Dollars and Sense

I listened to this amazing conversation between a person who was quoted a price in cents/kilobyte, and several Verizon representatives, all of whom are so addled by reliance on their computer screens that they are unable to grasp that they are mis-quoting a price by one hundredfold by failing to convert between dollars and cents. Then it got me thinking about why they should find it so difficult to multiply and divide by 100. It’s not that that can’t perform the trivial arithmetical calculations, it’s just that they experience a cognitive disconnect linking this operation with their intuition about how much something should cost. What we call “numbers” are in fact two different things: symbols that we manipulate using mechanical and representative operations (in this case, rational numbers or fractions that are ratios of two integers), and sensations relating to collections or volumes of objects that we intuitively experience and comprehend using body knowledge and experiential memories.

Why should it be so difficult for these Verizon people, all apparently USians, to handle such a simple operation as taking powers of ten? I think it’s to do with a lack of basic Metric education in the US. It seems obvious to me that in a culture where Metric conversion techniques are not routinely taught to schoolchildren, then the casual manipulation of powers of ten and powers of a hundred must become (when compared to other cultures) significantly less easy, common and apparently mind-numbingly abstruse and esoteric for a significant proportion of adults.

The unusual resistance of the U.S. to Metrication is both a symptom of and a driver of adult innumeracy.

Metric instills a basic intuition about powers of ten and orders of magnitude. Or at least, it will tend to, relative to indifferently scaled arbitrary measurements. Once you build this mental framework, it can be easily integrated into novel experiential learning.

I am unfortunately old enough to have begun primary school in a country using Imperial measurements that then switched to Metric. I can still recall being taught arithmetic as a young child, and being shown how to convert between ounces and pounds, and pounds and stone. That sucked, and made no sense.

Being indoctrinated into Metric within a few years reduced my cognitive load apppreciably, while enlarging my ability to estimate weights and measures. By exposing children to tanglible object weights such as 1g, 10g, 100g, 500g, 1kg, 5 kg and so on, one forms a consistent appreciation of mass. The same is true of learning distance.

I had to re-take basic physics and chemistry in a US university recently. I was quite shocked at how a significant proportion of the students had little conception of how much 1 ml was, or 10g, or 1m. It makes them even less able to relate the scientific measurements they read about and note down in lab to their own experience. Seriously, it’s a problem. Many of them had less cognitive ability to deal with weights and measures than a typical 10-year-old European child. USians now have the worst of both worlds: thanks to globalisation, pretty much all their commodities now carry measurements in grams and litres, but they are not really taught how to think Metric in school and so have little idea of how to work with them.

Powers of ten make life easier. I now saying that being taught Metric would have avoided this Verizon arithmetic abortion, but I think it might have increased the probability of finding a rep who got it.

Some might say that the basic reason for the communication disconnect is that dollars and cents are “different”, but I think comment in and of itself betrays a lack of Metric education.

I think the problem is that the Verizon people were incapable of intuiting on a fundamental level that the two are in fact the same thing, currency, but that the $ sign is a 100x multiplier of the ¢ unit. Or that the ¢ sign is a 100 divider of the $ unit.

As a pedagogy, Metric is based on the idea of as few fundamental units as possible, and everything else being created through powers of ten. It simplifies peoples’ cognitive grasp of the physical basis of their commoditised world, of how things are sliced and diced. I feel that is why, in the Verizon conversation, when the caller attempts to extend through analogy dollars and cents to metres and centimetres, it seems as if he may as well have been talking Etruscan to the representative.

As a measurement system, Metric helps people intuitively grasp that a centimetre is 100th of a metre. That a millimetre is 1000th of a metre. That a mL is 1000th of a litre. That a 1 cm³ cube of water (1cm each side) is a cubic centimetre, or cc, which weighs 1 gram and, were it to absorb 1 Calorie of energy, will exhibit a temperature increase of 1 Celsius. That a half-litre (a common unit of beer) is 500 mLs. Volume, length, and mass become inter-related linearly. A cent of something becomes immediately understandable as a 100th fraction of that something. Children are not taught to perform the same arithmetic with Imperial, so they do not gain early cognitive maps of powers of ten, and linear/log scaling.

This kind of linearity is how people experience matter in their daily lives: acceleration, momentum/inertia, impulse, etc. When experienced daily, Metric becomes not just an isolated abstraction as it is in the US (a slightly exotic measurement system used in specialised disciplines and for large soda containers), but instead woven into the fabric of experience through body and hand knowledge. It builds a communicative bridge between people in similar and even distant cultures.

Try interconverting between ounces and pounds, through a volume measurement, into lengths. Most people have very little idea. I know I couldn’t do it without a calculator. My wife, an American, even seems to have trouble occasionally identifying how many ounces are in a pound. 14 or 16? It all gets a little hazy even between people speaking “Imperial”.

In terms of communication, as well as being forced to learn a new language, USians now increasingly have to learn to speak different measurement languages anywhere outside the US. Even in former English-speaking Imperial holdouts such as Ireland and the UK, with all road signs being replaced as km, and all measurements (except, for now, the sacred pint) replaced as litres, communication has become slightly more complex. I recall reading a National Geographic with my little nephew (8), when he had to stop me to ask what the “strange numbers” were (F and lb).

Because of the external push of globalisation and standardised measures, and the internal push of people anxious to understand what the hell a “Celsius” is anyway, the US will eventually go Metric. But just as we see today, it will happen slowly, haltingly, and in a piecemeal and arbitrary fashion… creating anxiety and mis-communication as it progresses.

As a side note, upon reading the message on reddit, I immediately called the supervisor. The number was “not in service”.