From the title of this article, I instinctively feel that it should contain some kind of unsubtle Carry-On-style innuendo; that behind its apparent serious intent it will allude to matters both frivolous and trivial.  However, for anyone reading this in the same belief, let me be the first to disillusion you: it is actually as earnest and worthy as the sub-title, at least, suggests.

I genuinely do think that Orders of Magnitude are important, and yet it is a topic almost entirely overlooked during formal education and, as a consequence, a concept in which many adults find themselves woefully deficient.

Even now, I feel there is still an opportunity to flip this whole discussion on its head; throw in some entirely flippant comment, which will completely undermine my argument but, no, I am steadfastly determined to stick to the straight and narrow.

My first formal academic exposure to Orders of Magnitude was whilst studying A Level Physics.  That is quite a long way through the average student’s syllabus for a first encounter.  However, if you are confronted with Wikipedia’s definition of the concept, an A Level in Physics would seem scarcely sufficient to make the idea comprehensible:

            “An order of magnitude is an approximation of the logarithm of a value relative to some contextually understood reference value, usually 10, interpreted as the base of the logarithm and the representative of values of magnitude one.”

Simple then!

Thankfully, the Cambridge Dictionary provides a more understandable translation of the gobbledygook:

            “The approximate size of something, especially a number.”

There it is in a nutshell: a rough approximation of size.

I am literally having to fight back the urge to slip into Carry-On innuendo at this point, but I remain admirably committed.

And, so, just why are Orders of Magnitude important?  I believe that a sound comprehension of them is imperative to function in the modern world.  Thankfully, for anyone who has not taken A Level Physics, some understanding of Orders of Magnitude must be inherent in our nascent make-up.  On some fundamental level, we comprehend the size of things: the ocean is big; the waves are high; the current is strong.  However, when these physical descriptions are translated into numbers, we often find ourselves more at sea.

Is that ocean 10kms wide, or 10,000?  Is that wave 10cms high or 1000?  Is that current moving at 1mph or 100?

Typically, Orders of Magnitude operate by factors of ten.  They don’t require you to be deadly accurate; they just expect you to be within a relevant factor of ten accurate.  Can that be so very difficult?  Sometimes more difficult than it might seem.

I’ll give you an example, drawn from a semi-fictional real-life, but I am prepared to wager that something similar has probably happened to most people: I buy a chocolate bar priced at 95 pence from my local newsagent’s; the cashier rings up the amount of the bar, but omits the decimal point from before the 95, and unthinkingly reads off from the till: “That will be £95, please, sir.”  Without a knowledge of Orders of Magnitude, which warn you that you are being overcharged by a factor of 100––or two Orders of Magnitude––you might potentially find yourself £94.05 out of pocket on the transaction.  And whilst you might congratulate yourself that your own knowledge of Orders of Magnitude had saved the day, what of the cashier’s, who didn’t spot the anomaly in the first place?  The only potential inaccuracy in my scenario is the cashier’s inclusion of the words “Please, sir.”

Everyone makes decisions based on Order of Magnitudes all the time.  On a day-to-day level, I believe that the ability to accurately perceive one Order of Magnitude is fairly fundamental in order not to be late, get ripped off, or function at work: the distance to the shops is one mile rather than ten miles; a pack of four toilet rolls is sufficient for a week, not forty rolls; the refurb of my kitchen should cost £2,300 not £23,000––despite one builder’s quote; I have five friends rather than fifty friends, largely because of my strange fixation on Orders of Magnitude.

However, when it comes to larger, less frequently used quantities, I am prepared to concede a greater leniency regarding estimating Orders of Magnitude.  The distance from the Earth to Alpha Centauri for example: what’s your best guess?  By how many Orders of Magnitude would you expect to be amiss?  When considering such vast quantities, the number of Orders of Magnitude of inaccuracy will be correspondingly greater.  However, any estimate working in centimetres rather than light years, might also reveal another truth: as much as Orders of Magnitude are important, so too are Units of Measurement.  (The answer is approximately 4.3 light years, for anyone who is interested – Ed.)

© Simon Turner-Tree

Simon Turner-Tree counts his friends without relying on Orders of Magnitude.