uwot wrote: ↑Mon May 06, 2019 2:37 pm
Scott Mayers wrote: ↑Sun May 05, 2019 3:59 pmDoes this at least answer the question of "dimension" for my perspective that you can understand?
Gotta admit, I'm struggling. As far as I can gather, you are describing a 'dimension' as any route between two points. Again, correct me if I'm wrong. I think your approach shows the difference in our background. From a philosophical point of view, I get that mathematics can describe "lines", but the question that leaps out is 'Lines in what?' That's ontology for you. It's metaphysics, so superfluous to maths and physics, string theory which you mention, simply posits strings without saying what they are strings 'of'. Or what keeps them vibrating for nearly 14 billion years.
So, matter is curved lines? What keeps them curved?
First, note Newton's first law and how Einstein adapted this in his theory. Newton's concept treats all change as occurring in only straight lines as "normal". In GR, Einstein added that space can 'curve'. THIS doesn't specify WHAT occurs of things relative to themselves but to matter. So, light, for instance, is treated as following a curved path relative to some mass which is presumed as warping space. This is identical to stating that straight lines are not the ONLY 'normal' paths but that curves are also 'normal' with respect to mass.
What I do is add 'spins' as a dimensional factor by the perspective of those things that move through space. NOW normally things even spinning will still move in straight paths. BUT this is because they are limited to the lowest dimensions they happen to be in until something prevents them from resuming their normal straight-line paths. IF something cannot move in straight lines for ANY reason AND no point in space cannot not move, then a 'spin' factor can be added as a novel dimension in its own right. But the spin is at the level of the points of space themselves. Then the PATH still follows the rules of limitations of things moving in straight lines: nothing can go faster than the speed of 'light'. The speed, not the velocity is conserved.
So even in Einsteins' 'warped' space, light still transitions through it at the same speed but what is 'lost' linearly is gained by 'spin'.
This is just a matter of perspective. But Einstein's theory doesn't concern itself directly with the atomic level of particles themselves AND have a problem explaining how things like electrons don't fall into its nucleus. To me 'warped space' lacks theoretical expansion upon what it nor matter is. Thus, I am saying that mass is what causes the curvature illusively, fit to Einstein's theory BUT that the reality can be explained better and inclusive of matter itself if we treat spin as a factor that occurs in greater dimensions.
Now when something moves inertial, it IS in only one specific dimension even while other dimensions exist. Relative to something moving, it only persists as though that straight-lined path is ALL that exists relative to itself UNLESS something interferes to its transition through space. Then, if 'forced' to change, it takes the SIMPLEST dimensional change UP from where it is in. The optional directions are always perpendicular to the line of its normal path.
BUT, if something is prevented from moving to the first perpendicular direction based upon the forces imposed on such objects, it has to SKIP to the next higher dimension.
Note too that while we think of space as having 3 dimensions ignoring time or other factors assumed to NOT be in this space, it begs why '3' has some significance over binary options. The way I expressed it in the last post, a point itself is a dimension. THEN the second dimension is the line. Then think of the lines as wholes that extend perpendicular to itself to form a plane, this plane would then have for each line, two surrounding lines on either side of it for every line in a given plane. For the next higher dimension, it treats the whole plane as a unit and then a 3-D space is symmetric planes such that for every plane in this 3-D space has the property that it is symmetric in a binary way.
The next dimension up is not 'time' per se but velocity. And this can be expressed as a point jumping OVER a point tangent to it to its 'next' position. The 'points' are actually shells of a spherical locus of points. Because it cannot take all the points in each consecutive sphere outward, each possible point on these exist in independent worlds. But only one of two points (for symmetry) exist to each possible world from each point.
I have models I've created but cannot draw them yet (I need to figure out some graphics programming with more advanced calculus to eventually do this.) What I can do is formulate HOW one can do it for themselves and what the last post does. If you took care and have a good 'graphic' capacity to think of dimensions greater than 3, these are of change themselves in some way. The first kinds of changes are velocity, then acceleration. Then, since curves are also acceleration, this is just another kind of dimension. These are at the level of 'matter' and coexist in our space.
I know that I'm not doing it justice in this explanation as I'd like. I have shown some friends but it is dynamic. That is, I can't just draw merely one static model to represent this but have to present this in time to follow completely until I can find some means to model this using complex dynamic graphics on computers. [But I can try if you are patient. I literally had a lot of time to be able to do this first in my own head beforehand and so don't think I could summarize it simplistically.]
And so to at least the last question, what keeps them moving in curves?...they are moving in 'straight' lines relative to itself but appears as curves to us. Picture the three dimensions of space in just the Cartesian plane, Then to visualize the next SET of dimensions, imagine holding the origin in place and twisting the x, y, and z axis symmetric to each of its dimensions. For just the x, y dimensions, this will appear as two intersecting spirals from the origin perpendicular to each other (orthogonal, is the better word if you know this). [hint: they form what looks like your 'whirlpool' images and what I related to your means of selecting images.]