Are some infinities bigger than others?
|February 15, 2018||Posted by News under Cosmology, Intelligent Design, Mathematics, Philosophy|
It turns out that the set of all points on a continuous line is a bigger infinity than the natural numbers; mathematicians say there is an uncountably infinite number of points on the line (and in three-dimensional space). You simply can’t match up each point on the line with the natural numbers in a one-to-one correspondence.
If it is continuous (and some physicists think it may not be) then it will contain an uncountably infinite number of points. But that doesn’t mean it has to go on forever. As Einstein discovered, it may be curved in on itself to form a finite volume. More.
One would have thought that once we get involved with infinities, we are skirting the boundaries of measurement—at best.
See also: God as a necessary, maximally great, endless being vs. the challenge to an actual infinity
Reader: Weirdness of infinity shows that the universe is not infinitely old
Durston and Craig on an infinite temporal past . . .
At Quanta: Is infinity real?
Cosmologist: In an infinite multiverse, physics loses its ability to make predictions. And that’s okay.