Reading

[Keiji]

I just realized that for tetronians, reading would be difficult because there would be infinite possible directions one could read in. For us, we can only read in the left or right direction since there is only one arbitrary dimension in 3D (arbitrary meaning not the axis of gravity and not the camera normal). However, in 4D, there are two arbitrary dimensions, meaning tetronians would have to learn to read in ANY possible direction out of that plane.

Any thoughts on this?

[Nick]

You forgot up and down. I don't see why it would be so difficult. They would probably have a set pattern. For example, they might read along the z-axis until the the end, then move across to the next z-line on the right until the end, then move onto the next y-line underneath till the end of the page.

In other words, the same way we read, except instead of a single character occupying each x-y coordinate, it would a line of words extending down the z-axis.

[Keiji]

You forgot up and down.

No - that's the axis of gravity, so it makes sense that no matter how something is oriented, we always read it from top to bottom. Similarly, it makes sense that to read something, it has to be facing us, eliminating the axis of the camera normal. This leaves one dimension, which we've decided to read from left to right, and other cultures have decided to read from right to left. In 4D, you could read it in an infinite different number of angles, as there is a whole plane which is arbitrary like this.

[Nick]

When I said up and down, I meant Japanese-style. You could also read from bottom right to top left, or any other direction. I would hope that 4D creatures would be smart enough to make a system in which way to read, such as we did.

And why would 4D beings read in any direction other than straight along one of the axis'? You're not reading this sentence at a 45 degree angle. It doesn't matter if they have a lot of degrees to read at; we have 360, but we only use 1.

[bo198214]

The problem you mention, Keiji, would be the same problem, that astronouts would have to read a document. There is no gravitation, and so they have a whole plane as choice for reading direction?

I anyway dont know why you always make such a problem out of orientation in 4D (especially Wendy).

The gravitational direction as help for orientation is anyway merely by chance in our universe.
So by the same randomness a 4d world would have simply two (sensable) fields for orientation. For example one gravitational and one magnetic field.
And all the so problematic clock problems, which Wendy likes to report, vanish.

[Keiji]

The problem you mention, Keiji, would be the same problem, that astronouts would have to read a document. There is no gravitation, and so they have a whole plane as choice for reading direction?

No, because we usually live on Earth which does have gravity, so we get used to how our own vertical axis is different to the others.

[bo198214]

No, because we usually live on Earth which does have gravity, so we get used to how our own vertical axis is different to the others.

Then I dont understand your question. I see it that way:

We can put a coordinate system on each body by some predominant directed organs. For the human body this would be the eyes and the feets. The feets corresponding to the direction of gravity.

Similarly we can assume a third predominant directed organ in the body of the tetronian. For example there is a magnetic field or a proton stream in the world of the tetronian. And the tetronian always directs his body in such a way that this organ is aligned with this second field.

As long as we order these organs in a certain way for example eye->foot->second field organ (where foot is the first field (gravity) organ) and assume that the directions of these organs are linearly independent, we can set up a unique orthogonal system on the tetronians body. We would name the axes respectively:
1. backward-forward, 2. up-down, 3. wint-zant, 4. left-right
Where left-right is the remaining direction that is perpendicular to all the previous ones (where we define by convention what direction the left side is on this axis).

In the same way as we read 1. left-right, 2. up-down (, 3. backward-forward), A tetronian would read 1. left-right, 2. wint-zant, 3. up-down (, 4. backward-forward). Of course the book has to be aligned properly before reading, but usually one can easily endow the book with a corresponding coordinate system (at least by orientation of some asymetric letters). Backward-forward is anyway a special role because we/tetronians can not see what is behind a (hyper-)page.

Of course now you can ask, what if there is no such second field in the tetronians world? But than I reply back: what if there is no such first field (gravity) in the trionians world? The problem is similar.
We simply put a coordinate system onto the (assymetric) body (and onto asymetric letters) by the directions of some prominent organs (and by the direction of some unique features of a letter).

Of course there is some convention needed to what these unique features are. But given that, we merely need a convention of the order of these features. For reading of course backward-forward shall be the last direction if we want to avoid turning pages to much.
But for the ordering of the other directions there are even in the human world different conventions:
Chinese: 1. up-down, 2. left-right
Hebrew: 1. right-left, 2. up-down
Western: 1. left-right, 2. up-down
Dont know whether other of the 8 possible systems are/were in use.
Interestingly in Agyption culture it was possible to write the hieroglyphs from left to right as well from right to left, if you accordingly mirrored the signs.

[d.m.falk]

Of the written languages in use today, the most common direction of writing is left-to-right, top-to-bottom. Secondary is right-to-left, top-to-bottom (arabic, hebrew, maldivian/dhivehi). Then there is top-to-bottom, right-to-left (chinese, japanese, korean).... Then we get into top-to-bottom, left-to-right (mongolian, manchu, xine), and lastly left-to-right, bottom-to-up (Batak scripts of Indonesia), though these are now going to left-to-right, top-to-bottom. The ancient Filipino scripts- and this may still be true today, with those that still survive in use- were written bottom-to-top, left-to-right.

I don't buy the argument that gravity has anything to do with writing orientation, but out of convenience.

Further, who is to say Tetronians must have objects in 4 dimensions, or 3 as a maneuvering plane- I would think a two-dimensional piece of paper would be just as applicable in 4D as it would in 3D- it follows concervation of energy in the laws of thurmodynamice.

To me, applying "gravity" and "magnetics" to understanding the workings of spatial dimensions just doesn't work.

d.m.f.

[bo198214]

Wow, thanks for these informations.

Further, who is to say Tetronians must have objects in 4 dimensions, or 3 as a maneuvering plane- I would think a two-dimensional piece of paper would be just as applicable in 4D as it would in 3D

But why not use the full potential to write in so many dimensions as you can see at once.
A knot cord in 3d would probably also be enough for communication (perhaps in a Morse style) but who wants restrict oneself to 1 dimension, if you can see two at once. If I have to solve difficult mathematical problems I want to use as much possibilities as are there for visualization/presentation and not restrict my self to a knot cord!

So 2dimensional paper would something for the dumb tetronians.

- it follows concervation of energy in the laws of thurmodynamice.

Neither do I know what you mean, nor what it has to do with the dimensionality of canvas/paper for tetronians.

To me, applying "gravity" and "magnetics" to understanding the workings of spatial dimensions just doesn't work.

Its not to understand the workings of spatial dimensions, but for understanding the practicalities in a tetronians life. The fields I gave are anyway merely meant to introduce some asymetries in the trionian/tetronian's body (i.e. organs at the surface) to make it possible to attach a coordinate system to the body.

For example if we were rotation symmetric with the eye at the end of the axis of symmetry then in space there were no possibility to speak of left and right and up and down. We merely could denote the direction forward and backward, because we could not attach an individual coordinate system in unique way to our body. This would also be impossible if our species had so diverse bodies that we could not identify certain reference points which are to be found on *every* body.

If however there is an additional field or reference point/direction outside our bodies (which we will call *for convenience* gravity) and we were still rotation symmetric then we could establish an individual up/down as being the direction that is perpendicular to our viewing direction and lies in the plane of viewing direction and gravity (this works of course only if we not exactly looking into the direction of gravity) and having established those both individual directions we can also define left/right as being perpendicular to both.

For example we could say to someone "Roll to your left!" and he would know whereto to roll, unless he would stand on his eye or the opposite end of his eye.

[papernuke]

Wait but arent their eyes able to preceive in 4d? so wouldnt they be able to see the book as being "normal" to read like us?