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[Phys-L] Re: memorization +- understanding



RAUBER, JOEL wrote:

Isn't all calculation ultimately reduced to memorized procedures?

Yes and no ... and if yes, it's not necessarily a bad
thing.

Memorization and understanding are not mutually exclusive.

As a special case, _rote_ memorization means memorization
without understanding, which ought to be avoided if there
is a feasible alternative ... but not all memory is rote
memory.

In general, we have a highly-interconnected lattice,
consisting of
-- nodes representing primary facts (axioms and direct
observations)
-- nodes representing secondary (derived) facts
-- arcs that use logic to link the nodes together.

As an example of a known secondary fact: if you ask
me the square root of 1024, I can tell you the answer
in less time than it takes to ask the question. I just
know it. On the other hand, if I didn't know it, I
could rederive it in several different ways.

As an example of a secondary fact I don't know, I
have never bothered to memorize sqrt(10). But
since I know sqrt(1024), I can calculate sqrt(10)
very quickly: it's 12% less than 3.2.

Similarly, I have failed in my attempts to memorize
the mass of the proton in kg. On days when I need it,
I can keep it in short-term memory, but it never seems
to transfer to long-term memory. So whenever I need
it, I must refresh the cache by recalling Avogardro's
number (which I do manage to remember) and taking
the reciprocal (which I can do in my head, quickly
and easily).

If I did manage to memorize sqrt(10) or M_p, it would
not weaken my understanding of the fundamentals. It
would be in addition to -- not in lieu of -- the other
facts and relationships I know.

As an example of a rote fact, I know my aunt's phone
number. There are no arcs to or from this node, i.e.
this fact bears no logical relation to any other facts
I know.

Bottom line:
Understanding: good.
Memorization: _with_ understanding even better.
Memorization: sometimes necessary.
Rote memorization: sometimes the only option.