2. we should be here bold and resolute, as any (young) theorician : build our own theory, that is classification
$$ (natsci / philo ... )theorician\quad \rightarrow \quad (private \quad real \quad life) \quad learner $$
classify means : you have an \( x \), an \( y \), and (boldly) draw
$$ x \rightarrow y $$
3. Easy ? This is a negative, most of the time…
\( y \) is not of the same nature as \( x \): \( y \) is a ‘symmetry’, \( x \) is some real life ‘object’ : anything from minimal experience to macro ontos.
\( x \) is well-known-from-me, something-I-m-not-indifferent-to : a personal experience, something-I-often-play-with. Even conceptual, \( x \) is concrete-to-me.
\( y \) is eventually some abstract concept, more symmetrical… somehow more simple – balancing this with abstraction - than any \( x \), so that the compression \( x \rightarrow y \) could be significant : our purpose is to make…room.
4. As pointed out by Brown and Porter, the all point is to move from a ‘concrete’ (to the learner at least) collection of \( x_{\omega} \) to some more abstract \( y \)
One path to do that is to find some explicit relations between these \( x_{\omega} \)
The classic example of ‘cardinality’, our \( y \), as in https://golem.ph.utexas.edu/category/2008/10/what_is_categorification.html, make explicit the isomorphism between any finite set. Somehow, any child did that at some point…
Abstracting the detailed structure of these \( x_{\omega} \) unveils the symmetry \( y \).
5. Paradoxically, (student) learning is a long trip to forget (art of explicit building of) isomorphisms and keeping only \( y \) in mind. But real (life) learning tends to be rather a never ending explicit building of morphisms as new \( x_{\omega} \) flow in your mind…
That is : you should enforce your learning to learn ability, that is the art to design new \( y \) and new → between (old and new) \( x_{\omega} \) and (old and new) \( y \)
Hopefully, the more you do it, the more you are good at it… Note that be good at doing something, having learned it, is not as be good at learning anything !...
