[Singletoned]

> Piaget’s theory formulates a peculiarly inverted version of Ernst Haeckel’s biogenetic law that unites historical phylogeny and mental ontogeny in a recursive Möbius-band-like figure.

I've Googled quite a few words from that sentence and still can't wrap my head round it. Can anyone ELI6?

[tremens]

> Piaget’s theory formulates a peculiarly inverted version of Ernst Haeckel’s biogenetic law that unites historical phylogeny and mental ontogeny in a recursive Möbius-band-like figure.

Individual development (ontogeny) restates historical evolution (phylogeny). Haeckel’s biogenetic law says that as an embryo develops it will pass through its past historical states as a species. It's a long discredited 19th century scientific hypothesis.

Inverting the relationship would state that historical evolution is restating individual development OR in the other sense of inverting, they move in the opposite order to one another (Mathematicians: Euclid -> Topology, Kids: Topology -> Euclid).

Basically, kids build up knowledge of topology from everyday interaction with the world and then move onto Euclidean shapes with the knowledge of topology.

Mathematicians discovered it all in the opposite order, starting with Euclidean geometry and only later documenting topology.

[Singletoned]

Thanks. That seems a lot more understandable.

[gumby]

Tremens answered about Häckel; the Möbius strip part is Piaget’s model of learning which says that knowledge undergoes continuous rewriting rather than being simply accretive, a view which I would think should be unremarkable today.

Häckel came from a 19th century conception of “advancement” or “progres” — think of that absurd 19th century picture of various apes followed by a human, as if a human is somehow the “most evolved” of the animals. The idea of adaptation to the environment was alien (and apparently frightening) to most people in the West.

[zxcb1]

I found this helpful: https://en.m.wikipedia.org/wiki/Recapitulation_theory#Cognit...

[Singletoned]

Yeah, it was. So it's like how the order in which we learn philosophical ideas roughly mirrors the order in which they were discovered?

[gumby]

That was Herbert Spencer’s Belief, yes, as he had a rather reductio “Gadgrind” view of knowledge and worth (he is also the originator of the phrase “social darwinism” and, amusingly, is buried across from his rival Karl Marx. This simplistic view is pretty much dead these days.

[zxcb1]

I am still a bit confused, am I interpreting this correctly? From an individual perspective, embodied tacit knowledge precedes conceptualized knowledge. In this example the process of drawing refines the spatial skills / cognition required to grasp Euclidean geometry. And the process of cultural knowledge progression does not necessarily follow this developmental order?

[gumby]

Up to “and the process” yes, this is what Piaget taught. And that learning is a process of comtinuous rewriting of what you think you know, based on your experiences.

Separately: some people, like Spencer, who believe that “progress” has a direction, that “more advanced” societies have more universal knowledge that accumulates like stacking paper on a table, (and this was the challenge of Darwin) that humans are closest to god and all other creatures are inferior (you can see how this extends to a belief that there are different races (=breeds) of humans, both in genetics/god’s engineering and in culture).

Then tying the two together: you can look at the development of an individual human as an iterative, never ending and somewhat meandering process or you can say that you just have to transfer those stacks of paper, bottom to top, and then you’re done.

The connection between the two may sound absurdly tenuous but sad to say it is highly politicized and to this very day affects how schools are organized and funded, culture, politics, beliefs about right and wrong and how people should behave.

[zxcb1]

Ok, thanks! It seems to me that these aren’t mutually exclusive, rather complementary. The embodied approach, reminds me of the Montessori attitude of exploration / discovery and the metaphor of stacked paper, the industrial age, man as machine. How about seeing it as the difference between cultivating (complex, holistic, iterative, like ANNs) vs constructing (simple, compositional) or the principles of intuition and logic? Also, I suppose one may move in the other direction, from higher level conceptual to embodied understanding via iterative refinement.