mathematics

Archaeologists often define technology in terms of material products. People make stuff, and that stuff is technology.

But there's another way to think about the stuff we make: in terms of the information we need to make it. Technology is know-how, it's skill. It's something we learn how to do. Manufacturing may have physical side effects, but it's the cognitive software that lies at the heart of technology.

This usage is true to the etymology of the word, "technology":

from Gk. tekhno-, combining form of tekhne "art, skill, craft, method, system," probably from PIE base *tek- "shape, make" (cf. Skt. taksan "carpenter," L. texere "to weave;" see texture).

I mention this because, if we take this perspective on technology, then some "technology" may never be instantiated in material -- it may reside purely in the mind. That is the contention that Michael Frank and colleagues made in a 2008 paper about speakers of a language that does not have cardinal numbers above two [1]. Frank and colleagues set out to find whether this curious lack of number words causes Pirahã speakers to deal with numbers in experimental contexts differently from speakers of other languages.

The results showed that Pirahã speakers could complete number matching tasks, using strategies that were also widespread among non-Pirahã speakers in other contexts.

A total lack of exact quantity language did not prevent the Pirahã from accurately performing a task which relied on the exact numerical equivalence of large sets. This evidence argues against the strong Whorfian claim that language for number creates the concept of exact quantity (and correspondingly, that without language for number, any task requiring an exact match would be impossible). Instead, the case of Pirahã suggests that languages that can express large, exact cardinalities have a more modest effect on the cognition of their speakers: They allow the speakers to remember and compare information about cardinalities accurately across space, time, and changes in modality. Visual and auditory short-term memory are highly limited in their capacity and temporal extent (Baddeley, 1987). However, the use of a discrete, symbolic encoding to represent complex and noisy perceptual stimuli allows speakers to remember or align quantity information with much higher accuracy than they can by using their sensory short-term memory. Thus, numbers may be better thought of as an invention: A cognitive technology for representing, storing, and manipulating the exact cardinalities of sets.

At the moment, my twins are making great strides in math, at least compared to their skills six months ago. Then, their mastery of number depended on counting objects, which they tracked using fingers and toes. When they got to higher numbers, they would carry out operations by envisioning imaginary fingers and toes in their heads. Now, they have learned several different strategies to break up numbers and regroup or double them, allowing them to easily add and subtract two-digit numbers.

It's pretty cool to see it unfold, but it's essentially based on learning a technology of number. Numbers can be patterned to accomplish addition and subtraction in many ways, and with some practice and memorization, kids can attain a very rapid pace of solving problems. It's something that most of us have in their schooling somewhere, and there's nothing magical about it -- we just have to learn some algorithms and practice them.

The Pirahã are different from speakers of other languages with more cardinal numbers, because they do not have that particular shorthand. It's a significant aid to number processing, because words and concepts provide ways to escape the limits on human short-term memory. Frank and colleagues connect this research on number to other aspects of language and cognition:

Where does this leave the Whorf hypothesis, the claim that speakers of different languages see the world in radically different ways? Our results do not support the strongest Whorfian claim. However, they are consistent with several recent results in the domains of color ([Gilbert et al., 2006], [Uchikawa and Shinoda, 1996] and [Winawer et al., 2007]) and navigation (Hermer-Vazquez, Spelke, & Katsnelson, 1999). In each of these domains, language appears to add a second, preferred route for encoding and processing information. In the case of color, language enables faster performance in search, better discrimination, and better memory when target colors can be distinguished from distractors by a term in the participant’s language. However, verbal interference – which presumably blocks access to linguistic routes for encoding – eliminates this gain in performance, suggesting that the underlying perceptual representations remain unmodified. Likewise in the case of navigation: The use of particular linguistic devices allows (though does not require, see e.g., Li & Gleitman, 2002) efficient compressive navigational strategies. But again, under verbal interference these strategies are not accessible and participants navigate using strategies available to infants and non-human animals.

I would have written more subtle things about the Whorf hypothesis, and maybe I will some other time.

I very much like the idea that language itself provides the gears of a cognitive technology -- I think that is a very powerful one that we should apply more broadly in the past. It is misleading to see minimal stone tools, or the organic tools of other primates, as the simplest basis of technology. Technology begins with habits of mind, developed as strategies to better process regularities in the social environment. The powerful thing about language is that it gets in from outside. Children encounter regularities that have already taken hold in experienced minds. As I discussed last week ("Language bootstrapping the brain"), the process of language learning can proceed surprisingly well within brains with very different structural equipment.

One other observation of interest: Color and number words were "technologies" that were acquired surprisingly well by Alex the grey parrot. Talk about a very different kind of brain!

References

I ran across an interview between Anna Plutinski and population geneticist Warren Ewens.

I cannot say enough about Ewens' book, Mathematical Population Genetics. If you can work through it, you can do population genetics. It doesn't cover every au courant topic, but those will change next week anyway. And it's on Kindle now. Which I suppose probably looks pretty good on the DX, assuming the math displays well -- the book's format is just the right size for it.

Anyway, this interview from 2004 was probably conducted around the time the book was released. It covers pretty much the gamut of his career. I have to select some part to quote for you, so I'll select the passage that would be most likely to come out of my own math in my genetics class:

WE: Of course there is a strong possibility that the neutral theory is assumed not because it is appropriate but because the math of that theory is so very simple compared to the math applying for any selective theory.

AP: Can I follow that up? Do you think that that has lead to models of phylogenetic change that is not very well supported by the evidence?

WE: I think that that is quite possible. However, here we enter into another question. In mathematical population genetics theory you know from the very start that you are making big simplifying assumptions. You are in a very different position from a physicist, who might believe that his mathematical models describe reality exactly. No sensible population geneticist would make any claim along those lines. He or she is forced to simplify, because reality is so complicated that you don’t know it in any detail, and even if you did know it and used math describing it faithfully, the analysis would be impossible to carry through. So simplification is unavoidable. I do not know whether the use of the neutral theory is too much of a simplification and has lead us to incorrect and distorted views about the true evolutionary tree, it’s shape and dimensions, but I suspect that there has been quite a significant distortion.

There is much more at the link, some history of association testing, genetic draft, a lot on Ewens sampling theory, and a touch about his work here in Madison.

The Telegraph has a short article on Mark Pagel's research into reconstructing ancient languages:

Dr Pagel has tracked how words have changed by comparing languages from the Indo-European family, which includes most of the past and present languages of Europe, the Middle East and the Indian sub-continent.

He has been able to track the evolutionary history of Indo-European back using a computer and said that some of the oldest words were well over 10,000 years old even though the original Indo-European language is thought to date back no more than 9,000 years.

"I can say with confidence that there are sounds or words that predate Indo-European," he said. "If you look at 'thou', 'I' and 'who', we can now tell they are probably at least 15,000 to 20,000 years old. The sounds used then for these meanings were probably very similar to those used today."

Pagel is far from alone in reconstructing proto-Indo-European, of course, but he is introducing evolutionary methods to the problem -- called "glottochronology" -- in a unique way.

The press release from IBM is actually more infomative (the project used an IBM supercomputer for its analysis):

Looking to the future, the less frequently certain words are used, the more likely they are to be replaced. Other simple rules have been uncovered - numerals evolve the slowest, then nouns, then verbs, then adjectives. Conjunctions and prepositions such as: ‘and’, ‘or’, ‘but’ and ‘on’, ‘over’, ‘against’ evolve the fastest, some as much as 100 times faster than numerals. ‘Throw’ which is expected to evolve quickly, has a half-life of 900 years, there are 42 unrelated sounds for it across all the languages. In 10,000 years time, it will likely have been replaced in 10 of them – possibly including English, unless of course we all do our part to keep the word in circulation.

“50% of the words we use today would be unrecognisable to our ancestors living 2,500 years ago. If a time-traveller came to us, and told us he wanted to go back to that period, we could arm him with the appropriate phrase book, and hopefully keep him out of trouble” explained Mark Pagel, Professor of Evolutionary Biology at the University of Reading.

I'll have to wait to see the paper. I will be interested to get an idea of some of the dates they are proposing for language families and their relations.

There are still questions that would pose problems for this method. If we have to rely on highly-conserved words to do chronologies of language relations deeper than 5000 years, we are limited to a very small subset of words in any given language. How likely are these conserved words to be borrowed -- causing similarities without recent ancestry? Are the probabilities of change across many languages over a short time (the source of the statistic) really comparable to the probability of change in a few ancient languages over a long time?

UPDATE (2009-02-28): A linguistically-minded reader writes:

Regarding this recent post in your blog, I was surprised to see you actually recommend the press release by IBM and the University of Reading ("The press release from IBM is actually more infomative ..."). Even an amateur linguist like myself can see that it's crap. There's been considerable discussion on Language Log, starting from the BBC interview, where Pagel was induced to make a right fool of himself, linguistically speaking (which doesn't say anything one way or the other about his computer expertise, of course).

You can find the Language Log story here, along with comments. I always withhold judgment on a piece of work until I've read it myself, but I certainly sympathize with those who think the story was poorly reported in the press.

Particularly the one with the headline "Handy phrasebook for Doctor Who".