Infinity may be mentioned more often, but indefinity is more closely that which can be achieved. It does not claim something as grandiose as infinity, yet it can still be immense beyond anyone's imagination.
And it is not to claim that indefinity can ever replace infinity in mathematics, since that is clearly false -- try to divide any number by 0. The answer is not indefinite, it is infinity. But indefinity is more of a description of physical reality, where a quantum entity is not a continuum, nor is space a continuum of zero sized points so much as a set of locations that are occupied by something that can be measured.
So, in the physical world, unless there are truly an infinite number of objects all exactly crammed into an exactly boundless space that is infinitely large, then there is only an indefinity.
Mentally, one can construct sentences that logically conjugate all the permutations of concepts, even resulting in infinite infinities, and so forth. Yet not a single infinity can be demonstrated in a physical way. There is in a sense a real, kinetic and participatory indefinity. There is only a potential abstraction with which to demonstrate infinity.
I would think of indefinity as being a worker class and infinity as being upper class. The upper class has loftier speech, but the worker class provides for the leisure to speak it -- indefinity is the coal which is burned to light the artwork. I would think that Mark Twain might have had a mite more respect for the lesser of the classes.
After all, what is infinity but an immensely large bag packed with an uncountably immense number of zeros?
And it is not to claim that indefinity can ever replace infinity in mathematics, since that is clearly false -- try to divide any number by 0. The answer is not indefinite, it is infinity. But indefinity is more of a description of physical reality, where a quantum entity is not a continuum, nor is space a continuum of zero sized points so much as a set of locations that are occupied by something that can be measured.
So, in the physical world, unless there are truly an infinite number of objects all exactly crammed into an exactly boundless space that is infinitely large, then there is only an indefinity.
Mentally, one can construct sentences that logically conjugate all the permutations of concepts, even resulting in infinite infinities, and so forth. Yet not a single infinity can be demonstrated in a physical way. There is in a sense a real, kinetic and participatory indefinity. There is only a potential abstraction with which to demonstrate infinity.
I would think of indefinity as being a worker class and infinity as being upper class. The upper class has loftier speech, but the worker class provides for the leisure to speak it -- indefinity is the coal which is burned to light the artwork. I would think that Mark Twain might have had a mite more respect for the lesser of the classes.
After all, what is infinity but an immensely large bag packed with an uncountably immense number of zeros?
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