
Polynesian people used a kind of binary number system 600 years ago (2013) - ghewgill
https://www.nature.com/news/polynesian-people-used-binary-numbers-600-years-ago-1.14380
======
petersjt014
Of course, we _all_ know what they would have used if they were _real_ pros:

[https://en.wikipedia.org/wiki/Factorial_number_system](https://en.wikipedia.org/wiki/Factorial_number_system)

~~~
corysama
Hi, Peter. Welcome to Hacker News!

If you get downvoted, it's because HN community takes a somewhat strict
approach when moderating comments that contribute noise to the conversation.
"Nice article!" comments are routinely downvoted. As is sarcasm, witticisms,
memes, references and other styles of comments that occur frequently but do
not contribute to the discussion. It's a knowingly doomed attempt to hold back
the flood of noise that covers Reddit.

~~~
Others
That last part feels a little aggressive in this case... The Wikipedia article
he linked to is actually pretty interesting, relevant, and appropriate. Sure
the presentation is tongue and cheek, but so are half of the comments on this
site...

~~~
corysama
> but so are half of the comments on this site...

Yeah... There are a lot more jokes and sarcasm being voted up on HN these
days. It's always been around, but it used to be voted down a lot more. Can't
say I'm happy about that change. It seems the fate of all vote-based
communities to eventually devolve into Digg 3.0...

~~~
tray5
I agree that his comment didn't add all that much, but I think the snark on
your end was a bit more distracting and irrelevant than his comment, and
honestly his comment was kind of on topic. This site is thankfully strictly
moderated and usually the discussion in the comments is very on topic, jumping
at the chance to be smug like that degrades the quality of conversation much
farther then being semi-relevant with a bit of a joke. Downvote and move on

~~~
corysama
I started making comments like this after the tenth time seeing a green
account make a joke, get downvoted to hell and reply "WTF! Why is Hacker News
so mean to noobs!" (Peter was green an hour ago)

~~~
taneq
Wait, green means new?

~~~
tomsmeding
I believe it means "throwaway"

~~~
arethuza
Pretty sure it just identifies to logged in users that a particular account is
relatively new.

After all, who is to know that a "throwaway" account actually gets thrown
away?

------
netcan
The Polynesian history of the (european) middle ages keeps getting more
interesting and mysterious.

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.

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.

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.

~~~
openasocket
I'm having trouble imagining a society with mathematics (beyond just counting)
but not writing. Are there other known examples?

~~~
panglott
Those don't seem related to me at all. Quipu was an Incan record-keeping
system that we don't understand well. Abaci are very ancient calculation
devices that don't use writing. The oldest Mesopotamian and Roman versions
were just a table with pebbles on it. And that's where we get the word for
"calculate".

~~~
openasocket
They aren't required, it's certainly possible to have a number system and not
a writing system. But for anything where you need to do non-trivial arithmetic
or accounting you can't just do all that in your head and memorize the
results. You need some way of recording the results in a persistent way, even
if it's just tallies carved into a piece of wood. And I imagine any culture
that figures out a recording system for numbers would pretty quickly (in
historical terms, so like years or decades) develop a writing system. I could
be wrong of course, I haven't really formally studied ancient history.

Aside: Is Quipu not a writing system? I thought there was some evidence
indicating it was.

~~~
panglott
Pebble-tables are fine for that, but don't leave a persistant record. Mostly
when I hear "writing system" I think "linguistic writing system", a writing
system for language, rather than "mathematical writing system".

But IIRC a number of writing systems started off first as mathematical record
systems before developing to encode linguistic information. Maybe a good
example is cuneiform, which started off as tally marks in balls of soft clay
stored in jars, for tax purposes, which developed symbols for encoding what
kind of goods were being counted. Quipu may be similar, with more nascent
development as a linguistic system.

------
protomyth
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.

~~~
fishnchips
Oh wow, I didn't know that. Reminds me of the Aborigines who looked for shapes
and figures in the empty space between the stars as opposed to our own
ancients who'd rather 'connect the dots'.

~~~
cr0sh
Negative space astronomy - interesting...

------
_Codemonkeyism
"Polynesian people used binary numbers 600 years ago"

Disgrace to Nature for click bait. The number system might be clever but as
described is not binary numbers.

Especially the claim in the introduction

"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."

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.

Interesting the quote

“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.

It's only puzzling to scientists from "Department of Psychosocial Science" but
would not be puzzling to scientists from the "Department of Mathematics".

~~~
siosonel
The Polynesian people used binary numbers, but not only binary numbers. The
article's title is correct. What's sensationalist about that?

Is it an important finding? I think so. It helps shed light on the scientific
and technical originality of other cultures. It matters a lot to acknowledge
that knowledge does not always flow from west to east or north to south. It
helps to rid of the notion of there being 'advanced' and 'primitive' cultures.

Are the scientists from the "Department of Psychosocial Science" trying too
hard to make that case? I don't think so. Some people like me thinks this is a
newsworthy discovery. Apparently mathematicians would not agree but even so,
should they dictate that I should be dismissive of this article as well? The
way I see it, the article does not make outrageous or unfounded claims. I'm
free to appreciate that numbers have a certain universality as an abstract
concept or language that isolated people from different era and backgrounds
naturally converge to.

~~~
indolering
> Some people like me thinks this is a newsworthy discovery.

Because you don't understand math. Binary arithmetic is a painfully obvious
development. A bored high-schooler predisposed to mathematics would figure it
out in an afternoon.

And we've documented cultures using mixed base systems in the past. All this
would have taken is a single person to say, "Hey, some things are easier if
you do it this way" and taught all of their kids to use that system.

~~~
siosonel
How do you know I don't understand math? And if a high schooler could figure
this out, then Leibnitz own discussion or contribution to this topic is then
meaningless?

The main point is that the finding in the article has cultural significance,
rather than purely in terms of mathematics. I think you either don't
understand that or are not willing to see that. The article is not trying to
elevate a Polynesian people's contribution to mathematics. There is little
mathematical significance there as these people from 600 years did not
celebrate or promote their number system. Rather, the article explores how
mathematical knowledge arises and how it was used. Could there an underlying
commonality in the way humans learn and organize knowledge? That's an
interesting question to ask and is not diminished - but is in fact supported -
by the fact that the same knowledge gets rediscovered in multiple isolated
instances.

~~~
indolering
> How do you know I don't understand math?

Because if you had a deep appreciation for mathematical structures you
wouldn't be surprised by this development.

> And if a high schooler could figure this out, then Leibnitz own discussion
> or contribution to this topic is then meaningless?

Mostly, yes. Binary is useful for computers, but it's not like we use binary
algebra in our daily lives. FWIW, Leibnitz did a much better job at calculus
than Newton ... mathematical construct that has been "discovered" at least 3
times.

> The main point is that the finding in the article has cultural significance,
> rather than purely in terms of mathematics. I think you either don't
> understand that or are not willing to see that.

The OP was complaining about Nature screwing up the understanding of the
mathematics and chiding the social scientists for ignorant remarks about the
mathematics involved. I am also tired of seeing silly pop-science articles
being posted HN.

> Could there an underlying commonality in the way humans learn and organize
> knowledge?

Yes, it does and this finding does not contribute to what we already know
about mathematics and its relation to cognition [0]. I'm frankly a bit
embarrassed by my social science colleagues and Nature for not doing a better
job framing their findings more appropriately.

Sorry for being curt.

0:[https://en.wikipedia.org/wiki/Where_Mathematics_Comes_From](https://en.wikipedia.org/wiki/Where_Mathematics_Comes_From)

~~~
siosonel
I am not surprised by the mathematical development described in the article.
Rather, I appreciate that there is yet new evidence for what I believe about
human capacity and potential across cultures. I felt a small level vindication
and inspiration, not surprise.

I'm not sure why you insist on finding fault with what I understand or not, or
what you wrongly imagine my reaction is to this article. It's possible to
appreciate stories like that without being shallow or sensationalist. At the
same time, it is possible to be unnecessarily dismissive about something when
the focus is solely on technical aspects and lose the bigger picture of what a
story is about.

I think we agree that truly unique discoveries or inventions are extremely
rare. I did not get the sense that the article framed the islander's number
system as such. It's okay to disagree if you see the framing differently.

~~~
indolering
> I'm not sure why you insist on finding fault with what I understand or not

Again, I am just trying to validate the OP's points about social scientists
screwing up basic mathematics on Nature's website.

> At the same time, it is possible to be unnecessarily dismissive about
> something when the focus is solely on technical aspects and lose the bigger
> picture of what a story is about.

Agreed! I spend all my time on this stuff and it's the coolest thing ever ...
and I'm really sad that Nature doesn't come right out and say what you are
saying.

Again, sorry for being curt. I didn't mean to insult you, we really don't have
time to understand _everything_.

------
pfooti
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).

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).

0: [http://a.co/6gbRM1x](http://a.co/6gbRM1x)

~~~
adrianratnapala
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.

~~~
pfooti
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.

~~~
adrianratnapala
_Again, in this particular culture and economy, there wasn 't much of a need
to think about large numbers precisely._

I suppose so, but there's a reason I picked 87 years. It's a time-scale that
we care about when talking about people and society. We don't strictly need
precise numbers for that you could say "around when granddad was born" \-- but
if we do have precise numbers then we can and will use them.

------
1001101
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.

~~~
19eightyfour
That is weird, right? Where did the precise use of broken and unbroken lines,
in all the combinations necessary to represent binary 0 to 63 originate? It's
a compact representation to label 64 different things using 6 "sticks"...but
why did they do it like this? Were they aware of binary numbers?

~~~
chandler
> ...but why did they do it like this?

...because people are smart. People have _always_ been smart, it's one of the
defining attributes of humanity.

It strikes me oddly (not specifically your comment, but the general color
accompanying these kinds of articles)--there's a kind of ground assumption
that by looking into the past, one sees nothing but a gradually descending IQ.

~~~
jamesrcole
> _people are smart. People have _always_ been smart_

I don't disagree, but I think there's more to it than just that.

Our raw mental capabilities may have always been the same, but how smart we
are also depends on our learning. Learning gives us extra leverage. If you
have two smart people and one of them was trapped by themselves all their life
on a desert island and the other learnt a lot about (say) maths and science,
then the latter person could in practical terms have greater intellectual
capabilities.

Over the centuries we've made great gains in mathematical tools, scientific
knowledge, in democratizing education and in disseminating knowledge. And this
means over the centuries we've (as a species) obtained more leverage that we
can apply to our raw mental capabilities, giving us (overall) greater
intellectual capabilities.

~~~
chandler
> Our raw mental capabilities may have always been the same, but how smart we
> are also depends on our learning.

FWIW, I tend to equate "smart" with "cleverness," as a separate measure
distinct from "experience," for the same reason you describe--so what I
usually go by is something along the lines of:

 _Cleverness_ is a measure of "what can you do with what you have," whereas
_experience_ is a measure of "what do you have?"

> Over the centuries we've made great gains in mathematical tools, scientific
> knowledge, in democratizing education and in disseminating knowledge. And
> this means over the centuries we've (as a species) obtained more leverage
> that we can apply to our raw mental capabilities, giving us (overall)
> greater intellectual capabilities.

I don't think we've gained greater intellectual capabilities--our intellectual
capabilities are the same, we just operate in a completely different mental
environment than our priors did.

Moreover, having a different view of the world allows for different
connections to be made, and different potentials to be expressed (irrespective
of one's individual level of cleverness).

So, for example, by placing a priority on stories & views that encourage
greater investigation of the physical world, we get to where we are today. And
we can teach the next generation slightly different stories that optimize for
different kinds of usefulness.

To bring it to the HN contingent--if I learn a new programming language, I've
gained experience in different ideas and operate in a different mental
landscape. But I'm not smarter afterwards, and I wasn't dumber before.

------
ajarmst
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).

------
aaron-lebo
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).

~~~
yongjik
> 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?

~~~
jcranmer
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).

~~~
DrScump
Note, however, that the Australian aboriginals' oral histories (songlines)
lack any reference to coming from elsewhere, although DNA clearly demonstrates
otherwise.

In such cases, if any given generation omits an element from its oral history
(by choice _or_ mistake), it is lost forever.

~~~
flukus
There are two orders of magnitude difference in time though. Australian
Aboriginals have been on the continent for 40-60 thousand years, Polynesians
made it to Hawaii 800-2000 years ago.

------
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.

------
thinkingkong
If you think this is cool you might also find the Marshall Island stick
charts, and Polynesian navigation methods particularly intriguing. See

[https://en.wikipedia.org/wiki/Marshall_Islands_stick_chart](https://en.wikipedia.org/wiki/Marshall_Islands_stick_chart)

[https://en.wikipedia.org/wiki/Polynesian_navigation](https://en.wikipedia.org/wiki/Polynesian_navigation)

------
erpellan
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):
[https://web.archive.org/web/20170609082700/http://www.uh.edu...](https://web.archive.org/web/20170609082700/http://www.uh.edu/engines/epi504.htm)

------
janwillemb
_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._

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?

~~~
MichaelBurge
It's not at all like a Roman system except for the use of letters. You can
separate a natural number n into two parts:

n = 10 * q + k, where 0 <= k < 10 and q in N

q = 1 * K? + 2 * P? + 4 * T? + 8 * V?

where K?, P?, T?, and V? are 0 if the letter is absent and 1 if the letter is
present. n is a textbook base 10 decomposition, and q is a sparse binary
representation.

Roman numerals didn't use quotient/remainder or a geometric expansion at all.
Since the 'base' seems to switch between 2 and 5 each time, you can't cleanly
decompose it. And there was that weird subtractive case.

------
jloughry
Roger Bacon wrote about binary notation in the 13th century, although he
called bits `fingers'. John Wilkins credited Bacon in his book _Mercury, or
the Silent and Swift Messenger_ published in 1641.

Wilkins' book is basically a tutorial on communications security (COMSEC) that
touches on channel coding, reliability, secrecy, key management,
cryptanalysis, OPSEC, and data compression.

ETA: Wilkins takes a clear position on the full disclosure debate but cautions
of the hazard of experimenting with crypto technologies:

    
    
        `...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.'

------
whatshisface
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 the
global human standard is base-eleven.

Wait, what?

~~~
kobeya
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](https://en.wikipedia.org/wiki/Chinese_number_gestures)

------
userbinator
_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._

Interesting. Perhaps this is the very first use of binary-coded-decimal?

------
daxfohl
0b1001011000 years ago? Anybody?

~~~
DrScump
I keep forgetting the New Year and write 0b1001010111 on all of my checks.

------
jlebrech
Oh well, no more computers for us then
[http://www.cbc.ca/news/canada/north/cultural-
appropriation-m...](http://www.cbc.ca/news/canada/north/cultural-
appropriation-make-it-illegal-worldwide-indigenous-advocates-say-1.4157943)

~~~
torrent-of-ions
A guy in an English suit asking for cultural appropriation to be made illegal.
Oh the irony.

~~~
jlebrech
I find that funny, but remember everyone else is allowed to appropriate white
culture because reasons.

This just seems like tribalism to me, yet the same people want open borders
and freedom of movement, but not of ideas and culture.

------
erkose
Binary numbers have been in use since the balance scale was developed.

~~~
contingencies
This is not a bad point really. But taking that perspective, binary logic has
existed since all forms of classification, ie. any form of recognition
whatsoever, which all babies achieve innately (what is pain/hunger/warm/wet,
who is mum, is that a voice I hear, etc.) In short, all structured thought
requires binary logic, because otherwise classification wouldn't work, and
thus neither communication, memory, etc.

Full disclosure: I had a revelatory acid trip on this subject when a research
mathematician first explained to me set theory as essentially a derivative
matrix resulting from a boolean test.... the world as we perceive it is merely
sets! This explains children learning! Mind. Blown.

Bonus anecdote: If you like admiring early human achievements that have been
unfairly obscured from popular history, check out the Polynesian crab claw
sails.
[https://en.wikipedia.org/wiki/Crab_claw_sail#Performance](https://en.wikipedia.org/wiki/Crab_claw_sail#Performance)

------
Eire_Banshee
Meh. Ancient babylonians used a base-16 number system. Does it really matter
what number system they used?

~~~
spraak
Um... apparently not to you but to many of the readers here (as we can roughly
guess by the upvotes) it does matter.

