[AntonioLao]

It did not start with numbers but proportional patterns of living and utility things. Although some of these were exaggerated nevertheless the intended features were clearly defined. For painting: a bull, a horse, a fish, a stenciled right hand, or a stenciled left hand. For sculptures: a man, a woman, a child, or a lion man.

In Germany: the Lion Man of Hohlenstein Stadel carved mammoth ivory circa 28000 BC of the Aurignacian Period. In Austria: Venus of Willendorf carved and painted limestone and in France: Dappled Horses of Pech-Merle, charcoal and ochre on limestone both circa 25000 BC of Gravettian Period. Through the ages of space and time more and more of these mathematical patterns and designs were found in caves, archeological digs, and stone surfaces. In Spain: Altamira Bison circa 15000 BC of Magdalenian Period. In Italy: Addaura Cave Ritual Scene circa 11000 BC, Epipaleolithic Period. In Argentina: Hand Stencils circa 9500 BC, Late Pleistocene, Early Holocene Period. In Greece: Reclining Figurine, 6000 BC, Early Neolithic Period.
In every culture around the world a typical distinctive art form exists. But where and when these art forms became abstract representations then and only then marked the birth of numerals.

References: http://www.phaidon.com/Default.aspx/Web/30000-years-of-art-9780714847894
http://www-groups.dcs.st-and.ac.uk/~history/Indexes/HistoryTopics.html
http://en.wikipedia.org/wiki/History_of_mathematics
http://aleph0.clarku.edu/~djoyce/java/elements/toc.html

[Profpat]

But not the number 0, which came a lot later I believe. And with the binary system of 1 and 0 any thing can be represented. All our computer images, probably a hologram, maybe even a dynamic you and I Antonio.

Best,

Pat

[AntonioLao]

Originally Posted by Profpat But not the number 0

This would represent the background of a painting or the vacuum of physical existence.

[Profpat]

And one picture or image can be worth 10,000 words or formulas, or numbers.

[AntonioLao]

Originally Posted by Profpat And one picture or image can be worth 10,000 words or formula

Also a symbol is worth a thousand words but which words? These words are defined by subjective or objective interpretation.

[Profpat]

Well I'm really glad you hooked my up to the Borromean Rings. I'm still researching those babies. I guess it is the most simple form of the Brunnian links.

Thanks,

Pat

[AntonioLao]

Originally Posted by Profpat I guess it is the most simple form of the Brunnian links

http://en.wikipedia.org/wiki/Brunnian_link and http://en.wikipedia.org/wiki/Hopf_link
by comparison I still think Hopf link is the simplest.

[Profpat]

Thanks for the links. The one looks like a mobius strip.

[AntonioLao]

Originally Posted by Profpat The one looks like a mobius strip

Indeed it does! But Moebius is 2D while Hopf is 1D.

[Profpat]

I'll have to study these "links" ( pun intended ) some more. The other one reminds me of a complex Solomon's Knot.