For example, there's the RSA cryptographic algorithm, and the Marching Cubes volume iso-surface generation algorithm, just to name two of my favorites off the top of my head.
I don't consider either of these obvious. Nor do I subscribe to the notion that methods that harness the laws of mathematics are inherently less inventive than methods that harness the laws of physics.
Ok, I'll bite. What was the resolution of the monitor you threw away last year? And I assume by "resolution", you're speaking in terms of dot-pitch (shadow mask) or aperture grille pitch (Trinitron or equivalent), not just the frequency you're driving it at. I'd love a CRT monitor that has an actual *resolution* greater than 1600x1200, but I figured it would cost a couple grand and I wouldn't be able to get the thing up the stairs. Do you have make/model info?
I was about to suggest that but you beat me to it. So let me add a little suggestion: Instead of trying to carefully break the thing in the middle of the night, buy another identical device from wherever he got it (Home Depot, whatever) and take your time breaking it carefully. Then just swap the two in the middle of the night. Then return the properly-functioning one to the store for a refund.
against the idea that torture is by definition wrong.
I may agree with you that torture is wrong, in general. I may also assert that there are situations when it isn't. And whether or not it's effective is an entirely different matter. But what I object to at the moment is your erroneous use of the phrase "by definition". The alleged wrongness of it is not part of the definition of the word.
Now, it seems to me that not every kid out there gets a mobile phone. Shouldn't this push average WAY up?
Um, if a kid doesn't get a mobile phone at all, do you treat that as getting the phone at age infinity? If so, then the answer to your question is yes, and there may be a job for you in Bush's Social Security Administration.
Right of First Sale doesn't just apply to you and me.
Sure they have the right of first sale... up until the point where they sign a contract waiving it.
Denying that right through this system denies me the Right of First Sale
Nobody is denying you the right to sell it. The fact that prospective buyers won't find your used game particularly useful is not germane to the topic of your first sale rights.
and thus denies me my fair-use rights.
Apparently, you don't know what "fair use" means. "Fair Use" is a defense against allegations of copyright infringement. The only person who can violate your "fair use" rights is a judge who finds you guilty of infringment even when the fair use provisions apply.
I have never subscribed to this "just put your ideas down now; worry about the grammar later" school of thought. Such a process makes a chore of having to go back and correct the ideas to make them presentable, as if grammar and other finer points of writing were unnecessary burdens imposed by the teacher and other excessively picky individuals.
I don't think that's the intent. The intent is to focus on one problem at a time. First, what to say, then, how to say it.
I hope that you don't just code any old program and then go back later to fix compilation errors.
No, but when doing any kind of algorithmic work (and not just utilizing an API), I often write pseudo-code first, which is the equivalent of "just put your ideas down now". Of course, I do it on paper, since I already know how the compiler's going to feel about it.
If you could just fly in a rocket and see a bit red cement pole with "center of universe" painted on it, that would make a dandy absolute reference point.
Perhaps, but it doesn't change anything. Anything can serve as a reference point. The bottom line is that the laws of physics would still be invariant with respect to a Lorentz transform, which is pretty much all that Special Relativity states.
Within a group of 100 students, there are 100 choose 2 possible arrangements.
Something seems fishy about this, though that may be because it's 6:30 in the morning as I begin to write this.
It seems to me that there are (100 choose 2) possible pairs (not arrangements) of students. I think that to get the number of arrangements you first have to select 50 out of the 100 students to be the "left side", so to speak, of each pair. That's (100 choose 50).
Then, you have to select a permutation of the remaining 50 students to "line them up" with the first 50. That's (50!).
Then you have to correct for the over-counting: For any pair containing two people, A and B, where "A" was chosen as the left side of the pair and "B" chosen as the right, there's an isomorphic arrangement where A and B have changed positions. How many ways does this happen? Well, for any equivalence class of arrangements, you have 50 pairs that may or may not have their positions reversed, each representable as a bit in a 50-bit number. That's 2^50 isomorphisms per equivalence class.
So, the answer I get is (((100 choose 50)*50!)/(2^50)). Have I made an error somewhere?
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For example, there's the RSA cryptographic algorithm, and the Marching Cubes volume iso-surface generation algorithm, just to name two of my favorites off the top of my head.
I don't consider either of these obvious. Nor do I subscribe to the notion that methods that harness the laws of mathematics are inherently less inventive than methods that harness the laws of physics.
How many planets are there? Many Voted Early Morning: Just Slightly Under Nine.
Ok, I'll bite. What was the resolution of the monitor you threw away last year? And I assume by "resolution", you're speaking in terms of dot-pitch (shadow mask) or aperture grille pitch (Trinitron or equivalent), not just the frequency you're driving it at. I'd love a CRT monitor that has an actual *resolution* greater than 1600x1200, but I figured it would cost a couple grand and I wouldn't be able to get the thing up the stairs. Do you have make/model info?
(distance)^2 = (x2^2 - x1^2) + (y2^2 - y1^2) [super-script replaced with "^"]
This is a definition of distance-squared with which I was previously unfamiliar.
I once read an incomplete biography of Godel. But at least it was consistent.
I was about to suggest that but you beat me to it. So let me add a little suggestion: Instead of trying to carefully break the thing in the middle of the night, buy another identical device from wherever he got it (Home Depot, whatever) and take your time breaking it carefully. Then just swap the two in the middle of the night. Then return the properly-functioning one to the store for a refund.
against the idea that torture is by definition wrong.
I may agree with you that torture is wrong, in general. I may also assert that there are situations when it isn't. And whether or not it's effective is an entirely different matter. But what I object to at the moment is your erroneous use of the phrase "by definition". The alleged wrongness of it is not part of the definition of the word.
Now, it seems to me that not every kid out there gets a mobile phone. Shouldn't this push average WAY up?
Um, if a kid doesn't get a mobile phone at all, do you treat that as getting the phone at age infinity? If so, then the answer to your question is yes, and there may be a job for you in Bush's Social Security Administration.
Right of First Sale doesn't just apply to you and me.
Sure they have the right of first sale... up until the point where they sign a contract waiving it.
Denying that right through this system denies me the Right of First Sale
Nobody is denying you the right to sell it. The fact that prospective buyers won't find your used game particularly useful is not germane to the topic of your first sale rights.
and thus denies me my fair-use rights.
Apparently, you don't know what "fair use" means. "Fair Use" is a defense against allegations of copyright infringement. The only person who can violate your "fair use" rights is a judge who finds you guilty of infringment even when the fair use provisions apply.
Doggonit, make that twenty three pars a chromersomes.
I'm sure people at Harvard would equally hate the idea of someone from Texas like Bush dictating the dictionary.
Future Harvard Medical School lecture: "Each a them thar human cells has twenty-three chromersomes in its nukyulus."
The Unix world figured out that shadow password files are a good idea a long time ago.
I've always wondered about this. The security depends on denying access to the ciphertext?!? That sounds a lot worse than security through obscurity.
...that Uncle Joe and I are not related in any way, shape, or form.
Neither plot made any sense [...] the stories were predictible
So... you were able to accurately predict the precise manner in which they would be incomprehensible?
Is this an exploit that somehow grants malicious code access privledges even beyond the user's access level,
If it did, it should be characterized as a bug in Windows, not Word.
...I'd like there to be a patent-related story in which the inevitable "I'm gonna patent patents, har-dee-har-har" joke doesn't get modded "+5 Funny".
the infinitive "to the store"
Prepositional phrase. But you knew that. Nice troll, AC.
I have never subscribed to this "just put your ideas down now; worry about the grammar later" school of thought. Such a process makes a chore of having to go back and correct the ideas to make them presentable, as if grammar and other finer points of writing were unnecessary burdens imposed by the teacher and other excessively picky individuals.
I don't think that's the intent. The intent is to focus on one problem at a time. First, what to say, then, how to say it.
I hope that you don't just code any old program and then go back later to fix compilation errors.
No, but when doing any kind of algorithmic work (and not just utilizing an API), I often write pseudo-code first, which is the equivalent of "just put your ideas down now". Of course, I do it on paper, since I already know how the compiler's going to feel about it.
If you could just fly in a rocket and see a bit red cement pole with "center of universe" painted on it, that would make a dandy absolute reference point.
Perhaps, but it doesn't change anything. Anything can serve as a reference point. The bottom line is that the laws of physics would still be invariant with respect to a Lorentz transform, which is pretty much all that Special Relativity states.
Well, it's sort of fishy as 100 choose 2 returns pairs that may, for instance, be (a, b) and (b, a).
Well, no, that part's not fishy at all. The "k!" in the denominator of the formula for "n choose k" removes those duplicates from the count.
Within a group of 100 students, there are 100 choose 2 possible arrangements.
Something seems fishy about this, though that may be because it's 6:30 in the morning as I begin to write this.
It seems to me that there are (100 choose 2) possible pairs (not arrangements) of students. I think that to get the number of arrangements you first have to select 50 out of the 100 students to be the "left side", so to speak, of each pair. That's (100 choose 50).
Then, you have to select a permutation of the remaining 50 students to "line them up" with the first 50. That's (50!).
Then you have to correct for the over-counting: For any pair containing two people, A and B, where "A" was chosen as the left side of the pair and "B" chosen as the right, there's an isomorphic arrangement where A and B have changed positions. How many ways does this happen? Well, for any equivalence class of arrangements, you have 50 pairs that may or may not have their positions reversed, each representable as a bit in a 50-bit number. That's 2^50 isomorphisms per equivalence class.
So, the answer I get is (((100 choose 50)*50!)/(2^50)). Have I made an error somewhere?
or c) *IS* the Sun.
Moebius Fax?
A misnomer since the "Moebius" aspect was entirely left out. It's just a loop.
I'd say "formally rising" [...]
As opposed to "casually rising"? Or did you mean "formerly rising"?