APOD: Apollo's Analemma (2013 Sep 22)

Comments and questions about the APOD on the main view screen.
User avatar
neufer
Vacationer at Tralfamadore
Posts: 18805
Joined: Mon Jan 21, 2008 1:57 pm
Location: Alexandria, Virginia

Analemmata

Post by neufer » Sun Sep 22, 2013 10:23 pm

JohnD wrote:
Please, juts go back and count the number of annalemmas (annalemmae?) that have been APODS.

Too many....annalemmas are really rather boring.
http://www.perseus.gr/Astro-Solar-Analemma-070000.htm wrote:
More men have walked on the moon than have successfully photographed the analemma (see S&T, Dec/2003: 73).
And more men have walked on the moon than have successfully spelled "analemmata" :!:

Analemma (from Greek ἀνάλημμα "pedestal of a sundial")

Become a member of the Analemma Society or make a contribution:
http://www.analemma.org/ wrote:
Image
<<The Analemma Society, formed in 1998, is developing a park where students can learn abut the origin and nature of science as well as experience first hand the wonders of the Universe.

The Analemma Society has exciting plans for an Observatory Park at Turner Farm, supported by the Fairfax County Park Authority. The park will help the Analemma Society to achieve their goal of promoting science education through astronomy in the Northern Virginia area.

Great Falls, Virginia : Latitude N 38º 59' 40", Longitude W 77º 18' 45"

Observatory Park is an excellent place for students from Northern Virginia Schools and members of the community to observe and learn about the day and night sky. The Analemma Society hosts viewings of the night sky in Observatory Park on Friday evenings. A weather watch is provided below and we have a clear sky clock to closely monitor conditions for viewings each week. Please take a look and come out to join us!>>
Art Neuendorffer

User avatar
Nitpicker
Inverse Square
Posts: 2692
Joined: Fri Sep 20, 2013 2:39 am
Location: S27 E153

Re: APOD: Apollo's Analemma (2013 Sep 22)

Post by Nitpicker » Mon Sep 23, 2013 12:30 am

(Neufer, how is Jake LaMotta related to the scale on a sundial?)

The statement "More men have walked on the moon than have successfully photographed the analemma", is interesting to me. The shape of the analemma has been observed since ancient times, through the use of sundials. If one charts the position of the tip of the shadow cast by a sundial at the same time every sunny day throughout a year, one ends up with the shape of the analemma. Such a chart could also be described as a graph, and since it is a graph obtained using light, one could call it a "photograph". So, the analemma has likely been "photographed" successfully for centuries, even millennia.

I do not wish to detract from the impressive effort made by the photographer of this APOD, but we should also give credit to our ancient forebears, on whom be peace.

User avatar
neufer
Vacationer at Tralfamadore
Posts: 18805
Joined: Mon Jan 21, 2008 1:57 pm
Location: Alexandria, Virginia

Re: APOD: Apollo's Analemma (2013 Sep 22)

Post by neufer » Mon Sep 23, 2013 12:48 am

Nitpicker wrote:
(Neufer, how is Jake LaMotta related to the scale on a sundial?)

I do no wish to detract from the impressive effort made by the photographer of this APOD, but we should also give credit to our ancient forebears, on whom be peace.
Our ancient forebears... like Jake LaMotta.
Art Neuendorffer

User avatar
Nitpicker
Inverse Square
Posts: 2692
Joined: Fri Sep 20, 2013 2:39 am
Location: S27 E153

Re: APOD: Apollo's Analemma (2013 Sep 22)

Post by Nitpicker » Mon Sep 23, 2013 12:52 am

neufer wrote:Our ancient forebears... like Jake LaMotta.
He's still alive! :shock:

Edit: I feel compelled, now, to point out that I used the "shocked" emoticon to express my surprise that neufer should call Jake LaMotta an ancient forebear, not that Mr LaMotta is still alive. All the best to you Mr LaMotta (and you too neufer).
Last edited by Nitpicker on Mon Sep 23, 2013 2:29 am, edited 1 time in total.

User avatar
Beyond
500 Gigaderps
Posts: 6889
Joined: Tue Aug 04, 2009 11:09 am
Location: BEYONDER LAND

Re: APOD: Apollo's Analemma (2013 Sep 22)

Post by Beyond » Mon Sep 23, 2013 1:00 am

neufer wrote:Our ancient forebears...
Not to be confused with the ancient 3-bears, of Goldilocks fame, who were quite peaceable.
To find the Truth, you must go Beyond.

User avatar
neufer
Vacationer at Tralfamadore
Posts: 18805
Joined: Mon Jan 21, 2008 1:57 pm
Location: Alexandria, Virginia

Re: APOD: Apollo's Analemma (2013 Sep 22)

Post by neufer » Mon Sep 23, 2013 1:18 am

Nitpicker wrote:
neufer wrote:
Our ancient forebears... like Jake LaMotta.
He's still alive! :shock:
http://officialjakelamotta.com/index
Art Neuendorffer

Boomer12k
:---[===] *
Posts: 2691
Joined: Sun Apr 22, 2007 12:07 am

Re: APOD: Apollo's Analemma (2013 Sep 22)

Post by Boomer12k » Mon Sep 23, 2013 1:33 am

To infinity and BEYOND!!!!

:---[===] *

User avatar
alter-ego
Serendipitous Sleuthhound
Posts: 1123
Joined: Mon Apr 21, 2008 4:51 am
Location: Redmond, WA

Re: APOD: Apollo's Analemma (2013 Sep 22)

Post by alter-ego » Mon Sep 23, 2013 1:36 am

Ayiomamitis wrote: ...
You write that the view is from the southwest which means that one would then be looking northeast. Since the sun rises as far north as around 57 degrees azimuth (for my geographic location), I am not sure where the problem lies. This particular analemma is for 9:00:00 UT+2 which would place it slightly further south in relation to azimuth.

If there was any possibility of pursuing this exercise and which took three years to complete from the actual grounds, I can assure you I would have done it so as to avoid the digital composite involving the two underlying photos.
Hello Anthony,
First I'd like to commend you on both your effort and image. I enjoy the APOD collection from terrestrial to extra-terrestrial, including artistically creative examples the reflect real or perceived visualizations of astronomical phenomena. I think yours is a quality example, and the time and energy it took you to create the composite (using film no less as one of the components!). I personally don't have a problem with this image. I love analemma shots and their variations, and using an ancient Greek temple in the foreground provides an historically aesthetic perspective. Perfectly fitting the early, astronomy era.
By the way, there are interesting analemma views that I haven't seen yet so there is plenty of room for more creativity :)

Second, without judgment, I tend to be technical but I'm not a "hit man" searching for errors. With that said, I often do uncover discrepancies but I typically don't bring them up unless there is good reason to do so. I don't like complaining. APOD contributors (and forum members) don't deserve negative input. If and when some technical discussion is appropriate, I try to do so without being judgmental. I thought this was such a case, and I apologize if I upset you.

Your sincere response indicates an interest in any analemma position discrepancy, so I'll try to answer that now.
The sunlit temple didn't seem to fit the location of the analemma. The placement of the Winter Solstice sun is what I first noticed - it looked to be too far north. It was a strong suspicion, but I didn't have enough information to pursue it further. However, your image times provide me enough to be quantitative. I determined that Mt. Geraneia is in the background. I then identified the Winter Solstice sun azimuth ≈ 33°(East = 90°). That is much too far north. Using your exposure times at 9:00am (UT+2), and Corinth's Lat/Long, I simulated the analemma as viewed from the temple. I sampled the sun position every 14 days (26 locations), and I didn't care about daylight saving time as that detail is not warranted here.

It may be difficult to read the simulation's Alt/Az grid, but the analemma varies in azimuth (as viewed from the temple) between ≈90°(due East) and ≈130° (SE). The latter is the azimuth for the Winter Solstice sun. By my simulation, it appears the true position for the entire analemma is outside your field of view. Also, the simulation indicates the analemma is at a lower elevation than your image. I found your image better fit a 10:00am timing, but I'm uncertain about this and don't give that result much credence.

All in all, I'm confident your azimuth placement for the analemma is too far north by at least 90°. Honestly, I would have done exactly what you did with the images. In my mind, any variance from the analemma's true position is not important. You have a great image.

If your have further questions, I'd be happy to discuss them with you via my PM (if you prefer)
 
 
A pessimist is nothing more than an experienced optimist

User avatar
LocalColor
Science Officer
Posts: 266
Joined: Sat Mar 31, 2012 9:11 pm
Location: Central Idaho, USA
Contact:

Re: APOD: Apollo's Analemma (2013 Sep 22)

Post by LocalColor » Mon Sep 23, 2013 2:28 am

A person must be patient and consistent - and have luck of good weather to capture such an image. Hats off to the photographer! My smarter half has attempted this over the years, but we have so many cloudy days, and a very tall horizon to frustrate his efforts.

dawg65

Re: APOD: Apollo's Analemma (2013 Sep 22)

Post by dawg65 » Mon Sep 23, 2013 2:35 am

At the intersection or cross-over point shouldn't there be 2 close images of the sun, or did you capture the moment when the 2 images overlapped even though taken months apart? Amazing!

User avatar
Nitpicker
Inverse Square
Posts: 2692
Joined: Fri Sep 20, 2013 2:39 am
Location: S27 E153

Re: APOD: Apollo's Analemma (2013 Sep 22)

Post by Nitpicker » Mon Sep 23, 2013 4:52 am

dawg65 wrote:At the intersection or cross-over point shouldn't there be 2 close images of the sun, or did you capture the moment when the 2 images overlapped even though taken months apart? Amazing!
It appears to me that the Sun at the intersection point in the photo is from the June-to-December portion of the curve only. It doesn't appear to quite align with the December-to-June portion (which I suppose means it is not quite the intersection point, not that it matters to me.)

Having had a quick look at Google Maps and Stellarium (don't you just love the age we live in that we can do that?), I have to agree with alter-ego's analysis. If an alternative underlay shot of the temple could be taken, looking at a bearing of about 115 degrees, it would make this image more authentically beautiful (in my humble opinion).

But what is truly, authentically, beautiful, must be the single 35mm negative exposing all the Suns (without any underlay). I'd love to see a photo of the negative. It has a long history and a story to tell, and the photographer should be rightly proud of it.

A cynic might say that such a negative could be produced in a few minutes, by moving the camera around in a controlled fashion and shooting a sequence of frames at the Sun over lunch. Whilst that is perfectly true, it would not be authentic. That being said, such a hypothetical photo shoot might still be considered beautiful to some.

User avatar
Cousin Ricky
Science Officer
Posts: 466
Joined: Mon Aug 26, 2013 4:08 pm
Location: St. Thomas, U.S. Virgin Islands (+18.3, -64.9)

Re: APOD: Apollo's Analemma (2013 Sep 22)

Post by Cousin Ricky » Mon Sep 23, 2013 5:16 am

Joe Stieber wrote:
Anthony Barreiro wrote:My dear friend Bubbles made this analemma that tracks the Sun through the tropical zodiac (e.g. the September equinox is the beginning of Libra).
The sun's position at today's equinox (Sept 22, 2013) is in Virgo, about 38 degrees west of the modern Libra border. It looks like your friend is using an astrological position of the sun that doesn't consider precession.
Well, he did specify tropical zodiac, which is used by the sect of astrology that ignores precession.

(Unless I have it backwards. Not that it matters. :mrgreen: )

User avatar
Nitpicker
Inverse Square
Posts: 2692
Joined: Fri Sep 20, 2013 2:39 am
Location: S27 E153

Re: APOD: Apollo's Analemma (2013 Sep 22)

Post by Nitpicker » Mon Sep 23, 2013 5:45 am

The Tropical Zodiac (common to the Western world) is an idealisation of the Ecliptic, as it appeared ~2000 years ago -- a mere coordinate system if you will, dividing the Ecliptic circle into 12 equal angles. In modern times, the IAU has devised official boundaries for the 88 constellations, and the 13 which happen to straddle the Ecliptic, do not have equal angles on it.

The Tropical Zodiac locks the Northward Equinox (in March) to the start of Aries (the star sign), regardless of precession. This was closer to the reality 2000 years ago ... due to precession, the Tropical Zodiac is currently about one constellation offset from the official IAU constellations of the Ecliptic, give or take a constellation.

The thing which has always puzzled me about Astrology, is that it is measured by which constellation or asterism the Sun is "in" at the time ... but you can't see the stars when the Sun is up. Perhaps this adds to the mystery and helps to keep Astrology popular to this day? I dunno.

User avatar
Anthony Barreiro
Turtles all the way down
Posts: 793
Joined: Wed May 11, 2011 7:09 pm
Location: San Francisco, California, Turtle Island

Re: APOD: Apollo's Analemma (2013 Sep 22)

Post by Anthony Barreiro » Mon Sep 23, 2013 5:57 am

Cousin Ricky wrote:
Joe Stieber wrote:
Anthony Barreiro wrote:My dear friend Bubbles made this analemma that tracks the Sun through the tropical zodiac (e.g. the September equinox is the beginning of Libra).
The sun's position at today's equinox (Sept 22, 2013) is in Virgo, about 38 degrees west of the modern Libra border. It looks like your friend is using an astrological position of the sun that doesn't consider precession.
Well, he did specify tropical zodiac, which is used by the sect of astrology that ignores precession.

(Unless I have it backwards. Not that it matters. :mrgreen: )
Without regard to whether astrology has any predictive or descriptive validity, the tropical zodiac is simply an annual calendar, beginning at the March equinox when the Sun is at ecliptic longitude zero, the first point of Aries, and changing signs each time the Sun has travelled through 30 degrees of ecliptic longitude. It's still a useful system because it coordinates perfectly with the seasons, which are not affected by precession. You just have to remember that because of precession tropical signs don't match up with astronomical constellations. Also, the boundaries of our current astronomical constellations weren't drawn until 1930 CE, and the tropical zodiac has been in use for millennia. They're just different systems and each has its own uses.
May all beings be happy, peaceful, and free.

User avatar
DavidLeodis
Perceptatron
Posts: 1169
Joined: Mon May 01, 2006 1:00 pm

Re: APOD: Apollo's Analemma (2013 Sep 22)

Post by DavidLeodis » Mon Sep 23, 2013 10:39 am

On clicking the "Sun crosses" link the website knew my location. I know that can be done but it was still a bit disconcerting without first knowing that it would be done. On looking at an about us in the website it stated "Time and Date AS (AS - "Aksjeselskap") is a private, limited liability company owned by Steffen Thorsen. The company is based near Stavanger, Norway. It is registered in the Norwegian "Foretaksregisteret" (The register of business enterprises) as NO 988 375 713 MVA.". I hope it can be trusted not to use location information, nor whatever else it may have recorded, for commercial means.

User avatar
rstevenson
Quis custodiet ipsos custodes?
Posts: 2705
Joined: Fri Mar 28, 2008 1:24 pm
Location: Halifax, NS, Canada

Re: APOD: Apollo's Analemma (2013 Sep 22)

Post by rstevenson » Mon Sep 23, 2013 12:12 pm

DavidLeodis wrote:On clicking the "Sun crosses" link the website knew my location. I know that can be done but it was still a bit disconcerting without first knowing that it would be done. On looking at an about us in the website it stated "Time and Date AS (AS - "Aksjeselskap") is a private, limited liability company owned by Steffen Thorsen. The company is based near Stavanger, Norway. It is registered in the Norwegian "Foretaksregisteret" (The register of business enterprises) as NO 988 375 713 MVA.". I hope it can be trusted not to use location information, nor whatever else it may have recorded, for commercial means.
It's hard to imagine what sort of commercial advantage might be gained by that site by knowing your location when you access that page. The page has no means of knowing whether you're at home, or at an internet cafe, or a friend's house, or school or work, or on vacation in a foreign land.

I've run a couple of eComm sites for years and I can assure you that for some types of sites, knowing approximately where you are is quite helpful to the business, and is therefore not the sort of thing that would be shared with anyone else. But it's only helpful in the aggragate, and only to a business that can target the audience they discover through such means. (My two Canadian fine art greeting card sites couldn't change our products or in any other way I could imagine take advantage of the information, so for us, it was merely interesting that a few percentage of our site visitors were from South-east Asia.)

Knowing where you are when you access a web page is a trivial exercise for any web site, including the Asterisk itself. You should assume, if you're concerned about such things, that every page you visit is recording that information.

Rob

Guest

Re: APOD: Apollo's Analemma (2013 Sep 22)

Post by Guest » Mon Sep 23, 2013 12:32 pm

Thanks all for answering my question.
I had failed to realize that the time is measured from the edges of the sun and not the center.
That explains about 5 or 6 minutes of the difference.
And the atmospheric bending explains the rest.
It makes senses now.

User avatar
DavidLeodis
Perceptatron
Posts: 1169
Joined: Mon May 01, 2006 1:00 pm

Re: APOD: Apollo's Analemma (2013 Sep 22)

Post by DavidLeodis » Mon Sep 23, 2013 1:07 pm

rstevenson wrote:
DavidLeodis wrote:On clicking the "Sun crosses" link the website knew my location. I know that can be done but it was still a bit disconcerting without first knowing that it would be done. On looking at an about us in the website it stated "Time and Date AS (AS - "Aksjeselskap") is a private, limited liability company owned by Steffen Thorsen. The company is based near Stavanger, Norway. It is registered in the Norwegian "Foretaksregisteret" (The register of business enterprises) as NO 988 375 713 MVA.". I hope it can be trusted not to use location information, nor whatever else it may have recorded, for commercial means.
It's hard to imagine what sort of commercial advantage might be gained by that site by knowing your location when you access that page. The page has no means of knowing whether you're at home, or at an internet cafe, or a friend's house, or school or work, or on vacation in a foreign land.

I've run a couple of eComm sites for years and I can assure you that for some types of sites, knowing approximately where you are is quite helpful to the business, and is therefore not the sort of thing that would be shared with anyone else. But it's only helpful in the aggragate, and only to a business that can target the audience they discover through such means. (My two Canadian fine art greeting card sites couldn't change our products or in any other way I could imagine take advantage of the information, so for us, it was merely interesting that a few percentage of our site visitors were from South-east Asia.)

Knowing where you are when you access a web page is a trivial exercise for any web site, including the Asterisk itself. You should assume, if you're concerned about such things, that every page you visit is recording that information.

Rob
Thanks Rob for your reply.

Perhaps my mention of commercial interest was wrong, but my concern was that as the website knew exactly where I was then could it also be taking information about my home computer without my knowledge. Though I would expect that would be done without asking from dubious websites (which I would never knowingly visit) I was surprised that a link in an APOD was to a website that might be automatically taking and keeping information, as it is run by a private company. I assume that the Asterisk must know a lot about me by now. :wink:

User avatar
geckzilla
Ocular Digitator
Posts: 9180
Joined: Wed Sep 12, 2007 12:42 pm
Location: Modesto, CA
Contact:

Re: APOD: Apollo's Analemma (2013 Sep 22)

Post by geckzilla » Mon Sep 23, 2013 2:57 pm

David, it's likely simply extrapolating your location based on your IP. Anytime you transmit any information online you are giving that web server your IP. It's still anonymous to an extent because no one knows exactly who is using that IP but it is possible to find out more specific details but only your ISP should have access to that information, which I suppose could get told to law enforcement if you were involved in some kind of illegal activity. Anyway, it's harmless in my opinion.
Just call me "geck" because "zilla" is like a last name.

User avatar
rstevenson
Quis custodiet ipsos custodes?
Posts: 2705
Joined: Fri Mar 28, 2008 1:24 pm
Location: Halifax, NS, Canada

Re: APOD: Apollo's Analemma (2013 Sep 22)

Post by rstevenson » Mon Sep 23, 2013 5:49 pm

Yes, as geckzilla mentioned, they were likely only looking at your IP address. They could get more info than that by cross-collating with other data they either get themselves or buy, but in the case of that particular site, I'm guessing that's extremely unlikely.

On the other hand, if you buy books online by signing in with your Facebook account (which is something we're all being asked to do more and more) you'll be giving that book site a lot of information they'd love to see -- if you have a FB account, that is.

Rob

User avatar
Anthony Barreiro
Turtles all the way down
Posts: 793
Joined: Wed May 11, 2011 7:09 pm
Location: San Francisco, California, Turtle Island

Re: APOD: Apollo's Analemma (2013 Sep 22)

Post by Anthony Barreiro » Mon Sep 23, 2013 8:21 pm

Guest wrote:Thanks all for answering my question.
I had failed to realize that the time is measured from the edges of the sun and not the center.
That explains about 5 or 6 minutes of the difference.
And the atmospheric bending explains the rest.
It makes senses now.
Oh good.

I'm struck by how almost every "fact" in astronomy is actually an approximation, and how there will always be one more level of subtle complexity to explore. It's like the number pi, 3.14159 ... and however many more digits you want to compute. 3 is good enough for rough estimation, 3.14 for most purposes, etc.

I think the trick in learning about astronomy (and probably most everything else) is to gain a solid understanding of the first order of approximation before trying to understand the next. In this instance it is crucially important to understand why day and night are approximately equal at the equinoxes, especially when compared to the solstices. Once you've got that firmly in mind, then you can move on to understanding why the day is a few minutes longer than the night on the date of the equinox.

A problem can arise when someone with a deeper level of understanding of a particular phenomenon uses that understanding to gain a sense of personal superiority over someone who is still developing a more basic understanding. (That never happens here on Starship Asterisk, by the way.) It would be like a math teacher talking about the instantaneous rate of acceleration with a student who is still figuring out how to calculate average speeds.

Also, I find it helpful to remember that our ancient forebears (like Jake LaMotta) figured out a lot of this stuff without the benefit of timepieces, magnetic compasses, electronic calculators, personal computers, global positioning satellites, google maps, or any of the other modern conveniences we take for granted today. To my mind the wonder is that they got so much right, rather than how much they got wrong.

I guess my mind is wandering here and there on this first full day of autumn here in the northern hemisphere.
May all beings be happy, peaceful, and free.

User avatar
Anthony Barreiro
Turtles all the way down
Posts: 793
Joined: Wed May 11, 2011 7:09 pm
Location: San Francisco, California, Turtle Island

Re: APOD: Apollo's Analemma (2013 Sep 22)

Post by Anthony Barreiro » Mon Sep 23, 2013 8:25 pm

alter-ego wrote:
Anthony Barreiro wrote:... and the Sun's east-west movement at mean solar noon is caused by the Earth's elliptical orbit around the Sun.
Speaking just about the Sun's apparent motion, only the asymmetry of the figure "8" shape is due to the eccentricity of the Earth's orbit. Both the east-west and north-south solar movements are due to the obliquity of the ecliptic. If the Earth's orbit were perfectly circular, the analemma would still be there. Only the shape and orientation would be different.

Edit:
Below you can see the components to the analemma - the vertical axis is degrees and the horizontal axis minutes of time.
Analemma Components.JPG
Thanks, masked humanoid. I'm going to have to chew on this for a while.
May all beings be happy, peaceful, and free.

User avatar
Beyond
500 Gigaderps
Posts: 6889
Joined: Tue Aug 04, 2009 11:09 am
Location: BEYONDER LAND

Re: APOD: Apollo's Analemma (2013 Sep 22)

Post by Beyond » Mon Sep 23, 2013 10:45 pm

Masked humanoid :?: :?: Anyone can tell that the days are a little longer than the nights, because you always see light before you see the sun, and you always see light after the sun disappears. No fancy science stuff needed. :no:
To find the Truth, you must go Beyond.

User avatar
Anthony Barreiro
Turtles all the way down
Posts: 793
Joined: Wed May 11, 2011 7:09 pm
Location: San Francisco, California, Turtle Island

Re: APOD: Apollo's Analemma (2013 Sep 22)

Post by Anthony Barreiro » Mon Sep 23, 2013 11:15 pm

Beyond wrote:Masked humanoid :?: :?:
I was commenting on the nom de plume "Alter Ego." Makes me wonder who's behind the persona ... .
Beyond wrote:Anyone can tell that the days are a little longer than the nights, because you always see light before you see the sun, and you always see light after the sun disappears. No fancy science stuff needed. :no:
I think you're conflating two different threads. Alter Ego was enlightening me on the relationship between the Earth's orbit around the Sun and the shape of the Sun's analemma in the sky.
May all beings be happy, peaceful, and free.

User avatar
Beyond
500 Gigaderps
Posts: 6889
Joined: Tue Aug 04, 2009 11:09 am
Location: BEYONDER LAND

Re: APOD: Apollo's Analemma (2013 Sep 22)

Post by Beyond » Tue Sep 24, 2013 12:20 am

Ah, masked humanoid. Gotcha. You could be right about the conflating. Although i think i was mostly inspired by Guest's post, about 7 posts previous, i think, about measuring from the suns center and not the edges, causing a time discrepancy. Sometimes the ol' noggin gets something stuck in it and you don't realize how well it doesn't go with the conversation, until you put it out and someone points out the error. :yes:
To find the Truth, you must go Beyond.

Post Reply