# Thread: Bees from the sixth dimension

1. Join Date
May 2002
Location
Danbury,Ct. USA
Posts
1,964
Hi All,
Came across this connection between the bee dance and quantum mechanics. Anybody game to read it? If you look up "flag manifold" it will not make you feel good. For this article I think flag manifold=mathematically defined space.

From:
I Cite:
One day Shipman was busy projecting the six-dimensional residents of the flag manifold onto two dimensions. The particular technique she was using involved first making a two-dimensional outline of the six dimensions of the flag manifold. This is not as strange as it may sound. When you draw a circle, you are in effect making a two-dimensional outline of a three-dimensional sphere. As it turns out, if you make a two-dimensional outline of the six-dimensional flag manifold, you wind up with a hexagon. The bee's honeycomb, of course, is also made up of hexagons, but that is purely coincidental. However, Shipman soon discovered a more explicit connection. She found a group of objects in the flag manifold that, when projected onto a two-dimensional hexagon, formed curves that reminded her of the bee's recruitment dance. The more she explored the flag manifold, the more curves she found that precisely matched the ones in the recruitment dance. "I wasn't looking for a connection between bees and the flag manifold," she says. "I was just doing my research. The curves were nothing special in themselves, except that the dance patterns kept emerging." Delving more deeply into the flag manifold, Shipman dredged up a variable, which she called alpha, that allowed her to reproduce the entire bee dance in all its parts and variations. Alpha determines the shape of the curves in the 6-D flag manifold, which means it also controls how those curves look when they are projected onto the 2-D hexagon. Infinitely large values of alpha produce a single line that cuts the hexagon in half. Large' values of alpha produce two lines very close together. Decrease alpha and the lines splay out, joined at one end like a V. Continue to decrease alpha further and the lines form a wider and wider V until, at a certain value, they each hit a vertex of the hexagon. Then the curves change suddenly and dramatically. "When alpha reaches a critical value," explains Shipman, "the projected curves become straight line segments lying along opposing faces of the hexagon."

The smooth divergence of the splayed lines and their abrupt transition to discontinuous segments are critical--they link Shipman's curves to those parts of the recruitment dance that bees emphasize with their waggling and buzzing. "Biologists know that only certain parts of the dance convey information," she says. "In the waggle dance, it's the diverging waggling runs and not the return loops. In the circle dance it's short straight segments on the sides of the loops." Shipman's mathematics captures both of these characteristics, and the parameter alpha is the key. "If different species have different sensitivities to alpha, then they will change from the waggle dances to round dances when the food source is at different distances."

If Shipman is correct, her mathematical description of the recruitment dance would push bee studies to a new level.

Dickm

[size="1"][ December 23, 2005, 09:03 AM: Message edited by: dickm ][/size]

2. Join Date
May 2005
Location
chilliwack, bc
Posts
699
Very intresting. I remember reading an article that roughly summerized the mathimatical universe. i wouldn't doubt that there's an equation out there (albiet a big complex one) that explains...well...everything.

3. Join Date
Apr 2005
Location
Worthington, Pennsylvania USA
Posts
1,833
DICKM--Now that is heavy duty reading, thanks for sharing. After reading that artoc;e my mind is as quiescent as my bees.

4. Join Date
Apr 2005
Location
Worthington, Pennsylvania USA
Posts
1,833
See, I can not even type article.

5. Join Date
Jan 2001
Location
New York City
Posts
3,397
After reading the description, I have an
uncontrollable urge to play "Up, up and
away in my beautiful balloon" by the
60s pop group "The Fifth Dimension".

Like the "connection" found, the song
requires the use of lots and lots of
hot air. [img]smile.gif[/img]

"...projecting the six-dimensional residents
of the flag manifold onto two dimensions..."

Remember, a topologist can't tell his coffee
cup from his donut, as both are two-dimensional
compact manifolds. Never sit next to a
topologist at breakfast, as there is a 50/50
chance he will try to pour his coffee "into"
the donut, and the coffee will spill on your
suit.

6. &gt;Remember, a topologist can't tell his coffee
cup from his donut, as both are two-dimensional
compact manifolds. Never sit next to a
topologist at breakfast, as there is a 50/50
chance he will try to pour his coffee "into"
the donut, and the coffee will spill on your
suit.

OK Jim, you finally made me laugh out loud. [img]smile.gif[/img] And that probably proves I'm a geek.

7. Join Date
Mar 2005
Location
Odessa, Missouri
Posts
629
Chillard said:
I wouldn't doubt that there's an equation out there that explains everything"

Might be but there certainly is a statement made years ago by a beekeeper which explains everything.

"What we don't know is so vast it makes what we do know seem absurd" (Bob Harrison)

The article you read might have been by Steven Hawking as he has moved beyound the thinking of Einstein. An excellent book is "A brief History of Time" by Hawking. Todays world does not encourage the best minds and rather seems to do just the opposite.

You will only find one equation discussed in the above book because the publishers told Hawking that for each equation included in the book would halve the sales ( pg. 2 of the above book under acknowledgments).

8. Join Date
Mar 2005
Location
Erin, NY /Florence SC
Posts
3,558
I found the article rather Ruth-less!

9. Join Date
Dec 2004
Location
Totnes, Devon, England
Posts
1,020
Wow - I almost understood some of that! I'm going to run it past my daughter, who has just won a place at Oxford to study astrophysics. Maths was never my subject...

But don't these guys live in a weird world?

"The flag manifold (which got its name because some imaginative mathematician thought it had a "shape" like a flag on a pole) happens to have six dimensions, which means mathematicians can't visualize all the two-dimensional objects that can live there. That does not mean, though, that they cannot see the objects' shadows."

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