Verrrrrrrrry well stated. The 3rd panel doesn't worry me as it almost certainly approaches a limit, or at least my Calculus classes 30 years ago would lead me to believe that.
I've written a number of recursive algorithms, fractals included, and calculating area usage is a matter of finding...
Clever compound cartoon...Dying to figure out the formula to calculate the ink used.
There is a strange compound nature to this that I can *almost* calculate. This is just something nagging at me.
Take a look at this (IMHO) extremely clever cartoon...
Yes, well again, it's not because it's how I view the universe, it's an analogy involving something and a bend. This conversation got derailed by jumping on this as if it were an analogy of the universe, when I was trying to make it an analogy of causality not being causality.
Maybe I should...
What's poetic? You seem angry.
There's nothing mystical about, say, a 4D surface of a 5D balloon, nor the topological way of discovering it's "shape". Heck, people used to scratch their heads at walking north and getting closer to each other. But that analogy I used was just another magic...
If that's the case, and the "yes" is reassurring, then broadening this to all of physics:
Is it the case that whenever "thing" A (in our case, mass/momentum/etc) cannot exist without "effect" B, and "effect" B cannot exist without "thing" A, is it unreasonable to assume (generally) that "thing"...
Not quite. For #1 above, I'm already assuming (correctly or incorrectly) that a depression in spacetime *is* gravity. For #2 above, I'm already assuming that if the 4D low spot were created another way that it would draw objects toward its center.
The question is: is bent space actually...
Entirely incorrect. It's entirely valid to use an absurd postulation as an alternative way of explaining a prior question about something real. The notion of a "magic wand" has *nothing* to do with a magic wand per se. The question is not about magic, nor is it in particular "what does a...
Quick note on this. In all things, it's easiest for me to view time as just another dimension---makes more sense to me. So I'm assuming that bending space along anyone of the (for now, say 4) axes will beget (or be) gravity.
So given my magic wand: would'nt the external forces act on that bent region as if there were a mass there? <----broken way of saying it, I'll rephrase.
It sounds as if you both are in concert with that there are things that can act upon a mass independent of gravity. I suppose I have to...
It's fairly easily to visualize space bending as a result of the mass of an object, and that the bending of space is effectively gravity.
But if mass always results in bending space (how else could it hold it in this universe?), is it possible that mass and the bending of space is precisely...
Now you've nailed the semantic(?) problem. WHAT line, WHERE?
The one from (x1) to (x2)?
Or the one from (x1,y1) to (x2,y2)?
Or the one from (x1,y1,z1) to (x2,y2,z2)?
The first two don't tell me enough if in 3D space. (?)
If I'm frustrating anyone, please tell me. I'm still not...
[...returning...]
A parabola would be 2 dimensional because it cannot be described (shape and position) without both dimensions.
But in a 3 dimensional space it would have to be 3 dimensions to be able to fully describe the shape or position of it. A line, even along the face of a cube is...
As a software engineer for over 20 years I can tell you a few things. Not in order and forgive me for the hyperbole.
1. I would absolutely suggest *not* getting hired by a large company. Larger companies more often than not simply do not require you to wear enough hats. Further small...
Interesting. Basically N dimensions means that I need N pieces of information (cartesian coordinates, polar coordinates, or whatever) to find something within it. No?
...by which you reason that only 2 coordinates are needed with a 2 dimensional manifold regardless of whatever N dimensional...