Every one knew how laborious the usual Method is of attaining to Arts and Sciences; whereas by his Contrivance, the most ignorant Person at a reasonable Charge, and with a little bodily Labour, may write Books in Philosophy, Poetry, Politicks, Law, Mathematicks and Theology, without the least Assistance from Genius or Study.

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Gulliver's Travels:
Voyage to Laputa

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Fanciful. Preposterous. Absurd.
Archive for February 2006
'Anbar

#

According to Baby Name Wizard's NameVoyager, the name Amber peaked as a baby girl's name some time back in the early 1980's and has been in steep decline ever since.

One theory has it that, as with many other names that became popular after 1970, the rate of new name invention has simply outstripped demand and the name Amber, after receiving its requisite 15 minutes of fame in the top 10, has since been shoved out of the way to make room for newer and brasher upstarts, über-brattish names such as Tayla, Kayla, Brianna or Madison. Poor old Amber, meanwhile, has had to be content with ranking below 80 on the various baby name Top 100 charts out there.

Of course the other reason might be that enough people started to realise that the etymology of the word is Amber is in fact "the vomit of a sperm whale". Not quite the sort of thing parents usually like to think about when naming their daughters...[1]

OK I suppose I should "unpack" that statement just a little bit.

When people think of amber they normally think of that yellow fossilized resin stuff, that sometimes encases ancient little insects and can be fashioned into all kinds of pretty things like jewellery and ornaments. The word comes from the Arabic word 'anbar however this is really a mistranslation or misappropriation of the word. Whereas the Europeans meant to refer to a substance that the Romans knew variously as succinum, glaesum or glesum and the Greeks knew as elektron, the Arabs were actually referring to an entirely different substance which is today rendered into English as ambergris or "grey amber".[2]
Why devil's music do not please?
What sort of thing is Ambergrease?

— Samuel Colvil Whiggs supplication: A mock poem in two parts. 1687
What's not to like about ambergris? It is an extremely rare aromatic substance which is:
...soft, waxy, and so highly fragrant and spicy, that it is largely used in perfumery, in pastiles, precious candles, hair-powders, and pomatum. The Turks use it in cooking, and also carry it to Mecca, for the same purpose that frankincense is carried to St. Peter's in Rome. Some wine merchants drop a few grains into claret, to flavor it.

— Herman Melville Moby-Dick, or, the whale. 1851.
Ambergris has been highly prized since ancient times as an ingredient for making perfumes. Its scent is often described as both sweet and earthy and it also has the property of slowing evaporation and making other fragrances last much longer. A single drop of it is said to be able to keep its scent for decades and a single lump could supply the needs of perfume manufacturer for several years.

Ambergris is expensive due to its extreme rarity and for a long time the source of this wondrous substance remained a mystery. It was only ever found washed up on beaches. The locals would collect it and bring it to market.
The pieces that are found on the coasts of this sea (of India) are thrown there by the waves. One finds the amber in the sea of India, but no one knows where it comes from.

One only knows that the best Amber is the one found at Berbera and up to the ends of the land of the Zang (the East Coast of Africa), and also at Sihr and its surroundings. That amber has the shape of an egg and is gray. The people of that region go to find it, riding on camels during the moon-lit nights; they follow the coasts. They ride camels who are trained for that and who know how to look for amber on the coast. When the camel finds a piece of amber, it kneels down and its owner goes to collect it. One also finds pieces of amber floating on the water of a considerable weight. Sometimes those pieces are really big.

Abu Zaid al Hassan from Siraf & Sulaiman the Merchant, Travels in Asia, 851 AD


Collecting ambergris on the shores of the Indian Ocean.
15th century German illustration showing that the artist really had absolutely no idea of what ambergris is either.


The Arabs believed that it bubbled up from subterranean vents:
And there also is a spring of crude ambergris, which floweth like wax or gum over the stream banks, for the great heat of the sun, and runneth down to the seashore, where the monsters of the deep come up and, swallowing it, return into the sea. But it burneth in their bellies, so they cast it up again and it congealeth on the surface of the water, whereby its color and quantities are changed, and at last the waves cast it ashore, and the travelers and merchants who know it collect it and sell it. But as to the raw ambergris which is not swallowed, it floweth over the channel and congealeth on the banks, and when the sun shineth on it, it melteth and scenteth the whole valley with a musk-like fragrance. Then when the sun ceaseth from it, it congealeth again. But none can get to this place where is the crude ambergris, because of the mountains which enclose the island on all sides and which foot of man cannot ascend.

The Sixth Voyage of Sinbad the Seaman
The Chinese on the other hand referred to it as "Dragon's Spittle" because they believed that it was made from the congealed saliva that drooled from the mouths of dragons that slept on the sea floor.

As it turns out the Chinese were somewhat closer to the truth:
Ambergris is, in basic terms, what the sperm whale can't digest.

It's a combination of things like squid beaks and juice found inside sperm whales, but Mr Jury says that it is the quirky way the ambergris is released from the whale that really makes it off.

“They actually belch it out, and apparently those rare souls across the world who have actually heard this happen, say you can hear it for miles.”

Once the whale has belched up the ambergris it stays in the ocean for around a decade.

“If you were to take it… immediately after the whale has expelled it, then you would put it back in the water, because apparently the smell is horrific. But importantly it has to float around the oceans of the world for ten years… so that the sun and the water of the oceans can wash it, until all the nasties have gone and it assumes that sweetness that we're witnessing now.”

Mr Jury says scientists believe only about one per cent of sperm whales release ambergris.
The above quote comes from this article about a 15 kilogram lump of ambergris that was recently found washed up on a beach in South Australia.

The lump is currently being valued around US$300,000...


Original caption: "Loralee, is the lucky lady who found the ambergris pictured here on this beach south of Streaky Bay".

She's obviously pretty lucky but something about this photograph makes me think she's still not all that thrilled at sitting so close to a 15 Kg lump of whale vomit.


Praise is like ambergris;
a little whiff of it, by snatches, is very agreeable;
but when a man holds a whole lump of it to his nose;
it is a stink and strikes you down.

— Alexander Pope c.1720
See also:
Ambergris: Beachcomber's Bonanza
AMBERGRIS: A Pathfinder and Annotated Bibliography
Pieter Derideaux's excellent East African history website

[Note 1] Of course Amber is a very nice name and I hope all those Amber's out there won't take offence at my smart-arsedness.

[Note 2] The no-nonsense Germans call yellow amber bernstein which simply means "stone that burns".

UPDATE: I had originally snuck this link into the comments section below but I think it's interesting enough to make part of the post. On the chemistry and ethics of Ambergris.
Ambergris contains 46% of cholestanol type sterols (Sell 1990) including (+)-epi-coprosterine and the triterpene alcohol (-)-ambreine (25-45%), which is odorless, but this material is the precursor to other fragrant compounds formed by auto-oxidation, sunlight, and seawater such as (-)-gamma-cyclogeranyl chloride and (-)-gamma-bicyclohomofarnesal. The material is said to be able to retain its odour for centuries, and generally stays as an amorphous mass, with no tendency to crystallise. Mookherjee and Patel (1977) identified nearly 100 volatile substances in ambergris; they described some of the key components and their associated odours as follows:
  • g-homocyclogeranyl chloride: ozony-seawater (can be towards metallic)
  • a-ambrinol: moldy-animal-faecal
  • g-dihydroionone: weak tobacco
  • g-coronal: sea-water
  • ambroxan: moist, soft, creamy, persistent amber with velvety effect
The odour of a museum sample of grey ambergris examined by the authors team (Burfield 2000) is dry, slightly animalic, musty, earthy, and faintly fishy or seaweed-like in character. It has an exceptional radiance and has a dry, ambery, somewhat marine, long lasting dry-out. Ambergris was traditionally used in tincture form (3% dissolved in 95% alcohol).


— Modified from Monograph in Natural Aromatic Materials – Odours and Origins by Tony Burfield 2000

The article is fairly short but fulll of interesting tidbits about the present uses of ambergris and the implications for endangered sperm whales populations.

Splitters

#

INFERNO CANTO XXVIII

...No barrel, even though it's lost a hoop
or end- piece, ever gapes as one whom I
saw ripped right from his chin to where we fart:

his bowels hung between his legs, one saw
his vitals and the miserable sack
that makes of what we swallow excrement.

While I was all intent on watching him,
he looked at me, and with his hands he spread
his chest and said: "See how I split myself!

See now how maimed Mohammed is! And he
who walks and weeps before me is Ali,
whose face is opened wide from chin to forelock.

And all the others here whom you can see
were, when alive, the sowers of dissension
and scandal, and for this they now are split.

— Dante's Divine Comedy


Mohammed and his son-in-law Ali in the Ninth Abyss of Hell
Illustration by Gustave Doré, 1861.
Betrayal of the Zanj

#

In the tenth century a sea captain from the Persian port city of Seraf wrote a book which collected together various stories related to him by traders and seamen of life and adventures in the Indian ocean. The writer's name was Buzurg ("Big") ibn Shahriyar and his book was called The Wonders of India which survives today as a single copy kept at a mosque in Istanbul.

The excepted story below, which is the 31st tale in Buzurg's book, was one I first came across in a paraphrased form while reading Richard Hall's excellent book Empires of the Monsoon. Here it is in translation from the original from Pieter Derideaux's website. I've mentioned Pieter's site once before, it is fantastic resource of extracts from ancient and mediaeval authors who writing on subject related to the history of East Africa, the forbidding and mysterious land of "Zanj" [1].

When Buzurg was writing, traders from the Persian Gulf and Red Sea were routinely traveling to and trading with China, India, Indonesia and Africa. It was a world, however, that was virtually unknown to Europeans at the time .
Ismail'awaih told me, and several sailors who were with him, that in the year A.H. 310 [2] he left Oman in his ship to go to Quanbalu. A storm drove him towards Sofala [3] and the Zanj coast. Seeing the coast we had reached, the captain said, and realizing that we were falling among cannibal Negroes we were certain what our fate would be, we made the ritual ablutions and turned our hearts towards God, saying for each other the prayers for the dead. The canoes of the Negroes surrounded us and brought us into the harbor. There we cast anchor and went ashore. They led us to their king. He was a young Negro, handsome and well set-up. He asked us who we were, and were we were going. We answered that we had come to his land.

You lie, he said. It was by no means here you meant to land. It is only that the winds have driven you here in spite of yourselves. When we had admitted that he spoke the truth, he said: Bring ashore your goods. Sell and buy, you have nothing to fear.

We brought all our bales ashore and began to trade, a trade which was excellent for us, without any restrictions or customs dues. We made the king a number of presents to which he replied with gifts of equal worth or ones even more valuable. There we staid several months. When the time to depart came, we asked his permission to go, and he agreed immediately. The goods we had bought were loaded and business was wound up. When everything was in order, and the king hearing of our intention to set sail, accompanied us to the shore with several of his people, got into one of the boats and came out to the ship with us. He even came on board with seven of his companions.

When I saw them there, I said to myself: In the Oman market this young king would certainly fetch thirty dinars, and his seven companions a hundred and sixty dinars the lot. Their clothes are worth twenty dinars at the lowest. One way and another this would give us a profit of at least 3,000 dirhams, and without any trouble. Reflecting thus, I gave the crew their orders. They raised the sails and weighed anchor.

In the meantime the king was most agreeable to us, making us promise to come back again and promising us a good welcome when we did. When he saw the sails full with the wind and the ship began to move, his face changed. You are off he said. Well, I must say good-bye. And he wished to embark in the canoes which were tied up to the side. But we cut the ropes, and said to him: You will remain with us, we shall take you to our own land. There we shall reward you for all the kindness you have shown to us.

Strangers, he said, when you fell upon our shores, my people wished to eat you and pillage your goods, as they have already done to others like you. But I protected you, and asked nothing from you. As a token of my goodwill I even came down to bid you farewell in your own ship. Treat me then as justice demands, and let me return to my own land.

But we paid no attention to his words. As the wind got up, the coastline disappeared from sight. Then night wrapped us in her veils, and we reached the open sea.

When the day came, the king and his companions were put with the other slaves whose number reached 200 head. He was not treated differently from his companions in captivity. The king said not a word and did not even open his mouth. He behaved as if we were strangers to him and as if we did not know him. When he got to Oman, the slaves were sold, and the king with them.

Now, several years after, sailing from Oman towards Quanbalu, the wind again drove us towards the coast of Sofala on the Zanj coast, and we arrived precisely at the same place. The Negroes saw us, and their canoes surrounded us, and we recognized each other. Fully certain we should perish this time, terror stuck us dumb. We made the ritual ablutions is silence, repeated the prayer of death, and said farewell to each other. The Negroes seized us, and took us to the king's dwelling and made us go in. Imagine our surprise, it was the same king that we had known, seated on his throne, just as we had left him there. We prostrated ourselves before him, overcome, and had not the strength to raise ourselves up.

Ah he said, here are my old friends. Not one of us was capable of replying. He went on: Come, raise your heads, I give you the aman (save conduct) for yourself and for your goods. Some raised their heads, others had not the strength, and were overcome with shame. But he showed himself gentle and gracious until we had all raised our heads, but without daring to look him in the face, so strongly did remorse and fear affect us. But when we had been reassured by his save conduct, we finally came to our senses, and he said: Ah traitors. How have you treated me after all I did for you! And each one of us called out: Mercy, oh King! be merciful to us!

I will be merciful to you, he said. Go on, as you did last time, with your business of selling and buying. You may trade in full liberty. We could not believe our ears, we feared it was nothing but a trick to make us bring our goods to shore. None the less we disembarked them, and came and brought him a present of enormous value. But he refused it and said: You are not worthy for me to accept a present from you. I will not soil my property with anything that comes from your hands.

After that we did our business in peace. When the time to go came, we asked permission to embark. He gave it. At the moment of departure, I went to inform him. Go, he said, and may God protect you! Oh king, I replied, you have showered your bounty upon us, and we have been ungrateful and traitorous to you. But how did you escape and return to your country?

He answered: After you had sold me in Oman, my purchaser took me to a town called Basrah,- (and he described it). There I learned to pray and to fast, and certain parts of the Koran. My master sold me to another man who took me to the country of the king of the Arabs, called Baghdad-( and he described Baghdad). In this town I learnt to speak correctly. I completed my knowledge of the Koran and prayed with the men in the mosques. I saw the Caliph, who is called al-Muqtadir (908-32). I was in Baghdad for a year and more, when there came a party of men from Khorasan mounted on camels. Seeing a large crowd, I asked where all these people were going. I was told: To Mecca. What is Mecca? I asked. There, I was answered, is the house of god to which Muslims make the pilgrimage. And I was told the history of the temple. I said to myself that I should do well to follow the caravan. My, master, to whom I told all this, did not whish to go with them or to let me go. But I found a way to escape his watchfulness and to mix in the crowd of pilgrims. On the road I became a servant of them. They gave me food to eat and got for me the two cloths needed for the ihram (the ritual garments used for the pilgrimage). Finally, under their guidance, I performed all the ceremonies of the pilgrimage.

Not daring to go back to Baghdad, for fear that my master would kill me, I joined up with another caravan which was going to Cairo. I offered my services to the travelers, who carried me on their camels and shared their food with me. When I got to Cairo I saw a great river which is called the Nile. I asked: Where does it come from? They answered: Its source is in the land of the Zanj. And where? Near a large town called Aswan, which is on the frontier of the land of the blacks.

With this information, I followed the banks of the Nile, going from one town to another, asking alms, which was not refused to me. I fell, however, among a company of blacks who grabbed me. They seized on me, and put me among the servants with a load which was to heavy for me to carry. I fled and fell into the hands of another company which seized me and sold me. I escaped again, and went on in this manner, until, after a series of similar adventures, I found myself in the country which adjoins the land of the Zanj. There I put on a disguise. Of all the terrors I had experienced since I left Cairo, there was none equal to that which I felt as I approached my own land. For, I said to myself, a new king has no doubt taken my place on the throne and commands the army. To regain power is not an easy thing. If I make myself known or if anyone recognizes me, I shall be taken to the new king and killed at once. Or perhaps one of his favorites will cut of my head to get in his favor.

So, in prey of mortal terror, I went on my way at night, and stayed hid during the day. When I reached the sea, I embarked on a ship; and after stopping at various places, I disembarked at night on the shore of my country. I asked an old women: Is the king who rules here a just king? She answered: My son, we have no king but god. And the good women told me how the king had been carried off. I pretended the greatest astonishment at her story, as if it had not concerned me and events which I knew very well. The people of the kingdom, she said, have agreed not to have another king until they have certain news of the former one. For the diviners have told them that he is alive and in health, and safe in the land of the Arabs.

When the day came, I went into the town and walked towards my palace. I found my family just as I had left them, but plunged into grief. My people listened to the account of my story with surprise and joy. Like myself, they embraced the religion of Islam. Thus I returned into possession of my sovereignty, a month before you came. And here I am, happy and satisfied with the grace God has given me and mine, of knowing the precepts of Islam, the true faith, prayers, fasting, the pilgrimage, and what is permitted and what is forbidden: for no one else in the land of the Zanj has obtained a similar favor.

And if I have forgiven you, it is because you were the first cause of the purity of my faith. But there is still one sin on my conscience which I pray god to take away from me.

What is this thing, oh king? I asked. It is, he said, That I left my master, when I left Baghdad, without asking him his permission, and that I did not return to him. If I were to meet an honest man, I would ask him to take the price of my purchase to my master. If there were among you a really good man, if you were truly upright men, I would give you a sum of money to give him, a sum ten times what he paid as damages for the delay. But you are nothing but traitors and tricksters.

We said farewell to him. Go, he said, and if you return, I shall not treat you otherwise than I have done. You will receive the best welcome. And the Muslims may know that they may come here to us, as to brothers, Muslims like themselves. As for accompanying you to your ship, I have reasons for not doing so.

And on that we parted.
It should be noted that although this story and especially its punch-line would have undoubtedly delighted its Muslim readership, it is almost certainly not true. It is highly unlikely that anyone, African or otherwise would have been able to survive an overland journey from Cairo to the south of Zanj through the hostile territories of inland Africa. A more plausible though also very dangerous route would have been to hitch a ride down the Zanj coast from Mogadishu.

Nevertheless the story relates many things that must have been true about the daily dangers of the trade with Africa.

[1] Zanj - meaning "blacks" i.e. Africans. The ancient African port of Zanzibar which is located centrally on the East African coast derives its name from Persian Zanj-i-bar which means "the Coast of the Blacks". It was famous centuries ago for its exports of gold, ivory and slaves and more recently for its export of Farrokh Bulsara better known as Freddy Mercury.

[2] A.H. 310 - After Hijra i.e. 922 AD

[3] Sofala - located in present day Mozambique was a major trading port and the southernmost point were merchant shipping was willing to go due to the treacherous winds and currents that lay beyond.
Effigy

#


In some religions it is forbidden to depict the Danish.
No need to explain

#



All Things return to their natural state,
Bringing the original complete harmony to all.

Lao Tzu Talks to Be : An interpretation of the Tao Te Ching,
Establishing Harmony (65)


Spreadsheet

#


Livia Augusta
He showed marked respect to Livia Augusta [wife of Caesar Augustus], to whose favour he owed great influence during her lifetime and by whose last will he almost became a rich man; for he had the largest bequest among her legatees, one of fifty million sesterces. But because the sum was designated in figures and not written out in words, Tiberius, who was her heir, reduced the bequest to five hundred thousand, and Galba never received even that amount.

Suetonius,The Lives of the Caesars : Galba
Of course Tiberius never had any intention of giving Galba a penny but the technicality that he used to slash Galba's entitlement to a thousandth of the original amount relied upon the exploitation of a simple fact, one that was obvious even at the height of Roman power in the first century AD, that

Roman numerals totally suck!


I've noted previously the problems that many ancient number systems encountered when they came to trying to represent very large numbers. In that article I referred to the weaknesses of the Greek system which used letters to represent numbers 1, 2 ... 9 but then used a different set of letters to represent 10, 20 ... 90 and yet another to represent the hundreds. Naturally the Greeks found it easy to count up to 1000 (and be able to play also sorts of fun mathematical word games) but for higher numbers they then had to fall back on to various scaling rules. The system was inelegant but at least it was systematic, the Roman system was even less elegant and certainly less systematic.

To denote a number greater than 1,000 using the Roman system, the standard way was to rehash the old symbols but marking them with a bar over the top (a "vinculum") to indicate multiplication by one thousand. So V (i.e 5) with a bar over the top indicated 5,000, L (i.e. 50) with a bar indicated 50,000. Larger amounts could be shown by surrounding the number in a three cornered frame (open at the bottom) which indicated multiplication by one million. Livia's bequest to Galba was denoted as CCCCC enclosed in a three cornered frame (i.e 50 million) which Tiberius deliberately took to mean CCCCC with a bar over the top (i.e. 50 thousand).


Though cheated by Tiberius, Galba eventually got the last laugh by ending the Julio-Claudian dynasty when he became Empereror. Within only a few months, however, he was murdered in the Forum by his praetorian guard.

It's interesting to contrast this clumsy incremental approach to big numbers with what was already established practice in the old Mesopotamian city-states which were already extremely ancient even in the time of the Romans. Nearly two thousand years before Livia's last will and testament was read out, the scribes of ancient Sumer and Akkad routinely dealt with with large numbers which they wrote down by impressing tablets of soft clay with reed styluses. Their system starts out familiarly enough with the number of reed marks directly corresponding to the numeric value to be represented. By 10 however this becomes unwieldy so a different symbol is placed to the left which counts the tens.


This sequence could have theoretically carried on until 99 was reached but instead the Mesopotamians chose to limit it to 59. Just as with our modern decimal system where the unique symbols stop at 9, they used the place of the numerals as a way to multiply them by the base (in this case 60) raised by a power.

For example, a "1" placed to the left of a "57" would represent 1 x 60 + 57 i.e 117.

The sequence 1 57 46 40 would be 1 x (60 x 60 x 60) + 57 x (60 x 60) + 46 x 60 + 40



The base of 60 added a complicating wrinkle to the whole thing (one that we still see today reflected in the number of minutes we count in an hour and the number of degrees in a circle) but despite this it can be seen that the Mesopotamians used a place notation system which was remarkably similar to our own decimal system in many respects.

The system had some shortcomings, it was still possible to be ambiguous, unused columns had to contain blanks so that numbers like 3601 didn't get mixed up with 61. They did eventually come up with a symbol for zero which they could use to pad out numbers but they never fully systematised it as a true zero. They never used it at the end, for example, so the order of magnitude of a round number still needed to be guessed at by looking at its context.

Below is a famous example known simply as Plimpton 322. It was excavated from the ruins of the city of Larsa near Ur and dates from around 1800 BC during its last flourish of independence before all the old city-states of Sumer and Akkad were conquered by Hammurabi and unified under the control of the Babylon. The tablet was ruled with 15 lines and divided into four columns.


Ancient spreadsheet — older even than Visicalc.

Here it is transcribed into Indian numerals. First as base 60


width
diagonal
name
59 0 15 1 59 2 49
1
56 56 58 14 50 6 15 56 07 1 20 25
2
55 7 41 15 33 45 1 16 41 1 50 49 3
53 10 29 32 52 16 3 31 49 5 9 01 4
48 54 1 40 1 05 1 37 5
47 6 41 40 5 19 8 01 6
43 11 56 28 26 40 38 11 59 01 7
41 33 59 3 45 13 19 20 49 8
38 33 36 36 8 01 12 49 9
35 10 2 28 27 24 26 40 1 22 41 2 16 01 10
33 45 45 1 15 11
29 21 54 2 15 27 59 48 49 12
27 0 3 45 2 41
4 49 13
25 48 51 35 6 40
29 31 53 49 14
23 13 46 40 28 53
15

and then as decimal.

width diagonal name
0.9834 119
169
1
0.9492 3367
4825
2
0.9188 4601
6649
3
0.8862 12709
18541
4
0.8150 65
97
5
0.7852 319
481
6
0.7200 2291
3541
7
0.6928 799
1249
8
0.6427 481
769
9
0.5861 4961
8161
10
0.5625 45
75
11
0.4894 1679
2929
12
0.4500 161
289
13
0.4302 1771
3229
14
0.3872 28
53
15

Each of the columns has a heading. The fourth (rightmost) column heading is "its name" and its values number from 1 to 15. The second and third column headings are the "square of the short side" and "square of the diagonal" respectively. Both contain whole numbers which taken together form the short side and diagonal of a right angled triangle. The third side of this triangle which is not represented on this tablet would also be a whole number. Neat correspondences such as these do not just happen by chance, they need to be found. At the very least these values demonstrate that the ancient Mesopotamians understood Pythagoras' theorem and they knew it a good 1,300 years before Pythagoras was even born.

The first (leftmost) column heading is more cryptic "The takiltum-square of the diagonal from which 1 is torn out, so that the short side comes up", this implies some kind of of geometrical operation but the numbers speak clearly enough for themselves. They are perfect squares but ones that are fractional where we have to imagine a decimal point to their left. Another remarkable thing about them is that if you add 1 to them the numbers that result are also perfect squares.

Relating the first column to the second and third has been the subject of much mathematical debate over the past sixty years. Two theories predominate, one argues that their values are derived by trigonometric functions from the angle of the the triangle, in other words this tablet represents the first ever found trigonometric table (a quite advanced one in fact showing the squares of cosecants). However, this theory may be projecting greater mathematical prowess onto the Mesopotamians than they may have actually possessed, in the history of mathematics this would place them somewhere equivalent to the early European Renaissance.

A recent and perhaps more historically more satisfying theory argues that they are based on a list of reciprocals pairs. A complementary article provides a working out of the formulas involved.
Gender in the Marshes

#

..."I lived in the Marshes of Southern Iraq from the end of 1951 until June 1958...I spent these years in the Marshes because I enjoyed being there...Soon the Marshes will probably be drained; when this happens, a way of life that has lasted for thousands of years will disappear."

— The Marsh Arabs, Wilfred Thesiger,1964
Wilfred Thesiger lived with the Marsh Arabs of southern Iraq for many years. He was a keen observer and this excerpt provides a fascinating glimpse into how gender and trans-gender issues were dealt with in this traditional society. Unburdened by much of the baggage of more connected and modern societies these attitudes were straightforward, sensible and humane. This quote was taken from a post by emily0 at quench zine.
One afternoon, a few days after leaving Dibin, we arrived at a village on the mainland. The sheikh was away looking at his cultivations, but we were shown to his mudhif [guest house made of reeds] by a boy wearing a head-rope and cloak, with a dagger at his waist. He looked about fifteen and his beautiful face was made even more striking by two long braids of hair on either side. In the past all the Madan [Marsh Arabs] wore their hair like that, as the Bedu [Bedouin] still did. After the boy had made us coffee and withdrawn, Amara [one of Thesiger's boat boys] asked, 'Did you realize that was a mustarjil?' I had vaguely heard of them, but had not met one before.'A mustarjil is born a woman,' Amara explained. 'She cannot help that; but she has the heart of a man, so she lives like a man.'

'Do men accept her?'

'Certainly. We eat with her and she may sit in the mudhif. When she dies, we fire off our rifles to honour her. We never do that for a woman. In Majid's village there is one who fought bravely in the war against Haji Sulaiman.'

'Do they always wear their hair plaited?'

'Usually they shave it off like men.'

'Do mustarjils ever marry?'

'No, they sleep with women as we do.'

Once, however, we were in a village for a marriage, when the bride, to everyone's amazement, was in fact a mustarjil. In this case she had agreed to wear women's clothes and to sleep with her husband on condition that he never asked her to do women's work. The mustarjils were much respected, and their nearest equivalent seemed to be the Amazons of antiquity. I met a number of others during the following years. One man came to me with what I took for his twelve-year-old son, suffering from colic, but when I wanted to examine the child, the father said, 'He is a mustarjil.' On another occasion I attended a man with a fractured skull. He had fought with a mustarjil whom I knew, and had got the worst of it.

Previously, while staying with Hamud, Majid's brother, I was sitting in the diwaniya (brick guest house) when a stout middle-aged woman shuffled in, enveloped in the usual black draperies, and asked for treatment. She had a striking, rather masculine face, and lifting her skirt exposed a perfectly normal full-sized male organ. 'Will you cut this off and turn me into a proper woman?' he pleaded. I had to confess that the operation was beyond me. When he had left, Amara asked compassionately, 'Could they not do it for him in Basra? Except for that, he really is a woman, poor thing.' Afterwards I often noticed the same man washing dishes on the river bank with the women. Accepted by them, he seemed quite at home. These people were kinder to him than we would have been in our society.

— The Marsh Arabs by Wilfred Thesiger pp. 168-170
Alas, much of this ancient way of life was destroyed when Saddan Hussein drained the marshes and internally displaced hundreds of thousands of people. Given the hold of doctrinaire religious groups over the politics of post-Saddam Iraq, I can only guess that this tradition of acceptance would have become an early casuality of this tragedy.

If you are interested in reading my earlier postings about the Marsh Arabs start here with a post about the continuity of the role the marshlands played in Southern Iraq from the time of ancient Sumerians right up until the mid-20th century when it was occupied by Shia Ma'dan.

Then follow the sad tale of the marshland drainage carried out by Saddam as part of the plan to fight the 1991 insurgency and as collective punishment of an entire population — all under the watchful eyes of forces patrolling Iraq's southern "no fly zone". The article goes up to the attempts to partially restore the marshes since the overthrow of Saddam. An update on these efforts can be found here.

Finally, a reprint of a 20 year long anthropological project led by Edward Ochsenschlager to document the traditional marshland way of life as a way of informing and providing social context to archaeological digs in this ancient region.

You may also be interested reading this background on the marshy origins of the Noah's Ark story, Noah's archetype, Ziusudra, was a marshland sheik!
Eros ex Mathematica

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Actually, this is NOT at all what you're thinking.
The images in this room are created entirely from mathematical algorithms. If you find them offensive in any way, all I can say is that beauty (or obscenity) is in this case most certainly in the eye of the beholder.
The software used was Stephen Wolfram's ever popular software package for mathematicians, Mathematica.

Note to educators : this might be a good way to keep the kids from nodding off in class.

UPDATE: Of course let's not be coy about this, even algorithmic skin can leave us feeling exposed.