This is an odd but interesting story that may interest my Gentle Readers. I came across it through Clive Thompson’s Collision Detection, which pointed to a BBC article, but I found this nature.com article clearer. And, of course, for thems as understand such things, the abstract is available on-line from the National Academy of Sciences, and the entire article “Agrammatic but numerate” is available for a small fee (or through your university, research institution, or bowling league).
Anyway, it seems that Rosemary Varley and some colleagues at the University of Sheffield experimented with three aphasic men (with large left-hemisphere perisylvian lesions)(I think I went to school with Perry Sylvian) who despite severe grammatical impairment were able to parse mathematical ‘sentences’. That is, the men couldn’t easily differentiate subject and object in sentences such as ‘the girl chased the boy’ or ‘the hunter ate the lion’ but were able to decode such expressions as ‘30/90’ or ‘52-11’ correctly and consistently. The lesions that prevent reading not only don’t prevent calculating, but don’t prevent reading in math.
Well, and this surprises me. When I read an equation (say, x=(90 - [(3 + 17) * 3]), I think I read it in words. The translation is not word-for-word, but I would say something like “x is ninety less the amount of three plus seventeen, times three.” Or, more likely, I’d look at it and say “x is ninety minus three times three-plus-seventeen.” Either of those would use the part of the brain that in these fellows doesn’t function. Now, when I do the actual arithmetic, I don’t do it in words, I think, although it’s hard to tell. At any rate, it seems that it is possible to do the arithmetic without doing the language. Which is just cool. Even if it’s just a workaround that develops when the normal way doesn’t work. Perhaps particularly if it’s such a workaround.
In addition to just being cool, the experiment calls into (theoretical) question the attitude that some people take that language itself is what makes us human, that is, that human-ness and language are pretty much identical. Or at least that the things we think of as human, such as ... oh, self-awareness, the ability to reason, to use complex tools, to build for others, to pray, to negotiate, to make jokes, to imagine, to invent, to remember, the whole package, all those things are possible (and perhaps inevitable) simply because of language. I’ve been skeptical about this, although of course it’s a powerfully Scriptural view of humanity. Anyway, this doesn’t destroy that attitude (the people in question developed the lesions well after learning arithmetic and algebra, so if they are able to use the acquired skills without language, it doesn’t mean they could have acquired them without language, etc, etc), but it does bring a new light on its assumptions and conclusions.
Plus, of course, it’s just cool.
Thank you,
-Vardibidian.
how i read the equation “90 – ((3 + 17) * 3)”:
“90” “-” … “(“, “(“, “)”, “3+17”, “*3”, “from 90”
if that makes any sense. i don’t read it aloud in my head. reading it aloud would be something like
“ninety minus THREE PLUS SEVENTEEN, TIMES 3”
i don’t know chomsky’s cognitive work well enough to talk about how this changes what they assumed, if it does. i assume michael does and he will hurt me badly for what i am about to do wrong.
the quote in the nature article that “according to the view of cognition developed by linguist Noam Chomsky, language processing is a fundamental skill that is used for related grammatical tasks in the brain, such as certain mathematical ones” is somewhat vague – the question of what is the difference between “language processing” and “grammar” is difficult.
in particular there is a missing element, which angers me. we don’t know from any of these articles whether they could put letters in alphabetical order. i’m sorry but “90” is not analogous to “angry” in spite of the grammatical structure. “90” is hierarchical and non-arbitrary, “angry” isn’t. (90 = 9*10 + 0*1, but “angry” != A*10000 + N*1000 + G*100 + R*10 + Y*1, or any possible similar order of meaning – something like A=person N=doing G=reaction R=visible Y=attacking, where ANGRZ could mean “grateful”.)
if this proves a division between arbitrary and non-arbitrary parsing, that’s cool, and to me, not surprising. living with my mom as long as i did, i got to see her dyslexia at work in many ways, and saw her handle some astoundingly complex tasks without ever really being able to remember left from right.
(v: you added a variable to your formula; note that variables were not cited in the articles as part of the testing.)
from the abstract:
Despite severe grammatical impairment and some difficulty in processing phonological and orthographic number words, all basic computational procedures were intact across patients … To our knowledge, these results demonstrate for the first time the remarkable independence of mathematical calculations from language grammar in the mature cognitive system.
remarkable independence, or remarkable interdependence. there could still be a grammar facility, but perhaps higher function depends on the flavor of grammar, and the routine that handles arbitary flavor is busted.
vardibidian:
In addition to just being cool, the experiment calls into (theoretical) question the attitude that some people take that language itself is what makes us human, that is, that human-ness and language are pretty much identical.
allison and i were just talking about, thinking about, what was it like to be homo erectus (snicker) erec … oh i mean, what was it like to be us, without a voice box, or grammar facility, or whatever it was that turned us into poets. allison couldn’t imagine it where i had actually been thinking about that a lot lately, and, if you take away the language, we really have an extraordinary amount of other brainpower. incredible pattern matching capacity, just incredible. remember that we were easily using tools before we were talking.
so before we were poets, what were we? likely, as far as i can tell: singers. drummers. this is mathematical capacity, group activity, without abstraction.
Aw, Michael doesn’t hurt people. But Chomsky will hunt you down and eat your pancreas.
I don’t know if the aphasics could alphebetize, but they could recognize individual words, in which case I think there’s a good analogy that ‘5’ is like ‘dog’, if they are holding a picture of ‘5’ when they recognize it (and I’m really speaking vaguely, here). Now, I don’t have any sense of whether my image of ‘5’ is five pennies, or five lines, or five beats, but I know I have an image of 5ness, much the same as I have an image of dogness, which is independent of color, or size, or even (I think) shape.
Oh, and I should add that I did study math for a year or two at a reasonably high level; I can’t claim that I was ever fluent in it, but I could, on a good day, hold a halting sort of conversation in it with people who were. Anyway, the way that I ‘read’ an equation is probably strongly influenced by that experience, and is probably totally idiosyncratic.
Anyway, I think you raise really interesting points. I wonder how much of language is pattern-matching, and how much of pattern-matching is language. Not to get all Wittgensteinian, but is language use a tool for pattern-matching? If you imagine human-like-people developing without language, can you imagine them having the other kinds of pattern-matching we have? This is a question for the spec-fic readers as much as philosphers; the book I’m in the middle of does quite a lot with aliens, and languages, but assumes language in the aliens, if you see what I mean.
Thanks,
-V.
ah you beat me to it, but now i can add my thing using your grammar. as i see “us” we’re talking about “people-like humans,” not human-like people.
the distinction being a very broad, old, delineated culture. a known inheritance.
there are plenty of homo sapiens cultures on the earth that do not have the big inside/outside split of urban societies. i/we is very blurry – including things that to me, to you, are “clearly” external – very “they” – which we apply to both competitors and cooperators – that’s not how everybody does it.
there also seem to be various flavors of inside/outside in urban societies, though less distinct, unless you’re looking at an electoral map.
language has allowed us to manage our growth in incredible ways, finely tuning our resource use, developing very high tech answers to common problems. food, waste, housing, administration, etc.
but, if this world is an apple, we are still for all intents and purposes stuck living in the skin, digging out the meat of the fruit to supplement our now highly sophisticated diet. our gains are in self-gratification. there is competition to create, manipulate, and apply increasingly complex patterns found only in our newly abstracted ecology. is it make work? no, i think it’s critical, unavoidable, like sleeping. we see patterns, we want patterns, we will debate them, do them together; or we will die. lonely.
the essential difference to me between language and non-language is not one of existence or sophistication, but of raw power. my inherited gut sense says that a creature who could sing about the world, who could imagine it completely, in minute detail, was bound for the top of the food chain, unless they were incredibly tasty and slow.
yeah i don’t go for the “beasts of the field” kind of divisions. a human kid to me is obviously a very intelligent beast of the field, ready (from adult perspective) and waiting (from biological perspective) to be groomed into personhood.
i think we discussed something like this a while back, about human rights. i’m in about the same position, but a little more circumspect about dividing things. the best description i can offer, which i was thinking this morning before seeing your article, is that we are walking, talking, identical civilizations of single-celled animals. inside-out coral reefs, highly specialized, so that we can move great distances from the water (which we keep inside us) without using up every last bit of food. organs as ethnic groups or trade organizations. and then it all collapses back into the pool, and individual bits become new things.
i guess what this means is “people” is a compelling story we have passed through generations, in a variety of ways. that we like stories so much probably means that telling and hearing stories is a critical part of us, like running fast is to a cheetah. as i understand it, the whole thing of modern linguistics and cognitive science is that we’re geared to learn whatever story, in whatever style, but we want to learn a story, we want to share a story.
is a desire for narrative separable from pattern-matching, i don’t know. the city of critters is most effective when it forgets to live separately and engages the world as a community, i.e., an “individual” in a “community” of like non-groups. it becomes a repeating pattern when it starts liking itself better than other patterns.
is a comparative capacity separate from pattern-matching, i guess that’s where a lot of the science has been done, including this article. is comparative capacity necessary to lead a good life, i don’t know. it can be abused. racism, sexism, etc.
oh and relating to 5-the-value and dog-the-animal, i think there are big differences, fundamental differences… call it “repetitions” versus “comparisons.” “how many” is not subjective. “dog” is quite subjective, because there are many animals that have nearly every characteristic of a dog, but are cats, or bears. nothing is like 5. bear is not dog-point-two; 5.2 is absolutely both related to and separated from 5. (allison is reading this and disagrees because maybe it’s in how we learn it. dogs are everywhere, bears are in comparison to dogs. but i win because i say that we can’t round bears down to dogs, or say that a group of mixed dogs and wolves can be called “dogs” for the sake of expedient math.)
allison also points out that “dog” also has an emotional meaning – associations – well people can have lucky numbers – but, she says, “dog is a story, where 5 is not, to connect with what david was saying.”