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It’s one of the great philosophical puzzles of all time: given a square of a certain area, how do you construct from it a circle of equal area using only compass and line? The truth is you can’t. This was proven by Ferdinand von Lindeman in 1882, but it hasn’t stopped people from trying, even to the present day, the reason being it’s more than a geometrical puzzle.

Philosophically, we think of the earth and all things in it as the square, or the plane of existence, while the circle represents the whole, the unity, or heaven. And while geometry can measure out most things, the one thing it cannot do is provide a construction that derives heaven from the profane dimensions of the earth. The nub of the problem lies the strangeness of Pi.

At first glance Pi is a beguilingly simple number, the ratio of a circle’s circumference to its diameter. Divide the circumference by the diameter and you get 3.14159,… etc. The problem is “etc” is currently up to thirteen trillion places, and counting. The more we chase it, the further away it gets from us.

We assume from the evidence so far that Pi is an infinite and non repeating series, a transcendental number. It cannot be derived exactly by ratio, or by formula which means you can’t get to a circle equal in area to a given square, either by line and compass, or by supercomputer.

Or can you? Is there no intersection of line that gives us the radius of that circle? Can we not project it from the walls of the square? Might it not lie in inscribed circles? Can we get at it by projecting points of tangency? How about introducing other squares formed in harmonic series from the root square? Can we get projections from them?

Well,… no. Not exactly.

There are some very good approximations which the old philosophers must have had high hopes for when working within the accuracies permitted by actual line and compass. It’s only when we use computer aided design we get to zoom in and these constructions reveal their flaws. Then we stare through the gaps, not into the infinite void of Heaven, but at our own imperfections.

In my current work in progress, a guy drives himself nuts trying to square the circle. He represents the worst of our egoic tendencies, and he just can’t let it go even though it reduces him from a respected intellectual to the level of a suicidal crank. But he’s since had his revenge on me by having me fall under the spell of the conundrum myself. Yes, I know it’s impossible, but there’s still something beguiling about those approximations, at least to someone who grew up on Euclid and worked for a time on a drawing board with compass and line. I still have those compasses, forty years old now, and rendered obsolete some time around 1985 but there’s a definite beauty to them, also a creative potential, so I like to keep them clean out of respect, even though I rarely actually use them.

I stumbled across the approximation shown above, not with compasses, but with LibreCAD. I’m sure other would-be philosophers have found it too – I mean it’s hardly subtle. Indeed it’s a very simple and elegant construction that gives an answer accurate to within 0.13% of area. That sounds pretty good, but if you play the sums backwards, it yields an equivalent for Pi that’s only correct to the first two decimal places, so we’re a long way from attaining philosophical, spiritual or even just plain old mathematical transcendence.

What all this has to say about the human condition is that, at our worst, we can be self destructively pedantic in our quest for perfection, while at our pragmatic best we recognise a good approximation serves equally well.

This one’s a bit better – 3 decimal places:

pi

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group of friends hanging out
Photo by Helena Lopes on Pexels.com

Okay, so that title’s a bit tongue in cheek. I’ve no idea how to market a blog, other than by writing one, updating it a couple of times a week and poking around among other blogs and reading and following the ones I like. That’s blogging, and there’s no quick fix for a DIY hack. I’ve been at it ten years and it is what it is. I tell myself I’m a misanthropic old curmudgeon who doesn’t give a damn if anyone reads me or not, but that wouldn’t be true. I do like to know if people are reading me.

WordPress says I have 564 followers at the moment, which sounds a lot, but we must bear in mind only about twenty percent of those are really following and reading – the rest are just dumb barnacles stuck to the bottom of my boat, trying to sell me stuff, or people who have no interest in my writing and write “lifestyle” stuff and just want me to follow them back. This has to do with the Pareto principle, also known as the law of the vital few. But that still means I’ve got the ear of a hundred or so, and that sounds pretty good to someone who started writing in the days of typewriters and double lined manuscripts and lots and lots of rejection slips.

You can apply Pareto to all sorts of things, such as for instance how, in any organisation, twenty percent of the people do eighty percent of the work and how twenty percent of the people in the world hold eighty percent of the wealth, and so on. Now that’s all well and good, but when you see your blog hits have been declining over the past five years, you start to wonder if you’re missing a trick in not applying all the whizz-bang tools of the trade at your disposal, so to speak,… namely that odd bird: Twitter.

I’ve had a Twitter account for ages, but never really got the hang of it. Twittering seems to me like uttering a mumbled phrase or two in a room filled with a braying crowd, all of them slightly off their heads. It’s very unlikely anyone’s going to hear you. You’re just going to get drowned out by the noise, unless of course you single someone out and call them a dick-head, as many do of course, and cause a fight, but at the cost of the inevitable loss of your virtue.

Anyway,… by way of experiment I decided to give it another go and I’ve been tweeting all week, five to ten times a day in fact, just shooting out links to the blog and my books on Smashwords and Wattpad. And now, come Friday the results are in, and guess what?

1) Twittering like a canary all week attracts zero genuine visitors.

2) Twittering about your writing all the time takes a lot of effort and stops you from writing.

3) Twittering out links to your blog as a means of self marketing means you get a lot junk-blogs coming back at you trying to sell their marketing services, as no doubt will that marketing tag I’ve attached to this blog.

So, in conclusion, I remind myself, if you like blogging, which I do, then blog. Write your blog however the hell you want, and follow the blogs of others whose writing you like, because there’s a lot of good stuff out there, original, meaningful, soulful,… well, twenty percent of the time anyway, and that’s about the top and bottom of it. If the stats tell you your blog’s in decline or never gained any traction in the first place, live with it, or give it up. If you can’t give up, then don’t.

If you’re reading this, you count as one of my vital few, and you’re very welcome, so pull up a chair.

Fancy a cup of tea?

How’s life been treating you?

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Jepsons stone

Standing stone – Western Pennines – Nikon D5600 f5.6 1/650 Sec 125 ASA

There are no standing stones on Standing Stones Hill any more. We don’t know what happened to them, nor how many there were. There’s a story told by an old rambler of finding one fallen and half sunk in the peat of the moor – this would have been in the 1950’s – but I’ve spent a long time searching ever since and found nothing. Another story has one of the stones re-purposed as a lintel in a barn. But the nearest farms hereabouts were all dynamited in the 1920’s by Liverpool Corporation, then further bombarded as target practice by mortar and tank shells in the Second World War. You might say the hill has lost its original story then, is now mute and purposeless, except as a vantage point on waste and corruption, that while these more recent stories of the hill are not without local interest, it seems all stories, even the big ones come with a sell by date and, without adequate renewal, they lose their meaning and their purpose.

There are other stones on the moors, but none officially of Neolithic origin. You sometimes find them lurking in long runs of drystone walling. This way they escaped the rampage of pious vandals pedaling their own mendacious tales in more recent centuries. But the walls are hundreds of years old now and falling away to reveal these curious artefacts, and though their original stories have long since timed out, fresh ones begin leaking, all be it hesitantly, into consciousness. Are they not Neolithic? More medieval perhaps? Are they boundary markers? Hard to say, yet potential stories circle them like bees around a hive – it’s just that no one’s there to listen to them.

Your genuine Neolithic standing stone tends to show a lot of weathering, and not much by way of tooling. They tell us someone was here before us in this remoteness, that they had a purpose, now lost, yet perhaps these people knew something we do not. Lacking explanation though, we invent stories to fill the void, but they need a certain spark to truly catch fire, to make a difference and actually,… mean something.

The upright stone in the picture, above, is a fascinating one. It’s a few miles away from Standing Stones Hill, on the edge of the Western Pennines, yet has a good view of it. It  has more of a pillar-like shape than I’d expect of a truly ancient megalith and, though there is considerable weathering and little evidence of tooling, I’m not confident in stating its pedigree. However, its location on this outlying ridge, and its stunning sweep of the horizon, does grant it an impressive presence, all be it mute to its own past. But whether it’s truly Neolithic doesn’t matter for my personal purposes, which are those of paying homage to something immutable and notable, a thing to set ones bearings by, and of course from which to spin this, my own story. Stories are our life’s blood. They regulate the heart, they grant structure and bring calm to the stormy mind. But we need to be careful, because stories can also do immense damage.

The grand, overarching story of human history is that of suffering, of decay and renewal: a new king, a new idea, a new  myth arrives amid hopefulness at the banishing of the old, corrupt order. There is a fanfare and celebration, ushering in a renewed period of peace and plenty. But then the king dies in his turn, and his dynasty becomes corrupt, so a new challenger arises, a new king, a new story,… and so the cycle repeats.

We are living towards the end of one such story-cycle. The time of peace and plenty is over, and corruption dominates. The king is dead, his dynasty rendered ineffective by a mixture of inept and craven officials whose own paltry tales, void of hope, of imagination, are singularly evasive of necessary change, and they ring hollow in people’s ears. So the people turn away in despair, huddle into splintered groups, each inventing its own story in order to see them through, as one might light a candle against the immensity of endless night. And they hold to this guttering light against all reason, because a story, even if it’s a pleasing lie, will always trump the truth, if truth itself does not come with a more convincing story of its own.

This standing stone is an immutable reminder of the abiding reality of human existence, it being marked largely by suffering of one sort or another, and without a story to tell, that suffering has no meaning and human life is pointless. But individual stories are all well and good. I could invent a myth for my standing stone and it might entertain me for a while, get me from breakfast to bedtime, but it’s hardly likely to provide sufficient nourishment for anyone else. To sustain the coming generations we need a much bigger story to rescue the abiding fact of our existence from barbarism, and worse, from oblivion. We need an epic story, one that restores hope and meaning for everyone who calls these islands home, a story that rises above the mere venting of these old white-mens’ foetid spleens, a grim fact of the end-game that is such a feature and a stain upon our times.

Ideas anyone?

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the night sky
Night sky, Panasonic Lumix LX100 F1.7, 1 sec, 1600 ASA

It was probably winter when my father first showed me the bear. I would have been about nine, confused already, dazed by the world and feeling secure only in his company. I remember a winter sky, cold and black, the stars iced-white and my breath fogging the eyepieces of the Russian 8×24’s that were his pride and joy – though cheap as chips back then, the poor old Soviets already selling their souls for dollars amid a collapsing economy.

Prior to that his night-sky explorations had been aided by a pair of British-army cast-offs, circa 1912. I still have them, the stout leather case still smelling like new, but they were only marginally better than the naked eye. I don’t know what happened to those Russian bins. I think they got dropped, the prisms dislodged to produce a disconcerting double vision, and then my father died, and the night-sky didn’t seem important any more, not for a long time.

“You see that star there,” he said. “That’s Mizar. It forms a double with another star called Alcor. Do you see them both?”

Yes, I could indeed see both in those days, but that was half a century ago, fresh eyes, fresh mind, fresh soul.

“The Arabs used to say if you can see both,” he said, “if you can separate them, you have the gift of perfect eyesight.”

Really? That cheered me. I don’t think he realised how much. In father-son relationships, the smallest things can mean the most.

Nowadays, even with spectacles, and the optician assuring me I’m 20-20 when I’m wearing them, I can’t separate Alcor and Mizar any more. Eyesight is more than perfect lenses. It has to do with the mind as much as matter, and there’s something about that old Blakean thing about seeing through, not with the eye as well. But I do remember their names: Alcor and Mizar.

Now I’m sitting out in the back garden of my home in the rural north west of England, on a crazily warm, late September night. It must be twenty degrees still, and the sky is a soft midnight-blue, the air infinitely more inviting than those freezing stargazing nights with my father, back in the sixties. I am resting on a bench in shirt-sleeves, after a long day in the sun, and as the stars come out, I am thinking about him.

There’s a bright star directly overhead. I wonder what it is, point my phone at it and, via the Star Walk app, I learn it is Vega. Just like that! Marvellous isn’t it? I’ve heard of Vega, but try as I might it does not fit into the patterns I have fixed in my mind, patterns like the Bear and Cassiopea, and the Square of Pegasus and from Pegasus that simple route-map to Andromeda which still astonishes – that softly defined spiral that grows as the eye adjusts to darkness until it seems to fill half the sky and you wonder how on earth did I miss that: another whole galaxy, so many stars it blows the mind, and surely also so many lives,… out there.

No, try as I might I cannot separate Alcor from Mizar any more, except through binoculars – not those 1912 vintage things, though I suppose they would do, but a pair of cheap Chinese 10×42’s off Ebay, product of another era, another quirk of the global economy. Such a long time since the British made binoculars. Such a long time since we actually made anything.

The Rider, that’s what he called Alcor,… the Rider. One star riding upon another, as a man rides upon a horse,…

My father was an autodidact, self taught to a prodigious degree and in many disciplines, a collector of disparate technical knowledge, everything from electronics to geology to archaeology and ancient astronomy. His energy and enthusiasm had carried him from the coal face of the NCB to colliery deputy, about as far as a working man could aspire in those days, and much further than it would carry him now. But more than that, it always impressed me that other boy’s fathers did not know the names of stars, indeed barely ever glanced upwards on a clear night and wondered. But when my father saw the stars, he did not see them as an astronomer, aching to have the next comet named after him, but more as an early human might at the dawn of our most fundamental awakening, and simply wondering at his place in the world.

Betelgeuse – that’s the reddish star in the shoulder of Orion. Orion isn’t up tonight – he’s a winter constellation in western Europe, frosty nights and all that, and the deeper into winter you go he’s trailing the bright sparkly dog-star, Sirius – more names my father gave me, names with vivid pictures; the magic of myth. How neatly, how perfectly it all fits the contours of the mind. I still look for those names in the night sky, gain my bearings from them, my place in time.

Vega, was it? That star up there. So the app said, but it comes without a story, slips free from memory. I could look for it tomorrow but I’ve already forgotten its place in the sky. Technology advances, grants such a narrow window on the marvellous, but without the human element, the imagination, the story, these are dead things.

My garden is a wonderful place at night, spacious, lush green lawn, and unlike the place where I grew up, not overlooked, no neighbours wondering what the hell we were up to,  lurking about in the dark with binoculars. He would have loved it here, my father. He would have built a shed in it with an articulating roof to house a reflecting telescope. I smile when I imagine it. In its place I have a cabin where I sometimes write and explore the stars another way. But not tonight. Tonight I have lanterns hung out on hooks to stretch out this last gasp of summer, an Indian summer’s night, and since I am otherwise alone, I have the company of my father.

We’re not far from the equinox, he reminds me. That’s where the ecliptic plane intersects the horizon due east and west, spring and autumn, the line on which the Sun and the Moon and now the planets are strung out one by one and sink west, into tomorrow. Due west for me is an old oak tree, across the meadow that backs onto the garden. It was probably just a sapling when Newton was a lad. So much learning since then. It was his laws of motions that navigated men to the moon, and by that time the tree was old. I don’t know what it means, if anything.

There’s a star or something, just about to dip behind the tree.

“Neptune,” says my father.

Well, I don’t know. It might be. It’s a planet, that’s all I can say for sure, and I know that because he taught me you can resolve planets to a disk through binoculars, while stars are so far away – at least they were back in the sixties – that you could only make twinkly points of light of them even through the most powerful optics known to man.

I point my phone at it. “Yea, Neptune.”

“That’s amazing,” he says.

“Not really,” I tell him. “You used to explain it a lot better, tell it as a story, then it actually meant something.”

Tonight I’m no longer much, much older than he was when he told me these things. I’m not a man with a house and grown children, and forty years of work behind me, years of my life he never knew about. I’m just a kid, staring up at the night sky as it deepens and the stars twinkle softly, and I am looking at the Bear once more, with my father.

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Themagus_cover.jpgNick Urfe – young, middle class, self-loathing, classically educated prig and womanising misogynist finds escape, and half hearted employment teaching on a remote Greek Island. Here, he meets the wealthy recluse and aesthete Maurice Conchis who befriends him. Also living under Conchis’ protection is the mysterious and ever so winsome Lilly, with whom Nick falls in love. So far, so predictable then. But that’s your first mistake, and there will be many more if you try to second guess this outrageous labyrinth of a novel.

In short, Nick finds himself way over his head at the centre of a dark psychodrama in which he seems to be acting a part among a cast of other baffling, shape-shifting characters, with Conchis as director, manipulating him at every turn. Meanwhile Lilly transforms from one role to the next, becomes Julie, or her twin sister June, all of them leading Nick on, drawing him into deeper intimacy, then pushing him away. Does she really have feelings for him, or is she always simply acting the part Conchis has written for her? Who is the real Lilly/Julie/June anyway? Who is Conchis? Just when Nick begins to think he’s worked things out, and us with him, Conchis changes the narrative again,… reveals all that went before was a lie.

To what end are we playing this game is, of course, the question. Perhaps there is no end in the normal sense, and if we cannot trust the narrative why should there be a reliable end anyway?

As we, the reader, like the hapless Nick, are drawn ever more deeply into Conchis’s web we begin to wonder if the story is actually a psychological metaphor of the state of our own selves. Although at times inscrutable, like Conchis himself, this makes for an unsettling, disorientating and at times disturbing read. Hailed as an example of post-modern literature, The Magus shatters the accepted norms of story-writing where a protagonist works towards some goal and, in voyeuristic fashion, the reader simply follows along in the background to be gratified by a conclusion, neat or otherwise. Reading the Magus, Fowles drags us in with him, cautions us at every turn against trusting the story. Indeed, its occasionally ad-hoc nature has us wondering if he’s not just making it up as he goes along, that, like the Magus, he’s bamboozling us, with smoke and mirrors and none of it means anything other than what we project into it ourselves.

Peppered with psychological and mythological references, the story shifts from present to historical flashback, at times dramatic, erotic, horrific, and all of it quite possibly absurd. There is always the feeling here that if only I was as intelligent as the writer, and the critics who have lauded the story, I would know the difference; I would know, like Nick wants to know, if I was merely being taken for a ride, or if there was some point to the experience, that Conchis is more than simply a fraud at best, and at worst a dangerous psychopath.

Nick returns to England, penniless, disturbed by his experience, but seemingly also deepened by it. He’s more self-reflective, kinder to others, but like him we’re left wondering, waiting for a conclusion that never really comes, which suggest that if the story is indeed some kind of psychological experiment and we’ve come some way along the road to recovering our potential as a decent, self-aware human being, the final step is up to us. Nick is not the first young man to experience The Magus, and he won’t be the last,.. but who truly benefits? The subject, or Conchis?

Read as a straight novel, the main problem with the plot as “psychological experiment” is that nobody warrants that much elaborate attention, and former victims (or subjects) having been so abused and humiliated by Conchis in the process would probably be inclined to return to his island with a machine gun. Except angry loathing and a desire for revenge appear not to be a side effect of Conchis’ methods, just as the reader is left feeling disorientated, breathless and none the wiser, but rather more thoughtful and certainly not resentful of the time spent on this compelling, but ultimately bewildering labyrinth of a novel.

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The story of Dylan Thomas’ life provokes as much discussion as his poetical works. Subject of much myth-making, and many a biography by those who knew him, and others who claimed to know him but did not, his oft-times stormy character certainly left its mark on the poetry-world of the mid twentieth century. But for me his story is also a cautionary tale, granting insight to the near impossibility of making a dignified living by the arts, and worse, that sometimes to be blessed by a prodigious talent can also be a curse, one that more or less guarantees a premature and ignominious end after an all too brief a life of tortured insecurity.

Director Andrew Davies here picks up the story in the last year of the poet’s life, with Thomas, played by Tom Hollander, having been invited to New York by fellow poet, critic and admirer, John Brinnin, played by Ewen Bremner. He’d been to New York before, but seemed to have earned little from it, and was tempted back on this occasion with promises of a more lucrative collaboration with the composer Stravinsky.

Background biographical details are penciled in for us by flashback, though slanted overly towards a bucolic penury in rural Camarthenshire, centred around the famous boathouse at Laugharne. That Thomas also had a property in London, where he lived and worked extensively, especially during the war years, is blurred out in order to focus on this final, fateful, and largely self destructive episode, contrasting the beauty of this part of Wales, with the boozy squalor of New York .

His many biographies reveal a complex and, at times, disagreeable character, prone to drink and philandering, a man who could treat those around him appallingly. Yet he was also capable of great kindness and possessed of a certain sweetness, exuding an air of vulnerability and helplessness that the women he encountered found irresistible. It seemed he had only to be away from home for a moment to pick up another lover.

For all of his philandering though, the one true and somewhat stormy love of his life, was his wife, Caitlin, a woman possessed of a wild and fiery temperament, here plaid by Essie Davies. Sadly, they were not well matched, and in their later years she became for Thomas a woman he could neither live with nor without.

So, it’s November 1953 and he arrives in New York, a chain-smoking alcoholic, vulnerable, and burnt out. He sweats and vomits though readings of his work, suffers blackouts during rehearsals. He attends parties, celebrations, presses the hands of New York’s literati, regales them with his bonhomie, woos his audiences with dramatic readings of his work, but underneath he’s a man adrift, stricken by the recent death of his father, and unable to return home to his chaotic marriage. We have the impression he’s taking refuge, deliberately courting death, and indeed not so slowly killing himself with drink.

By turns dramatic, deeply moving but also funny, I felt the film did a fine job of presenting us with as dignified a portrait as possible of such a complex and difficult man, a man who’s flaws seemed very much on the surface of his being. I’m sure there’s nothing here that would disappoint even the most critical Dylan Thomas admirer.

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iateol cover second smallA dystopia is a nightmare vision of the future. It is Orwell’s 1984, it is Huxley’s Brave New World, it is the shock of what might yet be, and therefore, like the future itself, never actually arrives. Yet the world of 2019, would have seemed dystopic had we seen it coming in the 80’s, and though the 80’s were by no means the halcyon days, there is still a certain innocence attached to them, give or take the threat of mutually assured destruction. But there were no surveillance cameras perched on every conceivable vantage point, watching ordinary people going about their business, no cameras reading faces and putting names to them and we did not all willingly carry portable tracking devices that could read our minds and influence us by subliminal suggestion. Nor did we have governments willing to suspend the workings of parliament in order to push though controversial policies that might easily threaten our health and well-being.

As sinister as all that would have sounded in the 80’s, it’s perfectly normal to us, living now. We are it seems, an eminently adaptable species and this is perhaps one reason for our evolutionary dominance. We readily adapt to hardship, even those hardships we have created for ourselves, or are inflicted upon us by our fellow man. Today’s outrage is tomorrow’s normality. Yet we go on as if the ever more brutish externalities of our existence are of only secondary importance, for surely otherwise we would do something about them, especially when they start to hurt.

Many of us have long been conscious of a certain pathological polarisation in world affairs, fuelled by the rich man’s ever more desperate scramble for loot. This has led in turn to a Zeitgeistian volatility, aided and in large part amplified by our networked communications technology, a thing that can make a deafening amp-squeal out of even the most trivial dissent, or which can be used to distract us with candy from the contemplation of things others – the data-barons and their masters – would rather we ignored. In the UK, where I live, this volatility has of late of course been focused around the closely contested and highly controversial referendum to leave the European Union. In the three years since the vote, it has caused untold division at every level of society, unleashed the most intemperate language, and ushered in an era of utilitarian, political chicanery like nothing else I can remember.

Personally, I view it as a disaster on many fronts, and it has undoubtedly coloured my fiction writing. My current novel, The Inn at the Edge of Light, follows the life of a man from his twenties, in the 1980’s, through to old age, and his journey into a near distant dystopia, a future not too difficult to extrapolate from current trends. Needless to say his externalities do not improve much with time, but that he weathers such things so stoically shows what truly drives us are the same things that have always driven us – a place of our own to call home, freedom of relationship, of love, and something else, something irrational that gives us hope in the face of adversity, that even at the eleventh hour as the hangman approaches our cell, we hold out for a miracle, a last minute reprieve. Better still we shrug and say it doesn’t matter, that the truth, the essence, the meaning of our lives lies elsewhere.

There’s nothing I can do about the constitutional crisis, a thing so freely heralded this week from all but the usual swivel-eyed right-wing orifi, who, on the contrary, consider it all fair play and a bit of a wheeze. Yes, I can sign the petitions, register my objection, refute here and now, and even with touch of spittle-flecked vehemence, the somewhat condescending Moggian accusation of there being an air of “confection” in my dissent. But having done all that, I then turn back to seek a more soothing music in my words, and in the archetypal chatter in my head, and the ever beguiling images of my dreams.

At what point do we wake and realise we’re living in a dystopia? The truth is we never do, and anyway by the time it’s arrived it’s already too late to do anything about it.

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