Tag: maths

Unmixing the Steel

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12–17 minutes

A toy model of why purification is the wrong verb – offered for dissent.

Addendum: Please note that I have added an endnote to this post to explain the maths a bit better.

Preamble

I continue to press on colonialism, but this time I look at possibilities and probabilities of extricating colonial influences. I suggest that this is easier said than done. I am no expert in colonialism, post-colonialism, or decolonialism, but I have an interest in philosophical claims and maths, so here I am. Here, I attack a particular model using the metaphor of reconstituting from an alloy. This may be the wrong practical argument, but I address it all the same.

Decolonising decolonisation

There is a picture of decolonisation so intuitive that it barely announces itself as a picture. Something foreign was introduced. The task is to get it out. Sift the flour, strain the tea, remove the intruder, and what remains is ours again. The picture is tidy, it is emotionally satisfying, and it licenses a rule: identify the imports by provenance, discard them, keep the rest.

Let me say at the outset what this essay is not, because the register invites misreading. It is not a defence of the Enlightenment’s colonial rationale, which I regard as indefensible. It is not a claim that nothing should be dismantled. I hold no brief for borders, nations, or the machinery that enforces them, and I am not about to acquire one in the space of fifteen hundred words. The argument is narrower and, I think, more awkward: the subtraction rule cannot be applied, not because it is politically inconvenient but because it is arithmetically malformed. If you want to dismantle something, you need a rule that can actually be run. Provenance is not one.

Wrong metaphor, slightly better metaphor

The usual image is a solution – salt in water. Evaporate the water, and you get your salt back. The image quietly promises that separation is a matter of energy and patience.

Alloys are less accommodating. Steel is not iron with carbon loitering nearby; the hardness belongs to the compound, not to either constituent. Better still, steel’s properties depend on its thermal path as much as its composition. Identical carbon content, quenched rather than annealed, gives you a different material. The map from ingredients to properties is many-to-one and runs in one direction only. You cannot read the recipe off the blade.

That is the metaphor I want, and I want it because it makes a specific claim rather than a mood: the question which properties are the coloniser’s? is not hard to answer. It is malformed. The properties in dispute are compound properties. They have no constituent-level owner to be returned to.

So I built a small arithmetic model to see whether that claim survives being made precise, or whether it evaporates like most metaphors do when you make them count.

Unmixing_the_SteelDownload

What the model is for

Not evidence. Let me be blunt about this, since it is the first objection and it is correct. The model demonstrates nothing about actual history. The numbers are invented. There is no dataset, no measurement, no claim about any real polity.

Its use is different and, I’d argue, more honest than a model pretending to measure. It converts a rhetorical position into a set of rules, so that anyone who wants to disagree has to say which rule they reject rather than merely disliking the conclusion. That is a better argument than either of us shouting about purity. It also has the pleasant property of being able to embarrass its author, since a model can fail to produce the result you wanted, which is more than can be said for an essay.

The rules

Take a polity’s stock of practices – institutions, techniques, concepts, forms of life, whatever you like. Sort every element into three registers:

  • E : endogenous-tagged. Arose from the inherited repertoire.
  • X : exogenous-tagged. Imposed or imported from outside.
  • J : joint. Generated by combining the two, and therefore tagged to neither.

Two rules govern the dynamics.

Recombination. Each period, new practice is generated by combining two elements drawn at random from the existing stock. The offspring is E only if both parents are E. It is X only if both are X. Otherwise – mixed parentage, or a parent that is itself already joint – it is J.

Injection. During the colonial window, a fixed quantity is added to X each period from outside. This is the imposition proper: it does not arise from the stock, it is put there.

Then run two timelines. B receives the injection. A does not – except that A receives a fraction of it anyway, because no polity in the relevant centuries was sitting outside the world colonialism was busy making. Meiji Japan was not a control group. It was adapting to a treated world. In the causal-inference idiom this is an interference violation; I have simply written it in as a leakage parameter rather than confessing it in a footnote.

Finally, a property index sits on top of composition: P = E + 0.6·X + 1.8·J. The large coefficient on J is the whole point of the alloy metaphor. The compound has properties neither constituent had.

Sample output

Forty periods, injection running from period 5 to 25, recombination at 10% of stock per period:

periodEXJJ-share
5161000.0%
102542093.2%
15384415611.7%
205526318423.0%
257558647235.9%
3097789104849.6%
40139891399472.8%

Three things fall out, and the first is not a parameter trick.

One: the joint register is absorbing, so it eats everything. Any element with a J parent produces J. J therefore never shrinks and its share rises monotonically toward unity. This is a theorem about the rules, not an artefact of my invented numbers – any contact at all, given recombination and sufficient time, drives the untaggable share to dominance. By period 40, roughly three-quarters of the stock belongs to no one’s provenance.

Watch the X column, which is where the model earned its keep. X stalls at 91 while the total stock climbs past five thousand. The provenance-visible residue shrinks to 1.7% – not because the imposition faded, but because it was metabolised. What persists of the imposition is precisely the part that has stopped being taggable. I find this the most interesting output, since it says something the metaphor alone did not: coloniality outlives colonialism because it stops being legible as colonial.

Two: subtraction barely moves anything. Strip out every X-tagged element – perfect execution of the purificatory programme, no enforcement problems, no disputes about the list. The property index falls from 8,642 to 8,587. Six-tenths of one per cent. The property lives in J, which the provenance rule cannot see, let alone reach. The purist gets to burn the 1.7% that remains legible and call it a restoration.

Three: the control timeline identifies nothing. Over two hundred stochastic runs, the uncolonised timeline A returns a mean of 8,336 with a standard deviation of 1,249 – a 5th-to-95th percentile band running from 6,276 to 10,173. Colonised timeline B returns 8,571. That is 0.19 standard deviations from A’s mean: sitting comfortably inside the distribution, indistinguishable from an ordinary draw. The decolonising intervention shifts things by about 0.04 sd. Even if you grant a counterfactual – which the previous essay in this sequence argued you cannot, there being no determinate nearest world and no transworld-identical bearer – the counterfactual’s own variance swallows the effect whole.

The rule that survives

If provenance cannot be run, something else has to be. The model points at the alternative rather than merely clearing the ground.

A genetic rule asks: where did this come from? It is an origin test. It requires a counterfactual to answer, has no truth-value when the counterfactual is undefined, and – as the X column shows – targets a shrinking sliver of legible residue whilst the compound does the actual work. Applied in practice, an inoperable rule gets applied by proxy, which means provenance is assigned by whoever holds the pen. The purity test cannot be corrected, because it has already assumed its own criterion.

A functional rule asks: is this presently load-bearing in the reproduction of the asymmetry? It is answerable from what is in front of you, revisable when the answer changes, and indifferent to pedigree. Railways and germ theory arrived with the apparatus and do not sustain it. A racialised labour hierarchy sustains it, whatever its vintage. The question is not what a thing’s parents were but what it is currently holding up.

This is not a concession wrung out of anyone. The better decolonial work got here first and by a different route – Mignolo’s delinking is explicitly not restoration, and Táíwò’s objection to purity-by-provenance is that it insults the appropriative agency it claims to restore. Fanon, whose practice was cheerfully larcenous with Hegel, Marx and Sartre, would have had little patience for a rule that condemned an idea by its passport. The purificatory picture I am attacking is the popular one, not the serious one, and I would rather say so than enjoy an easy win.

What I want dissent on

Three specific places, since general disagreement is no use to anyone.

The absorbing rule. Is it right that mixed parentage yields an untaggable offspring? A critic might say that provenance is heritable – that a practice built from a colonial institution and a local one remains colonial in the relevant sense, and my rule assumes away the answer. I think that reply reintroduces the genetic test by the back door, but it is the strongest objection and I would like it pressed properly.

The coefficient on J. Nothing forces the compound to have emergent properties, and if the property index were merely additive the whole result collapses. Is emergence the right assumption, or have I built the conclusion into the arithmetic?

Whether the generalisation holds. I take this to be one instance of a wider pattern: there is no un-enframed baseline against which to audit a technology, no pre-wage self whose unalienated labour the wage-form displaced, no pre-Norman England to compare the settlement against. Every member of the family runs the same undefined counterfactual, and every purificatory programme in the set is malformed the same way. That is either an elegant result or an overreach dressed as one, and I am genuinely unsure which.

Endnote: On the constants

Several readers have asked where the coefficients in the property index came from. The answer is that I chose them, and since a toy model’s only real virtue is that its assumptions are visible, it is worth saying exactly what they do, what other values would mean, and – the more useful question – which results depend on them. The short version: almost none do.

What the index is

The index sits on top of the composition and reads:

P = E + κX·X + κJ·J

where each coefficient is a weight declaring how much a unit of stock in that register contributes to whatever the index tracks. The reader may fill in ‘functional capacity’, ‘productive capability’, or simply ‘the thing about the arrangement anyone would care about’; the argument does not depend on the interpretation. What matters is that the index is a stipulated relation between composition and property, not a measurement of one.

The coefficient on E is fixed at 1 by normalisation. It sets the unit and carries no claim. The other two do carry claims.

κX : how imported practice performs in situ. An imported practice was selected somewhere else, under other conditions. κX asks whether that provenance costs it anything, or gains it anything, once it is running here.

κJ : whether the compound exceeds its parts. This is the emergence parameter, and it is what makes the model an alloy rather than a mixture. Steel is harder than iron or carbon; if the joint register merely inherited the average of its parents, the metaphor would be idle.

What different ranges mean

κXreading
< 0imports subtract: a harm model, coherent but a different argument from this one
0 – 1mismatch: practices adapted elsewhere underperform in a setting that did not select them
= 1neutral; provenance carries no functional consequence
> 1selection: things get imported because they work, so imports outperform the average
κJreading
< 1degradation: hybrids are incoherent, syncretism costs something
= 1mixture, no emergence; the alloy metaphor abandoned
> 1alloy proper; the compound has properties neither constituent had

On restricting the ranges

I was asked whether κX ≤ 1 and κJ > 1 can be justified as constraints. My answers differ.

κJ > 1 is defensible, but only as interpretation. It is what the alloy metaphor asserts, so imposing it is less an empirical claim than a declaration of which model one is running. There is suggestive support in accounts of recombinant innovation – new capability arising from combination rather than from either parent – but suggestive is the correct word, and a critic who holds that hybrids typically underperform is making a coherent rival claim, not an error. The honest form of the constraint is therefore the inequality itself, κJ > κE, stated as the model’s premise rather than as a finding. And, as below, nothing turns on it.

κX ≤ 1 I would not impose, and I no longer use it. There is an argument for it: a practice selected in another environment has no particular reason to fit this one, so friction should be expected on average. But there is an equally good argument against, since the practices that travel are often the ones that travel because they work, which biases the other way. Neither argument is decisive, and the tie-break is not epistemic but rhetorical. This essay’s conclusion is that removing the exogenous register barely changes anything. Setting κJ low makes that conclusion cheaper to reach. Conservative practice runs the other way: choose the value that makes your own result harder to obtain, and report what happens across the range. The original draft used κX = 0.6, which quietly asserted that imported practice underperforms – an unargued substantive claim with an unfortunate resonance, and a thumb on my own scale. I have replaced it with 1.0.

What the constants actually carry

Very little, which is the point of saying so.

Across κX from 0.2 to 5.0 and κJ from 0.5 to 3.0, the effect of stripping every exogenous-tagged element at period 40 ranges from 0.14% to 11.8%, and stays under 3% everywhere except the corner where imports are stipulated to be worth five times native practice. At the neutral setting (κX = 1, κJ = 1 – no penalty on imports and no emergence at all, the metaphor entirely surrendered) the effect is 1.66%. Granting the purist’s own premise instead, that mixture degrades (κJ = 0.5), it is 2.61%. The identification result is similarly indifferent: the colonised timeline sits between 0.16 and 0.41 standard deviations from the uncolonised distribution’s mean across every pairing tested. There is no setting of these constants at which subtraction works or the control group identifies anything.

What does carry the argument is the absorbing rule – the stipulation that mixed parentage yields untaggable offspring – and, downstream of it, elapsed time. Holding the coefficients neutral, the effect of stripping X depends almost entirely on when you strip:

strip atX-shareΔP
t=85.3%5.3%
t=158.6%8.6%
t=256.6%6.6%
t=401.7%1.7%
t=600.3%0.3%

The curve rises while the injection continues and X accumulates faster than recombination metabolises it, peaks near the close of the colonial window, and decays thereafter toward nothing. This is the model’s substantive claim, and it needs no invented constant to make it: purificatory subtraction has a window, and the window closes on its own. Attempted immediately it is partially coherent. Attempted at generational distance it addresses a fraction of a per cent, not because the imposition faded but because it stopped being taggable.

Why they cannot simply be estimated

One might reasonably ask why I do not calibrate the coefficients against something rather than stipulating them. The reason is not laziness, and it is not incidental to the argument. To estimate κX and κJ empirically, one would have to measure the separate contributions of endogenous, exogenous, and joint practice to some outcome – which requires precisely the provenance attribution the essay argues is inoperable, assessed against precisely the counterfactual baseline it argues is undefined. The model cannot be calibrated for the same reason the programme it examines cannot be run.

I would rather state that plainly than have it discovered. It also means the appropriate dissent is not about the numbers. Anyone wishing to defeat the argument should attack the absorbing rule, where the whole weight rests; quarrelling with the constants defeats nothing, as the grid above concedes in advance.

Good, Bad, and the Quiet Arithmetic of Power

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4–7 minutes

The quickest way to derail any discussion of morality is to accuse someone of believing that ‘everything is relative’, so let’s start there. It’s a comforting accusation. It allows the accuser to stop thinking whilst feeling victorious. Unfortunately, it also misses the point almost entirely.

I am not claiming that everything is relative. I am claiming that ‘good’ and ‘bad’ are. More precisely, this particular binary pair does not track mind-independent properties of actions, but rather expresses subjective, relational, and power-inflected evaluations that arise within specific social contexts. That claim is not radical. It is merely inconvenient.

Audio: NotebookLM summary podcast on this topic.

Good and Bad as Signals, Not Properties

When someone calls an action ‘bad’, they are not reporting a fact about the world in the way one might report temperature or velocity. They are signalling disapproval. Sometimes that disapproval is personal (subjective: ‘this sits badly with me’), sometimes social (relative: ‘people like us don’t do this’), and sometimes delegated (relative: ‘this violates the norms I’ve inherited and enforce’. The word does not describe. It acts.

The same applies to ‘good’. Approval, alignment, reassurance, permission. These terms function less like measurements and more like traffic signals. They coördinate behaviour. They reduce uncertainty. They warn, reward, and deter.

None of this requires moral scepticism, nihilism, or adolescent contrarianism. It requires only that we notice what the words are actually doing.

The Binary That Isn’t

Defenders of moral realism often retreat to a spectrum when pressed. Very well, they say, perhaps good and bad are not binary, but scalar. Degrees of goodness. Shades of wrongness. A neutral zone somewhere in the middle.

This is an improvement only in the most cosmetic sense. A single axis still assumes commensurability: that diverse considerations can be weighed on one ruler. Intuitively, this fails almost immediately. Good in what sense? Harm reduction? Loyalty? Legality? Survival? Compassion? Social order?

These dimensions do not line up. They cross-cut. They conflict. Which brings us to the example that refuses to die, for good reason.

Stealing Bread

“I don’t mind stealing bread
From the mouths of decadence
But I can’t feed on the powerless
When my cup’s already overfilled”

— Hunger Strike, Temple of the Dog

Consider the theft of bread by a starving person. The act is simultaneously:

  • bad relative to property norms
  • good relative to survival
  • bad relative to legal order
  • good relative to care or compassion
  • and neutral relative to anyone not implicated at all,
    even if they were to form an opinion through exposure

There is no contradiction here. The act is multi-valent. What collapses this plurality into a single verdict is not moral discovery but authority. Law, religion, and institutional power do not resolve moral complexity. They override it.

What about ‘Mercy’?

When the law says, ‘Given the circumstances, you are free to go’, what it is not saying is: this act was not wrong. What it is saying is closer to:

We are exercising discretion this time.
Do not mistake that for permission.
The rule still stands.

The warning survives the mercy.

That’s why even leniency functions as discipline. You leave not cleansed, but marked. Grateful, cautious, newly calibrated. The system hasn’t revised its judgment; it has merely suspended its teeth for the moment. The shadow of punishment remains, doing quiet work in advance.

This is how power maintains itself without constant enforcement. Punishment teaches. Mercy trains.

You’re released, but you’ve learned the real lesson: the act is still classified as bad from the only perspective that ultimately matters. The next time, mitigation may not be forthcoming. The next time, the collapse will be final. So yes. Even when you ‘win’, the moral arithmetic hasn’t changed. Only the immediate invoice was waived.

Which is why legality is never a reliable guide to goodness, and acquittal is never absolution. It’s conditional tolerance, extended by an authority that never stopped believing it was right.

Power as the Collapse Mechanism

When the law says, ‘There may have been mitigating circumstances, but the act was wrong and must be punished’, it is not uncovering a deeper truth. It is announcing which perspective counts.

Mitigation is a courtesy, not a concession. Complexity is acknowledged, then flattened. The final judgment is scalar because enforcement demands it. A decision must be made. A sanction must follow. The plural is reduced to the singular by necessity, not insight.

Once this happens, the direction of explanation reverses. Punishment becomes evidence of wrongness rather than evidence of power. The verdict acquires moral weight retroactively.

From Ethics to Enforcement

At the local level, ‘good’ and ‘bad’ function as ethical shorthand. They help maintain relationships, minimise friction, and manage expectations. This is not morality in any grand sense. It is coordination under conditions of attachment and risk.

Problems arise when these local prescriptions harden into universal claims. When they are codified into rules, backed by sanctions, and insulated from challenge. At that point, the costs become real. Not morally real, but materially real. Fines. Exclusion. Imprisonment. Reputational death. Nothing metaphysical has changed. Only the consequences.

The God Upgrade

Religion intensifies this process by anchoring evaluative judgments to the structure of reality itself. What was once ‘bad here, among us’ becomes ‘bad everywhere, always’ is no longer a difference in perspective but a rebellion against the order of being. This is not ethical refinement. It is power laundering through eternity.

Not Everything Is Relative

To be clear, this is not an argument that facts do not exist, or that all distinctions dissolve into mush. It is an argument that ‘good’ and ‘bad’ do not behave like factual predicates, and that pretending otherwise obscures how judgments are actually made and enforced.

What is not relative is the existence of power, the reality of sanctions, or the psychological mechanisms through which norms are internalised and reproduced. What is relative is the evaluative overlay we mistake for moral truth once power has done its work.

Why This Is Ignored

None of this is new. It has been said, in various forms, for centuries. It is ignored because it offers no programme, no optimisation strategy, no moral high ground. It explains without redeeming. It clarifies without consoling.

And because it is difficult to govern people who understand that moral certainty usually arrives after authority, not before.

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Written by Bry Willis

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Refining Transductive Subjectivity

Posted in agency, fiction, identity, language, maths, morality, ontology, perception, philosophy, postmodernism, psychology, reality, societyTagged , , , , , , , , , , , , , , Leave a comment
3–4 minutes

I risk sharing this prematurely. Pushing the Transductive Subjectivity model toward more precision may lose some readers, but the original version still works as an introductory conversation.

Please note: There will be no NotebookLM summary of this page. I don’t even want to test how it might look out the other end.

Apologies in advance for donning my statistician cap, but for those familiar, I feel it will clarify the exposition. For the others, the simple model is good enough. It’s good to remember the words of George Box:

All models are wrong; some are useful.

The Simple Model

I’ve been thinking that my initial explanatory model works well enough for conversation. It lets people grasp the idea that a ‘self’ isn’t an enduring nugget but a finite sequence of indexed states:

S0→S1→S2→…→SnS₀ → S₁ → S₂ → … → Sₙ

The transitions are driven by relative forces, RR, which act as catalysts nudging the system from one episode to the next.

The Markov Model

That basic picture is serviceable, but it’s already very close to a dynamical system. More accurate, yes—though a bit more forbidding to the casual reader – and not everybody loves Markov chains:

Si+1=F(Si,Ri)S_{i+1} = F(S_i, R_i)

Here:

  • SiSi is the episodic self at index i
  • RiRi is the configuration of relevant forces acting at that moment
  • FF is the update rule: given this self under these pressures, what comes next?

This already helps. It recognises that the self changes because of pressure from language, institutions, physiology, social context, and so on. But as I noted when chatting with Jason, something important is still missing:

SiSi isn’t the only thing in motion, and RiRi isn’t the same thing at every step.

And crucially, the update rule FF isn’t fixed either.

A person who has lived through trauma, education, and a cultural shift doesn’t just become a different state; they become different in how they update their states. Their very ‘logic of change’ evolves.

To capture that, I need one more refinement.

The Transductive Operator Model

This addresses the fact that Si isn’t the only aspect in motion and there are several flavours of R over time, so Ri. We need to introduce the Transductive T:

(Si+1,Fi+1)=T(Si,Fi,Ri)(S_{i+1}, F_{i+1}) = \mathcal{T}(S_i, F_i, R_i)

Now the model matches the reality:

  • SS evolves
  • the pressures RR evolve
  • and the update rule FF evolves

RiRi can be further decomposed as Ri=(Rphys,Rsocial,Rsymbolic,…)Ri=(R^{phys},R^{social},R^{symbolic},…), but I’ll save that for the formal essay.

The self is not simply ‘what comes next’, but a rule that keeps rewriting itself as it encounters the world.

That is why this is transductive rather than inductive or deductive:
structure at one moment propagates new structure at the next.

What Transductive Subjectivity Isn’t

What TS rejects is the notion that the self is a summation of the SiSis and other factors; this summation is a heuristic that works as a narrative, and all of its trappings, but it is decidedly incorrect.

Self≠Σ(Si,…)Self≠Σ(Sᵢ, …)

Effectively,

Self≠∫0tExperiencedtSelf ≠ \int_{0}^{t} Experience \, dt

In ordinary life, we talk as if there were a single, stable self that sums all these episodes. Transductive Subjectivity treats that as a convenient narrative, not an underlying fact. For example, someone raised in a rigid environment may initially update by avoiding conflict; after therapy and a cultural shift, they may update by seeking it out when something matters. This fiction is where we project agency and desert, and where we justify retribution.

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Written by Bry Willis

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Two Four Two Three

Posted in language, maths, perception, philosophyTagged , , , , , , , , Leave a comment
1–2 minutes

This meme is not what I mean by language insufficiency, but it does capture the complications of language.

Image: Two Four Two Three

I found this image accompanying an article critical of AI – Claude.ai in particular. But this isn’t a Claude problem. It’s a language problem. I might argue that this could have been conveyed verbally, and one could resolve this easily by spelling out the preferred interpretation.

  • A: Two thousand, twenty-three
  • B: Four thousand, four hundred, thirty-three
  • C: Two thousand, four hundred, thirty-three
  • D: Four thousand, four hundred, twenty-three

So, this is not insoluble, but it is a reminder that sometimes, in matters like this, additional information can lead to clearer communication.

I’d also imagine that certain cultures would favour one option over another as it is presented above. As for me, my first guess would have been A, interpreting each number as a place position. I’d have expected teh double number to also have a plural syntax – two threes or two fours – but that may just be me.

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The Church of Pareto: How Economics Learned to Love Collapse

Posted in economics, maths, modernism, philosophy, psychology, societyTagged , , , , , , , , , , , , , , , , , , , , , , , , , 3 Comments

—or—How the Invisible Hand Became a Throttling Grip on the Throat of the Biosphere

As many frequent visitors know, I am a recovering economist. I tend to view economics through a philosophical lens. Here. I consider the daft nonsense of Pareto optimality.

Audio: NotebookLM podcast of this content.

There is a priesthood in modern economics—pious in its equations, devout in its dispassion—that gathers daily to prostrate before the altar of Pareto. Here, in this sanctum of spreadsheet mysticism, it is dogma that an outcome is “optimal” so long as no one is worse off. Never mind if half the world begins in a ditch and the other half in a penthouse jacuzzi. So long as no one’s Jacuzzi is repossessed, the system is just. Hallelujah.

This cult of cleanliness, cloaked in the language of “efficiency,” performs a marvellous sleight of hand: it transforms systemic injustice into mathematical neutrality. The child working in the lithium mines of the Congo is not “harmed”—she simply doesn’t exist in the model. Her labour is an externality. Her future, an asterisk. Her biosphere, a rounding error in the grand pursuit of equilibrium.

Let us be clear: this is not science. This is not even ideology. It is theology—an abstract faith-based system garlanded with numbers. And like all good religions, it guards its axioms with fire and brimstone. Question the model? Heretic. Suggest the biosphere might matter? Luddite. Propose redistribution? Marxist. There is no room in this holy order for nuance. Only graphs and gospel.

Jevons warned us…that improvements in efficiency could increase, not reduce, resource consumption.

The rot runs deep. William Stanley Jevons—yes, that Jevons, patron saint of unintended consequences—warned us as early as 1865 that improvements in efficiency could increase, not reduce, resource consumption. But his paradox, like Cassandra’s prophecy, was fated to be ignored. Instead, we built a civilisation on the back of the very logic he warned would destroy it.

Then came Simon Kuznets, who—bless his empirically addled soul—crafted a curve that seemed to promise that inequality would fix itself if we just waited politely. We called it the Kuznets Curve and waved it about like a talisman against the ravages of industrial capitalism, ignoring the empirical wreckage that piled up beneath it like bones in a trench.

Meanwhile, Pareto himself, that nobleman of social Darwinism, famously calculated that 80% of Italy’s land was owned by 20% of its people—and rather than challenge this grotesque asymmetry, he chose to marvel at its elegance. Economics took this insight and said: “Yes, more of this, please.”

And so the model persisted—narrow, bloodless, and exquisitely ill-suited to the world it presumed to explain. The economy, it turns out, is not a closed system of rational actors optimising utility. It is a planetary-scale thermodynamic engine fuelled by fossil sunlight, pumping entropy into the biosphere faster than it can absorb. But don’t expect to find that on the syllabus.

Mainstream economics has become a tragic farce, mouthing the language of optimisation while presiding over cascading system failure. Climate change? Not in the model. Biodiversity collapse? A regrettable externality. Intergenerational theft? Discounted at 3% annually.

We are witnessing a slow-motion suicide

We are witnessing a slow-motion suicide cloaked in the rhetoric of balance sheets. The Earth is on fire, and the economists are debating interest rates.

What we need is not reform, but exorcism. Burn the models. Salt the axioms. Replace this ossified pseudoscience with something fit for a living world—ecological economics, systems theory, post-growth thinking, anything with the courage to name what this discipline has long ignored: that there are limits, and we are smashing into them at speed.

History will not be kind to this priesthood of polite annihilation. Nor should it be.

What’s Probability?

Posted in maths, perception, philosophy, scienceTagged , , , , , , , , , , , , , , , , , , , , , , , , Leave a comment

The contestation over the definition of probability is alive and well—like a philosophical zombie that refuses to lie down and accept the tranquilliser of consensus. Despite over three centuries of intense mathematical, philosophical, and even theological wrangling, no single, universally accepted definition reigns supreme. Instead, we have a constellation of rival interpretations, each staking its claim on the epistemological turf, each clutching its own metaphysical baggage.

Audio: NotebookLM podcast on this topic.

Let us survey the battlefield:

1. Classical Probability (Laplacean Determinism in a Tuxedo)

This old warhorse defines probability as the ratio of favourable outcomes to possible outcomes, assuming all outcomes are equally likely. The problem? That assumption is doing all the heavy lifting, like a butler carrying a grand piano up five flights of stairs. It’s circular: we define probability using equiprobability, which itself presumes a notion of probability. Charming, but logically suspect.

2. Frequentist Probability (The Empiricist’s Fantasy)

Here, probability is the limit of relative frequencies as the number of trials tends to infinity. This gives us the illusion of objectivity—but only in a Platonic realm where we can conduct infinite coin tosses without the coin disintegrating or the heat death of the universe intervening. Also, it tells us nothing about singular cases. What’s the probability this specific bridge will collapse? Undefined, says the frequentist, helpfully.

3. Bayesian Probability (Subjectivity Dressed as Rigor)

Bayesians treat probability as a degree of belief—quantified plausibility updated with evidence. This is useful, flexible, and epistemically honest, but also deeply subjective. Two Bayesians can start with wildly different priors and, unless carefully constrained, remain in separate probabilistic realities. It’s like epistemology for solipsists with calculators.

4. Propensity Interpretation (The Ontology of Maybes)

Karl Popper and his ilk proposed that probability is a tendency or disposition of a physical system to produce certain outcomes. Sounds scientific, but try locating a “propensity” in a particle collider—it’s a metaphysical ghost, not a measurable entity. Worse, it struggles with repeatability and relevance outside of controlled environments.

5. Logical Probability (A Sober Attempt at Rationality)

Think of this as probability based on logical relations between propositions—à la Keynes or Carnap. It aims to be objective without being empirical. The problem? Assigning these logical relations is no easier than choosing priors in Bayesianism, and just as subjective when it comes to anything meaty.

6. Quantum Probability (Schrödinger’s Definition)

In quantum mechanics, probability emerges from the squared modulus of a wave function—so this is where physics says, “Shut up and calculate.” But this doesn’t solve the philosophical issue—it just kicks the can into Hilbert space. Interpretations of quantum theory (Copenhagen? Many Worlds?) embed different philosophies of probability, so the contestation merely changes battlegrounds.

Current Status: War of Attrition

There is no universal agreement, and likely never will be. Probability is used successfully across the sciences, economics, AI, and everyday reasoning—but the fact that these wildly different interpretations all “work” suggests that the concept is operationally robust yet philosophically slippery. Like money, love, or art, we use it constantly but define it poorly.

In short: the contestation endures because probability is not one thing—it is a shape-shifting chimera that serves multiple masters. Each interpretation captures part of the truth, but none hold it entire. Philosophers continue to argue, mathematicians continue to formalise, and practitioners continue to deploy it as if there were no disagreement at all.

And so the probability of this contest being resolved any time soon?
About zero.
Or one.
Depending on your interpretation.

Determinism and the Three-Body Problem

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The debate over free will often distils down to a question of determinism—indeterminism, hard or soft determinism, or something else. Poincare’s approach to the three-body problem is an apt metaphor to strengthen the deterministic side of the argument.

Quantum theory introduces aspects of indeterminism, but that doesn’t support the free will argument. Moreover, between quantum events, the universe is again deterministic. It’s simply been reset with the last exogenous quantum event.

Prima facia, Determinism and Chaos might seem strange bedfellows. And therein lies the rub. Chaos theory essentially tells us that even in a scenario of chaos, all possible outcomes can be calculated. They just must be calculated stepwise via numerical integration. Even this leaves us with estimations, as owing to Heisenberg’s Uncertainty Principle and the infinitude of slicing space, we can’t actually calculate the precise answer, although one exists.

My point is that not knowing what is being determined doesn’t invalidate the deterministic nature or process.

Value of Life

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Captain Bonespurs now has a flesh wound. Former president-elect Donald J Trump was the target of a not-so-sharpshooter yesterday. Immediately resorting to Godwin’s Law, I wondered if this was like the philosophical hypothetical asking, ‘Would you kill baby Hitler to prevent the eventualities that unfolded?’ Was Hitler the symptom or the disease? What about Donald J? Whatever the cause or motivation, not unlike the fire at the Reichstag, this event has galvanised his supporters. Let’s hope that the outcome doesn’t follow the same path. There is a fear that he’ll take a path similar to Hitler or Ceasar before him in a quest for power.

What is a life worth? The average US-American life is valued at around $7 million, give or take a few million. The number ranges between $1 MM and $10 MM depending on which agency you see. That they equate lives to dollars is curious enough, but that they can’t agree on a single figure is priceless.

For background, this value is used to determine intervention. For FEMA (Federal Emergency Management Agency), a human life is worth about $7.5 MM For the EPA (Environmental Protection Agency) it’s slightly more than $10 MM. Are these cats playing Monopoly? Nah.

The human life calculus considers factors like lifetime earnings potential and discounts it to Present Value. In action, assume there is a disaster. Let’s not use COVID-19. Instead, there is an island with 1,000 inhabitants. Using the $10 MM per person figure to simplify the maths, we would be justified in spending up to $10,000,000,000 to intervene in some potential disaster – $10 MMM or $1e10.

Human lifetime value is an average. Mr Trump has already shown himself to be worth more than $10 MM. I suppose this means that not all humans are created equal. No matter. Another logical question might be what is the cost of a person’s detriment to society. This is a question for a Modernist or someone who feels that a given configuration of society is preferred to all others – or at least some others. How much damage might one human do?

Trump enriched himself and his family and entourage in his first term. In Ukraine, Zelenskyy and his lot bilked the country out of billions. It’s nothing new, but do we subtract the costs from the benefits or is this a gross calculation?

Irrespective of the costs, the next four years ahead are expected to be tumultuous no matter which corporate-sponsored party prevails. Heads, they win; tails, the country – if not the world – loses.

Neglect and a Quarter Dozen

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I am going to neglect this blog for at least another day. I’ve got too many irons in the fire.

Why do we routinely say ‘half dozen’ but don’t tend toward ‘quarter dozen’ or ‘third of a dozen’? I know many people have maths deficits, but still. I don’t think even I will attempt to start this trend, but this thought crossed my head today.

I hope to return to reengage with this block, but until then, adieu.

Physics of Free Will

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Physicist, Sean Carroll, gives Robert Lawrence Kuhn his take on free will. I was notified about this when it was posted, and given the topical subject matter, I took the 8-odd minutes to listen to it straight away.

I wish I had been there to pose a follow-up question because, although he provided a nice answer, I feel there was more meat on the table.

Like me, Sean is a Determinist who feels that the question of determinism versus indeterminism is beside the point, so we’ve got that in common. Where I feel we may diverge is that I am an incompatibilist and Sean is a compatibilist. I could be interpreting his position wrong, which is what the follow-up question would be.

I say that Sean is a compatibilist because he puts forth the standard emergence argument, but that’s where my confusion starts. Just to set up my position for those who don’t prefer to watch the short clip, as a physicist, Sean believes that the laws of physics, Schrödinger’s equation in particular.

We have an absolutely good equation that tells us what’s going to happen there’s no room for anything that is changing the predictions of Schrödinger’s equation.

— Sean Carroll
Schrödinger’s Equation

This equation articulates everything that will occur in the future and fully accounts for quantum theory. Some have argued that quantum theory tosses a spanner into the works of Determinism and leaves us in an Indeterministic universe, but Sean explains that this is not the case. Any so-called probability or indeterminacy is captured by this equation. There is no explanatory power of anything outside of this equation—no souls, no spirits, and no hocus pocus. So far, so good.

But Sean doesn’t stop talking. He then sets up an analogy in the domain of thermodynamics and statistical mechanics and the ‘fundamental theory of atoms and molecules bumping into each other and [the] emergent theory of temperature and pressure and viscosity‘. I’ve explained emergence in terms of adding two hydrogen and one oxygen atom to create water, which is an emergent molecule with emergent properties of wetness.

My position is that one can view the atomic collection of matter at a moment as an emergent property and give it a name to facilitate conversation. In this case, the label we are applying is free will. But there is a difference between labelling this collection “free will” as having an analogous function to what we mean by free will. That’s a logical leap I am not ready to take. Others have equated this same emergence to producing consciousness, which is of course a precursor to free will in any case.

Perhaps the argument would be that since one now has emergent consciousness—I am not saying that I accept this argument—that one can now accept free will, agency, and responsibility. I don’t believe that there is anything more than rhetoric to prove or disprove this point. As Sean says, this is not an illusion, per se, but it is a construction. I just think that Sean gives it more weight than I am willing to.