everyday847

Originally Posted By: Khoth You don't need the axiom of choice to well-order the rationals. Any ordering you come up with to show they're countable will do (eg the one you get by writing them all down in an infinite plane and spiralling out from 0). Right: I'm saying that the axiom of choice is equivalent to something that's called something like the well-ordering principle that states that you can well-order any (nonempty?) set. Originally Posted By: Khoth I think the lexicographical ordering works if you extend it to negative numbers (just shove in -x after every positive x). No. What, by the lexicographical ordering, is the smallest negative rational number? If you can't answer that question, it's not a well-ordering. Ohh, are you proposing that you do something like 1, 1/2, 1/3, 1/4, ..., -1, -1/2, ... Yeah, I guess that works.

Originally Posted By: Celtic Minstrel Originally Posted By: Micawber Induction works on well-ordered sets. Being well-ordered is completely different from being countable, although the natural numbers happen to be both. But uncountable well-ordered sets are much studied. The rational numbers in the usual ordering are not well-ordered. But if I'm not mistaken, it's possible to well-order the rationals, isn't it? Perhaps using a lexicographical ordering? (ie 1, 1/2, 1/3, ..., 2, 2/3, 2/5, ..., 3, 3/5, 3/7, 3/8, ..., etc) Every set can be well-ordered if you're down with the axiom of choice, so yes--but the "lexicographical" ordering doesn't really work. For a well-ordering, every nonempty subset of the set you want to well-order has to have a least element. What's the smallest negative rational?

Originally Posted By: Like Mana from the Pacific Comparisons are by definition not equations. Equations require that equals sign. But your point is otherwise correct. —Alorael, who wouldn't be too sure about horses. He's fairly sure that's how dogs' brains work. His point is that the notion of comparing less than/ greater than (in the way that seems most obvious for real numbers) comes from mathematics, rather than from our external experience of real numbers. I don't find this to be accurate (though I'll readily admit that the reals look nice under that ordering--but I could well just be biased about it!).

Originally Posted By: Jadan Reguardless, Eating more or less is still a generic terminology involving mathematics. No, comparisons aren't defined in terms of mathematical relations. Quite the opposite; you can't define a field and hope that its structure will just tell you how to order its elements. (Though because of external intuition because we have concepts of eating more and less or whatever, some orderings seem more natural than others.)

Originally Posted By: Celtic Minstrel Originally Posted By: No_More_PLL_Ever some non-rational numbers, such as pi or the squared root of any prime number, have "names" and so any multiplication of them with a rational number has a "name" (maybe even addition can be dragged in this way). Not just the square root of prime numbers; the square root of any non-square number, the cube root of any non-cube, the nth root of any non-nth-power... and that's not the only set of functions that generates irrationals from rationals in a systematic way. There's the log functions, the trigonometric functions... even regular operations such as addition, subtraction, multiplication, division, and exponentiation. You're slightly misinterpreting, I imagine: he's not saying that "only the square roots of primes are irrational"; he's saying that "the square roots of primes can be said to have 'names' and then you can start generating the names of other irrationals from there." Nonetheless, you'd need the nth roots of all primes, plus a bunch more, and you'd still never accomplish the task because there are uncomputable numbers and as long as a number can't be computed, you can't meaningfully give it a name (since you can't call it 'log of pete' or 'cosine of mike' or much of anything else, as it can't be given as a function evaluated on some argument that can be computed by a finite, terminating algorithm.)

You're totally right, Slarty. Though, for what it's worth, a lot of qualities of written language can be interpreted in terms of features of spoken language. (Italics, perhaps, or, on the Internet, the use of <sarcasm> tags or something, could be effectively prosodic features. They certainly are as analogous to spoken prosody as certain qualities of signs in ASL can be said to be.)

Yeah, there's really no way to answer this question. There aren't objects with which we can interact that could interact with spirits or demons or whatever (unless you have a really strange construction of what a spirit or demon would be, were one to exist). The natural bridge is that you have to assume that magic (of some form; doesn't matter if it's FMA's alchemy, So You Want To Be a Wizard style, Robert Jordan style, D&D style, Spiderweb Software style, whatever) exists. That magic could be directed against the demon or spirit or it could be used to enchant a weapon. But since magic doesn't exist, this isn't real life; since neither demons nor spirits exist, I'm not too worried.

Originally Posted By: CRISIS on INFINITE SLARTIES Originally Posted By: Celtic Minstrel and the meaning of a word has nothing to do with grammar. Originally Posted By: everyday847 Well, from a linguistic standpoint Celtic Minstrel is right on the second point: the lexicographic representation of a language doesn't have anything to do with its grammar. 1) "The meaning of a word" and "the lexicographic representation of a language" (AKA, the lexicon) are not the same thing. 2) Even if you divorce "meaning" from all utterance-specific context and instead say "the imaginary, perfect dictionary definition of a word has nothing to do with grammar" you are still incorrect. We can perhaps pretend in our heads that we are thinking of the essential concept behind a given word, but the reality is that, when a concept is given representation in a word, that word has phonological, morphological, and of course, syntactic features that depend on the grammar and which, in addition to influencing the lexical form of the word, impact its meaning. To illustrate this point, show me how the intransitive lexical entry for "kill" can have the same meaning in a nominative-accusative and an ergative-absolutive language. It can't, even though the concept of killing is the same in both cases. Yeah, you're right.

Well, from a linguistic standpoint Celtic Minstrel is right on the second point: the lexicographic representation of a language doesn't have anything to do with its grammar. But that's the sort of boring point you can only make if you're okay with people who interject "2+2=4? who says I'm not working mod 3? pfaugh!" when you're clearly just adding numbers together not being strangled.

I'm skeptical.

Well, it's the name of Ahriman. There's plenty of analogy to the Christian devil if you are a Christian, I guess, but "the devil" came second.

Saraph observes "with his senses:" dynamite prose right there. Also, he hugs his sister for a straight hour? Impressive.

I'd sooner attribute Ahriman to Zoroastrianism, wouldn't you?

I'm holding my breath.

Steven Crane's collected poetry: the volume has Black Riders, War is Kind, and a few freestanding poems.

Originally Posted By: Dantius Originally Posted By: everyday847 While, of course, this is laughably improbable, it wouldn't be the first time that microorganisms irreversibly altered the composition of Earth's atmosphere. Correct me if I'm wrong, but aren't microbes the only thing that has irreversibly altered the earth's atmosphere? They are indeed.

I hardly trust cracked for the science of it; I'm a chemist. I meant only that potentially hazardous experiments in biological engineering are hardly new and that there's nothing especially apocalyptic about the fact that someone's made a bacterial genome from scratch. Lilith, the microbe in question wasn't causing any kind of disease; it would--supposedly--alter the atmosphere's ammonia content. While, of course, this is laughably improbable, it wouldn't be the first time that microorganisms irreversibly altered the composition of Earth's atmosphere. EDIT: whoops, missed that post. In any event, I'm not saying that it's particularly likely to. The oversight isn't that the scientists didn't realize that they were for-sure upping the ammonia content of the atmosphere to unsafe levels; it's that they didn't realize that there was a reasonable chance that they would.

Originally Posted By: Free as in phase space But when we get there, well, I don't see the dire predictions amounting to much. Jurassic Park doesn't turn disastrous because it's full of dinosaurs, it turns disastrous because it's full of dinosaurs and rather short on basic safety precautions. Now, creating problems I'll grant. Someone is likely to design, say, a pollution-eating microbe that ends up being a massively invasive species that ravages an ecosystem. It's just a matter of playing it as safe as possible and, if you're so inclined, praying. It's worked reasonably well for technology so far. This actually has basically happened before, as I recall. I believe it featured in a cracked article that I can't find at the moment, but the above almost happened--except the end result would have been the eradication of all edible plants had some wise scientist not reread the paper and cried foul.

Originally Posted By: Atrix Im dong the sack tenerva quest and i don't know how to get in when i use the dispel barrier spell on the barriers its say This barrier is to powerful to even be affected by this spell. If some one could tell me how to get in id realy appreciate it. The second set of three jobs for Levitt are clearing Fort Draco, lifting the siege at Fort Monastery, and aiding Tenevra. For the last, you have to talk to Ghall-Ihrno, who will mark you so that you can enter Tenevra. Though I haven't done any of Melanchion's quests yet, I imagine that that mark will still let you enter.

It depends on the situation. There are situations in which you want higher consistent damage (and the spellcraft route is thus profitable) and situations in which you would actually benefit more from damage with higher variance but a lower average. (You could string three 140% hits together and kill a baddie, even if infrequently, while it would always take four 120% hits to do so. Of course, the 120% hits are strongly advantaged if you're fighting a single boss that'll take you a large number of hits to kill.) Essentially, variance has value in and of itself because the enemies you fight have discrete chunks of HP that define their lives. If the goal of the game was to do x HP of damage to the game world, and all damage wasted on one enemy would spill over into the next, the higher average would be decisively better in every situation.

Originally Posted By: CRISIS on INFINITE SLARTIES Originally Posted By: Roy Dest in good strategic turn-based combat RPGs... the party itself uses AI to fight Uhhhh... no. Yeah, if there's a need for a quick-combat system or whatever, that means that a reasonably large number of combat encounters are so dull that you can't stand to do them yourself. That blows! That actually reminds me of the later stages of Revelations: The Demon Slayer. I was trekking away, I think up a mountain, and I kept on getting random encounters with monsters I knew I could defeat easily, and I really couldn't be bothered to do anything but the quick-combat feature.

This would make implementing artificial intelligence much more difficult. Suppose one of your characters has HP left within the range of possible damage that Goblin A might do with a typical strike. Goblin B is going to have to decide whether to target that character or another character before it's known whether that character survives the first blow. Or are you suggesting that this isn't a modification of the combat system, but just how the results of combat are displayed--so that, in fact, the goblins are able to strategize the same way and their actions are simply displayed at the same time? That's be more plausible, but either the AI would have to make a lot of bad decisions or it would appear sort of cheap.