Conceptual Science

“In this chapter we shall discuss one of the most far-reaching generalisations of the human mind…” With these words, Richard Feynman invites us into a grand intellectual adventure—one that stretches from ancient stargazers to the dawn of modern physics. In Chapter 7-1 of  The Feynman Lectures on Physics , the celebrated physicist sets out not merely to explain the law of gravitation, but to recount the profound journey of its discovery. That journey begins not with equations, but with awe. Feynman speaks of a nature so elegantly ordered that a single, simple law could describe the motions of planets, moons, and falling apples alike. But he is quick to remind us: such simplicity was not always obvious. It had to be uncovered, step by careful step, through centuries of observation, debate, and refinement. The Ancient View: Circles and Spheres Long before telescopes or satellites, early civilisations looked to the skies with reverence and curiosity. The Babylonians charted the stars a...

In Chapter 6-5 of  The Feynman Lectures on Physics , Richard Feynman steps into the philosophical and mathematical depths of quantum mechanics with his trademark clarity and humility. Here, he guides us through one of the most unsettling — yet illuminating — concepts in modern physics: the  uncertainty principle . Far from a dry equation in a textbook, Feynman presents this idea as a cornerstone of how we must think about nature at its most fundamental level. Let’s explore his explanations, the imagery he uses to bring the theory alive, and the historical context he subtly weaves throughout. From Convenient Approximation to Fundamental Reality Feynman opens the chapter by reminding us that probability was first used in physics as a  convenient tool . For example, to describe the behaviour of gases, it was far too complex to track the position and velocity of each of the ~10²² molecules. Probability offered a shortcut — not precision, but practicality. However, in the real...

Richard Feynman’s  Lectures on Physics  are celebrated not only for their intellectual clarity but for their rare ability to infuse deep physical principles with vivid, relatable imagery. In Chapter 6-4, “A Probability Distribution,” Feynman explores the nature of randomness, step-by-step motion, and the concept of a probability density—all through the lens of a slightly modified “random walk.” The section offers a gently meandering journey through one of the most foundational ideas in statistical physics: the Gaussian distribution. Feynman begins by returning to the concept of a random walk. Traditionally, this involves a particle taking steps either forwards or backwards, with each step being the same length. But now, he introduces a twist:  the step lengths themselves are allowed to vary unpredictably , although their  average length remains one unit . This modification makes the model far more realistic, more akin to the  thermal motion of molecules in a gas...

In Chapter 6-3 of  The Feynman Lectures on Physics , Richard Feynman introduces us to a simple but powerful concept: the  random walk . It’s a playful idea on the surface — a game involving coin tosses and small steps — but beneath it lies a deep insight into the nature of chance, measurement, and even atomic motion. A Game of Steps Imagine a player starting at a central point. At each turn, they flip a coin: heads means a step forward, tails a step back. With each toss, their position changes. It’s entirely random, so after many steps, where do we expect them to be? Feynman’s first answer is wonderfully intuitive: probably not far from where they started, but not exactly at the centre either. Sometimes they might wander off quite a bit, other times not much at all. If we were to track many such walkers, the average position would still be zero, because they’re just as likely to move left as right. But the average  distance from the starting point , regardless of directio...

In  The Feynman Lectures on Physics , Chapter 6-2 entitled  Fluctuations  explores a deceptively simple question:  How many heads do we expect to get if we toss a coin N times?  As always, Richard Feynman takes this common-sense query and uncovers a web of rich mathematical imagery, probabilistic nuance, and conceptual beauty that goes far beyond mere guesswork. Let’s unpack his thinking – and dive even deeper into the imagery and mathematics he uses to explain the statistical nature of coin tossing. The Empirical Setup – 100 Games of Chance Feynman begins not with a formula, but with an experiment. Suppose we toss a fair coin 30 times and count how many times it lands heads-up. This is repeated 100 times, and the results are recorded. The first three trials yield 11, 11, and 16 heads. Already, a hint of irregularity appears—why didn’t we see 15 heads, which seems the “expected” outcome? Feynman’s brilliance is to address the psychological trap of expectation . ...

“The true logic of this world is in the calculus of probabilities.” — James Clerk Maxwell It’s not often that one finds a physics text – especially one of such foundational stature as  The Feynman Lectures on Physics  – opening its arms to the messy, unpredictable realm of  probability . Yet in  Chapter 6  of Volume I, Richard Feynman does precisely that. Titled  “Probability” , this chapter forms an unusual but deeply insightful bridge between classical determinism and the probabilistic nature of modern physics. While most undergraduate physics courses plunge headfirst into Newton’s laws or Maxwell’s equations, Feynman pauses – he reflects, questions, and ultimately makes a compelling case: to understand the world at its most fundamental, we must first understand  uncertainty . A Physics of Guesses The chapter opens not with equations, but with a simple observation:  “Chance”  is part of everyday life. From weather forecasts to the likelihoo...