On Infinity

When D. Adams said, “an infinite number of worlds, simply because there is an infinite amount of space for them . ” imagine that he was thinking that it is infinite divisibility (of space) that justified for him the word “simply”. In other words imagine matter that must take up some space in its place. The place of this space is always divisible, so picture a line between two parts of this space as an operation that Adams could always do. Thus no matter how large or small of local area of matter occupancy is there is , as per the assumption, always an infinte number of lines drawn in the “universe” of this ”infinite’ space. Thus the number of material “worlds” is equipollent with the number of divisions argued for. If space is infinitely divisible even starting with an infinite spread of matter in its places there can be an infinite number worlds or an infinite amount of smaller divisions if the initial size is not infinite.So, when Adams, said, “not every one of them is inhabited”, I took him to mean that on one side or the other of at least one division there is some location that is only the place of impenetrable matter and not necessarily having life, a particular kind of organized matter, in it, but as he said “not every one of them” he must have meant that for every division one could not make an orthogonal cut to ALL of the divisions (infinite) and find life in every one. That was what he started with.Therefore, as there are only marginal placements where life may exist, these must be a finite cut-up of the original size no matter what size it is. In this way life only exists at a finite number of locations.I think this reasoning may be more than simply a mind game.I have begun to sketch how Panbiogeography via evolutionary graph theory may indeed justify thoughts about both the infinite (here the dashed lines indicate the infinite divisions of Adams etc) and finite variety. I would simply disagree with Adams that it can not be thought that life is not “in” every one of an infinte number of separations of physics’ space. What is required is a clear notion of a right angle biologically. This seems possible where graph theory may draw a topology that is not on geodesics. I have not proved this yet even for the fusion of the two kinds of graph theory I introduce here:http://axiompanbiog.com/vcarandtclaim.aspxWhat is required as a prerequisite in the thought is to show that Moran processes and HW equilibrium converge for a given track claim but because Panbiogeography do not guarantee equal weights the cause and correlation must be specified “into” the physics somewhat, which we were only assuming in Adams’ case (an infinite amount of space) (this *may* be a linguistic infinity of deep structure instead in reality).You could be correct if the space infinitly overdetermines the places the matter exists in the space but I take it Adams precluded that when he wrote "NOT EVERY"*****ONE*****. I took that to indicate that matter created the oneness but space bounded it, like Newton that Earth may be thought dynamically to a point(one earth- one point).

You know of course that one can add a finte number onto an infinite one and although this may be the same cardinal it can be a different ordinal number.Thinking about infinity is a bit like metaphyics. One must keep track not only of the current point one is on about but also the means taken to achieve the currency that got one to the strech one is considering.I think that Adams specified a specific way towards his conclusion. You seem to be thinking about infinity sans how one gets to an infinite thought itself, thus without the finite base from which Adams or you started the paradoxes threw off your sense of the perception itself. Just a guess.

What did he say about Tudwell's quote?

Az has not said that your quote IS a joke.I recall being puzzled by an Adams writing years ago, so I would like to know for sure what Adams said about your selection.It may be that all jokes aside, something can be gained when people who do not think infinity can be applied attempt to ply it's approach to reality.

Your quote was

quote:

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It is known that there are an infinite number of worlds, simply because there is an infinite amount of space for them to be in. However, not every one of them is inhabited. Therefore, there must be a finite number of inhabited worlds.

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"tweak on people's tails" referred back to "GOD" somehow or if at all. Your quote above, DID NOT!Cantor's reponse to Russell was very lengthy and not well considered in writing (Cantor went to see Russell and presented him with an extremely marginalized writing that Russell rejected somewhat) but the distinction of absolute and actual infinity is real enough for mathematicians.It seems to me your quote of Adams can be read in terms of actual infinities while the weak portion your cited may refer to absolute infinity and God but then I would go with yard of Russell's shoelaces and THEN show that because no one has said how a "tail" is related to point sets that is premature to use GOD TALK to determine where potential infinity gives way to the actual. This seems possible to me.Cantor was suggesting relations to Opticks actually and Soma is a long way from that. But no one has taken the possiblity beyond his barely cognizable artistic judgment that a painting (think- Writing on Infinity) and a symphony (think harmony of nature's laws) may NOT have the same infinity abstracted from them. Of course Frege was confident that no one would grab some sand and determine a transfinite thought with it but then again no one has gone beyond Russell's shoehotel of logic into one that with Kant could exist and which biologists may find perceptive for its current difference of geneotype and phenotype.

Yes, I do have a problem with leaving out words sometimes, but this time I am in Miami and the sand turned into a broken glass bottle that cut my foot. Too bad for Answers himself. I have no notion that I AM incorrect here, there will be no edit, only South Beach!!

It is in the forms...types, not the words I think.