“I can’t tell you how frustrated I am that after a couple of millennia, no one has effectively resolved Zeno’s paradox. So, I’m asking you, here, now, is space divisible or continuous? Between you and the computer or smart device where these words appear, is there a unified smoothness? Are there units of space?
“Does my confusion arise because I always link, but not in an Einsteinian way, space and time. Moving through space always takes me time, and I have a sense that I can divide time into nanoseconds. At any nanosecond or smaller unit, am I stationary in a spot, just the way a photo captures a single position of a runner? Frozen, as we say, in time and in a particular position in space. But that raises another question. What is the runner? If the runner occupies space and space is discontinuous, is the runner a whole? If space is discontinuous, is the runner a series of spatial units that we see as a whole because the brain is trained?
“See, I’m not very good at this. If the quantum physicists tell us that there is a foam of virtual particles coming into and going out of existence so that the vacuum of space isn’t really a vacuum, then in the 'position' where any virtual particle comes into existence—is that a unit? What’s with that paradox that keeps the brightest minds from resolving for us commoners what space is?
“I think continuum when I think of my life, but I know that a picture of me as a child seems to portray a unit I no longer am. Kindergarten me isn’t adult me. The link is merely one of my memory that imposes continuity of person. But if I impose that continuity on myself, do I not impose continuity on space, also? Then, like looking at that old photograph, is my looking at space an imposition of the brain? Is all movement just a series of saccades? That would make Zeno happy.
“I’ll grant that the divisibility of space doesn’t occupy my mind when I go to the store for bread, milk, and eggs. But in that trip, I am aware that I move in time and space, or that’s what I believe I do. And the trip seems both continuous and disjointed, every traffic light a punctuation mark on smoothness, every transmission shift, also. Any slight hesitation makes a unit.
“Common sense tells me that regardless of the paradox, I can reach the store. I don’t see myself going half the distance, half the remaining distance, half that remaining distance, ad infinitum. I get the bread, milk, and eggs, and return. The apparent smoothness of space becomes for me the real smoothness evidence by the completion of my trip.
“And yet, I’m still bothered by the possibility that the universe is discontinuous. It’s vegetable soup, not clear broth. And I’m bothered by the quantum foam and the virtual particles. Is space the matrix of matter or matter the matrix of space. Is motion through a continuum the way of the world, or is motion an illusion as Zeno argued?
“I just thought I’d bother you with the old problem to make you reassess your inferences and assumptions as you go about your day ‘moving through continuous space’ in measurable units of time. Or, should I say, ‘moving through continuous time’ by crossing measurable units of space?”
“Does my confusion arise because I always link, but not in an Einsteinian way, space and time. Moving through space always takes me time, and I have a sense that I can divide time into nanoseconds. At any nanosecond or smaller unit, am I stationary in a spot, just the way a photo captures a single position of a runner? Frozen, as we say, in time and in a particular position in space. But that raises another question. What is the runner? If the runner occupies space and space is discontinuous, is the runner a whole? If space is discontinuous, is the runner a series of spatial units that we see as a whole because the brain is trained?
“See, I’m not very good at this. If the quantum physicists tell us that there is a foam of virtual particles coming into and going out of existence so that the vacuum of space isn’t really a vacuum, then in the 'position' where any virtual particle comes into existence—is that a unit? What’s with that paradox that keeps the brightest minds from resolving for us commoners what space is?
“I think continuum when I think of my life, but I know that a picture of me as a child seems to portray a unit I no longer am. Kindergarten me isn’t adult me. The link is merely one of my memory that imposes continuity of person. But if I impose that continuity on myself, do I not impose continuity on space, also? Then, like looking at that old photograph, is my looking at space an imposition of the brain? Is all movement just a series of saccades? That would make Zeno happy.
“I’ll grant that the divisibility of space doesn’t occupy my mind when I go to the store for bread, milk, and eggs. But in that trip, I am aware that I move in time and space, or that’s what I believe I do. And the trip seems both continuous and disjointed, every traffic light a punctuation mark on smoothness, every transmission shift, also. Any slight hesitation makes a unit.
“Common sense tells me that regardless of the paradox, I can reach the store. I don’t see myself going half the distance, half the remaining distance, half that remaining distance, ad infinitum. I get the bread, milk, and eggs, and return. The apparent smoothness of space becomes for me the real smoothness evidence by the completion of my trip.
“And yet, I’m still bothered by the possibility that the universe is discontinuous. It’s vegetable soup, not clear broth. And I’m bothered by the quantum foam and the virtual particles. Is space the matrix of matter or matter the matrix of space. Is motion through a continuum the way of the world, or is motion an illusion as Zeno argued?
“I just thought I’d bother you with the old problem to make you reassess your inferences and assumptions as you go about your day ‘moving through continuous space’ in measurable units of time. Or, should I say, ‘moving through continuous time’ by crossing measurable units of space?”
RSS Feed