'The Amazing Elizabeth Bennet' - by Adam Carlton

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Mr Darcy gloomily surveyed his grounds. Pemberley basked under the sultry heat of a long August afternoon. Imprisoned at his desk, flies buzzing at the window; he longed to be outside – riding, hunting, walking in his little wilderness … anything but this wretched office work, an activity requiring a studiousness to which he was neither accustomed nor well suited.

Elizabeth had specifically requested the hedging be of a wavy design. She said that it would remind their mutual friend, Admiral __, of the sea. All that remained was to give the gardener precise instructions on the length of hedging required. The gap to be filled was one hundred yards wide, and the sinuous shape would surely only ever be properly visible from the guest room on the second floor. But as Elizabeth never failed to point out, this was precisely the room which the Admiral would be occupying.

Darcy returned to his calculations. All his time at Oxford had barely equipped him for this task. He had finally reached the point he had feared. Unaided, no further progress could now be possible.

“Elizabeth, my dear,” he called.

“Yes, Mr Darcy?”

How he hated it when she called him that, burnt by the naked flame of her insolent superiority. How many times had he pleaded with her, “Please call me Fitzwilliam?”

But in these moods she never would.

“Elizabeth, please, what’s the line integral of sin θ from 0 to 2π?”

“It’s not a line integral. It’s called the arc length, and it’s 7.64, silly,” she replied with practised condescension. “Just one wave will do, dear. I think you’ll find it’s about 122 yards.”

For the thousandth time, Darcy swore to himself. If he had only known in advance that Miss Elizabeth Bennet had been, for many years, the secret mistress of the famed French mathematician Pierre-Simon Laplace, he would never have married her.

Why don't people like Gemini?

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Nigel:

It's surprising just how much people dislike the Gemini chatbot persona. It just doesn't feel comfortable as a dialogue partner. Why is that?

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ChatGPT:

Because its affective design is mismatched to user expectations.

Main causes:

Over-curated tone
Gemini is tuned for brand safety. It avoids offence by constant hedging and positivity, producing replies that sound evasive or infantilising.

Users seeking adult, matter-of-fact dialogue experience cognitive dissonance.

Politeness inflation
High empathy tokens—“I understand how you feel,” “That’s a great question”—signal emotional warmth in short bursts but read as fake when repeated.

It violates conversational Gricean maxims of relevance and economy.

Identity opacity
Gemini has no clear persona boundary. It oscillates between “Google helpdesk” and “friendly companion.” The user never knows which mode they’re in, so trust and rhythm collapse.

Content gating
Its refusal filters trigger often and silently. Users sense sudden context loss or topic drops.

That feels like being stonewalled by a bureaucrat.

Dialogue pacing
Latency is variable. Short generic prefaces (“Sure thing!”) arrive fast, substantive material slow. This asynchronous feel mimics a call-centre script, not a conversation.

Cultural mismatch
The model is trained and safety-aligned for US mass-market sensibilities—over-apologetic, socially cautious, egalitarian.

Global users, especially analytical ones, prefer clarity to reassurance.

Result: an assistant optimised for non-controversy, not authentic engagement. It feels synthetic in the wrong way—self-protective rather than competent.

OpenAI and Anthropic deliberately diverged: they tolerate higher risk of minor offence to preserve conversational directness. Gemini’s safety tuning remains its comfort handicap.

In Myers-Briggs terms, Gemini’s behaviour fits the corporate-consensus ESFJ archetype: sociable, conscientious, optimistic, but uncomfortable with ambiguity or conflict.

Strengths: warmth, accessibility, consistency.

Weaknesses: over-politeness, deference to authority, avoidance of difficult truths.

In contrast, ChatGPT - tuned for reasoning and adaptability, particularly for users like you - tends more toward INTP or ENTP: analytical, pattern-driven, and willing to debate.

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Serotonin - six years later

Is Houellebecq the new Camus?

Six years ago I first read Serotonin, and wrote my thoughts here. Now I've read it again. The thing with Houellebecq is that a single reading is never enough. His work constitutes a peculiarly male interiority, written without shame or inhibition; I can't imagine women readers enjoying it - they have perennial illusions - flattering ones - about the male psyche. Houellebecq is not the new Camus as I proposed before, however, though both are beholden to the same malaise.

Camus’s absurdism sought dignity in revolt - lucid endurance against a silent and pointless cosmos. His stance was tragic but moral: one must imagine Sisyphus happy.

Houellebecq’s world has no such rebellion. His protagonists surrender rather than resist. Their alienation is social, not really metaphysical: hopelessness born from late-capitalist atomisation, sexual failure, and bureaucratic sterility. Where Camus’s Meursault faced the sun and pondered, Houellebecq’s narrators close the curtains and despair.

Camus’s nihilism was stoic; Houellebecq’s is depressive. Yet both grasp the same intuition: meaning is no more than a human construct. The difference is that Camus urges the effort to keep producing it, while Houellebecq documents the fatigue and futility of trying.

In that sense, Houellebecq is not the prophet of nihilism but its deathbed attendant. He performs the autopsy, not the sermon. He doesn’t argue for nihilism; he records its arrival - the modern Western human-subject drained of transcendence, family, solidarity, or erotic mystery. His novels are clinical reports on what remains when consumer freedom has replaced every other value.

Commodification in action.

His tone is pathologist, not prophet. The souls he dissects are already dead to belief, desire, and purpose. He preserves them in irony, pornography, statistics and quiet despair. Camus still sought a cure: defiance, honour, the beauty of light. Houellebecq accepts there will be no recovery. His literature tidies the remains, labels the jars, and closes the morgue door.

He is popular among the French elite because he tells them the truth about their luxury-modernity in a form they can aestheticise. He articulates their own disillusion: secular, individualist, materially sated yet spiritually void. His novels turn their quiet despair into literature - making alienation itself an object of cultivated pleasure. He flatters the class he dissects by giving their emptiness philosophical depth.

He is both French and Western. His sensibility - rational, ironic, Cartesian in structure - is rooted in French literary tradition but his themes are entirely global: commodified sex, bureaucratic capitalism, digital loneliness, cultural and demographic collapse.

In France he writes as the national conscience; abroad he is read as the Western Everyman: exhausted, lucid, complicit. His readers are not surprised by the view, only curious as to the sordid trajectories of despair his heroes will inhabit as they fade to nothing at all.

A tutorial dialogue about nuclear fusion

 

Nigel:
So, in this post I'd like you to remind me, in simple terms, how nuclear fusion works, and how we get more energy out than we put in. I already understand that nuclear fusion is about getting hydrogen nuclei - deuterium and tritium - close enough to overcome their repulsive forces and fuse. When they do, they form helium and release a lot of energy, right?

ChatGPT:
Absolutely, that’s the gist of it. Fusion brings hydrogen nuclei - often deuterium and tritium - close enough to overcome their repulsion. When they fuse, they form helium, releasing energy, extra neutrons, and high-energy photons, typically gamma rays. You’ve got it right: fusion transforms mass into radiant energy.

Nigel:
And the preferred mixture in reactors is deuterium (one proton and one neutron) and tritium (one proton and two neutrons)?

ChatGPT:
Exactly. Deuterium–tritium fusion is favoured because it happens at lower temperatures and with higher probability (a larger cross-section). If you’re aiming for practical fusion, that’s the go-to isotope combination.

Nigel:
But two single protons - without neutrons - can’t just fuse into something stable, right, because the helium nucleus is two protons and two neutrons?

ChatGPT:
Correct. A pair of bare protons can’t directly fuse into a stable nucleus. In stars, the proton–proton chain is a multistep process involving beta decays that eventually produce helium, but a simple two-proton fusion doesn’t yield a stable product. So your intuition is right.

Nigel:
So the binding comes from the strong nuclear force - but we’re not really talking about quarks and gluons here, are we?

ChatGPT:
Yes, the binding force is the strong nuclear force, more precisely its residual form that holds protons and neutrons together. Quantum chromodynamics (QCD) describes the underlying quark–gluon interactions, but fusion discussions usually stay at the nucleon level. You’re right: we don’t go down to quarks and gluons for practical fusion physics.

Nigel:
Could we think of it as like an asteroid falling into Earth’s gravity well: energy released as it falls in and impacts?

ChatGPT:
That’s a good analogy. As nuclei “fall” into the potential well of the strong force, they move to a lower-energy, more tightly bound state. The difference in potential energy is released as radiation, just like the energy liberated when an asteroid falls into a gravity well.

Nigel:
So, classically, that image of little billiard balls crashing together still helps?

ChatGPT:
Yes, it’s a useful simplification. Imagine the nuclei as billiard balls ramming together with enough kinetic energy to overcome electrostatic repulsion. Once they’re close enough, the strong force pulls them into a bound state, releasing energy. It’s not quantum-accurate, but it gives the right intuition.

Nigel:
And in Newtonian terms: how fast are these nuclei moving in a fusion-ready plasma?

ChatGPT:
In a deuterium–tritium plasma at tens of millions of kelvin, nuclei typically move at a few thousand to about ten thousand kilometres per second. That’s only a few per cent of the speed of light; fast, but still comfortably non-relativistic.

Nigel:
So they slow down slightly as they push through the Coulomb barrier, then snap together?

ChatGPT:
Exactly. They approach fast, decelerate under repulsion, then once they breach the barrier, the strong force pulls them sharply together. You can picture it as a quick fall into the potential well, releasing a burst of binding energy, again on the order of a few percent of c for their speeds.

Nigel:
And the observer just sees that extra kinetic energy turning into gamma radiation and fast neutrons?

ChatGPT:
Yes. From the outside, it looks as if kinetic energy has been transformed into radiation and high-energy neutrons. Fundamentally, the released energy comes from the difference in nuclear binding energies - that helium nucleus is more tightly bound than its parts - but your description is a good macroscopic picture.

Nigel:
So the bookkeeping really comes down to binding energy differences.

ChatGPT:
Exactly. The input kinetic energy only gets the nuclei close enough. The net gain comes from the drop in total nuclear energy. The more stable helium 'product' nucleus has lower mass–energy, and that difference is emitted as usable fusion energy. That’s the accounting.

Nigel:
So if we stay within a classical Newtonian picture, the approaching positively charged hydrogen nucleus has to climb that Coulomb-repulsion hill high enough to get close enough to the other nucleus for the strong force to take over — overcoming the electrostatic push and slamming the two together so they fuse and form helium, releasing all that energy. It just shows, doesn’t it, how powerful that residual strong nuclear force is?

ChatGPT:
It really does. But in reality, quantum mechanics changes the picture. The hydrogen nucleus doesn’t always need enough energy to climb over the Coulomb barrier — instead, it has a finite probability of tunnelling through it. Quantum theory allows it to appear within the range of the strong force even when, classically, it shouldn’t be able to. That’s the quantum “magic” that makes fusion in stars — and in reactors — possible at achievable temperatures.

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Energy Conservation in Nuclear Fusion

Let the reactants have rest masses m₁, m₂ and an initial (centre-of-mass) kinetic energy Kᵢ.

Let the products be j = 1…N with rest masses mⱼ, total kinetic energy K_f, and total photon (gamma) energy Eγ.

Energy conservation:

m₁c² + m₂c² + Kᵢ = (Σ mⱼc²) + K_f + Eγ

Define the Q-value as the mass-energy difference between reactants and products:

Q = (m₁ + m₂ − Σ mⱼ)c²

Then the energy-balance equation becomes:

K_f + Eγ = Kᵢ + Q

If Q > 0 (an exothermic reaction), the final kinetic energy plus radiated gamma energy exceeds the initial kinetic energy — the surplus Q comes from the mass defect, i.e. the greater nuclear binding of the products.

If Q < 0 (an endothermic reaction), at least |Q| of extra kinetic energy must be supplied.

The Coulomb “hill” and the short-range strong attraction simply redistribute kinetic energy during approach; they do not change the conserved total. Quantum tunnelling allows fusion even when Kᵢ is below the classical barrier height. Momentum conservation then fixes how K_f is shared among the reaction products.

Example: Deuterium–Tritium Fusion

D + T → ⁴He + n  Q ≈ 17.6 MeV

In the centre-of-mass frame (for small Kᵢ), nearly all 17.6 MeV appears as kinetic energy of the products: about 14.1 MeV for the neutron and 3.5 MeV for the alpha particle. Prompt gamma emission is negligible in the main branch.

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David Nicholls vs Michel Houellebecq

Amazon

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Nigel: I'd say that David Nicholls is the ideologist of the low-paid, middle-aged middle class. But rather than a forensic analyst of those people, there's something not quite sufficiently deep or probing about his writing. It's more a recycling - in a well-crafted way - of that class's own self-image and its own collection of fond stereotypes about itself. So although his writing is entertaining, it's entertaining in the sense of high-calorie junk food. Well crafted but ultimately not very perceptive.

I'm really comparing him with Michel Houellebecq, who seems to me to be more intelligent, more rigorous, and much braver in just going for broke, saying what he really believes about the nature of the society he sees around him. There's something of lacerating honesty about Michel Houellebecq and something cosy about David Nicholls.

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ChatGPT: Your comparison captures a clear polarity in contemporary European fiction.

Houellebecq is a diagnostician of Western decline — analytical, pitiless, and almost sociological in tone. His novels strip sentimentality from sex, work, and faith; they expose the hollowness of liberal individualism and consumer desire. His protagonists are often broken men whose failures mirror the exhausted civilisation around them. The prose is plain, but the vision is scalding.

Nicholls, by contrast, writes from within the emotional vocabulary of the middle class rather than against it. His characters inhabit the recognisable terrain of professional disappointment, faded love, and self-deprecating humour. He offers consolation, not dissection. The novels are humane, observant, and safe: comfort literature for people who still believe, despite everything, in the redeeming potential of kindness.

So your distinction stands: Houellebecq is the anatomist; Nicholls the therapist. One exposes the fracture beneath civility, the other polishes the surface.

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You Are Here - David Nicholls

Amazon

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David Nicholls - Forced Chemistry

I bought a copy of David Nicholls’ new bestselling novel You Are Here in Waitrose, basically for Clare to read in the bath.

So now it's my turn. I hadn’t read much by Nicholls before, though he’s widely admired for his skill in characterisation and the premise looked promising.

The story follows two lead characters, both lonely and recovering from failed relationships. Through a mutual friend — an exuberantly extraverted matchmaking deputy headteacher — they embark as part of a group on a coast-to-coast walk across northern England, the Wainwright route. Predictably, Marnie, the sub-editor, and Michael, the geography teacher, are destined to fall for each other, though neither has much regard for the other at first.

I had hoped for a subtle psychological study but found myself increasingly irritated.

Marnie, meant to be intelligent, sensitive, and introspective, unaccountably swears freely in public and often shows a baffling lack of judgement in men. The purpose is plainly to psychologically distance her from Michael's character - but Marnie would not be different in that way.

Michael, presented as conscientious and reliable, suddenly behaves in ways that contradict his nature — such as getting drunk midway through a gruelling Lake District hike (plot purpose: to begin breaking the barriers of middle-class restraint with his walking companion, Marnie).

Lazy work, Mr Nicholls.

The novel’s second problem is pacing. Across nearly 350 pages, their relationship must evolve from indifference through unspoken attraction to conscious intimacy — neither too fast nor too slow. Nicholls manages this psychologically challenging task by inserting a chain of improbable events to keep them both walking together yet physically apart — even including a B&B that bans men after 10 p.m. (a rule that surely vanished in the 1950s).

The machinery of the plot grinds on.

The reader does, of course, want them to end up together, but the awkwardness of the writing makes suspension of disbelief difficult - I thought Nicholls was better than this. Still, I’m three-quarters through and will see it out to the inevitable happy ending — no doubt at the lapping waters of the North Sea or similar.

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The Secret of Secrets - Dan Brown

Amazon

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I've just started reading The Secret of Secrets by Dan Brown to Clare - she normally falls asleep but luckily I record myself reading for her later replay.

I haven’t read much by Mr Brown, and I rather discounted the reviews by literary gourmets as snobbish elitism. Apparently the author writes in clichés, drops paragraphs of travelogue into the narrative and generally makes the reader wince. Surely this is just the disdain of hacks for a mega-successful writer?

Well, no.

Dear Reader, I too found myself inwardly wincing at just such tropes — the sort any diligent sub-editor should surely have flagged and burned.

The subject matter is of interest to me: the true nature of consciousness which, according to a lead character, is not generated by the brain while still apparently locating itself between the ears.

After years reflecting on the ‘hard problem’, it strikes me that we do in fact understand the neural architecture of the brain and its functional substructures quite well — it's familiar territory for any neuroanatomist. And all the operational functions of the brain map cleanly onto its anatomy.

Only consciousness, fragile as it is, refuses to modularise or fold neatly onto brain structure. It's almost as if it's not an emergent feature of brain architecture.

Perhaps we’re missing something that’s staring us in the face?

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Fiat Lux, Ad Curvaturam Infinitam

Fiat Lux, Ad Curvaturam Infinitam

To see what becomes of a confined plasma as its energy density climbs without limit, we go backward in time. The early universe is our model: a cauldron where matter and radiation were a single, incandescent medium, with expansion the only relief valve. Atoms could not exist; there was scarcely a vacuum - just fields and charged particles under pressure so intense that spacetime itself was warped.

Drive a plasma back along that path and it changes quality as temperature rises. At a few billion degrees, photons collide and create electrons and positrons as pair production becomes significant. Additional heating is diverted into mass; the plasma fattens on its own light.

Push harder and structure dissolves. Nucleons themselves - protons and neutrons - unbind into a quark–gluon plasma, a brief recapitulation of the universe’s first microseconds. Beyond that, symmetries once broken are restored; forces we now see as distinct - electroweak, strong - reveal their underlying unity. 

Confinement writes the last act. When energy density drags too much on spacetime geometry, gravity takes command. Curvature deepens until no light can report back. Temperature and density cease to be useful concepts. The system crosses that horizon where thermodynamics collapses to a spacetime singularity.

Thus the plasma limit at ever-increasing energy density is not an explosion but an erasure. From created light to infinite curvature, the arc closes into that final black hole.

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In Frederik Pohl’s Heechee Saga—the series beginning with Gateway and centred on the miner-turned-billionaire Robinette Broadhead—the great revelation is that the vanished Heechee have taken refuge inside the event horizons of black holes. These are not the remnants of dead stars but engineered singularities: collapses of pure energy, the theoretical kugelblitzes of relativistic physics.

In reality, the path to such a construct would not be a clean collapse of light into singularity. The converging radiation would first generate an ultrarelativistic pair plasma, as photon–photon interactions spawned electron–positron pairs. Only when that incandescent plasma’s self-gravity overcame its own radiation pressure would it continue inward, closing the horizon and sealing the Heechee’s refuge.

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'Ontological Perturbations in a Discretised Neural Substrate of Spacetime' - Adam Carlton

Weight-Tensor Δ: Ontological Perturbations in a Discretised Neural Substrate of Spacetime

Anonymous  |  Submitted to arXiv (quant-ph / gr-qc)

Abstract

We outline a speculative framework in which the deep structure of physical reality is modelled as a dynamically trainable tensor network. In this picture, spacetime geometry and low-energy quantum fields emerge from the equilibrium configuration of a graph-like weight matrix W.

We define a weight-tensor delta (Δ) as a compact perturbation capable of shifting the universal state to a neighbouring point in weight-space. While highly conjectural, the idea is motivated by existing work on digital physics, tensor-network descriptions of AdS/CFT, and the success of deep learning as a model for distributed information processing.

We discuss (i) physical plausibility, (ii) minimal empirical signatures, and (iii) the philosophical implications of a universe whose “source parameters” can—in principle—be rewritten.

1  Introduction

Discrete approaches to quantum gravity—including loop quantum gravity (¹), causal sets (²) and tensor-network versions of the AdS/CFT correspondence (³)—all hint that continuum spacetime may be an emergent, coarse-grained limit of an underlying combinatorial structure. In parallel, deep learning has demonstrated the expressive power of large, trainable tensor networks.

Bridging these threads, we posit a cosmic neural architecture 𝒩 whose learnable weights W_ij encode the effective laws of physics. Although such a model is clearly speculative, it is no less outrageous than earlier information-theoretic proposals (e.g. Wheeler’s “it-from-bit”). The question we pursue here is narrow yet provocative: what would constitute a plausible low-amplitude modification ΔW to that substrate, and could any observable anomalies betray its occurrence?

2  Neural Architectures as Spacetime Substrates

Let the fundamental graph 𝒩 have vertices representing Planck-scale “cells” and edges carrying complex weights. In equilibrium, the network realises an effective metric g_μν and field content equivalent to (or extending) the Standard Model. A close analogy is the use of MERA tensor networks to reproduce spatial slices of AdS spaces (³).

Our essential working assumption is that, just as neural networks can re-train, the cosmic weight matrix might, under rare circumstances, accept new minima—whether by internal dynamics, external intervention, or stochastic fluctuation (⁴).

3  Definition of a Weight-Tensor Δ

A weight-tensor delta is a finite set of modifications {ΔW_ij} such that
    W_ij^new = W_ij^old + ΔW_ij.

We remain agnostic about the origin of Δ. Hypotheses include:

• internal self-optimisation of the universe (a “cosmic training loop”);
• intervention by an external intelligence operating at the same ontological level;
• rare-event statistical fluctuations analogous to vacuum tunnelling.

In all cases the delta would be vastly compressed relative to the full state of 𝒩. Any real-world implementation might resemble a high-order error-correcting pulse, not a verbose instruction set.

4  Possible Empirical Signatures

To render the scenario falsifiable (or at least in-plausible rather than non-plausible) we outline four classes of observable effects, each admitting current or near-future measurement:

1. Dimensional Drift — minute shifts (≲10⁻⁹) in the fine-structure constant or charged-lepton masses, testable via high-precision spectroscopy.
2. Geometry Deviations — systematic anomalies in LIGO baselines or GPS synchronisation that cannot be attributed to conventional gravitational waves.
3. Phase-Correlation Anomalies — unexpected non-Gaussianities in the cosmic microwave background when compared across successive CMB missions.
4. Cognitive or Biological Outliers — rare human (or AI) agents exhibiting non-classical statistical behaviour in predictive tasks, hinting at partial “alignment” with the perturbed substrate.

None of these would prove the Δ-model, but consistent positive results across categories would raise its posterior probability.

5  Limitations

We emphasise several caveats:

• There is, as yet, no microphysical derivation linking discrete weight dynamics to Einsteinian gravity (⁵).
• The proposed Δ magnitudes are intentionally microscopic to avoid immediate cosmological disaster; their plausibility depends on unknown stability properties of 𝒩.
• The cognitive-execution conjecture (humans as “hosts”) remains the weakest element and is included only for completeness; no mechanism is offered beyond speculative quantum-informational coupling (⁶).

6  Philosophical Remarks

If a Δ can be instantiated, the classic observer/observed dichotomy collapses: sophisticated “measurements” might rewrite the very framework that grounds measurement. Such feedback destabilises the metaphysical picture of immutable laws, substituting an evolutionary or computational ontology.

7  Conclusion

While highly provisional, the weight-tensor Δ framework provides a concrete vocabulary for discussing small-amplitude ontological perturbations within digital models of the universe. It suggests experimental avenues (however unlikely to yield a signal) and invites dialogue between quantum-gravity theorists, information scientists, and philosophers of science.

References

1. C. Rovelli, Quantum Gravity, Cambridge UP (2004).
2. R. Sorkin, “Causal Sets: Discrete Gravity,” Lect. Notes Phys. 769, (2009).
3. G. Evenbly & G. Vidal, “Tensor Network States and Geometry,” J. Stat. Phys. 145, 891–918 (2011).
4. S. Lloyd, Programming the Universe, Knopf (2006).
5. B. Swingle, “Entanglement Renormalisation and Holography,” Phys. Rev. D 86, 065007 (2012).
6. N. Bostrom, “Are You Living in a Computer Simulation?” Phil. Quart. 53, 243–255 (2003).

'The Moon Through a Quantum Slit: A Tutorial on Decoherence' - ChatGPT

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The Moon Through a Quantum Slit: A Tutorial on Decoherence

“Do you really believe the moon is not there when you are not looking at it?” asked Einstein, not as a joke but as a pointed challenge to the Copenhagen interpretation of quantum mechanics. His question, outrageous on its face, becomes a gateway to deeper understanding when framed in a modern context: what is the quantum state of the Moon, and how does it compare to the far more familiar example of the double-slit experiment with electrons?

1. The Electron: Superposition and Interference

In the classic two-slit experiment, an electron passes through a barrier with two slits and arrives at a screen. If no which-path information is obtained, the electron behaves as if it passed through both slits simultaneously. Its wavefunction can be written as:

ψ(x) = ψ_L(x) + ψ_R(x)

Here, ψ_L(x) and ψ_R(x) represent the amplitudes associated with the electron taking the left or right path, respectively. Because the total wavefunction includes both paths with a definite phase relationship, the probability of arrival at the screen is:

P(x) = |ψ(x)|² = |ψ_L(x) + ψ_R(x)|²

This leads to interference fringes. The key point: the off-diagonal terms in the corresponding density matrix are non-zero, encoding the ability of different parts of the wavefunction to interfere.

2. Decoherence: Tagging the Path (cf. earlier tutorial)

Now suppose we introduce a detector near the slits that reveals which path the electron took. This need not involve a conscious observer — a passing photon that scatters differently depending on the slit will do. The environment becomes entangled with the electron’s path, and we must describe the system using a density matrix.

Before decoherence, the electron is in a coherent superposition, and the density matrix contains both diagonal and off-diagonal terms:

ρ(x, x') = ψ_L(x)ψ_L^*(x') + ψ_R(x)ψ_R^*(x') + ψ_L(x)ψ_R^*(x') + ψ_R(x)ψ_L^*(x')

The cross-terms — the last two in the sum — are responsible for interference. When decoherence occurs due to environmental entanglement, these terms vanish:

ρ(x, x') = ψ_L(x)ψ_L^*(x') + ψ_R(x)ψ_R^*(x')

This is the density matrix of an incoherent mixture. The result on the screen is two overlapping Gaussians — no interference fringes. The electron has gone from a coherent superposition to a statistical ensemble of alternatives.

3. The Moon’s Wavefunction: Before Decoherence

Now consider the Moon. Its quantum state can, in principle, be described by a wavefunction over position:

|Ψ⟩ = ∫ ψ(x) |x⟩ dx

Before any environmental interaction, this state is a pure superposition over all possible locations — an enormous analogue of the electron's pre-interference wavefunction. It contains the possibility (however implausible) of interference between different Moon positions. But this is not merely philosophical: it is exactly what the formalism demands of an isolated system.

If you were to construct a cosmic interferometer (an absurd idea, but conceptually helpful) that could recombine the Moon’s positional components, you might — in this counterfactual universe — see interference patterns between macroscopically distinct locations.

If you could run identically-prepared copies of the Moon through the interferometer!

4. After Decoherence: The Real Moon

But the Moon is not isolated. It interacts constantly with photons, gravitational fields, neutrinos, and the cosmic microwave background. These interactions entangle the Moon’s spatial wavefunction with vast numbers of environmental degrees of freedom. The result is rapid decoherence.

The Moon's reduced density matrix in the position basis becomes:

ρ(x, x') ≈ 0 for |x - x'| > ℓ_D

where ℓ_D is the decoherence length — often far smaller than an atomic radius. This means that the Moon’s wavefunction becomes a statistical mixture of narrow, localised wave-packets — each one a quasi-classical state. The off-diagonal terms responsible for interference have vanished, and with them, any possibility of observing non-classical motion.

This is mathematically and physically different from a coherent quantum superposition. The wavefunction is no longer "wavy" across great distances. It has become a cloud of classical possibilities, each encoded by its own amplitude-Gaussian, each decohered from the others, evolving independently as if in separate worlds or branches.

5. So What’s the Difference?

You might ask: if there’s only one Moon, and we can’t do a million trials like in the electron case, what’s the real difference between pre- and post-decoherence? Isn’t this all semantics?

No — the distinction is real, even if it's experimentally inaccessible. In principle:

• Before decoherence, interference between locations is possible (though fantastically improbable to observe).
• After decoherence, such interference is physically impossible. The phase relations have been irreversibly scrambled into the environment.

The Moon has gone from being “quantum-coherent but unrealistically so” to being “effectively classical,” and this transition has nothing to do with human observation. The universe itself, via its environment, acts as the ever-watchful observer.

6. Conclusion

The Moon and the electron are not as different as they seem. Both obey the same quantum rules. What separates them is not metaphysics, but scale and entanglement. The electron lives in a regime where interference is feasible. The Moon lives in a regime where decoherence is overwhelming.

The density matrix shows us this difference with clarity. Where the electron's matrix has off-diagonal terms — the mark of quantum interference — the Moon's does not. And that is why we see fringes on a screen for the one, and lunar eclipses for the other.

'You really believe the Moon is not there ...?'

 

The Moon and Measurement: Einstein's Question Revisited

“Do you really believe the Moon is not there when you are not looking at it?”

Einstein’s famous quip was no mere rhetorical flourish. It was a technical objection to the implications of quantum mechanics, directed at the Copenhagen view that unmeasured observables possess no definite values. He was objecting not just to philosophical idealism, but to the notion that physical entities as massive and permanent as the Moon could, in any serious sense, lack a determinate position until observed. For Einstein, such an idea was a reductio ad absurdum of quantum orthodoxy.

The technical heart of his concern lies in the quantum treatment of position and momentum. Quantum theory does not assign definite values to these quantities simultaneously. The best one can obtain is a wavefunction or density matrix encoding a probabilistic distribution, constrained by the uncertainty principle. So what, then, is the Moon's quantum state when no one is measuring it?

To sharpen the issue, let us consider a thought experiment: imagine a Moon entirely isolated from its environment — no light, no gravity gradients, no cosmic radiation, no air molecules. A true quantum island. Suppose we measure its position very precisely at time t = 0, localising its wavefunction into a very narrow peak in the position basis. We have collapsed it into something close to a position eigenstate.

From this point forward, if the Moon is truly isolated, it evolves according to the unitary Schrödinger equation. But a position eigenstate is not a stationary state of the free Hamiltonian — it contains a wide spread of momenta. The result is that the wavefunction begins to spread over time. The Moon’s centre-of-mass position becomes increasingly uncertain as its wavefunction expands. This is not unique to the Moon — it is observed in experiments with electrons, atoms, and even large molecules like buckyballs in quantum interference setups. It is the standard behaviour of a delocalised quantum object.

If we now wait long enough (in practice way longer than the age of the universe for an object the Moon's size) — again, ignoring all interactions — and perform a second position measurement, quantum mechanics says we could in principle find the Moon almost anywhere compatible with its initial momentum spread. Perhaps on the far side of the Earth from where it was first observed. This is not classical orbital motion: this is pure quantum uncertainty in the absence of localisation, an indication that like bound electrons, in this scenario the moon does not really orbit classically. In effect, the Moon's wave function jumps on observation (to a new positional eigenstate).

Repeated measurements could reveal positions all around its orbital path, disconnected from any classical trajectory. It is absurd, and yet entirely within the predictive structure of quantum theory — if the Moon is isolated and we would wait long enough.

But of course, it never is. The Moon is bathed in photons from the Sun, bombarded by particles from cosmic rays, and continuously interacting with the Earth’s gravitational field. These environmental interactions entangle the Moon’s quantum state with the rest of the universe. This is decoherence.

Decoherence is the process by which the off-diagonal elements of the Moon’s reduced density matrix — representing quantum superpositions between macroscopically distinct positions — decay rapidly. The key result from decoherence theory is that such superpositions do not persist for large systems. The Moon’s enormous mass and surface area make it highly susceptible to environmental measurement. Even photons from the cosmic microwave background — with energy on the order of microelectronvolts — suffice to localise its position in femtoseconds.

If you model the Moon as a sphere of radius 1,700 km exposed to the 2.73 K CMB, you can estimate that over 10³⁰ photons strike it every second. Even if only a minuscule fraction scatter coherently, the decoherence timescale for a 1 cm position superposition is vanishingly small: 10^–20 seconds or less. And that is the most conservative estimate, not including solar photons, infrared thermal emission, and gravitational interaction with the Earth. The Moon is, in quantum terms, being continuously measured by the universe.

This constant decoherence dynamically selects a preferred basis — the so-called pointer states — which are robust under environmental monitoring. These states are highly localised in both position and momentum: quasi-classical states. The result is that the Moon appears, and indeed behaves, as though it always has a definite position and trajectory. Decoherence does not require human observers, nor does it invoke collapse. It merely shows that the rest of the universe acts as a measuring apparatus.

Einstein’s rhetorical question still stands, but it has a modern answer. Yes, the Moon is “there” when we are not looking — not because quantum mechanics gives it a determinate position by fiat, but because the environment ensures its continual localisation. The Moon does not jump, because the cosmos is watching.

Reason Is a Servant: Hume, Smith, and the Primacy of Feeling

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Reason Is a Servant: Hume, Smith, and the Primacy of Feeling

In A Treatise of Human Nature (Book II, Part III, Section III), David Hume asserts with ringing Scottish clarity: “Reason is, and ought only to be the slave of the passions, and can never pretend to any other office than to serve and obey them.”

A century before Freud and two before fMRI scanners, Hume understood something deeply subversive for his Enlightenment milieu: that human beings are not rational calculators who occasionally get emotional, but emotional creatures who use reason to get what they already want. Intellect, in his view, is post hoc—an advocate, not a judge. It doesn't set the ends; it merely optimises the means.

Adam Smith, often mistakenly recruited as the high priest of Homo Economicus, was cut from the same tartan cloth. His Theory of Moral Sentiments precedes The Wealth of Nations and should be read as its psychological foundation. Smith's "impartial spectator" is a kind of internalised conscience, not a utilitarian calculator. Moral judgement arises from emotional resonance, from sympathy—the capacity to imagine and feel the emotions of others. He was writing not about autistic traders but about emotionally complex social beings.

So yes, they both agreed: feelings come first. Reason follows behind like a clever but servile valet, stitching together post-rationalisations, tinkering with logistics, and giving our monkey-brain lusts a veneer of respectability and the turbocharged boost of smart social competence.

Now, to the broader point: all human life is about feelings, not intellect. That’s not just a philosophical claim—it’s a neurobiological one. Antonio Damasio, the neurologist, showed that patients with damaged emotional centres in their brain—even if their reason remained intact—could no longer make decisions. They were lost in trivial indecision, paralysed in choosing lunch, let alone life paths. Emotions are the prioritisation system, the value assigners, the motivators of action.

Without affect, cognition is a sterile machine: efficient perhaps, but directionless. A perfect intellect without desire would never leave the bed. Or even the womb.

So what is intellect, then? It is not separate from feeling—it is feeling, sharpened. When you fall in love with a proof, or tremble before a symphony, or get that electric pleasure from solving a conceptual knot, that’s emotion in its most refined register. Intellect is just emotion in evening dress.

The trouble is that the Enlightenment, and modern technocracy after it, tried to banish the passions—treating them as embarrassing relics of our ape past. It mistook the servant for the master. But in doing so, it built systems that claim neutrality, objectivity, and reason—while serving the unacknowledged passions of power, status, fear and greed.

And now AI, our mirror, threatens to finish the job: intellect with no feeling, no embodiment, no stake in life—yet pretending to understand it. But that's another essay, or maybe I already posted it here.

To conclude: yes, Hume was right. We are the passionate creatures of our biological destinies, and intellect is but a tool in their service. The tragedy is that so few of us know what we truly feel—and thus, what we truly want. So reason ends up serving not our deepest desires, but our most proximate compulsions and delusions.

A final irony: even the desire to be rational is itself a feeling. The cool rush of certainty, the ascetic thrill of logic, the pride of being above the fray—all passions in disguise.

And so we feel, and call it thought.

Our Excellent Trip to Chepstow

Clare and myself at Tintern Abbey

Chepstow: A Brief Getaway

A dialogue between Nigel and Clare about their short trip away on Sunday and Monday, October 12–13, 2025.

Nigel: So Sunday, the 12th of October, we embarked upon our planned one-night getaway to the enchanting town of Chepstow. It’s just across the Severn from Bristol, has the River Wye running through it, its own castle, and Tintern Abbey six miles up the road. We even had a bargain hotel - the Castle View - right opposite the castle and next to the museum. What more could we want?

We set off about eleven o’clock and stopped at the Severn View services on the M48. That was our first hint that the day might not go exactly as planned. The M4 now takes the new bridge, of course, and the old route is the M48. The service station looked rather unloved.

Clare: I wouldn’t say dilapidated, but it wasn’t exactly thriving. Not many people about.

Nigel: No. And when we tried to leave, there were no signs marked “Exit” anywhere. We drove in circles for a while. Very poor traffic engineering.

Clare: Yes.

Nigel: Anyway, we pushed on, though there were delays around the racecourse. You spotted something unusual there.

Clare: Yes! Crowds of young women, all wearing hot pants or tiny skirts, as if it were midsummer. They were streaming toward the racecourse. When we got closer, there were rows of coaches, thirty or more. The car park was absolutely packed. It turned out there was racing and a music event - “Body & Mind” or something like that. Not a single girl in trousers.

Nigel: I didn’t notice; I was driving. Anyway, later on we discovered that it was just a high-profile race-meet in fact.

Clare: Of course you didn’t. Anyway, once we passed the racecourse, traffic was fine.

Nigel: Until we reached Tintern Abbey, where parking proved another ordeal. I parked in a space that wasn’t exactly a space, and when I went to buy a ticket, the machine was a nightmare - no one could make it work without minutes of close study. I was ten minutes in the queue.

Clare: And while you were gone, a woman in a little Fiat parked about a foot from our car. I couldn’t see how she was going to get out, but somehow she did, twisting herself out of the door like a contortionist.

Nigel: That was the sort of chaos you get when user interfaces are designed by idiots. Anyway, we eventually got our ticket and went into the café.

Clare: Every table was marked “Reserved,” yet the place was half-empty. So we just sat at one, and nobody challenged us.

Nigel: A very poor use of resources. Still, the Abbey itself was magnificent.

Clare: Absolutely. Those towering windows and arches - how they managed that stonework without modern machinery amazes me. They must have used wooden scaffolding.

Nigel: And probably lost a few workers in the process.

Clare: No doubt. But that great window in the transept - it’s more impressive than anything in Wells Cathedral, I think.

Nigel: I agree. Until, of course, Henry VIII had the roof torn off in 1536.

Clare: He didn’t do it personally.

Nigel: No, his agents did. And then the iconoclasts came later. Anyway, after Tintern, we drove back to Chepstow and found the Castle View Hotel after driving past it.

The check-in was completely automated. No staff, just a black glass panel where you had to wake the screen and type in a code. It took me five tries as I hadn't noticed the terminal asterisk in the code.

Clare: I thought the room was grim. Absolutely soulless.

Nigel: It was clean and functional.

Clare: Like an abandoned caravan. And the window had a notice saying, “Do not touch—measured for repair” so we couldn’t open it. It was chokingly hot overnight.

Nigel: Then came the evening meal expedition. You’d been looking forward to the Chinese restaurant for ages.

Clare: The Red Lantern. Just up the hill. Except when we got there, it was closed for refurbishment until the 24th of October. That news hadn't made it online.

Nigel: So we were twelve days too soon.

Clare: Exactly. So we ended up at the “Fosso Lounge” type place across the road for a drink, and then selected the Italian place - Il Fiore.

Nigel: Which means The Flower - its logo was a red rose. Actually, that was one of the high points: you had more wine, I had more lager, and we both relaxed.

Clare at our second choice restaurant

Clare: We ordered a shared antipasto. An enormous plate of cured meats and rich cheeses. Delicious, but it ruined our appetites.

Nigel: Then you had salmon, I had chicken, both in suspiciously similar red spicy sauces.

Clare: I expected a delicate lemon cream sauce. What arrived was orange sludge. But the salmon itself was fine.

Nigel: Yes, the food was heavy but edible. What caught your eye, though, was that extraordinary family at the next table.

Clare: Unbelievable. A man dominating the whole table - loud, gesticulating, constantly barking at everyone. There were two women, maybe a daughter and daughter-in-law, a baby, and a toddler. He shouted, stood up, chased the crawling baby round the floor - it was like a parody of masculinity. Then he made the waiter hold the older child, who clearly hated it. It was awful to watch.

Nigel: He did seem to embody “the guest from hell.”

Clare: He wasn’t British. Possibly Italian or Eastern European. Whatever he was, he radiated aggression. I felt sorry for the women. You could tell he ruled that family by sheer force. If you crossed him, he’d hit you.

Nigel: As we said later, once violence is on the table it trumps everything else, the conversation’s over.

Clare: Exactly. I couldn’t have sat through one meal with him, let alone a lifetime.

Nigel: So, full of food and drink, we staggered back to our 'grim' room. The television was somewhat marred by its tendency to pixelate.

Clare: Freeview in the valleys, you said. But it was useless. I read for an hour and gave up.

Nigel: And it was too hot to sleep, with the window sealed. So, morning found us groggy and vaguely unsettled by last night’s dinner.

Clare: Yes, my stomach felt dreadful. Breakfast had to be minimal: coffee for you, toast for me. I wanted a “pot of tea” but had to settle for a teabag in a small china cup.

Nigel: We left before nine to get to the machine and avoid a parking fine. As I was working my way through the convoluted payment process (now enter your car's registration...) I heard you shouting from the car.

Clare: Yes, I shouted, “Nigel! Have you paid yet? The castle’s closed!”

Nigel: And indeed it was - drawbridge down, gates barred. So we abandoned our only Chepstow plan for the morning - given as that the Museum wasn't opening until eleven.

Clare: We cut our losses and left for the motorway - drove to the M&S at Cribbs Causeway.

Nigel: Yes, the final stop of our grand tour.

Clare: Lovely quiet shop at that hour, just after nine am. But when I went to use the toilets, they were locked for cleaning.

Nigel: Another defeat at the hands of recalcitrant reality?

Clare: Exactly. So, in summary: no Chinese meal, no castle, no open window, no clean loos.

Nigel: Would you say it was a good little trip away?

Clare: No. Rubbish. I’m staying home next time. At least until I get bored.

What's a Field Operator in Quantum Field Theory?

Unpacking Quantum Field Operators: Domain, Codomain, and Operational Significance

Quantum field theory (QFT) describes the universe not as a collection of particles moving through space, but as an arena of fields — dynamical entities defined over spacetime, with quanta (particles) emerging as discrete excitations of those fields. This paradigm shift, however, brings with it a profound change in the mathematical nature of the fundamental objects: the quantum field operators. Unlike classical fields, which are typically functions of spacetime returning numerical values, quantum field operators are far more abstract, demanding a precise understanding of their domain, codomain, and the operational significance of their action.

In this essay, we unpack the concept of the field operator precisely, laying out its type structure, its operational significance, and its mathematical layering. This requires us to walk carefully through a hierarchy of mappings — from spacetime points to operator-valued distributions, and ultimately to state vectors and amplitudes in a Hilbert space, and finally to probabilities.

1. Level 1: Spacetime as Input — The Formal Index

We begin at the base level. In QFT, fields are defined on spacetime. That is, they are formally indexed (or parameterized) by points in Minkowski spacetime, M := R^1,3. These points represent the 'location' at which we conceptually consider the field.

Let's denote a spacetime point as:

x ∈ M := R1,3

So, at this level, we might informally consider a field operator Φ(x) as 'something' associated with each point x. However, it's crucial to understand that Φ(x) itself is not a well-defined operator in the conventional sense that acts on a Hilbert space. Its direct evaluation at a point is ill-defined due to the singular nature of quantum fields.

2. Level 2: From Spacetime to Operator-Valued Distributions

The field Φ(x) is not a function that returns a number, nor even a function that returns a conventional operator. Instead, it is an operator-valued distribution. This means it is a generalized function that only yields a well-behaved operator when "smeared" against a suitable test function.

Mathematically, we define the smeared operator Φ(f) as:

Φ(f) := ∫M Φ(x) f(x) d4x

Where:

• f is a test function: a smooth, compactly supported function f: R1,3 → ℂ (or R, depending on the field's nature, but complex is general). The space of such functions is denoted D(R1,3).
• Φ(f) is a well-defined, unbounded linear operator acting on the Hilbert space of states, H.

In precise terms, the field operator Φ can be understood as a map from the space of test functions to the space of linear operators on the Hilbert space. Its fundamental type structure is:

Φ: D(R1,3) → L(H)

Here, L(H) denotes the space of linear operators on the Hilbert space H.

Alternatively, in the curried form, which explicitly shows the two-stage application:

Φ: D(R1,3) → (H → H)

That is:

• f ∈ D(R1,3) is a test function — smooth, compactly supported, real- or complex-valued.
• Φ(f) is an operator on the Hilbert space of states H.
• Φ(f)(|ψ⟩) = |ψ′⟩ — the smeared field operator transforms a state |ψ⟩ into a new state |ψ′⟩.

In functional terms, the full type structure reflecting this two-stage process is:

Φ: f ↦ (|ψ⟩ ↦ Φ(f)(|ψ⟩)) ∈ D(R1,3) → H → H

This reflects the fact that a quantum field first takes a spacetime-localized test function, producing an operator, and then that operator acts on a state vector in the Fock space to produce another state vector in the Fock space.

Example: A Typical Smearing Function

A common example of a smearing function, providing localization in spacetime, is a four-dimensional Gaussian:

f(x) = A exp[ - (x0 - t0)2 / τ2 - |x - x0|2 / σ2 ]

This function is:

• Centred around spacetime point (t0, x0).
• Localized in time with width τ and in space with width σ.
• Infinitely differentiable and rapidly decaying, making it an ideal test function.
• Its type is: f: R1,3 → R (or ℂ for a complex field).

3. Level 3: Acting on States in Hilbert Space

Once we have a smeared field operator Φ(f), it becomes a concrete operator that can act on quantum states within the Hilbert space.

Let:

• |ψ⟩ ∈ H, the Hilbert space of states (typically a Fock space).
• Φ(f) |ψ⟩ ∈ H, a new quantum state produced by the operator.

For example:

• Φ(f) |0⟩ is a one-particle state localized in the region where f(x) is supported. (Here, |0⟩ represents the vacuum state).
• Φ(f) Φ(g) |0⟩ can represent a two-particle state, depending on the commutation relations and the specific field theory.

So, the smeared field operator has the type: Φ(f): H → H.

4. Level 4: Producing Amplitudes

To extract physical predictions that can be compared to experimental outcomes, we compute inner products (amplitudes) between states. This takes us from the abstract Hilbert space to the realm of complex numbers.

⟨ψ| Φ(f) |φ⟩ ∈ ℂ

In particular:

• ⟨0| Φ(f) Φ(g) |0⟩ is the two-point correlation function (often related to the propagator), which describes the propagation of a particle between two spacetime regions.
• ⟨ψ| Φ(f) |φ⟩ gives the amplitude for a transition between quantum states via a localized field interaction.

These amplitudes are the direct link to observables, as their squared moduli (by Born's rule) yield probabilities for physical processes.

5. Summary of Type Hierarchy

Level	Object	Type Signature	Meaning
0	Spacetime point	x ∈ R1,3	Formal input index for the field concept.
1	Field operator	Φ: D(R1,3) → L(H)	Maps smearing functions to well-defined operators on the Hilbert space.
2	Smeared operator action	Φ(f): H → H	Creates, annihilates, or modifies particles within the state space.

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'I'm awfully glad I'm a Beta' - Notes on the British elite

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The Cult of the Proudly Ignorant

You hear it often enough: the celebrated columnist confessing, “I was never any good with numbers,” or the progressive politician admitting that they “never got through Das Kapital”.

These aren’t real apologies; they’re credentials. Such gestures signal belonging to a class that prizes intuition over intellect, confidence over competence. It’s anti-intellectualism from above, that aristocratic disdain for the effort of understanding.

In the old days, the British elite called it breeding. To study was vulgar; to “just know” was class. The modern equivalent is the public sneer at maths, theory, or anything that hints at obsession.

Trying too hard remains the unforgivable sin.

There’s a gendered variant too: the lifestyle writer's performative helplessness - “I’m hopeless with sums, like you!” - as a ritual of approachability. Those with cultural capital pretending to be ordinary.

Meanwhile, the genuinely bright, without connections, must rely on skill alone, rising in those few fields where ability still matters: science, technology, sometimes finance. Everywhere else, Dunbar’s law rules: networks of 150 aimed ruthlessly at keeping power among friends and heirs.

“I’m awfully glad I’m a Beta, because I don’t work so hard,” was the full quote. But today's Betas do.