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See 4-D Space With 3-D Glasses
purpleant writes: "A hyperplane is a 3-dimensional space that slices through the 4-dimensional space, the same way a 2-dimensional plane can slice through our 3-dimensional space. The bounding hyperplanes can be extended infinitely so that they criss-cross through each other, chopping up hyperspace into many 4-dimensional 'chunks.' Again the inner chunks are finite, and they are distributed in shells around the core polytope. The
HyperStar applet displays those finite chunks, one shell at a time. The inner shells are complete -- each shell completely encases the previous shell. The outermost shells have holes in them."
4 dimensional space is relevant to slashdot, why?
In my complex analysis class at University, my professor said it was easy to visualize 4 dimensional functions. He proceeded to draw some kind of squiggle on the chalkboard and said, "There, just don't be close minded". We didn't laugh.
It the worlds first java-based kaladioscope!!
Now all I need s a webbrowser at the end of a tube and I can relive my childhood.
In Soviet Russia you dant have to put up with these crappy jokes
Eat it up you fucking geeks!
I thought the fourth dimension was time.....
Psycadelic baby!
From http://www.reactorcritical.com/#l1205
In Quake III Arena in 1280x1024 with 4x FSAA enabled, NV30 is going to be 2.5 times faster than the GeForce4 Ti4600.
In The Next Doom the board based on NV30 will be able to show 3.5 times or or even more of the performance the current Nvidia`s flagman has to offer us there.
NV30 will score three times more than the GeForce4 Ti4600 in 3D Mark 2001.
Effective HQ Pixel Fillrate (2x anisotropic filtering enabled) of the newcomer with will be about 2.7 times more than that of the fastest NV25.
As for pixel-shading speed, it will be 4 times of the NV25.
Think of the PORN!
"But the cars are all flashing me, bright lights are passing me, I feel life passing me by" - Stiff Little Fingers
... too bad I don't really have a clue what it means. *sigh* I guess this is why I'm not majoring in Math ;-)
As if trying to visualize the 4th dimension wasn't enough to give you a headache it comes with a 'cross-eyed' setting.
"A language that doesn't affect the way you think about programming, is not worth knowing" - Alan Perlis
FE:So, what's the closest you ever came to experiencing the fourth dimension?
Rucker: Well, there was this one time, we'd been partying all night, and I wanted to get a little higher. We were almost out of drugs, but I did have some acid. So I took it, but then I fell asleep. And when I woke up...
FE: Oh, I've been there. That's the fourth dimension?
so it's 5 am monday morning on the east coast and i decide to check out slashdot before going to bed for 4 hours of shuteye before work tomorrow (don't ask, crazy weekend). i am bleary eyed, brain dead, exhausted.
;-P
and i read "The bounding hyperplanes can be extended infinitely so that they criss-cross through each other, chopping up hyperspace into many 4-dimensional 'chunks.' Again the inner chunks are finite, and they are distributed in shells around the core polytope."
dudes! my functional iq right now is about 50! if you are going to post these kind of stories on slashdot, could you PLEASE post them around, say 3pm on a thursday? thanks
i should be awake by then, and i promise i will come back and try to wrap my mind around this story at that time... grumble, grumble
intellectual property law is philosophically incoherent. it is your moral duty to ignore it or sabotage it
Step 1: Make cool applet with shapes and colors. .....
Step 2: Explain shapes and colors with big words and things nobody knows anything about ie: hyperplanes, polytopes, and the fourth dimension
Step 3:
Step 4: Profit!!
I'm a minister!
PART 3
... show time.
... that ..." Becca reached for a reasonable excuse. Or, more appropriately, an unreasonable one. "I'm pregnant! I was going to tell you at lunch today."
Becca sat slightly apart from the others, who were deep into their "council of war". She shook her head as she looked from Lexie to Mr. Elliot to Mr. Devon.
"I still don't understand why we don't go to the police."
The three stopped and looked at her blankly. Mr. Devon finally spoke. "We don't have any proof. If the police move too suddenly, all the thief has to do is destroy my designs, and there's no evidence. I have no other copies of them."
"And besides," Mr. Elliot interrupted, "we have customers who are very sensitive to any kind of scandal. The smallest hint that we're having problems, and they'd be running back to Gucci as fast as their spike heels will take them. This must be handled quietly."
Becca sighed, for what felt like the forty third time that day. "So, do you at least have an idea of who could be behind this?"
Mr. Devon leaned forward. "The only designer that I know is having a show on Friday is Christof Kimmel. I had heard through the grapevine that he was having creative difficulties, but never would have imagined that he would stoop to stealing my designs. Of course, it is almost an honor to be considered good enough to steal from, but still..."
Becca broke in. "Fine. So what can we do that the police can't?"
Lexie looked up brightly. "I have a plan!"
'Why am I not surprised?" Becca asked herself. "Let's hear it," she said aloud. "Just remember, I have final veto power. If it's too dangerous, you don't do it, no appeals. Your father trusts me."
Lexie stood up and gestured dramatically. "Well, if we just took the designs back, they'd know that we figured it out, and they might try again. My dad told me about a case they had once, where they gave the bad guys some pictures of some really icky designs, and fooled them into thinking they were real. We could do the same thing."
"I'm not sure I could draw any 'icky' designs," the designer interjected.
"Oh, I'll help. I know just what the kids hate the most."
"And I have a dress left over from our 'Most Tasteless Design' party," Mr. Elliot said. "I can put it into one of our boxes, and they'll never know it isn't my little Alexandra's dress."
"Great!" Lexie jumped up. "Mr. Devon, get your sketch pad out, and let's get drawing! We've only got forty-five minutes before Fred is supposed to be meeting this guy. We've got to hurry!"
Becca stood, putting a hand on Lexie's shoulder to hold her still. "Wait, I hate to be the wet blanket here, but how do you propose to make the switch? If he's in a public place, there'll be witnesses. If he's back to his studio, we'll have to do some breaking and entering. Either way, I won't put Lexie at risk."
"I would never do anything that might hurt Miss Alexandra," Mr. Elliot said. "Mr. Peck would have my private parts on a plate, and I've grown quite fond of them."
"I'm sure he's going someplace public. We'll just follow Fred, then you guys will create a distraction, and I'll sneak up and make the switch, since I'm the smallest," Lexie explained. "That's all there is to it!"
"*You* have been exposed to Hollywood too long. This isn't some kind of action/adventure television show! Lexie, we don't know anything about where he's going," Becca said, exasperated.
"Oh, once we see the place, we'll figure out what to do. We just have to think on our feet."
'That girl has been hanging around Hannibal too much,' Becca thought. "No. No way. I absolutely forbid..." Becca stopped as Lexie looked up at her, her brown eyes glistening and pleading. "I cannot let you..." Becca saw Lexie's lower lip trembling, and was hit full force with the girl's I'm-So-Cute-How-Can-You-Refuse-Me-Anything pout. She sighed, for the forty fourth time. Templeton was going to have his work cut out with this one.
"OK, we'll see where Fred takes us. But if it looks too dangerous, " she waggled a finger in front of the girl's face, "you are out of it. Period. I really mean it."
Lexie leapt up and kissed Becca's cheek. Then she grabbed Mr. Devon's hand and pulled him from the room. The last thing Becca heard from her was, "Do you have neon pink and chartreuse markers?"
Yup. Temp was going to owe her big time for this one. She envisioned him laying on some tropical South American beach, with gorgeous women making obscene proposals to him. She pushed the image from her mind and started planning out everything he was going to have to do to make it up to her.
*****
"So, my beautiful blond man, will you come to my bed or not?"
Templeton Peck slowly backed up until his back was against the bars of his cell, putting as much space between himself and Pedro, the goat molester, as possible.
"Hannibal, any help here would be appreciated!"
"Oh, he's harmless, Face. Just don't go 'baaa' and you'll be fine," his commander said from the next cell.
"That's not funny, Hannibal."
"Face it, lieutenant. Can I help it if most members of the human race find you irresistable? You can't blame the man."
Face whirled around to give a scathing reply, then remembered who was at his back and quickly turned around.
"Relax, Face. Murdock and B.A. will have us out of here in no time -- probably before it gets dark. We definitely won't have to spend more than one night here, two at the most.
"I'll get you for this Hannibal. If you don't come up with something to get us out *now*, next time Lexie wants to go to the mall, her Uncle Hannibal gets to take her. Just imagine -- eight hours of trying on clothes and shoes and sighing over the pictures of River Phoenix in the teen magazines."
"Face, you wouldn't."
"Just try me."
There was a moment's silence, then...
"Guards!"
*****
Lexie looked over the top of her Teen Beat magazine at the man they were trailing. Fred had, predictably, decided that he felt much better, and left the shop after about forty five minutes. He had taken off on foot, with Lexie, Becca, the designer and the tailor following behind, doing their best to be incognito. Fortunately, Fred was not the most observant of men. Every so often he would turn and look back, causing them all to turn around suddenly or press themselves up against a building or hide behind something, like a teen magazine.
With one last longing look at River, Lexie put her magazine back into her bookbag. Fred had finally entered a restaurant, and it looked like it was time to flesh out the plan. Becca, as the least recognizable of the bunch behind her sunglasses, designer dress and borrowed blond wig, was elected to go inside and scout where Fred had gone.
She stood inside, as though waiting for someone. The maitre d' glided toward her, but she froze him with a baleful stare, and he smoothly turned away. Her frustration with Lexie was really helping with her Bitch persona today. Conveniently, she discovered that from where she stood, she could overhear Fred talking to another man she didn't recognize. Fred made a move to sit at the man's table, but the other made a violent gesture to stop him.
"You are not invited to sit with me. It would not do for one such as myself to be seen lunching with a peon such as yourself." As he spoke he handed a thick envelope to Fred.
"Christof, when will I come to work for you?"
"You will address me as Herr Kimmel, and you will never work for me. Do you think I would trust a man who would betray his own employer for money? For love, maybe. For sex, definitely. But never for something as coarse as money.
"But...I thought..."
"No, you did not think, and that is the crime that I can never forgive. Goodbye, Fred. I suggest you take this money and buy a ticket back to Pukwana, South Dakota, for you shall never work in this town again."
Becca watched as the dejected man slunk from the restaurant. She dropped her purse and took a look under the long tablecloth covering the table that the faux-designer was sitting at. Sure enough, there were a box and a folder there, of the types that Elliot used. She swiftly left to report her findings to her fellow conspirators.
Lexie's plan was very simple. Since he would be most likely to be recognized by Kimmel, Elliot would stay outside, watching in case of trouble. Becca and Devon would go into the restaurant and argue, distracting Kimmel and the rest of the patrons of the establishment, and then Lexie would sneak up and make the switch. It would be a 'piece of cake'.
Becca got a cold chill at those last words, for some reason, but shook it off. If Lexie got caught making the switch, all she had to do was pretend that what she held was hers. Lexie was very good at righteous indignation.
Devon was muttering as he and Becca entered the restaurant. "I don't know if I can do this. If Forest hears that I've been seen with a woman like this, he won't speak to me for a week."
Becca ignored him. She saw Lexie enter the restaurant and hide in a corner. It was
She said in her loudest, non-shouting voice, "So, where were you? Off with your secretary again? Do you have any idea how humiliating it is to stand around here waiting for you?"
Devon replied, equally loud, "About as humiliating as it is to have to be around you when you've been drinking Jack Daniels all morning. The least you could do would be to get intoxicated on a higher class of alcohol."
"What! I haven't had a drop all day!"
"Then you must have been drinking Jack the pool-boy or Daniel the gardener this morning!"
"You're getting the two of us confused again!"
At this time, the maitre d' approached. "Madame, monsieur. Do you have a reservation?"
"Of course we do," Becca said, still loudly, "under the name of Robinson."
The man looked apologetic. "There is no reservation under that name."
Becca whirled to Devon, and took the volume up a level. "What! You aren't even competent enough to make a reservation? You are such an idiot!"
She was feeling pride in her performance, and took a quick, sideways glance at Kimmel. He was ignoring them completely.
Becca looked at Devon in desperation. Any moment now they would be tossed out of the restaurant.
"I suppose you were too busy trying to find some new fashion designer to screw! Have you finally found a German one to add to your collection?" She chanced another look. Their prey had finally taken the bait. He had looked up, and was now riveted by the handsome man on the receiving end of the abuse she was spewing out.
"If I am, it's only because bringing my genitalia anywhere within 10 feet of you is to risk having them frozen off!"
"How dare you!" Becca grabbed a glass of wine from a passing waiter and flung the contents in the general direction of Devon, and in the exact direction of Kimmel. The wine hit him dead center in the face, dripping down his chest. Devon immediately rushed over to the other man. "Oh, I am so sorry. You must forgive my wife, she's... On the other hand, there is no reason why you should forgive the bitch, but I am sorry, none the less." He picked up a napkin and brushed at Kimmel's clothing. "Such a lovely shirt. You have exquisite taste." Devon smiled warmly at the man. He grabbed his hand and pulled him to his feet. "Let's go back to the kitchens, and see if we can get you cleaned up."
"What do you think you are doing?" Becca shrieked.
"Cleaning up after your messes, as usual."
Devon led him several steps away, and Lexie, seeing her chance, dove under the tablecloth, and set to switching the box and folder with those from her bag.
She froze as she heard voices coming back to the table.
"No, my dear boy. I am fine, truly. If you would like to make it up to me, though, you can join me for lunch."
Lexie thought her heart would stop when she saw two sets of legs appear under the tablecloth. She shrunk back against the legs that she recognized as Devon's. She had to dodge to one side as Kimmel brought one foot up, and rubbed it up and down Devon's leg. She was pretty sure that she was seeing something that she shouldn't for a few more years.
Becca also thought that her heart would stop when she saw that Lexie was trapped under the table. She grabbed a chocolate mousse from a nearby table.
"So, you like cleaning up my messes? Well, you should love cleaning this one up!" With that, she shoved the dessert fully into Kimmel's face, twisting slightly to try to get it under his eyelids. He jumped up, temporarily blinded by chocolate. Devon pulled Lexie from under the table, and she scampered from the room and out the door.
"Why are you acting so irrationally?" Devon said, looking for a way out now.
"Oh, darling, it's just that
"Oh, my sweetest heart. I'm so sorry I yelled at you. Let's go home and celebrate!"
They ran out of the restaurant, leaving the thieving designer messy, frustrated, and completely clueless.
As the four of them ran back to Mr. Elliot's shop, Becca spared a thought for Templeton. She hoped his mission had been as successful as theirs had been.
*****
The four men comprising the A-Team stood wearily in the suite of rooms belonging to the Princess Almira, feeling somewhat outclassed by their surroundings. All of them looked grimy and unkempt. B.A. had a his arm in a sling. Murdock had a bandage around his head. Face had a gorgeous black eye developing.
Hannibal alone had managed to escape without injury, and he managed to make 'grimy' look fashionable.
They were listening in disbelief to the words she was saying.
"You tell me that you have come to rescue me? But I need no rescue! I will be marrying Ramon soon, and we will be very happy. My papa, he is just a little over-protective. He wants me to marry some prince or duke, and will not listen when I tell him I would rather marry for money." She sighed. "He is so old fashioned."
She considered Hannibal for a moment, then stalked up to him. "Oh, but you are such a handsome man. Perhaps, if you were to ask, I might go with *you*." She twined her arms around his and up to his shoulders. She gave him one of her patented smoldering looks.
"Sorry, ma'am. I'm already in a committed relationship."
"That is even better. Then you will not want one with me."
Hannibal gently untangled himself from her. "As much as I appreciate the offer, ma'am, I can't take you up on it."
With a languid shrug she moved away. "I hate to see such brave, handsome men, who only came here to rescue me, after all, go away empty handed. I have decided. Whatever my father is paying you, I will have Ramon pay double. That will convince my papa that I am marrying the right man." She opened a safe and started pulling out money. "And we shall let you use our private plane, to return to your home."
There was an eruption from one of the members of the Team. "I ain't gettin' on no plane! I'll be walkin' home before I be gettin' on another plane! Hannibal, I'm gonna rip your..." The commotion stopped suddenly, and the large man slumped to the floor. Face smiled his most charming smile, and held up the small knock-out dart he had retrieved from his kit. He walked over to the princess. "Now, let's see about this additional payment you're making..."
*****
EPILOGUE
Rebecca yawned loudly as she walked downstairs to the kitchen. After she had measured out the coffee and started the pot she reached into the cupboard to pull out a mug. She lifted one up and read the words "World's Greatest Dad" on it. She smiled gently for a second before the smile slipped away from her face. Blinking her eyes rapidly, her hand tensed around the mug and she quickly put it back and grabbed another. Moving over to the now half-full pot, she poured herself a cup. After looking at the kitchen clock and seeing that it was only 6:30am, Becca decided against starting breakfast and wandered into the cozy breakfast nook just off the kitchen. Sitting on the loveseat, she propped her feet up and looked at the books and magazines lying on the end table next to her. Becca idly picked up a book - one of Lexie's Nancy Drew mysteries, smiling when she saw the finance magazine underneath.
Becca put the book down and wrapped both hands around her mug, inhaled the aroma deeply before taking a sip, then leaned her head back with a sigh of contentment. She and Lexie had picked up the dress the day before and had found the perfect necklace and earrings to go with it. Mr. Elliot had been so grateful for their help that he had arranged for a friend of his to come and do Lexie's hair for the dance. This night would be wonderful, if a certain father made it home in time.
Rebecca finished up her coffee and went back upstairs to shower and get dressed. When she came back down an hour later she heard the small tv in the kitchen and the sound of pots and pans banging together. Walking through the living room she nearly tripped over a suitcase in the middle of the room. Quickly running into the kitchen, Becca came to a sudden stop when she saw Templeton standing in front of the stove.
"You're home!"
Face had barely turned around before he was engulfed in a hug. He put a finger under her chin and lifted her face for a lingering kiss.
"Dad, you made it!" Face smiled against Becca's lips before pulling away to greet his daughter.
"I told you I would didn't I?" he said chidingly as he hugged Lexie.
"Yeah." Lexie squirmed out of Face's arms and landed on the floor.
"Dad! What happened to your eye?"
"Oh...that...just a small misunderstanding with a man named Pedro."
Rebecca remembering the food on the stove, quickly turned her attention to it before it burned.
"...and then Princess Almira had Ramon pay us double what her father had paid so that she could stay with Ramon. Which reminds me, I need to arrange a wire transfer to return the money we accepted from King Robert, since we didn't bring his daughter back. If you ladies will excuse me." Face smiled at his two favorite girls in the world and headed towards his den.
"I'll bring your breakfast down as soon as it's done," Becca called after him
"Don't bother, I'll be back in just a few minutes." Templeton's voice called from the hallway. Rebecca looked over at Lexie and they both smiled knowingly. Lexie went to one of the cupboards and pulled out a tray to carry the food down to the den while Becca started dishing out their breakfasts.
They were distracted when they heard a familiar name coming from the television.
"And today in fashion news, last night's show by German designer Christof Kimmel was an unmitigated disaster. Dresses mixing puce and florescent pink stripes with ruffles and bows from top to bottom has this reporter asking, 'What was he thinking?' or perhaps 'What drugs was he on?' These dresses look like they were designed by a twelve year old. After this debacle, Christof is finished in Hollywood. Next..."
Becca leaned over to shut off the tv, while Lexie sulked. "No way those look like they were designed by a twelve year old. I was aiming for six. If I'd wanted to, I could have made up something really good!"
Becca started chuckling. Lexie couldn't hold the pout and giggled. "We really got him, didn't we!"
"Yup, we got him good. That was a pretty good idea that you had."
"Uh-huh, and you know what I always say: I love it..."
"Lexie, don't you dare," Becca said warningly.
"...when a plan comes together!" Lexie dodged out of arm's reach, picked up the tray and hurried for the safety of her father's den.
Becca sighed, wondering how she'd ever gotten mixed up with this crazy bunch. Then she smiled, thinking of all the things Face was going to do to make up for the past week, picked up her cup, and wandered to the basement to join the party.
*****
Templeton Peck walked back to the table with two glasses of punch. He paused for a moment when he saw Lexie talking with her friends. He watched his daughter laugh at something one of her friends had said and he felt a pang in his heart at the realization that his daughter was growing up. In a few months, she would be a teen-ager and a few years after that she would be bugging him to teach her how to drive and she'd be...going on dates. He didn't want to think about that. It was too soon. He wasn't quite ready to share her yet. At that moment, Lexie looked up and saw him and her whole face lit up with an expression that she reserved only for him. His heart swelled even as he knew that he had been given the gift that was his Lexie at a very high cost and that someday he would have to tell her the secret of her past, but not tonight. Tonight was his night with her and he wouldn't share it with ghosts of the past. Taking a deep breath, he walked over to his daughter, smiling and nodding at her friends. Face put down the drinks he had been holding, turned to his daughter, bowed slightly and held out his hand.
"May I have the honor of this dance?"
The end
It's one of those OpenGL Windows 95 screensavers! :) Why didn't you just say so?
"Again the inner chunks are finite, and they are distributed in shells around the core polytope."
uhh yeah, but it all depends on the capacitive current getting to the space modulator
come on, lets do a thorough reporting job. You didnt even mention the fucking space modulator.
Looking directly at four-dimensional stereograms can *really* screw up your eyes. Caution or strong hallucinogenics advised.
I am a Karma Library.
It's already been invented. It's quite simple really. To travel forward in the 4th dimension, simply insert your pr0n tape into the device and hit Fast-Forward. To travel backward in the 4th dimension, hit Rewind.
I'm a minister!
mmm.. higher dimentional pizza.
If you set the Stereo mode to "Cross-eyed," you can view the picture in 3-D using the Magic Eye technique.
My Blog Sucks.
...now you go and give me a bastard headache looking at 3D images of a 4D environment on a 2D screen. Yowch.
I don't have a pair of 3d glasses, is there any kind of computer screen filter that has the same effect? Or do one's actual eyes need to be cross-eyed?
This sounds alot like Gene Ray, of Time Cube. Creepy, man.
How exactly do you think they are similar?
Hi guy. I am a short guy but i have a BIG, BIG HEART. ;-) I am a hot and handsome man, 34y/o, 139#, 5'6", athletic and slim body, very nice muscular hairy chest, masculine. I live in the gay city of Holland, MI. I am looking to make good friends. I love animals special dog, horse, tortoise and dolphin. I love nature, ocean, astronomy, Metaphisica and of curse the Internet. I do not talk about politics or religions, but i believe in God in my own way.
ooooooooooh, TRIPPY!
What post? The one you're carrying inside your rusty innards!
This isn't new. There have been real applications and Java applets, too that have been able to do this sort of thing. I've got an old app for the classic Mac OS called "HyperSpace" that does exactly this (draw multiple 3D cross-sections of 4-D hypercubes). It's a really, really old app.
Here
Less pretty but more understandable
BTW: things like the famous Stereoscopic Animated Hypercube have been around for quite some while. There even is a game around to be played.
Thanks to slashdot many people can actually find out about it.
the thing about opening our minds is right. :-)
We have always lived in three dimensions, so visualizing 4 dimensions Per Se is almost impossible coz our nuerons have been hardwired for 3 dimensions. So we can observe 4 dimensions in transit. For example if youwere a 2 dimensional being(thats not possible coz 3 is the minumum number of dimensions to sustain life) and a 3D sphere passed through your space, you will see a point, growing into a circle and then again into a point.
So if a 4D object came it would look like a morphing 3D object.
If mankind were able to create and use 4D's travel would be a whole new frontier. Esp since space-time is curved, Just imagine traveling a million miles instantaniosly
Confused! Go through stephen hawkings works! you will be even more so
My Aurora : http://www.youtube.com/watch?v=o91ZsGwJYyg
FB : https://www.facebook.com/TanveersPhotography
I would assume that if multiple dimensions exist, then we actually live in them already, it's just that we only have the ability to percieve the 4 obvious dimensions to us. While the other Nth dimensions are still existing just not eaqsily percieved by us. (AS in that quarks may in fact exist in the "4th dimension" (or properly termed by us as the 5th dimension.... don't start with the classic rock jokes!!) which would easily explain how some of them can exist in 2 physical "3d" locations at once.. existing in the "4d" space there will be multiple intersections from the "3d" space.... espically if the particle was elongated.
Is this a correct assumption?
Do not look at laser with remaining good eye.
If you think about it, it doesn't really make sense to be able to visualize a four-dimensional object using sight. Why? Because sight is a two-dimensional sense that on a daily basis we use to visualize three-dimensional space. Visualize trying to understand a 3D shape looking at a pinhole view of it (1D to 3D). Can't really be done, certainly not without a ton of staring at it.
Seeing as how it's so difficult to jump two dimensions in visualization, how do we do it? We use the only 3D sense that we've got... touch. Since we can "see" all sides of an object at once using touch, then we are truly experiencing that object in 3D.
So create some kind of device that you hold in your hands and moves around to simulate a hypercube. Simple answer :).
Find me in ~/.sig
We used to argue this in the computer science lab at college. Can the human mind gain visualization skills in four dimensional geometry? We came up with the following interesting answers:
p rod.html">Crystal Eyes</a>. Now there are liquid crystal on silicon solutions that are much cleaner, if not cheaper.
1. It's hard. We never see four diminsions. The brain would keep wanting to make one dimension some known continuim such as time, a color sequence, tone, or intensity. Only after this intermediate step would you get a true four dimensional geometry in your head.
2. You would need to have a true 3D display. Current rendering of three dimensional pictures flattened onto simple two dimensional screens would never work. Imagine using a laser pointer as a point source, and imagine that you had never seen a three dimensional object; now draw a three dimensional picture of a pick-up truck using the laser pointer. At the time, we were trying to get a simple three dimensional output, like <a href="http://www.stereographics.com/frames/frame-
We were students once, and poor.
After stareing at this for about 30 mins it made me wonder if God is a 4D being..
It's talking about a shape in 4 spatial dimesions, not 3 spacial dimensions and one time dimension. Also, movies aren't 3d - not even those red-cyan ones. If movies were truly 3d, you'
i finde ur ideers intreeging an wants to sib...sebsri...subscrib to ur news leter!
to learn more read some Kaku - one of the foremost scientist on hyperspace....(fixed link from previous post.
Hyperspace
People who have witty things here blow.
Hey, did anyone tell Tom Banchoff@Brown University
about this? He is the master when it comes to
4-d visualization. I still remember the opening
celebration of the Thomas J. Watson Jr. Center
for Information Technology at Brown when he
put on a music/graphics show projected outdoors
onto these huge screens.
http://www.math.brown.edu/~banchoff/
There was something similar done by a guy called Luke Dahl, only it was for audio.
:-)
It was a Markhov chain extrapolation of the 3d sound as perceived by a 3d being and using a series of normalizations and transforms.
It was called Frobenius Norm, and was a composition of how a 4-d sound would sound to a 5-d being, I think. I just remember it being "spiffy" and very addictive!
It was also featured in Woodstockhausen 2000.
It's full of stars!
Beware: In C++, your friends can see your privates!
A 3D sphere intersecting a 2D plane would create a circle, but you could only see the circle from a 3D view ontop of the plane.
If you were on the plain and had no concept of 3D, but still had depth perception, what you would see would be an arc. You could think its a circle, but without going around to the back and making sure the arc follows itself around the entire 360 degrees, you wouldnt know it was complete from just a single viewpoint on the 2D plane.
Morphing Software
Can the human mind gain visualization skills in four dimensional geometry? ... We never see four diminsions. The brain would keep wanting to make one dimension some known continuim such as time, a color sequence, tone, or intensity. Only after this intermediate step would you get a true four dimensional geometry in your head.
Your actually wrong in the second part. While our senses can't pick up more than 3D Sensory input our brain can very well imagine (and sense) more dimenions. It's simply a matter of training.
Indian Yogis would call that 'meditation'.
The stuff those kind of people talk about like "when time becomes irrelevant" and such isn't some mystical BS (at least not with the honorable ones) - it's actually what you expierience when your brain is trained apropriately. Or forced into such condition by (ab)use of drugs.
You can see "everything happen at once" like one would say. It's interesting that people reaching this kind of 'sense' have a syncronized activity of both halfs of the brain.
Normaly we don't have that. But Yogis and people who have trained meditation can actually achieve such 'brainsyncing' at will. (a tranquil enviroment given)
Tibetian meditation 'training' is known to train the same as modern biofeedback 'brainsyncing', often with a nearly identical setup like: "look at those 2 spots and see them as one".
We suffer more in our imagination than in reality. - Seneca
if a 3d sphere in a 2d perception looks like a circle growing and then shrinking over a long period of time, could time itself be just a approxmiation of objects that have more than just 3 diminsions? /andrew
as in, are we just in a single 3d plane and our perception of time is just things moving through it?
I don't know enough about hyperspace to properly explain this, is this what hyperspace is about though?
I have some GPL'ed 3-D Anaglyphic code here if anyone wants to play with this sort of 3-D rendering. Of course, you could also use jad to decompile that applet if you feel randy.
I thought hyperplanes are just 3D slices of data taken from any number of dimensions. So if you have an m x n matrix and want to visualize it, just take 3 of the columns.
... Until someone makes a videogame using these shapes. Maybe something funky like Frequency Cubed, Dance Dance Dance Revolution, or Duke Nukem 4D?
I'm serious though.
[PowerPoint] is a tool for capitalist presentation
High-dimensional (or multivariate) visualization is nothing new in the world of statistics & exploratory data analysis. Check out the freely available XGobi software or the new GGobi package. For a 100% Java version, see Blue Orca.
Read "And He Built a Crooked House". Heinlein did a bang up job of explaining a hypercube there using toothpicks and clay.
Phoenix
Don't be fooled--this is not a kaleidoscope! : )
hell
"..The bounding hyperplanes can be extended infinitely so that they criss-cross through each other, chopping up hyperspace into many 4-dimensional 'chunks.' Again the inner chunks are finite, and they are distributed in shells around the core polytope."
...must the best BOFH "Plausible Excuse" ever!
I can't even take this writeup right after waking up, never mind the article itself... it sounds way too much like the timecube guy for me...
the coolest club on
If you're into this sort of thing you should pick up Hyperspace by Michio Kaku, it's a very interesting book that does a pretty good job of explaining multiple dimensions in a way that most can understand.
How's my typing? Call 1-800-eta-shut
Hey guys! It is really a full-motion magicEye and if you squint your eyes it will come into focus -- A resume of Bernard Shifman, in an apparent attempt to spam the 4th dimension.
From excellent karma to terible karma with a single +5 funny post...
- Start with your typical 3x3 tic-tac-toe, on a piece of paper.
- Now add two more grids. Visualise each grid on top of the one before. It's not difficult to see how this is played. You can get three in a row on a single grid, just like normal. Or you can get three in a row by getting the middle square of each grid (3 in a row, vertically). And so on. This is basically tic-tac-toe in 3D. 3 sets of 3x3 grids. 3x3x3.
- Now, add another two sets of three grids. So now you've got 3x3 3x3 grids (still with me?). You can still win just like in the 3x3x3 version. But you've got another 3x3 ways in which to do it. The tricky part is, to visualise each possible `3 in a row', you've got to mentally `rotate in' any one (and only one) 3x3x3 cubic plane.
Sorry if that's difficult to follow. If you work it through on paper, you'll see what I mean. This is what being bored in math class will lead you to think of, when plain old tic-tac-toe just doesn't seem challenging anymore.- SMJ - (It's not just a name: it's a bad aftertaste.)
The correct definition of a hyperplane is here.
If you all want to understand hyperspace better you shoud pick up a copy of Michio Kaku's 'Hyperspace'. It covers most of the subject matter of flatland, and goes into more depth on the possibilities of higher dimensional space and unified field theory. It's a really interesting read and speaks on a level that most people can understand. I got alot out of it when I first read the book 6 years ago (I was 14 years old). I didn't get all the mathematics then, but the basic concepts were very well illustrated, and it got me started thinking even then.
-dewhite
Hello flonker,
Could you please post your telephone number? My lawyer would like to talk to you. I'm off to the hospital, cu guys.
"It's too bad that stupidity isn't painful." - Anton LaVey
In calculus, a slice of a higher dimensional shape represented in lower dimesional space is called a level curve. For instance, a level curve of a sphere is a circle. So a sphere is the level curve of a 4th dimensional solid.
I didn't see any source code --
If it is available, please say where!
Just thought I'd mention the interest.
this is all well and good..but a question or two. first of all, isn't it generally agreed that time is the forth dimension? please correct me if i'm wrong, here. therefore, the whole thing about watching the sections transform over the fourth dimension like it's some super fancy function is preposterous! how hard is it to see something change over time? my bottom line is this: it's as easily explained from the second to third dimension as it is from the third to fourth or even seventh to eighth. the author is just relating one dimension to the next dimension up the order. no matter what dimension you stand in, there is going to be one more that you are incapable of seeing higher up. if you treat the fourth dimension like it's something that we have as much control over as the first, second, or third then you will find, eventually, that you are mistaken. finally, your analogy to a 2-d being observing a 3-d object brings up an interesting point. we, as humans, have long realized that while we have control over three dimensions we exist, actually, in many (at least 5, i believe), but are held directly captive by the fourth (which would, in turn, be held captive by the 5th, etc). you say that our brains are hardwired to think in 3 dimensions. is it possible to imagine a purely 2-d existence?
Those who can, do. Those who can't, go into business for themselves.
I recently worked on a project (I am not the author) that modeled 4-D environments on the screen. We made a spaceship that had 4-D elements in it where doors would show or hide based on whether or not the correct hyperplane was in view.
There is a demo of the software that runs on windows and the navigation is very easy to figure out.
LOL... Wilhelm
A few people have posted with a comment about how they consider time to be the fourth dimension.
Sure, that's one way to think of it, but I think what this animation is attempting to describe is a fourth spatial dimension. That is, describing a geometry where 4 lines can be perpendicular to eachother, instead of the 3 that we are used to.
Saying the 4th dimension is time is an easy way out.
The damned thing does not work. I just get a blank grey screen no matter which button or slider I press or change.
Any n-1 dimensional plane cutting through an n dimensional space is a hyperplane. So, the correct wording of the story would have been "A hyper plane is a 3-dimensional space that cuts through a 4-dimensional space, just as a 2-dimensional hyperplane cuts through 3-dimensional space."
Posted from the wireless couch.
Haven't gotten to the M-Theory section yet.
(* If 2D lifeforms did exist (Planiverse suggests they would need zipper-like 2D organ structures) it's quite likely they would have some form of 'depth' perception - along a plane, of course. A sphere intersecting with their world could indeed be recognized as a circle, much like our brains can recognize the depth difference between a ball and a flat disc. *)
If a 4th dimensional biological entity intersected our dimension, it would probably look really really funky, like a bunch of morphing blobs. Imagine sitting there in a chair watching Bay Watch, and suddenly in the middle of the room small blobs of flesh appear, grow in size, but change shape in really really odd, unnatural ways, then disappear.
If that wouldn't make your skin crawl off, I don't know what would. It would even be odder than watching obese porn in reverse (not that I recommend it).
Note that there are some UFO reports of odd blobs appearing, morphing funny, and then just dissappearing. Long shot, I know, but you just never know what may have came our way before.
Table-ized A.I.
I COULD see all angles of the scenes at the same time. Of course, time stopped... Sorry.
CAn'T CompreHend SARcaSm?
Actually, a hyperplane is a subspace of a vector space, with the stipulation that all of the vectors in the subspace have one specific dimension in common (i.e. the same for all of them). A 0D point is a hyperplane of a 1D line, a 1D line is a hyperplane of a 2D plane, ...
E
If I'm understanding it right... It seems that while it is modelling 4D space, it's stil only displaying 3D at any given time. The question is, can you extend the mathematics of displaying 3D on a 2D screen, to displaying 4D on a (not yet available) 3D holigraphical projector?
It looked painful when Beavis blew Butthead from 2 dimensions to 3 dimensions on the Celebrity Deathmatch episode...
If the 4-D glasses are packaged with a fire extinguisher or another compressed air tank with a menacing looking hose (e.g. colonoscopy probe) watch out!
Good luck. I've read the book three times and always get hung up on it.