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# Department of Science, Math, & Technology

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4-dimensional life
Posted: Posted July 10th, 2007 by Tmeister
 (I was going to combine this with the other thread, but I figured it would get too confusing.) This will probably be much more interesting than 2D life. If you have a globular cell, then the membrane will be a 3-dimensional surface. Therefore, you can transport a large sheet into/out of the cell without breaking the membrane apart. This means that genetic information can be stored as sheets rather than strands, with both length and width being extremely long. The sheets can be compacted in the nucleus without rendering parts of it inaccessible. Proteins would likewise be formed out of sheets (rather than strands) of amino acids, so the extra dimension of storage is necessary. Large multicellular organisms could form. They would be supplied by vessels in the shape of hyper-cylinders (the shape of a sphere being swept through the 4th dimension). A highly interconnected nervous system and brain are possible. This universe provides many more degrees of freedom (literally and figuratively) to play around with than the 2D one. What would life be like? How would planetary systems work? How can you defend your nation's borders? Obviously I have only scratched the surface with this post.
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I like this idea and was planning to use something similar to explain the Etre and Vrendhalk, my gods and demons in my stories, respectively. I'll answer with my ideas when I have more time.

Posted July 11th, 2007 by bloodb4roses

For one thing a 4D entity could "walk through walls" from the P.o.V. of a 3D entity.

Posted July 11th, 2007 by eldin raigmore

Well, I never got into the biology of it, but as I stated, I'm trying to work out some 4D beings.

Aside from walking through walls, they could:
- disappear from your view, and be next to you on a different axis
- manefest in different forms depending on which way they are oriented when they enter a 3D space (possibly)
- take in more air, water, nutrients, etc.
- have more places to store things in what appears to be the same shape (a hepercube would look like a cube to someone in 3D)

But, I've also wondered how this would affect gravity, hypermass, hyper surface area, etc. And wonder if they would have more weight restrictions or if the added layer of geometry would help make their bodies more sturdy than a 3d beings.

Posted July 11th, 2007 by bloodb4roses

This and the 2d life bit are kind of on the edge here.

I know your intent was to get ideas on real world chemistry, but the problem there is that whenever you add a dimension, the fundamental world physics changes and all real world chemistry goes out the window.

I consider these to be science fiction because they seem to me to be speculation.

Were there more resident quantum physicists, somebody might have a useful hard science comment, but as it stands I don't think there's anything any of the forum members are qualified to comment on here from a hard scientific perspective (I'm guessing I've probably had the most hard science education here, and I know I can't- aside from saying that physics would be different, I can't tell you how or even really guess at it)

I personally think these two topics would be better suited for science fiction as, to my knowledge, there's just not enough science on these matters to give the posts much content here so any conversation is liable to devolve into speculation as opposed to hard science theory.

I could be wrong- Simon, maybe you can chime in here?

Let me know your thoughts on the matter- if you don't have any problem with a move, I (or Eldin) will bump them over there for you.

Sorry I don't have any good science comments on this one.

Posted July 11th, 2007 by Blake

Would central forces drop off by an inverse-cube law instead of an inverse-square law? That is, wouldn't such forces as gravity and electric or magnetic attraction or repulsion vary inversely as the cube of the distance between the bodies rather than inversely as the square of the distance?

(And in a 2D universe they'd very inversely as the distance, rather than inversely as the square of the distance.)

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I consider these to be science fiction because they seem to me to be speculation.
....
I personally think these two topics would be better suited for science fiction as, to my knowledge, there's just not enough science on these matters to give the posts much content here so any conversation is liable to devolve into speculation as opposed to hard science theory.
...
Let me know your thoughts on the matter- if you don't have any problem with a move, I ... will bump them over there for you. ...
I believe you are probably right. I will defer to you.

Posted July 12th, 2007 by eldin raigmore

Would central forces drop off by an inverse-cube law instead of an inverse-square law? That is, wouldn't such forces as gravity and electric or magnetic attraction or repulsion vary inversely as the cube of the distance between the bodies rather than inversely as the square of the distance?
If this is true, would whatever causes said forces have a larger force per unit (making things "similar" to three dimensions in our universe) or would they be the same per unit, effectively making the forces themselves seem weaker on a broad scale?

Posted July 12th, 2007 by bloodb4roses

Would central forces drop off by an inverse-cube law instead of an inverse-square law? That is, wouldn't such forces as gravity and electric or magnetic attraction or repulsion vary inversely as the cube of the distance between the bodies rather than inversely as the square of the distance?
If this is true, would whatever causes said forces have a larger force per unit (making things "similar" to three dimensions in our universe) or would they be the same per unit, effectively making the forces themselves seem weaker on a broad scale?
I'm not sure.
One version of the "11-dimensional universe" idea has it that in the RealWorld, gravity actually varies inversely as the cube of the distance at close distances -- something less than a millimeter. The idea is that the most expansive of the "rolled-up" dimensions is about that big (that is the diameter of the universe in this dimension is some macroscopic distance that is still pretty small -- less than a millimeter. Since gravity is so weak to begin with we can't detect the shift from the inverse-square to the inverse-cube unless we get two gigantic objects that close to each other and vary the distance between them within that distance. Hard to do.)
So it would make sense that everything is the same except the number of dimensions. In fact, having the forces carried by exactly the same particles, is part of the assumption that allows us to calculate the force varies as the inverse (n-1)st power, where n is the number of spatial dimensions. (Note that the particles themselves could be dimensionless points; photons and electrons are supposed to be, for instance). Also this would allow for a smooth transition from inverse-square to inverse-cube, or inverse-first-power to inverse-square, or whatever.

Posted July 12th, 2007 by eldin raigmore

Um... According to The Elegant Universe, most of the "rolled up" dimensions would be about the size of a string. I don't remember how small that was, but it's a hell of a lot smaller than a millimeter.

Then again, you also mentioned that this would be for the most expansive of the rolled up ones, so I don't know...

But if you had a universe with four "unrolled" dimensions, with certain parts that were 3D spaces, that might be different.

Posted July 12th, 2007 by bloodb4roses

Would central forces drop off by an inverse-cube law instead of an inverse-square law? That is, wouldn't such forces as gravity and electric or magnetic attraction or repulsion vary inversely as the cube of the distance between the bodies rather than inversely as the square of the distance?

Probably correct, though I don't know if there is any scientific relationship between the number of dimensions and the force drop-off laws. With an inverse-cube law, orbits are an unstable equilibrium: any disturbance to an orbit will sent the bodies spiralling towards or away from one another. This will apply to gravity, and maybe the "orbits" of electrons in atoms. So, in a 4D universe, you can't do orbiting the way we do it.

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Um... According to The Elegant Universe, most of the "rolled up" dimensions would be about the size of a string. I don't remember how small that was, but it's a hell of a lot smaller than a millimeter.

ISTR the idea was that only gravity would be able to travel along this dimension, explaining why it is so weak. Consider a magnet stuck on a fridge. The magnetism of the tiny magnet is strong enough to withstand the gravity of the entire Earth. Gravity is very weak.

To explain why the power law will change as the scale changes, an analogy:
Imagine treacle being poured into a long flat-bottomed trough (a universe with 1 unrolled dimension and 2 rolled-up ones). Initially, the distance it reaches is proportional to the cube root of its volume, as it forms a pile. When the pile gets bigger it tends to stay rather flat, so the linear extent of the treacle is proportional to the square root of its volume. When there is a lot more treacle, and it reaches several trough-widths along the trough, the distance it reaches is proportional to the volume of treacle.

Of course, the rolled-up dimensions in our universe do not have an edge but wrap round, and the force laws are inverses of the surface area of some space rather than the inverses of the volume of some space.

Now, what happens if your space is a fractal? You might get irrational powers in your forces, derived from the fractal dimension of the space.

Posted July 13th, 2007 by simon.clarkstone

This means that genetic information can be stored as sheets rather than strands, with both length and width being extremely long. The sheets can be compacted in the nucleus without rendering parts of it inaccessible. Proteins would likewise be formed out of sheets (rather than strands) of amino acids, so the extra dimension of storage is necessary.

I am not so sure about this. OTOH, proteins will need more data to produce, as there is so much more to each one. OTOH, splicing sheets is tougher than splicing strings, when doing reconbination.

This universe provides many more degrees of freedom (literally and figuratively) to play around with than the 2D one. What would life be like? How would planetary systems work? How can you defend your nation's borders?

There is some nice speculation on war and geography at http://tetraspace.alkaline.org/.

Posted July 13th, 2007 by simon.clarkstone

Would central forces drop off by an inverse-cube law instead of an inverse-square law? That is, wouldn't such forces as gravity and electric or magnetic attraction or repulsion vary inversely as the cube of the distance between the bodies rather than inversely as the square of the distance?

(And in a 2D universe they'd very inversely as the distance, rather than inversely as the square of the distance.)

Yes. And that means that in both 2D and 4D universes, atoms and planetary orbits would be unstable.

Posted July 14th, 2007 by WeepingElf

Would central forces drop off by an inverse-cube law instead of an inverse-square law? That is, wouldn't such forces as gravity and electric or magnetic attraction or repulsion vary inversely as the cube of the distance between the bodies rather than inversely as the square of the distance?

(And in a 2D universe they'd very inversely as the distance, rather than inversely as the square of the distance.)

Yes. And that means that in both 2D and 4D universes, atoms and planetary orbits would be unstable.
Why unstable?

Posted July 14th, 2007 by eldin raigmore

Would central forces drop off by an inverse-cube law instead of an inverse-square law? That is, wouldn't such forces as gravity and electric or magnetic attraction or repulsion vary inversely as the cube of the distance between the bodies rather than inversely as the square of the distance?

(And in a 2D universe they'd very inversely as the distance, rather than inversely as the square of the distance.)

Yes. And that means that in both 2D and 4D universes, atoms and planetary orbits would be unstable.
Why unstable?

I can't give you the mathematical details, but apparently an inverse-square law is necessary to create a stable equilibrium. In both an inverse-linear and inverse-cubed force field, perfectly circular orbits are possible, but even the slightest deviation from that will not lead to an elliptic orbit, but either to a spiralling movement to the center or to an escape. I read this in Scientific American a few years ago, and they will have good reason to say so.

Posted July 15th, 2007 by WeepingElf

I can't give you the mathematical details, but apparently an inverse-square law is necessary to create a stable equilibrium. In both an inverse-linear and inverse-cubed force field, perfectly circular orbits are possible, but even the slightest deviation from that will not lead to an elliptic orbit, but either to a spiralling movement to the center or to an escape. I read this in Scientific American a few years ago, and they will have good reason to say so.
(I posted in the other thread; I wish I'd read the above response first.)

Posted July 15th, 2007 by eldin raigmore

@ WeepingElf: But in 4D, who says that the orbit would have to be circular?

Posted July 15th, 2007 by bloodb4roses

@ WeepingElf: But in 4D, who says that the orbit would have to be circular?
I'm not WeepingElf; but, it would have to be, wouldn't it? In any central forces problem, any periodic solution lies in a plane.

Posted July 15th, 2007 by eldin raigmore

@ WeepingElf: But in 4D, who says that the orbit would have to be circular?
I'm not WeepingElf; but, it would have to be, wouldn't it? In any central forces problem, any periodic solution lies in a plane.

Sorry bout that.

I'm just thinking that we (on this board at least) really don't know all the intricacies of 4D worlds. I'm not saying you're wrong. But for all we know, orbits could be spheroid in 4D.

I know it's not really related to gravity, but aren't electron clouds like that? Who says the forces would be the same (in strength, how they act, etc) in a viable 4D universe anyway?

Posted July 15th, 2007 by bloodb4roses

I know it's not really related to gravity, but aren't electron clouds like that?

Electron clouds aren't really even orbits in that sense- they're wave functions, so it's not even a particle moving around. I don't think they can be compared at all anymore.

Anyway, the fundamental difference in forces is basically what I had said- everything would have to function fundamentally different for anything to work or make sense at all, but...

This is the science section, so the premise is that we're talking about real world physics.

Who says the forces would be the same (in strength, how they act, etc) in a viable 4D universe anyway?

The original poster, on account of asking for realistic scientific advise. ;)

This is why I think this should be in scifi, but people did offer sound science advice.

Posted July 16th, 2007 by Blake

Sorry bout that.
No apology was necessary afaik; but thanks anyway.

I'm just thinking that we (on this board at least) really don't know all the intricacies of 4D worlds.
That's probably true.

I'm not saying you're wrong. But for all we know, orbits could be spheroid in 4D.
Not if it's a "central force" generating the orbit, and there are just two bodies. The orbit will lie in a plane spanned by two vectors; one is the difference in their initial velocities, the other is the line along which the force is directed, which is (by definition of "central force") the line from one of them to the other. Two vectors can't span a space of more than two dimensions, even though it can be embedded in a space of more than two dimensions.

The orbit can appear helical to an observer who is traveling at a non-zero velocity relative to the two bodies; but even this helix is necessarily contained within a 3D subspace of the whole.

Any spheroidal solution, no matter how it comes about, would be at best a quasi-periodic solution rather than a periodic one.

But if there are several bodies not all of their orbits need to lie in the same plane. Star-and-planets systems in real life tend to have an "ecliptic plane"; a sort of "average" plane near which all or most of the planets' orbits lie. Perhaps that isn't something that would have to be common in another possible universe.

I know it's not really related to gravity, but aren't electron clouds like that?
Yes, for quantum-mechanical reasons, not only the aggregate of all the electrons' "orbits", but even each individual "orbit" (say, in a neutral hydrogen atom) is "like that"; which is one reason they aren't really "orbits", and one reason I don't think WeepingElf's argument leads to the conclusion that atoms would be impossible in 2D and 4D. (Though they still might be impossible; I just don't think that argument proves it. But I do think it might be effective in making it difficult to have gravitational orbits.)

I know it's not really related to gravity, but aren't electron clouds like that?
Electron clouds aren't really even orbits in that sense- they're wave functions, so it's not even a particle moving around. I don't think they can be compared at all anymore.
WHS.

This is the science section, so the premise is that we're talking about real world physics.
Who says the forces would be the same (in strength, how they act, etc) in a viable 4D universe anyway?
The original poster, on account of asking for realistic scientific advise. ;)
As I understand it and if I recall correctly, in quantum physics all forces are supposed to be carried by mediating "particles" (in quotes because a "particle" in quantum physics often doesn't satisfy our intuition about particles); and the strength of the field of a central force is distributed over the "surface" of a "sphere", consisting of all the points a set distance away from the center of force. This surface has D-1 dimensions if space as a whole has D dimensions; so its length (if D=2) or area (if D=3) or volume (if D=4) is proportional to the distance, or the square of the distance, or the cube of the distance, respectively. Thus the intensity of the force is inversely proportional to the distance, or to its square, or to its cube.

So if everything "we" "know" about physics were left the same except the number of spatial dimensions was raised to 4, this is what would happen.

This is why I think this should be in scifi, but people did offer sound science advice.
This is a tricky question, since the 11-dimensional view of the universe has been brought up seriously among the professionals and has not been completely repudiated. I'm not arguing against moving it; but I don't think I'll be the one to move it if it gets moved.

Posted July 16th, 2007 by eldin raigmore

http://conworlds.fun/cwbb/viewtopic.php?t=299 is the 2D thread on the CWBB. Tmeister was its Original Poster.
http://hi.gher.space/forum/ is still active!
http://hi.gher.space/wiki/Main_Page at least still exists.

Posted January 10th by chiarizio