APOD: Polar Ring Galaxy NGC 2685 (2014 Mar 14)

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Expand view Topic review: APOD: Polar Ring Galaxy NGC 2685 (2014 Mar 14)

Re: APOD: Polar Ring Galaxy NGC 2685 (2014 Mar 14)

by Nitpicker » Tue Mar 25, 2014 12:15 am

But back to footballs :ssmile: ... neither the 2-D nor 3-D variant of mandorla is suggested as a replacement for "football shaped", unless you specifically mean the precise shape of the mandorla. The term "football shaped", if it must be used, is best reserved for an intentionally loose description of an elongated circle or sphere. I still hold "oval" (a loose term in 2-D and 3-D) to be preferable to "football shaped" and in 2-D, it is even inclusive of lenticular shapes (no 3-D football could be correctly described as lenticular [well, maybe a partially deflated Soccer ball]).

Re: APOD: Polar Ring Galaxy NGC 2685 (2014 Mar 14)

by Nitpicker » Mon Mar 24, 2014 12:12 pm

Nothing to do with footballs or galaxies, just geometry ...

I must admit that, because of its other, less precise meanings, "lens" is not a brilliant name for the precise shape formed by the intersection of two planar circles. And aside from the two links I've already posted, I can't find much evidence of its use in this precise geometric way. Without concocting an ugly monster like "bi-circular-segment", I think we are only left with vesica piscis or mandorla, both of which are ancient words with religious origins, but which may be applied with validity to any intersection of two circles of the same radius. Given the choice, I would go for mandorla, as it is shorter and I like almonds more than fish guts. By extension, if the arcs had different radii, it could be called an asymmetric mandorla. Mandorla, mandorla, mandorla. I quite like it. Can anyone suggest a suitable adjective for mandorla, or even a name for a 3-D variant, which would be a volume or revolution about the radical axis (the line joining the pointy ends), not lenticular in 3-D?

Re: APOD: Polar Ring Galaxy NGC 2685 (2014 Mar 14)

by Nitpicker » Mon Mar 24, 2014 5:42 am

Chris Peterson wrote:
Nitpicker wrote:I think lens actually does have a precise meaning in a geometric context:
http://en.wikipedia.org/wiki/Lens_(geometry)
The existence of a very formal mathematical definition doesn't invalidate other, much more common definitions. Also useful, lens and lenticular are equally applicable to both 2D and 3D structures. So in the context of galaxies, they could refer to either the actual shape or to the shape in projection. (Of course, lenticular is also a galaxy classification, so there could be some confusion, given that many elliptical galaxies can be described geometrically as lenticular.)
It is no more formal than the definition of a square, circle, ellipse, rectangle, etc. I think the difference is that it is not as well known. See also:
http://mathworld.wolfram.com/Lens.html

Yes, "lens" certainly does have a few other meanings, but they are not relevant to my point in its context (which I didn't think I needed to explain, but it seems I did). I also think that "lenticular" and "shaped like a lens" are somewhat more relaxed descriptions than the geometric shape that is the "lens".

Re: APOD: Polar Ring Galaxy NGC 2685 (2014 Mar 14)

by Chris Peterson » Mon Mar 24, 2014 5:30 am

Nitpicker wrote:I think lens actually does have a precise meaning in a geometric context:
http://en.wikipedia.org/wiki/Lens_(geometry)
The existence of a very formal mathematical definition doesn't invalidate other, much more common definitions. Also useful, lens and lenticular are equally applicable to both 2D and 3D structures. So in the context of galaxies, they could refer to either the actual shape or to the shape in projection. (Of course, lenticular is also a galaxy classification, so there could be some confusion, given that many elliptical galaxies can be described geometrically as lenticular.)

Re: APOD: Polar Ring Galaxy NGC 2685 (2014 Mar 14)

by Nitpicker » Mon Mar 24, 2014 5:20 am

Chris Peterson wrote:
Nitpicker wrote: Agreed. Also, the left one could be just as correctly described as oval, or an oval. And whilst oval and lenticular do not have precise definitions, lens does, and only the one on the right side is a lens.
Nope, both are lenses. Lenticular has a precise meaning: shaped like a lens. And when referring to shape, lens just means biconvex. There is no constraint on either symmetry or the structure of the intersection between the two curves (which need not be circular).
In that case, we are back to having no word for the shape of the intersection of two circles. But, nope, I think lens actually does have a precise meaning in a geometric context:
http://en.wikipedia.org/wiki/Lens_(geometry)

Re: APOD: Polar Ring Galaxy NGC 2685 (2014 Mar 14)

by Chris Peterson » Mon Mar 24, 2014 5:10 am

Nitpicker wrote: Agreed. Also, the left one could be just as correctly described as oval, or an oval. And whilst oval and lenticular do not have precise definitions, lens does, and only the one on the right side is a lens.
Nope, both are lenses. Lenticular has a precise meaning: shaped like a lens. And when referring to shape, lens just means biconvex. There is no constraint on either symmetry or the structure of the intersection between the two curves (which need not be circular).

Re: APOD: Polar Ring Galaxy NGC 2685 (2014 Mar 14)

by Nitpicker » Mon Mar 24, 2014 4:54 am

Chris Peterson wrote:
Nitpicker wrote:
football_shaped.png
I did even less to turn your lens into a more realistic oval/lenticular football. But there is definitely still a need for the concept of the sharp lens shape, I just don't think it should be related to football.

(And owlice, I think you are right about lentils giving their name to the lens shape. Thank you for setting me straight.)
Note that either one of those shapes is quite correctly described as lenticular.
Agreed. Also, the left one could be just as correctly described as oval, or an oval. And whilst oval and lenticular do not have precise definitions, lens does, and only the one on the right side is a lens.

Re: APOD: Polar Ring Galaxy NGC 2685 (2014 Mar 14)

by Chris Peterson » Mon Mar 24, 2014 4:34 am

Nitpicker wrote:
football_shaped.png
I did even less to turn your lens into a more realistic oval/lenticular football. But there is definitely still a need for the concept of the sharp lens shape, I just don't think it should be related to football.

(And owlice, I think you are right about lentils giving their name to the lens shape. Thank you for setting me straight.)
Note that either one of those shapes is quite correctly described as lenticular.

Re: APOD: Polar Ring Galaxy NGC 2685 (2014 Mar 14)

by Nitpicker » Mon Mar 24, 2014 3:46 am

football_shaped.png
football_shaped.png (3.59 KiB) Viewed 562 times
I did even less to turn your lens into a more realistic oval/lenticular football. But there is definitely still a need for the concept of the sharp lens shape, I just don't think it should be related to football.

(And owlice, I think you are right about lentils giving their name to the lens shape. Thank you for setting me straight.)

Re: APOD: Polar Ring Galaxy NGC 2685 (2014 Mar 14)

by owlice » Mon Mar 24, 2014 3:29 am

Nitpicker wrote:Lentils got their name because of their lens shape. I love lentils. I say we reclaim the word "lens" as a popular shape name, for those nitpicky occasions where we really mean "lens" and not "oval". :ssmile:
Lentils came first; I'm reasonably certain the word "lens" comes from lentil, not the other way around.

I love lentils, too, especially lentil soup and lentil-bulgur salad. Nom nom nom! (Our Himalayan tripod cat's name is Lentil, more a reference to our initial perception of the size of his brain than anything else. He's a lovely very nice cat [except for the considering-people-prey thing].)
Nitpicker wrote:Prolate spheroid is not the correct term for an American football, despite what it says all over the internet.
That's why I said I'd probably just draw a football or find a picture of one.
Nitpicker wrote:But your particular shade of blue-green is so specific as to be barely useful to describe anything but itself.
According to you, one who is not able to see (or at least appreciate) the distinction. There are sounds in languages I don't speak that are different for a native speaker but the same for me; I cannot tell the difference between them. The sky is green, except it isn't. A football is oval, except it isn't. Does A=440, or does A=415? Or something else? Is it a microtone, or an Eb that is a little... well, flat? Annoying to my ear, perhaps, but for someone in a different culture, a perfectly good tone.

Re: APOD: Polar Ring Galaxy NGC 2685 (2014 Mar 14)

by geckzilla » Mon Mar 24, 2014 3:14 am

We have hexagonal and tringular and flat pencils, too. I'm not sure we have octagonal ones. Probably somewhere. Hexagons were too angular to pick on, though. So a lens with precise angles at the end is not mechanically useful to us, so we do not need a special name for it other than the name it already has, which works well in the optics world. You can imagine that if we did live in a world where this particular shape played a role in our every day lives, it would have a particular name. Something like the word football as it is known in the U.S., but known around the world. If you take this shape and round off just the bottom, you'd think you'd be that much closer to an oval. Instead, it turns into a teardrop. Waah.

Yes, I am still arguing because this argument amuses me.
Attachments
teardrop.png
teardrop.png (5.64 KiB) Viewed 712 times

Re: APOD: Polar Ring Galaxy NGC 2685 (2014 Mar 14)

by Nitpicker » Mon Mar 24, 2014 3:12 am

Chris Peterson wrote:
Nitpicker wrote:I say we reclaim the word "lens" as a popular shape name, for those nitpicky occasions where we really mean "lens" and not "oval". :ssmile:
The usual adjective is "lenticular", and I'm not sure where we would reclaim it from, as it remains in very wide usage.
In my world, it is uncommon to call the shape of the intersection of two circles a lens, or to say it is lenticular. But I'd like to see it become as common as the shape names: square, rectangle, circle, ellipse, oval and crescent (and their adjectives).

Re: APOD: Polar Ring Galaxy NGC 2685 (2014 Mar 14)

by Nitpicker » Mon Mar 24, 2014 2:55 am

geckzilla wrote:
Nitpicker wrote:You could delete only a tiny number of black pixels at the ends of your black and white lens shapes, such that I would be happy to suddenly start calling them oval. The difference is so minute, and it has a psychological component.
Oh, gosh. There are a few other shapes we could get rid of and just call slightly pointy ovals. Octagons are basically just circles with a few extra pixels. Why do we even have those? And yet a pencil shaped like an octagon will not roll. Luckily some brilliant minds managed to make that distinction.
I think you are just arguing for the sake of arguing now (and still selectively). I don't want to get rid of shapes. I was trying to say that all one has to do to convert a lens to an oval is to put a small radius on each end. Whether the shape has pointy ends or rounded ends makes very little difference to the overall appearance. In other words, the difference between some lenses and some ovals is arbitrary in practice, and we appear to arbitrate them differently.

Visually, there isn't much difference between a small octagon and a small circle. Mathematically and conceptually, there is a huge difference. Practically, there is just enough difference between a hexagonal pencil (octagonal? stop with the cultural differences already!) and a round one, to prevent the former from rolling off a sloping drawing board (which these days is also pretty conceptual).

Re: APOD: Polar Ring Galaxy NGC 2685 (2014 Mar 14)

by geckzilla » Mon Mar 24, 2014 1:58 am

Nitpicker wrote:You could delete only a tiny number of black pixels at the ends of your black and white lens shapes, such that I would be happy to suddenly start calling them oval. The difference is so minute, and it has a psychological component.
Oh, gosh. There are a few other shapes we could get rid of and just call slightly pointy ovals. Octagons are basically just circles with a few extra pixels. Why do we even have those? And yet a pencil shaped like an octagon will not roll. Luckily some brilliant minds managed to make that distinction.

Re: APOD: Polar Ring Galaxy NGC 2685 (2014 Mar 14)

by Chris Peterson » Mon Mar 24, 2014 1:45 am

Nitpicker wrote:I say we reclaim the word "lens" as a popular shape name, for those nitpicky occasions where we really mean "lens" and not "oval". :ssmile:
The usual adjective is "lenticular", and I'm not sure where we would reclaim it from, as it remains in very wide usage.

Re: APOD: Polar Ring Galaxy NGC 2685 (2014 Mar 14)

by Nitpicker » Mon Mar 24, 2014 1:42 am

geckzilla wrote:Do you call lenses or gibbous moons ovals? You could very coarsely define both of those as a ovals. The English language just isn't quite succeeding in this area. Kind of like how you don't have a word for the front of your elbow. You just call it the front of your elbow, unless you happen to be a doctor, in which case you might call it antecubital. Anyway, it's not my fault the English language has no word other than lens for this shape and that lens does not seem a proper word in many cases. It's a shame because it can be applied to quite a few things. Leaves, scales, petals, eyes, various nuts and seeds, spindles, many animals' pupils, etc...
You could delete only a tiny number of black pixels at the ends of your black and white lens shapes, such that I would be happy to suddenly start calling them oval. The difference is so minute, and it has a psychological component.

Lentils got their name because of their lens shape. I love lentils. I say we reclaim the word "lens" as a popular shape name, for those nitpicky occasions where we really mean "lens" and not "oval". :ssmile:

Re: APOD: Polar Ring Galaxy NGC 2685 (2014 Mar 14)

by Nitpicker » Mon Mar 24, 2014 12:12 am

Chris Peterson wrote:
Nitpicker wrote:Thank you geckzilla. That certainly does help to clarify what you mean by "football shaped, that is, symmetric and asymmetric lenses. But I really doubt that is what most people (even most Americans) mean when they use the term. Does anyone else have an opinion?
Context is everything. If the discussion were about footballs, the first of Geck's examples is the only one I'd consider valid. If the discussion were about galaxies, I'd consider one looking like any of the examples to be "football shaped". Seriously, as we all strain to see horses and witches in astronomical objects, nobody should have any problem with "football shaped" to describe anything that is even vaguely oval, ovoid, lenticular, or any number of other equally reasonable and substantially equivalent terms.
Thank you Chris. I'll note that the discussion of the shape here, has never been to describe an actual football. If we start defining the shape of a football as "football shaped" then I really think we should stay in bed and forget about it.

The difference we are arguing about here is only the degree of pointedness of the ends. Pffft (sound of deflating football of any shape).

(And geckzilla, yes, I think some of my photos of the gibbous Moon do make it look rather oval. It is only the idealized version -- an assymetric lens -- which has sharp points. Same goes for the American football.)

Re: APOD: Polar Ring Galaxy NGC 2685 (2014 Mar 14)

by geckzilla » Mon Mar 24, 2014 12:02 am

You see that one of those looks like a gibbous moon. I wouldn't call a gibbous moon an oval. Anyway, I'm not saying that anyone should call anything other than what they want. I'm saying it is in this shape category and not an oval. Do you call lenses or gibbous moons ovals? You could very coarsely define both of those as a ovals. The English language just isn't quite succeeding in this area. Kind of like how you don't have a word for the front of your elbow. You just call it the front of your elbow, unless you happen to be a doctor, in which case you might call it antecubital. Anyway, it's not my fault the English language has no word other than lens for this shape and that lens does not seem a proper word in many cases. It's a shame because it can be applied to quite a few things. Leaves, scales, petals, eyes, various nuts and seeds, spindles, many animals' pupils, etc...

Re: APOD: Polar Ring Galaxy NGC 2685 (2014 Mar 14)

by Chris Peterson » Sun Mar 23, 2014 11:53 pm

Nitpicker wrote:Thank you geckzilla. That certainly does help to clarify what you mean by "football shaped, that is, symmetric and asymmetric lenses. But I really doubt that is what most people (even most Americans) mean when they use the term. Does anyone else have an opinion?
Context is everything. If the discussion were about footballs, the first of Geck's examples is the only one I'd consider valid. If the discussion were about galaxies, I'd consider one looking like any of the examples to be "football shaped". Seriously, as we all strain to see horses and witches in astronomical objects, nobody should have any problem with "football shaped" to describe anything that is even vaguely oval, ovoid, lenticular, or any number of other equally reasonable and substantially equivalent terms.

Re: APOD: Polar Ring Galaxy NGC 2685 (2014 Mar 14)

by Nitpicker » Sun Mar 23, 2014 11:46 pm

Thank you geckzilla. That certainly does help to clarify what you mean by "football shaped", that is, symmetric and asymmetric lenses. But I really doubt that is what most people (even most Americans) mean when they use the term. Does anyone else have an opinion?

I understand "football shaped" to mean anything more or less like these shapes, but not necessarily so symmetric:
Not quite to scale, but accurate for shape.
Not quite to scale, but accurate for shape.
These can all be sufficiently described as ovals.

Re: APOD: Polar Ring Galaxy NGC 2685 (2014 Mar 14)

by geckzilla » Sun Mar 23, 2014 11:11 pm

Nitpicker wrote:
geckzilla wrote:Oval to me is rounder than a football. A football has some angularity to it which is very unlike an oval. This is pretty much like if you are in a culture which makes no distinction between green and blue and then you come to us and try to tell us that all of these blue things are green. The sky isn't green.
But your particular shade of blue-green is so specific as to be barely useful to describe anything but itself.
A shape can be extremely specific, can it not? A circle can be defined in as little as three parameters and is only ever one specific shape. To satisfy your desire for variety, however, I have attached several examples of what shape I consider the football to fall into the category of.
Attachments
lenses.png

Re: APOD: Polar Ring Galaxy NGC 2685 (2014 Mar 14)

by Nitpicker » Sun Mar 23, 2014 10:45 pm

geckzilla wrote:Oval to me is rounder than a football. A football has some angularity to it which is very unlike an oval. This is pretty much like if you are in a culture which makes no distinction between green and blue and then you come to us and try to tell us that all of these blue things are green. The sky isn't green.
But your particular shade of blue-green is so specific as to be barely useful to describe anything but itself.

It appears "football shaped", to you, is "very unlike" an oval, but a kind of lens, or a kind of lens with slightly rounded ends (which is actually an oval). Sorry, but that is so specific that it has introduced a level of confusion I previously never considered. I am starting to side with the Soccer nuts (but not quite). To me, a lens is so similar to an oval that they are barely worth discriminating between, unless you use technical terms. And "football shaped" could cover both (and more), in a loose, inclusive kind of way. The main point is that "football shaped" means not circular. I am almost certain that mine is the more universal meaning of the term, and this topic has not changed my opinion. But it has really been an eye-opener to me, and has strengthened my resolve to avoid the term "football shaped", as it is confusing, contentious and too informal for a wide audience.

I even went back through old APODs, looking for the shapes that were described as "football shaped". With the possible exception of this day's APOD, they all looked more oval than anything else.

Prolate spheroid is not the correct term for an American football, despite what it says all over the internet. A prolate spheroid is specifically the 3-D shape you get when you rotate a 2-D ellipse (a circle scaled linearly up or down in one axis) about its major axis. Geckzilla demonstrated graphically that this doesn't fit the American football. But given the right eccentricity, a prolate spheroid is closest to a modern Rugby ball. The American football started out life as a Rugby ball, and progressively became more pointy over time, with a smaller radius at the ends. The Rugby ball has also changed over the years, but not as much. An Australian football is a different ball again, which I emphasize only because I just read an old APOD which implied Rugby and Australian football were the same, when they are not at all. American football and the Rugby codes are more similar to each other, than any of the other codes.

Re: APOD: Polar Ring Galaxy NGC 2685 (2014 Mar 14)

by neufer » Sun Mar 23, 2014 6:50 pm

geckzilla wrote:
Oval to me is rounder than a football. A football has some angularity to it which is very unlike an oval. This is pretty much like if you are in a culture which makes no distinction between green and blue and then you come to us and try to tell us that all of these blue things are green. The sky isn't green.
Click to play embedded YouTube video.
http://www.seinfeldscripts.com/TheFatigues.html wrote:
  • The Fatigues
Jerry: So you saw Banya's act?

Abby: He got two minutes into that Ovaltine thing and I just couldn't take it anymore. Why is he so obsessed with Ovaltine?

Jerry: He just thinks that anything that dissolves in milk is funny.

Kenny Banya (reading): Why do they call it Ovaltine? The mug is round. The jar is round. They should call it round tine. That's gold, Jerry! Gold!

Re: APOD: Polar Ring Galaxy NGC 2685 (2014 Mar 14)

by owlice » Sun Mar 23, 2014 6:41 pm

geckzilla, that is a wonderful analogy!

Nitpicker, see geckzilla's post above! I guess if I ran across someone who had no idea what this shape was, I might use prolate spheroid. Biconvex lens doesn't quite cut it, as viewed from above the convex surface, a lens is often a circle. More likely, I would simply draw the shape or show an image of a football. It would never occur to me to use oval to describe the shape of a football.

An aside: when my son was just beginning to learn to talk, lima beans were ovs for "oval" (he was learning shapes, too, at that time). He loved these, and would get very excited when ovs were among the mixed frozen veggies on his tray. "Ovs! Ovs!" I've never seen anyone so excited about lima beans! (I am not a fan of them.)

Re: APOD: Polar Ring Galaxy NGC 2685 (2014 Mar 14)

by geckzilla » Sun Mar 23, 2014 5:37 pm

Oval to me is rounder than a football. A football has some angularity to it which is very unlike an oval. This is pretty much like if you are in a culture which makes no distinction between green and blue and then you come to us and try to tell us that all of these blue things are green. The sky isn't green.

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