4d paper & letters

[Keiji]

( administrator's note: this thread was split off from http://tetraspace.alkaline.org/forum/viewtopic.php?t=16 )

I was wondering if anyone knew of a term for the generalization one dimension up from row & column. The first dimension is a single row with multiple columns, each column with only one element. The second dimension adds multiple rows. What is a single row/column matrix as a unit? I was thinking that maybe the term "aisle" would work, using the analogy of theater seating. Then, when you extend rows and columns into the third dimension, you get multiple aisles.

If you look at Excel, you'll instantly come up with "Sheet". This also has a practical origin, as if you take a piece of paper, you can draw a table of 10 rows and 10 columns on it. If you photocopy that 10 times, you now have 10 sheets, each with 10 rows, each with 10 columns.

In 4d, they could draw "sheet tables" of 3 dimensions on swocks.

[alkaline]

using the term "sheet" does sound like a good suggestion. The problem with it is that it is also the name for a 3d piece of paper (which is obviously where you got the term). The terms 'row' and 'column' refer to lines of data, while 'sheet' refers to the object this data is on. The problem is that the term sheet could occur in the same context as rows and columns and thus cause confusion: "Look at the value in row 2, column 3 of sheet 5." This could either be a grid of data on a single swock, or multiple grids on different sheets of paper. I could see tetronians using both swocks and sheets. Compare to: "Look at the value in row 2, column 3 of aisle 5." This could only mean a grid on a single swock.

[Keiji]

Tetronians can't use sheets of paper. If they could, it would be infinitely thin, so a breeze would disintegrate it completely.

Just like we can't use lines to write on, 4d people can't use planes to write on, so they wouldn't need the term "sheet" to refer to anything but the 3rd index. (Indexes being column, row, sheet.)

[alkaline]

Well, i was thinking something analogous to a ticker in the third dimension. For stock market reports they used to use this long piece of paper that was only one printed line tall and printed out the stock prices one after the other. So, in the fourth dimension you could have a ticker, a sheet, and a swock. All of these would be the same thickness as our paper, just 4d thickness.

4d ticker = paper thickness * character height * character width * line of text length

4d sheet = paper thickness * character height * line of text height * line of text length

4d swock = paper thickness * line of text width * line of text height * line of text length

thus, a 4d sheet would be something different from a 3d sheet, but they would hold the same amount of data, just line a 3d ticker holds the same amount of data as a 2d "page" would. Maybe we should call 2d pages "tickers".

[Keiji]

Well, I see your point, but why would a 4d person want to write on a sheet?

Same reason that we write on sheets rather than "tickers".

[alkaline]

well, when you go from tickers to sheets, you expand the amount of data by quite a lot. A sheet is enough to hold a reasonable amount of data. A swock can hold much more data, and for a number of applications it would hold too much data.

Let's look at a random 3d book - it has 40 lines of text, and 12 words on each line. That is 480 words on a page, vs 12 lines for just a line of text on a ticker. Let's say a 4d swock is as "thick" as it is tall, so it would have 40 "aisles" of text. That's the equivalent of a 40 page book to us. That is more than a "unit" or "group" of data - that is several chapters worth.

Thus, i can easily see why tetronians (working term) would use sheets - if they just wanted to jot something down, take some notes, print out a grid of data, they wouldn't have to waste an entire swock. If they used a single swock for writing down every note to themselves during a course of a month, maybe they could fill it up. That wouldn't leave much flexibility for throwing notes away, because you'd waste so much of the swock.

i guess through this particular instance of an "object type" through the 2nd to 4th dimensions, we can see that you can't perfectly generalize upwards - variables don't expand at the same rate (here, the variables amount of data vs space to hold it).

[Keiji]

What would you rather carry about with you: a series of strips of paper (tickers) stapled at one end, or a pocket notebook?

What would a 4d person rather carry about with them: a series of sheets of paper, or a pocket swock?

It's hard to write on tickers, because they're so small. So by analogy, it would be hard for a 4d person to write on sheets because they're "small".

[alkaline]

i was thinking about the "small" aspect of sheets. They would probably end up having swocks that were small measurements on each side compared to the size of our sheets, like a third or half of the length & width. This would make it a little less "stretched" of an object, compared to a sheet. Also, stacking sheets might be a problem because they would easily fall over, but swocks wouldn't have that problem.

As far as a series of tickers stapled together, that would be very inconvenient for us to manipulate because there's so little you can store on each ticker. But, sheets aren't quite as inconvenient, because you can store more on a sheet than on a ticker. It doesn't seem quite as "silly". Thus, i can still see the use of sheets by themselves for post-its or something of that sort.

[Aale de Winkel]

note we trionians can write on a line, we however don't easily read morse code, so we prefer using 2 dimensional writing.
I do think tetronians might enjoy the 2 dimensional aspects of their 3 dimensional pictures.
I have no idea whether they would view 2 dimensional writing as we do morse code, it might well be a matter of taste.

So one could go either way, tetronians enjoy 2 dimensional aspects, enabling them also 2 dimensional writing,
or not in which case the n-onians use only n-1 dimensional writing.

Personally as a trionian, I might enjoy pe a multicolored line, and might view a statue-park as some sculpters writing. This way I've access to
writing in 1, 2 and 3-dimensional letters. Understanding it is quite another matter, I can't read chinese either though it is 2 dimensional writing.

[alkaline]

note we trionians can write on a line, we however don't easily read morse code, so we prefer using 2 dimensional writing.
I do think tetronians might enjoy the 2 dimensional aspects of their 3 dimensional pictures.
I have no idea whether they would view 2 dimensional writing as we do morse code, it might well be a matter of taste.

Well i personally believe it would have to do with separability of characters at quick sight. It is hard to tell apart the letters of morse code when we look at it quickly, but we can tell our latin letters apart pretty easily (with a couple exceptions) because if the relative distinctness between characters. I think that tetronians could use planar characters just fine, but they might find realmic characters to be even more distinctive and thus more effective in reading quickly without the problem of ambiguity between messy letters. In fact, if their characters were distinctive enough (which would be easier in tetraspace), it's possible they would never have a problem with messy characters.

[alkaline]

Personally as a trionian, I might enjoy pe a multicolored line, and might view a statue-park as some sculpters writing. This way I've access to
writing in 1, 2 and 3-dimensional letters. Understanding it is quite another matter, I can't read chinese either though it is 2 dimensional writing.

what does "pe" mean? you used it elsewhere and i just thought it was a typo, but you used it here again.

I'm not sure what you mean when you talk about a statue park. Is there some real-world statue that you are talking about? Or are you talking about an n-dimensional park viewed in a n+1 or n-1 dimension?

As trionians we wouldn't be able to "write" 3-dimensional letters with a pen on a piece of paper.

[Aale de Winkel]

pe stand for "par example" which means just somewhat else the ie "id est"
pe examplifies, while ie identifies.

A statue parc is erected by some dutch collectors near the city Arnhem (if I'm not mistaken).
Of course a trionian sculptur needs far more then just a pen, he simply has no acces to a tetronian pen.
But still a statue on its own tells knowledgeable people a complete story which might easily be seen as some books paragraph.
Statues put together the would make some chapter, while the whole parc forms a book.
So in our trionian world sculpters with great effort create the statues, while the keeper of the parc, creates the book from those statues.
according to his own insight or feeling or whatever.

Those three president, sculpted in that mounted, is also a sample of a statue-parc, containing three chapters in the usa history!
Mme Toussauds (and other Wax-museums) are samples of "statue-parcs".

[alkaline]

well statue parks seems to be a matter of art, while writing with a pen is a practical issue for everyone - it is the drawing with a pen that i was interested in. So yes, you could use 3d sculptures to "tell a story", but it is not it the language that you speak, it is in a more abstract form of communication. The problem with calling a statue park a story is that no two observers would get the same story from seeing the same statues - a matter of personal interpretation.

Are you talking about Mt. Rushmore? There are four heads there - George Washington, Thomas Jefferson, Theodore Roosevelt and Abraham Lincoln.

[Aale de Winkel]

you seem to be catching on but the dime has not fallen yet,
like a telegrapher is trained to distinguish seperate letters of morse-code.
someone who made a study of the poet life reads that poets poem quite
differently then someone with no knowledge of the (wo-)man
just as (as you said) statueparcs are interpreted in different ways

I can easily imagine a "startrek replicator" reduced to such a size that it
is a hand-held pen, dropping figures of the size of a travel chess board
allowing someone to write in 3-dimensional droppings
(of course this technology is not available yet, and startrek people enter
their three dimensional novels on the holo-deck)

Mt. Rushmore is probably seen by some history buf in quite a different
manner then some tourist.

[alkaline]

i'm not debating the fact that you can get across meaning through the use of art. I'm talking about concrete representation of spoken words using a written form. The use of creating 3d figures for "writing" is a pictographic method (verses a phonological method). it is a less efficient method, both for people learning to write and those learning to read, because there are so many more characters to learn. Us trionic beings don't need any more than 2d letters because we can make enough letters to represent all of the sounds we make - trying to use 3d letters just because we theoretically can seems like a fruitless effort.