It From Bit, Or From Metaphor

It is a fact oft-forgotten that the scientist has a mind that is very much like ours. One flooded by the same ephemeral streams of fancies, constantly struggling to solidify the ineffable into words. But above all: a lazy mind, sometimes so to a fault, supported by a brain that has limited computational capacities, and which is always in search for opportunities to offload the work onto the environment, much like how the poet seeks to discharge his emotions into a stanza.

So what the scientist does is to think patiently about his intuitions, wallow for a while amidst the airy wisps curling through his consciousness, in an attempt to find structure in them, as if the billowing mind-scape had contours in it if you look really, really hard. That way, he can then try to map – to arbitrarily associate – his ideas onto something external and discrete that is easy to quantify. By letting something else, a representation, stand in for his private thought, he sacrifices the rich experience of the real thing, in exchange for something that he and his collaborators can work mindlessly and mechanically with. Maybe they jot down an idea on a cafeteria napkin, apply some theorems to an equation on a blackboard, or let a computer grind through a dataset on the order of millions. The less brain it requires, the better.

It is this laziness that language is for. No two persons conjure up the exact same brain state upon reading the word “cat”, but the brain states are similar enough to produce roughly the same behaviour-guiding inferences. We may say that the brain states are “fungible”, and by mapping this overlap onto an external symbol – in this case a word – we get something that is sensorially impoverished but capable of cuing retrieval of information from the vastly more capacious long-term memory.

This way, our language can be seen as a culturally achieved notebook for storing intellectual resting-points that we now can use our computational resources to build upon instead of reinventing the wheel. The idea of language as an ever-shifting springboard for intellectual progress – something that transforms our thinking as much as it mirrors it – has by philosopher Andy Clark been compared to Mangrove trees. Mangrove trees grow in water, and quite like how islands emerge under Mangrove trees from soil accumulating between their roots, the coinage of a word becomes an island for further exploration in the balmy sea of thoughts our brains are bathing in.

Laziness is also what mathematics is about. To say that a fruit bowl contains three fruits is to disregard the fact that one may be a banana and the others two apples, and the number preserves no information about how the fruits are arranged. In some contexts, to represent the bowl by a number would be terribly insufficient, but across contexts, most people would at least agree that it contains three discrete objects. Like how all people generate fungible brain states upon reading a word, all people can easily extract numeracy – quantify – a fruit bowl. By doing so, people can reason about it using mathematical theorems inherited from other people living centuries ago, who themselves mapped their vague intuitions onto formal notations to play around with absent-mindedly. And because numbers are recursively defined (2 is 1+1, 3 is 2+1, etc.), we can offload their transformations to machines.

Perhaps it is due to the very same laziness that we also tend to forget this artificial, brain-serving, and brain-dependent nature of formalisms, and give them more metaphysical significance than they deserve, mistaking simulation for reality. Like how wars are fought over territory lines – lines that exist nowhere else than on our maps – we start unwinnable debates about abstractions as “true” or “untrue”. But when we take formalisms for what they are – external structures to bootstrap ourselves beyond our computational limitations – and give due recognition to the poetic impulse that led to their construction, a more fulfilling kind of insight becomes obtainable.

We see, for example, how deceptively simple concepts evolved gradually, carried and modified from mind to mind over the course of millennia, only recently mapped onto mathematical structures. The word “matter” was first coined by Aristotle, who borrowed the Greek word for “timber” to represent the stuff everything is made of, and acquired, during medieval times, the connotations of something solid and massy, proportional to our intuition of “resistance”. Later it was thought of as invisible corpuscles in an empty space. “Space” was conceived by Newton as an “immaterial medium”, and “gravity” was by him thought of as “Earth like a sponge, drinking up the constant stream of fine ethereal matter falling from the heavens, this stream by its impact on bodies above the Earth causing them to depend”. “Energy”, deriving from our intuition of “potential”, was in the early 1800s thought of as a ghostly substance like phlogiston and élan vital. When eventually we formulated it mathematically, enabling external manipulation, we were no longer required to consciously maintain such expensive imagery in our mind.

So when a scientist waxes lyrical, he does so a little bit less alliteratively than the poet, but his chalk-dry equations spring from sensibilities equally romantic. By encapsulating his experiences into formalisms, he lets formalisms flow through his mind in their stead, as building blocks on their hierarchical course towards self-complication.