Experimental prehistory & various digressions

Infinity Permeates Everything - a futile example with the Fractal Yupana

2024-01-16T21:21:00.004+01:00

Technically, it is not infinity. But practically, it is.

You would waste your whole life if you tried to count all the grains of sand on the nearest beach.

You would return to dust before you can count every individual cell in your body. Not only because you are continuously producing new ones, or because you can't see any of them.

In that sense, you are touching infinity, everywhere around and inside; you are made of "infinity".

So... it shouldn't be that astonishing to also find this kind of "infinity" in one single row of the Fractal Yupana.

Multiply the age of the universe by itself,
and multiply that result by the age of the universe...
and do that again with the lastest result... 10 times !
and then multiply that by 10 billions...

The result, in years, approximately 10 billions Googols (https://en.wikipedia.org/wiki/Googol) years, is the amount of time required to count from 1 to 100, by all the different ways there are to do that, by using a single row of a Fractal Yupana.

(This, assuming a few things, including the speed of your manipulations on a real yupana, taking no rest at all, living 1 Googol times as long as the current age of the universe... at least the universe is set to exist long after that https://www.science.org/content/article/way-universe-ends-not-whimper-bang )

By comparison, there is only 1 way to count from 1 to 100 with a Soroban. So, that would not be a way to appreciate "infinity".

Illustrations for an apparently unsubstantiated claim.

Number of ways you can "write" each number using a single row of the Fractal Yupana.

You can represent every number from 0 and 100 on one single row of a Fractal Yupana. Even though you would not do that, normally, except during multiplications, prefering to represent numbers from 0 to 9 on each row.

Click here for an interactive version

3 followed by 115 zeros... 3 quadrillons of googols !?

That is less than the total number of the different ways to count from 0 to 100 on a single row of a Fractal Yupana.

It is the result of the multiplication of the number of representations of each of the numbers from 0 to 100. That is a multiplication of 101 terms, and it is going to be huge (even though the 3 first ones and the 3 last ones are equal to 1). For instance, you have already 20 numbers that have at least 35 different representations: those from 38 to 57. That only is already greater than 35 multiplied by itself 20 times.

(a quadrillion of googols would be the american name for 10 to the power of 115, according to Encyclopedia Britannica : https://www.britannica.com/topic/large-numbers-1765137)

Comparison with other interpretations of the Yupana.

Let's first show the distribution of the numbers of ways to represent each number on one single row of the yupana. Then we'll compare the total number of ways to count from 0 to the maximum value on 1 row.

Yupana Dinamica / Inka.

You can count from 0 to 39 on a single row of the Yupana Dinamica (assuming, as for the Fractal Yupana, that you put 0 or 1 token on each spot). For instance, 145 is the number of ways to represent 18, same thing for 21.

click here for an interactive version

This may seem very grossly exaggerated. It is due to the fact that we count as being different two different spots in the same column, even though all spots in one column have the same value (example, each of the 5 spots of the 4th column have value 5). But we need (? not really) to do that if we are to compare with the interpretations of the Yupanas that give a different value to each spot.

If we consider as identical all the spots of one column, the number of ways to write a number falls down drastically. For instance, you'll have only 3 ways (5, 3+2, 2+2+1), instead of 12, to represent 5. And instead of 49 ways to represent 10, you'll have only 3 (5+5, 5+3+2, 5+2+2+1).

Yupana Chirinos-Rivera.

You can count from 0 to 66 on a single row of the Chirinos-Rivera's Yupana (assuming, as always, that you put 0 or 1 token on each spot). For instance, 70 is the number of ways you can represent 33.

click here for an interactive version clearer image

Comparison of the total number of ways to count from 0 using a single row.

Orders of Magnitude

115: Fractal Yupana (~ 1 followed by 115 zeroes)

81 : Yupana Chirinos-Rivera (~ 1 followed by 81 zeroes)

54 : Yupana Dinamica / Inka (~ 1 followed by 54 zeroes)

(about orders of magnitude, see https://en.wikipedia.org/wiki/Order_of_magnitude)

"One, two, many" is compatible with accurate calculations - example with a Fractal Yupana

2023-11-21T16:38:00.020+01:00

Some civilizations are said to not have names for quantities/numbers greater than one and two.

You can find interesting considerations about that on "The Number Warrior" blog article: Is one, two, many a myth (see link at the end of this article if you are interested).

note, 2024/3/3 : i just read some articles about "toki pona", an interesting conlang containing (originally) only 120 words, and only 3 words for numbers (wan=1, tu=2, mute=many); and about some efforts by the speakers to try to complete that set with other names, even trying to promote non-base 10 systems in order to keep close to the original set of 3 names for numbers. (If interested, try to read from here: https://sona.pona.la/wiki/Recommended_learning_resources).

Not having names for numbers greater than two doesn't prevent you from having an accurate representation for quantities. For example, you can still express exact quantities like "two and one", "two for each of your fingers", "two groups of two for each of the joints of your body", "two groups of two and one group of two and one", "two and one for each of the fingers of the members of our tribe" (and that's an accurate quantity, at least for an instant, even if you don't know how many members are in your tribe, as long as none of them looses a finger before you finish your sentence).

And not having names for numbers doesn't even prevent you from performing calculations. We are going to show that, with the example of multiplications performed with the Yupana, the (mythical or real) counting board of the Inca civilization. (Ok, the Inca civilization had names for numbers, but it's irrelevant here... as we plan to badly exaggerate with this concept).

note, 2024/3/3 : the previous remarks would not be totally true for "toki pona": it has no word for "fingers", "joints"... So... you can still have accurate mental representations for numbers by mentally using those equivalences; you would just find it hard to express them verbally, but that would not prevent you from expressing them graphically, or physically (with a counting board, or a khipu, or gestures, etc.).

First, there have been various hypotheses and representations for the Yupana and for the way it was used. But the most general representation is a plane counting board with rows and cells permitting to describe numbers in base ten. (All of that resembling a lot to the north European counting boards still in use in the XVII th century... hmm, does that seem suspect ? or is it just obvious ? because there may not be a lot of ways to design and use a counting board with numbers expressed in base 10).

Modern Yupana

Example below: image of a Yupana promoted under the name "Yupana Inka". It is generally used with a common method where the position of a token in one cell has no particular meaning, the number of dots/spots in a cell representing the value of the each of the tokens that will be put in the cell... knowing that each horizontal row represents a power of 10.

(image extracted from researgate.net - see link to the original at the end of this article)

Let's try to use only "one, two" to describe the standard Yupana, as "one, two" is enough to describe any size of "many" (ok, "one" alone is already enough for that, but well, it's easier with "one, two") :

- in each row, cells with "one", "two", "one and two", "one and a pair of twos" dots/spots.

- each token that will be put on the board will have the value of the cell in which it is put.

- value of one cell in the first (bottom one) row = quantity of dots/spots in it.

- from the second row upward, value of one cell = as many "pairs of the quantity represented in the leftmost cell of the row underneath" as there are dots/spots in the cell... or ..."twice the value of the leftmost cell in the row underneath" for each dot/spot in the cell... or accumulation, for "each finger in a primate" of the "value of the cell underneath";

- a column can also be attributed a value: number of dots/spots in any one of its cells

(ok, yes, we could orientate the counting board in various ways without really changing its interpretation and workings, we would just need to modify the spatial words in the description).

note, 2024/3/3 : and, ok, using "toki pona", we would not easily be able to formulate verbally those explanations... due to the lack of words, we would probably need a bunch of the existing "toki pona" words, with their caracteristically hyper-broad meaning, to try to describe a "row", a "column", a "spot", a "dot", etc... I don't think i'm going to try that, even if i learn a bit more of "toki pona" :-) . The other solution would be, as for every specialized human activity (think medecine, computers, linguistic, philosophy, etc.) to create a specially adapted set of technical words, designed to describe the matter, and only understood and used by the specialists.

Historical Yupana

You can see here a copy of the mythical/historical only known drawing of a Yupana, represented near an Inca accountant holding a quipu (a link to the original image is present at the end of this article).

We can notice that for some cells, some of the dots in the cell are colored differently, which may represent the presence of a token at a particular spot in the cell, with a particular value depending on this spot in this cell.

Following this principle, we can use a "fractal" interpretation of the Yupana that will allow big multiplications (and, obviously, also additions and subtractions, but that is already easy with the common use of the Yupana for which, instead, big multiplications may be cumbersome, unless we use a diversity of tokens having different values: one, two, three, five, for example). Only difference with the standard interpretation of the Yupana: the value of a token in a cell depends on its position in the cell.

Fractal Yupana

In this fractal representation of a Yupana, we have horizontal rows of rectangular cells that contain elliptic spots that contain rounder dots (that contain nothing).
And, yes, someone may already have described that clearly, but they may have named it something else than "fractal Yupana". A quick search on the internet, mid november 2023, didn't show obvious results (i even tried to ask bing's ai and google's ai (bard: seem to give satisfying and precise answers in general - but without references): they didn't find anything). So... i'm trying a description of my own.

The value of a token that will be positioned in a cell on the board will be :
- in/near a spot = quantity of dots in the spot multiplied by value of the cell
- well outside of any spot = value of the cell (= value of its first/lowest spot)

And as in the standard interpretation of the Yupana:

- value of a column: quantity of spots in any one of its cell (or value of its first (bottom one) cell);

- value of a cell in the first row (bottom one): quantity of spots in it;

- value of a cell in a row that is not the first one: quantity of spots in it multiplied by "twice the value of the leftmost cell of the underneath row" or accumulated "value of the cell just underneath" for "each of the toes in a human" or "value of its column" counted as many times as "twice the value of the leftmost cell of the underneath row";

- value of a row: one for the first row; for every subsequent rows: value of the row just underneath counted as many times as the "quantity of fingers in a marmoset";

And, sure, that could be simpler if it was described in base 10... but we are trying to be "one, two, many - compatible", by not using any name for numbers greater than two. We should be allowed to use the words "multiply by" as it is only "accumulated as many times as", a basic concept already used in the deepest prehistory... just guessing...

"One, Two, Many - compatible" multiplication with a fractal Yupana

Basic moves

First, let's consider a few simple (or less simple) moves illustrating the rules previously stated.

If there is no error here, the quantity represented in this portion of a fractal Yupana does not change (for us it would have a name: "five hundred"), only its expression changes, given as a variety of accumulations of group of quantities... (ok, for us that means "sums of products of numbers").

Neither the meaning of the expression nor the quantity that is expressed need to be known (or named) by the user who can just follow the simple rules to correctly transform at random (or at will) the expression of the quantity. Normally, the user would want do that during a calculation in order to obtain a simpler expression (with fewer tokens, requiring less attention, minimizing the risk of errors).

Basic multiplication moves

Multiplying with a fractal Yupana is just putting elementary products (without even knowing their name or their value) on the board, and simplifying the expression when desired. The only elementary products are those produced from two of the quantities "one", "two", "one and two", "one and a pair of twos" (thethat are structuring the board and with which any number can be expressed).

Placing an elementary product a x b in the right spot of a row is a visual task:

- on that row, find a cell that has a (or b) spots in it [it has a column of value a (or b)] and where one of the spots contains b (or a) dots,

- put the token in that spot.

Illustration :

Naturally, the row on which an elementary product is placed depends on the row of each of the constituents (factors) of the product: we show a simple and "mechanical" way of managing that aspect in the following video:

Here is the same multiplication, but performed with a real Fractal Yupana + a simplified technique using less chips. The handling of the chips on the board can become very natural and quick - with some training - if the chips have a convenient shape, becoming easy to seize, push and put aside:

A curiosity...

There are so many ways you can count from 1 to 100 using a single row of the yupana... see next post, to get a feel of this gigantic quantity... Here is one way to count from 0 to 100. It uses 4 of the ways to count from 0 to 25 on the first 3 columns, and the 3 ways to represent 25 using only the last column.

Selecting natural rattlebacks, 2 million years ago.

2021-04-12T11:46:00.013+02:00

There is one place on earth where you can discover the notion of "rattleback", find some natural rattlebacks, test them on the spot.

see video (same as below) : https://youtu.be/wMpCKqhEbBM?t=86

The possibility of "testing on the spot" is important, because first of all, it is what helps you discover that the very notion exists.

From the experimental archaeology session in this video, we won't hesitate :-) to assert that rattlebacks were discovered, by primitive human species, millions of years ago, on exceptional beaches, just like the one pictured in the video (Crovani / Argentella beach, Corsica).

Beaches of this type were probably few in number: you need to find absolutely smooth pebbles.

But over millions of years of evolution, no doubt :-) that, multiple times, our most primitive ancestors, made this discovery, while playing on one of those beaches, during their childhood :-)

Experiment : alternative versions of the Chartres Labyrinth

2020-04-06T22:20:00.005+02:00

Chartres Labyrinth - How many different versions can we create ?

I recently stumbled upon a famous labyrinth in Chartres (France), 12th century.

At first sight, Chartres Labyrinth is amazing. You can't immediately figure out how it works (entrance, exit, path, dead ends, ...). It appears on the paved floor of a religious building. When I was there, the labyrinth was visible under numerous chairs installed on the floor. In those circonstances, you try to follow the path of the labyrinth with your eyes, from a distance. But its concentric circles have a puzzling visual effect. You need to follow it for real, on foot.

After a while, trying to follow the path, avoiding the chairs, it appears that it is not a maze : it has only one path, no dead ends, the entrance and the exit are the same. The specialists use the term "unicursal".

Then a question arise : how many of those labyrinths can you create, following the same design and rules (more or less). If there are more than one solution, why choose this particular one.

This question can take a bit of time.. I guess mathematicians know the answer.
I finally managed (hardship with design softwares...) to produce some variants of the Chartres Labyrinth. There seem to be a lot more...

That could be the subject of a playful hoax : flooding the internet with images of alternative versions of the Chartres Labyrinth, and see if people get caught. Am I just trying that here, on a modest scale ?

Some alternative versions to the Chartres Labyrinth - 4 sectors - 11 circuits

this one has a small dead end and a short straight path that is an island ;

not perfect, because all the surface is not used

This one has 2 small dead ends : we should avoid that

this one contains a closed curved path that is an "island" (in the middle of the down right quarter) :

an example of what we should certainly avoid

this one is better, but still has a small dead end, and a straight island

this one is cool... only 2 small dead ends

but several branches to and from the central trunk

Same version, but without the dead end

Some alternative versions, Chartres-like Labyrinths - 5 sectors - 11 circuits

Not that bad, with five lobes, one dead end here

Two small dead ends, here

Same as before, but without the dead ends,

feels a bit unbalanced ?

Chartres like Labyrinth carved on a Tagua nut - finger labyrinth - hypnoglyph

The same labyrinth as before, carved on a Tagua nut,

to be used as a finger labyrinth

Chartres like Labyrinth drawn on a spherical surface - Potato

Another 5 lobes labyrinth, wrapped onto a potato :

The potato was granted the following version

of a five lobes Chartres-like Labyrinth :

Transposing - Chartres-like Labyrinth - Dodecahedron - 5 sectors - 11 circuits

The same version as before, after a transposition (by different method than for the potato) on the surface of a dodecahedron.

There, each circuit/level is represented by one face of the dodecahedron, among eleven of those. The last face represents the inner and the outer space (center and outside of the Chartres-like labyrinth). Each lobe, and each of the two central paths of the Chartres-like Labyrinth (the entry and arrival at the centre) is represented by a lane in which the path will be followed.

Here a video silently illustrating (or just suggesting) the process of transposition :

Another Chartres like Labyrinth carved on a Tagua nut - finger labyrinth - hypnoglyph

The next 5 lobes, 11 circuits Chartres-like labyrinth I'll make will be this one :

here, carved on a rather angular tagua nut

Computer program generated Chartres-like Labyrinths - javascript - Google Script

June 10, 2020 - I finally wrote my own prototype of a labyrinth generator computer program... it's still imperfect, limited by my incompetence and by some restrictions of the tools i could use (exploration with Google script + rendering in html and javascript). With Google script, despite the 6 minutes limit of running time, the whole exploration is possible for 11 circuits and 5 sectors (with some pruning to avoid disgraceful labyrinths)... but not all of the output via the log (don't know how to write elsewhere, yet). For the rendering, I've some improvements to do...

Some of the 42300 labyrinths found by the computer program

See here, 1 in 150 of the more than 42300 labyrinth the computer program has found. :

https://sites.google.com/view/labyrinths-examples/labyrinths-11-circuits-5-sectors-1-in-150

42341 labyrinths and a strange technical glitch

See how the technique used (canevas, in html) draws labyrinths that are more "decayed" when drawn farther from the origin.

click on the video below...

More info found : what other people had been doing...

Blogmymaze - Andreas Frei

April 10, 2020 - I find a blog, BLOGMYMAZE ( https://blogmymaze.wordpress.com ), that explores labyrinths, and examines a few cases of "11 circuits, 4 sectors" labyrinths :

https://blogmymaze.wordpress.com/2018/06/03/the-complementaries-of-the-three-very-interesting-historical-labyrinths-with-4-arms-and-11-circuits/

Mark Wallinger

April 10, 2020 - Someone has already done this kind of work extensively : in 2013, Mark Wallinger, British artist, has shown 270 distinct labyrinths, one in each of London tube station. There was also a catalog of that; see for instance :

https://bloggermymaze.files.wordpress.com/2015/10/tube_book_02.jpg?w=400&h=300&zoom=2

Jo Edkins

May 8, 2020 - An interesting blog compares existing (or having existed) mazes similar to the Chartres Labyrinth. It uses the rectangular transcription to ease the comparison.

Also shows some new designs. http://www.gwydir.demon.co.uk/jo/maze/chartres/index.htm ... this site will soon cease to exist, replaced by www.theedkins.co.uk .... where I was unable to find the same information about mazes... too bad...

Caerdroia - Labyrinthos - Andreas Frei, Hellen Galo, Tristan Smith, Jacques Hébert, ...

May 24, 2020 - Publications n°33 to n°39 of "Caerdroia - the Journal of Mazes & Labyrinths" are available in PDF versions on http://www.labyrinthos.net/digitaldownload.html. Particularly, among many other things, you'll see articles about :

- some variants of Chartres-like labyrinths, explanation from Andreas Frei about his way of cataloging labyrinths, in Caerdroia 39 (links to his website, in German, that seems rather empty) ;

- Amerindian mazes, in Caerdroia 38 ;

- how to create perfect labyrinths (Frei's graph + Hébert notation + 6 canonical labyrinths),by Ellen Galo, in Caerdroia 37 ; this article is also available in the archive of the most requested past articles... so... the subject is clearly interesting to a fair number of people :-)

- Kota labyrinths in southern India, in Caerdroia 36 ;

- how to analyze, design and scale up chartres-like labyrinths, by Andreas Frei, in Caerdroia 35 ;

- a computer program for generating medieval labyrinths, by Tristan Smith, in Caerdoia 35; we read that without enforcing strict enough rules about the properties of the labyrinths, there is ~5 million versions of a 11 circuits / 4 sectors labyrinth. The article links to Tristan Smith's website, where a good number (rapid count : more than 130) of alternative versions of Chartres-like labyrinths have been generated by the program (or with its help), using strict enough rules. The set of rules of Jacques Hébert gives just 20 "canonical labyrinths" that would be (i guess) the most "Chartres-like".

See https://www.otsys.com/~tsmith/daedalus.html ; the images of the labyrinths are in 4 pdfs ;

Also, the definitions corresponding to the rules that the program can respect are here https://www.otsys.com/~tsmith/properties.html (but the article in Caerdrioa is clearer : shows examples)

- a mathematical notation for medieval labyrinths, by Jacques Hébert, in Caerdroia 34;

surprise... Andreas Frei is actually also one of the authors of the blog Blogmymaze (see higher)...

The most requested past articles of Caerdoia are made available in the archive

http://www.labyrinthos.net/caerdroiaarchive.html#CaerdroiaIndex which also has a PDF listing all of the articles from 1980 to 2019... from which i extract this very small selection : the articles that may help in describing and creating variants :

#29 (1998)	Developing the Labyrinth: Alex Champion, p.43-51: re-drawing the classical labyrinth - new variants.
#34 (2004, pdf online)	A Mathematical Notation for Medieval Labyrinths, p.37-43: Jacques Hébert explains.
#35 (2005, pdf online)	The Cascading Serpentine, p.19-26: Andreas Frei examines the Chartres labyrinth structure.
#35 (2005, pdf online)	A Daedalus for the 21st Century, p.27-33: Tristan Smith’s software labyrinth builder.
#37 (2008, pff online)	Sigmund Gossembrot’s Labyrinth: A Very Special Design, p.41-44: Andreas Frei takes a look at an unusual labyrinth from the 15th century.
#37 (2008, pdf online)	Further Thoughts on ‘Perfect’ Labyrinths & How to Create Them, p.45-49: Ellen Galo dissects the structure of mathematically ‘perfect’ labyrinths.
#38 (2008, pdf online)	Two Labyrinths Compared: What They Have in Common, p.60-63: Andreas Frei takes a look at two apparently different labyrinths in early manuscripts.
#39 (2009, pdf online)	The True Design of Sens, p.28-32: Richard Myers Shelton compares the two known designs of the Sens Cathedral labyrinth and asks which is correct?
#39 (2009, pdf online)	A Catalogue of Historical Labyrinth Patterns, p.37-47: Andreas Frei describes the findings of his labyrinth design analysis project. Labyrinthos Archive 13
#40 (April 2011)	Greys Court: an invitation to symmetry, p.21-35: Richard Myers Shelton explores the symmetry inherent in certain labyrinths.
#40 (April 2011)	Considering the Duality of Labyrinths, p.40-47: Andreas Frei examines a hidden property of labyrinth designs.
#46 (July 2017)	Searching in the Mirror, p.34-48: Richard Myers Shelton completes his series on the geometry of symmetric labyrinth designs.
#48 (April 2019)	Basic Labyrinth Math, p.37-49: Richard Myers Shelton explains the rules of labyrinth structure.
#49 (May 2020)	Medieval Marvels: Fifty-Three Eleven-Circuit Manuscript Labyrinths, p.8-27: Jill K.H. Geoffrion & Alain Pierre Louët look at an extensive group of manuscripts produced prior to 1500

2020/09/13 - another description - with stricter rules - of what should be considered a Chartres-like labyrinth. In http://www.lavigne.dk/labyrinth/e6charst.htm. Chartres-like labyrinths would be made of a combination of those patterns :

to be continued....

Experiments : trying to locate the position of the sun - Sunstone - Iceland Spar - Optical Calcite -

2020-02-07T08:23:00.001+01:00

How to find the sun with a viking sunstone

We find various claims asserting the sun can be located, when not visible because of the clouds, with an Iceland Spar crystal. Some show experimental videos and conclude that their experiment proves that. I couldn't replicate the experiments. More precisely, I could replicate the experiment, but i couldn't see how it proved that the sun was actually located.

Conclusions of my first experiments

so far, no obvious way to tell which side is the sun ...

the sun is on the left or on the right, when "maximum" light polarization is detected

brainstorming for further tries [apparently, almost all nonsense : see "More information", lower]:

let light enter from different faces of the crystal;
really go do the experiment where the Vikings were said to use those crystals for navigation : North Sea, high latitude, on a boat ;
use refraction ; shape differently the hole that lets the light in ; use 2 crystals ;
use reflection on the inside of the faces of the crystal;
use crystals with various kind of inhomogeneities, giving complementary information ;

for example, explore the changes in colors and patterns in some crystals ;

detect the polarization from under the surface of the water;
ignore light polarization and the "Raleigh sky model", find some other model... (because the Raleigh sky model seems to have a symmetry that wouldn't allow to decide which side is the sun);

Videos of the my experiments :

More information

Not Calcite, but Cordierite, tourmaline, ... ?

Read on https://royalsocietypublishing.org/doi/10.1098/rsos.150406

"the Viking sunstones described in the old sagas could have been dichroic cordierite, andalusite and tourmaline or birefringent calcite (Iceland spar) crystals that could serve as linear polarization analysers."

Read on https://royalsocietypublishing.org/doi/10.1098/rsos.150406

"real calcite crystals also have disadvantages, and thus cordierite and tourmaline can also be at least as good sunstones."

Prerequisite step : calibrating and marking the crystal ?

Read on https://royalsocietypublishing.org/doi/10.1098/rsos.150406

[meaning not immediately clear for the lay person !]

"— Calibration step: In cloudless weather [...] rotate (adjust) the crystal until its well-determined orientation (e.g. minimal or maximal intensity of skylight transmitted through a dichroic sunstone, or minimal or maximal intensity difference between the two slots/spots of a birefringent sunstone), where it was fixed, and thereafter he calibrated the crystal by engraving the direction pointing towards the sun on the crystal surface.

— Navigation step 1: Applying this sunstone rotational adjustment under a cloudy or foggy sky at two different celestial points, the navigator could determine the directions perpendicular to the local E-vectors of skylight shown by the engraved straight markings of the sunstones, pointing towards the sun. [?? how many sunstones are needed ??]

— Navigation step 2: The intersection of the two celestial great circles crossing the sunstones parallel to their engravings gives the position of the invisible sun." [?? celestial circles crossing the sunstones ??]

Process for calibrating an Iceland spar (calcite)

"the calcite is rotated until the intensity difference between the two light spots is maximal. This occurs four times with 90° periodicity during a full 360° rotation of the crystal. [...] the Viking navigator [...] has to scratch only one straight mark (pointing towards the sun) onto the sunstone, and this sun mark can be used under all weather conditions to determine the position of the invisible sun."

You need two sun stones, not only one !?

Read on https://www.osapublishing.org/josaa/fulltext.cfm?uri=josaa-31-7-1645&id=294365

[another description, where we see that 2 sunstones are involved.
And we still have to find a proposal about how you perform that on a narrow crowded ship... maybe here, if you want to pay for access : https://www.osapublishing.org/ao/abstract.cfm?uri=ao-52-25-6185 ]

"Step 1 (Fig. 1A): Viking navigators are assumed to have determined the direction of skylight polarization in at least two celestial points with the use of two sunstones to estimate the position of the sun occluded by cloud/fog or being below the horizon. [...]

Fig. 1A

Step 2 (Fig. 1B): A short scratch on each sunstone could help the navigator to set two celestial great circles across the two investigated sky points parallel to the scratches being perpendicular to the local direction of skylight polarization. Then the navigator determined the above-horizon intersection of these celestial circles. According to the Rayleigh theory of sky polarization [9], this intersection coincides with the position of the invisible sun.

Fig. 1B

Step 3 (Fig. 1C): [... hypothesis for finding the geographical north ...] "

[better explained here, maybe, for who accepts to pay for science : https://www.osapublishing.org/ao/abstract.cfm?uri=ao-52-25-6185 ]

Other hints to evaluate

using 2 sunstones

in https://www.sciencedirect.com/science/article/abs/pii/S0262407915605553

Haidinger's brush : the easy / feasible method to test ?

Read on https://www.seeker.com/legendary-viking-sunstone-navigation-solved-1765489280.html

"if you look through the crystal in its depolarizing position and then pull it away suddenly from your line of sight, you can catch a glimpse of a faint, elongate yellowish pattern known as a Haidinger's Brush. The key here is that the ends of that yellow shape point directly toward the sun."

[ The thing is not self-explanatory... there are two opposite "ends" in this elongate pattern... and they can't both point directly toward the sun... ]

The study from where this assertion comes from is here:
https://royalsocietypublishing.org/doi/10.1098/rspa.2011.0369
[i'll need to try harder to understand the paper, because at first look, i can't see why we should find the direction of the sun with the Haidinger's brush... which is not directional... we find in the study this beautiful illustration, that is not as convincing as it seems to be

if you manage to see that magnificent Haidinger's brush, you can still rotate 180° and do the experiment again, then... would you not assert that the sun is in the opposite direction ? ]

Navigation by lead and line, and other means

Was it even necessary to locate the sun, the north or any direction ?

Read here how navigation by lead and line was used to determine where the boat was
https://www.cambridge.org/core/journals/journal-of-navigation/article/early-navigation-in-the-north-sea-the-use-of-the-lead-and-line-and-other-navigation-methods/EDA8012AE267C583E8F2EA14EE36E145/core-reader
[ok, not doable when crossing or exploring unknown deep seas]

The differences between natural and human flaking on prehistoric flint implements

2019-08-06T14:27:00.002+02:00

old (1939) but interesting paper, showing that the subject is studied at least since the end of the 19th century.

THE DIFFERENCES BETWEEN NATURAL AND HUMAN FLAKING ON PREHISTORIC FLINT IMPLEMENTS

By ALFRED S. BARNES

https://anthrosource.onlinelibrary.wiley.com/doi/pdf/10.1525/aa.1939.41.1.02a00080

AMERICAN ANTHROPOLOGIST ; 1939

Yupana - very handy for divisions

2019-02-10T19:38:00.007+01:00

The Yupana is also a handy tool for divisions.

There is a way to compute divisions with a Yupana, without any previous knowledge (almost) : no multiplication table, no division table.

If you use the classic interpretation for the yupana (1/2/3/5; sometimes labeled as Mendizabal's interpretation), the one basic thing that is useful to know is "10 = 5+3+2". Also basic and useful : "5=3+2", "3=2+1", "2=1+1" 😉

Illustrations here, with the classic interpretation of the Yupana 1/2/3/5 :

simple division, with explanations

big division, without explanation

If you use other interpretations of the yupana, it should be doable also, but with other basic notions. Notably for the interpretations of Chirinos, Chirinos-Hayakawa and Mendizabal-Hayakawa.

The process is very "automatic", probably also usable, in its principles, with any type of abacus where seeds are free to be moved everywhere (unlike the Soroban, for instance).

I guess that specialists will consider that this is a very well known process, maybe even the historic definition of the process of division 😊... But, well, for an ignorant like me, it is just perfectly suitable for Yupanas.

Process :

Recursively group seeds of the dividend around each seed of the divisor, in equal numbers.

Actually, the groups are to be made around the seeds of the divisor, or around their locations when multiplied by a power of ten : this depends on the difference between the orders of magnitude of the dividend and divisor.

A step of grouping ends when you can't make bigger (equal) groups, then :

- use the number of seeds of a group (same number for all groups, possibly = 0) as the next (or first) digit of the result,

- get rid of the seeds that were in the groups,

- move the remaining seeds (those of the dividend) one row up,

Repeat a new step of grouping with the remaining seeds that were moved up. Make groups of seeds around the seeds of the divisor [those seeds never move] or around their location when multiplied by a suitable power of 10,

When you think it's enough, after you have at least one digit of the result on the same row as the first digit of the divisor :

- position a decimal separator after the digit that is at the level of the first digit of the divisor,

- consider the remaining seeds [only those of the dividend] as the remainder of the division.

---------------------------------------------------------------------------------------------
Illustration here, with the classic interpretation of the Yupana 1/2/3/5 :

Maybe all that may be eased (less seeds) by using dice instead of seeds. Preferably some pre-Columbian Andean type of dice. Like one of those described here https://www.facebook.com/notes/museo-nacional-de-historia-natural-de-chile/el-ancestral-juego-de-dados-y-oráculo-del-quechucague-o-pichca/10154208849277919/

Found in Machu Pichu

Found in Huaca Tres Palos, Lima

The dice used by the promotors of the "Yupana Inka" may be interesting also, but making such beautiful dice would be a challenge ;

Image from https://www.youtube.com/embed/ZUOG_kTcFc4?start=476 (at 8:02)

2019/02/15 - Notes about the process of division with an abacus :

Wikipedia mentions a less efficient method : "A person can calculate division with an abacus by repeatedly placing the dividend on the abacus, and then subtracting the divisor the offset of each digit in the result, counting the number of divisions possible at each offset."

The History of the Abacus says nothing new (just mirrors our modern pencil and paper method)

The fundamental operations in bead arithmetics (with chinese abacus) : as we can guess about abaci with attached beads, the process has to be more like our modern process with pencil and paper (multiplications and subtractions).

How to do division on the abacus in easy steps : not so easy, requires knowledge of multiplication tables (as in the previous articles); normal... it details the use of a "soroban" (attached bead = limited possibilities).

The Most Promising... "Ancient Computers, Part I, Redisovery",by Steve Stephenson, at https://arxiv.org/ftp/arxiv/papers/1206/1206.4349.pdf

No yupana here, but tactics that may be applied to yupanas (maybe... I have to examine that in detail, and see if it can be done somehow with a yupana).
It mentions techniques where only a very small number of pebbles are needed, the potential of abaci with unattached beads/pebbles, divisions and multiplications without knowledge of tables and very automatic : exactly what we want.
Also in line here : https://ethw.org/Ancient_Computers
And more here : http://sks23cu.blogspot.com/2013/07/links-to-my-book-dvds-ancient-computers.html
And examples on the old Stephen Kent Stephenson's Youtube channel SKS23CU

Herodotos and the abacus may deserve more attention, as the proposed solution for division, at first look, resembles the one used higher with the yupana. Although it mentions subtractions that (in the process we described and tested above) we didn't need to perform (other that automatically remove sets of beads, without thinking).

Roman elementary mathematics doesn't seem helpful about easy automatic divisions.

Matematica Andina - La Yupana offers only to mirror the method we use nowadays for divisions.

Journal of mathematics and culture - volume 5 number 2 offers an article "the incan abacus : a curious couting device" (Molly Leonard and Chery Shakiban) that describes a way to perform multiplications and divisions by first preparing tables of multiples.

That's not very appealing if you try to find an automatic calculation process.
But there is a convincing argument : yupana calculations seem to have been a collaborative process involving 2 persons (quipucamayocs). And this hints for the possibility of them using some complementary and parallel processing, not only double checks.

2019/05/29 - Illustration of the division with a yupana

The basis for the process described earlier is illustrated by Oscar Pacheco Rios in a document dated 1999 "Del Quipu Incaico a la Yupana, El computador Ancestral", around page 57. Found here (at least) : https://www.andesacd.org/wp-content/uploads/2019/02/Del-Quipu-Incaico-a-la-Yupana.pdf

2019/11/29 - El tablero medieval de calculo - Jose Maria Nunez - 2003

http://funes.uniandes.edu.co/1522/1/100_Nuñez2003El_RevEMA.pdf

This article describes a simple process for the division : repeated subtractions, In principle, it is identical to the process I used with the yupana : the "grouping" represents a set of identical subtractions.

2020/07/14 - The process of division perfectly illustrated (with a simple example) on Herbert Apaza youtube channel, in 2015

In its principle, it's exactly the process i described (some years later). In practice, with bigger numbers, i guess we are forced to complicate the process that is used here, to avoid maximum confusion on the board.

Digression....

In this article (oups ! reference lost... but see reference about "schärlig" lower), we read that Europe was still using counting boards for computations, as late as in the XVIII th century.

We can infer that those counting boards were still in use in Europe, at the time of the invasion and conquest of the Inca empire (XVI th century). We should even try to verify if there were European counting boards in use, in Peru, 2 centuries after the Spanish conquest. This should have led to a better comprehension of the yupana. Basically, Europe and the Inca empire were doing the same thing, with not so different kinds of counting boards. Maybe for the Spanish, for the ignorant ones as well as for the learned ones, the yupana was just a counting board : no mystery, nothing deserving much attention, just a variant of what they already knew.

The most annoying / promising hypothesis is that the use of the European counting board may have been taught in Peru during the XVII th and XVIII th centuries. That would have touched only a small percentage of the population, but a non negligible proportion of those who were taught writing and counting, among which some native - or mixed blood - Peruvians. This would suggest a possibility of "discourse contamination" around the yupana.

But this hypothesis doesn't seem very promising, after a few hours of internet search :

1) apparently, already in 1590, "pen and ink" were used by the Spanish, at least for "very difficult computations". A citation from a Jesuit priest, Joseph de Acosta, praises the efficiency of the "Indians" of Peru for very difficult computations that would require that an able calculator use pen and ink.

2) in Spain, books in Spanish, about arithmetics with Arabic numerals, were available... See for instance this short study https://www.iejme.com/download/old-arithmetic-books-mathematics-in-spain-in-the-first-half-of-the-sixteenth-century-5935.pdf comparing five of them, printed in the first half of the sixteenth century, hence before the conquest of the Inca empire. Those 5 books were mostly targeting common people and accountants. At first sight, none of those books seem to make reference to counting tables !

2.1) See for instance, an extract, illustrating multiplications, from a book of commercial arithmetic from Spain (1546) "Suma de arithmetica pratica y de todas mercaderias" ... https://www.maa.org/press/periodicals/convergence/mathematical-treasure-commercial-arithmetic-from-spain-1546

3) The use of counting boards may have been limited to Northern Europe (or may have lasted longer there), because the south of Europe was more favorable of Arabic numeration.... see : https://hal.archives-ouvertes.fr/hal-01465419/document describing a book by Schärlig, about counting boards in Europe. Northern Europe only, with sources mainly from Switzerland and West Germany, but also Flanders (Spanish Netherlands), France (Lyon and Strasbourg) until 1792, England. Southern Europe is said to not have used counting boards, but Arabic numbers, for calculations. [scathing comments - in french - about the book and the author here : https://journals.openedition.org/crm/251... the author is criticized for not knowing how to do (and not doing any) bibliographical research].

My remark : the fascinating aspect of that would be that, for Southern Europeans, Inca and Norther European counting boards would have seemed equally strange and would have prompted the same kind of description: "they moved things on a board and where able to make difficult calculations".

4) Colonial education in South America may never have included counting boards. For example, in Guatemala, 1732, a book for teaching, in primary schools, arithmetical basic operations and resolution of problems in commercial environnements, "Aritmetica practica", written by Juan Joseph Padilla, seems to ignore the counting boards, and uses only the Arabic numeration. see : https://hal.archives-ouvertes.fr/hal-01465419/document. In the introduction, by Luis Radford, it is said to be structured like other "libros de abaci" (books that were not about abaci, but about the use of Arabic numbers) written in Europe at the end of the medieval era and after.

so... we can wonder whether any Spanish of the XVI th or XVII th century had ever seen a counting board before arriving in America... except if they had travelled in Northern Europe... and this could well have happened, as Spanish Netherlands was, with the territories or the ex-Inca empire, components of the Spanish Empire for more than 100 years (according to what i read on Wikipedia) :

- incorporation of the Inca empire from 1532 to 1572,

- existence of Spanish Netherland from 1556 to 1714

so... in theory, there was plenty of time for someone (any learned European or Peruvian) to have seen counting boards in the Netherlands - or elsewhere in Northern Europe - and also have lived some time in Peru and have seen or heard (if not outright invented a legend) about Inca counting boards.

Yupana - a viable Chirinos-Hayakawa interpretation ?

2019-01-06T12:51:00.000+01:00

The Chirinos-Hayakawa's Yupana

(I just invented this name, we'll see later if there is another name already in use for that thing)

Reminder about the Yupana

The Yupana, is said to have been a prehispanic counting tool / abacus used in the Inca empire. It is said to have been used, as many counting tools in the world, by moving various types of seeds or calculi on a board. The Inca counting board may have been a 4 column grid - according to one 16th century source, Guaman Poma de Ayala - with each column associated with a number of dots (1, 2, 3, 5). There is no definitive explanation of how to use a Yupana : no living ancestral knowledge, nothing clear (yet) found in historical records, only several modern interpretations and educational experiments in south american schools.

Notes : counting boards were still used in Europe, around the time of the conquest of the Inca empire by the spanish. Although the focus nowadays is set on the Guaman Poma 4 columns Yupana, various other tools are also called Yupana. Those that have been found have a number of cells carved into wood, stone or clay. With so few historical traces, nothing rules out that different types of Yupana / grid / counting board / abacus may have been in use simultaneously, for different purposes, different types of calculations or games. Particularly, as we know that the Inca empire was vast and diverse in cultures, languages and peoples.

Finding an efficient and "prehistoric" way to use a 4 columns Yupana

Important points for a viable interpretation of the yupana: paleo-compatible, efficient, reliable in complex computations, limited knowledge requirements (no multiplication tables), reduced number of manipulations, lower attentional requirements, lower memory requirements, possibility to track back errors.

A novel interpretation for the 4 columns Yupana

(I've not yet thoroughly verified if this interpretation has already been described before)

We can create another functional interpretation of the Yupana by mixing two systems :

the Andres Chirinos Rivera interpretation of the Yupana : basically, each dot in a row has a different value, from 1 to 11;
and a notation - not linked to Yupanas - demonstrated by Hayakawa Yoshinori on his youtube channel (早川吉則) : a notation that allows to blindly calculate, as with an abacus, as would do a computer, by using the successive powers of 2, with a very limited set of basic moves and almost zero knowledge requirements ;

The merge between Chirino's Yupana and Hayakawa's notation gives us a Yupana where :

each dot in a row represents a power of 2 : 1, 2, 4, 8, 16, 32, 64, and even more if we need it for special cases, up to 1024;

(if we needed even more, for special calculations we could increase the number of columns and use a "super-yupana")

each row, represents a power of 10, as required for a base 10 numeration system (Inca);
the first 4 dots in each row (1, 2, 4, 8) are sufficient to note any number in base 10;

3 other dots (16, 32, 64) are commonly used during calculations, particularly during multiplications
the remaining dots (128, 256, 512, 1024) may be useful in special cases;

for instance when we want to use fewer rows to note numbers ;
an example, extreme : 512256 may be noted with only 2 dots, on 2 rows.

The first experimentations show that the system is simple, "paleo-compatible", requires zero knowledge of multiplication tables, and need relatively few manipulations. But a high level of attention is still required from the operator. And there is still no obvious way to keep track of the successive operations, in order to find and correct an error.

Illustration 1 - values of the dots in the first row of the "Chirinos-Hayakawa" Yupana.

Video of a "big" multiplication with the Chirinos-Hayakawa's Yupana

Simpler version : Mendizabal-Hayakawa

I've tried a much simpler version, that could be called the Mendizabal-Hayakawa Yupana. It would give the values 1/2/4/8 to the columns, instead of the values 1/2/3/5.

After some experimentation, this Yupana appears to be easy to use, but the 1/2/3/5 marks in the cells are confusing and facilitate errors. We can still try to find a good reason for keeping those 1/2/3/5 marks in the cells. For instance by focusing on the great interest of the groupings by 2, by 3 and by 5 that occur frequently during calculations and that allow easy simplifications (5x8=40; 5x4=20 ; 3x4 = 12 ; 3x8=24).

Illustration 2 :

Video of a "big" multiplication with the Mendizabal-Hayakawa's Yupana

References and remarks

Articles

.... will be inserted later ...

Chirino's Yupana

Illustration 3 - values of the dots in the 2 first rows of a Chirino's Yupana

Example of basic use :

Hayakawa's "computer numerals"

Computer Numerals ... Education for all.

Illustration 4 - Hayakawa's notation -

Example :

Illustration 5 - Some numbers represented according to Hayakawa's notation

Yupana - A cursive handwriting for Yupana numbers

2017-11-17T16:02:00.000+01:00

I guess that historically there has never been a handwritten notation for yupana numbers ...

So ... there is one now ...

and it can easily be used to create an alphabet, for instance,

if we wanted to pretend that Incas were very close to having a writing system 😉

Illustrated here :

Dynamically explained here :

Few more explanations, google slides, static :
https://drive.google.com/open?id=1lIBZwoow8dBqOpw76z77pMInW69KAHTJDgJPanDyrxs

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and...

other links to attempts of the same kind (new number notations) from other folks:

Neanderthal gimbal project - (ok, that's not science) -

2017-10-05T18:15:00.002+02:00

A few videos where i try primitive techniques

in order to make prehistoric gimbals of various kinds

Growing yew trees for longbows, in sustainable yew groves ?

2017-01-14T17:32:00.004+01:00

Excerpts from

Arboretum et fruticetum Britannicum; or, The trees and shrubs of Britain
by John Claudius Loudon, Published 1838

https://archive.org/details/arboretumetfrut07loudgoog

https://ia802605.us.archive.org/16/items/arboretumetfrut07loudgoog/arboretumetfrut07loudgoog.pdf

About Yew, Taxus Baccata
27 pages, 2066 to 2093, a great deal of that is describing individual remarquable yew trees; there is also a few mentions of how to obtain straight trunks. Here are the excerpts.

"When drawn up by other trees, or being planted in masses, it takes somewhat the character of a fir; and may be found, thus circumstanced, whith a clear trunk 30ft. o 40 ft. high."

About bows, that no longer can be made from english yews

"Perhaps if yew trees were planted in masses, and drawn up to the height of 10 ft., with clear trunks, and cut down when they were of 6 in. or 8 in., in diameter, they might still be used for this manufacture."

I've seen yews of this diameter, growing almost "in masses" with clear trunks, but they were closer to 30 ft. in height. See this video, which is not part of the book, obviously

"The yew is admirably adapted for underwood; because [...] it thrives under the shade and drip of other trees. When planted in masses by itself, the trees are drawn up with straight trunks like pines and firs [...] There are some fine yew groves, with tall clean trunk, at Combermere, in Cheshire; [...] the yew, like [...] various other trees, usually seen as immense bushes, might easily be grown so as to throw all their strength into a clean straight trunk."

I didn't find anything else on the web about yew groves in Combermere (except here http://www.ancient-yew.org/userfiles/file/CheshireMarch2015.pdf were they guess it was in Combermere Abbey). No other trace... All destroyed long ago ?

Interestingly, preventive pruning doesn't even seem necessary. All you have to do is planting the tree in an environment that draws the tree up (in masses, or under the cover of other relatively tall trees). Simpler that what we read in "Introduction to Cultural Ecology / Mark Q. Sutton, E. N. Anderson (second edition, 2010)", http://xa.yimg.com/kq/groups/24970245/1577152732/name/Cultural+Ecology.pdf, page 123 :
"In Nevada and elsewhere, Indians made bows from staves of juniper wood [...] Planning far ahead, the Indians would select, prune, manage and nurture trees to grow straight and knot-free trunks that could provide bow staves, a process that could take decades. [...]. These trees were valuable resources that were constantly monitored, maintain and reused over hundred of years.[...] The same was done with yew trees in the Pacific Northwest and probably in old England"

See the cited article by Philip J. Wilke (1988) here : http://escholarship.org/uc/item/4v5249w9.pdf
The process described is more complex that just cutting a slender trunk and splitting it into bow staves. It is adapted to big trunks of more or less bushy trees. I guess the process would be much different with tree trunks cultivated to be 6 in. to 8 in. in diameter and growing straight, tall, naturally knotfree as a result of their growth in the shade of other trees.

More information about yews (but not about bows) :
http://onlinelibrary.wiley.com/doi/10.1046/j.1365-2745.2003.00783.x/epdf
http://onlinelibrary.wiley.com/doi/10.1046/j.1365-2745.2003.00783.x/full
British Ecological Society - Journal of Ecology 2003 - n° 229 - 91, 589 - 924

texts
Arboretum et fruticetum Britannicum; or, The trees and shrubs of Britain

by John Claudius Loudon, Published 1838

All discoveries involving fire were made in the first 10 KY !?

2016-12-07T21:01:00.001+01:00

"Proof" that all inventions about the uses of fire were made in a very short time.

We can read surprised or admirative comments about how strange it is that primitive people could have invented so many things, so early, once they had fire : boiling without containers, charring, making tar and glue, charcoal, transforming stones by heat (for knapping...), transforming clay in hard material, fumigating of meat, fish and skins, hardening of wood points, ....

But let's do the maths...

... and it will soon be clear that even made by mere chance, all inventions about the uses of fire were probably made in a very short time.

Parameters of the hypothesis :

200 K people,
from various early human species, and maybe some of them having relatively small brains and limited creativity,
15% of them all (30 K) having some knowledge of fire
... and using fire daily during 10 KY
1 fire for every 5 people (families), fire burning 5 hours per 24h, each day of the year

Fire used for cooking, for heat, for protection against beasts, for technological processes, for hunting.
Some people knowing how to create fire, other knowing only how to preserve fires or coals.
People from tribes who did not use fire would not be included in the calculation.
Results :
Total number of hours of experimentation : more than 100 billions hours
30 K / 5 * 10 K * 5 * 365 = 109 500 000 000 hours of experimentation.

This is a kind of primitive crowdsourcing, allowing for discoveries made by mere chance, during all kinds of events, in all kinds of environnements.

This is the equivalent of a continuous experiment lasting for more that 12 millions years !
30 K /5 * 10 K * 5 / 24 = 12 500 000 years.

That should be more than enough to make every possible primitive discovery about the uses of fire.

Next task : find real numbers and dates

When did fire began to be widely used by humans and pre-humans ?
200 KY, 400 KY, 1MY ago ?
How many humans and pre-humans lived at that time ?
Chimpanzees, now endangered, are still ~200,000 ;

Any reason for the first humans (from all human species), opportunist omnivores, with a wider range of habitats, to have been less numerous ?

Starting a list of publications where some hints should be found...

104,000 [288,000 in 1973] Bornean Orangutans, endangered
http://www.iucnredlist.org/details/17975/0

~100,000 Giraffes in 2015
[not human-like at all : much more specialized, endangered, big and not so "sustainable" beeing]
http://www.iucnredlist.org/details/9194/0

415,000 African Elephants in 2016,
[not human-like at all : much more specialized, endangered, very big and not so "sustainable" beeing]
https://www.theguardian.com/environment/2016/sep/26/african-elephant-numbers-plummet-during-worst-decline-in-25-years

900,000 American black bears in north america only
[not exacty human-like but also "opportunist omnivores"]
http://www.iucnredlist.org/details/41687/0

Chimpanzee (pan trogloditus only) population nowadays : ~200,000
http://www.iucnredlist.org/details/15933/0

The discovery of fire by humans: a long and convoluted process | Philosophical Transactions of the Royal Society B: Biological Sciences http://rstb.royalsocietypublishing.org/content/371/1696/20150164

"We know that burning evidence occurs on numbers of archaeological sites from about 1.5 Ma onwards (there is evidence of actual hearths from around 0.7 to 0.4 Ma); that more elaborate technologies existed from around half a million years ago, and that these came to employ adhesives that require preparation by fire. We know that both early modern humans and Neanderthals had sophisticated fire technologies, at least some of the time."

The Invisible Fire Starters: A usewear-based approach to identifying evidence of fire production by Neandertals - Sorensen, Andrew - 2012 - Marster thesis
https://openaccess.leidenuniv.nl/handle/1887/18337

Fire tamed 1 million years ago [Wonderwerk Cave site in South Africa’s Northern Cape province ]
Before that, the earliest reliable evidences were considered to be 0.4 million years old.
https://blogs.scientificamerican.com/observations/humans-tamed-fire-by-one-million-years-ago/

Making Soapstone/Steatite as hard as flint ? after firing, at ~950°C ?

2016-02-06T20:04:00.014+01:00

Soapstone / Steatite is marvelously easy to carve... and it can become hard and durable. Like clay, it has to be fired. Apparently for 1, 2 or 3 hours at ~950°C. Or, more interestingly : for 2 minutes only, at 1100 °C.

This is definitely worth a try. With very primitive means. Apparently the only technological requirement is knowing how to make big fires. Although, if we want 1100 °C, even for only 2 minutes, we'll probably need more than a big fire (some kind of kiln ? a strong and steady flow of air ?).

A few links and extracts :

added November 2021, modified December 2021: https://www.academia.edu/35753853/Experimental_Studies_of_Harappan_Steatite_Carving_and_Firing_Techniques (Experimental Studies of Harappan Steatite Carving and Firing Techniques, 2012, in Pakistan Heritage, by Gregg Jamison). Firing for 1 minute at 1100°C is enough to harden steatite to a hardness of 5. Firing the steatite one minute longer, or one hour longer, makes no much visible difference : it puts the hardness at 6 instead of 5. Chert was used to scratch the surface of the steatite after firing. These experiments did not include firing at lower temperatures, for longer durations.

added 2020 11 11 : https://egyptmanchester.wordpress.com/2018/01/19/the-use-of-steatite-in-ancient-egypt/

Ancient Egypt used steatite (hardness of Mohs 1) for small intricately carved objects, then fired them, probably in kilns, until they crystallize into enstatite (hardness of Mohs 5.5, close to that of granite);

(Manchester Museum)

http://cameo.mfa.org/wiki/Steatite

"Native steatite is so soft it can be scratched with a fingernail, but baking results in dehydration and hardening of the stone. Some ancient steatite carvings were glazed then fired which produced a mineral (enstatite) hard enough to scratch glass."

http://iosrjournals.org/iosr-jhss/papers/Vol20-issue2/Version-5/K020256672.pdf
"[...] the so-called Harappan script [... signs ] have the most peculiar and elaborate iconographies of Indus Civilization. It is represented on many stamp seals of fired steatite and corresponding clay sealing terracotta tablets [...]"

https://www.harappa.com/slide/group-incised-baked-steatite-tablets
"A group of 16 three-sided incised baked steatite tablets, all with the same inscriptions, were uncovered in mid- to late Period 3B debris outside of the curtain wall."

https://www.harappa.com/sites/default/files/pdf/Kenoyer%202005%20Faience%20Workshop.pdf

2005 Steatite and Faience Manufacturing at Harappa: New Evidence from Mound

E Excavations 2000-2001

A paper by Kenoyer, that describes (in particular) an experiment made in 2001 at Madison, Wisconsin : 3 hours of firing, maintained 1 hour at 935°C by continuously fueling wood.

"The experimental faience and steatite tablets were placed inside one canister, while a second

canister was overturned and placed on top as a lid. A narrow space was created between

the two canisters by using three splayed conical setters to raise the top canister slightly

above the lip of the first canister. This created a small, enclosed space that would be

insulated from the direct flame and ash. The canisters were placed on top of a layer of

wood fuel (pine and oak) and covered by additional fuel. After gradual heating, the entire

pile of fuel was ignited creating an extremely large bonfire. The tablets could be seen

through the space left open between the two firing canisters, and after approximately

three hours they reached a deep red orange color typical of relatively high temperatures.

Using a thermocouple (chrome-alumel) and digital pyrometer, the temperature of the

interior of the canister was documented at 935°C. By continuously adding fuel on top of

the canisters it was possible to maintain this temperature for about one hour, after which

the fire was allowed to die down."

From that, although kilns are mentioned in the paper, I understand that no kiln was used, but only "canisters" and "setters", put into a big pile of wood. Frustratingly, the article shows no drawing or photos of that experiment, so the reader is left alone to imagine what exactly the description refers to...

At least, we can find a few photos :

setters : https://www.harappa.com/search/site/setters

canisters debris : https://www.harappa.com/indus3/251.html

experiment with canisters (for firing faience) : https://www.harappa.com/indus3/256.html

experimental canisters : https://www.harappa.com/indus3/254.html

The way to put the "setters" in place is not clear; and the way they put 2 canisters one on top of the other seems odd and unstable (no surprise that impurities did enter into it).

A much earlier publication (1997) by Miller, university of Wisconsin-Madison, explores ancient kilns (or what's left of them and how this can be interpreted) from the indus civilisation;

https://www.harappa.com/sites/default/files/pdf/Miller_PotteryFiringStructuresKilns.pdf

http://community.ceramicartsdaily.org/topic/998-firing-rocks-with-clay-sculptures/
google image search, : images of Egyptian glazed steatite

http://www.nwssa.org/index.php?option=com_content&view=article&id=111:stone-corner-firing-soapstone-marapr-2002&catid=63:the-stone-corner&Itemid=62
Modern firing of soapstone, described; warnings about inclusions that can break a stone
Not very hot... but long... no hints about the hardness achieved : "to a high of no more than 500 degrees"; 24 hours of gradual heating, then 8 more hours.

http://archeosciences.revues.org/643
[about ancient beads from the sultanate of Oman] "We propose that steatite was used in the manufacturing process of the beads. The beads might have been made from soft steatite material and then hardened by firing at about 1000°C; the formerly soft beads thus became hard and durable. This hardening is due to the transformation of the steatite into synthetic enstatite which takes place at about 1000 °C."

http://www.academia.edu/11320048/_Cuire_des_statues_lusage_de_la_st%C3%A9atite_en_sculpture_%C3%A0_la_fin_du_Moyen_Empire_et_%C3%A0_la_Deuxi%C3%A8me_P%C3%A9riode_Interm%C3%A9diaire_GM_243_2014_p._23-32
(in french) Says that, around 1750 BC, Egyptians who were not rich enough had small sculptures made of steatite/sopastone, then baked at 900°C or higher so that they became as hard and durable as the statues made - from hardstones - for richer people.
« Cuire des statues » : l’usage de la stéatite en sculpture à la fin du Moyen Empire et à la Deuxième Période Intermédiaire.
"[...] Une cuisson à 900° C permet en effet de la durcir considérablement, de la rougir ou de la noircir (selon l’atmosphère de cuisson) [...] Sous l’effet de la chaleur, la pierre se déshydrate et, à partir d’une température de 900° C, se transforme en enstatite, d’un indice de dureté de 7 sur l’échelle de Mohs (au lieu de 1 pour la stéatite à l’état naturel) . Cette propriété est aujourd’hui utilisée par les artisans de la rive ouest de Louqsor pour produire des imitations de fritte, en enduisant d’une préparation à base de poudre de cuivre les pièces qu’ils ont réalisées en stéatite. Après cuisson à ciel ouvert, les reproductions d’amulettes et d’hippopotames sortent du foyer bleues, brillantes et très dures. [...]. Un simple four de quelques dizaines de centimètres de diamètre, creusé dans le sol, alimenté par un alandier et recouvert de briques a permis d’atteindre la température de 900° C en moins d’une heure. Un combustible particulièrement efficace et certainement aussi le moins onéreux pour cette opération s’est révélé être la bouse de vache séchée (utilisée encore aujourd’hui dans les campagnes égyptiennes). Lors d’une cuisson à ciel ouvert, en atmosphère oxydante, la stéatite rougit et obtient une couleur brun-rouge orangé, que l’on retrouve sur certaines statuettes de la XIIIe dynastie [...]. C’est probablement surtout une cuisson en atmosphère réductrice qui devait être utilisée. En effet, en refermant au bout d’une heure le four et en laissant se poursuivre la cuisson de la stéatite en enfumage pendant toute une journée, la surface obtenue était bien noire et dure. Un simple polissage a suffi ensuite à conférer à la pièce l’aspect luisant des statuettes du Moyen Empire."

http://annales.ensmp.fr/articles/1803-1804-1/82-84.pdf
(in french again) In the 18th century, artists were carving cameo from steatite/soapstone, then they baked them (to "red white" color) during 2 to 3 hours so that they become has hard as flint. They also had various ways for coloring the resulting stones. The paper also reports another experiment : making a paste with water and steatite/soaptsone powder, bake it (like clay), in hope of getting some hard rock : didn't work.

https://www.britishmuseum.org/pdf/Softstone%20in%20Arabia.pdf
"[... about small beads made from soft talc, then heated] The temperature at which enstatite crystallises is above 1200 C. This technology resembles that known from ancient India and Iran."
"[...] and other figurines (burials 634-638) made from a white heated form of steatite [...]"

http://link.springer.com/article/10.1007%2FBF00549373
The effect of firing temperature on properties of natural steatite and pyrophyllite
[The abstracts gives no practical new hint useful for prehistoric technology re-enactment : steatite hardens when heated above 900°C]
"Both materials were fired in hydrogen and air, over the temperature ranges of 950 to 1100° C and 1000 to 1150° C for the steatite and pyrophyllite, respectively. [...] The strength and hardness of the hydrogen-fired pyrophyllite was higher than its air-fired counterpart. The opposite result was observed in the steatite."

http://www.electronicsforu.com/EFYLinux/circuit/april2004/Steatite.pdf
a modern industrial process for firing steatite (but no information about the hardness obtained)

Cultural and social dimensions of the prehistoric Gulf Island soapstone industry - 1994 - Inge R. Dahm

http://summit.sfu.ca/system/files/iritems1/6548/b1696293x.pdf
Very interesting (artifacts description, culture, 200+km long distance exchanges, tools for carving soapstone, ...).
Apart from a few remarks like "this artifact appears to have been burnt", I couldn't find any discussion about a possible heat treatment of the soapstone artifacts and ornaments. Although this is a question that every reader would like to see answered : were those fragile artifacts hardened in some way, like in various other cultures, to withstand years of usage and... thousands of years in the ground ?
This being said, for many of this artifacs, especially labrets, softness may have been prefered to hardness: you don't want your teeth to be broken by a too hard stone labret. And the author regularly underscores the softness of the stone : maybe he verified it on most artifacts (? ... I didn't find any information about chemical analyses or hardness test).
About about physical properties, said to be "relevant to prehistoric soapstone carving", one information is the softness of the stone. And the only other information, rather irrelevant in prehistoric context is : "Fusability : Reaction to heat treatment. Soapstone will whiten and exfoliate when heated alone before a blowpipe and fuse to an enamel on the edges only". A few lines after that, another information that misses the point : "Soapstone can be heat treated to a hardness of 8 but will become brittle and will fracture or shatter on impact". Not very useful, because what we need to know is the amount of heat treatment - achievable with primitive means - that would confer some durability to (what variety and quality of) soapstone; and not the result of what appears extreme heat treatment (in other documents, heat treatments are said to harden soapstone to a hardness around 5 or 6).

Encyclopaedia Americana - 1800 - 1872
http://collections.nlm.nih.gov/bookviewer?PID=nlm:nlmuid-00110080RX11-mvpart
On page 583 (579) , about Steatite... here is a pinnacle of imprecision : "exposed to heat it, becomes much harder". Other nevertheless interesting information : "the variety of steatite called potstone is in hardness nearly the same as common steatite, but is more tenacious. [...] Steatite is not susceptible of a good polish; but its softness and tenacity [...] and its property of becoming hard by heat, render it a useful mineral in the arts. [...] The common steatite has even been employed for the purpose of engraving ; for, beeing easily cut when soft, it may be made to assume any desired form, and afterwards rendered hard by heat. It then becomes susceptible of a plolish, and may be variously colored by metalic solutions"

http://www.jstor.org/stable/124486
[protected content]
Glazed Steatite: An Investigation of the Methods of Glazing Used in Ancient Egypt (Jun., 1989)
"Whichever glazing method is used for steatie [...] the body becomes very much harder"

http://pubs.usgs.gov/circ/1951/0095/report.pdf
[Talc Investigation in Vermont - Preliminary report - 1951 - US departement of the interior - geological survey]
page 2 : "The pure, dense, crypto-crystalline variety of steatite known as "lava grade" is valuable because it can be machined into intricate forms and then heat-treated to great hardness with negligible shrinkage."

https://archive.org/stream/talcdepositsofst08page/talcdepositsofst08page_djvu.txt
[TALC DEPOSITS OF STEATITE GRADE, INYO COUNTY, CALIFORNIA]
"Lava-grade block talc is a variety of steatite dis- tinguished by its suitability for machining. It must be free of flaws and must not crack during firing. Formerly, lava-grade block talc was the only type of steatite used for insulators. Now, however, it is employed only in rela- tively small quantities for spacers in radar vaccuum tubes and for other specialized purposes. Since the discovery in the early 1920 's that pulverized talc could be used for making insulators, most steatite has been ground before firing. It is mixed with a binder, and pressed or extruded into the required shapes."

https://www.google.com/patents/US71919
[Letters Patent No. 71,919, dated December. 10, 1867. Henry Julius Smith, Boston]
"put the articles so formed in intimate contact with some kind of carbon, (I prefer finely-ground hone-coal or plumbago,) into a closed vessel, of suitable material for resisting heat, and submit the vessel and contents to heat for an hour or more, removing the same when a white heat has been reached. The articles are then found to be hard and tough. "
https://patentimages.storage.googleapis.com/pages/US71919.png

This corresponds probably to a temperature almost impossible to reach by prehistoric means.

Neanderthal superglue from birch bark - Experiments

2016-01-31T13:18:00.002+01:00

Big buzz this summer 2017 about 3 different and successful experiments
by P. R. B. Kozowyk, M. Soressi, D. Pomstra & G. H. J. Langejans.
Open paper on nature.com : https://www.nature.com/articles/s41598-017-08106-7
- Weight of the tar obtained = 9.6% of the weight of the bark (from Betula Pendula)
- Betula Alba would be the best species
- Several hours of burning with the "raised structure" technique [several hours : that's imprecise ! and from my experiments, I'm would tend to believe that 2 hours are more than enough]
- they seem to readily accept that "tar production is at least 200 thousand years old"

- Good news (obvious) : no real need for temperature control ;

Temperatures did vary during the experimentations, between less than 200°C and more than 400°C.
Suitable temperatures with birch bark : between 250°C and 500+°C
"The ability to strictly control temperatures to a narrow range between 340 °C and 370 °C for tar production is thus not as necessary as previously thought"

They have an excellent illustration about the compared tar yield, compexity of the 3 methods and the need to control (or not) the temperature :

This being said, we can't say that the use of a digging stick is a "complexity" : it can be replaced by "digging hands", and is something that every animal can do. We probably invented the digging stick long before we invented fire, which may be the most complex thing here :-)
OK, the complexity is in the number of steps needed... but do we really need to take this into account ? building a shelter requires a lot of steps; preparing one's tools for the next hunt requires a lot of steps; and even just making the spear for the next hunt requires lots of steps, knowledge and dexterity (finding a suitable piece of wood, preparing it, preparing a place for the spear point, finding flint or other suitable rock, knapping the rock, finding some adhesive or rawhide, hafting the spear point, ...).

Links to videos (timelapses) of the best ("raised structure") of the 3 methods here:
https://www.universiteitleiden.nl/en/news/2017/08/first-glue-neanderthals

A Method of Wood Tar Production, Without the Use of Ceramics
Grzegorz Osipowicz ; Reconstr. Exp. Archaeology EuroREA, 01/2005; 2:11-17.
Synthesis : http://www.keap.umk.pl/en/making-birch-tar-without-use-of-ceramics.html
Details : https://www.researchgate.net/publication/259583450_A_method_of_wood_tar_production_without_the_use_of_ceramics
There are interesting photos, and I would have loved seeing how was the glue accumulated at the bottom of the kiln, before its removal. The species of birch used in the experiment remains unknown.

Remarks, other links and other experiments
[no correct citations : a bunch of keywords, extracts and links]

From the above paper, we can guess that one primitive way of making glue from birch bark is not by producing tar first. In the described process, the tar mixes itself with charcoal : by "contamination" with carbonized birch bark.

Notes :
There are conflicting evaluations about the age of the piece of birch glue found at Königsaue : 40 000 years old or 80 000 years old. Older pieces of birch tar have been found in Italy (Campitello) : some say they are 200000 years old, others say that it's dubbious (see http://www.thesubversivearchaeologist.com/2012/02/of-birch-tar-hafts-and-caribou-fleshers.html).
From a short synthesis about the use of adhesives in Africa and Europe :
http://www.roceeh.net/fileadmin/images/Map_of_the_month/MoM_2010_12_Paleolithic_Adhesives.pdf

Still unclear to us ignorants... because we can read such different things here and there : Does the tar simply drip down, exuded in liquid form by the bark without going through a vaporized / gaseous state ? or does it condense itself from vaporized compounds ? or does it do both things, at various places in the kiln and at various stages of the process, depending on the temperature ?

Other apparently confusing elements :
"dry distillation", "destructive wood distillation", 300-400C, 340-400 °C, 220-280 °C, over 650°F [343°C], "released vapour is collected by a method which cools it down" , "wood tar is acquired during firing by it running through the holes into the smaller vessel placed underneath the big one" , "Without an airtight firing chamber, the wood tar would either evaporate or [...]", "limited air supply", Betula pendula Roth., Betula pubescens, ...

Much simpler techniques than "dry distillation" ?
http://www.academia.edu/11285848/To_see_a_world_in_a_hafted_tool_birch_pitch_composite_technology_cognition_and_memory_in_Neanderthals
"in simple covered pits (Pawlik 2004) or underneath stones inside a fire (Palmer 2007). It may even be possible through holding bark tightly wrapped around a stick inside the heart of a fire (Knul, pers. comm. 2011)".

As technologically simple as traditional charcoal making ?
http://www.continuitas.org/texts/benozzo_distillation.pdf
"[about (the very primitive) charcoal making in the XIX-XX in Itlay; page 35] the production of pitch was one of the secondary activities related to the making of charcoal (it was employed for covering roofs, or as a glue for tools, and the carbonai used to sell it together with charcoal"

Links and Experiments :

Grzegorz Osipowicz continues to experiment, and tries different types of kilns
http://www.academia.edu/4898914/New_experiments_with_a_mehod_of_birch_tar_production_without_the_use_of_ceramics

Neanderthal Superglue [2013; video]
https://www.youtube.com/watch?v=Dv81adCRQ2s
Shows a primitive process which result - after 8 hours of burning - is a very faint layer of tar on a small stone; no liquid.

Neanderthals 'used glue to make tools' ; Saturday, 19 January, 2002, 08:00 GMT
http://news.bbc.co.uk/2/hi/science/nature/1766683.stm
Keywords : Dr Dietrich Mania; Germany; Königsaue; Harz Mountains; Friedrich-Schiller University ; European Journal of Archaeology

"A sticky fingerprint on a fossilised blob of wood"
http://www.freerepublic.com/focus/f-news/608179/posts
keywords : Aschersleben; Harz Mountain; Heinrich Wunderlich; Professor Dietrich Mania of Freidrich-Schiller University in Jena ; more than 80 000 years old

Neanderthals Clever Enough To Make 'Superglue'
http://www.freerepublic.com/focus/fr/602648/posts
Extract :"The research, carried out at the Doerner-Institut in Munich, found the pitch was a birch pitch, which can be only be produced at temperatures of 300-400C"
keywords : Discovered in a lignite mining pit in the Harz mountains in Germany. Professor Chris Stringer, Natural History Museum in London. Professor Dietrich Mania of Freidrich-Schiller University in Jena

High-Tech in the Middle Palaeolithic: Neandertal-Manufactured Pitch Identified
http://eja.sagepub.com/content/4/3/385.abstract
European journal of archaelogy
keywords : Johann Koller,Ursula Baumer Doerner-Institut, München, Germany; Dietrich Mania , Friedrich-Schiller-Universität Jena, Germany

Neanderthals Defy Stereotypes
By Evan Hadingham ; Posted 01.09.13; NOVA
http://www.pbs.org/wgbh/nova/evolution/defy-stereotypes.html
Extracts : [...] distilling pitch from birch bark requires an oxygen-free environment and sustained temperatures of over 650° F [...] first discovery was made in 1963 at Kínigsaue, in then-East Germany. [...] Two small, hardened lumps of black material were found [...] one bearing a fingerprint and the other the impression of a wooden haft or handle. [...] In 2001, the lumps were dated to at least 40,000 years ago [...] birch bark pitch produced by the dry distillation process. Much older evidence was found at the Campitello quarry in central Italy. [...] two large lumps of black pitch, which covered the end of two stone flakes crafted in a typical Neanderthal style. The Campitello find dates back over 200,000 years [...] A third Neanderthal site at Inden-Altdorf, overlooking the Inde River in Germany and dating to around 128,000 to 115,000 years ago, features more than 80 stone tools flecked with black material, but the chemical analysis indicating that this was distilled pitch requires further confirmation.
[...] the team proposed that the Neanderthals had invented the following procedure: first, wrap a long strip of birch bark around a small pebble so that it forms a cigar-shaped roll. Next, dig a narrow pit, then set light to one end of the roll and place the burning end at the bottom of the pit. In the confined space at the bottom of the pit, the smoldering bark quickly uses up oxygen and causes the pitch to "sweat," or condense, out of the roll of bark onto the surface of the pebble. While still hot, the pitch is a sticky liquid that can be used immediately as glue.
[...] Although German experimental archaeologist Friedrich Palmer succeeded in earlier published experiments, in the NOVA program, he fails to produce more than a thin smear of pitch. In 2010, another team reported success by a variation on the technique: lay strips of bark on a flat stone surface, cover them with a couple of inches of sand to exclude oxygen, then build a fire on top. After a little over an hour, the team dug up the stone and found that enough pitch had dripped onto its surface to haft two or three spears or tools.However, the team succeeded easily on their first attempt only because they had a thermometer to judge if the fire was hot enough.[...] Archaeologist Wil Roebroeks, who witnessed Palmer's NOVA experiment, comments that its failure underscores the complexity of the process,[...]

Sticking with Neanderthals: Identifying Neanderthal Mastics and their Signatures
Joseph Walsh; Advisor: Bruce Hardy, PhD., David Heithaus
http://biology.kenyon.edu/HHMI/posters_2014/walshj.pdf

Ça colle pour l'homme de Neandertal
Par Sylvie BRIET — 22 janvier 2002 à 21:45
http://www.liberation.fr/sciences/2002/01/22/ca-colle-pour-l-homme-de-neandertal_391193
Extracts : [... ] En 1963, Dietrich Mania, paléontologue à l'université d'Iéna, découvre des outils et morceaux de poix datant de l'époque de Neandertal dans une carrière de lignite au nord-est des montagnes du Harz, près de Königsaue (Allemagne).[...] L'un des morceaux comporte une empreinte de doigt mais également la marque d'une lame de silex et celles de cellules de bois: ce morceau de poix, utilisé comme adhésif, fixait un manche en bois à une lame de couteau en silex. Tout le matériel découvert (comprenant d'autres pièces de bois et outils en silex) fut transféré au Landesmuseum à Halle. Sans être analysé plus avant car les techniques n'existaient pas.Trente-trois ans plus tard, le matériel est envoyé à l'institut Doerner. Des premiers résultats furent publiés en 1999. Cette fois, Johann Koller et Ursula Baumer ont établi la composition chimique [...] origine biologique [...] découvert que le niveau de bétulin (Betula verrucosa) est très élevé dans leurs morceaux de poix, comme dans l'écorce de bois de bouleau. [...] pour fabriquer une glue de cette qualité, il a fallu chauffer l'écorce dans une fourchette de température très étroite: entre 340 et 400 °C. [...] L'abondance du matériel annexe, les outils multiples suggèrent qu'il existe deux cultures sur ce site. L'une d'elles peut être attribuée aux premiers Homo sapiens modernes, la seconde revient clairement aux Néandertaliens. Restent des incertitudes sur les datations. Dietrich Mania, le paléontologue qui a découvert le site, n'a aucun doute sur l'âge des couches géologiques qui datent de 80 000 ans. Les morceaux ont été envoyés à Oxford (Grande-Bretagne) pour une datation au radiocarbone qui a donné 44 000 et 48 000 ans! La trop faible concentration en carbone pourrait expliquer cette différence et les chercheurs penchent pour la date géologique. [...]
European Journal of Archaeology de décembre 2001.

Neanderthal Glue Makers
[Video, 2008, National Geograhics]
https://www.youtube.com/watch?v=q7YT2HxWPVU
Claims to have a good idea of how Neandertals could have made glue from birch bark.
Illustrates the first steps, but doesn't show the end of the process nor success.
Evokes Native American Tribe in Canada having an ancestral technique for that, but doesn't name it, unfortunately...
keywords : Museum of Halle; fragment of ice age adhesive found in the 1960 in Königsaue in eastern germany; Dr Christian Heinrich Wunderlich, "no scientist has succeeded in making this pitch glue with the material Neandertals could have used"

Genotoxicity Assessment of Birch-Bark Tar—A Most Versatile Prehistoric Adhesive
http://file.scirp.org/Html/19560.html
Extract: "heating (pyrolysis) the bark of birch trees (e.g. European white birch Betula pendula Roth) under reducing conditions with limited air supply and a temperature of over 300˚C, the distillation product is an odorous dark-brown viscous pitch (Dudd & Evershed, 1999)."

Experimental explorations into the aceramic dry distillation of Betula pubescens (downy birch) bark tar.
First online: 21 June 2013.Peter Groom,Tine Schenck,Grethe Moéll Pedersen
http://link.springer.com/article/10.1007/s12520-013-0144-5?no-access=true
Extract : "[...] Though the experiments did not successfully produce tar as a finished product, they did lead to a better understanding of the dry distillation process [...]"

Traditional Glue, Adhesive and Poison Used for Composite Weapons by Ju/’hoan San in Nyae Nyae, Namibia. Implications for the Evolution of Hunting Equipment in Prehistory
Lyn Wadley , Gary Trower , Lucinda Backwell , Francesco d’Errico
PLOS; Published: October 28, 2015; DOI: 10.1371/journal.pone.0140269
http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0140269
Extract : "Western European Neanderthals heated birch bark for glue by Marine Isotope Stage 6 (MIS 6, that is, ~200,000–130,000 years ago) at the Campitello quarry site in Central Italy [1,2]. Stone tools from an occupation ~120,000 (120 ka) years old, in Inden-Altdorf, Germany, were hafted with birch bark pitch [3] and it was also discovered at Königsaue, Germany, where the geological-stratigraphic context suggests ages older than 80 ka [4]."

And here are my own experiments, not all failed
https://www.youtube.com/playlist?list=PL3DB4AC65A3ADEE03

More documents

Using Organic Materials in prehistory
Universtity College of London
https://www.ucl.ac.uk/archaeology/studying/undergraduate/courses/coursehandbooks/ARCL2041_organic_materials.pdf
[not about Neandertals] Werner Pfeifer describes an open distillation process and a closed distillation process; in both cases there are similarities with the kiln of Grzegorz Osipowicz ; but the result is very different : liquid tar, not hard glue.

Wood Tar in The Dnieper and Elbe Communities - VI-II Millenium BC
Slavomir Pietrzak; Baltic-Pontic studies; 2012
https://repozytorium.amu.edu.pl/bitstream/10593/13021/1/BPS-17_S_Pietrzak_WOOD%20TAR%20IN%20THE%20DNIEPER%20AND%20ELBE%20COMMUNITIES-VI%20%E2%80%93%20II%20MILLENIUM%20BC.pdf
[not about Neandertals]

When did humans learn to boil ?
John D. Speth, 2014
http://www.paleoanthro.org/media/journal/content/PA20150054.pdf
Humans may have, very early, boiled their food in skins, paunches, bark containers, by direct heating over a flame (without using heated stones, nor ceramic vessels). These techniques have been described in a number of Native American cultures. [see pages 57 to 59, in "Boiling in perishable containers without using heated stones"].
About birch glue :
"Birch tar can only be produced by a process of destructive (dry) distillation, in the absence of oxygen, and with temperatures maintained for several hours between a minimum of 340 ºC and a maximum of about 400 ºC (Koller et al. 2001; Peters et al. 2005: 335–337). [...] No one to my knowledge has yet adequately figured out how Neanderthals would have accomplished this complex feat of pyrotechnics without the aid of metal or ceramic containers (see Osipowicz 2005; Peters et al. 2005: 336–337; Palmer 2007; Meijer and Pomstra 2011; Groom et al. 2015)." [[what ? Osipowicz shows a way to do it, actually]]
The bibliograhy related to these extracts :
Groom, P., Schenck, T., Moéll Pedersen, G. 2015. Experimental explorations into the aceramic dry distillation of Betula pubescens (downy birch) bark tar. Archaeological and Anthropological Sciences 7, 47–58.
Koller, J., Baumer, U., Mania, D. 2001. High-tech in the Middle Palaeolithic: Neandertal-manufactured pitch identified. European Journal of Archaeology 4, 385–397.
Meijer, R., Pomstra, D. 2011. The production of birch pitch with hunter-gatherer technology: a possibility. Experimentelle Archäologie in Europa, Bilanz 2011, 199-204.
Osipowicz, G. 2005. A method of wood tar production, without the use of ceramics. euroREA 2, 11–17.
Palmer, F. 2007. Die entstehung von birkenpech in einer feuerstelle unter Paläolithischen bedingungen. Mitteilungen der Gesellschaft für Urgeschichte 16, 75–83.
Peters, K.E., Walters, C.C., Moldowan, J.M. 2005. The Biomarker Guide, Vol. 1. Biomarkers and Isotopes in the Environment and Human History. 2nd edition. Cambridge University Press, Cambridge.

Bâton de jet Gaulois - Urville-Nacqueville, Manche, France - Rainuré comme certains boomerangs et kylies australiens et bâtons de jets amérindiens

2016-01-16T15:00:00.001+01:00

Etude et expérimentations autour de la découverte d'un bâton de jet gaulois

sur le site d’Urville-Nacqueville (Manche)

Luc Bordes, Anthony Lefort, François Blondel et Thierry Meinel

http://revedeboomerang.free.fr/baton-urville2.pdf

Bâton de jet ; chasse aux oiseaux ; renforts en fer ; rainures longitudinales

100 av. J.C.

Trouvaille archéologique unique en France : en 2010

Comparaison avec d'autres bâtons de jets / boomerangs / kylies ; Europe et monde

Rainures purement décoratives ... Quels arguments ?

Les auteurs prennent pour acquis que les rainures longitudinales sont purement décoratives.

En même temps ils soulignent la présence de rainures du même type sur des boomerangs amérindiens et australiens. Alors... naturellement ... frustration manifeste du lecteur qui veut un début de "preuve" que cette convergence est uniquement décorative et non fonctionnelle.

Il existe peut-être un argument simple, dans ce cas précis où l'on affirme

que ce boomerang sans retour était utilisé dans un environnement humide :

les rainures mouillées ne joueraient plus leur rôle.
Il m'est arrivé de faire l'expérience dans un environnement boueux :

dès le second jet, le vol de mon boomerang sans retour s'est dégradé

(alourdi, les rainures boueuses, ...).

Il existe au moins une étude, résultat d'expérimentation en soufflerie, sur l'efficacité aérodynamique des rainures de boomerangs / bâtons de jets australiens.

Nelson, Reymond Charles. 'Groovy' Aerodynamics in Pre-European Australia.

Australian Journal of Multi-disciplinary Engineering, Vol. 2, No. 1, 2004: 1-7.

On trouve l'article sur internet, mais il est payant. Je l'ai acheté, lu et ... perdu... En fait, il n'offrait pas de preuve définitive, mais sa conclusion suggérait assez nettement une fonction aérodynamique pour ces rainures, pourvu qu'elles respectent certaines conditions.

La présentation de l'article est beaucoup plus catégorique (commerce oblige...) :

"[...] Wind tunnel tests show large drag force reductions in the case of throwing sticks and large lift force increases in the case of boomerangs. The fluting alone is responsible for the improved performance.[...]"

(http://search.informit.com.au/documentSummary;dn=520325129598400;res=IELENG

ou http://www.tandfonline.com/doi/abs/10.1080/14488388.2004.11464717)

Les bâtons de jet préhistoriques et leurs représentations

2015-05-16T20:53:00.002+02:00

Les bâtons de jet préhistoriques et leurs représentations: développement d'outils et de méthodes pour la mesure de leurs caractéristiques et l'évaluation de leurs fonctions

Luc Bordes, mémoire de Master 2 Préhistoire, Paléoenvironnement, et Archéométrie, Juin 2014

http://revedeboomerang.free.fr/memoire-LucBordes.pdf

Traditional boomerangs in India - Tamil Valari - வளரி

2015-01-04T22:08:00.007+01:00

I had taken for granted that boomerangs had been traditionally used in India.

But when I tried to know a bit more, I found only the same sentences repeated everywhere on the Internet.

So, I searched the Web more seriously... and gathered here every photo or comment about traditional Indian boomerangs. Most photos are from the British Museum, the Quai Branly Museum, the National Trust Collections, the Royal Collection Trust. The rest was found in the Higgins Collection, the Pitt Rivers Museum, a few commercial sites, blogs, forums or web pages. Comments generally come from old books found on archive.org.

I made screen copies of what was shown in my web browser when I zoomed on the interesting parts of the screen. Then I reworked slightly the resulting image (cropping, harmonizing sizes and orientations). This should not be a copyright violation (no commercial purpose, personal research, teaching of some kind, ...) and it's a protection against the change of url that may always happen on the other web sites. Beside that some web site (ex. Quai Branly Museum) don't even allow (bug ? or stupid policy ?) linking to their photos or web search results.

If you prefer,you can see :
- a quick Web tour without comments

- or a playlist : videos with experiments and visual explanations
(the comments are more often in Tamil language)

If you are interested in the cultural or historical aspect of the subject, you'll be able to read the books or web sites referenced below (although the reliable information that we can gather in english on this subject can seem very "shallow"). Anyway, the interesting thing for who (like me) is ignorant about India, is the unusual quantity of new names that we can't even associate with a vague category (tribes, castes, places, cities, persons, titles, languages, objects, historical events, ...). Add to this the fact that the place names have changed and that there were various ways of transcribing names in the roman alphabet. So, even by chasing such a limited subject as "boomerangs in India", you immediately encounter a fairly interesting quantity of unknown cultural and historical notions.

This search really began after a discussion with youtuber "Bangalorebobbel" who found an online version of "Castes and Tribes of Southern India", Edgar Thurston, 1909.

As usual this kind of old book is to be found on archives.org, where, maybe, any such search should begin (!?) : https://archive.org/details/castestribesofso01thuriala (pdf version :

https://ia600408.us.archive.org/33/items/castestribesofso03thuruoft/castestribesofso03thuruoft.pdf).

In that document, page 66, 70, 84/85, boomerangs are said to be a typical weapon of the Kallars/Kallan and Maravans (castes / tribes of the Tamil people in South India). Those boomerangs were made of wood, ivory, metal. The name of the weapon is written as "valai tadi" / "valari tadi" / "vellari thadi" / "vallari thadi" and is said to mean "bent stick". Page 77, 78 is mentioned a tradition : exchange of boomerangs between bride and bridegroom.
Associated place names : Madura, Madras [now Chennai] Museum, Pudukkottai, Tanjore [now Thanjavur] Armoury.

Actually this text partly comes from "Ethnographic notes in southern India : with 40 plates", Edgar Thurston, 1906; where a chapter is dedicated to boomerangs (page 555 to 559 ?? / 645 to 649) and a plate (XXXVII, page 556) with 2 boomerangs.
plate : https://archive.org/stream/cu31924023651023#page/n648/mode/1up

(I separated the image in two parts)

text : https://archive.org/stream/cu31924023651023#page/n645/mode/2up

This text also states that the Koli tribe of Guzerat [Gujarat, North Western India] used boomerangs. We can doubt that the author ever saw himself an indian boomerang as every assertion is attributed to other authors or personnalities or books : Mr Savile Kent citing Mr Balfour, General Pitt Rivers [ex Lane-Fox], Prof. E.C. Stirling, Egerton's "Indian and Oriental Armour", Dr G. Oppert citing the Dewan of Pudukkottai, Mr R. Bruce Foot, G.F. Dr Penha.

Egerton's "Indian and Oriental Armour" should contain some information about Indian boomerangs, but it is useless on archive.org which refers to googlebooks where (as usual) there is no means to read the thing normally.

About Pitt Rivers / Lane-Fox, an interesting article describing his experiments on boomerangs can be read on the Pitt Rivers Museum Web site, at http://england.prm.ox.ac.uk/englishness-PR-and-Boomerang-technology.html . We learn that Pitt Rivers made several facsimiles of Egyptian and Indian boomerangs seen in museums and that he successfully trained himself to throw them [so, this obsession about boomerangs is at least 130 years old in the west, may be more :-) ]. These are the 2 facsimiles of indian boomerang shown on the Web site (the egyptian one is beautiful also, but not given below) :

I can find only another boomerang photo (a ceremonial throwing stick, Madurai, Tamil Nadu) on Pitt Rivers Museum web site :
http://web.prm.ox.ac.uk/weapons/index.php/tour-by-region/oceania/asia/arms-and-armour-asia-138/index.html

October 12th 2017 - I find only 2 images (of the same object) in the ROYAL ARMOURIES COLLECTION web site
https://collections.royalarmouries.org/object/rac-object-10758.html
"Throwing stick (katariya, birra jungee)", "Dimensions: The length of the weapon is 443 mm (17.5in) max. width 5.7mm (2.0in). Weight: The weight of the weapon is 0.25 kg."; Associated Places : India, Hyderabad.

The same one - maybe, although it seems a bit more sturdy - as photographed in an exhibition of the Royal Armouries;
found (oct 12th 2017) on http://britseps.blogspot.fr/2012/11/ (toward the end of the post)

Chennai Museum Web Site only shows a bad quality photo of 2 apparently indian boomerangs but, strangely, the associated commentary is about australian Aborigines (although the comment is not very clear).

See this page, which also mentions the Khonds of Orissa without alluding to boomerangs : http://www.chennaimuseum.org/draft/gallery/02/02/ethnolg2.htm

2018 09 29 : I can't find this web page anymore, but there are now a good number of e-books on the web site of the Museum of Chennai. Some of them mentions boomerangs and valari,
In the Museum's journal of 1998-1999, there is an article written by a curator named Dr C. Maheshwaran : "Boomerangs in the collection of Chennai state museum". The article cites numerous times 150 years old british information (Thurston, Balfour), which suggests that reliable local information on the subject was not easily found in 1999.
http://www.e-books-chennaimuseum.tn.gov.in/chennaimuseum/images/books/GOVERNMENT%20MUSEUM%20CHENNAI%20MUSEUM%27S%20JOURNAL%20APRIL%201998%20-%20NOVEMBER%201999.pdf

In "The races of Man : an outline of anthropology and ethnography", Deniker, 1904 we read that boomerangs named "Singa" are attributed to the Khonds of Orissa [now Odisha, Eastern India] :

https://archive.org/stream/racesofmanoutlin00deniuoft#page/258/mode/2up

In "A study of traditionnal throwing sticks and boomerang tuning", Luc Bordes makes an analysis of the shapes and profiles of 5 Indian boomerangs (Valai thadi series of 5 boomerangs from Tamil Nadu) found in the Quai Branly Museum, Paris. See page 6 "a remarkable Indian Valari series" in http://revedeboomerang.free.fr/tuning2.pdf ; figure 12a is reproduced below :

Elsewhere, on http://revedeboomerang.free.fr/inde.html and http://revedeboomerang.free.fr/planisphere.jpg we find other photos of unknow origin, one is said to represent a Katariya / Katurea (from Gujarat), another represents some Valari and an australian-looking boomerang said to be from Southern India, Tamil Nadu.

After verification... the first image comes from http://www.oriental-arms.co.il/item.php?id=558 (a sold item). The second one is from one of the editions of "A glossary of the construction, decoration and use of arms and armor in all countries and in all times, together with some closely related subjects", by George Cameron Stone. We find in two places (page 346 & 348) the name "Guzerat" as the source of weapons that resemble more to the Tamil's Valari. (wrong attribution ? all mixed up : katari/valari/south india/katariya/gujarat ?) :

(Baroda = old name for nowadays Vadodara, third largest city in Gujarat (wikipedia))

Wilbraham Egerton published in 1880 a catalogue of the collections of the "India Museum" (1801-1879) : "An Illustrated handbook of Indian arms : being a catalogue of the arms exhibited at the India Museum". Some of the objects were reproduced in this catalog, and among them, some of the Indian boomerangs. We can see a rather well digitalized version of it; and here is a partial map of India where we can see what was called "Guzerat", the territory of the "Kolis", and "Baroda" https://babel.hathitrust.org/cgi/pt?id=hvd.tz1py2;view=1up;seq=8. Extract :

I can find only a few mentions of the Indian boomerangs in this publication, and only one illustration; pages 73, 74, 78, 81 :

Other boomerangs (southern Indian ones), mentioned, but not illustrated (apparently) :

Another "Katariya", made of brass, is shown on http://akaalarms.com/sold-very-rare-18th-century-indian-boomerang-ref-10327/

The comments let me wonder if it's a good idea to believe everything ... they seem to be like me : gathering information from every source... I would make every confusion between Katariya and Valari or Gujarat and Tamil Nadu when reading : "A very rare 18th Century Indian boomerang, traditionally used by the tribes of Gujerat and South India to hunt small animals, and protect livestock from predators. There are various names attributed to these items, Elgood* calls it a ‘Birundungi’ (referring to the South Indian variant); and Lord Egerton**, a ‘Katariya’ (referring to a boomerang used by Koles – a tribe of Gujerat). A lesser known source, Edgar Thurston*** provides some compelling research and calls it a ‘Valari’ or ‘Valai-Tadi’, referring to examples in the Tanjore Museum."

Another similar object, 30 cm long, steel, called Birundungi, said to be from South India is shown on http://akaalarms.com/sold-south-indian-steel-boomerang-known-as-a-birundungi-ref-10082/

Another "Katariya" from the Higgins Collection http://www.higgins-collection.org/artifacts/3485

18 1/4" O.L. 14 oz - Katariya, Gujarat, iron

October 12th 2017; found one image on http://ww.w.flight-toys.com/artifacts/tb423.html
"Iron Singa or Birugundi Boomerang from Southern India"; "Span = 35 cm ; Weight = 238 gm"
Comment [mostly repeating what we read elsewhere] : "This unusual throwing implement is a Tamil Valari or Birudungi Iron War Boomerang. This example was made out of low grade iron and the surfaces are heavily oxidized, but fully intact and functional. The more common steel form is called the Singa. The form of the Tamil boomerang is of very ancient origin, used in warfare and hunting. The term boomerang which has stuck amongst collectors is purhaps misleading as it does not return to the thrower. All surviving examples share several features in common, the ball or egg shaped knob for gripping, flattened deeply curved body, and a squared flaring end. It was made by the Kallars/Kallan and Maravans (castes / tribes of the Tamil people in South India). These boomerangs were usually made out of wood, ivory or metal. The local name for this type of boomerang is "valai tadi" / "valari tadi" / "vellari thadi" / "vallari thadi" all of which mean "bent stick". It is often a tradition that very fine Birugundi boomerangs were exchanged between brides and bridegrooms."

October 12th 2017 - A "birudungi" made of steel, presented as

"Old Indo Persian South Indian Steel Boomerang 'Birudungi" Warrior n Hunting" or "South Indian boomerang"; "Dimension :overall length 35 cm approx", ...

Image from https://www.worthpoint.com/worthopedia/indo-persian-south-indian-steel-440343259

Wikipedia says... "Indo-Persian culture" refers to those Persian aspects that have been integrated into or absorbed into the cultures of the Indian Subcontinent. From the presentation of this item, we could wonder whether Persian had boomerangs or steel boomerang. (first quick google searches about that topic didn't retrieve anything).

(October 12 2017) One image found of a Katariya said to pertain to the Worcester Art Museum ;
Titled "Katariya (boomerang)" ; origin : Gujarat; made of iron; 46.4 cm (18 1/4 in.), 14 oz (weight) and having small beads inside which make a rattling sound.
http://vps343.pairvps.com:8080/emuseum/view/objects/asitem/20130/332/invno-asc?t:state:flow=ef4f5ed2-f6fe-4765-8248-92e8b90da8a6

I first found mention of the Quai Branly collection on this page :
http://www.ashokaarts.com/shop/extremely-rare-tamil-valari-or-birudungi-wooden-war-boomerang-19th-century where they show another Valari :

profile and upper face

Extracts of the comment : "[...] its more common steel form it is known as Singa, it has various names in southern languages: Valari (Tamil), Katariya (Khol), Birra Jungee/Birudungi (Hyderabad), Vălaytădi (malayalam). [...] Similar examples can be seen in the British Museum, Quai Branly, Fitzwilliam and Liverpool Museum amongst others."

I found nothing about boomerangs on the Liverpool Museum Web site.

About the Fitzwilliam museum, I was not able to find any photo and their search tool is not very efficient compared to others... it's being replaced... so ... we can at least find a few verbal descriptions for 2 south Indian boomerangs donated by a man named Robert Taylor in 1879 :
http://webapps.fitzmuseum.cam.ac.uk/explorer/index.php?qu=robert%20taylor&oid=160097
length: 47.5 cm ; weight: 140 g ;
http://webapps.fitzmuseum.cam.ac.uk/explorer/index.php?qu=robert%20taylor&oid=160096
length, 46 cm , weight, 250 g [shorter but heavier]

Quai Branly Museum has a few wooden boomerang not shown to the public, but with photos on their Web Site : http://collections.quaibranly.fr/#71ea5d81-50c8-4054-a2c2-e1fcc19880b7
(searching for "boomerang inde" we find 4 results, all from South India, Tamil Nadu, Gasivaganga)

N° 71.1939.85.69 - 16 x 50,5 x 2,7 cm, 114 g

N° 71.1939.85.66 - 14 x 48,5 x 2,8 cm, 269 g

N° 71.1939.85.67 - 17 x 46,5 x 3 cm, 202 g

N° 71.1939.85.68 - 48 x 15 x 2,5 cm, 182 g

knobs

searching for "bâton de jet", we find 2 more boomerangs from India
http://collections.quaibranly.fr/#15e6b86d-c5d8-4982-9b00-ec0a2511ce1e

N° 71.1954.21.19 D - 50,5 x 18 x 3,1 cm, 250 g

N° 71.1950.86.2 - 47 x 14 x 3 cm, 309 g
[can't be flat, if the data is correct, by comparison with the other boomerangs]

The British Museum also has some boomerangs from India. Searching for india+boomerang gives 6 results, all named "Valari", one being strange in shape (and doesn't seem to be able to fly).
http://www.britishmuseum.org/research/collection_online/search.aspx?searchText=india+boomerang

metal valari from Madurai (?) 34cm x 5.5 cm; 219 g

ivory valari from Sri Lanka 47 cm x 7.4 cm, 120 g

ivory valari from Sri Lanka 48 cm x 7.3 cm, 140 g

wooden valari from Madras 46cm x 7cm, 231 g

wooden (mimosa) valari from South India 47cm x 6.8 cm, 159 g

valari, Indian club, from industan (?) 62 cm x 32.5 cm x 3.1 cm ; 480 g [probably not flat and unable to fly]

Searching for "india throwing stick" http://www.britishmuseum.org/research/collection_online/search.aspx?searchText=india+throwing+stick we find one more boomerang (in shape), this time it is said to have been made by Gond (said to be one of the most diffused tribe in India) but by the shape, it seems to be simply one more valari from south India (with a missing broken angle).

6.1 cm, 44.6 cm, 0.2 cm, 0.2 g [the alleged dimensions are clearly false]

Searching for "collery stick" ("collery" comes from Kallar) http://www.britishmuseum.org/research/collection_online/search.aspx?searchText=collery+stick we find one more southern indian Valari. This one related to : Thanjavur (city, formerly Tanjore), Maravar (Tamil tribe).

49.5 cm x 6.2 cm; 207 g

About the "collery stick" we find in "Military reminiscences : extracted from a journal of nearly forty years' active service in the East Indies", James Welsh, 1830, Volume 1, page 130 (https://archive.org/stream/militaryreminisc01wels#page/130/mode/2up) : " [...] taught me to throw the spear, and hurl the collery stick, a weapon scarcely known elsewhere, but in a skillful hand, capable of being thrown to a certainty to any distance within one hundred yards".

Little more information on the collery-stick / valari that had known James Welsh, on the Web page http://www.sivagangaiseemai.com/maruthupandiyar/maruthu-pandiyar-history6.html# (about the history of Maruthu / Marudhu / Mardoo brothers once rulers of Sivagangai) The text seems to replicate parts of James Welsh's text without always saying it, so it's not very clear where the information comes from).

From the blog Maya Devar comes another photo that spresents a dozen of Valari : http://mayadevar.blogspot.com/2009/04/poomarang-valari.html . By interpreting the automatic translation of the Tamil comments, I guess those Valari were exposed in the palace of the ex-ruling family in Ramanathapuram / Ramnad, South East India.

We can guess that most of those valaris are only slightly flattened : except the one in the center ; they may have been unable to really fly. 4 are broken in a way that let think they were not perfectly cut along the grain of the wood. Maybe because, for handiness, the knob had to diverge slightly from the overall curve.

On http://tamilnation.co/heritage/weapon.htm we find another article about boomerangs used by the Tamils (but no source is cited) : "Valari - An Unique Weapon of the Tamils". The url "tamilnation.co" is said to replace temporarily "tamilnation.org", so be sure to go there when this url doesn't work anymore. And there is an image of a valari that is said to have been found in Thondi (city, port, in Ramanathapuram District, Tamil Nadu). Associated person names : Dr Jeyachandrun (the man who holds the valari in the photo), Dr Jayabarathi (the author of the article)

On http://vikingsword.com/vb/showthread.php?p=56083 we find two photos.
The first one is of a metal boomerang, from the book of Robert Elgood (2004) "Hindu Arms and Ritual: Arms and Armour from India 1400-1865" where it is said to be on page 191 (also said : more boomerang from India to be seen on page 193 ; the author states that there are 6 types of boomerangs in India - [can't verify that, this book is too recent to be freely read online] ).

The second one is said to be from a "book Malbourough House" (I found on archive.org a catalog of "A CATALOGUE OF THE MUSEUM OF ORNAMENTAL ART AT MARLBOROUGH HOUSE PALL MALL (1856)" but there is only the part I ; the Division 14 - about weapons - may be in the second part; see it at http://hdl.handle.net/2027/chi.80791435). The photo represents a cluster of weapons labelled "CASE J". I show here only the #205 : something shaped as another ivory boomerang from India.

A few more boomerangs found by searching "throwing weapons" in the National Trust Collections (after having seen photos and detailed comment on Pinterest) http://www.nationaltrustcollections.org.uk/search/1?show=100.

http://www.nationaltrustcollections.org.uk/object/1180707.1 calamander wood, 44 cm

http://www.nationaltrustcollections.org.uk/object/1180707.2 calamander wood, 41 cm

http://www.nationaltrustcollections.org.uk/object/1183944, calamander wood, 49.6 cm

http://www.nationaltrustcollections.org.uk/object/1183941, calamander wood, 49.2 cm

http://www.nationaltrustcollections.org.uk/object/1180697, ivory and silver, 48.5 cm

"The Evolution of Culture and Other Essays", Pitt-Rivers, Augustus Henry Lane-Fox, 1906

extract from http://www.gutenberg.org/files/44844/44844-h/images/zill_t142g_plate15h.png

Plate XV, diagram 6, Indian Boomerangs

There may have been an interesting collection of Indian boomerangs at the Pitt-Rivers Museum in 1946; Large enough to deserve a catalog (?), from what we may infer from "Sir Francis made a valuable catalogue of our Indian boomerangs" (see the annual report of the curator of the Pitt Rivers Museum, in 1946, http://web.prm.ox.ac.uk/sma/index.php/museum-annual-reports/246-1945-46-annual-report.html )

From the Royal collection Web site : http://www.royalcollection.org.uk/collection-search/boomerangs

46.8 x 5.2 x 2.5 cm, rosewood, blades shod in silver, heavy knobs

Presented by H.H. The Rani of Shivaganga, Mysore

49.3 x 15.2 cm, rosewood, flat blade, iron band, heavy knob