Thanks, Your sentence within the tags looks the same as mine, but yours shows up and mine doesn't.![]()
Now I just have to feel all sad that a material that once was prized for arrowheads 'n' stuff is being used to "grit the path".
Infinity (meh). If you just happen to find an infinitely long straight line in space, a line that stretches without limitation or an end in both directions, is it possible to add a bit of extra length to the line and thereby make it a larger infinity, aka, Cantor?
There isn't an end to the line to add onto.Infinity (meh). If you just happen to find an infinitely long straight line in space, a line that stretches without limitation or an end in both directions, is it possible to add a bit of extra length to the line and thereby make it a larger infinity, aka, Cantor?
There isn't an end to the line to add onto.Infinity (meh). If you just happen to find an infinitely long straight line in space, a line that stretches without limitation or an end in both directions, is it possible to add a bit of extra length to the line and thereby make it a larger infinity, aka, Cantor?
What you can do is have every infinitesimal segment of the line grow at all times (becoming non infinitesimal) and then have the now finite segment's infinitesimal segments grow finite, etc. etc. with a steady expansion of the infinitely long line, at a steadily increasing pace.
Now, if you had a multidimensional, infinite object, expanding in all directions from all points at all times, with a bit of randomness thrown into the expansion, and various interference patterns created by varying rates of expansion (perhaps expansion along certain paths), with a bit of conscious awareness and desire thrown into it... who knows what you'd get.
There isn't an end to the line to add onto.
What you can do is have every infinitesimal segment of the line grow at all times (becoming non infinitesimal) and then have the now finite segment's infinitesimal segments grow finite, etc. etc. with a steady expansion of the infinitely long line, at a steadily increasing pace.
Now, if you had a multidimensional, infinite object, expanding in all directions from all points at all times, with a bit of randomness thrown into the expansion, and various interference patterns created by varying rates of expansion (perhaps expansion along certain paths), with a bit of conscious awareness and desire thrown into it... who knows what you'd get.
The problem of my little mind exercise is; the line, being infinite, it has no end in either direction, stretching forever in both directions (rather than being potentially infinite, a so called Cantor's 'infinity'), I can't imagine such a line expanding. Where would any particular section expand into? Nor are there loose ends at either end to expand, or grow. There are no 'ends' Apparently, its size (length) cannot be increased.
It would be a stretching operation performed on finite portions marked out on the line with a standard rule (1 meter), so a segment with finite length 1 meter would end up being 2 meters. This doesn't increase the total size of the line, it instead modifies it compared to a standard measurement.There isn't an end to the line to add onto.
What you can do is have every infinitesimal segment of the line grow at all times (becoming non infinitesimal) and then have the now finite segment's infinitesimal segments grow finite, etc. etc. with a steady expansion of the infinitely long line, at a steadily increasing pace.
Now, if you had a multidimensional, infinite object, expanding in all directions from all points at all times, with a bit of randomness thrown into the expansion, and various interference patterns created by varying rates of expansion (perhaps expansion along certain paths), with a bit of conscious awareness and desire thrown into it... who knows what you'd get.
The problem of my little mind exercise is; the line, being infinite, it has no end in either direction, stretching forever in both directions (rather than being potentially infinite, a so called Cantor's 'infinity'), I can't imagine such a line expanding. Where would any particular section expand into? Nor are there loose ends at either end to expand, or grow. There are no 'ends' Apparently, its size (length) cannot be increased.
What is colloquial is determined by the locution location.Your (and most peoples') main issue is that you're using colloquial terms to describe something that is subtle, and doesn't lend itself well to description in colloquial terms.
The problem of my little mind exercise is; the line, being infinite, it has no end in either direction, stretching forever in both directions (rather than being potentially infinite, a so called Cantor's 'infinity'), I can't imagine such a line expanding. Where would any particular section expand into? Nor are there loose ends at either end to expand, or grow. There are no 'ends' Apparently, its size (length) cannot be increased.
Your (and most peoples') main issue is that you're using colloquial terms to describe something that is subtle, and doesn't lend itself well to description in colloquial terms.
For example. there are no endpoints to the interval (0,1), but you probably won't complain too much if I make that interval longer. It also isn't too hard to find a map from (0,1) to (0,1) where every point gets farther apart from every other point. The resulting interval is the same, but it has arguably been 'expanded'.
It also isn't too hard to find a map from (0,1) to (0,1) where every point gets farther apart from every other point.
There isn't an end to the line to add onto.Infinity (meh). If you just happen to find an infinitely long straight line in space, a line that stretches without limitation or an end in both directions, is it possible to add a bit of extra length to the line and thereby make it a larger infinity, aka, Cantor?
What you can do is have every infinitesimal segment of the line grow at all times (becoming non infinitesimal) and then have the now finite segment's infinitesimal segments grow finite, etc. etc. with a steady expansion of the infinitely long line, at a steadily increasing pace.
Now, if you had a multidimensional, infinite object, expanding in all directions from all points at all times, with a bit of randomness thrown into the expansion, and various interference patterns created by varying rates of expansion (perhaps expansion along certain paths), with a bit of conscious awareness and desire thrown into it... who knows what you'd get.
There isn't an end to the line to add onto.
What you can do is have every infinitesimal segment of the line grow at all times (becoming non infinitesimal) and then have the now finite segment's infinitesimal segments grow finite, etc. etc. with a steady expansion of the infinitely long line, at a steadily increasing pace.
Now, if you had a multidimensional, infinite object, expanding in all directions from all points at all times, with a bit of randomness thrown into the expansion, and various interference patterns created by varying rates of expansion (perhaps expansion along certain paths), with a bit of conscious awareness and desire thrown into it... who knows what you'd get.
You might get a thread like this, liable to go everywhichway at any infinitesimal moment.