Studies on Ancient Greek Literature
The book is an analysis of Greek Hellenistic literature with the help of conceptual tools of cultural studies and media theory. Its main aim is to describe the cultural process during which Greek authors in the 4th and 3rd centuries B.C. made the “textualization of experience", that is, transferred phenomenalistically understood qualities of human sensory experience to the categories characteristic for textual description – as far as possible for them. This process is shown by examples from the works of Xenophon, Aristotle, Theophrastus, Philitas of Kos and Archimedes. The author also tries to show some of the consequences that the phenomenon of the Hellenistic textualization of experience had for the later epochs of European culture.
Chapter 7 Archimedes and his Sandreckoner
Literate man undergoes much separation of his imaginative, emotional, and sense life, as Rousseau (and later the Romantic poets and philosophers) proclaimed long ago.
Marshall McLuhan, Understanding media.
The Extensions of Man, chapter 9: “The Written Word.
An Eye for an Ear” (Routledge Classics edition, 2002, p. 88).
The development of specialist literature in the Hellenistic era and subsequent centuries was too broad to be analyzed within a single study, which, moreover, would have to include data from not only philology, but also science and history of science, not to mention detailed knowledge within individual fields. The number of texts belonging to this area overwhelms the recipient. It should be remembered that it is precisely in these epochs – from the end of the fourth century BC to the end of the second century AD – the majority of the ancient Greek-language literature preserved to our times was created. Most of this bulk of texts today is known only to specialists, precisely because it consists almost exclusively of “specialist” texts, i.e. non-literary, non-narrative, and intended for specific reading by a narrow circle of expert audiences, not by a wide literary or theatrical audience. The structure of these texts, the assumptions about their cognitive status and relation to reality, and finally their projected circulation in society are very different from the analogous properties of the texts from the earliest periods of developed Greek literate culture, in which their functioning and social roles were still strongly connected with the pre-literary forms of cultural messages, and thus maintained an integral bond with the whole of social life, they were not subject to internal specialization or limited to strictly defined proliferation and receiving circles. The phenomenon of specialization of the text began to be visible only at the very end of the classical era, which I tried to show in the previous parts of this book. In the Hellenistic period, it became the norm.←153 | 154→
The most extensive biographical encyclopedia of ancient scholars today, whose editors proudly point out that they have collected more material than can be found anywhere else, including the Realencyclopaedie der klassischen Altertumswissenschaft, contains 2,043 personal entries, the chronological distribution of which shows that the largest percentage of the authors of the Fachliteratur is in the first and the second centuries AD, but the beginning of the upward trend falls on the Hellenistic era.163 Nevertheless, as always in relation to antiquity, it should be remembered that we are dealing with a small fraction of the total text production of that time. One should also remember a certain arbitrariness in assigning ancient authors to the category of “scientists,” especially in the light of the investigations conducted here. Thales of Miletus is commonly regarded as the father of science; we are not sure whether he used the writing at all, and if so, whether he treated it as a fully-fledged tool for his thinking about reality. Almost certainly it was not for him what it was for Aristotle and his successors, who, by the way, nominated Thales as their spiritual protoplast knowing little more about him than we do.
If one wants to go beyond the traditional division of this literature in line with the network of modern scientific disciplines,164 then the antique professional literature, in its broadest sense, can be divided into two great disciplines shaped in accordance with the logic of cultural processes, which I try to illustrate in this book and whose foundations were laid by Aristotle and Theophrastus. The first one can be described as “structuring reality in the text.” This includes authors whose texts are “catalogues,” “systematics,” and “codes” of nature, that is, they are attempts to design ←154 | 155→the structure of reality available in research and in previously prepared descriptions so that the streams of chaotic sensory data are given the form of uniform, precise elements whose sets or aggregates make up a scientifically-acquired intelligible world. According to the modern classification, these works belong to such fields as zoology, botany, astronomy, and astrology, mathematics, musicology (called harmony in the antiquity), metrology, geography, paradoxography, and physiognomy. Within their framework, the physical reality available to the human mind at the then stage of development of observation techniques is included in text descriptions that design (and, from the point of view of the authors and readers of these texts, reproduce) its ordered structure by means of ordered structures of notation and description – divisions of the text into component elements designed to give, as a whole, a meaningful image that can be used for further theoretical investigations. The structuring tools here are textual tools shaped in the way I described earlier. The result of such scientific activities is to transfer the textual world order to the world itself – the world order in the text is considered to be the world order as such. This is the world in words. The project of the grainy, quantized structure of reality developed in the text is considered by human minds familiar to the text to be – if one can paraphrase Plato – truly existing essence.
The second great field of Fachliteratur is composed of textual instructions of practices, similar to those I analyzed on the example of Xenophon, but subject to the principles of textual absolutism derived from the writings of the Stagirite. These instructions – in the form of treatises on mechanics, agronomy, gromatics (delineating areas of cultivation), breeding, medicine, pharmacy, veterinary medicine, belopoics (constructing war machines), war strategy, alchemy, architecture, optics – include mainly manual and motoric practices, related to classes of repetitive activities that play a significant role in the functioning of the social system or in the influence of people on the natural world inhabited by them. What the instructions require, too, is specialist knowledge and performance skills.165 In addition to textbooks ←155 | 156→devoted to various technical and practical skills (also as “common” as gastronomy), this group also includes works more akin to “learning” in the modern sense, i.e. devoted to pure knowledge, not directly applicable in practice. However, this knowledge itself can also be regarded as a special class of practice – its collecting and processing often depend on careful observation or the design and execution of thoughtful experiments.
In this sense, ancient (and, to a large extent, modern) science is a class of specifically defined motoric, social and linguistic practices, whose characters influence each other, while remaining primordially dependent on the textual recordings of reality, which, in turn, make it possible to accumulate knowledge of all these practices in a way that exceeds the limits of direct human contact, which enables unlimited growth of the base material – and this arrangement forms the basis for the concept of “scientific experience,” which, as one can easily see, has little in common with the “experience” in the title of this book, although both types of “experience” are somehow linked to sensory data. However, the problem is that the material growing in the Fachliteratur texts does not contain non-verbal qualities of experience – also scientific – which, in turn, lies at the root of the problem of tacit knowledge in scientific procedures, a subject of a fierce discussion among philosophers and theoreticians of science for at least two hundred years. Nonetheless, most modern approaches to this problem assumed that tacit knowledge should not play any role in the constitution and development of scientific experimental knowledge, because it is not suitable for intersubjective textual communication.
Still, the boundaries between types of texts such as textualized practice, textual practice instruction, textual score of performance of a practice, catalogue/systematics/code, and finally the absolute text, i.e. mainly concerning itself and other texts – these boundaries have always (i.e. since the period in question here) been fluid in European culture. Even the most abstract philosophical inquiries sometimes manifest a connection with the realm of experience, even the most formalized theoretical descriptions are meant to confront experience. An absolute text – that is to say, one devoid ←156 | 157→of external references – is not possible in its pure form, even though it has permeated the dreams of many authors to come, and its closest realizations can be found in some experiments of twentieth century literature. But let us return to the Greek Fachliteratur.
I will try to demonstrate at least some of its important features – especially in relation to the first of the types distinguished here – on the example of a text which has gained fame in the history of mathematics and whose author is considered to be the most outstanding scientist of all antiquity (in the modern sense of the term “scientist”). What I have in mind is the shortest of Archimedes’ surviving works: Psammites.
Archimedes of Syracuse (ca. 285–212) is not only the greatest – in the opinion of his modern successors – but also the best-known antique scholar in contemporary popular culture, even though we know almost nothing about his life and person. Here, I do not consider him as a mathematician, whose ingenuity is the object of great admiration for modern scientists,166 but I consider his work as one of the important examples of a text-centered method of analyzing the reality present in the sensual experience of people using alphabetical writing according to the principles defined by the pioneers of abstraction, autonomy, and alienation of text from experience. In the case of Archimedes, we are dealing with an experience which, already at a phenomenal level, is detached from the Lebenswelt realm, because it is a proto-scientific experience that results from the textual bias in a particular way, very close to the modern scientific method167 and unprecedented in any of the previous authors discussed in this book.168 The profound admiration ←157 | 158→of modern scientists for Archimedes resulted, among other things, from the fact that he wrote about mathematical, physical, and mechanical problems almost as much as they did, at least in terms of textual reasoning structures. Before I move on to comment on this work, I will again pay some attention to biographical testimonies.
In popular books on the history of science, Archimedes appears mainly as a somewhat crazy person who jumps out of the bathtub, runs around the city naked, and shouts “eureka!” (or rather “heureka!”). Of course, the reason for his joy, unclear to the audience of this peculiar spectacle, was that he discovered – when looking at the water pouring out of the bathtub under the pressure of his body – a physical law later named after him. This picture perfectly fits the modern stereotype of a scientist “detached from reality” and, by the way, is also a model picture of the process of scientific heuresis. However, what interests me here is not the manifestations of this “detachment,” but the phenomena that led to it. It is impossible to prove the historicity of the episode with the bathtub, although it is not as fantastic as one often thinks, because “bathtub” in this case does not mean a white-enameled free-standing container, but an element of equipment of an ancient bath.169 However, it could be treated in the same way as I have previously treated the information about Theophrastus and Philitas,170 and ←158 | 159→the whole of Archimedes’ biographical tradition – which, despite the gaps in our knowledge mentioned above, is nevertheless richer than that of all other ancient scholars – also remains suitable for such an analysis.171 Its most important component is, of course, the story of his death at the hands of a Roman soldier as a result of a communicational misunderstanding during the conquest of Syracuse by the Romans led by consul Marcus Claudius Marcellus during the Second Punic War. We know this story mainly from Plutarch, who gives it in three versions.
For it chanced that he [Archimedes] was by himself, working out some problem with the aid of a diagram [epi diagrammatos], and having fixed his thoughts and his eyes as well [ten te dianoian kai ten prosopsin] upon the matter of his study [te theoria dedokos], he was not aware of the incursion of the Romans or of the capture of the city. Suddenly a soldier came upon him and ordered him to go with him to Marcellus. This Archimedes refused to do until he had worked out his problem and established his demonstration [pros ten apodeiksin], whereupon the soldier flew into a passion, drew his sword, and dispatched him.
Others, however, say that the Roman came upon him with drawn sword threatening to kill him at once, and that Archimedes, when he saw him, earnestly besought him to wait a little while, that he might not leave the result that he was seeking incomplete and without demonstration; but the soldier paid no heed to him and made an end of him.
There is also a third story, that as Archimedes was carrying to Marcellus some of his mathematical instruments [ton mathematikon organon], such as sun-dials and spheres and quadrants, by means of which he made the magnitude of the sun appreciable to the eye, some soldiers fell in with him, and thinking that he was carrying gold in the box, slew him. (Plutarch, Life of Marcellus 19)172
Of these accounts, the third is, so to speak, the most banal and repetitive in history. The first two, in turn, contain details that say a lot about the specifics of Archimedes’ intellectual work. He considers problems, which no longer rest on an experience of physical reality (i.e. “view” – “theoria” in the original sense of the term). Such experience, as we remember, provided the basis for the construction of the argument in Xenophon’s textbooks, its residual form still manifested itself in the epistemologies of Plato and Aristotle, while its absence became the cause of physiological problems of Theophrastus and Philitas. For Archimedes, this absence is no longer a problem, either physiological or even more so psychological or intellectual. On the contrary, the proper vehicle of his thinking is a record, text, chart, diagram, drawing: generalized written forms of mediating the reality experienced sensually in an insignificantly accidental way. The problems that haunted Plato and Aristotle do not exist at all for Archimedes because he does not see the need for any connection between the written record – which he sees as the vehicle and the means of thinking about reality – with that reality itself. In short, the record is for him a fully independent and alienated, natural and primordial entity. That is why it is submerged in “thoughts and eyes” to such an extent that his senses and mind stop receiving and processing any other external signals. The scientist’s perception is reduced because, in order to formulate judgements about the world, he does not have to experience the world at all. Instead, all that he needs is a symbolic notation of it, and not even on any solid ground, since one can draw figures on sand. What is more, the judgment derived in the form of a mathematical proof or physical law from such a generalized picture of the world is as universal as no judgment based on individual, ad hoc, and random sensory experience could be. Aristotle, making in Metaphysics sophisticated intellectual overturns in order to legitimize abstract textual categories, would probably be astonished to see how easily Archimedes omits the problem of their legitimacy because he no longer sees the need for such legitimacy. Undoubtedly, it was Stagirite who paved the way for him.←160 | 161→
In the second version, where Archimedes wants to ask the Roman soldier to let him finish the proof, we can hear the overtones of some idealized heroism, but here too we can see the effects of the alienation of the mind and body of the scientist from the realm of experience. These take the form of disregarding one’s own condition, which, when seen from the outside, is indeed very similar to heroism.
Plutarch’s accounts are not the only versions of Archimedes’ death. Here is the version presented by Livy:
While many shameful examples of anger and many of greed were being given, the tradition is that Archimedes, in all the uproar [tanto tumultu] which the alarm of a captured city could produce in the midst of plundering soldiers dashing about, was intent upon the figures which he had traced in the dust [intentum formis quas in pulvere descripserat] and was slain by a soldier, not knowing who he was… (XXV, 31)173
Livy omits the very act of murder, which is unsuitable for his ideological purposes because it does not give the glorious testimony of the intelligence of the Roman soldiers, but emphasizes, like Plutarch, the scientist’s deep focus on graphic representations of the problems on which he worked and his ability to “exclude himself” from the current, even extremely dramatic situation. Here, too, we get an example of the immersion of the mind in the medium of recording to the point of sensory deprivation, and this precisely how Livy understands Archimedes’ detachment. Cicero, in turn, interprets it differently:
A passion for miscellaneous omniscience no doubt stamps a man as a mere dilettante; but it must be deemed the mark of a superior mind to be led on by the contemplation of high matters to a passionate love of knowledge. What an ardour for study, think you, possessed Archimedes, who was so absorbed in a diagram he was drawing in the dust [in pulvere quaedam describit attentius] that he was unaware even of the capture of his native city [ne patriam captam esse senserit]! (De finibus bonorum et malorum, V 49–50)174
For Cicero, Archimedes’ behavior is a gesture of conscious intellectual heroism, not an effect of the medium of communication acting on the mind. Cicero values this behavior, placing it in a specific moral and political order. To see a similar symbolic interpretation of the scene of the Archimedes’ death in the twentieth century, let us look at the quotation from Alfred North Whitehead:
The death of Archimedes by the hands of a Roman soldier is symbolical of a world-change of the first magnitude: the Greeks, with their love of abstract science, were superseded in the leadership of the European world by the practical Romans. Lord Beaconsfield [Benjamin Disraeli], in one of his novels, has defined a practical man as a man who practises the errors of his forefathers. The Romans were a great race, but they were cursed with the sterility which waits upon practicality. They did not improve upon the knowledge of their forefathers, and all their advances were confined to the minor technical details of engineering. They were not dreamers enough to arrive at new points of view, which could give a more fundamental control over the forces of nature. No Roman lost his life because he was absorbed in the contemplation of a mathematical diagram.175
While remaining in the orbit of the humanistic interpretation of cultural history, Whitehead understands Archimedes’ death as an emblem of the conflict between the unselfishness of the pure thought of the Greeks and the brutal, interesting practice of the Romans. Today, the evolution of cultural phenomena is rarely seen in this way, but it should be noted that this evolution, as seen from the perspective of the investigations conducted here, also differentiates between Greeks and Romans. It seems that the culture of Roman antiquity has not brought significant innovations or even qualitative changes to the set of writing and reading practices produced by the Greeks. The only such phenomenon was the transition of the book shape from a scroll to a codex, which, while making it very easy to maneuver large parts of the texts to be read, did not change the essence of the relationship between the text and experience formed in the world of Greek culture.
The Roman erudite from the first century AD, Valerius Maximus, encloses the account of Archimedes’ death with a symbolic frame, saying that his abilities at the same time gave him life (because Marcellus wanted to get him alive as a great engineer who could be very useful to the Roman ←162 | 163→armies) and took it away due to a misunderstanding, and moreover, like all the previously quoted authors, he emphasizes his focus on written diagrams. It is also here where the most famous detail – the last words of the scholar – appears for the first time:
At is [Archimedes], dum animo et oculis in terra defixis formas describit, militi, qui praedandi gratia domum inruperat strictoque super caput gladio quisnam esset interrogabat, propter nimiam cupiditatem investigandi quod requirebat nomen suum indicare non potuit, sed protecto manibus pulvere “noli” inquit, “obsecro, istum disturbare”, ac perinde quasi neglegens imperii victoris obtruncatus sanguine suo artis suae liniamenta confudit. Quo accidit ut propter idem studium modo donaretur vita, modo spoliaretur.
But as Archimedes was drawing diagrams with mind and eyes fixed on the ground, a soldier who had broken into the house in quest of loot with sword drawn over his head asked him who he was. Too much absorbed in tracking down his objective, Archimedes could not give his name but said, protecting the dust with his hands, “I beg you, don’t disturb this,” and was slaughtered as neglectful of the victor’s command; with his blood he confused the lines of his art. So it fell out that he was first granted his life and then stripped of it by reason of the same pursuit. (Valerius Maximus, Memorable doings and sayings 8, 7, ext. 7)176
In the context of the comments made here, the words of dying Archimedes complete the picture of the textual alienation of experience.177 Placed in an extreme situation in which his own life is threatened, Archimedes does not show any self-preservation instinct at all, but he shows concern for the written record. This means that the truth about the world is hidden for him just in the record, and not in his own mind and body: not because Archimedes is not creative, but, on the contrary, because his great power of discovering and creating knowledge depends on the presence of the record, because its effects are no longer suitable for oral transmission, because they are expressed through concepts and relations of a strictly written nature, ←163 | 164→and from this it follows that the presence of the text is more important for their permanence than the presence of the mind which produced it.
This scene, together with the last words, was also described by the Byzantine authors. John Tzetzes (XII cent.) in Chiliades (II 145 Kiessling) attributes to him words: “apostethi, o anthrope, tou diagrammatos mou” [man, get away from my charts], and Joannes Zonaras, another Byzantine author from the twelfth century whose historical credibility in this case is, unfortunately, very low, cites probably the most interesting of all the versions of the story about Archimedes’ death, because, strangely enough, the last words of the scholar recalled (or invented) by this author are a strikingly accurate manifestation of the text’s advantage over experience:
…and they killed Archimedes. When he drew a diagram [diagramma gar ti diagraphon] and heard a soldier approaching him, he said “in the head, not in the record” [par’ kephalan, ephe, kai me para gramman]. And when that soldier stood in front of him, he thought for a moment [brachy te ephrontise] and said, “man, go away from the record” [apostethi, anthrope, apo tes grammes] with which he angered that one and was killed. (Epitome historiarum IX, 5; II 264–265 Dindorf, emphasis PM)178
The phrase “in the head, not in the record” can be understood either metaphorically, as “let it go on my head, not on the charts,” or in the more literal sense “let it hit my head, not the charts.” In both cases, Archimedes appears in an even clearer way as a man who cared more about the text than about his own mind and body. Here, however, he is already the phantasmatic Archimedes of Byzantine medieval erudites.
If we go back to Plutarch for a while, we will find other interesting biographical details with a little more credibility. In the Life of Marcellus (chapter 14, 4), he tells us about the magnificence of Archimedes’ scientific and engineering achievements:
To these [i.e. technics and mechanics] he had by no means devoted himself as work worthy of his serious effort, but most of them were mere accessories of a geometry practised for amusement [geometrias de paidzouses], since in bygone days Hiero the king had eagerly desired and at last persuaded him to turn his art somewhat from abstract notions to material things [apo ton noeton epi ta ←164 | 165→somatika], and by applying his philosophy somehow to the needs which make themselves felt [ton logon hamos ge pos di’aistheseos miksanta], to render it more evident to the common mind. (Life of Marcellus 14, 4)179
In Plutarch’s words, one can find confirmation of the theses presented here on the separation between the phenomenal experience and the textual record in the Hellenistic era. Archimedes, who, as already mentioned, omits the phenomenal realm in his intellectual work, is urged by the ruler to make politically beneficial use of his theoretical achievements. This theme is common as such – in the twentieth century we see it in the Manhattan Project, among others – but Plutarch uses characteristic expressions to discuss it: “apo ton noeton epi ta somatika,” which literally means “from what is thought/intellectual, to what is bodily/material,” followed by the terms logos and aisthesis, which can be expressed in this context as “text” and “experience.”
Plutarch unintentionally captured in these remarks the essence of one of the most important cultural processes accompanying the development of science. After Aristotle’s successors led in the Hellenistic period to an almost complete detachment of text records from the stock of given phenomenal experience, they received as a result a “pure theory;” an example of this is Archimedes’ Psammites, to which I will soon proceed. But their theoretical, abstract generalizations have not ceased to apply to the world of human life, although the sensual experience of this world was no longer at their root. This means that the theoretical texts revealed the potential for a reverse in their perception to the world of experience – but instead of being the results of that experience, they started to be its sources. Their content allowed to transfer it pragmatically back to aisthesis and to somatikon. The case of Archimedes is one of the first examples of the practical application of knowledge produced on the basis of a theoretical text. It is on such or similar practices of reverse recontextualization of textual abstractions that the edifice of modern science will be built. However, I stress again that for Archimedes himself, as we can infer from the quoted sources, the possibility of practicing his own theoretical knowledge was of no importance.←165 | 166→
However, the highly tensioned relationship between scientific theory and practice, defined in this way, did not arise only in the time of Archimedes. In the following sentences of Life of Marcellus, Plutarch continues his digressions on mathematics and engineering:
For the art of mechanics [organiken], now so celebrated and admired, was first originated by Eudoxus [of Cnidus, 408–355] and Archytas [of Tarent, his teacher, 428–347], who embellished geometry with its subtleties, and gave to problems incapable of proof by word and diagram [logikes kai grammikes], a support derived from mechanical illustrations that were patent to the senses [di’aistheton kai organikon paradeigmaton]. […] But Plato was incensed at this, and inveighed against them as corrupters and destroyers of the pure excellence of geometry [geometrias agathon], which thus turned her back upon the incorporeal things of abstract thought [apo ton asomaton kai noeton] and descended to the things of sense [epi ta aistheta], making use, moreover, of objects which required much mean [somasi] and manual labour. For this reason mechanics was made entirely distinct from geometry, and being for a long time ignored by philosophers, came to be regarded as one of the military arts. (14, 5–6, emphasis PM)180
These comments are interesting for many reasons. First of all, we learn that diagrams and charts have been present in Greek writing practices at least since the beginning of the fourth century (the case of Oenopides discussed earlier is unfortunately older, so the message of Plutarch does not clear our doubts about him; an even older case, which is Pythagoras’ mathematical thought, is almost entirely within the scope of legends and myths – however, it is worth recalling that Archytas and Eudoxus were Pythagoreans). Second, their abstract written form did not always meet the needs of early mathematicians, so they combined it with engineering practices, seamlessly combining abstraction of writing and experience of practice. Third, finally, Plato speaks on this issue and separates the realm of manual activities from the realm of abstract inquiries based on the “pure” text (and, in his own opinion, on Ideas). This decision is motivated by aesthetic and social arguments (“pure thought” is clearly a status symbol), and his overwhelming authority causes long-term degradation of the class of engineering practices in Greek society. This detail from the history of the Greek textualization of experience is another example of the ←166 | 167→interference of mediological and ideological factors in the history of the means of communication.
However, the conviction about the qualitative superiority of written abstraction over activities carried out in the world of sensual materiality gradually took root in the minds of Greek culture creators. Probably the progressive textualization of their intellectual practices overlapped with the perennial social rivalry in this culture for a position in the status hierarchy. Thus, Plutarch provides a suggestive account of Archimedes’ engineering successes in the fight against the Romans besieging Syracuse (in Plutarch’s report, we find the famous words of chief Marcellus about the “Briareus of Mathematics,” with which the fight is almost hopeless: here, Marcellus compares Archimedes to the mythical titan with hundred hands). After remarking on this, however, Plutarch quickly moves on to another subject:
And yet Archimedes possessed such a lofty spirit [phronema], so profound a soul [psyches], and such a wealth of scientific theory [theorematon], that although his inventions had won for him a name and fame for superhuman sagacity, he would not consent to leave behind him any treatise on this subject [syngramma], but regarding the work of an engineer [peri ta mechanika pragmateian] and every art that ministers to the needs of life as ignoble and vulgar, he devoted his earnest efforts only to those studies the subtlety and charm of which are not affected by the claims of necessity. These studies, he thought, are not to be compared with any others; in them the subject matter vies with the demonstration [pros ten hylen te apodeiksei], the former supplying grandeur and beauty [to megethos kai to kallos], the latter precision and surpassing power [ten akribeian kai ten dynamin hyperphye]. For it is not possible to find in geometry more profound and difficult questions treated in simpler and purer terms. (17, 3–5, emphasis PM)181
Archimedes’ intellectual pride stems from the detachment of the subject matter of his thoughts from any practice, any connection with action in the Lebenswelt realm. His proper domain is psyche, fronema, and theorema, i.e. those intellectual entities for which the proper, natural, material environment is the written record, and this record has a very high degree of autonomy in the world of practical actions. In this clear appreciation of the alienation of the thinking subject from the world of life, apart from psychological factors, there is also a role to play for the precision of written reasoning, which can be disturbed when combined with practical actions. ←167 | 168→Again we can see a reversal of the original relationship between the world and the text. The text is no longer a representation of the world, nor of its presence. Rather, it is the world that becomes a minor addition to the text. It does not completely disappear in the text – in this case the text would not be understood by anyone other than its author – but it succumbs to something like the Hegelian Aufhebung; deprived of existential autonomy, it becomes a silent, seemingly absent component of pure thought, supported and expressed in an autotelic record. The world is included in the text.
As Plutarch continues:
And therefore we may not disbelieve the stories told about him [Archimedes], how, under the lasting charm of some familiar and domestic Siren, he forgot even his food and neglected the care of his person; and how, when he was dragged by main force, as he often was, to the place for bathing and anointing his body, he would trace geometrical figures in the ashes, and draw lines with his finger in the oil with which his body was anointed, being possessed by a great delight, and in very truth a captive of the Muses. And although he made many excellent discoveries, he is said to have asked his kinsmen and friends to place over the grave where he should be buried a cylinder enclosing a sphere, with an inscription giving the proportion by which the containing solid exceeds the contained. (17, 6–7)182
The first part of this testimony is usually omitted by researchers and commentators with a somewhat embarrassing silence, but as long as it is authentic, it leaves no doubt as to the impact of Archimedes’ intellectual practices on his emotional and sensory realm. Once again, it should be reiterated that the problem of the physiology of higher intellectual processes awaits the researcher, who will finally move from the area of anecdotal curiosities to a serious discussion, the subject of which is worthy, if only because even the highest-class abstractor does not stop inhabiting his own body. Plutarch’s account confirms the previously formulated remarks about Archimedes’ sensory deprivation caused by the deep immersion of his mental realm in abstract writing categories – so deep that he uses as a writing medium the ashes then used in hygienic treatments. What is more – and this should be considered an extreme manifestation of his mental state – he also writes on his own body anointed with oil (the Greeks cleaned the ←168 | 169→body by rubbing it with oil mixed with ash and scraping it off with dirt) and this activity, as Plutarch discreetly suggests, brings him satisfaction that is close to sexual one, but it does so only in passing, as if on the occasion of the main activity, which is drawing on himself figures and diagrams associated with the current abstract intellectual process.
So what, to Archimedes, is his own body? Well, it does not perform any of the roles distinguished by modern psychology or phenomenology. It is neither a tool of existence in the world, nor a tool of action, nor of sensory perception, nor even of communication. It is a handy notepad used to write down the latest ideas. In Greek sources, we have messages about the records on the human body (the most famous of these bodies is the body of the semi-legendary lawgiver, Epimenides)183 but these are records of great importance and relevance to the social, religious, or political community to which the person having this body belongs. Archimedes’ body, in turn, is completely postponed, both as a carrier of the person and as a tool of being, and this disregard goes all the way to the grave where, according to Archimedes’ wishes, an image of one of his important mathematical discoveries was to be engraved – which indeed was the case, as Cicero later reports to have found exactly such an engraving (Tusc. V, 65). Looking at how Archimedes treated his own body, it is hard to imagine a greater advantage of an alienated text over the world of phenomenal experience.184
The depth of the recordings was, as we can see, at least as intense for Archimedes as for Theophrastus and Philitas, and ultimately had the same fatal consequences, but again – as when comparing these two cases – we ←169 | 170→can see an apparently subtle and indeed fundamental difference. Well, the reason why Archimedes dies is not because the texts he writes or reads destroy him physically, but it is because external circumstances suddenly interrupt his text-centered reflection on the generalized qualities of experience (commonly called “detachment from reality”). As was the case with Alexandrian philologists, whose attitude I analyzed in my previous book on the example of Didymus Chalkenteros, for Archimedes, too, the physical reality, the realm of existential and sensual experience, is only an insignificant addition to what is really important: pure thought, whose realization is a written record and which is connected with the Lebenswelt realm in a very indirect way. The difference with the Alexandrians, in turn, lies in the fact that for them the center of textual thinking was the past of their culture archived in the Library. For Archimedes, however, the text has no connection with the cultural situation, it is a tool of strictly abstract thinking, and its historical and cultural provenance has no meaning – that is why it can be written on sand or ashes, because the existence of the truth about the world contained in it does not depend on its presence and permanence, unlike in the case of culturally conditioned texts.
This is how the difference between the Naturwissenschaft and the Geisteswissenschaft within the meaning of Dilthey or, in more recent terms, between sciences and arts, is outlined. The basis of the two great fields is always the text, but their position in relation to their own historical conditions is different. In other words, a mathematician does not have to be interested in where the symbols and notations he uses come from (even if their shape and the extent to which they can be manipulated in the notation influence his thinking), while a literary critic or literary theorist should know the origin of the concepts he uses. Otherwise, he is in danger of falling into a cliché or nonsense – that is, he needs to have at his disposal a collection of past records recorded in a library or archive. However, as I will try to show, the separation of Archimedes’ thinking from the Lebenswelt realm is also not complete, at least in Psammites. The attempt I will make here to read this text will show, I hope, that even the human mind most abstracted from its own sensory system must maintain its connection with the realm of existence experienced in the body.
Psammites (in the Latin version Arenarius, in the English version Sandreckoner) is a short text that Archimedes addressed in the first sentence ←170 | 171→to the Sicilian ruler Gelon II.185 This text can serve as an example of a radical abstraction of the argument in a text practice alienated from the world, which mathematicians will then use, even if not directly influenced by it. Theoretical reasoning supported by recording tools is here freed almost entirely from sensual experience and retains only very few traces of it, which Archimedes uses as a basis for some parts of its reasoning in a way similar to that we have seen in episodes with bathing.
But first I propose a brief comment about the handwriting and the relationship between the oldest mathematical and astronomical inquiries and writing practices. As with most ancient Greek writings, the oldest manuscripts of Archimedes, the traces of which survived to our time, come from medieval Byzantium. Heiberg dated the archetype (the manuscript from which all known manuscripts originate) to the ninth/tenth century, and it is known that this manuscsript still existed in the sixteenth century, but was later lost.186 Based on philological analyses, the scholars found that the present form of the text was distorted in relation to the author’s version, which is more than a thousand years from the archetype. This was deduced mainly from the frequency of dialectal forms in Archimedes’ vocabulary. For me, however, a more interesting issue is the form of mathematical notation in his works; unfortunately, it is completely unresolvable. ←171 | 172→Medieval manuscripts of ancient mathematical texts often contain figures and diagrams illustrating the course of the argumentation, but we have no way of knowing how they relate to the original versions. Thus, we do not know what Archimedes’ original notation looked like, but almost certainly he used diagrams and graphical schemes when considering geometrical problems, as evidenced by the quoted references by Plutarch to his mania of drawing figures everywhere he could find useful surfaces. Graphic, but not textual presentation of ideas or mathematical problems is a very old phenomenon, much older than the Greek civilization. Therefore, it is not possible to say clearly what role such figures played in the written visualization of thought processes in the history of the Greek textualization of experience.
What is more, graphical visualization of numerical and spatial relations has had a strong connection with both mathematics and astronomy since the dawn of history – from the point of view of the history of written practices it is a very special connection. The numerical relations and spatial regularities observed by people since the beginnings of civilization coexisted in their minds with myths and religious beliefs about “what is above.” The experience of the starry sky was probably one of the earliest conscious experiences of our ancestors, long before the first pictograms have been drawn – this is evidenced by prehistoric buildings used, as we can assume today, for astronomical observations or for performing rituals related to phenomena in the sky. As a result of this eternal intimacy, the early mathematical and “diagrammatic” approaches of the Sumerians and Babylonians were born, followed by the astrological poems of Aratus and the figures, names, and mythical plots of the constellations, which gave the heavens (understood as both physical and cultural beings) a rich semantic and symbolic content. It can be assumed that the presence of writing and writing practices does not so much trigger a current of reflection here, but rather facilitates or accelerates it thanks to the aforementioned graphical and symbolic visualizations, which, however, were not created for the first time in the Greeks, but two thousand years earlier in Sumerians.187←172 | 173→
In Psammites, which occupies about a dozen pages of modern printing, Archimedes takes up the following problem: how many grains of sand would fill the whole cosmos?
The very existence of such a problem, the very possibility of formulating it and, above all, the intention to answer it in the form of a specific number rather than a symbolic suggestive verbal term, testify not only to the mental format of the author, but also to the advancement of “thinking techniques,” in the form of a notation and text, which Archimedes used to carry out the reasoning leading to the answer to this question. The point is that his whole reasoning was carried out in an environment of the text which enabled Archimedes to maintain the accuracy, scope, and precision that even the most developed oral-memory message could not provide. If we would like to defend Havelock and Ong’s theses about the unambiguously positive influence of alphabetical writing on human minds and civilization, Psammites could serve as a strong argument here, because it is a great example of the extension of the space available to the mind through text.
Let us start with the sand. Why does Archimedes choose this component of reality for his thought-observation-text experiment?
The motif of “sand incalculability,” present in human culture also since its oldest written history, is probably important here. Something is like grains of sand, when there is too much of it for the human mind to embrace ←173 | 174→and mark with numbers. The figure of the incalculable sand appears twenty-one times in the Bible,188 it is present in the Homeric epic, in Greek lyric and, as it seems, in a great number of other cultural texts from different eras, which, however, as far as I know, no one has ever calculated189 – and also certainly in the colloquial linguistic usage of many cultures and nations. This conviction, probably common to all people living in sand regions, results from the phenomenal experience enclosed by the work of symbols, from the feeling of astonishment and helplessness in the face of a stream of tiny grains passing through the fingers or in the footprints fading at the first blast of wind or the influx of a wave. Let us add to this image the still invincible monotony of the movement of the grains and the thought of the tiny thing growing to the enormity. This is enough to say that Archimedes’ intellectual choice – although it was probably partly due to practical, computational reasons – was also a clear provocation and challenge for his countrymen. To count what is incalculable and to fill the whole world with it – to prove the power of one’s own mind, going against the common idea.
Let us also think about the silent passivity of the sand. It is one of those elements of nature we experience, which – although it intrigues us with its extremes, both small and large – is strikingly indifferent to us. We cannot attribute to it any anthropomorphic intentions, as we do with so many other objects, creatures, and elements. Maybe European desert travelers or Bedouins or Tuaregs, struggling to survive in a sandstorm, had a different impression, as did the people who dug the Sphinx in Gizeh from the sands of the Sahara that absorbed it, but on a global scale almost all people who come into contact with sand perceive it, consciously or not, as an extremely passive existence. Even a stone provokes us to want to open it, but the grain of sand is too small for human stubborn inquisitiveness. The sea invites us, absorbs us, carries us, destroys us or shows the vanity of our efforts ←174 | 175→(also intellectual, as St. Augustine testifies). The sand can only show us the indifference of the passage of time. Therefore, being a part of the world of life, sand does not take part in it, it does not respond to the calls of human consciousness. This is also why sand is so well suited to introduce it into abstract reasoning.
Psammites begins with:
There are some, king Gelon, who think that the number of the sand is infinite in multitude; and I mean by the sand not only that which exists about Syracuse and the rest of Sicily but also that which is found in every region whether inhabited or uninhabited. Again there are some who, without regarding it as infinite, yet think that no number has been named which is great enough to exceed its multitude. […] But I will try to show you by means of geometrical proofs [apodeiksion geometrikan], which you will be able to follow [hais parakoloutheseis], that, of the numbers named by me and given in the work which I sent to Zeuxippus, some exceed not only the number of the mass of sand equal in magnitude to the earth filled up in the way described, but also that of a mass equal in magnitude to the universe [tou megethos ison echontos to kosmo].190
The opening of the argument consists in pointing out a certain element of the Lebenswelt with its reference to human consciousness – but only to immediately question the given colloquial experience and move on to abstract textual notions, because from the next sentence Archimedes enters into a polemic with Aristarchus of Samos (ca. 310–230 BC) about the size of the universe and its structure. Here is a fragment of this discussion:
His hypotheses are that the fixed stars and the sun remain unmoved, that the earth revolves about the sun in the circumference of a circle [tan gan hypotitheitai peripheresthai], the sun lying in the middle of the orbit, and that the sphere of the fixed stars, situated about the same centre as the sun, is so great that the circle in which he supposes the earth to revolve bears such a proportion to the distance of the fixed stars as the centre of the sphere bears to its surface. Now it is easy to see that this is impossible [touto g’eudelon hos adynaton]; for, since the centre of the sphere has no magnitude, we cannot conceive it to bear any ratio whatever to the surface of the sphere. (ch. 1)191
In these words, Archimedes gave us information about the heliocentric system which was over fifteen hundred years earlier than the Copernican one (Aristarchus’ writings on this subject are lost), but what is more important at this point is his rapid – within a few sentences – transition from phenomenal experience (the motif of sand) to full text abstraction, which is the discussion of proportions of celestial bodies, i.e. the conceptual analysis of such relations between elements of experience which are no longer perceptible in experience. Psammites’ whole is based – after the initial signaling of the motif of sand – only on such textual abstractions. In the subsequent sentences of this text, Archimedes constructs a geometrical reasoning, the aim of which is to determine the size of the cosmos, and the assumptions are derived from observational data concerning the size of the Earth and the apparent size of the Sun in the sky, and from the geocentric model derived from the discussion with Aristarchus, in which the center of the Cosmos coincides with the center of the Earth and its boundary is the sphere of fixed stars. The scarce observational data are superimposed with a system of notions reflecting in the text large-scale spatial relations, which remain far beyond the Lebenswelt boundary given to the human mind in the sensual experience, and this system itself has the primordial textually provenance – the notion record is here a matrix of physical space and relations taking place in it, similarly to what will happen in modern scientific texts (these are, however, supported by more advanced observations).
After such preparation, Archimedes begins to match both components of its concept – tangible sand and abstract space:
Given that the diameter of the universe is less than a myriad earth diameters it is clear that the diameter of the world is less than one hundred myriad myriad stadia [myriad=10,000]. These are my hypotheses regarding sizes and distances. Here now os what I assume about the subject of sand: if one has a quantity of sand whose volume does not exceed that of a poppy-seed, the number of these grains of sand will not exceed a myriad and the diameter of the grains will not be less than a fourtieth of a finger-breadth. I make these hypotheses following these observations: poppy seeds having been placed on a polished ruler in a straight line in such a way that each touches the next, twenty five seeds occupied a space greater than one finger-breadth. I will suppose that the diameter of the grains is smaller and to be about a fourtieth of ←176 | 177→a finger-breadth for the purpose of removing any possibility of ctiticizing the proof of my proposition. (ch. 2)192
Archimedes collides the extreme points of the scale of physical quantities known to him, one of which represents the smallest elements of physical reality discernible to the human eye, while the other – a large-scale structure of the cosmos accessible (as it is today) only through theoretical tools (that is, abstract verbal or mathematical notations). Let us note, however, that the estimation of the size of poppy seeds and the number of grains of sand corresponding to one grain of poppy is at least loose and Archimedes himself admits that he selects them in such a way that they best fit his deductions. This means that the elements he draws from the realm of Lebenswelt have no phenomenal significance, they are not components of the reality he actually experiences – they are quasi-realistic components of purely textual reasoning, embedded primarily in detached concepts, and their “experimental” provenance is a rhetorical trick by which Archimedes wants to make his reasoning more accessible to a layman, like King Gelon, and to have the strongest possible effect, colliding the nullity of grains of sand and poppy seeds with the vastness of space. We can see here a cluster of proto-scientific reasoning, rhetorical and persuasive practices, and the influence of the means of communicating the state of knowledge available to Archimedes on the form of knowledge which he created.
The next part of Psammites is devoted to deriving a nomenclature of numbers, which allows Archimedes to name the number of grains of sand filling the whole universe, the size of which he calculated earlier. The largest number having its own name in ancient Greece was myriad, corresponding to ten thousand in our notation. Without breaking the rules of Greek grammar, it could be multiplied at most to the form of myriad myriads myriads (myriakis myriais myriadessin, i.e. 10,000 x 10,000 x 10,000 = trillion, 1012), and already such a multiplication was not needed by the Greeks for anything, because in their world of life there were no phenomena whose description would require numbers of this order. It should also be remembered that they did not have a digital notation and all numbers in the positional notation were marked with letters, which made arithmetic and ←177 | 178→algebra very difficult for them (this is one of the reasons why these fields of mathematics developed much less well in ancient Greece than geometry).
Archimedes was fully aware of these conditions. This can be seen in the following sentence from the third chapter of Psammites:
It so happens [symbainei de], that tradition has given to us the name of numbers up to a myriad… [ch. 3, Vardi, p. 5]
The verb “symbaino” mainly means “to happen by chance,” and using this verb to describe any phenomenon gives it a clear mark of randomness. It seems that Archimedes wanted to emphasize the contingency of arithmetic terms that he had to use. With all the more freedom, therefore, he exceeded the conditions he had found and, using the exponential method, determined the number of grains of sand filling the cosmos at 1063. He did so on the assumption that the largest number of a particular row is the smallest number of the higher row, and then iterated this procedure into successive rows of numbers. Furthermore, he stated explicitly that the whole thought experiment with sand and the universe was just an excuse for him: Numbers named in this way could certainly suffice but it is possible to go still further. [ch. 3, Vardi, p. 6]
Then he freely develops his notation system (it is a purely verbal notation) and comes to the number which in our notation is 108000000000000000000 (one with eight quintillion zeros). The intellectual self-confidence of Archimedes, as emphasized by his researchers, allows him to go beyond any, even imaginary, relationship with experience to the purest mathematical abstraction; he demonstrates the potential of a system of notation based solely on in-text principles, because the numbers that eventually occur no longer determine anything, any size that is possible in the real world, not only that which people experience sensually but also any physical world at all possible within the human mind supported by theory and writing. I mentioned before that an absolute text is not possible – but Psammites’ final conclusions are close to it, and in later periods Archimedes will be followed by mathematicians developing theories and models that do not describe any of the worlds we know even the most theoretically. However, it is not certain whether a mathematical notation can be called a “text” in the sense in which scholars of humanities use it.193←178 | 179→
Psammites’ final sentences prove that Archimedes was fully aware of his intellectual alienation, but at the same time he defended his cognitive position with a sense of irony, in words addressed to the son and successor of Hieron II, the ruler who, according to Plutarch, strongly urged him to put the results of his intellectual works into practice:
I conceive [hypolambano], King Gelon, that among men who do not have experience of mathematics, such a thing might appear incredible. On the other hand, those who know of such matters and have thought about the distances and sizes of the earth, the sun, the moon, and the universe in its entirety will accept them due to my argument, and that is why I believed that you might enjoy [ouk anarmoston] having brought it to your attention. [ch. 4, Vardi, p. 9]
Psammites is an example of a radical departure of the textualized reflection beyond the Lebenswelt thanks to textual tools that organize and expand the realm of reflection as much as possible under the culturally defined conditions of notation (lack of digits, lack of possibilities of exponential notation, grammatical syntax of the Greek language). It shows textual traces of a generalized sensual experience, independent of the current historical, social, and cultural state of affairs. But this very approach to the physical reality in the textualized quasi-experience is already the result of specific processes in communication technology that lead to the production of abstract mental entities according to the instructions of the text, which is itself a collection of abstract post-Aristotelian concepts. The figure and work of Archimedes is one of the early examples of the advanced stage of “textual thinking” in European culture, in which the price for a huge extension of the range of reality available to the reflective human mind is a deep alienation of this mind and its associated body from the Lebenswelt realm – or, from a reality experienced and relived sensually, somatically. If we recall that Xenophon’s writings were created less than one hundred and fifty years earlier, we can realize how far the Greek text practices in the ←179 | 180→Hellenistic era have evolved – and the effects of this evolution have affected European culture throughout all centuries to come.194
163 See the diagram: The Encyclopedia of Ancient Natural Scientists. The Greek tradition and its many heirs, edited by Paul T. Keyser and Georgia L. Irby-Massie, Routledge 2008, p. 939.
164 As far as the general history of Greek science is concerned, two small books by G. E. R. Lloyd remain the basic studies: Early Greek Science. Thales to Aristotle, New York 1970; Greek Science after Aristotle, New York 1973. In the field of pure factography, George Sarton’s work is still irreplaceable: Introduction to the History of Science, three volumes in five parts, Baltimore 1927–1948 (antiquity is dealt in the first volume). Examples of contemporary elaborations about Fachliteratur are given in one of the footnotes to the chapter of this book devoted to Xenophon.
165 This literature shows a lack of studies on, for example, shipping technology or those aspects of the martial arts that are directly related to field combat. While this absence is not due to the poor preservation of the texts, it may mean that those classes of practices that were most dependent on non-verbal aspects of the knowledge of action were not then textualized. The problem of functional usefulness of the practice textbooks I have already pointed out when discussing Xenophon.
166 See e.g.: The Works of Archimedes edited in modern notation with introductory chapters by Sir Thomas Little Heath, Cambridge 1897 (22010), Preface, pp. V–IX.
167 Despite erroneous estimates of all the physical quantities that Archimedes calculates in Psammites. Anyway, the mistake in these estimates is not only due to the primitive nature of the observational techniques available in his era but also to the essentially text-centered position of all reasoning, which consists mainly in manipulating the textualized elements of physical reality.
168 Perhaps mathematicians earlier than Archimedes, especially Eudoxus and Euclid, also used similar methods of transforming proto-scientific experience into text. However, only small fragments of Eudoxus’ works survived, and the works of Euclid with Elements at the forefront have, according to philological research, undergone numerous interpolations that disturb the image of their original version. Previously, when mentioning Oenopides, I had already pointed out the difficulty in understanding how the earliest Greek mathematicians formed their reasoning in text messages. As we will see, Plutarch sheds some light on this problem in an information about Archimedes included in Life of Marcellus.
169 The ancient source of this message is Vitruvius (On architecture, book IX, preface 9–12), but we do not know where he got this information from.
170 Then it should be emphasized that although the stimulus of the intellectual process is a very expressive sensual experience – immersion of one’s own body in a bathtub filled with water – this element of sensuality is immediately alienated from the world of experience and transferred to the area of mental abstraction, where it becomes the basis for reasoning, which results in the formulation of a universal physical law. A completely identical structure has many other half-mythical stories about the heuresis of scientists, the most famous of which is the anecdote about Newton’s apple. The body of the scientist in these stories is an auxiliary tool of reasoning, not a tool of existence in the Lebenswelt. Such an attitude can only emerge in a culture with a very high degree of mediating phenomenal experiences by communication media that are alienated from the realm of primary sensual experience.
171 The testimonies concerning Archimedes’ biography were collected by Johann Ludvig Heiberg in his doctoral dissertation (Quaestiones Archimedeae, Hauniae [Copenhagen] 1879, this work also contains the first modern edition of Psammites with an extremely detailed critical apparatus). Heiberg (1854–1928) was a Danish scholar who specialized in editing of Greek mathematical and technical texts, until his time virtually untouched by classical philologists (if we do not count a little bit earlier works of Hultsch and Friedlein).
172 Plutarch’s Lives with an English translation by Bernadotte Perrin in eleven volumes, vol. V, Cambridge (Massachusetts), Harvard University Press, London, William Heinemann Ltd, MCMLXI (Loeb Classical Library 87), p. 487.
173 Livy with an English translation in thirteen volumes, vol. VI, Books XXIII–XXV, translated by Frank Gardner Moore, London, William Heinemann Ltd, Cambridge (Massachusetts), Harvard University Press MCMXL (Loeb Classical Library 355), p. 461.
174 Cicero, De finibus bonorum et malorum, with an English translation by H. Rackham, London, William Heinemann, New York, The MacMillan Co. MCMXIV (Loeb Classical Library 40), p. 451.
175 Alfred N. Whitehead, An Introduction to Mathematics, Williams & Norgate, London 1911, pp. 40-41.
176 Valerius Maximus, Memorable Doings and Sayings, Volume II, Books 6–9, edited and translated by D. R. Shackleton Bailey, Harvard University Press, Cambridge (Massachusetts), London 2000 (Loeb Classical Library 493), p. 235.
177 The most famous version of these words in later epochs – “Noli tangere [or ‘turbare’] circulos meos” [Do not touch/destroy my wheels] – does not appear in any of the ancient sources.
178 Ioannis Zonarae Epitome Historiarum cum Carolii Ducangii suisque annotationibus edidit Ludovicus Dindorfius, vol. II, Lipsiae 1869 (Bibliotheca Teubneriana), pp. 264–265.
179 Plutarch’s Lives, p. 471.
180 Plutarch’s Lives, pp. 471–473.
181 Plutarch’s Lives, pp. 479–481.
182 Plutarch’s Lives, p. 481.
183 This message is interpreted by Jesper Svenbro in the book Phrasikleia. An Anthropology of Reading in Ancient Greece, Cornell Univ. Press, Ithaca 1993 [French original 1988], ch. 7: True Metempsychosis: Lycurgus, Numa and the Tattooed Corpse of Epimenides, pp. 123–144. But his approach is completely different from the one presented here.
184 There is a certain similarity to such behaviors today with people who write “urgent matters” or telephone numbers on their hands or wrists – but in this case we are only dealing with an ad hoc use of the body surface as a recording surface, not with a deeply internalized practice embedded in the mainstream of someone’s life. In the Appendix, devoted to medieval scribes, I will come back to the issue of the somatic dimension of intellectual practices related essentially to the presence of the text.
185 I use the Heiberg edition: Archimedis Opera omnia cum commentariis Eutocii. E codice Florentino recensuit, latine vertit notisque illustravit J. L. Heiberg, vols 1–3, Lipsiae in aedibus Teubneri 1880-1881. The critical apparatus both in this edition and in Quaestiones… shows no major problems with the constitution of the Psammites’ text, even in parts containing numerical notations (most of the number names are written there in words). To understand the course of Archimedes’ speeches, Ilan Vardi’s commentary, available on the Internet under the title: Archimedes, the Sand Reckoner, is helpful. The works in earlier syntheses of Greek mathematics (among them especially the works of T. L. Heath, quoted here) also retain their value.
186 A detailed description of Archimedes’ textual tradition can be found in Prolegomena to the third volume of the Heiberg edition; see also a brief account in Heath, Works of Archimedes…, Introduction, pp. xxiii–xxxviii. nineteenth-century scholars (Hultsch, Heiberg, Heath, Schiaparelli) also deliberated whether the terms “graphe, graphesthai,” which are used in reference to the oldest Greek astronomers, should be understood as “writing” (i. e. “books, works”), or as “diagrams.”
187 An additional complication in thinking about the relationship between astronomy and writing is the special type of experience specific to the observation of the sky without the use of technically advanced observational instruments – namely, an exclusively visual experience, which means that “the sky” is an extremely unobvious element of the human Lebenswelt, at the same time close and distant, visible and unattainable. This state of affairs, resulting primarily from the physical and biological circumstances that shape our bodies and minds in the physical world, has had a great influence on the cultural perception of human position in the world. See Otto Neugebauer, The Exact Sciences in Antiquity, Dover Publications 1969, as a basic study on the early stages of mathematics in connection with the observational sciences. The fact that today’s astronomers still use the division of the celestial sphere into constellations whose images were mostly created in ancient times, and most of the stars visible without the help of optical instruments still bear their ancient names, is a clear example of the sustainability of culturally conditioned conventions in science. On astronomy in connection with historical periods of culture (i.e., the so-called archaeo-stronomy), see especially the extensive synthesis: David H. Kelley, Eugene F. Milone, Exploring Ancient Skies. A Survey of Ancient and Cultural Astronomy, 2 ed., Springer 2011.
188 Ilan Vardi, p. 12 with reference to Strong’s biblical concordance.
189 My attempts to find any scientific or even popular studies of the motif of “incalculable sand” in the literary and cultural imaginary have failed. On this occasion, however, I came across scientific reports from recent years, which concerned research aimed at experimentally determining the number of grains of sand in a certain unit of volume, which should be considered an involuntary and somewhat grotesque confirmation of the permanence of human fascination with this problem.
190 The Works of Archimedes edited in modern notation with introductory chapters by T. L. Heath, Cambridge University Press 1897 (reprint 2010), p. 221.
191 The Works of Archimedes, p. 222.
192 Since the translation of Heath is largely a paraphrase in manner of modern mathematical notation, here I pass from this quote on to the literal translation of Ilan Vardi available at: https://www.lix.polytechnique.fr/Labo/Ilan.Vardi/archimedes.html [2020.05.31].
193 There are many views on the meaning or meanings of the term “text” depending on different theoretical schools. In the semiological and structural sense, the notation of a mathematical proof, in which there are no signs of natural language at all, but only symbols of mathematical notation, is a text, but it is not a text in the sense of literary theory and literary studies. In the introduction, I have explained the understanding of “text” adopted in this book.
194 Continuing this theme, one should analyze the writings of Hellenistic authors specializing in mechanics and engineering, not just in pure theory. These included, for example, the Archimedes’ contemporary, Philo of Byzantium (ca. 280–220), the author of an extensive work called Mechanike syntaxis, which describes the principles of building seaports, artillery machines, pneumatic machines, automatic machines, and siege machines. In the same period, Ctesibius was active in Alexandria. His writings have not survived, but it is known that he invented a water clock, water organ, and valve. The culmination of Hellenistic engineering are the achievements of Hero of Alexandria (ca. 10–70 AD), mentioned in all the popular references to the history of science as the inventor of the first steam machine (the so-called “Hero’s engine”), which could not find practical applications in the ancient world. His writings, like those of Philo of Byzantium, have survived, but their analysis would go beyond the framework of this book. They represent a further stage in the design of scientific and technical practices based on a theoretical text, i.e. a return from the world of text to the world of life mediated by a theoretical text image. We do not know how widely used were the technical and engineering designs contained in the writings of Philo, Ctesibius, or Hero, but it can be assumed that at this stage of the development of specialist writing, mutual alienation of the text and experience is growing. We are probably dealing here with an alienation of specialist practices, dictated by text instructions, in the current social system, well visible in the case of Hero’s engine, which for positivist and Marxist historians of science and technology was a model example of “overtaking one’s own era and social formation by a brilliant underestimated inventor.” Authors such as Philo and Hero often stress the need for accuracy and precision in the execution of textbook instructions and contrast these features with the randomness of traditional older methods. Here is an example from the Belopoeika (Building Ballistic Machines) of Philo: “I assume you know that most people find this skill [ten technen] difficult to master [dystheoreton kai atekmarton]. […] For my purposes, therefore, the statement by the sculptor Polycletus will be suitable: ‘Perfection [to eu] comes from many numbers thanks to the precision of [dia mikron].’ The same is also true of this skill, because its effects depend on many numerical ratios, where even a slight deviation leads to serious errors in execution.” (Chapter 2, Philons Belopoiika (Viertes Buch der Mechanik) griechisch und deutsch von H. Diels und E. Schramm, Berlin 1919, pp. 7–8). The statement of the great sculptor, given by Philo, seemed quite mysterious to the scholars and became the subject of many conjectures which I cannot discuss here. In the following sentences, Philo speaks about the “ancient” people [archaious] whose designs worked only by chance, and they could not explain why that ←180 | 181→is and why the others did nott work as well. Here, Philo clearly contrasts the “tacit knowledge” that comes from the non-verbal transmission of practical experience and, as such, is – as in Aristotle’s Metaphysics – elusive and unworthy of attention, and precise knowledge based on the principles contained in the textbook, which is his own work filled with very detailed technical instructions for the design and construction of ballistic machines of greatest effectiveness. It is worth noting the disregard shown by Philo for the old traditional methods, which according to him can only be effective by chance. We see the same attitude in modern scientists when confronted with, for instance, “folk medicine.”←181 | 182→