Stars in the sky: An optical illusion

I was looking at Sirius last night, and I realised it very clearly looked five-pointed. Scan to another largish star, and sure enough, that seemed to have five pointy ends too.

Now, I’ve been camping in some pretty lonely places where the nearest (terrestrial) source of light was way, way over in the extremely distant horizon. Never has such a point source of light seemed five-pointed. So, it’s not a phenomenon that occurs because of distance.

What, then, causes this optical illusion?

If several stars showed 5 points, it probably wasn’t atmospheric turbulence.
Ice in the atmosphere usually gives four or six rays.
Minor astigmatism? Did anyone else see 5 pointed stars, or was it just you?

Do you wear spectacles or contact lenses?

Well, not last night specifically, but before that, yes. I’ve been in company where we’ve remarked about stars looking 4-, 5-, even 6-pointed. Varies, really. This is something I’ve noticed often before, but just thought to ask about today.

I do. The former.

How fortuitous! I just gave a lecture on this at the Christa McAuliffe Planetarium on Friday! (under my real-life name):

http://www.starhop.com/ssf.htm
In essence, the appearances of stars are determined by the limitations of our viewing apparatus (our eyes). The thing that causes stars to appear to have points is entoptic phenomena. You can see sketches of this done by Hermann von Helmholtz a century and a half ago, in his still-in-print book Physiological Optics. There are also some pix in M. Minnaert’s book The Nature of Light and Color in the Open Air (also still in print).

As noted above, you can see this effect more clearly if you’re myopic (I am), but I don’t think it’s necessary. A lot of people think it’s a diffraction effect ultimately due to structure in the crystalline lens in the eye. As far as I can determine, though, no one has definitively proven this, and there are a lot of structures in the eye that can cause this or contribute to it.
One quibble, though – you’ll notice that none of Helmholtz’ or Minnaert’s sketches (if you look them up) actually have five points. Furthermore, ancient depictions of stars typical;ly show them having four or six or eight points. (I showed several pictures of this on Friday night). This is true up through the Renaissance – six or eight points is the usual rule, with the occasional four-pointer. Furthermore, there’s some good ophysics behind this – diffraction patterns can’t have an odd number of points. A six-sided aperture, or a structure with sixfold symmetry, will give you a six-pointed star. But a five-sided aperture or figure with fivefold symmetry gives you a ten-pointed star. (On top of which, although you can tesselate a plane with four- or six-sided figures, you can’t do it with five-sided figures. And you can “tesselaste” a sphere with the five-and-six-sided figures of a truncated icosahedron – soccer ball shape – but that has more hexagons than pentagons.)

So whence the five-pointed star? I’ve never really seen one, myself. But I hazarded a guess on this. In the ancient world, the only five-pointed stars you see are from ancient Egypt. And the five-pointed stars there don’t look like the ones that you draw without lifting your pencil from the paper. The arms are of uniform width, right down to where they meet.
I think they’re inspired by starfish, which are abundant in the Eastern Mediterranean, and have just that shape. Furthermore, several varieties tend to sek out shade and avoid direct sunlight – just the way stars in the sky behave. Our own five-pointed stars started appearing in Western culture after the “rediscovery” of ancient Egyptian culture about two hundred years ago. “Endless knot” five-pointed penacle-type figures appeared before that, but they weren’t associatede with stars in the sky. So I think we have five-pointed stars because Egyptians associated starfish with the diffraction images of myopic stars, and we picked it up in the Egyptian art craze that began about the toime the Rosetta Stone was discovered. (Interestingly enough, one of the people instrumental in formulating our theories of diffraction and the wave nature of light was Thomas Young, who began the translation of the hieroglyphics on the Rosetta Stone (well before Champollion did).

Can’t you actually get five-pointed diffraction patterns from a Penrose tiled grating? I seem to recall reading something of the sort.

If you have a cite I’d love to see it. That’s not a challenge – it’s genuine interest.

I’ve got a stack of papers, both theoretical and experimental, showing that pentagonal apertures give you ten-pointed star patterns. It seems to me that anything with fivefold symmetry ought to give you the same.

Five fold diffraction patterns in Quasicrystals. I wouldn’t be too surprised if eye proteins could arrange themselves in this type of nonperiodic structure.

Interesting, but:

1.) X-ray Diffraction Patterns aren’t quite the same as the visible light patterns I discuss

2.) In any case, the diffraction pattern they give still has 10-fold, not 5-fold symmetry!

To expand just a bit on CalMeacham’s excellent post:

ISTR quite a bit of reliance in european renaissance “oriental” mysticism, up to and including Crowley and neopagans, of the five-pointed star symbolizing Man, the human soul, or the human spiritual body.

Of course, in this context, “oriental” means middle eastern, and almost always Egyptian. And rumors abound that many of the USA’s founding fathers dabbled in oriental mysticism, which would explain their use in the flag of the newly-emergent colonial democracy.

You’re right, although on the second count it may be just a poor picture. The article I linked to and several others certainly talked a lot about 5 fold symmetries. I expected to find an article on hologtaphic optical gratings that give a 5 fold pattern, but came up dry. Perhaps no one’s made one yet?

This thread makes me feel very ignorant.

::starts reading up on diffraction patterns, entoptic phenomena, and whatnot::

::head exlpodes::

That’s the interesting thing, though – structures and apertures with odd symmetries (3-fold, 5-fold, etc.) produce interference patterns with even symmetries – a result that I, myself, wouldn’t have predicted. But if you dig into the literature, you can find plenty of experimental and theoretical work to back it up. Weird and interestin’ stuff. And unexpected.

Don’t, please – it’s really all about pretty pictures. I’ll see if I can scare up some non-mathematical websites.

It’s only an even symmetry because you can’t see the phase. An interference pattern is basically a two-dimensional Fourier transform; the amplitude of the pattern from a constant-phase source has inversion symmetry, so it’s necessarily even. The phase of the interference pattern is antisymmetric under inversion.

In the intervening 12 years I’ve managed to forget all the details, but I recall the Mermin review article (Rev.Mod.Phys. 64 (1992) 3-49, as recommended in part of the site linked to by Squink) on quasicrystals and crystallographic classification being very, very good.

So, is it a fair assumption that unless I know oodles of calculus and even more oodles of college-level physics, I’ll never understand why stars in the sky might look pointy? No answers for laymen?

Well, shoot.

Thank you all for trying, though.

Stars look pointy because the lens of your eye acts as a crystal and diffracts the light along its planes.

Heh I think everyone got hung up on the impossible 5 pointed thing. I just went out and looked myself, and I saw many points, and they weren’t all symmetrically arranged around a circle. Probably due to slight imperfections in my eye, I saw 20 something odd points, with 7 bright ones and many faint ones. However, the 7 bright ones were arranged along the lines of an 8 pointed star, with one line missing. That direction simply wasn’t working for me as far as generating points goes. Being an artist, I’ve much practice noticing what I actually see as opposed to what I expect to see.

I think a similar thing happened to you. You probably saw a 6 pointed symetry, with one point missing due to imperfections in your eye. That’s not the same thing as a five pointed star…I highly doubt the 5 points were 72º apart around a circle. Instead you saw 5 bright lines that were a part of a more understandable symmetry, but not all lines in that symetry were bright.

For example ( on a hypothetical clock face)you might have seen lines at 12 o’clock, 2:30, 5:00, 7:30 and 10:00. While that might look like a 5 pointed star, what you are really seeing is a multiple of 6 sided symetry not being fully represented. There is no 5 symmetry here.

As to why you only see it when you look up at stars, perhaps the difference in curvature in your eye between looking horizontal and vertical is just enough to change which lines you see.

It’s not too hard to understand why stars sometimes look pointy. See this Astronomy Picture of the Day on refraction spikes in telescopic images for starters. With any luck someone will be along shortly with a good link on diffraction spikes produced by icey clouds. The trouble everyone is having with your question is that 5 pointed stars or diffraction patterns are so rare as to be mostly unheard of. That makes it hard to come up with an explanation of exactly what you saw in the sky.

Whoops. Sorry Cal. I went brain-dead, and forgot that you had already gotten a good start on the ice crystal bit. No offense intended.