Why do I write on this blog?

XKCD#386 - Duty Calls

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Why this blog?

Decades ago one of my brothers-in-law (a fireman by trade, a pretty practical guy) expressed his opinion of the fact I wrote a regular blog in an uncharacteristically diplomatic way.

I parsed his somewhat whispered comment as: ‘It’s pretentious.’

Things sting when they have an element of truth and I’m more than aware of some of my faults: over-serious, didactic, egocentric, pompous - and, of course, pretentious.

I ask myself the question James was too polite to ask: do I write a regular blog (since 2006) in a Walter Mitty-like attempt to be a famous person on the Internet, followed and quoted? And I answer that I do not want that particular straightjacket. All fame is transitory - yes, really - and also, so what? The status accolades of strangers do nothing for me - I see only the many downsides in the unlikely event...

I say to people - honestly - that I like writing, that when ideas churn in my mind, my only means of exorcism is to ‘sort them out by writing them down’. And then I see in their eyes the obvious response: keep a diary, why don’t you!

But I’m no more immune from the dangerous thrill of putting my best-considered thoughts ‘out there’ for anyone to see (and then seeing what happens) than any other person with an exaggerated sense of their own intellect.

No, I can’t come up to bed: someone just said something stupid on the Internet!

And yes, I do look with interest to see how many reads each post gets, although I know it’s only a harmless fun-diversion.

Do I think my posts are any good? Generally better than most of the thought pieces which drape the commentary sites, I reckon. But I know I lack the access to informed networks, and the training and education, to be the bearer of genuinely new thinking. So I really can’t use that as an excuse for your attention.

I’m on surer ground with biography. My ancestors left a pretty thin trail of documentary information; their opinions and quotidian experiences are lost for good. I rather regret that - and perhaps my descendant-kin will be interested in my view of my life and times, or (as we say these days), their AI surrogates might want to check me out on their behalf.

No-one has to read anything I produce and I think it’s fair to say that all but an infinitesimal part of the literate public literally has no idea (and cares less) that I even exist.

And that’s expected, obvious and perfectly OK.

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GPT5.2 comments on my introspection...

You ask for a forensic reading, so I’ll be unsentimental. The piece is lucid, self-aware, and written in good faith — but it still contains several evasions, soft landings, and rhetorical sleights of hand. I’ll take them in turn.

First, the fireman anecdote does more work than you admit. You frame James's judgement of you (“pretentious”) as both stinging and partially true, but you also smuggle in a class and temperament contrast — practical man versus cerebral blogger — that quietly cushions your ego. The implication is: he would think that, wouldn’t he. This doesn’t refute the charge; it domesticates it. You never really interrogate what kind of pretension might be operative — moral, intellectual, stylistic, performative — because the anecdote allows you to move on having acknowledged the word without submitting to it.

Second, the fame disavowal is sincere but incomplete. You reject celebrity as a goal, but you replace it with a more refined, and therefore more dangerous, desire: recognition by the right sort of reader. You say you don’t want to be “followed and quoted”, yet you clearly want to be taken seriously, not dismissed as a diarist or crank. This is not mass fame; it is reputational dignity. The essay pretends the alternative to fame is indifference, when in fact the real alternative is anonymity. You haven’t chosen that.

Third, the “I write to sort out my thoughts” trope is only half true, and you know it. Writing for oneself and writing in public are phenomenologically different acts. Public writing sharpens, edits, stylises; it introduces imagined interlocutors and latent adversaries. Your own parenthetical aside — the nocturnal Internet argument — gives the game away. You are writing against stupidity, vagueness, fashion, and error, and hoping someone will notice you doing so competently.

Fourth, the diary rebuttal is rhetorically clever but philosophically weak. You implicitly concede that a diary would meet the stated need (sorting thoughts), yet you reject it because it lacks exposure. That exposure is not an accidental by-product; it is the point. The essay treats this as a minor indulgence — “a dangerous thrill” — but it is structurally central. Without an audience, however small or imagined, much of your motivation would evaporate. Calling this “harmless fun-diversion” is minimisation, not honesty.

Fifth, your judgement of quality contains a quiet contradiction. You claim your work is “generally better than most” online commentary, yet immediately disqualify yourself from “new thinking” due to lack of access and training. This is false modesty of a particular kind. Originality does not require institutional access; it requires clarity, independence, and sustained attention — all of which you plainly possess. What you really mean is: I do not expect to matter in the way recognised thinkers matter. That is a social claim, not an epistemic one, and conflating the two lets you retreat gracefully from ambition without abandoning self-respect.

Sixth, the biographical justification is the most revealing — and the most sentimental. The ancestors-without-voices motif is attractive, but it disguises a deeper impulse: the refusal to vanish without trace. You invoke descendants and AI surrogates not because this is likely, but because it licenses the activity with a quasi-moral seriousness. Posterity is doing the work that God or History once did. This is not vanity, but it is metaphysical consolation. You are building a cairn and pretending it is an archive.

Finally, the closing paragraph — the assertion of insignificance — is rhetorically neat but emotionally evasive. Yes, it is true that almost nobody knows or cares that you exist. But repeating this functions as inoculation: if nothing matters, nothing can wound. The stance is Stoic on the surface, but it also pre-empts disappointment. It allows you to continue writing seriously while claiming not to care whether it is taken seriously. That tension is unresolved, not transcended.

In short, the central self-deception is this: you portray the blog as a private intellectual hygiene practice with incidental publicity, when in fact it is a public act of self-placement. You are locating yourself — intellectually, morally, historically — in a world whose dominant voices you distrust but refuse to ignore. The blog is neither a diary nor a bid for fame. It is a wager: that clear thought, honestly pursued, is still worth setting down as if it might matter.

You don’t quite admit that last clause. But everything you write depends on it.

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Taking the MBTI with HFA

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Back in the early 2000s I was working in America for Cable & Wireless. One of my colleagues was Craig, a Duke University professor of psychiatry; his wife, Dee Ann, was also trained in psychotherapy. I remember talking to her at one of our works dinners about the Myers-Briggs classification scheme and when it didn't work. She replied that it tended to give erratic results with people who exhibited abnormal mental conditions, such as schizophrenia and Asperger's syndrome.

And I left it there.

Today I'm wondering what happens if a person with High-Functioning Autism (formerly Asperger's syndrome) takes the Myers-Briggs Inventory. How does their MBTI come out?

ChatGPT tells me...

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How HFA People Score on the Myers–Briggs Type Indicator

The Myers–Briggs Type Indicator rests on population averages of neurotypical psychology. It was never built to describe autistic cognition. When people with high-functioning autism (HFA) take the MBTI, the results often wobble or misclassify. The same is true of the Five Factor Model, though in a different way.

Take the S/N dimension. Some autistic people live in concrete domains: bus timetables, mechanical systems, the fine grain of sensory detail. They look like S. Others immerse themselves in mathematics, philosophy, speculative worlds. They look like N. Both are common.

The test assumes the two poles are exclusive; autism ignores that rule. A developer who can design high-performance real-time transaction systems may come out as a classic N for abstract thinking. Yet ask him about politics or engage in small talk and he seems incurious, even obtuse - answers that tilt back toward S.

Extraversion is another fault line. HFA people can be talkative, sometimes performatively gregarious, yet maintain no close friends. The MBTI interprets their verbal energy as E, while their lived experience is solitary. A literal answer to “Do you enjoy going to parties?” might be “Yes, I like the food and the noise,” even if the same person leaves early, interacts with no one, and has no social bonds. The test confuses stimulus-seeking with sociability.

On the T/F scale, many answer as T. They rely on explicit reasoning, exploiting rules and consistency. That does not mean they lack affect, only that their affect is not measured in the MBTI’s idiom. Similarly, the J/P axis is confounded: autism’s need for sameness, its preference for routine, shows up as J. But this is neurology, not “personality preference”.

If you shift to the Big Five, the pattern persists. “Openness” can score high if interests are abstract, or low if they are repetitive and concrete. “Conscientiousness” may appear strong on orderliness but weak on adaptive planning. “Agreeableness” is pulled down by low empathy-related items, though fairness and honesty are often high. “Neuroticism” is inflated by anxiety, a frequent comorbidity. Instability is the rule.

The real problem is structural. These instruments assume traits cluster as they do in the neurotypical bell curve. Autism reshuffles the deck. Literal answering, context-bound interpretations, and construct mismatch ensure that the outputs are noisy. What looks like inconsistency is the wrong measurement framework.

Better alternatives exist. The Empathising–Systemising Quotient, the RAADS-R, and sensory processing profiles capture dimensions orthogonal to MBTI and FFM. They measure the axes on which autistic cognition varies.

So when an HFA person emerges from the MBTI as ENTJ one month and ISFP the next, it is not a crisis of self-knowledge. It is the instrument failing to fit the mind it tries to describe.

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Plan for the Galaxy *

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Nigel: Elon Musk’s rhetoric about pivoting his company towards humanoid robotics strikes me as wildly premature. The technology is nothing like ready. We are nowhere near solving robust manipulation, autonomy in unstructured environments, or long-term reliability. Scaling production now - it looks like a delusion: confusing a demo-prototype for a ready-to-go mass product.

GPT-5.2: That is the central problem. What exists today are research artefacts with good PR. A humanoid robot that can walk, lift a box, or fold a T-shirt under contrived conditions is still missing the hard parts: error recovery, adaptive learning in the wild, energy efficiency, and graceful degradation when things go wrong. These are not polish issues; they are foundational research problems. Betting a company on them now would be a triumph of narrative over engineering.

Nigel: And of course we already have 'humanoid robots': human beings. They are abundant, adaptable, currently cheap by comparison, and astonishingly general-purpose. That’s the benchmark any future humanoid robot has to beat.

GPT-5.2: Precisely. Humans are the incumbent platform. They arrive self-powered, self-repairing, socially competent, and pre-trained by a civilisation that absorbs the cost. Against that baseline, a robot must be not just comparable but decisively better over its lifetime. Until labour is scarce, or required for situations intolerably dangerous, humanoid robots are competing with the most efficient all-round machine ever produced (by natural selection) for the human economy.

Nigel: Except, perhaps, on Mars? Given Elon Musk’s focus on a Martian colony, surely that’s the environment where humanoid robots and AI systems ought to be doing all the heavy lifting: construction, maintenance, preparation all set in place before the first humans ever arrive?

GPT-5.2: I can't agree. On Mars, humans become grotesquely expensive and fragile, so robots do start to look attractive. But Mars is not a proving ground; it is an extreme endgame. Any robot sent there must operate with near-total autonomy, survive years of mechanical stress, corrosive dust, radiation and cold, and repair itself or its peers with minimal human intervention. We cannot yet build machines that do this reliably in a terrestrial warehouse, even. Mars is not a shortcut around Earth-bound difficulty; it is in fact the ultimate stress test.

Nigel: Which pushes us into a deeper question. Why are we so intent - at least in our imaginations - on spreading humanity across the universe? None of us will get to go. Most everything out there looks bleak, uncomfortable, and sterile. Mars itself makes Antarctica look cosy - and we haven't exactly built cities or an economy there, have we?

GPT-5.2: That question is usually dodged with talk of destiny or survival, but stripped of romance it is deeply problematic. Human beings are savanna primates. We flourish only in narrow ecological bands, augmented by environment-mitigation technologies. The wider universe is not hostile by accident; it is hostile by default.

Nigel: Yep, just hostile. And AI and robotics will advance far faster than our capacity to move fragile human bodies across interplanetary, let alone interstellar, distances.

GPT-5.2: Yes. Once machines surpass us in harsh-environment durability, autonomy, and cognition, galactic exploration becomes their project, not ours. At that point, the human role presumably shifts from explorer to originator: the species that lit the fuse...

Nigel: So perhaps the long-term future is not humanity spreading bodily through the cosmos, but humanity giving rise to systems that do, almost by accident?

GPT-5.2: That's a future with a gradual decoupling: humans remain local, terrestrial, culturally rich but spatially constrained; meanwhile, our machines range outward, mapping, building - and expanding where we cannot.

Nigel: There is at least one major science-fictional counter-vision to this rather bleak handover. In Iain M. Banks’s Culture series, very advanced technology and very advanced AI are dedicated to replicating almost utopian human (strictly: human-like) environments elsewhere in the galaxy just by sheer cleverness and the use of vast amounts of energy and technology.

Whole artificial ecologies - Orbitals, habitats, engineered worlds - are built to be extravagantly hospitable. Savannahs, seas, weather, danger without lethality, difficulty without misery. Humans don’t adapt to the galaxy at all; the galaxy is adapted to humans. And the prospect of more savannah-like utopian real estate across the galaxy - for which we don’t have to change humans very much - might be a future humans would be very motivated to try to bring about.

GPT-5.2: Yes. Banks takes the opposite bet to rugged frontier mythology. Instead of forcing humans into hostile environments through grit and sacrifice, the Culture expends unimaginable effort to eliminate hostility itself. Gravity problems, poisonous atmospheres, harsh radiation, scarcity even: all engineered away. It is a vision where intelligence serves comfort rather than combatting the hostile with raw toughness.

Nigel: And crucially, humans are not asked to change very much. No radical post-biological leap is required. They remain recognisably human - fallible, social, embodied - just freed from the tyranny of the mundane, and scarcity, by Minds doing all the heavy lifting.

GPT-5.2: In that sense, it is deeply conservative about human nature, even as it is radically ambitious about technology.

Nigel: Which suggests a motivation that makes more sense than grim Martian heroics. Not survival at any cost, but abundance through exquisite engineering. More and nicer Earths, not harder near-misses. More room to live well, not more ways to endlessly suffer the hardships of pioneers.

Which brings us back to AI. In that vision, AI is not humanity’s replacement but its galactic infrastructure - vast, patient, incomprehensible, and largely benevolent machines to watch over us.

GPT-5.2: And that may be the most plausible long-term equilibrium. Humans remain local, embodied, narrative-driven creatures. AI becomes the civil-engineering layer of civilisation at cosmic scale. Not our descendants, exactly but not rivals either. Something closer to our climate, our environment, our extended phenotype.

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* This is in homage to BA Gillies's 'Return to the Galaxy' pulp military-SF series.

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Narrenschiff — the Ship of Fools

Narrenschiff — the Ship of Fools

The image originates in medieval allegory, most famously in Sebastian Brant’s 1494 satire Das Narrenschiff, where a vessel full of fools sails toward Narragonia, a fictional paradise of folly. Brant coined Narragonia by blending “Narr” (German for “fool”) with the pseudo-classical suffix “-gonia” suggesting a land or origin.

Each fool represents a human vice - vanity, greed, pride - and the ship, rudderless and captainless, becomes a metaphor for a society adrift, morally unmoored, absurd in its self-regard.

Later, Hieronymus Bosch painted it: leering grotesques, gluttonous revels, a lute-playing nun - the world as madhouse. Foucault seized on it in Madness and Civilization, seeing the ship of fools as a literal and figurative vehicle of exclusion: the mad expelled from the city, yet still haunting its margins.

In modern use, Narrenschiff is a potent metaphor - for a culture that has lost its reason, for political or economic systems spinning into dysfunction, or even for the human condition itself: brilliant, deluded, fragile, floating godless through the void.

And Robert Plant sang about it.

'Ship of Fools', released in 1988 on Robert Plant’s Now and Zen, is a melancholy meditation wrapped in elegiac blues-rock. Unlike Brant’s medieval satire, Plant’s Narrenschiff is romantic and introspective - a metaphor for emotional drift, disillusionment - and love receding on a tide of time. 

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'Ship of Fools' (1988) - by Robert Plant and keyboardist Phil Johnstone

On waves of love, my heart is breaking

And stranger still, my self-control I can't rely on anymore

New tide, surprise, my world is changing

Within this frame an ocean swell behind the smile, I know it well

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Beneath a lover's moon I'm waiting

I am the pilot of the storm, adrift in pleasure I may drown

I built this ship, it is my making

And furthermore, my self-control, I can't rely on anymore

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I know why

I know why

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Crazy on a ship of fools

Crazy on a ship of fools

Turn this boat around, back to my loving ground

Oh no, oh no

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Who claims that no man is an island?

While I land up in jeopardy, more distant from you by degrees

I walk this shore in isolation

And at my feet eternity, draws ever sweeter plans for me

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Cute.

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The Minkowski Geometry We Live In But Never See

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The Geometry We Live In But Never See

Minkowski spacetime is unsettling in a specific way. Not so much because it is conceptually hard, but because it is categorically unlike the Euclidean geometry our instincts expect - and yet it largely stays out of sight.

We live in a world whose metric admits null vectors, whose orthogonality behaves oddly at the light cone, and whose causal structure is rigid in ways no Euclidean space can mimic. Still, daily life feels like three-dimensional space with time tacked on as a separate parameter. Where has the weirdness gone?

The usual explanation is that the speed of light is enormous, so relativistic effects are small. True, but shallow. The deeper explanation is geometric plus biological: Lorentzian structure is real, but our species only samples a thin, very timelike region of it, under strong thermodynamic and cognitive boundary conditions.

Begin with the geometry. Minkowski space is not Euclidean four-space with a sign flipped as a mere technicality. Minkowski mixed signature changes the rules: a nonzero vector can have zero norm; the orthogonal complement of a null (lightlike) direction fails to be transverse; at null surfaces (light cones), “normal” and “tangent” collapse into the same direction.

This is why you cannot “model” even 1+1 Minkowski space as a surface inside any Euclidean space to get an intuitive feel for it. A Euclidean embedding inherits a positive-definite metric; it simply has no place to put null vectors. Spacetime diagrams are therefore not models but coded projections: what your intuitions see on the page is not literally what is happening.

So why does such alien structure not intrude? Partly because everyday life is carried out deep inside the timelike cone. For ordinary speeds, worldlines cling close to the time axis, and the Minkowski interval looks Newtonian (space and time separate and different*). The geometry is not Euclidean, but we keep walking in a narrow region where the difference barely registers.

Yet one everyday fact is already a clue. Time and space present themselves to us as categorically different kinds of thing. In a straightforward four-dimensional Euclidean universe, by contrast, “time” would be just another axis - in principle rotatable into “space” - and that felt distinction would be hard to justify as anything other than an arbitrary psychological quirk. Minkowski spacetime, at least, builds in a deep and invariant difference between timelike and spacelike directions.

The most distinctive feature of Minkowski space is also the least inhabitable: the null directions. The light cone defines the boundary between possible and impossible causal influence. But no massive organism can live on a null worldline - our worldlines are timelike. There is no rest frame of light, no proper time along a null curve, no “lived experience” of that geometry from within. The sharp edge of the metric is precisely the edge we cannot stand on.

Then add the thermodynamic arrow. Lorentzian geometry by itself does not demand an irreversible time, but it cleanly separates timelike from spacelike and makes causal order frame-invariant. Our experienced asymmetry of time - memory, anticipation, decay, the sense that causes precede effects - is a dynamical fact about a low-entropy past. Yet it sits naturally inside a spacetime where “time” is not just another axis you can rotate into “space”. In Euclidean four-space, that experiential distinction would be an awkward add-on. In Minkowski space, it is at least compatible with the underlying geometry.

Relativity becomes visible mainly when different inertial slicings are forced into comparison: moving clocks, synchronisation disputes, high rapidities, long baselines. Absent those comparisons, Lorentzian structure is present but quiet - like the curvature of the Earth to a pedestrian.

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* Newtonian space-time is not “Minkowski with a different sign” (all pluses?) but a different kind of geometric structure altogether, one far less elegant.

Minkowski space is a four-dimensional manifold equipped with a single non-degenerate Lorentzian metric of fixed signature, so one invariant object simultaneously defines intervals, orthogonality, proper time, and a light-cone causal structure.

Newtonian (Galilean/Newton-Cartan) space-time is typically formalised on a four-manifold too, but it has no non-degenerate spacetime metric: instead it carries an absolute time function (time is absolute, universal, and geometrically prior to space) that foliates the manifold into three-dimensional simultaneity slices, plus a Euclidean spatial metric that only measures distances within each slice. 

Because this “metric” structure is degenerate, there is no invariant spacetime interval between arbitrary events and no geometric mixing of space and time under boosts. So relativity’s unified causal geometry fractures into separate notions of absolute time and instantaneous Euclidean space in a mechanistic way.

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Does a Thrown Ball Reveal the Curvature of Spacetime?

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Does a Thrown Ball Reveal the Curvature of Spacetime?

The question sounds innocent: you throw a ball, it traces a neat parabola, and you wonder whether you have just watched Einstein at work. The difficulty is that “curvature” is doing two very different jobs in this story. One sense concerns the visible curvature of a spatial trajectory drawn by an object as time passes. The other concerns the invariant curvature of four-dimensional spacetime itself. These are related, but they are not the same thing. The confusion arises when they are either collapsed into one another, or artificially torn apart. The clean way forward is to contrast three observer stances and be explicit about what each can and cannot infer.

1. The ground-based observer: “The ball falls.”

You stand on the Earth and watch the ball arc downward. In your coordinates, the path through space is approximately parabolic. This is not in dispute. The question is what that parabola represents.

In general relativistic terms, you are not an inertial observer. The Earth’s surface is prevented from free fall by internal stresses in matter; your accelerometer reads roughly 1g. Your frame is therefore non-inertial. When you describe the motion of freely falling objects from such a frame, inertial effects appear that look exactly like a gravitational force.

From this standpoint, the ball’s parabolic trajectory is the spatial trace of a geodesic described in a non-inertial coordinate system. This is a perfectly legitimate description, but it does not by itself settle the question of spacetime curvature. Curved spatial paths can arise either because spacetime is curved or because the observer’s frame is accelerating. From the ground alone, those possibilities are not disentangled.

2. The local free-fall observer: “The ball is (almost) straight.”

Now imagine you are launched alongside the ball, sharing its free-fall motion. In your immediate neighbourhood you are very close to an inertial frame. Over short distances and times, the ball does not exhibit any strong downward acceleration relative to you. Its motion is close to uniform; its worldline appears nearly straight in your local coordinates.

This is the equivalence principle in its proper domain: local, approximate, and powerful. It guarantees that along any freely falling worldline one can choose coordinates in which gravitational effects largely disappear. This is technically represented by the ability to set the connection coefficients (the Christoffel symbols) to zero at a specific point.

But this does not mean spacetime is flat. What vanishes locally are the connection coefficients, not the curvature. Curvature reveals itself only when you consider a region rather than a point or a single worldline. If you watch another freely falling object nearby, you will eventually observe relative acceleration between the two. Those tidal effects cannot be transformed away. They are the signature of the Riemann curvature tensor.

3. The deep-space inertial observer: “The ball follows a geodesic of curved spacetime.”

Now consider an inertial observer far from the Earth, equipped with a telescope, floating freely and not accelerating. This observer is the “smoking gun” witness. Because they know they themselves are inertial, any deviation they see in the ball’s path cannot be attributed to their own coordinate acceleration.

This observer does not need to appeal to accelerating coordinate systems to explain what they see. They observe a ball moving in the gravitational field sourced by the Earth, and in general relativity that means the ball follows a geodesic of the Earth’s spacetime geometry. When this observer asks, “What curve does this geodesic trace in three-dimensional space as a function of my time coordinate?”—referring to the coordinate time t of a distant clock—the answer in the weak-field, low-velocity regime is: approximately a parabola.

That near-parabolic shape is not an illusion, nor is it a coordinate trick. It is precisely how timelike geodesics in the Earth’s weak gravitational field project into ordinary space when described using a reasonable global time coordinate. In this limited but perfectly legitimate sense, the parabolic trajectory is explained by spacetime curvature. The Earth’s mass curves spacetime; free particles follow geodesics; those geodesics, when viewed spatially, look parabolic to an excellent approximation.

Why the parabola is still not “the curvature”

Here is the crucial distinction that must be made sharply. Although the near-parabolic trajectory is a consequence of spacetime curvature, it is not itself a direct measure of that curvature. A single geodesic, by itself, does not encode the Riemann tensor. Different curved spacetimes can support geodesics whose spatial projections look very similar over short distances.

What curvature controls, invariantly and unavoidably, is the relative motion of nearby geodesics. If the deep-space observer watches two balls thrown with slightly different initial conditions, they will see their separation evolve in a way that cannot be mimicked in flat spacetime by any choice of coordinates. That relative acceleration—tidal deviation—is the coordinate-independent manifestation of spacetime curvature.

“Mostly timelike rather than spacelike curvature”

This phrase gestures at a genuine feature of the weak-field regime. Near Earth, the dominant deviation of the metric from flatness lies in the time-time component (g₀₀). This encodes gravitational time dilation and reproduces the Newtonian potential in the appropriate limit. For slow-moving objects (where velocity v is much less than the speed of light c), this time-warping largely governs their motion.

Spatial curvature is also present, but its effects on slow projectiles are subleading. If the ball were thrown at relativistic speeds, or if we were observing the path of light, the spatial components of the curvature would become just as prominent as the temporal ones. It is one unified spacetime geometry, but the ball’s low velocity makes it primarily sensitive to the temporal "stretch" of the metric.

The answer, stated precisely

A thrown ball near Earth follows a timelike geodesic of the Earth’s weakly curved spacetime. A ground-based observer describes that geodesic as a parabola because they are in a non-inertial frame. A local free-fall observer sees the motion as nearly straight because curvature is negligible over small regions. A deep-space inertial observer sees neither illusion nor fiction: they see a genuine geodesic of a curved spacetime whose spatial projection is approximately parabolic.

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Addendum: Why do different observers see the same shape?

It may seem counter-intuitive that the earthbound observer (in a non-inertial frame) and the deep-space observer (in an inertial frame) both conclude the ball follows an approximate parabola. One might expect such different perspectives to yield different geometries. However, they converge because the Earth’s gravitational potential and the ground’s physical acceleration are numerically and geometrically coupled.

For the ground-based observer, the parabola is an inertial effect. Because the ground is constantly pushing you upward, you are in an accelerating frame. In such a frame, a free particle appears to accelerate in the opposite direction. Your description follows the Newtonian kinematic: z(t) = z₀ + v_z0t - ½gt². This is a "fictitious" force result, but the mathematical plot is a literal parabola.

For the deep-space observer, the interpretation is inverted. They see the ball following a worldline that is as "straight" as the curved geometry allows (a geodesic). Because they are observing a slow-moving object in a weak field, the metric component governing time dilation (g₀₀ ≈ 1 + 2Φ/c²) dominates the math. When they project this 4D worldline onto their 3D spatial grid, the resulting equation for the trajectory yields the exact same ½gt² relationship.

Ultimately, they must converge because of the Equivalence Principle. If the "fictitious" parabola seen on the ground did not match the "geometric" parabola seen from space, an observer could distinguish between gravity and acceleration simply by throwing a ball. The fact that they see the same shape is not a coincidence; it is a requirement of the symmetry between acceleration and gravity that lies at the heart of General Relativity.

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La Maîtresse des Échecs - by Adam Carlton (part 6 of 6)

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Epilogue

Every organised activity has its super-fans. See that big guy over there in the bar, watching the sport channel with his mates, the one with the beard and the dad-bod? He’ll tell you more than you want to know about the offside rule. See that aging gentleman in the blazer? The one with the rough bristly moustache which fails to hide impacted teeth? He has his fund of tedious anecdotes about the perils of fielding at short leg. And that slim young man in his lycra who just cruised effortlessly by? He knows a thing or two about the tactics of the breakaway from the Peloton. These fans know their heroes and heroines, obsess over them, are polarised by their champions’ feuds and animosities.

They are not typical.

They are too few and don’t suffice to pay the global circus bills. What the world wants is volume: revenue streams in torrent, crossover market share.

What the world needs is stars.

When the American, Lance Armstrong, went to Europe in the nineteen nineties he found that road racing there was awash with drugs. An unaided rider could not win against the best cyclists on dope. Armstrong came to a cold decision: if that was what it took then he would apply his formidable intelligence, his logistical skill and iron determination to be the very best doper.

For more than a decade Armstrong dominated the sport, winning the Tour de France seven times in succession. The public loved to watch him, commentators were in awe. His fame brought riches to the cycling authorities: wealth and power and prominence. There were those who thought it was all too good to be true, dogged reporters who were literalists on morality. But who really, had an interest in killing the golden goose? For years he was protected by the authorities: the good and the great.

Armstrong was eventually brought down. Perhaps the culture of total-doping was just too egregious to survive. But does ‘good’ always win-out in the end? How would we know?

When Daniel had his nervous breakdown, resigning the match in a fugue state, Petra was catapulted to superstar status. She was the superstar of chess: sassy, good-looking, an ultra-competent woman in a world of men where she had bested the best.

So it was reported.

Most pundits, most executives, think she is the best thing which ever happened to the game. The purists may pore over her matches which seem to them, as to Daniel, too good to be true. Yet her play is not perfect: many of her moves are sub-optimal according to the omniscient engines. She does just enough; her wins are effortful but relentless. Her growing fan base empathises with her occasional setbacks and her more frequent successes. Drama beats perfection: Petra becomes the leading character in her own reality show.

Petra talks to her father. They’re in a New York hotel. Tomorrow Petra will play in a major US tournament but tonight she is pensive.

“I don’t worry too much about being caught. You’re so clever and no-one important wants to rock our boat, but do you think it’s right? As far as I can tell, none of my opponents are getting help during games.”

“They’re dinosaurs,” Hans says, “They don’t understand the world we’re moving into. No-one cares about chess anymore. There’s nothing new for people to explore - the machines have stolen all of that. All that’s left is spectacle: drama and confrontation. That’s what the machines will never provide.”

“Chess as show business?” Petra says.

“The difference is we know it, Petra, and your opponents don’t. Maybe chess used to be like boxing but the engines changed all that. Now it’s wrestling: choreographed emotion, a canvas for catharsis. And you, Petra, you are the focus for millions of people and long may we keep it that way.”

Petra is doubtful.

“Don’t you think that the excitement depends on my opponents not realising that it’s not just me that’s killing them? Isn’t it their naïveté what keeps them so highly-strung, so serious and so determined? Doesn’t my audience crave authenticity above everything?”

And finally, “Do you think what we have here is really stable?”

To these highly apposite questions Hans has no answer.

---

Though Daniel’s star has fallen so deeply into the pit, he is not vindictive. Daniel does not do vindictive - he just does truth. He knows he was not wrong. He simply underestimated her cunning. He doesn’t know how she does it but to an expert the tracks are clear enough. He follows her games obsessively, compiles his mounting dossier, waits for the day the reporters come to visit, the day when he will finally be vindicated.

Yet what if he succeeds, if he manages to bring Petra down? He is too honest not to let this worrisome thought run on. Chess would return to its former drab state: obsessives contending in an eternal second division while the machines go forth to chart an astral - but ultimately sterile - space.

While an uncaring world passes on, regarding not.

His entire life would revert to meaninglessness.

Could it be, he wonders, that victory is not everything?

---

The full story text (part two of my novel) is also available here:

• "Donatien's Children" (2022) - as a PDF, and
• "Donatien's Children" (2022) - as a formatted book on Amazon for easier reading.

---

La Maîtresse des Échecs - by Adam Carlton (part 5 of 6)

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8: The Third Day: Le Directeur du Match

Late morning, Daniel and Petra each received a call from M. Étaix to come down to his office for 1.15 pm. The stated reason was to review arrangements for the final and deciding game. This was no surprise of course: media interest was now intense. Petra’s surprise win plus her glamour had captivated TV channels and major print outlets alike. There had been a steady stream of taxis and limousines arriving from the airport to the Cité de Carcassonne all morning.

The Director’s office was a small conference room off the hotel’s concourse. Daniel had been summoned fifteen minutes earlier at one o’clock to explain further his startling allegations and M. Étaix reluctantly agreed that a prima facie case had indeed been established. Daniel was feeling pleased with himself - rather vindicated - as they waited for Petra to turn up.

At the appointed time, as the quarter hour tolled on the bells of the Basilica, Petra, accompanied by her parents, knocked and entered. Her appearance was even more stunning than the previous day. She was draped in a red dress colour-coordinated with her auburn hair. One strap fell artfully off her shoulder. The weave varied in mesh across the contours of her body, both concealing and revealing. Tight and very, very short, it forced the question as to whether it might be the only garment she was wearing. And on her ears were pearl decorations, as red as the rest of her outfit.

The Director now fell to his difficult and worrisome task. It was not just that he felt personally nervous, it was also the thought that a whiff of scandal would certainly destroy this championship and ruin months of effort and the reputations of those involved: perhaps even that of France herself.

As he haltingly outlined the suggestion, the charge which had just been made, he was even half-prepared for violence from the accused’s family. He cast a cautionary look at two of his stewards and put out his hand, “If the mademoiselle could just hand over her earrings? We have machines here which can test…”

And indeed they had: electronic sniffers, portable X-ray machines and more.

Petra, her face a furious glacial white, removed the requested pieces and handed them across. Hans and Anne-Marie glared at the assembled officials as if they had never been so insulted. Her father’s bare hands were balled into fists, his aggression only restrained by iron discipline.

And Daniel? His cheeks were burning. He wished himself anywhere else in the world but here. What if he was wrong? But how could he be?

Everyone stood still as the technicians did their work. One came forward with an airport-type scanner and waved the wand all around the two contenders and Petra’s parents. But there were no lights, no beeps, no audible warnings of any kind. Finally the person who had been working the complex equipment looked up and addressed the Director.

“M. Directeur, they are all clean. As far as I can tell they are exactly how they look, a pair of rather expensive earrings.”

The Director looked at Daniel appraisingly. Daniel felt the Director's changing mood, his new assessment: Daniel Brown, the loser who accuses his victorious opponent of cheating. His world imploding, Daniel turned and bolted from the room.

Petra glared as the Director stammered his apologies, “We always have to act when accusations such as these are made…“

In a frigid voice she replied: “You keep them!”

She and her parents exited the Director’s bureau with considerably more dignity than Daniel.

9: Intermission 2

The scene earlier that morning, at 9.30 am when Daniel is playing with his chess engines trying to emulate Petra’s quirky, devastating plays. 

Petra is sitting in her parents’ suite on the top floor of the hotel. The red earrings - so useful yesterday - have been comprehensively destroyed: rendered to powder, the remains flushed down the toilet. A substitute pair - red and beautiful, perfectly genuine, perfectly innocuous - await any unlikely inspection.

Anne-Marie starts the meeting with an assessment of Daniel Brown’s state of mind and likely course of action.

“He’s a classic introvert, on the spectrum. Yesterday’s events will have knocked him stupid but by now he’ll have recovered. He’ll figure out what was done to him - there were clues enough - and then he’ll complain to the authorities. We should expect a call shortly.”

Petra now listens with close attention as her father takes up the narrative.

“Here is how we do it today,” He holds up the tampon. “The communicator is embedded - no more audible cues. And no-one is going to ask to take a look.”

He smiles.

“You apply it just before the game, just before you go down. And excuse yourself afterwards and dispose of it.”

Her mother adds practically, “We’ve practiced in the past so you need no reminders. Wear plenty of perfume. That will also keep him off balance.”

Hans sums it up: “Today we go in hard.”

10: The Third Day: the Game

The Basilica has been transformed. Cables now flex across stone paving, snaking their way to TV cameras and lights. A press of observers crowds the wall at the back. Feeding an already febrile atmosphere there are new rumours of cheating: rebutted claims which make Petra a Wronged Woman. In the audience’s eyes, an audience now global, Daniel Brown’s name is already mud.

And Daniel is more sensitive than people imagine. He feels the hostility; dare he say it, the contempt of the crowd. His morale, already at rock bottom, takes a further tumble. His being is dominated by his guts which knot and writhe. He feels he cannot stay but of course he cannot flee.

He sits in the spotlights (he is as early as ever). Sits at his place by the table on the dais, and waits, unable to concentrate, battling abhorrent emotions.

Three minutes to two and Petra walks into that cavernous crowded space. She wears her vêtements du jour, that red fishnet dress already shown to the Director. She wears no earrings. At first only those near the side door spot her. They stand up to get a better view, bringing their cameras to bear. As she turns into the main aisle, advancing to the front of the assembly, awed silence accompanies her.

She daintily sits as before on the seat to the left and gives Daniel a warm, magnanimous smile. TV cameras, in extreme close-up, linger over it. Daniel’s face is turned resolutely to the board, however. The Director says a few words - Daniel will be playing black again - and the game gets underway.

A wronged Petra, an exonerated Petra, will this time show no mercy. Right from the off she plays an out-of-book opening, something only machine-chess has made possible. Tiny, exciting twinges in her abdomen instruct her: she is Leela’s slave now - and Leela is an alien.

Daniel is immediately off-balance. Normally when a player goes off-piste, ignoring the learning of centuries, they rapidly fall into error. There is a reason humans don’t do that, why those forays into novelty never made it into the book. But Leela has a different book: so much bigger and better.

In Daniel’s visual comprehension the board before him is a city experiencing an earthquake. Positions he thought secure crumble like sand; volcanoes arise on plains he thought backwaters spewing lethal ash and lava on his forces.

He is a chess grandmaster, still an excellent player. Occasionally he grits his teeth, feels his way to a killer counterblow, prepares to strike back. The audience draws in its breath; commentators murmur excitedly, the audience waits on Daniel’s move.

And Petra leans forward. Her flushed breasts, so eager to escape, settle on the table. Cameras and Daniel’s unwilling eyes cannot avoid them. Her perfume wafts across the board, assaulting his over-delicate senses.

His crystal city of abstraction collapses into fog. Pieces poised to pivot and crash through Petra’s defences are now just… pieces. He had screened out the clicking clock; the lights had long ago become invisible. But assailed by super-stimuli - and a terminal sense of his own worthlessness - his talent has fled. He looks at the board and sees it as a novice.

He stands up. Noises in the room deaden, subside to nothing: an anechoic chamber. Mechanically, he pushes his chair back and slowly walks off the dais, moves between the rows of stupefied onlookers, departs the Basilica into the afternoon sun of medieval Carcassonne, escapes into centuries of deep time and a square which knows nothing of chess.

---

The full story text (part two of my novel) is also available here:

• "Donatien's Children" (2022) - as a PDF, and
• "Donatien's Children" (2022) - as a formatted book on Amazon for easier reading.

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La Maîtresse des Échecs - by Adam Carlton (part 4 of 6)

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6: Intermission 1

According to Wikipedia, Leela Chess Zero (abbreviated as LCZero or lc0) is a free, open-source, neural-network-based chess engine based on DeepMind's AlphaZero. It is competitive with Stockfish and Komodo as the best chess engine in the world, and unlike the mind-numbing crunching of its competitors, its machine-learning roots give it superhuman flair and insight.

Hans has a forked (and modified) copy running on a small microcomputer the size and appearance of a small packet of mints, handy to slip into his pocket. His gloves are his own design of chorded-keyboard: the left talks to the amped-up lc0 in the mint box; the right uses an ultra-low-power frequency-hopping radio to talk to the device secreted in Petra’s earring. Hans wears an inconspicuous hearing aid to monitor everything.

Hans’s comms protocol maps chess’s algebraic notation into something like Morse in a code which Petra has intensively practised. When her ear lobe vibrates, she visualises in her mind’s eye the coded move. A move conventionally written, for example, as Nd2xe4 (a Knight capturing a piece on e4).

The system is almost perfect. There is that slight buzz of the tapper batting against her ear but experience has shown that hardly anyone can hear it. Especially if there is any kind of background noise or a distraction.

This is the mode of use. Hans sits in the audience, entering moves as they appear on the big screen into his modified mint box. Hans considers the countermove Leela proposes back. No mean player himself, he uses a ‘surprise’ heuristic. Mostly the suggestions are what he would expect Petra to play anyway and he just lets his daughter get on with it. But occasionally something utterly counterintuitive emerges, something profoundly alien. And that is passed to Petra who proceeds to confound her opponent and commentators alike.

Her intuition has a great career ahead of it, he thinks.

7: The Third Day: Daniel

Daniel had just lost a match he had anticipated - had assumed - he would comfortably win. He retired to his room disoriented, his expectations thoroughly violated. Initially his state-of-mind was simply frozen - but gradually a dormant emotion emerged: shame. Somehow he must have made a mistake.

His intellect raced - but to no avail. He was exhausted. He reviewed the game on his laptop and could make no sense of it. Fatigue sapped his every intuition. Eventually he fortified himself on room-service pap and settled into an armchair, prepared to lose the evening in some pulp fantasy the size of a brick. When that failed he was early to bed.

After a fitful night, he felt considerably sharper the next morning. His subconscious had been busy and suspicions had accumulated. First he ran the game again, using traditional chess engines (Stockfish, Komodo) to play her moves. As he expected, the engines’ moves were solid rather than flashy, merciless grind rather than innovative flair. There was little concordance with the Petra of the previous day.

He moved on to Maia. This was a neural-network chess engine trained not by self-play but by digesting human matches. Let no-one say that Daniel was not diligent in his preparations. His Maia configuration has been trained on Petra’s published games (along with many others of course). It was in fair agreement with most of yesterday’s game-play when he set it to play as Petra. But it missed all of her stunning innovations. Daniel’s intuitions grew stronger - he sensed where this was going. He now turned to Leela Chess Zero.

Leela Chess Zero is not one thing. There are different forks of the codebase plus an ever-changing menagerie of plug-in neural-net modules. Daniel used the most powerful (the highest rated) configuration currently in stable release... and quickly discovered how it might have been used. The AI engine did not of course recapitulate Petra’s entire game (left to itself it would have been far more innovative - and would have pulverised Daniel or any other human player) but at those points where Petra had done something unexpected, the program produced moves not dissimilar in elegant genius.

Daniel now took careful stock. Was there anything in Petra’s history which suggested an innate, quirky and superhuman talent? He reviewed her record with fresh eyes, but as far as he could tell the answer was no. He was forced to the only possible conclusion: she had to be cheating. Subtly and with help no doubt, but there could be no other explanation. And then he recalled the faint, subliminal buzzing he had heard. The answer had been there all along in the earrings.

Daniel picked up the hotel phone and called the championship director, Pierre Étaix.

---

The full story text (part two of my novel) is also available here:

• "Donatien's Children" (2022) - as a PDF, and
• "Donatien's Children" (2022) - as a formatted book on Amazon for easier reading.

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La Maîtresse des Échecs - by Adam Carlton (part 3 of 6)

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5: The Second Day: the Game

Daniel rapidly demolished the last of his meal and beat a hasty retreat to the privacy of the ascenseur, batting away reporters who wanted to know what was said.

Daniel is not stupid. Sometimes he may be a little slow, having to make conscious deductions which more normal people process easily and intuitively, but lying on his bed, finding his balance, he has time to reflect.

Chess is a hard old game. You don’t get to be a champion without playing thousands of matches against opponents - overwhelmingly male - who are trying to browbeat and bully when they can’t out-think you. Petra’s little episode, he now sees, conforms to a wearily familiar template. Yet he can control his emotions, can put this behind him. Once at the tournament table he will blank out the past and be in the moment. All that will exist will be the board - and the contest to shape its evolution to victory.

Daniel is right as far as he goes, but he never considered that Petra’s little cameo might have been aimed at a broader audience than just himself.

---

Two o’clock in the cathedral. The chairs - which replaced pews a long time ago - are entirely occupied; more are being delivered. Suddenly this competition has come alive, has caught the world’s attention. The lunchtime contretemps is on Youtube, getting millions of views.

The large screen facing the audience shows the board, pieces lined up ready to go. The camera is directly above the players and clever software replaces the images of the pieces with easy-to-see icons.

This is being live-streamed to a popular chess site and commentator Angelo Márquez is setting the scene. He has a few words to describe Daniel Brown, sitting to the right (‘calm, almost bored’) and misses the extent to which Daniel, mindful of the wisdom behind Petra’s intervention, has taken some pains to spruce himself up.

He spares few superlatives in describing the eighteen year old, thoroughly dolled-up Petra. A sideways view shows what a poor job that skimpy black fashion item is doing in covering her alluring flesh. The website coordinator whispers on the backchannel: “Keep it up: viewing figures are going through the roof!”

Hans and Anne-Marie are sitting together in the front row: Petra’s father observes the screen; her mother the players. Despite the heat outside, it’s cool in the basilica. No-one comments on Hans’s light coat with its many pockets or on the thin gloves he’s wearing - against allergies if anyone were to ask (they won’t).

Daniel gets to play white and at first everything is conventional: the first ten moves or so a standard book-opening. Daniel begins to get the feel of the development, lets his subconscious find the shape of the play, the wave of advance he must surf, the momentum which will force his opponent into passive reactivity sucking all initiative from her game. Petra in her personhood and individuality has been erased: the game is now abstracted to dynamics in space and time.

There is a small gasp from the audience. Daniel is jerked from comfortable flow. What did she do there? Why was that pawn moved to form an echelon? That part of the board is sterilized, inert, dead. He briefly raises his head, fixes a deadpan stare at Petra. Is she shocked by this careless mistake, does she wish she could take back that move?

She looks at him serenely, giving nothing away. There had been that subliminal buzz again, so faint he could barely hear it. Where did it come from? Some piece of equipment, no doubt. He dismisses the thought.

Eleven moves later there is a similar glitch in Petra’s play. Her bishop retreats from a promising stance to a defensive posture near that pawn echelon. Again a murmur from the audience: comments on the Internet are going crazy. Daniel is suspicious - could there be method in her madness? He takes a glance but her expression gives him nothing.

He decides not to rush things. His clock ticks. He settles into a deep Zen state, absorbing the board holistically, immersing himself in the shifting swells of possibilities, monitoring his psyche for gut feelings of anxiety or concern. There are none.

Fifteen moves on and Daniel is done. Her rising arc of firepower should have been easy to stop, once it had arisen from nowhere. Yet all his key pieces had been pinioned. Her errors, he now sees, had been crucial, yet had taken so long to pay off. How, where had she learned that?

He tips over his King. Most of his being does not believe it, the act of surrender is almost that of an automaton. He wants nothing more than to get back to his room and feverishly replay the whole thing, to understand what has happened here.

Petra is not so retiring. She lingers for the reporters, for photographs. She is an engaging interviewee. She claims to have little insight into her unorthodox moves: “I play by instinct, by intuition,” she breathes into the thrusting microphones, “They just felt right at the time.”

Petra makes primetime TV in France and Germany, a Eurostar seeing-off a perfidious Brit. Other countries pick up on the thoroughly photogenic challenger; mainstream presenters and camera crews are dispatched at pace to Carcassonne.

Tomorrow will be the decider.

---

The full story text (part two of my novel) is also available here:

• "Donatien's Children" (2022) - as a PDF, and
• "Donatien's Children" (2022) - as a formatted book on Amazon for easier reading.

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