Mathematical Science & Technologies

Appendices

Appendix 1. The Essential Nature of Arithmetic

The following are extracted verbatim from the outstanding essay of A.D. Aleksandrov, A General View of Mathematics, specifically section 5, pp.17-19, on the Essential Nature of Arithmetic in [Aleksandrov/Arithmetic1956].

1. How did the abstract concepts of arithmetic arise and what do they reflect in the actual world?
“The concepts [of arithmetic] arose by way of abstraction as a result of the analysis and generalization of an immense amount of practical experience. They arose gradually; first came numbers connected with concrete objects, then abstract numbers, and finally the concept of number, in general, of any possible number. Each of these concepts was made possible by a combination of practical experience and preceding abstract concepts. This, by the way, is one of the fundamental laws of formation of mathematical concepts: They are brought into being by a series of successive abstractions and generalizations, each resting on a combination of experience with preceding abstract concepts. The history of the concepts of arithmetic shows how mistaken is the idealistic view that they arose from “pure thought,” from “innate intuition”, from “contemplation of a priori forms,” or the like.” [Aleksandrov/Arithmetic1956]

2. Why are the conclusions of arithmetic so convincing and unalterable?
“We see that the conclusions of arithmetic have been worked out slowly and gradually; they reflect experience accumulated in the course of unimaginably many generations and have in this way fixed themselves firmly in the mind of humankind. They have also fixed themselves in language; in the names for the numbers, in their symbols, in the constant repetition of the same operations with numbers, in their constant application to daily life. It is in this way that they have gained clarity and certainty. … What is essential here is not only the fact that they can be repeated at will but their soundness and perspicuity, which they possess in common with the relations among things in the actual world. This is the reason why the results of arithmetic are so convincing: its conclusions flow logically from its basic concepts, and both of them, the methods of logic and the concepts of arithmetic, were worked out and firmly fixed in our consciousness by [five] thousand years of practical experience on the basis of objective uniformities in the world around us.” [Aleksandrov/Arithmetic1956]

3. Why has the abstract concept of number and arithmetic taken so long to arise?
“Every abstract concept, in particular the concept of number, is limited in its significance as a result of its very abstractness. In the first place, when applied to any concrete object it reflects only one aspect of the object and therefore gives only an incomplete picture of it. … It is impossible to apply arithmetic to concrete problems without first convincing ourselves that their application makes sense in the particular case. If we speak of addition, for example, and merely unite the objects in thought, then naturally no progress has been made with the objects themselves. But if we apply addition to the actual uniting of the objects, if we in fact put the objects together, for example by throwing them into a pile, in this case there there takes place not merely abstract addition but also an actual process, and in general it may be impossible to carry it out. For example, the object may break, wild animals if placed together may tear one another apart, materials put together may enter into a chemical reaction and so the sum e.g. of a liter of water and a liter of alcohol will not yield two liters of mixture but 1.9 as a result of partial solution of the liquids, and so on. To put it briefly, truth is concrete, and it is particular important to remember this fact with respect to mathematics exactly because of its abstractness.” [Aleksandrov/Arithmetic1956]

4. What forces led to the development of mathematics?
“For arithmetic, the answer is clear from history. The forces that led to the development of arithmetic were the practical needs of social life. People learned to count and to work out the concept of number. Practical life, by posing more difficult problems, necessitated symbols for numbers. These practical needs and the abstract thought arising from them exercise on each other a constant interaction. The abstract concepts provide in themselves a valuable tool for practical life and are constantly improved by their very application. Abstraction from all nonessentials uncovers the kernel of the matter and guarantees success in those cases where a decisive role is played by the properties and relations picked out and preserved by the abstraction. In the case of arithmetic, this is the quantitative relations. … This is just a particular case of a phenomenon known to everyone, namely the interaction of experience and abstract thought, of practice and theory.” [Aleksandrov/Arithmetic1956]

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Appendix 2: The Invention of Writing: An Advancement of Bookkeeping

1. When was writing invented?
Proto-writing first appeared at the end of the 4th millennium BCE (c.3200) in southern Mesopotamia (Uruk) and Khuzistan (Susa). This was first purely numerical recording of quantities that had previously been recorded using tokens with the commodity understood from context; then the recording of the commodity separate from the quantity using pictographs; and then by end of 4th millennium, c.3200 proto-cuneiform in Uruk where both quantity and commodity were recorded in cuneiform encoded pictographs, followed by proto-Elamite in Susa c.3000. This led to then the standardization of cuneiform pictographs, followed by the next innovation c. 2500 in Fara where we see the early attempts at encoding phonetics to writing to reduce the number of individual signs needed and the burden on agreeing their meeting through cultural convention, as well as the application to the new conqueror language of Akkadian. See [Damerow/1999w].

The earliest writing appears between 3500 and 3100 BCE depending on which of the proto-writing materials one is willing to admit. Regardless, there still between 500 and 1000 years before the first readable cuneiform dating to c.2500 BCE (the school texts of Fara). [Nissen/1986]

Adam Falkenstein (1936) published ATU1: The Archaic Texts of Uruk, which recorded the archaic signs occuring in the first 620 tablets found at Uruk in the first three seasons of excavations there. In the 1980s, Hans Nissen, a student of Falkenstein, launched the Berlin Project that aimed to publish all texts found since Falkenstein’s publication. The difference was that since Falkenstein there was a group of texts the so-called “Lexical Lists” which went from 0.5% of known texts in 1936 to 15% in 1986 (50 years later) and were word-for-word ancestors of the ‘schooltexts’ from Fara (Shurrupak) and which are almost fully comprehensible. This has brought almost 70% of the archaic signs to be identified. (The remaining 85% of archaic texts are so-called economic or administrative texts, i.e. these are receipts, lists of expenses, of animals, of all kinds of goods, of raw materials.) [Nissen/1986]

Why writing? “It was the need to control an expanding economic unit (the Eanna temple) that prompted the introduction of controlling devices better suited for managing large quantities of information than the human memory.” [Nissen/1986, p.324] Writing was an advancement from other innovations in managing complex economy, namely cylinder seals, tokens, clay envelopes (bullae), numerical tablets, ideographic tags, and finally numero-ideographic tablets, and ultimately their standardization into cuneiform. [cf. Hoyrup/1991] “Writing appeared as the final solution to a number of economic problems which had probably been accumulating for a long time.” [Nissen/1986, p.326]

The evolution of writing over 1,100 years, from proto-cuneiform in Late Uruk period (3,100 BCE) to syllabic cuneiform during the Ur III period (2000 BCE). It took over 1,000 years to go from the first signs to the Ur III signs. (40 generations of 25 years each).

LU2 A Lexical List of Standard Professions, from 3200 BCE (Uruk IV) through to the Fara schooltexts.
Source: Englund/1998, p.104, Fig 32.
Transliteration: ORACC
Tablet attestation: MS 2429 (from Umma, c.3200-3000 Uruk III period)

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Appendix 3: Birth of the Universe up to the Early Period of Life on Earth

The difference between science and mythology Every culture has its own creation story that provides the whys and hows behind the way things came to be. Science, too, is a creation story, with the difference being that its whys and hows are connected in a chain of evidence that ties every claim back to principles that are in turn backed up either by experiment or are the result of observation with astronomical instruments or mathematical calculations based on physical laws, thermodynamics, and cosmological equations. [NAS, 1999], a 48pp book from the U.S. National Academy of Sciences, is an excellent comprehensive presentation, useful for its comprehensive approach, although it is by now dated.

The current scientific view of the story of the universe is based upon full-field (all-sky) astrophysical observations made between 2009-2013 by instruments aboard the Planck spacecraft (European Space Agency) positioned almost 1 million miles from the earth¹ and summarized in Chronology of the Universe [Wikipedia, 2023]

The Current Scientific View

What we believe happened depends on which of the two main cosmological theories we go with: lamba-cdm or mondian cosmology.

Theory 1 (lambda-cdm): if we assume the existence of a massive amount of, as yet undetected, dark energy (Lambda) and cold dark matter (CDM), then the Lambda-CDM model predicts, based on an analysis of the anomalies present in the cosmic background radiation at microwave and infrared frequencies, that the Universe formed in a “big bang” event 13.8 billion years ago (bya).² Now the Big Bang event itself was not an explosion (contrary to popular portrayal) but rather the abrupt appearance of extraordinarily rapidly expanding (inflating) universe in which spacetime itself (though not the matter in it) was stretching many times faster than the speed of light (10 light years in a tiny fraction of a second)³, and at extremely high temperatures (10^15 degrees Kelvin).⁴ Another tiny fraction of a second later, and the universe, now with its particles dispersed quite uniformly across the vastly inflated universe, entered hypercooling. during which time, the fundamental forces began acting and sub-atomic particles formed as described by the Standard Model of particle physics.

Over the next 20 minutes, sub-atomic particles combined to form photons (light energy) and matter, mostly hydrogen and helium, creating a super-hot (10 billion degreees Celsius, or 10^9 Kelvin K) glowing fog universe. This ambient energy was captured over the next 380,000 years in the formation of molecular bonds. The earliest molecules were hydrogen gas (H2) and, after much searching based on theory, also helium hydride has now also been identified as occurring naturally in space, confirming its place as one of the earliest molecules in the chemical evolution of the universe.⁵ The formation of molecular bonds over this period time enabled the universe to cool down a million-fold to a less hot 3000 K (c.2700*C), and become transparent. (Reminder, the Kelvin temperature scale is the same as Celcius except it is offset by 273 degrees, so that 0 Kelvin is absolute zero = -273C.)

It would take a further 10 million years (looking back in time this is still more then 13 billion years ago) before the early universe would cool a further 10-fold to reach the relatively pleasant 300K/27*C without any radiation heating from stars which had not formed yet. While these temperatures are suitable for liquids and therefore in principle for life as we know it (the so-called habitable era of the universe), in fact the dark, starless universe was not chemically rich enough yet to support either. Until the formation of stars there would have been very few elements heavier than lithium (3rd in the periodic table). Liquids and life (as we know them) require heavier elements which can only be forged through nuclear fusion, thus, in the nuclear furnaces of stellar nucleosynthesis.

This is one theory.

Theory 2: The other prominent alternative is a modified theory of gravity (MOND/MOG) that diverges from Newton/Einstein dynamics at very low accelerations, i.e. on the edges of galaxies or in the interaction between binary star systems. The gravitational modification due to Milgromian dynamics or Modified Newtonian Dynamics (MOND) is that for very low accelerations, e.g. on the scale of galaxies, the Milgromian law of gravity is inversely linear with distance instead of the inverse square law that holds within the solar systems or on earth. Considered another way, we might say that force is equal to the mass times the square of the acceleration as in the usual case. The complication is that, until 2021, MOND/MOG theories have not been able to fully explain the cosmic background radiation, nor the perceived homogeneity in distribution of matter throughout the universe, in every direction we look at (the isotropic property of space). As of 2021, MOND theories have been built that explain observations in the cosmic background radiation, providing the possibility of a MONDian cosmology.

Star formation⁶ began after 100 million years, ending the so-called “cosmic dark ages”. Nuclear fusion reactions in the stars began after 300 million years forming the heavier elements of the periodic table, carbon (6), nitrogen (7), oxgen (8), sulfer (16), which are needed for carbon based life and for liquids. The first galaxies of stars appeared at 400 million years.

Could life have existed in such a universe once stars had formed? Liquids (organic, inorganic, and water)⁷, contain elements made in stellar reactions which would have been available after star formation. Recent research (Loeb/2021) aims to shed light on whether liquids other than water (ethanol, propane, methanol, ammonia, hydrogen sulfide) could chemically sustain life to attempt an upper bound on the date when life could have started in the universe.

Our Milky Way galaxy began to form after 700 million years, and would take the next 4.5 billion years to evolve until it acquired its spiral arms through galaxy collision (8.7 billion years ago bya). It would take a further 4 billion years for our solar system to form (4.6 billion years ago).

Before we come to the formation and development of our solar system, let’s take a brief moment to look at the Milky Way (our galaxy): the edge of the Milky Way is about 1 million light years away from us. We are about 27k light years away from the center of our galaxy (i.e. we are off-center). At the center of the galaxy is a giant black hole Sagittarius A*, around which objects are orbiting at an astonishing 30% of the speed of light.

Closer to us is the nearest start system Alpha Centauri, of which Proxima Centauri is the nearest star to us, invisible to the naked eye, about 4.2 light years away, and would take 73,000 human years to get to with current thruster technology.

Our solar system, including the Sun, the planets, and the Earth-Moon system, formed during a tumultuous 100 million year period between 4.6 and 4.5 billion years ago (bya).

Taking a closer look at our solar system, with current thruster technology, it takes 9 months to journey to Mars and 1 year to Jupiter. Using our fastest spacecraft New Horizons, which can travel 30k miles/hr, or 1 million miles per day, it would take about 10 years to reach Pluto which is 3 billion miles away (a year of acceleration to top speed, a year of deceleration, and 8 yrs travelling at top speed). Compare this with the speed of light: 5 hours Sun to Pluto, 8 minutes Sun to Earth. Increasing our direct experience of the solar system requires further progress in robotic or manned space exploration.

Open questions remain: Is our Solar System in a Magnetic Tunnel? Telescopic observations match an analogy with camera observations inside a tunnel< It is believed that the early earth was molten and then cooled, forming a crust and holding surface liquid water creating oceans. During this time it is also believed that gravitational instabilities from the heavier planets may have pulled large numbers of asteroids from the solar system’s outer belt into the inner solar system where they collided with the Earth, moon, and many of the planets, leaving extensive cratering on planetary bodies and moons that did not have a thick enough atmosphere to protect themselves (Late Heavy Bombardment period) (e.g. our own moon).

Where did the water come from for the earth? Recent research finds that hydrogen-rich solar wind and oxygen-rich dust in the solar system can combine with irradiation from the sun to create flowing water that could have streamed onto early barren earth. What we believe today: Earth got its water from asteroids.⁸

How did the moon form?

Faint Sun paradox for early life. If the early Sun was smaller and dimmer, then the early earth would have been much colder. Were conditions really suitable for life on the early earth? greenhouse gases may have made the early earth habitable even when the early sun was too faint to warm it (faint sun paradox)

The first evidence of life on Earth are single-celled organisms (bacteria) which appear in the fossil record 3.8-3.7 bya (Early Archaen Era). Life evolved slowly over the next 3 billion years, along with major upheavals in the earth’s structure, atmosphere, climate, and surface geology. After the first billion years (i.e. 2.7 bya), simple multi-celled organisms appeared (algae, amoebas, mold, fungus). It took another 700 million years (to 2bya), for genetic material to begin being exchanged amongst prokaryotes. And from this point, another 900 million years (to 1.1bya) for the first sexually reproducing multi-cellular organisms to appear. It would take another 600 million years (to 538 mya), before the beginning of a radical acceleration of life’s diversity, the so-called Cambrian Explosion. (see Appendix 4 below).

As astronomical observation capabilities improve and we find more examples of earth like planets (e.g. TOI 700 e) and think that perhaps we might move to other planets, it’s worth remembering why we should not assume that there’s a planet B waiting for us: it has taken 3.2 billion years of joint evolution of earth and life, each impacting the other.

Where did the phosphorus come from in the early Earth that forms an essential element in DNA/RNA? Research suggests the biological phosphorus was releaesed by lightning strikes on a type of surface rock, a quintillion strikes during the chaotic period of the Earth’s development 4 billion years ago, that was followed by surge of life.

Evolution of higher complexity during the earliest stages of life on earth appears to have been driven by symbiosis. The earliest cilliates apparently absorbed instead of eating a nitrogen fixing bacterium, and developed an organism that can survive without oxygen by metabolising nitrogen. (Article here and here).

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Appendix 4: The Acceleration of Living Diversity (Cambrian Explosion) to the Dawn of Humanity

From 538mya, the diversity of life suddenly accelerates rapidly and a large number of species emerge during the so-called Cambrian explosion: fish, plants, reptiles. What caused this acceleration in diversity? We don’t know for sure. A new paper (2018) presents a provocative thesis – that the Cambrian explosion may have been triggered by the insertion of DNA brought in by a meteor or comet into the earthly mix. Whatever the cause, the next 200 million years saw life flourish in spectacular and unparalleled diversity.

This flourishing of life in its diversity came to an end 252mya with the most severe mass extinction to that point (the Late Permian extinction event) as a result of which 81% of marine life and 70% of land vertebrate life disappeared. The causes are thought to be massive volcanic explosions releasing 12x more carbon dioxide into the atmosphere than has occurred during the past 250 years due to the industrial revolution, driving acidification of the oceans, destruction of the ozone layer, increase in solar irradiation, and a global temperature rise of 8*C. It would take 20 million years before land life picked up again, stimulated by another major jump-start event which occurred 232 mya during the Carnian period. The greenhouse conditions on earth led to to 1-2 million years of heavier rainfall on what had been bocome an arid, dry Earth, accelerating life once again and boosting diversity.

This was the Cenozoic period (252-66mya) during which occurred the rise of large life on land and the dominance of the dinosaurs from 200 mya (the Jurassic period), including recently discovered super-massive dinosaurs.

The dominance of the dinosaurs lasted until the meteorite strike 66mya throwing up particulate matter in the atmosphere reducing sunlight reaching the surface and plunging the earth into a colder, darker phase. This triggered another mass extinction event that extinguished the dinosaurs, cooled the tropical earth. While mammals co-existed with dinosaurs at the end of the Jurassic period, they were small and filled specialized ecological niches. But mammals survived the meteorite strike that killed off the dinosaurs and thrived in the new, cooler, modern habitat, eventually becoming dominant. Primitive primates also existed from 66mya, migrating and evolving to the lineage in Africa c.13mya from which hominids would eventually emerge.

This was also the time of remarkable changes in the surface topography due to active plate tectonics (watch this simulation at 0.25x speed showing plate tectonic movement over the past 1 billion years).
And there are more surprises: massive ocean in the subducting zone beneath Earth’s crust. The massive fish shoals: lantern fish and a huge unharvested biomass

When we think about the remarkable diversity of life currently on earth (est. 1 trillion species overall, est. 8.7 million eukaryote species, of which only 1.2 million are known, mostly insects), and the even larger biodiversity lost (est. 5 billion extinct species), the question arises: if we could seed life in the universe using comets (panspermia), should we? Was the Cambrian explosion the result of such a seeding event?

Mass extinctions in the past have a lot to teach us about parallels to the present.

The Rise of Primates and the Dawn of Humanity

In the aftermath of the dinosaurs about 66mya, mammals flourished. There is evidence that primitive primates already existed at 66mya. The African primates from which our lineage descends appeared (13 mya).

Unknown common ancestor of chimps and humans

A look at the evolution of primates and hominids: grasping hand vs. dextrous hand

Wherever we look, we see affirmed the principle “Natura non facit saltus”, i.e. “Nature makes no leaps”. Everywhere there is gradation, diffusion, similarity with minor differences, advancement happening gradually through time. Wherever some jump, looking closer, the jump is found rather to have passed through more gradual stages that were not apparent in first appraisal.

The last known bifurcation between primates and hominin species was c.8mya when the evolutionary pathway of chipmanzees and humans diverged. At this time, the climate was warm, primates and hominins lived in the treelands on the edge of the growing savannah, in social structures.

Recent work has suggested that the simian hand with relatively shorter thumb length and longer fingers, evolved away from the hand shape of the last common ancestor of humans and primates which had relatively long thumb lengths. This simian “grasping hand” would have been i.e. better adapted for swinging through trees, for which a long thumb would have gotten in the way.

The dextrous hand by comparison with its relatively longer thumb, closer in size to the fingers, allows more dextrous hand work, at the same time making it less easy to swing in the trees, driving hominins to spend increasing amounts of time on the ground.

For a comparative understanding of the complexity of the evolved dextrous hand:

Anthropomorphic robotic hands approach human levels of dexterity, invented and engineered by a South Korean university. Another: Robot Hand moves closer to human abilities. Developed by a team of researchers in South Korea. Paper (Nature). Featured on Hackaday

By 6-7 mya, the earliest bipedal hominins have appeared in Africa (Sahelanthropus, Orrorin, Ardipithecus). Bipedalism has the advantage of hands free to hold tools or possessions, and the ability to see further. It is believed that bipedalism arose first using tree branches to guide bipedal ability and then free-standing on the ground. By 4mya, australopithecus was walking comfortably on 2 legs.

Tool use is another area where there significant gradation and diffusion and fewer apparent leaps the closer that we observe non-human tool use. Looking only at primates, we find that they use and make tools from natural resources: twigs and sticks for “termite fishing”, large leaves for wrapping or carrying, sticks for striking objects out of reach, even sharpening them for use as spears for stabbing and killing small mammals for food hiding in tree holes (2007), and unworked stones for cracking open nuts (hammer and anvil mode), hammering or throwing. Interestingly, we even see gender difference in chipmanzee use of inanimate objects, with female chimps using sticks or logs as dolls (2010 study). With primates able to develop and use tools despite their more awkward grasping hand (long fingered, short thumbed), it reasonable early hominins did similarly, with more capability from their more dextrous hand design (shorter fingered, longer thumbed).

The complication in all of this is concluding who developed and used the tools archaeologically. Unworked stones, for example, can be used for pounding, crushing, grinding, or to throw as a weapons, and yet stones used in this way are indistinguishable from naturally stone. Thus, the point where stone begins to be worked undeniably into tools with edges, becomes the earliest date from which we can say there is artifactual evidence for tool use, beginning 3.3 million years ago and marking the start of the Old Stone (Paeliolithic) Age. (see Appendix 5 below).

Hominin to Human (Part 2): Last Common Ancestor (LCA) concept, and Family Tree of Hominins

Hominin to Human (Part 1): Skeletal and Cranial comparisons

From 66mya to the Present. Life in the Cenozoic era – Tertiary and Quaternary Period, from the Paleocene to the Holocene Epochs.

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Appendix 5: Paleolithic (Stone Age) Culture from Lomwecki (3.3mya) to Shanidar (50kya)

The Paleolithic covers the time from the first stone tool wielding hominids (3.3 mya, Lomekwi3 site, W. Turkana, Kenya) until the end of the four ice ages (2.6mya-12kya). Primary subsistence mode was hunter-gatherer. A recent site which included Neanderthals and Homo Sapiens is Shanidar Cave (65,000 BCE), a Middle Paleolithic (Mousterian culture) site in the Zagros mountains of Iraq/Iran/Turkey border. The last paleolithich stage is Upper Paleolithic (from 50,000 BCE)

By 4 mya, we have comfortably bipedal hominins (Austraopithecine) in East Africa (Tanzania, Kenya, and Ethiopia). The appearance of worked stone tools in the archaeological record marks the beginning of the so-called stone age (paleolithic period). This occurs by 3.3mya, when we have the earliest archaelogical evidence of stone tools arising from a worked process (i.e. non-natural) (Lomekwi3 site in West Turkana, Kenya)[Harmand, 2015, Nature], pre-dating both the earliest Homo species and Oldowan tool culture by 700k years.

These earliest stone tools with sharp edges were created through blows delivered stone against stone and found at the Lomekwi site c. 3.3mya. However, we cannot conclude from this alone that they were made by hominins: [Proffitt, 2023] provides a plausible alternate hypothesis. Proffitt shows that wild macaques use stones to crack nuts (hammer and anvil mode) the result of which creates accidental fractures that are indistinguishable from Oldowan tools attributed to hominin production. Whether the tools from Lokemwi are the result of primate tool use or hominin tool use is to some extent immaterial. The point is that the use of stones for tools was now clearly deliberate. One possibility, the cracking of nuts using stones could have led to the accidental discovery of sharp edges followed by the intentional repetition of the behaviour now specifically for the purpose of obtaining the blades.

If we set aside simply struck stone tools, then the next evidence of an increase in sophistication in stone tool technology is 1 million years later, c.2.3mya, from the same W. Turkana area at the Lokalalei site [Delagnes,Roche, 2005]. These are bladed stone tools of Acheulean type, i.e. bifacial edges that show reworking to improve the blade (mode 2 tools) through a process of “knapping” or chipping away of small flakes.

Stone tool cultures – the shared knowledge of tool manufacture and use

Fundamental to the sustained development of stone tools is the notion of culture, or the transmission of knowledge (in this case lithic technology) between individuals. Here too animals display capability for the social transmission of behaviour, or culture.

Taking a look at stone tool sophistication, we can delineate five stone tool cultures stretching from simply struck stone tools from Lomekwi (c3.3mya) through to polished stone tools fixed in wooden hafts (14kya), (see Fossil & Tool Gallery). These stone tool cultures are classified according to the complexity required for their manufacture. “Simply struck tools are Oldowan (mode 1, unifacial). Retouched, or reworked tools are Acheulean (mode 2, bifacial). Retouching is a second working of the artifact. The manufacturer first creates an Oldowan tool. Then he reworks or retouches the edges by removing very small chips so as to straighten and sharpen the edge (this is called knapping the stone). Typically but not necessarily the reworking is accomplished by pressure flaking.” (Wiki, Oldowan). Stone knapping is not easy, nor was it likely to have been injury free. [Gala, 2023]

1. Lomekwian Tool Culture 3.3mya – these tools were flaked off unusually large flint cores, which were rotated for better edge creation. 3.3mya is 700k years before the start of the Quarternary Period of the 4 ice ages (from 2.6mya) (Wiki summary), produced before Homo species, likely by Kenyanthropus. Some flakes were worked on both sides (bifacial), demonstrating intentionality.
2. Oldowan tool culture (mode 1) , 2.6 mya to 1.7 mya. It is preceded by Lomwekian at 3.3mya (see above).
3. Acheulean tool culture (mode 2), 1.7mya to 160kya, but with the earliest bifacially worked stones coming from 2.3mya from the Lokalalei site in W. Turkana [Delagnes, Roche, 2005].
4. Mousterian tool culture (mode 3), 300kya to 40kya, (advanced bifacial), type site Shanidar Cave containing remains from both Neanderthal (c50kya) and Homo Sapiens.
5. Aurignacian tool culture (mode 4), 40kya to 20kya
6. Mesolithic culture (mode 5) also called Epipaleolithic – mixed material microliths, fine crafted polished stone blades hafted into wooden implements, from 14kya to 4kya (transition to copper, tin, and bronze)

Telling the story:

1. 4.2mya – Australopithecus species of man emerges. Long fingered and short thumbed. Easier to swing through trees.
2. The grasping hand – about 3mya there were changes in hand structure, shorter fingers and longer thumb, giving rise to the ability to form and use tools.
3. opportunistic wooden tools such as sticks to poke for termites, to hit hanging things out of reach, as weapons to hit other things
4. unworked stones e.g. for pounding, crushing, grinding, or to throw as weapons;
5. 3.3mya – 2.6mya – Lomekwi, Kenya – stone tool culture, still Australopithecus, pre-dating Homo species by 500ky – earliest known worked (or knapped) stones (mostly flint) into flakes for cutting, scraping

   From 2.6mya we have the start of the 4 ice ages marked by glacial advances and retreats.

   From 2.5 mya to 1.3mya we have Homo habilis (`handy man’), with more sophisticated stone tools near Oldowan in Tanzania.

6. Oldowan stone tool industry (mode 1), preparing cores which were struck and rotated as a result of which a variety of bladed tools could be made as desired e.g. cutting, chopping, scraping, pounding (2.6mya – 1.7mya, Oldowan, Ethiopia, homo habilis); – pebble tool stone industry

   Sophisticated stone tool creation industry. Earliest stone tools occurring in East Africa 2.5-1.5mya, late in the period of australopithecus and more during the stage of homo habilis (origin 2.3mya).

   “Why did early humans use flint to make tools? Flint was the most popular stone used to create tools because it was one of the sharpest instruments available and was easily chiseled or flaked into sharp points which were then used as tools. Flint is also very durable, making it one of the best resources for tools during the Stone Age” Flint Reference
   It is possible that, attempting to work the flint, that early man discovers the sparks that they can use to create fire on demand.

7. 2.3mya Homo species of man emerges with the first being Homo Habilis (“handy man”)
8. 2.0mya throwing shoulder evolved to allow fast, hard, accurate throws of a heavy spear to distances of 60-100m (homo erectus)

   At about the same time, homo species may have begun running and hunting across the savannah, which would have driven the evolutionary advantage of less body hair (more ability to sweat and dissipate heat).

   Stone knapping and the controlled use of fire

   From 1.9 mya to 400k ya we have Homo erectus.

   Note that, during this period from 1.9mya to 1mya, for almost 900,000 years, there were at least 3 species of humans overlapping and co-existing in the same range in eastern and north-eastern Africa (australopithecus, homo habilis, and homo erectus). Australopithecine disappeared from the fossil record about 1mya, replaced by Homo genera of the Hominidae family.

9. Acheulean (mode 2) stone tools, bifacially worked, thinner, sharper, more effective, creating hand axes and larger cutting tools (1.8 mya to 130kya, homo erectus).
10. Controlled use of fire suspected from c. 1.8mya (homo habilis) but currently controlled fire use only found dating back to 1mya, (Wonderwerk cave complex, South Africa, homo erectus)
11. 1.5 mya – earliest use of bone tools for digging (South Africa). Later bone tools were made by splitting apart or splintering bones with stones. Bone as a tool material.

    Throughout this period, waves of human ancestral migration leave Africa and populate the earth. Homo erectus remains of 1mya are found in the Jordan valley (Ubaidya site).

    By 700kya, Homo erectus man has learned to control fire, potentially accelerating the evolution of man to homo sapiens as a more protein rich diet could be consumed through cooking, leading to brain expansion. This theory is contested by the discovery of small brained human ancestors who were every bit as smart as the larger brained successors. (citation)

12. Why are human brains so large? Research with mini-brain organelles has shown that in humans, genetic encoding delays the release of a chemical that causes cells to separate, allowing brain cells to cluster for longer in humans than in other primates, resulting in larger brains with more neurons clustered to allow for more advanced thinking/processing.
13. By this point we have indisputed evidence that a distinct species of hominin, Homo species (habilis, erectus) has emerged distinct from the previous australopithecus species, though there is no abrupt transition and the evidence is sparse.
    

    Human Evolution Timeline, from Primates 55mya to Pre-Modern Humans 400kya

14. Did something (climate?) trigger the diverse modern human subspecies 500kya (neanderthals) and 300kya (homo sapiens).
15. Wood spears to kill large things have been found from 400kya (yew-hewn Clacton spear). These have been shown to have been able to be thrown accurately 60-100m.
16. Mousterian stone tool culture (400kya to 30kya, homo erectus/homo sapiens), including the Levallois technique for creating large, sharp knife-like stone tools using a prepared core in a tortoise-shell shape (mode 3). Also the earliest use of bone consistently to make tools 400kya, including a leather working bone lissoir. Leather working otherwise was with stone scrapers, also dated back to 400kya.

Anatomically Modern Humans

So what makes humans unique?

It appears to be a series of evolutionary adaptations that allowed humans to exploit and perfect a particular ecological niche. These include:

1. a dextrous hand,
2. the ability to throw hard, fast, and accurately (throwing is one of the few physical skills at which Homo Sapiens (and Homo Erectus) excelled
3. the controlled use of fire
4. loss of body hair (from among mammals),
5. a voicebox capable of supporting many vocalizations,
6. abstract symbolic association a word for a concept, religion, considerations of an afterlife
7. the ability to write and read.

With a dextrous hand, we have been able to fashion useful, precise tools. With the ability to throw, we have been able to hunt with spear thrown 100m with hard and with accuracy, enabling the capture of large and nutritious food, fueling growth of body and brain. The loss of body hair enabled long distance running without overheating, also useful in the hunt. The voicebox allowed a pallete of sounds from which with symbolic association could create rudimentary and then more complex language. Writing and reading allowed the recording of knowledge, its refinement, and dissemination beyond the scholar both in location and time.

Interestingly, it is NOT what we normally think of. When we consider what makes us human as distinct from animals, recent research has shown that each of the below abilities which we formerly thought were uniquely human, the capabilities have been observed in animals [Hauser]. These include the abiity to:

1. think and reason,
2. make and use tools, (including, surprisingly, the octopus)
3. communicate through body language, gesture, or vocally
4. feel emotions such as love, fear, jealousy, sadness,
5. bury their dead and grieve: elephants, dolphins, giraffes, chimpanzees, dogs, crows
6. have a sense of self, i.e. remember the past and plan for the future
7. create and transmit culture, e.g. during rearing of young
8. building purposefully (beavers & dams, spider & webs, birds & nests),
9. distinguish number (count), at least in an analog fashion that is accurate for small integers and semi-accurate as integers become larger
10. associate a stimulus (icon) with a physical experience (index) e.g. bell ringing with food appearance,
11. appreciate, display, and create art. In art, gorillas show an aesthetic sense, e.g. a gorilla might show its mother each other beautiful things, turning its face as if to say, no, but look at this, isn’t it beautiful?)

Can animals think, reason, learn, communicate, feel, grieve, love? All of the above. The gorilla Koko could use 1000 words in sign language, and could understand 2000 words of spoken English. Why couldn’t she speak? Gorillas have physiological limitations in their vocal cords and tongue muscles that prevent the production of sounds that humans can make for controlled speech. But that doesn’t limit their faculties for thought and a full emotional range.

The Development of Anatomically Modern Humans

Human Evolution Timeline, from Neanderthals 300kya to the emergence of writing 5kya (c.3000 BCE)

1. The (Earliest Homo Sapiens from 300kya, Morocco)
2. Aurignacian stone tool culture producing stone cutting blades shaped to be attached to a handle (80kya-23kya, Europe, homo sapiens). In materials overall, homo sapiens added bone to stone as a worked material. From 35-40kya, we have the earliest known human figurine (Venus statue), animal-human figurine (Lion-man), musical instrument (5-hole flute from a vulture bone), and realistic cave art (Chauvet cave). Including Cro-Magnon man in Europe, cave art, statuettes, and creation of artistic and ornamental objects, with high degree of artistry/craftsmanship
3. The bow and arrow is dated to 72-60kya, based on discovered and dated arrow tips
4. Magdalenian tool culture, (50kya-11kya), producing microliths, small sharp geometrically shaped instruments such as triangles or crescents which if placed on the end of a projectile or attached to a blade of wood or bone could form an effective weapon or tool.
5. A new find in Germany has uncovered what appears to be an instrument used to construct twisted plant fibre ropes: a mammoth tusk from 40,000 years ago, drilled with 4 holes, that were then used to make the weave. Article

   Stone-Age humans were mostly meat eaters, until they ran out of big game. This is another take on what led to human settlement. There is another reason expressed that the discovery of beer/alcohol led to the desire to settle down to cultivate this mind-altering drink.

   Last Glacial Maximum (LGM): 23,000-21,000 BCE – when glaciers maximally covered the earth’s surface, coldest temperature, lowest sea level. This means, it was about 6*C colder than today, sea level 125m lower than today, dryer, with dust levels 20-25x vs. the present. Europe was covered in ice from Cardiff to Denmark to mid-Germany/Poland, below this to Hungary was permafrost.

Artists conception of communal living in Shanidar cave (ca. 50,000 BCE)

The history & learning of craft:

1. knapping stone hand-axes and polished face hand-axes – to chop a piece of wood
2. knapping stone to make a knife – carving a piece of wood
3. drawing using charcoal and pigments made from berries
4. leather working using bone lissoir and fats to make it waterproof
5. barbequeing meats
6. skinning an animal
7. using sinews as thread
8. a bone awl to make hole
9. reeds and weaving to make baskets and mats
10. striking a fire with flint
11. building and tending a fire
12. building a shelter – lean to and pelts, or reed matts
13. building a shelter – with a roof
14. mud bricks, or mud grass wattle shelters
15. clay for pottery or sculpting
16. grinding wheat, barley, or cereal for flour or porridge
17. baking
18. hunting, tracking
19. making and throwing spears
20. making a bow and arrow
21. throwing stick
22. whirling slingshot
23. pull slingshot

The story so far know is: Australopithecus emerged c. 6-7mya, as first bipedal ape-like hominin. It took a long time for another change, 2.3mya with homo habilis, still ape-like. Then 1.8mya we have the earliest homo erectus, a human like fully bipedal hominin with smaller teeth, a body like ours, and an enlarged brain. The tipping point for this change may have been the controlled use of fire for on-ground night-time protection, warmth, and cooking (requiring smaller teeth/smaller gut). From here there branch off several homo species including neanderthals (origin 800-400kya). The final stage was the emergence of homo sapiens, our own species, discovered about 300kya in Morocco, or 200kya in Ethiopia.
Sources: evidence for 1MYA fire control at Wonderwerk cave complex in South Africa. / Homo Sapiens found as early as 300 kya in Morocco /

With the development of fire, and the ability to hunt cooperatively, and access to higher calorie intake, man’s brains became larger. The hypothesis is that tool use and the desire to carry ones tools, meant more and more walking on two legs, and less and less 4-legged walking or traveling through trees.

Three more species of humans fill out the story:

By 315kya, Homo sapiens had emerged based on fossil discoveries at site in Morocco and by 230kya at the Omo 1 site in the Ethiopian portion of the East African Rift Valley.

Homo sapiens neanderthalis appear about 130kya, and Homo sapiens sapiens (anatomically modern humans) appear about 100kya.

From 100kya onward, most of the Earth has been populated by hominid ancestors.

The last glacial period began 110kya and lasted to 12,000 BCE (14kya).

The Influence of Ancient Climate on Human Evolution

Correlation of major climate fluctuation with emergence of human species

Climate is the result of interactions between surface topography, ocean, atmosphere, and geological processes. It is both influenced by and itself greatly influences terrestrial life. In particular, climate and ecosystem changes are believed to have driven systematic migrations and explain (1) hominin ape ancestors origins in Western Europe migrating through Eastern Europe, Mediterranean, and thence to Africa to African apes and to early man in the savannas of Africa; (2) Homo erectus moving out of Africa into Europe, then leaving Europe for Northern Africa during a hundred thousand year cold spell, and re-entering Europe again as Homo Sapiens; (3) evolution of human species has been punctuated by major climate variation.

1. Tool-making Humans have existed across three major climatic epochs: originating at least 3.3mya (Lomekwi site) toward the end of the Pliocene (2.6mya), diversifying into multiple hominin species during the Pleistocene (starting 2.6mya) with the establishment of the dominant species homo sapiens c.100kya and the last of the Neanderthals c.30kya at the last glacial maximum (LGM) 27-20kya, followed by a final triple oscillation over 10k years ending at 11.7kya, c.9700 bce), and the current period of the Holocene (starting 9700 bce)
2. The Quaternary period (starting with the Pleistocene for all but the last 10ky) begins 2.6mya, roughly coinciding with the emergence of Homo erectus. It is a period of major climatic oscillations, with the general trend being cooler and dryer climate, punctuated by rapid drops in temperature leading to glacial formation and glacial advance of much of the temperate northern hemisphere (stadials) interspersed by temperature rises (inter-stadials). (It is called Quaternary because it follows the Tertiary period.) The Quaternary period is part of the last of the 6 major ice ages that the earth has been through from its formation 4b years ago. The first ice age was c2.9bya. The last, the Cenozoic ice age, began 34mya, and the Quaternary period is part of this last ice age. The holocene epoch (which we are now in since 10k BCE/12kya) could be considered an interglacial period that is still part of the Cenozoic/Quaternary ice ages.
3. The key point about these temperature changes is that they seem to have taken place rapidly, over the course of 1-5 decades, i.e. within the life-time of a human.
4. This would have exerted maximum pressure on humans for adaptation and survival, driving migration, search for different sources of food and freshwater, different sources of nutrition, chanaged pre-existing animal behaviours and migration paths, and impact the effectiveness of some skills while demanding improvement/advance in others to produce clothing, shoes, shelter, fishing, boating, etc.
5. Last Glacial Period – period of major glaciations from 115kya to 12kya.
6. The Last Glacial Maximum (LGM) occurs from 27kya to 20kya, i.e. ending c.18k bce. At this point, average global temparatures were 9*C, six degrees colder than current average global temperature, with sea levels at their local minimum 125m lower than current levels, and rainfall reduced by up to 90% (as water was locked away in glaciers). After this point, while the general trend is toward a warming climate, glacial melting, and rise in sea levels, there are still dramatic temperature oscillations occuring that drop into full glacial conditions for hundreds up to more than a thousand years.
7. The Dryas cold periods over the last 4k years of the ice age after the LGM. Oldest Dryas (lasted 300 years, from 13,000 to 12,700 BCE), Older Dryas (lasted 400 years, from 12,000 to 11,600 BCE), Younger Dryas (lasted 1200 years, from 10,900 to 9,700 BCE)

Paleolithic migrations

Hominid Migration out of Africa, 1.7mya to 1.4mya
Source: AtlasOfTheHumanJourney.com

Hominin Migration, 500kya to 125kya, source: AtlasOfTheHumanJourney.com

Reflections on climate health of today’s earth:
1) mass deaths of sea birds at sea:
2) refreezing the Earth’s poles. A few billionaires could do this:
3) lantern fish and a huge unharvested biomass

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Appendix 6: Culture in the Near East: From Mesolithic (during the end of the last ice age, c 18kya) to the Neolithic (rise of sedentism)

By about 50kya, a wave of anatomically modern humans (homo sapiens) left Africa and moved through the Fertile Crescent (Map of Pre-historic sites)

In this early period (48kya-35kya), we have both Neanderthal and Homo Sapiens occupying the same region, with the Neanderthal skeletons of Shanidar Cave in the Zagros mountains providing possibly the earliest evidence of human assault on Neanderthals. The Skeletons of Shanidar Cave, in the Zagros mountains of Kurdistan in northern Iraq, are Neanderthals from 65kya to 35kya. 10 nearly complete Neanderthal skeletons provide a remarkable picture. Neaderthals cared for their wounded and buried their loved ones in graves. There is evidence of murder of `Shanidar Three’ by a low-mass, low-kinetic energy projectile weapon, either by fellow Neaderthals, or by projectile-carrying homo sapiens who had entered the region. In contrast with the killing projectile, Neanderthals used heavy huntings spears thrust with great force at close range into their prey (large mammals). Humans had mastered lighter projectile spears, throwing these deftly and with some accuracy from further away. (Article 1, Wikipedia: Shanidar Cave, Article 2, Article 3). Shanidar, one of the few continuously occupied caves from 50kya to the present. [Solecki, 1979]

1. 21,000 BCE – 12,500 – Kebaran culture, microlithic stone tools, use of bow and arrow, domestication of dog, gathering and pounding of wild cereals, highly mobile/transhumance migratory patterns. Evidence for this culture is found during the period of warming and Early Holocene deglaciation in Northern Hemisphere after the LGM.
2. 12,500 BCE – sea level rise event
3. Polished stone tools mark the final stage (12 kya – metal use) in which grinding or polishing made smooth tools, which cut deeper, were more efficient, and helped humans clear swaths of land from forest to farmland.
4. Early Natufian – 12,500-10,800 BCE – settled society, use of wild cereals, domesticated dog, brewed beer, production of limestone plaster, in the warmer climate of the
   Younger Dryas – 10,800-9,500 BCE – was 1,000 years of sudden cold back to glacial temperatures (dropping 4-10*C in Northern Hemisphere), before finally yielding to the sustained warmer climate of the Holocene. Wild cereals not able to survive, flora unable to support sedentary residence, humans return to nomadic lifestyle.

5. Pre-Pottery Neolithic A (PPNA) – 9,500-8,500 BCE – climate warms back up, now wild cereals are cultivated, and sedentary lifestyle resumes

Kebaran culture in the Levant from 18,000 BCE

Natufian culture in the Levant from 13k bce to 9.7k bce at the end of the last glacial stadial (Younger Dryas). Natufian culture was semi-sedentary in the Levant, wandering around Jericho with its abundant springs.

After the last (fourth) ice age (ending c.12,000), transition between hunter-gatherer to increasingly sedentary subsistence mode.

Pre-Agricultural Sites:
Gobekli Tepe (9130 BCE) on the Anatolian/Syrian border is the earliest known temple site and is unique in that there is no evidence of sedentary living associated with it, or cultivation of grains. The limestone pillars weigh approx. 10-50 metric tons and would have required atleast 500 adults to move and place.

Starting to experiment with taming nature: wild cereal cultivation, domestication of the dog, domestication of other animals (sheep, goats), mix of semi-settled and nomadic herders. First evidence of bread 14,500 BCE and beer 11,000 BCE.

Nevali Cori
Karahantepe

Artists conception of Mesolithic life, combination of hunter and gatherer lifestyle.

References: Charvat/2002, Nissen/1988

By 14kya, the Paleolithic era is ending with the last ice age giving way (c.12kya) to the Younger Dryas inter-glacial period (holocene warming period c.10kya) lasting to the present time.

By 14mya man has mastered the bow and arrow, and we have evidence of domesticated dog living amongst men at the Palegawra site (17kya) in the Zagros mountains.

The change in climate and habitat triggers the start of the Mesolithic epoch in the transition from Paleolithic (nomadic hunter-gatherer) to Neolithic (settled farming).

As the last ice age receded around 12kya, the environment began to yield more plentiful food sources for hunter gatherers.

In the Mediterranean and Near East, wild grasses and cereals (wild barley, einkhorn and emmer wheat) increased, accompanied by lentils and various pulses.

Hunting moved from indiscriminate killing of a wide range of animals to a focus on a few species, particularly wild sheep, wild goats, and onager (wild donkey), supplemented less intensely by deer, wild boar, wild cattle, hare, wolf, fox, various birds, and other small mammals.

Gathering was turtles, hedgehogs, snails, other molluscs, and plant food.

For tools, they processed stone, bone (awls, knife handles, etc.), wood. To form axes, they used bitumin, a naturally occurring sticky tar, to attach stone or obsidian (black volcanic glass) blades into notched handles.

Stone tools were typically made of chert or flint, obsidian or quartz (hardest material)

Abundance spurred curiousity, new resources were opened (a variety of stones, raw copper, bitumen) and new technologies such as grinding and polishing stones and even the first steps in chemical production (lime plasters), were introduced.” (Charvat 2002:10)

Even in this period of plenty, there is evidence of violence between human beings.

By 11kya, they started to settle down in semi-fixed homes and experiment with mixed mode living — hunting, gathering, herding, and with wild crops.

By 10kya, man had domesticated other animals, not unsurprisingly first sheep and goats, given the heightened contact through hunting, and then cattle. By 9,500 ya, evidence exists of domesticated pigs.

By this point, housing was kept scrupulously clean, with lime plaster or clay interior walls, lowered floors, spiritual or ritual objects – statuettes, grave goods, body ornaments (necklaces, bracelets, rings). (Charvat 2002: 13)

“The essential characteristics of all human communities up to recent time—economic specialization, social differentiation and complex spiritual reflection of the visible world—may be documented in this period of time.” (Charvat/2002:15)

New Stone Age (Neolithic) and Rise of Sedentism

Now we enter the Neolithic period, in the Near East this is from 9500 BCE onwards, after the end of the Younger Dryas, last glacial period.

In agriculture there is experimentation with emmer wheat and einkhorn wheat, also cultivated peas, lentils, six-row bread wheat, oats, rye, linseed, and flax. They gathered wild cereals and also pistachio nuts from the highland woods.

Some of the dwellings (e.g. at Umm Dabahiyah) now have “fresco paintings geometrical patterns and figural scenes (an onager frieze, a hunting scene)” (Charvat 2002:19) — fresco paintings are with colored powders applied to fresh plaster so that upon drying, the painting is an integral part of the wall.

There is pottery, and ornamental decorations on pottery, houses with complex structures, including stairways for roof access, kilns for firing pottery, textiles and woven baskets.

In agriculture there is artificial irrigation leading to larger crop yields (sites Choga Mami and Tell es-Sawwan inter alia). There is also clear evidence that Neolithic peoples were experimenters, cross-breeding cereal grasses to obtain domesticated variations that are in use to this day (four-row emmer wheat, six-row variations, with non-shattering stems in order to preserve the grains when harvesting). Charvat 2002:30

This was their main achievement – the advance and experimentation in securing additional food sources and improving and perfecting these through genetic interventions.

Dogs were used to assist in both shepherding and hunting. As shepherding added more species (goats, sheep, cattle, pigs), hunting targets changed away from wild goats to gazelle and onagers, presumably because wild goats would be added to the herd. Gazelles and onagers are harder to hunt, requiring the coordination of numerous hunters with a single purpose. They also consumed more fish, mussels, turtles, and crabs.

The settlements consisted of several houses, in some cases (Tell es-Sawwan) with a fortification ditch (3m deep, 2.5m wide) surrounding the houses, together with a rampart with buttresses (reinforced defensive walls). Houses were built of clay bricks, sometimes formed in molds, and the floors bore an occasional coating of bitumen (tar) or gypsum, otherwise reed mats, or stamped earth. Some of the village streets were paved.

By Neolithic time, civilization was complete — societies had structure, religion, economic specialization, surplus food, art, and community.

Planting and harvesting of grain was in place by 6900-6000 BCE.

“The Neolithic food-producing economy was no fun … human remains at the site show evidence of physically demanding work, including collapse of neck vertebrae due to carrying heavy loads on the head (remember that the wagon would not be invented until the Chalcolithic period [from 4000 BCE on].” The digging, threshing, grinding, harvesting, irrigation, water carrying, load carrying — all of this was human labor. (Charvat 2002:32)

One wonders if in the Neolithic times ideas of slavery led to raids on nearby settlements in order to coerce others to carry out food-producing work.

Lifecycle of lambs and sheep: “Lambs are born around Christmas (for confirmation by the Near Eastern data see Wright, Miller and Redding 1980, 271; Wright, Redding and Pollock 1989, 108–109; Hruška 1995, esp. pp. 82–83) and in May they are usually grown enough to walk even over heavy ground and to be weaned so that sheep can be milked from that time on. In May the shepherds with their herds usually ascend the summer pastures whereupon the sheep are sheared and new wool employed to settle all accounts, debts and obligations that the shepherds or their masters might have incurred before, the season of cheesemaking following in the months of June and July. (Charvat 2002:39)

There is some evidence that Neolithic cultures were migratory, moving seasonally between lowlands (winter) and highlands (summer), and taking advantage of whatever combination of subsistence methods worked in each circumstance. So there was agriculture, herding, hunting, gathering, but looks like there may have been migrations twice a year, (Charvat 2002:47) I.e. the sites were permanent but the people in them were not (Charvat 2002:40) Non-nomadic domesticates are the pig, which cannot travel long distance. Another sign is larger cemeteries indicating territorialization of human communities. (Charvat 2002:39)

Homo Sapiens migration – from Paleolithic to Neolithic, 10,000 years onward
source: AtlasOfTheHumanJourney.com

Genetic analysis shows it was the same peoples who settled the Polynesian Islands, including Easter Island, between 830 and 1360, over the course of 17 generations (30 years per generation). Each of these 21 islands has a similar ancient relic/megalith culture, and speak the same language.

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Appendix 7: Domestication of Animals

Others:

• Dog – Domestication, 14kya Palegawra; 10kya Idaho. How did this come about? Russian and US scientists have identified a gene (SorCS1) in foxes that leads to exaggerated friendliness and tameness behaviour (2018). A tameness gene may have made a few wolves seek human affection. If female, this may have led to pups with the same gene, and over the course of hundreds of generations of animals, to dogs.
• Donkey – domesticated 5000 BCE in East Africa. Entered mid-East c. 2500 BCE

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Appendix 7b: Foraging Foodstuffs: What the Wild would have held for ancient hominins and still holds for us today

1. 12 wild nuts in N.American and Europe – boiled, roasted, floured

Appendix 8: Near Eastern Cultural History: from pre-Pottery 7500 BCE through to Uruk city state period 4000 BCE

List of all settlements, villages, and cities

Culture around settlements, herding, farming, but also transhumance seasonal migration between lowlands and highlands.

Type sites: Jarmo (7090BCE), an agricultural community of 150 people, or 25 houses, in the foothills of the Zagros mountains during the early Neolithic. Jarmo has evidence of agriculture, animal husbandry (sheep, goat, pigs), domestication of emmer and einkhorn wheat, barley and lentils, foraging of nuts acorns, pistachios, and early pottery.



Artist conception of Neolithic lifestyle.

Bonkuklu Hoyuk, a site from 8500 BCE, small site

Catalhoyuk in Anatolia, Turkey is dates from c.7500 BCE and is interesting as it was a proto-city with permanent settlement homes for between 5,000 and 7,000 individuals. (Compare to Jarmo village which had 150 homes.)

• Ubaid (6500-3800 BCE)/Chalcolithic (4500 BCE) – transition to permanent unwalled settlements with specialized craftspeople (potters, weavers, metalworkers), cultivation of grain under arid conditions through the use of irrigation canals (some up to 5km long) requiring large collective labor efforts, the growth of an extensive trade netowrk, and the building of temples. First known settlement in S.Mesopotamia is Tell el-Ouelli (Ubaid 0) (6500 BCE-5400 BCE), 4km SE of Larsa, 25km SE of Uruk. Next is Eridu (Ubaid 1) up to 4,000 residents in 20-25 hectares, irrigation agriculture, limited use of copper metal tools, expansion of art and aesthetics, and the beginnings of stratification of society, professional specialization, and the clustering of villages around centers


Artists conception of Ubaid life (unwalled settlements, communal labor, irrigation agriculture, copper supplementing stone and wood tools)



Ubaid period cultures, c.6000 BCE onwards.

• City-State Period (4,000 BCE-2,900 BCE) – early bronze age, expansion of settlement size to large cities with walls (Uruk, Ur, Susa), with up to 50,000 residents in 6 km2 (Uruk c.2900BCE), hierarchical society with an established elite (temples and lords), warrior class, slavery, long distance trade, large surpluses and the controlled use of labor for prestige buildings – emergence of writing, the state, arithmetic, ancient book-keeping. Uruk city (founded in Eridu Ubaid 1 period 5,000 BCE onwards) originated as two separate temple sites to Innana and An (Kullaba district).See FAQ1 for discussion of middle-chronology dating of Mesopotamian events from Early Dynastic onward


Uruk City, founded in Ubaid 1 (Eridu) period 5,000 BCE as two temple sites, Eanna (to Inanna) and An, consolidated into a single walled urban site, eventually with an intricate inter-city canal system allowing heavy goods (wood, stone, etc.) to be brought into the city by boat from outposts, colonies, and distant trading partners (Venice in the desert)

For history after ED period, see Part 2: The Mathmatics of Uruk and Susa, Appendix

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Bibliography & Further Reading

Mesopotamian Mathematics: From prehistoric metrological tokens to writing and the earliest recorded mathematical practice (3200 BCE and onwards)

1. Denise Schmandt-Besserat, 1977, An Archaic Recording System and the Origin of Writing,”; Syro-Mesopotamian Studies I., 1977, pp.31-70; [Besserat/1977]
   This first publication of her findings builds on prior work of Amiet (1966) on Susa findings, on Oppenheim (1959) on Nuzi findings including an inscribed bulla from 2000-1500BCE, and on Falkenstein (1936) on archaic signs (proto-writing). Subsequent detailed investigations of Besserat’s hypothesis have supported the following points (1) sealed bullae containing tokens provide the evidence of the use of tokens for accounting commercial transactions, (2) that this transition from tokens to inscribed bullae provides a key missing link between pre-writing numerical practice, proto-writing, and the proto-cuneiform that followed, (3) that this critical transition happened c.3200 BCE in Uruk (aka Warka) in southern Mesopotamia. The rest of her many claims in subsequent publications have been demolished, in particular the claim that clay tokens were an accounting system in wide use across the Near East. See critical reviews by Zimansky/1993, Englund/1993, Englund/1998, and the use of contextual archaeology to close the case on Besserat’s speculations, see masters thesis Niemi/2016, and Bennison/2018
2. Tonje Niemi, 2016, Near Eastern tokens. A contextual analysis of near eastern tokens from the 7th to the 4th millenium BC, Master’s thesis, The University of Bergen [Niemi/2016]
   Based heavily on the work of Charvat/2002, Niemi reviews the claims of Besserat using contextual archaeological analysis. She finds, as have Damerow, Englund, Nissen, and others, that while the evidence for token use for book-keeping is convincing in the 4th millenium site layers, there is insufficient contextual evidence for mathematical use of tokens in any other strata due to (1) insufficient quantity of token finds across time and location to be draw significant conclusion, and (2) contradictory micro-local finds of the tokens suggesting use of tokens for other purposes (e.g. funerary rites, game pieces, etc.)
3. A. Leo Oppenheim, April 1959, Journal of Near Eastern Studies, 18:121-128, “An Operational Device in Mesopotamian Bureaucracy“. [Oppenheim/1959]
   Oppenheim describes a bulla containing 48 tokens dated from 1500 BCE that also contains a cuneiform description of the reading of these tokens as itemizing types of sheep and goats (male, female, young, old ,etc.). Unfortunately, between cataloging the tokens and analysis in the museum, the tokens got separated from the bulla, so the opportunity to assign token type to animal type is lost.
4. Joran Friberg, 1984, Numbers and Measures in the Earliest Written Records, Scientific American, Feb 1984, Volume 250, Number 2, pages 110-118 [Friberg/1984]
5. Hans Nissen, Peter Damerow, Robert Englund, (transl. by Paul Larsen) 1993, Archaic Bookkeeping: Early Writing and Techniques of Economic Administration in the Ancient Near East; University of Chicago Press; [NissenDE/1993]
6. Robert Englund, 2004, Proto-Cuneiform Account-Books and Journals, in Hudson/Wunsch Creating Economic Order, CDL Press, pp.23-46 [Englund/2004]
7. Marvin Powell, 1971, Sumerian Numeration and Metrology, PhD Dissertation, University of Minnesota. [Powell/1971]
8. Robert Englund, 2001, Grain Accounting Practices in Archaic Mesopotamia [Englund/2001]
9. Peter Damerow, 1999, The Origins of Writing as a Problem of Historical Epistemology, Max Planck University Preprint P114, Invited Lecture at Multi-Origins of Writing Workshop, March 1999 [Damerow/1999w]
10. Hans Nissen, 1986, Archaic Texts from Uruk (ATU2), World Archaeology, Vol 17, Issue 3 [Nissen/1986]
    Outstanding discussion of what we know about the evolution of writing and how we have been able to decipher it.
11. Robert Englund, 1998, Texts from Late Uruk, published in J. Bauer, R. Englund and M. Krebernik, Mesopotamien: Späturuk-Zeit und Frühdynastische Zeit (transl. Mesopotamia: Late Uruk Time and Early Dynastic Time) OBO 160/1, Freiburg Switzerland 1998, 275pp. [Englund/1998]
12. Mesopotamian Mathematics: Some Historical Background, Eleanor Robson, 2000. [Robson/2000]
13. Mathematics in Ancient Iraq: A Social History, Eleanor Robson, 2008, Princeton University Press, Download Chapter 1 (Academia.eu) [Robson/2008]
14. Mathematics and Early State Formation, Jens Hoyrup, 1991 [Hoyrup/1991]
15. [Hoyrup/1991b] – Changing Trends in the Historiography of Mesopotamian Mathematics: An Insider’s View, Jens Hoyrup, 1991

    Geometric Mathematics in the Ubaid Period

16. Shamil Kubba, 1990, The Ubaid Period: Evidence of Architectural Planning and the Use of a Standart Unit of Measurement (the “Ubaid Cubit”) in Mesopotamia. Paleorient, 16(1), 45-55. [Kubba/1990]
17. Jean-Daniel Forest, 1991, The Ubaid System of Length Measures (in French), Paléorient, 1991, vol. 17, n°2. pp. 161-172 [Forest/1991]
18. Amir Soudipour, 2007, Architectural and Conceptual Analysis of Mesopotamian Temples from Ubaid to Old Babylonian Period, Feb 2007, Masters of Arts thesis, Bilkent University, Ankara, [Soudipour/2007]
19. Eleanor Robson, 2000, The Uses of Mathematics in Ancient Iraq: 6000 BCE-600BCE, in Selin’s Mathematics Across Cultures [RobsonSelin/2000]
20. Jens Hoyrup, 2011, Mesopotamian Calculation: Background and Contrast to Greek Mathematics, Genova, 17-19 Nov 2011, Congress IX Societa Italiana di Storia della Matematica, [Hoyrup/2011]

    On the Interpretation of Notched Bones (18,000-35,000 BCE) as Prehistoric Mathematical Artefacts

21. On the Impossibility of Close Reading: The Case of Alexander Marshack, James Elkins, Current Anthropology, vol 37 #2, April 1996, [Elkins1996]
22. Obituary and achievements of Alexander Marshak prolific self-taught anthropologist who introduced the interpretation of notches on prehistoric artefacts as mathematical (calendars, arithmetic records, and a representation of primes), Dec 2004, NY Times, [Marshack/2004]
23. The Roots of Civilization: The Cognitivie Beginnings of Man’s First Art, Symbol, and Notation, Alexander Marshack, 1971 [Marshack/1971]
24. History of Mathematics, David Burton, 1982 [Burton/1982]

    Controversy over the interpretation of the Ishango Bone

25. The Fables of Ishango, or the irresistable temptation of mathematical fiction, Olivier Keller, Aug 2010, BibNum [Keller2010]
26. The Bone that Began the Space Odyssey, Dirk Huylebrouck, 1996, Mathematical Intelligencer, vol 18 #4, pp.56-60 [Huyle/1996]
27. The Ishango Artefact: the Missing Base 12 link, Vladimir Pletser, Dirk Huylebrouck, 1999, Forma, vol 14, pp.339-346 [PletserHuyle/1999]
28. Does the Ishango Bone indicate knowledge of Base 12?, 2012, Vladimir Pletser, ArXiv.org, [Pletser/2012]
29. Rebuttal by Pletser and Huylebrouck, 2015, ArXiv.org, [PletserHuyle/2015]

    Language and the Number Concept

30. Numerical Cognition without Words: Evidence from Amazonia, Peter Gordon, October 2004, Science vol 306 #496, [Gordon/2004]
31. Number as a Cognitive Technology: Evidence from Piraha language and cognition, Michael Frank, Daniel L. Everett, Fedorenko, Gibson, April 2008, Cognition vol.108, pp.819-824 [FEFG/2008]
32. Quantity Recognition Among Speakers of an Anumeric Language, Caleb Everett, Keren Madora, 2012, Cognitive Science, vol. 36, pp.130-141, [EM/2012]
33. Levi Conant, 1896, The number concept: Its origin and development, Republished in The World of Mathematics by James R. Newman; Vol.1; pp.432-442; 1956; Simon & Schuster, [Conant/1896]
34. Numbers and numerals, David Eugene Smith and Jekuthiel Ginsburg, 1937. Republished in The World of Mathematics by James R. Newman as “From numbers to numerals and from numerals to computation”; Vol.1; 1956; pp.442-465; Simon & Schuster, [SG/1937]
35. Mathematics from the Birth of Number, Jan Gullberg, W.W.Norton, 1997, [Gullberg/1997]
36. Number Systems [NS]

    The Piraha, the first known culture without numeracy

37. Brazil’s Piraha Tribe: Living without Numbers or Time, Rafaela von Bredow, May 3, 2006, Der Spiegel, [Piraha/2006]
38. Has a remote Amazonian tribe upended our understanding of language? John Colapinto, April 2007, The New Yorker Magazine [Piraha/2007]
39. Cultural Constraints on Grammar and Cognition in Piraha: Another Look at the Design Features of Human Language, Daniel L. Everett, August 2005, Current Anthropology vol 46 #4, [EverettD/2005]
40. Interview with Daniel Everett: Clarifying 1985 and 2005 views (PDF), April 4th, 2014

    Genetic and Evolutionary origins of speech and language

41. Liebermann & McCarthy, 2007, Tracking the Evolution of Language and Speech: Comparing Vocal Tracts to Identify Speech Capabilities, UPenn Museum Expedition, Vol.49, No.2, Summer 2007, (PDF available)
42. Grammar Came Later: The Gradual Evolution of Language, Nov 2016, Daniel L. Everett, Journal of Neurolinguistics
43. FOXP2 gene associated with speech and complex vocalization
44. FOXP2 gene in mice makes them smarter, 2014, New Scientist
45. 2018 study challenging recent selection of FOXP2 in humans
46. Babel’s Dawn, Edmund Blair Bolles, : a look at the multidisciplinary evidence concerning the origin of speech in humans. Review. Blog.
47. A Survey of the Semiotic Progression Towards Language in the Archaeological and Physiological Record, Daniel Everett, Nov 7, 2018, CIDRAL
48. The American Aristotle: The Semiotics of C.S. Peirce, Daniel Everett, 2017, Aeon Semiotic progression is from index -> icon -> symbol

    Paleolithic archaeological record of early hominins
    Definition: Stone Tools are defined by the complexity required for their manufacture. “Simply struck tools are Oldowan. Retouched, or reworked tools are Acheulean. Retouching is a second working of the artifact. The manufacturer first creates an Oldowan tool. Then he reworks or retouches the edges by removing very small chips so as to straighten and sharpen the edge. Typically but not necessarily the reworking is accomplished by pressure flaking.” (Wiki, Oldowan), Wiki, See Mode 1 (Oldowan, unifacial, simply struck), Mode 2 (Acheulean, bifacial, retouched), Mode 3 (Mousterian, advanced bifacial), Mode 4 (Wiki, Acheulean).

49. Paleolithic Cultures (Wiki)
50. Fossil & Tool Gallery
51. Knapping as a Skill, and Risk of fatal lung disease from dust inhalation Lithic Technology and Lithic Production
52. [Gala, 2023] – The Injury Costs of Knapping, American Antiquity, 2023, (Online article), (Research summary), (News coverage)
53. [Proffitt, 2023] – Wild macaques challenge the origin of intentional tool production, Science Advances, 2023, (Online article), (News Coverage) – study finds that monkeys using stones to crack nuts (hammer and anvil mode) create accidental fractures that are indistinguishable from Oldowan tools attributed to hominin production. Could also indicate how hominins accidentally discovered the sharp edges and then began to create such edges intentionally.
54. [Harmand, 2015] – 3.3 million year old stone tools from Lomekwi3, W. Turkana, Kenya, Nature, May 2015. (Online article), (BBC coverage)
55. [Delagnes,Roche, 2005] – Stone Knapping in Lake Turkana area 2.3mya, 2005 – Lokalalei site, W. Turkana, Kenya, bifacially reworked bladed stone tools; Online PDF
56. [Callaway, 2017] – Emergence of Homo Sapiens, at 315,000 years ago, based on fossils discovered at Jebel Irhoud site, Morocco, Online article]
57. [Vidal, 2022] – Nature, 2022, Emergence of Homo Sapiens, currently 230,000 years ago based on fossils from Omo I site in Ethiopian Rift Valley, discovered in 1960s, News coverage
58. [Solecki, 1979] – Contemporary Kurdish Winter-Time Inhabitants of Shanidar Cave, Iraq, Ralph Solecki, World Archaeology, Vol.10, No.3, Feb 1979, (Online article)

    Human Cultures and Lithic Industries

59. Lomekwian Tool Culture 3.3mya – these tools were flaked off unusually large flint cores, which were rotated for better edge creation. 3.3mya is 700k years before the start of the Quarternary Period of the 4 ice ages (from 2.6mya) (Wiki summary), produced before Homo species, likely by Kenyanthropus. Some flakes were worked on both sides (bifacial), demonstrating intentionality.
60. Oldowan Tool Culture in the Lower Paleolithic, 2.6 mya to 1.7 mya, giving way to Acheulean. It is preceded by Lomwekian (see above)
61. Acheulean tool culture, 1.7mya to 160kya, giving way to Sangoan or Mousterian
62. Mousterian tool culture, 300kya to 40kya, Mode 3, type site Shanidar Cave containing remains from both Neanderthal (c50kya) and Homo Sapiens.
63. Aurignacian tool culture, 40kya to 20kya, Mode 4
64. Epigravettian, 26kya to 14kya
65. Mesolithic culture – Mode 5 and Epipaleolithic Near East
66. Kebarran culture – Microlithic tools, bow and arrow, domestication of the dog, c14kya. Type site: Palegarwa in Kurdistan
67. Natufian culture – Sedentary or semi-sedentary lifestyle even before the introduction of agriculture. Earliest site with bread c.14,400 BCE. Type site: Jericho (c.10,000 BCE onward)
68. Pre-Pottery Neolithic – includes such sites as Gobekli Tepe, Catalhoyuk, and Jarmo

Neurological Studies of Animals, and the Cognitive Precursors of Mathematics

Talented and Gifted Animals, Stanislas Dehaene, 1997, Chapter 1 of The Number Sense: How the Mind Creates Mathematics, Oxford University Press, 274pp. Animal brains are hardwired for an analogue form of counting.

Crows Rival Human Toddlers in Counting Skills, Rachel Nuwer, May 2024, Scientific American

Varanoid Lizards of the World, Eric Pianka and Dan King (eds), 2004 [Pianka,King/2004]

Tales of Monitor Lizard Tails, and Other Perspectives, Murpy, 2019 [Murphy/2019]

Animal Communication: Animal World’s Communication Kings, Rebecca Morelle, May 1, 2007, BBC News

Animal Emotions and Cooperative Empathetic Behaviour: Orcas, Aug 10, 2018

Basic math in monkeys and college students. JF Cantlon, EF Brannon, 2007, Duke University Study, PLoS Biol 5(12): e328,

The ability of birds to count, O. Koehler, Bulletin of Animal Behavior; Vol.9, pp.41-45, 1950; Nature; Vol 168; Issue 4270, pp.373-375, 1951; Republished in The World of Mathematics by James R. Newman; Vol.1; pp.489-496; 1956; Simon & Schuster, [Koehler/1950]

Revising the Triune Brain model of Paul MacLean

The Number Sense, Bruce White, We are born with a number sense, though we have to learn to count.

History

Hans Nissen, 1995, Western Asia before the Age of Empires [Nissen/1995]
Succinct, 8-page summary of Mesopotamian history.

Land, History, and Geography, 2011, Notes from course on Sumerian at Masaryk University (Czech)

Petr Charvat, 2002, Mesopotamia Before History, Taylor & Francis (Revised edition of Ancient Mesopotamia 1993), [Charvat/2002]
Detailed description, based on archaelogical finds, of how the Near East went from Paleolithic to Mesolithic to Neolithic to Chalcolithic, before arriving at the Uruk period of city states. Each find site is reviewed in detail, and an interpretation is given covering all aspects of the associated culture (material conditions, social practice, art and ritual, modes of sustenance, food and commensality, individual work profiles, housing conditions, etc.)

Kevin Cathcart, 2011, The Earliest Contributions to the Decipherment of Sumerian and Akkadian (PDF online)

L.W. King and R.C. Thompson, 1907, The sculptures and inscription of Darius the Great on the Rock of Behistûn in Persia : a new collation of the Persian, Susian and Babylonian texts, The British Museum [Behistun/1907]

Thorkild Jacobsen, 1939, The Sumerian King List, University of Chicago Press [Jacobsen/1939]
Provides an account, written toward the end of the Sumerian period, and before the conquest by Babylon, of the Sumerian lineages, from Eridu to the flood, to Kish and Uruk (Gilgames), to Ur, to the Akkadian conquest (Sargon), the Sumerian reconquest Ur III, and finally to Isin. Here the King List stops c.1753 BCE. What we know is that within 50 years (and one more transition to Larsa), the dissolution of the Sumerian dynastic lineage would occur with the conquest by Babylon under Hammurabi, a brother of the next to last regent of Larsa (Warad-Sin). See Uruk and Susa, appendix for details.

Madeleine A. Fitzgerald, 2002, The Rulers of Larsa, PhD Dissertation, Yale University [Fitzgerald/2002]
Gives a detailed history of Larsa and its environs in the aftermath of Ur III (early 2nd millenium), when Isin was hegemonic. Discusses evidence for the gradual growing in strength of Larsa until its pre-eminence, the waning of Isin, the rise of Babylon, and ultimately the defeat of Larsa (see Mathematics of Uruk and Susa, appendix for establishing chronology for these events). Shows the relative insecurity in these cities and the way in which fortunates waxed and waned in the human timescales of a generation. Shows that rulers were succeeded quite rapidly in times of conflict (probably death in battle), and that militarily successful rulers had long reigns. Detailed discussion of the year name system on which synchronist approach to relative chronologies are based.

Staurt Manning, et.al, 2016, Resolving Mesopotamian Chronology: Integrated Tree-Ring Radiocarbon High-Resolution Timeframe to resolve Earlier Second Millenium BCE Mesopotamian Chronology, PLOS Journal, July 2016 [Manning/2016]
Summary: Carbon-14 dating of tree rings shows that absolute dating of Mesopotamian events can be accurate to +/- 8 years. Of the 5 major chronologies, only the Middle (MC) and Middle-Low (L-MC) chronologies are compatible with the data. The fall of Babylon is now established as between 1587-1595 BCE.

The Story of Man, Carleton S. Coon., Alfred Knopf, second edition, 1962, [Coon/1962]

The Essential Nature of Arithmetic, pp.17-19, in A General View of Mathematics, A.D. Aleksandrov, 1956 (Russian), 1963 (English), Chapter 1 (pp1-64) from Mathematics: Its Content, Methods, and Meaning, by Aleksandrov, Kolmogorov, Lavrentev (1999, Dover republication) Describes the dialectical nature of mathematics, and how arithmetic arose from the human experiences of unimaginable generations (see Appendix 1 for extract). [Aleksandrov/Arithmetic1956]

Mathematical developments against developments in human history. [Timeline]

Scientific Investigation of the Past

[Walsh/2010] – Does Newton Feign a Hypothesis? Kirsten Walsh, Oct 2010, Early Modern Experimental Philosophy Project. – On the difference between theory and speculation in scientific thought, and prehistorical interpretation.

[NAS, 1999] – “Science and Creationism: A View from the National Academy of Sciences, 2nd ed., 48pps, 1999, U.S. National Academy of Sciences. Online and PDF

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1. The reports (2013-2018) analyzed anomalies in the cosmic microwave background (CMB) radiation and extracted signals from the early formation of the universe, the classification and distribution of matter across the universe, and investigated the fundamental physics of the cosmos. ↩
2. With measurement error of 1500 years per million = 0.15% = 15 bps (basis points) + +/- 21 million years. Sources: Wikipedia: Chronology of the Universe and Wikipedia: Planck Collaboration results ↩
3. Although general relativity establishes that matter cannot travel faster than the speed of light, it says nothing about how fast space itself, or gravity waves, can travel. As an example, physicists studying the theoretical physics behind warp drives use this as support for faster than light travel for a space bubble being propelled by gravity: “a real-life warp drive would use massive ammounts of energy, to create enough gravitational pull to distort spacetime in a controlled fashion, allowing a ship to speed along inside a self-generated bubble that itself is able to travel at essentially any speed.” (Adams, Popular Mechanics, Aug 15, 2023) ↩
4. Source: 2nd last paragraph of Overview of Lambda-CDM model, or the dark energy/cold dark matter model ↩
5. Hydrogen is not stable as an atom, only as a molecule H2 formed from two non-decaying atomic hydrogen isotopes (protium 1-H at 99% abundance with atomic mass 1 and 0 neutrons, and deuterium 2-H at 1% abundance with 1 proton and 1 neutron). Helium is stable as an atom with two non-radioactive isotopes (atomic masses 3-He and 4-He). It does not exist as a molecule He2 unless at cryogenic temperatures. Hydrogen is normally found as a gas, becomes a plasma at high temperatures e.g. in stars and lightning, and then becomes liquid and then metal under extremely low temperature and pressures such as in the interior of Jupiter. ↩
6. What is a star? It is a stable nuclear fusion reactor safely contained by gravity which forms around the star through its density curving spacetime around it, unlike the magnetic containment that is so difficult for us to get right on earth. ↩
7. Water H2O has unique properties for a liquid. Ethanol CH3-CH2-OH, also called ethyl alcohol or grain alcohol, is naturally formed when yeast ferments carbohydrates in e.g. wheat/barley malt (beer), grapes (wine), or potatoes (vodka). Propane C3H8, also called liquified petroleum gas or LPG, naturally occurs during natural gas processing and crude oil refinement, is a non-toxic clean fuel.. Methanol CH3-OH, also called wood alcohol, is highly toxic and causes irreversible vision loss if consumed. Ammonia NH3 is corrosive/flammable molecule, naturally formed by the body as a waste product (urea) when proteins are broken down into amino acids. Hydrogen Sulfide H2S is the rotten eggs/swamp gas smell of decay, which is flammable and toxic, and produced by volcanoes and hot springs, but also naturally by bacteria in the mouth and gut when breaking down proteins, and metabolized by the and released from the body through urine, faeces, or flatulence. ↩
8. Water: unique properties for a liquid, most of the weight of humans, with precious little only 3% freshwater on earth. Freshwater bodies of water are, e.g. highland lakes fed by rivers and streams running off from hills and mountains, without a high sediment load with earth based salts which otherwise accumulate. In the UK, Loch Ness has more freshwater (263 billion cubic feet) than all the lakes and rivers of the UK combined. ↩