roice writes "Rubik's junkies and puzzlers will be interested in this software rendered four-dimensional
analog of Rubik's Cube. With over 1.75E120 possible combinations, it's
a mind bender. Free versions are available for both Windows and Linux, and
they even publish their source code for download. Solving it will get your
name listed in their Hall
Of Fame, and there is also a running competition for the most efficient
solution. To help get you started, you can check out a solution algorithm based
on techniques used to solve the popular three-dimensional version."
Heck with solving it. There are some things that just aren't worth solving. Now where can I find a software rendered four dimensional analog of a hammer and nail?
I don't know. It looks like a more complex 3D version that's just real togh to build with plastic.
Maybe it's because I read some quack's claim that the 4th dimension was time. In which case a 4D rubics cube would solve itself over time or be onsolvable because it rescrambled while you were trying to solve.
Maybe it's because I read some quack's claim that the 4th dimension was time. In which case a 4D rubics cube would solve itself over time or be onsolvable because it rescrambled while you were trying to solve.
The 4th dimension is whatever you define it as. There's no "true" 4th dimension. Einstein had the idea that time could be treated in a fashion similar to that of the spatial dimensions, and so, in his work, he defined the 4th dimension as the temporal dimension.
However, for this program's purposes, it's assumed that we're talking about the 4th *spatial* dimension. You can (kinda) visualize it if you think of the progression of first 3 dimensions: a line (1st d) can be rotated 90 degrees to itself to form a square (2nd d) which can be rotated 90 degrees to itself to form a cube (3rd d). The 4th dimension is thus hypothesized as the space defined by a cube rotated 90 degrees to itself.
(Granted, I'm no mathematician, so if someone has a better understanding, please correct me.)
If you've ever read the story "And He Build a Crooked House" by Robert Heinlein, it contains a very good description of what a four-dimensional hypercube would look like. Imagine a small cube in the middle, six cubes surrounding it (one on each side, squashed together so that they share faces), and one big cube on the outside. Alternately, imagine two intersecting cubes (one corner of each cube is in the middle of the other cube), where each face of one cube is connected to each face of the other cube by another cube. Confused yet? So am I! Read the story, it's quite interesting.
This puzzle uses the first model mentioned above, except that you can only see seven cubes at once (the outer cube is hidden so that it won't block the view of the others). If you rotate the model (with Shift-left or Shift-right click), the outer cube comes into view.
Those are only descriptions of a hypercube that is projected onto a three-dimensional space or intersected with a three-dimensional space.
A real hypercube looks like a hypercube, not a cube with lines or anything else... of course you need to be five-dimensional to perceive the whole thing at once.
In general you need N+1 dimensions to perceive an N-dimensional object; for example, we can only fully perceive two dimensional objects all at once. Three dimensional objects we only see a particular side of, an
after taking calc III, Ive come up with a great way to describe 4d objects.
Example, take a room, it has 3 standard dimensions, now lets add another dimension, lets say temperature. Now we have a 4d object, we could even try and make a function to model temperature based on postion, temp = f(x,y,z);
You can even do neat things like make 3d objects out of 4d objects by taking a level surface of the 4d object. In simpler terms, take all of the points in the room that are one temperature, that will form a 3d o
Here's a Java animation that will show you a 2D projection of a 4D hypercube:
http://dogfeathers.com/java/hyprcube.html
It's really tough to wrap your head around another spatial dimension. Books like Flatland and Realware make the comparison to a 2D person's world being interrupted by one of us.
For example, if you were 2D, living on your flat plane, and a 3D person passed an orange through the plane, you would perceive it as a round shape which grew out of nothingness, got bigger and changed shape for awhile, then shrank and disappeared.
A 3D person could also see into your house, because a 2D person would just build four walls and no ceiling or floor. Similarly, a 4D creature could see through all of us and our buildings, because we only build in three dimensions.
You sound like you could borrow my Rubik's Square. It only took me about half an hour to solve, once I realized that all the squares are the same color.
Here's a solving technique that works everytime: Simply twist and turn the cube until all sides match up. No additional tools required or embarassing adhesive related situations to deal with...
you know how long I've been working on my three dimensional one? over a year. Perhaps I'm stupid, but that thing is impossible to solve. Anyone have any clue how long it would take a computer to solve your standard rubics cube through brute force?
you know how long I've been working on my three dimensional one? over a year. Perhaps I'm stupid, but that thing is impossible to solve.
Maybe somebody subjected you to one of my favorite old tricks. Take one corner off of a solved cube and rotate it so that the colors don't match the rest of the cube. Reassemble in this orientation. Presto: unsolveable cube.
Maybe somebody subjected you to one of my favorite old tricks. Take one corner off of a solved cube and rotate it so that the colors don't match the rest of the cube. Reassemble in this orientation. Presto: unsolveable cube.
Kinda funny -- I've inadvertently subjected myself to this same trick as a child. It always took so long to scramble the thing, it was easier to take it apart and put it back together in random order. Little did I realize there was a very good chance of creating an unsolvable cube.
Furthermore, I went so far as to buy a "how to solve the rubik's cube" book. Followed every goddamn step in that thing, and was pissed when it wasn't working. Eventually I tried it on my sibling's and it worked, and I came to the conclusion that mine was defective. Not sure how long it took me to figure out how mine became defective, but the blame was fully mine.:)
Gotta say, trying to solve an unsolveable puzzle sure kept me busy. It may have gotten my frustration tolerance up high enough that I can stand to debug those really nasty programs....
Maybe somebody subjected you to one of my favorite old tricks. Take one corner off of a solved cube and rotate it so that the colors don't match the rest of the cube. Reassemble in this orientation. Presto: unsolveable cube.
Way back in the mists of time I tried that on my school's Rubik's wizard. I took three pieces and rotated them. Gave it to the wizard and waited. Five minutes later he returned the almost complete cube, pointing out the _one_ piece he was unable to get right as it had been rotated.
The best way to solve a given cube is called "God's algorithm" to us Rubik's geeks (I can average about 50 s. solving a cube, which is ok, but not phenomenal). It's 18 moves [www2.vo.lu]. The method behind it is far too complicated for a person to do without a computer to assist, but using a rather simple method [olympus.net], a person can very easily solve a cube in around 65 moves, but slowly. The record-breaking solution times are closer to a hundred moves, but rather than remembering a move-efficient but thought-intensive way to solve it, one remembers many more algos that whose situation can be recognized much more quickly.
And for the previous posts asking how long it takes a computer to do it... it's very, very low. Under a second. Many people can do it, manually (a computer just has to give the moves, it can ignore the time required to actually turn the cube) in under 20 seconds [speedcubing.com] (For the people out there in disbelief, Dan Knights has a video of him actually doing it in 17, it's for real. I won't post the link, because I'm not going to be responsible for slashdotting his site).
There's a huge difference between a computer solving it "brute force", and a person or computer solving it through established algorithms. By brute force, just twirling the cube until the solution popped up, it would take on average however long it takes your computer to process half of the possible combinations. That's quite a long time. However, a computer solving a cube how we would, focusing on time rather than least amount of moves, could easily solve more than one a second.
Neat game. It's been around a while. I've been able to solve 7 random twists. The first thing you have to do is start with a ordered cube and see what happens when you twist it different ways. Not consistently, though. The trick is to figure out what the last move probably was, reverse it, the one before it, reverse that, and so on. After 3 random twists, you might be able to make a bad guess and recover from it. After 7, one wrong turn is a good reason for starting over. Never was able to solve a r
Just a word of warning to the foolish and brave. Before you tackle the 4^4 hypercube, make sure you buy an ergonomic mouse and mousepad. My guess is you'll probably develop super-carpal tunnel syndrome before you even you match one side of the damn cube. Also be sure to stockpile a few extra mouses, there's no knowing how many of them you'll be throwing against the wall.
What do you mean extra mouses? I may just go see the page and.... oops, there goes my mouse, trowing itself against the wall. And I though quake 3 arena was bad for it....
For those spared this atrocity, it was a Saturday morning cartoon featuring, I kid you not, a living Rubik's Cube. It was an idea that filled me with loathing even at that age, and I can't tell you what it was about because I always switched to something else as soon as it came on.
The 1980s certainly seemed the nadir of American animation...
Yes, I remember (I try to blot out the memory but it keeps COMING BACK!!) But I still think the MC. Hammer cartoon was worse. Anyone remember Mr. T's show?
Information on the "Rubik, The Amazing Cube" television show
Premiered on ABC: September 10, 1983-September 1, 1984.
The series ran for 1 year, and had a total of 12 episodes. It was originally broadcast as "The Pac-Man/Rubik, The Amazing Cube Hour" on Saturday mornings in colour with each Rubik segment lasting 22 minutes.
The Plot --------
Rubik is discovered by a young boy (Carlos) who brings the colourful cube to life - after he aligns all the cube's sides - an sets out on a magical adventure tour along with h
I suspect that this could be solved in a reasonable amount of time with a heuristic search algorith, such as ACO or a genetic algorithm using the number of matches as a heuristic.
Obviously, brute force, even at a massively parallel execution, is completely out of the question.
My problem with this is that it rotates so fast, that I can't figure out what the effect of a rotation is supposed to be. The speed also makes learning by observing it solving itself useless... just some flashes and 0.25 seconds later it's done. Any way to slow it down?
Puzzled by the cube? Try renting two (relatively low-budget, unknown) sci-fi flicks.
- Cube [imdb.com]: Buncha people, trapped in a buncha cubes, with a buncha deadly traps.
- Cube 2: Hypercube [imdb.com]: Buncha people, trapped in a hypercube, with less deadly traps but more confusion as to wtf is going on.
Both movies are fairly puzzling in their own right, with that sort of "unknown" sci-fi ending that is commonly found in lower-budgeted movies (e.g. Pi).
Douglas Hofstadter wrote a couple of excellent columns on Rubik's cube and variations on the theme for his Metamagical Themas column in Scientific American back in the eighties (you can buy his collected columns in this book [amazon.com]). In particular, he talks about the various ways you can modify the basic 3x3x3 cube concept - for example, 4x4x4 cubes, 3x3x3 tetrahedra, alternate colour schemes, and so on (along the way, investigating the spark of inspiration that encourages people to try out different variations on a theme - something he refers to elsewhere in his books as 'conceptual slippage' - this hypercube would be a 'slip' along a different axis to those hofstadter explores - I'm sure he'd appreciate it:) ). He goes into plenty of detail about the mathematical approaches you can use to solving the cube, and some intriguing analogues to subatomic physics that crop up in the maths of rubik... anybody wanting an introduction to the kinds of topics the people behind this hypercube are exploring could do worse than to read those articles.
There's also some excellent stuff in that book on Lisp, quantum mechanics, chaos theory, Alan Turing, and nuclear war... great selection of articles by an extremely interesting mind.
That would be like having regular 3D rubik's cube and not be able to turn the white face.
Not quite. It's like having a physical 3D rubik's cube and not being able to see all 6 faces at the same time. You can however turn a physical cube around so you can see the hidden face. It's a similar idea in this one. The way to see the hidden "face" is given in the FAQ:
Q: I can turn a real cube around so that I can see the hidden faces, can I do something similar to see the invisible eighth "face"? A: Yes. If yo
Great. (Score:5, Funny)
Re:Great. (Score:5, Funny)
Parent
Is this actualy 4D ? (Score:5, Interesting)
Maybe it's because I read some quack's claim that the 4th dimension was time. In which case a 4D rubics cube would solve itself over time or be onsolvable because it rescrambled while you were trying to solve.
Parent
Re:Is this actualy 4D ? (Score:5, Informative)
The 4th dimension is whatever you define it as. There's no "true" 4th dimension. Einstein had the idea that time could be treated in a fashion similar to that of the spatial dimensions, and so, in his work, he defined the 4th dimension as the temporal dimension.
However, for this program's purposes, it's assumed that we're talking about the 4th *spatial* dimension. You can (kinda) visualize it if you think of the progression of first 3 dimensions: a line (1st d) can be rotated 90 degrees to itself to form a square (2nd d) which can be rotated 90 degrees to itself to form a cube (3rd d). The 4th dimension is thus hypothesized as the space defined by a cube rotated 90 degrees to itself.
(Granted, I'm no mathematician, so if someone has a better understanding, please correct me.)
Parent
Re:Is this actualy 4D ? (Score:5, Informative)
This puzzle uses the first model mentioned above, except that you can only see seven cubes at once (the outer cube is hidden so that it won't block the view of the others). If you rotate the model (with Shift-left or Shift-right click), the outer cube comes into view.
Parent
Nope... (Score:3, Informative)
A real hypercube looks like a hypercube, not a cube with lines or anything else... of course you need to be five-dimensional to perceive the whole thing at once.
In general you need N+1 dimensions to perceive an N-dimensional object; for example, we can only fully perceive two dimensional objects all at once. Three dimensional objects we only see a particular side of, an
Re:Is this actualy 4D ? (Score:3, Interesting)
Example, take a room, it has 3 standard dimensions, now lets add another dimension, lets say temperature. Now we have a 4d object, we could even try and make a function to model temperature based on postion, temp = f(x,y,z);
You can even do neat things like make 3d objects out of 4d objects by taking a level surface of the 4d object. In simpler terms, take all of the points in the room that are one temperature, that will form a 3d o
Re:Is this actualy 4D ? (Score:5, Interesting)
http://dogfeathers.com/java/hyprcube.html
It's really tough to wrap your head around another spatial dimension. Books like Flatland and Realware make the comparison to a 2D person's world being interrupted by one of us.
For example, if you were 2D, living on your flat plane, and a 3D person passed an orange through the plane, you would perceive it as a round shape which grew out of nothingness, got bigger and changed shape for awhile, then shrank and disappeared.
A 3D person could also see into your house, because a 2D person would just build four walls and no ceiling or floor. Similarly, a 4D creature could see through all of us and our buildings, because we only build in three dimensions.
Parent
nooo (Score:5, Funny)
Re:nooo (Score:5, Funny)
I'm sure this 4D version will be just as easy...
Although I'm not sure how I'll peel off the colored stickers and rearrange them with this software version.
Hmmm
Parent
Re:nooo (Score:3, Informative)
Bah, as long as one minute? You are slow.
Check out this site [speedcubing.com], especially the multimedia section. There are videos of guys that solve the cube in less than 20 seconds!
Re:nooo (Score:5, Interesting)
Jason
ProfQuotes [profquotes.com]
Parent
Not interested... (Score:4, Funny)
Re:Not interested... (Score:5, Funny)
Parent
Re:Not interested... (Score:3, Funny)
Technique number one (Score:5, Funny)
Um, though that may be a little hard with the program, I'll admit.
Maybe if I apply the screwdriver to the ~~++5#Q%NO CARRIER
Re:Technique number one (Score:2)
Apply a screwdriver to it; reassemble in the proper order.
My favorite "solving" technique was a lot simpler... peel off the stickers and arrange them into the solution.
neurostarRe:Technique number one (Score:3, Funny)
Re:Technique number one (Score:5, Funny)
That's a violation of your End-User License Agreement and the DMCA.
Please lie face down on the ground, with your legs and arms apart. BSA agents will be arriving shortly to take you into custody.
Schwab
Parent
damn it.... (Score:5, Interesting)
Re:damn it.... (Score:5, Informative)
He made a software/hardware 3D rubics cube solver using LEGO mindstorms, a quickcam, and VB.
Parent
Re:damn it.... (Score:3, Informative)
Re:damn it.... (Score:5, Informative)
Maybe somebody subjected you to one of my favorite old tricks. Take one corner off of a solved cube and rotate it so that the colors don't match the rest of the cube. Reassemble in this orientation. Presto: unsolveable cube.
Parent
Re:damn it.... (Score:5, Funny)
Kinda funny -- I've inadvertently subjected myself to this same trick as a child. It always took so long to scramble the thing, it was easier to take it apart and put it back together in random order. Little did I realize there was a very good chance of creating an unsolvable cube.
Furthermore, I went so far as to buy a "how to solve the rubik's cube" book. Followed every goddamn step in that thing, and was pissed when it wasn't working. Eventually I tried it on my sibling's and it worked, and I came to the conclusion that mine was defective. Not sure how long it took me to figure out how mine became defective, but the blame was fully mine.
Gotta say, trying to solve an unsolveable puzzle sure kept me busy. It may have gotten my frustration tolerance up high enough that I can stand to debug those really nasty programs....
Parent
Re:damn it.... (Score:3, Funny)
Way back in the mists of time I tried that on my school's Rubik's wizard. I took three pieces and rotated them. Gave it to the wizard and waited. Five minutes later he returned the almost complete cube, pointing out the _one_ piece he was unable to get right as it had been rotated.
You were close... (Score:5, Informative)
And for the previous posts asking how long it takes a computer to do it... it's very, very low. Under a second. Many people can do it, manually (a computer just has to give the moves, it can ignore the time required to actually turn the cube) in under 20 seconds [speedcubing.com] (For the people out there in disbelief, Dan Knights has a video of him actually doing it in 17, it's for real. I won't post the link, because I'm not going to be responsible for slashdotting his site).
There's a huge difference between a computer solving it "brute force", and a person or computer solving it through established algorithms. By brute force, just twirling the cube until the solution popped up, it would take on average however long it takes your computer to process half of the possible combinations. That's quite a long time. However, a computer solving a cube how we would, focusing on time rather than least amount of moves, could easily solve more than one a second.
Parent
thats an easy one (Score:5, Funny)
duh...just peel off the stickers.
Re:thats an easy one (Score:3, Funny)
Umm (Score:2, Funny)
*Four* dimensional Rubiks Cube? (Score:5, Funny)
What, you have to step into the future to solve it? :-D
Re:*Four* dimensional Rubiks Cube? (Score:2)
I solved the 4th Dimentional Cube! (Score:2)
That's what you get when you mess with the timeline!
Tried it a while back. (Score:2, Interesting)
Is it me (Score:2)
Be pepared... (Score:5, Funny)
Re:Be pepared... (Score:2)
Anyone remember "Cubey"? (Score:4, Interesting)
The 1980s certainly seemed the nadir of American animation...
Re:Anyone remember "Cubey"? (Score:2)
Not "Cubey", (Score:3, Informative)
Premiered on ABC: September 10, 1983-September 1, 1984.
The series ran for 1 year, and had a total of 12 episodes. It was
originally broadcast as "The Pac-Man/Rubik, The Amazing Cube Hour"
on Saturday mornings in colour with each Rubik segment lasting
22 minutes.
The Plot
--------
Rubik is discovered by a young boy (Carlos) who brings the colourful cube
to life - after he aligns all the cube's sides - an sets out on a magical
adventure tour along with h
heuristic search (Score:2)
Obviously, brute force, even at a massively parallel execution, is completely out of the question.
When I was a kid (Score:5, Funny)
Now I just get drunk and masturbate a lot.
Already done it. (Score:2)
Most efficient solution (Score:5, Funny)
2) Click SOLVE
Two clicks... anyone do better?
Re:Most efficient solution (Score:5, Funny)
3) PROFIT?
Parent
Rotates too fast (Score:3, Insightful)
Movie References (Score:5, Informative)
1-D Rubik's Cube! (Score:5, Funny)
The interface is simple: just look at it. Quantum mechnaics dictates that observing it changes it's state so just assume it's solved.
Here is a magnified version:
If you still have trouble with it, my book will be coming out pretty soon.
Hofstadter's the best source for rubik weirdness (Score:5, Informative)
There's also some excellent stuff in that book on Lisp, quantum mechanics, chaos theory, Alan Turing, and nuclear war... great selection of articles by an extremely interesting mind.
Re:Lego Solution (Score:5, Funny)
It's LEGO, not LEGO's, not Lego's, not lego's, not lEGO's, not leGO's, not legO's, not lego'S, not LeGo's, not lEgO'S.
It's not LEGOS, legos, LEGOS'.. ITS LEGO
"I have one LEGO, I have two LEGO, I have many LEGO. I enjoy playing with LEGO"
1 LEGO = LEGO
2 LEGO = STILL LEGO
No farking S!!
Ok I feel better now.
Parent
Re:Not complete (Score:3, Informative)
Not quite. It's like having a physical 3D rubik's cube and not being able to see all 6 faces at the same time. You can however turn a physical cube around so you can see the hidden face. It's a similar idea in this one. The way to see the hidden "face" is given in the FAQ:
Q: I can turn a real cube around so that I can see the hidden faces, can
I do something similar to see the invisible eighth "face"?
A: Yes. If yo