In the movie 2001 a black cuboid with side ratios 1:4:9 detected on the Moon through its anomalous magnetic properties sends a radio pulse in response to sunlight.

Given a particular such semigroup satisfying axioms derived from a multiway system, one can see whether the operator representations of particular strings are equal—and if they are not, then it follows that the strings can never be reached from each other through evolution of the multiway system.

In practice, moving one's finger slowly through water gives a Reynolds number of about 100 (so that a regular array of dimples corresponding to eddies are visible behind one's finger), walking in air about 10,000, a boat in the millions, and a large airplane in the billions.

There seems to be no simple characterization, say in terms of paths through networks, of which can, but for successive t the total numbers are {4, 12, 32, 80, 200, 496, 1208, 2916, 6964, 16476, 38616, 89844, 207544, 476596, 1089000, 2477236, 5615036} or roughly 2.25 t .

(Typical of the time was the statement of Leonardo da Vinci that "no human inquiry can be called science unless it pursues its path through mathematical exposition and demonstration".)

All these railroads go through flat empty terrain that previously had only a few nomadic inhabitants—and no settlements to define a route.

Detailed ideas about infinite sets emerged in the 1880s through the work of Georg Cantor , who found it useful in studying trigonometric series to define sets of transfinite numbers of points.

For each complete update of a rule 90 sequential cellular automaton, the pictures below show results with (a) left-to-right scan, (b) random ordering of all cells, the same for each pass through the whole system, (c) random ordering of all cells, different for different passes, (d) completely random ordering, in which a particular cell can be updated twice before other cells have even been updated once.

At times there have been hopes of so-called dynamical symmetry breaking giving the same effective results as the Higgs mechanism, but without an explicit Higgs field—perhaps through something similar to various phenomena in condensed matter physics.

The total number of configurations in rule 30 that repeat with periods that divide 1 through 10 are {3, 3, 15, 10, 8, 99, 18, 14, 30, 163} .