Mendelian dynamics and Sturtevant’s paradigm
M. Gromov · Contemporary mathematics - American Mathematical Society · 2008
This a brief introduction to the formal genetics centered around two mathematical ideas going back to Gregor Mendel and Alfred Sturtevant. Preambule. The road from biology (or from any branch of science on the fundamental level) to mathematics goes in several ( often Brownian rather than straight) paths in parallel. • Identifying a class of phenomena–”particular trees in a forest”–that appear with a regularity suggesting an underlying (mathematical) structure. (Are there non-mathematical structures?) • • Designing and performing experiments/observations purifying and amplifying what is seen by the naked eye (e.g. by planting our ”trees ” to an ”artificial soil”). •• • Making (often implicitly) ad hoc hypotheses, (e.g. continuity, symmetry, functoriality) – that provide a logical framework for the experimental data. For example, the ”theory of coin tossing ” derives its mathematical beauty