Fred should not see anything

[ben1787]

the idea of two dimensional space is that there is only that. two dimensions. Fred should not be able to see at all. He exists only in height and length but when he is described as seeing a line in front of him or a dot that should not theoretically be possible for the is no width in front of him. There is nothing for him to see!! Please answer soon. This really bothers me. This means that in the case of the tetrasphere or the tetranail through the safe, there should be nothing for a three dimensional bob to see either. Just like there is no 3rd dimension in 2d space, there is no fourth dimension to see in 3d space.

[jinydu]

Please reread the article more carefully. Fred can see cross-sections of 3D objects, which are of course 2-dimensional.

[Keiji]

Actually, the plane may lie directly through the gaps between the atoms in the 3D object, in which case Fred would see nothing. If however the plane lied inside the atoms, he would see the object.

[Hugh]

Jinydu, I don't think that 2d Fred sees 2d cross-sections of 3d objects - say for example a circle section of a sphere. He looks along his infinitely thin plane "edge on", which would be a 1d line, which cannot be seen.

iNVERTED, even if the plane lay inside the atoms, it would still only be a 1d slice of them to look at, which still, couldn't be seen.

[thigle]

analogously, [in for ex. steiner's book "fourth dimension,..."] the following is noted: (very free quote)

*1d being would see just within his space - within the line of 1d existence. in other words, only the endpoint of however long object(segment) within this 1d line-world is observed.
*in 2d, a planar being looking any direction within his plane, sees just the edge (1d) of whatever planar object obstructs his view within his 2d reality.
*in 3d a massive space-like being looking any direction, see just 2d pattern of optic flow within the FOV. the sense of depth is caused by integrated binocular vision, one-eyed people whose other eye sight was restored have to learn to understand & perceive depth sometimes as hardly as we 4th dimension.
*in 4d, we perceive 3d. we are thus at least 4-dimensional, just thinking about the eye-sense.

it is erroneous to think that because organ of sight is [apparently] 3d, the seer, the act of seeing is 3d too. for perception (not just visual) for sight of nD object, structure of the perceiver is surely n+1 dimensional. as brown says in Laws of form: "...to distinct is to contain already..."

[jinydu]

Well, the 1D line would be visible to Fred; although his brain would probably interpret it as a side of a 2D object. After all, when 3D beings look at a cube, they see only a plane (or planes), a 2D object.

[faranya]

Well, maybe there isn't anything he should be able to see, but does that really matter? It's used to help visuilize the concepts of the dimentions

[Hugh]

Well, maybe there isn't anything he should be able to see, but does that really matter? It's used to help visuilize the concepts of the dimentions

If a theoretical 2d being couldn't actually see anything because it looks at everything "edge on", this does make a difference in how we think we view the space around ourselves. A 1d line of vision, in my opinion, could not be seen, so even if this being found itself in 3d or 4d space, it still couldn't see anything around itself. It would actually see 2 less dimensions (0d) than what it was (2d).

We see with a 2d extending x/y plane of vision at any glance. All higher dimensions than the two we see, we look at "edge on" in any one glance. All possible higher spatial dimensional axes are perpendicular to our viewing plane, wherever we aim it. So wherever we would aim our plane of vision in higher than 3d space, we would only see what we would think is 3d space around us.

[pat]

If that's the case, then the fact the we can see anything means either that there is no fourth spatial dimension or that our eyes and everything in our universe has some extent in that spatial dimension.

The prior isn't very interesting for our purposes. And, the latter is pretty awkward.

[Hugh]

Hi Pat,

It might be awkward to think of us as having some extent of our bodies in a fourth spatial dimension, but if the universe is actually 4d, then we would be 4d too. Our vision of our body is only a 2d extending plane of it at any time, so we only see a 3d "slice" of it, or of someone else at any time. It's a limited view.

How would we see a 4d hypersphere in front of us? A 3d "slice" of it; a sphere. Same thing.

[pat]

The same way we'd see a spherinder in front of us.

The awkward comes in thinking we might be only a few microns thick in that dimension or that we might have a more varied shape in that dimension that we have no clue about. There's further awkwardness to think we have some extent in some dimension yet have no ability to turn any of our joints out of our hyperplane.

[Hugh]

Hi Pat,

The awkward comes in thinking we might be only a few microns thick in that dimension or that we might have a more varied shape in that dimension that we have no clue about.

I think that either is possible.

There's further awkwardness to think we have some extent in some dimension yet have no ability to turn any of our joints out of our hyperplane.

If we're only seeing a 3d slice of our bodies, we wouldn't see those tiny aspects of it turning out of our hyperplane. We would have to remember that we see only the surface of what we look at. What is turning or moving in the higher dimensions happens on the level of the smallest component of matter. We're only looking at a compilation of the 2d surface of each of those components that face our directional view at any time. Think of a 4d matrix turning around, but not as a whole, but each one of the tiny individual points within it turning around itself. Does that make sense?

[thigle]

hugh wrote:

If we're only seeing a 3d slice of our bodies, we wouldn't see those tiny aspects of it turning out of our hyperplane. We...see only the surface of what we look at. What is turning or moving in the higher dimensions happens on the level of the smallest component of matter. We're only looking at a compilation of the 2d surface of each of those components that face our directional view at any time. Think of a 4d matrix turning around, but not as a whole, but each one of the tiny individual points within it turning around itself. Does that make sense?

it does not only give sense, but it corresponds to my experience of 4-space as micro-compact. this roughly corresponds to some ideas in:
Spin-Mediated Consciousness Theory http://www.arxiv.org/abs/quant-ph/0208068
Spin-Mediated Consciousness Theory: An Approach Based On Pan-Protopsychism http://cogprints.org/2579/

the other question, dual to this approach, is: how do you see it globally ? i mean, one way to think it is the one you state. other would be global approach. what is the relation between these 2, compactified & global ?

quite coherent, although a bit lenghty, is this 'global' approach article on glome: http://users.adelphia.net/~44mrf/

[Hugh]

Hi thigle,

That last site you mention leads to Michael R. Feltz's pages on Hyperspheres, Hyperspace, and the Fourth Spatial Dimension. It used to be available at bright.net but it hasn't been there for some time. Thanks for finding it. There is a lot of information and possibilities there to look at.

I think the fourth spatial dimension is actually, very large. It's just our view of it is limited because we can only see the surface of things at any time. We can't see the dimensions of each individual tiny part of matter.

If we and the universe are 4d, not only what we're looking at but what we're looking with is 4d too. (That's where I think the VRI comes in.)

That spin-mediated consciousness theory is fascinating... the quantum mind, entanglement, etc.... it would sure be great to actually know how it all really works.

[thigle]

hi hugh. you state that: "

If we and the universe are 4d, not only what we're looking at but what we're looking with is 4d too.

according to tony smith: http://www.valdostamuseum.org/hamsmith/allspaces.html the spacetime of universe we're in is RP1xS3 and internal symmetry space is CP2, both being 'embedded' in octonionic structure.
but then, i don't understand tony's theory...
but, as much as i get it, i think that he says that there are TWO 4-dimensional complementarities (physical spacetime & exotic internal symmetry spaces) within the macro-space of many-worlds ('the pluriverse'). so the 'at-hand' (=potentialy experientiable) fields for objects/events of consciousness would be BOTH the (global?) 4-dimensionality of our spacetime AS WELL AS (micro?) 4-dimensionality of internal timespace.
so (as somehow stated by Kent Palmer in his 'Deep Math' article) the 8 dimensional milieu is composed of spacetime/timespace fusion ?

[Hugh]

Hi thigle,
Whoa, that's one link with a lot of other links to a lot of stuff!

but then, i don't understand tony's theory...

I must admit, most of it is beyond me too. I can understand a pluriverse - a macro-space of all possible worlds. Hearing about internal symmetry spaces makes me think about viewing different ones with VRI flips.

Spacetime/timespace fusion?

[thigle]

i think tony says somewhere that each point of our physical 4d spacetime is one whole internal symmetry 4-space. (and each point of pluriverse a whole 4d spacetime).
my experience correspond to this:
consider mind(=experiencing=perception) as active and consciousness as mind's function - the passive pole of experience. you can cosider consciousness spacelike and minfd time like. so you got space and time to begin with.
now if i concentrate my attention at a point of space, visible through external eye-sense, and hold it in unmovingly in such one-pointedness for amount of time necessary, this brings about an experience of stability of mind. that means, no matter what phenomena manifest, a certain unmoving quality of the observing aspect of experience is present and stable. the unmoving quality within movement, this one-pointedness, corresponds to SPACETIME aspect of experience. space quality prevails, but is indivisible from happening - the time.
then wholeness (of SPACE ), this unmoving quality of awareness is blended with moving qualities in experiencing - the breath, the blink of an eye, a neighbour yelling, car starting, storm thundering, becoming wet...one finds calm not only in calmness but in the fieriest dynamics and motion and touch and whatever as well. the movement becomes integrated, a moving within unmoving. this would correspond to TIMESPACE level.
when both moving and unmoving, appearances(mind) and consciousness, become embedded in awareness, their hyperdialectics is resolved as one taste fusion : what accomodates this timespace is a SPACETIME, chiasmic to it. what expresses spactime is timespace. they are indivisible in awareness. thus said as fusion.

or you might realize it as ubiquitous, omnipresent, empty matrix.

[thigle]

or awareness is on the soliton level beyond octonions ? i truly don't know

[Hugh]

I truly don't know either.

[lordofduct]

We could assume that just like ourselves in 3space we evolved to physically make an organ to perceive depth by binocular vision.

A 2D being may also do the same but under the constraints of 2D. As sight is actually the collection of intensity in light the 2D being may possibly use a similar binocular view like us in a little bit of a different way.

Our binocular vision takes into account two axiis. up down and left right. By laying both images a top of each other and comparing the two by lining up the edges of each surface and the account of how much distortion it takes (recognized by where the eyes must be angled) we can estimate the depth of objects by figuring how close one object is compared to others.

Well a 2D being would see light as well but the creature would only notice it's height. up and down. So it could, the vision itself could take on any look it the mind of the creature just like vision is different between 3D creatures. (for instance a flounder with two eyes on top of it's head... or a chameleon with it's eyes on each side, or how about a spider with its bajillion eyes. Stop being so chauvanistic and realize the human binocular vision is not the only thing.) Again an idea of depth can be taking from this... as depth to a 2D being is actually left right to us.

so here are two possibilities...

oh crap, ran out of time... I will be back in an hour with some drawings... eeeey

But yes it would see, it would see changes in intensity in light from top to bottom. This is if they develop a tool to see anyways... let alone if life could even EXIST in 2D!

[Hugh]

Hi lordofduct,

The problem with using drawings to represent what a 2d being would see is that the lines themselves are 2d, not 1d. There is a thickness to them that wouldn't really exist in a 2d plane. A 1d line only has one dimension so it's infinitely thin, so it couldn't be seen.

[lordofduct]

first I didn't finish what I had to say as work got really busy, and now im busy with some study material...

but, a 2D object would have a thickness left and right and up and down.

As for the process of receiving the light... no matter how thin it were, the light would also move through this spacial dimension (assuming there is light, if not, well sight is lost inherantly). The process of capturing the light would change intensity from top to bottom depending the infinitly thin edge it bounced off of, as it is the same infinitly thin width as the objects edge....

nevermind debating what is infinitly thin. Size just like time and speed is relative to the one perceiving it. Because as the object is infinitly thin and approaching zero, so is the entity seeing, and so is the realm they are in... if it ever reched zero though the being would cease to exist. So assuming they are still at some width that they do not understand, that width is still enough to exist and allow light to travel for sight.

The sight would most likely be completely different to how we see.

proof width is relative is in our own sight. We have peripheral vision, which has a flaw. Things towards the edge of our sight is stretched a little bit. If you stared at a wall of dots equally spaced that stretched left and right out of your line of vision the dots towards the side lines of sight would seem further apart then the ones at the center of vision.

I also read how someone considers the idea of our own dimension being infinitly thin being awkward.... but it is not.and is totally plausible considering the largest size there is. Which we do not know, but do know is much larger then us and possibly even larger then the universe. That is a very big number. To find area located under such a width represented on a graph as a line as it dives towards zero would only require an extremely fast rate of decline as it approaches.

For this to be possible (but not proven of course) is to look at other instances this occurs. How about time... a number that is rather large. Then take another number that seems rather large to us... our perception. We see our length of existence to be rather long. the tens of thousands of years we have been here seems so long. But in comparison to the age of Earth it's paper thin... Earth in comparison the the age of the universe is also thin making our length of existence drop much lower.

It is all relevant to your unit rate vector. As it gets larger we get smaller.

[lordofduct]

thickness of the object into the 3rd dimension is irrelevant because the light reflecting is also trapped with in the dimension. and that light would still reflect back to the light receptor or eye of the entity.

like so:


the perception of this light could be seen in so many ways, possibly not in fullscreen... but still there could be a measure of the amount of light received from top to bottom of the points of vision.

A depth (left right) could be implemented by 2 eyes one on top the other. The two images when layed on top of each other would allow the brain to estimate the difference in angles of the light reflecting at the bottom or top edges of the object they are looking at giving a sense of distance (left right) they are from it in comparison to objects further away or closer.



The two images would create an angle in the difference of light of each object. Objects A's angle of difference (theta) compared to the angle of difference at the edge of object B would give the sense of depth (left right) to the person viewing.

Again, I stress the thickness is irrelevant as the light itself is the same thickness (almost nothing) and still MUST reflect off the object... it can not just pass through it.

This is all still dependant to the existence of a light source.

[Hugh]

Because as the object is infinitly thin and approaching zero, so is the entity seeing, and so is the realm they are in... if it ever reched zero though the being would cease to exist. So assuming they are still at some width that they do not understand, that width is still enough to exist and allow light to travel for sight.

It is less than approaching zero in thickness, it actually is zero in thickness. That's the problem. Try doing the drawings from the perspective of the 2d being looking "along the plane" with only 1d lines and you'll see. A 1d line can't be drawn, or seen.

[lordofduct]

If you are saying it has a thickness it is a 2D plane existing in a 3D realm that the objects on can not leave. if it were to actually reach zero it would no longer exist as the 3D realm it exists in requires that extremely small thickness to occur. So essentially you are saying that the 2nd dimension doesn't exist without the 3rd being there?

If that isn't what you are saying... the thickness would not matter. Looking downward onto the 2D realm from our realm (like in the drawings above) you can move the objects around in 2 dimensions. Up down and left right. These objects will collide; will they not? If light exists in the realm then it too will collide; will it not? When light collides with an object it reflects off.

If that reflected light then collides with another object that can receive light then it will receive it.

You keep thinking that as you look through your eye you must take a 3rd person perspective to the light coming into it. This is not so.

Our eyeball takes light in where as it has little tiny receptors across a surface and each one measures the intensity of different colors. Other light receptors of different creatures may take in different measurements then color (or luminence) but instead maybe temp. or UV intensity... many different things.

Now our eyes have theses receptors layed across a surface in one layer. Kind of like a 2D surface. Each receptor receives its data of the intensity in light and sends it to the brain along with which recepto it is... mathematically you could consider it like.

R(3,5)=80%
where receptor at x=3 and y=5 in the grid of receptors is receiving light of intensity 80%.
R(3,6)=81%
...
R(52,12)=88%
....
R(100,100)=80%

Now say you have a 2D object with a surface of an eye. That surface is 1 dimensional. So instead of rows and columns it only has 1 single row of receptors. It would send the data to the brain possibly like:

R(1)=80%
Meaning the receptor at spot 1 on the row is receiving an intensity level of 80%.
...
R(2)=81%
R(3)=81.5%
...
...
R(8 )=80%

Our eyes don't actually see depth or height, or length... it's just a grid of receptors. If ANYTHING could exist in the 2D realm these receptors could also. The thickness is irrelevant!


The brain does not receive an image, it receives a table of values and coordinates. All it is saying is that object 'light' has bombarded and reflected off of object 'receptor x'. the brain then takes these coordinates of 1 dimension and puts them together in a row like they should. Now how the brain actually interprets it and displays it to the entity is unknown to us as this can be done in any of a way.

Go for it try and tell me that the brain would HAVE to display it in an x,y plane like our own sight... then explain to me how a freaking spider sees or a flounder or a chameleon. The brain can interpret these quantities and display them however they freaking like!

-----
I must add, these coordinates the brain receives are actually more complex then how I put it. Each receptor receives several quantities across a large angle of different things... not just intensity, but also color values and other things, this massive amount of data can be described in a matrix... but I'm not gonna write all that out; instead I kept the numerical values simple for explanation.

[lordofduct]

How about for a second way of sight to verify what I am saying. Let's imagine the creature sees the same way a blind cave salamandar would... using sound waves. Or any creature using sound waves.

Refer to number 1 of the image below

Say the creature produces a sound and the waves bounce off an object in front of it, those waves then come back to the creature... the size of the wave has changed since leaving it and that change can be used to tell the creature how far an object is from itself.

Refer to number 2 of the image below.

OR say fred was round and had tiny little ears all over its body on it's edge that were very accurate and recognizing how long it took a sound to travel out and then reflect and return down to the nanosecond. The red lines in the image below represent the sound and the length of time in nanoseconds it took for the sound to return. The length of time can then paint a picture for the brain to tell how far in any given direction there is an object.


AGAIN, thickness is irrelevant. As long as objects (including sound waves and light) exist in the 2D realm they will bombard eachother and reflect when put into movement in 2 dimensional directions. Recording the strength of bombardment, the speed of the objects movement, and the angle the bombardment occurs at the creature can then create a picture of what is going on around them.

You really must throw away these chauvanistic ideas that sight is interpreted the same way as humans interpret things. Seeing your surroundings can be put together in so many ways using light (sight), sound (hearing), touch (like snakes use vibrations in the ground to paint a picture of how far a moving creature is), smell (dogs can use smell to tell them how far away in what direction something of interest is) and even taste (insects use taste to paint a map of where they have been along with where other members of its tribe and of other species have been, then can use this to tell how far away from home they are).

[Hugh]

if it were to actually reach zero it would no longer exist. So essentially you are saying that the 2nd dimension doesn't exist without the 3rd being there?

It is actually at zero thickness, that 1d line, so you're saying that it would no longer exist, and I would say that 2d life probably could not exist. The 2nd dimension does exist, as two perpendicular axes of possible directional movement. If there is life confined to it, all I'm saying is that it couldn't see anything within it.

Looking downward onto the 2D realm from our realm (like in the drawings above) you can move the objects around in 2 dimensions. Up down and left right. These objects will collide; will they not?

If there is no thickness to the surfaces, how could they collide? Where would they meet if there is no thickness to their edges?

I understand what you are saying about the line of receptors but again, think of what these receptors are looking at; nothing, zero.

[lordofduct]

so your saying 2D objects can not collide!?

really?

So if a squares edge comes in contact with another squares edge they continue passing on through eachother? wow! how the hell did this happen?

If we can mass a 2D object (which yes we can... go to physics and calculus and you will learn howto), and one 2d object of a mass f passes through another 2d object of another mass g then the point of crossing would have to be a combination of both mass's. Which well means that something occured there! So even IF things didn't collide, they'd would atleast have to combine!

Having mass alone means they would collide anyways... because for them to take up the same amount of space while still combining mass you'd have to compress the particles making up the objects.

[lordofduct]

If there is no thickness to the surfaces, how could they collide? Where would they meet if there is no thickness to their edges?

thickness doesn't matter for collision. collision is two objects making contact. the line y=x+2 crosses the line y=-x+2 at the point (0,2). That point (0,2) is a point of collision!



Your statement about life probably not existing in 2D... well I could easily believe and agree with that. But then we are not positive so you can not denounce it all together.

[Hugh]

If we can mass a 2D object (which yes we can... go to physics and calculus and you will learn howto), and one 2d object of a mass f passes through another 2d object of another mass g then the point of crossing would have to be a combination of both mass's. Which well means that something occured there! So even IF things didn't collide, they'd would atleast have to combine!

Okay, I agree. Maybe within this "combination", there could be a recognition or awareness of presence.

thickness doesn't matter for collision. collision is two objects making contact. the line y=x+2 crosses the line y=-x+2 at the point (0,2). That point (0,2) is a point of collision!

It would be more of a co-existence than collision wouldn't it?

Your statement about life probably not existing in 2D... well I could easily believe and agree with that. But then we are not positive so you can not denounce it all together.

Agreed. Anything is possible, some of it is just more unlikely.