[originally from November 27th, 2014]
There seems to be a special case of mind projection fallacy where people assume there’s an hierarchy of knowledge, and infer this hierarchy from their own experience of coming to the point where they are now (which is a sensible thing to do assuming the hierarchy exists – then there’s only one path to a certain piece of knowledge). That appears to be heavily influenced by formal education, that indeed organizes knowledge in this way.
For example: “This person talks about spectra. Clearly they learned trigonometry, then limits, then infinite series, then integration, then linear algebra, then Hilbert spaces, then Fourier series, and now know what spectrum is”. And they’re baffled that such person knows nothing about dot products, but is still comfortable with equalizers and spectrograms, because apparently they learned it practically rather than theoretically.
Another example is how I thought that understanding Schrödinger equation is a prerequisite for using bra-ket notation (which I don’t quite understand yet) until I met people who consider the former a much more complicated and high-level topic.
Or the fact that programmers with hacker-ish background, who grew up playing with computers, and learned programming as a next logical step after acquiring tons of practical (but not all that relevant) computer skills, are baffled to see programmers without suck background, who just learned programming as their major.
You don’t assume that every architect has built dozens of dog huts and tree houses as a kid, do you? But I would hypothesize that is this was someone’s path to the architecture major, they would probably be baffled at their classmates’ limited ability of the actual construction.
I would probably agree that some very highly specific pieces of knowledge may have universal prerequisites (although in most cases you should be able to get rid of them by reorganizing concepts), but in general they’re just floating around waiting to be learned. It’s very far from the pyramid people believe it to be.