a cultural gymnasium for the curious runner
Calculus is the mathematics of rates of change (differential) and of the accumulation of quantity (integral). Applied to running, for instance, it can yield information about how fast you are changing your accumulation of distance from a certain point. To do this, it looks at all the tiny distances you have run in each small instant of time and then adds them up....and there's the rub.
Zeno and his school had challenged the Pythagorean notion that both space and time were made up of discrete, indivisible units, that a section of a line, for instance, is a finite number of points, and its length is the sum of the lengths of each point.
But since a point with any length, however small, can always be divided again and again ad infinitum, thought Zeno, it is plainly not an indivisible unit; we are driven to conclude that such discrete points cannot have any length at all. But adding together a series of points of zero magnitude would always give any line's extension as zero length, which is absurd: space must therefore be continuous, not discrete, and it can be infinitely divided.
However, Zeno also designed other paradoxes to show that even this continuous space and time could NOT be sliced up infinitely without contradiction!
He did this by showing that any motion of any kind through such 'slices' required the completion of an infinite number of small trips in a finite time, which he regarded as impossible. For Zeno, space and time were neither discrete nor continuous, but unchanging, contrary to our perceptions. Motion is thus illusory.
Now the theory of calculus has a view which casts doubt on Zeno's dismissal of these slices of continuous space and time. It, too, analyses a continuity by inspecting and adding up its ever-smaller constituent slices, but it introduces the crucial idea of an approaching end-limit to the slicing process. At this limit, the magnitude of the slice would be zero, and so all the slices together become a continuity when they become infinitely small.
Looking at thinner slices more frequently gives a better approximation of what's going on overall, until, in the limit, we have a precise picture of each moment of the journey, and these can be integrated to describe that journey. As we'll see, this way of looking at infinity and infinitesimals suggests that Zeno was wrong - an infinite number of trips CAN be made in a finite time.
Could it be that any kind of logic or modelling we choose to use, even today, is somehow inherently flawed? Well, there have certainly been challenges, even for arithmetic.
If the mathematical description of a real world situation is accurate enough, progress can be made by playing with the mathematical model according to certain logical rules. Any conclusions reached can then be mapped back on to the real world, where theories can be proposed and experiments devised to test them.
It's a big 'if', though.'The map is not the territory' may be a truism, but it places the fidelity of the model centre-stage when it comes to the credibility of the theories derived from it.
The writer Jorge Luis Borges tells of a country in which cartographers are striving to create ever more accurate maps, until they triumphantly produce one that is the same size as the country itself, apparently the only guarantee of its real accuracy, consistency and completeness! Of course, it proves unwieldy: 'In the Deserts of the West, still today, there are Tattered Ruins of that Map, inhabited by Animals and Beggars', wrote Borges, but the point of the tale is in its title, 'On Exactitude and Science'.
The story has echoes of both Shelley's 'Ozymandias' and may also be a nod to the devastation wrought on the 'map' by Kurt Godel, who had shaken the foundations of mathematics in the 1930's by proving that any axiomatic arithmetical system, any 'map', must be incomplete and inconsistent, in that there are unprovable truths within it.
A note on calculus
Running in Philosophy and Language
This is "motion towards", isn't it, boy?....'
It all started when Zeno and his chums in the Greek colony of Elea (in modern Italy) were busy pondering the nature of reality and whether it conforms to our perception of it. In their deliberations, they used the 'reductio ad absurdum' method of argument, i.e., applying logic to a proposition to test whether it leads to any contradiction that would fatally undermine it.
Now, I'm not sure which is more absurd, the fact that I was overtaken by a giant Scooby Doo during the Cardiff Marathon, or Zeno's insistence that I wasn't, despite all appearances to the contrary. Does the evidence of my own eyes not trump his sophistry? After all, as Alice said to the Red Queen, 'In our country, you'd generally get to somewhere else if you ran very fast for a long time'.
Well, let's see what Zeno has to say in his famous paradox. He imagines a race between Achilles and a tortoise, in which the latter has a head start. Using an apparently impeccable logic, Zeno offers a proof that as long as it keeps moving, this slowest of beasts can never be overtaken, even by this fastest of Achaean warriors. Indeed, in another of his paradoxes, he shows that 'in every way but experience' (as Tom Stoppard put it in his play 'Jumpers'), neither Achilles nor the tortoise can possibly move at all!
As he attempts to catch up with the tortoise, Achilles always has to first reach the tortoise's starting location for that same time interval, by which time the continually moving tortoise will always have moved on, albeit by an increasingly tiny distance. This applies to all subsequent time intervals, however small, and so the tortoise will always be in front of him, and thus can never be overtaken.
Since we do actually perceive tortoises being overtaken all the time in the world around us, mostly by St. David of Attenborough on the Galapagos Islands, then either Zeno's logic or our perception must be flawed. Those who would dispute his logic are invited to dismantle his argument by identifying the errors within it. If they cannot do so, asserts Zeno, then the alternative must be admitted: the 'overtaking' we witness must be an illusion, at best a superficial manifestation of an underlying, more fundamental reality.
Perhaps unsurprisingly, Diogenes the Cynic pooh-poohed all of this when he first heard it. Living up to his name, he just got up and walked out, overtaking others as he did so, thereby proving to his own satisfaction the falsity of the proposition.
However, 'stating the bleedin' obvious' has few academic credentials in philosophy departments, despite its iconic status as Sybil Fawlty's specialist subject on Mastermind. Diogenes' stunt didn't really address or identify any logical errors in Zeno's argument, only the conclusion. There was still some explaining to do.
And there still is: attempts by mathematicians and philosophers to resolve the problem of one man chasing a tortoise still provoke animated exchanges on the nature of infinity, the incompleteness of mathematical systems, the limits of calculus and the continuity of spacetime - now that's what I call a fecund paradox!
Zeno then purported to prove that ANY motion we perceive in nature is illusory, a notion that would later inform the Platonic view that our senses can only perceive the reality of 'ideal forms' imperfectly. We only see 'shadows on the cave wall' (Plato), or as 'through a mirror, darkly' (St. Paul). Even today, shadows of particle collisions in a real cave of actual mirrors at the Large Hadron Collider at CERN seem to be darkly confirming the limits of 'knowability' at the most fundamental levels of nature, where all is probability, not certainty. Luckily for us and our survival, though, things seem to be more predictable outside the sub-atomic realm.
Anyway, back to more important things, such as running from A to B: according to Zeno, you must first travel half the distance, and then half the remaining distance (i.e., a quarter of the original), then an eighth, and so on ad infinitum, always having to cover half the remaining distance to B, traversing an ever-smaller slice of distance and time before you can reach the next slice. Zeno argues that there is always another slice, and that you would have to cross an infinite number of slices to actually reach B, which would take an infinite time, and so you'd never get there.
By extension of this argument, nothing can really move at all - 'eppur si muove', as Galileo said of the earth, 'and yet it moves' - so is there an Achilles' heel to Zeno's logic? For some, the advent of calculus resolved the paradox; for others it merely begged further questions hidden in its assumptions.
Suffice to say here that calculus brought in the crucial idea of an end-limit to the slicing process, and then used the mathematics of convergent series to add up the infinite number of these ever-smaller slices of time and distance. As the running totals accumulate, they each seem to converge towards a finite value, so that at the end-limit of this process, we can anticipate a value for the distance covered and the time taken to do so, implying that you DO actually arrive at B in a given time.
We could plainly never actually count the infinite number of slices or add them up, any more than Zeno could, because it would literally take forever, but our mathematical logic claims to be able to calculate their sum where Zeno's couldn't.
Satisfied? - Hmm, I thought not, but let's see if translating these words into maths is any more convincing. If x is the distance required to be covered, and S is the sum of all the parts of that distance suggested by Zeno, (i.e., half of it, followed by a quarter of it, etc.),
then S = x/2 + x/4 + x/8 +............
and doubling each side of the equation would be equally true:
2S = x + x/2 + x/4 + x/8 +......
Subtracting the first equation from the second, it can be seen that all the right-hand terms will cancel out, bar one, and so you are left with
S = x
So the infinite number of fractional distances that Achilles runs through, bit by bit, are logically proven to add up to an amount equal to the total distance required to be covered, whatever it is. Unlike Zeno's logic, ours is at least not in conflict with our perception that he can indeed get past the tortoise.
Note that this subtraction involves the weird properties of infinite series. Even one of the inventors of calculus, Gottfried Leibniz, considered the infinitely large and the infinitely small to be ideal entities 'not of the same nature as appreciable quantities'. It would take Cantor's set theory proofs of the1880's to place the idea of infinity on the kind of solid foundations acceptable to mathematicians. (Limitations of space and intellect prevent me from going into the details of set theory here.)
Most mathematicians seem content to assert that Zeno's paradox has been resolved; they have confidence in the logic of convergence analysis and the notions of infinity that underpin it. We CAN actually traverse an infinite number of slices in a finite time, it seems, and thus there is no paradox, and motion is not illusory. Phew.....Aesop's fabulous tortoise DID overtake the hare (although Zeno would agree that it was because the hare stopped moving forward), and fleet-footed Achilles DID catch up with princely Hector outside the walls of Troy, never mind a tortoise.
For some philosophers, however, it remains a metaphysical problem for which the proposed solutions lack rigour. Wittgenstein, for instance, was sceptical about bringing calculus to the party, mainly because it uses limits to tackle infinity, a word which means 'limitless', while others have noted that Zeno has assumed motion on the part of both Achilles and the tortoise in order to prove that motion is impossible, and so the paradox is there from the start.
Philosopher Pat Corvini agrees that the paradox arises from Zeno's formulation of the problem, which for her is a false syllogism: the statement that Achilles must run through an infinite number of divisions of space is a mathematical abstraction, while the statement that he cannot do so relates to the physical world. The first cannot logically be applied directly to the second to reach a conclusion.
George Lakoff is even more suspicious about mathematics itself, a discipline whose foundations had been shaken by Kurt Godel's 1930's proof that any axiomatic arithmetical system must be incomplete and inconsistent, in that there are always unprovable truths within it.
Lakoff argued that mathematics as a model of reality is fundamentally constructed as much by our imagination as by our reason, neither of which are disembodied repositories of truth. Our biology limits and structures the way we think, even about mathematical abstractions, and we cannot just think anything. We have built complex mathematical concepts and language through metaphors sourced from our everyday human experience of the physical world around us - extension, for instance, or enclosure (subitising would be another example, where you know there are, say, five objects in front of you without counting them). We don't discover maths, we invent it, says Lakoff, and there is no perfect, pre-existing, absolute truth in its logic.
Conversely, and intriguingly for those who consider that mathematics has shown Zeno's ideas to be wrong-headed, the Nobel laureate, Werner Heisenberg, insisted that 'physics is on the side of Plato', adding that nature consists ultimately of mathematical 'forms'. Another pioneering physicist, Max Tegmark, goes even further in his 2014 book, 'The Mathematical Universe': 'Time and physical motion are illusory', he writes. 'Mathematics doesn't describe the universe......it IS the universe', and that includes us. Maths is thus not invented, but discovered, and we are all 'mathemes'.
So, are we the Number made Flesh? 42, maybe? Well, if so, one particular island of reverse entropy created by these numbers and ratios and relationships between quantities became Zeno himself, and his running paradox moved this debate forwards.......assuming such motion is possible, of course.
From Aristotle to Russell, solutions to Zeno's riddle have been proposed without delivering a knockout blow, and modern physics also has something to say about those infinitely divisible slices of time and space. Quantum theory, for instance, places limits on the smallest units measurable (Planck length and time), while relativity theory discourages any inappropriate fragmentation of the spacetime continuum into separate time and space categories.
Applying Occam's razor to shave away the more unlikely theories with the grandest assumptions has often been a mantra in generating scientific hypotheses, but where would you apply it? To the Platonic forms or to the infinity-taming calculus?
Meanwhile, as you ponder that, a 182-year-old giant tortoise called Jonathan still runs around the island of St. Helena today at an average speed of 0.17 mph, having been first taken there during the reign of William IV, a decade after Napoleon Bonaparte had died there. It seems appropriate to end with this photograph of him overtaking a Boer prisoner and his guard in 1900.
Running in Language (Part 1)
Did you know that 26.2 mile races are named after a vegetable? Or that a gym was a gathering place for nudes and scholars? Ever wondered why Nike and ASICS are so called? Or that jogging was done horizontally in the old days?
The rich and often surprising linguistic roots of everyday running words can be traced in the record of their usage, including their metaphorical adoption in everyday speech and the arts. The semantic diversity of running terms used in non-running contexts, for instance, can shed light on the way we form ideas, and philosophers have not been slow to investigate this 'shaping' of our concepts.
Take the word 'run', for instance (seen above in Monica Bonvicini's 2012 sculpture in London's Olympic Park): it is defined as moving faster than a walk while never having both or all feet on the ground at the same time. It is easy to forget how often this word is used in our language in circumstances which have nothing to do with either feet or the ground.
Indeed, they often involve no physical motion at all: we speak of running out of options as time runs out and the bills run up; we run risks and organisations, we run into trouble and out of money. We feel run down, running a fever or a temperature, maybe with runny noses or running sores. Candidates and rivers and tights all run, we have running jokes and totals......and our imagination can run wild, run away with itself and run the whole gamut of emotions!
Many of these examples have, at best, an abstract sense of motion - we can feel we are 'running around in circles' while standing still, for instance. The consequent opportunities for punning have not been lost on comedians: 'Brave men run in our family', quipped Bob Hope in 'The Paleface', while my maths teacher, Mr. Christie, used to tell us to pay attention to the blackboard 'while I run through it again'.
In politics, the linguistic convention that British candidates 'stand' for parliamentary seats while Americans 'run' for Congress has been wryly noted as a reflection of the spirit of each nation, the one insular, static and heavy with inertia, the other pioneering, dynamic and full of momentum. (Discuss.)
Our current running words were brought to these shores by invaders, settlers and classical Greek scholars: after the Latin of the Romans and the Anglo-Saxons' Old English had eclipsed almost all of the indigenous Britons' Celtic language, Norman French dominated for three centuries until a new, confident Middle English emerged. As pronunciation changed and the language lost its inflected nature, i.e., dropped many of its word endings, it evolved into Modern English.
Over the centuries, the figurative use of 'run' has extended the general meaning of physical motion into so many other arenas of endeavour and abstract thought that the word has acquired a new richness as part of a more nuanced everyday language.
The origins of the word 'run' are to be found in two Old English verbs: 'rinnan'/'yrnan' meant 'to run, flow' (intransitive, past tense 'ran', past participle 'runnen'), while 'earnan' was the transitive 'to ride to, to reach by running, etc.'. Both are assumed to have evolved separately from a common Proto-Indo-European word coined thousands of years before, and both have a more general sense of movement than the athletic definition. This has evidently fed into many of the modern metaphors mentioned above.
Beyond that there is no real consensus on how the very first primitive speakers selected and shaped sounds that became agreed by all their peers to refer to that object or this action, although a possible scenario has been imagined: in his script for the 1981 action film Quest for Fire, set 80,000 years ago, Anthony Burgess suggested that a word for 'run' would have been one of the earliest and most essential collaborative signals for the Neanderthals as they tried to survive by hunting animals and outwitting our own Cro-Magnon ancestors - actually, he used two words, 'djan vitrash', meaning 'go quickly'.
The Latin for 'to run' ('currere', past participle 'cursus') gave us our modern English words 'course' and 'current', while 'courier' and 'corridor' came to us via the Romance languages (i.e., ones derived from Latin, such as Italian and French), as did the Spanish 'corrida', a bullfight, originally 'corrida de toros', running of the bulls.
The Exeter Book (c.975 AD) has an Anglo-Saxon riddle that exploits the more general meaning of 'yrnan' in the original Old English:
'I am swifter than he, at times stronger; he is more enduring. Sometimes I rest; he must run on.
I dwell in him forever, as long as I live; if we two are parted, I am doomed to death.'* (answer below)
In time, 'yrnan' had become 'ronnen', past participle, 'y-ronne', and we can see the Anglo-Saxon and Latin influences side by side in the first few lines of Chaucer's 14th century Middle English storyfest, The Canterbury Tales (seen above in a manuscript that Chaucer himself may have supervised).
As the pilgrims gather in spring, the sun appears to lie half way across the constellation of Aries:
'...............................and the yonge sonne
hath in the Ram his halfe cours y-ronne'
Up until late medieval times, the same word was often spelt differently within the same text, although 'ronne' was always pronounced as 'run'. As the need for a standard written language became clear, mostly driven by the requirements of law and trade and disseminated by the new printing, 'run' became the Modern English spelling.
It took a while, though. Shakespeare's First Folio still has two different spellings of the word in 'A Midsummer Night's Dream', for instance. When Demetrius tells his stalker, Helena, 'Ile run from thee', she replies three lines later 'Runne when you will, the story shall be chang'd'. Even in 1860, George Eliot writes of the rural gentry who belonged 'to a generation with whom spelling was a matter of private judgement' in her novel 'The Mill on the Floss'.
By the time of Rudyard Kipling's 1895 paean to stoicism, 'If-', the standardisation of spelling was complete:
'If you can fill the unforgiving minute
with sixty seconds' worth of distance run....'
Three-letter words of one syllable tend to be stable over time, although today's SMS texting language is making inroads into this. Go to four letters and it may be a different story, though, as in the famous catchphrase of comic book hero Alf Tupper, 'The Tough of the Track':
Most runners know that so much about running is in the head. In struggling up hills or long distances, they are running through a psychoemotional challenge every bit as immediate as the physical one. Their brain is screaming 'stop' along with the rest of their body, and this needs to be overridden if progress is to be made. Any thinking during or about running, however, can only use the concepts we each have at our disposal, as expressed in a limited language that has evolved over millennia to form communicable ideas, not least to ourselves.
For many linguistics researchers, cognitive scientists and even mathematicians, evolution of the use of particular words gives insight into the way we conceptualise the world around us. Language enables us to represent to others that which we perceive with our senses and the concepts we form, including abstract ideas, but this begs the question whether the linguistic tools at our disposal determine and constrain the way we think, or vice versa.
In his bestselling attempt to articulate 'What I Talk About When I Talk About Running', Haruki Murakami writes that, for him, running is not merely exercise, but a metaphor, in his case for fulfilling his human potential by 'awakening to an awareness of the fluidity of action itself'.
However, it may be that metaphor has had a more fundamental role in the formation of concepts. The 'embodied cognition' thesis posits that all aspects of our mind are rooted in biology, in our flesh. As a frinstance, the cognitive scientist and linguist, George Lakoff, has proposed that our understanding of the simpler, more familiar interactions of our body with its environment, such as our awareness of space or enclosure, has contributed to an understanding of more complex concepts, such as emotions or mathematics, through the use of metaphors, a kind of mapping of one domain of experience on to another.
Linguistic evidence, combined with experimental and clinical investigations into the neural correlates of mental behaviour, has led to theories about the nature of consciousness itself.
So, 'run' may be just a syllable, little more than a grunt, really, but it has developed from a more general meaning of fast flow, as in a river or reaching somewhere quickly, into scores of nuanced metaphors that enrich the English language.
American poet Emily Dickinson wrote a line about 'the undeveloped freight of a delivered syllable', the half-grasped meaning, but it could be equally applied to the multiple meanings of 'run'. Remember this the next time you are running up hills or bills while feeling run down, or running across a large semantic field.
* The answer to the riddle: a fish in a river.
In part two of this exploration of running language, which will follow hard on the heels of this one (whoosh, there goes another metaphor), you can read about the origins of common running terms.....and find out the explanations for the introductory teasers left hanging here.
Running in Language (Part 2)
Our exploration of the etymology of common running terms continues, beginning with an explanation of those teasers in part one:
MARATHON - from the Greek word for 'fennel', derived from others meaning 'grow thin', a supposed property of these bulbous herb vegetables.
Marathon is a coastal plain to the east of Athens and its fennel fields were the site of the famous battle against a Persian invasion attempt in 490 B.C.. From here the legendary courier, Pheidippides, ran the 25-odd miles over the hills to the capital to announce the Athenian victory, after which the city's women would weave fennel-stalks in symbolic commemoration.
Nearly 2,400 years later, at a time when Classics was considered to be an essential part of education (and coincidentally when fennel, as an ingredient of absinthe, happened to become trendy in bohemian culture), the organisers of the first modern Olympics in Athens in 1896 were inspired by the tale to hold a 'marathon race' covering the same route.
GYMNASIUM - from the Greek 'gymnos', naked, and 'gymnazein', to exercise, literally 'to train naked'. When Homer Simpson passed a sign saying 'Gym' while out jogging, his attempt at pronouncing this strange word - 'Geim? What's a geim?' - at least got the original hard 'g' right.
Greek athletic competitions were held in the nude, both for aesthetic reasons and as a tribute to the gods (and in some cases to confirm the gender of the athlete). As the Greeks recognised the relationship between athletics, health and education, gymnasia also became places of intellectual pursuit: Plato's Academy and Aristotle's Lyceum were both gymnasia, while Galen and Hippocrates would emphasise the medical importance of gymnastic exercise.
The academic sense of 'gymnasium' as a secondary high school persists in Germany and other European countries, while nudity in gyms doesn't. (Discuss.)
NIKE - the American sports company changed its name in 1971 from Blue Ribbon Sports to Nike, the winged Greek goddess personifying strength, speed and victory. Her figure inspired the designs of the famous emblems of both Rolls Royce cars and Honda motorcycles, as well as the original football World Cup, the Jules Rimet trophy.
'Nike' is the Greek word for victory and the root of the name Nicholas; it was uttered by Pheidippides in his dying breath after his epic run from Marathon.
ASICS - the name of the Japanese sportswear firm is an acronym for Anima Sana In Corpore Sano, Latin for 'a healthy soul in a healthy body', derived from a phrase of the Roman satirical poet, Juvenal.
JOGGING - from the Old English 'sceacan', to move the body or a part of it rapidly back and forth, Middle English 'shoggen', to move with a jerk. The modern words 'shake', 'shock' and 'shag' also appear to have derived from these, but the modern sense of jogging seems to have come from its17th century use to describe the jolting gait of horses being exercised.
FOOT - Old English 'fot', plural 'fet'. The foot unit of length is an example of the way early units of measurement were often based on parts of the human body and named after them, in this case from the supposed average foot length of Anglo-Saxon men.
As an indication of the stress patterns or syllable length in poetry, the metrical foot was taken from music, probably from keeping time by tapping the foot (not to be confused with the Napoleonic metric foot, defined as a third of a metre). The Roman poet Horace berates mediocre poets whose 'verse runs on tender feet', while his Greek contemporary, Meleager, claims to have taught his muse 'to run on barbed feet'.
The phrase 'My foot!' expressing a contemptuous contradiction was a twentieth century euphemism for the previously common 'My arse!', although ten minutes in the company of either The Royle Family or my family would seem to indicate that the latter has made a comeback.
'Footing the bill' comes from the Victorian practice of tallying costs and writing the total at the bottom, or 'foot', of an invoice.
ATHLETE - Greek 'athlos', contest; 'athlon', prize. The Old English term was 'plegmann', play-man (glad that didn't stick - 'And the World Plegperson of the Year Award goes to.....').
RACE - Old English 'raes', a running, a rush.
PACE - from the Latin 'passus', stride, from the past participle of 'pandere', to stretch. The meaning of 'rate of motion' first appeared in the 13th century, while 'pacemaker' was first used in late Victorian times to mean a rider or boat that set the pace for those in training.
RUN - (see previous blog article)
In other languages:
RUN is the indigenous name of a tiny Indonesian spice island, 3km x1km, which played an extraordinary part in English history. During the reign of James I, it became the first English overseas colony, precipitating many battles with the Dutch over the valuable spices to be exclusively found there, especially the nutmeg and mace.
Now part of the Banda Islands in modern Indonesia, it was ceded to the Dutch at the Treaty of Breda after the Anglo-Dutch Wars in the mid-1600's. In return, the Dutch handed over the island of Manhattan, including New Amsterdam, which had been occupied by the Duke of York (the future James II), hence the city's new name, New York.
So, Run for New York - a fair trade? Ask the indigenous peoples: Manhattan had been bought from them for $24, while Run was simply....well, overrun.
Having run the Marathon marathon, I'd quite fancy a Run run......
RAN, the Japanese for 'chaos' or 'rebellion', is the title of a 1985 Akiro Kurosawa film based on Shakespeare's King Lear and Japanese legends.
RAN is also the Old Norse name, meaning 'sea' or 'robber', of (you've guessed it) a sea-robber in the Icelandic Eddas of Scandinavian myth, a goddess who was a literal fisher of men.
RÚN is the Irish Gaelic for 'secret'.
COURSE - (see previous blog article)
STADIUM - from 'stadion', the ancient Greek unit of distance measurement used for footraces. The running track at Olympia was one stadion long at just under 200 metres.
In the King James Bible, 'stadion' was translated from the original Greek of the gospels as 'furlong', a similar English distance which is still used in horse racing - it had originally been the approximate 'furrow length' that oxen could plough in a field without resting. Luke 24.13 describes how, after the Resurrection, two of the apostles "went that same day to a village called Emmaus, which was from Jerusalem threescore furlongs".
In English, 'stadium' came to mean 'running track' in the 1600's, and had acquired its modern meaning by the early 1800's.
CHAMPION - in the context of combat, the Latin for 'field' is 'campus', and this fed into the Romance languages - hence the French 'champion' for a combatant, as well as the plurals favoured by chanting football fans in the Italian 'campiones' and Spanish 'campeones'.
The archaic feminine, 'championess', is found in English writing such as Edmund Spenser's epic poem, 'The Faery Queene', Samuel Richardson's 1748 novel, 'Clarissa', and Charles Kingsley's distinctly non-PC adventure story, 'Westward Ho!' (which has a Devon town named after it, exclamation mark and all!).
WALK - Old English 'wealcan', to roll, toss, move round. A walker was someone who 'fulls' cloth, i.e., treads on it to clean and thicken it (in Latin, 'fullare'), hence the common names Walker and Fuller. Running over a trace or scent to spoil it thus became the Middle English 'foilen', to foil.
SPRINT - from the Scandinavian root, 'sprenten', to spring, dart or leap.
BOLT - from the Old English 'bolt', a short, stout arrow.
AGONY - from 'agon', Greek for 'assembly for a contest'.
HIPPODROME - from the Greek 'hippo' ('horse') and 'dromos' ('course'), as used in chariot races; the name was used in modern times for places where circuses were held, and later for theatre. 'Dromeas' means 'runner'.
OLYMPIAD - the period of four years between successive ancient games held in honour of Zeus at Olympia. The word derives from the genitive of 'Olympia', 'Olympiados', and was used by the ancient Greeks to date historical events.
Zeus is the father of the gods - his Roman name is Jupiter, from 'deus pater', literally 'god-father'.
There have been many writers who have strung some of these running words together to great effect, but perhaps none more elegantly than the man described by George Orwell as 'almost as good a novelist as it is possible to be.......while holding untenable opinions.' Running Muse will be looking at what he made of a particularly eventful athletics meeting next week (see here).