On Infinity

Actually I'm in calculus at the moment. I know what a limit is, at least in relation to lines and graphs, but I've never dealt much with sequences. What you're saying makes sense, but I wouldn't be able to prove it mathematically. I did, and I quite enjoyed it. Very strange.

Sounds like you were right, though, like Creavolution, I wouldn't say a line is finite on one end. It certainly has a starting point, but that doesn't make it finite. I remember someone (cavediver, I believe) called the sort of line you're describing as semi-infinite. And if you cut an infinite line in two points, you would have two semi-infinite lines and one finite line.But that's just infinite lines. Infinity itself is a whole different matter.

Yes, I have trouble conceptualizing "infinity itself" separately from an infinite "thing".

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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.

The interesting thing is that the semi-infinite line is "as big as" the infinite line. to see that, cut the semi-infinite line in an infinite number of pieces (each one a meter long), put all the odd ones together making a semi-infinite line, put all the even ones together making a second semi-infinite line, and finally tie both semi-infinite lines together making one infinite line

In the late 80’s I participated in the early versions of these message forums. They were dial-up bulletin boards. At the time they were the coolest way to communicate across the country. Douglas Adams was a regular on one of them. He was into “techno stuff” as he liked to call it.The “infinity” subject was as much debated there as has started here.Just like Ulan Colluphid’s blockbuster trilogy, “Where God Went Wrong,” “Some More of God’s Greatest Mistakes” and “Who Is This God Person, Anyway?” the “infinity” issue was a tweak on peoples’ tails. Adams, who was an ardent atheist, liked to poke fun in his trademark subtle way. He was well aware of the logic error in the “infinity” joke but was set on tickling some of his Oxford collogues.He used a lot of logical absurdities in his work. Gotta love it.Edited by AZPaul3, : No reason given.

What did he say about Tudwell's quote?

Ha! I should have known. Douglas Adams is a smart guy, and with as much illogic as there is in the rest of the book, it should have been obvious that it was a joke. But either way, it helped me gain a deeper understanding of the concept of infinity.

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.

Yeah, he did. He didn't reference any specific quotes from Adams himself, but he seems rather knowledgeable on the subject, so I take his word.

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.

The 'tweak on people's tails' did refer back to God, but only as a comparison. AZPaul3 wrote:

quote:

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Just like Ulan Colluphid’s blockbuster trilogy, “Where God Went Wrong,” “Some More of God’s Greatest Mistakes” and “Who Is This God Person, Anyway?” the “infinity” issue was a tweak on peoples’ tails.

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Emphasis mine. I think Paul was just saying, "Like the trilogy of books about God, the part on infinity was a joke."

Unfortunately Douglas Adams passed away in 2001.His most revered books, The Hitch Hicker's Guide to the Galaxy series, Dirk Gently, the Meaning of Liff, were ALL jest. He was a comedian. Sort of a David Berry kinda guy.None of his books were intended to be real. They were all SciFi comedy. Like Lewis Carroll, he used logic to the absurd.abe: The Ulan Colluphid books I cited were all figments of Adam's imagination.Edited by AZPaul3, : Well, I sort of thought I might explain something since it seemed to me that maybe, just maybe, some, not having taken the opportunity to enjoy said tomes, might not understand what it was to which, in my usual verbose and borderline cognitive way, I was referring, sorta.

If it turns out that infinity is just a figment of our imagination, i. e., the word is something like 'slithy tobes', it sounds like something that might exist but we're not sure and we have to get on with the poem, then Adams might just have (had) the best grasp of infinity of anyone.

You do realize don't you that you are quite incorrect about this?