On 2001-11-06 06:42, David Hall wrote:
I'm about as far from being a mathematician as can be <font size=-1>(this is a warning that I really don't know what I'm talking about here)</font>, but I've been thinking about it and I have an observation to make about the paradox of the infinite halves. Please tell me if I get anywhere close to having a legitimate point here. [img]/phpBB/images/smiles/icon_smile.gif[/img]
Doesn't the paradox require a continuous rate of movement? I.E, the action has to be something that can be infinitely divided up to begin with. In such a case, I can see a mathematical
paradox. But in most real-life situations, movement is not continuous, but is broken up into discrete units. Take, for example, footsteps.
As long as you are approaching the wall, you would have a constant velocity of x centimeters per unit of time, the distance and time it takes to make one stride. There is no way to break that down into halves. One step per second is one step per second. You can't say that the man suddenly is taking only half a step. In the end, there would always be a final point in which the distance to the wall is less than the length of one pace, and therefore the wall would be reached in that one final step, no matter what kind of halving goes on mathematically.
I think it's likely that all physical movement has to follow this discrete-interval type of movement, if only down to the Planck length. [img]/phpBB/images/smiles/icon_smile.gif[/img] In which case, the paradox becomes impossible in physical terms.
Ok, That's my thought. Now everybody is welcome to come piling onto me and show me what a real moron I am. What am I doing wrong here? Don't hold back. I'm ready for a whuppin. [img]/phpBB/images/smiles/icon_biggrin.gif[/img] [img]/phpBB/images/smiles/icon_biggrin.gif[/img] [img]/phpBB/images/smiles/icon_biggrin.gif[/img]