In response to Travis's Nov. 12 post in response to my comment in response to his Nov. 7 post.
Travis:
Upon rereading your previous post (Nov. 7) I realized that what you were talking about is not necessarily a common first language on a global level, but rather a global second language. This feels much more acceptable to me.
My initial concern was regarding a common first language. In any given language, when a person is trying to translate to a different language, there is inevitably a word or phrase which doesn't quite translate. In switching to an international first language, each of these nuances would be lost. Each frame of mind, each instance of a thought process these words represent would be eliminated by the steamroller of a common first language. Similarly, systems of logic based on syntax outside of those of the new global language would not translate into the new first language. These lost paths to ideas could be the key to the next scientific breakthrough or a better theory connecting the different kinds of human experience.
In the new context of a global second language, I find the idea much less intimidating. The main risk, in my mind, associated with such an endeavor is that the common second language may become the only language, or so dominant as to essentially be the only language, and all of the above concerns about a common first language recur. (There are also the concerns for the literary world as seen in the link below.)
As for the choice of English, I still feel, in the long run, it is a fairly arbitrary choice. Any such global language will inevitably change. Change seems to be the only constant in history. I people say this is the first time in history these conditions exist, but that's what the previous empire said. Rome can never predict it's own fall. English might be the best choice now, but I doubt it will eternally be so.
You mention in the Nov. 12 post, possibly changing English. Noah Webster suggested something similar to distinguish American English from it's colonial parent. His changes can be seen in colour and color, and other differentiations in spelling, but this was only the start of his ideas for spelling reformation. He wanted to go so far as to do away with silent e and other superfluous letters in words, so that eventually English would be purely alphabetic in its phonetics., each letter making one unique sound. A would-be useful trait for a global second language.
For an interesting perspective on what could come of English as an international second language, check out the free online book "English Next" found here: http://goingglobal.corante.com/archives/2006/02/24/english_as_a_second_language_english_as_a_global_language.php
For a look at what may be lost on a literary level: http://www.cepr.org/press/DP2055PR.htm
Tuesday, November 27, 2007
Monday, November 26, 2007
Subtitles
In response to E Pluribus Unum, Comprende? (http://money.cnn.com/news/newsfeeds/articles/newstex/IBD-0001-21160351.htm)
Americans can speak Spanish, and still be American. Or should we edit the words on the Statue of Liberty to read, "Give me your tired, your poor, Your english-speaking masses yearning to breathe free..."
Multilingualism is not an affront to the identity of the United States. The author, in alluding to the previous waves of immigration "wanting to be American", overlooks the time it takes for new citizens to learn a language. Often it was only the second generation who learned English out of necessity and a desire to pursue opportunities for advancement. To get certain jobs, knowledge of English was necessary. This is still the case today.
So why is a two women speaking Spanish while sorting clothing cause enough to be fired. It seems to me, that this is an overreaction to the point of paranoia. For an employer to require English as a prerequisite makes sense where customer interaction is involved. Some fields, such as health care professions, have even started looking for people who can speak spanish. Communicating with the customer is key for business, so it makes sense that job options would be limited by language skills. What is slightly more confusing, is why do they matter for positions in which there is no customer interaction? This is not as simple as limiting people's freedom of dress with a dress code as the columnist implies. There are outside laws and societal as to appropriate dress for work and public, and also limits to what people can control through a dress code. (e.g. religious garb.) There is no such correlation for mandatory language. In a situation where miscommunication is not an issue, and it does not disrupt or affect the work of other employees, I feel that discriminating for work based on language is unjust.
Similarly, I don't believe clinging to laws or ideas of the past and what being American has meant is the best justification. In the 19th century, that meant no Irish. Jim Crow laws and constitutional justification of slavery, that a slave was only three-fifths of an American citizen, show that laws must change with perspective and time.
Assimilation, however, seems like an inevitability. The new culture(s) affect America and over time, through pushing and pulling, the country again has "assimilated" to a new culture. As long as the majority of media is in English and education remains predominantly in English, then learning English is a near inevitability for the next generations. I mean it's not like there are spanish only television stations, separate music awards for latin music, or spanish dubbing on national television networks.... oh, wait.
Is it possible "Transmido en SAP" (forgive my spelling, Spanish, and memory), the words at the bottom of the screen before major television programs indicating the availability of Spanish dubbing, could lead to a permanently bilingual country? Possibly. It enables spanish speaking immigrant communities to truly isolate themselves in a language the way their 20th century European counterparts could not. If a person wanted to enjoy the scope of American media entertainment, English was a prerequisite in a way it is not any more. A solution to this problem (if indeed someone feels it is a 'problem' that needs a 'solution') comes in a very simple form. Subtitles. On TV, movies, and everywhere. This subtle script exposes Spanish-speakers that would otherwise be isolated to English, while simultaneously allowing them access to a wider range of media. And the next generation, would be exposed to English before their reading picked up, and be put in situations where they want to learn the language and what is being said. (It could even be sold as an attempt to up Spanish literacy.)
This is the secret behind the Israeli population's understanding of Hebrew.
This is a real exchange I heard over dinner at my cousin's house:
--I didn't know you speak English. Are your parents American or do you just watch a lot of TV?"
--I watch a lot of TV.
Over time watching TV, hearing the words, and reading the screen, people pick up the language.
But if this doesn't happen, and for the first time, the third generation doesn't embrace English over their grandparent's tongue for daily use. I'd encourage the columnist not to think of this specifically as the balkans, but as any European state where dialects and languages vary greatly within a single countries borders. Change is not the end of the world; just the end of the world that was.
Americans can speak Spanish, and still be American. Or should we edit the words on the Statue of Liberty to read, "Give me your tired, your poor, Your english-speaking masses yearning to breathe free..."
Multilingualism is not an affront to the identity of the United States. The author, in alluding to the previous waves of immigration "wanting to be American", overlooks the time it takes for new citizens to learn a language. Often it was only the second generation who learned English out of necessity and a desire to pursue opportunities for advancement. To get certain jobs, knowledge of English was necessary. This is still the case today.
So why is a two women speaking Spanish while sorting clothing cause enough to be fired. It seems to me, that this is an overreaction to the point of paranoia. For an employer to require English as a prerequisite makes sense where customer interaction is involved. Some fields, such as health care professions, have even started looking for people who can speak spanish. Communicating with the customer is key for business, so it makes sense that job options would be limited by language skills. What is slightly more confusing, is why do they matter for positions in which there is no customer interaction? This is not as simple as limiting people's freedom of dress with a dress code as the columnist implies. There are outside laws and societal as to appropriate dress for work and public, and also limits to what people can control through a dress code. (e.g. religious garb.) There is no such correlation for mandatory language. In a situation where miscommunication is not an issue, and it does not disrupt or affect the work of other employees, I feel that discriminating for work based on language is unjust.
Similarly, I don't believe clinging to laws or ideas of the past and what being American has meant is the best justification. In the 19th century, that meant no Irish. Jim Crow laws and constitutional justification of slavery, that a slave was only three-fifths of an American citizen, show that laws must change with perspective and time.
Assimilation, however, seems like an inevitability. The new culture(s) affect America and over time, through pushing and pulling, the country again has "assimilated" to a new culture. As long as the majority of media is in English and education remains predominantly in English, then learning English is a near inevitability for the next generations. I mean it's not like there are spanish only television stations, separate music awards for latin music, or spanish dubbing on national television networks.... oh, wait.
Is it possible "Transmido en SAP" (forgive my spelling, Spanish, and memory), the words at the bottom of the screen before major television programs indicating the availability of Spanish dubbing, could lead to a permanently bilingual country? Possibly. It enables spanish speaking immigrant communities to truly isolate themselves in a language the way their 20th century European counterparts could not. If a person wanted to enjoy the scope of American media entertainment, English was a prerequisite in a way it is not any more. A solution to this problem (if indeed someone feels it is a 'problem' that needs a 'solution') comes in a very simple form. Subtitles. On TV, movies, and everywhere. This subtle script exposes Spanish-speakers that would otherwise be isolated to English, while simultaneously allowing them access to a wider range of media. And the next generation, would be exposed to English before their reading picked up, and be put in situations where they want to learn the language and what is being said. (It could even be sold as an attempt to up Spanish literacy.)
This is the secret behind the Israeli population's understanding of Hebrew.
This is a real exchange I heard over dinner at my cousin's house:
--I didn't know you speak English. Are your parents American or do you just watch a lot of TV?"
--I watch a lot of TV.
Over time watching TV, hearing the words, and reading the screen, people pick up the language.
But if this doesn't happen, and for the first time, the third generation doesn't embrace English over their grandparent's tongue for daily use. I'd encourage the columnist not to think of this specifically as the balkans, but as any European state where dialects and languages vary greatly within a single countries borders. Change is not the end of the world; just the end of the world that was.
Thursday, November 15, 2007
In Lieu of Other Things
I think this cartoon, from xkcd.com (a really funny site if you want to check it out), adds a certain statement about how quickly linguistic imperialism, change or elimination of languages as the result of conquering, is overlooked in debates on language. In fact even the Queen's English is a decendent of a combination of early French and German languages superimposed on one another through conquest.
Monday, November 12, 2007
TV Eats Your Baby's Brain
In response to: Baby DVDs may slow early language acquisition (http://www.dailytimes.com.pk/default.asp?date=11/13/2007%209:00:12%20AM) and 'Baby genius' DVDs delay language skills (http://www.theage.com.au/news/tv--radio/baby-genius-dvds-delay-language-skills/2007/10/17/1192300839626.html)
As it turns out, all those hours of staring at a television screen of swirling shapes and classical music, although distracting for baby and giving a break to mommy, are not actually increasing the child's inteligence. At least not on a language level. Infact, a study from the University of Washington says just the opposite, that babies that for each extra hour per day of brain-boosting programming under names like "Baby Einstein" and "Brainy Baby" reduced the word recognition test scores by 17 points in infants between 8 and 16 months. This effect ballances out by age 24 months, when 'Baby Einstein' catches up with 'Sponge Bob', 'Sesame Street', and 'Oprah', none of which showed negative impact on language development.
The only kids who demonstrated a noted positive difference on the tests were those who were read to by parents once a day.
This says a lot about language development in toddlers. That, surprisingly enough, children need to be exposed to language to learn it. A child obviously can't pick up a language without hearing it. But this doesn't explain how those children showing a gap in language abilities at 16 months are caught up by 24 months. (Any ideas?)
Due to the social nature language, those children who are read to out perform thos who have learned from TV. Those children in contact with parents as they read them a book receive other cues to use to help understand the meaning of new words, and possible side conversation of the book providing another context for the text, not to mention probably being in a happier emotional state better for learning.
The idea of baby genius tapes is the result of a game of scientifically-innacurate telephone coming from "the Mozart Effect". In 1993 "Nature" published a study conducted at UC Irvine showing ADULTS did better on spatial reasoning tests after hearing Mozart. (http://encarta.msn.com/encnet/departments/elementary/default.aspx?article=classicalmusic) Through press buzz on the story, and public connecting 2 and 2, from this it is obvious that Mozart makes babies smarter.
Since Mozart must make babies smarter, it only makes sense that a DVD around the composer's work would be twice as effective by adding a visual component. Ta-dah! Baby DVD's are a $100 million industry.
In short, read to your kids, don't let a TV do it for you.
As it turns out, all those hours of staring at a television screen of swirling shapes and classical music, although distracting for baby and giving a break to mommy, are not actually increasing the child's inteligence. At least not on a language level. Infact, a study from the University of Washington says just the opposite, that babies that for each extra hour per day of brain-boosting programming under names like "Baby Einstein" and "Brainy Baby" reduced the word recognition test scores by 17 points in infants between 8 and 16 months. This effect ballances out by age 24 months, when 'Baby Einstein' catches up with 'Sponge Bob', 'Sesame Street', and 'Oprah', none of which showed negative impact on language development.
The only kids who demonstrated a noted positive difference on the tests were those who were read to by parents once a day.
This says a lot about language development in toddlers. That, surprisingly enough, children need to be exposed to language to learn it. A child obviously can't pick up a language without hearing it. But this doesn't explain how those children showing a gap in language abilities at 16 months are caught up by 24 months. (Any ideas?)
Due to the social nature language, those children who are read to out perform thos who have learned from TV. Those children in contact with parents as they read them a book receive other cues to use to help understand the meaning of new words, and possible side conversation of the book providing another context for the text, not to mention probably being in a happier emotional state better for learning.
The idea of baby genius tapes is the result of a game of scientifically-innacurate telephone coming from "the Mozart Effect". In 1993 "Nature" published a study conducted at UC Irvine showing ADULTS did better on spatial reasoning tests after hearing Mozart. (http://encarta.msn.com/encnet/departments/elementary/default.aspx?article=classicalmusic) Through press buzz on the story, and public connecting 2 and 2, from this it is obvious that Mozart makes babies smarter.
Since Mozart must make babies smarter, it only makes sense that a DVD around the composer's work would be twice as effective by adding a visual component. Ta-dah! Baby DVD's are a $100 million industry.
In short, read to your kids, don't let a TV do it for you.
Thursday, November 8, 2007
Language as Society: Change and Transition
In response to: The language of world communication (http://www.nationnews.com/editorial/306156905562860.php)
The term Bajan refers to both the people and the street language of Barbados. The word originated from a heavily accented pronunciation of "Barbadian", "Barbajan", which later became shortened. The term grew to become a label for at first the uneducated, but eventually all of the people of Barbados.
Although there official language of Barbados is English, Bajan, a dialect of English, prevails among Barbadians in daily life.
Felicia C, a poster on Yahoo Answers explains it thus:
"As a Bajan (Barbadian), I have to say that we will try to speak proper English
(ie what we call "the Queen's English") when speaking to tourists or formal
situations but we have little use for it otherwise, and most conversations
between Bajans take place in the dialect."
(http://answers.yahoo.com/question/index?qid=1006060114358)
The author of the article objects to this proliferation improper English. Part of the cause, in their mind, is a negative social stigma about those who speak properly. The article comes in support of the statements of Chief Education Officer Wendy Griffith-Watson, who is trying to undo this stereotype, and encourage the everyday use of formal English.
The author of the article goes on to connect this everyday use of an informal tongue with general decline of society and all the shady morals demonstrating "increasing disrespect for law and order". If the people speak slang in the street, the whole world will fall apart?!
In particular they cite the ZR (Route Taxi) Culture and kids opting for use of privately run Public Service Vehicles over government sponsored Buses. These alternate modes of transportation are bastions of a Bajan counter culture. Since the government has kept the prices on Transport Board Buses fixed for the past 15 years, PSV operators must keep their prices low to compete. The crews running such conveyances, necessary for commuters in Barbados, are kept in a lower earning bracket, meaning only the less educated take on these jobs. The term ZR culture stems from the perceived looseness and illicit actions of some crews or patrons of PSV's. (Check out "http://barbadosfreepress.wordpress.com/2007/07/17/public-service-vehicles-in-barbados-we-love-them-but/")
But is there necessarily a relationship between what may be seen as the crumbling of society and slang language? This author, like many others we have encountered in our news stories for BBC language advisers and government controlled standards to preserve language integrity, is of the conservative mindset that languages need to be preserved in its current, 'proper' form. This is dramatically apparent in their opening sentence, quoting Shakespeare. It is common in this mindset to relate changes in language to negative changes in society.
Here is an interesting fact: No one talks like Shakespeare anymore! Languages change. This is not to say that languages should have no standards whatsoever, but in the case of Bajan, which has taken root throughout Barbados, maybe it is the solution to, rather than the cause of, societal problems.
As with many dialects with origins among slave populations, there is a lingering external association between foolishness or stupidity and Bajan. This can be seen in the case of the Jamaican dialects in any number of ads for the latest spiced rum. By insisting on the use of proper English these stereotypes are reinforced.
Why not, rather, embrace and institutionalize Bajan? If its deficiencies preventing it from being a "formal language" are grammar and structure, create them. There is a risk that this would not be acceptable to speakers of Bajan, which is known for its constant fluidity and adaptation, but it could create a positive cultural self-identity, that the Bajan is truly valid in culture and language.
The term Bajan refers to both the people and the street language of Barbados. The word originated from a heavily accented pronunciation of "Barbadian", "Barbajan", which later became shortened. The term grew to become a label for at first the uneducated, but eventually all of the people of Barbados.
Although there official language of Barbados is English, Bajan, a dialect of English, prevails among Barbadians in daily life.
Felicia C, a poster on Yahoo Answers explains it thus:
"As a Bajan (Barbadian), I have to say that we will try to speak proper English
(ie what we call "the Queen's English") when speaking to tourists or formal
situations but we have little use for it otherwise, and most conversations
between Bajans take place in the dialect."
(http://answers.yahoo.com/question/index?qid=1006060114358)
The author of the article objects to this proliferation improper English. Part of the cause, in their mind, is a negative social stigma about those who speak properly. The article comes in support of the statements of Chief Education Officer Wendy Griffith-Watson, who is trying to undo this stereotype, and encourage the everyday use of formal English.
The author of the article goes on to connect this everyday use of an informal tongue with general decline of society and all the shady morals demonstrating "increasing disrespect for law and order". If the people speak slang in the street, the whole world will fall apart?!
In particular they cite the ZR (Route Taxi) Culture and kids opting for use of privately run Public Service Vehicles over government sponsored Buses. These alternate modes of transportation are bastions of a Bajan counter culture. Since the government has kept the prices on Transport Board Buses fixed for the past 15 years, PSV operators must keep their prices low to compete. The crews running such conveyances, necessary for commuters in Barbados, are kept in a lower earning bracket, meaning only the less educated take on these jobs. The term ZR culture stems from the perceived looseness and illicit actions of some crews or patrons of PSV's. (Check out "http://barbadosfreepress.wordpress.com/2007/07/17/public-service-vehicles-in-barbados-we-love-them-but/")
But is there necessarily a relationship between what may be seen as the crumbling of society and slang language? This author, like many others we have encountered in our news stories for BBC language advisers and government controlled standards to preserve language integrity, is of the conservative mindset that languages need to be preserved in its current, 'proper' form. This is dramatically apparent in their opening sentence, quoting Shakespeare. It is common in this mindset to relate changes in language to negative changes in society.
Here is an interesting fact: No one talks like Shakespeare anymore! Languages change. This is not to say that languages should have no standards whatsoever, but in the case of Bajan, which has taken root throughout Barbados, maybe it is the solution to, rather than the cause of, societal problems.
As with many dialects with origins among slave populations, there is a lingering external association between foolishness or stupidity and Bajan. This can be seen in the case of the Jamaican dialects in any number of ads for the latest spiced rum. By insisting on the use of proper English these stereotypes are reinforced.
Why not, rather, embrace and institutionalize Bajan? If its deficiencies preventing it from being a "formal language" are grammar and structure, create them. There is a risk that this would not be acceptable to speakers of Bajan, which is known for its constant fluidity and adaptation, but it could create a positive cultural self-identity, that the Bajan is truly valid in culture and language.
Monday, November 5, 2007
The Death of a Signing Chimpanzee: An Excercise in Anthropomorphising
In response to: An African chimpanzee and its language of signs (http://www.hindu.com/2007/11/02/stories/2007110257872200.htm)
Washoe, a chimpanzee who learned over 250 words in American Sign Language, died last Tuesday. Some scientists considered her to be the first nonhuman to acquire human language. But is 250 signs enough to count as language? Even tame estimates of the number of words used by the average English speaker places them in the thousands.
Not to mention, Washoe's use of language appeared to be limitted to single words used to identify something she wanted or to gain a reward. The examples cited on the web page clearly lacked Chomsky-an recursion in her signing. There was no indication she had the ability to string her signs into longer sentences for what could be called language.
Clear examples of her linguistic shortcomings can be found in any of the History and Timeline section of FriendsofWashoe.org.
Looking specifically at the entry Washoe Gives Birth to Sequoyah (http://www.friendsofwashoe.org/timeline_sequoyah_birth_and_death.shtml), the many instances where Washoe's 'language' fail are glaring. The narrator is still using treats when he goes for a walk with her in the woods. More notably, when he has to communicate with her about her baby, whether it be getting permission to take it away, or getting her to return it, he is limmitted to knocking Washoe out, or using tootsie pops to reach his goal. It appears much more like he mastered interaction with Chimpanzee's on their terms, rather than the team successfully managing to establish communication on the level of human language.
It seems each point along this timeline suffers from anthropomorphising, as the observers project human emotions and the language that comes with them onto the subjects they were studying. It comes as a natural consequence to assuming she has language. How could something that communicates like a human, not feel like a human?
This mistake is a greater misstep than past occurences of invading cultures evaluating local customs through the lens of what they consider civilized. There is no common basis to assume we understand an animal's thought process, and to project human interaction onto them is a mistake. That is not to say that animals do not have 'emotion' (I use the term loosely here due to it's largely human connotation.) but to assume they model Human feelings, when our reactions vary greatly culture to culture, there is clearly no basis for species to species correlation.
Washoe, a chimpanzee who learned over 250 words in American Sign Language, died last Tuesday. Some scientists considered her to be the first nonhuman to acquire human language. But is 250 signs enough to count as language? Even tame estimates of the number of words used by the average English speaker places them in the thousands.
Not to mention, Washoe's use of language appeared to be limitted to single words used to identify something she wanted or to gain a reward. The examples cited on the web page clearly lacked Chomsky-an recursion in her signing. There was no indication she had the ability to string her signs into longer sentences for what could be called language.
Clear examples of her linguistic shortcomings can be found in any of the History and Timeline section of FriendsofWashoe.org.
Looking specifically at the entry Washoe Gives Birth to Sequoyah (http://www.friendsofwashoe.org/timeline_sequoyah_birth_and_death.shtml), the many instances where Washoe's 'language' fail are glaring. The narrator is still using treats when he goes for a walk with her in the woods. More notably, when he has to communicate with her about her baby, whether it be getting permission to take it away, or getting her to return it, he is limmitted to knocking Washoe out, or using tootsie pops to reach his goal. It appears much more like he mastered interaction with Chimpanzee's on their terms, rather than the team successfully managing to establish communication on the level of human language.
It seems each point along this timeline suffers from anthropomorphising, as the observers project human emotions and the language that comes with them onto the subjects they were studying. It comes as a natural consequence to assuming she has language. How could something that communicates like a human, not feel like a human?
This mistake is a greater misstep than past occurences of invading cultures evaluating local customs through the lens of what they consider civilized. There is no common basis to assume we understand an animal's thought process, and to project human interaction onto them is a mistake. That is not to say that animals do not have 'emotion' (I use the term loosely here due to it's largely human connotation.) but to assume they model Human feelings, when our reactions vary greatly culture to culture, there is clearly no basis for species to species correlation.
Thursday, November 1, 2007
Requiem for a Three
In response to: Language makes maths a rough ride for students (http://www.eastandard.net/mag/mag.php?mnu=details&id=1143976743&catid=316)
Every day at 2:15, I go to get my brain smashed by a sledgehammer. Who knew two numbers and a letter could have this effect? 51H has five one hour classes per week. There's one other notable category of classes that share this kind of scheduling at Stanford: languages.
Unlike lecture based courses, where it is more beneficial to have a day for newer material to sink in, languages are better learned through constant exposure, as often as possible, so less time is spent going over what may have been forgaotten between installments.
So why 51H? Why not the other math courses? The nature of 51H is such that it is like learning a new language, the language of proof. The standard 50 series focuses on techniques for manipulation of numbers and terms, whereas 51H is designed to look at the language from where these manipulations are derived. This is a language with it's own set of gramatical rules, based on a strict logic not to be broken. Interestingly enough, the rules for manipulations of numbers are largelt expressed without numbers, inorder to express generality. (I miss 4. It was such a pleasent number) Similarly, if you were studying the syntax of a language, the terms like noun and verb would be far more useful than the specific instances table and kick.
But does this kind of language actually fall under the language acquisition mechanism, as Chomsky views it? Or under the Boroditsky-an model, does the learning device have to create a new program for learning Proof, or can it fall largely under the previous systems used for language?
John Hawks posted in his blog on just this subject (http://johnhawks.net/weblog/reviews/brain/function/math_localization_language_2006.w) citing a recent study showing subjects suffering with aphasia, similarly had trouble with calculation. His hypothesis is that math is expressed through language, and this would account for the proximity of the centers of the brain.
I personally would like to think, that math can exist as a language unto itself, but it would follow without roots in a language of productive human interpretation, where would such a language spring from? Or if it is inherent in the universe, from where would it be percieved?
Every day at 2:15, I go to get my brain smashed by a sledgehammer. Who knew two numbers and a letter could have this effect? 51H has five one hour classes per week. There's one other notable category of classes that share this kind of scheduling at Stanford: languages.
Unlike lecture based courses, where it is more beneficial to have a day for newer material to sink in, languages are better learned through constant exposure, as often as possible, so less time is spent going over what may have been forgaotten between installments.
So why 51H? Why not the other math courses? The nature of 51H is such that it is like learning a new language, the language of proof. The standard 50 series focuses on techniques for manipulation of numbers and terms, whereas 51H is designed to look at the language from where these manipulations are derived. This is a language with it's own set of gramatical rules, based on a strict logic not to be broken. Interestingly enough, the rules for manipulations of numbers are largelt expressed without numbers, inorder to express generality. (I miss 4. It was such a pleasent number) Similarly, if you were studying the syntax of a language, the terms like noun and verb would be far more useful than the specific instances table and kick.
But does this kind of language actually fall under the language acquisition mechanism, as Chomsky views it? Or under the Boroditsky-an model, does the learning device have to create a new program for learning Proof, or can it fall largely under the previous systems used for language?
John Hawks posted in his blog on just this subject (http://johnhawks.net/weblog/reviews/brain/function/math_localization_language_2006.w) citing a recent study showing subjects suffering with aphasia, similarly had trouble with calculation. His hypothesis is that math is expressed through language, and this would account for the proximity of the centers of the brain.
I personally would like to think, that math can exist as a language unto itself, but it would follow without roots in a language of productive human interpretation, where would such a language spring from? Or if it is inherent in the universe, from where would it be percieved?
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