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

111–120 of 125 posts

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

#111

Post by openasocket »

baseethrowaway wrote: post #50
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. E…

What's "information density"? Is there a formula for that? Googling didn't turn up anything

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

#112

Post by panglott »

openasocket wrote: post #107
panglott wrote: post #104

Earlier quoted context omitted.

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".

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 fo…

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.

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

#113

Post by walterstucco »

coldtea wrote: post #58
honestoHeminway wrote: post #53

Earlier quoted context omitted.

Proposed solution - a colour picker of Information quality as vote tool? Factual disputed - Factual accurat? (Red - Black) Information Rich - Information Poor? (Black - Faded Text)

That's what Slashdot did. Didn't help very much in the general case.

Slashdot is still a better community than HN

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

#114

Post by adrianratnapala »

pfooti wrote: post #48
adrianratnapala wrote: post #42

Earlier quoted context omitted.

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", o…

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.

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

#115

Post by petersjt014 »

corysama wrote: post #54
tray5 wrote: post #52

Earlier quoted context omitted.

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…

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)

I certainly understand where you're coming from and what you're probably thinking of (Eternal September is the name I know it by)--but I did try to make my comment both relevant and funny. I personally think I did okay there, but I'm fine with disagreement on that part.

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

#116

Post by 1001101 »

natch wrote: post #32
1001101 wrote: post #11

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.

Came here to say this. https://en.m.wikipedia.org/wiki/I_Ching And as you know each hexagram was composed of two groups (trigrams) of three pairs. Similar to bytes and nibbles. Even though the superstition is unfounded, the trigrams could combine in any way to refer to concepts and expositions that could give a lot of food for thought. Quite a nice system and very elegant because of its basis in binary numbers. Edit:…

I was thinking of the Shao Yang (binary) arrangement, rather than the original King Wen arrangement, which would have been created during SY's lifetime (1012-1077). This is the version Leibniz examined [1]. But, yes, as you point out, if you go back to the King Wen version, even earlier. If only Leibniz was around today!

[1] https://www.jstor.org/stable/1399337?seq=1#page_scan_tab_con...

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

#117

Post by corysama »

petersjt014 wrote: post #115
corysama wrote: post #54

Earlier quoted context omitted.

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)

I certainly understand where you're coming from and what you're probably thinking of (Eternal September is the name I know it by)--but I did try to make my comment both relevant and funny. I personally think I did okay there, but I'm fine with disagreement on that part.

I don't disagree. I shoulda waited to see if you were downvoted first before commenting. Meanwhile, I thought my comment was nice. I used to get a lot of support for a slightly less polite version of the same message. But, apparently today a lot of people read it as aggressive, snarky and smug :P

That's the problem when forums have a lot of sarcasm. It becomes even more difficult for anyone to judge your intentions. When people in "witty" forums say mean/dumb things they get surprised by how many readers think they are serious. And, some of them respond with mean/dumb things in seriousness. And, in not-seriousness... Usually there's an indistinguishable mix. And, even when you say something constructive, a lot of people will assume a negative intention and get upset that you are so disparaging.

So, yeah. Every few months I get in the mood to welcome a witty noob. Doesn't always go well :P

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

#118

Post by jacobolus »

panglott wrote: post #104
openasocket wrote: post #99

Earlier quoted context omitted.

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

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".

As far as I know the invention and use of counting boards went hand-in-hand with written (cuneiform) records. Or at least, we don’t have any evidence of earlier positional counting boards, only artifacts like tally sticks and piles of (non-positional) tokens.

The Sumerian society that developed cuneiform numeration/writing was a large bureaucratic urban society built on complicated debt/taxation/social organization.

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

#119

Post by jacobolus »

ajross wrote: post #98
jcranmer wrote: post #45

Earlier quoted context omitted.

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.

It sounds like pedantry, but it's important: history can't be recorded if there isn't any recording being done. Again, current evidence has the long count preceeding written language in Mesoamerica. That time frame only works for the mesopotamian and nile river civilizations.

While we’re at it, the (positional) Mesopotamian sexagesimal system evolved around 2000 BC, and had a placeholder “zero” symbol for empty places sometime before 0 AD.

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

#120

Post by baseethrowaway »

openasocket wrote: post #111
baseethrowaway wrote: post #50

Earlier quoted context omitted.

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. E…

What's "information density"? Is there a formula for that? Googling didn't turn up anything

Probably a bad translation on my part from my native language. I meant radix economy, which is ideal with radix e.

https://en.wikipedia.org/wiki/Radix_economy

"e has the lowest radix economy

...

A base with a lower average radix economy is therefore, in some senses, more efficient than a base with a higher average radix economy."

Post reply on HN