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The Developmental Spiral
A Curious and Unexplained Universal Phenomenon


Spiral Symmetry in the Universe

Our Apparently Accelerating Succession of Ages—A Simple and Ever-Tightening Developmental Spiral


Coming Eras: Proposed Details

Alternative Era Scheme: Trend Reversal in Differentiated Networks


Computational Closure and the Developmental Singularity: A Very Speculative Post-Tech Singularity Proposal

A speculative consideration of accelerating cycles of developmental emergence.

What is it about the spiral shape that human mind finds so intellectually and visually enticing?
Has the universe somehow 'tuned us' to an intuitive understanding of its importance?

There is much still to be learned on this topic, but for now you may enjoy,
Spiral Symmetry, by Istvan Hargittai and Cliff Pickover, 1992,
The Golden Ratio, by Mario Livio, 2003, about logarithmic spirals,
and, on prime number spirals, as great places to start.

If we live in a universe of finite space, time, energy, matter, and compressibility, our history of spiraling emergence must have a limited number of turns ahead.

Our Apparently Accelerating Succession of Ages— A Developmental Spiral




Hominid Age (Genus Homo, behavioral mimicry language)

Archaic Age (Homo sapiens sapiens, vocal language)
Tribal Age (Cro-Magnon human, pictographic language)
Agricultural Age (horticulture/husbandry, writing systems)
Empires Age (autocracy, organized warfare)
Artifice Age (organized religion, prescientific inquiry)
Scientific Age[1]
Industrial Age
Information Age
Symbiotic Age
Autonomy Age
Tech Singularity


2,000,000 yrs ago

90,000 yrs ago
40,000 yrs ago
9,000 yrs ago
3,000 yrs ago
1,500 yrs ago
380 yrs (1500-1770 AD)
180 yrs (1770-1950)
70 yrs (1950-2020)
30 yrs (2020-2050)
10 yrs (2050-2060)
Circa 2060

While my own best current intuition expects a 2060 A.D. singularity, Vernor Vinge, Ray Kurzweil, Marvin Minsky, Richard Coren, James Wesley, Damien Broderick, Robin Hansen, Eliezer Yudkowsky, Nick Bostrom, and a number of other scholars have proposed a range of ETA's between 2020 and 2140, with 2020-2060 presently representing the majority of predictions, clustering around a 2040 mean.

Note that each major age has lasted less than half the previous—this is characteristic of a double exponential, hyperbolic, or "asymptotic" function. Era choice is arbitrary, but the compression is apparently not.
Some non-bold ages since hominid emergence are omitted above for clarity. Bold ages are examined below in a bit more detail:




Technological Subcycles

1390-1500, 110 yrs, Final Pre-Scientific Revolution
1500-1600, 100 yrs, 1st Scientific Revolution
1600-1690, 90 yrs, 2nd Scientific Revolution
1690-1770, 80 yrs, 3rd Scientific Revolution

1770-1840, 70 yrs, 1st Industrial Revolution
1840-1900, 60 yrs, 2nd Industrial Revolution
1900-1950, 50 yrs, 3rd Industrial Revolution

1950-1990, 40 yrs, 1st Information/Computer Revolution
1990-2020, 30 yrs, 2nd Information/Computer Revolution

2020-2040, 20 yrs, 1st Symbiotic Revolution
2040-2050, 10 yrs, 2nd Symbotic Revolution

2050-2060, 10 yrs, Multiple Autonomy Revolutions

Circa 2060 Technological Singularity


Prominent Features

(1323-82: Coordinate Geom., Exponents, Series)
Copernicus Heavenly Bodies (1543) Vesalius (1543)
Bruno (1600), Kepler (09) Galileo (32) Descartes (37)
Newton Principia (1687, 1704) Linnaeus (1735)

"CWT: Coal, Wood, Textiles" Watt Steam Eng, 1769
"SST: Steam, Steel, and Telegraph"
"ICE: Internal Combustion, Chemistry, and Electricity"

"Dig. Computers, Engineering, Multinationals, Television"
"Planetnet, Global Entertainment, Trade, and Security"

"GUI,CUI,&NUI(Agents), Peace/Equity/Justice Era"
"Deep Symbiosis, Global Telepresence, Minor Magic"

"Progressive Autonomy, Developmental Intelligence"

"AI, Earthpark."
Shortly after: Uploads and Full Nanotech.

Coming Eras: Proposed Details

A 30-year cycle, from 1990-2020: Building out the 1st generation Internet Grid (the so-called "stupid network"), early intelligence amplification (IA), commercial biotechnology, ongoing miniaturization, weak nanotech (academic evolvable hardware), 2nd generation robots, early evolutionary computing. Major national and international trade, sociopolitical, and security convergence reforms (G8, WTO, UN, IAEA, etc.) begin.

A 20-year cycle, from 2020-2040: The modularly intelligent, distributed, semi-ubiquitous first-generation Conversational Interface network, creating impressive, commercial intelligence amplification (IA), via very coarse-grained personality capture in lifelogging systems. Powerful biotech (isolated "medical miracle" therapeutics, negligible human bio-augmentation due to equity and ethical concerns), early computational nanotech (true evolvable hardware), 3rd generation adaptive robots, commercial evolutionary computing, ongoing significant sociopolitical reform, and peace/justice/equity crusades become dominant. Early Transparent Society, accelerating compassion begins. Age of Materialism slowly unraveling (economizing, creative free time, voluntary simplicity increasing in first world economies).

A 10-year cycle, from 2040-2050: Second generation conversational interface, with second generation personality capture/first-generation 'uploading' (strong interior modeling of the attention, drives, motives, past history, emotional state, etc. of the interfaced human), leads to a new, deeper symbiosis with our semi-intelligent machines and networks. Yet IA strategies (intelligence amplification, direct human empowerment), while still the dominant change drivers in this ere, are progressively being overshadowed by AI strategies (artificial/autonomous intelligence, indirect human empowerment), as significant though still limited autonomy emerges in our ubiquitous AI platforms. More powerful biotech ("Common Miracles"), limited human augmentation, mature computational nanotech, 4th generation self-reconfiguring robots, mature evolutionary computing. Sociopolitical systems and major power groups begin to see their impending extinction/transformation. Personal, social and spiritual transformations become big issues. Materialism loses further ground. By mid-2040's, most humans are still singularity-unaware, but hundreds of millions across the globe sense an approaching "hurricane" of change.

2050: Era of Strong Autonomy. The 10-year cycle is followed, in this caricature, by progressively shorter 5-, 2-, and 1-year cycles, each substantially more autocatalytic. Human support of and adjustment to successive technology paradigms becomes steadily less necessary, as each is noted to be more self-regulating, self-provisioning, self-repairing, self-directing, self-generating, and involving low level bottom-up evolutionary developmental processes that are increasingly opaque to top down human observers. Technological safety and oversight will likely be one of our central concerns and enterprises at this time. Nevertheless, we will be sheparding a substrate that will be increasingly more self-balancing, and rapidly self-correcting in its mistakes. At this stage, most human-machine interfaces will be impressively seamless and human-centric, involving a range of what may be termed "second-generation uploading" techniques: capture and instantiation of the personality, intentionality, and experience history of the user into all the machine systems we use.

Circa 2060: Technological Singularity. The AI (and shortly thereafter, AI's) claim self-awareness. Autonomous Technological Intelligence emerges on Earth. True, third-generation uploading of human personality and conscious architecture to the machine substrate begins to occur in an accelerating fashion thereafter, driven by human curiosity and highly ethically constrained autonomous intelligence, proceeding in a technically reversible process, at least at first. Note: this particular projection proposes 2060, but the above intervals are only a guess at this stage. See other singularity timing predictions for a range of current guesses in this space.

Alternative Era Scheme: Trend Reversal in Differentiated Networks

When we consider history in terms of trend reversals in differentiated networks (with widely varying, nonclonal nodes), rather than in terms of disruptive technological punctuations, we can can see the possibility for defining another, even less arbitrary set of developmental eras. Furthermore, the most clear and possibly most valuable cusps and inflection points (trend reversals) seem to be those involving not just isolated environments, but the entire network of the leading edge of local intelligence.

Using this methodology, we can state that Earth's techno-bio-socio-political networks arrived at a kind of singularity, or global phase change, about thirty years ago, when a number of trends broke and are now accelerating in a reverse direction. Circa 1970, shortly after humanity's first foray into the "beautiful desolation" of space, we reached a peak in global nuclear arms buildup, and simultaneously passed an inflection point in total world population and the second derivative (rate of growth) of total world energy consumption (a result of the stunning energy efficiency of each new generation of our increasingly intelligent machines, and the sharply limited energy needs and increasing sustainability ethics of biological humans). As I've written elsewhere, a kind of "technological contraceptive" limiting our procreation and marginal per capita consumption seems to be rapidly spreading across the planet, superceding our primal urges to reproduce and consume with even deeper desires for personal and child development. We are learning social self control (not fast enough for the sustainability minded among us, but we are changing behaviors nonetheless) amid a world of accelerating plenty.

I would suggest that the next major network phase change singularity, involving a necessary peaking and inflection of a number of still slowly growing trends (e.g., individual and state violence, nationalism, fundamentalism, anarchic individualism, authoritarianism) must arrive at the dawn of the conversational interface era, circa 2020.

This would give a current interval of fifty years (1950-2020) between major cultural phase changes (sociotechnological 'singularities') at the present time. An alternative analysis, from the birth of the transistor in 1950 to the emergence of the conversational interface circa 2020, would give seventy years for the current 'Information Age' era.

It is tough to say without good quantitative modeling whether either of these models would suggest a technological singularity earlier or later than the 2060 estimation. We would need to do some careful trend measurement in previous eras, note their length, and then apply a simple mathematical regression model. Any volunteers?

Computational Closure and the Developmental Singularity --
A Very Speculative Post-Tech Singularity Proposal

Post 2060: Strong ("Drexlerian") nanotech arrives. Technology increasingly begins to seem "magical" from the perspective of unaugmented human biology, though the bulk of the physics behind the "magic" remains easily comprehensible, once explained to any human. Human-machine integration becomes ever more seamless at all scales. Voluntary biological "uplifting" or "uploading" into the machine substrate (reversible by law, but rarely done in practice) begins, slowly at first, and then in earnest, after a brief era (20 years? 200?) of increasingly more accurate predictive simulation of the human substrate by our technological successors. Full AI simulation of the human thoughtspace will eventually occur in the same manner and for the same reasons that humans today attempt to understand and predict the realtime genetic and proteomic behavior of bacteria, in our multimillion dollar "metabolome" simulations. From our perspective, the uploading process will seem like simple outmigration and expansion of our own consciousness in a new phase of personal and collective growth, with both differentiation and fusion in attempts to optimize internal and environmental learning.

Serious future thinking leads us to strongly suspect that human and biological uploading will be only a small part of the coming global metasystem transition, to use Valentin Turchin's and Francis Heylighen's worthy phrase. Local AI simulation systems are very likely to become so powerful they begin to understand the general history of universal and local biological development in essentially closed, statistically predictable terms. Even though chaotic, nonlinear systems (e.g., weather, human behavior, conscious thought) remain fundamentally unpredictable in their details, this has historically never stopped them from becoming statistically predictable and probabilistically simulable (as in Probabilistically Checkable Proofs), to a point of rapidly declining utility of computation. This declining utility apparently leads information processing systems to seek new, more generative computational domains.

Such effective and approximate local closure has occurred in countless real and abstract domains before, as in mapping the physical Earth (e.g., post-Columbus cartography, or post-GPS location systems), or in countless other knowledge domains of observably declining generativity (e.g., classical music, number theory, Newtonian physics). Computational closure is rapidly occurring at even the highest scales in mapping all physically observable astronomical events (e.g., Martin Harwit, Cosmic Discovery, 1981) and at the lowest scales in decoding the fundamental physical structure of spacetime (Brian Greene, The Elegant Universe, 1999). Closure is a profound, universal, accelerating, and still poorly understood information processing phenomenon.

Assuming local intelligence continues our six billion year trend of accelerating increase in STEM (space, time, energy, and matter ) compression (the most likely assumption, for this author), this will lead, in very short time, to a local system capable of universal simulation, a theoretical proposal popularly known as an "omega computer" ("omega" only in relation to computational utility within this universe, however).This would be a post technological singularity AI network capable of approximately (e.g., effectively, never completely) modelling all prior and future realms of universal development that are allowed by our fixed and finite physics. Just in case you think future intelligence might get somehow transcend physical limits and persist within this universe indefinitely, you should know that our most current cosmologial models involve not simply "heat death" billenia from now, but an impending accelerating universal senescence (see Mario Livio, The Accelerating Universe, 2000).

I think the central conclusion we are tempted to draw from this early evidence is as follows:

"Inner space" (zones of great STEM compression and universe simulation and recreation capacity), not "outer space" (expansion off Earth, or even the present human sphere of living), may be a constrained developmental destiny for postbiological intelligence, very soon in cosmologic time.


More Circumstantial Evidence for Closure -- The Growth and Limits of Computation

Seth Lloyd, in "Computational Capacity of the Universe," Physical Review Letters, June 2002, estimates the upper limit of how much computing power the entire universe has expressed since the beginning of time. His proposed number, 10^120 logical operations, is quite large, but necessarily bounded, or finite. Lloyd cleverly compares this number with the estimated total computation that has been accomplished by all human-made computers that have ever run (e.g., our local pre-AI network and its databases), yielding 10^31 operations to date. It is quite impressive that half of this latter total was produced within the last two years, using his estimate of a fixed Moore's law doubling time of two years. In other words, the marginal velocity of local computation is quite rapid.

Even given the fixed two-year doublings in Lloyd's preliminary model, he notes it may take only another 300 doublings, or only 600 years, before all the available energy in the universe (or more realistically, our local physical resources) are employed in computation. Thus he implicitly proposes that we have roughly 600 years until we reach an asymptote, or in my language, a developmental singularity, a technological system that has reached the limits of its acceleration, and that perhaps is close to the limits of computational complexity as well.

Just how far down do observed trends in STEM efficiency and density of computation scale? Is there a natural limit? Rolf Landauer of IBM did important work in this area (e.g., C. H. Bennett and R. Landauer, "The Fundamental Physical Limits of Computation", Scientific American, 48-56, July, 1985). Bennett, Landauer, and others have found no minimum energy requirements, and researchers in this area have proposed reversible computing paradigms which would be able to communicate with "arbitrarily small" energy levels within known physical law ("How Much Energy Does it Take to Send a Bit? Perhaps None.", IBM, June 28, 1996). This suggests a universe that supports accelerating efficiencies and compressions of computation as far down as we can see.

If, then, the physical substructure of the universe supports our historically-observed double exponential growth of local computation all the way down to the Planck scale, the fundamental fabric of spacetime in the Standard Model of physics then we can expect the continued success of mesocomputation, nanocomputation, quantum computation, femtocomputation, and perhaps eventually, even Planck computation via new universe creation within the multiverse as some cosmologists have proposed. (See John Leslie, Universes, 1996, Lee Smolin, The Life of the Cosmos, 1997; Martin Rees, Before the Beginning, 1998 for more on the multiverse, and some tentative universal replication hypotheses).

Let us now propose two revisions to Lloyd's 600-year estimate. First, two-year doublings in price performance in today's fastest-growing computational systems are not fixed, but have actually shrunk to less than 14 months (in some estimates, less than 12 months) over the last five years within graphics chips (e.g., Nvidia), which currently represent the first generation "visual cortex" of our still-brainless PC's, and apparently the current leading edge of marginal computational development rates on our planet. Thus we see that 300 remaining doublings to the developmental singularity might be accomplished in as little as 140 years, which would be consistent with Richard Coren's estimate (The Evolutionary Trajectory, 1998) of a fundamental "phase change" in the structure and nature of local intelligence circa 2140. This phase change would be consistent with my prediction of universal transcension.

Second, if these doublings in computational operations of local intelligence have to occur via a relentless local STEM compression, as appears evident, then we may expect our post-tech singularity AI's to chart an accelerating course to a local developmental singularity, and subsequent universal transcension to another multiversal domain. More on these quite speculative yet apparently fundamental issues in my forthcoming book.


Footnote 1. We might consider defining Greek culture (circa 400 BCE) as the start of the Scientific Age on this planet. But I would suggest that a better definition of the emergence of an Age must involves a distributed "network" transition, not a few examples that aren't sustained. The key point here is that Greek culture wasn't able to survive long in the developmentally primitive environment in which it managed to emerge.

Greek culture was an isolated and unique emergence among the typical militant hierarchical religious civilizations of the day. Scholars such as Daniel Robinson of Georgetown University have noted that it was the unusual type of monotheistic religion invented in Greece, one which allowed unprecedented individual liberty of inquiry, that was probably the single most important factor responsible for their stunning scientific and political advances. This new form of government, and the permissiveness of its religious memes, wasn't long tolerated by the other theistic autocracies in the region at that time.

Unfortunately, many experimental cultures are often born without "immune systems," and Greece was apparently no exception. Scholars like R.J. Rummel have argued convincingly that democracy is intrinsically less suited for initiating warfare than autocracy, particularly in environments where communication networks are low quality and quantity. So the Greek experiment was highly vulnerable to overthrow from the start. Both Greek science and Athenian democracy appear to me to be forms of civilization and political organization that were unsupportable, on average, in a world before literacy and telephones, a world where widespread inter-state violence was sanctioned by the typical religions of the day, a world of empires and artifice, one where escalating "arms races" were still occurring among state actors, and one where barbarian hordes could easily overthrow any but the most coordinated (and at that time, necessarily autocratic) defense systems.

We see early temporary emergences of "advanced forms" occur in other developmental systems, such as in the early false starts that occur in oogenesis, or limb buds that emerge early in embryos and then revert, long before the eventual developmental transition actually occurs. We don't call those local aborted efforts the start of an "Age", and for the same reason I wouldn't call Greek culture the start of the Scientific Age. By this definition, the spirit of scientific inquiry (both hypothesis and empiricism, practical or formal) would not become broadly popular for another thousand years after the Greeks first demonstrated its great potential.

Picking a specific date of sustained, distributed emergence is always dicey, but I'd place it near the beginning of the 1500's, in my own (admittedly arbitrary) choice. Johannes Gutenberg invented the movable type printing press in 1450. But fifteenth century culture wasn't yet ready for the implications of this radical technology, so for the first sixty years his press was almost solely used for automating the copying of Bibles. {Perhaps the same is happening with the new tools of the web: it takes a "blogging generation" to grow up, fluent in them, before we fully realize what they can do to accelerate change.)

Fortunately, by the early 1500's, enterprising Europeans had understood the value of the press for increasing literacy in general, and a bona-fide printing boom occurred, one that branched into all subjects of human inquiry. That was a clear and irreversible network transition, occurring across the European theatre. Some scholars would date the start of the Scientific Age with the publication of Francis Bacon's Novum Organum in 1620. Some would date it still later, with the publication of Isaac Newton's Principia Mathematica in 1687. I would presently argue it started circa 1500, as the desire for individual literacy and free inquiry and discussion are key elements that allowed our modern scientific methodology to emerge. In short, the phase change singularity of scientific thinking emerging as a sustainable planetary culture, apparently wasn't yet possible in the time of the Greeks, and to date it from that point would miss the intrinsically social nature of the computational processes involved. Some date between 1500 and 1700 seems most accurate, from my perspective.


Accelerating change is apparently inevitable. The future is an untold story of emergent events, some of which seem to be inherent in the developmental structure of the universe.
Let's discover them, together.