4d object visualization ..

Discussion in 'Physics & Math' started by planaria, Mar 14, 2004.

  1. planaria Well-Known Member Registered Senior Member

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    honestly i dont understand people and their inability to see 4d objects

    .. a ball that moves through time can be described as a string ..
    what is actually hard is visualizing COMPLEX 4dimensional shapes.. (try to visualize every detail of 2 galaxies colliding .. 5dimensional cubes are also easy it is simply a cube that move both ways in time at the same time.. so in a sense the cube can stretch through time as well as move through it ..

    the best definiton of dimensionality that i have heard is simply giving something a new way to move.. although i would add that things like color , meaning , taste , conductivity, etc, can all add a form of "dimension" to an object.

    the very definition of dimensions is whats really confusing to me .. because a dimension can be so many different things ..

    what do you classify dimensions as ..
     
  2. 1100f 6anned Registered Senior Member

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    I neither do not understand the people that have have difficulty to visualize a 11 dimensionnal space. This is very easy, you visualize a space in N dimensions and take N = 11. :D
     
  3. CTEBO Well-Known Member Registered Senior Member

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    I try to explain multi-dimensional models to this science-minded friend of mine and I am absolutely baffled at his inability to even visualize 3 dimensions from a 2-D drawing let alone 4 or 5 dimensions. Is it difficult to visualize 11 dimensions? Yes, of course, we don't need 1100f's sarcasm to point that out. I cannot visualize 11 dimensions.
    Come to think of it I cant even visualize 4 dimensions. The best I can do is visualize a 3-D representation of a 4-D object, or at best draw a 2-D model of a 3-D representation of a 4-D object, but some people can't even do that!!!
    A 4-D cube can easily be visualized. Picture a cube. It has 8 corners so label them in your head A1, B1, C1, D1, E1, F1, G1, and H1. Then picture a smaller cube floating at the center of the larger cube. Label this smaller cube's corners A2, B2, ... H2 in correspondence with A1, ... H1. Now, finally, draw a line connecting A1 to A2, a line connecting B1 to B2 and so on. Once this is done you have successfully made a 3-D model of a 4-D cube. The only thing is that in 4 actual dimensions, ALL the angles of the object you just created are 90 degree angles (yes even the angles created by the lines connecting the two cubes' respective corners).

    I once thought that the only explanation for existence (not just space-time) must be an infinite dimensional system. Basically a dimension for every dichotomy in nature, be it physical or conceptual (up/down, sacred/profane, hard/soft, subjective/objective, etc) But then I figured that I was taking the notion of dimensions a bit too liberally.

    You asked what a dimension actually is and I think the physical definition of it has alot to do with coordinates. Classical thinkers where sure that there were only 3 dimensions because you never needed more than 3 coordinates to precisely specify a location in space. Time was introduced as a fourth dimension cuz we needed a 4th coordinate to specify the location of an "event" (not just an object). I personally believe in 10-ish dimensions, but not in the string theory sense. I think the extra dimensions are extended, not curled up. Why don't we see them? I am inclined to think that this is a result of our binocular vision and not some feature of the universe as a whole. Why can't we move through them? We are actually moving through them all the time (me thinks).
     
    Last edited: Mar 14, 2004
  4. John Connellan Registered loser Valued Senior Member

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    Oh yeah, thats because it is impossible.

    A string is a 3D object

    exactly

    No, I've always thought of dimensions being numbers solely describing the position of an object in space-time. It has nothing to do with properties of objects (like colour) but I might be wrong here.
     
  5. planaria Well-Known Member Registered Senior Member

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    The only thing is that in 4 actual dimensions, ALL the angles of the object you just created are 90 degree angles (yes even the angles created by the lines connecting the two cubes' respective corners).

    mathematically yes.. but visually no .. for instance what i mean by visualizing a 4d object as a string i meant more as a visual tracer .. for instance when a bright light pases infront of your eyes you see the path that it took. you are in essence seeing a visualization of a 4 dimensional object.

    percieving things mathematically and perceiving them visually do not always lead to the same results.

    i wonder what it would be like feel a 4dimensional object .. or to smell a 4dimensional smell that would be interesting ... i wonder if we feel and smell these already and dont even realize it ?
     
  6. Rappaccini Redoubtable Registered Senior Member

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    Smelling four-dimensional smells?

    This doesn't seem like real physics or mathematics to me.
     
  7. John Connellan Registered loser Valued Senior Member

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    No as I have said above, smell is a property of an object not a dimension the object is in. Another way of differentiating between these two is that dimensions will apply to the universe as a whole whereas properties will not.
     
  8. planaria Well-Known Member Registered Senior Member

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    actually smell is more a form of measurment imo . but this is off topic ..

    but to put this to rest i think it depends on what you concentrate on for visualization.. if you are a hardcore mathematician it will be impossible for you to visualize a 4d object .. because you do not think visually you think numerically ..

    although im sure there are exceptions to this rule .. but by and large lots of mathematicians seem to have this.
     
  9. FNG2k4 Well-Known Member Registered Senior Member

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    I wonder what it would take to see in 4 diminsions?

    Math helps plot out 4d objects in a 3d graph helping us view a 4d object.
    http://research.microsoft.com/~hollasch/thesis/chapter4.html

    A smell or sense of touch of a 4d object would be the similiar as a being in a flatland (2d plane) touching a cross section of a sphere (a circle). He gets an accurate discription of a sphere but he has to wait until the sphere crosses through his plane. while the sphere is in his plane he recognizes it only as a circle. In his case he senses an x and y axis but not a z axis. No matter what this 2d guy does he is unable to view the height of a sphere. Similiarly in a 3d view the only way we can see a 4d object is by 3d slices of the object as the objects moves through our 3 dimensions. We are limited to sensing only a 3d slice of the object at a time.
     
  10. planaria Well-Known Member Registered Senior Member

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    which is why tracers from light shining/moving at your eyes is a perfect example.. its not slices its a blur

    as for smelling and touching ...i think smelling a 4dimensional object would be smelling a 'blur' of all the smells that it could emit through time.

    touching is a similar idea..

    imagine being able to feel a big rock while at the same time simultaneously being able to feel it in rubble dust reforming into another rock etc..

    it would be very confusing to be sure ..


     
  11. FNG2k4 Well-Known Member Registered Senior Member

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    No its a slice we dont get a blur of that information we get a slice of it.

    If time is the 4d that slice is now.
     
  12. John Connellan Registered loser Valued Senior Member

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    I was talking about the other form of the word 'spell' which is the scent of an object. That is a property. U are talking about the verb 'to smell' i guess? That is indeed a measurement (or 'sense') of the surroundings. I can't see why a 4d object would 'smell' any different to a 3d object with the same scent?!
     
  13. planaria Well-Known Member Registered Senior Member

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    ok lets say there is a 4d tomatoe.. the reason that it would smell different is because we run into 4d tomatoes all the time.. a tomatoe in 3 space dimensions and 1 time dimension grows, ripens , rots, so you would smell all these smells at the same time.. since the 4d object is a sum of a 3d tomatoe through time. i guess a 4d tomatoe can also be an interval of time of a tomatoe too .. so you would smell all the possible smells of that the tomatoe can emit through that interval.

    i guess you are right about emitting smell and smelling.. but if there is no observer , then was there ever a smell :)
     
  14. zonabi free thinker Registered Senior Member

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    i am very interested in this subject, and spend countless hours trying to explain the fourth dimension to my friends and even people on here.

    could someone try and explain to me how the 5th, 6th, and 7th ... etc dimensions work? A person once told me some mathematical explanation of like 10 to the negative 33 thousand or some odd number, but this made no sense to me really, i guess i am more of a visual person.

    I can understand up to the 4th dimension, Time. and i have made several theories regarding Time, most of them based around my assumption that there are many "layers" of time that overlap one another, to create the "dimension" of time.

    But my mind stops there, and i cannot figure out what they mean when they say theres up to 11 dimensions? Although i do not doubt it for a second, I just cannot comprehend it at this time... can someone shed some light on this?

    on the 4d object visualization- i think it boils down to this:
    - you either CAN or CANNOT visualize it. plain and simple.
    some people just dont have the visual or mathematical mind power to envision more than what they see in front of them. o well, their loss right?!
     
  15. Pete It's not rocket surgery Moderator

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    I guess you mean 'visualize', rather than see.
    It's a cognitive limitation... simple 3D visualization is instinctive, requiring no abstract thought. Increasing complexity requires more and more abstract thought.

    All people have a limit, even in 3D (or 2D). Have you ever tried to solve a complex 2D puzzle like this one in your head?

    With non-trivial 4D objects, it's much harder.
    Try this, for example:
    How many different 4D shapes can be constructed with exactly 4 hypercubes?
    How many of those shapes are reflections of another?
     
  16. planaria Well-Known Member Registered Senior Member

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    i have a qeustion

    lets assume : a 4d cube is a 3d cube that can move in 1 time dimension,, but does that mean the cube can move in any direction or can it only move in a straight line .. ? ?
     
  17. Pete It's not rocket surgery Moderator

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    The assumption is false, unless you can equate time units with length units, and the 3D cube exists motionless for a length of time equal to the width of the cube. Before an after the time segment, the 3D cube must not exist.

    Throwing in relativity, in which "motionless" is only meaningful for a specified frame, complicates things. I think you'd need to use Minkowski space.

    I'm not sure how a 4D cube in Minkowski space would appear... I don't know if the concept is even meaningful.
     
  18. planaria Well-Known Member Registered Senior Member

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    what it doesnt exist ? 3d cubes move in time all the time..

    i guess my next question would be , where do you seperate time and space from reality in order to do this .. because in reality a 3d cube with 1 time dimension can move in any direction it wants .. (except back and forth in time at the same time i suppose) .. so i guess to answer that riddle about how many different 4d shapes can be constructed with exactly 4 hypercubes is a hugely large number .. since in essence looking for away at a 4d hypercube it could look like a vibrating string or a string in a loop .. or whatever shape .. personally i equate motion with time.. so that can create a lot of shapes .. for more than i have the memory or experience for.

    that 2d puzzle is easy if you cheat just rotate the whole thing 90 degrees :) ( i would need to play a lot of rubix cube to get the skill to figure that 2d problem out)
     
  19. Pete It's not rocket surgery Moderator

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    Making it a long 4D prism, not a 4D cube.

    Making complex 4D shapes. Thinking about time as a fourth dimension is a bit restrictive in this discussion. Just forget time, and think about a 4th spatial dimension instead.

    No, a hypercube is a very specific shape. It's not flexible at all.

    A cube has six square faces, a hypercube is a has eight cubic blocks (a word I chose to describe the next step up from a face. ie vertex, edge, face, block).

    A cube has 6 faces, 12 edges, 8 vertices.
    A hypercube has 8 blocks, 24 faces, 32 edges, and 16 vertices

    On a cube, each square face is surrounded by four other square faces on planes at right angles to the first face.

    On a hypercube, each cubic block is surrounded by six other cubic blocks in spaces at right angles to the first block.

    Now do you see why visualizing 4D is hard?
     
  20. planaria Well-Known Member Registered Senior Member

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    uhm actually, there really very easy to visualize.. with practice.

    but i understand more now why people have such a hard time with them

    Now do you see why visualizing 4D is hard?[/QUOTE]
     

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