Shadows

[DogmaJerk]

Hi folks

Haven't scanned the site thouroughly yet, but I have read the adventures of Fred Bob and the rest...Very interesting.

Anyway, I wanted to point out the connection to shadows. Shadows in flat land are one dimensional. (That is if the ground plane is truly flat, not round like "earth") The shadow of any object will fall directly in line with the ground plane, no matter what shape or size of the 2-d being. (Of course I have noticed that a shadow could be cast onto an upright-standing bush for instance, but we're talkin groundplane) Likewise my shadow in realmspace can be measured accoring to two dimensional space on the pavement. Therefore the shadow of a four dimensional person could be projected onto its groundspace (realmspace) and stand at any angle three dimensionally. One could theoretically witness what would appear as a featureless silouhuette moving about freely, with no apparent relation to sun positioning or light conditions.

Cool, so if I saw one of these shadows standing still, I could maneuver around it beholding different sides of this three-dimensional massless specter, just as I move around my podium, my cat, my dad. If I were to poke my head in, would the entire room appear darkened from my view inside? Is this shadow train of thought even plausible? What kind of light source is required?

[sup2069]

Very interesting, I never thought of shadows. As far as to your answer I do not know.

[alkaline]

yes you are right in how the shape of the shadow would appear to us. It is a different question altogether though about the interaction of light between different dimensions. Light would have to come from tetraspace to realmspace, and a tetronian object would have to block this light at a certain place so that a region in realmspace would appear darker because of this blockage. However, all of this is based on the assumption that tetronian light would interact with realmspace in the first place.

[Splatt]

light in 3d travels in a line, so would light in 4d travel as a plane. but the problem with this argument is what would light be in 2d?

[alkaline]

no, light travels in a line in every dimension. Light "particles", called photons, move in a single direction. The path of an object is always a line, no matter what the dimension. Be careful not to over-generalize the dimensional-analogy: something that is a line in one dimension isn't always a plane in the dimension above it. It all depends on the nature of what you're dealing with.

[Splatt]

i guess what i'm thinking is, why do things have to have the same properties that they have in 3 dimensions. as i sit here thinking about it, what even says a four dimensional being would use the same light we use to see. we look around and see surfaces with light, but a four dimensional being wouldn't be able to use the same light that we use.

[alkaline]

Well, there are two approaches you can take to studying the fourth dimension:

1. Assume the same physics as the third dimension, except for an extra dimension to move in.
2. Build 4d physics from the ground up.

Number 1 is the best for introducing basic 4d concepts, and most lay people would be confined to that type of study of the fourth dimension. Sometime i want to start into number 2, building physics from the ground up. This requires a bit of knowledge of advanced physics, so it could take a while to develop. That is the type of physics that you are proposing - and it's something i'm quite interested in.

Also, you are quite right that 4d physics doesn't *have* to have the same properties as 3d physics. Using practicality though, we could probably rule out certain things. For light to move in a "plane", its front end would have to be a line, possibly infinite - this requires a line, possibly infinite, to emit this "string" of light. If light could only take this form, then it point sources of light wouldn't exist, only linear ones would. That would make for a very strange universe.

[Keiji]

Doesn't seem strange to me.

[Splatt]

well i was thinking about this on my way to school and this is what i came up with.

In 2 dimensions the only light they would "see" would be light that is travelling along their same plane, any light that goes through any other way would simply be a point. thats why i don't think they would use light the same way we do.

In 4 dimensions light could very easily extend as a plane and we only see light as a travelling line. but as you said if we consider that the physics would be faily similar they may have light like we have x-rays but don't use it to see the way we do. i would think that an entity would use something else to look around that we may only partially be aware of. we could take gravity for example. you mentioned in another post that energy dissipated in a lower dimension would be relatively weak, well it seems to me that thats what gravity could be. imagine that the planets and suns are simply sitting in gravity wells created by objects in higher or lower dimensions.

[Aale de Winkel]

I do think in any dimension photons ar pointlike particles.

The regular wave/particle dualism is of course also present.
ie lots of photons bombarded at a wall with some slits will give an interference pattern beyond that wall.

I assume that in flatland those pattern will be the same as in realmspace (when there are two holes in the line before the bionian sun)

I don't see why tetrionian photons would give different patterns, though that depends on what a tetronian "slit" might be.

I do think all the force-intermediar particles (gravitons, photons, gluons etc.) ought to be seen as pointlike particles, and therefore travel in straight lines, until they interact with some object (pe light reflecting of an object).
This view makes 4d-physics somewhat computable as our ordinairy physics. Having string-like photons, one end caught by an object the photon wraps around the object, or get stretched out since one end is reflected by an object while the other end travels further. The latter looks plausible but makes I think uncalculable physics.

Not all trionian objects should aquire trength in tetronian space, letting the force intermediaries remain as they are makes things simpler. Gravity is in all dimension concidered along the y-axis (I call it the 'vertical' myself, since y for me has a coordinate-function), so a graviton is concidered point-like, why should a photon suddenly be a string, or even plane!

Concidering string/plane like photons of course would make some alternate physics, for me I keep it as close as possible to the familiar trionian physics.

[Jay]

The lack of these shadows at least proves there are no 4-d objects near us on earth. We don't see these 3-d shadows in everyday life, which means there are no 4-d objects to block light coming from the 4th dimension here. However, maybe somewhere else in space, these shadows are abundant, coming from a 4-d world.

[Jay]

Here's an interesting thought.

Any shadow in 1-d would be completely pitch black, because all light from the light source would be blocked.

Most shadows in 2-d would be fairly dark, but not pitch black, because the light that passes the being continues to spread out afterwards and lighten the shadow.

Here in 3-d, most shadows are barely even black, for the same reasons as in 2-d. In addition the expanding light has more areas to penetrate the shadow from.

Maybe the reason we can't see the 3-d shadows of 4-d objects is because they simply aren't that dark at all, or not enough to be perceived by our standards.

[alkaline]

Following along your line of thought from 1-d to 3-d, then a 4d shadow would indeed be fainter than a 3-d shadow. I don't think it wouldn't appear at all, though - it would have at least some measure of darkness. I think the reason that shadows are as faint as they are in realmspace is that there are that many more directions for ambient light to lighten the shadow. In tetraspace, there are even more directions for ambient light.

[Keiji]

tetronian shadows cannot be projected into realmspace simply by casting the shadow through realmspace. if we cast a trionian shadow through planespace, bionians would not be able to see it because the dust particles are either one side of the plane or the other, as planes have zero thickness.

for us to see a tetronian light or darkness, they would have to insert a tetronian wedge into realmspace to reflect the photons, since tetronian wedges have a constant realmar surface which will lie directly on any given realm if intersected with it in any way.

[alkaline]

Maybe they could even project an image into realmspace by placing a tetronian mirror at an angle to realmspace. Then, whatever was above us in tetraspace would be reflected into our space. If they rotated it, we would see morphing images on the mirror, but to us it wouldn't look like the mirror was moving at all.

[Keiji]

that is very possible in fact