originally posted on one of my several now defunct blogs, called

On Engineering, on 25th September 2012

The relationship between engineers and numbers is often an uneasy one. Engineers are by and large mathematically literate after all those years at university, but we don’t necessarily feel at home in the world of maths. It’s a subject that we feel is to be dropped at the earliest opportunity.

Once we enter employment, we don’t need maths anyway. We learn the formulae and relationships that are pertinent to the subject matter at hand - and forget the rest. If we do happen to need something from “the rest”, we generally know where to unearth it and, after some thought, can apply it.

My own mathematical world is rather limited. I need to interpret test data, certainly, but have found that it’s the qualitative information that I extract that is useful rather than any best-fit curves or dynamic equations of state. I do sometimes need to calculate friction coefficients, but since the formulae are simple enough to encapsulate in a spreadsheet, I don’t actually need to know what precisely those formulae are (but I can find them if required).

If mathematics is one aspect of this relationship between engineers and numbers, numeracy is the other. Whatever results we get out of testing, or whatever design information we wish to convey, I need to talk numbers with colleagues, suppliers or customers. Given that I’ve living and working in Germany, these discussions often take place in German. Now, whilst I’m pretty good at the language from a linguistic standpoint, I have a real problem with German numbers.

I’d like to point out at this juncture that I was never bad at simple additions and subtractions in English. But the quirks of the way the German language treats numbers make me stumble when naming or hearing numbers in isolation and often I’ll simply give up if I need to engage in a little mental arithmetic.

The problem is that German numbers are - partially - enunciated backwards.

If I want to say the number 65 in English, I have a nice mental image: sixty-five - 65. However, German tells us the smaller number first: fünf-und-sechszig. This means that my innate numerical image is messed up and I need to hold figures in a buffer before I can complete my own natural image: (5)´6 -> 65.

My internal workings are a very fast version of this:

“OK, he’s just said the number five, and there’s an “and” being said, so there will be a number coming before it… So, what is it, then?… Wait for it… Ah, OK, so it was a sixty. What was the first number again? A five. So, that sixty was the tens digit and five was the unit digit, so he meant to say sixty five.”

That usually works, as I say, when numbers are mentioned in isolation. But having to perform arithmetic with them seems to be a mental effort too far.

“So, he wants me to take five and sixty, then subtract eight and twenty. So that means… scramble…scramble….seven and thirty.” My German colleagues, who have grown up with this nonsense, can cope with this much better than I have been able to and are therefore usually much faster at computing the answer and beat me to it, meaning that, after a short while, I gave up even trying.

The mental effort is compounded by larger numbers where the hundreds are spoken first, then come the units, followed by the tens. So these end up as:

“Six hundred two and fifty.”

My internal numerical imaging is so strong that as well as my problems in parsing and understanding the numbers I hear, I have problems in saying them, too. This has caused at least one near miss in my time as an engineer in Germany, where I told a prototype builder to make something one hundred and fifty eight millimetres long, rather than one hundred five and eighty millimetres. Thank goodness for sketches and prints, is all I can say to that.

I know German primary school teachers who have confirmed that the German numbering system really does create difficulties for children at school - but given that quite a lot of German engineering seems to work reasonably well, it does not seem to be a handicap for life.

Other languages have their idiosyncrasies, notably (in my experience, anyway), French with its sixty-fourteen (for 74) and four-score-and-three (for 83): but since these quirks are still sequential, I can cope (but still hope that the Belgian “septante, octante” and “nonante” take over the francophone world). Maltese numbers are so complicated that they have been almost completely done away with and replaced by the English; but there is even a slight hiccup in logic in English: “thirteen”, “fourteen” and so on are a version of the German, with their singles being named first. But it’s such a short sequence of exceptions to the rule that I would treat them along with “eleven” and “twelve” as practically being units in their own right.

If you’re a German reading this, I’d be fascinated to know what your mental processes are for this, and whether you feel that you’re at some kind of mental processing disadvantage because of it; or even if you feel that it’s a kind of mental brain training that gives you that additional edge.

If you’re an Asian right-to-left reader reading this, I wonder if your mental image of numbers is different to mine, or whether the western numeral notation system has become so dominant that you think sixty five as a six followed by a five.

Now of course, it can sometimes simply not matter which way the numbers crop up…

554 + 445 = 999

545 + 454 = 999

… But by the time I’ve worked that out, it’s too late: I’m frazzled and am looking for the nearest pen - or a cup of coffee.