# Masterpiece conquest: the “100 birds” problem and Arno Schmidt

**Posted:**September 11, 2016

**Filed under:**History, Literature, People |

**Tags:**15-puzzle, Abu Kamil, Alcuin of York, Alexander the Great, Archimedes, Archimedes palimpsest, Arno Schmidt, Aryabhata, B.L. Van Der Waerden, Babylon, Bhakhshali manuscript, Bhaskara, Brahmagupta, Caspar Thierfelder, Cattle problem, China, Christoff Rudolff, Diophantine equations, Diophantus, Euclid, Fibonacci, George Rippey Stewart, India, Jamshid al Kashi, Kuttaka, Leonardo of Pisa, Mahavira, Mathematics, Problema Bovinum, Pythagoras, Samarkand, Sataspes, Seki Takakazu, Wasan, Zhang Quijian Leave a comment

“*Once, when we were revising the map of the world, Aristotle and I worked through every travel report! The quite natural phenomenon of birds seeking food from a mob on the move and choosing a route in the direction of the only hospitable region, was of course immediately declared to be a new portent. Yet another example that the common people, even as eye-witnesses, simply cannot give reliable evidence.*“

From “Alexander or What is Truth”, Arno Schmidt (1949)

**I. The “100 birds” problem**

**A bird cornucopia**

It seems that the first occurrence of this specific problem is found in Zhang Quijian’s (or, spelled differently, Chang Ch’iu Chien) “*Mathematical Manual*”, a Chinese mathematical text, dating probably from the 5th century A.D. It is a rather simple mathematical puzzle, still to this day occasionally met in quite a few variations in textbooks and recreational Mathematics books. Its original version, problem 38 of chapter 3 in the Chinese text, reads:

“*If a rooster is worth 5 coins, a hen 3 coins, and three chickens together 1 coin, how many roosters, hens and chickens, 100 in total, can be bought for 100 coins?*“

Though at first it seems that there might not be enough information to solve it, the problem can be reduced to a system of two linear Diophantine equations (i.e. indeterminate equations of which only integer solutions are of interest) with three unknowns, which indeed possesses infinite solutions. However, given the particular conditions of the problem (i.e. that there are 100 birds and 100 coins in total), the solutions that are physically possible are only three. Zhang Quijian lists in his text all three of them (which are (4, 18, 78), (8, 11, 81), (12, 4, 84), where in each bracket the first number stands for the number of roosters, the second for the number of hens and the third for the number of chickens), yet without providing any details about how they were computed. After Zhang Quijian, and for more than a millennium, variations of the problem appear in several texts with a remarkably wide geographical dispersion, from the British islands to Japan. The English scholar Alcuin of York (8th century), teacher of Charlemagne, includes in his fifty-three “*Propositions for Quickening a Young Mind*” (“*Propositiones Alcuini Doctoris Caroli Magni Imeratoris Ad Acuendos Juvenes*“) six birds-free variations of the problem, bearing striking similarity to the Chinese original:

**Problem #5**: *Propositio de emptore denariorum*

“*A certain buyer said: ‘I want to buy 100 pigs with 100 denarii in such a way that a mature boar is bought for 10 denarii; a sow for five denarii; and two small female pigs for one denarius’. How many boars, sows, and small female pigs should there be so that there are neither too many nor too few of either pigs or denarii?*“

**Problem #32**: *Propositio de quodam patrefamilias*

“*A certain head of household had 20 servants. He ordered them to be given 20 modia of corn as follows: The men should receive three modia; the women, two; and the children half a modium. How many men, women and children must there have been?*“

Two more problems follow, **problem #33** (“*Propositio de quodam patrefamilias*“) and **problem #34**: (“*Propositio de alio patrefamilias erogante suae familiae annonam*“) which are identical to problem #32 with the number of servants changed to 30 in the former and to 100 in the latter.

**Problem #38**: *Propositio de quodam emptore in animalibus centum*

“*A certain man wanted to buy 100 various animals for 100 solidi. He wished to pay three solidi per horse, one solidus per cow, and one solidus per 24 sheep. How many horses, cows and sheep were there?*“

**Problem #39: ***Propositio de quodam emptore in oriente*

“*A certain man wished to buy 100 assorted animals for 100 solidi in the East. He ordered his servant to pay five solidi per camel, one solidus per ass, and one solidus per 20 sheep. How many camels, asses and sheep were obtained for 100 solidi?*“

In order to solve for example problem #34, following a modern approach, one could start by assuming that A is the number of men, B is the number of women and C is the number of children. Then each of those groups of people would receive 3A, 2B and C/2 bushels of corn respectively and a system of two Diophantine equations is produced:

A+B+C=100

3A+2B+C/2=100

By eliminating C we get 5A+3B=100 from which it follows that 3B is smaller than 100 and that B is a multiple of 5 and therefore six solutions are possible: B=5 or 10 or 15 or 20 or 25 or 30. The corresponding values of A are 17, 14, 11, 8, 5, 2 and those of C are 78, 76, 74, 72, 70, 68. An almost identical system of indeterminate equations appears also in the Bhakhshali manuscript, a versified Indian text found on birch bark in 1881, of which only fragments had survived. The date of the manuscript is quite uncertain and is under debate, ranging from as early as 4th century until as late as 12th century. There is one almost complete statement and solution of a system of Diophantine equations, almost identical to Alcuin’s problem #32:

A+B+C=20

3A+3B/2+C/2=20

Only a few decades after Alcuin, a similar, yet more demanding, “100 birds” problem appears in Mahavira’s “*Ganitasarasangrasa*” (“*Compendium of the essence of Mathematics*“), a wonderful, versified Sanskrit collection of arithmetic rules and problems organized in nine chapters. In paragraph 152 of book VI we find this problem:

“*Pigeons are sold at the rate of 5 for 3, sarasa birds at the rate of 7 for 5, swans at the rate of 9 for 7 and peacocks at the rate of 3 for 9 pana. Someone was told to bring 100 birds for 100 pana for the amusement of the King’s son, and was sent to do so. What does he give for each of the kinds of bird that he buys?”*

“*Pana*” or “*karshapana*” were ancient Indian coins current from the 7th century BC onwards while “*sarasa*” birds are sarus cranes. In Mahavira’s text there is a brief description of an algorithmically organized rule for producing one solution of the problem, depending on the selection of suitable multipliers. In modern terms, his problem can be reduced to a system of two Diophantine equations with four unknowns and possesses 16 physically possible solutions. A few decades after that, similar problems are included in the wonderfully titled “*Kitab al-tair*” (“*Book of Birds*“), consisting of only six problems, a small text of the Egyptian mathematician Abu Kamil Shuja ibn Aslam (9th – 10th century). Two of these problems read:

“*100 birds of three species are purchased for 100 dirhams. Ducks are 5 dirhams each, 20 sparrows cost 1 dirham, and chickens are 1 dirham each. How many of each species are bought?*“

“*With 100 dirhams buy 100 birds of 4 types: geese at 4 dirhams each, chickens at 1 dirham each, pigeons at 1 dirham for two and starlings at 1 dirham for ten.*“

The second problem is as demanding as Mahavira’s in that it can be reduced to a system of two Diophantine equations with four unknowns yet its full solution is somewhat tedious as it possesses 98 solutions (a discussion of which can be found here). Abu Kamil’s approach was unique as he was the first to concentrate on the fact that such a problem may have a great many physically relevant solutions and, in his introduction of the “*Book of Birds*” he even explained that this very fact was what made him write this little book:

“*I found myself before a problem that I solved and for which I discovered a great many solutions; looking deeper for its solutions, I obtained two thousand six hundred and seventy-six correct ones. My astonishment about that was great, but I found out that, when I recounted this discovery, those who did not know me were arrogant, shocked, and suspicious of me. I thus decided to write a book on this kind of calculations, with the purpose of facilitating its treatment and making it more accessible.*“

Quite remarkably, the first of Abu Kamil’s problems mentioned above is identical to Alcuin’s problem #39. Even more remarkable is the fact that, as Alcuin’s text is older, one could rather precariously conclude that the “*Book of Birds*” seems to be pointing towards Europe, indicating a flow of “mathematical fluids” from West to East, yet Alcuin himself in his text chose to make a direct reference to the East, possibly pointing towards the opposite direction. About four centuries after Alcuin’s time, his problem #33 repeats identical in the 11th chapter of the famous “*Liber Abaci*” (“*Book of Calculations*“) of Leonardo of Pisa (widely known as Fibonacci, 12th-13th century), only this time involving birds, like the eastern problems of Abu Kamil and Zhang Quijian:

“*A certain man buys 30 birds which are partridges, pigeons and sparrows for 30 denarii. A partridge he buys for 3 denarii, a pigeon for 2 denarii and 2 sparrows for 1 denarius, namely 1 sparrow for 1/2 denarius. It is sought how many birds he buys of each kind.*“

And about two centuries after Fibonacci, a variation appears in faraway Transoxiana and Tamerlane’s capital Samarkand. In his “*Miftah al-hisab*” (“*Key to Arithmetic*“, 1427) the Persian astronomer and mathematician Jamshid al-Kashi discusses this example:

“*One duck costs four coins, five sparrows cost one coin and one rooster costs one coin. One buys 100 birds for 100 coins. How many birds can he buy?*“

In early 16th century, the first German textbook of Algebra, a book under the peculiar title “*Behend **U**nd Hübsch Rechnung Durch Die Kunstreichen Regeln Algebre So Gemeinicklich Die Coss Genent Werden**” *(*“Nimble and Beautiful Calculation Via the Artful Rules of Algebra [which] are so Commonly Called ‘Coss’ “*) written by Christoff Rudolff (1499 – 1543) repeats a problem identical to problem #32 of Alcuin. A rather easy, though somewhat peculiar variation of the problem appears in “*Arithmetica Oder Rechenbuch*” (“*Book of Arithmetic*“, 1587) of the German calendar maker Caspar Thierfelder, which relates the so called “*Regula Virginum*” (Rule of Maidens) or “*Regula Cecis*” (Rule of Drinks) i.e. the custom of charging different prices for the drinks of men, women and maidens:

“*47 people, men, women, and maidens together spent 47 gr., each man gave 5 gr., each woman 3 gr., and each maiden 1 hr. How many persons of each kind were there?*“

Here “gr.” stands for “*groschen*“, a coin widely used in central Europe from the 13th century onwards, while “hr.” means one half of a groschen. This is a particularly easy variation as it does not take long to conclude that there are only five different possibilities (1, 2, 3, 4 or 5 men) for the number of men such as the total cost will not exceed 47 and only for only one of them (3 men) the numbers of women and maidens remain positive integers. Finally, emerging from the tradition of “*wasan*“, the Japanese art of calculation, problems involving systems of Diophantine equations such as those discussed above appear in works of Seki Takakazu’s school (17th – early 18th century).

**Mathematical osmosis**

The repeated appearances in both eastern and western mathematical texts of this emblematic “100 birds” problem, as quite reasonably all the above problems may be collectively named, seem to indicate an osmosis, a flow of “mathematical fluids” between cultures within a time span of a millennium the least, in a rather confusing and unclear manner, with conflicting arrows pointing sometimes eastwards and other times westwards. Diophantine equations bear the name of the obscure yet ingenious Diophantus of Alexandria (3rd century AD), owing to his “*Arithmetica*“, a work organized in 13 books of which only 6 have survived. It is a collection of 189 problems (with solutions) related to equations, both determinate (1st book) and indeterminate (books 2 to 6) of which the author examines only positive integer or rational solutions and usually restricting his study in finding just one possible solution, yet without any attempt to describe a general method: each problem is solved by a unique, individualized approach. Apart from its algebraic interest, Diophantus’ “*Arithmetica*” is the first attempt of a major advance from the rhetorical Algebra, i.e. one that is carried out by hard to follow verbal descriptions, to the syncopated Algebra, which makes use of abbreviations, and sets up a system of mathematical notation. Though in the text are found some far more challenging problems related to Diophantine equations and though the theory required for solving the linear Diophantine equation ax+by=c (the one related to the “100 birds” problem) was already present in Greek Mathematics, at least since the time of Euclid (4th century BC, i.e. more than half a millennium before “*Arithmetica*“), Diophantus apparently made no attempt to study it. A possible explanation is that the specific problem was considered trivial and of no interest as opposed to other problems in “*Arithmetica*“, that involved squares and cubes, which are far more relevant for the “geometric” Greek Algebra. And even after Diophantus, the linear Diophantine equation does not appear in extant Greek mathematical texts. Yet, in the course of several centuries before Diophantus, the Greeks had bothered themselves with far more challenging problems of indeterminate equations. According to the historian of Mathematics B.L. Van Der Waerden (1903 – 1996) in his “*Science Awakening*” (1954), the Pythagoreans (6th century BC) had studied the Diophantine equation

x2-2y2=1

and had solved it in a way proving that it possesses an infinite number of solutions. The problem of dividing a square number into two squares, a problem examined in “*Arithmetica*“, is attributed in “*Commentary on Euclid*” by Proclus (5th century) to Pythagoras (6th century BC), involving “side” and “diagonal” numbers, later on described by Theon of Smyrna (1st century). A problem from the Constantinople manuscript known also as the “*Archimedes palimpsest*” (10th century), which is a medieval copy of ancient Greek works, asks for two rectangles such that the perimeter of the second is three times that of the first and the area of the first is three times that of the second, a problem that can be reduced to a system of two Diophantine equations with four unknowns. And of course, the notorious “*Problema Bovinum*“, the cattle problem attributed to Archimedes (3rd century BC), is a quite remarkable indeterminate system of 7 equations with 8 unknowns and an extra difficulty of demanding certain sums to be square or triangular numbers. The answer to the problem ,which is simply the sum of all unknowns and represents “*the number of cattle of the sun which once grazed upon the plains of Sicily*“, was found to be approximately equal to 7.76X10^206544. The flow of ideas between the Mediterranean shores and the Indian subcontinent was greatly stimulated after Alexander’s campaigns in Asia and the subsequent founding of Greek satrapies by the great conqueror’s Diadochi. Moreover, after late second century BC, direct trade links were established between the Greeks and the Hindus. The German writer Arno Schmidt (1914 – 1979), through his alter ego, describes this link passionately in his post-apocalyptic novella “*Dark Mirrors*” (1951):

“*After Eudoxus, as the first Greek had officially opened the sea route to India in the days of Ptolemy Euergetes, commercial enterprises assumed truly gigantic dimensions. I recommend you include the really interesting “facts” in your repertoire: how they sailed up the Nile from Alexandria to Coptus; and from there traveled by caravan to Berenica on the Red Sea, where the India fleet was waiting with up to 120 (!) large freighters. They necessarily remained close to land as far as Oecilis at the exit of the Red Sea, of course; but from there the convoy traversed with the July/August monsoon, sailing 40 uninterrupted days on the open sea […] the 1800 miles to Barygaza, etc. on the Malabar coast; and returned in December. And from the time of Hippalus the Sailor on, this voyage was undertaken with massive escort for centuries, year after year, causing Pliny to declare the value of exports at 50 million sesterces, the imports at 5 billio*n”.

Almost a millennium after Alexander and three centuries after Diophantus, the linear Diophantine equation ax+by=c was included in the rhetorical, versified, verbally ornate Algebra texts of the Hindu mathematicians Aryabhata (5th – 6th century AD), Brahmagupta (7th century AD), Mahavira (9th century), whose “100 birds” problem was discussed above, and Bhaskara (12th century AD). The Indian approach was algorithmic, employing a method or rule known as “*kuttaka*” (liberally translated as “pulverisation”) which reduced the initial Diophantine equation to an equivalent problem with smaller coefficients, without any particular concerns for demonstration though. Osmosis between Chinese and Hindu Mathematics is considered certain and, though priority is under dispute, Aryabhata and Zhang Quijian were contemporaries (6th century AD). It was then that the “100 birds” problem was first documented in the Chinese “Mathematical Manual”.

**II. A masterpiece conquest**

**A passionate defense of the Greeks**

In 1946 the American professor of English George Rippey Stewart (1895 – 1980) published “*Man, an Autobiography*“, a work of “speculative anthropology”, excerpts of which appeared in the “*Reader’s Digest*” issue of July, 1947. Three years later he made considerable impact with his science fiction novel “*Earth Abides*” in which a deadly disease brings humanity back to the starting point. At that time Arno Schmidt was working on “*Alexander or What is Truth*“, a novella discussing the questions of historical truth and cultural osmosis. And in 1951, Schmidt wrote the post-apocalyptic novella “*Dark Mirrors*“ in which humanity, in similar manner as in Stewart’s novel, is brought back to the starting point by a nuclear holocaust. In it Schmidt, again through his alter ego, one of the last survivors on earth, appears absolutely furious against Stewart and especially against Stewart’s point of view concerning the cultural contributions of the Greeks:

*” I flung the Reader’s Digest against the wall, heaved a sheet of paper into my typer and rattled off (oh, was I fuming!)*

*[…]*

*… for your ‘man’ the overriding issue is ‘civilization’, i.e. to use your definition from p.175b: ‘the mass of such things as agriculture, metalworking and social tradition’ (not art or science, of course, none of that! The word culture does not even occur in your work – except on p.169a where in an ironic line you speak of those who are more enthusiastic about poetry than about plows); but civilization: that gives ‘control over the outside world’ and for you that is the essential ‘rough and easy way’, the decisive criterion by which to compare epochs, or, as you state it more clearly and precisely, to ‘test’ them. And as if hastening to make us palpably aware of the full weight of your test of civilization, you also apply it with remarkable impartiality to the Greeks. First you make the rise of Hellenic culture so easy to comprehend: ‘Not having much regular work to do, they had to pass the time in various ways. Thus the Greek citizens were able to develop art, athletics and philosophy’. Sounds quite plausible, doesn’t it? And so simple! – How true: for thousands of years before and after them, rulers and priests had no such idle time available to them?! And the equally work-shy South Sea Islanders, or Teutons, or the denizens of cloisters, etc., had none either! And nevertheless, not only did they not develop any of the arts and sciences (not to mention philosophy), not only did they not understand them when they met up with them, but in fact did their best to suppress them! For certain people – around 99 percent – culture is, after all, boring: do you know that?! – True, the artist and thinker requires his leisure; but that sentence, like the one about pigs and sausage, does not work in reverse. ‘A great deal of nonsense has been written about the Greeks in general and about the Persian Wars in particular…’ : granted : I have your book here in my hand!*

*[…]*

*…something that your beloved ‘intelligent Egyptians or Babylonians’ or those ‘in many ways more admirable’ Persians could have learned from the Greeks: how one writes universal history, with objectivity and apt comprehensiveness, instead of with the narrow-minded, overweening, false and wooden tone of the chronicles of the Egyptians or the local gossip-columns of the Old Testament.*

*[…]*

*You summarize: ‘Throughout the breadth of the world, there is in use no important invention which can certainly be credited to the Greeks.’ On the basis of which I (even I, Professor George R. Stewart!) conclude, ‘that the Greeks neither made civilization nor saved it, not even re-made it very notably.’ Thank you! Now at last, we occidental neurotics, so long hindered by our praejudicium antiquitatis, can see things clearly!”*

These are all included in a letter compiled by the story’s main character on May 20, 1962, one of the last people alive after the nuclear war that erupted in the mid-fifties, a letter that is never to be sent and never to be received by the notable professor. “*Just recall to mind what humanity looked like!*” he says at some point of the story. “*Culture!?: one in a thousand passed culture on; one in a hundred thousand created culture!*” His letter is closed with utter contempt towards the American scholar:

“*…we had to wait for your book, this bonanza of nonsense, to inform us about how the history of humankind is taught in the US! We have been accustomed till now to ascribe in brief the following to the Greeks: that they were the first to develop and employ the spirit and method of Western research. We owe them such important independent findings as the exact measurement of the earth’s sphere, and, as a result, maps with objects fixed by longitude and latitude. In astronomy, star catalogues, geo- and heliocentric world views etc., are likewise Greek discoveries; biological systems are based on their work; could you solve Diophantine equations? Compare Greek cultural achievements – statues, temples, epics, dramas, etc. – with any and all previous and contemporaneous achievements: greater men than either of us have been enraptured by them! Philosophy – – well, you folks over there have not got that far yet.- We are and shall remain of the opinion that, in spite of the Stewart test, the totality of our intellectual existence, emerging out of the last two crests of culture, the renaissance and the classic-romantic age, is based, as were those crests themselves, on the Greek way.*

*[…]*

*It may be humiliating that your nation has as yet made no contribution to great culture – with the exception of Edgar Poe; but even that day too will come! (Though not through your efforts!)*

*May your toilets always flush;*

*with sincerest contempt”*

**The “100 birds” problem and Arno Schmidt**

Schmidt’s mention of Diophantine equations in “*Dark Mirrors*” might not be superficial. Firstly, because he had repeated this argument in his triptych “*Leviathan*“ (1949) when through the personage of Pytheas of Massalia he claimed that *“Herodotus is the best example, of how even grand, deeply educated, rich minds are apt to making ridiculous errors when scientific – especially mathematical – education is missing. He had heard something about the roundness of the earth, as taught and proved centuries ago by Pythagoras, Thales, Anaximander – and he thinks that this is related only to our own world! He maintains that what they meant is that this round disk floats on Oceanus, which of course is opposed by him, relied upon his good and wide geographical knowledge; […] He had understood nothing of all this…” * Now this argument was similarly employed to organize an attack against the distinguished American professor of English who was obviously missing mathematical education. Secondly, because in “*Alexander or What is Truth*” he had already strategically used Diophantine equations and the “100 birds” problem in particular to indirectly support an argument. The story in “*Alexander*” unravels in small paragraphs of first person narration and inner monologue, as was usual in Schmidt’s works, describing a time when Alexander the Great, quite unbelievably, was dying in Babylon and his empire was about to be torn in pieces by his successors. Schmidt’s alter ego in the story this time is Lampon of Samos, a 18 year old Greek student of the great Aristotle (also the teacher of Alexander), who travels to Babylon in order to meet his uncle Aristodemos, one of Alexander’s guards. Schmidt is notorious for his demanding prose form, his linguistic acrobatics and his mind games inspired from his own vast readings. His encyclopedic texts are highly interactive in the sense that they require the engagement and participation of the reader and a kind of “homework” to be done in parallel to reading, clarifying the author’s continuous direct references or allusions to Literature, History, Geography, Astronomy and even Mathematics. At some point, Lampon and his friend and co-traveler Hipponax, “*out of pure uselessness*”, exchange challenging problems, one of which (in a rather obvious anachronism) is a description of the 15-puzzle and the other is a variation of the “100 birds” problem:

“*Watching quickly gets to be a bore**: Hipponax (who is staying with the baggage this evening, ‘holding position’, as he says in the army jargon of the day), sat down next to me, and out of pure uselessness we exchanged riddles and magic tricks. I made a 16-square field for him, filled them at random with the numbers 1-15 and had him use the open field to shift them back into normal order (he’d never seen that one). In return he explained: ‘The vendor next door has 3 kinds of wine, at 10, 3 and 1/2 drachmas a jug; here are 100 drachmas: bring me 100 jugs,’ and added: ‘It’s not the answer that’s interesting, that’s easy to find. But rather the exact mathematical method for solving it, by way of setting up equations -‘ Well yes, in this heat you can’t always be clever.*“

Apart from Art and Literature, Schmidt displayed particular interest in Mathematics as an amateur and apparently felt admiration for the world of Science and Mathematics, a sentiment that is emblematically expressed in “Enthymesis” (1949): “*Who can only be great? Artists and Scientists! Nobody else! And amongst them, the humblest is a thousand times greater than the great Xerxes*”. After the war he even claimed at some point that he voluntarily canceled his studies of mathematics and astronomy at the university of Wroclaw during the Nazi regime, when his sister married a Jewish businessman. Later on, while employed in a textile factory as a stock accountant , he had for some years worked privately in compiling tables of logarithms with ten correct digits, a quite tedious yet futile occupation. Within his texts one can find numerous direct or indirect references to mathematical concepts, ideas, metaphors often in connection to the history of Mathematics, indicating that his remarkable amount of reading included mathematical texts. And sometimes these references are blunt as a sketch of an attempted “quick proof” of some proposition in the post-apocalyptic “Dark Mirrors” (1951), using mathematical symbols and jargon, and at the same time subtle and ironic as when this proof is soon uncovered to be nothing else than a proof of Fermat’s last theorem, for which Schmidt’s alter ego comments that “*the symbols drew themselves out nimbly from my pencil, and I bungled merrily along”*. It therefore seems quite possible that he was fully aware of the global historical character of the “100 birds” problem, which was employed in “Alexander” as an emblem of a masterpiece conquest, one “*that endures and bears fruit*“. He presents his characters, two representatives of “*the literary nation*“, as early as three centuries before Christ, casually and “*out of pure uselessness*” on their way to Babylon discuss a puzzle that was destined to be studied in non-Greek mathematical texts of scholars in both East and West for at least the next 18 centuries after that time. Schmidt has Hipponax make clear that “*It’s not the answer that’s interesting, that’s easy to find. But rather the exact mathematical method for solving it, by way of setting up equations”*. Far beyond any algorithmic approach of finding answers, this may be a reference to the Greek mathematical tradition that led to Diophantus’ syncopated Algebra and the establishing of a mathematical language, a major transition in the history of Mathematics and Culture in general.

**Towards hospitable regions
**

In “Alexander” Schmidt repeatedly makes allusions to the natural process of mixing of ideas, cultures, peoples and to the flow of cultural juices like the “*natural phenomenon of birds seeking food from a mob on the move and choosing a route in the direction of the only hospitable region*“, as opposed to the forced and unnatural, mongrel mixing attempted by Alexander. Lampon and Hipponax are accompanied by the traveling actors Agathyrsus and Monika whose repertoire includes a play named “*Sataspes*” (named after the Persian navigator) and another named “*At the Well*” which for Lampon is “*a shallow piece of propaganda, which obligingly celebrates Alexander’s melting-pot policies and features at the end: a Macedonian sergeant who marries a Persian farmgirl”*. When on the outskirts of Babylon Agathyrsus appears determined to go by way of Borsippa (Birs Nimrud), telling to Lampon about the “*venerable Chaldean University*” and the Assyrian manuscripts kept there. The “*orientalized” *great conqueror who demanded “*proskynesis*“, to be worshipped as a god, had “*adopted pasha posturings and an unsavory entourage” *and had won over the Greeks, “*the literary nation*“, by his calculated moves, forcing upon them a melting-pot policy, after which “*the arts as a whole […] would be irreparably ruined […by his…] decree that they be united with oriental swank*“. And “*…it’s likely that […] he had already made a quite conscious decision to distance himself from the Greeks; because their free and open behavior toward him was unbelievably scandalous to Asians accustomed to quite different ways. So he coldly weighed the power at his disposal, and has since set everything at the ready so that he can at any time rely solely on the orient*“. At some point, Lampon of Samos quotes his teacher, the great Aristotle:

“* ‘The highest ideal would of course be a harmonious world empire; a united and thus peaceful ecumene…’ Hipponax suddenly grew quite irate: ‘Your Aristotle is an idiot’, he shouted ‘he knows nothing of the world: how can someone drivel on about a world empire composed of 100 nations totally divergent in language, custom, religion?! Europe alone can never be united.’ He got hold of himself again; said coldly, indignantly: ‘I had considered Aristotle and your kind to be more reasonable; but an isophrene (a line of equal stupidity: clever!) binds all human beings without exception. And nations.*” Alexander’s conquest bears no stamp of a masterpiece. “*Let me tell you what a masterpiece of conquest is*“, Hipponax says in Schmidt’s story, “*it’s something that endures and bears fruit, over centuries […] But what happened here was: Persia, a loosely federated state of 100 different peoples, was penetrated here and there along various thin frontiers by a strong, usually victorious, army of good professional soldiers, was systematically plundered, and occupied at several strategic spots. The nations were not conquered at all: countless mountain peoples, in Asia Minor, – ah, everywhere – are free as birds; many isolated fortresses defy him still: who along the Indus or among the Scythians still cares about Alexander? Partisans everywhere. So the country has not been <organically> conquered; a reasonable, humane commander would never have agreed to such an undertaking for that matter; he would have seen the madness in advance. Had he limited himself to Asia Minor, as Parmenion so urgently recommended to him when Dareios offered peace, Alexander could have been a benefactor of mankind: he could have established a new, wonderfully rich basis for Greece, for Greek culture in general, triumphantly energizing it well into the future. 200 years later, some wise successor would have known what to do next”*. And “*trembling like a flame*“, Hipponax concludes: “*You show me the place where one blade of grass grows because of Alexander: I can show you for each, 100 where nothing prospers!!!*“

For Schmidt, any attempt to conquer the world by force is un-Greek: the world was actually being conquered by Greek Art, Culture, Philosophy, Science, Mathematics and the arrows of the cultural flow naturally radiated from the Mediterranean shores “*choosing a route in the direction of the only hospitable region” *. A great leader would be one who would recognize this cultural greatness instead of plunging into the madness of an ephemeral, futile world campaign, as Alexander did. Such a leader would be a benefactor of mankind, establishing “*a new, wonderfully rich basis for Greece*“, allowing the Greek spirit to be dispersed through a natural, long-term osmosis. It seems that his mention of the emblematic “100 birds” problem is another of his mind games, as he presents his readers with a puzzle quite familiar to many, that could be still found in modern textbooks and that was included in Rudolff’s “Coss”, the first German textbook of Algebra. More than this, it is a puzzle that permeates the mathematical tradition of both western and eastern cultures for almost two millennia and a symbol of the slow, continuous natural mixing of cultures. At another point, having arrived in Babylon and while Alexander is dying, Lampon describes to his uncle Aristodemos the latest scientific advances of the Greeks:

*“I had to report about our latest geographical conclusions; he was chiefly interested in Pytheas of Massilia’s Periplus; he demanded all the details that I could still recall (and there were lots of them; it is in fact most important work) ‘Think of that,’ he said, ‘up there then, it’s continually light – constant day and sunshine, right? And yet it starts snowing the further north you go? How did you explain that?’ I laid out for him one of the new hypotheses, and he nodded appreciatively: ‘So the sun’s orbit around the fixed globe of the earth is not constantly at the level of the equator (something we’ve known for a long time now really!) but somewhat above it: which explains the light. (And at the same time explains as well Herodotus’ curious report: <the Phoenicians had the sun on their right as they sailed around Africa>!) – And since the rays strike at a very shallow angle given the curvature of the earth – about like our mornings, when it’s still cold as hell. – Hm. That would explain the chill then -‘ He pondered this for a moment, shoved critical lips forward and nodded gently: ‘Quite plausible’ he then said in conclusion, ‘and that’s how our knowledge of the mechanics of the universe continually advances.’*

The difference between this guard of Alexander, the Greek soldiers in general, and the army that Alexander wished to create is immense. The appearance of Alexander’s Bactrian Legion in the outskirts of Babylon disgusts Lampon:

“*Soldiers drilling: on a large field. The Baktriana Legion (Hipponax explained) under Greek instructors: big rough Persian louts from the mountains, with high chests and broad brows; physical elite (‘They all swear an oath to Iskander as they call him’ The boom of a marching song: ‘…3…4…: with lances high, our phalanx ranks closed tightly…’) Other boats beside and behind us; small talk and laughter arose above the water’s disk.*

*Bodies: that’s the way you select horses and oxen; or breeds of dogs perhaps (but Plato does call them the dogs of state!). Robust souls. – Human beings should be judged by that which distinguishes human beings from other living things: by their intelligence. –*“

In that, Schmidt presents his characters, ordinary representatives of the “*literary nation*” being far ahead of their time culturally, continually doubting the great conqueror Alexander, casually discussing about the Arts, Theater, Mathematics and Science in a way that remained advanced for many centuries thereafter, as was the case with the “100 birds” problem, even discussing the 19th century 15-puzzle, as they themselves are part of a great flow of cultural and scientific ideas between the Mediterranean shores and the East.