I confess that I had no idea of what the Infinity symbol was before I was requested to design this Cloth, but I am glad I had to learn about it. How fascinating!
I like to work on projects that teach me something, whatever it is about knitting or not. Thank you, Jolene! 
= The mathematical symbol for infinity is called the lemniscate (lemniscus in latin = pendant ribbon). The lemniscate is patterned after the device known as a mobius (named after a nineteenth century mathemetician Mobius) strip. A mobius strip is a strip of paper which is twisted and attached at the ends, forming an 'endless' two dimensional surface.
Now I know why the Moebius Scarf was named that way... 
= But the religious and cultural aspects of the infinity symbol predate its mathematical origins. Circles and loops are reminiscent of the idea of life being conceived as an eternal, often times seasonal cycle, that endlessly repeats itself - endless reincarnation.
= In the tarot, it represents the balance of forces and is often associated with the magician card.
= The symbol as a tattoo would stand for the state or quality of being infinite. It is best described as a figure eight on its side, and is used to denote what is limitless and without boundary or end.
Sources: Wikipedia - About.com - Numericana - Vanishing Tatoo
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