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The Shaggy Steed of Physics

timothy posted more than 10 years ago | from the smarty-jones-is-dumb dept.

Science 181

Sarusa writes "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 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.

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FUCKING NERDS - GET A DATE AND A LIFE (-1, Troll)

Anonymous Coward | more than 10 years ago | (#10250296)

Stop reading this shit, your not a 20th level mage with 25 charisma!

Re:FUCKING NERDS - GET A DATE AND A LIFE (-1, Offtopic)

MarsDefenseMinister (738128) | more than 10 years ago | (#10250326)

You know NOTHING of D&D, obviously. Now roll your D12, save vs. moderators.

Re:FUCKING NERDS - GET A DATE AND A LIFE (-1, Troll)

mobby_6kl (668092) | more than 10 years ago | (#10250346)

>Stop reading this shit, your not a 20th level mage with 25 charisma!

Yeah I'm not a 20th level mage with 25 charisma. That's why I'm reading this shit.

FP (-1, Offtopic)

Anonymous Coward | more than 10 years ago | (#10250297)

Once again!

-DT

fp for mercatur's return (-1, Offtopic)

Anonymous Coward | more than 10 years ago | (#10250302)

Praise be!

fp (-1, Offtopic)

Anonymous Coward | more than 10 years ago | (#10250310)

fristy pist for mercatur.net

First post! (-1, Offtopic)

Anonymous Coward | more than 10 years ago | (#10250311)

Shagadelic!

Huh? (-1)

Anonymous Coward | more than 10 years ago | (#10250312)

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

I just stopped reading right there. What does this have to do with news for nerds?

Re:Huh? (1, Interesting)

Anonymous Coward | more than 10 years ago | (#10250338)

I know, it sounds like the beginnings of a bad porno.

Re:Huh? (1, Funny)

Anonymous Coward | more than 10 years ago | (#10250689)

I know, it sounds like the beginnings of a bad porno.

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

Re:Huh? (1)

Gentlewhisper (759800) | more than 10 years ago | (#10250502)

"I just stopped reading right there. What does this have to do with news for nerds?"

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 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...

Re:Huh? (1)

gcaseye6677 (694805) | more than 10 years ago | (#10250851)

This book is too nerdy even for nerds. I'm sure I'm not the only one who doesn't want to work post-graduate-level mathematics just to read a folk tale.

Fair Warning (5, Funny)

D3 (31029) | more than 10 years ago | (#10250318)

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"

Whoever wins, YOU LOSE. (0, Offtopic)

Fecal Troll Matter (445929) | more than 10 years ago | (#10250561)

"Knowing what I know today, we still would have gone on into Iraq."

-George Dubya

Aug 02 04

"Yes, I would have voted for the authority. I believe it was the right authority for a president to have."

-John Kerry

Aug 10 04

Never forget..

1,000+ and counting U.S. troops dead in Iraq.

10,000+ and counting Iraqi civilians dead in Iraq.

0 Weapons of mass destruction found in Iraq.

0 Democratic governments running in Iraq.

Magic you say? (1)

zippo01 (688802) | more than 10 years ago | (#10250322)

I tap a forest and 2 plains, and couter The druids "my little pony" spell...

wtf (-1, Redundant)

phyl0x (656298) | more than 10 years ago | (#10250324)

jesus, i didnt even get through the review without loosing all interest...

Re: REJOICE! (4, Funny)

lukewarmfusion (726141) | more than 10 years ago | (#10250360)

Huzzah! Interest has been loosed upon the internet by phyl0x, the great emancipator. No longer shall interest be bound and forced to live and work as a slave to...well...ummm....

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

Re:wtf (2, Funny)

Anonymous Coward | more than 10 years ago | (#10250380)

without
loosing all interest...

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 (1, Funny)

Anonymous Coward | more than 10 years ago | (#10250573)

i'd like to be the third person to tell you that you used the wrong word. maybe this massive humiliation will help you remember?

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

Anonymous Coward | more than 10 years ago | (#10250330)

SPOILER! Scroll down to read below.





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

A lighter physics book... (4, Interesting)

tcopeland (32225) | more than 10 years ago | (#10250334)

...is O'Reilly's Physics for Game Developers [oreilly.com] .

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... (4, Funny)

johnnyb (4816) | more than 10 years ago | (#10250392)

I thought game developers got to make up their own physics :)

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

tcopeland (32225) | more than 10 years ago | (#10250464)

> [link to Programming from the Ground Up]

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

Too light (5, Interesting)

Animats (122034) | more than 10 years ago | (#10250655)

Speaking as the author of a physics engine for animation [animats.com] , "Physics for Game Developers" is a bit too light 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.

Re:Too light (1)

ben_place (710556) | more than 10 years ago | (#10251198)

There's a related book, an ACM prizewinner, on the N-body problem.
Don't tell us the prizewinning book's name or anything, because then we might read it.

But seriously, what is it?

Re:A lighter physics book... (0)

Anonymous Coward | more than 10 years ago | (#10251003)

why should i read a book from rightwing nutjob.

Long review? (3, Insightful)

tinla (120858) | more than 10 years ago | (#10250340)

Maybe I'm in a minority of 1, but that review didn't seem very long to me. Sure its longer than a jacket summery... but it hardly does as far enough to be in-depth let alone deserve a warning.

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

Re:Long review? (0)

Anonymous Coward | more than 10 years ago | (#10250356)

Maybe I'm in a minority of 1, but that review didn't seem ver

Jeez! Enough with the War & Peace recital! You're sending me to sleep here!

Re:Long review? (1)

nusratt (751548) | more than 10 years ago | (#10251331)

"didn't seem very long to me. Sure its longer than a jacket summery..."

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

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

erick99 (743982) | more than 10 years ago | (#10250354)

For folks like myself who would like to know more about what the book covers, but is not going to spend several weeks working through the math and learning math. Perhaps the content goes beyond what can be known without doing the math, I don't know. Hell, how could I?

Cheers,

Erick

Re:The Shaggy Steed of Physics For Idiots (3, Insightful)

AuMatar (183847) | more than 10 years ago | (#10250473)

Are you looking to learn physics or understand physics? You can have Kepler's laws explained to you in a page or two, and learn enough to use them in basic ways. TO understand physics, you need to do the math. If you don't, you can memorize a bunch of equations but you'll never understand where those equations come from.

The poster is a huge nerd (0, Flamebait)

atrizzah (532135) | more than 10 years ago | (#10250364)

But that's OK I guess. Sounds like a good book, albeit way over my head

Re:The poster is a huge nerd (1)

ircubic (813042) | more than 10 years ago | (#10250384)

Oh my, how unbelievably rare to find a nerd on a site that has "News for Nerds" in it's logo...

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

halivar (535827) | more than 10 years ago | (#10250365)

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.). But at 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... (4, Funny)

Tired and Emotional (750842) | more than 10 years ago | (#10250517)

> Otherwise I can't recommend it -- the book is gibberish if you can't follow the math.

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 (3, Funny)

hackronym0 (812439) | more than 10 years ago | (#10250373)

RTFS - Read The Frelling Summary

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 (1)

bandy (99800) | more than 10 years ago | (#10250496)

PDWD - Packed Deep With Dren

Re:time for a new acronym (1)

Nykon (304003) | more than 10 years ago | (#10251086)

This book is rated M++
For too much math :)

Most of them (2, Funny)

MikeMacK (788889) | more than 10 years ago | (#10250375)

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 (2, Interesting)

rokzy (687636) | more than 10 years ago | (#10250410)

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.

Re:Most of them (2, Funny)

MikeMacK (788889) | more than 10 years ago | (#10250456)

I've heard of them, unfortuneately my professors obviously haven't.

Re:Most of them (3, Insightful)

Christopher Thomas (11717) | more than 10 years ago | (#10250498)

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 (1)

sxtxixtxcxh (757736) | more than 10 years ago | (#10250420)

i read this one... true to the form of physics books, there was an unexpected plot twist at the end.

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 (1)

Marxist Hacker 42 (638312) | more than 10 years ago | (#10250461)

I thought it was really easy to get into Milliways. And then all sorts of neat stuff happens- the cow comes by and asks what steak it can donate for your dinner, and later on the universe will be ending for your entertainment.

Re:Most of them (4, Informative)

wass (72082) | more than 10 years ago | (#10251227)

The reviewer raves about this book (despite not recommending it at the end), but IMHO misjudges the level or prerequisites of the reader that this book might interest. I'm a graduate physics student who didn't read this book (actually I never heard of it until now), but I'd like to throw in some comments that differ from those of the reviewer.

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 Steed is 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 a graduate-level student of math or physics..." Most of the material covered seems to be the standard fare that the typical undergraduate physics major will encounter, and some of these topics will likely be encountered several times prior to graduation.

Small nit-pick (1)

Seydlitz (690174) | more than 10 years ago | (#10250395)

Perhaps I'm behind the times, but aren't gravitational force-carrying particles simply conjecture at this point in time? Yes, they're logical and fit nicely into our understanding of the three [four] fundamental forces, but they aren't scientific fact yet by any means of the term - perhaps at most a theory that makes sense, but we've found impossible to test. But like I said, maybe I'm just behind the times.

gravitational force-carrying particles conjecture (1)

RedLaggedTeut (216304) | more than 10 years ago | (#10250686)

Seydlitz says:
Perhaps I'm behind the times, but aren't gravitational force-carrying particles simply conjecture at this point in time?
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. Peter Schaefer

So no attractive particles for me, if feasible, although you could make up one if it makes calculations easier :-)

Re:Small nit-pick (3, Informative)

Chuckstar (799005) | more than 10 years ago | (#10250817)

Gravitons (the gravitational force carrying particles) are still very much hypothetical. They are postulated merely because all other forces seem to have a particle that carries them. Certain quantum theories of gravity require them, but no one has a really good quantum theory of gravity yet anyway. However, the fact that gravity does not act instantaneously has been observed. So there does need to be some way to propogate gravity from one location to another. There does need to be some type of wave, particle, or both transmitting gravitational information at the speed of light (or very close to that speed).

Confused? (1)

AcidFnTonic (791034) | more than 10 years ago | (#10250403)

Anyone here care to explain to someone not yet finished with higher level maths.....?

Layman's translation (3, Informative)

Dhaos (697924) | more than 10 years ago | (#10250677)

Ok, a little layman summary:

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, the main thrust of the book is apparently related to the three-or-more body problem. In it, the same basic equation is used. But since every body is being influenced by every other body, which are in turn being influenced by every other body, it gets very messy. Well-nigh uncalculateable, at least by people. The calculus just becomes too complex.

Fortunately, the two-body problem establishes a good enough model, allowing for us to model the motion of planets in our solar system, so long as we take into account that there's some wobble we have to throw in.

Now, I know this didn't explicitly cover the math, but basically, the book takes all of what I just said and builds it up from very basic to very complex mathematics.

Or thats my understanding, anyway.

Re:Layman's translation (1)

rpresser (610529) | more than 10 years ago | (#10250756)

You neglected the important fact, made strongly in the review, that the first half of the book is devoted to deriving the commonly known equations, including Newton's,, that govern the two-body problem.

I want very strongly to read this book....

Re:Layman's translation (0)

Anonymous Coward | more than 10 years ago | (#10251000)

I pressume that he derives a mathematical formalism called analytical mechanics. This formalism is mathematically equivalent to Newtons law.

Inappropriate (3, Funny)

MikeMacK (788889) | more than 10 years ago | (#10250442)

The Arch-Druid then instructed him thus: "Take," said he, "yonder little shaggy steed, and mount him immediately

Kind of inappropriate if you ask me.

Re:Inappropriate (0)

Anonymous Coward | more than 10 years ago | (#10251034)

and then the hero replied pray sir wont it be appropriate to put it in vfstab.

shaggy lost dog story (2, Insightful)

Doc Ruby (173196) | more than 10 years ago | (#10250453)

I glean from the review that the book is a detailed examination of the two-body model for object interactions, from femtoscopic to macroscopic, in the original, untranslated mathematical language. But what has all that got to do with a small, shaggy horse? I can guess from the Slashdot summary that the model is like the small Irish steed, guiding its rider to exciting, unknown places. But does that mean that the long review isn't as relevant to a synopsis as the Slashdot summary, and that the first line of this post is the capsule review proclaimed impossible by the reviewer?

I want to read it! (1)

DonDiablo (158580) | more than 10 years ago | (#10250493)

Ohh, I am salivating already! Thanks for the reference!!!

Current Amazon sales rank. . . (3, Informative)

Sialagogue (246874) | more than 10 years ago | (#10250500)


1,082,811

Math Explains Nothing (0, Troll)

Louis Savain (65843) | more than 10 years ago | (#10250507)

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.

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. Math does not explain anything. On the contrary, it is the math that cries for a physical explanation.

As an example, neither Newtonian's inverse square law nor Einstein's GR equations explain why things fall. They just describe the motion of massive bodies with respect to one another.

Re:Math Explains Nothing (3, Insightful)

stevelinton (4044) | more than 10 years ago | (#10250540)

The don't explain why things fall, but they explain with superb beauty and conciseness how things fall. Asking why things happen is verging into the realm of philosophy, rather than physics.

Re:Math Explains Nothing (-1, Troll)

Louis Savain (65843) | more than 10 years ago | (#10250593)

Asking why things happen is verging into the realm of philosophy, rather than physics.

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.

Re:Math Explains Nothing (1)

Aardpig (622459) | more than 10 years ago | (#10250696)

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 Google Newsgroups for "Louis Savain"; you're sure to get a taste of his clever fusion between conspiracy theory and moronic pseudoscience!

Re:Math Explains Nothing (-1, Offtopic)

Louis Savain (65843) | more than 10 years ago | (#10250861)

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.

And your opinion matters to me because...?

Re:Math Explains Nothing (1)

Aardpig (622459) | more than 10 years ago | (#10250972)

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 (1)

Aardpig (622459) | more than 10 years ago | (#10250995)

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 (0, Offtopic)

Louis Savain (65843) | more than 10 years ago | (#10251076)

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?

And your point is...?

Re:Math Explains Nothing (1)

photon317 (208409) | more than 10 years ago | (#10251281)


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 functioning of the reality we live in, whatever it is. You can only ask for a causal Why at the lowest layers of current physics (at any given time) for two reasons - either as a philosophical side-track that has little to do with furthering physics, or to prompt the unpeeling of another layer in the physics onion (Why do protons and neutrons and electrons behave as they do? Aha, it's those damn quarks, we've unravelled another onion layer, yay for physics, and so forth). Eventually we'll reach the very bottom, if one exists.

Re:Math Explains Nothing (1)

feyhunde (700477) | more than 10 years ago | (#10250699)

It's where you draw the line.

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 (1)

cens0r (655208) | more than 10 years ago | (#10250705)

Do you really think biologists and psychologysts have any idea of what's going on? They have no idea why animal brains work the way they do. They just treat things they don't understand as a black box to be ignored. All biology is really just chemistry, and all chemistry is just physics.

Re:Math Explains Nothing (2, Insightful)

Too Much Noise (755847) | more than 10 years ago | (#10250732)

Physics is based on causality also - at several levels, too. Who'd have thought!

Here's a clue: a model of the Universe (or parts of it) is just that - a model. Meaning it describes the howaccurately enough, but does not explain the why . And guess what - causality is part of the reason.

But hey, don't let reason stand in the way of a good troll. This is /. after all.

Re:Math Explains Nothing (1)

RobiOne (226066) | more than 10 years ago | (#10250945)

Math really does not explain much. It only serves as a tool to express ones observations and presumptions.

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

Re:Math Explains Nothing (1)

strook (634807) | more than 10 years ago | (#10250890)

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 (1)

pla (258480) | more than 10 years ago | (#10251009)

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 layer to this, since Charles might have intercepted the box from Alice, replaced her lock with his own, send the box on to Bob, intercepted it on the return, and replaced his own lock with Alice's. They call this the "Man in the Middle" attack.

The solution? A fourth party, Diane, sells pre-locked box-and-key pairs, and can "certify" that a given key belongs to a given lock which belongs to a given box. Thus, Bob can make sure the lock and box both came from Alice, and can Alice can know that she gets back the same box (in case Charles smashed the original box open and managed to use an entirely new box with the same lock).


Satisfied?

Re:Math Explains Nothing (1)

Stalyn (662) | more than 10 years ago | (#10250994)

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.

No Math is probably the only language expressive enough to somewhat communicate all those beautiful visual images I can create in my head.

Mod parent down... (1)

Aardpig (622459) | more than 10 years ago | (#10251042)

...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 (2, Insightful)

Tungbo (183321) | more than 10 years ago | (#10251049)

"Math does not explain anything. On the contrary, it is the math that cries for a physical explanation."

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:Math Explains Nothing (1, Insightful)

wass (72082) | more than 10 years ago | (#10251350)

Yes and no.

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 one of the most central concepts to quantum mechanics, yet you wouldn't understand what eigenstates or wavefunctions are without some knowledge of math. If you explain it using only words, you're still beating around the bush, and basically it's the math that you would be describing.

Finally, to prove your example is crap, please explain using words why things fall. If your description involves anything about gravitons or Higgs bosons, please explain why they form, why gravitons should be spin-2, what a spin-2 boson field implies, etc, without using math. Basic answer - you cannot.

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

andy314159pi (787550) | more than 10 years ago | (#10250523)

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. This type of posturing is probably the kind that you see in this book. The problem being described is actually found in just about every undergraduate modern physics textbook and every physical chemistry textbook. The way mathematical physics is delivered to an audience usually sends them as far away from the subject as possible. It is really possible for somebody to write the "kinder, gentler" textbook of mathematical physics. The subject is a pain in the ass, but not as much a pain in the ass as those who teach and practice it.

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

feyhunde (700477) | more than 10 years ago | (#10250603)

Not all. I had a physics prof who was married to a math prof. They both have their own research areas that scare the heck outta me with the math, but know how to tone it down to undergrads. My undergraduate courses got overhauled and replaced by a new pilot program that breaks the work up into problem types. This makes mathmatical physics much easier to deal with then subject area. Rather than skipping to the hardest parts 'cause you gotta finish mechanics before em' you go in a much more sensible manor. We had an entire course on wave motion, going from a string to a spring to em waves in coax to hydrogen atoms. It makes is much easier to understand when you can always point back a few steps with a clear every day example.

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

deglr6328 (150198) | more than 10 years ago | (#10250768)

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 (1)

N7DR (536428) | more than 10 years ago | (#10251062)

Gosh, I wonder what the artistic physicists think...

If it isn't beautiful, it isn't true.

correction to the equation (1)

coast99 (782648) | more than 10 years ago | (#10250539)

The exemplary equation does not make much
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 (1)

phobos13013 (813040) | more than 10 years ago | (#10250579)

Im really surprised at some of these responses... i would really have expected most of you folks out there to be able to understand the chain rule and poisson notation. Granted its a little lame to be in a fantasy book, but sounds pretty interesting and a good quality review. Thats my two bits.

Re:Is This /. or (1)

MustardMan (52102) | more than 10 years ago | (#10250724)

Chain rule I can see. Poisson brackets are not exactly common in the IT/CS crowd that tends to be drawn to /.

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 (1)

phobos13013 (813040) | more than 10 years ago | (#10250803)

ok, i didnt rtfa till after i posted but still even if it is a textbook (the price shoulda gave it away...) the review didnt give hint to this fact. Only following the bnr link did i get it. Anyway, i wasnt going to read it either way.

Re:Is This /. or (0)

Anonymous Coward | more than 10 years ago | (#10250979)

The real problem is that the reviewer has only read one book one analytical mechanics, so he cannot compare with oither books on the same subject. He has written a review that would fit any book on analytical mechanics. The only news is that the book also includes a chapter about symmetry, and relates to quantum mechanics.

Re:Is This /. or (0)

Anonymous Coward | more than 10 years ago | (#10251038)

Obviously you haven't read the responses to the stories about nano-tech :)

Another very good book (5, Informative)

phr1 (211689) | more than 10 years ago | (#10250594)

Structure and Interpretation of Classical Mechanics, by Gerald Jay Sussman and Jack Wisdom:

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.

What he really means about the math (0)

Anonymous Coward | more than 10 years ago | (#10250624)

Mr. Oliver opines that anyone with basic undergraduate math should be able to handle it.

What this really means is that the book is an entire treatise in the failure of the American educational system to produce people who know these things.

I took 3 semesters of calculus, DiffEq (twice), and Discrete Math, and another class that mostly consisted of proving things which I condidered more of a logic class but was in the math department anyway, and I don't recognize most of the things in the review. Poisson brackets? Hooke motion?

Re:What he really means about the math (0)

Anonymous Coward | more than 10 years ago | (#10250897)

Pressumably you studied math and this is a physics book :)

Anyway here is a link for you: http://mathworld.wolfram.com/PoissonBracket.html

The restricted three-body problem... (4, Informative)

Aardpig (622459) | more than 10 years ago | (#10250639)

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... (0)

Anonymous Coward | more than 10 years ago | (#10251101)

My astrodynamics professor as an undergrad told those of us in class that if we could solve the unrestricted three-body problem, he would put us in for a PhD.

Re:The restricted three-body problem... (2, Interesting)

kavau (554682) | more than 10 years ago | (#10251386)

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.

Horse eh? (1, Funny)

Anonymous Coward | more than 10 years ago | (#10250645)

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.

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? (1)

kahei (466208) | more than 10 years ago | (#10250869)

...of uniform density.

We also assume the prince to be perfectly rigid.

Slightly OT.. (2, Insightful)

Capt'n Hector (650760) | more than 10 years ago | (#10250680)

[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:

<latex>
LaTeX code goes here...
</latex>

Re:Slightly OT.. (0)

Anonymous Coward | more than 10 years ago | (#10250733)

MathML. Mozilla supports it, and there are already TeX->MathML converters out there.

Re:Slightly OT.. (2, Informative)

gatzke (2977) | more than 10 years ago | (#10251110)


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/
http ://pear.math.pitt.edu/mathzilla/Examples/marku pOftheWeek.mhtml

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)

Correct me if I'm wrong (2)

DanielMarkham (765899) | more than 10 years ago | (#10250916)

But isn't physics built on math? And isn't math built on philosophy? And don't we still not have a good understanding of how gravity and electromagnetic radiation act? (take dark energy for one example, or the gravitational anomalies dealing with eclipses)

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 create a calculus randomly and see where it goes, a la genetic programming, for instance? Might make a neat science fair project.

Re:Correct me if I'm wrong (0)

Anonymous Coward | more than 10 years ago | (#10251119)

An x86 should do it!
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