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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.'"
Neal Stephenson was right! Its Snow Crash!
<fnord>OBEY</fnord>
Ever seen Hanna-Barberas Brave Starr? The bad dude's name was an indian named Tex-Mex of the Hexagon.. or something.
Um, 7 bits gives you 128 values, not 1500. Or it wasn't binary. Or the position mattered. Or something.
I want to delete my account but Slashdot doesn't allow it.
I'd be *really* impressed if they had Duke Nukem 3.
Read reviews of shopping cart software
That means that the Incas were a bit advanced! :P
Any technology distinguishable from magic, is insufficiently advanced.
I reckon they were prolly trying to say one of three things (in order of likelyhood)...
1) first post !
2) All your base are belong to us
3) imagine a beowulf cluster of these things
...was made by 1's and 0's I could have been out of my elementary school in less than 5 years!
The world is made up of just 10 kind of people: who understands binary code, and who does not.
Apple iProduct. Non importa cosa sia, lo comprerete!
And if they washed and shrank them, would that have been data compression?
SCO to Hell
The more we learn, the more we forget. For example, who can tell me the best mix for bronze? Not many now. How about what's best to plant after sowing rye for two years? As we continue to move into a more technological society, there is quite a bit of knowledge we are losing. Remember the famous ancient battery?
I'd suggest that if we got off of our superiority high horse, we'd find that we've always been quite ingenious. 7-bit though, that's what I find interesting. Wonder where 7 bits comes from. 10 or 5 --that I'd understand. 7, perhaps someone who'd been in a terrible accident?!
...tizzyd
Think about it for more than 0.5 seconds why don't you. ASCII code is only 7 bit and it can represent every word in the English (and many other) languages.Just because you have a 7 bit code does not mean you cant repeat values made up from that code.
Next time think before you say someone doesn't know what they are talking about and make yourself a fool.
that the Incas OWN SCO ????
The Chinese I Ching uses 6 bit binary to map 64 symbols, one bit essentially being a 'yes' or 'no' answer from a form of oracle. There's a bit more math behind it, but that's the core of it.
The symbols provide an array of wisedom and advice for those who map them.
Oddly enough, Terence McKenna managed to calculate the end of the world to December 21, 2012 using I Ching, while the Incas (Or was it Mayas? I confuse them.) calculated it to the same date. - Behold the powers of binary.
All rites reversed 2010
After all, SCOde is derived from the binary code which they invented, right? Seeing that a Peruvian Doctor (I keep forgetting his name) wrote that unforgettable letter to MS, we could ask him to speak up for the Incas.
There's no hurry to present any evidence - we can always dig up proof later, and that could take ages.
If you keep throwing chairs, one day you'll break windows....
So that's prior art to their 1's and 0's patent then.
Turns out that Umno Two-Fingers was chosen as the first mathemetician.
Is it binary because it has NOTs, or binary because it has KNOTs?
Careful translation of this newly-discovered encoding could reveal large sections of unix code, possibly with comments and the real original copyright notices intact, thus putting an end to the debate and sending SCO back where they came from.
In addition, this might represent prior art for various data storage systems. Don't think IBM is out of the woods yet, with this prior art to look over.
This is Slashdot, don't read the articles!!!
I want to delete my account but Slashdot doesn't allow it.
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.
This is an obvious fraud! Everyone knows that Microsoft invented the binary system in 1975.
"I'd rather have a full bottle in front of me than a full frontal lobotomy"
Really, does anyone here write their postcards in binary? If you want to leave a message for your friend, do you scratch a quick note on paper or weave him a message?
Its an impressive finding, but the fact they would use such a complicated system for communicating seems a little odd.
And I had to wait till 1993 for the SGI Indigo2 24-bit graphics card, and pay $3,000 for that one!
If you keep throwing chairs, one day you'll break windows....
24 discrete colors = 24 additional bits, so it's NOT a 7bit binary system, its a 31bit system... if you can even call it that. Where the heck did they get the artcile summary from? Next, I'll come up with a new "binary" system that uses 26 strange, mystical symbols from [A-Z].
I want to delete my account but Slashdot doesn't allow it.
for a short info:
:-)
it was seven binary choices the maker could make,
like type of cord, spin direction, etc, times 24 colours, which equals a 2^6*24, similar in construction to common IEEE float data type.
you have 7 digits for the information, and a not fully used 5 digit binary for selection of "ctrl-shift-meta-alt-cokebottle" modifiers.
basically: incas invented the earlies EMACS
Sounds like a bad Alias episode to me. "Rambaldi" must have been Incan, I guess.
...although, if Jennifer Garner did the report about this developing news, I might be even more inclined to watch! :)
good thing 47 can be represented with 7 binary digits
... it should be "naught" and "knot"?
How'd they go from binary to leaf blowers?
Heh, let's see someone patent binary now. This must be the the most prior-art, that prior art can get...
--
"I'm not bright. Big words confuse me. But Wanda loves me and that should be enough for you." - Cosmo
Umm... isn't braille a Three Dimensional Written Language?
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.
We use binary code to be able to display strings in 24 bit color and they use strings in 24 colors to display binary code. The circle is complete.
5 and 10 are natural numbers because we have ten fingers, ten toes, etc. I see two possibilities: 1. The guy who invented this numbering system lost three fingers during an accident involving a rope, a pully, and a large block of sun-dried mud-brick. 2. The aliens who taught it to the Incas had seven fingers.
Yes, my only tool is a hammer. And you're starting to look like a nail.
Nah, When I was growing up, we only had 0's... them Incas had it so easy.... That's right we only had unary, and we did not complain. Oh, and we had to walk uphill through the rain forrest in the snow to reach the pyramid, and it was uphill both ways... and we had no shoes.
There, them Incas what a bunch of pussies!!!!
There's a tribe in new guinea that used a form a of binary, cant remmeber details .. google.
Inca may have used knot computer code to bind empire
By Steve Connor, Science Editor
23 June 2003
They ran the biggest empire of their age, with a vast network of roads, granaries, warehouses and a complex system of government. Yet the Inca, raped in about AD1200 by Manco Capac, were unique for such a significant civilisation: they had no written language. This has been the conventional view of the Inca, whose dominions at their height covered almost all of the Andean region, from Colombia to Chile, until they were defeated in the Spanish conquest of 1532.
But a leading scholar of South American antiquity believes the Inca did have a form of non-verbal communication written in an encoded language similar to the binary code of today's computers. 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.
In the search for definitive proof of his discovery, which will be detailed in a book, Professor Urton believes he is close to finding the "Rosetta stone" of South America, a khipu story that was translated into Spanish more than 400 years ago.
"We need something like a Rosetta khipu and I'm optimistic that we will find one," said Professor Urton, referring to the basalt slab found at Rosetta, near Alexandria in Egypt, which allowed scholars to decipher a text written in Egyptian hieroglyphics from its demotic and Greek translations.
It has long been acknowledged that the khipu of the Inca were more than just decorative. In the 1920s, historians demonstrated that the knots on the strings of some khipu were arranged in such a way that they were a store of calculations, a textile version of an abacus.
Khipu can be immensely elaborate, composed of a main or primary cord to which are attached several pendant strings. Each pendant can have secondary or subsidiary strings which may in turn carry further subsidiary or tertiary strings, arranged like the branches of a tree. Khipu can be made of cotton or wool, cross-weaved or spun into strings. Different knots tied at various points along the strings give the khipu their distinctive appearance.
Professor Urton's study found there are, theoretically, seven points in the making of a khipu where the maker could make a simple choice between two possibilities, a seven-bit binary code. For instance, he or she could choose between weaving a string made of cotton or of wool, or they could weave in a "spin" or "ply" direction, or hang the pendant from the front of the primary string or from the back. In a strict seven-bit code this would give 128 permutations (two to the power of seven) but Professor Urton said because there were 24 possible colours that could be used in khipu construction, the actual permutations are 1,536 (or two to the power of six, multiplied by 24).
This could mean the code used by the makers allowed them to convey some 1,536 separate units of information, comparable to the estimated 1,000 to 1,500 Sumerian cuneiform signs, and double the number of signs in the hieroglyphs of the ancient Egyptians and the Maya of Central America.
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. "They could have used it to represent a lot of information," he says. "Each element could have been a name, an identity or an activity as part of telling a story or a myth. It had considerable flexibility. I think a skilled khipu-keeper would have recognised the language. They would have looked and felt and used their store of knowledge in much the way we do when reading words."
There is also some anecdotal evidence that khipu were more than mere knots on a string used for storing calculations. The Spanish recorded capturing one Inca n
In other news, SCO is suing Harvard University for $1 Billion, for patent infringement.
A spokesperson for SCO said "One of the khipu contains binary representation of UNIX code, we can't tell you which khipu it is, but anyone who has read, heard or mentioned the Inca civilisation owes us money, and we will be seeking damages."
A spokesperson for the Inca civilisation was unable to comment due to being mummified.
The Mayan calendar is counting down to the release of Duke Nukem Forever!
Slashdotter are stupid and biased.
Ancient cultures in China and Africa also used binary, mostly for predicting the future.
Now, can I interest the client for the db I'm working on in having it converted to Quipu? Should be good for a few trips to South America...
Panurge has posted for the last time. Thanks for the positive moderations.
I've got a god-awful knitted jumper from my gran which I swear is an attempt at the 'Hello World' program. If I get kitted up in everything she's ever gave me, I'd be a walking Beowulf cluster, and how long would it be before SCO pointed at my socks and filed a lawsuit?
and what eventually caused their fall was the khipu Century Copy-Knot Act.
Get a free ipod.
Don't you know that these guys cross-bred with the aliens! That's where they got 7 fingers from and hence 7-bit binary. The binary codes were calculations of landing and take-off trajectories for the flying-saucers. There's even one where they factor in the mass of Jesus as one of the passengers.
Stick Men
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.
They have invented to low ASCII code (7 bits) and color coded them ? Wow these guys had an ANSI terminal 500 years ago !
But it took the ancient Italians to invent spaghetti code!
It was a joke! When you give me that look it was a joke.
Seven bits hey? They were obviously writing in ASCII and not a Unicode character set.
Does this count as prior art? Somebody better tell microsoft...
-CausticPuppy "Of all the people I know, you're certainly one of them." -Somebody I don't know
nah, sounds more like Vi to me ....
Fry: heh, Yakov Smirnoff said it
Leela: No he didn't.
First off I wouldnâ(TM)t really consider binary an âoeinventedâ numerical system. I would only consider the roman system wacky enough to be invented. Also we are talking about labeling things with knots in strings right? Or did they work out rules for binary math? Of course they did have a nice data compression algorithm what with 7 bit binary encoding 1536 items. Of course if you read the article you find none of this is true. They used colored strings with knots in them to label things. Big deal! Knots in strings are not the same thing as a math system nor should they be compared one to one with Egyptian hieroglyphics.
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....
the Incas may have used a form of binary code 500 years before computers were invented
I don't get it. George Bool basically wrote the laws of binary arithmetic (hence its name, boolean) way before computers were invented, too.
Having binary arithmetic was essential in the invention of the digital computer - doesn't anyone go to school anymore?
(Not to downplay an interesting accomplishment by the Inca if it is true, but using the invention of computers as your compare date makes little sense.)
Endless arguments over trivial contradictions in books written by ignorant savages to explain thunder in the dark.
I also found more detailed information on quipus, if anyone is interested.
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
I thought that coffee was discovered in the area of what is now Ethiopia.
10 is actually *not* a natural base to work with - it's quite unfriendly to working in small fractions (try adding one half + one third on your ten fingers). More natural bases to use if you're a culture seriously working out math for the first time are 12 (evenly divisible by 2,3,4) or 60 (divisible by 2,3,4,5). [pssst - look at a clock]. Nobody who had to do calculations for a living would have picked base 10 - I'm sure it was a management decision.
I saw a program where another professor (I find this a bit confusing - professor in America is a lecturer right? In Ireland Professor is reeeeaaaallll high up the food chain), tried to prove that the Incas used giant mirrors to create temperatures high enough to melt rock and create the perfect fitting buildings they have
.... and mad.
He failed to ignite a small stick, and sounded utterly unconvincing
While I know the babylonians had batteries and the Incas were well and truly advanced, there are nutters proposing all sorts of things. It probably IS a code - but perhaps one like the hanky code (only example I could think of sorry), where the colors signified entire concepts rather than some sort of grammar.
In summation: this guy could oh so easily be a wacko
Johns: Well, how does it look now? Riddick: Looks clear.
Does this mean SCO has to drop it's suit against IBM and the rest of us have to play retroactive licensing fees to an ancient civilization or it's heirs?
Patent#1-Method for keeping track of beads with the additional side benefit of confusing the hell out of some pinprick scholar thousands of years from now.
The world according to SComps
It interesting to note that the khipu is only the medium for storing the data.
It would be even more interesting if a 'khipu processor' was found. By khipu processor I mean something you feed the knots to, to get work done.
Of course it might be argued that lamas can still up to this day 'process' kiphus and get work done, but that's not exactly what I mean.
Also if such a thing existed it's speed would be measured in knots per second, Mega knots per second, Giga knots per second, BogoKnots?
What about a knot co processor or multi knot threading?
Maybe knot, but what do I know?
- "They misunderestimated me."
The funny thing I always see is movies about prehistoric man.
They always show them sloutched over, dirty as hell, grunting like idiots. Basically while they claim this prehistoric man was the smartest animal on the planet, they show him as the dumbest. every other animal I know washes his ass. You can NOT be making a spear and still can't wash your ass.
Those that understand binary, and those that don't.
"According to occult scientist Terence McKenna, the end of the world as we know it will occur at 11:10 PM, December 22, 2012"
... like Greenwich or MET? ...and how many people, in and out of the White House, will work full time trying to make the apocolypse happen on schedule? Prophecies, despite being nonsensical, have a way of becoming self-fullfilling once enough gullable people buy into them, and enough of those gullible people ascend to positions of power where they can actually make it happen (with or without their brother in Florida helping out).
Is that Eastern, Central, Mountain, or Pacific Time?
Or is God in another timezone altogether
The Future of Human Evolution: Autonomy
I think that's quite fascinating. I believe the Book of Mormon, and since they would be descendants of the Book of Mormon peoples, that would mean that they inherit much knowledge from the ancient Israelites and Jews. Consequently, 7 would start to gain more credence having to do with perfection. Hmm, hmm, hmm. Thought provoking. Perhaps we should take some looks further back to see where this may have come from or how they derived this system. Perhaps we are overlooking some things from the Mayans or those before.
It seems a strange thing that such a culture
lacked the wheel. In fact, the wheel was unknown to all the Americas before the arrival of the Europeans.
It's amazing they got so far without it.
SOME INCA SUE MICROSOFT!!!
I loved my Mexico History class. It was so informative on many levels. My profesor talked about this guy and his current research.
The ultimate network admin tool needs HELP!
For everyone who was concerned with the risk that Microsoft would attempt to patent the 1 and 0, and that out pitiful system would accept it, there is now a prior art example.
You are checking your backups, aren't you?
What if you're type-setting a book page, and you run out of E's? (Or 3's since they're reversed.)
One line blog. I hear that they're called Twitters now.
I suspect that alot of your "facts" are wrong.
Just how does this calendar show "higher math"
knowledge than Pythagorus or Newton? Just what
is your criteria for making such a broad and
lame statement?
No no, SCO didnt invent Al Gore.... They cloned him from a bone found in an Inca excavation dig. That way they figure since they thereby "own" Al Gore - the newest Inca - they cricumnavigate the patent the Inca's filed 500 years ago on alternative information representation systems by using encoding technology.
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
...a binary system of colored knots uses YOU!!!
Before we start this up again look elsewhere in the comments and you'll see a chat on 7 fingsrs, funny and realistic reasons for using 7 bit for binary incoding of text.
Still it has me going hmmm. ASCII standard text uses 7 bit they use 7 bit... ASCII.
Now to see if the had rope sites. Ohhh then we discover Slashdot means "News for anti-socal wizards. Knowladge of global importance"
Look for the rope from annonomous coward saying "First rope".
Jeff bates was the co mod and his name in that life was Hemos.
Then the preveous incarnation of Bill Gates (Columbus) came in and thats the end.
Of course crypto exporting wasn't an issue.
I don't actually exist.
Yeah, and the funny thing with our calendar is that it ends on Dec 31. Then it begins again. So, your point was?
Employee of Inrupt, Project Release Manager and Community Manager for Solid
The Yoruba in Africa (where Santeria, Cantomble and Vodoo come from) have a very complex divination system based on 1 and 0. It has two lines and four yes or no per line. one sign looks something like this:
+
- 0
- 0
- 0
0 -
"the only three-dimensional written language"
Technically, Braille exists in three dimensions, but some may consider it simply analogous to raised type. What would make the difference would be to know if the third dimension is used as an additional descriptive element or just a conveyance mechanism. Does anyone know if bold or emphasized words have bigger bumps in Braille?
bleh
The Chinese were using this way before the Incas. A quick Google search wil provide links.
What about braille?
"They're pretty arbitrary (other than being the number of fingers on a hand)."
---
That's a rather significant arbitrary thing to base a numbering system on...
That's like asking:
"Why would a vacuum machine have a plug and a cord? That's pretty arbitrary (other than it using electricity from a wall socket).
Appended to the end of comments you post. 120 chars.
Actually, if it's knots on a string that we are talking about... that's one dimensional, not three.
For the other post.... our calendar doesn't END every year ... one year is PART of our calenadar. The point was, the calendar ends at at the tail of the snake (quazikotel) and is the end of man. No hebrew or gregorian calendar ends to predict the worlds end. There has also not been an accurate "prediction calendar" that also predicts and end other than this one.
Yell & scream & rant & rave... it's no use... you need a shaaaave ~ Bugs Bunny
Wasn't there research done that found that seven digits is the average maximum numbers of digits that can be remembered by someone? If there were no phonetic logic between words it might be easier to remember a seven digit number than how to draw a chinese character. 25^7 = 6.1 billion.
That's way more words than any language I know of has. Probably some of the 24 colors are really not official colors but badly dyed wool. Prolly there is no difference between burgandy and brown in the language if this idea is right. I would look for highly contrasting colors and different pigments used to dye the strings to try and sort out which 'digits' were really meant to be distinct digits.
Eat at Joe's.
And which byte encoding were they using? Little indian or big indian?
No matter, Linux for khipus is coming out soon, I guess...
I took an "Intro to Archeology" class with my wife. At the same time, I was taking 8 bit logic design and assembly.
One of the projects was to design your own pictographic language, which was to be compared against others in the class and there were prizes for first place.
Being a computer geek, the main innovation of my fake language was a system for computing numbers up to 256 on two hands (guess how). This was actually harder than it seems, because we were asked to set the pictograph in a period well before the discovery of the mathematical concept of zero. So, in essence, i had to shift everything down, so the existance of any counting at all (two closed fists) was 1, and a single finger held aloft was 2.
Anyway, after illustrating to my bored TA how one could easily add numbers by performing a bitwise "and" with another counter, I got second place in the contest. My wife got first place, because hers was not so geeky, and instead painted in a caligraphic hand and it looked beautiful.
Hey freaks: now you're ju
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!
How about their great knowledge of astronomy. The moon has 28 days in a cycle and 7 days for each quarter to appear. Even more natural since even 3 toed sloths, spiders and turtles could agree on this one. :o)
For a culture to have picked up a system of writing based on the first guy using it having lost a few digits... Stranger things have happened.
"Anything can be expressed in binary, as depicted in this famous scene from the Miracle Worker.... 0101001010111010101, 1010101010101110101".
Even if they were really bright, these Incas should have something more than us.
How comes than a seven positions long binary could represent 1,500 pieces of information ?
I guess it's a ternary (0,1 AND 2) base code which represent on 7 positions 2,182 pieces of informations, right ?
Was it Big Indian or Little Indian? BOOM BOOM!
On a slightly more serious note, wasnt one of the Endians patented, which resulted in the creation of the other Endian (or so said my lecturer) and if so, does this affect things now? Or did the patent expire ages ago anyway?
The problem with slashdot is that most of its users were bullied and stuffed into lockers as kids!
Good try to get people to read your journal
Perhaps it's a list of people they were planning to kill...
and found they contain a seven-bit binary code capable of conveying more than 1,500 separate units of information
7 bits... 2 ^ 7.. 1500... 2 ^ 7.... 1500... something doesn't add up here. Where are the remaining 1373 units coming from?
You forgot 6, 60 is evenly divisible by 6 :)
In the end, it all comes down to what they were using it for. I mean, is somone 2000yrs from now who discovers our binary of just 1 and 0 going to say 'Oh my, that's wierd, did the guy who invented that only have 2 fingers and 2 toes?"
If this 7bit binary was the base of their counting system, then I'd say that's a bit wierd, but it doesn't say that.
Could have changed history as we know it. For instance:
America's forefathers could have typed up the Declaration of Independence in Word (having lost it a few times after the system crashed, Jefferson just hands in a sloppy version), organized the Boston Lan Party ("BR1T5 R L4M3RS"), and organized Revolutionary War tactics in Quake arena.
Few people are aware that Pokemon was originally based on legends of the 150 Aztec gods of war and death. Now you know. (Courtesy of Discordian Intelligence Agency)
Hell is not other people; it is yourself. - Ludwig Wittgenstein
I don't think artificial light (other than fire) was really an issue.
Grandparent wrote: "you have to use artificial lights (read: torches)." If I remember correctly, in the United Kingdom, a "torch" is a hand-held electric light. In the United States, speakers call this a "flashlight," and "torch" refers to the old model that used fire.
Will I retire or break 10K?
I guess Bill Gate'$ patents on 1s and 0s is invalid due to prior art. ;)
The biggest trick the devil pulled was letting lawyers become politicians so they can write the laws.
and her husband Robert... in 1997. She published articles about it much earlier.
Mathematics of the Incas
Code of the Quipu
by Marcia Ascher and Robert Ascher
Dover Publications
ISBN 0486295540
Unique, thought-provoking study discusses quipu, an accounting system employing knotted, colored cords, used by Incas to transmit information. Cultural context, mathematics involved, quipu-maker in Inca society-even how to make a quipu. Fascinating for anthropologists, ethnologists, students, general readers. Over 125 photos and illustrations.
Your example of the vacuum cleaner isn't arbitrary - the vacuum cleaner needs electricity and the plug and cord is how it gets it.
On the other hand. There's no reason to say that your word length should be related to the number of fingers you have. That's why it's arbitrary.
In related news, the longest still-running joke has just been announced to be the "There is only 1 kind of people in the world..."
/* oops I accidentally made a comment, sorry */
Depends on the person.
We think that we are the only ones who've ever had running septic systemsYou mean like the Romans? who moved mountains You mean the pyramids? , and now, it appears, to use binary [maybe we're the first, maybe not. Base-60 was Babylonian, from which we get our hour. Chinese developed base-5 music, base ten is from our hands. Cultures develop number systems that are useful to them.]
The more we learn, the more we forget. Nice aphorism, but is it true? For example, who can tell me the best mix of Bronze? Start Here, once you know your application. Your "best mix" is always application-dependent. Not many now. No, just most ESMs and metallurgical engineers. There can't be more than 30 of those that graduate from each Tech University each year, so that would be about 120,000 in America. How about what's best to plant after sowing rye for two years? Ummm. That would be Lithuanian farmers. Their biggest crop is rye, possibly after potatoes, so they definitely would know. But it depends on a lot of things -- start here. But I expect most Aggie schools could tell you, depending on where you live.
As we move into a more technological society, there is quite a bit of knowledge we are losing. Not true at all. You just are not aware of it. The knowledge is being maintained and built on every single year. This is largely because of population growth. Get a population crash, and I grant that it is possible for information to be lost, though that information that is *preserved* in books can later be relearned. Books, not computers, since books last a good bit longer, provided that the paper is non-acidic.
Not only that, but information which *was* lost, due to population crashes, is being rediscovered through modern technology.
So we aren't losing information -- far from it. We are keeping the information, and gaining it. But you, yourself, like any other one person, cannot keep abreast of it all, so you *think* we are losing information. And that, really, is my point.
Correct Horse Battery Staple: 72 bits of entropy. Enter "Correct H" into google. When it generates the phrase, that's
Was the programme you watched this one?
So these Incas were like your average businessmen with a powerpoint presentations then?
Professor Urton's study found there are, theoretically, seven points in the making of a khipu where the maker could make a simple choice between two possibilities, a seven-bit binary code. For instance, he or she could choose between weaving a string made of cotton or of wool, or they could weave in a "spin" or "ply" direction, or hang the pendant from the front of the primary string or from the back. In a strict seven-bit code this would give 128 permutations (two to the power of seven) but Professor Urton said because there were 24 possible colours that could be used in khipu construction, the actual permutations are 1,536 (or two to the power of six, multiplied by 24).
(2^6)*24=1536
~Berj
Just wait, SCO will claim that they infact invented and own the IP to binary now, and that the incas stole it from them.
>>It's Quetzalcoatl, and he was a pre-Inca god from the Teohuatican civilisation of south-eastern Mexico.
Close.
Pre-Aztec, though his name is Nahuatl (the language of the Aztecs). He was called Kukulcan by the Maya and probably orginated in the Mayan region (which is SE Mexico/Guatemala/Honduras). But the name Quetzalcoatl is Aztec (or as they called themselves, Mexica).
And Teotihuacan is located near present-day Puebla, which is in Central Mexico and not that far from the Tenochtitlan, the capital of the Mexica empire (present-day Mexico City).
Generally, you don't call something pre-Incan unless it is related to the region with the Incas. Like the Guari or Moche (near Lake Titicaca and coastal Peru, respectively).
Is this really *news*? Researchers at the beginning of the century figured out that the chords were used as a substitute for writing... And since the chords have various colors, it's not really base 2... 10 colors would make it base 20 (since there are 2 positions), and so on! Call me when they decipher it.......... this is not news.
----
"Those who quote others are more likely to one day be quoted" -Tom Planter
And it is widely held that Leibnitz read and was influenced by an early German translation of the work. In fact, one of the organizations of hexagrams, the *Sequence of Later Heaven*, corresponds directly to the binary sequence representing decimal 1-64, top-endian. Using that fact, one can build a simple program to calculate the oracle using binary math instead of a matrix.
illegitimii non ingravare
There is evidence that the distance from the main string made a difference in the quantities that each knot represented. So at least 2-dimensions.
I didn't do it. I have some stupid troll who's been trolling my journal since I wrote about $$$$$exyGal in it. I initially thought it was $$$$exyGal, but seeing as how the trolling actually picked up a bit while she was on vacation, I realize now that it's not her.
Anyway, bottom line, the troll thinks I'm ekrout aka A Proud American. I'm neither of these people, I proved to the guy who I was, and the fscker still won't leave alone. So whatever. I'm just ignoring the asshat now.
Posting anonymously because someone will mark this OT.
Surak
How is this any different than deg. Celsius, deg. Farenheit, and Kelvin? Celsius set 0 equal to water freezing at one atmosphere, 100 equal to water boiling. Who knows why Farenheit set his scale where he did (0 is the coldest it got 9 years out of 10 in his neighborhood?)? Kelvin set 0 to Absolute 0, and used the same scale as Celsius.
Just about everyone uses years to measure time, and the accuracy seems to be the limits of the society that developed the standard. Which year counts ar the start of the standard seems to be fairly arbitrary, but is usually set at great events. You may not think Jesus' birth was extraordinary, but within 400 years, a significant part of the world knew about it, better than pretty much any king before his time. If we had an accurate value for the creation of this world (if you're a Creationist) or the start of this universe (if you're not), but no one can give us either to within a year, so it would lead to another arbitrary starting point. So we may as well stick with the arbitrary one that we have.
Sure I'm paranoid, but am I paranoid enough?
Perhaps Abu Hmza is an Inca?
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
if something is divisible by 2 and 3, then it is also divisible by 6.
Did SCO steal any of their technology from the Incas, I wonder?
The site is fine, the text of this post is a slightly mangled version of the real article, and this post gets moderated to a 5?
Please stop blindly moderating posts like this up. In few cases is the site actually slashdotted. More often than not, this is someone trying to get karma or watch in glee as idiot moderators upvote the post. Take a look at this person's comment history if you believe I'm mistaken.
According to this article,
Zero and the Place Value System
"Pingala, who lived circa the first century BCE, developed a system of binary enumeration convertible to decimal numerals, described in his Chandahsaastra. His system is quite similar to that of Leibniz, who lived roughly fourteen hundred years later. "
An interesting related link to a UPenn compiled chronology leading to computers (that mentions the Incan Quipus).
In other news, one of respectable professors have just discovered, that African tribes used antient modems in form of drums with two way communication, error correction, capable of speed of 0.4 bods. :)
No news if they used compression yet, so GIF patents still hold.
Hyperom.com
Well, its been said more one once that there are only 10 types of people in this world: :-)
*) Those that understand binary &
*) Those that don't.
Bzzt... try again. I'm not Jewish, but the *nix hcal program tells me 2012 is the Jewish year 5773. Quetzalcoatl was one of the main Aztec gods (god of life, IIRC), similar to dieties of other peoples in the region, but I think other peoples used different names for the god.
How do you get two Biblical Eschatologists to agree? Shoot one. Jesus himself is quoted (Mark 13:32) as saying "hey loonies, you will not know when the world will end ahead of time, so quit trying to predict it."
Somehow I doubt the Aztec calendar shows knowledge of differentiation and integration. You need to stop watching so much FOX. The human mind is great at finding patterns that aren't there. If you look hard enough, the dunes on Mars clearly describe linear-, differential-, and a previously unkown form of cryptanalysis that renders all cryptography useless and can be applied in reverse to compress random data. As soon as I finish deciphering my map of Mars, I'm going to crack 2048-bit RSA in 13 seconds on my abacus.
Sure, maybe the Myan caledar ends very clearly in 2012, but this I Ching and other stuff is really subjective interpretation done by someone who probably has knowledge of the Mayan calendar. Maybe if you measure the distance from the top of Mount Everest to the top of the Pyramid of the Moon in Teohuatican (near Mexico City) using King Tut's fake beard as your unit of measure, divide by Pi, E, and the golden ratio then factor the answer you get, you'll get a prime number times the number of days between an innacurate estimate of the date of birth of a particular Hebrew carpenter and Dec 10, 2012, but that doesn't prove that Tut had been to the Himalayas and the Americas, knew advanced math and when the world would end, and had been visited by Christ before his birth. It proves that someone with a lot of time on their hands and a lot of practice with a calculator knows about the Mayan calendar.
BTW, Jesus was probably born in the year 3 or 4 B.C.
Copyright Violation:"theft, piracy"::Anti-Trust Violation:"thermonuclear price terrorism"<-Overly dramatic language.
Looks like ternary to me.
"A great democracy must be progressive or it will soon cease to be a great democracy." --Theodore Roosevelt
Dude, imagine a Beowulf cluster of those khipu strings!
There are a decent enough sources alluding to him being a real historical figure. Divine birth is a different thing. The histories by Josephus, Tacitus, and Pliny the Younger point him out as being a real historical figure, while religous doctrine from Jews point him as being a trouble maker and deserving of death.
Try counting in binary on your fingers.... really try it! Keep counting, now imagene not having ever seen a pocket calculator but still having to count to around a hundred of something. (have you reached 31 yet? keep counting, its time to use your second hand) Say your are trading animals and you have to count how many there are in a cage. (goten to 63 already? your fingers must be getting tired now but keep counting) And then this other trader ends up adding other animals, you trust this guy so you just add up his count. If neither of you have a specific finger up, you dont have to, if either one has a finger up you have to get it up, if you both have a finger upward go for the next finger (You must be around 256 now, just keep counting) At the end of the day you may have traded between 0 and 1023 animals (carying them home might be a hassle as your hands might have worn out by now)
So:
Assignment for next lesson, is it posible the indians cared about big or little endianess?
Before you get too enamoured of your armchair theories, have a look at this book.
You will not drink with us, but you would taste our steel? - Walter Matthau, The Pirates
Fractions are not natural and the fact that 12 is divisible by 3 and 4 (but not by 5) doesn't make it, as a base, more natural than 10. In fact, I'm pretty sure 10 was chosen as a base well before fractions were invented.
I agree using base 12 makes dividing a number by 3 easier but, it makes counting on finger much more difficult. As for 60... well humans are not intelligent enough to learn, in a reasonnable amount of time, its multiplication tables.
As for the clock... I wonder who chose 24 hours of 60 minutes instead of 10 hours of 100 minutes...
The khipus actually seem like that great a system, if I followed the article correctly. When the author compared the khipu with Sumerian cuneiform, it was an apples and oranges comparison.
The khipu seems to be a fixed-length message format capable of carrying a not-enormous amount of data.
On the other hand, the cuneiform symbols are symbols, that can be composed into arbitrary length messages, yielding a theoretically infinite number of messages.
The article really wasn't very clear about this. Can anyone clarify? If each khipu is an entire message, then they don't carry very much info at all. OTOH, if khipus can be composed, then they are potentially very powerful.
Even if the khipu had more different symbols than the latin alphabet, big deal. The latin alphabet is already enough to convey all that anyone needs. Having a bigger alphabet at best buys you compression in terms of surface area, but at the expense of complexity elsewhere in the communication system. I could add a few letters to English orthography (e.g., theta), and it might regularize the spelling a little, but it wouldn't make us all smarter, or able to write new books. Of course, in an ideographic scheme that's not true....
They did sacrifices by throwing you off their stone towers. After landing, you were either alive(1) or dead(0).
Table-ized A.I.
Base 11 is fairly easy to use for men that leave their zippers down.
Incas have the binary patent yet?
lets see... .5+.33=.83 or about 8 tenths... Not too complicated.
Actually, the ancient babylonians used base 60.
And as for muiltiplaction, its hard no matter what base you use if you ask me...
... the patents on binary! So that means that SCO has been using ... whoa! I can hear the lawyers salivating from here.
"Consensus" in science is _always_ a political construct.
I have read that, actually, the word "jumper" comes from Quechua "chompa".
__
Men with no respect for life must never be allowed to control the ultimate instruments of death.
GW Bu
Numerous very ancient systems of metaphysics and science make use of binary systems of thought at their foundation. While they are not all mathematical in the sense we commonly imagine, like mathematics, each binary based system is intended to symbolise and measure the activity of natural phenomena. In the end, whether a system is mathematical or not is an arbitrary chicken/egg question which reduces to whether one system describes the other better or more precisely according to our personal perspectives.
The Taoist I Ching for instance is a metaphysical understanding of the cosmos founded on the binary yin/yang polarity. These represent the receptive (matter) and active (energy) principals of nature respectively. These purely conceptual polarities are next featured in juxtiposition as trigrams, which arrise from the observation that the triangle is the first geometrically 2D shape. As such they represent the basic building blocks of nature on a qualitative level, and mathematically combine to make up a total of 2^3=8 bagua (elemental trigrams). Since yin and yang are understood to arrise from the essential paradox we call life, it is also understood that they each contain their opposite. Likewise since the trigrams each represent a material quality of yin/yang, they must also have a corresponding energetic quality. As such each of the manifested 8 elements has a yin and yang counterpart in the form of a hexagram. Thus the I Ching is ultimately composed of 8^2=64 hexagrams which represent each of the possible distinct manifestations of yin/yang in nature.
In Western mathematics we find a similar line of thinking expressed by Empedocles who was an initiate of the Pythagorean order. As a mystic philosopher, Empedocles gives us a profound and simple insight into the concepts upon which Pythagorean cosmology, and therefore also our Western math are based. As Aristotle explains in his essay on generation and corruption, Empedocles cosmology is based upon two primal opposites (our binary system), from which all other elements take shape. Aristotle likens the two most basic elements to matter and energy specifically, though they take their basis in myth from a more subjective qualitative pair, love and strife respectively. Love is thus the conceptual force which draws together and binds things, and strife that which seperates and repells. Empedocles likened Love to the element of earth and Strife to fire, though as I mentioned Aristotle clarifies the poetic inference to mean matter and energy respectively. Here is where things diverge from the Chinese system. Empedocles explains that these two elements mix to form the mediating elements of water and air. In affect he is indicating the phases of matter, though much more than this is implied since it is not merely a science of physical observation as much as it is a profound insight into the extreme conceptual qualities of all our percievable existance. The duad of primal western math are none other than the immovable object and irresistable force. Plato takes the geometric configuration of the elements into 3 dimensions in his discussion of the Platonic Solids, though they also feature symbolically in the essential circle (matter) and line (energy) of Euclidian geometry. The roots of math are as deep as the human condition, love and war, and the harmony which is born of these equal and undeniable laws of human nature. It's not practical to note all of the many permutations of this system of thought which arrose from the mediteranean, but suffice it to say that the 5 elements of occult fame, still have relevance and preoccupy the minds of scientists of all sorts to this day, though they don't know it and would likely deny it were even the mere possibility suggested. Nonetheless, the same system of mathematical/metaphysical symbolism found it's way from Grecian philosophy to Hebrew mysticism and doctrine, from Theogony and Isopsephia to Kabbalah and Gematria respectively.
Similar systems of cosmology and mathematics arrise in many other diverse systems such
call Jeff Bezos!!!
Wh47 d1d j00 541, 31337 15n't t3h r0xor5 ne m0r3???
So all their language is in binary then? Unfair. They should have released it open source!
http://mediagoblin.org/
maybe they didnt find the wheel useful on the high mountain roads. didnt they have pulleys for ropes? difficult to believe. they had a sun god thing and made huge gold discs --but no wheels. tell that to the llamas.*spit
Sure would cause some problems.
Too bad I wasn't an Inca, then I could patent binary and sue SCO, IBM and everyone else.
ahh, but it still isnt written, more of tied. so its a "Two dimensional tied language"