Well, this prettymuch has me comfused..... But now Im wondering.... How do you say "I" and "a" in pig latin? Normally, you take the first letter of the word, add the suffix "-ay" to it, and then place it at the END of the word.... yes, I do realize that this is entirely off topic...
If you realise it's entirely off topic then go make a new one. Tank, you're talking about a one dimensional universe with the line analogy. Two dimensions mean you can walk forwards-backwards and left-right but there is no up-down. When discussing dimensions it's futile to attempt to bestow human attributes to sub or supra dimensional beings. As for time, obviously energy is the driving force behind everything, without energy nothing would be possible. But you should think of time as the road and energy as the engine of a car driving along. Besides which, time is inextricably entangled with energy and the rest of the universe as shown by time dilation at extremely high speeds. The point is units of time are arbitrary, time itself is far more complicated. Sam
Okay. You make a good point about time. But if the line I described before was horizontal instead of vertical (which simply implies a rotation of perspective), the line is simply what you can see. And a line is still a two-dimensional object, only a point is a one-dimensional object. If I could draw what I mean it would make a lot more sense, I bet you. An arc on Mrs. Circle would be allocated to "see," her vision (as we 3D beings perceive a plane), would perceive a line. Going further down, a point, or one-dimensional being would be incapable of any perception at all. Along this line Mrs. Circle sees, different colours, and line segments can be seen, but any sense of depth is negated, as two oncoming circles, one further away could easily be seen as a pair of circles, one young, one old, approaching at the same time. Does that make sense? It kind of does to me, but you can never be too sure.
It doesn't to be honest, but mainly because I think you've got your dimensions mixed up. A line is a one dimensional construct because it goes up and down (or left and right, or back and forth), this is one plane. A dot would be zero dimensional as there is no movement in any direction but this is only possible in theory as obviously any dot can be broken down to a circle which is two dimensional. Link. In the picture in the link above we see a dot (zero dimensional), a line (one dimensional), a square (two dimensional) and a tesseract (four dimensional). Tesseracts hurt my head but they're the fourth dimensional projection of a cube, here is an applet which shows you the progression from dot to tesseract. The problem with discussing dimensions above the three we are accustomed to is not only because the fourth dimension (ignoring the idea of time being a dimension) is something we exist in but cannot consciously perceive or affect but also because we are using computer monitors, a two dimensional medium. If you try the applet in the above link you'll see the limitations for yourself. Sam
I have seen the tesseract thing before. Is that the one which has the inner cube continually being rolled outwards? The "Dr. Quantum visits Flatland" link you put up has a segment where the Doc shows what the Flatlanders see when he puts his finger through their world, but he still shows what it would look like from a top view, or a third dimension. Try and imagine what you would see if you were at that intersection: an impassable barrier, obscuring your view on that one side, appearing virtually out of nowhere. And a point could even be considered a sphere, couldn't it? And then, which I don't want to do, is go subdimensional, relative to the point-sphere. I'm three posts away from a time-travel-paradox-induced headache.
I don't think a point would be a sphere because it would have to have some radius which would extend it to three dimensions.
But how do you describe a point? We can't, because we live in a three-dimensional existence. Maca is probably closer with a circle, but to us, a point is still a definable geographical representation, even though (in terms of zero-dimensionality - I'm conceding that point, Sam), it isn't. So a point is simply the "zen" of dimensions. It can't actually be seen, because to be seen implies an object to be possessed of dimensions. It just is. So to truly achieve inner peace, to be one with everything, you have to go smaller, instead of bigger?
I don't know what your getting at with "achieving inner peace" but to me, a point is simply a mathematical representation of a position in space. There's as much mystery in contemplating points as there is in contemplating infinity.
Meh, I guess I'm just reading too much into it. But a point doesn't exist in three-dimensional terms, right? It has no depth, height, or width, it simply exists. The whole "inner peace" spiel was just to illustrate an acceptance of that which can't be truly identified, or whatever, in our Universe.
I would say that a point does exist in three dimensions, three dimensional space is made up of points. Take Cartesian space for example. The origin is labeled as (0,0,0). There is a point (1,1,1) in that space as well as (x,y,z) points. You can connect lines between them. They can be connected through curves. These points don't have dimension in 3d space but collectively make up the space.
I was meaning the point itself doesn't have any dimensions, so a single point doesn't exist, but two points constitute a line, three constitute a plane, and so on, is that right? So the presence of a point is evidenced by its position in space relative to another point, which may or may not include the origin, is that right? And just to clarify, I'm not at all qualified to make any of these assumptions, I just piece together things well, and read a lot.
I would say that you're more than qualified to ponder. A point on its own, would have no dimension I suppose but I don't think the existence of that point is dependent on its dimension. If you just had a point and no others, that space would have no dimensions (i.e. it would have no degrees of freedom) but it is still there, existing in its space.
I never want to hear you say degrees of freedom ever again....ever. Brings about bad memories and....ugh.