Friday, December 07, 2007

Photo Hunters: Long: ". . . and birds perch on the phone lines."

Photo: Sparrows on a Fence. Taken in New Haven, CT in October 2007.

The photo will open, horizontally, in a new window when clicked.

Text: Letters to a Young Mathematician. Ian Stewart. Basic Books: 2006. New York. pp 46-48.

"From a distance they look like sheet music, fat little blobs on rows of horizontal lines. There seem to be special places they like to perch, and it’s not at all clear to me why, but one thing stands out. If a lot of birds are perching on a wire, they end up evenly spaced.

"That’s a mathematical pattern, and I think there’s a mathematical explanation. I don’t think the birds 'know' they ought to space themselves out evenly. But each bird has its own 'personal space,' and if another bird gets too close, it will sidle along the wire to leave a bit more room, unless there’s another bird crowding it from the other side.

"When there are just a few birds, they end up randomly spaced. But when there are a lot, they get pushed close together. As each one sidles along to make itself feel more comfortable, the 'population pressure' evens them out. Birds at the edge of denser regions get pushed into less densely populated regions. And since the birds are all of the same species (usually they’re pigeons), they all have much the same idea of what their personal space should be. So they space themselves evenly.

"Not exactly evenly, of course. That would be a Platonic ideal. As such, it helps us to comprehend a more messy reality.

"You could do the math on this problem if you wanted to. Write down some simple rules for how birds move when the neighbors get too close, plonk them down at random, run the rules, and watch the spacing evolve. But there’s an analogy with a common physical system, where that math has already been done, and the analogy tells you what to expect.

"It’s a bird crystal.

"The same process that makes birds space themselves regularly makes the atoms in a solid object line up to form a repetitive lattice. The atoms also have a 'personal space': they repel each other if they’re too close together. In a solid, the atoms are forced to pack fairly tightly, but as they adjust their personal spaces, they arrange themselves in an elegant crystal lattice.

"The bird lattice is one-dimensional, since they’re sitting on a wire. A one-dimensional lattice consists of equally spaced points. When there are just a few birds, arranged at random and not subject to population pressure, it’s not a crystal, it’s a gas.

"This isn’t just a vague analogy. The same mathematical process that creates a regular crystal of salt or calcite also creates my 'bird crystal.'"
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58 comments:

  1. Do you know, until I read this, I just took it for granted that birds lined themselves up relatively equally on a phone wire. I didn't realise there was an actual mathematical equation to it...amazing, yet it's one of those things we see all the time and never think about.

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  2. Very interesting Andrée, and a great photo for the theme. Birds are not so stupid after all.

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  3. I love the photograph of the birds on the line. Works so well for this theme and I find the spacing interesting. When I used to feed birds on my deck wall ledge (still do in particularly bad weather), I notice that they have there own space even when relatively close together. Different from a line but I guess the same principle. I hope you have a pleasant weekend.

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  4. Very very nice shot. I like how you got very close. Birds are so tough for me. They always fly away.

    Mine will be up at midnight EST.
    http://www.benspark.com/photo-hunters-long-120807.html

    Please come by and visit. It is of my favorite road photo.

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  5. You always have nice pictures of yummy birds to look at.


    Hugs...G

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  6. Nice shots. Have a great weekend.

    Oh yes, mine is up too.

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  7. Nice long line of birds on that fence.

    What I have observed recently about pigeons on a phone wire is that they are bunched together on each side of the pole. I figure that they don't sit in the center because of the droop--the wire more stable and less wobbly closer to the pole. And close together because--it's COLD out there!

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  8. that is one of the best photos of the week! great shot.

    happy hunting.

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  9. interesting!
    love that shot, too ...

    happy weekend!
    My PhotoHunt post

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  10. I love this photo! It reminds me of the animated film Monsters where at the beginning of the film, it shows some birds on a line. And when a huge ugly bird joined them, they boycott it. They got hurt when they tried to harm the ugly bird. A funny cartoon.

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  11. That's neat, what a cool submission for the theme.

    My LONG picture is up too! :)

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  12. Great choice for our theme this week.

    I've been noticing the birds all lined up on power wires and other places lately. Didn't realize that math was involved.

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  13. Wonderful and amazing! Thanks for dropping by ;)

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  14. Now my neck hurts ! Had to turn my head to see the sparrows ! That's so funny seeing them sitting in a line !

    PS Poor Arthur's peaceful time is finished, Rosie is full back again, lol !

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  15. I love the photo! Nice take on the theme. Happy weekened ;)

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  16. great shot! wow, i love photo essays! great info. thanks. :)

    happy weekend! :)

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  17. Now that's a long photo!.....

    http://kennyljs.com/

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  18. What a wonderful post. Not only do we get a great photo but now I will never look at birds on wores the same way again! Have a great weekend

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  19. lol I just love it. In SD in the summer they are on our barbed wire fence but not all in a row like that, Thanks for sharing that great photo.

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  20. Great shot and very interesting reading. Thanks!

    Happy Weekend.

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  21. This is really creative "long" photo~!!!!!! I am so admiring~!!!!

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  22. Great shot of the birds and thanks for the interesting read.

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  23. This is my favorite Long today. I think I need to study those birds for a little bit longer...

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  24. Wow! I love the picture by itself, but with the explanation and quotes it's amazing!

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  25. Good shot and good read. Thanks.

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  26. Hi....cool photo!! I love your photo layout style...that's cool.

    And, sure you can put the recipe card up on your recipe blog...I'm flattered.

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  27. How very interesting! I learned something new! Thanks so much for stopping by Long on Pollywog Creek, too! Hope your weekend is long in delights!

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  28. Thanks for the interest info along with the pretty photo! :)

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  29. Great idea for the theme! Happy photo hunting, and have a great weekend :)

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  30. When my hubby and i see birds all lined up on a wire we always comment that they are "ON LINE"....computer using!! smile.

    Sandy

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  31. ugh! mathematical calculations- that would take too "long"! How about just figuring they leave enough space between themselves so that they have room to spread their wings for takeoff? Nice picture!

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  32. Nice shot! And I never thought about birds having personal space issues. Very interesting, thanks. :)

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  33. Cool photo! That is certainly a long line of birds. Very interesting information! Thanks for sharing. :)

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  34. That is absolutely an amazing post! Now I'll think of salt crystals ever time I see birds on a line!

    Beautiful shot :-)

    Thanks for visiting!

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  35. That's a great shot and a terrific post! Very interesting :-)

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  36. That is such a cute picture of those birdies! I just love watching birds' antics!

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  37. I noticed that about birds, but didn't know there was a mathematical explaination for it. We, like birds, also like our "space" like when standing in a long line. Great photo! Have a good weekend.

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  38. I really think you did a wonderful job on this weeks theme!! Thanks for your visit! Have a great weekend!! Grams

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  39. terrific photo! and nifty math connection!

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  40. What a great pic! And I'm amazed to discover that your sparrows are the exact same species that we have here in the UK. Have a great weekend!

    My LONG pics are up at Siani's Pot-Pourri.

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  41. I was just about to comment about species of sparrows when I though I'd look to see what I had said last week about woodpeckers and nuthatches, only to find I've commented on the wrong post, the wrong blog, or messed it up altogether! Never mind, I love the picture, especially end on:)

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  42. I never thought of horizon being or could be use in the math term of long.
    One of my son grade school teacher said people who tend do there math in horizon style thinks more in algebra.

    Mine up now

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  43. I never thought of horizon being or could be use in the math term of long.
    One of my son grade school teacher said people who tend do there math in horizon style thinks more in algebra.

    Mine up now

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  44. A really thoughtful take on this week's theme. Thank you for that quote, I have often seen birds rowed up like that. Now I can understand why. :)

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  45. Beautiful, long line of birds...
    Thanks for the visit!

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  46. very interesting!great photos of the birds too..Mine is up too have great weekend!

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  47. that is so cute :D
    and great info
    - ideru ( http://ideru.kansaiblogger.com )

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  48. Thank you for the interesting information, wouldn't have known that there is something mathematical about them sitting on a wire :) Love your photo of the birds sitting atop the fence.

    Have a great weekend, Andree :)

    Julie
    http://teacherjulie.com/2007/12/07/photo-hunt-long/

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  49. Wow, what awesome photos you take!!! I just visited your other blog (all photos of birds mostly) and was quite impressed. We are studying birds in school (homeschool) and I'm going to show the kids your site. Love the LONG photo hunt picture as well!
    Have a great day,
    Elinor

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  50. I loved the creative way you have arranged the shot. never thought of it!

    And the accompanying story is fascinating. Personal space is important not only to us, it appears.

    Interesting, do Mediterranean birds keep a shorter distance between them, like Mediterranean people?

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  51. original and interesting idea for the theme!a space for the birds...the nature is so perfect!

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  52. What a fabulous photo. i love watching birds and seeing their behaviour. Sara from farmingfriends

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  53. Got your comment on my blog, and this is TOO funny. I always wondered why the birds kind of knew exactly what to do on the wire. They all sit like they have a perfect spot, and exactly in an even spaced row! Birds must be mathematical geniuses!
    --JB

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  54. Hi there, your post been recommended by JB since I saw his arrangement of birds. I think we under-estimate birds, they are in fact intelligent creatures. However, I was thinking, may be they arrange themselves in the patterns or spaced equally, because they know how much space they need to take off. Anyway, this is very interesting, I started some bird watching this year, so I will consider this into my observations. Nice blog you have too. Anna :)

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