The Exponential Development of Process

It has often been observed over the last few centuries that time appears to be accelerating as trains, automobiles, and airplanes have radically increased the speed of travel and concomitantly shrunk subjective distances in space. For the pioneers who crossed North America in covered wagons, this trip was a long and perilous journey, but for us it is a several-hour flight accompanied by relatively mild discomfort. Similarly, the inventions of the telegraph, the telephone, and the internet have facilitated the acceleration of communication, so that in the mid-nineteenth century, the Pony Express, combined with the limited extent of the telegraph which only went as far as St. Joseph, Missouri, was the fastest way to send a written document from the East Coast to the West, a trip that took about ten days, whereas now one can communicate almost instantaneously through satellite video conferencing with someone in Shanghai or Mozambique. However, despite the common recognition of this acceleration, the idea that this increasing speed of experience is exponential in nature does not appear to be intuitive for most people, as our brains and our conceptual tools have evolved primarily in the context of linear phenomena.

Exponential Growth

Plotted on a linear graph, this exponential progression starting with one and doubling at each integer along the horizontal axis reaches one billion in about thirty doublings.

It is unclear precisely when the quality of exponentiality was discovered, and by whom, but several persistent stories place this discovery during the first millennium C.E. in India or Persia in coincidence with the invention of Chess. A classic narrative, related by the Persian poet Ferdowsi in his epic poem “Shahnameh” sometime around 1000 C.E., tells of a mathematician named Sessa, described as the inventor of the “Game of Kings,” who pleased his king so greatly by his invention that the monarch told Sessa to name his reward. The mathematician’s request seemed simple and reasonable: place one grain of rice on the first square of a chess board, and double the number for each of the sixty-four squares, so that the second square would contain two grains, the third four grains, the fourth eight grains, and so on. The king, thinking this a rather modest request, quickly assented. However, when the king’s treasurer calculated the total after some difficulty and delay, it turned out that the king had agreed to give Sessa more than eighteen quintillion grains of rice, which amounts to about four hundred billion tons, far more than was contained in the entire kingdom, far more even than the world currently produces in a year. In some versions of the story, Sessa is put to death for his impertinence, while in others he is made the new king. However, the key point is that this exponential growth starts out seeming fairly linear, though clearly accelerating, but by the time the doublings are well into the double digits, the growth becomes startlingly explosive.

Ray Kurzweil, the inventor of such profoundly transformative and pervasive technologies as the first omni-font optical character recognition system, the first flatbed scanner, the first text-to-speech synthesizer, and the first keyboard synthesizer capable of reproducing realistic instrumental sounds, and since 2012 Director of Engineering at Google, has been one of the primary figures in applying exponentiality to the growth of technology. In his Law of Accelerating Returns, Kurzweil demonstrates that not only technology, but the evolution of life and mind for which technology appears to be an extension, has progressed exponentially, though this acceleration is only now becoming rapid enough that individuals are beginning to have an intuitive sense of it in their lifetimes. The capacity very quickly to adapt to extreme novelty is one of the most marked qualities of the human organism, so that about three decades ago as of this writing, the internet did not exist, and a few decades before that, computers were essentially glorified calculators, but we can hardly imagine living without these inventions.

Now, as Kurzweil has often pointed out, our “phones” actually contain computers that are at least a thousand times more powerful and a million times less expensive than the building-sized supercomputers of the mid-nineteen sixties, which means that our pocket devices are a billion times more capable per dollar of computation, adjusted for inflation, than the most advanced computers were fifty years ago.[i] Kurzweil places the many innovations that have led to this situation, cross-referenced to a slew of authoritative encyclopedic sources, on a graph that traces a strikingly smooth exponential curve through periods of inflation and rapid economic growth, as well as through depressions and wars. And similarly, he places on a graph the emergence of biology through the information-conserving novelty of DNA, the emergence of mind through the information conservation of neural patterns, the emergence of computational technology through the information conservation of hardware and software, and the incipient merging of biology and technology through the embeddedness of humanity in global networks and the embedding of increasingly tiny and powerful information processors in the human brain and body. Without reproducing Kurzweil’s research in detail, it must suffice to say that it is difficult to imagine a credible argument against the ineluctable mountain of data he has amassed to support his primary hypothesis. Any lingering skepticism about this phenomenon appears to be driven primarily by the hegemony of linear common sense that has been dominant in modernity. As is true of most of the concepts discussed in these pages, exponential acceleration seems to be a higher-order common-sense characteristic of the emerging mode of thought.[ii]

Exponential Development of Process

Exponential development through emergent stages plotted on a logarithmic graph. The figures given are approximate, representing orders of magnitude rather than precise dates, which continue to be the subject of debate.

[This post is an excerpt from The Dynamics of Transformation: Tracing an Emerging World View.]

[i] This figure will almost certainly be outdated by the time the present book is published.

[ii] The majority of arguments leveled against Kurzweil generally seem to take two forms. First, his critics often mention Kurzweil’s intention to resurrect his deceased father once technology becomes sufficiently advanced. While certainly a quirky ambition, this critique is the clearest kind of argumentum ad hominem, and thus fallacious. Just because Kurzweil holds some unconventional ambitions does not invalidate his discoveries. If we judged new theories based on the theorist’s personal eccentricities, many transformative revolutions would not have occurred, including Newtonian physics, as Isaac Newton was a truly bizarre and pugnacious individual. Second, and perhaps more plausibly, some critics have claimed that Kurzweil’s predictions are overly optimistic, that such an exponential trajectory cannot possibly continue. And it is definitely possible that some unknown factor, whether ecological catastrophe or collective human choice, will inhibit the current trajectory. However, it seems to me that such critics must bear the burden of proof, as it appears more likely that processing power will continue to follow the smooth exponential curve that it has traced for billions of years than that it will deviate from this trend, if such an exceptionally consistent movement on such a vast scale can be described as such.

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