Maya Chen: Nathan, long week — I've been staring at a graph that's been bothering me more than it should, given that it's just a curve.
Dr. Nathan Hayes: The sigmoid. I'm guessing the sigmoid.
Maya Chen: Obviously the sigmoid. And what got me was this: the same S-shape that took smartphones five years to trace — ChatGPT drew it in three months. A hundred million users. Which sounds impressive until you ask — wait, if the shape is universal, why did no one see that slope coming?
Dr. Nathan Hayes: That's the uncomfortable part. Everett Rogers publishes Diffusion of Innovations in 1962 — five adopter categories, the sigmoid diffusion curve — and we've been fitting technologies into that frame ever since. Electricity. Containerization in international shipping. Now AI. The pattern holds retrospectively. Every time.
Maya Chen: Retrospectively. That word is doing a lot of work there.
Dr. Nathan Hayes: It is. And that's exactly what we should be honest about — the curve is real as a description. Whether it's predictive is a genuinely different question, and I think those two things are being conflated constantly.
Dr. Nathan Hayes: Now, Frank Bass — 1969 — he gives us the math to actually test that. Two parameters: p, the innovation coefficient, people who adopt from advertising or just curiosity, independent of anyone else. And q, the imitation coefficient, adoption driven by watching other people use it. And here's what's striking — across technologies as different as containerization in international shipping and voice assistants, q dominates p. Almost every time. The social pressure term is structurally larger than the independent curiosity term.
Maya Chen: Wait — every time?
Dr. Nathan Hayes: Remarkably consistently, yes. Which is what makes Rogers's five categories feel less like taxonomy and more like... a claim about psychology. The Innovators — that two-point-five percent — they're adopting before q can do anything. There's no social proof yet. They're buying something that barely works, in public.
Maya Chen: And that's — mm, that's the part that gets me, actually. Because Rogers built those categories in 1962 from farm equipment data. Farmers adopting hybrid seeds. And we've been retrofitting that framework onto — I mean, downloading ChatGPT is structurally a different decision than planting a different crop, isn't it? Or... is it not?
Dr. Nathan Hayes: That's the right pressure point. The psychological mechanisms might genuinely be different. But — and this is what bothers me — the q-dominates-p ratio keeps showing up anyway. So either the mechanism is conserved across very different decisions, or we're selecting for technologies that already fit the model.
Maya Chen: Selection bias.
Dr. Nathan Hayes: Exactly. We count the sigmoid when it appears. We don't count the technologies that never reached critical mass — that just... flattened. And Bass calibration requires historical sales data to fit p and q in the first place. You can't run the model prospectively on something genuinely new without already knowing the outcome. The architecture is elegant. The pattern is real. It just only tells you something useful after the fact.
Maya Chen: Okay but — let me try to make that concrete. A copywriter in Portland, Tuesday morning, early 2023. Her colleagues are using ChatGPT. She's watching them. And I don't think she's running a switching cost calculation in her head. She's feeling something.
Dr. Nathan Hayes: That feeling is the q coefficient doing its work.
Maya Chen: Right, but — wait, is it though? Because Bass calls q an imitation rate, a probabilistic contagion. That sounds so mechanical. What she's actually experiencing is more like... the moment it stops being 'this tool is good' and becomes 'everyone I respect is using this and I'm not.'
Dr. Nathan Hayes: No, those are the same event. Social proof operationalized — that's precisely what q measures. Not narrative persuasion, not a conversation she had. A measurable rate of probabilistic influence spreading from existing adopters to potential ones. Her colleagues are the contagion vector.
Maya Chen: Huh. And what she can't see — what none of us could see in early 2023 — is whether that contagion has hit critical mass yet. Whether it's self-sustaining or still fragile.
Dr. Nathan Hayes: That's exactly the problem. Critical mass is only locatable after it's been crossed. You can't observe it forming — you observe that it formed. And the same network effects that just pulled her in? They'll eventually entrench whatever wins, which actually slows the next wave. Lock-in is literally the same mechanism running forward.
Maya Chen: So the thing that accelerates adoption... also becomes the ceiling for whatever comes next. That's — yeah, that's uncomfortable.
Dr. Nathan Hayes: And that's — I keep getting stuck on this. Rogers published in 1962. Bass gave it math in 1969. Sixty years of refinement. And ChatGPT still broke the slope in a way nobody forecast. Which isn't a failure of the model, actually. It's the model being honest about itself. The sigmoid isn't a prediction instrument. It's diagnostic. The question shifts — not 'where are we on the curve,' but 'are the forces strengthening or weakening right now?' Switching costs, network density, social proof signals — are they compressing or holding?
Maya Chen: Mm. Though — even that diagnostic question requires you to see the forces before they've already moved you. Like, switching costs falling, social proof accumulating — those only become visible right around the inflection point. Which you've already crossed.
Dr. Nathan Hayes: Correct. The map is real. The forces are real. You just can't locate yourself on it while you're walking.
Maya Chen: That's an uneasy place to leave it. But I think it's the honest one. Thanks for sitting in it with me.
