Paradox. I guess two docs are better than one, eh? (Heh-heh.)
I just finished the article by Nick Hugget at http://plato.stanford.edu/entries/paradox-zeno/. Sometimes I wonder whether my brain is half the size of someone like Hugget or if I'm just not utilizing what is there. Either way, the result is the same! I simply confess that, though I understand Zeno's paradox, I just don't understand Hugget's explanation in standard OR non-standard mathematics. I applaud those who do! What does seem clear to me, however, is that the current space/time continuum is what it is, and I find it interesting that we are ever in search of how it operates (e.g., has anyone read something of the Haldron Collider located on the border of Switzerland/France lately?) Anyway, the most sensible thing I read in the Hugget article was the following:
“Our belief that the mathematical theory of infinity describes space and time is justified to the extent that the laws of physics assume that it does, and to the extent that those laws are themselves confirmed by experience. While it is true that almost all physical theories assume that space and time do indeed have the structure of the continuum, it is also the case that quantum theories of gravity likely imply that they do not. While no one really knows where this research will ultimately lead, it is quite possible that space and time will turn out, at the most fundamental level, to be quite unlike the mathematical continuum that we have assumed here.”
Two thoughts: (1) science tells us that the universe is currently expanding, so my question is what is outside of the current universe? If we could reach there, would it have the same properties as our space/time continuum? (2) Could it be that what is outside of our space/time continuum is what we define as the present; i.e., outside the constraints of time & space? If so, are we somehow connected to it?
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Wow... Some really interesting thoughts here. I unfortunately know next to nothing about the space-time continuum (or whatever it turns out to be!). But I like your thought about the borders being something like the present, which in many ways doesn't seem to exist.
ReplyDeleteYour thoughts about the limits of space and time being something like the present, which we experience as persons all the time but cannot "pin down," as it were, made me think of some of Kant's thoughts about space and time.
In short, these two things, for Kant, were only realities within human subjects. Space and time were subjective conditions for the possibility of anything appearing to our senses at all as an object. We simply have to conceive of any being (thing) as in space and time, and this raises interesting questions about some of the stuff you are on about above. Kant thought that it was a mistake to think of space and time as something "outside" us, but rather as features necessary to our cogntion and perception of anything.
Interesting stuff!