The Prehistoric Origins of Mathematics

3rd ed. Aug 2023 (expanded appendices). 2nd ed. Nov 2019 (revised to include advances in linguistics, genomics, interpretive theory, and Mesopotamian mathematics); 1st ed. (Dec 29, 2009)

Part 1 in Ancient Mathematics series. (Part 2: The Mathematics of Uruk and Susa 3500-3000 BCE, Part 3: Exploring Cuneiform Culture 8500-2500 BCE)

Abstract
How far back in time can we trace mathematical understanding and mathematical practice? When did humans acquire the neurological circuitry for the cognitive and linguistic capabilities on which mathematics depends? Advances in multiple disciplines over the past 30 years have fundamentally changed what we know about our past and about the biological capacity for, and cultural impulses behind, cognitive precision (language, number sense, cultural transmission). Exploring these questions will take us on a journey across archaeology, Assyriology, artifact analysis (close reading theory), anthropology, genomics, linguistics, neurobiology, and animal cognition.

We proceed backwards in time from c.3000 BCE, at the dawn of written mathematics (archaic bookkeeping) in Sumeria (modern S.Iraq). From here we will move to the prehistoric evidence of practitioner geometry in the cultures of the late Neolithic as evidenced in the layout of permanent houses, granaries and temples (c.5000 BCE in Ubaid culture), and in geometric pottery designs (c.6000 BCE, Halaf and Samarran cultures). Further back, we see the appearance of plain tokens from c.7000-8000 BCE, the same plain tokens that we know were used for counting by herders and which were instrumental in the invention of writing for book-keeping purposes within the temple institutions running centralized economic control in the urban city-states. Looking beyond the Near East, in Paeleolithic/Neolithic Europe and Britain there is evidence for monolithic monuments c.4000-7000 BCE oriented toward midwinter and midsummer solstice that suggest an awareness of the periodicity of the solar and lunar cycles, and the relation of the solar cycle to the seasons.

Before 10,000 BCE marking the start of the warming period (holocene) that began after the retreat of the 4th glacial period, the density of artifactual evidence is insufficient to draw firm conclusions: there are fewer than 5 isolated finds of artifacts between 70,000-18,000 BCE (one find per 10,000 years), with contested interpretations. So we switch to indirect evidence (genetic, anthropologic, and linguistic) to establish the capability of symbolic thought in anatomically modern humans (H. Sapiens) from c.200,000 BCE onwards. Here culture becomes a critical factor, under-scored by the fascinating example of the modern Piraha tribe in Brazil that have broken previous assumptions about the inevitability of symbolic thought in anatomically modern humans. The Piraha are the only known tribe/people whose language and culture appear not to have progressed beyond an analog notion of magnitude similar to that of higher animals, skipping entirely the granular linguistic numeracy present in every other known language, primitive or modern. Why? It appears to be cultural: the Piraha reject the value of future planning and are completely non-materialistic. This leads to an interesting philosophical observation: quantitative mathematics initially develops within a culture that values planning and material control.

From anatomically modern humans c.200,000, we jump backwards to c.2.4 million years ago and consider the capacity for conceptual thinking implicit in the tool-making capability of early hominids. We look at C.S. Peirce’s “semiotic model” (index, icon, symbol) of conceptual and linguistic development, and conclude that bladed tool-making (Lokalalei site evidence) required at least stage 2 or stage 3 conceptual development. Having gone back as far as we can with the capabilities of humans and hominids, we consider the origin of number sense in humans, animals, birds, and reptiles, and trace back the neurological circuitry supporting an analogue number sense to a latest common ancestor (LCA), a stem reptile that would have existed some 260 million years ago.

A set of Appendices provide additional color on:

1. Appendix 1: Dialectic nature of arithmetic (and mathematics),
2. Appendix 2: Invention of writing and the advancement of book-keeping
3. Appendix 3: Birth of the universe up to the early period of life on earth (Pre-Cambrian Eon)
4. Appendix 4: Acceleration of living diversity (Cambrian explosion period) to the dawn of humanity (Pliocene epoch)
5. Appendix 5: Paleolithic (Stone Age) Culture from Lomweki (3.3mya) to Shanidar (c.50kya)
6. Appendix 6: The Mesolithic, the last glacial maximum (26kya) to settled life 10,000 BCE)
7. Appendix 7: Timeline for domestication of animals.
8. Appendix 7b: Foraging for Food – What the wild landscapes might have held for ancient humans (and still today)
9. Appendix 8: Near Eastern Cultural History: from pre-Pottery Neolithic (c7500 BCE) to city states Uruk period (c4000 BCE)

A list of recommended readings, most of which can be downloaded freely, is provided in the Bibliography.

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This is a long paper (62pp) with many images and tables.
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1. Evidence from the dawn of written mathematics (c.3000 BCE): accounting with clay tokens.

By 3,200 BCE (5200 years ago) there is indubitable evidence for mathematical practice within the sophisticated cultural context of Neolithic Sumerian city states with a strong centralized control of production resources and economic activity through temple-statal administration. This led to the breakthrough advancement of proto-writing: scribes used the clay tokens typically kept in “bullae” (clay envelopes) to impress upon flattened clay tablets to create the earliest known system of accounting, or book-keeping. In this context, the token combined quantity and commodity, so correct interpretation required knowing the context of the transaction. Within 50 years, there was a further advance: pictographic signs that could specify commodity separately from quantity. Over the next 500 years, temple and state control of economic planning and supply chain management grew more extensive and more ambitious, developing syllabic writing, standardizing traditional metrologies (the same signs could still take on different values depending on metrological context), and improving arithmetic technologies (the emergence of the sexagesimal system, reciprocal tables, other aids to calculation/computation/solving problems).

The strongest archaeological evidence of mathematical practice dates to at least 3,200 BCE (5200 years ago) in ancient near eastern city-states. Archaeological finds in the past century have shown that geometrical clay tokens which appear to have been used for counting and measuring across the region, became established at this time in the Sumerian city-state of Uruk (southern Mesopotamia/Iraq) as the standard administrative procedure for recording commercial transactions (archaic book-keeping). Similar finds have been made in Elamite Susa (Zagros mountains/western Iran), a rival city-state to Uruk. [NissenDE/1993], [Friberg/1984].

Key to this conclusion were the finds by Denise Schmandt-Besserat of tokens enclosed in clay “bullae”, or sealed clay envelopes, with matching token-impressions on the clay surface. ([Besserat/1977], [Oppenheim/1959]) The impressed indentations made by pushing the tokens into the wet clay are also the earliest examples of proto-writing. [Damerow/1999w]

The meaning of these impressions can be worked out from the historical sequence of clay tablets that initially record token-impressions only with no additional written context, to later the juxtaposition of number signs with additional signs indicating the commodity (e.g. 3 sheep), and finally the use of separate cuneiform signs for number and for commodity. [Nissen/1986], [NissenDE/1993], [Robson/2000].

There is evidence of elaborate systems of metrology (measurement) that linked the tokens variously to different length, area, volume, weight, and time units, in nested factors of 2,3,6, and 10. The decipherment of these metrologies was based on painstaking studies of hundreds of archaic tablets with numbers matched to those in cuneiform tablets using the associated cuneiform symbols (see below on the number system). [Powell/1971], [Nissen/1986], [Nissen/1993], [Englund/2004] The situation with ancient Sumerian metrologies was similar to
customary measures in medieval Europe, see also Mathematics of Uruk and Susa)

What must be remembered is that the mathematical and metrological understanding that is captured in the earliest tablets in 3200 BCE was pre-existing and hence pre-dated 3200 BCE, before writing. It was the technology of book-keeping through writing that was the invention of the time (see the next section).

How far back did the use of plain tokens for counting and measurement go?
We have clear evidence for their use c.3200 BCE for administrative purposes associated with temple management of Ubaid period economy controlling surpluses and labor. Before 3,200 BCE, while plain tokens are find in many sites, they are without sufficient context (e.g. the bullae with imprints) to conclude definitively that they were used for counting and measurement. Thus we can provide only a date range for the start of plain token use for counting and measurement, from 8,000 BCE to 3,200 BCE (see [Niemi/2016: 33-34], and [Bennison/2018: 20-22]).

Archaic Tablet Texts
From 3,200 BCE onwards, there is increasing archaeological record of clay tablets [Friberg/1984]. The anthropological and sociological work of Nissen, Damerow, Englund, Hoyrup, Robson, and several others, have led since the 1980s to an understanding of how the temple economy evolved the scribal-statal system built around written accounting practice [Hoyrup/1991]. Mathematically, this proceeded over 1000 years (i.e. from 3200 BCE to 2300 BCE) in various stages: (1) an initial stage in which quantity and commodity were combined in a single token/impression; (2) adding pictographic symbols for representing the commodity for which the number provided the quantity; (3) logographic cuneiform (writing with the wedge-end of a reed) in which the symbol represented the full word or idea, giving no indication of the pronounciation; (4) syllabic representation of spoken language using the same cuneiform symbols enabling Sumerian and Akkadian scribes to record concepts and literary ideas as well as numerical transactions. [Nissen/1986], [Robson/2008]

Sumerian written and spoken numerals

The cuneiform representation of the Sumerian/Akkadian/Babylonian number system is ADDITIVE, and in this way has the same sense of cumbersomeness common to all additive systems (e.g. Roman numerals). This is because of the shortage of symbols. The Sumerians had two symbols: a symbol for 1 (vertical wedge) and a symbol for 10 (horizontal wedge nail end only). All numbers up to 60 (their base) were written by accumulations of these symbols. The digits 1 to 9 were expressed by writing the requisite number of 1’s, either consecutively or bundled together in groups of three with one group on top of another. Similarly the ‘digits’ 10, 20, …, 50 were expressed by the requisite number of 10’s, etc. The symbol for 60 was the same symbol as for 1, interpreted by context or, in a far-reaching innovation, BY POSITION. Thus the number 147 would be represented by two symbols of 60, two of 10, and seven of 1. The digit 0 was not used and presumed to be understood from the context, although in the later Babylonian period it was denoted by a wedge. [Roy, 2003]

How were the numbers spoken? (A * next to an s renders it as ‘sh’ in pronounciation). 1-10 were: Dis*, min, es*, limmu, ia, as*, imin, ussu, ilimmu, u. Then higher number formation in a similar structure as with many languages that take 10 as base. u-dis*, u-min, etc.
The spoken numbers show a fascinating linguistic pattern, with some trace of base 5 (the numbers 6 through 9 are named as 5+1,…,5+4, though not consistently), strongly base 10 structure (the numbers 11-19 are 10+1,…,10+9), some trace of base 20 (40 is nimin, or 2×20), and mixing (50 is 2×20+10). Finally the sexagesimal unit 60 is reached (ges) and the pattern repeats.
There is an ambiguity in the verbalizing of numbers higher than 60 (gesh). Is gesh-u 70 (=60+10) or 600 (=60×10)? Apparently both, with the amount resolved in context. Compare the linguistc structure of languages from Inuit (base 20), western languages (nominally base 10 but with various inconsistencies in formulation) [Gullberg, 1997, 7-60], and east Asian languages (base 10 with clean structure). [Takasughi, 1996]

The deciphering of cuneiform languages: Sumerian, Akkadian, Babylonian, and Old Persian

How do we know what these signs mean? Our understanding of cuneiform is relatively recent, with pioneering deciphering work beginning from 1838 (CE) onwards [Friberg/1984]. But our understanding of Mesopotamian mathematics is burdened by how we came to this understanding. Before 1850, the major investigators were Edward Hincks, Henry Rawlinson, and Jules Oppert, who collectively deciphered the language working off the tri-lingual Behistun Inscription (see section below). From the 1850s onward, the focus was on deciphering specific tablet finds. The first set of tablets discovered pre-1945 were very different from the ones from 1945-1951 (Susa tablets). The investigators of the first set of tablets were either philologists (language studyiers, Abraham Sachs, Goetze) or mathematicians (Neugebauer, Thureau-Dangin) but rarely both. Neugebauer was the closest to both, and he, as well as others, fell victim to using modern symbolism, and interpreting Babylonian discussions in an modern, even pre-modern context. By the time the next set of data had come in, there had been several decades and multiple secondary sources telling the story that Babylonian mathematics was the antecedant of the Greek mathematics, and that Babylon was the origin of the stream that fed the rest of Western Mathematics. Thus, in terms of what is known about Babylonian mathematics, one should disregard all that was thought to be known up to the 80s, and certainly the received knowledge that is in textbooks and histories even through the 2010s. The new knowledge began in the 1970s from a revised look by Marvin Powell and Joran Friberg at existing works, and by Denise Schmandt-Besserat at archaeological findings. All three showed that Mesopotamian mathematics needed to be seen in historical development. [Hoyrup/1991b: 27]. The new knowledge from the 1980s is not only from new sources, corrected transliterations, and better translation/interpretation (e.g. Hoyrup’s conformal translations), but also new information about cultural context (scribal roles, social/economic/political/military trends, use of clay tokens, and location of finds — i.e. exercise books, teacher training (e.g. Susa tablets), scrapheap (exams/discards), problem sets with abbreviated solutions for instructors. These insights were contributed by Hans Nissen, Robert Englund, Peter Damerow, Jens Hoyrup, Joran Friberg, and Marvin Powell, who, amongst others, were part of the Berlin Workshop on Concept Development in Babylonian Mathematics. [Hoyrup/1991b]

Behistun: from Herodotus to Old Persian to Babylonian Akkadian
The trilingual Behistun Inscription is to cuneiform writing what the rosetta stone (discovered 1799) is for the understanding of Egyptian hieroglyphics. The Inscription was engraved into the face of sheer cliffs near the ancient crossroads of Behistun (Kermanshah province of Iran) by the Achaemenid (Persian) king Darius the Great (Darius I) in 550 BCE. Its message proclaiming his conquest of all the lands and his right to rule, was intended for the entire Near East, and so was written in the three major cuneiform languages of his day: Old Persian (his own language), Elamite (the language of Susa), and Babylonian Akkadian (the semetic language understood across Assyria and Mesopotamia). All three languages had died even by 400 BCE and over the millenia fanciful suggestions were put forth as to what the inscription signified. Additional background on the Behistun Inscription (2017)

In 1802, Grotefend had deciphered ten of the 37 symbols of Old Persion. Sir Henry Rawlinson started in 1835 using Grotefend’s efforts. He found the first part of the Inscription contained the same list of Persian kings as given in Herodotus (400 BCE) but in their Persian forms. By 1838 Rawlinson had succeeded, in part due to the fact that Old Persian used an efficient syllabic representation of 37 characters. In 1844 and 1847 he studied the Babylonian section. Edwin Norris, a colleague, completed the study of the Elamite section by 1855. By 1855 [Rawlinson/1855] and Norris with a few others (Hincks 1854) had deciphered all three cuneiform sections: Old Persian (37 characters), Elamite (131 characters) and Babylonian (500 characters, more than 10x the number for syllabic Old Persian). The decipherment of Akkadian and Sumerian (Cathcart, 2011 paper)

From Old Persian to Babylonian to Akkadian to Sumerian
Behistun provided the key to Babylonian through Old Persian, which is accessible through Middle and Modern Persian (Farsi). Babylonian (and Assyrian) Akkadian are derivative dialects of an older Semetic language Akkadian. Their decipherment was completed by Hincks, Rawlinson, and Oppert in the mid 1800s, and from 1956 through 2011, the 26-volume Akkadian dictionary was compiled by University of Chicago (freely available online). To get to Sumerian we needed to rely on Sumero-Akkadian bilingual texts, and fortunately there are many, primarily the sign lists written by the early scribes that lived during the time of the transition from Sumerian city states to the Akkadian Empire, after Sargon unified the Sumerian city states under his rule. History of Akkadian (2003)

Deciphering proto-cuneiform (pictographs) from Sumerian cuneiform

Deciphering an unknown but syllabic written language is hard. Deciphering the meaning of pictographs is harder still. To get to the meaning of the proto-literate writings it has taken the efforts of the Berlin group, a cross-disciplinary group of researchers who have used computer aided digitization of dozens of fragments to complete the work begun in 1936 by Adam Falkenstein who first published the Archaic Texts of Uruk (ATU).

Nissen 1986 (p.317) explains: even in 1936 it was recognized that a few texts were lists. Later more lists were discovered. And it was noticed that these proto-cuneiform lists corresponded word for word, position for position with the same lists almost 600 years later which were written in Sumerian cuneiform which by this time we did understand.

Let us now leave 3,200 BCE, the dawn of writing and move back further into the previous period, when the mathematics was developed that the scribes of Uruk and Susa would later capture.

2. Mathematical practice in the transition between Neolithic to Chalcolithic (Ubaid period): evidence from 8,000 BCE

Tokens of the kind associated with the start of tablet accounting are found in Neolithic settlements across the Near East dating back through 8000-7000 BCE. Between 6,000 BCE and 4,000 BCE (8000 to 6,000 years ago) there is evidence of (1) painted pottery showing elaborate designs using sophisticated symmetries, and (2) layout of prestige buildings (eg temples, shrines) showing architectural competency in geometric design (rectangles with proper corners suggesting knowledge of 3:4:5 or 5:12:13 ratios) and use of moulded bricks (standardized dimensions per site, but not across time).

Anthropological context
The formation of settled society occurred from 12,000 to 10,000 BCE, with evidence for the deliberate cultivation of crops occurring c.9,000 BCE. This coincides with the time after the last ice-age receded from the Near East (c.12,000 BCE). Early Neolithic settlements were small, without walls, whose residents combined cultivation of crops and management of domestic livestock (primarily sheep and goats) within a largely egalitarian social structure. [Charvat/2002]

By c.6000 BCE, we see a clear shift into the transitional Neolithic-Chalcolithic Ubaid period culture, with larger settlement sizes, semi-permanent dwellings, further specialization in crafts, and emerging evidence of hierarchical social status. [Charvat/2002] The results were quite remarkable and are part of the documented acceleration in Neolithic cultural sophistication. [Charvat/2002] (See Appendix 6 for more details on what life was like then.)

This was a time of practitioner level mathematical knowledge, what Hoyrup describes as sub-scientific, learned “on the job”, in terms of procedures, in apprenticeship arangements. [Hoyrup/1988], [Hoyrup/1989], [Hoyrup/1994]. Evidence for sub-scientific, practitioner level mathematical understanding can be found in the artifacts of Neolithic life: designs in pottery showing geometric regularity and the exploration of geometric patterns; building layouts showing an understanding of form, symmetry, composition; an understanding of seasonal regularity and calendarized activities: migration, planting, harvesting, all of which required reasonable mastery of the solar calendar (without which seasonal regularity is impossible); and number, which is required in cooperative behaviour: equitable distribution gains from hunt or harvest, planning for the retention of sufficient seed for sowing next season’s crop, and trade/exchange across increasingly longer distances. All of these have socio-anthropological-archaeological evidence in the period between 8000-4000 BCE. We may thus pull backwards the date of the development of mathematical understanding to this period from c.9,000 to 6,000 BCE, i.e. from the period of the deliberate cultivation of crops and management of small livestock (sheep, goas) to the period of sophisticated Neolithic practitioner technology within larger permanent settlements with longer distance trade and hierarchical organization.

Let’s look at each:

(1) painted pottery dating from 6,000-4,000 BCE show designs that use complex mathematical symmetries, and rotational frieze patterns, providing evidence for strong geometrical stylisation [RobsonSelin/2000].

Hassuna culture: painted and applique designs on pottery from the Yarimtepe I site (in Iran):

Samarran culture: Pottery from Samarra from 6000 BCE-4000 BCE show confidence in geometrical form:

In the photo below of the Samarra Bowl (c.4000 BCE), we see:

“Four stylised herons catch fish in their mouths while eight fish circle round them. An outer band of stepped lines moves outwards, countering the swirling effect of the animal figures.” [RobsonSelin/2000]

(2) analysis of nine successive temple layouts at Eridu (first Sumerian city mentioned in the King List) from Temples XVII c.5750 BCE through Temple VI, and comparison to other Ubaid period sites (6,500 BCE – 3800 BCE) show an architectural discipline in which prestige and communical buildings began to be laid out with increasing sophistication resulting in the use of modules with dimensions suggesting the use of a standardized length measure (Ubaid cubit of 0.72cm) as well as knowledge of side ratios of right triangles (3:4:5, and 5:12:13). [Kubba/1990], [Forest/1991] makes similar findings at Tell Hammam et-Turkman, Soudipour/2007.

In addition to geometry, there appears to be some significant master builder experience involved even in the choice of orientation of the temple layout to maximze sunlight. From the earliest temple site (Temple XVII), all the buildings have a fixed orientation with corners at compass points N,E,S,W, creating a northwest-southeast axis.

“The fact that buildings were built in such a way that their corners were made to face the central axis indicates an excellent knowledge of climatic matters. When the corners of the building face the north-south axis, the four sides of the building receive maximum sunlight, the northeastern and south eastern wall receive the sunlight until midday and the northwestern and the southwestern walls receive the sunlight after midday. Thus, all four sides of the building receive sunlight daily” (Youkana, 1997: 63)”

Why have complex temple building activities not yielded written mathematical evidence?
Essentially, it is due to what could be considered guilds in the early society. The guild of master builders had their own domain knowledge. The guild of temple administrators (SANGA) and chief administrators of a city (EN) had their own domain knowledge, essentially that of a quartermaster (senior individual supervising stores and distributing supplies and equipment) crossed with bookkeeper/accountant (recording of financial transations, including purchases, sales, receipts, payments). The invention of written mathematics was in the guild of the quatermaster/bookkeeper in the context of running an increasingly complex temple economy. The builders had no such practical pressure/problem for which written mathematics was needed.
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Jens Hoyrup explains: “Temple building must have involved a fair measure of practical geometrical knowledge, but evidence from later times suggests that this knowledge was the posession of master builders and did not communicate with the mathematics of the literate managers.” (Hoyrup/2011 p.4)

Sophisticated naive geometrical knowledge and its associated geometrical algebra appears more or less fully clothed in scribal mathematics at the end of the Ur III period in the northern periphery of the Ur III empire (Eshnunna, c.2030 BCE) leading eventually to the sophisticated Old Babylonian mathematics that Neugebauer was able to decipher. [Hoyrup/1985], [Hoyrup/1990], [Hoyrup/1993], [Hoyrup/1996], [Hoyrup/2002]. The traditional practitioner, guild-level knowledge of geometry understood by the master builders and field surveyors (rope stretchers) appears to have remained unchanged through to Islamic mathematics when al-Khwarizmi documented it as the science of the al-jebr guild, in his masterwork “Algebra”, through which this knowledge made its way to medieval Europe, persisting still in its naive geometrical form until the 1500s (Pacioli), finally dying in the work of Viete who transformed algebra into a symbolical instead of rhetorical discipline in the 1590s. [Hoyrup/1994] When was it discovered? Again, we can give no firm date, but we can give a range, from 6,000 BCE during the extensive temple building and agricultural organization of larger settlements during the Ubaid period, through to 2,030 BCE when it first appears in the written record.

The interaction between culture and mathematical development

By the end of the Ubaid and at the start of the Uruk period, settlements were for the first time able to generate significant food surpluses through centralized management of labor resources directed to building large-scale irrigation systems to improve food output. The resulting economic and social changes, the transition from settlements to city-states, the rise of an established urban elite, and the shift to a redestributive, centrally controlled temple-economy drove the use of tokens as accounting devices, as we have seen above. [Charvat/2002], [Niemi/2016]

In this and the previous period, what we have seen is that mathematical practice has arisen within a social context. It has been developed (invented?) and perfected within that social context for an application with a social purpose (accounting, recording of commercial transactions, state management of labor and food surpluses, design of prestige buildings, or the manufacture of status goods). Through its use, mathematics then affects and in many cases transforms the culture it arises within, and shifts it in new directions, which in turn affect the direction of further mathematical practice. See [Hoyrup/1991] and [Robson/2008] for examples of how the culture of the scribal schools varied from Uruk to Akkad to Ur to Hammurabi‘s Babylon to the fall of Babylon, a period covering 1500 years.

By this time, the essential concepts for mathematics are present in the archaeological evidence: counting (using tokens for tracking quantities of sheep, goats, male, female, kids), keeping time (migration of animals being hunted, transhumance behaviour, right times for sowing and reaping), shape and symmetry in craft (symmetry present in the bifacial working of Mode 2 stone tools in which both sides are worked to improve the quality of the edge and to produce a blade, symmetry and shape in reed weaving, symmetry and shape in pottery, and in the decorative patterns that adorn it), practical matters of building and measuring (lengths of poles, doorways, size of sleeping areas, circular mud dwellings). Progress into settled life has been through the desire to exert control over subsistence security and to improve the material quality of life. In this context, experience has been gained on how to do things efficiently, and on the underlying methods for this control. Sufficient agricultural surplus allow practitioners to specialize and refine their craft and develop the technologies they use. All these practitioner level knowledge are attested to in the archaeological records of the Neolithic Near East.

3. Exploring tthe Paleolith: limitations of direct archaeological evidence, and a look at controversial claims dating mathematical practice to 70,000 BCE.

Before 10,000 BCE, there are a few isolated finds with controversial mathematical or calendrical interpretations, but nothing convincing. For example, we exclude the Ishango, Lebombo, and Wolf bones, and exclude also the engraved ochre from Blombos Cave. The argument for their mathematical nature (Marschak) is based on close reading of their markings and association with tallies, prime number groupings, or calendric tabulation. But the notches on the bones (for example) could have non-mathematical hypotheses, e.g. to improve their grip for use as a tool or weapon. These finds do not pass Newton’s test (1713) against speculation: “Hypothesis non fingo” meaning “[I am certain if] I need feign no hypotheses!” [Walsh/2010].

Can we find direct evidence of mathematical practice in the Paleolithic before humanity became settled?

There are two problems with older archaeological evidence: the first problem is that many materials that may have been part of mathematical practice are bio-degradable and would not have survived (e.g. markings on sand with a stick, tallies on wood). Those that could survive (pebbles, bones) lack any cultural context to confirm mathematical usage. For example: notches on bones could suggest tallying, arithmetic, an understanding of prime numbers, or pre-historic calendar cf. [Marshack/1971]. But they could equally well be explained by non-mathematical intent, e.g. to improve the grip of the object used as a hammer or club [Elkins/1996].

The second problem is that the paeleolithic finds are isolated geographically (Ishango bone in Uganda, Lebombo bone in Swaziland, and Wolf bone in the Czech Republic) and in time (dated between 18,000 and 35,000 BCE). There is little to no archaeological context of the finds that would suggest mathematical intention, which therefore relies entirely on interpretation of marks which remain tenuous and highly controversial (cf. Claim [Marschack/1971] and rebuttal [Elkins/1996]; Claim [Huylebrouke/1996], and rebuttal [Keller/2010]).

Similar problems beset the interpretation of an engraved red ochre lump from S.Africa dated to c.70,000 BCE. Suggestions of geometric decoration are hard to conclude without repetition or other context. They could also have been attempts at cleaning the point of a blade, or use as a cutting board, or scrapings to release coloured powder from the ochre for pigment dye.

These are the circumstances surrounding all paleolithic artifacts discovered so far to which a mathematical culture has been ascribed. We simply do not have enough archaeological context on why or what they were carved for in order to interpret them. Unfortunately, speculative interpretations have made their way into news media and non-specialist literature covering ethno-mathematics and, regrettably, even into textbooks on mathematics history. The interpretations have ranged from lunar calendars and fertility tallies, to multiplication tables and prime number lists. As an example, textbook historian David Burton follows Marshack and represents a current enthusiastic popularization when he writes of the Ishango bone: “It had been used for reckoning time “in sequences of numbers that agree with the number of days included in successive phases of the moon.” [Burton/1982] [Burton/1982], [Huyle/1996], [PletserHuyle/1999].

More critical recent scholarship has drawn important cautions: [Elkins/1996] takes apart Marshack’s microscopic readings of notched bone and highlights the repeated unjustified leaps in going from evidence to conclusion. [Keller/2010] summarizes:

“The siren song of mathematical illusion is never far away when it comes to prehistoric artifacts. A notch may be nothing more than a mark [unless] one is obsessed with arithmetic [in which case the sign joins] the common denominator of all the ethnographic artifacts of this kind [showing] item by item [bijective] symmetry between objects and signs. Faced with the raw artifacts of prehistory, it is impossible to know … whether the markings are decorative or not, and if they are not, whether we are dealing with an artificial memory system.” (Keller/2010)

4. Re-examining the Paleolithic for indirect evidence of symbolical capability in humans from 315,000 years ago

We have seen that all the conceptual precursors for mathematics are directly present in the archaeological record by 6,000 BCE (end of Section 2 above). How far back can we trace them? We have seen in Section 3 that we don’t have high enough artifact density to categorically assert their presence. So we turn now to consider the indirect evidence which we do have to support the claim that capability for mathematical thinking (number, shape, time, change) were present in the Paleolithic culture of anatomically modern humans, i.e. from 315kya.

As early as 230kya, the archaeological record (Omo 1 site in the Ethiopian side of the Rift Valley) shows changes in human species as anatomically modern humans (H. sapiens) diverged from Homo Erectus. New finds in Morocco (Jebel Irhoud site), push this date back to 315kya (though some contest whether the latest finds are H. Sapiens). Evidence of complex behaviour (ritual burial of the dead, cooperative hunting, the controlled use of fire, language capability) suggests the capacity for symbolical thinking that would be a prerequisite for any sort of mathematical practice (counting, bijection, keeping a tally, measuring, symmetry, or abstract artistic design).

In light of the previous section, we do not currently have direct conclusive evidence of mathematical practice from before 10,000 BCE. But if we modify the question to inquire when humanity developed the symbolic capability to support numeracy, then we can go back further to 315,000 years ago (note this is the last 9% of human presence on earth, which stretches back 3.5 million years).

Archaeological evidence shows that intelligence, communication, and social living stretch back to 315,000 years ago (Middle Pleistocene), when humans had already evolved into what is essentially their modern form, Homo Sapiens, and were using speech, tools, fire for warmth and cooking, were hunting large adult animals, and had diversified into all of the major races. By the time of the fourth glacial advance 100,000 years ago (Upper Pleistocene), anatomically modern humans (H. Sapiens) dressed and sewed skins, were able to live beyond the frost line, had a culture of arts and crafts and a ceremonial society that buried the dead and showed solicitude to the aged and maimed. (See Appendix 4 for details of life in the paleolithic to the start of the neolithic.) Presumably, then, there would already have been utility in comparing, for example, the number of men in a hostile encampment with those in the home group, and in communicating this numerical information for group action. Similarly, a builder or toolmaker needing material for a particular purpose would have needed to specify dimensions, even if roughly. An elder needing to know how long a hunting party had been absent before setting off to investigate would have needed to mark time.

Until early in the current century, the prevailing opinion was that humankind developed symbolic capability between 50,000 year ago and 315,000, coincident with the emergence of anatomically modern humans (H. Sapiens). This was based on:
(1) the discovery of the earliest human art (cave paintings, jewelry/decorative power),
(2) anthropological evidence of ritual burial of the dead,
(3) anthropological evidence of cooperative hunting which presumes the ability to communicate intentionally and with precision,
(4) the practice of language, indicated by earliest presence of the human version of the FOXP2 gene which regulates learning and complex speech, combined with the assumption that (a) the ability to speak implies that speech and language occurred, and (b) that any language, no matter how primitive, must be symbolic and include at least a rudimentary number concept (e.g. one-two-many, or even one-many). The correctness of this last assumption was justified by the evidence of all known primitive languages encountered before the 1970s) (cf. [Conant/1897], [Smith/Ginsburg/1937] and [Gullberg/1997])

These views have changed in the past 20 years following extensive analysis and study of the Piraha people of the Brazilian Amazon discovered by Western sociologists and anthropologists in the 1970s, whose language surprisingly has no numerical concepts at all [Piraha/2006]. The Piraha (both the people and their language) provide observational evidence that there can exist a state of being in which symbolic capability is present but numerical capability in language and culture does not result. [C.Everett/2016] [DL.Everett/2018]

Language and the Number Concept

Speech had previously been viewed as a proxy indicator of numeracy, since before the Piraha every language and culture previously known had numeric concepts. [Conant/1896]: “We know of no language in which the suggestion of number does not appear, and we must admit that the words which give expression to the number sense would be among the early words to be formed in any language.” The unusual language and culture of the Piraha people has no numbers, not even the “one”-“two”-“many” pattern found in other primitive languages. They become the first known counter-example, in the process changing our view of what language is and how it may have evolved. [SG/1937], [Piraha/2006], [Piraha/2007], [Gordon/2004], [FEFG/2008], [EM/2012]

Studies of the Piraha suggest that numerical capability appears to require three things: (1) the capability for symbolic thought (e.g. grasping the notion of bijection, which underpins discrete comparison); (2) a mechanism to keep the count (e.g. fingers, marks/notches, pebbles, or linguistic counting words), and, taken for granted before the Piraha, and, most importantly perhaps, (3) a culture that assigns value to planning, forethought, and material acquisition, all of which are supported by numeracy. The Piraha culture rejects planning, forethought, and is non-materialistic to the extreme, resulting in placing no value for number in their culture. As a result, not only have they not developed any mechanisms for counting, but they actively resist the learning and retention of these mechanisms when they are introduced to them, despite being able learners of other things [Gordon/2004], [Frank, DL.Everett/2008], [C.Everett/2016].

This places the development of mathematical practice within cultural context once the fundamental neurological ability for symbolical thought exists. While one may indeed grasp the notion of bijection, without a mechanism to keep a precise tally one cannot actually count, only match. How the tally itself is made is less important and can take many forms: visually by using fingers of the hands or creating marks or notches, physically by collecting pebbles or other tokens or calculi, or linguistically using by words and/or signs. But without valuing the act/outcome of counting/accounting/planning, the Piraha example shows that humans essentially fall back on what appears to be a biologically innate analogue number sense that is also present in animals, birds,¹ and even some reptiles, but which decreases in precision as magnitudes get larger. This is why animal counting degrades quickly beyond four or five. [Gordon/2004] [Everett/2012], [Dehaene/1997] Note the 2024 results in carrion crows (May 2024, Scientific American).

The evidence for speech

What evidence exists for speech? Genomic investigations into speech defects have identified the FOXP2 gene as a critical link to and enabling factor of speech control. Absence leads to non-viability, reduction leads to significant vocal disability. While the FOXP2 gene is expressed in birds, mice, primates, and humans, the human variation is different from all the others. The modern functioning version has been present in humans between 120,000-260,000 years ago, either the last common ancestor of Neanderthals and Homo sapiens, or specific to Homo sapiens. And so we form the basis of the argument: the capability for complex vocalization means the ability to realize speech and language. From language comes symbolism. Within a culture that valued planning, control, and materialism, the number concept can develop. All of the pieces for were therefore in place by 230,000 years ago (FOXP2 gene by 260,000 years ago, evidence of social/cooperative living by 315,000 years ago). (Origin of speech)

5. Paleo-anthropological evidence from 2.3 million years ago and the semiotic model of human conceptual development

The earliest known stone tool fossils are from the Lomekwi3 in W. Turkana (Kenya) dating back 3.3 mya. These stone tools are mostly single strike flakes taken from large cores that were rotated before striking. Their dating makes them interesting as there were no Homo species at the time, and it is suspected that perhaps Kenyanthropus are the knappers. [Harmand/2015] However, the most interesting find is the next one, artifacts from Lokalalei, Kenya (in the same Turkana region) from 2.3mya (1 million years later) which show the emergence of sophisticated stone knapping techniques among the early hominids there. [Delagnes,Roche/2005] By now it could be Homo Erectus, or continue to be Kenyanthropus or AAustralopithecus. If these were the simple split-stone variety (one strike, one split, use the edges that result), it would not be a surprise since the simpler Oldowan stone tool culture dates already from 2.6mya. What is surprising is that these stone tools from Lokalalei were made using the complex multi-strike techniques for forming blades from a carefully selected blank flint core using a sequence of strikes to create a razor sharp tapered edge. This technique requires considerable experience with how stone shatters as well as advance planning requiring to visualize how the sequence will work to create the tapered edges.

Except for the Lokalalei site, such tools are only found in the fossil record from 1.7mya onward (Acheulean culture), some 600,000 years later.

Looking at C.S Peirce’s semiotic model for conceptual and linguistic development (see below), we have in the Lokalalei stone knapping process two indications of early hominids having reached Stage 3 symbolic behaviour: the considerable planning requirements to shape the blade, and the cultural transmission (teaching) of the technique. This provides a terminus ante quem (latest date) of 2.3 million years ago for abstract symbolic thought.

Using C.S. Peirce’s semiotic progression (index, icon, symbol) for evaluating linguistic and conceptual development.

C.S. Peirce’s semiotic model posits that conceptual and linguistic development pass through 3 stages: physical/index, associated icon, and abstract symbolic (cf. [Everett/2017]). This makes it a useful model for empirically situating any given activity and placing it within the 3 sequential states.

Index conditioning (Stage 1) is the ability of creatures with a nervous system to perceive an “index” (physical stimulus) and produce an appropriate response (e.g. recoil from a hiss, be wary of yellow and black insects, recognize footprints or smells). This capability gives intelligent animals and humans have the ability to recognize and respond to sounds (bell, word, clap, sound of water suggesting presence of water) or visual cues (hand signal, position of ears, baring of teeth, etc.) or any of the other senses. Both the perception of stimulus and the pathways for response are biological and neurological. This is what allows a variety of animals, birds, and reptiles to possess a number sense and to perceive shape, time, and change (the cognitive precursors of mathematics). Memory, adaptation, and trained learning are forms of index conditioning.

Icon communication (Stage 2) involves the intentional use of signs (“icons”) chosen because of their close association with the intended physical meaning (e.g. smoke for fire, a figurine for motherhood, a stick drawing for a person, or a footprint or smell for the creature that caused it). Stage 2 is the understanding and use of “icons” which are associations intentionally chosen to represent physical phenomena (e.g. picture of cow, picture of fire, emojis, etc.). The majority of animals have not been found to be able to reach stage 2, with the exception of some primates, but even when they do show the ability to understand icons, they do not show the ability to take these learnings back to their communication with each other.

Symbolic communication (Stage 3) involves the intentional selection of arbitrary signs whose meaning is established by cultural convention (e.g. male/female signs, traffic light colors, arbitrary gestures, tallies, arithmetic signs, numerals, etc.). Stage 3 is the use of abstract symbols, i.e. signs that are purely arbitrary and require establishment by cultural convention in order to interpret. Examples include symbols such as $ or £ or traffic light green for go/red for stop, a heart sign for love, sign language, alphabet, logograms, words/names, and NUMBERS. ²

Over the past 20 years, the fieldwork approach to linguistics has challenged the Chomskian theory of language acquisition in early humans. The importance of the Piraha to theories about prehistoric language development and numeracy is that they provide field evidence that anatomically modern humans have not reached Stage 3 in the semiotic progress, remaining at Stage 2, apparently by cultural choice.

Inferring human capability from the fossil record

The making of effective bladed stone tools for cutting and scraping requires the ability to think abstractly and to conceptualize and foresee the consequence of a certain way of striking the stone to create a certain kind of fracture. When done expertly, the resulting blades are sharper than razors, sharper than surgical knives. Indeed, in the modern era of medicine, before super thin metal blades could be produced, surgical knives were indeed made from expertly knapped flint.

Stone tool-making among early humans is considered to be an aspect of transmitted culture based on the ability to consistently produce such artefacts through broad geographic regions and through time. The first of these cultures, the Oldowan c.2.6 mya produced simple split stones, but already this was enough to show that communal sharing of knowledge had developed in early hominins to enable this method of production to continue unbroken for the next 900,000 years (till 1.7mya). At this point, it was replaced by the improved Acheulean tool-making method of the late Homo Erectus period (1.7 mya). Evidence from [Delagnes,Roche/2005] have shown that similar exceptional stone knapping capability to produce bladed tools were present at the Lokalalei site 2.3 million years ago. This kind of complex stone knapping was highly dangerous as evidence from modern lithic workers attempting to reconstruct the old ways have found out (sharp fragments flying off at high velocity, with the makers wearing no gloves, no shoes, no protective eyewear, no trousers).

The archaeological data and evidence of sophisticated bladed stone tool creation at Lokalalei provides two arguments for humankind reaching Stage 3 symbolic capability at least by 2.3 million years ago, almost 14x earlier than the earliest Chomskian estimates: the capability itself, and the ability to transmit that knowledge.

6. Culture transmission and the cognitive precursors for mathematics in animals: back to 260 million years ago

How early does culture transmission in animals manifest itself? When does the analog perception of number appear in animals? Around 260 million years ago, neurological and biological evolution had progressed to the last common ancestor of birds and mammals, a reptile that shared the brain circuitry of both and which underpins the index/response mechanism that gives an analog number sense (small numbers) to animals, birds, and monitor lizards (reptiles).

Culture transmission and iconic or symbolic association are necessary conditions for mathematical understanding. Cultural transmission in order to teach the understanding and use of complex ideas, tools, or technology. Iconic/symbolic capability to be able to recognize and work with quantity, form, and the perception of change.

The presence of culture (socially transferred knowledge) has been observed in chimpanzees (Oct 2009 study) who share tools and teach tool use (Oct 2016 study).

Adult members of the Piraha tribe use what appears to be a biologically innate analogue number sense that is also present in animals, birds, and even some reptiles. The precision of this number sense decreases as magnitudes get larger, and explains why animal counting accuracy degrades quickly beyond four or five, cf. [Everett/2012], [Dehaene/1997].

Do number sense (but perhaps not measurement or counting per se) and the perception of shape and change (but perhaps not their description or communication) occur outside human species? Investigations have found evidence of number sense in animals (birds, dogs, monkeys, dolphins). Perception of the passage of time, the ability to distinguish one from many (in particular, quantities other than two), and the ability to distinguish shapes from each other, have all been documented in various animals. [Koehler/1950]

“A man was anxious to shoot a crow. To deceive this suspicious bird, the plan was hit upon of sending two men to the watchhouse, one of whom passed on, while the other remained; but the crow counted and kept her distance. The next day three went, and again she perceived that only two retired. In fine, it was found necessary to send five or six men to the watch house to put her out in her calculation. The crow, thinking that this number of men had passed by, lost no time in returning.’ From this he inferred that crows could count up to four.” John Lubbock, _Nature_, Vol. XXXIII. p. 45., from [Conant/1896].

“A nightingale which was said to count up to three. Every day he gave it three mealworms, one at a time. When it had finished one it returned for another, but after the third it knew that the feast was over….” Lichtenberg, _Nature_, Vol. XXXIII. p. 45., from [Conant/1896].

“Dinah, my spaniel, … was overlooking half a dozen of her new-born puppies, which had been removed two or three times from her, and her anxiety was excessive, as she tried to find out if they were all present, or if any were still missing. She kept puzzling and running her eyes over them backwards and forwards, but could not satisfy herself. She evidently had a vague notion of counting, but the figure was too large for her brain.” Galton, _Nature_, Vol. XXXIII. p. 45, from [Conant/1896].

The semiotic perspective highlights that perception and response to indexes (unintentional physical associations) is common to all living things that can think (sense their environment and choose a response).

If we ask when this analogue number sense may have developed in animals, this takes us back much further. Primates go back to 13 million years ago, birds to 150 million years ago, mammals to 220 million years ago, taking us back to the last common ancestor of birds and mammals having the same brain structure, which would have been a stem reptile c.260m years ago. A research paper in 2024 on crows that count concludes a 320 million date for a common ancestor, and presents evidence that this common ancestor would not have had the capability that the crows have, providing a limitation on the level of counting sophistication in the evolutionary progression.

Dating the capability for mathematical cognition then becomes a question of the timeline of intelligent, perceptive life itself. The intelligent tree-dwelling primates of 13 million years ago likely had the mental capacity for cognition of the precursors of mathematics. Are animals able to progress from the lowest rung (indexes) of Peirce’s 3-step evolution to the next rung (icons)? Experiments have shown that animals can proceed from icon to correct decision (this is learning and cataloguing new indexes e.g. Pavlov’s dog, trained monkey, crow), the challenge not yet demonstrated (as far as I am aware) is of an animal taking the stimulus, and picking the right descriptive icon, i.e. classification. Similarly, I am not aware of a non-human animal intentionally adopting a completely arbitrary symbol or sign, whose interpreted meanings need to be established as part of a cultural convention, unless we take animal language to be such an example.

Can we pin an upper time limit to the existence of a brain capable of perceiving number, shape, change, time and responding? Studies have shown that an analog number sense (recognition of numbers smaller than 6 in an analog/imperfect way) exists in mammals (dogs, monkeys), birds (parrots, crows) and even reptiles (monitor lizards, [Pianka/King 2004, Murphy 2019]). Neurological studies have established that in mammals, it is the mammalian neocortex (evolved 220 mya) that is the seat of complex cognitive functions such as sensory perception, spatial reasoning, learning and memory, decision making, motor control, and conceptual thinking. In birds, it is the DVR (dorsal vernicular ridge) that provides neocortical-like functioning. Both the neocortex and the DVR have been found to develop out of the same region in the embryonic brain. This points back to the neurological circuitry of a common ancestor of mammals, birds, and monitor lizards, i.e. a stem reptile (amniote) existing some 260 million years ago.

7. Conclusions

How far back do we have evidence for mathematical practice? What about the cognitive, social, and cultural aspects needed for its cognitive precursors?

We have seen in this article that:

Direct evidence for mathematical knowledge exists from c.6,000 BCE or 8,000 years ago.

Humans developed the capability for abstract thought around 2.3 million ago based on ability to create bladed stone tools requiring multiple precise strikes to a flint core, Lokalalei site evidence. The application of bladed stone tools drove innovation through to 315,000 years ago, by which point the last of the major evolutionary changes leading to anatomically modern humans was complete.

The intrinsic ability to perceive number, size, shape, time, and change trace back beyond humans themselves and into mammals and birds, back some 260 million years ago, to the last common ancestor of mammals and birds.

If we tell the story in the correct order, it looks like this:

1. c.220m years ago the mammalian neocortex, and by 150m years ago the dorsal vernicular ridge (DVR) in birds had evolved, and these are the neurological seats of cognitive recognition the index/response mechanism that underlies the analog number sense (for small numbers) that is documented in mammals and birds. The number sense documented in monitor lizards (reptiles) would push the date further back to a reptilean common ancestor of mammals and birds, a stem reptile, c.260m years ago, sharing the neurological circuitry common to both. In birds, their brains developed further developing what appears to be magnetoreceptors in bird retinas that are sensitive enough to transmit changes in orientation vs. earth’s magnetic field directly to the brain, essentially working like a neurally integrated compass, and allowing long distance migration
2. The extinction event for land dinosaurs which occurred at 66 million years ago (mya) touched off a rapid cooling off period in global temperatures, present in geologic evidence. The disappearance of the dinosaurs led to the proliferation of mammals into the ecological niches vacated by the dinosaurs. Mammals it turns out, had existed since c. 200 mya, but had remained small, mostly nocturnal, and either tree-dwelling or burrowing, to avoid competition with the dominant dinosaurs. From 34 mya to 23 mya the Earth transitioned from a tropical world to modern ecosystems. From 23 mya to 2.6 mya the cooling continued. Primates were already living in trees by 13 million years ago, and hominids had branched off between 7.5 to 5.6 mya. At 2.6 mya, the four ice ages began (Pleistocene period) with the last glacial retreat occurring around 12,000 years ago (12 kya) and the inter-glacial warming period (holocene) beginning 10 kya. [Coon/1996]. See Timeline (PDF) of Early Human Life, from 55mya to 5kya (Tom Conklin, 2009)
3. Around 2.3m years ago, we see in the fossil record (Lokalalei) the first appearance of technologically complex stone knapping tool-making to create blades by early human species, that provide evidence of the progression of human-kind from index/response (shared with animals) to iconic/symbolic thinking.
4. As early as 315,000 years ago, we see in the archaeological record (Omo 1), changes in human species as anatomically modern humans emerge, and we have evidence of complex symbolic behaviour, which in principle could support numeracy.
5. Around 6,000 BCE (8000 years ago) there is evidence of elaborate pottery with mathematical designs, disciplined building layouts showing the use of a standardized length measure and an understanding of principles of geometry including the application of right triangles.
6. By 3,200 BCE (5200 years ago) there is indubitable evidence for mathematical practice in clay tokens and bullae (“envelopes”) in Mesopotamian city states within a centralized temple economy and a scribal-statal context. This is the earliest known system of metrology (counting and measuring), of writing, and of book-keeping (accounting)

But of course, we continue to uncover more about our prehistoric past, so the story of the prehistoric origins of mathematics is undoubtedly not yet complete.

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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 earth³ 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).⁴ 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)⁵, and at extremely high temperatures (10^15 degrees Kelvin).⁶ 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.⁷ 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 formation⁸ 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)⁹, 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.¹⁰

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)

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   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]
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    Geometric Mathematics in the Ubaid Period

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    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)
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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. How do birds migrate long distances? The answer appears to be magnetoreceptors in bird retinas that are sensitive enough to transmit changes in orientation vs. earth’s magnetic field directly to the brain, essentially working like a neurally integrated compass. ↩
2. if we think of language as symbolic, the question is at which stage animals that communicate with each other, do so. ↩
3. 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. ↩
4. 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 ↩
5. 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) ↩
6. Source: 2nd last paragraph of Overview of Lambda-CDM model, or the dark energy/cold dark matter model ↩
7. 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. ↩
8. 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. ↩
9. 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. ↩
10. 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. ↩