One Summertime (or, Measuring a summer’s day)

As I was saying yesterday, summers tend to be all too short in this part of the world.

This fact was confirmed for me today when, having put on shorts and a t-shirt this morning because this week’s glorious summer weather appeared to be continuing, I found myself having to cycle home from work in my shorts and t-shirt in the rain.  As I went along, I cheered myself up by singing a rendition of George Gershwin’s Summertime (with a fairly heavy dose of irony).

This lead me inadvertently to the invention of a new unit for the measurement of distance.

As you may recall if you’ve been reading this blog for long enough or have browsed far enough through the archives, a while ago I ran a series of posts about units of length, relating them all to the span of the Menai Suspension Bridge (NB that link is actually to one of my blog categories; most, but not all, of the posts relate to that particular series).

It just so happened that I started singing Summertime (one complete run through at moderate tempo) more-or-less as I was getting on to the bridge and I finished it at about the time I reached the far end.  Therefore, it occurred to me that I could measure the length of the bridge (or anything else for that matter) in terms of the length of time it took to sing the song.

I therefore (loosely) define a Summertime to be the unit of length equal to the distance traversed on a bicycle while singing the eponymous song.  Of course, it’s not a particularly precise definition since it depends on how fast you ride and how fast you sing (which are not necessarily directly correlated).  On the basis of one measurement, given that the length of the Menai Suspension Bridge is about 256.3 meters and rounding up due to a combination of the inherent lack of precision in the definition of the Summertime and the fact that I hadn’t actually quite reached the bridge when I started singing, the conversion factor seems to be 1S = 300m approx.

And of course, that’s not all that much shorter than the length of a typical British summer. 🙂

 

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A life measured in coffee spoons

Recently, I’ve been getting stuck into the poetry of T. S. Eliot.

As I mentioned  some time ago, his Old Possum’s Book of Practical Cats is one of my favourite works of poetry.  It’s also the part of Eliot’s work that I know best, having read it many times.  I own two printed copies, one with illustrations by Edward Gorey and the other (the standard Faber edition, I think) illustrated by Nicholas Bentley.  Both are fine sets of illustrations (and the two are quite different in style from each other), which complement the poems nicely.

I have also had a copy of Eliot’s Selected Poems (Faber, 1954) for a few years, although I don’t think I’ve read quite everything in there.  This anthology, which was put together by Eliot himself, contains many, though not all, of the poems from his earlier published volumes.  It includes The Wasteland, which is probably his most famous poem.

Quite recently, I picked up an electronic copy of Eliot’s Complete Poems, mostly to get hold of Four Quartets (probably his second most famous work, which I particularly wanted to read after having read about it).  I also got a couple of commentaries on his work, some of which is quite obscure and benefits from a bit of study to understand what it’s getting at (although it is perfectly possible to derive much enjoyment from it without picking up on all, or indeed any, of the references).

Although I’ve mostly been reading my new electronic anthology (with a view to reading all of Eliot’s published poetry before too long), I have been dipping into my dead tree editions as well, mainly for the sheer tactile pleasure of handling real books.  I discovered a couple of passages I had underlined in The Love Song of J. Alfred Prufrock, one of Eliot’s earlier poems (dating to around 1918, as I recall) and the source of the title of his first published anthology: Prufrock and Other Observations.  Evidently these underlined passages were the bits which most leapt out at me on my first reading of the poem, several years ago, and they are still amongst my favourite bits of it.

The first is a single line that I find particularly appealing:

I have measured out my life with coffee spoons.

I’m not sure precisely what Eliot had in mind when he wrote that line but, as someone who drinks quite a lot of coffee (and rarely goes for as much as a whole day without at least one cup), I like the idea of somehow using coffee spoons (or rather, the cups of coffee that you make with their aid) as a measure of the passing of your life.

I have no idea how many cups of coffee I have actually consumed in my life.  Based on a rough estimate of 2 cups per day for the last 25 years (since I was about 11), and assuming 365 days per year (i.e. ignoring leap years etc.), it’s something like 18,250 cups.  It’s not uncommon for me to only have one cup in a day (although, as I said, I rarely miss a day entirely) and I have been known to have a lot more than two cups, so I suspect that’s probably a fairly low estimate and it would probably be safe enough to round it up to 20,000.  That’s something to ponder next time I’m lying awake at night.

Anyway, back to the poetry symposium…

The other passage is slightly longer, and is an explicit reference to Shakespeare’s Hamlet (the play, not the character):

No! I am not Prince Hamlet, nor was meant to be;
Am an attendant lord, one that will do
To swell a progress, start a scene or two…
Full of high sentence but a bit obtuse;
At times, indeed, almost ridiculous —
Almost, at times, the Fool.

I would guess that the attendant lords in question are probably meant to represent Rosencrantz and Guildenstern (who were such minor characters that Tom Stoppard felt inspired to redress the balance by rewriting the Hamlet story from their perspective in his excellent play Rosencrantz and Guildenstern Are Dead).  This passage is quite apt for someone who used to dream of being famous (and preferably also rich) but is now quite content to live in relative obscurity and does his best not to take himself too seriously.  Not, of course, that I have anyone in particular in mind with that description.

I have missed out a few lines from the middle of that second quote.  If you like the bit I’ve quoted (or even if you don’t), I’d recommend reading the whole of The Love Song of J. Alfred Prufrock.  This particular passage comes from quite near the end, while the coffee spoon one is near the middle (my edition doesn’t give line numbers and I can’t be bothered to count them).

155.891 smoots (or maybe two)

When I started my occasional series of posts about length measurements just over a year ago, I mentioned that there were two reasons why I had chosen to use the Menai Suspension Bridge as the reference object for all the different units (to be measured via the Google Maps DMT wherever possible).  One reason was that I regularly traverse this landmark.  The other, as I said, was a bridge-related connection to one of the units which was to be related in due course.  Now is the time!

The smoot is a unit that originated in October 1958 when a bunch of engineering students at MIT used one of their number (Oliver Smoot, later to be Chairman of the American National Standards Institute (ANSI) and President of the International Organization for Standardization (ISO)) as a measuring stick to measure the length of the Harvard Bridge.  One smoot is equal to Oliver Smoot’s height (at the time of the measurement), which was 5’7″ (i.e. 67″ or 1.7018m). The bridge’s length was measured to be 364.4 smoots plus or minus one ear, with the “plus or minus” intended to express uncertainty of measurement.  That’s about 620m in the rather more boring but somewhat more common metric system.

The Menai Suspension Bridge, according to my measurement on Google Maps, is 155.891 smoots long, so it’s a bit less than half the size of the Harvard Bridge.  Incidentally, the Menai Suspension Bridge looks very similar to the Széchenyi Lánchíd (Széchenyi Chain Bridge) in Budapest:

Széchenyi Chain Bridge, Budapest

The Budapest bridge was actually built about 15 years later by a different engineer (and modelled on a bridge over the Thames).  Wikipedia lists its length as 375m, which Google Calculator tells me is about 220 smoots.

In case you’re wondering about the possibility of two smoots indicated by the title of this post, it’s actually a reference to two Smoots since Oliver has a cousin, George Smoot, a physicist who won the Nobel Prize (for physics, unsurprisingly) in 2006 and has appeared as a guest star on The Big Bang Theory (which is quite appropriate since much of his physics work has been on the big bang).   Arguably, George is more famous than his cousin although I’m not aware that he has any units named after him.  I decided to go ahead and write this post after I discovered (from Wikipedia, where else?!) that today is George Smoot’s birthday.  So, happy birthday George (in case you should ever happen to read my blog, which is admittedly fairly unlikely)!

10444.7 inches (or 31334.1 barleycorns)

If you’ve been following my blog for a while, you may remember that early last year I started a series of posts on the subject of units of length measurement based on the Distance Measurement Tool feature of Google Maps, using the span of the Menai Suspension Bridge as a test object for comparing the different measurements.

The last couple of units I looked at (beard-seconds and Olympic swimming pools) were decidedly esoteric, but both derived essentially from standard metric units (a beard-second is 5nm and a swimming pool is 50m so it’s not surprising that, as I’ve just noticed, an Olympic swimming pool is exactly 10,000,000,000 beard-seconds long).

This time I want to return (mostly) to somewhat more mainstream units and also diverge from the metric path as we consider inches and related measurements. These form the length part of the so-called Imperial system of measurements which, according to Wikipedia, was formally introduced to the UK by the Weights and Measures Act of 1824, although the actual units themselves are somewhat older. Since 1995, all Imperial measurements in use in the UK are defined in terms of metric units and measuring devices used in trade are legally required to display metric measurements. In practice, many people continue to use Imperial measurements for many purposes.

In principle, I’ve always been a firm supporter of the metric system as it makes a lot more logical sense to me. For instance, I find it much easier to remember that there are 1000 millimetres in a metre and 1000 metres in a kilometre than to remember that there are 12 inches in a foot and 5280 feet in a mile (I had to look that last one up on Google!). However, a couple of years ago I read an interesting book entitled About the size of it (by Warwick Cairns, published in 2008 by Pan Books), which advances the thesis that Imperial units are actually based on various measurements relating to the human body and are thus easier for people to visualise.

For instance, a foot (which is about the same as 30cm – apparently it’s actually 304.8mm) is the length of a standard British size 10 boot, which is the average shoe size for an adult male. As it happens, my feet are size 10. This is obviously fairly approximate as individual boots (for a size 10 foot) vary somewhat in length but it means that it’s quite easy to pace out a length of, say, roughly 6 feet and consequently somewhat easier (or so Mr Cairns says, and I’m inclined to agree with him) to visualise a length of 6 feet than one of 1.8m.

An inch (now officially 25.4mm) is, according to Cairns, essentially the thickness of a human thumb. Although different people have hands of different sizes there is, apparently, less variation in the thickness of thumbs than you might think and certainly they are close enough to a standard size to be quite useful for approximating distances.

I would have to do some experimenting to be sure, but I’m fairly certain that I’m more accurate when I try to estimate (suitable) distances in feet or inches than when I try to do it in metric units (despite my best efforts, in the past, to make myself work in metric). For accurate measurements or calculations, metric would still be my first choice in general, but for estimating or visualising distances (on a human scale, at least) I have always found imperial units to be somewhat more natural and now I have a better understanding why that is.

Another Imperial unit that Cairns mentions, which as far as I can tell was not included in the Weights and Measures Act, is the barleycorn. This, as the name suggests, is the length of an average grain of barley and happens to be exactly a third of an inch. Although no longer regularly used as a unit of measurement, the barleycorn is apparently the basis of the British system of measuring shoes. Here’s a condensed explanation (see Cairns’ book for more detail): A child’s size 0 shoe is based on the size of an average child’s foot when they first start needing shoes, which is 4 inches (aka. 1 hand – you can probably guess where that unit came from); thereafter, shoe sizes go up in barleycorns (e.g. a size 1 is 4 inches + 1 barleycorn, i.e. 4.33 inches, size 2 is 4 inches + 2 barleycorns, size 3 is 4 inches + 3 barleycorns, i.e. 5 inches, etc.); a child’s size 12 shoe is 8 inches (or 2 hands) long (i.e. 4 inches + 12 barleycorns (4 inches)). The next size up (8 inches + 1 barleycorn) is considered a child’s size 13 or an adult size 0 and thereafter the adult sizes continue by adding barleycorns. This means that an adult size 10 is 8 inches + 11 barleycorns or 11.66 inches (11 and two thirds, to be precise), slightly shy of a foot (i.e. 12 inches); the discrepancy is explained by the fact that shoe sizes measure the size of the insole, which is slightly smaller (by about a barleycorn, in fact) than the external size of your boot. In other words, if I want to measure distances in feet as accurately as possible, I should put on a fairly sturdy pair of boots.

The span of the Menai Suspension Bridge, as measured with the Google DMT for the purposes of this blog series, is 10444.7 inches, which is the same as 31334.1 barleycorns or 870.393 feet.

5.30591 Olympic swimming pools

It’s been a while since the last entry in my series on length measurements, so I thought it was about time for another.  Since I’ve been thinking about ancient Greece recently, it seemed appropriate to go for an ancient Greek unit of measure.  However, apart from one of a number of different cubit measures (which I’m planning to write about later), there were no  Greek units amongst the list of measurements that I prepared from the Google maps DMT when I first planned the series. Checking back with the DMT, it seems that this was because there weren’t any to choose from rather than just that I didn’t pick any for my list.

Employing a bit of lateral thinking, the closest I could come up with from my list was the Olympic swimming pool.  I suspect that if swimming featured in the ancient Olympic Games (it’s not mentioned in the Wikipedia article, but that doesn’t necessarily mean it was never contested) they didn’t use a standard size pool.  A swimming pool used for the modern Olympics, though, is supposed to have a standardised length of 50m.  It also has other details (such as width, water temperature, number of lanes and minimum depth) standardised according to the FINA specification, but it is the length (the greater of the two horizontal dimensions) that is used when an Olympic swimming pool features in Google’s DMT.  As far as I’m aware, it’s not a particularly common unit of length for measuring things other than swimming pools (the other common size of pool for competetive use being 25m, or half Olympic size).

As the title of this post indicates, the span of the Menai Suspension Bridge is about 5.3 Olympic swimming pools.  I suppose that means that swimming across the straits would be equivalent to doing 5 lengths of the pool (ignoring the added difficulties imposed by the strong currents and the distinctly sub-spec water temperature).  In any case, I think I’ll stick to cycling across the bridge rather than swimming under it.

I was interested to note that the Google DMT’s list of units didn’t include the σταδιον (stadion, plural: stadia; usually anglicised as stadium or stade), which is one of the better known ancient Greek distance units.  The problem could be that there is no single authoritative conversion factor from metres to stadia: although a stadion was defined as 600ft (according to Herodotus), there were several conflicting definitions of a foot in use at the time (dependent on geographical location) and hence a stadion in one place could be longer or shorter than one somewhere else.

Apparently the stadion unit was named after a running race over that distance, and the race in turn was named after the building in which it took place; as you might expect, this building also gave rise to the modern word “stadium” as a sports venue.  Wikipedia is slightly confusing as the stadion unit page says an Olympic stadion was about 176m, while the stadion race page says that the stadion race track at Olympia was about 190m long.  It could be that the stadion unit began life as the length of the race track and later standardised as 600ft and that the definition of a foot in use at Olympia was 1/600 of 176m, thus leaving the race track slightly longer than the new definition of a stadion.

Taking the definition of 1 stadion = 176m, the Menai Suspension Bridge measures about 1.5 stadia.  Using the length of the Olympic racetrack (1 stadion = 190m), it is about 1.4 stadia.

5.30591e+10 beard-seconds

It’s about time for the next part in my series about units of length measurement and this time I’ve decided to go for one of my favourites: the beard-second.

I had not heard of this particular unit until I came across it in the Google Maps DMT, but it is sufficiently established to appear in a Wikipedia article (albeit not a page unto itself).  This doesn’t go into great detail (or, indeed, any detail) about its history but defines it to be the length an average beard grows in one second.  There are at least a couple of more precise definitions in terms of established units – 1 beard-second is either 100 angstrom (which is the same as 10 nanometres) or 5 nanometres.  Apparently Google uses the latter definition for its calculations.

This unit is supposedly inspired by the light-year but useful for very small distances instead of very large ones.

The span of the Menai Suspension Bridge, as measured with the Google DMT for the purposes of this blog series, is  5.30591×1010 beard-seconds (5.30591e+10 in the computer-friendly version of scientific notation, in case your browser doesn’t support the HTML5 <sup> tag).  If you’re not familiar with the notation, that means roughly 5 followed by ten zeroes (that is, about 5o billion in the American sense of the word, which seems to be becoming accepted as the international standard version).  In other words, if I sat at one end of the bridge, I’d have to wait a very long time for my beard to grow long enough to reach the other end!

265.296 Metres

To kick off my series about length measures and the Google Maps DMT, I decided to start with one of the more common (and, arguably, useful) units on offer: the metre (m).

The metre (or meter to our American cousins) is one of the seven basic units of the SI system of measurements favoured by the world scientific community, which is the modern form of the metric system.

There have been several definitions of the metre since it was first proposed by English philosopher John Wilkins in 1668.  Apparently Wilkins proposed setting 1m to be the length of a pendulum with a half-period (IIRC that’s the time taken to swing from one extreme to the other – a full period being the time to complete a swing there and back again) of 1 second.  During the eighteenth century this original definition vied with another that defined the metre as one ten-millionth of the length of the Earth’s meridian along a quadrant (that is the distance from the equator to the North Pole) at sea level.

When the French Academy of Sciences defined their metric system in 1791 (around the time of the French Revolution), they opted for the latter definition, since the length of the pendulum required to give a 1s swing is affected by the slight variations in strength of the earth’s gravitational field at different location while the length of the meridian is constant (assuming, of course, you can measure it with sufficient accuracy in the first place).  As far as I can tell, this was the first official definition of the meter.

For nearly a century, from 1875, the length of the metre was defined to be the length of a specific metal bar measured under specified conditions (the gory details, along with a lot more information about historical definitions of the metre, can be found in the Wikipedia article linked above).  This was replaced in 1960 by a definition based on the wavelength of a particular line in the emission spectrum of Krypton-86 in a vacuum (presumably a constant for all Kr-86 atoms and therefore a, theoretically, more easily transferable measurement than the length of a single metal bar kept in Paris).

In 1983 the current definition of the meter was agreed, namely the length of the path travelled by light in vacuum during a time interval of 1  ⁄   299,792,458 of a second.  This is, of course, dependent on the definition of a second (which I won’t go into now, as this is supposed to be an article about length measurements) and the constancy of the speed of light in a vacuum (one of the cornerstones of Einstein’s theories of Relativity).

As an SI unit, the metre comes supplied with a whole bucketload of standard prefixes to denote decimal multiples of the basic unit.  This means that you can write distances from the very small (e.g. the diameter of a helium atom is about 0.0000000001m or 0.1nm (nanometres)) to the very large (e.g. the diameter of the sun is about 1,400,000,000m or 1.4GM (gigametres)) without excessive leading or trailing zeroes.  For everyday purposes, kilometres (1,000m) and millimetres (0.001m) are especially useful.

The span of the Menai Suspension Bridge (shore to shore, as measured using the Google DMT) is 265.296m.  My regular commute to work (using approximate start and end points, measured using the Google Maps navigational tools and my usual route) is 4.2km.