When science and technology meet social and economic systems, you tend to see something akin to what the late Stephen Jay Gould called "punctuated equilibrium" in his description of evolutionary biology. Something that has been stable for a long period is suddenly disrupted radically--and then settles into a new equilibrium.1 1.See Stephen Jay Gould, Punctuated Equilibrium, Cambridge, MA: Harvard University Press, 2007. Gould pointed out that fossil records show that species change does not advance gradually but often massively and disruptively. After the mass extinctions that have occurred several times across evolutionary eras, a minority of species survived and the voids in the ecosystem rapidly filled with massive speciation. Gould's theory addresses the discontinuity in fossil records that puzzled Charles Darwin.

Yamaha's self-playing piano has been intricately designed to mimic the celebrated 20th-century Canadian pianist and Bach interpreter down to the finest musical detail. Yamaha has invented a piano that not only plays itself, but also mimics one of the best pianists and Bach interpreters of the 20th century – Glenn Gould. The piano was born of Yamaha's Dear Glenn project, which uses machine learning to teach the artificial intelligence that drives the instrument's self-playing capability the interpretative idiosyncrasies and stylistic nuances of Gould's playing. In a video released by Yamaha, the'Glenn Gould as AI' piano performs Bach's Goldberg Variations in a concert setting – offering audiences, it is hoped, as close a version of the late Gould's performances as they can ever hope to see live. The self-playing aspect of the piano was made possible by the same technology used for Yamaha's existing Disklavier instrument.

In his brilliant, provocative 1966 essay, The Prospects of Recording, Glenn Gould proposed elevating – pardon the pun – elevator music from pernicious drone to enriching ear training. In his view, the ubiquitous presence of background sound could subversively train listeners to be sensitive to the building blocks, structural forms and hidden meanings of music, turning the art form into the universal language of the emotions that it was destined to be. In a not-unrelated development, Gould had somewhat recently traded the concert hall for the recording studio, an act echoed by The Beatles' release in 1967 of Sgt. Peppers' Lonely Hearts Club Band, an album conceived and produced in a multi-track recording studio and never meant to be played in concert. And while Gould's dream of a transformative elevator music never quite panned out, it is clear that from the 1940s through the '60s -- from Les Paul and Mary Ford's pioneering use of overdubs in How High the Moon, to the birth of rock and roll with Chuck Berry's "Maybellene" in 1955, and on to Schaeffer, Stockhausen, Gould, The Beatles and many more -- a totally new art form, enabled by magnetic tape recording and processing, was born.

We provide sharp worst-case evaluation complexity bounds for nonconvex minimization problems with general inexpensive constraints, i.e.\ problems where the cost of evaluating/enforcing of the (possibly nonconvex or even disconnected) constraints, if any, is negligible compared to that of evaluating the objective function. These bounds unify, extend or improve all known upper and lower complexity bounds for unconstrained and convexly-constrained problems. It is shown that, given an accuracy level $\epsilon$, a degree of highest available Lipschitz continuous derivatives $p$ and a desired optimality order $q$ between one and $p$, a conceptual regularization algorithm requires no more than $O(\epsilon^{-\frac{p+1}{p-q+1}})$ evaluations of the objective function and its derivatives to compute a suitably approximate $q$-th order minimizer. With an appropriate choice of the regularization, a similar result also holds if the $p$-th derivative is merely H\"older rather than Lipschitz continuous. We provide an example that shows that the above complexity bound is sharp for unconstrained and a wide class of constrained problems, we also give reasons for the optimality of regularization methods from a worst-case complexity point of view, within a large class of algorithms that use the same derivative information.

In 2013, an algorithm determined Eric Loomis' six-year prison sentence in Wisconsin for attempting to flee a traffic officer and operating a motor vehicle without the owner's consent. No one knew how the software, Correctional Offender Management Profiling for Alternative Sanctions, or COMPAS, worked--not even the judge who delivered the sentence. Analyses conducted by ProPublica later found the predictive artificial intelligence used in this case, which attempts to gauge the likelihood of an offender committing another crime, to be racially biased: A two-year study involving 10,000 defendants found that the A.I. routinely overestimated the likelihood of recidivism among black defendants and underestimated it among whites. The U.S. Supreme Court declined to review Eric Loomis' case, so the sentence stands. Increasingly, A.I. has the power to alter the course of people's lives.

When it comes to the world of "big data", whoever has the most data has an advantage. And whoever has the most and best data scientists with the best tools to crunch that data usefully, build on that advantage. That's a key reason CIOs now look at all the data their companies collect and enlist data scientists and new tools to try to wring competitive advantage from what they learn. Entire economic blocs and countries are also upping the investment ante as they seek to slake their thirst for data and the riches machine learning and other AI technologies can bring. For example, the European Union's Digital Market Commission in April said it would increase its artificial intelligence R&D spending to $1.8 billion.

It is particularly interesting to note how close to the mark he was in his predictions of the state of the art in hardware. However, in his own specialty area - learning - he underestimated the difficulty of developing systems that learn from experience. We can only hope that we will not be as far off in actuality as we believe George Orwell to be, or as far off in our time scale as were Charles Babbage and his almost equally famous interpreter, Lady Lovelace Where, then, will the computer be in 1984? Computers are not going to get much bigger; in fact, they are going to get very much smaller, that is smaller in physical size, while retaining all of their presently envisioned computational capabilities. They will, of course, have access to very much bigger memories, memories which in fact can contain the total sum of man's recorded information, but this is already technically possible today.

Big data, the Internet of Things, and artificial intelligence hold such disruptive power that they have inverted the dynamics of technology leadership. When science and technology meet social and economic systems, you tend to see something akin to what the late Stephen Jay Gould called "punctuated equilibrium" in his description of evolutionary biology. Something that has been stable for a long period is suddenly disrupted radically--and then settles into a new equilibrium.1 1.See Stephen Jay Gould, Punctuated Equilibrium, Cambridge, MA: Harvard University Press, 2007. Gould pointed out that fossil records show that species change does not advance gradually but often massively and disruptively. After the mass extinctions that have occurred several times across evolutionary eras, a minority of species survived and the voids in the ecosystem rapidly filled with massive speciation.

The following correction was printed in the Guardian's Corrections and Clarifications column, Thursday April 22 2004 The seminar at which Stephen Jay Gould was rigorously questioned by Dennett's students was Dennett's seminar at Tufts, not Gould's at Harvard. Dennett wrote Darwin's Dangerous Idea before, not after, Gould called him a "Darwinian fundamentalist". Dan Dennett is a sailor, with a billowing white beard and moustaches that he twiddles when thinking. He uses "salty" as a term of praise and has just bought a 42ft boat that sleeps five and could, if he wished, cross the Atlantic. His passion for sailing may be the best way to approach his philosophy. In both, un-charted and dangerous areas are to be navigated by explorers ingeniously equipped. Like all sailors, he has stories. One concerns a French couple he met when sailing off Greenland. They were on their honeymoon, sailing from France to Iceland, then Greenland, and finally, in one long reach, from Greenland to the Falklands.

Little Theater has a tiny orchestra pit, with room for only a handful of players, and a modest budget. So when it mounts a big musical like "Beauty and the Beast," it brings in an electronic ringer. A laptop computer, loaded with a program called OrchEXTRA, serves as a "virtual orchestra," from strings to woodwinds, drums to horns, giving the music such a rich sound that audience members may wonder how a full Broadway orchestra fits into the tiny pit. "As far as sound quality, these things are great," says Dorian Boyd, the sound designer/technician for Little Theater, referring to OrchEXTRA. Virtual orchestras are much better than the early systems of just a few years ago, he says, which could sound like "video game music."