Monday, February 21, 2011
A Linguist's Overview of Numeric Digit-Base Systems
From the title you may think this is a mathematics post, but don’t be fooled. This post is about the language of math, and more precisely the use of different digit-base systems in different languages; languages may differ not only in the words they use to count, but also in their fundamental system for counting and therefore conceiving of mathematical notions (though the final, ultimate understanding of course remains the same).
Most modern societies use a base-10, or “decimal” system:
A few languages that use(d) a decimal (base-10) system: Incan languages like Quechua and Aymara, Chinese languages, Vietnamese, Japanese, Korean, Thai (Japanese, Korean, and Thai decimal systems were adopted from the Chinese system).
The Hindu-Arabic numeral system, first developed in India, is a base-10 system, corresponding of course with languages that use a base-10 counting system.
Variations of Hindu-Arabic numerals are used in places that speak the following languages (but are not limited to them, especially in the modern age): Western languages, Arabic, Farsi, Indian languages, Burmese, Khmer, and Thai.
If we have a base-10 system in the English language, then why do “eleven” and “twelve” seem to be independently named? By the logic of the decimal system, shouldn’t eleven be called “oneteen” (one-ten) and twelve “twoteen” (two-ten)? They are, after all, followed by thirteen (three-ten), fourteen (four-ten), and fifteen (five-ten), right?
Although many European societies, such as those in the British Isles, used a duodecimal, or base-12 numeric system for measurements (one foot = 12 inches), monetary units, and time (12 months, 12 zodiac signs), the words eleven and twelve are actually thought to originate from the Proto-Germanic “ainlif” (one is left) and “twalif” (two are left). Still, in modern English this comes across as an irregularity.
French, although decimal-based, has the irregular use of base-20 for numbers 80 through 99. 80 is called quatre-vingt (4 x 20). 85 is quatre-vingt cing (4 x 20 + 5), 90 is quatre-vingt dix (4 x 20 + 10), and 95 is quatre-vingt quinze (4 x 20 + 15).
The Sumerians strategized a base-60, or sexagesimal system that was later passed on to the Babylonians. This system was used (and in many cases, is still used) to measure time (60 seconds in a minute, 60 minutes in an hour), angles, and geographic coordinates.
This base-60 system was not, however, derived from the Sumerian language itself, and the cuneiform numeric system was actually a decimal system.
The Duodecimal System (Base-12):
Languages that use a duodecimal (base-12) system are rare. Chepang (spoken in Nepal), Mahl (spoken on Mincoy Island, India), and Nigerian languages such as Janji, Gbiri-Niragu, and the Nimbia dialect of Gwandara all use a base-12 number system. J.R.R. Tolkein’s Elvish languages also use a duodecimal system.
The Mayans (and other Mesoamerican cultures) used a base-20 system:
Other digit-systems used in different languages include the following:
Computers use a binary, or base-2 system to store data:
Computer programmers, who are after all human, use a hexadecimal (base-16) system instead of the binary system:
Web page colors are based on this system. Combinations of red, green, and blue (the primary colors of light) are represented as (R,G,B) = #RRGGBB. For example, #000000 = (0,0,0) = 0 Red, 0 Green, 0 Blue = WHITE; #FFFFFF =(256 Red, 256 Green, 256 Blue) = BLACK. Likewise, #FF0000 = red, #00FF00 = green, and # 0000FF = blue.
Those of us who are not computer programmers would have a difficult time with the hexadecimal system. Likewise, I imagine it must be difficult for a language learner trying to crossover from one digit-base system to another. I am sure this has happened in history where two or more cultures have collided. Would merchants have argued in an open marketplace over basic trade units? Would colonialist pedagogues have been puzzled by their native subjects’ seeming lack of comprehension in basic math? They may have been unaware that what appears to be a logical brick wall is in fact a linguistic barrier.
I hope this post has done more than make you realize that certain languages use different digit-base systems than our familiar base-10. Depending on what digit-base is used in your language’s counting system, individual numbers can take on a different meaning or level of significance. Think of how many times you refer to the number ten. “I’ll be there in ten minutes,” or saying to an obnoxious child “I will count to ten.” Or that demonical professor who wants a ten-page essay on quantum physics. Ten is just a handy, familiar number in our minds, and this is only because we speak a language whose number system is ultimately based on the number of fingers we have. If we were Huli speakers, 225 would be more significant than 100, and your professor would want a 15-page essay instead of ten pages. And if we spoke a base-8 language, we might celebrate our 64th birthday as though it were our 100th.
-------------------------------------------------------------------------------------
A book I came across in my research for this post:
Numbers, Language, and the Human Mind
By Heike Wiese
I found this on books.google.com, so if you are interested you may also type in the name/author of this book at that search engine.
Most modern societies use a base-10, or “decimal” system:
0 1 2 3 4 5 6 7 8 9
10 …
A few languages that use(d) a decimal (base-10) system: Incan languages like Quechua and Aymara, Chinese languages, Vietnamese, Japanese, Korean, Thai (Japanese, Korean, and Thai decimal systems were adopted from the Chinese system).
The Hindu-Arabic numeral system, first developed in India, is a base-10 system, corresponding of course with languages that use a base-10 counting system.
Variations of Hindu-Arabic numerals are used in places that speak the following languages (but are not limited to them, especially in the modern age): Western languages, Arabic, Farsi, Indian languages, Burmese, Khmer, and Thai.
If we have a base-10 system in the English language, then why do “eleven” and “twelve” seem to be independently named? By the logic of the decimal system, shouldn’t eleven be called “oneteen” (one-ten) and twelve “twoteen” (two-ten)? They are, after all, followed by thirteen (three-ten), fourteen (four-ten), and fifteen (five-ten), right?
Although many European societies, such as those in the British Isles, used a duodecimal, or base-12 numeric system for measurements (one foot = 12 inches), monetary units, and time (12 months, 12 zodiac signs), the words eleven and twelve are actually thought to originate from the Proto-Germanic “ainlif” (one is left) and “twalif” (two are left). Still, in modern English this comes across as an irregularity.
French, although decimal-based, has the irregular use of base-20 for numbers 80 through 99. 80 is called quatre-vingt (4 x 20). 85 is quatre-vingt cing (4 x 20 + 5), 90 is quatre-vingt dix (4 x 20 + 10), and 95 is quatre-vingt quinze (4 x 20 + 15).
The Sumerians strategized a base-60, or sexagesimal system that was later passed on to the Babylonians. This system was used (and in many cases, is still used) to measure time (60 seconds in a minute, 60 minutes in an hour), angles, and geographic coordinates.
This base-60 system was not, however, derived from the Sumerian language itself, and the cuneiform numeric system was actually a decimal system.
The Duodecimal System (Base-12):
0 1 2 3 4 5 6 7 8 9
A B 10 11 12 13 …
Here, A=10, B=11, 10=12, etc…alphabetic letters represent numbers from 10 to the duodecimal base of 12. Numbers eleven and twelve have independent names in languages that employ the duodecimal system.
Languages that use a duodecimal (base-12) system are rare. Chepang (spoken in Nepal), Mahl (spoken on Mincoy Island, India), and Nigerian languages such as Janji, Gbiri-Niragu, and the Nimbia dialect of Gwandara all use a base-12 number system. J.R.R. Tolkein’s Elvish languages also use a duodecimal system.
The Mayans (and other Mesoamerican cultures) used a base-20 system:
0 1 2 3 4 5 6 7 8 9
A B C D E F G H I J
10 11 12 13 ….
In this system “10” represents 20. Alphabet letters are here used to represent the numbers that are between 9 and the Mayan digit-base number 20; what we call the “teen” numbers would not have been known as “sixteen” (six-ten) or “seventeen” (seven-ten) but would have had their own independent name.
Other digit-systems used in different languages include the following:
Base-4: Chumashan languages (native to southern California). Number names were structured according to multiples of 4 and 16.
Base-5 (quinary): Gumatj, Nunggubuyu, and Kuum Kopan Noot are all quinary languages indigenous to Australia. Saraveca, an extinct language spoken in what is now Bolivia, was also quinary.
Base-15: used in the Huli language of Papua New Guinea. In Huli, fifteen is called ngui, thirty is ngui ki (15x2), and 225 is ngui ngui (15x15).
Base-24: Kakoli (a.k.a. Umbu Ungu, of Papua New Guinea). Tokapu means 24. 48 is tokapu talu (24 x 2). 576 is tokapu tokapu (24 x 24)
Base-27: Telefol and Oksapmin, also in Papua New Guinea.
Base-32: Ngiti (Democratic Republic of Congo) is base-32 with base-4 cycles.
Computers use a binary, or base-2 system to store data:
0 1 10 11 100 101 110 111 1000 1001
0 1 2 3 4 5 6 7 8 9
The top row represents the computer’s base-2 digit system, and the bottom row is there so you can compare it to the base-10 system.
Computer programmers, who are after all human, use a hexadecimal (base-16) system instead of the binary system:
0 1 2 3 4 5 6 7 8 9
A B C D E F 10 …
(10=16 here)
Web page colors are based on this system. Combinations of red, green, and blue (the primary colors of light) are represented as (R,G,B) = #RRGGBB. For example, #000000 = (0,0,0) = 0 Red, 0 Green, 0 Blue = WHITE; #FFFFFF =(256 Red, 256 Green, 256 Blue) = BLACK. Likewise, #FF0000 = red, #00FF00 = green, and # 0000FF = blue.
Those of us who are not computer programmers would have a difficult time with the hexadecimal system. Likewise, I imagine it must be difficult for a language learner trying to crossover from one digit-base system to another. I am sure this has happened in history where two or more cultures have collided. Would merchants have argued in an open marketplace over basic trade units? Would colonialist pedagogues have been puzzled by their native subjects’ seeming lack of comprehension in basic math? They may have been unaware that what appears to be a logical brick wall is in fact a linguistic barrier.
I hope this post has done more than make you realize that certain languages use different digit-base systems than our familiar base-10. Depending on what digit-base is used in your language’s counting system, individual numbers can take on a different meaning or level of significance. Think of how many times you refer to the number ten. “I’ll be there in ten minutes,” or saying to an obnoxious child “I will count to ten.” Or that demonical professor who wants a ten-page essay on quantum physics. Ten is just a handy, familiar number in our minds, and this is only because we speak a language whose number system is ultimately based on the number of fingers we have. If we were Huli speakers, 225 would be more significant than 100, and your professor would want a 15-page essay instead of ten pages. And if we spoke a base-8 language, we might celebrate our 64th birthday as though it were our 100th.
-------------------------------------------------------------------------------------
A book I came across in my research for this post:
Numbers, Language, and the Human Mind
By Heike Wiese
I found this on books.google.com, so if you are interested you may also type in the name/author of this book at that search engine.
Friday, February 11, 2011
Where do zombies come from?
Did you know that the English word zombie has African roots? The word-concept nzumbi (ghost, spirit) was first brought to the Caribbean by slaves who spoke Kimbudu (spoken in Angola). In the Carribean it developped into the creole word zonbi; the word also evolved into a superstition of a corpse that could be manipulated by supernatural power and made to obey commands.
Incidentally, a "zombie" is also a voodoo snake deity of West African origin in Haiti, parts of the southern United States, and Brazil. I do not know if this is related to the Kimbudu-origin "nzumbi" (with lack of evidence, I tend to think not), but it is an interesting coincidence nontheless.
(http://kawann.k1.online.fr/atilye-de.htm)
nzumbi (Kimbudu) > zonbi (Carib. Creole) > zombie (English)
Incidentally, a "zombie" is also a voodoo snake deity of West African origin in Haiti, parts of the southern United States, and Brazil. I do not know if this is related to the Kimbudu-origin "nzumbi" (with lack of evidence, I tend to think not), but it is an interesting coincidence nontheless.
(http://kawann.k1.online.fr/atilye-de.htm)
Tuesday, February 8, 2011
Aphasia—Loss of Language
Aphasia is the loss of language due to damage to part or parts of the brain that are responsible for language. Damage may be brought about by head injuries, strokes, tumors, infection, or dementia.
Damage to the left or right temporal lobe (though normally in the left) results in Wernicke's Aphasia (fluent aphasia). A person with Wernicke's Aphasia will speak in long sentences that are hard for others to understand (it is also hard for such a person to understand others). They may add unnecessary or even invented words to their speech. Because the left temporal lobe is not close to any motor movement areas of the brain, Wernicke's Aphasia is not usually accompanied by weakness or paralysis of the body.
Broca's Aphasia, a type of non-fluent aphasia, occurs with damage to the frontal lobe. A person with Broca's Aphasia speaks in short, concise sentences that eliminate small words like "is" or "the." Though strained to speak, an affected person has no comprehension problem when listening to others. Broca's Aphasia is frequently accompanied by right-side weakness or paralysis, since the frontal lobe also controls motor movement.
Global Aphasia (non-fluent) is a result of damage in extensive areas of the brain's language areas, resulting in limited speech and comprehension abilities and extreme difficulties with communication.
Below are some examples of sentences that may be spoken by persons with aphasia. Remember, while Wernicke's is characterised by long, drawn-out speech with superfluous or made-up words, Broca's speech is identified by its brevity.
Wernicke's:
Broca's:
[Source for all above information: National Institute on Deafness and Other Communication Disorders' website, at this url: http://www.nidcd.nih.gov/health/voice/aphasia.asp]
As you can see, not every aspect of language is controled by one single area of the brain, in fact different aspects of language are controlled by parts of the brain that are separated from one another. I believe this to be an advantageous development, since in the event of a head injury causing a form of aphasia the chance of losing all language capabilities whatsoever is lessened. That is my best guess, not actually being a neurologist myself.
After reading about this I would also be interested to know 1. How do the mechanics of the brain work in regards to language and communication, and 2. How and to what effect do the language-areas of the brain correspond with motor skills? If you are reading this and you know anything about this, please feel free to share your knowledge.
Damage to the left or right temporal lobe (though normally in the left) results in Wernicke's Aphasia (fluent aphasia). A person with Wernicke's Aphasia will speak in long sentences that are hard for others to understand (it is also hard for such a person to understand others). They may add unnecessary or even invented words to their speech. Because the left temporal lobe is not close to any motor movement areas of the brain, Wernicke's Aphasia is not usually accompanied by weakness or paralysis of the body.
Broca's Aphasia, a type of non-fluent aphasia, occurs with damage to the frontal lobe. A person with Broca's Aphasia speaks in short, concise sentences that eliminate small words like "is" or "the." Though strained to speak, an affected person has no comprehension problem when listening to others. Broca's Aphasia is frequently accompanied by right-side weakness or paralysis, since the frontal lobe also controls motor movement.
Global Aphasia (non-fluent) is a result of damage in extensive areas of the brain's language areas, resulting in limited speech and comprehension abilities and extreme difficulties with communication.
Below are some examples of sentences that may be spoken by persons with aphasia. Remember, while Wernicke's is characterised by long, drawn-out speech with superfluous or made-up words, Broca's speech is identified by its brevity.
Wernicke's:
"You know that smoodle pinkered and that I want to get him round and take care of him like you want before.”
Broca's:
"Walk dog.” (meaning "I will take the dog for a walk.")
"Book book two table." (meaning "There are two books on the table.")
[Source for all above information: National Institute on Deafness and Other Communication Disorders' website, at this url: http://www.nidcd.nih.gov/health/voice/aphasia.asp]
As you can see, not every aspect of language is controled by one single area of the brain, in fact different aspects of language are controlled by parts of the brain that are separated from one another. I believe this to be an advantageous development, since in the event of a head injury causing a form of aphasia the chance of losing all language capabilities whatsoever is lessened. That is my best guess, not actually being a neurologist myself.
After reading about this I would also be interested to know 1. How do the mechanics of the brain work in regards to language and communication, and 2. How and to what effect do the language-areas of the brain correspond with motor skills? If you are reading this and you know anything about this, please feel free to share your knowledge.
Saturday, February 5, 2011
Language and Dialect Quote
"One should not think that a dialect is a "badly spoken" language: it is indeed a full-fledged language, with a specific grammar and lexicon. If however it is said today that Italian, Spanish or French are languages, it is not because they are richer, handsomer or better structured than Leonese, Napolitan or Picard, but because they have acquired more prestige by becoming literary and official languages for constituted States. The idioms that were the starting points of these three languages, respectively the Tuscan dialect of Florence, the Castillan dialect and the dialect of the Ile-de-France, were themselves, originally, but dialects spoken on a reduced geographical area."
- Henriette Walter, in L'aventure des langues en Occident, p132.
Friday, February 4, 2011
Colorless Green Ideas: The Experiment
"Colorless green ideas sleep furiously."- Noam Chomsky
This revolutionary sentence was composed by Noam Chomsky in 1957 to demonstrate that, contrary to popular opinion of the time, grammar is NOT the fundamental underlying structure of language. The sentence, though in agreement with the grammatical structure of Standard English, is nonsensical. In other words, meaning is not necessarily dependent on sentence structure.
I will break down Chomsky's sentence structure word-by-word: Adjective. Adjective. Subject. Verb. Adverb.
Now I will write a new sentence that makes more concrete sense but which follows the exact same grammatical structure:
"Colorful little fish swim quickly."
What I will do next is to mix up the word order of my sensical, structurally sound (by mainstream English standards) sentence and see if meaning may still be derived from it:
"Quickly swim fish little colorful." (Adv. V. Sub. Adj. Adj.)
"Fish colorful little swim quickly." (Sub. Adj. Adj. V. Adv.)
"Little fish colorful quickly swim." (Adj. Sub. Adj. Adv. V.)
"Swim little colorful fish quickly." (V. Adj. Adj. Sub. Adv.)
"Colorful swim quickly little fish." (Adj. V. Adv. Adj. Sub.)
What these sentences do is to make a mishmash of ideas (colorless green ones, of course) that form a picture in the mind of, well, colorful little fish swimming quickly. DEFINITE MEANING MAY STILL BE DERIVED FROM A NON-STRUCTURALLY SOUND SENTENCE, HOWEVER NOT FROM A STRUCTURALLY SOUND SENTENCE THAT HAS NO DEFINITE MEANING IN ITSELF.
If I were to alter the sentence "Colorless green ideas sleep furiously" in the same way, it would also make about as much sense as in its original form. :)
Thursday, February 3, 2011
Intro to Assyriology
For this post I will draw a few basic points from this interview with Pennsylvania State University's Assyriologist Gonzalo Rubio: http://www.livescience.com/history/dead-languages-sumerian-akkadian-assyriologist-q-a-101213.html
Sumerian and Akkadian were the languages of Ancient Mesopotamia, which is approximately the region of present-day Iraq. They were spoken during the Bronze Age in the "Cradle of Civilization." Ancient Mesopotamians had the first complex urban civilization in the world that gave rise to writing and advances in art, science, mathematics, and politics.
Sumerian was first spoken around 1300 BC (5000 years ago). Sumerian and Akkadian are both dead languages. They employed a writing system called cuneiform.
Sumerian is very similar in structure and grammar to other, more modern Semitic languages like Arabic and Hebrew. Akkadian, on the other hand, has a completely different structure; Rubio says that Akkadian sentence structure is comparable to the sentence structure of Japanese, Turkish, Finnish, Hungarian, and many Native American languages. This does not mean that Sumerian is related to any of those languages, it is only a comparison based on one single, very specified aspect of language.
Rubio and other Assyriologists analyze documents such as myths, legal texts, economic documents, poems, sales receipts, scientific and scholarly texts, and letters.
Sumerian and Akkadian were the languages of Ancient Mesopotamia, which is approximately the region of present-day Iraq. They were spoken during the Bronze Age in the "Cradle of Civilization." Ancient Mesopotamians had the first complex urban civilization in the world that gave rise to writing and advances in art, science, mathematics, and politics.
Sumerian was first spoken around 1300 BC (5000 years ago). Sumerian and Akkadian are both dead languages. They employed a writing system called cuneiform.
Sumerian is very similar in structure and grammar to other, more modern Semitic languages like Arabic and Hebrew. Akkadian, on the other hand, has a completely different structure; Rubio says that Akkadian sentence structure is comparable to the sentence structure of Japanese, Turkish, Finnish, Hungarian, and many Native American languages. This does not mean that Sumerian is related to any of those languages, it is only a comparison based on one single, very specified aspect of language.
Rubio and other Assyriologists analyze documents such as myths, legal texts, economic documents, poems, sales receipts, scientific and scholarly texts, and letters.
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