(net time : 293 min)

Unit 10

Advantage of maths: simplicity, economy of effort, generality and precision

Q1: axiom?

Q2: no need to experiment?

Most of the contents are known in statistics courses

Unit 11

symmetry: invariance under transformation

              temporal (displacement, scaling, reversal, periodicity), permutation, dynamic (conserved quantity)

              internal/external

natural classification: actual objects in the world;  artificial classification: convenient way of making reference

top-down (attribute, sort) and bottom-up (inductive principle)

3 aspects of a type (sensory, abstract, linguistic)

              typology: a classification used for sorting

              taxonomy: hierarchically ordered classification, each level is a typology

3 conditions of typology(structural): clear boundary, completeness, exclusive types.

4 scales of typology(interpretation): consistency, equivalence, equidistance, independence

3 conditions of typological variables: universality, qualitative difference, logical independence

4 scales of typological variable attributes: nominal, ordinal, interval, ratio

linguistic map of the parameter space.

method of comparison: compare similarities and differences.

              use in science – classification, historical reconstruction, generalization, hypothesis testing

phylogenetic taxonomies: family tree with hierarchy, constructed bottom-up and top-down, used to estimate evolution times.

              total time = mutation number * year per mutation

              mutation number =2 for 2 difference, =1 for 1 difference

Fig 11.3.1

models

3 types: strategic(bottom-up), tactical(top-down), simulation

9 stages: question->variables and parameters ->existing resource -> analytical tool -> basic model -> preliminary testing -> formalize, simplify, enrich -> hypothesis -> conceptual framework/paradigm

6 criteria: accuracy, relatedness, transparency, robustness, fertility, ease of enrichment(scalable)

5 values: suggest principles, indicate new direction, reach beyond observation, highlight relation in big data, overview for organizing and interpreting data

3 dangers: map for the territory (纸上谈兵, 按图索骥), bed of Procrusters (削足适履，all nails in one’s eye with hammer), unrelated (买椟还珠)

Q10: evolution

Q11: Mendel, hereditary, chromosome, gene, DNA.