Is a line a shape?

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Or is a curved line a shape and a straight line not?
And is a dot a shape?

And if all of these things are true - which is the MOST boring?

― The Bitter Tears Of Little Lord Travolta (nordicskilla), Friday, 1 October 2004 01:17 (twenty-one years ago)

The greatest book ever.

― Ned Raggett (Ned), Friday, 1 October 2004 01:19 (twenty-one years ago)

None of those things are shapes. Shapes have area and lines and points do not have area.

― Dan Perry '08 (Dan Perry), Friday, 1 October 2004 01:21 (twenty-one years ago)

They're one-dimensional and therefore shapeless.

― jaymc (jaymc), Friday, 1 October 2004 01:34 (twenty-one years ago)

correct.

― RJG (RJG), Friday, 1 October 2004 01:34 (twenty-one years ago)

None of those things are shapes. Shapes have area and lines and points do not have area.

They're one-dimensional and therefore shapeless.

So..there's no getting round either of these issues? They are statements of fact that cannot be contested?

― The Bitter Tears Of Little Lord Travolta (nordicskilla), Friday, 1 October 2004 02:07 (twenty-one years ago)

Let me ask you another question then...are they art?

― The Bitter Tears Of Little Lord Travolta (nordicskilla), Friday, 1 October 2004 02:08 (twenty-one years ago)

Wait JUST a minute...a dot is ROUND isn't it???

― The Bitter Tears Of Little Lord Travolta (nordicskilla), Friday, 1 October 2004 02:12 (twenty-one years ago)

and if a dot is in fact round, could a line be characterised as a series of dots....

― gem (trisk), Friday, 1 October 2004 02:14 (twenty-one years ago)

A dot is not round.

― jaymc (jaymc), Friday, 1 October 2004 02:17 (twenty-one years ago)

Or, I dunno, a dot may be round, but a POINT is not round.

― jaymc (jaymc), Friday, 1 October 2004 02:17 (twenty-one years ago)

And a dot that is round is obv. not a point but a circle.

― jaymc (jaymc), Friday, 1 October 2004 02:18 (twenty-one years ago)

so what shape is a point?

― gem (trisk), Friday, 1 October 2004 02:18 (twenty-one years ago)

A point looks round to me.

― The Bitter Tears Of Little Lord Travolta (nordicskilla), Friday, 1 October 2004 02:19 (twenty-one years ago)

I know it must seem like I'm playing devil's advocate here, but I'm pretty sure this is the process by which science is made.

― The Bitter Tears Of Little Lord Travolta (nordicskilla), Friday, 1 October 2004 02:20 (twenty-one years ago)

If a point looks round to you, then it's not a point.

― jaymc (jaymc), Friday, 1 October 2004 02:21 (twenty-one years ago)

dot1 P Pronunciation Key (dt)
n.
A tiny round mark made by or as if by a pointed instrument; a spot.

― The Bitter Tears Of Little Lord Travolta (nordicskilla), Friday, 1 October 2004 02:21 (twenty-one years ago)

So a point is different to a dot?

― The Bitter Tears Of Little Lord Travolta (nordicskilla), Friday, 1 October 2004 02:21 (twenty-one years ago)

Yes. I conceded that a dot was round.

― jaymc (jaymc), Friday, 1 October 2004 02:22 (twenty-one years ago)

But a dot, which is round, can be made by a pointed instrument.

Dictionary.com says so!

xpost-oh

― The Bitter Tears Of Little Lord Travolta (nordicskilla), Friday, 1 October 2004 02:22 (twenty-one years ago)

"point: A dimensionless geometric object having no properties except location."

― jaymc (jaymc), Friday, 1 October 2004 02:23 (twenty-one years ago)

Surely the tip of any point is round, or at least rounded?

xpost-oh shit, you win

― The Bitter Tears Of Little Lord Travolta (nordicskilla), Friday, 1 October 2004 02:23 (twenty-one years ago)

how can a geometric object have no properties? this is different to a "point" that you can see marked on a page?

― gem (trisk), Friday, 1 October 2004 02:24 (twenty-one years ago)

Well...I AM pleased I didn't put money on this! I have bills to pay.

― The Bitter Tears Of Little Lord Travolta (nordicskilla), Friday, 1 October 2004 02:24 (twenty-one years ago)

since if it is visible and can be differentiated from a dot, surely it must have properties?

― gem (trisk), Friday, 1 October 2004 02:24 (twenty-one years ago)

In fairness, def. 5 of "point" is " A mark or dot used in printing or writing for punctuation, especially a period."

But the definition I gave (9a) is probably closer to what we're talking about.

― jaymc (jaymc), Friday, 1 October 2004 02:25 (twenty-one years ago)

gem, I think jaymc has us cornered.

I suppose we could just deny the truths inherent in his posts and form some sort of fundamentalist breakaway sect, but time and popular opinion will always be against us. Do you think you can take that sort of heat?

― The Bitter Tears Of Little Lord Travolta (nordicskilla), Friday, 1 October 2004 02:27 (twenty-one years ago)

Hmmm, gem raises a good point, though (OH NO haha).

Can a point actually exist in the real world?

― jaymc (jaymc), Friday, 1 October 2004 02:27 (twenty-one years ago)

I mean, maybe it's just one of those mathematical hypotheticals.

― jaymc (jaymc), Friday, 1 October 2004 02:27 (twenty-one years ago)

Adam, have you ever seen Show Me Love? Should I watch it now?

― jaymc (jaymc), Friday, 1 October 2004 02:28 (twenty-one years ago)

I think any point that can be created in the physical world has to have a shape of some kind.

xpost-I have seen it, it is good. Yes, watch it now. It is not as good as Together though.

― The Bitter Tears Of Little Lord Travolta (nordicskilla), Friday, 1 October 2004 02:29 (twenty-one years ago)

xpost well i think that's what the definition you used suggests jaymc... but i guess it makes no sense to me that something with no geometric properties can be differentiated from something that does have geometric properties (i.e. roundness). i am stupid though.

― gem (trisk), Friday, 1 October 2004 02:29 (twenty-one years ago)

also, i think this is a very cool question adamrl, even if the answer is obvious to everyone else!!

― gem (trisk), Friday, 1 October 2004 02:29 (twenty-one years ago)

I'm a bit stupid, too. It's no wonder we agree!

― The Bitter Tears Of Little Lord Travolta (nordicskilla), Friday, 1 October 2004 02:29 (twenty-one years ago)

Okay. Together is teh classic, yes.

― jaymc (jaymc), Friday, 1 October 2004 02:30 (twenty-one years ago)

but i guess it makes no sense to me that something with no geometric properties can be differentiated from something that does have geometric properties (i.e. roundness)

That's only because you're skipping over "except location." A point isn't an object in that sense: it's a place. It's no more hypothetical, and no more a shape, than a set of latitude and longitude coordinates (which would be, after all, a point).

― Tep (ktepi), Friday, 1 October 2004 02:30 (twenty-one years ago)

I think this question forces you to think outside the box. You know, because boxes are three-dimensional.

― jaymc (jaymc), Friday, 1 October 2004 02:31 (twenty-one years ago)

And your point is?

― The Bitter Tears Of Little Lord Travolta (nordicskilla), Friday, 1 October 2004 02:31 (twenty-one years ago)

Oooh, Tep: yes, very good.

― jaymc (jaymc), Friday, 1 October 2004 02:31 (twenty-one years ago)

sorry, couldn't resist.

xpost

― The Bitter Tears Of Little Lord Travolta (nordicskilla), Friday, 1 October 2004 02:31 (twenty-one years ago)

I object to your line of questioning, Adam.

― jaymc (jaymc), Friday, 1 October 2004 02:31 (twenty-one years ago)

But whatever, I'm in no shape to have this conversation right now.

― jaymc (jaymc), Friday, 1 October 2004 02:32 (twenty-one years ago)

pointless.

― The Bitter Tears Of Little Lord Travolta (nordicskilla), Friday, 1 October 2004 02:32 (twenty-one years ago)

It's no more hypothetical, and no more a shape, than a set of latitude and longitude coordinates

yes i agree - that's why i was wondering why we were comparing them as if they were in the same class of objects though

― gem (trisk), Friday, 1 October 2004 02:33 (twenty-one years ago)

"Objects"? Hmmm....

― The Bitter Tears Of Little Lord Travolta (nordicskilla), Friday, 1 October 2004 02:33 (twenty-one years ago)

Not to get off on a tangent, but this thread is not a good sine.

― oops (Oops), Friday, 1 October 2004 02:34 (twenty-one years ago)

i guess that's why i said "if it's visible" up there because i guess it depends on what definition of point you use, as jaymc already alluded to....

*brain explodes*

― gem (trisk), Friday, 1 October 2004 02:34 (twenty-one years ago)

haha stop it with the maths jokes i keep laughing and workmates are staring

― gem (trisk), Friday, 1 October 2004 02:34 (twenty-one years ago)

I knew I'd spend the evening maths debating.

― The Bitter Tears Of Little Lord Travolta (nordicskilla), Friday, 1 October 2004 02:35 (twenty-one years ago)

are your co-workers a bunch of squares or something?

― oops (Oops), Friday, 1 October 2004 02:35 (twenty-one years ago)

yes, highly conservative work environment. LAUGHTER IS NOT PERMITTED.

― gem (trisk), Friday, 1 October 2004 02:36 (twenty-one years ago)

hehe at squares by the way

― gem (trisk), Friday, 1 October 2004 02:36 (twenty-one years ago)

Integral[1/(cabin) d(cabin)] = log(cabin) + c = houseboat.

― Leeeter van den Hoogenband (Leee), Friday, 1 October 2004 02:37 (twenty-one years ago)

Leee, no smart people humor allowed!

― The Bitter Tears Of Little Lord Travolta (nordicskilla), Friday, 1 October 2004 02:40 (twenty-one years ago)

ok i am still confused/stupid

a set of latitude and longitude coordinates

sooooo is this how we define a line? not something you can see on a piece of paper-loike?

― gem (trisk), Friday, 1 October 2004 02:41 (twenty-one years ago)

because surely something you can see on a piece of paper has "area"?

― gem (trisk), Friday, 1 October 2004 02:41 (twenty-one years ago)

Aye, saucy Leee(s).

― Tep (ktepi), Friday, 1 October 2004 02:41 (twenty-one years ago)

If you can see it on a piece of paper, it isn't a line. It's a very, very thin filled-in rectangle.

That sounds like a crappy answer, but that's why people don't like math.

― Tep (ktepi), Friday, 1 October 2004 02:42 (twenty-one years ago)

But yeah: a line is a series of points extending from X to Y, A to B, Chicago to my pants, etc. Just like a point is only a location, a line is really a distance, but it's a specific distance -- the distance from Chicago to my pants -- not just a quantity ("many miles + shoes").

― Tep (ktepi), Friday, 1 October 2004 02:43 (twenty-one years ago)

Or is a curved line a shape and a straight line not?

so is this original question is asking about shapes (i.e. really thin filled in rectangles) and not lines?

(i think i was alright at maths in school and uni, promptly forgot it all though)

― gem (trisk), Friday, 1 October 2004 02:44 (twenty-one years ago)

That sounds like a crappy answer, but that's why people don't like math.

Yes, now you remind me.

― The Bitter Tears Of Little Lord Travolta (nordicskilla), Friday, 1 October 2004 02:44 (twenty-one years ago)

re: curved line

A line has one dimension, yet can exist in higher dimensions. In this case, it can exist in two dimensions, yet remains one-dimensional.

A different take: imagine a solid box. Its faces all have (surface) areas, and these areas have but two dimensions, yet they exist in 3-space. Same with your line.

Lines, lattitude, points, etc. don't exist IRL except purely as conceptual abstractions (e.g. time).

I think there's a mathematical defn. of a dot, which is distinct from a point because the former has dimensionality.

― Leeeter van den Hoogenband (Leee), Friday, 1 October 2004 02:58 (twenty-one years ago)

re: curved line

A line has one dimension, yet can exist in higher dimensions. In this case, it can exist in two dimensions, yet remains one-dimensional.

A different take: imagine a solid box. Its faces all have (surface) areas, and these areas have but two dimensions, yet they exist in 3-space. Same with your line.

Lines, lattitude, points, etc. don't exist IRL except purely as conceptual abstractions (e.g. time).

I think there's a mathematical defn. of a dot, which is distinct from a point because the former has dimensionality.

― Leeeter van den Hoogenband (Leee), Friday, 1 October 2004 02:59 (twenty-one years ago)

WTF, my computer sez "You have inserted a blank DVD" -- it's not blank, dude, I got it from Netflix!!

― jaymc (jaymc), Friday, 1 October 2004 03:00 (twenty-one years ago)

No Swedish teenage lesbians for me tonite :(

― jaymc (jaymc), Friday, 1 October 2004 03:00 (twenty-one years ago)

Nuts to double posting and poxy fulography!

More math humorologism:

TS: dog seats vs. monkey seats!11!

I really don't want to go on reading Hegel.

See jaymc, the blankness can exist within the DVD-space, along the same principles I previously mapped out.

― Leeeter van den Hoogenband (Leee), Friday, 1 October 2004 03:01 (twenty-one years ago)

I've had some compatibility issues with discs from Netflix that've done that with my girlfriend's DVD player (or, weirdly, played only in black and white).

ILX (or my ISP) is being all weird on me; anyway, gem, neither you nor Adam were being stupid, it's just one of those things no one who doesn't work with a protractor for a living ends up remembering unless someone asks about it on a message board while they're skimming the debate thread.

― Tep (ktepi), Friday, 1 October 2004 03:10 (twenty-one years ago)

the explanations are cool tep and leeeee! i like that words can have so many definitions anyway, i think that is where i got a bit confused. i will file it in my "learned something for today" section of my brain! thank you.

also my ilx is weird too.

― gem (trisk), Friday, 1 October 2004 03:11 (twenty-one years ago)

(Ned is otm in the first answer, btw -- Norton Juster's association with Hampshire College was one of my main reasons for going there, although he retired the year before I started. The Chuck Jones short is at least as good as the book.)

― Tep (ktepi), Friday, 1 October 2004 03:15 (twenty-one years ago)

Probably been said, but if you draw a line, that's a shape [albeit a very narrow one]. A line's really just conceptual and can't be physically represented, for that physical representation would have to be multidimensional in order for it to exist.

― Core of Sphagnum (Autumn Almanac), Friday, 1 October 2004 04:33 (twenty-one years ago)

When trying to explain planes and other 2-dimensional things, my hs geometry teacher told us to think of them as comparable to a shadow.

― oops (Oops), Friday, 1 October 2004 04:36 (twenty-one years ago)

Yeah, and when trying to explain one-dimensional things, think of Bush's rhetoric.

― Core of Sphagnum (Autumn Almanac), Friday, 1 October 2004 04:58 (twenty-one years ago)

http://www.timkcbooks.com/pictures/steadman_little.jpg

Little dot com, the blob of ink.

I love this book.

― Trayce (trayce), Friday, 1 October 2004 05:32 (twenty-one years ago)

Brett Whiteley's doing kids' books now?

― Core of Sphagnum (Autumn Almanac), Friday, 1 October 2004 06:19 (twenty-one years ago)

If a line had only one dimension then it wouldn't fill any space on a piece of paper, thus you could draw infinite lines on one piece, surely?

― Sick Mouthy (Nick Southall), Friday, 1 October 2004 07:14 (twenty-one years ago)

Anybody remember that cartoon that was just lines interacting? I *think* it was Chuck Jones but I'm not sure...

― Spencer Chow (spencermfi), Friday, 1 October 2004 07:27 (twenty-one years ago)

Drawn lines are three-dimensional - the ink has thickness as well as breadth. Conceptual straight lines are one-dimensional. Curved lines can have fractional dimension, somewhere between 1 and 2. I think calling, for instance, a parabola a shape is not unreasonable or unusual, even though Dan is technically correct.

― Martin Skidmore (Martin Skidmore), Friday, 1 October 2004 18:20 (twenty-one years ago)

I love that line cartoon. Haven't seen it in ages .. but I love those old documentaryish Chuck Jones cartoons.

― dave225 (Dave225), Friday, 1 October 2004 18:23 (twenty-one years ago)

(x-post hah)
I second Ned OTM for first answer. That book rules.

― AaronHz (AaronHz), Friday, 1 October 2004 18:24 (twenty-one years ago)

Curved lines can have fractional dimension, somewhere between 1 and 2

Martin, can you explain this a bit more? It seems really interesting, I'd like to understand it. (I ahve maths up to A-Level further maths, but no further).

― Gravel Puzzleworth (Gregory Henry), Friday, 1 October 2004 18:26 (twenty-one years ago)

It's not the easiest thing to explain. The idea kind of started with Peano's contrived 'curve' that visited every point in a plane, so it was indistinguishable from a 2-d shape. Fractals (that's what we are talking about here) have a fractional dimension relating to how much of a plane they fill. Do you know the Koch curve? Imagine a straight line, three inches long; replace the middle inch with two inch-long lines, obviously at an angle to the originals to fit them in, something like _/\_; then divide the four sections you have in a similar way, and do the same thing. Repeat ad infinitum. This has a fractional dimension of 1.26 - because it contains four one-third-sized Koch curves (and so on all the way down), its dimension is log4/log3. Obviously most things are more complicated than that. The generalised way of computing fractional dimension is more like this: draw the curve on a grid. Count the number of squares it passes through. Halve the size of the squares and count again. At the limit, the rate at which the proportion of counted squares decreases is the fractional dimension. On this basis, I've seen the British coastline quoted as 1.28 and cloud outlines at 1.35. Does that help at all?

― Martin Skidmore (Martin Skidmore), Friday, 1 October 2004 19:02 (twenty-one years ago)

The greatest book ever.

-- Ned Raggett (ne...), October 1st, 2004.

only related on a severe tangent but it's worth reading +Godel, Escher & Bach_ too...

― firstworldman (firstworldman), Friday, 1 October 2004 19:03 (twenty-one years ago)

I love that line cartoon. Haven't seen it in ages .. but I love those old documentaryish Chuck Jones cartoons.

Does anyone know what it's called or if it's available on video?

― Spencer Chow (spencermfi), Friday, 1 October 2004 19:05 (twenty-one years ago)

The Dot and the Line? Or are you talking about something else? The Chuck Jones adaptation is fantastic. Won an academy award.

http://www.imdb.com/title/tt0059122/

― Colin Saunders (csaunders), Monday, 4 October 2004 04:47 (twenty-one years ago)

Martin just melted my brane but I think he was proving me right.

― Sick Mouthy (Nick Southall), Monday, 4 October 2004 11:03 (twenty-one years ago)

Boxes aren't necessarily three dimensional. Although we can't perceive the 4th dimension, it's possible to give an illustration of the properties of a 4 dimensional box or tesseract.

Tesseracts look a bit like either this:

http://www.math.uni-hamburg.de/home/moeller/tesseract.jpg

or this:

http://www.cyber-shaktipat.org/relax/tesseract.jpg

― Markelby (Mark C), Monday, 4 October 2004 11:32 (twenty-one years ago)

"point: A dimensionless geometric object having no properties except location."

I've been in pubs like that.

― Billy Dods (Billy Dods), Monday, 4 October 2004 12:31 (twenty-one years ago)

Tesseracts don't exactly 'look' like that - the first is a 3-d construct that, if folded through a fourth dimension, could become a tesseract, in the same way that a paper marked and shaped into a set of six linked squares can be folded in the third dimension into a cube. The second is a very misleading 3-d projection of a tesseract, but it misrepresents it. Obviously we can't see a tesseract, since we don't have 4-d vision. I think we can stick with 'box' meaning a 3-d object.

― Martin Skidmore (Martin Skidmore), Monday, 4 October 2004 15:15 (twenty-one years ago)

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