Friday, August 28, 2015

The Sothic Cycle, Corrected

The Sothic Cycle, Corrected

by Brendan Bombaci

Copyright 2015
All Rights Reserved
ISBN 978-1-329-51731-8


Sothic Cycle” is the name given to the astrophysical discrepancy between the 365-day ancient Egyptian solar year and the heliacal rising of Sirius. An estimated duration of the cycle (1,461 years) has been used to more accurately date events in ancient Egyptian historical records, but fails to account for (1) the 400-year leap cycles which subtract extra leap days that accumulate as an artifact of leap years being useful only for a solar year of 365.25 days rather than the actual 365.2422 days, as well as (2) the precession of equinoxes, a cycle so-called because it desynchronizes any given constellation on the ecliptic from the spring equinox sunrise by one degree every 72 years (coming full circle in nearly 26,000 years). In this brief article I describe these complications and the mathematics that must be used to correct for the multi-decade error in the Sothic Cycle caused thereby.

Keywords: Sothic Cycle, Sirius, calendar, Egypt, Precession, relative dating, calibration, intercalation, leap year


The Sothic Cycle is a name given to the no longer observable but once confusing desynchronization and resetting of the heliacal rising of the star Sirius (“Sothis” in Greek) with sunrise on the first day of the ancient Egyptian solar year. This was caused by a lack of leap year intercalation. It has been rightly asserted by historians and archaeologists that this cycle caused the numerous discrepancies seen in ancient Egyptian history regarding the start of the solar year, but it is causal only in part. It has been and still is an incomplete application of the cycle to simply multiply the 4 years it takes to acquire a Leap Year day by 365.25 days in order to derive its duration. As such, the cycle has been imprecisely determined to be 1,461 years.  There are two mechanisms that are unaccounted for, one unavoidably astrophysical and the other merely mathematical.


The current school of thought on the Sothic Cycle originated in historian Eduard Meyer’s original 1904 realization about it when researching Egyptian historical records. His idea was soon professionally perpetuated, starting with its uncritically promotional inclusion in an annex of the influential Egyptian history textbook from 1924, “A History of Ancient Egypt, 2nd Ed.,” written by the Rockefeller-funded professor J.H. Breasted of the University of Chicago (Mackey 2003). This annex was titled “Chronological Table of Kings,” and in it Breasted boldly altered known ancient Egyptian historical dates via Meyer’s Sothic Cycle calculation, calling them “astronomically fixed.” His Sothic Cycle calibration method became granted, but criticism of it existed prior to my own. 

Perhaps the earliest criticism, published by Luby (1941), was of the incorrect application of leap year mechanics in this cycle. As such, he calculated the Sothic Cycle duration by dividing 365.2422 days per year by 0.2422 (to obviate both leap years and leap cycles), and was satisfied with the resulting solution of 1,508 years. Rose (1994) later called for a wider acceptance of the idea that Egyptians used a 3-year “triennium” from time to time when the 4-year quadrennium (after which one degree of sky would precess) desynchronized from the actual rising of Sirius. She offers an elaborate but oddly estimated accounting for the discrepancy between the Egyptian 365-day and actual solar year lengths, resulting in a declaration that the Sothic Cycle is actually 1452 years in duration. More recently, it has been suggested that the value used for the current cycle “is not totally exact: the Sothic cycle is not fixed because of the proper motion of the star and the length of [the] Sothic year evolves over time” (Quiles et al. 2013:424, emphasis added). The authors provide no explanation for this statement, however.


The Sothic Cycle Mechanism

The first of the two missing factors in the current value of the Sothic Cycle is the leap cycle (Seidelmann 2005) that Luby corrected for. With his simple math in mind, we don’t need to retroactively remove 3 leap years per every 400 years of the current value (a process that can easily lead to error). In as much, to reveal the actual duration of the cycle, we can begin by resetting it to a value of 1,508 years.  Starting there, we must account for the much more slowly slipped degrees of celestial/solar alignment, caused by the Precession of Equinoxes or “Platonic Great Year” cycle. That cycle, in total, was estimated by the Hebrews to resolve in 25,920 years (Hebra 2003) when it realigns the rise of the sun at the spring equinox with a particular sub-degree of the ecliptic. This number was either (1) approximated to the actual precession duration to be well-rounded for the Babylonian sexagesimal or “base 60” divisional system that our modern timekeeping and navigation systems are based on, or (2) actually quite representative of the precessional duration as it existed then, when the Earth’s axial tilt (the cause for precession) was at a different degree of obliquity.  In as much that 1,508 years divided by the 72 years in one degree of said precession is an extra 20.244 shifted degrees during that time, we must deduce that the cycle actually completes sooner than 1,508 years: 20.244 times the 4.058 years in one degree of properly intercalated Sothic Cycle shift equals 82.15 years. Subtracting this from 1,508 gives a corrected ancient Sothic Cycle duration of 1425.85 years. Recently, however, we have come to recognize with advanced technology that precession takes 25,772 years to complete, so each degree takes 71.6 years rather than 72, meaning that 21.06 extra degrees or 85.467 years would have to be subtracted from the 1,508 year basis, giving a Sothic Cycle duration of 1422.533 years.  Until it is proven that axial tilt changes affect the duration of precession, it may be best to use this latter calculation.  For purposes of dating events within dynasties, the variance is somewhat negligible.

Additional Factors

There has been another critique of the Sothic Cycle which calls into question the original historical dates offered by Censorinus (which the cycle became cross-referenced with), pointing out a lack of historical specificity in astronomical viewing locations, as well as differences in calendrical system nuances between geographically and temporally distanced population groups whose accounts we reference, and even differences in star-shrouding atmospheric haze over the millennia and periodically during extreme weather regimes (O’Mara 2003). It appears that there is a multitude of factors we must consider, outside of celestial mechanics, to derive a veritable astronomical referencing system. An example of some very recent and impressively thorough research, that can easily hit that mark with a future revision including the Sothic Cycle correction, is the Bayesian modeled period-matching of solar, lunar, and Sothic calendars, cross-referenced with radiocarbon dating, performed by Quiles et al. (2013) for the purposes of providing an absolute chronology for the 18th Dynasty. 


Much research continues to use or attempt usage of the currently valued Sothic cycle referencing system as either a result of it being presumed totally verified by the peer review process, and/or a result of there being no better tool for the task. By the data I provide, it becomes obvious that this following leads (1) researchers to depend upon and publish work based on officially granted but actually confounded data, and (2) therefore a vast readership of journals, textbooks, and magazines to a misguided trust in the results. It is now apparent that we must not only realign the historical dates that we do surely know of with this proposed Sothic Cycle correction, but also reevaluate a large number of dates by way of deeper textual research and correlation of it with absolute dating methods used on germane artifacts and features. There is hope yet for justifiably method-skeptical Egyptologists (and for all who aren’t but should be), and for those archaeologists and historians working with other cultures who derive their relative dating from Egyptological work.


Hebra, Alex, Measure for Measure: The Story of Imperial, Metric, and Other Units, The John Hopkins University Press (2003), 53.

Mackey, Damien F., ‘Fall of the Sothic Theory: Egyptian Chronology Revisited,’ Journal of Creation 17, issue 3 (2003), 70-73.

O’Mara, Patrick, ‘Censorinus, The Sothic Cycle, and Calendar Year One in Ancient Egypt: The Epistemological Problem,’ JNES 62, no. 1 (2003), 17-26.

Quiles, A., E. Aubourg, B. Berthier, E. Delque-Količ, G. Pierrat-Bennefois, M.W. Dee, G. Andreu-Lanoë, C. Bronk Ramsey, and C. Moreau, ‘Bayesian Modeling of an Absolute Chronology for Egypt’s 18th Dynasty by Astrophysical and Radiocarbon Methods,’ JoAS 40 (2003), 423-432.

Rose, Lynn E., ‘The Astronomical Evidence for Dating the End of the Middle Kingdom of Ancient Egypt to the Early Second Milennium: A Reassessment,’ JNES 53, no. 4 (1994), 237-261.

Seidelmann, P. Kenneth, ed., Explanatory Supplement to the Astronomical Almanac, University Science Books (U.S. Naval Observatory: Washington, D.C., 2005), 580-581.

Saturday, August 15, 2015

A Horological and Mathematical Defense of Philosophical Pitch

A Horological and Mathematical Defense of Philosophical Pitch

By Brendan Bombaci

All Rights Reserved

Copyright 2013 Lulu Press

ISBN: 978-1-304-36230-8



I propose an alteration of the concert pitch standard outlined in ISO 16.  As of now, it is set to A440 (A=440Hz), which has been chosen subjectively (rather than empirically as based upon the mathematical or geometrical values of art composition), as most all other concert pitch standards have been chosen throughout history.  I have sought out various ways to make a compositionally cogent concert pitch standard, and I have succeeded at finding one that is perfectly tailored to synchronize with both the sexagesimal timekeeping system upon which all music is measured, and the 5 Limit Tuning system.  It is well-known that this form of just intonation is the most consonant of all tuning systems, including that of equal temperament (whether or not equal temperament mostly corrects for the arguably noticeable near-Wolf fifths of just intonation).  In as much, it is perfectly suited to be the model tuning system for this innovative new pitch standard, especially when one considers its fractional values for deriving each note of the chromatic scale.  I will now explain both of my justifications in detail with some corroborative horological references.

Time In

It should be imagined that Western music - with an original meter basis of 4/4 that originally hinged upon the second hand of the clock for metering rhythm (a la the 120bpm Roman standard for marches) even before the second was academically identified [5] - should have a pitch frequency that is similarly correlated.  When tuning music to A440, most of the pitch frequencies are not whole numbers; the first octave of B (B1), for example, is 61.74Hz.  If this were set to 60Hz instead, being the only note of the chromatic scale which comes close to synchronizing with the clock as a fractal continuance of the sexagesimal system, we would find the middle C note, C256, at the “scientific” or “philosophical” pitch of Joseph Sauveur (a mathematician, physicist, and music theorist) [1] and Ernst Chladni [1, 2], “the father of acoustics.”  At the first octave of C, we would have the value of 1Hz, perfectly matching the second hand complication (movement).

Using 5 Limit Tuning set to C256, the frequencies of notes C4 (256), G4 (384), E4 (320), D4 (288), and B4 (240) are reducible to, respectively: 1, 3, 5, 9, and 15.  You may notice that these notes, C, E, G, B, and D respectively, rearrange to a set of “stacking thirds,” in perfect chordal harmony.  With the lowest C also standing in for its multiples of 2, 4, 8, 16, and 32, all of the numbers which are member to that set of stacking thirds are the very same numbers which comprise the numerators and denominators by which every chromatic note is derived from unison (except 45, but this is still a harmonic of 15).  This makes for more mellifluous tonal vibrations.  In addition, the numbers 1, 2, 3, 4 and 5 represent the most commonly used values for meter in classical and modern music (with the 3 also standing in for its multiple of 6).  There are also important historical implications to this system, making it more geometrically and even astronomically intrinsic.

The helek (helakim, pl.) is an ancient and still used unit of time in Hebrew horology [3], from which the second of modern global timekeeping was extrapolated.  Further preceding helakim were units of the same duration but with the Babylonian names barleycorn or she, but, no matter which name is used, all effectively mark the passage of 1/72nd of one degree of celestial rotation in a day.  There are 1080 helakim per hour, and therefore 25920 helakim per day, which, in total, represent the number of years in one astronomical Precession of the Equinoxes.  This gives a discrete measurement unit that relates each “moment” to a visibly interesting astronomical cycle that has captured the imaginations of many cultures worldwide.  Half of a day is akin to half of a precession of equinoxes, thereby; and likewise, periods of 2160 helakim are similar to the 2160 years of one astrological Age, meaning there are 12 Signs that pass in one day.  Many historical European clocktowers, such as the Torre dell’Orologio in Venice, graphically purvey this along with the 24 hour segments.  The conversion between helakim and seconds is this: 1 helakim = 3.333 seconds, or 18 helakim = 60 seconds.  72 helakim, like the 72 years that pass in one of 360 degree of celestial precession, are equal to 4 minutes.  4 minutes multiplied by the whole 360 degrees equals 1440, the amount of minutes in one day.   This is also the frequency in Hertz of the F# (the 7th interval, or perfect chromatic center) when the chromatic scale is tuned with the Philosophical Pitch and 5-Limit Tuning System. 

Making the transition from helakim to seconds would only be a matter of deciding that the sexagesimal “navigational” system should also be standard for the measurement of time, for better precision.  Musicians of the Middle Ages would have noticed that the twelve divisional factors of that system (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60) are attractively coherent with four of the five stacking thirds frequencies of the new 5 Limit Tuning system which was designed to fix Pythagorean tuning dissonance in thirds intervals.  With the addition of the fifth stacking third (9/18/36hz, etc.: the 2nd interval D note), they altogether cross-correlate with all aforementioned time measurement references within the Precession of Equinoxes, paying ultimate homage to the more prolific origins of timekeeping (remember: 18 helakim per 60 seconds). 

On a more esoteric note, the contemporary system also corresponds in some cases to culturally relevant “sacred” geometrical figures, whether or not any ancient musicians played note values that represented the same cosmic motions their timing system held to.  Some of the latter include the conversions: 1440/3.333 = 432.0432 (a value considered by some to be the “spiritually” correct concert pitch), 216/3.333 = 54.054 (1/8th of the latter value, and the number of years in one Exeligmos or Triple Saros eclipse prediction cycle that the Greeks discovered), 360/3.333 = 108.0108 (1/4th of the first value, and a number of great importance in Buddhist and Hindu tradition), and 240 / 3.333 = 72.072 (the number of years in one degree of equinox precession, and the “tetragrammaton” value given to the Hebrew name for Christ  -YHWH).  No less, the latter two solution values are the same as the degrees of key angles within a pentagram that reference the phi ratio and Fibonacci sequence (a fundamentally common pattern which all biological matter utilizes for efficient growth, and one that has been venerated throughout history via great artworks), and the faces of the dodecahedral (soccer ball shaped) Cosmic Microwave Background itself [4] that shows how our cosmos expanded from the Big Bang.  Interesting as they are, these solution values are not the note values we should make standard in our chromatic tuning system, but rather intriguing sign posts that show the astro-horological bases for certain compositional conventions in both secular and religious visual (including architectural) and sonic art.

For the sake of remaining true to horology in sonic form, harking back to but making better sense than the “Music of the Spheres,” the usefulness and the intricate aesthetics of tuning to C256 is inarguably better than any other standard.  It also becomes far more intuitive to explain, due to whole number relationships, how various notes interact with one another and with tempo bases.  Any “brighter” compositional sound, such as desired by proponents of A440, can be manifested by simply transposing a song.  Although utilizing this proposed standard alters interval relationships (because just intonation is not equally tempered), it offers a new way to experience music, with the same revolutionary impact that modes within a key provided for mood and depth when choral music was innovated.  Now, slight dissonances will be heard in a number of modes stemming from any key.  Many Western composers prefer this and use just intonation specifically to achieve enhanced dramatic effect; some people who do so are: John Luther Adams, Glenn Branca, Martin Bresnick, Wendy Carlos, Lawrence Chandler, Tony Conrad, Fabio Costa, Stuart Dempster, David B. Doty, Arnold Dreyblatt, Kyle Gann, Kraig Grady, Lou Harrison, Michael Harrison, Ben Johnston, Elodie Lauten, György Ligeti, Douglas Leedy, Pauline Oliveros, Harry Partch, Robert Rich, Terry Riley, Marc Sabat, Wolfgang von Schweinitz, Adam Silverman, James Tenney, Michael Waller, Daniel James Wolf, and La Monte Young.  Perhaps, with the rationality I provide in this article, many more yet will.


1.  Bruce Haynes. History of Performing Pitch: The Story of “A,” pp 42,53 (Lanham, Maryland: Scarecrow Press, 2002).

2.  Ernst Florens Friedrich Chladni.  Traitéd’acoustique, pp 363 (Paris, France: Chez Courcier, 1809)

3.  Hebra, Alex.  Measure for Measure: The Story of Imperial, Metric, and Other Units, pp 53 (The John Hopkins University Press, 2003)

4.  Luminet, Jean-Pierre, Jeffrey R. Weeks, Alain Riazuelo, Roland Lehoucq, and Jean-Phillipe Uzan.  Dodecahedral Space Typology as an Explanation for Weak Wide-Angle Temperature Correlations in the Cosmic Microwave Background.  Nature 425:593-595.

5.  Sachau, Edward C.  The Chronology of Ancient Nations. (Kessinger Publishing, 2004). 

Friday, August 14, 2015

Symbolic Thought in Neandertals: A Preponderance of Evidence

Symbolic Thought in Neandertals:
A Preponderance of Evidence

By Brendan Bombaci

This work is licensed under a
Creative Commons Attribution 4.0 International License.
ISBN: 978-312-15922-8


There has long been a debate as to whether Neandertals have had modern human culture, and thereby symbolic thought.  They are said by many to have shared only the pre-Aurignacian, Mousterian tool industry with Homo sapiens.  The Aurignacian has been considered a more advanced industry with specialized blades, and, found with Homo sapiens, representative of advanced thought.  Recently added to Neandertal repertoire, however, are blades from the Chatelperronian industry and tool kits from others including the Protoaurignacian.  No less, Aurignacian finds, also inclusive of symbolic artifacts (figurines, jewelry, etc.) are not always associated with modern humans, and similar symbolic artifacts have also been found in the Mousterian Neandertal context, one bone flute and 11 redated Spanish cave painting sites, respectively.  Observations of symbolism and intent in primate play, Dunbar’s Social Brain Hypothesis, archaeological evidence of group tactical hunting, and anatomical and genetic characteristics, altogether show a high likelihood that Neandertals had language similar to humans.  Such language is different from primate language in that it is an open call system whereby particular sounds can mean different things in different contexts, and are not solely used for one situation or meaning; it is thereby symbolic.  Although Homo sapiens occupation in England has been pushed back to 42-44ky BP, and in Southeastern Italy to 43-45ky BP, possibly hinting that they culturally influenced Neandertals, I argue that the prevailing evidence suggests Neandertals had cognition on par with modern man and therefore did not die out due to either ill preparation for climate change or defeat by a “better” culture.


Blade technology and symbolism, via inscription, painting, burials, or ornaments, have been the widely proclaimed hallmarks of the Upper Paleolithic and thereby anatomically modern humans, AMH (Roebroeks 2008:919).  There is an apparent technological industry transition between 40-30kya, from the Neandertal-only Middle Paleolithic Mousterian tradition to transitional ones that seem to lead to the Upper Paleolithic Aurignacian (Roebroeks 2008:918).  Many have attributed that industry as only relative to Homo sapiens because of human remains (and tentatively, at the time of their discovery, no Neandertal remains) associated to a small portion of myriad Aurignacian contexts and because the transition period marks the gradual decline of Neandertal habitation sites.  Some say this evidently suggests that Homo sapiens ousted Neandertals with a more-advanced cognitive power (Wolpoff et al. 2004).
However, there is now evidence from two sites in France that a special blade tool was being manufactured by supposedly “Middle Paleolithic” Chatelperronian Neandertals (Straus 2005:55).  Decorations have been found on Chatelperronian bone awls, a type of tool which is implicitly associated with intensive planning (for time-consuming tailoring, e.g.), both aspects suggesting that “far from being an intrusive behavior, poorly assimilated and limited to a few bartered objects, symbolism permeates all aspects of Chatelperronian life” (Wolfpoff et al. 2004:537).  Due to its specialized style, the Chatelperronian has been argued to be a tool industry with no relation to Cro-Magnons at all and (Roussel 2013).  Due to modern redating methods, and reviews of recognizable mixed industry variances in tool types between assemblages, including those with both Mousterian and Upper Paleolithic types, the creation of the Aurignacian complex is in the process of being partially credited to Neandertals in general (Jankovic et al. 2006:461, 463-4).  Indeed, the definition of particular assemblages as representative of certain industries is fallible, as “pattern searches on the commonly accepted archaeological monitors of human adaptation [...] have consistently shown a temporal and spatial mosaic wherever the transition interval is recorded” (Wolpoff 2004:537).  The Bachokirian, Bohunician, and Protoaurignacian are now being tentatively accepted as proxies for Neandertal presence (Roebroeks 2008:923). 
One red quartz Acheulean biface, the likes of which have not been seen anywhere else, found in an apparently ritualistic burial context, could be proof of symbolism as far back as 400kya (Carbonell and Masquera 2006), with the last common ancestor of Homo sapiens and Homo neanderthalensis, that is, Homo heidelbergensis.  That such symbolism would not carry forth with both ancestral lineages is preposterous, but this assertion has been scrutinized.  New archaeological dating evidence (Higham et al. 2010) has determined that there is substantial stratigraphic mixing at Grotte du Renne and therefore that the symbolic artifacts priorly associated to Neandertals there (d’Errico et al. 1998) should now be put under more intense review.  However, the same archaeological team (Higham et al. 2005) also redated the Vindija site specimens to 32kya, and found no such cross-site inferred stratigraphic mixing (Mellars 2010).  This fastens the prior suggestion of Neandertal occupation before anatomically modern humans (AMHs) there and the craftsmanship of Upper Paleolithic (UP) materials found on site and likely elsewhere (Jankovic et al. 2006).  Bone tools found there even have analogues in the “Mousterian” site of Divje Babe, Slovenia (Jankovic et al. 2006:462).
Recent ultrafiltered radiocarbon date retesting of Homo sapiens skeletal remains at Vogelherd place them between 3.9-5ky BP and corroborate that the Aurignacian industry there is not associated to these intrusive bones, suggesting that it was possibly Neandertals (Conard, Grootes, and Smith 2004) who carved the 31-36ky-old stylish mammoth-ivory animal figurines and báton percé that are found at levels IV and V (Conard and Bolus 2003:341).  No less, a 50ky old Mousterian core with artful striations, found in Quneitra (Syria), seemingly sketching the unseen pattern of wave force from a point of percussion, may be an example of an “external information system” (d’Errico et al. 2003:21, 32) for teaching tool manufacture.  Statistical analyses of raptor claw distributions and striations on them have also shown likelihood that Neandertals were using such items for symbolic purposes, at least in Italy and France (Morin and Laroulandie 2012).  If such creations aren’t evidence enough of symbolic Neandertal cognition, perhaps another item from Divje Babe is: the oldest bone flute yet dated and X-ray tomography analyzed (>46ky old) – the only one in Mousterian rather than Aurignacian or later context (Tuniz 2012, Turk et al. 2006).  Nobody can say now that the >42ky old bird bone flute and various human figurines found in Aurignacian context at Geissenklosterle, Germany (Higham et al. 2012) are certainly Homo sapiens creations.
Paul Mellars (2010) displays some apparent bias in favor of the artless Neandertal theory generally and outright accepts the preconception that the Aurignacian is only AMH relative, determined, even, (as is popular) that the Chauvet cave paintings were made by AMHs (Mellars 2006:934).  This is now open for debate due to uranium series redating of paintings in 11 caves in Spain – at Altamira, Tito Bustillo, and El Castillo –  (Pike et al. 2012) that put the ages of seven of them (including bison and horse figures, rectangles and ovals, hand print stencils, and anthropomorphic figures) between 29.7-41.4ky BP, spatially relative to the latest Classic Neandertal occupation at El Sidron Cave nearby (Wood et al. 2013) and temporally relative to southern Iberian sites generally (Blain et al. 2013, Jennings et al. 2011), with the rest of them at a period >5ky later of early modern human occupation of Portugal (Duarte et al. 1999, Trinkaus 2005:210).  This makes it quite possible that the Neandertals in the region shared their artistic ideations and techniques with the oncoming Homo sapiens groups they interbred with.  There is also a Mousterian pigment-dyed seashell find in northern Italy, dated to 47.6 cal ky BP, that may further describe the Neandertal artistic processes (Peresani et al. 2013). 
The Shanidar IV Flower Burial has been reinterpreted from being very ritualistically symbolic (Sommer 1999) to mostly chance (Merlin 2003:300), due to faunalturbation.  Many of the palynologically inferred plant species are medicinal, however, with one specimen found abundantly there, Ephedra, being psychoactive and amphetamine-like.  As this species has been used worldwide for religious and intellectual purposes over millennia (Merlin 2003:300-2), its inclusion may renew the funeral suggestion and offer a new understanding of Neandertal ideations about death and beyond.  Their ignorance of this local plant’s qualities is unlikely, as Neandertals surely tested local flora for edibility and are known to have consumed chamomile (Hardy et al. 2012:620), another bitter and non-nutritive, psychoactive plant (Viola et al. 1995).
Dunbar’s Social Brain Hypothesis works on the well-observed premise that in primates and humans, the total number of neurons and synapses as well as the relation between sizes of specific frontal lobe areas, correlate to social network sizes; and, excluding total neocortex size from this (since optical regions, which are specialized in Neandertals, do not relate to social mentalizing), fossil AMHs could keep track of 139 people and Neandertals could track 114 (Pearce, Stringer, and Dunbar 2013:5).  This is obviously a limit on societal structure depth and breadth, but it is also a near-par range.  Dunbar (2003:176) notes that grooming, vocal chorus bonding, social language development to faciliate large groups, and then grammatical language, were all part and parcel of social brain evolution in hominids.  He has suggested that Neandertals may have only had social language (2003:177) – the third mentioned evolutionary step, but the aforementioned inferred social network sizes from 2013 suggest otherwise.  Archaeological evidence of group tactical hunting (mass assemblages of near-mature reindeer and bison, implying seasonal faunal congregations) at two Late Pleistocene sites, Mauran and Les Pradelles, suggests abstract communication, “active cooperation, and a defined role for everyone: thus, a social organization” (Rendu et al. 2012).  Though the speculation may be dubious, because of possibly simple systematic rejection of juveniles and elders, as well as rough dating resolution, it is still likely that such behavior was necessary to overcome their lack of both anatomical ability to run with any speed comparable to Homo sapiens in such open-air environments (Cartmill and Smith 2009:379-80) and accultured physiological ability to throw spears at any distance (Schmitt and Churchill 2003:104, 106-7, 111-2).
There are also various anatomical and genetic facts that suggest a high likelihood of symbolic Neandertal speech.  Recent primate observations of symbolism in representational play (Lyn, Greenfield, and Savage-Rumbaugh 2006) bolster the notion that even 5mya, our ancestors had symbolic cognitive capacities whether or not ecological constraints could afford them extensive external development of them.  Recent reconstructions of the (Kebara) Neandertal vocal tract show that they had a very modern vowel space, hyoid bone, and low laryngeal positioning (d’Errico et al. 2003:28, Wolpoff et al. 2004:535, Martinez et al. 2008).  Internal and external earbone analyses have shown that early Homo sapiens and Neandertals likely acquired the same exact capacities for language reception from Homo heidelbergensis, as ear bones from the Qafzeh and Amud specimens corroborate by being within the range of human variation (Dediu and Levinson 2013:6).  Their respiratory muscles were similar to modern humans, as inferred by matching thoracic vertebral canals, giving a cortical control which allows for proper breath and volume modulation required for vocal imitation and learning (Dediu and Levinson 2013:6-7).  Genetic sequencing of the Vindija Neandertal has allowed us insight into the fact that Neandertals and modern humans share the same FOXP2 gene involved in speech production and comprehension (Dediu and Levinson 2013:4, Shriberg et al. 2006, Turner et al. 2013), orofacial movements (Krause et al. 2007:1), and probably meaningful gestures (Shriberg et al. 2006) and literacy (Turner et al. 2013).


I must make a few remarks regarding recent revisions on human occupation dates in Europe.  Hublin (2012) notes that mineralogical ash dating techniques in tool deposit contexts have revealed “a series of initial Upper Paleolithic assemblages spread from the Levant (Emirian) to Bulgaria (Bacho-Kirian) and Moravia (Bohunician) [...that] may well document an early episode of modern colonization of [eastern] Europe as old as 50,000y” (Hublin 2012:13472, emphases added).  14C dating of Kent’s Cavern (in 1989) and Oase I specimens (in 2003) originally put the earliest human occupation of Europe at nearly 35kya (Trinkaus 2005:210), however, in 2011, “using a Bayesian analysis of new ultrafiltered bone collagen dates in an ordered stratagraphic sequence,” Higham et al. (2011) provided dates of 44.2-41.5kya for the Kent’s Cavern maxilla, and, Benazzi et al. (2011) reclassified the Grotta del Cavallo teeth from Neandertal to AMH via microtomography and associated a recent Bayesian age model redating of the shell beads on site (45-43kya) to those teeth as well.  So it seems that the human population spread closer to Neandertal territory from the eastern sites, first to Italy and then England, with the latter destination suggesting possible travel through Germany and thereby Vogelherd, casting doubt yet again on the makers and owners of the artifacts there. 
However, the tools from the Levant, Bulgaria, and Moravia are only presumed to be associated with Homo sapiens, based on the now-refutable Danube Corridor hypothesis (Conard, Grootes, and Smith 2004); no skeletal remains are in context.  In 2008, Joris and Street published their view that these technologies are proxies for Neandertal presence (Roebroeks 2008:923).  Also, the Kent’s Cavern maxilla is only relatively dated to “a small selective sample of fauna from an old and poorly executed excavation” (White and Pettitt 2012:392), so should not be thought of as an early representation of AMH occupation in western Europe.  Also, even if it is early, it was only found in context with two Aurignacian blades (Higham et al. 2011:521), so its age is not associated with any truly typological assemblages, let alone uniquely symbolic artifacts.  The Grotta del Cavallo inhabitant would appear to be an exception to this critique, being at the type-site for the Uluzzian industry, but the fact that only deciduous molars were measured, without reference to any other (non-present) teeth or jaw morphology, makes the conclusions highly questionable.  Also, similar beads have not been found amongst other Neandertal sites, which suggests that even if AMH were using such symbols, this type of art either did not get shared with or was not interesting to other Neandertals.  It too implies nothing as of yet.  Especially being that the species on site was apparently making or using Aurignacian-transitional tools, it would not, i.e., discredit slightly earlier Neandertals from association with the Mousterian-context ochered shell in northern Italy.  Finally, Roebroeks (2008:920) highlights difficulties in assuming much about Neandertal technological capacity and ingenuity, since there is a lack of permanent occupation sites likely due to biologically determined, ephemeral central place foraging (instead of long-distance hunting).  


In light of all evidence provided that reveals the most probable reality of Neandertal symbol utilization, it is safe to assume that Neandertals did not die out due to cognitive incompetence amidst an inundation of Homo sapiens, or, therefore, due to inability to culturally adapt to climatic circumstances.  Their cold-adapted bodies (Cartmill and Smith 2009:374-6) worked well enough for them to thrive in the cold let alone in refugia during glaciations (Beeton et al. 2013), undoubtedly including the most recently dramatic snap amplified by two volcanic eruptions in Italy around 40ky BP (Golovanova et al. 2010:680), which Hublin (2012) refers to for the aforementioned mineral ash relative dating of AMH presence in Europe.  A study of ecocultural niche modeling (partially tainted by the assumption that the only tool industries associated to Neandertals are the Mousterian, Chatelperronian, and Bohunician) shows that populations of anatomically modern humans and Neandertals had an inverse relationship in magnitude over spatiotemporal location, suggesting that Neandertals did not disappear due to climate change but due to an influx of AMH in their territory (Banks et al. 2008).  However biased the model, this may be true.  One way that human DNA differs from that of Neandertals is with the gene SPAG17 which codes for the beating of sperm flagellum (Gibbon 2010:684).  If a lack of this gene, or other general issues, caused Neandertals to reproduce less effectively than the Homo sapiens around them – even a 2% difference in mortality would cause their extinction in 30 generations (Roebroeks 2008:924).  But there was no abrupt extinction.  They didn’t really die out at all. 
Neandertal survival into the Upper Paleolithic throughout Europe is becoming more and more recognized by ancient morphological (Rougier et al. 2007, Trinkaus 2005:217-222) and mtDNA mosaics (Zilhao 2006:192), and now modern nuclear DNA (Green et al. 2010) – the latter of which presents a major challenge to determinations of nonexisting Neandertal gene flow in AMH specimens after 30ky BP.  If reproductive success depended upon cognitive similarity between people as it widely does today, with selfish selection for those that do not have any mental inability or disorder, e.g., we can deduce that Neandertals and Homo sapiens were very alike and attracted to each other more than sexually.  This appeals to logic because of how much of a time investment is needed for the cultural admixing and acculturation that must take place during reproduction and the following parental and group cooperation implied by its success.  There are likely very human – symbolic – reasons why Neandertals and Homo sapiens wished to combine legacies, and, just as Neandertals did not genetically perish, modern cultures too are a result of that relationship.


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