He’d picked up on an obscure technique – differentiating parameters under the integral sign – not in the usual curriculum. Feynman explains:
The result was, when guys at MIT or Princeton had trouble doing a particular integral, it was because they couldn’t do it with the standard methods they had learned in school. If it was a contour integration, they would have found it; if it was a simple series expansion, they would have found it. Then I come along and try differentiating under the integral sign, and often it worked. So I got a great reputation for doing integrals, only because my box of tools was different from everybody else’s, and they had tried all their tools on it before giving the problem to me [[xvi]].
A different set of intellectual tools, a different model, a different perspective on how something works may be a valuable asset.
Speaking at the USC Business School in 1994, Warren Buffet’s investment partner, Charlie Munger (1924–2023) offered advice to financial analysts that applies equally well to scientists and engineers [[xix]]:
What are the models? Well, the first rule is that you’ve got to have multiple models – because if you just have one or two that you’re using, the nature of human psychology is such that you’ll torture reality so that it fits your models.
Figure 1.11 shows Munger as well as renowned military strategist, Colonel John Boyd (1927–1997). Boyd devised what he called the “OODA Loop” of Figure 1.12 to understand the conceptual demands of tactical air combat. The acronym stands for Observe, Orient, Decide, Act: a four-phase framework describing how warfighters and others can react and adapt to rapidly changing conditions.
Observations include all the available data regarding the unfolding situations. A practitioner orients themselves with respect to the available observations and the broader context by applying models, or as Boyd characterized them, “doctrines.”
As Boyd put it, “If you’ve got one doctrine, you’re a dinosaur. Period” [[xx]]. Having oriented themselves, a practitioner is ready to decide upon a course of action and follow through. The faster one can cycle through this process and adapt to quickly-moving circumstances, the more likely one can outpace an adversary’s thinking and take the initiative in a confrontation. Much more may be said about the OODA loop concept [[xxi]], and a more contrarian view is also available elsewhere [[xxii]].
Models are central to the decision-making process, as shown in the graphical representation of the (much simplified) OODA loop of Figure 1.12. The ability to bring multiple models to bear in deciding, acting, and solving problems is as much an advantage for investors and scientists as it is for warfighters. Be it the scientist’s physical and mathematical models, the investor’s financial and economic models, or the tactician’s doctrines and war plans, mastering a broad variety of different perspectives offers an analytic advantage relative to those who rely only on a narrow range of conventional approaches.
This book offers those who read it a unique model, a new perspective on what reality is and how it works. To truly appreciate and take advantage of it, however, we have to step back a moment to consider what models are and how they work.
Many models may be useful depending on the circumstances, but they are often contradictory or incompatible taken to certain limits or in particular contexts. The Earth may look flat locally, but in the broader context, it is spheroidal. By what rules do models “compete” against each other? When they contradict, how do we determine which is correct? What are the patterns or cycles that govern how models evolve, compete, and displace each other? How do we discover what is really real?
Before we can consider and evaluate a new physical model, these are the kinds of questions we must be able to answer. To answer these questions requires an understanding not only of physical principles, but also of how we reached those conclusions.
[i] 1955 November, Biographical Memoirs of Fellows of the Royal Society, Volume 1, Albert Einstein 1879-1955 by Edmund Whittaker, Start Page 37, Quote Page 54, Published by Royal Society, United Kingdom.
[ii] Clark, Ronald W., Einstein: Tis Life and Times, 1972, p. 418. Note that this quote may be apocryphal – it is not sourced from Einstein’s written works and appears attributed to him second hand. See: https://amzn.to/3ujt2Ta
[iii] Portrait of Ernest Rutherford from the portrait by Oswald Birley in the Royal Society. Credit: Wellcome Collection. CC BY
[iv] Portrait of Albert Einstein, 1947. This image is available from the United States Library of Congress's Prints and Photographs division under the digital ID cph.3b46036. See: https://commons.wikimedia.org/wiki/File:Albert_Einstein_Head.jpg
[v] See: https://upload.wikimedia.org/wikipedia/commons/0/06/Richard_Feynman_1959.png
[vi] Feynman, Richard, The Feynman Lectures on Physics, Vol. 1, (New York: Basic Books, 2015, originally, 1964), Lecture 1, "Atoms in Motion"; section 1-2, "Matter is made of atoms"; p. 1-2. See: http://amzn.to/2wDTPY8
[vii] Schantz, Hans G., “Electromagnetic Models and Their Application,” Proceedings of the 2017 Antenna Applications Symposium, Allerton Park, Monticello, Illinois, 2017.
[viii] Gottschall, Jonathan, The Storytelling Animal: How Stories Make Us Human, (New York: Houghton Mifflin Harcourt, 2012). See: http://amzn.to/2vwu0ZU
[ix] Pickover, Clifford A., Keys to Infinity, (New York: John Wiley & Sons, 1995), p. xiv. See: http://amzn.to/2uQbIk8.
[x] Gottschall, Op. Cit., p. 17.
[xi] Hertz, H., The Principles of Mechanics Presented in a New Form, London: Macmillan And Co., Ltd., 1894, p. 1.
[xii] Popper, Karl R., Quantum Theory and the Schism in Physics, London & New York: Routledge, 1982, p. 44. See: https://amzn.to/3urvy9K
[xiii] “Eratosthenes and the Circumference of the Earth,” Nature 152, 473 (1943). https://doi.org/10.1038/152473a0
[xiv] Nuclear weapon test Bravo (yield 15 Mt) on Bikini Atoll. The test was part of the Operation Castle. The Bravo event was an experimental thermonuclear device surface event. US Department of Energy, March 1, 1954. See: https://en.wikipedia.org//wiki/Castle_Bravo#/media/File:Castle_Bravo_Blast.jpg
[xv] Mortensen, Fred N., John M. Scott, and Stirling Colgate, “How Archival Data Contribute to Certification,” Los Alamos Science, Number 28, 2003, pp. 38-46. See: https://fas.org/sgp/othergov/doe/lanl/pubs/las28/mortensen.pdf
[xvi] Richard P. Feynman, “Surely You’re Joking, Mr. Feynman!” (New York: W.W. Norton & Company, 1985), p. 87. See: https://amzn.to/49F7sZp
[xvii] See: https://en.wikipedia.org/wiki/Charlie_Munger#/media/File:Charlie_Munger_(cropped).jpg
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[xviii] See: https://en.wikipedia.org/wiki/John_Boyd_(military_strategist)#/media/File:Boyd56.jpg
#/media/File:Boyd56.jpg){kind=link}
[xix] Tren Griffin, Charlie Munger: The Complete Investor, (New York: Columbia University Press, 2015), p. 43. See: https://amzn.to/3SJUKma
[xx] Ford, Daniel, A Vision So Noble: John Boyd, the OODA4 Loop, and America’s War on Terror, (Warbird Books; 2017 edition, originally published 2013), p. 115. See: https://amzn.to/3sANqhY
[xxi] Macris, Alexander, “On Strategy, Part II,” Contemplations on the Tree of Woe, November 15, 2023. See:
[xxii] Kratman, Tom, “Indirectly Mistaken Decision Cycles,” See: https://www.baen.com/decisioncycles. Undated. Accessed November 16, 2023.
[xxiii] After: https://commons.wikimedia.org/wiki/File:OODA.gif
Simplification Makes It Easier . Yet most people think that true advancement means more complexity
I never thought about the fact that on a large enough scale you can either be straight, or level, but not both. Cool!