Mrs Whatsit Sez: It's a Tesseract

May 8, 2003 11:57 AM

A Hypercube is "One of the simplest four-dimensional structures that we can imagine...[Google cache]. It is the four-dimensional analogue of an ordinary cube."
It's confusing, but Drew's words and pictures here will probably wrap your head around the concept. If you're already a Math-Head, you may find this more interesting, and it leads us to this fun interactive tesseract. Or you can draw your own.
Want even more fun?: This Hypercube is just out on video (in the US; 3/03 in the UK), this tesseract has been around since '62, and this one is has just been released.
[Yes, tesseracts & h-cubes were previously discussed here & even waaay back here.]
posted by Shane (23 comments total)

Ho hum.... I was expecting another timecube. Now THERE'S some good science!
posted by Espoo2 at 12:01 PM on May 8, 2003

nah, actually this is pretty cool.
posted by Espoo2 at 12:02 PM on May 8, 2003

And you can Live In One . . .theoretically.
posted by blackfly at 12:07 PM on May 8, 2003

Nice title there shane! and [this is good], 'specially since my mind's still twisted from seeing this for the first time last night.
posted by WolfDaddy at 12:10 PM on May 8, 2003

I was expecting another timecube.
Damn! That's perfect! It should have been in my links!
"Cubeless education - is a deadly evil." LOL! Thanks, espoo!

More mind-bending fun:
Imagine a person who lives in 4 spatial dimensions, watching a hypercube rotate. The 4-dimensional person has a 3-dimensional retina in each of its 2 eyes (two eyes suffice for depth perception, even in 4D). Each retina records a 3-dimensional image.
posted by Shane at 12:10 PM on May 8, 2003

If I ever get my head wrapped around this stuff, it will probably be in much the same way that cars are wrapped around trees. I already have plenty of trouble with geometry in the first three dimensions...
posted by zztzed at 12:14 PM on May 8, 2003

There's an old anecdote about an ordinary guy talking to a mathematician.
Ordinary guy: "How can you possibly work with four-dimensional spaces? How could you imagine a four-dimensional object?"
Mathematician: "It's quite easy. I just imagine n-dimensional spaces for integer values of n, in general. Then, I set n=4."
posted by CrunchyFrog at 12:33 PM on May 8, 2003

If I ever get my head wrapped around this stuff, it will probably be in much the same way that cars are wrapped around trees.

For some reason, this makes me think of the Navidson Record in House of Leaves.
posted by kaibutsu at 12:36 PM on May 8, 2003

I think I.... almost... kinda...

Nope, sorry lost it. Over my head.
posted by canucklehead at 12:37 PM on May 8, 2003

Yeah, it's too bad Cube 2 was just a rehash of the original's plot line. Moving through time was a cool concept.
posted by graventy at 12:39 PM on May 8, 2003

This is great, thanks :).
(I've been interested in hypercubes ever since Carl Sagan mentioned them in Cosmos) ;) .
posted by plep at 12:40 PM on May 8, 2003

My eyes crossed and made this work for a second, but then adimensional shambler showed up and dragged me intointo that dark cyclopean space between worlds where the black goat nurses her thousand young and amorphous Azathoth writhes to the maddening tunes of invisible and accursed flutes. Kinda sucks but at least they have DSL.
posted by PinkStainlessTail at 12:43 PM on May 8, 2003

See also :- Flatland.
Imagine how a 2-d person could comprehend a 3-d world... then extrapolate...
posted by plep at 12:46 PM on May 8, 2003

I could understand it if it made any damn sense.

/disgruntled.
posted by goethean at 12:47 PM on May 8, 2003

...then a dimensional shambler showed up and dragged me into that dark cyclopean space between worlds where the black goat nurses her thousand young and amorphous Azathoth writhes to the maddening tunes of invisible and accursed flutes...

Some people have all the luck. Or drugs.
posted by Shane at 12:52 PM on May 8, 2003

I found the first cube film rather decent, the second one much less so (but it did have the saving grace of forever kniggit...)
posted by dorian at 1:07 PM on May 8, 2003

Slip Azathoth a twenty and she'll take off the breastplate of hissing snakes. Nothing you can do about the damn flutes, though -- the maitre d' claims "all the other customers love 'em."
posted by languagehat at 1:07 PM on May 8, 2003

It's things like this that make me think scientists are all in on some eleborate joke to make the rest of us look like fools for actually believing in all these theories.

Gravity, hah!
posted by lychee at 1:28 PM on May 8, 2003

Damn, blackfly beat me to it.

I love that story. Anyone ever try to film it yet? It would make a great Twilight Zone.
posted by pmurray63 at 2:46 PM on May 8, 2003

Higher dimensions are great to speculate about. As a kid, I was fascinated by the idea of other dimensions. How would higher-dimension creatures interact with us? What would we see?

If a hypersphere ( a 4-d sphere) passed through our world it would not be too unlike a 3-d sphere, a ball, passing through a sheet of paper. First, we would see a small point which would then grow and grow until it reached a maximum size and then shrink again and finally disappear. Thats the easiest case, but by studying "slices" of more complex geometric shapes you can get an idea of what more complicated intersections would look like.

I still have my old drawings of polytope cross-sections as well as unfoldings, that is higher-dimensional objects which have been cut and flattened, like a cardboard box.

The explanatory power of higher dimensions really made its appearance with Einsteins theories of our 3-d space as elements of a higher geometry. Unfortunately, Kaluza-Klein type theories (theories which represent forces as higher dimensions) have had limited success, despite being the forerunner of modern string theories.
posted by vacapinta at 3:45 PM on May 8, 2003

And, as an addendum, string theory/M theory postulates eleven dimensions. We can't see the unfamiliar ones because they're rolled up tightly -- go more than (IIRC) 10^-40 meters in any of them and you're back where you started; the universe is effectively 3 dimesnional, like a piece of paper is effectively 2 dimensional even though it has a thickness.
posted by Tlogmer at 5:15 PM on May 8, 2003

hypercubes bring back memories of my undergrad graph theory classes. easy way to impress a girl? "oh me? I'm just studying n-dimensional hypercubes"

(they're actually fairly simple)
(come to think of it, no girls were ever impressed)
posted by krunk at 5:31 PM on May 8, 2003

Damn, blackfly beat me to it.

Well, at least I can mention that I love that story.

Damn, pmurray63 beat me to it.

Well, at least I can put in a [this is g

Damn.

OK, then, I'm outa here.
posted by soyjoy at 7:31 PM on May 8, 2003