1: Introduction
At the outset of his Annals , which was his last work, published around AD 118, Tacitus states that he wrote sine ira et studio (‘without anger or zeal’), that is, in an objective and dispassionate frame of mind devoted to an uninflected portrayal of historical truth. The announcement is part of his self-fashioning as a muckraker above partisan emotions who chronicles the sad story of early imperial Rome: the decline and fall of the Julio-Claudian dynasty (AD 14–68) in the Annals and the civil war chaos of the year of the four emperors (AD 69) followed by the rise and fall of the Flavian dynasty (AD 69–96) in the (earlier) Histories . But his narrative is far from a blow-by-blow account of Roman imperial history, and Tacitus is an author as committed as they come – a literary artist of unsparing originality who fashions his absorbing subject matter into a dark, defiant, and deadpan sensationalist vision of ‘a world in pieces’, which he articulates, indeed enacts, in his idiosyncratic Latinity. 1 To read this Latin and to come to terms with its author is not easy: ‘No one else ever wrote Latin like Tacitus, who deserves his reputation as the most difficult of Latin authors.’ 2
This introduction is designed to help you get some purchase on Tacitus and his texts. 3 We will begin with some basic facts, not least to establish Tacitus as a successful ‘careerist’ within the political system of the principate who rose to the top of imperial government and stayed there even through upheavals at the centre of power and dynastic changes (1). A few comments on the configuration of power in imperial Rome follow, with a focus on how emperors stabilized and sustained their rule (2). In our survey of Tacitus’ oeuvre , brief remarks on his so-called opera minora (his ‘smaller’ – a better label would be ‘early’ – works) precede more extensive consideration of his two great works of historiography: the Histories and, in particular, the Annals . Here issues of genre – of the interrelation of content and form – will be to the fore (3). We then look at some of the more distinctive features of Tacitus’ prose style, with the aim of illustrating how he deploys language as an instrument of thought (4). The final two sections are dedicated to the two principal figures of the set text: the emperor Nero (and his propensity for murder and spectacle) (5); and the senator Thrasea Paetus, who belonged to the so-called ‘Stoic opposition’ (6). None of the sections offers anything close to an exhaustive discussion of the respective topic: all we can hope to provide are some pointers on how to think with (and against) Tacitus and the material you will encounter in the set text.
2.1 Tacitus: life and career
Cornelius Tacitus was born in the early years of Nero’s reign c . AD 56/58, most likely in Narbonese or Cisalpine Gaul (modern southern France or northwestern Italy). He died around AD 118/120. 4 His father is generally assumed to have been the Roman knight whom the Elder Pliny (AD 23 – 79) identifies in his Natural History (7.76) as ‘the procurator of Belgica and the two Germanies.’ We do not know for sure that Tacitus’ first name ( praenomen ) was Publius, though some scholars consider it to be ‘practically certain.’ 5 His nomen gentile Cornelius may derive from the fact that his non-Roman paternal ancestors received citizenship in late-republican times ‘through the sponsorship of a Roman office-holder called Cornelius.’ 6 Our knowledge of his life and public career is also rather sketchy, but detailed enough for a basic outline. If we place the information we have or can surmise from his works on an imperial timeline, the following picture emerges:
|
Dates |
Reigning Emperor |
Tacitus |
|---|---|---|
|
54 – 68 |
Nero |
Born c . 56 |
|
68 – 69 (January) |
Galba |
|
|
69 (January – April) |
Otho |
|
|
69 (April – 22 December) |
Vitellius |
|
|
69 – 79 |
Vespasian |
In Rome from 75 onwards (if not earlier) 77/78: marriage to Julia Agricola, daughter of Gnaeus Julius Agricola (dates: 40–93; governor of Britain 77–85) |
|
79 – 81 |
Titus |
80s (or even earlier): Membership in the priestly college of the Quindecimviri sacris faciundis c . 81: Quaestor Augusti (or Caesaris )? |
|
81 – 96 |
Domitian |
88: Praetor 89–93: Absence from Rome, perhaps on official appointments |
|
96 – 98 |
Nerva |
97: Suffect consul (after the death of Verginius Rufus) 98: Publication of the Agricola and the Germania |
|
98 – 117 |
Trajan |
c . 101/2: Publication of the Dialogus ? c . 109–10: Publication of the Histories 112–13: Proconsulship of Asia |
|
117 – 138 |
Hadrian |
Died not before 118, c . 120? ? Shortly before: Publication of the Annals |
Overall, we are looking at an impressive career both in Rome and in provincial government, which he entered at an early age and sustained throughout his life. As Birley notes with respect to one of his earliest appointments: ‘His membership of the XVviri , prestigious enough at any stage in a man’s career, had come early. Often senators did not get into this élite priestly college or one of the other three of equal status until after being consul. Further, in 88 the XVviri had a particularly important role: supervising the Secular Games.’ 7 Tacitus managed to remain active in public life through several regime changes: he seems to have done equally well under emperors he excoriates in his writings (in particular Domitian) and under emperors he deems worthy of praise (Nerva, Trajan). This raises an interesting, and potentially awkward, question, well articulated by A. J. Woodman: ‘Tacitus’ smooth progression from office to office – and in particular his relatively early acquisition of a major priesthood and his culminating proconsulship of Asia – bespeak of someone who was more than happy to take advantage of the political opportunities which the system had to offer and whose debt to the emperors listed in the preface to the Histories [on which see below] was not inconsiderable. It is thus all the more curious that, as usually interpreted, his treatment of the early empire in the Annals represents a general indictment of the system from which he had derived such personal benefit.’ 8 Curious indeed. Does Tacitus just indict specific emperors? Or certain dynasties? Or the entire system of the principate? Or only variants thereof? And why? The scholarly verdict is divided…
2.2 Tacitus’ times: the political system of the principate
It is easy to think of Roman emperors as omnipotent rulers who could do (and did) whatever struck their fancy. The truth is more complex – and arguably more interesting (if less sensational). The duration and success of an emperor’s reign depended not least on the way he interacted with a range of individuals and groups, which needed ‘to accept’ him: 9
It would be misleading… to conceptualize the emperor as an omnipotent monarch capable of dominating his far-flung empire. The structural limitations to the practical power of Roman emperors were simply too great. Aristocratic competitors could be very dangerous, especially those in command of legions stationed in the periphery. From such potential pretenders to the throne the threat of usurpation could never be extinguished entirely. Less acute but more constant pressure came from those groups within Roman imperial society that were capable of meaningful collective action in the public sphere. Especially significant were the senate, the plebs urbana of Rome, and the legionary armies. With these influential collectivities the emperor was in constant dialogue, both real and symbolic, interacting with each in a highly prescribed manner calculated to elicit the public displays of consensus, or ‘acceptance’, upon which imperial legitimacy ultimately rested. 10
In addition to the social groups identified by Noreña, we should recognize the imperial family and the court, its personnel, and its social dynamics as major factors in how power worked during the principate. Relatives with ‘dynastic’ credentials joined ambitious aristocrats as potential pretenders to the throne. 11 (Nero kills off in cold blood one such, Junius Torquatus Silanus, in our set text: see Annals 15.35 and Section 5 below.) The daily proximity to the emperor turned female figures of the court (mothers, wives, mistresses) into potential power brokers but also potential victims of imperial whim: Agrippina and Poppaea are prime examples of both in Tacitus’ Nero-narrative. The same is true of the emperor’s closest advisors and high-ranking members of his staff, frequently highly skilled (and highly loyal) freedmen. Senatorial sources tend to look askance at such – from a republican point of view – ‘interlopers’ in the Roman field of power. Neither women nor freedmen shared in political decision-making in republican times, but now could wield greater influence than many a distinguished senator, simply because they had easy access to, and the ear of, the emperor. The same goes for the prefect of the Praetorian Guard, the bodyguard of the emperor and the most significant military presence in the city of Rome.
What made being a Roman emperor so difficult was the fact that each constituency brought a different set of expectations to bear on their princeps : 12 the ideal emperor of the army was never going to be the ideal emperor of the senate was never going to be the ideal emperor of the people. Moreover, the groups were in latent rivalry with one another for access to the emperor and for his attention, which caused potential problems in those settings – such as public games – when he interacted with several simultaneously: gestures of special proximity or favour towards the plebs, for instance, might miff the ruling élite (and vice versa). Finally, the groupings themselves were not necessarily homogeneous. At the opening of Annals 16, for instance, Tacitus reports in disgust that the urban plebs reacted to Nero’s public performance as cithara player with enthusiasm and delight, yet goes on to note with grim satisfaction that this (from his point of view) shameful disgrace of imperial dignity scandalized and saddened those common people who had travelled to the city from remote places in the countryside where the values of old Italy were still alive. 13
The relation between the emperor and the senatorial ordo , i.e. the politically active members of the élite, was especially fraught, and for various reasons. In comparison with republican times, the aristocracy was particularly affected by the ‘massive and unprecedented relocation of power and authority in the Roman world’ brought about by ‘the advent… of the imperial regime we call the principate.’ 14 Élite Romans experienced – and had to cope with and negotiate – ‘concrete social and cultural dislocations … in the face of the emperor’s power – for example, a reduction of the opportunities and rewards for displaying military prowess, and a perceived aggravation of certain problems associated with flattery.’ 15 They now occupied a paradoxical position in the field of power. On the one hand, they remained rulers of the world: emperor and senators governed the empire together (with the emperor having exclusive control over the army), in close interaction with local élites. (The interaction of centre and periphery is one of the main topics of the first few chapters of the set text.) On the other hand, they were subordinate to the princeps and had to accommodate his existence – not least because the emperor put a cap on senatorial rivalry, preventing the senate from dissolving into suicidal infighting and kicking off civil war. For the Roman aristocracy remained a highly competitive body: senators who pursued a public career vied for prestigious appointments, acted as patrons for others with like ambitions, and desired glory. In contrast to republican times, however, success and effectivness in these roles and undertakings depended in large part on being in favour (or at least not on bad terms) with the emperor – though, as we shall see in Section 6, defying the emperor could also yield a type of fame.
The mutual reliance of princeps and ruling élite in governing the empire and the fact that inner-aristocratic competition over posts and honors now inevitably revolved around the figure of the princeps promoted novel forms of behaviour among the senators. Rituals of consensus, in which senators demonstrated their proximity and loyalty to the princeps , became important; senators vied with each other for recognition by the emperor; some tried to get ahead by charging others with disloyalty: the figure of the informer ( delator ) who broke with group-solidarity and tried to get others charged with treason ( maiestas ) – an extreme form of aristocratic rivalry to acquire a position of influence close to the princeps – populates Tacitus’ historical narratives; 16 others endeavoured to make a name for themselves by pursuing a collision course with the emperor – often much to the chagrin of their senatorial peers (see Section 6 below on Thrasea Paetus). Observers with a literary bent (such as Tacitus or Pliny) are often as scathing about their fellow-senators as they are about the behaviour of specific emperors, evaluating senatorial conduct on a moralizing scale that ranges from servility on the one hand to a defiant embrace of republican libertas on the other: ‘The instances of servile behaviour that Tacitus chronicles are legion, and all readers will have their favourites; any selection that is not copious is false to the tone of his writing.’ 17 This is for sure an accurate description of what Tacitus does in his narrative, but we shouldn’t assume that his categorical grid of servitus vs. libertas yields an accurate interpretation of senatorial conduct in imperial Rome – however tempting this may be. As Egon Flaig asks, (as he means it) rhetorically: ‘Were the 600 highest ranking persons of an enormous empire of 60–80 million inhabitants really slaves at heart?’ 18
For members of the senatorial aristocracy, the emperor would ideally conform to the image of the civilis princeps – a ruler in other words who aligned his forms of interaction with the senate according to proto-republican norms and values: freedom of speech; strict limits to adulatio ; recognition of the value of republican office which emperor and other aristocrats could hold or aspire to, especially the consulship; investment in a private status – as if an ordinary citizen – in dress and appearance. From an emperor’s point of view, balancing ritual elevation with ritual humility – to be part of the society, not above society – was entirely functional: ‘An emperor whom ritual and ceremonial raised above the level of human society, whose power was represented symbolically as deriving from “outside”, from the gods, owed nothing to the internal structure of the society he ruled. To act, by contrast, as a member of that society, as the peer of its most elevated members, was (symbolically) to associate autocratic power with the social structure. Civility both reinforced the social hierarchy by demonstrating imperial respect for it, and strengthened the autocracy by linking it with the social structure.’ 19 Not all emperors felt necessarily obliged to try to confirm to this image (their reigns often came to an abrupt end…); and as we shall see in Section 5 below, different emperors had different notions of what ‘civility’ consisted in.
Consideration of the underlying ‘structure’ of the imperial system also helps to put our sources into perspective – enabling us to read them as highly rhetorical and personally and politically committed views on, rather than entirely accurate representations of, historical realities. Just taking our imperial sources at face value results in the kind of history one gets in the (highly engrossing and actively emetic) BBC-series Horrible Histories , where the ‘Rotten Romans’ feature prominently – and Nero gets the final riff in the ‘Roman Emperor’s Song – Who’s Bad?’, topping the pops against classic competition: the apparently certifiable sociopaths Caligula (emperor 37–41), Elagabalus (218–222), and Commodus (180–192). 20 But the composition of literature by members of the ruling élite was never a neutral activity; rather, it was itself implicated in the imperial configuration of power, in the jostling for position, in exercises of self-promotion: Pliny, Tacitus, and Suetonius wrote (mainly) for fellow aristocrats about a shared world dominated by the emperor – and used their works to define their own status, position, and prestige within it.
Rhetorical myth-making is rampant in Roman historical writing. Most notoriously, our sources show an avowed interest in portraying emperors who for one reason or other fell out of favour as mentally deranged. In many a text, early imperial Rome comes across as a society ruled over by lunatics besotted with power and keen to act on every depraved instinct. Tacitus contributed his share to our image of Roman emperors as evil freaks. Over the last few decades, however, scholarship has increasingly started to question this picture, arguing that your favourite salacious anecdote about imperial Rome (such as Caligula appointing his horse to the consulship) may just be too good to be true – and is in fact a distorting rumour put into circulation posthumously by individuals and groups much invested in blackening the reputation of the deceased emperor. 21 Could it be that our sources are so hostile to certain emperors not because they were deranged – but that they look deranged because our sources are so hostile?
This possibility may come as a let-down. But it shouldn’t: critical debunking of historiographical myth-making is in itself an exciting exercise that opens insights into a foreign culture. Fascination shifts from history to the ‘making’ of history, from the allure of alleged facts to the power of historical fabrications. The question as to why these sensationalizing stories have emerged and been able to colonize our imagination so effectively is arguably just as interesting as trying to put an emperor on the psychiatric couch on the basis of insufficient and distorted evidence. What went down in imperial Rome was not just the power of the sword but the power of the word, especially when it came to shaping (or disfiguring) posthumous reputations.
2.3 Tacitus’ oeuvre: opera minora and maiora
From the very beginning of Roman historiography in the late third century BC political achievement and authoritative prose about historical events or figures had gone hand-in-hand. The composition of historical narratives in a range of genres was very much the domain of senators. As Ronald Syme puts it: 22
In the beginning, history was written by senators (first a Fabius, and Cato was the first to use the Latin language); it remained for a long time the monopoly of the governing order; and it kept the firm imprint of its origins ever after. The senator came to his task in mature years, with a proper knowledge of men and government, a sharp and merciless insight. Taking up the pen, he fought again the old battles of Forum and Curia. Exacerbated by failure or not mollified by worldly success, he asserted a personal claim to glory and survival; and, if he wrote in retirement from affairs, it was not always with tranquillity of mind.
It is thus telling that Tacitus’ literary career begins in earnest only after he had reached the pinnacle of public life: the Agricola or De vita et moribus Iulii Agricolae appeared in the year after he held the consulship (AD 98). His literary debut also coincided with a major upheaval at the centre of power. AD 96 saw the end of the Flavian dynasty through the assassination of Domitian and the crowning of Nerva as emperor at the age of 65, after years of loyal service under Nero and the Flavians. Pressure from the Praetorian Guard and the army more generally soon compelled Nerva to adopt Trajan as his eventual successor, and Tacitus’ first literary activities fall within this period of transition and change, which he himself marks out as a watershed in politics and culture. In fact, he explicitly links the demise of Domitian (and his oppressive regime) to the renaissance of creative efforts in the literary sphere. 23 His writings in and of themselves thus advertise the current system of government as a good one (or at least an improvement over what had come before) and signal Tacitus’ (new) political allegiances. (Much of the bad press that has come down to us on the last Flavian comes from writers in the reign of Trajan – Pliny, Tacitus, Suetonius, above all – keen to paint the past in black and the present in white, thereby promoting both the reigning emperors and themselves.)
The Agricola is difficult to classify in generic terms. Prima facie , it is a ‘biography’ of his father-in-law Gnaeus Julius Agricola; but it also sports striking affinities with various forms of historiographical writing, not least the works of Sallust (the last ‘republican’ historiographer) or, in its year-by-year account of Agricola’s governorship of Britain, annalistic history. It also includes a brief ethnographic excursion on the British (10–12). But arguably the most striking features are the three chapters of prologue (1–3) and epilogue (44–46) that Tacitus devotes almost exclusively to an attack on the principate of Domitian, which had just come to a violent end. 24 The historical material, the overall outlook, and the timing of the publication all reek of a republican ethos.
Tacitus’ next work builds on the ethnographic pilot paragraphs in the Agricola . His Germania or De origine et situ Germanorum is an ethnographic treatise on the German tribes, which he uses as a mirror to reflect on contemporary Rome. 25 Soon thereafter Tacitus published the so-called Dialogus ( Dialogus de oratoribus ), in which he employed yet another genre (the dialogue) to explore whether or not the quality of public oratory had deteriorated under the principate – a traditional preoccupation going back to Cicero who already diagnosed the rise of autocracy as fatal for high-quality speech in the civic domain owing to a disappearance of freedom of expression. These three works are often labelled Tacitus’ opera minora , his ‘minor works.’ They are all ‘historical’ in one way or another and thus set the stage for the two major pieces of historiography: the Histories and the Annals .
The Histories
The opening paragraph of the Histories contains the most detailed self-positioning of Tacitus as a writer of history and is worth a detailed look. Already the opening sentence – Initium mihi operis Servius Galba iterum Titus Vinius consules erunt : ‘I begin my work with the second consulship of Servius Galba, when Titus Vinius was his colleague’ – is jaw-dropping. What makes it so, is not so much what’s in it but what isn’t. At the beginning of AD 69, when Tacitus begins his Histories , Galba was not just consul for the second time – he was also emperor! As Nero’s successor he had already been in power since 6 June 68. Tacitus, however, blithely glosses over this not entirely insignificant fact, preferring instead to give a historiographical shout-out to Galba in his role as ‘republican’ high magistrate. This programmatic keynote sets the tone for the rest of the work – and the remainder of the opening paragraph ( Histories 1.1): 26
nam post conditam urbem octingentos et viginti prioris aevi annos multi auctores rettulerunt, dum res populi Romani memorabantur pari eloquentia ac libertate: postquam bellatum apud Actium atque omnem potentiam ad unum conferri pacis interfuit, magna illa ingenia cessere; simul veritas pluribus modis infracta, primum inscitia rei publicae ut alienae, mox libidine adsentandi aut rursus odio adversus dominantis: ita neutris cura posteritatis inter infensos vel obnoxios. sed ambitionem scriptoris facile averseris, obtrectatio et livor pronis auribus accipiuntur; quippe adulationi foedum crimen servitutis, malignitati falsa species libertatis inest. mihi Galba Otho Vitellius nec beneficio nec iniuria cogniti. dignitatem nostram a Vespasiano inchoatam, a Tito auctam, a Domitiano longius provectam non abnuerim: sed incorruptam fidem professis neque amore quisquam et sine odio dicendus est. quod si vita suppeditet, principatum divi Nervae et imperium Traiani, uberiorem securioremque materiam, senectuti seposui, rara temporum felicitate ubi sentire quae velis et quae sentias dicere licet.
[Many historians have treated of the earlier period of eight hundred and twenty years from the founding of Rome, and while dealing with the Republic they have written with equal eloquence and freedom. But after the battle of Actium, when the interests of peace required that all power should be concentrated in the hands of one man, writers of like ability disappeared; and at the same time historical truth was impaired in many ways: first, because men were ignorant of politics as being not any concern of theirs; later, because of their passionate desire to flatter; or again, because of their hatred of their masters. So between the hostility of the one class and the servility of the other, posterity was disregarded. But while men quickly turn from a historian who curries favour, they listen with ready ears to calumny and spite; for flattery is subject to the shameful charge of servility, but malignity makes a false show of independence. In my own case I had no acquaintance with Galba, Otho, or Vitellius, through either kindness or injury at their hands. I cannot deny that my political career owed its beginning to Vespasian; that Titus advanced it; and that Domitian carried it further; but those who profess inviolable fidelity to truth must write of no man with affection or with hatred. Yet if my life were to last, I have reserved for my old age the history of the deified Nerva’s reign and of Trajan’s rule, a richer and less perilous subject, because of the rare good fortune of an age in which we may feel what we wish and may say what we feel.]
Tacitus here takes us on a flash journey through Roman history, from the foundations of Rome way back when down to his own times, with Actium and Augustus, AD 69 (the year of the four emperors), and the Flavian dynasty as major pit stops. Onto this chronological skeleton, Tacitus hangs systematic comments on the (changing) political regimes, which he matches to the (changing) outlook of Latin historiography. His basic thesis of an inextricable link between the political environment and the quality of writing it sponsors raises some awkward questions about his own literary efforts. Tacitus confronts this challenge head-on by scripting a mini-autobiography into his opening salvo that outlines his political career and his approach to historical writing. If we extrapolate the information Tacitus has packed into his opening paragraph and present it in the form of a table we get the following:
* Unlike the opening of the Annals (for which see below), Tacitus here glosses over the fact that initially Rome was ruled by kings, in the process playing down the traditional assumption that primeval monarchy was simply ‘natural’.
In his history of Rome and Roman historiography, Tacitus posits two key watersheds: 31 BC and AD 96. This generates a tripartite scheme. In republican times, the political set-up produced and enabled outstanding authors. By contrast, the period from Actium until the death of Domitian, dominated as it was by the Julio-Claudian and Flavian dynasties, was not conducive to literary talents: contemporary accounts are marred by various flaws to do with the wider political milieu. With the rise to power of a new type of princeps committed to republican norms in the wake of Domitian, could historiography, too, regain its former heights and produce an account of the previous epoch that avoids the inevitable deficiencies of contemporary voices? Without being too explicit about it, Tacitus seems to be answering this question in the affirmative: only now, under Trajan, so he seems to be saying, has the time come for writing the history of the earlier emperors, thereby advertising the job he is minded to take on himself.
Tacitus approaches his task in inverse chronological order: in the Histories , he revisits the year of the four emperors and the rise and fall of the Flavian dynasty (AD 69–96); in the subsequent Annals , he covers the period from the death of the first to the death of the last of the Julio-Claudian emperors, that is, Augustus to Nero.
The Annals
As in the Histories , Tacitus uses the opening sentence of the Annals for a grand sweep through Roman history from the very beginning down to imperial times ( Annals 1.1):
Urbem Romam a principio reges habuere; libertatem et consulatum L. Brutus instituit. dictaturae ad tempus sumebantur; neque decemviralis potestas ultra biennium, neque tribunorum militum consulare ius diu valuit. non Cinnae, non Sullae longa dominatio; et Pompei Crassique potentia cito in Caesarem, Lepidi atque Antonii arma in Augustum cessere, qui cuncta discordiis civilibus fessa nomine principis sub imperium accepit. sed veteris populi Romani prospera vel adversa claris scriptoribus memorata sunt; temporibusque Augusti dicendis non defuere decora ingenia, donec gliscente adulatione deterrerentur. Tiberii Gaique et Claudii ac Neronis res florentibus ipsis ob metum falsae, postquam occiderant, recentibus odiis compositae sunt. inde consilium mihi pauca de Augusto et extrema tradere, mox Tiberii principatum et cetera, sine ira et studio, quorum causas procul habeo.
[Rome at the outset was a city state under the government of kings: liberty and the consulate were institutions of Lucius Brutus. Dictatorships were always a temporary expedient: the decemviral office was dead within two years, nor was the consular authority of the military tribunes long-lived. Neither Cinna nor Sulla created a lasting despotism: Pompey and Crassus quickly forfeited their power to Caesar, and Lepidus and Antony their swords to Augustus, who, under the title ‘princeps’, gathered beneath his empire a world outworn by civil conflicts. But, while the glories and disasters of the old Roman commonwealth have been chronicled by famous writers, and intellects of distinction were not lacking to tell the tale of the Augustan age, until the rising tide of sycophancy deterred them, the histories of Tiberius and Caligula, of Claudius and Nero, were falsified through cowardice while they flourished, and composed, when they fell, under the influence of still rankling hatreds. Hence my design, to treat a small part (the concluding one) of Augustus’ reign, then the principate of Tiberius and its sequel, without anger and without partiality, from the motives of which I stand sufficiently removed.]
And, as in the Histories , he stakes a claim to superiority over previous accounts: his history of the Julio-Claudian dynasty, written in retrospect, surpasses earlier, contemporary sources in veracity by virtue of his dispassionate handling of the subject matter. In the one manuscript that preserved the opening books of the Annals the text is presented under the title Ab excessu divi Augusti . Our conventional label Annals has therefore ‘no ancient authority’, but it is nevertheless ‘a happy choice in that it reminds the reader that Tacitus, most original of Roman historians, wrote within the traditional framework of year-by-year narrative’ (more annal ysis on this to come in a moment). 27 In fact, at one point Tacitus himself refers to ‘the Annals ’ as ‘his annals’ ( Annals 4.32.1): 28
Pleraque eorum quae rettuli quaeque referam parva forsitan et levia memoratu videri non nescius sum: sed nemo annalis nostros cum scriptura eorum contenderit qui veteres populi Romani res composuere.
[I am not unaware that very many of the events I have reported, and shall report, may perhaps seem little things, trifles too slight for record; but no parallel can be drawn between these annals of mine and the work of the men who composed the affairs of the Roman people of old.]
What are annals? This type of historiography, which originated in the second centry BC, gets its name from its policy of year-by-year recording ( annus = year). 29 Notable features include dating of the years with reference to the two high magistrates who entered into office at the beginning of the year (‘when x and y were consuls…’ is the most conspicuous annalistic tag) and attention to signs of interaction between the res publica and the supernatural sphere (such as prodigies). As such, the genre came with certain formal expectations and under the principate carried a potentially built-in political ideology: it was a distinctively republican mode of writing.
Tacitus felt by no means bound to a strictly chronological presentation of his material. There is evidence that he even re-ordered material across year-boundaries – in violation of his own principle suum quaeque in annum referre (4.71: ‘to record each event in its year of occurrence’). And within the year, he operates freely to generate special effects, not least through the striking juxtaposition of distinctive narrative blocks. The set text offers a superb example: Nero’s decision not to proceed with his plan to visit the East and in particular Egypt (15.36) segues seamlessly into an orgy that turns Rome into Egyptian Alexandria (15.37), which is followed abruptly by the Great Fire of Rome (15.38) as if moral chaos entails physical destruction. 30 The sequence owes itself to Tacitus’ selection and arrangement of the material, and the order in which he narrates these events hints at – even if it does not expressly articulate – an interpretation of Nero’s world and the historical forces at work therein.
Yet, however much he was free-lancing generically, his commitment to annalistic history remains fundamental to the politics of his prose – and literary originality. 31 One could argue that Tacitus generated a new generic hybrid – ‘imperial annals’ – insofar as he superimposed an annalistic structure on imperial history, thereby integrating a republican way of ordering time with another ordering principle, the reigns of individual emperors. 32 To write imperial history in annalistic form was a choice that ensured a paradoxical tension in the very make-up of his text. Or, in the words of John Henderson: 33
The annalistic form of ‘our Annals ’ (4.32) binds the work to the politics of the res publica , consular figureheads leading a yearly change of the guard to link human with solar time. Annals are the voice of the tribune, the censor, the consul, of that Rome, they can speak no other language. It was not possible to write Annals before (in the myth of respublica libera ) Brutus expelled the Tarquins. … What Tacitus documents under the flag of dispassion (so: laments, protests, contemns?) is collapsed into the reigns of emperors, as Livian history of Rome Ab urbe condita is ousted by Tacitean history of the Caesars’ re-foundation Ab excessu divi Augusti .
Only parts of the Annals , which, on the most plausible reconstruction, originally added up to 18 Books, have survived. Here is what we have (and what we haven’t):
|
Book |
Years Covered |
Emperor(s) |
|---|---|---|
|
1 |
14 – 15 |
Augustus, Tiberius |
|
2 |
16 – 19 |
Tiberius |
|
3 |
20 – 22 |
Tiberius |
|
4 |
23 – 28 |
Tiberius |
|
5 |
29 |
Tiberius |
|
6 |
31 – 37 |
Tiberius |
|
[ Lost: 7 – 10 |
37 – 47 |
Caligula, early years of Claudius ] |
|
11 |
47 – 48 (first part) |
Claudius |
|
12 |
48 (rest) – 54 (first part) |
Claudius; book ends with Nero’s ascent to the throne |
|
13 |
54 (rest) – 58 |
Nero |
|
14 |
59 – 62 (first part) |
Nero |
|
15 |
62 (rest) – 65 (first part) |
Nero |
|
16 (breaks off in ch. 35 with the death of Thrasea Paetus) |
65 (rest) – 66 (first part) |
Nero |
|
[Lost ? 17 – 18 |
? 66 (rest) – 68 (till the death of Nero) ? |
Nero ] |
One conspicuous aspect of the Annals that the table illustrates nicely is a change in policy after the Tiberius-narrative in how Tacitus distributed his material across books. Throughout his account of Tiberius’ reign, a new book coincides with a new year and hence new consuls – in traditionally annalistic fashion. In the Claudius- and Nero-narratives, Tacitus abandons this practice. As a result the beginnings and ends of books – always marked moments – foreground imperial themes. Consider:
End of Book 11 : execution of Claudius’ wife Messalina
Beginning of Book 12 : choice of Agrippina (Nero’s mother) as new wife
End of Book 12 : death of Claudius and Nero’s ascent to the throne
Beginning of Book 13 : murder of Junius Silanus
End of Book 13 : the death – and revival (!) – of the arbor ruminalis , the tree that 830 years ago gave shadow to Romulus and Remus when they were babies 34
Beginning of Book 14 : Annalistic opening (‘under the consulship of Gaius Vipstanus and C. Fonteius’, i.e. AD 59), followed by the failed and successful murder of Agrippina 35
End of Book 14 : Exile and murder of Nero’s first wife Octavia; preview of the conspiracy of Piso
Beginning of Book 15 : War in the East
End of Book 15 : Honours for Nero in the wake of the conspiracy of Piso
Beginning of Book 16 : the ‘treasure of Dido’ (a hare-brained idea to solve a financial crisis)
2.4 Tacitus’ style (as an instrument of thought) 36
Tacitus is one of the great prose stylists to write in Latin. Indeed, to be able to read him in the original is held by some to be in itself sufficient justification ‘to believe that learning Latin is worthwhile.’ 37 But readers of Tacitus weaned on Ciceronian Latin are in for a disquieting experience. While it is important to bear in mind F. R. D. Goodyear’s point that Tacitean style is protean (both across his oeuvre and within a single work) and his writings constitute an ‘endless experiment with his medium, the discontent with and reshaping of what had been achieved before, the obsessive restlessness of a stylist never satisfied that he had reached perfection’, it is nevertheless possible to identify some pervasive features that are also amply on display in the set text. 38
(a) Where Cicero aims for fullness of expression ( copia verborum ), the name of Tacitus’ game is brevity ( brevitas ), not least in how he deploys ellipsis and asyndeton. As Ronald Syme puts it, ‘The omission of words and connectives goes to ruthless extremes for the sake of speed, concentration, and antithesis; and stages in a sequence of thought or action are suppressed, baffling translation (but not hard to understand).’ 39
(b) Whereas Cicero’s diction tends to be conservative, Tacitus delights in the unusual lexical choice. 40
(c) Cicero takes pride in balance and symmetry; Tacitus goes for disjunctive varietas . His ‘studied avoidance of syntactical balance and the pursuit of asymmetry’ is in evidence throughout the set text and noted in the commentary. 41
(d) One particular Tacitean technique of throwing syntactical symmetry off-balance is to unsettle ‘the relationship and respective weight of main clauses and subordinate clauses.’ 42 As Ronald Martin put it: ‘[Tacitus] makes use, far more than any other Latin writer, of sentences in which the main clause is completed early and the centre of gravity is displaced to appended, syntactically subordinate, elements.’ 43 The first sentence of the set text (15.20.1) is an excellent case in point.
(e) More generally, Cicero and Tacitus differ in their deployment of irony – which advances to something of a master-trope in Tacitus. O’Gorman defines irony as ‘a mode of speaking which establishes an unquantifiable distinction between a statement and “its” meaning’ and adds an important clarification: ‘A crude definition of an ironic statement would define the meaning as opposite to what is said, but it is better to conceive of the meaning of an ironic statement as different from what is said, not exclusively or even necessarily its opposite.’ 44 She aptly calls on Cicero, who equates irony with dissimulation ( de Oratore / On the Ideal Orator 2.269): 45
Urbana etiam dissimulatio est, cum alia dicuntur ac sentias, non illo genere, de quo ante dixi, cum contraria dicas, ut Lamiae Crassus, sed cum toto genere orationis severe ludas, cum aliter sentias ac loquare.
Irony, that is, saying something different from what you think, is also elegant and witty. I don’t mean the kind I mentioned earlier, saying the exact opposite (as Crassus did to Lamia), but being mock-serious in your whole manner of speaking, while thinking something different from what you are saying.
As O’Gorman puts it: ‘Irony depends upon the divergence in sense between utterance ( quae dicuntur ) and the unsaid ( quae sentias ). But the nature of the unsaid is indeterminable; all we know about it is that it is aliud – other than what is uttered.’ 46 In the case of irony in Cicero’s orations, however, it is often rather obvious what Cicero thinks, even if it is not what he says: an orator, after all, relies on his eloquence to produce tangible results (a verdict of innocence or guilt, a decision on a matter of policy) and therefore must communicate what he means. Also, for an ironic utterance to be witty, both meanings, the stated and the implied, must resonate simultaneously. In contrast, Tacitus’ use of irony is more opaque. And indeed he often leaves it unstated of what precisely he means – even if we realize that authoritative irony is in play: in his works, irony is not a local phenomenon, applied for special effect – it is an ubiquitous feature of his narrative and authorial voice, the counterpart to his claim to be in ruthless pursuit of the truth. In Cicero, irony is an occasional figure of speech; in Tacitus, it is a pervasive mode of critique.
This leads to a more general consideration: as with his resourceful manipulation of genre, style in Tacitus is a formal instrument of thought – an essential aspect of how he defines his authorial voice. His style ought to be embraced as a means and a medium of political commentary. 47 It enacts his interpretation of history: it is as dark, difficult, and fractured as the world in pieces he sets out to describe. If the empire struck, Tacitus strikes back – often with a dark sense of humour, manifesting itself in ‘arch wit, appalled satire, sleazy innuendo, surreal coincidence …’ 48
In part, Tacitus thereby addresses the problem of authenticity. How do you develop an authentic voice on subject matter suffused with fraud and deceit? How do you avoid your own authorial project, your own rhetoric becoming subsumed by the imperial vices you set out to chronicle and expose? One way is to deploy irony to shift and hide. As a result, coming up with the definitive interpretation of Tacitus is a bit like trying to find a stable position in quicksand. Or, as Henderson puts it, ‘he’ll never be caught with his rhetorical trousers down, his work is ironized beyond anything so crude. Instead, his text writes in “anti-language”, held always just beyond reach of secure reading, recuperative comprehension, not a “story” but a deadly serious challenge to think out, re-think and be out-thought by “the consular historian”.’ 49
2.5 Tacitus’ Nero-narrative: Rocky-Horror-Picture Show and Broadway on the Tiber
Tacitus’ portrayal of Nero is in some respects more restrained than those of other contemporary sources. Examples from the set text include his selective Taci-turn-ity in reporting Nero’s alleged sex crimes and his judiciously aporetic stance on whether the emperor was responsible for setting Rome afire. But his Nero, too, is a murderous pervert with disgusting inclinations (such as a penchant for Greek culture…) and a prolific contributor to imperial Grand Guignol (as the French call theatre that specializes in naturalistic horror shows) – to begin with, unwittingly so. Here is the first sentence of the Nero-narrative ( Annals 13.1.1–2):
Prima novo principatu mors Iunii Silani proconsulis Asiae ignaro Nerone per dolum Agrippinae paratur, non quia ingenii violentia exitium inritaverat, segnis et dominationibus aliis fastiditus, adeo ut C. Caesar pecudem auream eum appellare solitus sit: verum Agrippina fratri eius L. Silano necem molita ultorem metuebat, crebra vulgi fama anteponendum esse vixdum pueritiam egresso Neroni et imperium per scelus adepto virum aetate composita insontem, nobilem et, quod tunc spectaretur, e Caesarum posteris: quippe et Silanus divi Augusti abnepos erat. haec causa necis.
[The first death under the new principate, that of Junius Silanus, proconsul of Asia, was brought to pass, without Nero’s knowledge, by treachery on the part of Agrippina. It was not that he had provoked his doom by violence of temper, lethargic as he was, and so completely disdained by former despotisms that Gaius Caesar [sc. Caligula] usually styled him ‘the golden sheep’; but Agrippina, who had procured the death of his brother Lucius Silanus, feared him as a possible avenger, since it was a generally expressed opinion of the multitude that Nero, barely emerged from boyhood and holding the empire in consequence of a crime, should take second place to a man of settled years, innocent character, and noble family, who – a point to be regarded in those days – was counted among the descendents of the Caesars: for Silanus, like Nero, was the son of a great-grandchild of Augustus. This was the cause of death…]
The imperial principle is evidently in play here: the book doesn’t start with the new year and the new consuls, but with a new series of imperial murders. As such it looks back to the beginning of the Tiberius narrative – and forward to the set text: 50 later on in his reign, the grown-up Nero takes care of business himself and kills off another Junius Silanus without the help of his mother (by then herself a murder victim) because he was a potential pretender to the throne, having similar dynastic credentials. The incident is part of the set text: see 15.37. More generally, Tacitus makes it abundantly clear that all of Nero’s reign lives up to its ominous beginnings, as the youthful emperor starts to ring the changes on murder. A (very) selective survey may include reference to his ‘fratricide’, insofar as Nero does away with his stepbrother Britannicus, the son of his predecessor Claudius and third wife Messalina (Agrippina, the mother of Nero, was Claudius’ fourth spouse). 51 Matricide follows, the gruesome slaughter of Agrippina. 52 Nero’s two wives Octavia and Poppaea Sabina (implicated in the murder of her predecessor) fall victim to, respectively, deliberate and accidental ‘uxoricide’, the latter combined with ‘foeticide’: Poppaea was pregnant at the time when Nero, in a fit of anger, kicked her to death. 53 The set text concludes with the unsuccessful attempt at the ‘senicide’ of Seneca, a failure made up for in the wake of the Pisonian conspiracy. 54 The surviving portion of the Annals ends with a killing spree (or wave of suicides) that includes the death of Thrasea Paetus. 55 In addition, ancient sources – though not necessarily Tacitus – charge Nero with ‘urbicide’, that is, the killing of the city of Rome in the great fire ( Ann . 15.38–4, part of the set text).
But Subrius Flavus, one of the conspirators around Piso, singles out not only matricide and arson as his reason for treason, but a third factor of a rather different nature: Nero’s attempt to turn Rome into an ancient variant of Broadway, with the emperor himself getting top billing. 56 This was part of a more general embrace of public spectacle moralists like Tacitus considered frivolous and Greek: Nero’s reign is marked by a heavy investment in festivals (including his own, the Neronia ); games, not least chariot-races; the whole culture of mousike (including poetry competitions and singing to the lyre); and the building of Greek cultural institutions such as gymnasia . Towards the end of his life, he even took his talents abroad, first to Southern Italy (a step covered in the set text: see 15.33), then with a trip to Greece (AD 66–67, i.e. not covered in the surviving portion of the Annals ). Relying on Tacitus and other sources, Ted Champlin argues that ‘Nero’s progression from private to public performance, and from amateur to professional, develops in three distinct stages’ both for music and charioteering: 57
|
Stage 1: AD 54–58 |
Rigorous programme of training in music; attention to circus entertainment and religious attendance at the games |
|
Stage 2: AD 59–63 |
Singing before the people on stage at his private Juvenalia; racing before a private audience in a specially built circus |
|
Stage 3: AD 64–68 |
Performance of music and racing in public |
The theme runs throughout Tacitus’ Nero-narrative, from 13.3 (where we catch the youthful Nero exercising his singing and charioteering) to, presumably, his death in the lost portion of the Annals . Suetonius reports that Nero’s final words were ‘ qualis artifex pereo ’ (‘What an artist dies in me!’). 58 In Tacitus, an avowed Hellenophobe, Nero’s artistic inclinations receive an exceedingly bad press. 59 But once placed in context, matters are not that simple. Ted Champlin has recently challenged the once orthodox view that Nero’s sponsorship of, and participation in, these activities was a total turn-off: 60
Despite the moral strictures of the authors who report Nero’s actions, the social context must be seen as an ambiguous one, and public attitudes as deeply ambivalent. Many of his people surely disapproved of their emperor’s games and the damage done to his imperial dignity, but many more just as surely applauded him. His actions sprang from patterns of behavior familiar in contemporary noblemen and approved by ancient precedent, and his people encouraged him. Killing relatives and rivals, real or imaginary, was cold political reality; performing in public may have been a fantasy, but it was one shared by a large part of Roman society. Whether it could be seen as part of the supreme imperial virtue, civilitas , is a matter for debate.
From this point of view, Nero’s cultivation of his showbiz talents and his desire to turn himself into the biggest star of the imperial entertainment industry were not meant to offend, but to act out one version of the ideal princeps . In part, as Champlin goes on to show, Nero succeeded – which accounts for his enormous popularity with certain segments of the population long after his death. One group he did not manage to win over were certain authors of the Trajanic age (Pliny, Tacitus, Suetonius), who are largely responsible for fixing Nero’s image in historiography – and thus for posterity (including us…). They are all scathing about Nero’s stage-performances and investment in spectacles as a way of defining his public image. In his Panegyricus , a speech of praise composed for the emperor Trajan, Pliny the Younger notes the contrast between Nero’s and Trajan’s style of imperial leadership as follows (46.4–5):
Idem ergo populus ille, aliquando scaenici imperatoris spectator et plausor, nunc in pantomimis quoque aversatur et damnat effeminatas artes, et indecora saeculo studia. ex quo manifestum est principum disciplinam capere etiam vulgus, cum rem si ab uno fiat severissimam fecerint omnes.
[And so the same populace which once watched and applauded the performances of an actor-emperor (sc. Nero) has now even turned against the pantomimes and damns their effeminate art as a pursuit unworthy of our age. This shows that even the vulgar crowd can take a lesson from its rulers, since a reform so sweeping, if once started by an individual, can spread to all.]
2.6 Thrasea Paetus and the so-called ‘Stoic opposition’
The first figure we encounter in the set text is not the emperor Nero but a senator by the name of Thrasea Paetus (or Paetus Thrasea). He had an illustrious political career, rising to the rank of consul in AD 56 (early in Nero’s reign), even though he frequently embarked on a course of collision with the emperor. Within the literary world of the Annals , he is a character of structural significance. His appearances (and absences) are always well-timed and strategic: ‘Though he [sc. Thrasea Paetus] had been suffect consul in A.D. 56, he does not appear on the pages of Tacitus till two years later. Indeed Tacitus carefully controls his appearances to produce a consistent pattern of one who continuously sought, not always without success, to uphold libertas senatoria .’ 61 One striking example of this policy involves his presence in the first few chapters of the set text (15.20–22), which form the tail end of Tacitus’ account of AD 62. As such, his direct speech here correlates with his appearance (including a direct speech) at the beginning of Tacitus’ account of the same year (14.48–49). These paragraphs cover the trial of Antistius and form a ‘twin’ to 15.20–22. The passage is lengthy, but, quite apart from its structural significance, also offers acute insights into the relationship between senate and emperor and into the character of Thrasea Paetus.
(49) Libertas Thraseae servitium aliorum rupit, et postquam discessionem consul permiserat, pedibus in sententiam eius iere, paucis exceptis, in quibus adulatione promptissimus fuit A. Vitellius, optimum quemque iurgio lacessens et respondenti reticens, ut pavida ingenia solent. at consules, perficere decretum senatus non ausi, de consensu scripsere Caesari. ille inter pudorem et iram cunctatus, postremo rescripsit: nulla iniuria provocatum Antistium gravissimas in principem contumelias dixisse; earum ultionem a patribus postulatam, et pro magnitudine delicti poenam statui par fuisse. ceterum se, qui severitatem decernentium impediturus fuerit, moderationem non prohibere: statuerent ut vellent; datam et absolvendi licentiam. his atque talibus recitatis et offensione manifesta, non ideo aut consules mutavere relationem aut Thrasea decessit sententia ceterive quae probaverant deseruere, pars, ne principem obiecisse invidiae viderentur, plures numero tuti, Thrasea sueta firmitudine animi et ne gloria intercideret.
[(48) In the consulate of Publius Marius and Lucius Afinius, the praetor Antistius, whose reckless conduct in his plebeian tribuneship I have already mentioned, composed a number of scandalous verses on the princeps , and made them public at a well-attended banquet of Ostorius Scapula, with whom he was dining. He was thereupon accused of treason by Cossutianus Capito, who, by the intervention of his father-in-law Tigellinus, had lately recovered his senatorial rank. This was the first revival of the statute; and it was believed that what was sought was not so much death for Antistius as glory for the emperor, whose tribunician veto was to snatch him from death after he had been condemned by the senate. Although Ostorius had stated in evidence that he had heard nothing, the witnesses for the prosecution were believed; and the consul designate, Junius Marullus, moved for the accused to be stripped of his praetorship and put to death according to ancient custom. The other senators were approving the motion, when Thrasea Paetus, with a great show of respect for Caesar and a most vigorous attack on Antistius, argued that it did not follow that the penalty a guilty defendant deserved to suffer was the one that ought to be decided upon, under an outstanding princeps and by a senate not fettered by any sort of compulsion. The executioner and the noose had long since been abolished; and there were punishments established by laws under which punitive measures could be decreed without implicating the judges in brutality or the age in infamy. In fact, on an island, with his property confiscated, the longer he dragged out his criminal existence, the deeper would be his personal misery, and he would also furnish an excellent example of public clemency.’
(49) The autonomy of Thrasea broke the servility of others, and, after the consul had authorized a vote, everyone supported his opinion, except a few dissenters, among whom Aulus Vitellius [sc. the future emperor] was the most active sycophant, who levelled his abuse at the very best, and, as is the wont of cowardly natures, lapsed into silence if anyone replied. The consuls, however, not daring to put the senatorial decree into practice, wrote to Caesar about the general consensus of opinion. He, after some vacillation between shame and anger, finally wrote back that ‘Antistius, unprovoked by any injury, had uttered to the most intolerable insults against the princeps . For those insults retribution had been demanded from the senators; and it would have been appropriate to fix a penalty matching the gravity of the offence. Still, as he had in mind to check undue severity in their verdict, he would not interfere with their moderation; they must decide as they wished – they had been given liberty even to acquit.’ These words, and others like it, were read out, and his resentment was plain to see. The consuls, however, did not change the motion on that account; Thrasea did not withdraw his proposal; nor did the remaining members withdraw their support for what they had approved; one part, lest they should seem to have placed the emperor in an invidious position; a majority, because there was safety in their numbers; Thrasea, through his usual firmness of spirit, and a desire not to lose any of his glory.]
The passage offers excellent insights into the fraught relations between senate and princeps , achieving two things in one: (i) it illustrates some of the (unwritten) social scripts that both parties could follow to ensure more or less smooth interactions on sensitive issues; (ii) and it shows what happens when one stubborn character like Thrasea Paetus refuses to play by the rules. Let’s have a look at the script that everyone tacitly followed before Thrasea’s intervention. It would have involved a death sentence passed by the senators followed by a pardon from the emperor. If this scenario had played itself out, everybody would have benefited. First, the defendant: he would have received a slap on the wrist, but not lost his head. Second, the senate: trials of treason put this body in a difficult position. Irrespective of the merits of the case, their actions in such matters were themselves open to critical scrutiny: mild treatment of the defendant could be interpreted as manifesting latent sympathies with the culprit, whereas (overly) harsh punishment, while being a sign of outraged loyalty, could be interpreted as kow-towing to a tyrant. But when it was understood that senatorial severity was a first step in a dialectic that set the princeps up for an act of mercy, senators had good reasons for leaning towards passing a harsh verdict since they knew it would not be executed – while also pleasing the emperor. Third, the princeps : Nero hoped for a verdict of guilty and a capital sentence as an opportunity to display his mild disposition by pardoning the defendant despite his evident guilt – a scenario in which he would get the best of both worlds: a firm show of senatorial loyalty, plus personal credit for behaving like a civilis princeps .
Tacitus’ narrative makes it clear that everyone involved played according to this script – until Thrasea Paetus decided to interfere. Then chaos ensued. The senators were put on the spot. As soon as the capital sentence ceases to be unanimous, as soon as alternatives are available, they find themselves in a double bind. Once a milder option is on the table, they lose face if they remain in favour of the death penalty; but voting in favour of the milder proposal – they know – will incur the displeasure of the princeps . The dilemma is rendered more uncomfortable by the fact that individual senators could exploit the opportunity to score points for themselves. In this case, Aulus Vitellius opposed Thrasea Paetus, in the full knowledge of endorsing the alternative favoured by the princeps – and (one assumes) in the hope of being rewarded for this show of loyalty. Viewed like this, what Tacitus calls senatorial servility ( servitium ) emerges as pragmatism and common sense, and what he calls the independence ( libertas ) of Thrasea Paetus as a rather irritating act of self-promotion that leaves everybody else worse off.
Let’s look at the fall-out: by arguing for a more lenient sentencing by the senate Thrasea Paetus pre-empts the role that Nero expected to play himself. (Reading his speech intertextually with Caesar’s position in the senatorial debate over the fate of the Catilinarian conspirators as reported by Cicero (in his fourth speech against Catiline) and Sallust (in his Bellum Catilinae ) heightens the affront: it implies that Paetus is here play-acting as emperor by imitating the founding figure of the Julio-Claudian dynasty.) 62 The senate (including the consuls who had proposed the death penalty) are forced to change tack. The princeps is deprived of his opportunity to show mercy and grudgingly concedes what he would have gladly imposed. Aulus Vitellius aggravates the divisions within the senate for personal gain (just like Thrasea). Everyone is insecure and anxious once the princeps has been upset. The episode thus illustrates Tacitus’ earlier critical comment on Thrasea’s adversarial stance towards the princeps , when he notes that Thrasea’s ostentatious departure from a senate-meeting as protest against excessive adulation of the emperor ‘caused danger for himself without initiating freedom for the rest’ ( Annals 14.12.1: sibi causam periculi fecit, ceteris libertatis initium non praebuit ).
Within the senate, then, Thrasea’s refusal to play along in what was ultimately a carefully orchestrated social drama that enabled senators and emperor to negotiate their positions vis-à-vis one another, was bound to prove divisive: it forced all other senators to adopt a much more exposed stance on the matter. From the point of view of the retrospective historiographer, of course, Thrasea’s intervention was a godsend: it provided Tacitus with the opportunity to assess the character of the senate as a whole and of specific individuals on a spectrum of possibilities, ranging from ‘unscrupulous opportunist’ to ‘servile’ to ‘principled and independent.’ At the same time, it is important to note that Tacitus enables his readers to appreciate how disruptive a figure Thrasea Paetus was. He could, for instance, easily have enhanced Thrasea’s apparent heroism by suppressing the information that Nero planned to pardon the accused in any case: this would have made it much more difficult for his readers to recognize the social script that was playing itself out before Thrasea interfered. Moreover, he identifies Thrasea’s desire for glory as the primary motivating factor behind his intervention. This entails a tension between a principled commitment to republican norms (such as a libertas ) and the self-seeking desire to inscribe oneself in the memory of the Roman people ( gloria ) – at whatever cost. 63
It is worth linking this discussion to Tacitus’ biography – and authorial preferences. The type of the ‘principled troublemaker’ or, to use a more positive label, ‘martyr of republican libertas ’ is a recurrent figure in Tacitus’ oeuvre , with Thrasea Paetus, who was invited to commit suicide under Nero, and his son-in-law Helvidius Priscus, who met the same fate under Vespasian, leading the way. Their seemingly upright conduct and apparent adherence to a set of old-fashioned norms and values, their courage, and defiance to death, make for excellent foils for bad emperors. 64 But Tacitus’ own position vis-à-vis this kind of senatorial peer was decidedly ambivalent – and unsurprisingly so. Both he himself and his father-in-law Agricola had stellar careers under ‘bad’ emperors. It is therefore not without interest that Tacitus in the Agricola explicitly contrasts the futile, self-serving desire for immortality through heroic suicide that motivated the martyrs with the commitment to civic duties and service to the res publica that underwrote the public career of his father-in-law ( Agricola 42.3–4):
proprium humani ingenii est odisse quem laeseris: Domitiani vero natura praeceps in iram, et quo obscurior, eo inrevocabilior, moderatione tamen prudentiaque Agricolae leniebatur, quia non contumacia neque inani iactatione libertatis famam fatumque provocabat. sciant, quibus moris est inlicita mirari, posse etiam sub malis principibus magnos viros esse, obsequiumque ac modestiam, si industria ac vigor adsint, eo laudis excedere, quo plerique per abrupta sed in nullum rei publicae usum ambitiosa morte inclaruerunt.
[It is characteristic of human nature to hate whom you have harmed: but the natural disposition of Domitian, quick to anger, and the more inscrutable the more implacable, was nonetheless mollified by the moderation and circumspection of Agricola, because he was not trying to call forth fame and death with obstinacy and empty boasts of freedom. Let those, whose habit it is to admire what is forbidden, know that even under bad emperors there can be great men; and that obedience and unassuming conduct, as long as they are coupled with effort and initiative, can attain the same degree of praise that many more achieve through perilous courses of action and self-promoting deaths that are of no use to the commonwealth.]
In this passage, at least, Tacitus seems to recommend a middle course between suicide and servility, well captured by D. Sailor: ‘a life that bears unmistakable signs of autonomy, signs that suffice for acquiring prestige, but that nonetheless do not lead inevitably to an encounter with the regime’s violence. Being killed by the regime was… the lone incontestable proof that you had not surrendered your autonomy to the princeps ’ domination and that you did not recognize the legitimacy of his coercive powers. But there were also alternative “careers” that argued, though less conclusively, for the possibility of both staying alive and securing real distinction for considerable autonomy.’ 65 And this may explain why his portrayal of figures like Thrasea in his later historiographical works, while overall positive, also hints at the dysfunctional aspects of their personalities.


1.8: Why It Matters- Communicating in Business
Why learn to effectively communicate in business?
Business is about people. We exist to serve people with our products and services, to employ them and pay them to do work, to purchase the supplies and merchandise we need to operate. To be in business is to be surrounded by people who interact with you, who require something from you.
Communication is the connection between people. It could be a shared photograph, a letter or a smoke signal, but as long as one person is sending a message and another person is understanding it, communication is happening.
The successful professional builds and maintains relationships, completes tasks, directs teams, and expresses ideas via effective communication. To be successful you’ll need to be an effective communicator: you need to be understood.
Playwright George Bernard Shaw is quoted as saying, “The single biggest problem in communication is the illusion that it has taken place.” This module is the first step in dispelling the illusion. Here we will talk about the elements of communication—recognizing the pattern of good communication, the types of communication you’re likely to see in the workplace, and the kinds of tools you can use to effectively build your message, deliver it, and be understood by your audience.
Contributors and Attributions
- Why It Matters: Communicating in Business. Authored by : Freedom Learning Group. Provided by : Lumen Learning. License : CC BY: Attribution
- wocintech (microsoft) - 152. Authored by : WOCinTech Chat. Located at : https://flic.kr/p/FsLAtL . License : CC BY: Attribution


Defining Monopoly
A monopoly is an economic market structure where a specific person or enterprise is the only supplier of a particular good.
learning objectives
-
Differentiate monopolies and competitive markets
A monopoly is a specific type of economic market structure. A monopoly exists when a specific person or enterprise is the only supplier of a particular good. As a result, monopolies are characterized by a lack of competition within the market producing a good or service.
Monopoly
: The graph shows a monopoly and the price (P) and change in price (P reg) as well as the output (Q) and output change (Q reg).
Characteristics of a Monopoly
A monopoly can be recognized by certain characteristics that set it aside from the other market structures:
-
Profit maximizer:
a monopoly maximizes profits. Due to the lack of competition a firm can charge a set price above what would be charged in a competitive market, thereby maximizing its revenue.
-
Price maker:
the monopoly decides the price of the good or product being sold. The price is set by determining the quantity in order to demand the price desired by the firm (maximizes revenue).
-
High barriers to entry:
other sellers are unable to enter the market of the monopoly.
-
Single seller:
in a monopoly one seller produces all of the output for a good or service. The entire market is served by a single firm. For practical purposes the firm is the same as the industry.
-
Price discrimination:
in a monopoly the firm can change the price and quantity of the good or service. In an elastic market the firm will sell a high quantity of the good if the price is less. If the price is high, the firm will sell a reduced quantity in an elastic market.
Sources of Monopoly Power
In a monopoly, specific sources generate the individual control of the market. Sources of power include:
-
Economies of scale
-
Capital requirements
-
Technological superiority
-
No substitute goods
-
Control of natural resources
-
Network externalities
-
Legal barriers
-
Deliberate actions
Monopoly vs. Competitive Market
Monopolies and competitive markets mark the extremes in regards to market structure. There are a few similarities between the two including: the cost functions are the same, both minimize cost and maximize profit, the shutdown decisions are the same, and both are assumed to have perfectly competitive market factors.
However, there are noticeable differences between the two market structures including: marginal revenue and price, product differentiation, number of competitors, barriers to entry, elasticity of demand, excess profits, profit maximization, and the supply curve. The most significant distinction is that a monopoly has a downward sloping demand instead of the “perceived” perfectly elastic curve of the perfectly competitive market.
Key Points
-
A monopoly market is characterized by the profit maximizer, price maker, high barriers to entry, single seller, and price discrimination.
-
Monopoly characteristics include profit maximizer, price maker, high barriers to entry, single seller, and price discrimination.
-
Sources of monopoly power include economies of scale, capital requirements, technological superiority, no substitute goods, control of natural resources, legal barriers, and deliberate actions.
-
There are a few similarities between a monopoly and competitive market: the cost functions are the same, both minimize cost and maximize profit, the shutdown decisions are the same, and both are assumed to have perfectly competitive market factors.
-
Differences between the two market structures including: marginal revenue and price, product differentiation, number of competitors, barriers to entry, elasticity of demand, excess profits, profit maximization, and the supply curve.
-
The most significant distinction is that a monopoly has a downward sloping demand instead of the “perceived” perfectly elastic curve of the perfectly competitive market.
Key Terms
-
monopoly
: A market where one company is the sole supplier.
-
differentiation
: The act of distinguishing a product from the others in the market.
LICENSES AND ATTRIBUTIONS
CC LICENSED CONTENT, SPECIFIC ATTRIBUTION
-
Monopoly market.
Provided by
: Wikipedia.
Located at
:
en.Wikipedia.org/wiki/Monopoly_market
.
License
:
CC BY-SA: Attribution-ShareAlike
-
Perfect competition.
Provided by
: Wikipedia.
Located at
:
en.Wikipedia.org/wiki/Perfect_competition
.
License
:
CC BY-SA: Attribution-ShareAlike
-
Monopoly market.
Provided by
: Wikipedia.
Located at
:
en.Wikipedia.org/wiki/Monopoly_market
.
License
:
CC BY-SA: Attribution-ShareAlike
-
Boundless.
Provided by
: Boundless Learning.
Located at
:
www.boundless.com//management...ifferentiation
.
License
:
CC BY-SA: Attribution-ShareAlike
-
Boundless.
Provided by
: Boundless Learning.
Located at
:
www.boundless.com//economics/...ition/monopoly
.
License
:
CC BY-SA: Attribution-ShareAlike
-
Imperfect competition after regulation.
Provided by
: Wikimedia.
Located at
:
commons.wikimedia.org/wiki/Fi...regulation.svg
.
License
:
CC BY-SA: Attribution-ShareAlike


11.5: Ramsey's Theorem
By this time, you are probably not surprised to see that there is a very general form of Ramsey's theorem. We have a bounded number of bins or colors and we are placing the subsets of a fixed size into these categories. The conclusion is that there is a large set which is treated uniformly.
Here's the formal statement.
Let \(r\) and \(s\) be positive integers and let \(\textbf{h}=(h_1,h_2,…,h_r)\) be a string of integers with \(h_i \geq s\) for each \(i=1,2,…,s\). Then there exists a least positive integer \(R(s:h_1,h_2,…,h_r)\) so that if \(n \geq n_0\) and \(\phi:C([n],s] \rightarrow [r]\) is any function, then there exists an integer \(\alpha \in [r]\) and a subset \(H_{\alpha}⊆[n]\) with \(|H_{\alpha}|=h_{\alpha}\) so that \(\phi (S)= \alpha\) for every \(S \in C(H_{\alpha},s)\).
We don't include the proof of this general statement here, but the more ambitious students may attempt it on their own. Note that the case \(s=1\) is just the Pigeon Hole Principle , while the case \(s=r=2\) is just Ramsey's Theorem for Graphs . An argument using double induction is required for the proof in the general case. The first induction is on \(r\) and the second is on \(s\).


4.8: Outcome- Soil Profiles and Types
Describe and compare typical soil profiles and basic soil types.
This section provides information on the different types of soil and soil profiles. You will become familiar with different soil types, their components and common locations.
What You’ll Learn to Do
- Identify the measurable components of soil: sand, silt, and clay.
- Identify the primary soil horizons: organic, topsoil, subsoils, and C horizon.
- Identify three common (and important!) types of soil: pedalfer, pedocal, and laterite.
Learning Activities
The learning activities for this section include the following:
- Reading: Soil Texture and Composition
- Reading: Soil Horizons and Profiles
- Reading: Types of Soils
- Self Check: Soil Profiles and Types
Contributors and Attributions
CC licensed content, Original
- Authored by : Kimberly Schulte and Lumen Learning. Provided by : Lumen Learning. License : CC BY: Attribution


2.2: Recent Research Historical Variation in Khipu and Figures
-
- Last updated
- Save as PDF
The most complex system of writing (using the word in a broad sense) that Andean peoples possessed before the Spanish invasion of 1532 was the cord- and knot-based medium called khipu (Quechua) or quipu (Spanish). The material makeup of khipu is a story of variation over time, with some longue durée continuities. Khipu had a brief, spectacularly productive heyday as the official medium of the Inka state (established some time during the 15th century ce until 1532 ce). The great majority of all the 600-odd more or less complete khipus held in museums and accessible private collections are catalogued as imperial Inka artifacts, but new radiocarbon results show that some date from the Spanish colony (Cherkinsky and Urton, forthcoming). The Ethnologisches Museum in Berlin and the American Museum of Natural History in New York have the largest collections. Online offerings suggest that an unknown number of them (some fake) are in other hands. Inka khipus were largely standardized in format and material content ( Figure 1 ).
But Inkas are not the only principals in this story. The cord medium underwent a long, varied evolution both before and after khipus’ brief Inka florescence. Both pre- and post-Inka khipus differed widely from Inka ones in physical substance and form. This chapter consists of a historical and a functional section. In the first half I discuss material attributes of Inka, pre-Inka, and post-Inka khipus, respectively, with emphasis on change. By contrast, in the second half of this chapter I emphasize material continuity: material traits that make a khipu a khipu, and how they affect culture as lived through inscription. For the spatial distribution of the evidence discussed, see the map in Figure 2 .
Figure 1: Khipu demonstrates repeating colour sequence. 64-19-1-1-6-2 of the Musée de l’Homme (now in Musée du Quai Branly).
Figure 2: Map showing main locations mentioned in the text.
Figure 3: Basic khipu terminology and structure (Ascher and Ascher 1997: 12, fig. 2.7). By permission of Marcia Ascher and Robert Ascher.
Figure 4: Three common knots used in Inka khipus: Left: Inka long knot of value four, used in units place; center, simple (s) knot; right, figure-eight (E) knot (Ascher and Ascher 1997: 29, fig. 2.11). By permission of Marcia Ascher and Robert Ascher
Figure 5: A khipu with arithmetical values. The topcord sums the values of pendants, and the topcord’s subsidiary those of the pendants’ subsidiaries (Ascher and Ascher 1997: 31, fig. 2.14). By permission of Marcia Ascher and Robert Ascher.
Figure 6: Paired khipu from Puruchuco: these two Inka-era specimens (UR 66–67) were rolled together, and bear similar color patterning. Photograph courtesy of Gary Urton.
Figure 7: Khipus of Wari affiliation, several centuries earlier than Inka examples, bear information in the form of colored thread lashed around pendant cords. American Museum of Natural History T-223. Photograph courtesy of Carmen Arellano.
Figure 8: Wrapped sticks from funerary context at the Paracas site of Cerrillos. Photograph courtesy of Jeffrey Splitstoser
Figure 9: Wrapped sticks of late prehispanic and / or colonial dates in the collection of the Peabody Museum, Harvard. Photograph courtesy of William Conklin
Figure 10: Mummy from Chuquitanta with wrapped sticks. Photograph courtesy of Berndt Herrmann.
Figure 11: A herder’s khipu from modern Peru, studied by Carol Mackey in the late 1960s (in Quilter and Urton 2002: 334). It analyzes a herd of llamas by reproductive status.
Figure 12: In Tupicocha, Peru, 1995, Celso Alberco assumed the presidency of his ayllu (a network of families) by donning its khipu. Author’s photograph.
Figure 13: A khipu belonging to ayllu Segunda Satafasca of Tupicocha. The overall design matches canonical Inka design. Author’s photograph.
Figure 14: Kaha Wayi, the house of ritual and traditional governance in Rapaz. It houses a large collection of vernacular khipus. Author’s photograph.
Figure 15: In 2004, Toribio Gallardo shows Rapaz’s khipu collection. Author’s photograph.
Figure 16: Some Rapaz khipus bear textile figurines. Author’s photograph.
Figure 17: An Inka-era khipu with all its knots removed. Photograph courtesy of Gary Urton.
Figure 18: Felipe Guaman Poma de Ayala drew this Inka postal runner with a khipu labeled “letter” (1980 [1615]: 178).
Figure 19: Inka khipu bound in fascicle for storage. Photograph courtesy of William Conklin.
Figure 20: Khipu(s) 41-2-6993 of the American Museum of Natural History are apparently marked as a pair by common attachment to a single end knob. Author’s photograph.
Figure 21: The Tupicochan practice of twisting an entire khipu into a single huge knot. Author’s photograph.
Figure 22: The 1590 de Murúa manuscript illustrates cooperative reading and finger-sorting of cords (de Murúa 2004: 124 verso).
Figure 23: At Laguna de los Cóndores, some Inka-era khipus found with enshrined mummies were tied to each other. Photograph courtesy of Gary Urton.
Figure 24: The Peabody Museum at Harvard holds a ring-shaped set of five conjoined khipus. Photograph courtesy of the Peabody Museum.


27.3: Guide for writing a proposal
selected template will load here
This action is not available.
Write a few short sentences briefly summarizing the aim of your experiment, how it will be conducted, and how precise of a result you expect to obtain.
Clearly describe, in as much detail as required, the method/procedure that you will use to carry out your experiment, and how you will analyze the results. Justify the choices that you made (no need to say you chose to use a ruler because you will need to measure a distance, but perhaps say why you need to measure a given distance, or that you chose to measure something in a particular way as it would reduce the corresponding uncertainty). Provide a list of the equipment that you will need. Also, propose a method of assessing whether or not your project was successful.
Consider the following questions:
Provide the names of team members, and assign relevant duties to each member. Give a rough outline of the timeline to conduct the experiment, to analyze the data, and to report on the results.


12.4: Historical Notes
Kruskal's algorithm was published in 1956 by Joseph B. Kruskal in a three-page paper that appeared in Proceedings of the American Mathematical Society. Robert C. Prim published the algorithm that now bears his name the following year in The Bell System Technical Journal. Prim's paper focuses on application of the minimum weight (or length or cost) spanning tree problem to telephone networks. He was aware of Kruskal's prior work, as they were colleagues at Bell Laboratories at the time he published his paper. It turns out that Prim had been beaten to the punch by Czech mathematician Vojtěch Jarník in 1929, so some refer to Prim's algorithm as Jarník's algorithm. (It was later rediscovered by Dijkstra, so some attach his name as well, referring to it as the Dijkstra-Jarník-Prim algorithm.) Edsger Dijkstra published his algorithm for finding shortest paths in 1959 in a three-page paper appearing in Numerische Mathematik. In fact, Dijkstra's algorithm had been discovered (in an equivalent form) by Edward F. Moore two years earlier. His result appeared in Proceedings of an International Symposium on the Theory of Switching.


3.4: Gravitational Potential Energy
Learning Objectives
- Explain gravitational potential energy in terms of work done against gravity.
- Show that the gravitational potential energy of an object near surface of Earth is given by product of its mass, height, and gravitational acceleration.
- Show how knowledge of the potential energy as a function of position can be used to simplify calculations and explain physical phenomena.
Work Done Against Gravity
Consider lifting a weight (of, say, 5 kg, which weighs about 50 N) from the floor to a table surface at a height of 1 meter from the floor. In lifting this weight, you have done work, both in the usual sense (if you do this lifting of weight over and over, you will eventually get tired) and in the scientific sense we defined in the earlier section (\(W=F d\), and you applied an upward force as you displaced the weight upward by 1 meter). One thing is different in this scenario, however. Earlier, in describing work-kinetic energy theorem, we said that net work done on an object changes the kinetic energy of the object (\(\Delta \mathrm{KE}=W_{\text {net }}\)). But in this case, if you imagine lifting the weight very slowly up to the height of the table, you will find that the kinetic energy of the weight does not change. It starts at zero and remains at zero throughout this very slow motion. What is going on here?
The key difference is that, for this weight, there are now two forces acting on it as it is being lifted. The gravitational force pulls downward, while the force you apply is directed upward. If you are lifting the weight very slowly, then its acceleration is very close to zero, so the net force on it is zero (\(F_{\mathrm{net}}=0\)), which means the net work done on the weight is also zero (\(W_{\text {net }}=F_{\text {net }} d\); the applied upward force does positive work, while the downward gravitational force does negative work).
While this is a correct description (the negative work done by the gravity cancels out the positive work done by the applied force), this description misses something. Specifically, you can see that this weight that has been lifted by 1 meter does have more energy than a weight that was resting on the floor. This is how you can see it: if you let go of the weight (after removing the table), as the weight originally at 1-meter height reaches the floor, it gains a substantial kinetic energy as it continues to be pulled by gravity. Rather than saying that this kinetic energy simply appeared as the weight fell through the 1-meter height, we opt for the description that this weight already had this energy, when it was at rest at the 1-meter height, just in a form that was not kinetic energy. We call this energy associated with the height of objects the gravitational potential energy , \(\mathrm{PE}_{g}\). And in this example, the energy originally came from the work done by the applied force—rather than considering positive work done by the applied force to be cancelled out by the negative work done by the gravity, we say that this positive work done is stored as positive \(\mathrm{PE}_{g}\).
This phenomenon of potential energy turns out to be quite general and goes beyond the gravitational force. There are other forces in nature where negative work done by these forces turns into positive potential energy. We call these forces conservative forces , which will be the subject of the next section. For the purpose of this section, following is the quick derivation of formula for \(\mathrm{PE}_{g}\) (everything in terms of symbols now). In lifting the weight of mass \(m\) through a height \(h\) slowly, you have to apply a force equal to its weight, \(mg\). So the work done is \(W=F d=m g h\), and since it's this work done that is stored as gravitational potential energy, the gravitational potential energy must be:
\[\mathrm{PE}_{g}=m g h. \nonumber \]
Converting Between Potential Energy and Kinetic Energy
Gravitational potential energy may be converted to other forms of energy, such as kinetic energy. If we release the mass, gravitational force will do an amount of work equal to \(mgh\) on it, thereby increasing its kinetic energy by that same amount (by the work-energy theorem). We will find it more useful to consider just the conversion of \(\mathrm{PE}_{\mathrm{g}}\) to KE without explicitly considering the intermediate step of work. (See Example \(\PageIndex{2}\).) This shortcut makes it is easier to solve problems using energy (if possible) rather than explicitly using forces.
More precisely, we define the change in gravitational potential energy \(\Delta \mathrm{PE}_{\mathrm{g}}\) to be
\[\Delta \mathrm{PE}_{\mathrm{g}}=\mathrm{PE}_{\mathrm{gf}}-\mathrm{PE}_{\mathrm{gi}}=m g h_{\mathrm{f}}-m g h_{\mathrm{i}}=m g\left(h_{\mathrm{f}}-h_{\mathrm{i}}\right)=m g \Delta h \nonumber\]
Note that \(\Delta h\) is positive when the final height is greater than the initial height, and vice versa. For example, if a 0.500-kg mass hung from a cuckoo clock is raised 1.00 m, then its change in gravitational potential energy is
\[\begin{aligned}
m g \Delta h &=(0.500 \mathrm{~kg})\left(9.80 \mathrm{~m} / \mathrm{s}^{2}\right)(1.00 \mathrm{~m}) \\
&=4.90 \mathrm{~kg} \cdot \mathrm{m}^{2} / \mathrm{s}^{2}=4.90 \mathrm{~J}.
\end{aligned} \nonumber\]
Note that the units of gravitational potential energy turn out to be joules, the same as for work and other forms of energy. As the clock runs, the mass is lowered. We can think of the mass as gradually giving up its 4.90 J of gravitational potential energy, without directly considering the force of gravity that does the work .
Using Potential Energy to Simplify Calculations
The equation \(\Delta \mathrm{PE}_{\mathrm{g}}=m g \Delta h\) applies for any path that has a change in height of \(\Delta \mathrm{h}\), not just when the mass is lifted straight up. (See Figure \(\PageIndex{2}\).) It is much easier to calculate \(m g \Delta h\) (a simple multiplication) than it is to calculate the work done along a complicated path. The idea of gravitational potential energy has the double advantage that it is very broadly applicable and it makes calculations easier. From now on, we will consider that any change in vertical position \(\Delta \mathrm{h}\) of a mass \(m\) is accompanied by a change in gravitational potential energy \(m g \Delta h\), and we will avoid the equivalent but more difficult task of calculating work done by or against the gravitational force.
Example \(\PageIndex{1}\): The Force to Stop Falling
A 60.0-kg person jumps onto the floor from a height of 3.00 m. If he lands stiffly (with his knee joints compressing by 0.500 cm), calculate the force on the knee joints.
Strategy
This person’s energy is brought to zero in this situation by the work done on him by the floor as he stops. The initial \(\mathrm{PE}_{\mathrm{g}}\) is transformed into KE as he falls. The work done by the floor reduces this kinetic energy to zero.
Solution
The work done on the person by the floor as he stops is given by
\[W=-F d, \nonumber\]
with a minus sign because the displacement while stopping and the force from floor are in opposite directions. The floor removes energy from the system, so it does negative work.
The kinetic energy the person has upon reaching the floor is the amount of potential energy lost by falling through height \(\Delta \mathrm{h}\):
\[\mathrm{KE}=-\Delta \mathrm{PE}_{\mathrm{g}}=-m g \Delta h, \nonumber\]
The distance \(d\) that the person’s knees bend is much smaller than the height \(\Delta \mathrm{h}\) of the fall, so the additional change in gravitational potential energy during the knee bend is ignored.
The work \(W\) done by the floor on the person stops the person and brings the person’s kinetic energy to zero:
\[W=-\mathrm{KE}=m g \Delta h. \nonumber\]
Combining this equation with the expression for \(W\) gives
\[-F d=m g \Delta h. \nonumber\]
Recalling that \(\Delta \mathrm{h}\) is negative because the person fell down , the force on the knee joints is given by
\[F=-\frac{m g \Delta h}{d}=-\frac{(60.0 \mathrm{~kg})\left(9.80 \mathrm{~m} / \mathrm{s}^{2}\right)(-3.00 \mathrm{~m})}{5.00 \times 10^{-3} \mathrm{~m}}=3.53 \times 10^{5} \mathrm{~N}. \nonumber\]
Discussion
Such a large force (500 times more than the person’s weight) over the short impact time is enough to break bones. A much better way to cushion the shock is by bending the legs or rolling on the ground, increasing the time over which the force acts. A bending motion of 0.5 m this way yields a force 100 times smaller than in the example. A kangaroo's hopping shows this method in action. The kangaroo is the only large animal to use hopping for locomotion, but the shock in hopping is cushioned by the bending of its hind legs in each jump.(See Figure \(\PageIndex{3}\).)
Example \(\PageIndex{2}\): Finding the Speed of a Roller Coaster from its Height
(a) What is the final speed of the roller coaster shown in Figure \(\PageIndex{4}\) if it starts from rest at the top of the 20.0 m hill and work done by frictional forces is negligible? (b) What is its final speed (again assuming negligible friction) if its initial speed is 5.00 m/s?
Strategy
The roller coaster loses potential energy as it goes downhill. We neglect friction, so that the remaining force exerted by the track is the normal force, which is perpendicular to the direction of motion and does no work. The net work on the roller coaster is then done by gravity alone. The loss of gravitational potential energy from moving downward through a distance \(h\) equals the gain in kinetic energy. This can be written in equation form as \(-\Delta \mathrm{PE}_{\mathrm{g}}=\Delta \mathrm{KE}\). Using the equations for \(\mathrm{PE}_{\mathrm{g}}\) and KE , we can solve for the final speed \(v\), which is the desired quantity.
Solution for (a)
\[-\Delta \mathrm{PE}_{\mathrm{g}}=\Delta \mathrm{KE} \nonumber\]
becomes
\[-\left(\mathrm{PE}_{\mathrm{gf}}-\mathrm{PE}_{\mathrm{gi}}\right)=\frac{1}{2} m v_{\mathrm{f}}^{2}-\frac{1}{2} m v_{\mathrm{i}}^{2} \nonumber\]
Noting that the initial speed is zero, and using the formula for gravitational potential energy, we have
\[-\left(m g h_{\mathrm{f}}-m g h_{\mathrm{i}}\right)=\frac{1}{2} m v_{\mathrm{f}}^{2} \nonumber\]
Taking the initial height as zero gives
\[-m g h_{\mathrm{f}}=\frac{1}{2} m v_{\mathrm{f}}^{2} \nonumber\]
Solving for the final speed, we find that mass cancels and that
\[v_{\mathrm{f}}=\sqrt{-2 g h_{\mathrm{f}}} \nonumber\]
Substituting known values,
\[v_{\mathrm{f}}=\sqrt{-2 g h_{\mathrm{f}}}=\sqrt{(-2)\left(9.80 \mathrm{~m} / \mathrm{s}^{2}\right)(-20.0 \mathrm{~m})}=19.8 \mathrm{~m} / \mathrm{s} \nonumber\]
Please note that the height used above was negative. This is because we chose the initial height to be our reference level for gravitational potential energy. Our final height is 20 meters below that reference level.
Solution for (b)
Again \[-\Delta \mathrm{PE}_{\mathrm{g}}=\Delta \mathrm{KE}. \nonumber\]
Thus,
\[-\left(\mathrm{PE}_{\mathrm{gf}}-\mathrm{PE}_{\mathrm{gi}}\right)=\frac{1}{2} m v_{\mathrm{f}}^{2}-\frac{1}{2} m v_{\mathrm{i}}^{2} \nonumber\]
Taking the initial height as zero leads to
\[-m g h_{\mathrm{f}}=\frac{1}{2} m v_{\mathrm{f}}^{2}-\frac{1}{2} m v_{\mathrm{i}}^{2} \nonumber\]
Rearranging gives
\[\frac{1}{2} m v_{\mathrm{f}}^{2}=-m g h_{\mathrm{f}}+\frac{1}{2} m v_{\mathrm{i}}^{2} \nonumber\]
This means that the final kinetic energy is the sum of the initial kinetic energy and the gravitational potential energy. Mass again cancels, and
\[v_{\mathrm{f}}=\sqrt{-2 g h_{\mathrm{f}}+v_{\mathrm{i}}^{2}} \nonumber\]
Now, substituting known values gives
\[v_{\mathrm{f}}=\sqrt{-2 g h_{\mathrm{f}}+v_{\mathrm{i}}^{2}}=\sqrt{(-2)\left(9.80 \mathrm{~m} / \mathrm{s}^{2}\right)(-20.0 \mathrm{~m})+(5.00 \mathrm{~m} / \mathrm{s})^{2}}=20.4 \mathrm{~m} / \mathrm{s}. \nonumber\]
Discussion and Implications
First, note that mass cancels. This is quite consistent with observations that all objects fall at the same rate if friction is negligible. Second, only the speed of the roller coaster is considered; there is no information about its direction at any point. This reveals another general truth. When friction is negligible, the speed of a falling body depends only on its initial speed and height, and not on its mass or the path taken. For example, the roller coaster will have the same final speed whether it falls 20.0 m straight down or takes a more complicated path like the one in the figure. Third, and perhaps unexpectedly, the final speed in part (b) is greater than in part (a), but by far less than 5.00 m/s. Finally, note that speed can be found at any height along the way by simply using the appropriate value of \(h\) at the point of interest.
We have seen that work done by or against the gravitational force depends only on the starting and ending points, and not on the path between, allowing us to define the simplifying concept of gravitational potential energy. We can do the same thing for a few other forces, and we will see that this leads to a formal definition of the law of conservation of energy.
Section Summary
- Work done against gravity in lifting an object becomes potential energy of the object-Earth system.
- The change in gravitational potential energy, \(\Delta \mathrm{PE}_{\mathrm{g}}\), is \(\Delta \mathrm{PE}_{\mathrm{g}}=m g \Delta h\), with \(\Delta \mathrm{h}\) being the change in height and \(g\) the acceleration due to gravity.
- The gravitational potential energy of an object near Earth’s surface is due to its position in the mass-Earth system. Only differences in gravitational potential energy, \(\Delta \mathrm{PE}_{\mathrm{g}}\), have physical significance.
- As an object descends without friction, its gravitational potential energy changes into kinetic energy corresponding to increasing speed, so that \(\Delta \mathrm{KE}=-\Delta \mathrm{PE}_{\mathrm{g}}\).
Glossary
- gravitational potential energy
- energy associated with height of objects on the Earth