oh yeah? so in 2-D it's the 'inverse law' (1/dist^1) and in 1-D the 'constant law' (1/dist^0 = 1)??
Exactly. If you find some way to make a force propogate in only one or two dimensions (good luck) you'll see it stays strong at greater distances. Consider a point object (object A) in three dimensional space that has an attractive force. Consider another point object (object B) at a certain distance (d) from it that is affected by A's force. A's force affects every point d away from it (every point on the sphere of radius d) equally strongly. As increases, the surface area of the sphere also increases, and the magnatude of the force is diluted. The surface area of a sphere is something like 4/3*pi*d^2. I may be misremembering, high school geometry was a long time ago, but I know the d^2 part is right. So in three dimensions, the force is diluted according to an inverse square law.
In two dimensions, the points affected by object A's force at distance d are the points on the circle centered at A. The length of the circumfrence of the circle is proportional to d, so in two dimensions, the force is diluted according to an inverse law. In only one dimension, there are just the same two points being affected at any given distance, their size does not increase in any way as d increases, so the attraction to object A remains constant.
It all depends on what norm you are using. What tells you that in these other dimensions - if they exists - the Euclidean norm should be used??
The Euclidean norm in fact isn't being used. If the extra dimensions were as close to being Euclidean as the familiar four are, we would notice pretty fast that gravity wasn't obeying an inverse square law. Our experimental results would be absurdly far from Newton's predictions. All the talk about measuring the size of the other dimensions is about measuring how non-Euclidean the universe is.
It really hurts to read this stuff: "two dimensions extend a millimeter". WTF??? since when have dimensions got lengths? Some dimensions aren't even measured in centimeters (->time).
Time isn't measured in centimeters because we were measuring time long before we knew it was a dimension like length, width, and height. We percieve it differently, so we use different units. The conversion factor between meters and seconds is the speed of light, if I remember my freshman physics course correctly. As for the length of a dimension, consider a two-dimensional creature living on the surface of a torus (doughnut shape). The creature can move in two directions. It finds that if it goes in one direction, it reaches its starting point fairly soon, but it takes a while longer in the other direction. Our universe is sort of like the surface of that torus, just a lot harder to visualize. The dimensions that bend back on themselves have a finite length.
I really liked Hugh Jackman's Wolverine, even though it's an easy part to play...
An easy part to play??? Jackman played a dynamic character so smoothly that I didn't even notice the transformation until the movie was over and I was thinking back to the beginning. The writers deserve a lot of the credit for this too, but most actors would have botched it completely. Jackman pulled it off admirably. I was as impressed with his acting as with Patrick Stewart's, and Stewart is my favorite actor.
As good as Jackman and Stewart were, though, I have to say that Ian McKellan stole the show. A sympathetic, sane bad guy? It would have been much easier, and much less effective, to play Magneto as a monomaniacal nut case who lost his mind along with his respect for ordinary humans. The script would have allowed it, too. The same lines spoken by a bug-eyed, angry fanatic would have sounded loony. Instead, you find yourself understanding Magneto's ideas, almost even agreeing with them.
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Let's just hope one of the Pizza Hut drives doesn't pilot it. That baby will be totaled in minutes!!!
On the other hand, if it doesn't get wrecked, it'll probably be breaking the speed limit. Faster than light travel, here we come!
oh yeah? so in 2-D it's the 'inverse law' (1/dist^1) and in 1-D the 'constant law' (1/dist^0 = 1)??
Exactly. If you find some way to make a force propogate in only one or two dimensions (good luck) you'll see it stays strong at greater distances. Consider a point object (object A) in three dimensional space that has an attractive force. Consider another point object (object B) at a certain distance (d) from it that is affected by A's force. A's force affects every point d away from it (every point on the sphere of radius d) equally strongly. As increases, the surface area of the sphere also increases, and the magnatude of the force is diluted. The surface area of a sphere is something like 4/3*pi*d^2. I may be misremembering, high school geometry was a long time ago, but I know the d^2 part is right. So in three dimensions, the force is diluted according to an inverse square law.
In two dimensions, the points affected by object A's force at distance d are the points on the circle centered at A. The length of the circumfrence of the circle is proportional to d, so in two dimensions, the force is diluted according to an inverse law. In only one dimension, there are just the same two points being affected at any given distance, their size does not increase in any way as d increases, so the attraction to object A remains constant.
It all depends on what norm you are using. What tells you that in these other dimensions - if they exists - the Euclidean norm should be used??
The Euclidean norm in fact isn't being used. If the extra dimensions were as close to being Euclidean as the familiar four are, we would notice pretty fast that gravity wasn't obeying an inverse square law. Our experimental results would be absurdly far from Newton's predictions. All the talk about measuring the size of the other dimensions is about measuring how non-Euclidean the universe is.
It really hurts to read this stuff: "two dimensions extend a millimeter". WTF??? since when have dimensions got lengths? Some dimensions aren't even measured in centimeters (->time).
Time isn't measured in centimeters because we were measuring time long before we knew it was a dimension like length, width, and height. We percieve it differently, so we use different units. The conversion factor between meters and seconds is the speed of light, if I remember my freshman physics course correctly. As for the length of a dimension, consider a two-dimensional creature living on the surface of a torus (doughnut shape). The creature can move in two directions. It finds that if it goes in one direction, it reaches its starting point fairly soon, but it takes a while longer in the other direction. Our universe is sort of like the surface of that torus, just a lot harder to visualize. The dimensions that bend back on themselves have a finite length.
I really liked Hugh Jackman's Wolverine, even though it's an easy part to play...
An easy part to play??? Jackman played a dynamic character so smoothly that I didn't even notice the transformation until the movie was over and I was thinking back to the beginning. The writers deserve a lot of the credit for this too, but most actors would have botched it completely. Jackman pulled it off admirably. I was as impressed with his acting as with Patrick Stewart's, and Stewart is my favorite actor.
As good as Jackman and Stewart were, though, I have to say that Ian McKellan stole the show. A sympathetic, sane bad guy? It would have been much easier, and much less effective, to play Magneto as a monomaniacal nut case who lost his mind along with his respect for ordinary humans. The script would have allowed it, too. The same lines spoken by a bug-eyed, angry fanatic would have sounded loony. Instead, you find yourself understanding Magneto's ideas, almost even agreeing with them.