Computer languages are also mostly equivalent in their handling of general programming issues—and indeed among widespread languages the only substantial exception is Mathematica, which supports symbolic, functional and pattern-based as well as procedural programming.

Quantum effects Over the years, many suggested effects have been thought to be characteristic of quantum systems: • Basic quantization (1913): mechanical properties of particles in effectively bounded systems are discrete; • Wave-particle duality (1923): objects like electrons and photons can be described as either waves or particles; • Spin (1925): particles can have intrinsic angular momentum even if they are of zero size; • Non-commuting measurements (1926): one can get different results doing measurements in different orders; • Complex amplitudes (1926): processes are described by complex probability amplitudes; • Probabilism (1926): outcomes are random, though probabilities for them can be computed; • Amplitude superposition (1926): there is a linear superposition principle for probability amplitudes; • State superposition (1926): quantum systems can occur in superpositions of measurable states; • Exclusion principle (1926): amplitudes cancel for fermions like electrons to go in the same state; • Interference (1927): probability amplitudes for particles can interfere, potentially destructively; • Uncertainty principle (1927): quantities like position and momenta have related measurement uncertainties; • Hilbert space (1927): states of systems are represented by vectors of amplitudes rather than individual variables; • Field quantization (1927): only discrete numbers of any particular kind of particle can in effect ever exist; • Quantum tunnelling (1928): particles have amplitudes to go where no classical motion would take them; • Virtual particles (1932): particles can occur for short times without their usual energy-momentum relation; • Spinors (1930s): fermions show rotational invariance under SU(2) rather than SO(3); • Entanglement (1935): separated parts of a system often inevitably behave in irreducibly correlated ways; • Quantum logic (1936): relations between events do not follow ordinary laws of logic; • Path integrals (1941): probabilities for behavior are obtained by summing contributions from many paths; • Imaginary time (1947): statistical mechanics is like quantum mechanics in imaginary time; • Vacuum fluctuations (1948): there are continual random field fluctuations even in the vacuum; • Aharonov–Bohm effect (1959): magnetic fields can affect particles even in regions where they have zero strength; • Bell's inequalities (1964): correlations between events can be larger than in any ordinary probabilistic system; • Anomalies (1969): virtual particles can have effects that violate the original symmetries of a system; • Delayed choice experiments (1978): whether particle or wave features are seen can be determined after an event; • Quantum computing (1980s): there is the potential for fundamental parallelism in computations.

But the idea of treating complexity as a coherent scientific concept potentially amenable to explicit definition is quite new: indeed this became popular only in the late 1980s—in part as a result of my own efforts.

In the 1600s the philosophical idea that the only way to get information with certainty is from the senses led to emphasis on observable aspects of communication, and to the conclusion that there is no way to tell whether an accurate transfer of abstract thoughts has occurred between one mind and another.

Nevertheless, by the 1930s, the Second Law had somehow come to be generally regarded as a principle of physics whose foundations should be questioned only as a curiosity.

But the science I have developed in this book opens up an area so vast that the twenty years I have spent investigating it have allowed me to explore only tiny parts.

But the languages were primarily intended only for specifying numerical calculations.

The way the path integral for a quantum field theory works, each possible configuration of the field is in effect taken to make a contribution Exp[  s/ ℏ ] , where s is the so-called action for the field configuration (given by the integral of the Lagrangian density—essentially a modified energy density), and ℏ is a basic scale factor for quantum effects (Planck's constant divided by 2 π ). … But while this works for QED, it is only adequate for QCD in situations where the effective coupling is small.

For almost all textbooks tend to discuss only those cases that happen to come out this way.

But I found that active research on what had been called cellular automata had more or less petered out (with the slight exception of a group at MIT at that time mainly concerned with building special-purpose hardware for 2D cellular automata). … And in fact I still vaguely assumed that if simple initial conditions were used, only fairly simple behavior would be obtained. … And I do know that for example on June 1, 1984 I printed out pictures of rule 30, rule 110 and k = 2 , r = 2 totalistic code 10 (see note below ), took them with me on a flight from New York to London, and a few days later was in Sweden talking about randomness in rule 30 and its potential significance.