Number as cognitive technology

4 minute read

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 Frank:Piraha:2008. 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 Pirah 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 Pirah 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 participants 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!