frish's paradox

first blog! boooosh! 21st century, here i come!! forgive my excitement everyone but this is truly a momentous event not only for me but indeed for everyone on the interwebs. for the first time, i shall grace the ignorant masses with brilliance and eloquence generously poured from the deep and heavy bucket of wisdom that is my brain into the dixie cups of stupidity you people con off as a noggin.

wow, no one is friggan gonna read these…

okay, okay… so the paradox i am about to propose to you isn’t technically called frish’s paradox. some douchebag named zeno apparently thought of it like 32 million years ago or something and it’s really called zeno’s paradox. i only found this out after i googled what was on my mind and stumbled upon a heart-braking wikipedia article reminding me yet again that there is no such thing as an original thought left in this world… awesome.

this paradox managed to squeeze its way into my head during philosophy class somewhere between trying to disprove skepticism and asserting universal determinism. haha… big words make me sounds smart. anyways, this is the thought i had:

say that i extend my arm in a punching motion straight out from my chest. for the sake of simplicity, let us imagine that my fist moves two feet in a straight line away from my body. now, in that motion of extension, before my fist could be fully extended at two feet, it had to first be extended away from my body by one foot at some point prior to its extension of two feet. it is not possible for my fist to reach the full extension of two feet if first it was not extended one foot. likewise, in order for my fist to be extended one foot, it must first at some point prior to being extended one foot be extended from my chest by one inch. it is not possible for my fist to be in the position of being one foot away from my chest in this scenario if it was never extended first by one inch. i think you can all feel where this pattern is leading…

if we assume that distance is infinitely divisible, the pattern never ends and there is always a smaller distance that must be reached before a movement can be extended any farther. the problem i run into then, is how can we make that initial movement, that smallest little movement of extension, if we have to first be extended by even a smaller distance, and yet a smaller distance before that, and a smaller distance before that, ad infinitum?

the obvious implication of this paradox is that motion is not possible because a movement through space can never begin. however, it would seem that even a most casual observation of the universe is enough to contest that even though this paradox seems to present us with the only conclusion that motion is not possible, things do in fact move.

after thinking about it for a bit, i decided that there are only two ways to get around this paradox. the first solution would be to assert that there is in fact a smallest degree of movement, a smallest unit of space, that something can move through that acts as the basis for all greater movement. if this were true, we wouldn’t need to reach any smaller extension before reaching this smallest level of extension because by definition, no smaller extension exists. i honestly don’t know how realistic this idea is though… the second “solution” is to somehow change our understanding of space or perhaps just our understanding of movement through space. maybe time is involved somehow… i dunno.

anyways, in the little wikipedia article mentioned earlier (you know, the heart-breaking one), an interesting theory by a philosopher by the name of peter lynds is proposed as another solution. he says that “an object in relative motion cannot have a determined relative position (for if it did, it would not be motion), and so cannot have its motion fractionally dissected as though it does as in the paradoxes.” in other words, you cannot say that your fist must be extended by one foot before it can be extended by two because while it is in motion it literally cannot be said to have any extension from anything at all. i’m not sure i fully understand how he is defining motion here but i certainly think his theory very interesting and definitely challenges the way i understand space and motion.

so pretty much right now i’m stuck trying to think of a better solution to this problem than mr. lynds', cuz honestly, i think his solution is just a way of dancing around definitions. oh, and if you decide to talk about this paradox say at the dinner table, or at school, or at a funeral, or whatever… if you referred to it as frish’s paradox, it would really just be a small thing you can do to help make the world a better place. thanks for reading!
here’s the wikipedia article on several of zeno’s paradoxes and proposed solutions:

http://en.wikipedia.org/wiki/Zeno%27s_paradoxes