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September 11th, 2008

What is a Constellation?

(This post is a collection of some ideas I had in a conversation with Dan Korman about six months ago, at the APA Pacific in Pasadena.)

Are there such things as constellations?  I’ll presume that there are such things, which then of course raises the question of what they are.  The natural thought is that a constellation is a collection of stars, which means that it’s a bunch of balls of hydrogen and such, each glowing from the heat of its fusion, scattered across large expanses of space.

But this seems to give the wrong persistence conditions.  Consider the constellation of <A href=http://en.wikipedia.org/wiki/Orion_(constellation)>Orion</a>, which is probably the most easily recognizable and visible constellation in the northern hemisphere (unfortunately, at this time of year in the southern hemisphere it doesn’t rise until about 1 am, and whenever it does appear it’s upside-down).  If <A href=http://en.wikipedia.org/wiki/Epsilon_Orionis>the middle star in his belt</a> were to suddently cease to exist, it seems that we wouldn’t say that Orion has ceased to exist (as would be the case if Orion were just a set of stars), but rather that Orion’s belt is now missing a buckle.  Similarly, if a new, extremely bright star were to appear in the vicinity of <A href=http://en.wikipedia.org/wiki/Lambda_Orionis>Orion’s head</a>, we would say that Orion’s head is now brighter, and not that we’re looking at a new constellation.  So we might suggest that a constellation is not a set of stars, but is rather an object composed of them.

Now, when I say “in the vicinity of”, it doesn’t actually matter how close this new star is to the star that already exists there – the star that currently serves as Orion’s head is about 1000 light years away, while <A href=http://en.wikipedia.org/wiki/Gamma_Orionis>Orion’s right shoulder</a> (the less bright one) is only about 240 light years away.  A new bright star could count as an addition to Orion if it was over 1000 light years away (like the head and middle of the belt), or if it was closer to the shoulder, or if it was only 1 or 2 light years away, in which case it would be much closer to the stars in <A href=http://en.wikipedia.org/wiki/Crux>the Southern Cross</a> than it would be to most of the other stars in Orion.  The important thing is just what angle you’d have to look at to see it from Earth.

Thus, I suggest that rather than being composed of stars (as in the actual glowing balls of gas), a constellation is composed of beams of light reaching Earth. [UPDATE: see comments for a modification of the “beam of light” view.]  To be part of Orion, it doesn’t matter where the ball of gas is in relation to the other balls of gas (after all, a few of those balls of gas are closer to stars in constellations that can’t even be seen from most of the northern hemisphere than they are to most of the other balls of gas in Orion), but it does matter what angle the beam of light reaches Earth.  As further confirmation of this view, note that if the middle star in Orion’s belt were to explode right this instant and stop shining, we wouldn’t actually say that Orion has lost his belt buckle yet – that wouldn’t happen for another 1300 years.  Although the ball of gas would no longer exist, the beam of light reaching the Earth still would for quite a while.

This suggestion then raises another question – if constellations are composed of beams of light rather than of balls of gas, then are constellations really made of stars?  I think the natural answer here is that the word “star” is actually ambiguous between a glowing ball of gas and a beam of light reaching the Earth, and that constellations are composed of the latter but not the former.  As it turns out, a few “stars” aren’t really beams of light from individual glowing balls of gas at all.  Some of them are <A href=http://en.wikipedia.org/wiki/Binary_star>binary star systems</a> (for instance, <A href=http://en.wikipedia.org/wiki/Sirius>Sirius</a>, which is the brightest “star” in the sky, and which you can find conveniently by following the line of Orion’s belt down and to the left (reverse the directions in the Southern hemisphere of course).  And the bright middle “star” in Orion’s belt [sword] is actually <A href=http://en.wikipedia.org/wiki/Orion_Nebula>the Orion Nebula</a>, which is a cloud of gas that is giving birth to many stars in the other sense.

Of course, not just any beam of light coming down to Earth counts as a star – some are planets, some faint ones are asteroids or moons of planets, and some are man-made satellites.  (For instance, a few weeks ago I was able to spot the International Space Station using a guide <A href=http://heavens-above.com/PassSummary.aspx?satid=25544&lat=0&lng=0&loc=Unspecified&alt=0&tz=CET>here</a> – you’ll need to input your own location and time zone for that to be helpful.)  Presumably, for a beam of light to count as a star in this sense, it must be bright enough to be visible to the naked eye, but also stable enough that it doesn’t noticeably move from year to year, and must come from far enough away that it doesn’t noticeably move as the observer moves from point to point on Earth.  But constellations in the ordinary sense I would say are composed of these sorts of stars, and not of balls of gas in space.

Thus, I think it’s incorrect to say (as we standardly do) that stars are glowing balls of gas in space, and that constellations are made of stars.  This involves an equivocation on the word “star”.  Stars in one sense tend to be created by stars in the other sense, but the examples pointed out above show that one can exist without the other.

(Astronomers do have terms for certain natural collections of balls of gas, like <A href=http://en.wikipedia.org/wiki/Star_cluster>star clusters</a>, which are balls of gas of the relevant type that are gravitationally bound to one another.  They also have a<A href=http://en.wikipedia.org/wiki/Constellation>technical use</a> of the term “constellation” to refer to one of 88 specific regions of the sky and all the stars in them – thus for instance, the astronomical constellation of <A href=http://en.wikipedia.org/wiki/Crux>Crux</a> consists not just of the five stars of the Southern Cross seen on <A href=http://en.wikipedia.org/wiki/Flag_of_Australia>the Australian flag</a> (for some reason the <A href=http://en.wikipedia.org/wiki/Flag_of_New_Zealand>New Zealand flag</a> has only four stars) but actually has <A href=http://en.wikipedia.org/wiki/List_of_stars_in_Crux>at least a dozen</a> stars.  However, they use the technical term <A href=http://en.wikipedia.org/wiki/Asterism_(astronomy)>“asterism”</a> for something very much like the ordinary term “constellation”.)

Posted by Kenny Easwaran in Uncategorized

15 Comments »

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15 Responses to “What is a Constellation?”

  1. Jonathan Ichikawa says:

    Some beams of light are stars? Most stars are emitted by stars? Stars fly through the universe at the speed of light and bombard the earth? These all sound pretty implausible.

    I guess you must think that it’s true that “last night I looked up in the sky and a whole bunch of stars hit me in the eye.” I don’t think that’s a true sentence of English.

  2. Andrew Bacon says:

    Interesting. But I don’t think that quite accounts for our talk of stars – as Jonathan points out – even if it works for talk of constellations. In particular you said:

    “if the middle star in Orion’s belt were to explode right this instant and stop shining, we wouldn’t actually say that Orion has lost his belt buckle yet – that wouldn’t happen for another 1300 years.”

    I don’t think that confirms the view that stars aren’t the super hot balls of gas we usually associate with stars. I think rather it is better to say that Orions buckle isn’t a star, and that constellations, more generally, aren’t composed of stars but rather beams of light.

    I think its quite plausible that the names of stars were introduced in such a way that they designated whatever caused the light we can see (for example Hesperus and Phosphorus codesignate, even though it is only a few light minutes away, so you would always be talking about a different light beam in the evening/morning respectively. Also people succeeded to refer to it by ‘the morning star’ even though it is a planet.) But the names for constellations presumably were introduced to refer to patterns. I don’t think at the time people knew that the patterns would change so drastically depending on were you were located in the universe, thus the difference between fusions of stars and constellations wasn’t apparent.

    P.S. I thought the Orion Nebula was the middle star of his sword, not his belt?

  3. Kenny Easwaran says:

    Jonathan: The first sentence sounds implausible, but not obviously false. The second is tough to say just because of the equivocation. I’m not sure about the third. But the last one does strike me as problematic.

    So perhaps I shouldn’t be talking about the beam of light, but rather the bright point in the sky. It sounds platitudinous, rather than false, to say that stars are bright points of light in the sky. However, the sky isn’t the same thing as space. But the sky isn’t anything on Earth either. Rather, the sky is some sort of collection of lines of sight out from the earth, or something like that. It’s very bright in some directions, and most of those bright points are stars.

    But there’s still a question about what points in the sky are, since they’re not points in space, and they’re not points in any individual’s visual field. I think this was another issue I remember talking about with Dan now that I think of it – in addition to 3d space, and individual visual fields, there’s also the sky, which has some properties of each (though it’s more like a visual field in most ways, I would think).

  4. Kenny Easwaran says:

    Andrew: It sounds strange to me to say that constellations aren’t made of stars. However, I wouldn’t totally rely on this intuition of mine. If I were to substitute “bright point in the sky” for “beam of light”, would the things you point out sound better? I’d need to say something more about the identity conditions of these bright points in the sky, because the planets move around noticeably from night to night (and even a few stars move noticeably over the course of several decades and centuries), but it seems that this might work without requiring that the names always refer to whatever causes the bright spot. (After all, it’s really not clear whether the ancients even thought there was something causing the bright spots, or just thought of them as some sort of primitives.) And of course, there might be interpersonal or intertemporal variation in the extension of “star” as to whether it includes all the bright spots in the sky (including ones caused by planets and satellites) or just the relatively stationary ones.

  5. Carl Ehrett says:

    The ideas in comments 3 and 4 seem to me unlikely to allay the sort of worries in comment 1 as long as you conceive of the sky as a collection of lines of sight. Presumably, the bright points in the sky would in that case be (something like) those lines of sight that intersect sources of light. And, as one might expect, individuating points as collections of lines has strange consequences.

    For example, even if this prevents that “a whole bunch of stars hit [us] in the eye”, it will still, uncomfortably, be true that stars intersect our eyes, and perhaps even that Betelgeuse (e.g.) in fact fills all the space around and above me (since all that space is within a line of sight of that star).

    Of course, it is possible to hold the sky to be a collection of lines of sight, and yet hold the points of light in the sky not to be some subset of those lines. But I doubt whether, going that route, it will be possible to get right the relationship between star and sky. The points of light should, I think, wind up as part of the sky (rather than merely in the sky). But they don’t seem to be part of any collection of lines of sight.

  6. Jonathan Ichikawa says:

    Kenny, equivocation is a feature of arguments, not sentences. We do not, in general, reject sentences that use ambiguous words in different ways. (At the pool tournament: “There was a commercial break after each break.” Editing the cooking show: “Now cut to the part where he cuts the third cut of beef.”)

    This sentence sounds obviously false:

    “Stars often emit stars, which travel to Earth.”

    According to your view, there should be a true reading of this sentence. If there is a true reading, then, for Gricean reasons, we should expect it to be the dominant one. But it’s just clearly not.

  7. Chad Carmichael says:

    Hi Kenny. You suggest that constellations are not collections of stars because collections do not have the right persistence conditions. A star might be destroyed, for example, in which case you claim the collection would cease to exist while the constellation persists. Perhaps there is a sense of ‘collection’ on which this is true. But isn’t there an ordinary sense of ‘collection’, for example the one we use to talk about baseball card collections and the like, on which collections can gain and lose members? Why not say that a constellation is a collection in this ordinary sense? One reason you might think constellations cannot be ordinary collections is that the stars could become so scattered that they no longer make a figure from the perspective of earth. In that case, you might think, the constellation is destroyed but the collection persists. However, this doesn’t suggest to me that constellations are not ordinary collections. Rather, it suggests that ‘constellation’ is a phase sortal—it applies to an ordinary collection of stars at the phase of that collection’s existence during which the collection is appropriately arranged. When the collection is so arranged that it ceases to make a figure, that collection ceases to be a constellation.

  8. Michael Kremer says:

    I’m with Chad Carmichael here. The motivation for turning from stars (great glowing balls of gas) to beams of light was to solve certain puzzles about persistence conditions. But those same puzzles can be raised about other things we’re inclined to call “collections” — for example, chess sets. Let me tell a true story that seems to me to motivate the point. My wife has a chess set that is made up of reproductions of the Lewis chessmen. When we moved, four pawns from the set were lost. We didn’t say that the set ceased to exist, but that the set was now missing some pawns. (Similarly to what we would say if Orion lost his buckle.) I then found a company (on the Isle of Lewis!) that makes such pieces, and after I sent them one of the pawns (we had four left, of course) they made and sent me some reproductions. In fact, they sent six new pawns, so the set now has two extra pawns. Moreover, the original pieces were made of crushed marble, but the new pieces are made of a resin compound. So now the set has some pieces made of crushed marble and some made of resin. (This is similar to what we would say if Orion acquired a new star.) Same puzzles, but no move to beams of light is going to help here. There may be an analogous move, but there seems to be a broader pattern requiring some deeper analysis.

  9. Kenny Easwaran says:

    Re 7 and 8:

    That’s probably right about collections. But I now no longer think that the persistence conditions are the relevant argument (sorry for being a moving target). We definitely need to address persistence conditions for collections in general for the reasons both of you bring up, but the move to constellations not being composed of glowing balls of gas is motivated by other considerations.

    First of all, as I mentioned in the post, the actual location of a glowing ball of gas is irrelevant to whether it counts as part of Orion or not – instead, all that matters is which direction it is located from Earth, and how bright it appears from Earth. (Moving the central star in Orion’s belt by 100 light years in any direction wouldn’t affect whether it’s part of Orion, but for some of the closer stars, even much smaller movements would affect their membership of Orion. There are hundreds of millions of stars in the relevant direction to be part of Orion, but only a dozen or two of them are bright enough when seen from Earth to count.)

    Another issue is the fact that constellations are located in the sky, but they don’t seem to be located in space. I now think the question I should have started with is “what is the sky?” rather than “what is a constellation?” After all, not everything in space is in the sky – imagine a twin Earth that orbits the sun exactly opposite to Earth (which is a perfectly stable orbit). This twin Earth wouldn’t be in the sky at all, since it would always be blocked by the sun. Also, two things can be at the same place in the sky (as I believe Venus and Mars were a week or two ago), without being at the same point in space. My instinct is to repeat what I suggested above and say that the sky is just the collection of all lines of sight from the Earth, much as a visual field is the collection of all lines of sight from the retina (or is at least related to this collection of lines of sight in some close way). My main worry about this is that birds, planes, and Superman are sometimes in the sky, without being far enough away to make sense of which line of sight they occupy.

    I’m still troubled by Jonathan’s points about ambiguity (especially given the way I’ve seemingly referred to the ball of gas star by means of the bright point in the sky star at several points above). But I’m not sure how serious a worry this is. Does a Cartesian dualist have to deny that the pronoun “I” can ever refer to my body rather than my soul? Then it would be false to say that I ran into a tree the other day when I wasn’t looking where I was walking. And if the word is treated as ambiguous, then it looks like Descartes should be able to say things like “I am connected to me by my pineal gland”, which sounds exceedingly awkward at best. I take it that there are fairly decisive arguments against Cartesian dualism, but that this isn’t one of them. Perhaps the better treatment here is to say that each of these words only literally refers to one of the things (“I” refers to the soul, “star” refers to the ball of gas) but that one can also refer to the other with the same word by means of metonymy. And it seems more difficult to use a word both metonymously and literally in a single sentence than to use an ambiguous word in two different ways. “Downing Street declared yesterday that Downing Street should be repaved.” “The White House told Congress that the White House should be repainted.” I think those sound awkward, though maybe they’re still not as bad as Jonathan’s examples.

    But thanks for the comments!

  10. Chad Carmichael says:

    It seems right that location alone doesn’t deterine whether a star is part of Orion. Luminosity is also important. But how does it follow from this that Orion is not an ordinary collection?

    If constellations were not in space, then that would be a reason to deny that they are ordinary collections of stars, since ordinary collections of stars clearly are in space. But I don’t see why I should agree that constellations are not in space. Perhaps Kenny has in mind that constellations are not in space because they are in the sky and nothing in the sky is in space. But it seems pretty clear that there are stars in the sky. And certainly stars are in space. So it seems that being in the sky doesn’t stop something from being in space as well. So I say that constellations are ordinary collections of stars that are both in the sky and in space. (Perhaps ‘in’ means different things in the two claims.)

    Finally, it doesn’t seem right to me that the sky is a collection of lines of sight. If earth were suddennly annihilated, the sky would cease to exist. But the relevant lines would remain. And, if the earth were moved across the galaxy, it seems to me that the sky would move with it. But the collections of lines of sight from the earth would be different after the move. So that collection must not be the sky.

  11. Kenny Easwaran says:

    Location and luminosity suffice to determine whether a star is part of Orion or not. But they seem to determine it only by means of determining brightness and position in the sky. So it would be more natural (though clearly not absolutely required) to think of the constellation as a collection of things that have brightness and position in the sky as characterizing properties, rather than position and luminosity.

    I think the point you’ve already made about collections saves the “sky as collection of lines of sight” thesis from your objections. Just as a stamp collection can survive replacement of some of its members (and even all of them, if the replacement is done in the appropriate way), and the stamp collection could also be destroyed without any of its members being destroyed (if say each stamp is sold off to a different collector in a different part of the world), so too could the sky be destroyed without any of the lines of sight being destroyed, or the sky could continue to exist with all the lines of sight changed if they were replaced by the appropriate means (like moving the Earth).

  12. Chad Carmichael says:

    I think I can say on my view that brightness and position in the sky are what explain whehter a star is or is not a part of Orion. Of course I also have to say that the brightness and position in the sky of Orion is determined by its location in space and the brightness of its constituent stars. But that seems ok.

    If we each have a stamp collection, I think we can trade some stamps without trading collections. But if I suddenly trade all my stamps for all of your stamps, I think we trade collections. Similarly, if Earth is suddenly transported across the galaxy, the collection of lines of sight is just swapped out altogether. Collections can’t undergo that kind of sudden, complete change.

    It seems implausible to me that the collections of lines of sight would be destoyed if the earth were destroyed. We can imagine an astronaut might remain floating in space after earth is annihilated, and that she can see along the same lines of sight. The sky, I claim, would cease to exist. The collection of lines of sight would remain (if there ever was a collection of these in the ordinary sense of ‘collection’, anyway).

  13. alan nelson says:

    In Astronomy, such names as ‘Orion’ refer to areas on the surface of the celestial sphere. So luminosity is not a criterion for an objects being “in” the constellation—different star maps have different resolutions.
    On a good star map, the boundaries between the constellations are marked off just as political boundaries are marked on terrestrial maps.

    Asterisms are actually closer to what I think has been discussed here. They are fixed bunches of stars: big dipper, “the” southern cross. If one picked out about a dozen stars and called it “Orion”, that would be an asterism. [this doesn’t settle whether it is bodies or lights that are being picked out by ‘star’, of course].

  14. Dan Korman says:

    Hi Kenny,

    Really interesting post! You say that one of the main motivations for the collection-of-bright-points theory is that the location of a star is irrelevant to whether it’s part of a given constellation. I take it that what you have in mind is something like this: Let A be the set of stars associated with Orion and let B be some random set of stars that look from earth to be completely scattered but actually are no less scattered (relative to one another) than the ones in A. You want to say: there’s no ontologically significant difference between the stars in A and the ones in B that could explain why the ones in A compose something, and the ones in B don’t. So the only thing that could explain why the ones in A compose something is that we find their arrangement interesting. And that makes the facts about composition (and about what exists) objectionably mind-dependent. On the other hand, when it comes to bright points, at least we can appeal to their spatial proximity in explaining why them compose something.

    But if that’s what you have in mind, I’m not sure how the move to bright points helps. After all, take some bright point in the vicinity of Orion’s bright points but that’s not part of Orion. Orion’s bright points together with this additional bright point don’t jointly compose a constellation. But again, there seems to be no difference between (i) Orion’s bright points and (ii) Orion’s bright points together with this extra one that could account for why the former but not the latter compose something, other than the fact that we find their arrangement interesting.

    There are a few ways of dodging the problem, but they’re all going to be available to star-theorists too. For instance, suppose composition is unrestricted. Any plurality of bright points compose something — it’s just that which ones get classified as constellations is determined by how they look to us. But the star-theorist can say the same thing if they’re willing to accept unrestricted composition: whether some stars compose something isn’t at all mind-dependent; all that’s mind-dependent is which fusions meet the conditions for being a constellation (and it’s no surprise that that should be mind-dependent).

    Another possibility is that constellations are artifacts. Just as states came into existence when we started drawing boundaries on a map of North America (or perhaps as soon as we started conceptually carving up North America), constellations came into existence when we started drawing boundaries on a map of the night sky (ditto). But again, both the point-theorist and the star-theorist can help themselves to this explanation.

  15. Kenny Easwaran says:

    Alan – I briefly mentioned those points in the last parenthetical remark in my post, but it’s good to have them further spelled out.

    Hi Dan,

    Those are some interesting points. If there really were a very bright point right near Orion, I’m not sure whether we’d say that it was or wasn’t part of Orion. I suppose we could have a situation where Cassiopeia (the W-shaped thing) gradually drifted through Orion, and then we’d say that the stars belonged to one or the other, but in ordinary circumstances, I would have thought that proximity alone would make a bright point part of a (newly misshapen) constellation. But I’m not sure. I’ll have to think about that.

    As for constellations being artifacts, that’s an interesting idea too. But I think you’re right that both points of view allow for that explanation. So in that case I’d have to rely more on arguments about what the sky is made of than the points about constellations themselves.

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