Experts on innovation always agree that it is speeding up ‘exponentially’. But is that true?
In 1965, in just four pages, the later co-founder of Intel, Gordon Moore, noted that the ‘complexity for minimum component costs’ of integrated circuits – that is, the number of transistors per chip that yielded the minimum cost per transistor – had roughly doubled each year from 1962 to 1965. Though he hardly needed to say so, that pattern is an exponential one. Still, Moore added that there was no reason to believe that it would not remain nearly constant for at least another 10 years. 
Moore’s extrapolation, however valid, is no unbending law of the future of the whole of electronics. To extend it beyond electronics is still less permissible. Innovation in pharmaceuticals, for example, is slowing. 
When boosters of IT rave about exponential growth, they should really say ‘accelerating, but only for the moment’.  While we wouldn’t rule out everyone owning five mobile phones, exponential growth tends, more rapidly than linear growth, to move toward infinity. And right now, the world’s technological growth is not tending toward infinity. Indeed since the West re-encountered economic crises in the early 1970s, the US in particular has had a kind of secret crisis of innovation, despite all the technological advances it has undeniably registered. 
The re-animation of frozen corpses
The US inventor-forecaster Ray Kurzweil believes that disease-fighting micro-robots in the human body, artificial intelligence, and the reanimation of frozen corpses are technologies that will move in such an exponential style, they will transform life ‘irreversibly’ by 2045.  Yet technologies much less exotic than these always irreversibly transform life: the breakfast cereal, for example, cannot easily be dis-invented. Yes, the diffusion of the endlessly cited iPhone is faster than that of domestic appliances in the 1920s. But the development of the Internet-enabled mobile phone has taken decades – and in genetics, James Watson, Francis Crick and Rosalind Franklin first published on the structure of DNA back in 1953. 
Perhaps people think that innovation is accelerating because they feel they have little control over their lives. Yet while earlier surges of innovation embraced a whole range of sectors, today’s advances don’t quite do that. It’s time for something better.
Agricultural, first and second industrial revolutions
In Britain the agricultural revolution embraced Jethro Tull’s mechanical seed drill (1701), Joseph Foljambe’s patented, lightweight, iron-fitted Rotherham Plough (1730, bought by George Washington and eventually factory-made), and Andrew Meikle’s grain threshing machine of the 1780s. It took in Flemish crop rotation, Flemish hydrology, and the selective breeding of animals. By raising productivity on the land, the agricultural revolution made cheap food and a surplus population of workers available for the first industrial revolution.
That began with the manufacture of wool (Kay’s fly-shuttle, 1733), and improved productivity in garment manufacture. Finished cloth was bleached with sulphuric acid and chlorine, and patterned with cylindrical printing. Downtimes in mills fell as components and frames came to be made of iron, leather belts replaced pulley-ropes, and gearing and shafting were rationalised. Blast furnaces turned out iron at high levels of purity, and, unlike mills and windmills, steam engines worked year-round. They modernised coal mining; and, with the commercial application, after 1776, of James Watt’s improvement on Thomas Newcomen’s steam engine (1705), the science of thermodynamics took off. The design, precision and smooth operation of metalworking tools improved and, with that, the standardisation of bolts and screws.  Britain’s James Brindley pioneered canal building; America’s Benjamin Franklin hit upon the wood-burning stove and lightning conductor, and France’s Joseph Marie Jacquard devised, about 1800, punched cards to control the weaving of silk.
Spanning the decades around 1900, the second industrial revolution included electric power and motors, organic chemistry and synthetics, the internal combustion engine and automotive devices, precision manufacture and assembly-line production.  Steel, petrochemicals, printing and papermaking, lighting and vacuum tubes and cathode ray tubes, packaged goods, soaps and cleaners, cameras and film cameras, surgery and anaesthesia: all these advanced dramatically. So did the railways. There emerged mechanical typesetting, mechanical refrigeration, diesel locomotives, electric trolley cars, steel ships, modern submarines, chain-driven bicycles, gyrocompasses, safety razors, department stores, radio and the telephone.  Herman Hollerith’s tabulating machine assisted in the first US Census (1890), laying the basis for IBM.  In December 1903 the Wright Brothers performed their first powered flights, and in 1912 the discovery of Bakelite was announced. To control the flow of goods brought about by steam-powered factories and locomotives, typewriters and telegraphs multiplied. 
What’s up, Doc?
Previous waves of innovation, then, were international, and prefigured some of what we now know as IT. Importantly, they coincided with major social, economic and political upheavals, and new hopes in the possibility and necessity of progress. In that context, the first and second ‘industrial’ revolutions were wide-ranging, more or less conscious attempts to save heaps of time in production processes.
After 1939 things were a little different. Many innovations came about that were all new: atomic bombs and nuclear reactors, transistors and integrated circuits, mass-produced homes, microwave ovens, manned space flight, lasers, xerography, the mouse, PCs, the graphical user interface, the World Wide Web, the Internet search, 3D TV. Significantly, though, many other innovations sprang from earlier developments: radar, cybernetics, television, mass aircraft carriers, ballistic missiles, synthetic rubber, plastics, mass-produced penicillin, and the Green Revolution with high-yield, disease-resistant wheat.
Is mankind, though, moving in decisive style beyond this, the still formidable post-war legacy of innovation?
After the Holocaust and the gulags of the 20th century, the 21st sorely lacks a background culture of optimism about progress. There are few great quests to lighten the load of work: for instance, robots have spread in industry, but still do little in hospital or home. It is labour utilisation, not innovation, that has brought the principal boost to the world economy in recent years.
It’s true that there’s forward movement in the controlling of IT by voice, face and gesture, in nuclear fusion, cleaner coal, carbon capture and storage, the capture of CO2 from the air, bio-fuels, batteries and all-electric cars, wind turbines, photovoltaic panels, geothermal energy, hydrology, desalination, early warning systems for bad weather, synthetic biology, stem cell research, neurobiology and much else besides. But there is little to compare with the sweeping grandeur of earlier revolutions.
The emphasis is not on revolutionising production, but rather on finance, home insulation, consumer goods, and consumer services (though something like civilian supersonic transport is out). Innovation has come to mean not step-changes in the making of wealth, but something vaguely akin to the continuous improvement programmes developed in post-war Japanese car factories. There are few new miracle cures, wonder materials or truly rapid transformations of the energy scene. Above all, it is impossible to see even the silhouette of a range of mutually reinforcing innovations, creating new industries across a broad front.
That, though, was the pattern in previous industrial revolutions.
Right now, the second decade of the 21st century badly needs a wave of new industries. Where, for instance, are tomorrow’s radically new means of production? The principles around which mankind should go innovating have never been more vital.
 Gordon Moore, ‘Cramming more components onto integrated circuits’, Electronics, Vol 38, No 8, 19 April 1965. The interpretation of complexity and minimum cost is by Jon Stokes, ‘Classic.Ars: understanding Moore’s law’, ars technica, 27 September 2008, on http://arstechnica.com/hardware/news/2008/09/moore.ars.
 Some see pharmaceutical companies as having ‘risen to the challenge’ of increased regulation and cost discipline: see Stephen Scypinski, ‘Editorial: Speed and Efficiency in Pharmaceutical Development’, Journal of Pharmaceutical Innovation, 18 August 2009, on http://www.springerlink.com/content/c572151612628732/fulltext.pdf. However for critics drug firms focus more on ‘me-too’ innovations than on fundamental ones. In a paradox, just when Big Pharma is attacked for its excessive market power, it has ‘a professional sense of gloom’ about prospects. See Frank A Sloan and Chee-Ruey Hsieh, Pharmaceutical Innovation: Incentives, Competition, and Cost-benefit, Cambridge University Press, 2007, p10, and Richard A Epstein, Overdose: How Excessive Government Regulation Stifles Pharmaceutical Innovation, Yale University Press, 2006, p7.
 Compound interest, like parts of biology and physics, works exponentially; but IT rarely moves as xt, where x is a constant number bigger than 1, and t, the exponent, represents time elapsed. While Moore’s ‘law’ shows few signs of reaching its limits, in the rest of IT growth tends to be sub-exponential or polynomial. Still more restrictively, around 1980, Metcalfe’s law suggested only that the dollar value of a network proceeds as the square of the number of ‘compatibly communicating devices’. For a discussion, see Simeon Simeonov, ‘Metcalfe’s Law: more misunderstood than wrong?’, 26 July 2006, on http://blog.simeonov.com/2006/07/26/metcalfes-law-more-misunderstood-than-wrong/
 ‘Industrial innovation’, noted President Jimmy Carter in a major speech on the subject, ‘is an essential, but increasingly overlooked factor in a strong and growing American economy’. See Carter, ‘Industrial Innovation Initiatives Remarks Announcing a Program To Encourage Innovation’, White House press briefing, 31 October 1979, in John T Woolley and Gerhard Peters, The American Presidency Project [online], Santa Barbara, on http://www.presidency.ucsb.edu/ws/?pid=31627. More than two years earlier, Carter had favoured new, unconventional sources of energy, but only as last of 10 principles: the ‘cornerstone’ of his response to the energy crisis of 1973-4 was energy conservation. See Carter, ‘The President’s Proposed Energy Policy’, televised speech, 18 April 1977, on http://www.pbs.org/wgbh/amex/carter/filmmore/ps_energy.html
 Ray Kurzweil, The Singularity is Near: When Humans Transcend Biology, Viking Adult, 2005, p7. For a pessimist vs an optimist on the rate of technological change, see Jonathan Huebner, ‘A possible declining trend for worldwide innovation’, Technological Forecasting & Social Change, 72, 2005, on http://accelerating.org/articles/InnovationHuebnerTFSC2005.pdf, and John Smart, ‘Measuring Innovation in an Accelerating World’, Acceleration Studies Foundation, no date, on http://accelerating.org/articles/huebnerinnovation.html. Two critiques of the view that the speed of change is accelerating are Bob Seidensticker, Future Hype: the Myths of Technology Change, Berrett-Koehler, 2006; Steven Schnaars, Megamistakes: Forecasting and the Myth of Rapid Technological Change, The Free Press/Collier Macmillan, 1989.
 David Landes, The Unbound Prometheus: Technological Change and Industrial Development in Western Europe from 1750 to the Present, Cambridge University Press, 1969, pp84-85, 87, 90-91, 95, 99, 101-2, 104-5.
 Ibid, p235.
 See, among others, Alfred Chandler, The Visible Hand: the Managerial Revolution in American Business, Harvard University Press, 1978.
 Kevin Maney, The Maverick and His Machine: Thomas Watson, Sr. and the Making of IBM, Wiley, 2003.
 James Beniger, The Control Revolution: Technological and Economic Origins of the Information Society, Harvard University Press, 1986.