Do the points on a line touch?

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― Alan (Alan), Wednesday, 26 November 2003 12:21 (twenty-two years ago)

only the ones that are in love.

― neil simpson (neil simpson), Wednesday, 26 November 2003 12:23 (twenty-two years ago)

You can walk down them, if that's what you mean.

― Andrew Farrell (afarrell), Wednesday, 26 November 2003 12:25 (twenty-two years ago)

I read a book that said they DO and it is because of irrational numbers. Then again the book also said x=msd*(?? = power of three so god knows.

― Sarah (starry), Wednesday, 26 November 2003 12:26 (twenty-two years ago)

what book?

― Alan (Alan), Wednesday, 26 November 2003 12:34 (twenty-two years ago)

~~Topsy and Tim Go Swimming~~.

Actually I believe it is my grebt popular Maths book about INFINITY: called The Mystery of the Aleph, the Kabbalah and the Search for Infinity, or some variant thereof. It is rather good but becomes completely impenetrable to my thick skull a good way in.

― Sarah (starry), Wednesday, 26 November 2003 12:36 (twenty-two years ago)

On the one hand, you can't find two points that touch because there will always be a gap between them. On the other hand, there will always be another point in that gap.

― Andrew Farrell (afarrell), Wednesday, 26 November 2003 12:37 (twenty-two years ago)

His theory was that without irrational numbers on the number line, you'd see a line sure but there would be infinitely many little "holes".

― Sarah (starry), Wednesday, 26 November 2003 12:37 (twenty-two years ago)

.. in the line.

Or something. This is from one of the bits which didn't utterly lose me but I wouldn't take my word on it.

― Sarah (starry), Wednesday, 26 November 2003 12:39 (twenty-two years ago)

do you still have that book?

― Alan (Alan), Wednesday, 26 November 2003 12:41 (twenty-two years ago)

What if the ball is out.

That book sounds like the kind of fodder that would make my head burn up in RAYGE.

― Pete (Pete), Wednesday, 26 November 2003 12:43 (twenty-two years ago)

Well, apart from yon rational numbers, the other numbers can be split into the ones that you can describe as a solution to an equation (like the square root of two, which is just x^2 = 2, easy peasy) and the transcendental numbers, which just ... are. Like e, and pi, and theis new number I came up with called Bob. Bob goes 1.3354438883893482555...I can keep this up all day you know...233244298867498...

― Andrew Farrell (afarrell), Wednesday, 26 November 2003 12:46 (twenty-two years ago)

You'd think Pete, but there's only a teeny tiny bit about the Kabbalah and that's quite FUN! It is not my other popular maths book from which I decided Cantor was a benny (I think I may have changed my opinion on this).

Alang yes I do, you can borrow if you want - also I can give you your N64 back - I've not finished Zelda but I have had it for ages and I guess I can play the version on the gamecube...

― Sarah (starry), Wednesday, 26 November 2003 12:46 (twenty-two years ago)

Pete, you would probably be some happier with the Lakoff book on maffs I just finished with.

― Alan (Alan), Wednesday, 26 November 2003 12:46 (twenty-two years ago)

sarah, ha ha I was playing zelda ooT on my GC only last night - it's still stands up against recent games in all but graphic resolution.

― Alan (Alan), Wednesday, 26 November 2003 12:48 (twenty-two years ago)

Cantor was a Benny. And that hotel of his will never be clean.

I have a Lakoff interest in this subject (ho ho).

― Pete (Pete), Wednesday, 26 November 2003 12:54 (twenty-two years ago)

I was told that a line is infinitly small in all but one direction (and obviously the opposite direction), and a point is infinitly small in all directions.

― Johnney B (Johnney B), Wednesday, 26 November 2003 12:54 (twenty-two years ago)

Think is that these are imaginary points and imaginary lines so depending on how you define your imaginary terms a line could be made up of points, or a discontinuity of points (points within points).

― Pete (Pete), Wednesday, 26 November 2003 13:00 (twenty-two years ago)

yeah, it depends how you define your points and your lines.

and how you define touch.

― ken c, Wednesday, 26 November 2003 15:21 (twenty-two years ago)

I remember Terry Griffiths once using these kinds of argument to dispute a ref's touching ball judgement.

― Eyeball Kicks (Eyeball Kicks), Wednesday, 26 November 2003 15:32 (twenty-two years ago)

i wish i were there to hear that, he has the best accent ever.

― ken c, Wednesday, 26 November 2003 15:38 (twenty-two years ago)

Touching ball rule though is merely reerees being nice to the fella. Ie if you play it in that direction it will be a push shot and I'll hafta do you. Sonny.

― Pete (Pete), Wednesday, 26 November 2003 17:34 (twenty-two years ago)

I really thought this was going to be about American football.

― Dan Perry (Dan Perry), Wednesday, 26 November 2003 17:38 (twenty-two years ago)

Points on a line are purely intellectual inventions. As such, they conform exactly to their definition. Part of the definition of a point is that it exists in one dimension only. One upshot of this definition is that points cannot "touch", because they have no surface area. However, they can and do exist infinitely near to one another.

Don't worry if this does not make any sense in a physical world. Euclid never worried about such trivialities.

― Aimless, Wednesday, 26 November 2003 17:58 (twenty-two years ago)

I thought points existed in no dimensions? Unless the scientific world has finally come around to my long-held belief that the first dimension should be time.

― nabiscothingy, Wednesday, 26 November 2003 18:01 (twenty-two years ago)

Time is DIMENSION ZERO.

― Pete (Pete), Wednesday, 26 November 2003 18:02 (twenty-two years ago)

nabisco otm.

― Sterling Clover (s_clover), Wednesday, 26 November 2003 18:04 (twenty-two years ago)

Except inasmuch as the ordering of dimensions is arbitrary; points don't exist in time, generally speaking.

― Casuistry (Chris P), Wednesday, 26 November 2003 18:07 (twenty-two years ago)

Yes, nabisco is right about the zero dimensionality of points. I misspoke. The first dimension is extension == lines.

― Aimless, Wednesday, 26 November 2003 18:07 (twenty-two years ago)

Anyway I know nothing about this stuff but I like to think that things with no dimensions can't touch. Because what's "touching?" There's nothing there to touch. Touching has a physicality and a senuality to it, and points don't have bodies. They don't get to rub up against one another and make pleased noises. In this sense maybe they're like a metaphor. There they are. We want to think of them as "part" of the line, but they're not, because they have no substance. We want them to touch, to interrelate, to form a community, but no. It's, you know, tragic. Like the whole Xeno / Achilles thing. Achilles will never win the race! He will forever subdivide the difference but he can never actually achieve what he's destined to achieve!

In this sense I think that points and lines are beautiful and sad and we should keep them that way: let's not cobble together some practical easier-to-imagine Hollywood ending where suddenly they all get to touch.

― nabiscothingy, Wednesday, 26 November 2003 18:18 (twenty-two years ago)

"I can feel" - TM Bride Of Pinbot. (Pointbot)

― Pete (Pete), Wednesday, 26 November 2003 18:20 (twenty-two years ago)

Well, I would say that 'points' the concept have no dimensionality and 'points' the physical entity obv. has dimension depending on the physical line in which they are contained. But why are we worrying about things that exist in our heads? LET'S TALK ABOUT REAL TANGIBLE THINGS LIKE FEELINGS PEOPLE

― Dean Gulberry (deangulberry), Wednesday, 26 November 2003 18:31 (twenty-two years ago)

We're talking about the feelings of points! The loneliness! The alienation! Wrap your head for one second around the existential dilemmas of a point.

― nabiscothing, Wednesday, 26 November 2003 18:40 (twenty-two years ago)

http://www.northsouth.com/art/dotandlinecover.gif

― Ned Raggett (Ned), Wednesday, 26 November 2003 18:44 (twenty-two years ago)

There are so many things to debate in here that I hardly know how to start, but while I agree that since these are all made-up things we can make up the answer, and what the hell might 'touch' mean here anyway, I would find it extremely hard to argue that in theoretical terms there could be some space between these points.

If we believe in string theory, we do eventually reach a limit, but it doesn't bear too much resemblance to points and lines.

― Martin Skidmore (Martin Skidmore), Wednesday, 26 November 2003 20:38 (twenty-two years ago)

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