Original Usenet thread from alt.ascii-art, started 10 Jun 1997.
HyperCube (Diamond Explained)
alt.ascii-art
· 26 messages · 10 Jun 1997 - 27 Jun 1997
In article <mar...@news.ricochet.net>, "The Right Rev. Felix Roy Mariposa, Prophet" <mar...@ricochet.net> waffles on >In article <339...@garnet.fsu.edu>, Michael Naylor ><mna...@garnet.fsu.edu> wrote: > >> This is _not_ a diamond... this is a hypercube, a four-dimensional >> object. It's a cube that's been stretched into another dimension. > >> Michael > >In article <juo...@g-grids.demon.co.uk>, salesman ><sal...@g-grids.demon.co.uk> wrote: > >> Your telling me you can se something in that other than a bunch of lines >> ? wow. I can't see any 3-d'ness at all realy. Or 4-dimensioness. Hang on >> .. isn't time the 4th dimension ? >> -- >> Salesman's Warcraft 2 Page >> http://www.g-grids.demon.co.uk > > The idea behind the hypercube is this: As in Mike's sig below, we can >see a three-dimensional cube in a collection of two-dimensional lines: > > ---- __ __ () _ _ __ __ _ _ __ __ ___ ___ o >| \_|_\ | \/ |--| '(| =| | \| |/o \ " /|_/ O | O ) () o >|_|_| | |_\__/_|__|_|_|__| |_|\__|_/\_|_|___|__/|_\_\ o_/||\/ > \|__\| Michael Naylor, mna...@math.fsu.edu, (904) 644-8433 _/\_ > > So, by getting the angle right, we have the representation of a 3-D >object in 2-D. By taking that logic a step further, it should be >theoretically possible to make a four-dimensional object visible in a >three-dimensional representation... if you can just get the angle right. > > Yes, time is the fourth dimension - that's the paradox of the hypercube; >it makes it supposedly possible to "see" time in three dimensions, which >common sense tells us is absurd. > > Back to ASCII art: how the hell are you supposed to have a 2-D ascii >representation of a 3-D representation of a 4-D object? Sorry, Mike, I >agree -- it looks like just a bunch of lines. To make an ASCII Hypercube... >I don't think that's possible on a flat computer screen. Well I just can't imagine what a 2-d (even a 3-d) representation of a 4- d object would look like. (Even with normal art). If a hyber cube does exist that makes you think you are seeing 3-d and time, I would love to see a pic. > > (But just my luck, Joan Stark's going to do it, post an ASCII hypercube, >and I'll look like a fool.) > >FRM > -- Salesman's Warcraft 2 Page http://www.g-grids.demon.co.uk
In article <339...@garnet.fsu.edu>, Michael Naylor <mna...@garnet.fsu.edu> waffles on >I was 'thumbing' through Scarecrow's collection, and came across this. >This is _not_ a diamond... this is a hypercube, a four-dimensional >object. It's a cube that's been stretched into another dimension. >(Didn't draw it, just setting the record straight). > >Cheers, > >Michael > > >[I believe this next one is a diamond.] > _________ > /|\ /|\ > / | \ / | \ > /__|__/ \__|__\ >|\ | | | | /| >| \ |----|--| / | >| /\-\---|---/\ | >|/_____|\|_____\| > \ | \ / | / > \ | / \ | / > \|/ \|/ > -------- > I just spent a few secs staring at this realy hard, and I can quite clearly see 4 cube shapes (like the ones in mikes sig), but I don't see how this represents 4-d. To me it represents 4-cubes-overlapping-each- other-bit :) -- Salesman's Warcraft 2 Page http://www.g-grids.demon.co.uk
In article <339...@garnet.fsu.edu>, Michael Naylor <mna...@garnet.fsu.edu> wrote: > This is _not_ a diamond... this is a hypercube, a four-dimensional > object. It's a cube that's been stretched into another dimension. > Michael In article <juo...@g-grids.demon.co.uk>, salesman <sal...@g-grids.demon.co.uk> wrote: > Your telling me you can se something in that other than a bunch of lines > ? wow. I can't see any 3-d'ness at all realy. Or 4-dimensioness. Hang on > .. isn't time the 4th dimension ? > -- > Salesman's Warcraft 2 Page > http://www.g-grids.demon.co.uk The idea behind the hypercube is this: As in Mike's sig below, we can see a three-dimensional cube in a collection of two-dimensional lines: ---- __ __ () _ _ __ __ _ _ __ __ ___ ___ o | \_|_\ | \/ |--| '(| =| | \| |/o \ " /|_/ O | O ) () o |_|_| | |_\__/_|__|_|_|__| |_|\__|_/\_|_|___|__/|_\_\ o_/||\/ \|__\| Michael Naylor, mna...@math.fsu.edu, (904) 644-8433 _/\_ So, by getting the angle right, we have the representation of a 3-D object in 2-D. By taking that logic a step further, it should be theoretically possible to make a four-dimensional object visible in a three-dimensional representation... if you can just get the angle right. Yes, time is the fourth dimension - that's the paradox of the hypercube; it makes it supposedly possible to "see" time in three dimensions, which common sense tells us is absurd. Back to ASCII art: how the hell are you supposed to have a 2-D ascii representation of a 3-D representation of a 4-D object? Sorry, Mike, I agree -- it looks like just a bunch of lines. To make an ASCII Hypercube... I don't think that's possible on a flat computer screen. (But just my luck, Joan Stark's going to do it, post an ASCII hypercube, and I'll look like a fool.) FRM -- Do you hate Spam in your e-mail? Don't just delete it, do something about it! Report incidents of Spam, and get the offender kicked off the net. Do this: 1. Check the header for the REAL domain name that the Spam was sent from -- often Spammers disguise their email address. 2. Send a forward of the Spam to their Postmaster. The Postmaster's address will be "postmaster@[domain name here]". Put the domain name from the header in place of [domain name here]. 3. Any reputable ISP will cancel the Spammer's account immediately. The Right Rev. Felix Roy Mariposa, Prophet mar...@ricochet.net O- ULC <*>
In article <WK0...@g-grids.demon.co.uk>, salesman <sal...@g-grids.demon.co.uk> wrote: > Well I just can't imagine what a 2-d (even a 3-d) representation of a 4- > d object would look like. (Even with normal art). If a hyber cube does > exist that makes you think you are seeing 3-d and time, I would love to > see a pic. That's why the hypercube is only a theory -- it SHOULD be possible, but in realistic, practical terms it doesn't exist. Outside of advanced math classes, the best use of the hypercube is as an example of where logic ends and common sense begins. FRM -- Do you hate Spam in your e-mail? Don't just delete it, do something about it! Report incidents of Spam, and get the offender kicked off the net. Do this: 1. Check the header for the REAL domain name that the Spam was sent from -- often Spammers disguise their email address. 2. Send a forward of the Spam to their Postmaster. The Postmaster's address will be "postmaster@[domain name here]". Put the domain name from the header in place of [domain name here]. 3. Any reputable ISP will cancel the Spammer's account immediately. The Right Rev. Felix Roy Mariposa, Prophet mar...@ricochet.net O- ULC <*>
Hehehehe! Time _can_ be viewed as another dimension, and it sometimes
is called "the fourth dimension". However, there is nothing wrong with
assuming more space dimensions than your usual three. In reality,
actually, space has a bit of a "lumpiness" or "curvature" to it, and it
really does bend into at least four dimensions.
Here's the idea: Start with a zero dimensional point
.
Now stretch that point in one direction, call it the 'X' direction.
._._._._._._._.
You get a one-dimensional line (pictured here as a line segment).
Stretch that line in another direction at 90 degrees to the first
direction, say, the 'Y' direction.
._._._._._._._.
:_:_:_:_:_:_:_:
:_:_:_:_:_:_:_:
:_:_:_:_:_:_:_:
:_:_:_:_:_:_:_:
:_:_:_:_:_:_:_:
:_:_:_:_:_:_:_:
You get a plane in two dimensions (pictured here as a square). Stretch
that plane in a direction that is 90 degrees to both the X and Y
directions (like, the Z direction) and you get space (pictured here as a
cube).
._._._._._._._._
:\ \
: \ \
: \._._._._._._._\
: :_:_:_:_:_:_:_:
: :_:_:_:_:_:_:_:
\ :_:_:_:_:_:_:_:
\ :_:_:_:_:_:_:_:
\ :_:_:_:_:_:_:_:
\:_:_:_:_:_:_:_:
Now, just stretch space in another direction that 90 degrees to the X,
Y, and Z directions (say, the W direction) and you've got the fourth
dimension... or stretch this cube in the W direction and you've got a
hypercube.
"Now wait a minute", I hear you say. "I can see the X, I can see the Y,
and I can see the Z, but ain't nobody gonna convince me there's a W
direction!"
Well, why not? After all, we draw these three dimensional objects on
two dimensional screens. In my cube drawing above, here's the
directions: ._
^ |\
| \
<---- X ----> Y Z
| \
v _|
That Z direction isn't really 90 degrees to the X and Y, but it's easy
to imagine it is. So let's make a W direction on our paper, say this
way:
_
/|
/
W
/
/
|_
And lets drag our cube in that direction:
______________
;\ \
/: \ \
./.:_ \_____________\
:\ \/:_:_:_:_:_:_:/:
: \ /\:_:_:_:_:_:_/_:
: \/____________\/:_:
: |_:_:_:_:_:_:_|:_:
: |_:_:_:_:_:_:_|:_:
\ |_:_:_:_:_:_:_|:_:
\ |_:_:_:_:_:_:_| /
\ |_:_:_:_:_:_:_| /
\|_:_:_:_:_:_:_|/
et voila, a hypercube! (this one is semi-solid... see those diagonal
faces, those should all be solid).
Back to the 'diamond' in question:
> _________
> /|\ /|\
> / | \ / | \
> /__|__/ \__|__\
>|\ | | | | /|
>| \ |----|--| / |
>| /\-\---|---/\ |
>|/_____|\|_____\|
> \ | \ / | /
> \ | / \ | /
> \|/ \|/
> --------
This is supposed to be a transparent hypercube, like the cube in my sig,
where you can see all the edges. The artist captured the essentials,
but I think s/he needed to make it much bigger... a hypercube has lots
of edges!
I think these figures are right (I never tried to counts edges and faces
of a hypercube before!)
Dimensions Vertices Edges Faces
Point 0 1?
Segment 1 2 1
Square 2 4 4 1
Cube 3 8 12 6
H-cube 4 16 30 18
Anyways, hypercubes are fun and make great paperweights, just be careful
not to drop your car keys into them.
:)
Michael
--
---- __ __ () _ _ __ __ _ _ __ __ ___ ___ o
| \_|_\ | \/ |--| '(| =| | \| |/o \ " /|_/ O | O ) () o
|_|_| | |_\__/_|__|_|_|__| |_|\__|_/\_|_|___|__/|_\_\ o_/||\/
\|__\| Michael Naylor, mna...@math.fsu.edu, (904) 644-8433 _/\_
In article <339...@garnet.fsu.edu>, Michael Naylor <mna...@garnet.fsu.edu> wrote: > Hehehehe! Time _can_ be viewed as another dimension, and it sometimes > is called "the fourth dimension". However, there is nothing wrong with > assuming more space dimensions than your usual three. > Now, just stretch space in another direction that 90 degrees to the X, > Y, and Z directions (say, the W direction) and you've got the fourth > dimension... or stretch this cube in the W direction and you've got a > hypercube. Well, to continue this thread (and, yes, I know this ain't alt.physics), time IS the fourth dimension, not "can be." The trick is that the separation of Time and Space is an artificial distinction -- physics tells us that Time and Space are two manifestations of the same thing, no different from width, depth or height. And yes, the fourth dimension is 90 degrees off from the other three... If you've followed all that, you should have a headache by now. The problem with this discussion, despite Michael's valiant attempt, is that hypercubes are almost impossible to draw on paper/computer screens. Michael's was a good start, but it takes a 3-D model to best show what we're talking about. > Anyways, hypercubes are fun and make great paperweights, just be careful > not to drop your car keys into them. > > :) > > Michael That's not funny! My cat once thought a hypercube was just another cardboard box -- so he jumped in it to play... no one's heard from him since. If anybody sees him, he's a greyish tabby who answers to the name "Schroedinger." FRM -- Do you hate Spam in your e-mail? Don't just delete it, do something about it! Report incidents of Spam, and get the offender kicked off the net. Do this: 1. Check the header for the REAL domain name that the Spam was sent from -- often Spammers disguise their email address. 2. Send a forward of the Spam to their Postmaster. The Postmaster's address will be "postmaster@[domain name here]". Put the domain name from the header in place of [domain name here]. 3. Any reputable ISP will cancel the Spammer's account immediately. Fight Spam! Join CAUCE (Coalition Against Unsolicited Commercial Email) at http://www.cauce.org/ and tell your Congresspeople how Spam mailings hurt you. Help protect genuine Internet commerce: Outlaw UCE Spamming. (This anti-Spam signature is available rent-free. Use it as your own.) The Right Rev. Felix Roy Mariposa, Prophet mar...@ricochet.net O- ULC <*>
I was 'thumbing' through Scarecrow's collection, and came across this.
This is _not_ a diamond... this is a hypercube, a four-dimensional
object. It's a cube that's been stretched into another dimension.
(Didn't draw it, just setting the record straight).
Cheers,
Michael
[I believe this next one is a diamond.]
_________
/|\ /|\
/ | \ / | \
/__|__/ \__|__\
|\ | | | | /|
| \ |----|--| / |
| /\-\---|---/\ |
|/_____|\|_____\|
\ | \ / | /
\ | / \ | /
\|/ \|/
--------
--
---- __ __ () _ _ __ __ _ _ __ __ ___ ___ o
| \_|_\ | \/ |--| '(| =| | \| |/o \ " /|_/ O | O ) () o
|_|_| | |_\__/_|__|_|_|__| |_|\__|_/\_|_|___|__/|_\_\ o_/||\/
\|__\| Michael Naylor, mna...@math.fsu.edu, (904) 644-8433 _/\_
In article <339...@garnet.fsu.edu>, Michael Naylor <mna...@garnet.fsu.edu> wrote: > You may call time the fourth dimension if you wish, but it is no more > the "official" fourth dimension than, say, width is the offical second > dimension. In fact, if you've ever drawn a distance vs. time graph like > we all probably have in physics class, then you've designated time as > either the first or second dimension. It's all what you want to call > it. Ok, point taken. I should have said that the accepted convention is to call time the fourth dimension. >As for time being 90 degrees from length, width, and depth, well... > that's like saying that red is 90 degrees away from blue. If you drew > it that way on a color wheel, then fine, but make sure we have some kind > of frame of reference or the statement is meaningless. Again, I should have been a little more clear: as I remember learning it, each dimension is 90 degrees off from the previous one (with the first being an arbitrary frame of reference for the ones after it). So, if we call time the fourth dimension, then it is 90 degrees from the third dimension, which by convention would be one of the three spatial dimensions. > > The problem with this discussion, despite Michael's valiant attempt, is > that hypercubes are almost impossible to draw on paper/computer screens. ^^^^^^ > Michael's was a good start, but it takes a 3-D model to best show what > we're talking about. > Hypercubes are not impossible to draw on paper or computer or a > blackboard... we've just seen several examples. Unless you mean that > cubes and other 3-D objects are impossible to draw in two dimensions as > well, which you could argue. My point was that to really start to see this, you should see a 3-D model of what a hypercube might look like -- I've seen some pretty good ones, but not only is it beyond me how to draw them on paper, I couldn't even hope to ASCII 'em. > > > >That's why the hypercube is only a theory -- it SHOULD be possible, but in > >realistic, practical terms it doesn't exist. Outside of advanced math > classes, the best use of the hypercube is as an example of where logic > ends and common sense begins. > The hypercube is not where "logic ends", it is a very logical extension > of the concept of dimension. It exists as surely as any mathematical > object. I was trying to wrap my post up quickly, but since there is NOTHING brief about this thread, I'll go verbose... I use "realistic" as short-hand for the way we percieve the world, which is primarily in 3-D. We percieve time, too, as the fourth dimension, but in a far less tangible way, and DEFINITELY seperate from our three tangible, spatial dimensions. But according to physics, time and space are the same thing -- and the hypercube is an example of that. A solid object, with equal sides and vertices, that has four dimensions. In short, time made as tangible as the "spatial" dimensions. So, our sensory input, which is views space in three dimensions, doesn't reconcile with an object that can only exist in four-dimensional space. This is what I meant by "common sense" -- the way we're used to seeing the universe. But since the universe existsi in four dimensions (at least), hypercubes DO exist, but can't be percieved by our senses, which only see the universe in three. This is how I learned Hypercubes, at least... not in math class (oh, those many years ago), but in AP Physics (even more years ago) as an illustration of the 4-D universe. (I can anticipate a reply arguing that we can sense the passage of time -- well, yes and no. Yes, we sense the PASSAGE of time, but only as an infinite progression, not the same as the perception a spatial dimension, which time is no different from. So we sense time the same we sense distance by falling off a cliff.) Now if anybody mentions the fifth dimension, I will sharpen all 30 edges of a hypercube until they are razor-sharp, come to your house with it, and insert it in you. FRM "The Fifth Dimension? Didn't they get to Number 3 with 'Baby, I Want your Love Thing'?" -- Dave Lister, "Red Dwarf" -- Do you hate Spam in your e-mail? Don't just delete it, do something about it! Report incidents of Spam, and get the offender kicked off the net. Do this: 1. Check the header for the REAL domain name that the Spam was sent from -- often Spammers disguise their email address. 2. Send a forward of the Spam to their Postmaster. The Postmaster's address will be "postmaster@[domain name here]". Put the domain name from the header in place of [domain name here]. 3. Any reputable ISP will cancel the Spammer's account immediately. Fight Spam! Join CAUCE (Coalition Against Unsolicited Commercial Email) at http://www.cauce.org/ and tell your Congresspeople how Spam mailings hurt you. Help protect genuine Internet commerce: Outlaw UCE Spamming. (This anti-Spam signature is available rent-free. Use it as your own.) The Right Rev. Felix Roy Mariposa, Prophet mar...@ricochet.net O- ULC <*>
On Wed, 11 Jun 1997 18:48:45 +0100, salesman <sal...@g-grids.demon.co.uk> wrote: >>I think these figures are right (I never tried to counts edges and faces >>of a hypercube before!) >> >> Dimensions Vertices Edges Faces >>Point 0 1? >>Segment 1 2 1 >>Square 2 4 4 1 >>Cube 3 8 12 6 >>H-cube 4 16 30 18 Your explanations and drawings are quite good, but -sorry to tell you- your figures are wrong The tesseract, or hypercube, has -4 dimensions, -16 vertices -OK so far-, - 32 edges, not 30 (not too hard to see; you have 12 edges in the cube you begin with, another 12 edges in the cube you end with, and eight edges connecting each vertex in the first cube with its homologue in the second cube) -24 faces, not 18 (again, 6 faces in cube 1 plus 6 faces in cube 2, plus 12 faces connecting each edge of cube 1 with its homologue in cube 2) -and last but not least, 8 cubical "faces" (cube 1, cube 2, and 6 cubes connecting each face of cube 1 with its homologue in cube 2)
Whoa! Hold on! Let me address each point (and I promise a new ascii drawing at the end of this post, so we can pretend we're still in this newsgroup *grin*) FRM writes: > Well, to continue this thread (and, yes, I know this ain't alt.physics), >time IS the fourth dimension, not "can be." The trick is that the separation of Time and Space is an artificial distinction -- physics tells >us that Time and Space are two manifestations of the same thing, no different from width, depth or height. And yes, the fourth dimension is 90 >degrees off from the other three... If you've followed all that, you should >have a headache by now. You may call time the fourth dimension if you wish, but it is no more the "official" fourth dimension than, say, width is the offical second dimension. In fact, if you've ever drawn a distance vs. time graph like we all probably have in physics class, then you've designated time as either the first or second dimension. It's all what you want to call it. As for time being 90 degrees from length, width, and depth, well... that's like saying that red is 90 degrees away from blue. If you drew it that way on a color wheel, then fine, but make sure we have some kind of frame of reference or the statement is meaningless. > The problem with this discussion, despite Michael's valiant attempt, is that hypercubes are almost impossible to draw on paper/computer screens. Michael's was a good start, but it takes a 3-D model to best show what we're talking about. > >That's why the hypercube is only a theory -- it SHOULD be possible, but in >realistic, practical terms it doesn't exist. Outside of advanced math classes, the best use of the hypercube is as an example of where logic ends >and common sense begins. Hypercubes are not impossible to draw on paper or computer or a blackboard... we've just seen several examples. Unless you mean that cubes and other 3-D objects are impossible to draw in two dimensions as well, which you could argue. The hypercube is not where "logic ends", it is a very logical extension of the concept of dimension. It exists as surely as any mathematical object. In "realistic, practical terms", even something as simple as a square does not exist. A square is an abstraction, even the most precise tools or computers can create a "real" square. Fun discussion, Reverand! Here's my new hypercube (thanks Veronica!) ( AAAAAaaaaaaaa! ( () ) ) ________ // ) () |\ \ // ( \\__ \ ______\// \__) | | | | | \ | | \|_______| // \\ (( || \\ || ( () || ( () ) ) Hyper-Cube -- ---- __ __ () _ _ __ __ _ _ __ __ ___ ___ o | \_|_\ | \/ |--| '(| =| | \| |/o \ " /|_/ O | O ) () o |_|_| | |_\__/_|__|_|_|__| |_|\__|_/\_|_|___|__/|_\_\ o_/||\/ \|__\| Michael Naylor, mna...@math.fsu.edu, (904) 644-8433 _/\_
On Wed, 11 Jun 1997, The Right Rev. Felix Roy Mariposa, Prophet wrote: > Now if anybody mentions the fifth dimension, I will sharpen all 30 edges Parallel universes don't exist, and if they did, they'd deny their own existance. (I have proof, mail me for it... <g>) > of a hypercube until they are razor-sharp, come to your house with it, and > insert it in you. You can no more insert a 4D object in to me (a 3D object) than you can insert me (3D) into the surface of a piece of paper (2D). :D BTW, since a 2D object is lacking a dimension, it could physically slice me in two (nasty paper cut), and to a 4D object, I also lack a dimension, therefore inserting one into me would probably slice it in two! Happy wibbling... -- Carl R White | e-mail...: crw...@-comp.brad.ac.uk | finger...: crw...@-dcsun1.comp.brad.ac.uk | web......: http://www.student.comp.brad.ac.uk/~crwhite/ Anti-Spam and Uncle-Pek measures in place & .sig fixed too...
Carl R. White wrote: > > On Wed, 11 Jun 1997, The Right Rev. Felix Roy Mariposa, Prophet wrote: > > > Now if anybody mentions the fifth dimension, I will sharpen all 30 edges > > Parallel universes don't exist, and if they did, they'd deny their own > existance. (I have proof, mail me for it... <g>) > > > of a hypercube until they are razor-sharp, come to your house with it, and > > insert it in you. > > You can no more insert a 4D object in to me (a 3D object) than you can > insert me (3D) into the surface of a piece of paper (2D). :D > > BTW, since a 2D object is lacking a dimension, it could physically slice > me in two (nasty paper cut), and to a 4D object, I also lack a dimension, > therefore inserting one into me would probably slice it in two! > > Happy wibbling... > > -- > Carl R White | e-mail...: crw...@-comp.brad.ac.uk > | finger...: crw...@-dcsun1.comp.brad.ac.uk > | web......: http://www.student.comp.brad.ac.uk/~crwhite/ > Anti-Spam and Uncle-Pek measures in place & .sig fixed too... Depends on which is harder, you or the hypercube; and which was moving. For instance, you can take a plastic cylinder, and use it to make a hole in a piece of paper, and you'd get a 3-D thing inserted into a 2-D one (cylinder moving, paper still). Or you can take a cylinder, slowly rub the edge of the paper against it so it gets that cutting effect (the cylinder would have to be of a soft substance -- say jello) until the paper slices the cylinder in half, with one half under the paper, and the other on top -- voila, 2-D thing inserted into a 3-D thing (cylinder still, paper moving). But, if you were to just throw the two together, the cylinder (of plastic, not jello) would probably win. OTOH, if you were to throw together a jello cylinder and sheet of plastic, plastic wins (variation on paper, rock, scissors -- jello, plastic, hypercube :) -- .--. |~~| .-------. Kevin Kreamer |~~| |.-----.| <kre...@centraltx.net> |--| || KCK || "A feature is a bug with seniority." | | |'-----'| |__|~'-------'
Carl R. White wrote: [ 8< ] > You can no more insert a 4D object in to me (a 3D object) than you can > insert me (3D) into the surface of a piece of paper (2D). :D > [ 8< ] how do we know that you are a 3D object? (you look pretty 2D from where I'm sitting...) -- 8] *paranoia*
In article <Pin...@dcsun4.comp.brad.ac.uk>, "Carl R. White" <crw...@computing.bradford.academia.unitedkingdom> wrote: > On Tue, 10 Jun 1997, salesman wrote: > ._____________________. > |\\. /|\ > | \ \. / | \ > | \ \ / | \ > | \ \. / | \ > | \.__\_______/____L____\ > | |\. \_____/ _|_--""| > | | \L\.___L\.-" | | > | | | | | | | | > | | _|_|___|_| | | > |__.==|="__\L____\|=._| | > \ | / \ \ | > \ | / \. \ | > \ | / \. \ | > \ | / \.\ | > \L/___________________\| > > I always thought the above was a 2D representation of the 3D > representation of a 4D cube (hypercube), assuming there was a fourth > directional dimension... :-) > Carl R White | e-mail...: crw...@-comp.brad.ac.uk I've seen a variation of this in 3-D, that had the lines radiating inward to form the inner cube's edges (don't expect me to ascii it). But yes, this is a possible representation, but so is the one that started this thread. Since it's theoretical, a hypercube could look like this, for all we know: :~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-. |`. /~\~~~~~~~--. `. (At least it would explain | `. \_/_______--' `. where the meat comes from.) | `:========================================: | | ,dP""8a "888888b, d8b "888b ,888" | FRM | | 88b " 888 d88 dPY8b 88Y8b,8888 | | | `"Y8888a 888ad8P'dPaaY8b 88 Y88P888 | | | a, Y88 888 dP Y8b 88 YP 888 | | | `"8ad8P'a888a a88a;*a888aa88a a888a | | | ;*;;;;*;;;*;;;*,, | | | _,---'':::';*;;;*;;;*;;*d;, | | | .-' ::::::::::';*;;*;dII; | | | .' ,<<<,. :::::::::::::::ffffff`. | | | / ,<<<<<<<<,::::::::::::::::fffffI,\ | | | .,<<<<<<<<<<I;:::::::::::::::ffffKIP", | | | |<<<<<<<<<<dP;,?>;,::::::::::fffKKIP | | | | ``<<<<<<<dP;;;;;\>>>>>;,::::fffKKIPf ' | | | \ `mYMMV?;;;;;;;\>>>>>>>>>,YIIPP"` / | | | `. "":;;;;;;;;;i>>>>>>>>>>>>>, ,' | ! | `-._``":;;;sP'`"?>>>>>=========. | `. | `---..._______...|<[Hormel | | `. | `=========' | `:====================================(FL): -- Do you hate Spam in your e-mail? Don't just delete it, do something about it! Report incidents of Spam, and get the offender kicked off the net. Do this: 1. Check the header for the REAL domain name that the Spam was sent from -- often Spammers disguise their email address. 2. Send a forward of the Spam to their Postmaster. The Postmaster's address will be "postmaster@[domain name here]". Put the domain name from the header in place of [domain name here]. 3. Any reputable ISP will cancel the Spammer's account immediately. Fight Spam! Join CAUCE (Coalition Against Unsolicited Commercial Email) at http://www.cauce.org/ and tell your Congresspeople how Spam mailings hurt you. Help protect genuine Internet commerce: Outlaw UCE Spamming. (This anti-Spam signature is available rent-free. Use it as your own.) The Right Rev. Felix Roy Mariposa, Prophet mar...@ricochet.net O- ULC <*>
Shimrod (csg...@wing.rug.nl) wrote: >The Right Rev. Felix Roy Mariposa, Prophet wrote: >> That's not funny! My cat once thought a hypercube was just another >> cardboard box -- so he jumped in it to play... no one's heard from him >> since. If anybody sees him, he's a greyish tabby who answers to the name >> "Schroedinger." Some thoughts on Schrodinger... ============= Schrodinger's Cat or Schrodinger's Can ? ============== Subject: Re: Schrodinger's Cat Newsgroups: sci.physics,rec.humor,alt.ascii-art From: Col...@equinox.gen.nz (Colin Douthwaite) Date: Sun, 11 Sep 94 14:01:34 +1200 Howard Wiseman (hm...@phyvc.auckland.ac.nz) wrote: : In article <Pin...@dsys.cc.conncoll.edu> : Lance D. Ritchie, ldr...@conncoll.edu writes: : >Can anyone tell me more about this? : (Schrodinger's Cat) : >I would especially like any references : >which discuss it. I know I have heard the phrase before. I vaguely : >recall something about a cat in a box, and about how one would know : whether : >or not the cat was dead without opening the box. But, upon reflection, : this : >sounds quite silly. Help! : > : Look in just about any popular book on quantum physics. e.g. : "Quantum Physics: illusion or reality" by A. McRae (I think), or : "In search of Schrodinger's Cat" by John Gribbon (I think) --------------------------------------------------------------------------- From: eng...@primenet.com (Lawson English) Newsgroups: sci.physics Subject: Re: Schrodinger's Can Date: 31 Jan 1995 06:47:41 GMT Message-ID: <3gkmed$ic...@news.primenet.com> Andy Watson (And...@ix.netcom.com) wrote: : Yes folks, it's true! : Erwin Schrodinger was in fact sitting on the can when he : made his many intuitive discoveries of QM. In fact, he : was in the classic "Thinker" pose as he did so... Did you observe this, or is this merely heresay? ------------------------------------------------------------------------- From: Col...@equinox.gen.nz (Colin Douthwaite) Newsgroups: sci.physics,alt.ascii-art,rec.humor Subject: Re: Can someone please explain Schrodinger's Can to me Date: 31 Jan 1995 03:06:04 GMT Mahipal Singh Virdy (vir...@pogo.den.mmc.com) wrote: : Schrodinger's Can? Can? Can what? [H,A]=HA-AH...HA, HA funny. : ANd they said the Internet wasn't good for laughs. :-) : In article <3g05b4$qm...@eplet.mira.net.au>, : Adrian J.F Land <bun...@werple.mira.net.au> wrote: : >Hi There.. : > : >From time to time I have seen various articles replying : >to thoughts on 'Schrodinger's Cat'.. : >Unfortunatly I cannot find the original article but it : >looks right up my alley - So could someone please : >explain it to me.. : > : >BTW - pitch the explanation at Secondary School level : >please! : > : "..right up my alley"? Wink, wink. : I'm sorry Adrian. I couldn't resist. Otherwise, if not for this : post, my day would've been without Laughter. Typing mistakes do : happen. But the distance between the letter T and the letter n are : too far apart for this to have been accidental. Or so I thought. : Thanks a bunch. : Mahipal, : Someone else will momentarily explain to you the Paradox of the : Cat. I'm too busy laughing. = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = ____ ____ _ _ ____ ____ ___ _ _ _ ____ ____ ____ . ____ [__ | |__| |__/ | | | \ | |\ | | __ |___ |__/ ' [__ ___] |___ | | | \ |__| |__/ | | \| |__] |___ | \ ___] ____ ____ _ _ | |__| |\ | |___ | | | \| = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Which Can was Schrodinger actually sitting on ? This Can ? //////// |:---[.] |( _J | ^ ( _| / \_____) / _____ \ | / \ \ _________ | | | | ./ ./ \ /\ /\__ | ./ ./ | | | \/--- _ ./ ./ | \ \ ) ) /________ / o | | >_____/_____)_) | | | \__________/ | | |__ ________ / \ | | / ./ ------- .\ | | | | / ./ \.\ \ \\ | | / ( ) ) \ |\ | | / \. ./ / \ | \ !--------------\ \._______./ / \ | | ! `============' | | | \ I | | | > I | / | / \ |________/____| < > (_________)____) ___\________________________/________________________________ Or this one ? //////// |:---[.] |( _J | ^ ( _| / \_____) / _____ \ | / \ \ | | | | \ /\ /\__ | | | \/--- _ Eep. \ \ ) ) _ _ / | >_____/_____)_) ( )( ) ___ \__________/ ____ \../-' \ ______________________/ \ / \///___/// | | / .====='/ \ \ / \_ _ _ _ \ /________________________________________________________/\ | |=======================================================| \ | | SCHRODINGER'S CAN | | | | | | | | /\_/\ | | | | / o O \_____-------------_________ | |_____|__ | ( ~ ) ____ \ | (_______)_) | \`---'/ / ) ) | | | \___/ / / / / | | | \ ________\ / /__/ | / | \ / / / | / | / / / / | / | _/ / __/ / | / | (___/ (_____/ | / | | / |_______________________________________________________|/ ------------------------------------------------------------------------- From: Col...@equinox.gen.nz (Colin Douthwaite) Newsgroups: sci.physics,alt.ascii-art,rec.humor Subject: Re: Entwisle's Dog meets Schrodinger's Cat Date: 6 Dec 1994 06:47:42 GMT Message-ID: <3c11ee$fv...@southern.co.nz> David Howard,Ph3751,Rm368 (dav...@ist.flinders.edu.au) wrote: > I was explaining the idea of Schrodinger's Cat to a fellow > PhD student. In particular, the role of the observer... > What if the observer was a dog (named for said fellow PhD student) > rather than a human? ... > If you take the position that the dog is concious, so that the > situation is the same as that for a human observer, then what > about the case where the observer is a mouse (which had better > hope the cat collapses to "dead" ;-) )... > Comments anyone? For example, the "real" name for > Entwisle's dog if this idea has been considered before... ------------------------------------------------------------------------- Subject: Entwistle's Dog meets Schrodinger's Cat ------------------------------------------------------------------------- ROWWWWRR! /\_/\ |/ |o -| =(__*__)= . ,' U ', )) 8''''' , , '''''8 )\\ // ''''''. .'''''' _``\`,- '''' ''- ,,,/ / .' '. .---'a> , < ,<' << ,<, ' / \ .' , '., `v^w ' , << ,< ' < < / \ Eep. .' , ,, ''8 ````--' \ ,,,---''/ <' // _ _ / ,, ,'',, ',.' ''''' !! ;; ( ' / \ ( )( ) ___ , ''',,' ', '8 !!</ \ `\ / \../-' \_ '''' '' <</ / /</ \///___/// (FL) <</ .====='/ -Matthew MacIntyre- ------------------------------------------------------------------------- Entwistle's Dog meets Schrodinger's Cat ()() ____ (..) /|o | /\/\ /o| o| __c\db/o.. /o_|_o_|_________ / \ /______________________________\ / \ /________________________________\ , , / \ |\___/| ,-. /__________________________________\ |o o|_______________ | | { } \ w / \`. ,',' <____________________________| _`---' , |.`--' ,' | DOG BOX > (____``\ |```` ( \ `---' {____________________________| ______ (________|````````\ /) < } / DOG \ ) // |____________________________| /___________\ (_// \\/ \||// |// \\/ -cfbd- \||// [ mouse & cheese by Row ] Was the dog dead or alive ? Did the cat take a free lunch ? Around this part of the world, anyone ending up in the dog-box would be considered more dead than alive :-) --------------------------------------------------------------------------- Malcolm S. Craill (s.c...@mactropolis.co.nz) wrote: >We might be onto something with the tumble driers. >In my youth I taught our cat to navigate through some quite >difficult mazes made from ABC beer crates. These were overlapped >in such a way as to allow the cat to go left or right, up and down. >The crates are of course open ended wooden boxes with small holes >on all remaining 5 faces to allow the subject of the experiment >(the cat) to anticipate the next option avilable around the corner. >This may be an important factor. >The cat later vanished for several days after being last seen in >the vicinity of the beer crates. It later reappeared inside the >clothes drier. The drier had it's door closed at the time that the >cat was discovered. ____________________ | o o o ....... | |--------------------| | ____ | | ,-' `-. | | / /\ /\ \ | | :| (o|o)' |] | | \ =(^)= / | -David Moore- | `-.____,-' | | | ==================== djm The question is was your cat dead or alive when you discovered it in the clothes dryer ? The answer is important because it may provide a solution to the Schrodinger's Cat problem which still creates much difficulty for physicists. =========================================================================== Bye,
<The tesseract, or hypercube, has <-4 dimensions, <-16 vertices -OK so far-, <- 32 edges, not 30 (not too hard to see; you have 12 edges in the cube <you begin with, another 12 edges in the cube you end with, and eight <edges connecting each vertex in the first cube with its homologue in <the second cube) <-24 faces, not 18 (again, 6 faces in cube 1 plus 6 faces in cube 2, <plus 12 faces connecting each edge of cube 1 with its homologue in <cube 2) <-and last but not least, 8 cubical "faces" (cube 1, cube 2, and 6 <cubes connecting each face of cube 1 with its homologue in cube 2) Ah! Thank you Frank, I can't count very well, I'm afraid. Never thought of the cubical "faces"... very cool! Would a 5th dimensional hypercube then have 24 cubical "faces" and 8 hypercubical "faces"? These things get complicated quickly! -- ---- __ __ () _ _ __ __ _ _ __ __ ___ ___ o | \_|_\ | \/ |--| '(| =| | \| |/o \ " /|_/ O | O ) () o |_|_| | |_\__/_|__|_|_|__| |_|\__|_/\_|_|___|__/|_\_\ o_/||\/ \|__\| Michael Naylor, mna...@math.fsu.edu, (904) 644-8433 _/\_
Colin Douthwaite wrote: > > Veronica Karlsson (e93...@sm.luth.se.nospam) wrote: > > >surely _this_ must be a hyper-cube: > > > ________ > >|\ \ > >| \ ______\ > >| | | > >| | hyper | > > \ | | > > \|_______| > > Hmm...that depends who or what you are...Dougal can't read so he > thinks it's a Sugar Lump. :-) > > .,,,,,. > .%;;;;;;;%`\ \ / > / ` /`"'''"'`\ \ \ _ / > / / ~ 6 6 ~ \ \ ("'"; > / / .,,,,,. \ \``'.,,,.. ;"'" > / : ::;;;;;:: ; \ \ ```'' \ > / : `'''''` ; \ \ \ \ \ \ \ > / `, _ ,' \ \ \ \ \ > -cfbd- / \ `''`(_)``''` / \ \ \ \ > / // \ : . . . : / \ \ ; \ \ \ \ ; > / // \\ ; ; ; ; // \ /\ ; ; , ' ^ ^ '^ ^ ' > _______` '' ` `` '' `' ` ' ` > |\ \ > | \ ______\ > | | | > | | hyper | > \ | | > \|_______| > > Bye, Pleeeeeeeease, show us the "before and after" pictures... :D -- :) Veronica Karlsson ( e93...@sm.luth.se http://www.ludd.luth.se/~vk/ ) ( llizard's fanclub: http://www.ludd.luth.se/~vk/llpages )
On Fri, 13 Jun 1997 14:36:24 +0200, Veronica Karlsson <e93...@nospam.sm.luth.se> wrote: >> >surely _this_ must be a hyper-cube: >> >> > ________ >> >|\ \ >> >| \ ______\ >> >| | | >> >| | hyper | >> > \ | | >> > \|_______| Not a hyper-cube, but I hope you like the object: .----------------------------------------------------------------------. |_.-._.-._.-._.-._.-._.-. _.-._.-._.-. _.-._.-._.-._.-._.-._.-._.| |_.-._.-._.-._.-._.-._. .::db .-._.-._. .::db .-._.-._.-._.-._.-._.-._.| |_.-._.-._.-._.-._.-._ .::d88b -._.-._ .::d88b -._.-._.-._.-._.-._.-._.| |_.-._.-._.-._.-._.-. .::d8888b .::d8888b ._.-._.-._.-._.-._.-._.| |_.-._.-._.-._.-._.- .::d88!::::::::::::d888888b _.-._.-._.-._.-._.-._.| |_.-._.-._.-._.-._.- \ Y88\_________\ Y888888P _.-._.-._.-._.-._.-._.| |_.-._.-._.-._.-._.-. \ Y8888P ._.-. \ Y8888P ._.-._.-._.-._.-._.-._.| |_.-._.-._.-._.-._.-._ /dbY88Pdb _.-._ /dbY88Pdb _.-._.-._.-._.-._.-._.| |_.-._.-._.-._.-._.-. /d8P_YP Y8b .-. /d8P_YP Y8b .-._.-._.-._.-._.-._.| |_.-._.-._.-._.- /d8P .-.\ Y8b /d8P .- \ Y8b -._.-._.-._.-._.-._.| |_.-._.-._.-._ .::db/d8P _.-. \.::db/d8P _.-. \ Y8b ._.-._.-._.-._.-._.| |_.-._.-._.-. .::d88bYP ._.-. .::d88LSP ._.-._ \ Y8b ._.-._.-._.-._.| |_.-._.-._.- .::d8888b .::d8888b`b _.-._. \ Y8b:db _.-._.-._.-._.| |_.-._.-._. .::d88!::::::::::::d888888b`b .-._.- \ YPd88b .-._.-._.-._.| |_.-._.-._. \ Y88\_________\ Y888888Pd8b .::d8888b -._.-._.-._.| |_.-._.-._.- \ Y8888P -._.- \ Y8888P!::::::::::::d888888b ._.-._.-._.| |_.-._.-._.-. \ Y88Pdb ._.-. \ Y88Pdb_________\ Y888888P ._.-._.-._.| |_.-._.-._.-._ \__YP Y8b _.-._ \__YP Y8b`P -._.- \ Y8888P -._.-._.-._.| |_.-._.-._.-._.-._. \ Y8b .-._.-. /d\ Y8b .-._.-. /dbY88P .-._.-._.-._.| |_.-._.-._.-._.-._.- \ Y8b -._.- /d8P\ Y8b -._.- /d8P_YP _.-._.-._.-._.| |_.-._.-._.-._.-._.-. \ Y8b /d8P _\ Y8b /d8P _.-._.-._.-._.-._.| |_.-._.-._.-._.-._.-._ \ Y8b:db/d8P ._ \ Y8b:db/d8P ._.-._.-._.-._.-._.| |_.-._.-._.-._.-._.-._. \ YPd88bYP -._. \ YPd88bYP -._.-._.-._.-._.-._.| |_.-._.-._.-._.-._.-._. .::d8888b .::d8888b .-._.-._.-._.-._.-._.| |_.-._.-._.-._.-._.-._ .::d88!::::::::::::d888888b -._.-._.-._.-._.-._.| |_.-._.-._.-._.-._.-._ \ Y88\_________\ Y888888P -._.-._.-._.-._.-._.| |_.-._.-._.-._.-._.-._. \ Y8888P .-._. \ Y8888P .-._.-._.-._.-._.-._.| |_.-._.-._.-._.-._.-._.- \ Y88P _.-._.- \ Y88P _.-._.-._.-._.-._.-._.| |_.-._.-._.-._.-._.-._.-. \__YP ._.-._.-. \__YP ._.-._.-._.-._.-._.-._.| `----------------------------------------------------------------------' Solid 3D -- Lennert Stock - Demon Internet WebDemon - http://www.demon.nl/
Frank Newhouse wrote: > > On Wed, 11 Jun 1997 18:48:45 +0100, salesman > <sal...@g-grids.demon.co.uk> wrote: > > >>I think these figures are right (I never tried to counts edges and faces > >>of a hypercube before!) > >> > >> Dimensions Vertices Edges Faces > >>Point 0 1? > >>Segment 1 2 1 > >>Square 2 4 4 1 > >>Cube 3 8 12 6 > >>H-cube 4 16 30 18 > > Your explanations and drawings are quite good, but -sorry to tell you- > your figures are wrong > > The tesseract, or hypercube, has > -4 dimensions, > -16 vertices -OK so far-, > - 32 edges, not 30 (not too hard to see; you have 12 edges in the cube > you begin with, another 12 edges in the cube you end with, and eight > edges connecting each vertex in the first cube with its homologue in > the second cube) > -24 faces, not 18 (again, 6 faces in cube 1 plus 6 faces in cube 2, > plus 12 faces connecting each edge of cube 1 with its homologue in > cube 2) > -and last but not least, 8 cubical "faces" (cube 1, cube 2, and 6 > cubes connecting each face of cube 1 with its homologue in cube 2) Making the above table: Dimension Points Lines Squares Cubes H-Cubes H-H-Cubes Point 0 1 Line 1 2 1 Square 2 4 4 1 Cube 3 8 12 6 1 H-cube 4 16 32 24 8 1 H-H-cube 5 32 80 80 40 10 1 etc. the number of Y-dimensional objects in an X-dimensional object is 2 x number of Y dimensional object in an X-1 dimensional object + number of Y-1 dimensional objects in an X-1 dimensional objects. Is theis a bit clear? No? reread! Still not clear? No? Bummer! :-) It sounds a bit complicated, but once you get it it's quite simple example: number of lines in cube: 2 x number of lines in squares + number of points in square == 2*4 + 4 = 12 Greetz, -- _____ _ _ _ ,-'`. | __| |_|_|_____ ___ ___ _| | _ _ _ _ ___ ,'`.,-'`. |__ | | | | _| . | . | | \ / \ |\| ' | /`.,'`.,-'`. |_____|_|_|_|_|_|_|_| |___|___| |_/ \_/ | | | (`./`-,'`.,-'`. _ _ _ _ _ _ \.\.( `,'`.,-' Herman Hiddema |_) /| |\| | / ` )`\ |.|`,' Venuslaan 147 c | /"| | | | \_, ,' \/`) /.| 9742 KN Groningen ,-'"`-. / \,'\/`( ( The Netherlands //// / @ @ \ \\\\ \,'`./`./`.\ tel. 050-5775373 \ :=| ,._,. |=: / \ ,'\ /\ ) mailto:csg...@wing.rug.nl || ,\ \_../ /. || \ ,; \,' http://huizen.dds.nl/~shimrod/ ||','`-._))'`.`|| `: \.' `-' (/ `-' `./ Now there's a man who knows where his towel is!
Benjamin Francisco P. wrote: > > > ._____________________. > > |\\. /|\ > > | \ \. / | \ > > | \ \ / | \ > > | \ \. / | \ > > | \.__\_______/____L____\ > > | |\. \_____/ _|_--""| > > | | \L\.___L\.-" | | > > | | | | | | | | > > | | _|_|___|_| | | > > |__.==|="__\L____\|=._| | > > \ | / \ \ | > > \ | / \. \ | > > \ | / \. \ | > > \ | / \.\ | > > \L/___________________\| > > > I always thought the above was a 2D representation of the 3D > > representation of a 4D cube (hypercube), assuming there was a fourth > > directional dimension... :-) > > Actually, the above is the best representation possible for our senses, > of a hypercube. The first method described (Creating 2 n-1 dim hc's and > joinig ends works), points (0dim) become lines (1dim) lines become > squares (2dim), squares go to cubes (3dim) and so on. Thwe trouble with > all representations, is that, just like the previous 3, the joining of > the 2 (n-1)dimensional hypercubes MUST be done at right angles to ALL > the other dimensions used. In the first 4 (point, line, square, cube) > that is just fine, cuz we can visualize the succesive dimensions. But we > just CAN'T represent correctly a hypercube, because we can't imagine the > 4th dimension, to draw the lines along THAT dimension (The weird > hexagons drawn earlier are only 3d figures, because the lines joining > the cubes are along one of the first 3 dimensions, not the fourth) > The most accurate way would be for you to look at the drawing above, and > try to imagine the lines connecting the 2 cubes being at right angles to > all the lines they join. Tough huh? Well, don't worry, you CAN'T because > we see the world in a 3d way, so you can't imagine a 4th d. Like you > can't invent new colors. Sure you can invent new colors. Add a mixture of red, green, and blue that no one has done before. > In any case, I think a cube in our world is still a hypercube. Ok, so > time is not the official 4th dimension, but it is still a dimension at > right angles to all the others (of course) and cubes in our world DO > continue on time, they don't just vanish. So they have an extention into > another dimension (They probably extend into all dimensions, along with > everything in the world, we just aren't equipped to notice it). Now try > again, to imagine 2 cubes connected by lines at right angles to all the > others. Do you understand why the cube above is still not an exact > representation of a hypercube? After all, a 3d cube drawn on paper > hardly resembels the real thing huh? > > -- > I know the truth, and the truth hurts! -Isamu Dyson > The end comes before chaos - Kefka > > Benjamin Francisco P > Bfr...@puc.cl A cube in our world is a hypercube only if its length along the 4-D is equal to the lengths along the other 3 dimensions. Otherwise, its a hyper-rectangle. Time is the "official" fourth dimension, according to Einstein and physicists following him. Einstein saw the universe as a complete 4-D continuum, where you can "turn" it, and the fourth dimension will take the place of another one of the dimensions -- kinda like if you turn a regular cube, the width becomes the length or the height depending on which way you turn it. We can then represent a hypercube after we come up with a way to reconcile the time/length difference -- come up with a way to convert between meters and minutes, for instance. The other problem with the time-hypercube is the concept of world lines. World lines are lines on a regular cartesian plane, but with the y-axis being replaced by the t-axis (t for time), that show how a certain thing or set of things travel with respect to time and some other dimension, like length. An example is in order. If you go in a straight line for 2 meters and it takes you 4 seconds to do it (and you did it at a constant velocity), then the graph would be a slanted line : (secs)^ 4 + * | / 2 + / | / x <-+---+---+--> v 1 2 (meters) y with the equation : y = (1/2 sec/meter)x World lines can be plotted for a hypercube, for instance, or all atoms in the universe (on a *huge* graph). The interesting thing is that if you were to plot all atoms, then you'd have countless lines curving this way and that, some of them coming together to form something, say a hypercube, for a while, and then diverging when the hypercube is destroyed. But the lines don't begin or end, they are infinite in both directions -- the graphical illustration of the law of conservation of matter. The other cool thing is you can plot energy as well as matter, even on the same graph, because E=MC^2. The way this is a problem for hypercubes, is that if you plot it, all of the atoms inside are plotted as lines with no ends, therefore the hypercube is plotted as a line (or collection of lines, depending on how you want to do it) with no end. therefore, a real cube with side = 2m plotted becomes a hyper-rectangle with sides 2m,2m,2m,infinite seconds. Have fun in ascii.physics land! -- .--. |~~| .-------. Kevin Kreamer |~~| |.-----.| <kre...@centraltx.net> |--| || KCK || "Everything that can be invented has been invented." | | |'-----'| --Charles H. Duell,U.S. Office of Patents, 1899. |__|~'-------'
In article <199...@ladder02.news.aol.com>, spu...@aol.com (Spunk1111) wrote: > In article <mar...@news.ricochet.net>, > mar...@ricochet.net (The Right Rev. Felix Roy Mariposa, Prophet) writes: > > > Now if anybody mentions the fifth dimension, I will sharpen all 30 > edges > >of a hypercube until they are razor-sharp, come to your house with it, > and > >insert it in you. > > Wasn't the 'Fifth Dimension' a rock group?? hehe > -joan I believe they got to number 2 on the charts with "Baby, I want your Love Thing." Their careers fizzled, however, when their follow-up album was a long-winded discussion of 4 dimensional objects set to a disco beat. FRM ASCII hypercube, viewed from distance of 30 meters and 4.2 years: ---> ' <--- -- Do you hate Spam in your e-mail? Don't just delete it, do something about it! Report incidents of Spam, and get the offender kicked off the net. Do this: 1. Check the header for the REAL domain name that the Spam was sent from -- often Spammers disguise their email address. 2. Send a forward of the Spam to their Postmaster. The Postmaster's address will be "postmaster@[domain name here]". Put the domain name from the header in place of [domain name here]. 3. Any reputable ISP will cancel the Spammer's account immediately. Fight Spam! Join CAUCE (Coalition Against Unsolicited Commercial Email) at http://www.cauce.org/ and tell your Congresspeople how Spam mailings hurt you. Help protect genuine Internet commerce: Outlaw UCE Spamming. (This anti-Spam signature is available rent-free. Use it as your own.) The Right Rev. Felix Roy Mariposa, Prophet mar...@ricochet.net O- ULC <*>
>> Veronica Karlsson (e93...@sm.luth.se.nospam) wrote: >> > ________ >> >|\ \ >> >| \ ______\ >> >| | | >> >| | hyper | >> > \ | | >> > \|_______| Am I the only one here who can't help but think about Infocom's 'Spellbreaker'? First the hypercube, and now *this*... WRITE "HYPER" ON FEATURELESS WHITE CUBE BLORPLE "HYPER" CUBE -- Support the anti-Spam amendment! /<-= Admiral Jota =->\ Join at http://www.cauce.org/ -< <-= jot...@tiac.net =-> >- \<-=- -= -=- =- -=->/
Veronica Karlsson (e93...@nospam.sm.luth.se) wrote: >Colin Douthwaite wrote: >> >> Veronica Karlsson (e93...@sm.luth.se.nospam) wrote: >> >> >surely _this_ must be a hyper-cube: >> >> > ________ >> >|\ \ >> >| \ ______\ >> >| | | >> >| | hyper | >> > \ | | >> > \|_______| >> Hmm...that depends who or what you are...Dougal can't read so he >> thinks it's a Sugar Lump. :-) >> .,,,,,. >> .%;;;;;;;%`\ \ / >> / ` /`"'''"'`\ \ \ _ / >> / / ~ 6 6 ~ \ \ ("'"; >> / / .,,,,,. \ \``'.,,,.. ;"'" >> / : ::;;;;;:: ; \ \ ```'' \ >> / : `'''''` ; \ \ \ \ \ \ \ >> / `, _ ,' \ \ \ \ \ >> -cfbd- / \ `''`(_)``''` / \ \ \ \ >> / // \ : . . . : / \ \ ; \ \ \ \ ; >> / // \\ ; ; ; ; // \ /\ ; ; , ' ^ ^ '^ ^ ' >> _______` '' ` `` '' `' ` ' ` >> |\ \ >> | \ ______\ >> | | | >> | | hyper | >> \ | | >> \|_______| > >Pleeeeeeeease, show us the "before and after" pictures... :D OK then...here's Dougal _after_ eating the hypercube... .,,,,,. .%;;;;;;%`\ / /`"'''"`\ \ // -# @- \ \ // .,,,,,. \ \``'.,,,.. /: ::;;;;: ; \ \ ```'', /: `'''` ; \ \ \ \ \ \ \ /`, _ _ ,' \ \ \ \ \ ("'"; " `` V ''` ' ` `' ` ' ` `'` ' `"" "'" __ . h |\ y r \|_ Bye,
Rumor has it that on Fri, 13 Jun 1997 21:59:50 -0500, Kevin Kreamer
<kre...@centraltx.net> wrote:
% Benjamin Francisco P. wrote:
% A cube in our world is a hypercube only if its length along the 4-D
% is equal to the lengths along the other 3 dimensions. Otherwise, its a
% hyper-rectangle. Time is the "official" fourth dimension, according to
% Einstein and physicists following him. Einstein saw the universe as a
% complete 4-D continuum, where you can "turn" it, and the fourth
% dimension will take the place of another one of the dimensions -- kinda
% like if you turn a regular cube, the width becomes the length or the
% height depending on which way you turn it. We can then represent a
% hypercube after we come up with a way to reconcile the time/length
% difference -- come up with a way to convert between meters and minutes,
% for instance.
The answer is...42!
Sorry, sorry, sometimes I just can't help myself. Trying to imagine a line 6
hours long blew my mind.
Does this mean that a hypercube could only exist for X secs before colapsing
into a "regular" cube?
Where X secs = 2 metres.
Or are all hypercubes really hyperRectangles until the end of time?
<shakes head vigorously to clear the clutter>
I'm getting a headache, I think I'll go read some nice, simple cultural
anthropology or something.
Sleeper
"It tasted better when I thought it was deer meat."
-over heard at a soup kitchen serving tofu chilie.
Sleeper wrote: > > Rumor has it that on Fri, 13 Jun 1997 21:59:50 -0500, Kevin Kreamer > <kre...@centraltx.net> wrote: > > % A cube in our world is a hypercube only if its length along the 4-D > % is equal to the lengths along the other 3 dimensions. Otherwise, its a > % hyper-rectangle. Time is the "official" fourth dimension, according to > % Einstein and physicists following him. Einstein saw the universe as a > % complete 4-D continuum, where you can "turn" it, and the fourth > % dimension will take the place of another one of the dimensions -- kinda > % like if you turn a regular cube, the width becomes the length or the > % height depending on which way you turn it. We can then represent a > % hypercube after we come up with a way to reconcile the time/length > % difference -- come up with a way to convert between meters and minutes, > % for instance. > > The answer is...42! > > Sorry, sorry, sometimes I just can't help myself. Trying to imagine a line 6 > hours long blew my mind. > > Does this mean that a hypercube could only exist for X secs before colapsing > into a "regular" cube? > Where X secs = 2 metres. > I don't think it would collapse into a regular cube, because time would continue to flow, and so in that case it would end up as a hyperrectangle. For it to be a hypercube, the shape must become a cube at a given time and then stop being a cube X seconds later, because we can not stop time. (if we could stop time, it would be easy -- make a cube at a given time, then stop time X seconds later -- voila, hypercube!) You could break the cube in half after X seconds, and then you'd have a hypercube 2m*2m*2m*Xsec, that just finished being a hypercube (viewing the cube from a 4-D perspective). The drawings that were posted were attempts (many of them very good attempts) to represent two-dimensionally a fourth-dimensional view of a cube lasting for X seconds, if I understand the concept correctly. <now I shake my head to clear the clutter :) > > Or are all hypercubes really hyperRectangles until the end of time? > <shakes head vigorously to clear the clutter> > All quarks are really hyperwhatevers (because they won't always necessarily retain a cube shape throughout the course of time), until we can divide a quark. Then all whatever's-the-smallest-part-of-matter becomes hyperwhatevers until the end of time (or until we can break it down further). I hope I helped clear it up <g> > I'm getting a headache, I think I'll go read some nice, simple cultural > anthropology or something. > > Sleeper > > "It tasted better when I thought it was deer meat." > -over heard at a soup kitchen serving tofu chilie. Maybe rocket science will be easier ;) BTW, to pull this thread at least a little back towards the topic of ascii-art, here's what we all wish would fall out of a hypercube if we ever found one (MONEY !!!): | | | | | | | | | | | | | | | | .:::. | | | | | | ::':::: | | | | :.:::': | ____________ .-'''-. KCK::::.:: | .' .' : : ':::' | .' .' : : | | : : ;KCK ; | | : : '-...-' | ______ : : | | :KCK .' .' | | | : .' .' '.'__________.' .'''. : : : : :KCK : '...' -- .--. |~~| .-------. Kevin Kreamer |~~| |.-----.| <kre...@centraltx.net> |--| || KCK || "A feature is a bug with seniority." | | |'-----'| |__|~'-------'
In article <5nqcgt$tr3$4...@mnementh.southern.co.nz>, cfb...@southern.co.nz (Colin Douthwaite) wrote: > [...] > From: eng...@primenet.com (Lawson English) > Newsgroups: sci.physics > Subject: Re: Schrodinger's Can > Date: 31 Jan 1995 06:47:41 GMT > Message-ID: <3gkmed$ic...@news.primenet.com> > > Andy Watson (And...@ix.netcom.com) wrote: > : Yes folks, it's true! > > : Erwin Schrodinger was in fact sitting on the can when he > : made his many intuitive discoveries of QM. In fact, he > : was in the classic "Thinker" pose as he did so... > > Did you observe this, or is this merely heresay? > > ------------------------------------------------------------------------- > > From: Col...@equinox.gen.nz (Colin Douthwaite) > Newsgroups: sci.physics,alt.ascii-art,rec.humor > Subject: Re: Can someone please explain Schrodinger's Can to me > Date: 31 Jan 1995 03:06:04 GMT > > Mahipal Singh Virdy (vir...@pogo.den.mmc.com) wrote: > > : Schrodinger's Can? Can? Can what? [H,A]=HA-AH...HA, HA funny. > : ANd they said the Internet wasn't good for laughs. :-) > > : In article <3g05b4$qm...@eplet.mira.net.au>, > : Adrian J.F Land <bun...@werple.mira.net.au> wrote: > : >Hi There.. > : > > : >From time to time I have seen various articles replying > : >to thoughts on 'Schrodinger's Cat'.. > : >Unfortunatly I cannot find the original article but it > : >looks right up my alley - So could someone please > : >explain it to me.. > : > > : >BTW - pitch the explanation at Secondary School level > : >please! > : > > > : "..right up my alley"? Wink, wink. > > : I'm sorry Adrian. I couldn't resist. Otherwise, if not for this > : post, my day would've been without Laughter. Typing mistakes do > : happen. But the distance between the letter T and the letter n are > : too far apart for this to have been accidental. Or so I thought. > : Thanks a bunch. > > : Mahipal, > : Someone else will momentarily explain to you the Paradox of the > : Cat. I'm too busy laughing. Hey, that was me laughing back then. It's still funny. > = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = > > ____ ____ _ _ ____ ____ ___ _ _ _ ____ ____ ____ . ____ > [__ | |__| |__/ | | | \ | |\ | | __ |___ |__/ ' [__ > ___] |___ | | | \ |__| |__/ | | \| |__] |___ | \ ___] > > ____ ____ _ _ > | |__| |\ | > |___ | | | \| > > = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = > > Which Can was Schrodinger actually sitting on ? [trim] /\ "If the line between science fiction and / science fact doesn't drive you crazy, /\ \ then you're just not tr(y)ing!" \ /\/\ / \ \/ Mahipal / == \ / \/\/ The |meforce> Paradox \/ http://www.geocities.com/Athens/3178/mew3.html -------------------==== Posted via Deja News ====----------------------- http://www.dejanews.com/ Search, Read, Post to Usenet
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