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. But a study now shows that a kind of binary system was already in use 300 years earlier among the people of the tiny Pacific island of Mangareva in French Polynesia.
The discovery, made by analysing historical records of the now almost wholly assimilated Mangarevan culture and language and reported in Proceedings of the National Academy of Sciences, suggests that some of the advantages of the binary system adduced by Leibniz might create a cognitive motivation for this system to arise spontaneously, even in a society without advanced science and technology.
...
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. 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.Bender and Beller show that this system retains the key arithmetical simplifications of true binary, in that you don't need to memorize lots of number facts but follow only a few simple rules, such as 2 × K = P and 2 × P = T.
(Score: 0, Offtopic) by kurenai.tsubasa on Friday June 16 2017, @05:31PM (4 children)
<sarcasm>See, misogynerds? There's nothing complicated about computer programming at all! You just make it complicated because you hate women and minorities and want to chase them out of the field. If it weren't for you misogynerds, all computer software would be written by womyn-born-womyn and be free of bugs. You may also hate handicapped people if you've rejected systemd.</sarcasm>
(Score: 2) by DeathMonkey on Friday June 16 2017, @05:38PM (3 children)
<sarcasm>...</sarcasm>
I don't believe you.
(Score: 2, Insightful) by kurenai.tsubasa on Friday June 16 2017, @08:01PM (2 children)
Oops! You're not an AC! I need new glasses.
Well, let's revisit the comment without the <sarcasm />.
What is your proof that they have not found more proof that misogynerds have conspired to make programming languages inaccessible to womyn-born-womyn by using a naïve approach to base 2 where the first digit position is not base 2?
(Score: 2) by DeathMonkey on Friday June 16 2017, @08:32PM
I.....wait.....what?
Parsing that last sentence is like trying to solve one of those Google interview puzzles. Is that a quadruple negative?
(Score: 2) by tfried on Saturday June 17 2017, @07:52PM
Was your first unrequited love a Polynesian feminist, or something?
(Score: 2) by Adamsjas on Friday June 16 2017, @05:50PM (8 children)
Q: Why didn't barefoot people use base 20?
A: Because sharks.
(Score: 2) by bob_super on Friday June 16 2017, @05:56PM (7 children)
Primitive men wanted base 21, and women base 22.
(Score: 2) by JNCF on Friday June 16 2017, @06:18PM (6 children)
Neither fingers nor peni have 21 states; you can count higher with one hand of binary digits than you can with all 21 of your unary digits.
(Score: 2) by bob_super on Friday June 16 2017, @06:25PM (5 children)
I like counting in binary, but every time I get to 0b00100, someone punches me in the face.
(Score: 2) by JNCF on Friday June 16 2017, @06:39PM (4 children)
Next time you should activate your web-shooters by quickly counting up to 18 (or 9, depending on which side you start from).
To pick apart my original comment, I should have said that fingers and peni don't have 21 states that are easily discernable for the purposes of human counting. Even with just two states counting based on a boner could still prove difficult.
(Score: 2) by bob_super on Friday June 16 2017, @06:46PM (3 children)
Given that fingers can reliably attain three distinct states, but toes and other parts can't, it might be more efficient to count in base 3, hands-only.
Still a problem when reaching 00100, 00200, or in the UK 00220
(Score: 2) by JNCF on Friday June 16 2017, @08:31PM (2 children)
I'm assuming that knuckle joints aren't being used for state, since I have the most trouble moving those independantly. Given that state 0 is two curled joints, state 1 is the uncurling of the joint nearest the knuckle, and state 2 is the uncurling of both joints, can you hold your hand in the 02020 position? My middle finger can't move lower than 1 while its neighbors are both fully extended. I've considered a system that uses different bases for different fingers to allow for higher numbers, but that ruins all of the nice tidy rules we get from working in a consistent base. It's a trade-off.
(Score: 2) by bob_super on Friday June 16 2017, @08:58PM (1 child)
After all these political fights, it's nice to see an SN discussion reach peek geek.
(Yes I can fold my 4th and 5th fingers independently).
(Score: 2) by JNCF on Friday June 16 2017, @09:27PM
I can fold my 4th and 5th independently enough to count on, it's the combination of my index and ring fingers both being simultaneously fully extended that prevents me from fully folding my middle finger. I wouldn't be surprised if some, or even most, people are capable of the task. Given that binary takes us all the way to 1023 on ten fingers, I could see arguing that it's a good enough standard for visually conveying numbers if even just 20% of the population possesses my inferior knuckle architecture.
We should really start CRISPRing people into having hands that are conducive to counting in a dozenal system, obviously.
(Score: 4, Insightful) by weeds on Friday June 16 2017, @06:36PM (5 children)
So they had a name for 10, 20, 40, and 80. By combining the names you could get representations of numbers. Aside from 10, 20, 40, and 80 not being all of the powers of 10, how is this in any way "binary" (a number system based on place values and 0 and 1)?
Kind of like ten x one hundred is one thousand and ten x one thousand is ten thousand. You get that for free when your named numbers are based on a common multiplier...
What is TPK x TK7? Too hard? How about TPK + TK7?
This looks a lot more like Roman Numerals than any place valued number system not to mention a base 2 number system.
Help me out here...
Get money out of politics! [mayday.us]
(Score: 0, Redundant) by kurenai.tsubasa on Friday June 16 2017, @07:53PM (1 child)
Sorry, can't help you. It's irrefutable proof that assigned males are using an unnatural definition of “binary” to exclude womyn-born-womyn and minorities from tech careers. Obviously, this is a more pure form of binary than our misogynist base 2 system.
If only we hadn't conspired to prevent, with our insistence on base 10, base 8, or base 2 notations, womyn-born-womyn from writing something like this:
for (uintV_t i = 0; i < TK7; i++) {
std::cout << i << std::endl;
}
Unfortunately, being a misogynerd, I would not be able to determine more precisely exactly what a uintV_t is. It might only hold values up 1 before the value represented as 80 in our misogynist notation, but it could also be quite different in ways a misogynist like me would not be able to anticipate. I only have experience with misogynist data types such as unit8_t.
(As a side note, we misogynists of course know that doing that with a uint8_t and expecting the cout object to print numerals would require casting i to int before the insertion operator. Also of course, we know that this depends on how a uint8_t is typedefed, because we have intentionally created these complications as a means of excluding womyn-born-womyn. I'm certain that a more natural system such that these noble people in TFS used would simply know whether the programmer, being a superior and complete being such as womyn-born-womyn are, intended to output some emojis and playing card suits or numerals.)
I'm certain that c+= has always had support for the syntax above. Always. We're also still at war with Eastasia.
AC didn't believe I was serious about sarcasm, so I will omit the sarcasm tags on this attempt and try to be more serious.
(Score: 3, Insightful) by takyon on Friday June 16 2017, @09:53PM
You should write more journals.
[SIG] 10/28/2017: Soylent Upgrade v14 [soylentnews.org]
(Score: 2) by JeanCroix on Saturday June 17 2017, @01:08AM
The archeologists in question simply don't understand binary..?
(Score: 2) by tonyPick on Saturday June 17 2017, @07:36AM
Clearly they were simply mistranslating from the 2,000 year old Chinese...
http://www.historyofinformation.com/expanded.php?id=454 [historyofinformation.com]
Link spotted on the HackerNews thread on the same topic. And looking at the delivery times on those letters, isn't it sort of awesome to live in the future at times?
(Score: 2) by tfried on Saturday June 17 2017, @07:34PM
Not quite. The striking thing about Roman numerals is that they are clearly not based on an understanding of powers. They have "digits" for 1, 5, 10, 50, 100, 500, 1000, but each "digit" will typically have to be represented by a multitude of signs. Such as XLII for a mere 42, or inscrutable beasts like MCMXCVIII. It's not surprising that this system was replaced by the Arabic system, worldwide. (And still we see fascinating proofs of innumeracy in inconsistencies such as sixteen / twenty-six - or even the French soixante-dix-sept ("60+10+7")).
The interesting bits about this are that a) the system probably developed independently, b) it is apparently based on an understanding of powers, and the representation of digits, c) it is unique in using two different bases (one of which happens to be 2).
(Score: 1, Insightful) by Anonymous Coward on Saturday June 17 2017, @01:12AM
(Score: 2) by Entropy on Saturday June 17 2017, @02:30AM (2 children)
So no, they didn't have binary. 0 has been a surprisingly illusive concept throughout history.
(Score: 2) by AthanasiusKircher on Saturday June 17 2017, @02:41AM (1 child)
Just because a system lacks zero doesn't mean it isn't binary (at least in terms of number base systems). Binary just implies based on powers of 2, like decimal implies based on powers of 10. In common parlance, people use decimal to also imply a place value system that has zero, but the Roman numerals are also decimal.
But what's being described here sounds more like a hybrid system. Just like sexigesimal systems were popular historically, but often tended to really be hybrid decimal and senary systems in practice.
(Score: 2) by Entropy on Saturday June 17 2017, @08:44PM
While that is true, sort of...Not having zero really screws stuff up.