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Charles R. Giardina

LucentTechnologies,Whippany,NJ,UnitedStates(Retired)

Cover image

Title page

Dedication

List of figures

Preface

Acknowledgments

Chapter 1. Introduction to quantum many-sorted algebras

Abstract

1.1 Introduction to quantum many-sorted algebras

References

Chapter 2. Basics of deep learning

Abstract

2.1 Machine learning and data mining

2.2 Deep learning

2.3 Deep learning and relationship to quantum

2.4 Affine transformations for nodes within neural net

2.5 Global structure of neural net

2.6 Activation functions and cost functions for neural net

2.7 Classification with a single-node neural net

2.8 Backpropagation for neural net learning

2.9 Many-sorted algebra description of affine space

2.10 Overview of convolutional neural networks

2.11 Brief introduction to recurrent neural networks

References

Chapter 3. Basic algebras underlying quantum and NN mechanisms

Abstract

3.1 From a vector space to an algebra

3.2 An algebra of time-limited signals

3.3 The commutant in an algebra

3.4 Algebra homomorphism

3.5 Hilbert space of wraparound digital signals

3.6 Many-sorted algebra description of a Banach space

3.7 Banach algebra as a many-sorted algebra

3.8 Many-sorted algebra for Banach* and C* algebra

3.9 Banach* algebra of wraparound digital signals

3.10 Complex-valued wraparound digital signals

References

Chapter 4. Quantum Hilbert spaces and their creation

Abstract

4.1 Explicit Hilbert spaces underlying quantum technology

4.2 Complexification

4.3 Dual space used in quantum

4.4 Double dual Hilbert space

4.5 Outer product

4.6 Multilinear forms, wedge, and interior products

4.7 Many-sorted algebra for tensor vector spaces

4.8 The determinant

4.9 Tensor algebra

4.10 Many-sorted algebra for tensor product of Hilbert spaces

4.11 Hilbert space of rays

4.12 Projective space

References

Chapter 5. Quantum and machine learning applications involving matrices

Abstract

5.1 Matrix operations

5.2 Qubits and their matrix representations

5.3 Complex representation for the Bloch sphere

5.4 Interior, exterior, and Lie derivatives

5.5 Spectra for matrices and Frobenius covariant matrices

5.6 Principal component analysis

5.7 Kernel principal component analysis

5.8 Singular value decomposition

References

Chapter 6. Quantum annealing and adiabatic quantum computing

Abstract

6.1 Schrödinger’s characterization of quantum

6.2 Quantum basics of annealing and adiabatic quantum computing

6.3 Delta function potential well and tunneling

6.4 Quantum memory and the no-cloning theorem

6.5 Basic structure of atoms and ions

6.6 Overview of qubit fabrication

6.7 Trapped ions

6.8 Super-conductance and the Josephson junction

6.9 Quantum dots

6.10 D-wave adiabatic quantum computers and computing

6.11 Adiabatic theorem

Reference

Copyright

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List of figures

Figure 4.6 Tensor vector space. 72

Figure 4.7 Operations involving tensors. 75

Figure 4.8 Tensor product of Hilbert spaces. 76

Figure 5.1 Polyadic graph involving matrix operations. 83

Figure 5.2 Illustration of identical operands in polyadic graph. 86

Figure 5.3 Bloch sphere. 87

Figure 6.1

Figure 6.2

Bound state and scattering state tunneling effect. (A) Bound state, (B) Scattering state, (C) Normalized bound state solution, (D) Tunneling effect. 108

Cooper pair tunneling. Based on (Frolov, 2014), (A) Frolov Barrie, (B) Cooper Pair Tunneling, (C)

Voltage-Current Dead Zone. 118

Figure 6.3 (A) Parallel Circuit, (B) Energy levels within cosine type boundary. 120

Figure 6.4 Adiabatic process following Zwiebach, (A)

Hamiltonian, (B) Energy Separation, (C) Path

Crossing Hamiltonian, (D) Non Crossing Paths. 126

Figure 7.1 Simple elements in H1 ⊗ H2 and pure states.

Figure 8.1 Polyadic graph for subgroup in Banach algebra.

and right ideals.

8.3

Figure 8.4 Graph for homomorphisms involving C* algebra.

Figure 8.5 GNS construction between A C* algebra and a Hilbert space. GNS, Gelfand-Naimark-Segal.

Figure 10.1 General and specific algebraic quotient spaces. (A) Mappings in quotient space, (B) quotient space, line in plane.

circular interval.

Figure 10.5 Manifold with two charts and transition mapping.

Möbius stick figure.

Figure 10.1

Two types of lattices. (A) Square pattern lattice, (B) more general lattice.

Figure 10.1

Hopf fibration S0 → S1 → S1. (A) Original circle; (B) Twist applied to circle; (C) Folding operation.

11.2 Lie group MSA graph.

Figure 12.1

Figure 13.1 Spectra for operator L in l1 and its dual in l∞ .

Figure 14.1 Canonical hypergroup polyadic graph.

Figure 14.2 Partial isometry mappings.

Figure 14.3 Polyadic graph for partial isometry [U, U*] nonzero.

Figure 14.4 Polyadic graph for a symplectic vector space.

Figure 15.1

Ladder operators for Fock spaces. (A) Bosonic Fock space, (B) Allowable operations in Fermionic Fock space.

Figure 15.2 Young diagram obtained from the Maya diagram (see Example 15.9).

Figure 15.3 Young diagram to find Maya diagram.

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independence, he knew so well how to preserve an appearance of opposition even in his eulogies and flatteries, that public opinion did not cease to favour him. Besides, the most illustrious defenders of the vanquished cause, Pompey, Cato, Scipio, Bibulus, were dead. Of all those who had occupied with honour the highest posts under the old government, he alone remained; consequently it was usual to regard him as the last representative of the republic. We know that on the Ides of March, Brutus and his friends, after having struck down Caesar, while brandishing their bloody swords, called for Cicero. They seemed to recognize him as the head of their party, and to give him the credit of the bloodshed that they had just committed.

It was, then, circumstances rather than his own will that caused him to play so great a part in the events which followed the death of Caesar.

I shall narrate later[60] how he was led to engage in that struggle with Antony, in which he was to perish. I shall show that it was not of himself and voluntarily that he began it. He had quitted Rome and did not wish to return. He thought that the time for resistance under legal forms had passed, that it was necessary to oppose to Antony’s veterans good soldiers rather than good reasons, and he was not wrong. Convinced that his part was finished, and that that of the men of war was about to begin, he set out for Greece, when a gale cast him on the coast of Rhegium. Thence he repaired to the port of Velia, where he found Brutus, who was also preparing to leave Italy, and it was he who, always scrupulous, always the enemy of violence, asked him to make once again an effort to rouse the people, and once more to attempt the struggle on the basis of law. Cicero yielded to the request of his friend, and although he had little hope of success, he hastened to return to Rome there to offer this last battle. This was the second time that he came, like Amphiaraüs, “to throw himself alive into the gulf.”

Brutus did him a good service that day. The desperate enterprise in which he engaged him, almost in spite of himself, could not be useful to the republic, but was serviceable to Cicero’s glory. This was perhaps the grandest moment in his political life. In the first place, we have the pleasure and almost the surprise of finding him firm and decided. He seems to have freed himself from all that hesitation that usually troubled his conduct; and besides, it was scarcely possible to

hesitate then, for the question had never been so clearly stated. At each new development of events, the parties stood out more clearly. For the first time, the ambition of Caesar, of which everybody knew, by rallying round the Roman aristocracy all those who wished, like it, to preserve the ancient institutions, had enlarged the limits of this party and modified its programme. By taking into itself new elements it changed in name as in character; it became the party of order, the party of honest men, of the “optimates.” It is thus that Cicero loves to name it. The meaning of this name was at first rather vague, after Pharsalia it became more precise. As at this moment there was no longer any doubt of the intentions of the conqueror, as he was seen to openly substitute his authority for that of the senate and people, the party that resisted him took the name proper to it, and which nobody could any longer refuse it; it became the republican party. The struggle was fairly begun between the republic and despotism. And, that doubt might be still less possible, despotism after Caesar’s death showed itself to the Romans under its least disguised and, so to say, most brutal form. A soldier without political genius, without distinction of manners, without greatness of soul, at once coarse, debauched and cruel, asserted by force his right to the inheritance of the great dictator. He did not take the trouble to hide his designs, and neither Cicero nor anybody else could be deceived any longer. It must have been a great relief to that mind usually so undecided and uncertain to see the truth so clearly, to be no longer perplexed by shadows, to have such a complete confidence in the justice of his cause, and after so much doubt and obscurity at last to fight in clear daylight. We feel that his mind is at ease! how much freer and more lively he is! what ardour there is in this old man, and what eagerness for the fight! None of the young men about him show so much decision as he, and he himself is assuredly younger than when he strove against Catiline or Clodius. Not only does he begin the struggle resolutely, but, what is more unusual with him, he pursues it to the end without giving way. By a strange contrast, the most dangerous enterprise that he had ever undertaken, and which was to cost him his life, was precisely that in which he best resisted his usual fits of discouragement and weakness.

Immediately on his return to Rome, while he was still inspired by the ardour that he had acquired at Velia from his conversations with Brutus, he went to the senate and ventured to speak there. The first

Philippic, compared with the others, appears timid and colourless; what courage, however, did it not need to pronounce it in that unconcerned city, before those frightened senators, at a few paces from the furious and threatening Antony, who by his spies heard all that was said against him! Cicero ended then as he had begun. Twice, at an interval of thirty-five years, he raised his voice alone, in the midst of a general silence, against a dreaded power which would not tolerate resistance. Courage, like fear, is contagious. The courage that Cicero showed in his speech awakened that of others. This freedom of speech surprised at first, then shamed those who kept silence. Cicero took advantage of this first revival, which was still rather hesitating, to assemble a few persons round him and find some defenders of the almost forgotten republic. Here was the difficulty. There were scarcely any republicans left, and the most determined had gone to join Brutus in Greece. All that could be done was to appeal to the moderates of all parties, to all those whom Antony’s excesses had shocked. Cicero adjured them to forget their old enmities and to reunite. “Now,” said he, “there is only one vessel for all honest men.”[61] Here we recognize his usual policy. It is again a coalition that he tries to form as at the time of his consulship. This part is clearly that for which he has most taste and which suits him best. By the pliability of his character and his principles he was fitter than anybody to reconcile opinions, and the habit he had of approaching all parties made him not a stranger to any, and he had friends everywhere. Thus his undertaking appeared at first to succeed very well. Several of Caesar’s generals readily listened to him, those especially who thought that, in the main, they lost less by remaining citizens of a free state, than by becoming subjects of Antony; and ambitious subalterns, like Hirtius and Pansa, who, after the master’s death, did not feel themselves strong enough to aim at the first place, and who would not be contented with the second. Unfortunately it was still but a collection of chiefs without soldiers, and never had there been more need of soldiers than at that moment. Antony was at Brundusium, where he was waiting for the legions he had sent for to Macedonia. Enraged by the unexpected resistance that he had met with, he proclaimed that he would avenge himself by pillage and slaughter, and he was known to be the man to do so. Every one thought that already he saw his house sacked, his estate parcelled out, his family proscribed. Fear reigned everywhere, men

trembled, hid themselves and fled. The most courageous sought on all sides for some one who might be called upon to defend the republic. No aid was to be hoped for but from Decimus Brutus, who occupied Cisalpine Gaul with some legions, or from Sextus Pompey, who was reorganizing his troops in Sicily, but this aid was distant and doubtful, and ruin was near and sure. In the midst of this general panic, the nephew of Caesar, the young Octavius, whom the jealousy of Antony, and the distrust of the republicans had up till then kept away, and who impatiently awaited the opportunity of making himself known, thought that this opportunity had come. He went through the environs of Rome calling to arms his uncle’s veterans who were settled there. His name, his liberality, the promises he lavished soon brought him soldiers. At Calatia, at Casilinum, he found three thousand in a few days. Then he addressed the leaders of the senate, offered them the support of his veterans, demanding for sole recompense that they would acknowledge him in the efforts he was about to make to save them. In such distress there was no means of refusing this help without which they would perish, and Cicero himself, who had at first shown some distrust, let himself be seduced at last by this young man who consulted him, flattered him, and called him father. When, thanks to him, they had been saved, when they saw Antony, abandoned by some of his legions, obliged to leave Rome where Octavius held him in check, the gratitude of the senate was as lavish as their fear had been great. The liberator was loaded with dignities and honours. Cicero, in his eulogies, raised him much above his uncle; he called him a divine young man raised up by heaven for the defence of his country: he stood surety for his patriotism and fidelity; imprudent words for which Brutus reproached him severely, and which the event was not long in falsifying!

The events that followed are too well known for me to have need of repeating them. Never had Cicero played a greater political part than at this moment; never had he better deserved that name of statesman that his enemies denied him. For six months he was the soul of the republican party, which was re-constituted at his call. “It was I, said he proudly, who gave the signal for this awakening,”[62] and he was right in saying so. His voice seemed to restore some patriotism and some energy to this unconcerned people. He made them once more applaud those grand names of country and liberty

that the Forum would soon hear no more. From Rome, the ardour gained the neighbouring townships, and gradually all Italy was roused. This, however, was not enough for him, he went still further to raise up enemies for Antony and defenders for the republic. He wrote to the proconsuls of the provinces and to the generals of the armies. From one end of the world to the other he chid the lukewarm, flattered the ambitious, and congratulated the energetic. He it was who incited Brutus, always undecided, to seize Greece. He applauded the bold stroke of Cassius, which made him master of Asia; he urged Cornificius to drive Antony’s soldiers from Africa; he encouraged Decimus Brutus to resist in Modena. The promises of support that he invited with so much earnestness arrived from all sides. Even enemies and traitors dared not openly refuse him their co-operation. Lepidus and Plancus made emphatic protestations of fidelity. Pollio wrote to him in a solemn tone “that he swears to be the enemy of all tyrants.”[63] On all sides his friendship is demanded, his support solicited, men put themselves under his protection. His Philippics, which, happily, he had not time to revise, are scattered through the whole world, very nearly as he spoke them, and with the vivacity of the first sketch, preserve traces of the interruptions and applause of the people. These passionate harangues carry everywhere the passion of these grand popular scenes. They are read in the provinces, they are devoured in the armies, and from the most distant countries evidence of the admiration they excite arrives to Cicero! “Your robe is even more fortunate than our arms,” says a victorious general to him, and adds, “In you the consular has conquered the consul.”[64] “My soldiers are yours,” wrote another to him.[65] The credit of all the good fortune of the republic was attributed to him. It was he who was congratulated and thanked for all the successes that were obtained. On the evening that the victory of Modena was known at Rome, the whole people went to his house to seek him, conducted him in triumph to the Capitol, and wished to hear from his own mouth an account of the battle. “This day,” he wrote to Brutus, “has repaid me for all my trouble.”[66]

This was the last triumph of Cicero and the republic. Success is sometimes more fatal to coalitions than reverses. When the common enemy, hatred of whom has united them, has been conquered, private dissensions break out. Octavius wished to weaken Antony in order to obtain from him what he wanted; he did not wish to destroy

him. When he saw him flying towards the Alps, he made overtures to him, and both together marched on Rome. From that time nothing remained for Cicero but “to imitate brave gladiators, and seek like them to die honourably.”[67] His death was courageous, whatever Pollio, who, having betrayed him, had an interest in calumniating him, may have asserted. I would rather believe the testimony of Livy, who was not one of his friends, and who lived at the court of Augustus: “Of all his misfortunes,” says he, “death is the only one that he bore like a man.”[68] This, it must be confessed, was something. He might have fled, and at one moment he tried to do so. He wished to set out for Greece, where he would have found Brutus; but after some days’ sailing with contrary winds, suffering from the sea, tormented above all by regrets and sadness, he lost heart for life, and was landed at Gaeta, and went back to his house at Formiae to die there. He had often thanked the gale that took him back to Velia, the first time that he wished to flee to Greece. This it was that gave him the opportunity to deliver his Philippics. The storm which drove him ashore at Gaeta has not been less serviceable to his fame. His death seems to me to redeem the weaknesses of his life. It is much for a man like him, who did not boast of being a Cato, to have been so firm at this terrible moment; the more timid he was by temperament the more I am touched at finding him so resolute in dying. Thus, when, in studying his history, I am tempted to reproach him with his irresolution and weakness, I think of his end, I see him as Plutarch has so well depicted him, “his beard and hair dirty, his countenance worn, taking his chin in his left hand as his manner was, and looking steadily at his murderers,”[69] and I no longer dare to be severe. Notwithstanding his defects he was an honest man, “who loved his country well,” as Augustus himself said on a day of sincerity and remorse. If he was sometimes too hesitating and feeble, he always ended by defending what he regarded as the cause of justice and right, and when that cause had been for ever conquered, he rendered it the last service it could claim from its defenders, he honoured it by his death.

II

CICERO’S PRIVATE LIFE

I

Those who have read Cicero’s correspondence with Atticus, and know what place questions of money occupy in these private communications, will not be surprised that I begin the study of his private life by endeavouring to estimate the amount of his fortune. The men of those days were as much concerned about money as the men of to-day, and it is perhaps in this that these two periods, which men have so often taken pleasure in comparing, most resemble each other.

It would be necessary to have at hand the account-books of Eros, Cicero’s steward, in order to set down with exactness the expenses of his household. All that we know with certainty on this subject is, that his father left him a very moderate fortune only, and that he increased this greatly, while we cannot say precisely to how much it amounted. His enemies were in the habit of exaggerating it in order to throw suspicion on the means by which it had been acquired, and it is indeed probable that if we knew the total it would appear to us considerable; but we must take care not to judge of it according to the ideas of our own time. Wealth is not an absolute thing; a man is rich or poor according to the position in which he lives, and it is possible that what would be wealth in one place would scarcely be a competency elsewhere. Now we know that at Rome wealth was far from being so evenly distributed as it is among us. Forty years before the consulship of Cicero, the tribune Philip said that, in that immense city, there were not two thousand persons who had a patrimony;[70] but these possessed all the public wealth. Crassus asserted that, in order to call himself rich, it was necessary for a man to be able to support an army out of his revenues, and we know that he was in a position to do so without inconvenience. Milo contrived to get into debt in a few years to the amount of more than seventy million sesterces (£560,000). Caesar, while still a private person, expended, at one time, one hundred and twenty million sesterces (£960,000) in order to make a present of a new Forum to the Roman

people. This outrageous extravagance implies immense fortunes. In comparison with these, we can understand that Cicero’s, which scarcely sufficed for the purchase of a house on the Palatine, and which the adornment of his Tusculan villa almost exhausted, must have appeared very moderate.

In what manner had he gained it? It is not without interest to know this in order to reply to the ill-natured reports that his enemies circulated. He says somewhere that the means by which a fortune was honestly made at Rome were commerce, contracting for public works and farming the taxes;[71] but these means, very convenient for people in haste to enrich themselves, could only be used by those who had no political ambition; they excluded from public honours, and consequently did not suit a man who aspired to govern his country. We do not see, either, that he acted like Pompey, who invested his funds in an important bank and shared in the profits; at least there remains no trace in his letters of undertakings of this nature. Nor could he think of making money out of his works. It was not the custom then for an author to sell his works to a bookseller; or rather, the trade of a bookseller, as we understand it now, scarcely existed. Usually those who wished to read or possess a book borrowed it of the author or of his friends, and had it copied by their slaves. When they had more copyists than they needed for their own use, they made them work for the public and sold the copies they did not want; but the author had nothing to do with the profits they drew from them. And finally, public offices could not have enriched Cicero; we know that they were less a means of making money than an occasion of expense and ruin, either by the price it was sometimes necessary to pay for them, or by the games and entertainments that were expected from those who had obtained them. It was only in the government of provinces that immense gains were made. It was on these gains that the ambitious nobles usually counted to repair the waste of their fortunes that the luxury of their private life and the profusion of their public life had caused. Now Cicero deprived himself of this opportunity by yielding to his colleague Antony the province that, according to custom, he ought to have governed after his consulship. It has been suspected, indeed, that he then made with him some bargain by which he reserved to himself a share in the handsome profits that he relinquished. If this bargain existed, which is doubtful, it is certain it was not kept. Antony pillaged his province,

but he pillaged it for himself alone, and Cicero drew nothing from it. Twelve years later, without having desired it, he was appointed proconsul of Cilicia. We know that he remained there only a year, and that, without doing any illegal act, and while securing the happiness of his subjects, he contrived to take back two million two hundred thousand sesterces (£17,600), which gives us an idea of what might be gained in the provinces when they were pillaged without scruple. Besides, this money did not profit Cicero; he lent part of it to Pompey, who did not return it, and it is probable that the civil war caused him to lose the rest, since he found himself without means at its close. We must seek, then, elsewhere for the origin of his fortune. If he had lived in our days we should have no trouble in learning whence it came. It would be sufficiently explained by his ability as an advocate. With an eloquence such as his, he would not fail now-a-days to enrich himself quickly at the bar; but at that time there was a law forbidding orators to accept any fee or present from those for whom they had pleaded (lex Cincia, de donis et muneribus). Although it was the work of a tribune, who had made it, says Livy, in the interest of the people,[72] it was at bottom an aristocratic law. By not allowing the advocate to draw a legitimate profit from his talent, it kept away from the bar those who had nothing, and reserved the exercise of this profession for the rich as a privilege, or rather it prevented it becoming really a profession. I think, however, that this law was always very imperfectly obeyed. As it could not provide against everything, it was scarcely possible for it to prevent the gratitude of clients finding some ingenious method to escape its severity. If they were really determined to pay in some manner for the services which they had received, it seems to me that the law could only with difficulty prevent it. In Cicero’s time, they did not fail to violate it openly. Verres told his friends that he had divided the money he brought back from Sicily into three parts; the most considerable was to corrupt his judges, the second to pay his advocates, and he contented himself with the third.[73] Cicero, who on this occasion laughed at Verres’ advocate, Hortensius, and at the sphynx that he had received on account, took care not to imitate him. His brother affirms that up to the time when he was a candidate for the consulship he had never asked anything from his clients.[74] Nevertheless, whatever scruples we may suppose him to have had, it is very difficult to admit that he had never profited by their good-will.

No doubt he refused the presents that the Sicilians wished to make him when he had avenged them on Verres; perhaps it would not have been prudent to accept them after such a notorious trial, which had drawn all eyes upon him, and made him powerful enemies; but some years afterwards I see that he allowed himself to accept the present made him by his friend Papirius Poetus, for whom he had just pleaded.[75] It consisted of some fine Greek and Latin books, and Cicero loved nothing so much as books. I notice also that when he had need of money, which happened sometimes, he preferred to apply to rich men whom he had defended. These were less harsh and more patient creditors to him than others, and it was natural that he should profit by their influence after having aided them by his eloquence. He tells us himself that he bought the house of Crassus with the money of his friends. Among them, P. Sylla, for whom he had just pleaded, alone lent him two million sesterces (£16,000). When he was attacked for this in the senate, Cicero got out of it with a joke; which proves that the lex Cincia was no longer much respected, and that those who infringed it had no great fear of being prosecuted.[76] It is very possible, then, that those nobles whose honour or fortune he had saved, that those towns or provinces that he had protected against greedy governors, that those foreign princes whose interests he had defended in the senate, above all, those rich societies of farmers of the taxes, through whose hands passed all the money that the world sent to Rome, and whom he served so vigorously by his reputation or his eloquence, had often sought and sometimes found an opportunity of testifying their gratitude. This generosity appears to us now-a-days so natural that we should scarcely blame Cicero for not having always rejected it; but we may be sure that, if he sometimes thought that he might accept it, he always did so with more moderation and reserve than the greater number of his contemporaries.

We know one of the most usual forms, and, as it seems, one of the most legal by which this generosity showed itself. It was the custom at Rome to pay, after death and by will, all debts of gratitude and affection contracted during life. This was a means that offered itself to the client of discharging his obligations to the advocate who had defended him, and it does not appear that the lex Cincia threw any obstacle in the way. We have nothing like it among ourselves. At that time, the father of a family who had natural heirs might withdraw

from his fortune any amount that he wished, and give his relations, his friends, and all who had been useful or agreeable to him, a good share of his estate. This custom had become an abuse. Fashion and vanity had come to have a large share in it. A man wished to appear to have many friends by inscribing the names of many persons in his will, and naturally the most illustrious were inscribed by preference. Sometimes people were brought together in it who seldom met anywhere else, and who must have been surprised to find themselves there. Cluvius, a rich banker of Puteoli, left his estate to Cicero and Caesar after Pharsalia.[77] The architect Cyrus placed among his heirs both Clodius and Cicero, that is to say, the two persons who most heartily detested each other in Rome.[78] This architect, no doubt, regarded it as an honour to have friends among all parties. It even happened that a man set down in his will people whom he had never seen. Lucullus augmented his immense wealth by bequests which unknown persons left him while he governed Asia. Atticus received a good number of legacies from people of whom he had never heard, and who only knew him by reputation. How much more then must a great orator like Cicero, to whom so many were under obligation, and of whom all Romans were proud, have been often the object of this posthumous liberality! We see in his letters that he was the heir of many persons who do not seem to have held a large place in his life. In general, the amounts left to him are not very large. One of the largest is that which he inherited from his old master the Stoic Diodotus, whom he had kept at his house till his death.[79] In recompense of this long-continued affection, Diodotus left him all his savings as a philosopher and teacher. They amounted to a hundred thousand sesterces (£800). The union of all these small legacies no doubt made up a considerable sum. Cicero himself values it at more than twenty million sesterces (£160,000).[80] It seems to me, therefore, that there is no doubt that these legacies, with the presents he may have received from the gratitude of his clients, were the chief sources of his wealth.

This wealth was composed of property of different kinds. He possessed, firstly, houses in Rome. Besides that which he inhabited on the Palatine, and that which he had from his father at Carinae, he had others in Argiletum and on the Aventine which brought him in an income of eighty thousand sesterces (£640).[81] He possessed numerous villas in Italy. We know of eight very important ones

belonging to him,[82] without reckoning those small houses (diversoria) that the nobles bought along the principal roads to have somewhere to rest when they went from one domain to another. He had also sums of money of which he disposed in different manners, as we see in his correspondence. We cannot estimate this part of his wealth with exactness; but according to the practice of the rich Romans of that time, it may be affirmed that it was not less than his houses or estates. One day when he is asking Atticus to buy him some gardens that he wishes, he says to him, in an off-hand way, that he thinks he may have about six hundred thousand sesterces (£4800) in his own hands.[83] We have here perhaps one of the most curious differences that distinguish that state of society from ours. Now-a-days scarcely any but bankers by profession handle such considerable sums of money. Our aristocracy has always affected to look down upon questions of finance. The Roman aristocracy, on the contrary, understood them well, and thought much about them. Their great wealth was used to further political ambition, and they did not hesitate to risk a part of it to gain adherents. The purse of a candidate for public honours was open to all who could be of use to him. He gave to the poorest, he lent to others, and sought to form with them bonds of interest which would attach them to his cause. Success usually followed those who had put the greatest number of men under obligations. Cicero, although less rich than the majority of them, imitated them. In his letters to Atticus he is almost always writing about bills and dates of maturity, and we see in them that his money circulated on all sides. He is in constant business relations, and as we should now say, has a running account with the greatest personages. Sometimes he lends to Caesar, and sometimes borrows of him. Among his numerous debtors are found persons of all ranks and fortunes, from Pompey to Hermogenes, who seems to have been a simple freedman. Unfortunately, counting them all, his creditors are still more numerous. Notwithstanding the example and advice of Atticus, he ill understood how to manage his fortune. He constantly had costly fancies. He would have at any price statues and pictures to adorn his galleries and give them the appearance of the gymnasia of Greece. He ruined himself to embellish his country houses. Generous out of season, we see him lending to others when he is constrained to borrow for himself. It is always when he is deepest in debt that he has the greatest desire to buy some new villa. He does not hesitate,

then, to apply to all the bankers of Rome; he goes to see Considius, Axius, Vectenus, Vestorius; he would even try to soften Caecilius, the uncle of his friend Atticus, if he did not know that he was inflexible. Nevertheless he bears his troubles with a light heart. The prudent Atticus tells him in vain that it is disgraceful to be in debt; but as he shares this disgrace with a great many people it seems light, and he is the first to joke about it. One day he told one of his friends that he was so much in debt that he would willingly enter into some conspiracy, if any one would receive him, but that since he had punished Catiline’s he inspired no confidence in others;[84] and when the first day of the month arrives, when payments become due, he is content to shut himself up at Tusculum and leave Eros or Tiro to argue with the creditors.

These embarrassments and troubles, of which his correspondence is full, make us think, almost in spite of ourselves, of certain passages in his philosophical works which appear rather surprising when we compare them with his mode of living, and which may easily be turned against him. Is it really this thoughtless prodigal, always ready to spend without consideration, who exclaimed one day in a tone of conviction that moves us: “Ye immortal gods, when will men understand what treasures are found in economy!”[85] How dared this ardent lover of works of art, this impassioned friend of magnificence and luxury, how dared he treat as madmen people who love statues and pictures too well, or build themselves magnificent houses? He stands self-condemned, and I do not wish to entirely absolve him; but while we pronounce on him a severe sentence, let us remember the times in which he lived, and let us think of his contemporaries. I will not compare him with the worst men, his superiority would be too evident; but among those who are regarded as the most honourable, he still holds one of the foremost places. He did not owe his wealth to usury like Brutus and his friends; he did not augment it by that sordid avarice with which Cato is reproached; he did not pillage the provinces like Appius or Cassius; he did not consent like Hortensius to take his share of this pillage. We must then acknowledge that, notwithstanding the blame we may lay upon him, he was more scrupulous and disinterested in money matters than others. In the main, his irregularities only injured himself,[86] and if he had too much taste for ruinous prodigality, at least he did not have recourse to scandalous gains in order to satisfy it. These

scruples honour him so much the more as they were then very rare, and few people have passed, without stain, through that greedy and corrupt society in the midst of which he lived.

II.

He does not deserve less praise for having been honourable and regular in his family life. These were virtues of which his contemporaries did not set him an example.

It is probable that his youth was austere.[87] He had firmly resolved to become a great orator, and that was not to be done without trouble. We know from himself how hard the apprenticeship to oratory then was. “To succeed in it, he tells us, a man must renounce all pleasures, avoid all amusements, say farewell to recreation, games, entertainments, and almost to intercourse with one’s friends.”[88] This was the price he paid for his success. The ambition by which he was devoured preserved him from the other passions, and sufficed him. His youth was completely taken up with study. When once these early years were passed the danger was less; the habit of work that he had formed, and the important affairs in which he was engaged might suffice to preserve him from all dangerous impulses. Writers who do not like him have vainly tried to find in his life traces of that licentiousness which was so common around him. The most ill-disposed, like Dio,[89] banter him about a clever woman, named Caerellia, whom he somewhere calls his intimate friend.[90] She was so in fact, and it appears that she was not wanting in influence over him. His correspondence with her was preserved and published. This correspondence was, it is said, rather free in tone, and seemed at first to give some occasion to the malicious; but it must be remarked, that Caerellia was much older than he; that, far from being a cause of dissension in his household, we only see her intervening to reconcile him with his wife,[91] in fact that their acquaintance seems to have begun in a common liking for philosophy;[92] a sedate origin which does not forebode unpleasing consequences. Caerellia was a learned lady whose conversation must have been very pleasing to Cicero. Her age, her education which was not that of ordinary women, put him at ease with her, and, as he was naturally quick at repartee, as, once excited by the animation of

conversation, he could not always govern and restrain his wit, and as, besides, by patriotism as by taste, he put nothing above that free and daring gaiety of which Plautus seemed to him the model, it may have happened that he wrote to her without ceremony those pleasantries “more spicy than those of the Attic writers, and yet truly Roman.”[93] Later, when these rustic and republican manners were no longer in fashion, when, under the influence of the gradually developing court life, the rules of politeness were being refined, and manners were becoming more ceremonious, the freedom of these remarks no doubt shocked some fastidious minds, and may have given rise to illnatured remarks. For our own part, of all that correspondence of Cicero which is now lost, the letters to Caerellia are those perhaps that we most regret. They would have shown us better than all the rest the habits of society, and the life of the fashionable world at that time.

It is thought that he was about thirty when he married. It was towards the end of Sulla’s rule, at the time of his first oratorical successes. His wife, Terentia, belonged to a rich and distinguished family. She brought him in dowry, according to Plutarch,[94] 120,000 drachmae (£4440), and we see that she possessed houses in Rome, besides a forest near Tusculum.[95] It was an advantageous marriage for a young man just beginning political life with more talent than fortune. Cicero’s correspondence does not give a very good impression of Terentia. We imagine her as an economical and orderly, but sharp and disagreeable housewife, with whom it was difficult to live at ease. She did not agree very well with her brotherin-law Quintus, and still less with Pomponia her sister-in-law, who, however, did not agree with anybody. She had that influence over her husband that a determined and obstinate woman always has over a careless and irresolute mind. For a long time Cicero left her absolute mistress of the household, he was very glad to shift on to somebody else those occupations that did not suit him. She was not without influence on his political life. She advised him to take energetic measures at the time of the great consulship, and later she embroiled him with Clodius, from dislike to Clodia, whom she suspected of wishing to allure him. As no gain came amiss to her, she succeeded in entangling him in some financial affairs, that Atticus himself, who was not over scrupulous, did not think very honourable; but there her power ended. She seems to have remained a stranger, and

perhaps to have been indifferent to her husband’s literary glory. In none of Cicero’s works, in which the names of his daughter, his brother, and his son recur so frequently, is there any mention of his wife. Terentia had no influence on his mind. He never confided to her his private opinions on the most serious affairs of life; he never admitted her to share in his opinions and beliefs. We have a curious proof of this in his correspondence. Terentia was devout, and devout to excess. She consulted soothsayers, she believed in prodigies, and Cicero did not take the trouble to cure her of this eccentricity. He seems even, somewhere, to make a singular distribution of labours between her and himself; he shows her respectfully serving the gods, while he is occupied in working for men.[96] Not only did he not disturb her devotion, but he showed a consideration for her which surprises us. When he was about to start for Pompey’s camp, he wrote to her: “At last I am free from that uneasiness and suffering that I experienced, and which caused you so much concern. The day after my departure I recognized the cause. During the night I threw off pure bile, and felt myself relieved as if some god had been my doctor. Evidently it was Apollo and Aesculapius. I beg you to return thanks to them with your usual piety and zeal.”[97] This is strange language in the mouth of that sceptic who wrote the treatise On the Nature of the Gods; but Cicero was, no doubt, one of those people, like Varro and many others, who while they make little use themselves of religious practices, think that they are not bad for the common people and for women. There has survived a whole book of letters from Cicero to Terentia, which contains the history of his household. What strikes one on opening it is that, as we get further on, the letters become shorter, the last are no more than short notes. And not only does the length of the letters diminish, but their tone is no longer the same, and marks of affection become more and more rare. We may then conclude that this affection was not of the kind that increases with time; that common life, which strengthens true personal unions, enfeebled this one. Instead of being strengthened, it was worn out by length of time. The earlier letters show an incredible passion, and this in spite of the fact that Cicero had been married nearly twenty years; but he was then very unfortunate, and it seems that misfortune makes people more tender, and that families feel the need of drawing closer when heavy blows fall on them. Cicero had just been condemned to exile. He departed very sorrowfully from

Rome, where he knew that his house was burnt, his friends persecuted, his family ill-treated. Terentia had behaved very energetically, she had suffered for her husband, and suffered with courage. On learning the manner in which she had been treated, Cicero wrote to her despairingly: “How wretched I am! And must a woman so virtuous, so honourable, so gentle, so devoted, be thus tormented for my sake!”[98] “Be assured, he tells her elsewhere, that I have nothing dearer than you. At this moment I think I see you, and cannot restrain my tears!”[99] He added with still more effusion, “Oh, my life, I would wish to see you again, and die in your arms!”[100] The correspondence then ceases for six years. It recommences at the time Cicero left Rome, to go and govern Cilicia, but the tone is very much changed. In the single letter remaining to us of this date, affection is replaced by business. It has to do with a legacy that had fallen in very opportunely for Cicero’s fortunes, and of the means of turning it to the best account. It is true he still calls Terentia his very dear and much-desired wife, suavissima atque optatissima, but these words have the appearance of polite phrases. However, he shows a great desire to see her again, and asks her to come as far as she can and wait for him.[101] She went as far as Brundusium, and, by a lucky chance, she entered the town at the same time that her husband arrived in the harbour; they met and embraced on the Forum. It was a happy moment for Cicero. He returned with the title of imperator and the hope of a triumph; he found his family united and joyous. Unfortunately the civil war was just about to break out. During his absence parties had broken with each other; they were about to come to blows, and immediately after his arrival Cicero was obliged to make choice between them, and to take his side. This war not only injured his political position, it was fatal to his private happiness. When the correspondence recommences, after Pharsalia, it becomes extremely matter-of-fact. Cicero returns to Italy, and lands again at Brundusium, no longer triumphant and happy, but vanquished and desperate. This time he does not wish to see his wife again, although he never had more need of consolation. He keeps her at a distance, and that without much ceremony. “If you come, he tells her, I do not see how you can be useful to me.”[102] What makes this answer more cruel is, that, at the same time, he sent for his daughter, and consoled himself with her conversation. As to his wife she gets nothing more from him than short notes, and he has the courage to tell her that he

does not make them longer because he has nothing to say.[103] At the same time he refers her to Lepta, Trebatius, Atticus, and Sicca, to learn what decisions he has taken. This shows clearly enough that she no longer enjoyed his confidence. The only mark of interest he still gives her is to ask her, from time to time, to take care of her health, a superfluous recommendation, since she lived more than a hundred years! The last letter he addressed to her is just what a man would write to his steward to give an order. “I expect to be at Tusculum the 7th or 8th of the month, he says; be careful to prepare everything. I shall, perhaps, have several persons with me, and very likely we shall remain some time. Let the bath be ready, and let nothing be wanting that is necessary to comfort and health.”[104] A few months afterwards, the separation which this tone foreshadows, took place between the couple. Cicero divorced Terentia after more than thirty years of marriage, and when they had children and grandchildren.

What motives drove him to this disagreeable extremity? Probably we do not know them all. Terentia’s disagreeable temper must have often caused those little quarrels in the household which, repeated continually, end by wearing out the most steadfast affection. About the time that Cicero was recalled from exile, and a very few months after he had written those passionate letters of which I have spoken, he said to Atticus: “I have some domestic troubles of which I cannot write to you,” and added, so that he might be understood: “My daughter and my brother love me still.”[105] We must think that he had good reason to complain of his wife, to leave her thus out of the list of persons by whom he thought himself loved. It has been suspected that Terentia was jealous of the affection Cicero showed to his daughter. This affection was somewhat excessive and so exclusive as possibly to wound her, and she was not a woman to endure this without complaint. We may believe that these dissensions prepared and led up to the divorce, but they were not the final cause of it. The motive was more prosaic and vulgar. Cicero justified it by the waste and misuse of his money by his wife, and several times he accused her of having ruined him for her own benefit. One of the most curious characteristics of that age was that the women appear as much engaged in business and as interested in speculations as the men. Money is their first care. They work their estates, invest their funds, lend and borrow. We find one among Cicero’s creditors, and

two among his debtors. Only, as they could not always appear themselves in these financial undertakings, they had recourse to some obliging freedman, or some shady business man, who watched their interests and profited by their gains. Cicero, in his speech for Caecina, coming across a character of this sort, whose business was to devote themselves to the fortune of women, and often to make their own at their expense, depicts him in these terms: “There is no man one finds oftener in ordinary life. He is the flatterer of women, the advocate of widows, a pettifogging lawyer by profession, a lover of quarrels, a constant attendant at trials, ignorant and stupid among men, a clever and learned lawyer among women, expert in alluring by the appearance of a false zeal and a hypocritical friendship, eager to render services sometimes useful but rarely faithful.”[106] He was a marvellous guide for women tormented with the desire of making a fortune; so Terentia had one of these men about her, her freedman, Philotimus, a clever man of business, but not very scrupulous, who had succeeded at this trade, since he was rich and himself possessed slaves and freedmen. In early days Cicero often made use of him, doubtless at the request of Terentia. It was he who got for him at a low price some of the property of Milo when he was exiled. It was a profitable piece of business, but not in very good taste, and Cicero, who felt it to be so, speaks of it with some shame. On his departure for Cilicia he left the administration of part of his property to Philotimus, but he was not long in repenting of it. Philotimus, like the steward of a great house, paid less attention to his master’s interests than to his own. He kept for himself the profits he had made on the property of Milo, and on Cicero’s return presented him an account in which he figured as his creditor for a considerable amount. “He is a marvellous thief!”[107] said Cicero, in a rage. At this time his suspicions did not go beyond Philotimus; when he returned from Pharsalia he saw clearly that Terentia was his accomplice. “I have found my household affairs, said he to a friend, in as bad a state as those of the republic.”[108] The distress in which he found himself at Brundusium made him distrustful. He looked more closely into his accounts, a thing that was not usual with him, and it was not difficult for him to discover that Terentia had often deceived him. At one time she had retained sixty thousand sesterces[109] (£480) out of her daughter’s dowry. This was a handsome profit, but she was not negligent of small gains. Her husband caught her one day pocketing

two thousand sesterces (£16) out of a sum he had asked her for.[110] This rapacity completed the irritation of Cicero, whom other causes no doubt had soured and hurt for a long time. He resigned himself to the divorce, but not without sorrow. We do not break with impunity the bonds that habit, in the absence of affection, ought to draw closer. At the moment of separation, after so many happy days have been passed together, so many ills supported in common, there must always be some memory which troubles us. What adds to the sadness of these painful moments is, that when we wish to withdraw and isolate ourselves in our sorrow, business people arrive; we must defend our interests, reckon and discuss with these people. These discussions, which had never suited Cicero, made him then suffer more than usual. He said to the obliging Atticus, when asking him to undertake them for him: “The wounds are too recent, I could not touch them without making them bleed.”[111] And as Terentia continued making difficulties, he wished to put an end to the discussion by giving her all she asked. “I would rather,” he wrote, “have cause to complain of her than become discontented with myself.”[112]

We can well understand that the wags did not fail to make merry on the subject of this divorce. It was a just retaliation after all, and Cicero had too often laughed at others to expect to be spared himself. Unfortunately he gave them, a short time after, a new opportunity of amusing themselves at his expense. Notwithstanding his sixty-three years he thought of marrying again, and he chose a very young girl, Publilia, whom her father, when dying, confided to his guardianship. A marriage between guardian and ward is a real stage marriage, and the guardian generally has the worst of it. How did it happen that Cicero, with his experience of the world and of life, allowed himself to be drawn into this imprudent step? Terentia, who had to revenge herself, repeated everywhere that he had fallen violently in love with this young girl; but his secretary, Tiro, asserted that he had only married her in order to pay his debts with her fortune, and I think we must believe Tiro, although it is not usual that, in this kind of marriage, the elder is also the poorer. As might be foreseen, trouble was not long in appearing in the household. Publilia, who was younger than her step-daughter, did not agree with her, and, it appears, could not conceal her joy when she died. This was an unpardonable crime in Cicero’s eyes, and he refused to see her again.

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Table of Contents

Copyright

Notices

List of figures

II

CICERO’S PRIVATE LIFE

I

II.