Talk:Tesseract/Archive 1

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Text from 2001

Am I correct that the 4th demension is not time? If so, it should be pointed out (as mathematical demension does not have a meaning for me yet), as I assumed it was before I looked at the web site. - Eean

Try looking up time. This article is not an in-depth mathematical explanation of a 4D object. It's a simple definition. Maybe you could read dimension. ~BF

There is no such thing as the 'mathematical 4th dimension'. Dimensions don't exist by themselves; dimensions are attributes possessed by spaces, and it makes no sense to talk about a 'mathematical 4th dimension' without reference to which space it is a dimension of. In this case, it doesn't matter how many dimensions the space has, so long as it has at least four. And "translating a cube" won't give you a hypercube -- IIRC, translation is merely a change of position.

Talking about a "mathematical 4th dimension" is redudant and confusing -- there is no other sense of dimension that could apply in this context than the mathematical one. And the set definition given for a tesseract might give the mistaken conclusion that all tesseracts have that definition, when only one particular tesseract does. -- SJK

It would be cool if someone added some information on what is called "Latin hypercubes". I won't, because I don't understand the subject, but I find them utterly fascinating. They appear to have uses in solving optimization problems and maybe something to do with nonparametric statistics. {{n8chz

TARDIS question

The TARDIS in the science fiction series Doctor Who has properties analogous to the hypercube, being appreciably larger on the "inside" than it is on the "outside".

I've just cut this from the article, since it doesn't make sense to me. I can't think of any sense in which a hypercube is larger on the "inside" than it is on the "outside". -- Oliver P. 15:58 Mar 22, 2003 (UTC)

Could have been supposed to be a reference to how you could fold up a 3D elephant and put it in a tesseract, if you don't mind the elephant being bent, in the same way you can put a large piece of paper in a small box. But phrased like it is, it of course doesn't make any sense... كسيپ Cyp 16:17 Mar 22, 2003 (UTC)

Aha! That's an amusing idea. I'll have to write a paragraph on methods of crumpling up elephants and putting them inside tesseracts in the elephant article... ;) -- Oliver P. 22:44 Mar 22, 2003 (UTC)

In fact, you don't necessarily have to fold the elephant. Consider a line and a square. In a square with side 1m you can fit (without bending) a line with length sqrt(2)m. A one-dimensional owner of the square could put the line in it, and provided that the square was positioned so that its projection onto the owner's dimension was of length 1, the owner would think of sqrt(2)-meter line as being inside a 1-meter long container. Of course, all objects are "larger on the inside than on the outside" for people from lower dimensions, since the "outside" of such an object is an infinitely small portion of it. A person capable of using a tesseract as a container should have no problems with placing the tesseract in such way that only a very small corner of it sticks out into 3D. Think "tip of the iceberg". -- Lament

Heavy

Shit! This thing is insane. I never learned about this in university. Why not? I learned about fuckin matrices and shitty negative number graphs. But 4D cubes? Wow!That is the only thing apart from pi that is interesting in maths. If only u could put it onto a 2D screen tho--Thewayforward 18:29, 17 Feb 2005 (UTC)

No cursing please. Thanks. Oh, and you can, it looks like an octagon with the star inside of it. -Scythe33

Don't know where it is, but there is a website where you can see and manipulate a hypercube (not a real one obviously - just an image on a screen.) its pretty cool, comes with a demonstration of how it is formed, starting from the point and adding dimensions, allowing manipulation of the current object (line, square, cube) at any point. I'll see if I can find it. Vimescarrot 22:27, 6 January 2006 (UTC)

No cursing?! --Imitationleather 19:59, 25 February 2006 (UTC)

Glory Road

I took the reference in Glory Road to be to the Banach-Tarski paradox. How would it work with a 4-dim object? I don't see it (the protagonist reports being able to follow each unfolding individually. --Trovatore 02:18, 22 July 2005 (UTC)

Time??

Isn't the 4th Dimension time? What does this shape have to do with progressing in time? Although I understand why they would try to consider it a a 4D figure, doesn't it have to be liked somewhat to time? Zachorious 08:39, 17 November 2005 (UTC)

The 4th dimension doesn't have to be time. One can easily imagine a 4-dimensional universe with time as the 5th dimension. The tesseract lives in this (imaginary) 4-dimensional world. Mathematically speaking, it lives in 4-dimensional Euclidean space rather than 4-dimensional Minkowski space. -- Fropuff 15:19, 17 November 2005 (UTC)

Hypercube definition in computing

The definition we were given in computer science lectures allowed for a hypercube to be extruded outwards from 1 dimension, 2 dimensions, 3 dimensions and so on up to N dimensions. The examples here all appear to assume a maximum of 4 dimensions?

Mathematicians (as opposed to computer scientists like you and me) refer to 3-D cubes, 4-D tesseracts or hypercubes, 5-D hyperhypercubes, etc. CS people just call them all hypercubes and put a number on them to indicate the dimension. We could definitely use a section in this article explaining the difference in terminology. DenisMoskowitz 20:40, 29 November 2005 (UTC)

Etymology

Any idea where the word "tesseract" comes from? -- wr mar-8-2006

Apparently it's tesseres aktines = 'four rays' in Ionic Greek. —Tamfang 17:59, 8 March 2006 (UTC)

The Myriad Tesseract

Please read very slowly and carefully:

I'm sure you were all introduced in early childhood that 10 ones equal a ten, 10 tens equal a hundred, and 10 hundreds equal a thousand, with symbols of a 1 unit, a 10 line/stick, a 100 square, and a 1000 cube. Any Internet site showing the next term, namely, a myriad tesseract (made of 10 thousand cubes) in Java?? 66.245.73.39 01:54, 6 Dec 2004 (UTC)

I haven't seen anything along these lines, but holy crap that would rock. Hard. The major problem I see is that it's hard enough to visualise a hypercube in 2-D with only lines and shading, imagine how hard it would be to see if you had that many more shapes in it!! aubrey 07:11, 15 March 2006 (UTC)

Glory Road / Doctor Who Dates

James Gifford reports that that Glory Road was created as early as April 1962 (http://www.nitrosyncretic.com/rah/ftp/nhol.pdf), and it was certainly with his publishers by May 1963 (http://www.lib.utexas.edu/taro/tamucush/00232/tamu-00232.html). We also know that Glory Road was published in serial form starting in July 1963 - this would probably have been on the news-stands in June 1963, so creators of Doctor Who could have read it while creating/writing the show (work started in March 1963, first aired November 1963, according to Wikipedia). With this in mind, I've deleted the suggestion that Heinlein might have taken the idea from Doctor Who; if anything, the reverse is more likely, particularly as Heinlein has been quoted elsewhere as being interested in the "fourth dimension" as early as his Annapolis days. Realistically, though, the idea was "in the air" at the time, so perhaps most likely is that the foldbox and the TARDIS were simply independent creations. RomanSpa 02:51, 14 March 2006 (UTC)

parallel*piped

The spelling of parallelepiped has cycled a couple of times. Etymology often helps: the second element is the noun epipedon (plane surface), from epi (on) + pedon (ground), according to the American Heritage Dictionary. —Tamfang 05:32, 13 April 2006 (UTC)

In searching the internet, some references seem to use the terms with different spellings interchangably, but others use both terms with specific and different technical meanings, are you sure this is just a spelling issue?--Technicaltechy 12:03, 13 April 2006 (UTC)

Well, if the -o- form is an independent word, I for one am curious to know its meaning and etymology. —Tamfang 07:12, 14 April 2006 (UTC)

I don't know if there are any good references, but answers.com makes a distinction. Don't know whether it is defensible or not. | parallelopiped| parallelopiped--Technicaltechy 15:01, 14 April 2006 (UTC)

Looks like two ways to say the same thing. By "prism" we usually mean "right prism" (one whose sides are rectangles), but a parallelepiped is indeed a (general) prism whose bases (and sides) are parallelograms. —Tamfang 18:33, 14 April 2006 (UTC)

Mish's question (folding the net)

The example given of a net of a tesseract must be impossible, how can you fold the net so that it is possible to create a tesseract? please explain :) —The preceding unsigned comment was added by 80.177.171.199 (talk • contribs) on 23:26, 13 June 2006.

The cube at the center stays in the samme place. You then fold the six stacks coming off each face of the central cubes until they're pointing at 90 degrees to the 3-plane the first cube is in. When this happens, their faces approach each other and join. Then, the cube at the end of the 2-cube stack is folded over again, to be parallel to the plane of the first cube, and its faces join with the un-joined faces of the other folded cubes.

It's exactly like folding an ordinary box from a cross-shape piece of paper, except that you have to wrap your mind around the idea of folding things at right angles to reality as we know it. I'll see if I can produce an animated .gif, as this would be handy to link from the net's caption. --Christopher Thomas 01:56, 14 June 2006 (UTC)

I've made an animation, and linked it from the caption of the net in the article. --Christopher Thomas 03:52, 14 June 2006 (UTC)

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