Refining Transductive Subjectivity

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:

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.

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(Sᔹ, 
)

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.

Questioning Traditional Families

I neither champion nor condemn tradition—whether it’s marriage, family, or whatever dusty relic society is currently parading around like a prize marrow at a village fĂȘte.

Audio: NotebookLM podcast on traditional families.

In a candid group conversation recently, I met “Jenny”, who declared she would have enjoyed her childhood much more had her father not “ruined everything” simply by existing. “Marie” countered that it was her mother who had been the wrecker-in-chief. Then “Lulu” breezed in, claiming, “We had a perfect family — we practically raised ourselves.”

Now, here’s where it gets delicious:

Each of these women, bright-eyed defenders of “traditional marriage” and “traditional family” (cue the brass band), had themselves ticked every box on the Modern Chaos Bingo Card: children out of wedlock? Check. Divorces? Check. Performative, cold-marriage pantomimes? Absolutely—and scene.
Their definition of “traditional marriage” is the vintage model: one cis-male, one cis-female, Dad brings home the bacon, Mum weeps quietly into the washing-up. Standard.

Let’s meet the players properly:

Jenny sprang from a union of two serial divorcĂ©es, each dragging along the tattered remnants of previous families. She was herself a “love child,” born out of wedlock and “forcing” another reluctant stroll down the aisle. Her father? A man of singular achievements: he paid the bills and terrorised the household. Jenny now pays a therapist to untangle the psychological wreckage.

Marie, the second of two daughters, was the product of a more textbook “traditional family”—if by textbook you mean a Victorian novel where everyone is miserable but keeps a stiff upper lip about it. Her mother didn’t want children but acquiesced to her husband’s demands (standard operating procedure at the time). Marie’s childhood was a kingdom where Daddy was a demigod and Mummy was the green-eyed witch guarding the gates of hell.

Lulu grew up in a household so “traditional” that it might have been painted by Hogarth: an underemployed, mostly useless father and a mother stretched thinner than the patience of a British Rail commuter. Despite—or because of—the chaos, Lulu claims it was “perfect,” presumably redefining the word in a way the Oxford English Dictionary would find hysterical. She, too, had a child out of wedlock, with the explicit goal of keeping feckless men at bay.

And yet—and yet—all three women cling, white-knuckled, to the fantasy of the “traditional family.” They did not achieve stability. Their families of origin were temples of dysfunction. But somehow, the “traditional family” remains the sacred cow, lovingly polished and paraded on Sundays.

Why?

Because what they’re chasing isn’t “tradition” at all — it’s stability, that glittering chimera. It’s nostalgia for a stability they never actually experienced. A mirage constructed from second-hand dreams, glossy 1950s propaganda, and whatever leftover fairy tales their therapists hadn’t yet charged them ÂŁ150 an hour to dismantle.

Interestingly, none of them cared two figs about gay marriage, though opinions about gay parenting varied wildly—a kettle of fish I’ll leave splashing outside this piece.

Which brings us back to the central conundrum:

If lived experience tells you that “traditional family” equals trauma, neglect, and thinly-veiled loathing, why in the name of all that’s rational would you still yearn for it?

Societal pressure, perhaps. Local customs. Generational rot. The relentless cultural drumbeat that insists that marriage (preferably heterosexual and miserable) is the cornerstone of civilisation.

Still, it’s telling that Jenny and Marie were both advised by therapists to cut ties with their toxic families—yet in the same breath urged to create sturdy nuclear families for their own children. It was as if summoning a functional household from the smoking ruins of dysfunction were a simple matter of willpower and a properly ironed apron.

Meanwhile, Lulu—therapy-free and stubbornly independent—declares that raising oneself in a dysfunctional mess is not only survivable but positively idyllic. One can only assume her standards of “perfect” are charmingly flexible.

As the title suggests, this piece questions traditional families. I offer no solutions—only a raised eyebrow and a sharper question:

What is the appeal of clinging to a fantasy so thoroughly at odds with reality?
Your thoughts, dear reader? I’d love to hear your defences, your protests, or your own tales from the trenches.