"I've said this molecule is unstable and doesn't exist dozens of times in organic chemistry class, but as it turns out, the molecule had different ideas," Northwestern chemistry professor Joseph Lambert said.
Q: You've been calling something unstable for a while, but it turns out it was stable. What do you do?
You said First off, Drake's equation was meant to map our ignorance, not as a serious attempt to enumerate the number of planets with intelegent life, and I have claimed that this isn't the case. Fortunately you have now quoted Drake disagreeing with you on the first point:
You: "Drake's equation was meant to map our ignorance..." Drake "The purpose of the equation was to help focus the conference..."
Three points:
The quote you attribute to Drake is from his biography, not his autobiography.
Clipping a quote at the point it starts to go against you is silly trick. The full sentence was:
The purpose of the equation was to help focus the conference attendees' attention on the crucial questions that needed to be answered in order to determine the chances of SETI's success. (Emphasis added)
Saying that something was meant to map our ignorance may arguably differ from saying that it was meant to focus attention on questions that need to be answered, but I can't see how any reasonable person can claim that it disagrees.
If it weren't for the fact that you seem to have posted reasonable things on other threads, I'd be tempted to think I was being trolled.
Just for the record, Be sold all its assets to Palm except the right to litigate; we (I'm a proud stockholder) are sueing, not Palm. I haven't sold my stock & don't intend to. Have you read the case? People have odd perceptions; they think a company like Microsoft (or Enron) can't fall just because it hasn't so far. This is 90% of the power they wield.
But back to AMD, my point about game theory was this: giving in to coercion in a case like this dosn't remove the threat, it simply defers it 'till the next time they want something from you. Whereas exposing the fact of the threat often makes it impossible for it to be carried out. If someone threatens to kill you and make it look like an accident unless you do as they say, your best bet is to publish far and wide the facts of their threat, so that the cost of acting on it becomes too great. Often (but not always) your chance of successfully beating the coercion gambit fall with time, since one of the main things the bully will do with their power is make it harder and harder for you to resist. So at any given point in time, you are better off resisting than going along and hoping things get better.
Case in point, if Microsoft has implied that they won't support AMD products in in their software (or break things, as they've done in the past, say with Digital Research & others), AMD should announce the fact.
From Drake's biography: "The purpose of the equation was to help focus the conference attendees' attention on the crucial questions that needed to be answered in order to determine the chances of SETI's success."
He didn't, as you state "come up with the Drake equation during the Green Bank conference"--he was one of the organizers of the conference, and used the equation to structure the agenda.
MarkusQ, big kudos to you for the first correct, appropriate in context, use of "beg the question" I have ever seen on this site. It is misused *vastly* more often than it is used correctly, so it's a relief to see it right for once. Way to go.
Thanks. I was once chastized for using it correctly by someone who was so used to seeing it used incorrectly that he misinterpreted my post in an odd way that let him see the misuse he expected. Jeesh.
-- MarkusQ
P.S. *smile* Am I correct in deducing that you from your user ID that you eat processed starches?
Perhaps. But if it were just coercion, it would seem like there would be better strategies than giving in; for example, making a stand (and reporting the attempted coercion) is much more effective from and underdog such as AMD, and from a game-theory point of view makes more sense in the long run.
First off, Drake's equation was meant to map our ignorance, not as a serious attempt to enumerate the number of planets with intelegent life
Mike Connell:
"So I sat down and thought, "What do we need to know about to discover life in space?" Then I began listing the relevant points as they occurred to me." - Frank Drake describing how he came up with the Drake equation during the Green Bank conference.
I'm confused. Your tone ("This is tripe") seems to imply that you disagree with me, but the quotation from Drake you offer is exactly what I was refering to: he didn't sit down calculate the likelyhood of life in space from what we knew but rather sat down to list what we would need to know (and clearly did not, and for many points still do not). He was, as I stated (and as he has stated elsewhere) more interested in mapping out what we would need to learn than in computing an "answer."
So, are you disputing this (and if so, in what way?) or am I just confused about the intent of your post?
Windows, however, allows me to choose my hardware manufacturer. I can buy NT and then buy any x86 chip (there used to be quite a few) to run it on. I'm not tied down and I think that's what he's getting at.
Ah, but you are tied down; in fact, you're tied down to a pool that includes AMD. I think the point is that AMD is tied to providing for this pool (by sunk R&D, for example) even more strongly than you are tied to buying from it (by Windows). Elsewise his testimony seems unmotivated.
First off, Drake's equation was meant to map our ignorance, not as a serious attempt to enumerate the number of planets with intelegent life, just as if someone asked me how fast a car I'd never seen or heard of was, I might answer "take the distance from where it stops to where it stops and divide by the time it takes" as a (slightly) more informative way of saying "I don't know." Then I suppose these clowns would come along and say "But the driver might have taken side trips! What if he forgot his sun-glasses and had to go back for them? You aren't accounting for acceleration/deceleration time! What about the wind?", etc.
Secondly, "the moon is vital to life" is one of those science fiction plot ideas that predates science fiction. It comes in many forms, but I've never seen one that doesn't beg the question (we couldn't have evolved without the moon because the moon causes X, we are the only example of us we have, and evolved with X; therefore we needed the moon to evolve). It sometimes makes me wonder at the sagacity of whoever coined the term "lunatic."
Third, many of the things they drag in are by no means established (and several are in fact in doubt). For example, we don't know where the Earth got its water, so we can't say if the process is common or not. We have only detected large extra-solar planets because that's all we know how to look for. We don't know that a stable climate is needed for the evolution of complex life (some argue that an unstable climate is required, lest you get stuck at a local addaptive maxima.
Anyway, I could go on, but you get my point: this is tripe.
I found the statements made by Sanders to be very odd. There must be something more to this that we aren't seeing, else why would he make so many statements that are 1) clearly wrong and 2) at odds with AMD's past positions on what is good for the industry? Specifically:
"most no Microsoft OS only run propritary hardware"--in the microcomputer industry at least, this has never been true. CP/M, for example, ran on a variety of 8 & 16 bit hardware, as did MOSS, Forth, etc., and in the Unix world it's even more absurd. To see my point, just turn the question around: if you were developing a new processor and needed an OS for it, would your first thought be to try to port Windows?
AMD has been very clear about how bad they think it would be for Intel to keep the hardware analogues of "API" information a secret, and how good they think it is for the free world to have multiple sources for x86 processors.
As I typed this, I think I answered my own question. Do you suppose he's worried (or has been convinced) that the only thing keeping alternative processor architectures out of the main stream it the difficulty of porting Windows? Does he fear a flood (or even strong trickle) of non-x86, and thus non-Intel/AMD processors might weaken AMD's strategic position?
there is reason why Ctrl-V and Ctrl-X are used for copy and cut in Windows, it's just because this is the way Wordstar does this !
Wordstar used Ctrl-KC for copy and (because it used a concept called "persistant blocks") didn't have a cut-to-clipboard--the closest thing it had was either move (Ctrl-KV) or delete-block (Ctrl-KY).
If you really think my analogy wasn't any good, why not support that with evidence having to do with viruses, instead of saying that analogies are wrong?
Sorry, I thought it was obvious (and note, I never said that "analogies are wrong"). For starters:
It is very hard to learn much about a biological virus by looking at the "source code" (DNA/RNA sequence); it is often quite easy to learn everything you need to know to prevent infection by a computer virus just by looking at the source code.
Computer viruses are written by people; biological viruses are not. Likewise, computer systems were designed by people, whereas people were not. This effects everything from the distribution of responsibility for failures to the effectiveness (and need for timeliness in) warnings, etc.
It is beyond our present technology to distribute "patches" or "upgrades" to correct the weaknesses that allow our bodies to be exploited by biological viruses. It is quit easy (and common place) to do this with computer systems.
A fatal biological virus kills a person (murder); a fatal computer virus takes down a system that may subsequently have to have its software reloaded (vandalism, possibly theft).
Computer viruses are much simpler than biological viruses.
It is quite legal to publish information about biological viruses in a form that is accessible to anyone who cares to read it. This particular point strengthens your analogy, but weakens the conclusion you try to draw from it.
Biological viruses operate at a scale in time and space that makes them very hard to detect, manipulate, etc. Computer virues operate in a space that is totally open to us; you do not need rare or prohibitively expensive equipment to study them, nor do you need years of specalized training (a month or so should suffice, given that you're starting about where a "pre-med" student does).
I could go on and on. If it weren't for the choice of names and cultural assumption of similarity, I don't think people would be so fond of this particular analogy. For example, we don't hear advertisements, religions, etc. lumped in this category, but the argument to do so is just as strong as the one for lumping computer and biological viruses. Do you propose that it should be illegal to discuss religion with people who aren't theologians? Should it be illegal to distribute advertising copy?
I like the idea of thinking about biological and computer viruses in the same way.
Sure. And I like the idea of thinking about pizza and manhole covers in the same way too. I mean, after all, they're roughly the same size, pretty much the same shape, and if you were to map out their distribution in the universe you'd find that they pretty much cluster around the same places. Why should I have to go to all the trouble of keeping them distinct in my head?
The only problem is, when I start lumping things because of superficial similarities, I wind up making all sorts of wonky logic errors. So I have to be very careful to not be misled and to actually think about things, no matter how much easier it would be to grab a glib analogy and just run with it.
Using spread spectrum technology greatly increases bandwidth available
This just isn't true, any more than weaving around increases the width of a roadway. Sure, it might let you dodge some obstructions, but in the process you become an obstruction to other trafic. The total amount of information that can be carried doesn't increase. Just like in the weaving-around-on-the-road analogy, you have to ask, what would happen if everyone did this? The answer, of course, is that to a good first aproximation all those other SS broadcasters would look like noise to you; so the ambient noise level goes up and the S/N ratio falls, meaning less information gets through.
How much less? well, in an ideal world, if you do everything right you only lose exactly as much as you thought you'd gained. TNSTAAFL.
Each photon you reveive can only tell you so much. You can't beat the uncertanty principle with hand waving.
Jabber, AIM, MSN, and others use TCP. In fact, the only client I know of that ever used UDP was ICQ, but that was an older protocol that is no longer being used
I think his point was that Jabber is like UDP in that you aren't sure that any particular message will get through, but then you don't pay the overhead of making sure.
Why not eat your enemies it would give you incentive to kill kill kill !!!
Well, for one thing, you'd still have to carry in all the condements, etc. For another, most of my enemies aren't backpackers, so I'd have to haul them in too. And lastly, given what I think most of them are full of, I'm not sure I'd like the taste.
I haven't found MREs to be all that objectionable. The thing to remember is that you don't eat them when you're staying in a five star hotel, just as you wouldn't sleep on the ground or catch rain water to drink. Conversely, you don't haul an espresso machine and a queen sized bed on your back for fifty miles just so you'll have "all the comforts" at the end of the day.
If you think in terms of food quality per Kg hauled (and remember that it's frequently you that's going to be doing the hauling), MREs are great--much better than trying to scrounge for twigs and berries, or going hungry.
Outside of the i18n community, I haven't seen this style of abbreviation anywhere. If you have a better suggestion for an abbreviation, we'd be happy to hear it.
I don't have an alternative abbreviation to propose; I have a deep irony to point out. The whole point of internationalization is to make things that are only accessable to speakers of one language (generally English) accessable to people who speak other languages. That this process is denoted by a cryptic polyglyph that isn't obvious to native speakers of any language and is justified by obscure referrence to one particular language (which is English!) is (quite litterally I suppose) too ironic for words.
-- MarkusQ
So, I wonder, do people who have trouble spelling occasionally write i17n or i19n? Or is it more common for them to write i18n but omit the wrong sequence of letters?
I can think of about thirty possible interpretations and none of them make sense.
On licence plates, you only have a few characters to work with. On message boards, if you are doing something illegal and want to escape simple minded pattern searches, your are trying to be cryptic. But in a headline? What is the point?
I mentioned that I run linux (lee-nucks) [which is how Linus pronounces it in some sound clip that is stuck somewhere in my default RH install. His pronuciation, however, was (lie-nucks) [ assuming you prounuce the lie as an american would, with a long I]. I looked a bit like a fool; i feel, because I didn't pronounce it his way, even though his way was wrong.
I was caught in this debate many years ago, and someone produced a digitized sound-bite from Linus with the "lie-nucks" pronunciation. After much confusion we realized that the sound file he had gotten off the web was someone else reading a statement attributed to Linus. The source if this misleading sound file?
"Time flies like an arrow" has three valid syntactic parsings. Only one makes sense semantically, though.
Depends on how deep you push the boundary of syntax; some grammars distinguish article-ambiguities, e.g.
Fat Tony likes a feast.
Fat Tony likes a girl.
which raises the number of parsings to at least four. And for any a priori "the line between syntax and semantics should be drawn here" you can come up with, someone can doubtlessly construct an "easy to please/eager to please" counter example.
The MSGPL license, for GPL implementations of MS protocols need only include the clause that changes must be available in source code form or in binary digits tattooed across the backside of the author, and that a license fee of one wet honey glazed ham is due if the software is used consecutively for more than sixty thousand years.
Even better, if you can get them: a pair of twenty sided quantum-entangled dice. That way, both sender and receiver can extend the pad at need, just by rolling up more numbers.
The only tricky part is reading the dice without looking at them. There are several ways to do this, but none of them actually work in practice and at least one of them is suspected of causing space-time errosion (& thus you will need to file an Environmental Impact Statement, including the plain text of the message being sent, thus reducing the utility of the system).
Another problem is keeping the dice cold. They have to be kept very, very cold, and of course this is very very expensive (C = A*exp(K-T)+B*N, where C is cost, K is Boltzman's constant, T is the temp., A and B are arbitrary constants related to local tax laws, and N is undefined).
But the main advantage of using quantum dice is that it would be too nerdly for words (at least three equations would be required) and you could probably get your picture in some magazine, wearing a white lab coat with coloured lights hitting you from odd angles.
-- MarkusQ
P.S. The original post was sound, but if you buy any of this post, I have a startup I'm trying to fund...
Slashdot Mirror
"I've said this molecule is unstable and doesn't exist dozens of times in organic chemistry class, but as it turns out, the molecule had different ideas," Northwestern chemistry professor Joseph Lambert said.
Q: You've been calling something unstable for a while, but it turns out it was stable. What do you do?
A: Increment the version number and release it!
-- MarkusQ
Three points:
If it weren't for the fact that you seem to have posted reasonable things on other threads, I'd be tempted to think I was being trolled.
-- MarkusQ
Just for the record, Be sold all its assets to Palm except the right to litigate; we (I'm a proud stockholder) are sueing, not Palm. I haven't sold my stock & don't intend to. Have you read the case? People have odd perceptions; they think a company like Microsoft (or Enron) can't fall just because it hasn't so far. This is 90% of the power they wield.
But back to AMD, my point about game theory was this: giving in to coercion in a case like this dosn't remove the threat, it simply defers it 'till the next time they want something from you. Whereas exposing the fact of the threat often makes it impossible for it to be carried out. If someone threatens to kill you and make it look like an accident unless you do as they say, your best bet is to publish far and wide the facts of their threat, so that the cost of acting on it becomes too great. Often (but not always) your chance of successfully beating the coercion gambit fall with time, since one of the main things the bully will do with their power is make it harder and harder for you to resist. So at any given point in time, you are better off resisting than going along and hoping things get better.
Case in point, if Microsoft has implied that they won't support AMD products in in their software (or break things, as they've done in the past, say with Digital Research & others), AMD should announce the fact.
-- MarkusQ
From Drake's biography: "The purpose of the equation was to help focus the conference attendees' attention on the crucial questions that needed to be answered in order to determine the chances of SETI's success."
He didn't, as you state "come up with the Drake equation during the Green Bank conference"--he was one of the organizers of the conference, and used the equation to structure the agenda.
I stand by my interpretation (which seems to be reasonably common).
-- MarkusQ
Thanks. I was once chastized for using it correctly by someone who was so used to seeing it used incorrectly that he misinterpreted my post in an odd way that let him see the misuse he expected. Jeesh.
-- MarkusQ
P.S. *smile* Am I correct in deducing that you from your user ID that you eat processed starches?
-- MarkusQ
Mike Connell:
I'm confused. Your tone (" This is tripe") seems to imply that you disagree with me, but the quotation from Drake you offer is exactly what I was refering to: he didn't sit down calculate the likelyhood of life in space from what we knew but rather sat down to list what we would need to know (and clearly did not, and for many points still do not). He was, as I stated (and as he has stated elsewhere) more interested in mapping out what we would need to learn than in computing an "answer."
So, are you disputing this (and if so, in what way?) or am I just confused about the intent of your post?
-- MarkusQ
Windows, however, allows me to choose my hardware manufacturer. I can buy NT and then buy any x86 chip (there used to be quite a few) to run it on. I'm not tied down and I think that's what he's getting at.
Ah, but you are tied down; in fact, you're tied down to a pool that includes AMD. I think the point is that AMD is tied to providing for this pool (by sunk R&D, for example) even more strongly than you are tied to buying from it (by Windows). Elsewise his testimony seems unmotivated.
-- MarkusQ
This is tripe.
First off, Drake's equation was meant to map our ignorance, not as a serious attempt to enumerate the number of planets with intelegent life, just as if someone asked me how fast a car I'd never seen or heard of was, I might answer "take the distance from where it stops to where it stops and divide by the time it takes" as a (slightly) more informative way of saying "I don't know." Then I suppose these clowns would come along and say "But the driver might have taken side trips! What if he forgot his sun-glasses and had to go back for them? You aren't accounting for acceleration/deceleration time! What about the wind?", etc.
Secondly, "the moon is vital to life" is one of those science fiction plot ideas that predates science fiction. It comes in many forms, but I've never seen one that doesn't beg the question (we couldn't have evolved without the moon because the moon causes X, we are the only example of us we have, and evolved with X; therefore we needed the moon to evolve). It sometimes makes me wonder at the sagacity of whoever coined the term "lunatic."
Third, many of the things they drag in are by no means established (and several are in fact in doubt). For example, we don't know where the Earth got its water, so we can't say if the process is common or not. We have only detected large extra-solar planets because that's all we know how to look for. We don't know that a stable climate is needed for the evolution of complex life (some argue that an unstable climate is required, lest you get stuck at a local addaptive maxima.
Anyway, I could go on, but you get my point: this is tripe.
-- MarkusQ
I found the statements made by Sanders to be very odd. There must be something more to this that we aren't seeing, else why would he make so many statements that are 1) clearly wrong and 2) at odds with AMD's past positions on what is good for the industry? Specifically: As I typed this, I think I answered my own question. Do you suppose he's worried (or has been convinced) that the only thing keeping alternative processor architectures out of the main stream it the difficulty of porting Windows? Does he fear a flood (or even strong trickle) of non-x86, and thus non-Intel/AMD processors might weaken AMD's strategic position?
I wonder.
-- MarkusQ
there is reason why Ctrl-V and Ctrl-X are used for copy and cut in Windows, it's just because this is the way Wordstar does this !
Wordstar used Ctrl-KC for copy and (because it used a concept called "persistant blocks") didn't have a cut-to-clipboard--the closest thing it had was either move (Ctrl-KV) or delete-block (Ctrl-KY).
-- MarkusQ
If you really think my analogy wasn't any good, why not support that with evidence having to do with viruses, instead of saying that analogies are wrong?
Sorry, I thought it was obvious (and note, I never said that "analogies are wrong"). For starters:
I could go on and on. If it weren't for the choice of names and cultural assumption of similarity, I don't think people would be so fond of this particular analogy. For example, we don't hear advertisements, religions, etc. lumped in this category, but the argument to do so is just as strong as the one for lumping computer and biological viruses. Do you propose that it should be illegal to discuss religion with people who aren't theologians? Should it be illegal to distribute advertising copy?-- MarkusQ
I like the idea of thinking about biological and computer viruses in the same way.
Sure. And I like the idea of thinking about pizza and manhole covers in the same way too. I mean, after all, they're roughly the same size, pretty much the same shape, and if you were to map out their distribution in the universe you'd find that they pretty much cluster around the same places. Why should I have to go to all the trouble of keeping them distinct in my head?
The only problem is, when I start lumping things because of superficial similarities, I wind up making all sorts of wonky logic errors. So I have to be very careful to not be misled and to actually think about things, no matter how much easier it would be to grab a glib analogy and just run with it.
-- MarkusQ
Using spread spectrum technology greatly increases bandwidth available
This just isn't true, any more than weaving around increases the width of a roadway. Sure, it might let you dodge some obstructions, but in the process you become an obstruction to other trafic. The total amount of information that can be carried doesn't increase. Just like in the weaving-around-on-the-road analogy, you have to ask, what would happen if everyone did this? The answer, of course, is that to a good first aproximation all those other SS broadcasters would look like noise to you; so the ambient noise level goes up and the S/N ratio falls, meaning less information gets through.
How much less? well, in an ideal world, if you do everything right you only lose exactly as much as you thought you'd gained. TNSTAAFL.
Each photon you reveive can only tell you so much. You can't beat the uncertanty principle with hand waving.
-- MarkusQ
Jabber, AIM, MSN, and others use TCP. In fact, the only client I know of that ever used UDP was ICQ, but that was an older protocol that is no longer being used
I think his point was that Jabber is like UDP in that you aren't sure that any particular message will get through, but then you don't pay the overhead of making sure.
-- MarkusQ
Why not eat your enemies it would give you incentive to kill kill kill !!!
Well, for one thing, you'd still have to carry in all the condements, etc. For another, most of my enemies aren't backpackers, so I'd have to haul them in too. And lastly, given what I think most of them are full of, I'm not sure I'd like the taste.
MREs seem a lot easier and more appitizing.
-- MarkusQ
I haven't found MREs to be all that objectionable. The thing to remember is that you don't eat them when you're staying in a five star hotel, just as you wouldn't sleep on the ground or catch rain water to drink. Conversely, you don't haul an espresso machine and a queen sized bed on your back for fifty miles just so you'll have "all the comforts" at the end of the day.
If you think in terms of food quality per Kg hauled (and remember that it's frequently you that's going to be doing the hauling), MREs are great--much better than trying to scrounge for twigs and berries, or going hungry.
--MarkusQ
This is good news because it isn't that good for you to subsist on nothing but Twinkies.
--MarkusQ
Outside of the i18n community, I haven't seen this style of abbreviation anywhere. If you have a better suggestion for an abbreviation, we'd be happy to hear it.
I don't have an alternative abbreviation to propose; I have a deep irony to point out. The whole point of internationalization is to make things that are only accessable to speakers of one language (generally English) accessable to people who speak other languages. That this process is denoted by a cryptic polyglyph that isn't obvious to native speakers of any language and is justified by obscure referrence to one particular language (which is English!) is (quite litterally I suppose) too ironic for words.
-- MarkusQ
So, I wonder, do people who have trouble spelling occasionally write i17n or i19n? Or is it more common for them to write i18n but omit the wrong sequence of letters?
i18n is short for internationalization. It is abreviated as i18n because there are 18 characters between the i and the n.
Thanks. Now that you mention it, I've even seen that before. But I still think it's pointless obfuscation. Or should I say:
T4s. N1w t2t y1u m5n i0t, I'(2)ve e2n s2n t2t b4e. B1t I*segfault* s3l t3k it'(1)s p7s o10n.
-- MarkusQ
and i18n's Itself
What the heck does "i18n's" mean?
"ilen is"?
"ilaten is"?
"ilsn is"?
"belonging to ilsn"?
I can think of about thirty possible interpretations and none of them make sense.
On licence plates, you only have a few characters to work with. On message boards, if you are doing something illegal and want to escape simple minded pattern searches, your are trying to be cryptic. But in a headline? What is the point?
And what does this mean?
-- MarkusQ
I was caught in this debate many years ago, and someone produced a digitized sound-bite from Linus with the "lie-nucks" pronunciation. After much confusion we realized that the sound file he had gotten off the web was someone else reading a statement attributed to Linus. The source if this misleading sound file?
MSNBC of course.
-- MarkusQ
Depends on how deep you push the boundary of syntax; some grammars distinguish article-ambiguities, e.g.
which raises the number of parsings to at least four. And for any a priori "the line between syntax and semantics should be drawn here" you can come up with, someone can doubtlessly construct an "easy to please/eager to please" counter example.-- MarkusQ
Brilliant! If I had points I'd mod you up!
-- MarkusQ
Even better, if you can get them: a pair of twenty sided quantum-entangled dice. That way, both sender and receiver can extend the pad at need, just by rolling up more numbers.
The only tricky part is reading the dice without looking at them. There are several ways to do this, but none of them actually work in practice and at least one of them is suspected of causing space-time errosion (& thus you will need to file an Environmental Impact Statement, including the plain text of the message being sent, thus reducing the utility of the system).
Another problem is keeping the dice cold. They have to be kept very, very cold, and of course this is very very expensive (C = A*exp(K-T)+B*N, where C is cost, K is Boltzman's constant, T is the temp., A and B are arbitrary constants related to local tax laws, and N is undefined).
But the main advantage of using quantum dice is that it would be too nerdly for words (at least three equations would be required) and you could probably get your picture in some magazine, wearing a white lab coat with coloured lights hitting you from odd angles.
-- MarkusQ
P.S. The original post was sound, but if you buy any of this post, I have a startup I'm trying to fund...