Of course, we <i>all</i> know what they would have used if they were <i>real</i> pros:<p><a href="https://en.wikipedia.org/wiki/Factorial_number_system" rel="nofollow">https://en.wikipedia.org/wiki/Factorial_number_system</a>
The Polynesian history of the (european) middle ages keeps getting more interesting and mysterious.<p>Evidence for polynesian contact with the Americas is mounting. Regardless, the medieval coonization of all the pacific islands is evidence of seamanship and navigation skills European mariners didn't achieve until well into the age of sail. European sailing was much more trade/cargo oriented & we know a lot less about "pre-contact" polynesian maritime cultre so it's hard to do put the technologies side-by-side. That said, it looks the polynesian ability to aim for and land on small remote islands circa 300CE was not surpassed by any other culture until the 18th century.<p>Then there's the strange case of Easter Island with it's giant stone statues. Giant stone statues & "how-the-f%£$-did-they-do-this" megalithic monuments have existed for a long time (EG the sphinx), but these are usually produced by populous civic cultures. "High civilization" to use an out of date term. For a tiny island to produce this kind of an artistic culture without obvious predecessors or descendants is strange.<p>As always in prehistory (in the literal, "before written records" sense), what we know is very little. But, it wouldn't be hard for me to believe that surprising numerical or mathematical systems existed there. It's a culture that has surprised us to the point of disbelief several times.
A couple of Native American tribes used octal because base 8 works for the number of things you can carry between the fingers. Would have made computing a bit simpler if that had been adopted instead of base 10.
"Polynesian people used binary numbers 600 years ago"<p>Disgrace to Nature for click bait. The number system might be clever but as described is not binary numbers.<p>Especially the claim in the introduction<p>"Binary arithmetic, the basis of all virtually digital computation today, is usually said to have been invented at the start of the eighteenth century by the German mathematician Gottfried Leibniz."<p>implying Leibnitz didn't invent binary and equate the existence of 4 numbers (10,20,40,80) which lack the simplicity of 2 states by representing it with KTPV with the invention of the binary number system is sensationalist.<p>Interesting the quote<p>“It’s puzzling that anybody would come up with such a solution, especially on a tiny island with a small population,” Bender and Beller say.<p>It's only puzzling to scientists from "Department of Psychosocial Science" but would not be puzzling to scientists from the "Department of Mathematics".
If this stuff is interesting to you, you should read about Geoff Saxe's work [0] with the Oksapmin people of Papua New Guinea. This book is newish (and I haven't read it, but I've read almost all of the studies the book is built on) and synthesizes a couple of decades of research into how these people count and talk about number and how that practice changed over time (there's some fascinating conclusions about how the base changed from base-27 to base-20 when western money, in particular the 1 pound : 20 shilling ratio, came to be more widely-used).<p>And yeah, more or less base-27. They used body parts to refer to numbers 1-27, and often anything higher than that was just "a lot", but they could count more using the system if needed. How the Oksapmin people mingled both traditional counting and modern arithmetic is pretty fascinating (and says a lot about the underlying cognitive processes that make humans able to reason about number).<p>0: <a href="http://a.co/6gbRM1x" rel="nofollow">http://a.co/6gbRM1x</a>
While not intended to be used mathematically, the I Ching hexagrams developed around 1000AD represented the binary numbers from 0-63 (2^6), as discovered by Leibniz who was quite fond of binary himself.
While the described system has some powers of 2, which is interesting, it is a far cry from positional binary. It most certainly does not prefigure the system described by Leibniz, nor the application of arithmetical operations to logic, which was the profound insight in question. This shares far more with things like the base-60 fractions used by Mesopotamians than anything recognizably similar to modern binary and logic systems. (Which of course derive a great deal from Aristotle, significantly more than 600 years ago).
The ability of the Polynesians to settle huge stretches of the Pacific might be one of the most impressive human achievements ever.<p>Odds are they reached South America even if we never find direct evidence (there is some).
> Mangarevans combined base-10 representation with a binary system. They had number words for 1 to 10, and then for 10 multiplied by several powers of 2<p>Because base-10 seems to originate from two handfuls of fingers, I wonder why they didn't end up with a base-5 representation with a binary system?<p>> takau (K) means 10; paua (P) means 20; tataua (T) is 40; and varu (V) stands for 80<p>By using their numeral for five (say, F) to mean 5 in this scheme, they could have gotten rid of their numerals for 6 to 9. So 157 would be VTPKF2 instead of VTPK7.
If you think this is cool you might also find the Marshall Island stick charts, and Polynesian navigation methods particularly intriguing. See<p><a href="https://en.wikipedia.org/wiki/Marshall_Islands_stick_chart" rel="nofollow">https://en.wikipedia.org/wiki/Marshall_Islands_stick_chart</a><p><a href="https://en.wikipedia.org/wiki/Polynesian_navigation" rel="nofollow">https://en.wikipedia.org/wiki/Polynesian_navigation</a>
This reminds me of the story of ancient Ethiopians using binary maths. I read about it a while back and finally managed to track it down (the original link seems dead): <a href="https://web.archive.org/web/20170609082700/http://www.uh.edu/engines/epi504.htm" rel="nofollow">https://web.archive.org/web/20170609082700/http://www.uh.edu...</a>
<i>They had number words for 1 to 10, and then for 10 multiplied by several powers of 2. The word takau (which Bender and Beller denote as K) means 10; paua (P) means 20; tataua (T) is 40; and varu (V) stands for 80. In this notation, for example, 70 is TPK and 57 is TK7.</i><p>To my non-mathematically trained ears this doesn't sound like a binary system at all, but more like the highly inefficient Roman system. Am I missing something?
Roger Bacon wrote about binary notation in the 13th century, although he called bits `fingers'. John Wilkins credited Bacon in his book <i>Mercury, or the Silent and Swift Messenger</i> published in 1641.<p>Wilkins' book is basically a tutorial on communications security (COMSEC) that touches on channel coding, reliability, secrecy, key management, cryptanalysis, OPSEC, and data compression.<p>ETA: Wilkins takes a clear position on the full disclosure debate but cautions of the hazard of experimenting with crypto technologies:<p><pre><code> `...the chiefe experiments are of such nature, that
they cannot be frequently practised, without just cause
of suspicion, when it is in the Magistrates power to
prevent them.'</code></pre>
Computers use base two because their most natural unit can occupy one of a couple states: 0 or 1. One, two, base two.<p>Human hands, on the other foot, have ten fingers. Since our favorite mapping between things and integers is finger counting, we naturally end up with more than two states. Zero, one, two, three, four, five, six, seven, eight, nine, and the fully-extended state, ten. That's eleven states, which is why the global human standard is base-eleven.<p>Wait, what?
<i>They find that the former Mangarevans combined base-10 representation with a binary system. They had number words for 1 to 10, and then for 10 multiplied by several powers of 2.</i><p>Interesting. Perhaps this is the very first use of binary-coded-decimal?
Oh well, no more computers for us then <a href="http://www.cbc.ca/news/canada/north/cultural-appropriation-make-it-illegal-worldwide-indigenous-advocates-say-1.4157943" rel="nofollow">http://www.cbc.ca/news/canada/north/cultural-appropriation-m...</a>