Yoruichi-san
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Posts posted by Yoruichi-san
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Reading old XKCD, I came across this and it made me think of brainden ;P. Then I thought it would cool to have a thread to post things, images, comics, quotes, news, w/e, that makes us think of our cyber-home.
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Actually, I think I'm gonna step back from the crazy experimental mafias and do something simple and popular next. In honor of the new Batman movie, going to (finally) finish making Justice League Unleashed ;P. I should have the setup done by this weekend, will start sign-ups sometime next week if there are no objections.
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Sorry, been really sick lately. Too feverish to think up a clever way of working the hint into a story, so...
(a square, sitting on it's base) -> (1,1,1)
(a rectangle, sitting on either base) -> (1,1,1)
(isosceles triangle, non-equal angle pointing up) -> (1,0,0)
(ninja star) -> (0,0,1)
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Well, this batch was certainly cleverer than the last. But they saw points, not the point. They did understand why a square was better than a rectangle and an equilateral triangle was better than isosceles. They did not see the infinite beauty that was around them.
She smiled to herself. Father had yet to engender a thing that could defeat her.
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A rectangle is pretty, I'm sure you'll agree,
But that a square is better is plain to see.
While isosceles is firmly in the race,
For the triathlon, equilateral takes first place.
On such beauty you may want to reflect,
Or rotate them around with your intellect.
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She was bemused at the latest pack of new toys Father had sent to sniff around her gateway. They seemed clever enough, and they had gotten past the first few rooms, true, but they would never get past this room. Creatures like them, so entrenched in the computational, would never be able to see the beauty around them, to understand it and its import. No, this was why she was what she was, why she must be what she must be and must do what she must do. Father had failed before, and here he would fail once more.
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First, an excerpt from the wikipedia page for "decimal."
And another excerpt from the page for "0.999..."
So since decimal places are the digits after the decimal point, it seems there is one pair of equal decimal expansion representations for each positive integer and each negative integer. And this is exactly the set of all the numbers that fit the OP. Any other terminating decimal expansion will have the pair of representations equal at one or more decimal places.
It is interesting that 0 fails in this regard. The method of decimal representation we use has no way of approaching 0 with repeating 9's due to the fact that adding value in a decimal place always increases the distance from 0.
If you change the OP to require a different digit in each place (not just decimal place, and can't simply not have a value explicitely put in a place (ie, both 0's in hundreds place of 34 and 67)), you find that at least one number needs to be infinite. You obviously cannot have an infinite number equal to a finite one. But what about two infinite numbers?
Sure, if you subtract the decimal representations of two infinite numbers created by an infinite decimal expansion, you could end up with a finite decimal expansion. But it seems it isn't possible in the case where the digits are different at every position. If you try the "trailing 9's" approach you end up with ....99999.9999... = ...00000.0000..., but the number on the right is 0, while the other is infinite. But are all infinite numbers created by this decimal expansion method equal anyway? For instance, is ...22222.2222... = ...11111.1111... ? You can keep subtracting 1 from both and never reach a negative number (or even a finite number). I'm thinking every infinite number created using this method of decimal expansion is equal (and equal to aleph-naught), and so the subtraction of the decimal expansions doesn't really apply since all are the same number/concept... and the difference is simply undefined. Sure, there are higher degrees of infinity, but they are essentially 2^(one of these infinite number) or more in "value."
Hyperreals sound interesting. I can't, at the moment, understand how there can be a non-zero infinitesimal. I'll quickly look that up. It seems that they handle it essentially like the different degrees of infinity, and just call all the infinitesimals nonzero. It seems to me like they are kept as two separate concepts, and when you order values you order them first by its "standard part" and then by the infinitesimals included.
Anyone have thoughts on any of this or disagree vehemently on a point?
You should also take a look at surreal numbers, which is somewhat related. It's a notation that involves taking the numbers "between" other numbers and is a very interesting way of looking at infinitesimals
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That would explain the "vertically labeled" bit I was confused about.
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It's a wedge shape, so that's the way it would look.
And yet the plot says there were 16 installments. Typo, Y-san?
Yeah, something weird happened with the copy-pasting. Part got repeated. Here:
(1,0,0), (0,1,0), (0,1,0), (0,1,0), (0,1,0), (0,0,0), (0,0,0), (1,1,1), (1,1,1), (0,0,0), (0,1,0), (0,0,0), (0,1,0), (0,0,0), (1,0,0), (0,0,1), (1,1,1), (0,0,0)
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The third door capitulated with nary a contest. Captain Wraith smiled as he watched his underlings march through it. Father must be proud...
The room they entered now was very round, perhaps even perfectly round, with cornflower blue walls (or perhaps it was better to say ‘wall’). There were no paintings or displays, the wall was a pristine barren blue. The ceiling was a metallic looking dome, and In the center of the room was a round table a shade lighter than the walls on which levitated a large metallic sphere whose surface took on a bluish hue as it reflected the color of the room.
Around it were several large, translucent, wedge shaped buttons, which were vertically labeled: (0,0,0), (0,0,1), (1.0,0), (0,1,0) and (1,1,1)
Cautiously, Orin approached the table. When he was within touching distance of it, it seemed to sense it presence and the (1,0,0) button lit up for a moment, then turned back off. Orin glanced back at Captain Wraith, who nodded, and then pressed gingerly down on the button.
A moment later, the (1,0,0) button lit up again (and turned off), and a moment later, the (0,1,0) button lit (and turned off). Orin mimicked the pattern. Then it was (1,0,0), (0,1,0), (0,1,0). Orin continued to repeat the shown series. After the sixth installment of the series, it became somewhat difficult for Orin to remember, but with the forthcoming aid of the other agents, he managed to get each within a few tries. The sixteenth installment was:
(1,0,0), (0,1,0), (0,1,0), (0,1,0), (0,1,0), (0,0,0), (0,0,0), (1,1,1), (1,1,1), (0,0,0), (0,1,0), (0,0,0), (0,1,0), (0,0,0), (1,0,0), (0,0,1), (1,1,1), (0,0,0)
But after he had repeated it correctly (yes, he and all the rest of agents were certain that it had been correct), instead of continuing on to the next installment, the buttons remained dark.
“I’m guessing we have to figure out the rest of the series for ourselves,” Wraith spoke up after a few moments. “I have an idea, but...it seems dependent on style...”
Father’s voice came. “Yes, but I believe the Witch gives beauty the benefit of a doubt.”
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Defining my coordinate system (and orientating the cat the mouse) so that mouse starts at (s,s), wgere s=length of one side, cat starts at (0,s). Also defining mouse speed = v, and X(t) to be my function of the x position of the cat at time t. At time t, the mouse's distance from its starting point is vt. The cat's distance from it's starting point is X, the velocity of the cat is nv. Hence the distance b/w the cat and the mouse will be sqrt((s-X)2+v2t2).
Then the speed of the cat, in the x-direction, dX/dt = nv(s-X)/sqrt((s-X)2+v2t2)
To be honest, it's been a while since diffEQ, so I don't recognize the equation or way to solve it off the top of my head. Bonanova and fabpig are probably right about it being a catenary. But solve this differential equation, and you will have the function (you can put it in terms of y, if you want, instead of t, by using the relation b/w the vt and y). You know it will take tf=s/v for the mouse to reach it's destination, so plug that in, put the other side equal to s (the total X-length the cat travels in that time), and solve for n.
Further correction. Somehow I always inadvertently put a - instead of a +...
Haven't had a chance to further work on a solution, though. I'm thinking u-sub or trial and error (guess the general form of the solution and then solve for constants).
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..that Father is working with the Witch to find a group worthy enough to track down and destroy the Devourer of Worlds.
Holy c...how do you do it...
Is entitled "The Power of Green" ;P
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Uh oh, MM is here...time to go hide the plot hints...and the silverware...
I'm kind of curious to know what happens when we run out of tries...
Mm...hmm...*taps fingers together in imitation of Mr. Burns*
Well done, everyone! The stuff for the next segment is on my comp at home, so it will up this evening. Meanwhile, please don't break anything...including the plot twists ;P.
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This is getting surreal...
...or perhaps you're trying to push us to our limits ;P
(On a totally unrelated and being a smart@z note in answer to the OP...scientific notation, anyone?
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The second door defeated, the triumphant agents marched through, managing enough manner not to jostle each other on their eager way.
The doorway led into another room, with sky blue walls and two doors on each side, a door opposite them, and, of course, the door they entered through. Above each door on the side hung a panel of LED’s displaying a series of numbers. Next to each door was another keypad, though the screen on these looked different and the keypads only had numbers.
Orin stepped to the first door on the left. The LED display above it read: 33-29-19-22-13-15. He shrugged and entered the numbers into the keypad. The door clicked open, and the curious agents struggled to get a peek inside. A small alcove with nothing of interest: clothes on hangers hung on a rack, old shoeboxes stacked on the ground and hatboxes stacked on the shelf above.
Orin moved on to the next door. Its LED read: 36-17-14-22-13-14-16. Again, he inputted the numbers, and the door clicked open. Inside was a bedroom, with pastel flowered wallpaper and stuffed animals lining the walls, and a crib in the center with a mobile of the solar system rotating above it.
Next he moved to the doors on the right. The first, whose LED read: 35-21-15-26-14-19-19-37, made Orin frown and Wraith smile as they glanced its tiled floor, sink, and toilet. “At least she’s considerate enough to provide amenities,” the captain joked.
The last side door, 22-15-17-23-16, was walled with impressive bookshelves fraught with antiquated but well-maintained tomes and contained a large mahogany desk atop which lay strewn papers and pens.
Orin turned back towards the group to make a comment, but stopped when he noticed the LED display above the door by which they had entered: 13-36-15-14-21-36-33-13. It, though, had no keypad.
The final door on the diametric wall was the opposite. It had a keypad, but no LEDs. On the very left of the keypad display, partitioned from the rest of the display with a |, was the number 3.
“I’m guessing that’s the way we have to go,” Wraith remarked. “Well, better get started.”
Orin shrugged. It seemed too easy, but maybe he should try the number from the door they had entered by? He stepped up to the keypad and did so, then pressed [enter]. The keypad display flashed. Could it have been that easy?
The door didn’t budge, but the 3 changed to a 2.
“Hmm...I’m going to guess that’s the number of tries we have remaining and I’m further going to guess that we don’t want to know what happens when we run out of tries,” Wraith remarked. “We better think this one through...”
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The effervescently tempered agents were effulgent with ideas. They tried more codes, but the door remained immutable.
Orin was still ruminating over everything that had occurred. There was something they were missing. All these things so far, the first door, the second door, the pictures, they had to connected somehow, but how? The code for the first door, so specific. An equivalent effect could have been gotten with different numbers in the 2nd, 4th, and 6th positions, it was only the 1st, 3rd, and 5th that really mattered. But yet that number...he had a feeling that it had been specifically chosen for a reason. The pictures as well, an odd selection, not a collection you'd expect anyone to have chosen for aesthetic purposes. Why that number, and why those pictures? Could it be...
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Janine pursed her lips as she listened to other end of the link. Boys, always picking up on specific words rather than hearing the meaning of the message itself. She sighed deeply. Then one of them said something that made her perk up. Finally, a guy who actually listened!
Orin, meanwhile, was pondering. "So...if not a coincidence..."
Two eager agents were keen to try their proposed solutions on the door. The first entered a series of numbers. The door didn't budge. The other one followed quickly with a similar series. Nope, no cigar.
Orin furrowed his brows more deeply, staring at the door. The silvery blue door that was identical in every way to the door that had come before. Then an idea began to form in his mind. Hmm...maybe...?
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Defining my coordinate system (and orientating the cat the mouse) so that mouse starts at (s,s), wgere s=length of one side, cat starts at (0,s). Also defining mouse speed = v, and X(t) to be my function of the x position of the cat at time t. At time t, the mouse's distance from its starting point is vt. The cat's distance from it's starting point is X, the velocity of the cat is nv. Hence the distance b/w the cat and the mouse will be sqrt((s-X)2-v2t2).
Then the speed of the cat, in the x-direction, dX/dt = nv(s-X)/sqrt((s-X)2-v2t2)
To be honest, it's been a while since diffEQ, so I don't recognize the equation or way to solve it off the top of my head. Bonanova and fabpig are probably right about it being a catenary. But solve this differential equation, and you will have the function (you can put it in terms of y, if you want, instead of t, by using the relation b/w the vt and y). You know it will take tf=s/v for the mouse to reach it's destination, so plug that in, put the other side equal to s (the total X-length the cat travels in that time), and solve for n.
Oops, making a correction. I want the x-component, not the y-component. Also, I realized this whole thing might be easier if I put in terms of theta(t), instead of X(t). Will try when I have time.
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Defining my coordinate system (and orientating the cat the mouse) so that mouse starts at (s,s), wgere s=length of one side, cat starts at (0,s). Also defining mouse speed = v, and X(t) to be my function of the x position of the cat at time t. At time t, the mouse's distance from its starting point is vt. The cat's distance from it's starting point is X, the velocity of the cat is nv. Hence the distance b/w the cat and the mouse will be sqrt((s-X)2-v2t2).
Then the speed of the cat, in the x-direction, dX/dt = nv2t/sqrt((s-X)2-v2t2)
To be honest, it's been a while since diffEQ, so I don't recognize the equation or way to solve it off the top of my head. Bonanova and fabpig are probably right about it being a catenary. But solve this differential equation, and you will have the function (you can put it in terms of y, if you want, instead of t, by using the relation b/w the vt and y). You know it will take tf=s/v for the mouse to reach it's destination, so plug that in, put the other side equal to s (the total X-length the cat travels in that time), and solve for n.
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The agents were making progress, cracking the enigma. They cut through five of them like a hot knife through butter. But the last one, they weren't so sure about.
Janine's voice came over the neuro-link. "I don't suppose you boys would get it," she said in a cheerful, joking tone. "After all, it's us girls who have to do all the cooking. You just wait until the end and claim the glory of carving."
"I think I see now..." Orin spoke up a moment later. "But...what are we supposed to do now? Is the fact that the door is the same color as the previous just a coincidence? Or perhaps it was just to save on building material costs?"
There was muffled sound over the neuro-link. Was it...could it have been...a laugh? Then Father's voice came on, composed as ever. "No, Orin, I do not think that is it."
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The agents continued to concentrate. A few of them thought it might have to do with hex values.
"Perhaps," Father responded. "But the Witch has no particular interest in the computational. She likes to play."
"Or maybe we have to research the pictures?" One suggested.
"That I doubt," was the great Father's reply. "The second picture, I believe it is a private picture, I recognize the destination, and professional pictures taken there are of a much higher quality. I also do not believe the destination itself has anything to do with the solution. You should search for some element in the picture, or related to the picture. The tool itself, I suspect, you will have to search for, as it is not something easily memorized in its entirety."
Wraith considered for a moment, then his eyes glazed as if he was looking at something through his neuro-link. "Yes...hmm...that seems to work. It would seem 209 is the most straightforward of the bunch. It's exactly what's in the picture."
(Aside: Yes, I did take the second picture myself
. It's Huang Long/Jui Zhai Gou in Northwest China, and truly breathtaking if you ever get a chance to go. And no, that has nothing to do with the puzzle ) -
When I keep hitting 'refresh' to see if the number of views on my topic has gone up.
When I feel sad when it hasn't
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The agents pondered over the puzzling pictures. One took note of what Father had said. "Perhaps we have to find the words that are associated with these pictures?"
"That seems like a sound plan," Father's voice in their heads intoned. "Also, be aware that the questions will never have letters or words, but the answers might."
Another stroked his chin pensively. "Perhaps something to do with the metal of the door and the way the color blue is associated with these things?"
"Perhaps...but the Gateway is not as much about the color itself as what the color represents. Not all the objects inside the blue Gateway will be related to blue."
Wraith nodded, an idea coming to him. "Well, blue is objective, right? Maybe the Chromatic Witch is using a tool here, to express some element of these pictures. Something that does not change when one changes borders..."
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6. Muffle (I think it's pronounced "mul-eh")
Edit: Love 7 by the way...great song ;P
Generals
in Games
Posted · Edited by Yoruichi-san
Hmm...seems interesting. Hope I'll have time...
5-Star: Hirkala
1. Admiral Molly O'Mae
2. Gerenal MikeD
3.Captain Aaryan
4.valkyrie phillip
5. grand master overlord general tyrant supreme ruler Flamebirde
6. Cadet Brainiac100
7. [Genetic experiment created by splicing together the DNA of Julius Caesar, Cao Cao, and Napolean Bonaparte] Y-san
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Take that. Gratimerxie
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