George Hrabovsky

Before we begin, here's a bit of background on my mathematical education. I have taken math up to Calculus II and got a pretty good grade, but I never went further then that. Thus, when someone starts mentioning Lagrangians and Hamiltonians, and the Principle of Least Action, Curls, Grads and all of that my eyes begin to glaze over. That didn't happen with this book, and I will attempt to explain why.

In the Preface to the book, Professor Susskind talks about how he felt an itch to help people get into Physics. So he was teaching courses up in California, where he lives and found it to be fun. This is mainly because the people he was teaching had seen a bit of how life is and wanted to satisfy their curiosity. The second author on this book, George Hrabovsky stumbled on some of his work and wanted to do a book together. Thus was this book written.

Now this book starts by assuming some things. The first is that you have had some advanced math, but are now rusty. The second is that you had some experience with Physics. So the book is split into eleven chapters, or as they are called in the book, Lectures. It covers everything you need to know in Classical Mechanics, and gives a good enough mathematical grounding to segue into Quantum Mechanics, but that is another book; one that by chance I happen to own.

The Theoretical Minimum starts with The Nature of Classical Physics, where they talk about Phase States and goes on to familiarize you with some math. It covers Trigonometry, Spaces, Vectors, Integral and Differential Calculus, Dynamics, Partial Differentiation, Poisson Brackets, the Hamitonian, the Lagrangian, and a few more subjects.

Susskind and Hrabovsky also go at a good pace, in my opinion. While they don't hold your hand, they don't exactly throw you into the deep end right off the bat. When something is explained or introduced, Susskind and Hrabovsky explain the terminology and what the symbols are and what they do. I had read a book on Classical Mechanics and Quantum Physics; it was far beyond my level, but the author also expected you to know what the heck a Bra-Ket was or what a Lagrangian did. Back on the Theoretical Minimum though. Since they explain the symbols used, you don't have to invent weird names for them, or call it a "thingie" as I tend to do when I am overladen with Greek Letters. I can recognize the capital Sigma, and many others, but I do mix up the names sometimes.

Thus, I feel that this is a good book for someone like me and others that may be rusty at Classical Mechanics. This is more than enough to earn an excellent score of five out of five.… (mais)

Math is just a skill, like any other and not everyone can do it. What gets my goat is the "anyone can do anything if only they try hard enough "attitude. No, they can't. Some people are good at certain skills and not other, and others have different skills. I happen to be good at math. I get annoyed when people say "Ooh, you must be so clever!" when I tell them. No - I just have that particular skill - I can no doubt be as dumb as the next person at something else. As Courtney Barnett puts it: "The ambulance driver thinks I'm clever 'cos I play guitar /I think she's clever 'cos she stops people dying." Laughing at general illiteracy isn't so funny, because that is a relatively simple skill that most of us can learn, and it hurts people not to have it; but Quantum Mechanics? Come on, no one groks it, and it really doesn't matter for most of us.

The innumeracy and scientific illiteracy that is being normalised is part of the social environment which enables a powerful minority to continue to dominate and exploit a majority by ensuring that as few people as possible have the necessary logical skills and knowledge to seriously question the stories they are told about the world. Accepting this kind of thing as "humour" is accepting a narrative which says that math and science are things that only a tiny number of geeky people care about or understand on account of its alleged "difficulty" and irrelevance. It's all part and parcel of the maintenance of power. In truth, math and science are not that hard until they get to work on us school to persuade us that they are. They also get to work on suppressing our creativity. There's nothing funny about this at all. Mass literacy has been accepted as a necessary evil and it's no longer acceptable to be proud of illiteracy.

Why aren’t more kids learning Physics? It has to be a combination of teaching methods and the way physics is stereotyped in the media. Physics is an absolutely fascinating subject. It's about understanding the very fabric of reality. What could be more interesting than that? It depresses me that most people seem to see the subject as being dry and dull. It really isn't. On top of that, people who study physics have to do it because they love physics, and many people do love it. However, there is virtually no prospect of future employment in the field in Portugal.

A lot of physics at degree level can be downright dull IF NOT TAUGHT RIGHT. You really have to be interested in why things are the way they are from an early age to circumvent that, and I find it hard to believe that gawking at Carl Sagan (the one I grew up with) on the telly is going to make that happen. I can't remember having role models as such - I just loved taking things like hifi, toasters, phones and bikes to bits to see what made them tick (or to see if they'd worked when I'd put them back together...), and finding math equations extraordinarily beautiful. Yes, there's the sexy stuff like astrophysics (relatively easy as much of it was qualitative when I studied it), but to have even the barest of a good all-round grasp of physics as a whole, you have to have done the fairly sophisticated mathematical groundwork, get your head around such utterly scintillating concepts like statistical mechanics, thermodynamics and Fourier optics, before you can set the world alight with your re-jigged theory of quantum gravity (which I did study after I finished my Computer Science college degree).

Moving in a little closer to the book’s content. His explanation of the Lagrangean is something I've never seen done this way before. We have determined experimentally that we can represent very generally the laws of physics by deriving them from a condition which states that a certain quantity (called the Action) must be kept minimum. The action is differently defined for each system, but always represented as the integral between two points in time of another quantity (Called the "Lagrangian Quantity") that is a function of position and velocity at any point in time. Since the action must be kept minimum, the derivative of it (with respect to position) must be kept 0. Both position and velocity are considered to change with respect to time. As such, we can write:

dAction/dx = d/dt(dLagrangian/dv)-dLagrangian/dx = 0 (Euler-Lagrange Equation)

By selecting the Lagrangean function to equal KE-PE, the above equation derives Newton's 2nd law of motion. Brilliant. Moreover, the lagrangean's form can be changed in order to change coordinate system. By doing so first and then solving the Euler-Lagrange equation, the laws of motion for even Non-Inertial Reference Frames can be readily computed (as long as they are non-relativistic), such as in a circularly moving Reference frame. Like so, fictitious forces (those observed in NIRFs but not in IRFs) can be calculated, such as the Coriolis force.

[Paraphrased] "There are some things you only want to experience once, like a book. You don't want to read the same thing over and over again. But there are other things, like music, that you'll want to listen to continually because it just feels good. I hope my lectures are like that... (Paraphrased)." Why yes, Professor Susskind, the lectures in your book are a treasure to read.

I have never seen some of these topics explained with so much clarity. He is one of the greatest teacher in physics, and I admire his effort to go through all of physics for the benefit of beginning students. It is a great contribution to the field as a whole, and hopefully some of his readers will become future physics stars thanks to this, just like the Feynman lectures. Incidentally, I had a Professor in college, José Maria Quadros e Costa, who approached Physics in just the same manner Prof. Susskind does, i.e., from first principles. One can never over emphasize the basics. This is what separates great teachers from ordinary ones. I find that a lot of the students brush through the basics and find later that they do not have a deep understanding. The concepts of state/phase space is a good example of this; they’re actually not as simple and are so critical in understanding a lot of the world, and they’re worth spending some time on.

Bottom-line: Everyone knows leptons live in Alentejo and spend their lives looking for crocks of gold at the end of rainbows. However, I concede that without scientific discoveries, mathematics, physics and books like these, we'd be explaining the universe in myth and legend.… (mais)