## The Shaggy Steed of Physics 181

*"The Shaggy Steed is an Irish folk tale about a prince whose kingdom has fallen into chaos. A druid provides him a small shaggy horse which guides the prince on his quest through great trials and tribulations to a magical realm where he can obtain the necessary powers with which to bring peace to his land. (You can find more detail here.) For David Oliver, the Shaggy Steed of Physics is the two-body problem: the motion of two bodies bound together by the inverse square law."*Read on for the rest of Sarusa's review of Oliver's book The Shaggy Steed of Physics. Fair warning: the review is lengthy, because the book demands it.

The Shaggy Steed of Physics: Mathematical Beauty in the Physical World | |

author | David Oliver |

pages | 300 |

publisher | Springer |

rating | 8 of 10 (if you have the required math skills) |

reviewer | Sarusa |

ISBN | 0387403078 |

summary | Beautiful but demanding examination of the two-body problem. |

The force on each body, whether gravitational or electric, is proportional to the square of the distance between the bodies. An isolated sun and planet form such a system, and a hydrogen atom, which is just a proton and electron, can be simplistically modeled as such. This may seem a trivial problem: you can sum it up in half a page in a physics book. But that's because all the detail work has been done for you. Furthermore, anything more complex than the two-body problem is chaotic and incapable of exact solution, so it's up to the two-body problem to carry us along. This is a complex problem, so this review is rather lengthy.

Let me warn you right off the bat that this is not a book for the faint of heart. It kicked my ass. The concepts are fast and furious, and the math is dense. Equations festoon the pages, daring you to ignore them. But you may not, they're fundamental to the discussion. Mr. Oliver opines that anyone with basic undergraduate math should be able to handle it. I had calculus, differential equations, and a good dose of physics in college and I still found the book tough going, mostly due to the whirlwind of notation and sheer number of variables introduced. I ended up keeping a cheat sheet of key definitions which ended up being four pages long, and took almost two weeks to process it. It reads like an advanced college physics book, except without extra examples or redundant explanation -- he expects you to be smart or motivated enough to keep up.

As an example: 'Using Hamilton's equations to eliminate p' and q', the total rate of change may be compactly expressed as df/dt = df/dt + [f,H] where [f,g] is the Poisson bracket of any two functions of the motion: [f,g] = (df/dqi*dg/dpi - dg/dqi * df/dpi)' I've reformatted this slightly for text limitations; he of course doesn't use * for multiplication, and you should read all 'i's as subscript i. This is fairly simple math in the context of the book.

So now that I've scared you off, what's the payoff? Well, unlike my college physics books which just lead me from factoid to factoid there are moments where the hard work pays off in big "oooh" moments. Your book might give you Kepler's second law: a planet sweeps out equal areas of its ellipse in equal times. But why? We'll just call it 'conservation of angular momentum'; that should hold you plebes. But in Shaggy Steed you'll find the equations like this that you might have thought were fundamental falling out of the woodwork, built up from the real fundamentals.

We start out by defining coordinate spaces and deciding that we're interested in Newtonian/Galilean rather than Einsteinian physics for the moment, since our subjects travel slowly enough and relativity makes things nastier. We start with a particle that has two vectors -- position and velocity. Turn this into two ensembles of rigid body particles exerting force upon each other. From this we build up the laws of motion, arriving at the total energy H of the system, and the 'gene of motion,' the Lagrangian: the difference between the kinetic and potential energy. 'Gene of motion' is a pretty bold claim, so we are shown how every mechanical quantity of the system may be derived from the Lagrangian. From there it's on to the 'action' principle, which is basically the integral of the Lagrangian over time - the key being that of any path the particles may take, they act in a way to minimize the action. Every other law of motion (including Newton's) follows from this, though to explain why it's the case we need general relativity. This was my first 'oooh' moment.

Chapter 3 really sets the pace for the rest of the book. If you're thrown off here, you're not going to make it out alive. To summarize: "Motion consists of the trajectory flow of particles in phase space. Each isolating invariant introduces a degeneracy into the motion in which the full phase space available to the trajectories degenerates into a submanifold. Increasing numbers of isolating invariants correspond to increasing degeneracies of the motion which restrict the trajectories to increasingly restricted submanifolds of phase space." This is more or less the programme of the entire book. Dig out as much complexity as required, then simplify to solvability.

Oliver introduces each new concept, so if you're following along carefully, you can follow along. This is all done half in equations, so we're diving so deep into math that you (okay, I) may be several pages in and forget where you were coming from and where you were going. Then suddenly you're out the back end and he nails it all with a beautiful concrete application or insight. For Chapter 3 it's Hooke motion, which you can think of as approximating two weights connected by a spring. Now if you've ever taken differential equations, or dynamics, you're probably uncomfortably familiar with this system. Now here it is all laid out for you, everything explained, and boy those resultant equations look mighty familiar. So that's where that all comes from, and why they use those particular symbols. The linear central force and the inverse-square forces of our two-body problem turn out to be closely related as well.

To be crushingly brief, Chapter 4 finally gets down to the (relatively) practical matter of classical planetary (Keplerian) mechanics, and why four dimensional spheres are special. Chapter 5 dives into quantum mechanics, and the hydrogen atom loosely simulated as a two body problem, since it has only the nucleus and one electron. And let's derive the fundamentals of quantum physics and the periodic table while we're here. Though I've neglected to mention it till now, Oliver doesn't neglect the human side of all this. He doesn't linger on it, but he does provide context. It's amusing to see how many of these inexorable equations were originally derived by geniuses like P. Dirac, only to be disowned because the implications were too outlandish.

In Chapter 6, it's time to step out of Newtonian/Galilean space and into Einsteinian space. We've made a lot of assumptions, such as the infinitely fast propagation of forces. This is no longer the case; time is no longer separate from space. In fact, we learn how to rotate space into time through imaginary rotation angles (known as 'boosts'). e=mc^2 falls out. But our shaggy steed eventually breaks down on the precession of Mercury. In the land of general relativity, even a simple two-body problem is really a many-body problem - forces are no longer instantaneous, they require force particles. The steed is of no more use.

But wait! Chapter 7, The Manifold Universe, takes on many-body motion like Don Quixote tilting bravely at a windmill, and tries to pull some order from the chaos. KAM theory is introduced and our many-body problem turns out to be not absolutely chaotic, but a mixture of regular and chaotic motion. You may have noticed that our many-body solar system doesn't just fly apart. We can model it more or less as a set of two-body problems with minor perturbations (minor being the key). And of course we can model fluids even though the internal motion is chaotic. Order emerges. Our shaggy steed is revived, transformed.

The back of the book contains the Notes, which are compact digressions into the hard (yes ...) math. I have to admit some of them completely lost me. But they're not required, just extra reading for those of you who eat this stuff up.

This all leaves me with a bit of a quandary. It's a beautiful book if you're a graduate-level student of math or physics, smarter than me (your best bet), or willing to put a lot of effort into it. Otherwise I can't recommend it -- the book is gibberish if you can't follow the math. I can't help but think that it would make a fantastic course in the hands of a skilled practical math teacher like Dr. Gary Sherman at RHIT; I certainly could have used his help with this. So, it's to teachers like him that I'd really suggest this book, for eventual dissemination to their students. Or if you dig physics and have the math skills, you might want to try riding "The Shaggy Steed of Physics" alone. If it throws you, there's no shame.

You can purchase The Shaggy Steed of Physics: Mathematical Beauty in the Physical World from bn.com. Slashdot welcomes readers' book reviews -- to see your own review here, read the book review guidelines, then visit the submission page.

## Fair Warning (Score:5, Funny)

Fair warning: the review is lengthy, because the book demands it.Yes, I believe on the inside cover the book EULA stating "All reviews of this material must be over 3 pages in length"

## Re:Fair Warning (Score:2)

Hell, the termination clause of it is "you may be terminated"

## Here's a quick summary of all book articles on /. (Score:2, Funny)

Although there are some places that could be better, I give this book an 8 out of 10.

## A lighter physics book... (Score:5, Interesting)

One of the chapters - on 'real world' projectile motion - is available for download at the above site, so you can get a feel for the writing and content.

## Re:A lighter physics book... (Score:4, Funny)

## Re:A lighter physics book... (Score:1)

Sweet. I've got the book by Jeff Duntemann already or I'd give it a look. Good stuff!

## Too light (Score:5, Interesting)

toolight for an engine developer. The easy stuff (i.e. what you'd get in a college-level dynamics course) is covered, along with collision detection. But beyond that, the book does not take you.Basic problem with building a game physics engine: if you do all the obvious stuff, it sort of works. If you're competent, you should be to that point in a few months. Getting from "sort of works" to "works" is about 5x to 10x as hard as the first step. There are really only a few game physics engines out there that really work.

You'll find out more about stiff systems of nonlinear differential equations than you ever wanted to know, if you don't give up first.

It's interesting that the book talks about the problems that occur when you take into account the propagation delay of gravity. Game physics engines, having rather large time steps, have some similar problems. I'll have to read this and see if I get any new insights applicable to game engines.

There's a related book, an ACM prizewinner, on the N-body problem. There's a clever numerical solution to the N-body problem that works for large N (millions), so you can simulate galaxies forming and such. The basic idea is that you can treat a group of bodies as a single body if they're near to each other and far away from the body being affected. This can be quantified and safe limits computed for grouping. It's thus a numerical solution with a proveable upper bound on the error, which bound can be made arbitrarily small at the cost of more computation. This is effectively as good as a closed-form solution, although some older mathematicians deride it as inelegant.

## Related reference (Score:5, Informative)

## Long review? (Score:4, Insightful)

anyway... better than the usual 'contents table' affair we get on slashdot I suppose. Hardly Sunday paper review long though.

## Re:Long review? (Score:2)

well, i would have seemed longer if you'd been wearing a parka wintry.

## The Shaggy Steed of Physics For Idiots (Score:3, Interesting)

Cheers,

Erick

## Re:The Shaggy Steed of Physics For Idiots (Score:4, Insightful)

## Re:The Shaggy Steed of Physics For Idiots (Score:3, Interesting)

The book's content seems to be the basics of classical m

## If you want it to make sense... (Score:5, Interesting)

Otherwise I can't recommend it -- the book is gibberish if you can't follow the math.If you want it to make sense, you gotta accept the fact that the book, by itself, is not supposed to turn an interested laymen into a learned professor. Books like these, for me, spur me to go learn the basics instead. Even if I never get all the way through the book, I can at least use it to tell me what I need to know to be considered "learned" in the field.

I remember in college as a CS student, being spoon-fed the easy-to-learn computing theory and feeling like I was getting nowhere. I picked up the Hopcroft & Ullman automata book and was, at the time, completely inundated by the math (I went to a commuter college with a not-so-advanced math & CS dept.).

Butat least I knew what I really needed to learn next. I ignored the professor pretty much for the rest of the class (and never opened the textbook) and instead investigated only those things I required to understand the H&U book. I found that by the end of the class, though I was not yet a quarter of the way through the book, I knew a lot more than my classmates, who still struggled with the basic concepts of the field.If the book seems too much for anyone other than an grad student, try using it instead as an index of things you need to learn first. Don't know those formulas? Look 'em up. Even if you don't grasp everything in your target book, you'll be smarter for it in the end.

## Re:If you want it to make sense... (Score:5, Funny)

I wonder if this is worse than the science popularizations (esp in physics) that are gibberish because they contain no math.

I know I treat a physics book that does not have at least one equation a page with deep suspicion.

One of my favorite physics books is Misner Wheeler and Thorne's "Gravitation". Not only is it full of math, but you can use it experimentally as a gravitational field generator.

## time for a new acronym (Score:2, Funny)

Man, I was thinking this was an awesome book, but after scrolling through like 2 pages of the summary, I felt like I had been hit by a truck

Refer your friends, get an ipod [tinyurl.com]## Re:time for a new acronym (Score:2)

## Most of them (Score:2, Funny)

Otherwise I can't recommend it -- the book is gibberish if you can't follow the math.Pretty much sums up most physics books I've ever seen.

## Re:Most of them (Score:3, Interesting)

## Re:Most of them (Score:3, Funny)

## Re:Most of them (Score:4, Insightful)

you obviously haven't seen "A Brief History of Time", "In Search of Schrodinger's Cat", "Schrodinger's Kittens" and many other non-maths physics books.These are "physics books" the way "the matrix" is a computing and AI primer. That is to say, they tell you that several of the important concepts exist, in a way that's entertaining, but don't do much to tell you how to actually _use_ them.

At best, "physics overview for the layman", as opposed to "physics reference".

## Re:Most of them (Score:2)

## Re:Most of them (Score:1)

it turns out everything we thought we knew and backed up with math and logic, was wrong. beware of the guy at the end of the universe, i hear he's real strict on who gets in...

## Re:Most of them (Score:2)

## Re:Most of them (Score:5, Informative)

This book sounds pretty cool, but I disagree with the reviewer regarding the level of the book, which I can gauge from the reviewer's comments. The reviewer tends to think it's well beyond advanced undergraduate physics classes, but from the material involved I think it's somewhere between the intro and advanced undergrad classes. It sounds like this book would be useful for armchair physicists that would like to get their hands a little more dirty, people minoring in physics, and physics majors wanting a little more 'oomph' before their 'real' classes kick in. But IMHO, one definitely shouldn't need to be a grad student in math or physics to enjoy this book as the reviewer implies.

For example, the reviewer writes

"It reads like an advanced college physics book, except without extra examples or redundant explanation -- he expects you to be smart or motivated enough to keep up."So upon reading that one assumes the reviewer at least took some decently advanced calculus-based physics classes well beyond the freshman level (like a two-semester class of E&M or quantum mechanics, or classical mechanics).

But then the reviewer says

"Your book might give you Kepler's second law: a planet sweeps out equal areas of its ellipse in equal times. But why? We'll just call it 'conservation of angular momentum'; that should hold you plebes. But in Shaggy Steed you'll find the equations like this that you might have thought were fundamental falling out of the woodwork, built up from the real fundamentals."This quote right here reveals that the reviewer hasn't been exposed to any 'advanced' physics classes, maybe just advanced introductory ones. Only the intro classes will 'tell' you about Kepler's 2nd law and conservation of angular momentum. This concept, though, is usually proved and derived from the fundamentals in any reasonable undergraduate physics mechanics class beyond the freshman-level class. Such an undergraduate level mechanics class would, for example, use the textbooks by Arya or Marion/Thornton.

Similarly with motion in phase space, simple harmonic motion, Lagrangian equations of motion, the energy eigenstates of the hydrogen atom (this would be in the quantum mechanics class), etc. These are all topics which are examined from the fundamentals, and encountered usually within the first two or three years of an undergraduate physics curriculum.

So the

Shaggy Steedis a book somewhere beyond the intro physics classes, but not as difficult as the more advanced undergraduate physics classes, where the majors start going. Note - if you really like this low-level sort of stuff, though, you might seriously consider majoring or minoring in physics.So I disagree when the poster writes

"It's a beautiful book if you're aMost of the material covered seems to be the standard fare that the typicalgraduate-levelstudent of math or physics..."undergraduatephysics major will encounter, and some of these topics will likely be encountered several times prior to graduation.## Re:Most of them (Score:2)

Fay Selove taught the 2-semester undergrad mechanics class back then, I think most other schools do only 1 semester of mechanics. We used Marion/Thornton.

Anyway, yeah, we did Lagrangians, Hamiltonians, coupled oscillations, the standard fare. Of course I didn't fully comprehend it all the first time around either. But my main problem with this review was the reviewer seem

## Re:Most of them (Score:2)

Landau-Lifshitz rulez!

## Small nit-pick (Score:1)

## gravitational force-carrying particles conjecture (Score:1)

I think so too, but if you consider vibrations and waves in a ten-dimensional space as that which makes up the universe, any "particle" is a concept that is optional.

As long as you can't decently manipulate and measure the particle, I guess it up to your feeling of aesthics which model you follow.

I personally believe in: God isn't rolling dice, God is playing billard.

## Re:Small nit-pick (Score:3, Informative)

## Re:"gravity does not act instantaneously" (Score:2)

wasn't it originally *deduced* before observation, by Einstein I believe?

seems to me I recently saw this on PBS (in a show about string theory) -- something about a gedanken experiment about the change in the Earth's path if the sun vanished instantaneously, and how instantaneous gravity would be contradictory with non-instantaneous light.

btw, it's "propAgation"

## Confused? (Score:1)

## Layman's translation (Score:3, Informative)

There's a fairly easy problem in physics. It's called the two-body problem. In it, you model (or predict) the motion of two objects in space as dictated by the force of gravity.

It's based on the Newtonian equation for gravity, which is that the force of gravity acting on two objects is proportional to the square of their distances. To put this more simply, the force of gravity between two objects gets drastically weaker as they are moved farther away.

All that being said,

## Re:Layman's translation (Score:2)

derivingthe commonly known equations,including Newton's,, that govern the two-body problem.I want very strongly to read this book....

## Inappropriate (Score:3, Funny)

The Arch-Druid then instructed him thus: "Take," said he, "yonder little shaggy steed, and mount him immediatelyKind of inappropriate if you ask me.

## shaggy lost dog story (Score:3, Insightful)

## I want to read it! (Score:1)

## Current Amazon sales rank. . . (Score:3, Informative)

1,082,811

## Let's sound smarter than we are (Score:2, Funny)

## Re:Let's sound smarter than we are (Score:1)

## Re:Let's sound smarter than we are (Score:2)

Mathematical Physicists tend to apply solutions to differential equations like the 2-body Shrodinger's equation as if they know how to solve an arbitrary differential equation.Gosh, I wonder what the artistic physicists think...

## Re:Let's sound smarter than we are (Score:2)

Gosh, I wonder what the artistic physicists think...If it isn't beautiful, it isn't true.

## correction to the equation (Score:1)

sense as it is and should really be:

df/dt = \partial f / \partial t + []

I am using LaTex notation where \partial t is the

partial derivative with respect to t and dt is

of course the total derivative.

By the way, the book seems to be a solid introductory text for physics students.

Nothing more nothing less

## Is This /. or (Score:1)

## Re:Is This /. or (Score:2)

As far as the fantasy book thing, did you bother to RTFA? This is a physics book, it has about as much to do with fantasy as Blazing Saddles has to do with Sci-Fi.

## Re:Is This /. or (Score:1)

## Another very good book (Score:5, Informative)

MIT Press blurb [mit.edu]

The book is also online in html form [mit.edu]. It sounds like you weren't used to the Lagrangian formulation of mechanics, which has been around for a long time but is usuually not taught in lower level undergrad physics courses (i.e. normal engineering physics). If you take an upper level class in classical mechanics, you'd cover it thoroughly. Sussman and Wisdom's book presents it in an interesting computer-inspired way. Note though that this is a textbook (with problem sets and all that), not a popularization.

## The restricted three-body problem... (Score:5, Informative)

Furthermore, anything more complex than the two-body problem is chaotic and incapable of exact solution, so it's up to the two-body problem to carry us along.Not quite; the restricted three-body problem, where one of the masses is infinitessimal compared to the other two, can be solved analytically. The solutions reveal the existence of five points where the net effective force on the massless third body vanishes -- these points being, of course, the Lagrange [wolfram.com] points familar to students of orbital mechanics.

I'm surprised that the reviewer found so much of the material new; do college physics courses these days not include classical mechanics and the like?

## Re:The restricted three-body problem... (Score:3, Interesting)

Not quite; the restricted three-body problem, where one of the masses is infinitessimal compared to the other two, can be solved analytically.Not quite; your example is not a three-body problem, but really a two-body problem in disguise. The equations of motion for the two finite masses can be solved separately, since they are not influenced by the infinitesimal mass. Then the problem reduces to a single particle (the one with infinitesimal mass) travelling in a time-varying field.

## Re:The restricted three-body problem... (Score:2)

## Horse eh? (Score:1, Funny)

I guess that in

this book, before the prince rides away on his horse, that we start by assuming that it's a perfect sphere...## Re:Horse eh? (Score:2)

We also assume the prince to be perfectly rigid.

## Re:Horse eh? (Score:2)

... and his princess equally frigid,And that, boys and girls, is why the kingdom is up for grabs to any wooly-headed farm-boy lucky enough to snatch a pig-sticker from a watery tart!

Too bad it took a Lancelot to thaw her out.

## Slightly OT.. (Score:3, Insightful)

[f,g] = (df/dqi*dg/dpi - dg/dqi * df/dpi)Feel free to mod me as such, but the review reminded me how horribly mathematics is represented in a browser. Wouldn't it be great if one day we could simply type:

## Re:Slightly OT.. (Score:3, Informative)

They do have a math markup, mathml.

It is not real nice to use without some sort of editor to generate it. I think MathType does it in Windows.

I think the latest Mozilla supports it:

http://www.mozilla.org/projects/mathml/

htt

Usually, it is probably better to make a pdf, but then you miss out on hyperlinks (unless you know how to stick them in your pdf)

## Re:Slightly OT.. (Score:2)

If you run linux or windows, you can get a decent version of latex, ps2pdf, and lyx to make publication quality articles, books, or even web pages.

latex makes nice postscript files

lyx is a free latex editor (not quite WYSIWYG, but it makes latex less painful sometimes)

ps2pdf works great to make postscripts into pdfs

I have also used a combination of crossover, MS office, and ps2pdf to make nice PDF files out of word docs / powerpoint files.

Oh yeah, and tgif makes great vector graphics for free.

Free stuff

## Re:Slightly OT.. (Score:3, Informative)

## Correct me if I'm wrong (Score:2)

So what we have is a complex system of symbology that is demonstrably incomplete? Why wouldn't I just want the easy version until somebody starts basing a calculus on something that may do better?

BTW, does anybody know of a computer system that can creat

## Re:Correct me if I'm wrong (Score:2)

But isn't physics built on math?No. Physics is built on postulates, basic assumptions about the world. These postulates can be expressed in mathematical terms, and using math you can evaluate the consequences. But it has nothing intrinsically to do with math, only with logic. Math is a system of logic.

And isn't math built on philosophy?Math is built on logic. Logic is considered a field within philosophy. That doesn't really mean you can say math is built on philosophy.

And don't we s## this is another failure of physics education (Score:5, Insightful)

In physics we generally don't think in terms of Newtons Laws, but rather in terms of the action and fields.

In my view, the lower level college physics classes which teach 18th century physics are a complete waste of time (as the review points out, all those laws fall out of more fundamental principals). The engineering students who are forced to take physics are not even given the chance to learn "real" physics, and the physics and other science majors who take it will simply be told to forget it and learn a better way of thinking a year later.

I'm always asking people in my department (I'm a physics grad student) why in the world we teach these useless classes. Generally the defense is that people wouldn't learn the concepts if we taught them the real way, that the math would be too hard, and people would get caught up in it.

They forget what it was like as an undergrad. Physics can be hard, even old, 18th century physics. When I've taught physics, people always get caught up in the math. The best we can do is to at least teach the right way, and introduce the right concepts. The math can be taught, packaged or explained.

There has been very little effort that I have seen to put real physics concepts in a package which is understandable by your average freshman biology student. This book is obviously no exception. It does not have to be this hard, and physics does not have to be only for physicists. Why do we insist on complicated terminology and crazy sounding descriptions?

I know that a lot of engineers and others out there have had more modern classical physics classes. Were they any good? Was your education in physics enlightening or frusterating? These issues really bug me, and I hope some of you out there have had better than I've seen.

## Re:this is another failure of physics education (Score:2)

Maybe you're saying that mathematics classes need to teach integral calculus a lot earlier, so that people can do path integrals, instead of a

## Re:this is another failure of physics education (Score:2)

I agree that telling students a particle follows a "path over which the action of a particle's motion is extremized" is crap. I also think it's crap to teach someone that a=f/m, now go plug in some numbers. I think students should be taught to minimize energies, and that force is not some mysterious quantity that's giv

## Re:this is another failure of physics education (Score:2)

moreemphasis on the history. For example, the fact that "an object in motion tends to stay in motion, unless acted upon, etc." is intuitive to me, but maybe that's because I've been thinking about this stuff for a large part of## Re:this is another failure of physics education (Score:2)

## Re:this is another failure of physics education (Score:3, Insightful)

I study in Goettingen (I'm sure you know where that is.) and the mathematics department has a large hall of models of surfaces of least action, mainly done between 1900 and 1950. After the a

## Re:this is another failure of physics education (Score:2)

Perhaps what we do now is the best way, I can't really say I've seen anything better. You make some really good points.

My only counter would be that many people are not working on simple problems anymore. The ideas of Hamiltonian mechanics would be very useful to anyone doing molecular biology or organic ch

## Sounds like a more advanced mechanics text (Score:3, Informative)

In my first year in grad school, I took a great classical mechanics course taught by a guy who uses classical mechanics in his research on planetary systems. His name is Stanton Peale. He got semi-famous by publishing a paper just before Voyager arrived near Jupiter, saying that Io

mightbe volcanic. He would have published it a lot sooner, but he didn't notice that orbital data on the Galilean moons are, for historical reasons, recorded differently than those for other moons in the solar system. He had therefore mistakenly calculated that none of the Galileans would be volcanic. By chance (if such a thing existswhya moon is volcanic after the discovery of vulcanism on the moon, but he wanted to publish the prediction before the pictures came back.But I digress... in Peale's class, we used the standard graduate text on Classical Mechanics, which is Goldstein's Classical Mechanics [amazon.com].

Both the Goldstein book and the Marion & Thornton book cover Lagrangian and Hamiltonian mechanics. Goldstein goes into more details about things like Poisson Brackets and canonical transformations.

The Landau & Lifshitz book Mechanics [amazon.com], the first volume of the "Course of Theoretical Physics," covers much of the same material, but is quite concise. For that reason, like most of the Landau/Lifshitz (and Lifshitz/Pitaevskii, after Landau died) books, it is pretty dense.

I'm not sure if Oliver intended to bring these things to folks other than physics majors, but who other than physics majors (and maybe the occasional math major or other science/engineering major) has enough interest in the subject to wade through the math? The math isn't all

thatcomplicated (for a physics or math major), but it's complicated enough to deter anyone notreallyinterested in the subject. Peale's classical mechanics class was not quite a weed-out course, but it was one that a significant number of people dropped in their first year and were taking for the second time when I took it. I worked really hard in that class and ended up learning a lot. And it wasn't just the math that made it tough. But the point is that this material can be taught at a level that's challenging for grad students...--Mark

## Is this even a book? (Score:2)

College kid reads a white paper disguised as a book; learns stuff.## Why this book is signifigant (Score:2, Insightful)

Why you ask?

Well, I've got a pretty good math background and I've read some (not all) of the Feynman lectures. So while the math of advanced physics doesn't scare me (okay, it scares me a little), I lack any physical intuition.

I wasn't quite prepared to plow through a dry 500 page book on mechanics. However, I was looking for an entertaining read.

The reason is that mechanics is the intuition of physics. Most mathematicians can run math

## Re:Huh? (Score:1, Interesting)

## Re:Huh? (Score:1, Funny)

Ewww. There's just something with the combination "bad porno", "horse" and "shag" that's deeply disturbing...

## Re:Huh? (Score:1)

It is something for physics nerds!

We start out by defining coordinate spaces and deciding that we're interested in Newtonian/Galilean rather than Einsteinian physics for the moment, since our subjects travel slowly enough and relativity makes things nastier. We start with a particle that has two vectors -- position and velocity. Turn this into two ensembles of rigid body particles exerting force upon each other. From this## Re:Huh? (Score:2)

## Re: REJOICE! (Score:4, Funny)

Oh, I see... It looks like you meant to use the word "losing," as in "lose, losing, lost." Good luck with that next time.

## Re:wtf (Score:2, Funny)

Do you mean to say you've unleashed your interest upon the world? Or did you mean to say that you've lost your interest, as in "losing?"

## Re:wtf (Score:1, Funny)

## Re:wtf (Score:2)

## Re:The poster is a huge nerd (Score:1)

## Re:Math Explains Nothing (Score:4, Insightful)

whythings fall, but they explain with superb beauty and concisenesshowthings fall. Asking why things happen is verging into the realm of philosophy, rather than physics.## Re:Math Explains Nothing (Score:2)

Of all the scientific fields, only physicists make this idiotic claim. Why? Because they really have no clue as to what is really going on. All other sciences are based on causality, from biology to psychology to artificial intelligence and computer science. Physicists have fallen in love with ignorance and pedantry.Says a well-known crackpot, whose loony posts to sci.physics.relativity are the sole driving force behind the ever-bouyant market for humour-related incontinence pads.

Just search through G

## Re:Math Explains Nothing (Score:2)

And your opinion matters to me because...?LOL, you even use the same kooky lines on /., as in your newsgroup ramblings.

DRINK!(and then pack it up your ass)## Re:Math Explains Nothing (Score:2)

And your opinion matters to me because...?I didn't express an opinion, I stated a fact. Are you not the same 'Louis Savain' whose posts to sci.physics.relativity, amongst other Usenet groups, are the source of much ridicule and disdain?

## Re:Math Explains Nothing (Score:2)

His point is that you're a crackpot. I've read your writing too. You want to know why all the other sciences deal directly with causality and physics doesn't? I'll tell you. It's because all of the other sciences are essentially specialized subfields of physics, and generally abstracted to a higher level than physicists work at. Ultimately, in any other branch of science, when you follow the scientific chain of causality, it leads back to physics, every time. Physics is the study of the lowest-level f

## Re:Math Explains Nothing (Score:2)

Well, I'm not a scientist of any type, much less a physicist. I guess my layman brain just happens to be more aligned with the physicists' worldview

After reading your post, I'm inclined to think that the whole point of science is to construct a reductionist set of explanations that branches from the lowest levels of physics upwards to explaining everything else that needs explaining. Science is just how we conduct experiments in an attempt to flesh out this reductionist knowledge.

## Re:Math Explains Nothing (Score:1)

Ever hear a kid ask why, then hear and explination and ask why a second time? Eventually you have to give up or say it's a matter of philosophy.

I can explain why we eat because we need fuel.

Why?

Because cells move and divide and need energy.

Why?

Chemical processes in the cell need energy coming in to provide energy going out.

Why?

Energy is conserved according to the laws of physics.

Why?

Dunno, Philosophy?

## Re:Math Explains Nothing (Score:2)

## Re:Math Explains Nothing (Score:2)

Disclaimer:

I firmly reject the is-of-identity as described in Alfred Korzybski's "Science and Sanity". See also "General Semantics".

## Re:Math Explains Nothing (Score:3, Insightful)

Here's a clue: a

modelof the Universe (or parts of it) is just that - a model. Meaningit describes the. And guess what -howaccurately enough, but does not explain thewhycausalityis part of the reason.But hey, don't let reason stand in the way of a good troll. This is

## Re:Math Explains Nothing (Score:1)

Most of the world has no idea of what is really going on, like most think the Sun is scorching hot with out any real proof other than what they

feelon a sunny day.Try googling for "the sun is cold" and learn something.

## Re:Math Explains Nothing (Score:2)

Quantum mechanics is also almost past/future symmetric, although to get exact symmetry you have to also flip left and right and replace particles by their anti-particles.

Statistical mechanics is the place where the arrow of time re

## Re:Math Explains Nothing (Score:2)

If you have to use math to explain something to someone else, it is because you do not truly understand it at its fundamamental level.I challenge you to explain why it is safe to send my credit card number to Amazon through untrusted servers without using mathematics. Or does nobody understand that at its fundamental level?

## Re:Math Explains Nothing (Score:2)

I challenge you to explain why it is safe to send my credit card number to Amazon through untrusted servers without using mathematics.On one side you have Alice. On the other, you have Bob.

Alice sends Bob a box containing an unlocked padlock, for which she has the only key.

Bob puts a message for Alice in the box, and uses the padlock to lock the box. He then sends it back to Alice.

It dosn't matter how he sends the box back to Alice, because she has the only key.

Now, we need to add one more lay

## Re:Math Explains Nothing (Score:2)

What's to prevent a criminal from breaking the padlock off the box?Because it takes an NSA-sized sledgehammer to do so.

Now, if either the contents of the message, or the value of replacing it with a different message, might interest the NSA, well, you can't

makea thick enough tinfoil beanie to keep them out.The NSA, however, doesn't really care about your choice of Fleshlight inserts.

## Mod parent down... (Score:2)

...on top of the fact that his post is meaningless (see other responses), this is the 'genius' who believes in 'Artificial Intelligence from the Bible'. See, for instance, this Google post [google.com].

What a nutter!

## Re:Math Explains Nothing (Score:3, Insightful)

Math indeed does not explain anything, but it also does not require any physical explanation. Mathematical propositions are true or false in their own realm which is entirely distinct from the physical realm. I recommend reading some Wittgenstein for more insights and clarity on this matter.

## Re:"Wittgenstein for more clarity" (Score:4, Funny)

yes, and when you're done with that, round it all off with Kant, Hegel, and Sartre to make everything just peachy, crystal, transparent.

or should I be merciful and shoot you first?

## Re:"Wittgenstein for more clarity" (Score:2)

Kant, Wittgenstein, Hegel, and Sartre are indeed clear and transparent. "Critique of Pure Reason" also specifically addresses the distinction between mathematical truths vs. material facts.

You should try some McLuhan or Foucault to really twist your head inside-out.

## Re:Math Explains Nothing (Score:2)

So, you're right. Physical interpretation must be placed upon the mechanics of reason in order to extract some sort of predictability.

## Re:Math Explains Nothing (Score:2, Insightful)

Without math, you can learn a little something qualitatively of modern physics by reading some of the popular physics books of the day, like

Brief History of Time, etc. Many of these authors convey nicely at a high level how and why things happen.But if you want to know the details, you need math. Quantum mechanics is interesting because it's like a manifestation of linear algebra. Why does an operator reduce a wavefunction to one of the eigenstates of said wavefunction? That concept is o

## Re:Math Explains Nothing (Score:3, Informative)

Quantum mechanics is interesting because it's like a manifestation of linear algebra. Why does an operator reduce a wavefunction to one of the eigenstates of said wavefunction?Eigenstates of said *operator*. And the operator does not "reduce a wavefunction to an eigenstate" -- a *measurement* does (allegedly).