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Incas Used Binary?
Abhijeet Chavan writes "An article in the Independent
reports that a leading scholar believes the Incas may have used a form of binary code 500 years before computers were invented.
'Gary Urton, professor of anthropology at Harvard University, has re-analysed the complicated knotted strings of the Inca - decorative objects called khipu - and found they contain a seven-bit binary code capable of conveying more than 1,500 separate units of information...If Professor Urton is right, it means the Inca not only invented a form of binary code more than 500 years before the invention of the computer, but they used it as part of the only three-dimensional written language.'"
10 or 5 would make sense only in a 10-base culture. Anybody now which base the Incans used?
Perhaps they didn't have a '0' (like the romans) and started of with 1 meaning an empty hand wich could mean 11 as a base?
Purely guesswork.
//Patrik Graeser
Why would you understand 10 or 5? They're pretty arbitrary (other than being the number of fingers on a hand).
They were probably encoding other symbols and they had between (2^5) 32 and (2^6) 64. So, 7 was the logical choice. If we wanted to encode the letters (A-Z), the numbers (0-9), and some basic punctuation (.,-;) we'd need exactly 7 bits too.
Using 24 colors seems rather stupid to me. What if you're out of pigment #21? And what about when it's dark and you have to use artificial lights (read: torches) -- will you be able to tell that a dot is burgundy and not brown?
Occam's razor dictates that the professor is wrong.
Anyhow, archeologists a few thousand years from now will probably look at an old copy of WIRED and say the same thing about us.
Regards,
--
*Art
No: Selecting one of 24 colours is NOT 24 bits. Each Knot may be wool/cotton, ply/crossply, front/back, and so on, plus black/white/red/green... But for each variable you may have only one of each pair and one of the 24 colours. The article is exactly right if you read it carefully.
Consciousness is an illusion caused by an excess of self consciousness.
This is not new. It has been generally surmised that quipus (khipus, qipus) served as a carrier of complex informations. See e.g. this page for pictures and info.
According to the article, the quoted scientist merely says that the permutations possible in a quipu weaving might indicate a septary (not, by any means, a binary) code. He also says he's looking for a Rosetta stone equivalent.
Well, do go on looking, old fellow. But I wouldn't hold my breath waiting for a whip-toting archaeologist-hero to stumble out of a collapsing jungle temple with a quipu-to-English dictionary under his arm. Remember, the Incas were one of the more institutionally stupid (and thus, extinct) civilizations in history - after independently inventing the wheel, they used it for children's toys exclusively.
And he expects to unearth the original quipu RFC? It's probably in quipu, too. And eaten by a llama.
Considering we're talking about a society/civilisation from 600 years ago (minimum) I don't think artificial light (other than fire) was really an issue.
And if you're out of pigment #21, just make some more. (At a guess)
I say we take off and nuke it from orbit. It's the only way to be sure...
That is a poor interpretation. 1536 possibilities allows someone to encode 10.6 bits of information. To encode 1536 "separate units" of information, each unit must represent no more than 1/145th of a bit. That is a very, very small amount of information, equivalent to having someone tell you something you were already 99.5% sure was true, such as "wow, this poker hand is not a straight!" or "guess what, my birthday this year does not fall on Friday the 13th".
It may be closer to the truth to say their knot language had 1536 different symbols, as compared with the 50-or-so letters, numbers, and punctuation marks we use in English.
Patrick Doyle
I mod down every jackass who puts his moderation policy in his sig. Oh, wait a sec....
I also found more detailed information on quipus, if anyone is interested.
There are 'several' strings (how many?) and there are 3 permutations for the strings mentioned (the ones in the above post). For each string there are 24 colours (that should have been fun differentiating 24 colours made with 'primitive' dying methods - 'is that dark-blue or midnight-blue is this one corn yellow or straw yellow?')
... I'm probably wrong but it sounds quite hard) are in fact 6 colours in 4 different shades that are due to archeological effects - surrounding matter of the artifacts, exposure to light, cleaning solutions used.
... sorry can't describe it better ... post-lunch lethargy.
So for each string there are 24+3+ maybe a couple more possibilities. Let's say base-29.
Were does the 7 bit binary come in then?
Also the bloke says "This could mean the code used by the makers allowed them to convey some 1,536 separate units of information".
It could. It could be the 24 colours were 24 crops (or different items, perhaps including livestock) and the 4 different variations for each string meant we've got loads, got none, got a few, haven't counted yet. Far less sophisticated than binary.
It could be that the 24 colours (someone do a list of 24 colour names that are easily recognisable
However, 'I have discovered a writing system comparable with that of Sumerian cuneiform' is sure to persuade an ongoing grant.
Also, while I'm enjoying my rant, using binary where positions in the code have different values we need to know the ordering - in fact it's vital. Permutations vs. combinations. Also I'd query (as I've hinted above) the value of describing a simple on/off indication for several positions as being n-bit binary. It feels wrong to me
pbhj
The only caveat to this calendar is that it ends in the year 2012. So far every celestial event, if the demise of the Inca empire was predicted accuartely. (Down to Hale Bopp, Halley's comet, moon and sun eclipses, civilzations, etc etc)
What's interesting about the calendar ending in 2012 is that this is a generally accepted year for The AntiChrist to appear by Bibilical eschatologists. It is also generally the year that is predicted by the Hebrew calendars for the Messiah (the true year 2000 to them I believe) - someone correct my factoids if I'm wrong.
Yell & scream & rant & rave... it's no use... you need a shaaaave ~ Bugs Bunny
Makes just as much sense as comparing all dates to the birthday of one Jesus, son of Joseph the carpenter. It's just an arbitrary point in time that is supposed to demonstrate something. Relating the time to George Boole's accomplishment would have been more informative, that's true, but I don't think most of the people even know who Boole was, not to mention when he lived (I don't know when he lived. 19th century?). Hell, not too many people know when the first electronic computers were built, either, but they have more clue about it than Boole.
Hell is not other people; it is yourself. - Ludwig Wittgenstein
Each separate knot has six variables with two possible values (I gave three from memory, there are three more) and one with 24 values - colour. Therefore each knot represents a kind of "super byte" which can hold a single value from 0 to 1535. The data is not in the string but in the joins between strings. From a base string, there are multiple strings, with each not having 1536 possible values. From each string, substrings, sub-sub-strings and sub-sub-sub strings may be appended. Each append operation adds another "superbyte". The number of strings is indetermiante, because, as the article says, effectively the data spreads out in 3-space.
Of course, I don't reckon they used it to maximum density, and the use of the bits may well have been representational. But it might be that it in facts encodes a chapter/paragraph/sentence/word structure. Simple sentences ("Fred owes Bill 5 goats") would be base plus one level of attached strings - a fairly simple level of encoding, with a super-byte at each knot. But it would not be diffcult to generalise from this onec it became common. In fact, this would tend to happen automatically if Bill tied all his IOUs onto one "backing string": from spine, substring identifies debtors, sub-substrings identify multiple debts.
Consciousness is an illusion caused by an excess of self consciousness.
The possible explanation is, that the evolution of writing is affected by the evolution of mental structures and categories: the Incas saw everything unfamiliar as supernatural, having been isolated from other cultures. The Aztecs and (particularly) the Mayas had had contacts with other cultures besides their own, so they know what it means to be conquered by a more advanced civilization.
Hell is not other people; it is yourself. - Ludwig Wittgenstein
It's a fact that e.g. shepherds from the Caucasus mountains have used binary for counting sheep for a long long time, possibly as long as they have had sheep. And that would make the use of binary much older than the Inca civilization. They used, and still uses, binary as a way of counting sheep easily with the fingers. 10 bits, 1024 sheep. It's extremely easy to let your fingers count in binary, if you have something to rest your fingers on (try with the edge of a table). You can count without thinking, just letting the fingers run while you e.g. read a newspaper. I use that shepherd method myself sometimes. When you're done with the counting just read the value from the current finger setting (you're a hacker, you can do that, right?)
TA
The cover of the MySQL book by New Riders has a picture of Mayan ruins.
How weird is that?
Hammer of Truth
It's Quetzalcoatl, and he was a pre-Inca god from the Teohuatican civilisation of south-eastern Mexico.
The mathematics needed for accurate astronomical records and calendars aren't so special either - the ancient Britons had most of them figured out for the stone circles, purely from centuries of observation and orally transmitted knowledge. The (apocryphal) Book of Enoch also contains sophisticated astronomical references, possibly remembered from the Egyptians, but related to both moon-based and solar circle observatories.
Counting and long observation from fixed points is all that is needed for astronomy - in fact there's not a lot more involved even now!
oh brave new world, that has such people in it!
I'm not so impressed that the Incas used a complicated system of tying colored knots on string that *kinda* resembles binary when you consider how much easier it would've been to just write the information down.
Hey, troll, I almost took your bait.
Then I realized that most everyone reading slashdot is bright enough to recognize that a library of strings tied around your waist is a hell of lot easier to carry on mountain trails than the same amount of information packed into clay tablets or animal skins. Or even books (assuming that the local resources would provide a paper analog).
More durable, and easier to store, too. Plus, binary encoded strings (to use the proper name for such a system) could be easily duplicated in quantity by illiterate children.
So perhaps the mystery of how the Incan Empire came to be comes down to their having discovered a method of mass publication, and the use of child labor in their publishing houses.
</tongue-in-cheek>
Let's start with 3. Scroll down to the bottom of the Independent's article, and note the identical construction of the Sumerian stone and the Rosetta stone. Both translated the same thing into 3 languages.
AFAIK, there's never been a stone with a transcription in two languages (which would be logical for treaties, etc), or evidence of the same transcription being later added to (which would be logical when new trading routes are formed). No. We only get the same text in three forms, all carved at the same time.
Three is also considered "lucky". To the best of my knowledge, this isn't a new myth but one that extends as far back as is tracable.
Four is a nice symbolic number. You can do a lot with squares. Squares, four-pointed symbols, etc, seem to be common in early symbols. Four seems to have also been a common number to symbolise completeness. The four horsemen, for example.
Seven, again, seems to have a lot of ancient significance. Again, it's a "lucky number" and has a lot of mythological references.
However, as you've probably figured out by now, most of this is for European cultures. The natives of the Americas were there a long time before European culture flourished.
If we see the same numbers in Inca culture, we can conclude one of two things. Either these numbers were sufficiently handy that cultures were more likely to use them than some other set, OR the numbers gained importance prior to the Arctic crossing into America.
The first possibility seems the more logical. After all, farmers used 3-stage and 4-stage crop rotation, not because these numbers were mentioned in mythology, but because that was a really good number of stages to have in a crop rotation scheme.
(In fact, many of today's farming problems are likely caused by the lack of crop rotation in many places. Farmers tend to replant the same crop in the same place, relying on fertilizers to make up for the exhaustion of the soil.)
Also, triangles and squares are much easier to construct with primitive tools than, say, duodecagons or fractals. This makes three-sided and four-sided shapes vastly more preferable to something more complex.
Septahedrons (seven-sided shapes) aren't particularly common, true, but once you have 3 and 4 as "magic numbers", then 7 and 12 automatically gain some "special" significance.
It's a small world and it smells funny; I'd buy another if it wasn't for the money; Take back what I paid (SoM)
Absolutely. After all, the ancient Egyptians had an algorithm for multiplying large numbers based on addition and the fact that every number can be written as a power of two (although they never literally wrapped their minds around that last part).
What they did was this:
Say you want to multiply 17 and 31.
1 * 31 = 31
2 * 31 = 31 + 31 = 62
4 * 31 = 62 + 62 = 124
8 * 31 = 124 + 124 = 248
16 * 31 = 248 + 248 = 496
17 = 16 + 1, so 17 * 31 = 496 + 31 = 527
For that matter, the Babylonians counted in base 60 and used floating point numbers.