Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Polynesian people used a kind of binary number system 600 years ago (2013)

nature.com

Post reply on HN
Print view View original

41–50 of 125 posts

Re: Polynesian people used a kind of binary number system 600 years ago (2013)

#41

Post by jcranmer »

yongjik wrote: post #16
aaron-lebo wrote: post #6

The ability of the Polynesians to settle huge stretches of the Pacific might be one of the most impressive human achievements ever. Odds are they reached South America even if we never find direct evidence (there is some).

> Odds are they reached South America even if we never find direct evidence (there is some). Isn't sweet potatoes in Polynesia (which originated from South America) pretty much a proof?

The origin of Polynesian sweet potatoes being from an old visit to South America is the most plausible origin story, but the lack of anthropological evidence is also a powerful dissuading factor. There's no oral stories of either the Polynesians or the South Americans of such a voyage taking place, like there was for the Viking colonization of Vinland (recalled in the Icelandic sagas).

Re: Polynesian people used a kind of binary number system 600 years ago (2013)

#42

Post by adrianratnapala »

pfooti wrote: post #39

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 t…

Did they use 27 as a radix when they went for bigger numbers?

For example and Oksapmin might have say "four score and seven years ago", using their 27-numeral vocabulary to supply words for "four", "seven" and "twenty", but in this case the (closest thing to) a radix is 20, not 27.

Re: Polynesian people used a kind of binary number system 600 years ago (2013)

#44

Post by ajross »

jcranmer wrote: post #36
whatshisface wrote: post #3

Computers use base two because their most natural unit can occupy one of a couple states: 0 or 1. One, two, base two. 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…

What you're missing is that positional numeral systems developed relatively late--in recorded history, which is well after number systems start to be encoded in language. Earlier numeral systems are counting systems, where zero isn't a proper number but rather a signifier for a lack of stuff. Let's look at numbers in natural languages. In English, we start with 12 basic numbers--one through twelve--and then we start…

> What you're missing is that positional numeral systems developed relatively late--in recorded history,

Mesoamericans were carving base-20 long count dates at least as early as they were writing words, actually. The oldest complete date is 36 BCE. This was a true number system, including a glyph for zero.

Re: Polynesian people used a kind of binary number system 600 years ago (2013)

#45

Post by jcranmer »

ajross wrote: post #44
jcranmer wrote: post #36

Earlier quoted context omitted.

What you're missing is that positional numeral systems developed relatively late--in recorded history, which is well after number systems start to be encoded in language. Earlier numeral systems are counting systems, where zero isn't a proper number but rather a signifier for a lack of stuff. Let's look at numbers in natural languages. In English, we start with 12 basic numbers--one through twelve--and then we start…

> What you're missing is that positional numeral systems developed relatively late--in recorded history, Mesoamericans were carving base-20 long count dates at least as early as they were writing words, actually. The oldest complete date is 36 BCE. This was a true number system, including a glyph for zero.

We're still talking ~2,000 years ago, which I consider recorded history (basically, the distinction between history and prehistory is roughly ~6,000 years ago). Certainly much, much newer than language.

Re: Polynesian people used a kind of binary number system 600 years ago (2013)

#46

Post by vorg »

> 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

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?

> takau (K) means 10; paua (P) means 20; tataua (T) is 40; and varu (V) stands for 80

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.

Re: Polynesian people used a kind of binary number system 600 years ago (2013)

#47

Post by [deleted] »

kobeya wrote: post #5
whatshisface wrote: post #3

Computers use base two because their most natural unit can occupy one of a couple states: 0 or 1. One, two, base two. 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…

There's a lot more possible states than eleven. 32 if you count just whether a finger is extended. More if you allow crossing fingers, interaction between hands, etc. And this isn't theoretical either: https://en.wikipedia.org/wiki/Chinese_number_gestures

[deleted]

Re: Polynesian people used a kind of binary number system 600 years ago (2013)

#48

Post by pfooti »

adrianratnapala wrote: post #42
pfooti wrote: post #39

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 t…

Did they use 27 as a radix when they went for bigger numbers? For example and Oksapmin might have say "four score and seven years ago", using their 27-numeral vocabulary to supply words for "four", "seven" and "twenty", but in this case the (closest thing to) a radix is 20, not 27.

for the most part, they didn't go for bigger than 27 very often. At the time Saxe started studying them in the late 1970s, they were living very close to nature, and often didn't have cause to need to accurately count higher than that (if you have one or two fish, the distinction is important - if you have 27 or 28, less so).

But yes, the word fu (not foo, but enjoyably similar) which kind of means "a full amount", or enough, and was used as "one radix", so people do something like fu + another number word to mean 27 + that other number. I don't remember if there was evidence of treating it like a radix (like multiple fu + something), but I don't think that happened.

Again, in this particular culture and economy, there wasn't much of a need to think about large numbers precisely. Which is part of what makes all this pretty fascinating - humans have some inbuilt capacity to reason about numbers (some studies of babies show that they can distinguish between two and three of things just as readily as two hundred to three hundred, sort of a visual field scale independence - I'd have to dig to find that study, I read it about eight years ago, I think it was in nature), but beyond a certain level it becomes intrinsically intertwined with our development of language and other conceptual frames.

Re: Polynesian people used a kind of binary number system 600 years ago (2013)

#49

Post by Chinjut »

whatshisface wrote: post #3

Computers use base two because their most natural unit can occupy one of a couple states: 0 or 1. One, two, base two. 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…

What actually happened, probably, is that humans first counted by putting things in correspondence with fingers; actual bijections between fingers and things. This naturally led to ten, the number of fingers total and thus a grouping size of understandably frequent use, becoming a very significant number (culturally, linguistically, etc.). Ten was a very significant number for a very long time before positional notation with its digits and bases was invented. (The Romans had no digits, but they loved their fives and tens)

And thus, when such notation for numerals WAS invented, it felt quite natural to take ten as base, it being such a significant number.

Re: Polynesian people used a kind of binary number system 600 years ago (2013)

#50

Post by baseethrowaway »

whatshisface wrote: post #3

Computers use base two because their most natural unit can occupy one of a couple states: 0 or 1. One, two, base two. 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…

Maybe a coincidence (I don't know details of computer history), but another interesting reason why binary is used might be information density.

Base e (2.71...) has highest information density. Of course, computers can't use irrational numbers as their base, so base 3 would be a closest pick. However, base 3 is much harder to represent in digital logic, so base 2 is a better pick and is still relatively close to e.

EDIT: Finally found a reference. https://en.wikipedia.org/wiki/Non-integer_representation#Bas...

I wonder if the idea originated before Hayes described it in 2001. Now it looks more likely to be a coincidence :)

Post reply on HN