Mathematical Models to Calculate the Acceleration of Innovation Across Time
= "the planetary macro-evolutionary acceleration in the last 4 billion years can be described by a single hyperbolic equation quite accurately".
Context
Andrey Koroyatev on the Singularity thesis:
"Note that some big historians take such “mathematically grounded” predictions rather seriously. The most prominent among them is Akop Nazaretyan. In his article with a symptomatic title “Mega-history and Its Mysterious Singularity” in the Russian Academy of Sciences flagship journal he maintains the following: “The solar system formed about 4.6 billion years ago, and the very first signs of life on Earth date back to 4 billion years. Thus, our planet became one of the (most likely, numerous) points on which the subsequent evolution of the metagalaxy was localized. Although its acceleration was noted long ago, anew circumstance has been discovered of late. The Australian economist and global historian G.D. Snooks, the Russian physicist A.D. Panov, and the American mathematician R. Kurzweil compared independently, proceeding from different sources and using different mathematical apparatuses, the time intervals between global phase transitions in biological, pre-social, and social evolutions (Panov 2005a, 2008; Kurzweil2005; Snooks 1996; Weinberg 1977). Calculations show that these periods decreased according to a strictly decreasing geometrical progression; in other words, the acceleration of evolution on the Earth followed a logarithmic law” (Nazaretyan 2015: 356)."
Description
Andrey Korotayev:
1.
"A twofold increase in macroevolutionary development rate tends to be accompanied by a fourfold increase in the acceleration speed of this development rate; an increase in macroevolutionary development rate 10times tended to accompanied by 100 times increase in the acceleration speed of this development rate; and so on...”
For example:
- "around 18 000 BCE we would find that planetary macroevolution occurred at the scale of tens of thousands of years, around200 000 years before present (BP) – at the scale of hundreds thousands of years (around one global phase transition per 100 thousand years), around 2 million BP – at the scale of millions of years, around 20 million BP – at the scale of tens of millions of years, around 200 million BP – at the scale of hundreds of millions of years, and around 2 billion BP – at the scale of billions of years
- around 1 CE macroevolutionary shifts (e.g. Axial Age revolution) tended to happen at the scale of one per millenium
- “around 1800 CE a typical rate of global macroevolution was about one macroevolutionary shift ( e.g., Industrial Revolution) per century” – that is macroevolution around that time proceeded at the scale of centuries"
2.
"The analysis .. appears to indicate the existence of sufficiently rigorous global macroevolutionary regularities (describing the evolution of complexity on our planet for a few billion of years), which can be surprisingly accurately described by extremely simple mathematical functions. At the same time this analysis suggests that in the region of the singularity point there is no reason, after Kurzweil, to expect an unprecedented (many orders of magnitude) acceleration of the rates of technological development. There are more grounds for interpreting this point as an indication of an inflection point, after which the pace of global evolution will begin to slow down systematically in the long term."
Discussion
Andrey Korotayev :
"It is shown that the mathematical analysis of the series of events (described by Kurzweil in his famous book), which starts with the emergence of our Galaxy and ends with the decoding of the DNA code, is indeed ideally described by an extremely simple mathematical function (not known to Kurzweil himself) with a singularity in the region of 2029. It is also shown that, a similar time series (beginning with the onset of life on Earth and ending with the information revolution – composed by the Russian physicist Alexander Panov completely independently of Kurzweil) is also practically perfectly described by a mathematical function (very similar to the above and not used by Panov) with a singularity in the region of 2027. It is shown that this function is also extremely similar to the equation discovered in 1960 by Heinz von Foerster and published in his famous article in the journal “Science” – this function almost perfectly describes the dynamics of the world population and is characterized by a mathematical singularity in the region of 2027. All this indicates the existence of sufficiently rigorous global macroevolutionary regularities (describing the evolution of complexity on our planet for a few billion of years), which can be surprisingly accurately described by extremely simple mathematical functions. At the same time it is demonstrated that in the region of the singularity point there is no reason, after Kurzweil, to expect an unprecedented (many orders of magnitude) acceleration of the rates of technological development. There are more grounds for interpreting this point as an indication of an inflection point, after which the pace of global evolution will begin to slow down systematically in the long term."
How seriously should we take the prediction of “singularity” contained in such mathematical models?
Andrey Korotayev:
"Should we really expect with Kurzweil that around 2029 we should deal with a few order of magnitude acceleration of the technological growth? I do not think so.
...
What are the grounds to expect that by Friday, November 13, A.D. 2026 the world population growth rate will increase by a few orders of magnitude as is implied by von Foerster equation? The answer to this question is very clear. There are no grounds to expect this at all. Indeed, as we showed quite time ago, “von Foerster and his colleagues did not imply that the world population on [November 13, A.D. 2026] could actually become infinite. The real implication was that the world population growth pattern that was followed for many centuries prior to 1960 was about to come to an end and be transformed into a radically different pattern.
...
Note that in case of global demographic evolution the transition from the hyperbolic acceleration to logistic deceleration started a few decades before the singularity point mathematically detected by von Foerster.
...
Panov got involved in the study of the processes of the slow-down of the global technological-scientific growth (Panov 2009, 2013).As LePoire puts it, “Big History trends of accelerating change and complexity with related increases in energy use may not be sustainable. The indications of potential slowdown in the rate of change in economies, technology, and social response were investigated. This is not to say that change will stop, just the rate of change will not accelerate. In fact, at the inflection point in a logistic learning curve only half of the discoveries have been made."
Details
"Modis – Kurzweil list contains 27 “canonical milestones”, whereas Panov’s series only includes 20 “biospheric revolutions”. Thus, at least 7 Modis – Kurzweil milestones have no parallels in the Panov series."
Modis Time-Series
"Some Modis “milestones” from his 2002 article in the Technological Forecasting & Social Change:
(1) Origin of Milky Way, first stars – 10billion years ago.
(2) Origin of life on Earth, formation of the solar system and the Earth, oldest rocks –4 billion years ago.
(3) First eukaryotes, invention of sex (by microorganisms), atmospheric oxygen, oldest photosynthetic plants, plate tectonics established – 2 billion years ago.
(4) First multi-cellular life (sponges, seaweeds, protozoans) – 1 billion years ago.
(5) Cambrian explosion/invertebrates/vertebrates, plants colonize land, first trees, reptiles, insects, amphibians – 430 million years ago.
(6) First mammals, first birds, first dinosaurs– 210 million years ago.
(7) First flowering plants, oldest angiosperm fossil – 139 million years ago.
(8) First primates/asteroid collision/mass extinction (including dinosaurs) – 54.6million years ago.
(9) First hominids, first humanoids – 28.5million years ago.
(10) First orangutan, origin of proconsul –16.5 million years ago.
(11) Chimpanzees and humans diverge, earliest hominid bipedalism – 5.1 million years ago.
(12) First stone tools, first humans, Homo erectus – 2.2 million years ago.
(13) Emergence of Homo sapiens – 555,000years ago.
(14) Domestication of fire/ Homo heidelbergensis – 325,000 years ago.
(15) Differentiation of human DNA types –200,000 years ago.
(16) Emergence of ‘‘modern humans’’/earliest burial of the dead – 105,700 years ago.
(17) Rock art/proto writing – 35,800 years ago.
(18) Techniques for starting fire – 19,200years ago.
(19) Invention of agriculture – 11,000 years ago
(20) Discovery of the wheel/writing/archaic empires/large civilizations/Egypt/Mesopotamia – 4,907 years ago
(21) Democracy/city states/Greeks/Buddha[≈ Axial Age] – 2,437 years ago.
(22) Zero and decimals invented, Rome falls, Moslem conquest – 1,440 years ago.
(23) Renaissance (printing press)/discovery of New World/the scientific method – 539years ago
(24) Industrial revolution (steam engine)/political revolutions (French, USA) – 225years ago.
(25) Modern physics/radio/electricity/automobile/airplane – 100 years ago.(26) DNA structure described/transistor invented/nuclear energy/WWII/Cold War/Sputnik – 50 years ago.
(27) Internet/human genome sequenced – 5 years ago "
Panov series
"0. The origin of life – 4 · 109 years ago. The biosphere after its appearance was represented by nucleus less procaryotes and existed the first 2–2.5 billion years without any great shocks.
1. Neoproterozoic revolution (Oxygen crisis) – 1.5 ·109 years ago . Cyanobacteria had enriched the atmosphere by oxygen that was a strong poison for anaerobic procaryotes. Anaerobic procaryotes started to die out and anaerobic procaryote fauna was changed by an aerobic eucaryote and multicellular one.
2. Cambrian explosion (The beginning of Paleozoic era) –590–510 · 106 years ago. All the modern phyla of metazoa (including vertebrates) appeared during a few of tens of million years. During the Paleozoic era the terra firma was populated by life.
3. Reptiles revolution (The beginning of Mesozoic era) –235 · 106 years ago. Almost all paleozoic Amphibia died out. Reptiles became the leader of the evolution on the terra firma.
4. Mammalia revolution (The beginning of the Cenozoic era) – 66· 10 6 years ago . Dinosaurs died out. Mammalia animals became the leader of thee volution on the terra firma.
5. Hominoid revolution (The beginning of the Neogene period) – 25–20 · 106 years ago19. A big evolution explosion of Hominoidae (apes). There were 14genera of hominoidae between 22 and 17 millions years ago – much more than now. The flora and fauna became contemporary.
6. The beginning of Quaternary period (Anthropogene)– 4.4 · 106 years ago 20. The first primitive Homo genus (hominidae) separated from hominoidae.
7. Palaeolithic revolution – 2.0–1.6 · 106 years ago21. Homo habilis, the first stone implements.
8. The beginning of Chelles period – 0.7–0.6 · 10 6 yearsago2\. Fire, Homo erectus.
9. The beginning of Acheulean period – 0.4 · 10 6 years ago. Standardized symmetric stone implements.
10. The culture revolution of neanderthaler (Mustier culture) – 150–100 · 103 years ago. Homo sapiens neandertalensis. Fine stone implements, burial of dead men (a sign of primitive religions).
11. The Upper Palaeolithic revolution – 40 · 10 3 years ago. Homo sapiens sapiens became the leaderof cultural evolution. Development of advanced hunter instruments – spears, snares. Imitative art iswidespread.18 570 · 106 years ago according to Panov 2005b.19 24· 106 years ago according to Panov 2005b.20 4–5 · 106 years ago according to Panov 2005b.21 2–1.5 · 106 years ago according to Panov 2005b.22 0.7 • 106 years ago according to Panov 2005b.
12. Neolithic revolution – 12–9 · 10 3 years ago. Appropriative economy [foraging] had been replaced by productive economy [food production].
13. Urban revolution (the beginning of the Ancient world)– 4000–3000 B.C. Appearance of state formations, written language and the first legal documents.
14. Imperial antiquity, Iron age, the revolution of the Axial time – 800–500 B.C. 23. The appearance of a new type of state formations – empires, and a culture revolution. New kinds of thinkers such as Zaratushtra, Socrates, Buddha, and others.
15. The beginning of the Middle Ages – 400–630 CE. 24D is integration of Western Roman Empire, widespread Christianity and Islam, domination of feudal economy.
16. The beginning of the New Time [Modern Period],the first industrial revolution – 1450–1550 CE 25Appearing of manufacture, printing of books, the New time culture revolution etc.
17. The second industrial revolution (steam and electricity)– 1830–184026. Appearance of mechanized industry, the beginning of globalization in the information field (telegraph was invented in 1831), etc.18. Information revolution, the beginning of the post industrial epoch – 1950. The main part of population of industrial countries work in the field of information production and utilization or in the service field, not in the material production."
More information
- Foerster H. von, Mora P. M., Amiot L. W. 1960.Doomsday: Friday, 13 November, AD 2026 Science 132 (3436): 1291–1295
- Modis T. 2002. Forecasting the growth of complexity and change. Technological Forecasting and Social Change 69(4): 377–404. DOI: https://doi.org/10.1016/S0040-1625(01)00172-X
- Modis T. 2012. Why the Singularity Cannot Happen. In Eden A. H., J. H. Moor, and E. Steinhart. (Eds.). Singularity Hypothesis: A Scientific and Philosophical Assessment. Berlin: Springer. P. 311–346. DOI: https://doi.org/10.1007/978-3-642-32560-1_16
- Panov A. D. 2005b. Scaling law of the biological evolution and the hypothesis of the self-consistent Galaxy origin of life. Advances in Space Research36(2): 220–225. https://doi.org/10.1016/j.asr.2005.03.001
- Panov A. D. 2011. Post-singular Evolution and Post-singular Civilizations. Evolution 2: 212–231
- Panov A. D. 2017. Singularity of Evolution and Post-Singular Development. From Big Bang to Galactic Civilizations. A Big History Anthology . Volume III. The Ways that Big History Works: Cosmos, Life, Society and our Future / Ed. by B. Rodrigue, L. Grinin, A. Korotayev. Delhi: Primus Books. P. 370–402