Would someone tell me how this happened? We were the fucking vanguard of shaving in this country. The Gillette Mach3 was the razor to own. Then the other guy came out with a three-blade razor. Were we scared? Hell, no. Because we hit back with a little thing called the Mach3Turbo. That's three blades and an aloe strip. For moisture. But you know what happened next? Shut up, I'm telling you what happened--the bastards went to four blades. Now we're standing around with our cocks in our hands, selling three blades and a strip. Moisture or no, suddenly we're the chumps. Well, fuck it. We're going to five blades.
Your analogy of ill-gotten wartime loot is kind of funny. When the descendants of dinosaurs come looking for their ancestors bones, we will have to cough them up.
I was wondering why that blue jay was giving me such a crap talking-to this morning.
Are there any applications for it within our understanding of physics?
The existence of monopoles is a possible "explanation" for the quantization of electric charge. Maxwell's Equations are only self-consistent if:
1. magnetic monopoles don't exist, and charge is not quantized; OR
2. magnetic monopoles do exist (at least one, somewhere), and charge is quantized.
As charge is quantized, it has always been a strong argument for monopoles' existence. Of course, perhaps Maxwell's Equations aren't applicable at the quantum level, but so far they've done a damned good job of being consistent and predicting and explaining things.
Not to nit-pick, but how is a circular argument "perfectly valid?" A circular argument is the opposite of valid. A circular argument is an argument made in support of the proposed proof of a claim by presenting the original claim in said support. That's the opposite of valid.
Erm. The parent poster was saying that calling the metamaterials periodic is tautological, but not untrue; it wasn't implied that circular reasoning is a valid form of logic.
Yes, because as I mentioned in an earlier post (as have others), time is usually considered a parameter, rather than a dimension, except in SR and GR. And a single dimension can hold a vector or tensor (or higher-order generalization of these) form. A vector potential, for example.
By saying that sound is 1D, you've basically said that, "No matter how I move my head, I'm going to hear the same sound, _but_I'm_only_allowed_to_move_along_a_certain_path_." It doesn't allow for spherical or circular spreading. Nor does it allow for interactions with objects in a room.
I don't think you're getting that you can measure any field at a single point in space (it's what it _means_ to be a field, or be characterized by a field equation). That has nothing to do with whether the field is 1D, 2D, 3D, more-D, or can be characterized as having a non-integer dimension (as in the limits of many statistical mechanics models like irreducible Ising models).
Um... you understand that the microphone's position is in 3D space, right? And one can use accelerometers rather than microphones, which record 3D movement, not just a scalar pressure.
Only infinitely far from a point source in an unbounded medium, or if you're talking about compressional or transverse waves on a 1D object (plane waves in an infinite half-space; naiive guitar string waves, etc.). Otherwise, sound is intrinsically 3D, and is much harder to model accurately (usually) than electromagnetic waves, because things like Lamb waves, Love waves, etc. lead to the need for tensor descriptions rather than the usual vector descriptions.
Actually, your parent poster is correct: a transverse wave like on a string can be parametrized by one coordinate, since the displacement isn't a dimension. So both compressional and transverse waves on a string can be said to be 1D _in_space_: give an x-coordinate, I can tell you the displacement at a given time (or, if you're masochistic, take the one spatial dimension to be the length along the string from some origin).
2D: ripples on a pond. Need an (x,y) to specify the location; the other number is the displacement (or density, or velocity; doesn't matter).
3D: ripples in a volume, such as sound waves in an unbounded medium, electromagnetic waves in space, etc. There are two ways to be "off" by one dimension in problems such as these:
1) count time as a needed dimension (usually, it's treated as a parameter, especially for time-harmonic problems, but sometimes it's really needed, as in SR and GR);
2) not take advantage of symmetries in the problem, which can sometimes collapse the problem to a lower dimension (or _almost_ lower dimension).
Though it's not specifically a *tech* book (more a science thing), I helped co-author a chapter for a book published by Cambridge.
I hadn't worked with them before, though my co-authors had. I had lots of questions about the contract (re-use of published material, what our responsibilities were, and so on). The publisher was very helpful in figuring them out, and explaining to me what each thing meant (and accepted a couple of changes for future contract versions). The book itself is of high quality, in cover, printing, typesetting, figures, etc., and the turnaround time for reviewing and editing was good.
I'm quite happy with them.
So a college degree in engineering apparently barely starts to touch on many of the concepts that have been explored by mathematicians.
Of course. But then most mathematicians, shown a cooling tower, would have no idea how to optimize it, or how to perform an FEM analysis on a structure, or how to calculate the SNR in a radio system, or any of a tremendous number of things that engineers can do. And if you ask a topologist, say, questions that a computer scientist would find commonplace, he may well founder. They're all based, ultimately, upon such things as Fourier series, but different disciplines take different tacks.
One thing I've learned is that truly good thinkers will recognize when they're bumping up against something new, try to associate the new things with what they already know, and *not* be afraid to get some of the details wrong. If the mapping between the new and the old is even mediocre, that's often good enough to make some tremendous strides and learn the new material. Don't knock engineering know-how!
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Would someone tell me how this happened? We were the fucking vanguard of shaving in this country. The Gillette Mach3 was the razor to own. Then the other guy came out with a three-blade razor. Were we scared? Hell, no. Because we hit back with a little thing called the Mach3Turbo. That's three blades and an aloe strip. For moisture. But you know what happened next? Shut up, I'm telling you what happened--the bastards went to four blades. Now we're standing around with our cocks in our hands, selling three blades and a strip. Moisture or no, suddenly we're the chumps. Well, fuck it. We're going to five blades.
What're you -- some kind of dirty hippy? C'mon, Mavis, we're goin' to McDonald's.
Come on, I've teed it up for you, now knock it out of the park!
Maybe we can make a touchdown from that half-court shot, as you so nicely handicapped the goalie.
Makes the tunes more hoppy.
Huh. In that case, I've got two fiddles right here.
Filter error: Please use less whitespace.
Sorry, man. You'll just have to buy a stronger desk.
Yep. http://xkcd.com/612/
Your analogy of ill-gotten wartime loot is kind of funny. When the descendants of dinosaurs come looking for their ancestors bones, we will have to cough them up.
I was wondering why that blue jay was giving me such a crap talking-to this morning.
Are there any applications for it within our understanding of physics?
The existence of monopoles is a possible "explanation" for the quantization of electric charge. Maxwell's Equations are only self-consistent if:
1. magnetic monopoles don't exist, and charge is not quantized;
OR
2. magnetic monopoles do exist (at least one, somewhere), and charge is quantized.
As charge is quantized, it has always been a strong argument for monopoles' existence. Of course, perhaps Maxwell's Equations aren't applicable at the quantum level, but so far they've done a damned good job of being consistent and predicting and explaining things.
Everyone edit all the biographies to say that people died in 1997. Then we can say whatever we want!
...had shut off all seaports and airports sooner.
Not to nit-pick, but how is a circular argument "perfectly valid?" A circular argument is the opposite of valid. A circular argument is an argument made in support of the proposed proof of a claim by presenting the original claim in said support. That's the opposite of valid.
Erm. The parent poster was saying that calling the metamaterials periodic is tautological, but not untrue; it wasn't implied that circular reasoning is a valid form of logic.
So you can have a hash of hashes, or an array of arrays, but you can't get arrays in your hashes or vice versa.
Yo, Puppy, I heard you like arraying your hashes and hashing your arrays, so we put ... Oh, nevermind.
Explain to me how it's a dimension. And use the standard, physics/math definition of 'dimension', please. No making shit up.
Yes, because as I mentioned in an earlier post (as have others), time is usually considered a parameter, rather than a dimension, except in SR and GR. And a single dimension can hold a vector or tensor (or higher-order generalization of these) form. A vector potential, for example.
Correct me if I misunderstand you (surely I am): Are you saying that all _scalar_ fields are of one dimension?
The sound is what we hear.
Erm. Okaayyyy....
By saying that sound is 1D, you've basically said that, "No matter how I move my head, I'm going to hear the same sound, _but_I'm_only_allowed_to_move_along_a_certain_path_." It doesn't allow for spherical or circular spreading. Nor does it allow for interactions with objects in a room.
I don't think you're getting that you can measure any field at a single point in space (it's what it _means_ to be a field, or be characterized by a field equation). That has nothing to do with whether the field is 1D, 2D, 3D, more-D, or can be characterized as having a non-integer dimension (as in the limits of many statistical mechanics models like irreducible Ising models).
Um... you understand that the microphone's position is in 3D space, right? And one can use accelerometers rather than microphones, which record 3D movement, not just a scalar pressure.
I think that was his point :)
Only infinitely far from a point source in an unbounded medium, or if you're talking about compressional or transverse waves on a 1D object (plane waves in an infinite half-space; naiive guitar string waves, etc.). Otherwise, sound is intrinsically 3D, and is much harder to model accurately (usually) than electromagnetic waves, because things like Lamb waves, Love waves, etc. lead to the need for tensor descriptions rather than the usual vector descriptions.
Actually, your parent poster is correct: a transverse wave like on a string can be parametrized by one coordinate, since the displacement isn't a dimension. So both compressional and transverse waves on a string can be said to be 1D _in_space_: give an x-coordinate, I can tell you the displacement at a given time (or, if you're masochistic, take the one spatial dimension to be the length along the string from some origin).
2D: ripples on a pond. Need an (x,y) to specify the location; the other number is the displacement (or density, or velocity; doesn't matter).
3D: ripples in a volume, such as sound waves in an unbounded medium, electromagnetic waves in space, etc. There are two ways to be "off" by one dimension in problems such as these:
1) count time as a needed dimension (usually, it's treated as a parameter, especially for time-harmonic problems, but sometimes it's really needed, as in SR and GR);
2) not take advantage of symmetries in the problem, which can sometimes collapse the problem to a lower dimension (or _almost_ lower dimension).
Though it's not specifically a *tech* book (more a science thing), I helped co-author a chapter for a book published by Cambridge.
I hadn't worked with them before, though my co-authors had. I had lots of questions about the contract (re-use of published material, what our responsibilities were, and so on). The publisher was very helpful in figuring them out, and explaining to me what each thing meant (and accepted a couple of changes for future contract versions). The book itself is of high quality, in cover, printing, typesetting, figures, etc., and the turnaround time for reviewing and editing was good.
I'm quite happy with them.
Why are those eyes downcast?
So a college degree in engineering apparently barely starts to touch on many of the concepts that have been explored by mathematicians.
Of course. But then most mathematicians, shown a cooling tower, would have no idea how to optimize it, or how to perform an FEM analysis on a structure, or how to calculate the SNR in a radio system, or any of a tremendous number of things that engineers can do. And if you ask a topologist, say, questions that a computer scientist would find commonplace, he may well founder. They're all based, ultimately, upon such things as Fourier series, but different disciplines take different tacks.
One thing I've learned is that truly good thinkers will recognize when they're bumping up against something new, try to associate the new things with what they already know, and *not* be afraid to get some of the details wrong. If the mapping between the new and the old is even mediocre, that's often good enough to make some tremendous strides and learn the new material. Don't knock engineering know-how!
"100101000101011111001001000100101000100100001"!