tag:blogger.com,1999:blog-701878382459611272.post442673022222765054..comments2023-08-15T06:32:58.350-05:00Comments on Philosophy KTL: How Chunky is Space?Amos Hunthttp://www.blogger.com/profile/00262758674894498892noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-701878382459611272.post-78250686036647157922010-02-16T00:12:15.837-06:002010-02-16T00:12:15.837-06:00I shall endeavor then to be more genuinely polemic...I shall endeavor then to be more genuinely polemical in the future. What I was apologizing for really was my pretense that I had foreseen your explanation, which is to say that perhaps I was apologizing only to myself, since I don't believe anyone else was aware that I was making any such pretense.<br /><br />But do you honestly mean to say, Sebastian, that there is no motion except in six cardinal directions?Amos Hunthttps://www.blogger.com/profile/00262758674894498892noreply@blogger.comtag:blogger.com,1999:blog-701878382459611272.post-86836708604421190822010-02-10T18:49:38.200-06:002010-02-10T18:49:38.200-06:00Yes, but Amos, the fact that you cannot measure th...Yes, but Amos, the fact that you cannot measure the distance without resorting to some smaller unit does not prove that the unit you are using to measure exists. Suppose I presented you with the following argument:<br /><br />There are 31,556,926 seconds in a year. Let us say that I have dividend income from investments in the amount of 30,000. This means that every second I make about 9/100 of a penny. Therefore, pennies must in fact be divided into hundredths.<br /><br />I think you will agree that this argument is flawed. The fact that a discrete quantity can be theoretically measured at a smaller level does not make the quantity any less discrete or the division "discovered" any more real. Thus it is with space. Granted that the hypotenuse is not a whole unit--all this means is that we must resort to fiction to quantitatively measure in the first place.<br /><br />Therefore I must conclude that your objection, clever as it is, happens to be wrong.<br /><br />Also, no apologies are necessary as to your tone. I hardly found it polemical, and I am (at any rate) a fan of polemics.Sebastianhttps://www.blogger.com/profile/06634050682365973346noreply@blogger.comtag:blogger.com,1999:blog-701878382459611272.post-68096606050782352322010-02-10T10:48:40.089-06:002010-02-10T10:48:40.089-06:00Sebastian, please excuse the polemical tone in my ...Sebastian, please excuse the polemical tone in my reply to your comment.Amos Hunthttps://www.blogger.com/profile/00262758674894498892noreply@blogger.comtag:blogger.com,1999:blog-701878382459611272.post-80522202996161982662010-02-09T23:54:23.509-06:002010-02-09T23:54:23.509-06:00The classical problem of the incommensurability of...The classical problem of the incommensurability of the hypotenuse of a triangle to the sides clearly refutes your explanation.<br /><br />No single three-dimensional shape reiterated through space could possibly answer to the description you give. Perhaps you will say that cubes serve the purpose? They do indeed, provided we only ever ask about the distance between two units of space which can be found on a line perpendicular to their adjacent plane surfaces. However, if I ask for the distance between two units in space arranged "around a corner" from each other, it will be impossible to give their distance in terms of the same basic unit. Instead, a further division of space will be necessary.Amos Hunthttps://www.blogger.com/profile/00262758674894498892noreply@blogger.comtag:blogger.com,1999:blog-701878382459611272.post-42970337552368885642010-02-09T18:51:37.909-06:002010-02-09T18:51:37.909-06:00Mr. Hunt,
While it may be that you have in fact d...Mr. Hunt,<br /><br />While it may be that you have in fact divined my conclusion, I would suggest that you have not sufficiently examined the possibility that the units are "at no distance from each other." Suppose we take a random smallest possible unit of space. This unit will be surrounded (most likely) by other equally small units. Since each unit abuts each other unit the distance between each unit from the edges will be zero. From the center the distance between any other unit's center will be exactly one unit, assuming that the units are all of the same shape and size.<br /><br />Thus the discreteness of space will still be preserved.Sebastianhttps://www.blogger.com/profile/06634050682365973346noreply@blogger.com