gonegahgah wrote:[...]Step 28. Immersing our 3Der in a 4D image via direct brain stimulation:
This shows how 3Der hooked up to a box that is receiving multiple pictures from a great number of rooms.
Hmm. I'm not sure I understand why we would need so many rooms. I thought it should be sufficient to use something like Patrick Stein's nD ray-tracer and deliver slices of the 3D projection volume into whatever is stimulating the brain cells?
[...]The biggest problem with this is that there is no feedback to help the 3Der grow and interact with their environment such as hands.
Yeah, that would be the second big stumbling block once we figure out how to deliver 3D data to the brain directly. Clearly, contemporary 3D VR motion sensors will be inadequate, since they can only capture 3D motion of our 3D limbs. Perhaps this can somewhat be mitigated by designing a set of controls manipulable by our 3D hands that control a virtual 4D arm (or arms) that manipulate the virtual 4D environment -- then it'd be a matter of learning how to operate a "4D robot" that serves as our surrogate body in the 4D world.
[...] Although this would allow us to see inside the cubes that form the faces of the tesseract across the rooms; this approach would fail to allow us to see the compound faces of the end cubes; which a 4Der can. The 4Der can see 4 of the cube-'faces/volumes' at once of a tesseract (like we can 3 of the square faces at once of a cube).
I think if our hypothesis is correct, and the brain is able to rationalize a set of 3D nerve impulses into coherent 3D image, then we shouldn't have a problem with this at all. The 4D simulator will deliver the 3D array of pixels including lighting and shade, parallax, and what-not, and, assuming our brain is able to make any sense of this data, we should be able to perceive the cube's volume directly, judge its angle with the light source(s) based on the 3D shading within it, and infer the square boundaries where it touches the other cells in the tesseract.
[...] I think we need an extra eye and we need to place it in a series of parallel rooms that are looking at the cube from a different aspect. I'll have to think some more about that though...
I'm not sure if that relates to the debate on the need for three eyes yet - though I had already been pondering about where the 4Der's third eye would lay if they had three eyes. [...]
On my way home today, I thought a bit more about the whole number-of-eyes issue. I've come to the conclusion that only two eyes are needed for stereoscopic vision in any dimension. Except for some exceptional cases which are unlikely to occur (or aren't very important) in real-life, it doesn't really matter which direction the binocular disparity happens in. I believe that any correspondence between the number of eyes and the dimension of space only depends on the advantage conferred by the widening of one's lateral peripheral vision.
First, let's talk about stereopsis. Since we have two eyes, what each eye sees isn't exactly the same as the other; the difference is called binocular disparity. Our brain instinctively tries to reconcile these two different images by inventing a 3rd dimension, by means of which the difference between the two images can be rationalized. This produces a 3D model out of the 2D images that we see.
Now, our eyes are spread out horizontally, so the disparity in the two images lie in the horizontal direction. For example, if we were looking at a vertical pole in front of us, its position relative to the background will appear shifted differently when seen from each eye; when our brain tries to reconcile this disparity, it constructs a 3D model where the pole "protrudes" from the background; i.e., we see 3D depth. What about a horizontal line? If the line is infinite (or at least, extends beyond our field of vision), and completely featureless, then there will be no binocular disparity, and we wouldn't be able to tell if it was part of the background, or something in front. If our eyes were laid out vertically instead, then we would see the vertical disparity of the line, and we'd be able to tell where it is in relation to the background. So here we see a difference between horizontal binocular vision (i.e., "normal" vision) and vertical binocular vision (if our eyes were laid out one on top of the other).
However, such cases are contrived; your average general object isn't a featureless infinite line or any featureless infinite construct that is vertically or horizontally homogenous. Our world is filled with all manner of shapes, most of which are irregular; even smooth objects like very long tree trunks or pipes aren't completely homogenous; they usually have enough features that binocular disparity will still happen. In other words, if your two eyes were lined up vertically on your face instead of horizontally, you'd still be able to perceive depth without any problems.
Where would this make a difference, though? It makes a difference when we consider peripheral vision. If your eyes were lined up vertically, you'd have a wider range of vision vertically; you'd be able to detect peripheral movements above or below your field of vision. Since we're mostly confined to the ground by gravity, though, this expanded vertical range of vision is largely useless: it's usually just the floor or ground below you, and a largely empty sky above. The interesting things lie mainly on the across dimension, to use wendy's terminology. Having two eyes horizontally laid out expands our horizontal range of vision -- very useful because that's where most of the interesting things are. The fact that two eyes also give binocular vision is a happy coincidence.
In 4D, the same applies: having just two eyes is good enough to have binocular disparity -- save for exceptional, contrived cases which aren't really that important in real-life situations. However, having 3 or 4 eyes laid out in a planar fashion will enhance lateral peripheral vision -- remember that, as gonegahgah repeatedly pointed out, in 4D there aren't just left and right, but a whole 360° of sideways. Having only 2 eyes will limit peripheral vision to mainly two opposite directions; having 3 or more eyes will have a better coverage of the 360° of periphery.
So I think one can get by with just 2 eyes in 4D, though for better peripheral vision, 3 or 4 would be more advantageous.