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

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

#91

Post by acjohnson55 »

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…

Yep!! That's what's commonly misunderstood about the "invention of zero". Positional numbering is the part that's actually innovative. This hit me when I was a math teacher and trying to consider our algorithms for arithmetic from first principles. I was teaching high school students how to work with exponential expressions with variables, which seems very esoteric, unless you realize that you've been doing it for years implicitly.

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

#92

Post by 1001101 »

jamesrcole wrote: post #87
19eightyfour wrote: post #80

Earlier quoted context omitted.

I agree. People are also arrogant. We like to look back and think "how quaint" and we are better than them. It's humbling to think that we actually weren't. But it's probably not very adaptive to think that way. Since, believing we are better now, by falsely diminishing the whatever metric of the past, probably helps us keep going forward to create the bright future. Hopefully without repeating the mistakes of the pa…

I think that it's fair to say that, in the past, people were (overall) a lot more ignorant about the character of the world and the universe, and that this led them to (overall) believe a lot more incorrect things. This is not to beat our chests in a "we're better" kind of fashion, but just to acknowledge that we have the benefits of the knowledge that people who came before us built.

As time goes on, you have more giants standing on the shoulders of other giants, and so on. Our feeble wetware is going to look pretty inferior to the digital cognitive systems of the next millennium, so we would do well to stay humble :)

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

#93

Post by protonfish »

iamcurious wrote: post #85
_Codemonkeyism wrote: post #59

"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…

>implying Leibniz didn't invent binary Humanity is really old. At most, we can say that Leibniz was the last to invent it.

Leibniz recognized the concept of binary in the hexagrams of the I Ching and even published a paper on it. http://www.historyofinformation.com/expanded.php?id=454

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

#94

Post by siosonel »

_Codemonkeyism wrote: post #59

"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…

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.

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

#95

Post by indolering »

siosonel wrote: post #94
_Codemonkeyism wrote: post #59

"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…

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…

> 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.

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

#96

Post by handojin »

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.

The I Ching hexagrams don't represent numbers. They're not ordered numerically and any of the traditional sequences and they're not used to perform arithmetic. The individual lines represent (AFAIK) 2's, 6's, 3's, and 9's depending on whether the line is male or female, moving or static.

The correspondence between the hexagrams and the binary numbers nothing more than a necessary consequence of the representation chosen: the number of states of a string of 6 characters in a system of 2 symbols.

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

#97

Post by spraak »

Eire_Banshee wrote: post #90

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

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

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

#98

Post by ajross »

jcranmer wrote: post #45
ajross wrote: post #44

Earlier quoted context omitted.

> 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.

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.

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

#99

Post by openasocket »

netcan wrote: post #88

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…

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

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

#100

Post by 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.'
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