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Riddle Me This, Batman! in General
Electric Sheep One
Member # 3431
Profile #102
Ah; I see your point. Thanks for the very clear answer.

I guess I'm too used to physics, where one indeed often has to be careful about orders of limits, but where the right thing to do is almost always to keep everything finite until the final answer, and only then take the limit.

Our limit ordering problems almost always arise because huge but finite quantities have been approximated as infinite, and although you can sometimes retain the infinite limits and come out okay with fancy footwork, the really correct thing to do is to remember that in fact it's all finite.

[ Tuesday, August 22, 2006 02:39: Message edited by: Student of Trinity ]

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Posts: 3335 | Registered: Thursday, September 4 2003 07:00
Riddle Me This, Batman! in General
Electric Sheep One
Member # 3431
Profile #100
And I guess I'm asking, "Are you sure?" The answer you've given is old hat; I'm asking for a rethinking, not just a reiteration.

If 0.999... is not by definition an infinite series, what is its definition? And if it is, isn't it indeed the limit as 1 is approached from below?

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Posts: 3335 | Registered: Thursday, September 4 2003 07:00
Riddle Me This, Batman! in General
Electric Sheep One
Member # 3431
Profile #97
I did not say it was approaching; I said it was the limit. I would be surprised if you could define infinite decimal representations without some invocation of limits. If you can, go ahead; I'd be happy to see it.

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Posts: 3335 | Registered: Thursday, September 4 2003 07:00
Riddle Me This, Batman! in General
Electric Sheep One
Member # 3431
Profile #94
Isn't 0.999... more specifically equal to the limit as you approach 1 from below? It seems as though it ought to be. So then 1/(1-0.999...) would be positive infinity, with unambiguous sign.

So how come we can't do things like this to make the limit as you approach 1 from above? Writing 1.000 ... 001 doesn't really work, does it?

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Posts: 3335 | Registered: Thursday, September 4 2003 07:00
Idea for realsing creations in Geneforge 4: Rebellion
Electric Sheep One
Member # 3431
Profile #36
I have no doubt the creations can get around any controls the Shapers could impose. What they can't get around is Jeff's G rating.

Anyway, Eyebeasts just like to watch.

[ Sunday, August 20, 2006 12:49: Message edited by: Student of Trinity ]

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Posts: 3335 | Registered: Thursday, September 4 2003 07:00
School in General
Electric Sheep One
Member # 3431
Profile #46
The thing everyone says about writing is that you indeed learn it by writing. Why not write a bunch of little essays and get a degree that may later give you some security in which to write? Hunger is not inspirational. And life as an English major still leaves plenty of time to write your own stuff.

And give yourself some credit. Nothing's going to screw up your own style if you don't let it.

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Posts: 3335 | Registered: Thursday, September 4 2003 07:00
Dinosaurs Are Alive in General
Electric Sheep One
Member # 3431
Profile #45
Job 41:1-34: The speaker is God, questioning Job. (King James Version; I deleted the verse numbers and made up paragraphs.)

quote:

Canst thou draw out leviathan with an hook? or his tongue with a cord which thou lettest down? Canst thou put an hook into his nose? or bore his jaw through with a thorn?

Will he make many supplications unto thee? will he speak soft words unto thee? Will he make a covenant with thee? wilt thou take him for a servant for ever? Wilt thou play with him as with a bird? or wilt thou bind him for thy maidens? Shall the companions make a banquet of him? shall they part him among the merchants?

Canst thou fill his skin with barbed irons? or his head with fish spears? Lay thine hand upon him, remember the battle, do no more.

Behold, the hope of him is in vain: shall not one be cast down even at the sight of him? None is so fierce that dare stir him up: who then is able to stand before me? Who hath prevented me, that I should repay him? Whatsoever is under the whole heaven is mine.

I will not conceal his parts, nor his power, nor his comely proportion. Who can discover the face of his garment? or who can come to him with his double bridle? Who can open the doors of his face? his teeth are terrible round about. His scales are his pride, shut up together as with a close seal. One is so near to another, that no air can come between them. They are joined one to another, they stick together, that they cannot be sundered.

By his neesings a light doth shine, and his eyes are like the eyelids of the morning. Out of his mouth go burning lamps, and sparks of fire leap out. Out of his nostrils goeth smoke, as out of a seething pot or caldron. His breath kindleth coals, and a flame goeth out of his mouth.

In his neck remaineth strength, and sorrow is turned into joy before him. The flakes of his flesh are joined together: they are firm in themselves; they cannot be moved. His heart is as firm as a stone; yea, as hard as a piece of the nether millstone.

When he raiseth up himself, the mighty are afraid: by reason of breakings they purify themselves. The sword of him that layeth at him cannot hold: the spear, the dart, nor the habergeon. He esteemeth iron as straw, and brass as rotten wood. The arrow cannot make him flee: slingstones are turned with him into stubble. Darts are counted as stubble: he laugheth at the shaking of a spear.

Sharp stones are under him: he spreadeth sharp pointed things upon the mire. He maketh the deep to boil like a pot: he maketh the sea like a pot of ointment. He maketh a path to shine after him; one would think the deep to be hoary.

Upon earth there is not his like, who is made without fear. He beholdeth all high things: he is a king over all the children of pride.
The four other Biblical references to Leviathan are much briefer, but one of them mentions that it is a type of serpent. I somehow have the idea that it is usually identified as a type of crocodile.

[ Sunday, August 20, 2006 04:07: Message edited by: Student of Trinity ]

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Posts: 3335 | Registered: Thursday, September 4 2003 07:00
Riddle Me This, Batman! in General
Electric Sheep One
Member # 3431
Profile #86
The obvious answer is: ...

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Posts: 3335 | Registered: Thursday, September 4 2003 07:00
Riddle Me This, Batman! in General
Electric Sheep One
Member # 3431
Profile #81
Since we're all having so much fun with this one, or at any rate the number of posts in this thread is becoming arbitrarily large, perhaps it's time for the Prisoner's Dilemma.

Two partners in crime are being tried separately. A sharp prosecutor makes the same proposal to each one: rat on the other, for a reduced sentence of 5 years, so that the prosecutor can score a major conviction on the other one and get him put away for 20. If neither crook confesses anything, circumstantial evidence will send them both to jail for 10 years. If they both try to rat on each other, the credibility loss will make the biggest case fall apart, but they'll both look bad enough to pull 15 years.

So each prisoner has the choice to collaborate with the prosecution or not. If both collaborate they get 15 each; if both keep quiet, they get 10; if only one collaborates, he gets 5 and the other gets 20.

The orthodox, game theory answer to this problem is clear. Prisoner A should figure that if prisoner B collaborates, he should collaborate too to get 15 instead of 20 years. And if prisoner B doesn't, he should collaborate to get 5 instead of 10. So either way, he should collaborate.

The funny part is that both prisoners' reasoning should be the same, so both should collaborate, and both get 15 years. Whereas if they had not bothered with game theory, and just stuck to the crooks' code, they would both have kept quiet and gotten away with 10 years each. Somehow game theory makes the outcome worse.

If you haven't heard this one before, it's actually important. It is used as a simple model for all kinds of dismayingly bad real world problems.

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Posts: 3335 | Registered: Thursday, September 4 2003 07:00
School in General
Electric Sheep One
Member # 3431
Profile #24
Yeah, classes just ended a couple of weeks ago here, and I began recovering, oh, yesterday. They start again near the end of October. September has a completely different meaning to me now.

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Posts: 3335 | Registered: Thursday, September 4 2003 07:00
Oopsie Daisy (Ver 5.5) in General
Electric Sheep One
Member # 3431
Profile #7
Good translation should not generally be word-for-word; but if that were the goal, there is no 'the' in d'escalier.

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Posts: 3335 | Registered: Thursday, September 4 2003 07:00
Shaper hypocrisy vs. Shaper tragedy (SPOILERS) in Geneforge Series
Electric Sheep One
Member # 3431
Profile #173
High officials in the executive branch of the US government are always good at hitting people with shotguns.

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Posts: 3335 | Registered: Thursday, September 4 2003 07:00
Oopsie Daisy (Ver 5.5) in General
Electric Sheep One
Member # 3431
Profile #5
I was just thinking of posting about pensée d'escalier, but now it's too late.

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Posts: 3335 | Registered: Thursday, September 4 2003 07:00
Oopsie Daisy (Ver 5.5) in General
Electric Sheep One
Member # 3431
Profile #4
Absolutely. Everyone knows that the artificial gravity machine was front page news all over the world. Airlines would all be obsolete already, if they could just succeed in turning the thing upside down without it falling over like this.

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Posts: 3335 | Registered: Thursday, September 4 2003 07:00
Faustian theory of aging in General
Electric Sheep One
Member # 3431
Profile #9
Or you develop a nice signature, and then you have to change it again.

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Posts: 3335 | Registered: Thursday, September 4 2003 07:00
Icshi's Whereabouts in Richard White Games
Electric Sheep One
Member # 3431
Profile #19
More of an Ex-exarch, then.

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Posts: 3335 | Registered: Thursday, September 4 2003 07:00
Story LIne in Geneforge 4: Rebellion
Electric Sheep One
Member # 3431
Profile #2
I don't know about 'by far'. I think G2 and G3 work well as logical developments. But G1 was definitely a bit better. Everything kind of worked, and the only loose end that was there for me was that there was no indication of just how the PC was growing in power so quickly. That got taken for granted as part of CRPG convention, when in fact the Geneforge-y theme of the game offered a great opportunity to make it an important working part of the story.

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Posts: 3335 | Registered: Thursday, September 4 2003 07:00
Faustian theory of aging in General
Electric Sheep One
Member # 3431
Profile #5
The next ten. From now on.

It may be worth distinguishing serious learning of big things, like becoming fluent in a new language, from just picking up scraps of novelty. Most serious subjects have a learning surface that's pretty gently sloped around the periphery, and you can easily absorb some fun facts. At some point, though, you learn enough to realize that you've been playing on the beach of a continent, and that to explore the interior would take years of hard work. That's the part that is hard.

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Posts: 3335 | Registered: Thursday, September 4 2003 07:00
Riddle Me This, Batman! in General
Electric Sheep One
Member # 3431
Profile #64
Right. You could have average probabilities equal (in the sense that I had in mind) if half of the families always had boys, and half always had girls. Then if nobody cared about the sex of their children there would be equal numbers of each; but if everybody wants one boy, you get half the families with one son and the other half with huge numbers of daughters, for a whopping gender imbalance.

I think Shaw was kind of a loon, and I don't really know whether he ever propounded this theory. But it goes to show something, I figure. Maybe that there's often a fine line between idealized model and straw man.

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Posts: 3335 | Registered: Thursday, September 4 2003 07:00
Faustian theory of aging in General
Electric Sheep One
Member # 3431
Profile #0
Here is my Faustian theory of aging, which is perhaps not wholly sincere, but which I do fear holds all too much truth.

Middle age is about getting smart. You get smart by coming to take for granted all the things that took you years to figure out at first. Because the trick to being smart is that already knowing is a lot faster than learning. So the trick to being really smart is simply to stop learning and start already knowing. You stop wasting so much time and energy wondering whether you really understand anything, and start assuming that you already know the answer and just have to spit it out. And once you've done enough learning, you can do this. While it works, it works great. For ten years or so, I figure, you can be amazingly smart.

Then all the things you take for granted, and that thereby make you smart, start not being true any more. Now you're Faustus in Act V. Now you no longer know anything, and even though you might not actually be so much worse than a young person at learning things, you're far too used to the speed of already knowing things to go back to the slowness of learning, which was after all so miserably slow that no-one who had ever tasted better could stomach it. So you become a stupid old person.

I'm currently trying to decide whether trying to beat this pattern is worth risking the loss of those ten good years. Because in the end you're going to die, no matter how long you keep learning, and to achieve anything significant, maybe you need those ten years of higher efficiency than learning can ever deliver.

The tragedy isn't that you get seduced away from life-long learning; learning really is horribly slow, and a human lifetime of learning is unlikely to dent the universe. The tragedy is that the time of knowing doesn't last. But it would be worse if it did, because it could only last if the world stood still and no-one ever achieved anything.

It's mortality's first harmonic, the inherently necessary mortality of human competence.

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Posts: 3335 | Registered: Thursday, September 4 2003 07:00
Riddle Me This, Batman! in General
Electric Sheep One
Member # 3431
Profile #52
That is indeed the easy answer. If every birth gives equal chances for girls and boys, no rule for deciding when to try another birth can change the odds. Alorael, do your infinite sums again. I might confess that I didn't see it so well the first time I heard it, myself. Maybe I had a hunch even then about the hard answer. Or maybe I was kind of dumb as a beginning grad student, and slowly got somewhat better.

Thuryl has the right idea for the hard answer.

[ Tuesday, August 15, 2006 13:14: Message edited by: Student of Trinity ]

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We're not doing cool. We're doing pretty.
Posts: 3335 | Registered: Thursday, September 4 2003 07:00
Shaper hypocrisy vs. Shaper tragedy (SPOILERS) in Geneforge Series
Electric Sheep One
Member # 3431
Profile #167
quote:
Originally written by Randomizer:

I think I read about a solution in a Ray Bradbury short story. You attach a device to everyone's head with any intelligence so when they think they get assaulted with so much noise that they lose their concentration. It lowers everyone down to the level of the idiots.
Web boards are the beta version.

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Posts: 3335 | Registered: Thursday, September 4 2003 07:00
Quick thought about boss battles in Geneforge 4: Rebellion
Electric Sheep One
Member # 3431
Profile #14
You're fighting with blades, fire, teeth, acid, all those good sorts of things. And after 14 rounds your enemy is going to suddenly drop dead, without a scratch, as if from a heart attack? You have to see the damage accumulating. Without creating a dozen or so extra skins for every creature in the game, which is not exactly Spiderweb's level of graphical sophistication, a health bar is the only way.

For special monsters that showed no apparent damage until suddenly collapsing, for whatever reason, Jeff could always keep the health bar at full and then kill with a script.

[ Tuesday, August 15, 2006 00:55: Message edited by: Student of Trinity ]

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Posts: 3335 | Registered: Thursday, September 4 2003 07:00
Brief Geneforge 4 Update in Geneforge 4: Rebellion
Electric Sheep One
Member # 3431
Profile #17
But if you're a Servile put lots of points into Leadership, or else whenever you take one of those dialog options that ends in '(Lie.)', your nose will grow even longer.

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Posts: 3335 | Registered: Thursday, September 4 2003 07:00
Riddle Me This, Batman! in General
Electric Sheep One
Member # 3431
Profile #41
Another little statistical puzzle. I once heard the following theory attributed to George Bernard Shaw. Suppose the average probabilities of a baby being born male or female are equal (and to forestall pointless kibitzing, let both be 50% for the sake of this discussion). Nevertheless (the theory argues) there end up being more girls born than boys, because many families want to have at least one boy, so they keep having children until they get one, resulting in disproportionately many families with several sisters and one baby brother.

The easy version of the puzzle, which is the one I heard, is to show that this theory couldn't possibly work. The slightly harder version, which I believe I invented, is to show that it easily could.

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Posts: 3335 | Registered: Thursday, September 4 2003 07:00

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