That’s a toughie…but I’ll work on it.
42
Yes, pick the other door.
Funny, I thought you said “Hieronymous Bosch.”
Here’s a link with a definitive answer.
http://www.ravenna.com/blackhole.cgi?6
“The problem with the world is that everyone is a few drinks behind.” - Humphrey Bogart
x = 0
Yer pal,
Satan
Hmm, I’m disappointed…I thought if I left another blank post dangling out there, I’d get a lot more comments. Apparently not.
Ah, well. Trolling aside, see if any of you can explain this to me in terms that make sense to a mathematical moron. I take this material from page 295 of Goodbye, Darkness, by William Manchester; (Boston: Little, Brown, and Company, 1979):
____________________
/ 2 2 2 2 2
ds= V c dt —dx —dy —dz
I don’t have a good program for this, so if it looks screwy, it’s ds equals the square root of c squared times dt squared minus dx squared minus dy squared minus dz squared.
Supposedly this is something called “Minkowski’s Clock Paradox”, and I have never been able to find anybody who can explain to me what it means. I asked several different math profs in school, and only one of them came up with a partial answer; he said he thought it had something to do with the relationship of distance to time on the surface of a moving sphere. If that’s the case, then I am assuming that “d” means “distance”, “s” means “sphere” or “surface”, “t” means “time”, and “x”, “y”, and “z” are variables of some description. I have no clue as to what “c” might be. So, what does it mean, all you brilliant people out there who are smarter than I am? I await your explanations.
Pickman’s model wrote:
Lemme help with the notation:
ds = SQRT(c[SUP]2[/SUP] * dt[SUP]2[/SUP] - dx [SUP]2[/SUP] - dy[SUP]2[/SUP] - dz[SUP]2[/SUP])
(The secret for the exponents is to use the following HTML sequence: <SUP>2</SUP> . )
The truth, as always, is more complicated than that.
And regards your question:
The various "d"s do not stand for distance. They are the differential symbol. “dt” means an infinitessimally small change in t, “dx” means an infinitessimally small change in x, etc… Furthermore, x y and z are all spatial coordinates, and t is time. c is of course the speed of light. It’s a problem from Relativity.
The truth, as always, is more complicated than that.
Thanks, Tracer; however, I’m still foggy on this. Okay, so it’s relativity, but what does it mean? Or is it one of those things that pertains more to philosophy than math, like, if I skip a stone across a pond, does that mean that skipping it is what the future was? Or, can you put your foot into a running stream and pull it back out of the same stream, or is it a different stream, since time, distance, and water have all changed since putting your foot in to begin with? I don’t follow.
I’m not entirely sure myself, as I’ve never wrestled with Minkowski’s Clock Paradox (unless this is the same thing as the Twin Paradox with a different name).
However, I do know that in Relativity, time is usually treated as one more component in a 4-dimensional space-time vector. I.e. instead of saying something is at position (x, y, z) at time t, Relativitists would say that something is at a spacetime “position” of (x, y, z, ct). t is multiplied by c, here, to make the units come out the same, among other reasons.
Quick-N-Dirty Aviation: Trading altitude for airspeed since 1992.
Okay, so if “d” represents a very small change in the variable that follows it, then “s” obviously must stand for “speed”, I would guess. Ergo:
the change in speed equals the square root of:
the speed of light squared
multiplied by
the change in time squared
minus
the change in “x” squared
minus
the change in “y” squared
minus
the change in “z” squared.
I am assuming that all these differential designations are multiplied by the variable that follows them, as in dt[SUP]2[/SUP] equals d times t[SUP]2[/SUP], right?
So in other words, this would pertain to a moving sphere; say, planet Earth, and x,y, and z could be New York, Cairo, and Rangoon, for example?
(I’m sorry if I’m appearing to be terribly dense, but you have to remember, with my math skills, I have trouble balancing a checkbook.) 
And the speed of light is still figured at 186,300 miles per second (299,792.8 kilometers per second), is it not?
Dude, try a search on the web. I got 26 hits on metacrawler with ‘minkowski clock paradox’. This one seems kinda readable; http://www.weburbia.com/physics/twin_spacetime.html
Trouble with your checkbook? Do the math profs help with those questions as well?
Pickman’s Model wrote:
Uh … no. x, y, and z are the three rectangular spatial coordinates for any ONE point in space. I.e. x could be the distance north of Cairo, y could be the distance east of Cairo, and z could be the distance above Cairo. Cairo would, by this definition, have (x,y,z) coordinates of (0,0,0). A plane flying directly over Cairo at an altitude of 5,000 meters would have (x,y,z) coordinates of (0,0,5000m). A man standing 1000 meters to the north and 2000 meters to the west of Cairo would have (x,y,z) coordinates of (1000m,-2000m,0).
Quick-N-Dirty Aviation: Trading altitude for airspeed since 1992.
You are speaking of the “Twins Paradox”, heres a link…read. I will not attempt to explain it since my grasp is marginal at best and I tok a semester course on it.
http://math.ucr.edu/home/baez/physics/twin_paradox.html
By the way, s doesn’t stand for speed, speed is almost always v for velocity a vector, rarely the scalar speed. V is more commonly defined as “dx dy dz” as in change in x, y and z over time.
Your equation is not correct either. dx[sup]2[/sup] etc. is against convention. It unclear if your squaring the derivative or showing a second partial derivative.
Ah, HA! So my conception was way out in left field. It must have been the “sphere” idea that threw me off…it seems like all this has to do is with the relationship of time to distance (like, does it travel in a straight line, or does it curve?), and nothing to do with speed or the shape of a particular surface.
Thanks, Tracer, Dorf, and Omniscient, for your explanations and links. I read both links, by the way; I could grasp some of it, but once I got into the heavier stuff, it was the same sensation I used to get in Algebra class: I could feel the circuit breakers in my brain begin to snap off, one by one, until the formulas magically changed into gibberish right in front of me bleedin’ eyes. Mathematical comprehension for me is sort of like pouring water into a glass: you can only fit do much in, and after that, you can keep pouring if you want to, but all it’ll do is just run off the top. I’m SO glad I was a History major.
In any event, I know more than I did, and I do appreciate the help. Thanks again guys!
Now I have to ask Pickman, where the hell did you stumble across this?..and what made you so interested in it?..I mean I’ve come across all sorts of higher Physics questions, and I just skip right over them. They make almost no sense to me, and I personally believe that most of them are hoeee anyway.(yes, that’s the technical term for B.S.). I’m all for expanding my horizon, but damn you went waaaayyyy beyond the call of duty there…
I haven’t lost my mind, I have a tape backup around somewhere.
LOL. It came from William Manchester’s book, Goodbye, Darkness, which is a combination memior and historical account of the war in the Pacific in World War II.
Manchester himself was a Marine, and he was telling about the times he and the guys in his company would be huddled down in holes during a lull in the fighting, and somebody would introduce some groovy concept to talk about. Many of them were draftees and college-educated (there was no deferment for college students in WW II the way there was in Vietnam), and one guy, named Wally Moon, was a budding physicist who’d been at MIT. He was the one who introduced Minkowski. Manchester wrote the equation down in his diary, but had never been able to understand it. He said there were four Phi Beta Kappas in his section, but when Wally started going into the 4th and 5th dimensions, he started to lose his audience. Another guy named Knocko told him, “Bubba, this is too deep for Dixie. The day they introduce an entrenching tool into Alabama, it’ll spark an industrial revolution.” I’d have to agree with that; not the part about Alabama, but about it being too deep for Dixie. Too deep for me, too.
Anyway, I was intrigued by this funny-looking equation, that’s all. I wanted to know what it meant, what it was about. None of my math profs in college could tell me, like I said; so I just thought I’d throw it out here and see what came up. Interesting, but as I said, I believe I’ll stick to History. The equations I saw in those two links above looked about as comprehensible as Klingon written in kanji to me.
As an aside, if anybody is interested, Goodbye, Darkness is one of the best books I ever read, bar none. I’d recommend it to anybody. It’s out of print in hardcover, but you can find it in a Dell paperback edition at any good bookstore. Buy it and read it—it is excellent, in every sense of the word. Something there for everyone, I think.