Instructables

Make a "real" tesseract - 4D cube.

Picture of Make a
4Dcube.jpg
This is easy, like making a real 3D cube out of anything.
I did it for the first time using popsicle sticks.
It was hard so I don't recommend using popsicle sticks,
maybe skewers and super balls.

I call this a real tesseract because although it's stuck in 3D space,
it has all it's edges of equal length, just like a real cube or a real square.

Often tesseracts are illustrated as a small cube inside a big one.
Not this one! And No, this is not an "impossible object" illusion!

Why did I Make this?
1.A sculpture and to see how hard it was.
2.Imagining the possibilities of making (the frame of) a
"flux conductor" or a "flux inductor" ...
maybe even a "flux capacitor".
3.Wondering what would happen if I made the items in "why #2".
4.It's about time I Make something new on here!

A flux conductor or inductor would perhaps be a wire that follows a
"hamiltonian circuit path" around the hypercube.
That means a wire that goes to each corner only once,
of a square object of any amount of dimensions.

Tesla had not much more than wire to use as electronic parts.
Who knows what an electric tesseract might do?

This model was inspired by the 2D drawing of a hypercube (tesseract).
A Cube is an object with 6 sides which are squares.
A Hypercube is an object with 8 sides which are cubes.
 
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Step 1: Make a cube

Picture of Make a cube
This should be easy, just make two squares and then add equally long
lines between them.

It's not so easy with ice cream sticks. I cut angles on the ends so they
were shaped like parallelograms (with a miter) hoping they would line
up perfectly at the corners. I did not do any math to see if 45 degrees
is the correct angle, and still now have not.

In "junkyard mode", I propped it up with cans barely successfully while
I glued it.

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aortlieb7 months ago
I recommend using K-NEX pieces, since they work really well.
Anakataract10 months ago
lbenedetti is correct. The reason the x y and z sides of a tesseract have uneven sides is because the tesseract we are familiar with is just a 3D shadow of the real thing. If you take a wirefram cube and shine a light on it the shadow is a square with a smaller square inside of it. Pop it up a dimension, and boom, you've got a tesseract.
lbenedetti3 years ago
The only problem that I have not read on here yet is the fact that his representation of the tesseract has equal sides. As Carl Sagan states when an object moves down a dimension it loses it's regular properties meaning that it is no longer made up of right angles and equal lines. Sagan shows this perfectly by taking a
3-D glass cube and showing it's reflection on a flat (2-D) surface. If you were to take the tesseract from the 4th dimension to the 3rd it would no longer have the 90 degree angles or the equidistant sides.

http://www.google.com/imgres?imgurl=http://www.daviddarling.info/images/tesseract.jpg&imgrefurl=http://www.daviddarling.info/encyclopedia/T/tesseract.html&usg=__sRSSsqg9gVUhaOvOxUVpRRa3094=&h=575&w=780&sz=21&hl=en&start=0&sig2=nnRKgkMmVVcDVUhhz5xvVA&zoom=1&tbnid=rg8cN7q13FrV1M:&tbnh=145&tbnw=196&ei=OVjSTejsD4-Bswa734GkCQ&prev=/search%3Fq%3Dtesseract%26um%3D1%26hl%3Den%26safe%3Doff%26sa%3DN%26biw%3D1120%26bih%3D602%26tbm%3Disch&um=1&itbs=1&iact=rc&dur=397&page=1&ndsp=15&ved=1t:429,r:0,s:0&tx=55&ty=57
ningo7 years ago
A more appropriate title might be "a projected tesseract"; this is no more a tesseract than two squares joined by lines in the plane, of length equal to the sides of said squares, is a cube.
VIRON (author)  ningo7 years ago
I agree mostly. But it's definitely 3-D and can be used as a model or frame for education and experiments. Since I haven't done them yet, I can't make any claims. It is reasonable to expect nothing unusual will happen.
mikesty VIRON7 years ago
It's definitely 3D, but you said it was real and 4D.

You can't create a non-3D object in a 3D universe.

(perhaps with the exception of a Nobius strip)
you can create a "2-d" object: a shadow is a 2 dimensional "object" in a 3-dimensional world.
Not really. Not enough coordinates means we won't be able to interact with it. Too many coordinates mean we just use the 3 standard coordinates.
With the fact that a 2 dimensional object casts a 1d shadow and a 3d object casts a 2d shadow, does that mean that a 4d object casts a 3d shadow?
If it did, I could see in the future all kinds of strange things being created as by-products of the fourth dimension, possibly even in a state of matter?
A shadow isn't an object. You see an object when light strikes it, bounces off and hits your eyes... basically. Where there is no light, since something is obstructed, it casts a shadow.
An "Object" is relative to the space in which it resides. In two-space, there is no light, since light is both a particle and a wave. Hence, a shadow can be considered an object. Also, if you don't like the shadow analogy, what about a projection?
Right, which is why my conjecture is that the number of dimensions an object has = the number of dimensions in the universe that possesses it.

What is two-space? You're losing me here.

The same applies for projection.
1-space = 1d 2-space = 2d 3 space = 3d etc. those terms are used in vector math, generally, when you expand theorems in the second dimension into the third, fourth, etc.

Since a shadow does not reflect light, it is most definitely not 3 dimensional. However, it IS an object. An example of an object that doesn't reflect light is glassware in a glass of oil. The Object DOES NOT reflect light; the light passes right through it.

Just because you can't see something doesn't mean that it isn't an object. IE Air, light doesn't bounce off of it much, but it's still an object.
You cant create a REAL 4-D or higher object in a 3-D world. I
you're right. However, the concept here is if we can express a 3D Object on a 2D surface, we can express a 4D object in a 3D Universe.
VIRON (author)  mikesty7 years ago
Just think about this: A hologram is a 3D or possibly 4D image on a flat plane. The 4th dimension is usually time on animated holograms, but imagine a ... hologram of ... a 4D mirror that reflects any light coming from a 4th space dimension toward you. What might you see? If there are no real 4D objects, a hologram of one must (and can) be synthesized or computer generated. If a flat hologram can hold a 3D image, a 3D hologram should be able to hold a 4D image. But that's in a short time ago and a galaxy not very far away. (bent star wars ref.) Also, fractals are real and have dimensions which are fractions. On second thought, most of them are full of "imaginary numbers"-sorry that's just a math joke. Snowflakes and rivulets and leaves are real fractals.
mikesty VIRON7 years ago
the 4th dimension is usually time? i don't know if it ever is :) is that hologram really flat though? and is the image really 3D?
Fine, 4 spatial dimensions! What this is, is taking a 2D drawing of a 3D object, and making it 3D. So now its a "drawing" of a 4D object in 3D.
Right. That's why it's a "projected" tesseract.
there are two other ways to represent a tesseract.

one is enclosed, which is basically a large cube with a smaller cube inside, with its corresponding vertexes joined together with lines (in this version, like the next, has 8 'rooms', one in the center, 6 represented by the warped cubes along the sides, the top and bottom, and the 8th one being the surrounding space around this figure, which is easier to understand in the second figure).

the other figure is inside-out (or unfolded), and looks like four cubes stacked on top of each other, with four more cubes connected along the sides of the second to the bottom cube on the stack (depending on how you unfold it). it looks like an upside down 3D crucifix (this figure also has 8 'rooms', but they're more ... corporeal ...in this shape.... the 'outside' room is now the room in the middle of the 4 protruding cubes, the 'center' cube from before is now the very top cube, the 'top' cube should now be at the bottom of the figure, and the 'bottom' cube should now be second from the top, right under the 'center' room. the 4 rooms around the sides of the enclosed figure should now be the ones protruding outward.)

this figure you've made does demonstrate all 8 rooms, but it's a bit more confusing visually.

the purpose of the 4th dimension of this shape is that it allows you to move from one 'room' to the other in a straight line and come back to where you started. it doesn't really have anything to do with time travel in the commonly used sense, but simply uses the 4th dimension as a way to fold across the 3rd to come back to where you started. unfortunately, since all walls are connected to the walls of the other cubes, once inside such a structure it would be impossible to exit. every exit in this 'crooked house' would lead to one of the other 7 rooms. an awesome short story by Robert A. Heinlein called "And He Built a Crooked House " explains how being inside this theoretical structure would work, though takes an artistic license with how they get out of it. you can read it here: http://www.scifi.com/scifiction/classics/classics_archive/heinlein/heinlein1.html

hope that helps anyone who doesn't understand what they're making with Popsicle sticks. :P
Correct me if I am wrong, but your second visualization of the tesseract ("upside down 3D crucifix) is actually the net of a tesseract. It's like how if you unfold a cube you get a crucifix divided into 6 squares. When you "unfold" a tesseract you get the 4 stacked cubes with 4 cubes surrounding the second to last level.
exactly.
AAAHHHHH I"M FREAKING OUT ... so there is more then one god??
Corey we're not talking about god or gods. Off topic or typo error?
if there is an alternate dimension?
time is just the perception of change
Yup :)
um 4D is a measure of time (example if i leave an ice cube out in -0 tempature will it stay? yes! but if i leave it out in 100 degrease tempature? no!
bubbaflamm6 years ago
It is definitely 4D. The fourth dimension is time, and as it exists for any measurable time it has a 4th dimension. The shape doesn't make it 4D, only makes the 4th dimension a bit easier to imagine.
Actually if it did have the dimension of time it can be anywhere at any time. For example: it could appear and disappear, and then 4 appear in different places. Also, time as a dimension isn't accepted by every scientist.
BUT, a tesseract has a different kind of dimension (another dimension of space, but it still has 4 dimensions). The 4th dimension of the tesseract is the "W-axis"... the directions are: left, right, up, down, forward, backward, ana, upsilon, wint, kata, delta, and zant.
Goto:
http://en.wikipedia.org/wiki/Fourth_dimension
hg341 mcdonn1234 years ago
a tesseract is the 5th dimension
The 4th dimension is just another direction to move in, its a spatial dimension.
I've often wondered if there would be any interesting weirdness resulting in a toroidal transformer wrapped with wire similarly to a Hopf fibration. Obviously, it wouldn't quite be the same thing since wire would cause the fibers to intersect, but I'm convinced there has to be some difference in efficiency or some odd property not present in your standard iron doughnut. Just a thought - maybe you've tried it. I might if I get bored enough one day.
for a great way to understand how to perceive another dimension watch "flat land" available @watchmovies.net
dizzyd6 years ago
First off Mikesty: It's a Mobius Strip, not a Nobius Strip. And they are only mathematically achievable. In real life the object must be created with something that at one point had two planar surfaces, making the 3D reality unattainable. Second off the Tesseract with a "cube inside of a cube" does not satisfy the needs of elementary geometry. A square by it's definition is a parallelogram and a rectangle. The definition of a rectangle is that all angles in the shape are 90 degrees and the definition of a parrellelogram is that all sides are parallel. Take a look at the 3-D renderings of the cube within a cube and tell me what you see wrong with this? No imagine a 4-D shape with nothing, but right angles and parallel sides and tell me your brain doesn't blow up. It's like posing the question of where the universe ends....if it ends what's next? If it is contiguous ie. a sphere, then where does that sphere reside? Your mind is incapable of grasping infinity and also of grasping a fourth dimension. Until you can learn to accept that fact, no knowledge can be gained.
iKill dizzyd6 years ago
you just blew my mind with the last few sentences... makes me wish i was on lsd or acid or any other hallucinogenic we could then have a 3 hour long conversation about how the world will end XD
dizzyd iKill6 years ago
Let me elaborate a little more for your psychedelic needs. Think about how the solar system is set up, and how the traditional atom is set up..... Positively charged center with negatively charged electrons orbiting the nucleus. Sun = Emits energy, Planets = absorb energy ie. positive, negative. Now consider my earlier comments about grasping infinity. Are you a Universe, your couch, your table, your computer, are these all universes? They are made up of atoms. This is highly unlikely, but I just wanted to trip you out again.
iKill dizzyd6 years ago
lol 10 hours to late i robotripped last night and that would have fun to read but this is the funniest paragraph ive ever read i hope you enjoy it... "You could end up walking out your room naked with a beanie on your head mumbleing about how cold it is while your eyes are the size of frizbiez and you begin to try to make yourself a bowl of corn flakes using tongs, oven mitts and a jug of pineapple juice while all that time your parents and staring at you in disbelief ready to call the rehab to get you off those evil drugs."
lawl
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