Lectures

The “Thinking like a …” series (to be determined)

The “Say what?” series

THINKING LIKE A PHYSICIST

John Healy (draft 5-28-2024)

Visualizing escaping Earth's gravity
Visualizing escaping Earth’s gravity

TABLE OF CONTENTS

  • Introduction
  • Overview
  • Examples
  • The mindset of a physicist
  • The physicist’s toolkit
  • Communicating physics
  • The limits of physics?
  • Notes
  • References

INTRODUCTION

In every discipline of study there’s a range of personalities, approaches, specializations, and skill levels. So, to define “thinking like a physicist” is somewhat presumptuous – to characterize an essential mindset without reduction to cliché.

Yet, the topic has been covered well enough, if only indirectly or anecdotally. There’re enough case examples which highlight particular distinctions. And career physicists who teach and write about how they see the world and find practical solutions to situations where most might not.

So, my position is that “thinking like a physicist” is something that can be taught. Albeit teaching that is something even famous physicists might not do well. And my personal experience – suffering through lackluster teaching in college, and being a teacher myself – provides some insights.

There’re some caveats, naturally. Physics involves lots of math, which typically constrains its audience – those even interested in studying the subject. So, when physics = math, even its big ideas can be pointless.

But this challenge is not confined to physics. Math and mathematical models pervade practically every discipline, and are essential to interdisciplinary research and applications.

And math is only part of a physicist’s toolkit. In fact, I’ve read of graduate school advisors saying to their students that innovation and insight are more than just doing math. There’s time to become proficient in the math.

Mathematical physicist Paul Dirac stated, “Mathematics is only a tool and one should learn to hold the physical ideas in one’s mind without reference to the mathematical form.” – “Tales of the Quantum: Understanding Physics’ Most Fundamental Theory” by Art Hobson

OVERVIEW

Many of the aspects of “thinking like a physicist” apply to other disciplines (and vice versa). And to our personal, everyday lives.

Thinking like a problem solver **

“Physicists, especially, love to look for general rules to make sense of disparate observations.” – Why We Die: The New Science of Aging and the Quest for Immortality (2024) by Venki Ramakrishnan

  • Make an organized list or table
  • Use logical reasoning
  • Solve a simpler problem (or break into simpler problems or steps)
  • Identify too much or too little information (eliminate unnecessary information)
  • Look for a pattern
  • Make a model or use objects
  • Work backwards
  • Draw a picture or diagram
  • Guess and check
  • Simulate a problem
  • Use multiple strategies
  • Write an equation

** The problem-solving strategies used when I taught middle school math, strategies applicable to much more than math.

An organized, layered model – Geographic Information System

EXAMPLES

  • The general gas equation PV=nRT is an example of thinking like a physicist, namely, simplifying gas molecules as microscopic balls: pressure, volume, and temperature not being actual properties of any molecule, but as emergent statistical properties useful for everyday practical applications.

THE MINDSET OF A PHYSICIST

Framing complexity

• “The Hardest Thing To Grasp In Physics? Thinking Like A Physicist” by Chad Orzel (August 29, 2016) – You need to know not just how to do calculations that treat cows as spheres, but when it’s appropriate to do that.

“… so what do I mean by, ‘Think like a physicist?’ It’s something I’ve been intermittently talking about since I started blogging here at Forbes, a very particular approach to problem-solving that involves abstracting away a lot of complication to get to the simplest possible model that captures the essential elements of the problem. … This kind of simplified model-building isn’t completely unique to physics, but we seem to rely on it more heavily than other sciences. … This kind of quick-and-dirty mental modeling is efficient and also extremely versatile. When you find that the simplest approximation doesn’t quite match reality, it’s often very straightforward to make a small tweak that improves the prediction without needing to start over from scratch (moving from point cows to spherical cows, as it were). And you can iterate this process, slowly building up a more and more accurate model from lots of steps that are individually pretty simple. Of course, while it’s a powerful method for thinking about the world, it also has its pitfalls.”

Traits

  • Curiosity
  • Tolerance of uncertainty (patience with ambiguity)
  • Analytical reasoning
  • …

Scoping a problem

  • What’s important, what’s not (essential features)
  • Abstraction, smoothing
  • Suppressed dimensions (Nick Lucid, The Science Asylum)
  • Approximations
  • Mathematical tricks
  • Rules of thumb (e.g., Occam’s Razor)

THE PHYSICIST’S TOOLKIT

“Bohr was a master at building models that made sense of some observations, while strategically ignoring others.” – Wilczek, Frank. Fundamentals: Ten Keys to Reality (p. 208). Penguin Publishing Group. Kindle Edition.

“Most of science is a search for simple, stable properties that can answer questions which interest us.” – Ibid. (p. 214).

  • Scientific method (see References, cf. Sagan’s Demon-Haunted World: Science as a Candle in the Dark)
  • Reality check
  • Math
  • Models (as simplifications)
  • Collaboration

COMMUNICATING PHYSICS

“A good representation can make the difference between usable knowledge and knowledge that is there ‘in principle,‘ …” – Wilczek, Frank. Ibid. (p. 216).

  • Demonstrations
  • Visualizations
  • Analogies
  • Story telling

THE LIMITS OF PHYSICS?

“The world is simple and complex, logical and weird, lawful and chaotic.” – Wilczek, Frank. Fundamentals: Ten Keys to Reality (p. 207). Penguin Publishing Group. Kindle Edition.

“Scientists who define themselves narrowly fail to enrich their minds, but people who avoid science impoverish theirs.” – Ibid. (p. 219).

So, what falls outside the purview of physics?

There’s a long history on this topic, which remains a vibrant contemporary discussion. Particularly around the concept of truth.

Witness Lucretius‘ The Nature of Things written ~50 BC, a treatise on science and philosophy.

One of the achievements of the Greek mind between the eighth and the fifth centuries was a process which might be called separation or differentiation. They discovered that fact is different from fiction and that history is different from myth, that theology and philosophy are different ways of talking about the world, and that each of these is different from natural science. – Lucretius. The Nature of Things (Penguin Classics). Penguin Books Ltd. Kindle Edition. Introduction by Richard Jenkyns.

Some physicists (and scientists) have written books. For example:

• Sean M. Carroll‘s The Big Picture: On the Origins of Life, Meaning, and the Universe Itself (2016). He discusses what we know (and don’t know) – about the world, reality, the universe – within a framework of “poetic naturalism.”

• Carl Sagan‘s book The Demon-Haunted World: Science as a Candle in the Dark (1996) contrasts science with magical thinking, pseudoscience, and antiscience. His chapter “The Fine Art of Baloney Detection” is a classic on critical thinking (and media literacy).

• In Frank Wilczek‘s book Fundamentals: Ten Keys to Reality, his chapter “Mysteries Remain” addresses some remaining “great questions.”

A special quality of humans, not shared by evolution or, as yet, by machines, is our ability to recognize gaps in our understanding and to take joy in the process of filling them in. It is a beautiful thing to experience the mysterious, and powerful, too. – Wilczek, Frank. Ibid. (p. 205). [1]

Wilczek’s last chapter in Fundamentals includes a section “Beyond Science: Complementarity as Wisdom,” citing examples from art, models of the mind, which reflect “different (complementary) ways of processing reality” – paths to insights. He invokes a spirit of tolerance and humility:

Thus, complementarity is an invitation to consider different perspectives. Unfamiliar questions, unfamiliar facts, or unfamiliar attitudes, in the spirit of complementarity, give us opportunities to try out new points of view and to learn from what they reveal. They foster mind expansion. Why not bring this spirit to supposed conflicts between art and science, or philosophy and science, or religion A and religion B, or religion and science? It can be illuminating to look at the world in different ways. – Ibid. (p. 219).

Notes

[1] From my poems …

• from “Sisyphus in the back yard”

the gods sported and faded from the press,
the universe returning as its own address.
what Olympus was now passes to us —
we scale ourselves and return Sisyphus

Copyright © 1975, 2017 John P. Healy

• the beasts at the end of my desk

can we live without myth?
what sustains us,
what enables us to acknowledge the unknown in peace
while working to understand it?
what preserves wonder
without regressing all to mean utility?

• midstream

connected, together midstream
partially — as some
mind-ed to then-when or down
shape the influx from infinities
into a stability.
yet, adding to, subtracting,
leaving still euclidean non-visible
out from the relative,
even as we do

References

  • An Introduction to Scientific Research by E. Bright Wilson, Jr. (Professor of Chemistry, Harvard University). McGraw-Hill Book Company, Inc. © 1952. Particularly, Chapter 3 “Elementary Scientific Method.” [A paperback book which was either recommended reading or given to me when I was a freshman in college.]
  • The Character of Physical Law by Richard Feynman. The Messenger Lectures at Cornell 1964. The M.I.T. Press © 1965. Particularly, Chapter 2 “The Relation of Mathematics to Physics” and Chapter 7 “Seeking New Laws.”

• Thinking Like a Physicist, Physics Problems for Undergraduates by N. Thompson. Taylor & Francis (January 1, 1999).

In this unique collection of problems and solutions, selected from examination and tutorial questions used in the University of Bristol, the reader is encouraged to apply basic physical principles, judicious assumptions and approximations, and simplified ‘models’ of complex situations, and to consider the limitations of the resulting solutions – in short to ‘think like a physicist’.

• How do I think like a physicist? (2023)

[Excerpts from replies]

To add to this, approximations are key. Solving things “correctly” is almost never a good idea in physics. Understanding when you can take approximations is very important.

To me, “thinking like a physicist” is not being satisfied until you’ve explained the real world and how the math applies to it. The math is nice and it is quite an important step, but the physics is in the next steps beyond the math (and sometimes in choosing which math to use and when/how to apply it).

… physicists do not need to use maths with the same level of rigour as mathematicians. They are satisfied with approximations and will do many things that would make a mathematician cringe, all in the name of simplifying the problem enough such that it is solvable yet still able to yield a good enough approximate solution for the particular use case at hand.

• Can You Think Like a Physicist?

Yes, anyone can learn to think like a physicist. It requires curiosity, creativity, and a willingness to question and challenge assumptions. With practice and exposure to scientific concepts and methods, anyone can develop the critical thinking skills and mindset of a physicist.

While there are many benefits to thinking like a physicist, it is important to remember that it is just one way of viewing the world. It may not always be applicable or useful in certain situations or fields. It is also important to remain open-minded and consider other perspectives and approaches to problem-solving.