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Did Polynesians invent the binary system centuries ago?

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File:Binary clock.svg
Binary clock/Alexander Jones & Eric Pierce

Or more? It’s possible:

Each system has subtle advantages depending on what sort of counting and calculations are needed. The decimal system is handy considering that people have 10 fingers. But when it comes to division, other systems are better. Because 10 has only two prime factors (2 and 5), dividing by thirds results in an annoyingly infinite approximation (0.3333 … ) whereas the base-12 counting system produces a nice finite solution. (Indeed, some mathematicians have advocated for a worldwide switch to base-12.) Binary, meanwhile, has a leg up on decimal when it comes to calculation, as Leibniz discovered 300 years ago. For example, although numbers in binary become much longer, multiplying them is easier because the only basic facts one must remember are 1 x 1 = 1 and 0 x 0= 1 x 0 = 0 x 1 = 0.

But Leibniz may have been scooped centuries earlier by the people of Mangareva, a tiny island in French Polynesia about 5000 kilometers south of Hawaii. While studying their language and culture, Andrea Bender and Sieghard Beller, anthropologists at the University of Bergen in Norway, were astonished to find a mathematical system that seems to mix base-10 and base-2. “I was so thrilled that I couldn’t sleep that night,” Bender says. It could be not only the first new indigenous arithmetic system discovered in decades, but also the first known example of binary arithmetic developed outside Eurasia. – Science

Also: Did you know that some mathematicians advocate a switch to base-12 counting?

Binary here.

Indeed , a Wigner put it, 'a miracle confronts us':
The Unreasonable Effectiveness of Mathematics in the Natural Sciences - Eugene Wigner - 1960 Excerpt: ,,certainly it is hard to believe that our reasoning power was brought, by Darwin's process of natural selection, to the perfection which it seems to possess.,,, It is difficult to avoid the impression that a miracle confronts us here, quite comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions, or to the two miracles of the existence of laws of nature and of the human mind's capacity to divine them.,,, The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning. http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html An Interview with David Berlinski - Jonathan Witt Berlinski: There is no argument against religion that is not also an argument against mathematics. Mathematicians are capable of grasping a world of objects that lies beyond space and time …. Interviewer:… Come again(?) … Berlinski: No need to come again: I got to where I was going the first time. The number four, after all, did not come into existence at a particular time, and it is not going to go out of existence at another time. It is neither here nor there. Nonetheless we are in some sense able to grasp the number by a faculty of our minds. Mathematical intuition is utterly mysterious. So for that matter is the fact that mathematical objects such as a Lie Group or a differentiable manifold have the power to interact with elementary particles or accelerating forces. But these are precisely the claims that theologians have always made as well – that human beings are capable by an exercise of their devotional abilities to come to some understanding of the deity; and the deity, although beyond space and time, is capable of interacting with material objects. http://tofspot.blogspot.com/2013/10/found-upon-web-and-reprinted-here.html Mathematics is the language with which God has written the universe. Galileo Galilei Nature by Numbers - Fibonacci - video http://vimeo.com/9953368
Alexander Vilenkin commenting on Euler's Identity, e^ipi+1=0 , states:
"It appears that the Creator shares the mathematicians' sense of beauty." - Alexander Vilenkin
Dr. Craig weighs in here
Mathematics and Physics – A Happy Coincidence? – William Lane Craig – video http://www.metacafe.com/w/9826382 1. If God did not exist the applicability of mathematics would be a happy coincidence. 2. The applicability of mathematics is not a happy coincidence. 3. Therefore, God exists.
Here is a humorous reaction to a mathematical problem in physics:
“It always bothers me that in spite of all this local business, what goes on in a tiny, no matter how tiny, region of space, and no matter how tiny a region of time, according to laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out. Now how can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one stinky tiny bit of space-time is going to do?" - Richard Feynman – one of the founding fathers of QED (Quantum Electrodynamics) Quote taken from the 6:45 minute mark of the following video: https://www.youtube.com/watch?v=obCjODeoLVw
I don’t know about Feynman, but as for myself, being a Christian Theist, I find it rather comforting to know that it takes an ‘infinite amount of logic to figure out what one stinky tiny bit of space-time is going to do’:
John1:1 "In the beginning was the Word, and the Word was with God, and the Word was God."
of note: ‘the Word’ in John1:1 is translated from ‘Logos’ in Greek. Logos is the root word from which we derive our modern word logic http://etymonline.com/?term=logic Music:
Joy Williams - 2000 Decembers ago https://www.youtube.com/watch?v=4W8K3OhxVSw
Ethiopians have also long used the same mathematical approach to multiplications as computers do these days by using powers of two and divisions.
A Night Of Numbers - Go Forth And Multiply - video http://www.youtube.com/watch?v=Nc4yrFXw20Q
a few related notes:
"Either mathematics is too big for the human mind or the human mind is more than a machine" ~ Kurt Godel "Nothing in evolution can account for the soul of man. The difference between man and the other animals is unbridgeable. Mathematics is alone sufficient to prove in man the possession of a faculty unexistent in other creatures. Then you have music and the artistic faculty. No, the soul was a separate creation." Alfred Russel Wallace - An interview by Harold Begbie printed on page four of The Daily Chronicle (London) issues of 3 November and 4 November 1910. Geometric Principles Appear Universal in Our Minds - May 2011 Excerpt: Villagers belonging to an Amazonian group called the Mundurucú intuitively grasp abstract geometric principles despite having no formal math education,,, Mundurucú adults and 7- to 13-year-olds demonstrate as firm an understanding of the properties of points, lines and surfaces as adults and school-age children in the United States and France,,, http://www.wired.com/wiredscience/2011/05/universal-geometry/
This man 'sees' pi as a landscape that he walked through to over 20,000 digits
Math Genius Computes in the Blink of an Eye - video http://www.youtube.com/watch?v=Xd1gywPOibg
The man also 'sees' pi and other numbers, and equations, as well;
The Man Who Draws Pi - A Case of Acquired Savant Syndrome and Synesthesia Following a Brutal Assault: Excerpt: “Everything that exists has geometry”, says JP, who acquired amazing mathematical abilities after a mugging incident in 2002. He was hit hard on the head, and he now experiences reality as mathematical fractals describable by equations. Light bouncing off a shiny car explodes into a fractal overlaying reality, the outer boundaries of objects are tangents, tiny pieces that change angles relative to one another and turn into picture frames of fractals during motion, and the boundaries of clouds and liquids are spiraling lines.,,, Mathematicians and physicists were taken aback: Some of JP’s drawings depict equations in math that hitherto were only presentable in graph form. Others depict actual electron interference patterns.,,, Despite his lack of prior training, JP is the only person in the world to have ever handdrawn meticulously accurate approximations of mathematical fractals using only straight lines. He can predict the vectors for prime numbers in his drawings, and his drawing of hf = mc^2, which contains all the style elements of his earliest drawings, is remarkably similar to an actual picture of electron interference patterns, which he found years after first drawing the pattern (see Fig 7, 8). http://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B0GEjtSycjTKNDU4ZmVhNjktNDk2OC00MjBhLTk5ZmQtYzBhYTRkM2ZlNmU4&hl=en
Along that line;
Is Integer Arithmetic Fundamental to Mental Processing?: The mind's secret arithmetic Excerpt: Because normal children struggle to learn multiplication and division, it is surprising that some savants perform integer arithmetic calculations mentally at "lightning" speeds (Treffert 1989, Myers 1903, Hill 1978, Smith 1983, Sacks 1985, Hermelin and O'Connor 1990, Welling 1994, Sullivan 1992). They do so unconsciously, without any apparent training, typically without being able to report on their methods, and often at an age when the normal child is struggling with elementary arithmetic concepts (O'Connor 1989). Examples include multiplying, factoring, dividing and identifying primes of six (and more) digits in a matter of seconds as well as specifying the number of objects (more than one hundred) at a glance. For example, one savant (Hill 1978) could give the cube root of a six figure number in 5 seconds and he could double 8,388,628 twenty four times to obtain 140,737,488,355,328 in several seconds. Joseph (Sullivan 1992), the inspiration for the film "Rain Man" about an autistic savant, could spontaneously answer "what number times what number gives 1234567890" by stating "9 times 137,174,210". Sacks (1985) observed autistic twins who could exchange prime numbers in excess of eight figures, possibly even 20 figures, and who could "see" the number of many objects at a glance. When a box of 111 matches fell to the floor the twins cried out 111 and 37, 37, 37. http://www.centreforthemind.com/publications/integerarithmetic.cfm
I've always thought that base 12 would make an ideal monetary system because it's so rich in divisors for its magnitude. Dozens would also facilitate trade in commodities. Thumbs count as 2 each. ;-) -Q Querius
Mapou, I agree. I think there is a lot we don't know about ancient polynesia. Collin
It does not surprise me. Centuries ago, Polynesians perfected a system that allowed them to navigate thousands of miles between island specks in the pacific without a compass. They did it mostly by observing the waves in the ocean. And, of course, there's the mystery of Easter Island. Mapou

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