It sounds like they want to say they are synonymous. Isomorphic implies that each category has the same[1] internal structure. Given that the author doesn't spend much time developing the ontology of want nor the ontology of thought, it's hard to make an isomorphic connection between the two realms.

For me a stronger essay would be to say, "Give people a reason to change their minds," or "Strong products give people a reason to change their minds." Connecting "I would never get into someone else's car," or "I would never let strangers stay in my home," to reasons why we would change our mind on those topics, is a better conceptual framework for creating things people want.

We can identify loads of things we wouldn't do, and conceive of ideas that might make people change their minds. Even better, we can find pairs of things that people want and the assumptions they have that are preventing them from getting what they want, and create a product that connects the two. Either way, that's not exactly the author's essay.

1. Or for the sake of the grace, similar internal structure.

I agree, it’s a bit of stretch.

In my mind the mapping and inverse mapping were defined in these two paragraphs:

“I think altering thinking at scale requires people wanting that thing, otherwise you wouldn’t get network effects and scaling would be impossible.

Also, I think that making something people wants requires altering the way they think. When you make something new you ask people to reconsider their existing habits and first principles. This mental shift, however small, is what leads to mass adoption and users falling in love with your product.”

It implies that for every thing people want there's a corresponding change to the way they think.

There's a subset where that's true, but "Iso" is a stronger sort of morphism than what we have here. It must preserve structure everywhere to be an isomorphism.

Yeah, perhaps I don’t want to use isomorphic as it sort of implies a universal quantifier. I think the relationship is weaker than isomorphism in retrospect.

EDIT: On the other hand, all external stimuli changes the way we think, we are meaning making machines. Where there is something we try and make meaning of it.

I think scale matters in terms of things impact on our thinking, but fundamentally the argument could be made that for all things people want there are changes in the way they think.

Maybe clarifying “novel things” people want would be clearer.