*(Students frequently rise to the challenge when teachers raise the bar. Give them something to stretch their minds with and students will go at it with vigor and purpose. Elementary statistics is a transfer course at California’s community colleges for the CSU/UC systems. A major part of this course is probability, the workhorse of statistics. What if community college students were asked to read Richard Feynman’s lecture on probability? What would they make of it? Feynman (1918-1988) won the Nobel Prize for physics in 1965 for his seminal contributions to quantum electrodynamics. He is celebrated for his physical insights and for his ability to clarify complex concepts for the general audience. His fame grew when he gave a series of lectures on physics at the California Institute of Technology for undergraduates from 1961-1963 that became the three-volume “The Feynman Lectures on Physics.” More than four decades later, the “Red Books” are still being read and still continue to inspire.. The lectures are now available online. His lecture on probability intrigued several community college students who found it instructive and challenging. Second of a 2-part series).*

Eitaro’s understanding took a leap when he studied Feynman’s classification of probability: chance and likelihood, fluctuations, random walk, probability distribution and the uncertainty principle. “Unlike the text where the author discusses probability without telling how one concept relates to the other, Feynman describes the essentials of probability and statistics in clear and simple terms. He starts his lecture with the simplest concept of probability – coin toss - and builds toward the Heisenberg uncertainty principle in a way that seems at once natural and logical. The more you flip a coin, the more the chance of landing heads or tails will be closer to 50In a random walk, if the deviation from expected value is greater than the number of trials, we can assume a flaw. Fluctuation is the deviation of a particular set of observations from the most likely outcome. The uncertainty principle represents a strange fuzziness in nature. Our most precise description of nature must be in terms of probabilities. Although some scientists don’t like nature described in terms of probabilities, they haven’t found a way around it. At least not yet.

Instead of reading the lecture, Camren understood Feynman’s lecture more by watching his YouTube videos. “After watching him I came to realize the man wasn't just a gifted scientist, he was a passionate teacher. It takes passion to teach and his lecture touched me because he was able to make something that I was unfamiliar with feel as if I understood it all along within 60 minutes!” The lecture was based on an understanding of how to determine the reality of something that is unknown. By using probability Feynman was able to explain the characteristics of physical laws. In the fundamentals of physics there are probabilities, and nature herself does not know which path things will take. That’s why you have to sum all possibilities.

Although Rajan did not understand all of it, he found the lecture very interesting. Probability is an extension of guessing. We guess because we do not have full knowledge of a certain situation. Because we are able to guess mathematically, probability guesses tend to be more accurate than guessing whimsically. The uncertainty principle is an expression of probability in some sense. It is essential to describe events at the atomic level. While some physicists believe that uncertainty is not inherent in nature, they have been unsuccessful in proving their theory.

Braxton didn’t understand everything in Feynman's probability lecture either. She knew words like density, chance, and standard deviation, but “I found his mind far more complex than mine, and I cannot think at such a high level, especially when it comes to math.” She liked that Feynman spent time defining what “chance” was and how we ordinarily use the word: the chance of rain, the chance of living for hundred years, the chance of an earthquake, the chance of a nuclear war. “Life is a guessing game, and the theory of probability helps make the guesses a little more logical, helping us make better, more educated guesses.” Braxton wishes that most of her teachers were like him but given that Feynman is a genius, it is unrealistic to expect other teachers to be like him. “Still, other teachers can learn from him. Too bad they don’t!”

Jenna also found it hard to understand Feynman’s lecture on probability. “It was long and he used some words that made it difficult for me to fully grasp what he was trying to say. However, there were some things that I took away from his lecture. The first part was all about chance and probability. We often use the word chance to show that we are making a guess about something. We use the word probability when we are going to test something that is repeatable. However, nothing is exactly repeatable. But that is not that big of an issue as long as we try to make it as similar as possible. Feynman went on to talk about ‘random walk’ which I had never heard of before. It is fair to assume that the average distance traveled in a random walk is zero because there is equal chance of going forward or backward. However, once you start to move either way, you have a tendency to stray farther and farther away from the zero line. In these problems, there is always the chance of deviation or error. None of these problems are going to be always exactly what we assume them to be. Most of the time, they won’t be what we assumed, but they will be close to the deviation we calculate. What I found startling was when he asserted that nature is probabilistic. Certain things in life and in nature cannot be known with certainty. Nature is not deterministic because ‘the most we can know is in terms of probabilities.’ I found this statement fascinating. It has certainly given me reasons to master probability.”

Blake has heard of Feynman before and saw his videos on YouTube. “It is clear that his mind works in very interesting ways. He looks at things from different perspectives. Of course we all want to look at things from different perspectives but our minds are not as powerful as Feynman’s. That’s why he is, or was, Feynman. While I understand the coin toss problem in the context of probability, what really captured my imagination was how Feynman went on to connect simple ideas to profound ideas. His explanation of the uncertainty principle, which I don’t understand completely, was still interesting enough that I read it several times over. if you force a particle into a particular spot, the particle ends up having a high speed, and if you slow down a particle, it ends up spreading out, which makes it hard to pinpoint. That’s where probability comes in. Nature acts in this way when describing things in terms of quantum mechanics, where you don't always know exactly what's going on.”

Kolin followed Feynman’s ideas fairly well but found his attitude toward knowledge even more educational. “When the most profound questions get answered, they reveal yet more questions. There is no end to knowledge. We just keep looking and thinking and even if we can understand only a little bit of how nature works, that’s satisfying enough.”

Nancy found Feynman’s lecture brilliant. “The physicist’s enthusiasm for science is unmistakable, and his capacity to communicate the topic is unparalleled. Truly, Professor Feynman was the teacher of teachers. It is incredible how he is able to organize and present such complicated information to people like me who have only an entry-level understanding. Although I did not grasp everything in the lecture, I was able to follow his step-by-step explanation and understand the logic he was trying to convey. His final words in the lecture summarize his point of view: ‘The future is unpredictable and even nature herself does not know.’”