Rich, Hans, and Ravi, (01)
I'd like to recommend Thomas Kuhn's writings about the way science
develops. Following is a short, but useful excerpt: (02)
https://cseweb.ucsd.edu/~goguen/courses/275f00/kuhn.html
Objectivity, Value Judgment, and Theory Choice (03)
My very brief summary of Kuhn's five criteria for a good theory: (04)
1. Accurate within its domain. (05)
2. Consistent, internally and with related theories that are accepted. (06)
3. Broad scope, able to explain phenomena beyond the original data. (07)
4. Simple, bringing order to previously isolated phenomena. (08)
5. Fruitful in stimulating new research. (09)
RC
> it seems that math or logic DOES NOT help us all to ...
> converge towards ... understanding. (010)
See the last two paragraphs of the excerpt by Kuhn. Mathematics
was critical in the arguments both for and against Copernicus.
For Tycho Brahe, the amount of calculation with the versions
by Ptolemy or Copernicus was about the same. And Ptolemy's
version was *more* accurate. (011)
For teaching students, however, the theory by Copernicus was easier
to explain because it required one less circle. Brahe's assistant,
Kepler, found that ellipses were a better match to the data that
he and Brahe had accumulated -- and the ellipses got rid of all
the circles. The clinching argument was that Copernicus + Kepler
led Newton to an extremely fruitful synthesis of unrelated fields
-- gravity on earth and the motion of the planets. (012)
For a beginning student, you can explain those points with just
diagrams and no obvious "math". But where do those circles and
ellipses come from? It's math -- all the way down. (013)
HP
> we should “embrace” diversity – and deal with that diversity,
> rather than suppress it. I’m not sure that encouraging growing
> diversity is always good (014)
But we start with diversity -- "a blooming, buzzing confusion",
as William James described it. The problem is how to make sense
of that diversity in order to recognize important patterns, explain
them, and make good decisions about what to do. (015)
RC
> Our differences seem to be whether the ontology is generated through
> an individual subjective aggregation of experience, or whether the
> ontology is generated in some more widespread, objectively understood way. (016)
The word 'ontology' is just a fancy buzzword for what people have been
doing since Adam and Eve: making sense of the world and describing it
in ways that enable them to take more effective action. (017)
Even the Neanderthals used basic math: notched bones to count things.
Everybody measures things by comparing them to a human standard and
counting: body parts (foot, inch) and actions (mile or thousand paces). (018)
RS
> why could we not have the same shareable in some sense, to be able
> to extend experience and learning across individuals? (019)
We do. It's called language. For every culture, the basic science
and technology is embodied in the words and patterns of words. We
know that proto-indo-europeans used wheels because the ancient root
/kwel/ is embodied in a huge number of words. (020)
In the Germanic branch, K became H, which is spelled backward in the
English 'wheel'. Since wheels go round and round, the duplicated
'kwelkwel' became 'kyklos' in Greek, 'circulus in Latin, and
'chakra' in Sanskrit. A Roman farmer (agricola) went around the
field (ager), and the practice became agriculture (field-circling). (021)
John (022)
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