The Biological Basis of 3 Spacial Dimensions

[NanoByte]

All you theoreticians fool around with any number of "dimensions", but humans normally perceive in exactly 3 orthogonal spatial dimensions. Given this constraint on spatial perception, a human tearing apart a human head finds 3 orthogonal semicircular canals in the inner ear, neural signals from which are processed in the brain somewhere where data from the senses are also coordinated. Is not our three-dimensional spatial perception due to this particular trio, which of course is then perceived as aligned in 3 mutually perpendicular dimensions? If not, to what is it due?

Now, take a Flatlander or a Hyperhuman. . .? And what's in various lower animals' heads? And is this a scientific or a philosophical question? Is it a rational question? Oh, yes, and you bionic types with a programmatical number of dimensions. . .?

OK, unless I get rewired, I probably wouldn't understand your answers anyhow.

Ray

[C K Dexter Haven]

Sorry, friend, but you only see a two dimensional picture of what you're looking at. You can't see around corners or behind objects. The two dimensional image that your eyes report to your brain has excellent perspective, so that you have "depth perception", but that's not the same thing as seeing three dimensions.

[NanoByte]

I didn't say that humans saw in 3 dimensions; I said they perceived in 3 dimensions. That is, they model their worlds in 3 dimensions (in their normal reality, apart from any mathematical extentions drummed up in ivory towers), whatever senses are involved in any particular case of perception.

My rather ill-formed question tries to wonder over the reason the magic number, 3, comes up; but I don't quite figure this is really a question within objective science.

Ray

[C K Dexter Haven]

Fair enough, Nano, you did say "perceive" and I read too fast. Sorry.

On the "objective" bit, there are a number of mathematical theorems that are easily proved in dimensions above 3, but are false for dimensions 3, 2, and 1. So 3, in terms of dimensions, does have some objective "magic" about it.

[Nickrz]

I see everything twice!

[cornflakes]

Ok, stand in the middle of a flat desert. Move in one direction. Now, stop moving in that direction and move in another direction that does not take you partly in the direction you were originally going. You are now moving at right angles to your original direction; if you were moving in, say, direction X, you are now moving in direction Y. If you jumped straight up, you would be moving in still another direction, which could be called direction Z.

You could also express any motion in terms of two axes of rotation and the distance from a reference (30 degrees west, 25 degrees up and 3 miles out), but we tend to travel in straight lines more than we go round in circles (unless you work with radar.)

[matt_mcl]

Wait a minute. Ordinary humans *do* see in three dimensions; that their eyes move in concert permits them to perceive depth by parallax, and not just length and height. However, my eyes were damaged in surgery when I was a child, and so they don't move in concert. I see a slight double image all the time, and I can't perceive depth at all well, except for cognitively (I know it's a big sofa far from me and not a little sofa close to me).

[JoeyBlades]

NanoByte writes:


a human tearing apart a human head...


Such imagery...


...finds 3 orthogonal semicircular canals in the inner ear...


Part of the vestibular system used for balance.


Is not our three-dimensional spatial perception due to this particular trio, which of course is then perceived as aligned in 3 mutually perpendicular dimensions?


I think it's the other way around. Since we move about in 3-space, the vestibular
system evolved to detect relative changes in our orientation within 3-space.



If not, to what is it due?


I think the easy answer is the best. We perceive 3 spacial dimensions because that's all there is. Think about the ways that we can perceive things in three space. We use our eyes to assemble images and using tricks of perspective and visual cues, our brains assemble a 3D model of what we're looking at. However, vision is not the only mechanism that we use to perceive in 3D. Certainly touch is a 3 dimensional perception mechanism and under the right conditions, the auditory senses perceive in 3D.


matt_mcl wrote:


Wait a minute. Ordinary humans *do* see in three dimensions;


Sorry friend, that's merely illusion. Binocular vision gives you a sense of depth perception, but that is merely one of a batch of two dimensional inference tricks that our brain uses to construct three dimensional models. Have you ever seen one of those old stereographs? They are generally made of wood and have a binocular-like viewer. The user puts in cards with two pictures on them. Each picture is taken from a slightly different vantage point. Each eye sees a different two dimensional image, but the human brain merges these images and perceives a three dimensioanlity... Another, similar example, are autostereograms (AKA "Magic Eye", AKA "Hollusions"). Clearly the actual image is two dimensional, yet when viewed properly, the brain perceives three dimensions.

Think of it this way, if you really saw in three dimensions, you would be able to see the backside of objects at the same time you look at their fronts.

[NanoByte]

CK, matt & Joey, as to 3D vision:

Whether we "see" in 3 dimensions is a side issue not really impacting what I was striving for, but I'll comment on that here first:

'See' is not a technical term in objective science and is clearly (NPI) a subjective concept. I don't see (NPI again) why one should limit one's use of this word, in referring to sensing visual information in order to build one's internal model of a portion of external physical reality considered to be in 3-dimensional space, in such a way as to exclude visual-axial displacement information -- however determined, although most especially from stereopsis achieved through two transversely displaced 2D-image detectors (eyes). You should be lord of all you (can) survey. The verb 'to see' is clearly normally used as a subjective correlate to the objective coordinate functioning of both eyes, both optic nerves, the visual cortex and part of the cingulate gyrus, I believe. In any case, you don't normally claim seeing is only what goes on in one eye at a time. Would you deny me the right to say that a certain blue car and red car are straight in front of me, and that I can see that the blue one is approximately twice as far away from me as the red one?

You claim that one only sees in 3 dimensions if one can see on the hidden side of an opaque object. It seems to me, that if you say that, you'd also have to say that one does not have full hearing capacity if one can't hear what's said behind a soundproof door. If you block a part of your signal (either sound or light waves), yes you don't "hear" or "see" some particular feature of what may be the target, but you still "look"/"see" or "listen"/"hear", in general, in full capacity only as limited by details of the given scenario.

Do you see what I mean in all n dimensions? ;) (Actually, at present, I no longer have any stereopsis, due to almost no sight (absolutely no central vision) in one eye, as a result of glaucoma; but I still "see" in 3D -- though not as well (as the owner of a certain parked vehicle early on unfortunately became aware of).)

CK:

So 3, in terms of dimensions, does have some objective "magic" about it.

Hmm. If it does, how come so many people embue that number with so much mysticism (F, S & HG, e.g.)?

Nickrz:

I see everything twice!

Once in the IN basket and once in the circular file?

cornflakes:

. . .we tend to travel in straight lines more than we go round in circles. . .

Speak for thyself! How do I get off this merry-go-round? ;)

Joey:

quoting me:

"Is not our three-dimensional spatial perception due to this particular trio, which of course is then perceived as aligned in 3 mutually perpendicular dimensions?"

I think it's the other way around. Since we move about in 3-space, the vestibular system evolved to detect relative changes in our orientation within 3-space.

Well, I guess, from an engineering standpoint, in making a general-purpose gismo designed to move in a well-controlled manner in 3 dimensions, you'd stick 3 gyros, in mutually perpendicular orietations, into the thing. Then, if you put a quite complex processor in that entity and stick on a few types of sensors and effectors, I guess a human would figure the job was done properly, considering all these components to be interwired in an effective manner.

What I was trying to get at, I guess, was really a sort of complex notion of a mix of neurobiology and metaphysics. I mean, philosophically, you can start dualistically either from "out there" having 3 (or however many) dimensions and assume conformity occurs to that, as implied above -- or from "in here" having n dimensions (viewed objectively as n-dimensional neural nets), which is also applicable to a mode of programming the above processor. This latter case does not make necessary an assumption that "reality" is inherently 3-dimensional -- wherein, in such above implementation, the processor could be allowed to have the capability of modifying the gyro system to any configuration optimal for some given environment in which its ingenuity might find itself. Perhaps, in communicating with such an entity, you would find that, if it were smart enough to symbolically communicate with you in refined abstract terms, it would shun, in a conversation with you, any consideration of its physical environment's being discussed in terms of 3 dimensions, preferring some other number of dimensions, integral or fractal.

Without getting involved in such as the above artifact, one might look at the question in evolutionary and developmental neurobiological terms as follows: You have species of organisms evolving, and individuals of all of them developing, neurologically and otherwise, around such peripheral components as vestibular systems, in the case of mobile organsms, and around other sensory organs -- with a gradually more centralized brain containing various sorts of neural-net configurations designed to coordinate these organs in a manner which would allow these individuals and species to survive in various changing environments. Then, depending on how such vestibular or similar organs, along with other sensory organs, interactively evolve with their coordinating brain cortices, might not such organs as the vestibular one come up with other than 3 reference bases, or might not the intercontrolling neural nets set the key number of reference bases within themselves? And then, should any of these species evolve to the point of feeling a silly need to write on blackboards, whiteboads, monitor screens or Etch-a-Sketches -- mightn't they preferably postulate, on the first order, solid geometries not so compatible with Euler's rules -- to the extent, even, of dimensionalities of other than 3?

Well, that's all garbled pretty messily, but maybe you get the idea.

Ray (Holy Mother, Daughter and Favored Witch -- except when traversing wormholes)

[metroshane]

the human head weights 8 lbs!

------------------
We live in an age that reads to much to be wise, and thinks too much to be beautiful--Oscar Wilde

[tracer]

It almost sounds like the OP is saying: "Maybe the universe has 4 or 5 (or more) space dimensions in it, but since our biology limits us to perceiving only 3 dimensions, those are the only ones we're aware of."

If that's true, all that's needed is the right mutations and we'll be able to see inside each others' stomachs.

[capybara]

Ok, this may sound stupid, but Hell...
Am I remembering a bt of horse puckey from elementary school which says that the fourth dimension is "time"? If this is considered so, then we do experience the fourth one, then. Just not all at once, of course. Maybe the operative word should be "experiencing" dimensions instead of "sensing"?

[NanoByte]

M. K.:

Or maybe you could say that we do experience the other three. . .but just not all at one place. ;)

-----

Well, tracer's sort of on the right track.

But look at it more abstractly: Whether something is a "space" dimension, "time" dimension, or some other kind of dimension, is really determined by the facts of how it correlates to neural activity that closely interacts with whichever of your plug-N-play I/O peripherals, or otherwise with far-out ideaware downloaded from physicists and mathematicians playing upon your notion of a "dimension". Maybe that more-massive interconnection found in Einstein's brain between [I forget which two brain parts] on one side permitted him to experience a less-intellectualized, more-intuitive "experiencing" of hyperdimensionality that combines space and time dimensions and maybe even some of those other six that mathematical reality-weavers think should be packed in with the first four. My head really isn't very intuitively facile with those things, but I understand the forces are tooling up these days to shove new genetically engineered neurons into our old Alzheimer's-wracked thought organs, so maybe I can get a supercharged refill.

Ray (Only space-time will tell.)

[matt_mcl]

Think of it this way, if you really saw in three dimensions, you would be able to see the backside of objects at the same time you look at their fronts.

What? Why?

I look at the sofa across from me in the computer room. I can see that it is tall and that it is long. I'm told an ordinary human can see that it's deep, too. Voilà, three dimensions, no cubist bullshit. What are you talking about with this seeing behind things stuff?

[NanoByte]

So he's a simultaneous front-door/back-door sort of voyeur, I guess is what Joey says.

Ray

[DSYoungEsq]

Funny. I perceive in four dimensions, though after 39 years of one of them, I wish that perception would slow down. ;)

[JoeyBlades]

matt_mcl,

You asked:


What are you talking about with this seeing behind things stuff?


Think of it this way. Let's say you're standing in your computer room. In front of you, you see your sofa. You see that it is a three dimensional object right? Now close your eyes... while they are closed, I'm going to slip on a pair of special glasses that have two high resolution pictures of your sofa, each taken from a slightly different vantage point. Now open your eyes. Can you tell the difference? If I've done a good job in my photo reproduction and as long as there are no other visible cues (like photograph edges) you can't tell the difference between the two. Of course, if you were to move your head around or walk around the room, you could tell the difference, but now you're simply panning in three space and your brain is interpolating a 3D model. For you to actually see in three dimensions, your vision has to exist three dimensionally, and you would necessarily be able to see objects from all sides simultaneously.

Cubist bullshit, indeed...

[DougC]

the human head weights 8 lbs! - Metroshane
- - - So it needs to be deep fried for twenty-four minutes until it's done.
-
-
- - - I once asked the question "If we had three eyes could we see in four dimensions?" - I saw a darn interesting article about dimensions/human perceptions once a long time ago. In it, some researcher was asked placed a four-dimensional object in our hand, what would it look like, and if we'd recognize it as such. He said no, because we as humans (and as many animals are) are stuck with the perception that works best for where we exist. He noted that jellyfish have a simpler, more accurate perception of space because they are symmetrical about an axis. They have eyes all the way around their edge and so don't have a "left" and "right" side, and have no use for the concept of "sidedness". If you asked them "where something was" they'd have an entirely different way of describing its location than what you would consider obvious, but theirs would be more precise. The way they would describe any object they see (if they could do so) would be more accurate because it would be more dependent on the object rather than any preconceived expectation of what it should look like. - MC

[NanoByte]

DSYoungEsq:

But does anyone directly perceive in 4 spacial dimensions? I think you would have to have really mutant original wetware, as well as having suckled on a Klein bottle or something.

Joey:

Your argument just plain doesn't make any sense. Do you know of anyone else, preferably someone of scientific or philosophical authority, who argues this position of yours, which apparently claims that only simultaneous VRML is 3-dimensional sight? The fact that our 3D vision can be deluded certainly does not make it have less dimensional capability. An atmospheric mirage is, per se, 2-dimensional. It deludes one's vision. Then do you say, "People don't have even 2-dimensional vision, just 1-dimensional."? If I play a sound clip of a cat, and someone looks for a real cat, does that mean (s)he can't hear? Three-dimensional per-/conception needn't even relate to light receptors. Consider the congenitally blind and deaf, who no doubt first model in 3 dimensions only with their proprioceptive senses (as also probably everyone does in the womb). Would you also say they don't exhibit 3-dimensional perception unless they feel around to the far side of something, opposite to them? Neo-cubist?

MC:

So it needs to be deep fried for twenty-four minutes until it's done.

Perhaps mine is overdone. . .but wouldn't that make my ideas more solid?

If we had three eyes could we see in
four dimensions?

I'm not so sure that the number of dimensions we can per-/conceive in bears any relationship to our sense of sight. I'm not up on evolutionary biology, but I believe vertebrates evolved the eye anew, ignoring what those simpler critters came up with in the way of sight. So maybe some vertebrates got around in 3 dimensions, i.e., that which they actually thought of in 3 dimensions, prior to inventing their eyes. Of course, if you're blind, you still recognize things in terms of 3 dimensions. One can also assume this for those born blind and for moles, blind fish and whatever, right? Clearly, the use of other senses -- hearing/audiolocation, proprioceptive sensing and sonar (bats, cetaceans) -- develops a neural model that assigns 3-dimensionality to space.

As to jellyfish:

If you asked them "where something was" they'd have an entirely different way of describing its location than what you would consider obvious, but theirs would be more precise.

So, you're now claiming I'm beneath a jellyfish?! ;) I guess I just wonder a little about you people who think you can talk to jellyfish.

The way they would describe any object they see (if they could do so) would be more accurate because it would be more dependent on the object rather than any preconceived expectation of what it should look like.

You know, there's absolutely no way I can buy that. First off, they're bound to have been born with a rudimentary instinctual model of how their prey is distributed in space, to such extent as is necessary to catch some. Probably they have a little learning capacity also, which would build on such a kernel. But the end result would still remain extremely crude in some ways our visual systems would be more sophisticated in, although perhaps more precise in a limited number of ways that suits their needs for catching such prey. Also, there are all kinds of jellyfish. I don't know much of anything about jellyfish, but I suspect some detect their prey, and maybe other things, more by ion/electric sensation or tactile sensation of water movement than by vision.

Admitting no empirical knowledge of the limited nervous systems of jellyfish having circular arrays of many eyes about a (capital-caudal axis?), I suppose, if their maw (whatever you call it) is also symmetrical about this axis, and they have no preferential side for relating to any protective or resting surface, they would indeed have no need for an angular reference point on this circle; but they would need to know the eye-plane off-axis distance to any pertinent object, the object's orientation about its axis of symmetry relative to something of itself -- if not a reference point on the circle, perhaps the axis-transverse vector of its present direction of movement, and some measure of the angle of the object forward from this plane up to its axis of symmetry and aft somewhat towards same.

I think scientists have studied the nervous systems of some jellyfish almost in their entirety, because I think they have only some tens of thousands of neurons, but I don't actually know what someone with such knowledge would say in respect to their actual neural modeling of space.

Myself:

You appear to have screwed up on at least one thing, though it's not germane to the central issue of your OP:

In my artifactual example -- "3 gyros"? As some sort of orientation sensors, roughly equivalent to the semicircular canals of the animal vestibular system, to be used in 3-dimensional space, I was first going to say "3 accelerometers". I now think that would've been closer, and maybe 3 sensors on one gyro would even have been better, though I wonder, on a system designed to be quick moving. So what is a rough equivalent to the vestibular system? Three accelerometers, two level detectors and a damped plumb bob? The human animal normally lives in and has evolved in, not just a space with 3 dimensions, but one also with a gravitational field having both a magnitude and a direction.

Ray (Hey, I was an EE, not one of those MEs I insult now and then. ;) )

[JoeyBlades]

Nanobyte,

You wrote:


Would you also say they don't exhibit 3-dimensional perception unless they feel around to the far side of something, opposite to them?


Whoa, Nellie! I never said we don't perceive in three dimensions, only that we don't see in three dimensions. There are very different concepts.


Do you know of anyone else, preferably someone of scientific or philosophical authority, who argues this position of yours...


No, but then I haven't been looking... For the record, I haven't heard anyone (reputable) claim the opposite either. however I stand by my original statement. I'll see if I can dig up someone of a higher authority or a better proof for you.

[JoeyBlades]

Oops! That should have read "They are very different concepts" or "These are very different concepts". Doh!

[DougC]

- - - The example wasn't supposed to create the illusion that jellyfish have eyes that can see the way ours do, or that they have enough marbles to chat with you about it. The point was that we are stuck with much of our perception because of the vision/brain setup that we have. We have two eyes placed side by side, and so much of our perception is based on dividing everything into "two sides". Certain jellyfish (man 'o wars are one, I thinks) are round with eyespots all around; therefore they have no use of the terms "left" and "right".
- - - The reason their method of description is more precise is this: use, for example, any object whose location is known to you. Now imagine if you stood someone else next to you, and tried to give them directions on how to find it without using the terms "left" or "right", or even "up" or "down" - (two terms based on gravitational influence). You will have to orient them entirely with other objects along the entire distance; hence, you will have given them a more accurate set of instructions than if you could say "turn left at this point" or "turn right at that point".
- - - He also noted that a "better" method of spacial orienting would be four different directions radiating away from each other at equal angles (as a tetrahedron) because our triple axis method is incorrect; it requires negative measures of spacial distance that can't exist in reality. The tetrahedron method has (at least) one distance as zero but never requires negative numbers to describe where any point lies. The problem is, it isn't instinctive; a problem he chalked up to our built-in perceptive methods. - MC.

[JoeyBlades]

OK, after extensive searching (minutes) I've turned up nearly zilch. Not to be daunted... I'll try to make my point clear through a few developments and examples.

First, a philosophical test. Not a proof, per se, but food for thought. Let's say that you do have a kind of vision that allows you to see around objects and potentially see them simultaneously from the front and the back... what would you call this kind of vision? Certainly not 4 dimensional vision...

By the way, computer imaging jargon for the interpretation of 3D information from 2D images is 2.5D. The image modeling uses a technique known as shape-from-x where x is one or more of the visual cues such as shading, texture, countour, focus, stereo, motion, and other photometric and geometric inverse approaches...


OK, let's talk about what it means to see in three dimensions. I'll start by establishing a framework for my discussion. Let's say that the first dimension is X and this is the left-to-right dimension. The second dimension is Y and is the top-to-bottom dimension. Finally, the third dimension is Z and is the depth dimension (i.e. near or far).

Now, when I look at a scenario with one eye, the image is captured in two dimensions (X and Y). This image itself has no Z component, though through some of the visual cues mentioned above I can infer some 3D characteristics. If I open the second eye, I get a second 2D image. From this I can gather a few more visual cues, but I still have no actual Z component in my vision.

So what does it mean to add a Z component to our vision? I can visualize this in at least two ways... One I call the three degrees of freedom method and one I call the Z slice method... Hey, I'm making this up on the fly. As I said, I couldn't find anything about this kind of stuff anywhere.

The three degrees of freedom method is a pixelated approach. If I break my 2D image down to it's smallest X and Y components resolvable by the vision system, then in a 3D image, I have to account for the Z position of any pixel in the 3D image. Imagine that each pixel is resolved by three line segments. One that traverses the X dimension, one that traverses the Y dimension, and one that traverses the Z dimension. The intersection of these three line segments defines a 3D pixel. Just as a 2D image is the composite assemblage of pixels in 2 dimensions, a 3D image is the assemblage of pixels in 3 dimensions. Since pixels on the back sides of objects are within the legitimate 3-space, they would necessarily be visible. Another way to think of this is that the complexity of a 2D image is a square function X*Y and the complexity of a 3D image is a cube function X*Y*Z.

The Z slice method may sound somewhat familiar. It's similar to CAT or MRI scan imaging techniques already in use today in modern medicine. The composite three dimensional image is constructed by merging information from multiple 2D planes at ever increasing depths in the Z direction. Just as computers can reassemble these images into a 3 dimensional model, so too would a 3D vision system. The only difference being that a 3D vision system should be doing this in real-time, where scanning imaging systems today must use a time slice methodology.

Constraints? Same as any 2D system. Pixels will be black if no photons are being reflected. Aspect ratios are not infinite for real world systems (i.e. we can't see infinitely in the X and Y dimensions). Some correlary to peripheral vision could constrain a 3D vision system.

Of course, all of this is mostly hypothetical, since aside from scanning CAT, MRI, and X-Ray systems, I'm not aware of anything that even comes close to this in the real world, but hopefully I've made my point. True 3D vision must allow the viewing of all points on a three dimensional model simultaneously (within the constraints listed above - though there could be others).

[tracer]

BTW, it's "spatial", not "spacial".


-- tracer, who has never watched the Spacial Olympics.

[JoeyBlades]

tracer writes:


BTW, it's "spatial", not "spacial".


Ummm... actually, it's both. Either are accepted forms. Look it up.