People From St Petersburg

"Music is a pastime, a relaxation from more serious occupations."

"I am not a Jacob wrestling with God, but a Job lying on his dung-hill. I have assimilated Western thought and its clarity, but, in fact, I am solidly rooted in the passive Eastern nature and remain rebellious to any action. The book, the cell, the presence at the altar and at lengthy church ceremonies, and above all the solitude and withdrawal from the world -- this is the atmosphere which suits me; it is there that I feel like a fish in the water. I cannot lead an active and contemplative life at the same time. You know how much I love the Jesuits, but their ideal (to unite contemplation with action) is not within my means."

"When I feel overwhelmed by misfortune, the greatest joy that the Lord can give me is to go to the altar, to put my forehead against it (as on the day of my ordination to the priesthood), and to feel the presence of the only reality. Not only does calm return, but my body seems to be annihilated; the only true life begins, the life of that which is intangible.""

"If the Soviet Government orders me to act against my conscience, I do not obey. As for teaching the Catechism, the Catholic Church holds that children must be taught their religion, no matter what the law says. Conscience is above the law. No law which is against the conscience can bind."

"My whole life has been based on two principles: the love of the Church to which I am united, and the love of my country, which I adore. If I do not care whether I am sentenced to ten years imprisonment or to be shot, it is not because I am a fanatic... Since I joined the Catholic Church my sole object has been to reconcile my country to that Church which I believe to be the One True Church."

"The true messianism of the Russian Church is not what the Slavophiles have imagined, but it is the example of suffering. It is in this way that she shows that she is the continuation of Christ in this world."

"So they march with sovereign tread… Behind them limps the hungry dog, and wrapped in wild snow at their head carrying a blood-red flag soft-footed where the blizzard swirls, invulnerable where bullets crossed – crowned with a crown of snowflake pearls, a flowery diadem of frost, ahead of them goes Jesus Christ."

"Hell and damnation, life is such fun with a ragged greatcoat and a Jerry gun!"

"Blok was probably the greatest Russian poet since Pushkin; although internationally less well known than Rilke and Valéry, he is of their stature and importance. He revolutionized Russian versification by making use of a purely accentual technique. He knew, as so few now know, that only the poetry of suffering – whether it is a poetry of joy or not – can be great. His own poetry, for which he burnt himself out, demonstrates this."

"O, my Russia! O, wife! The long road is clear to us to the point of pain. Our road – like a Tatar arrow of ancient will has pierced our breast."

"What message, years of conflagration, have you: madness or hope? On thin cheeks strained by war and liberation bloody reflections still remain."

"When rowan leaves are dank and rusting And rowan berries red as blood, When in my palm the hangman's thrusting The final nail with bony thud, When, over the foul flooding river, Upon the wet grey height, I toss Before my land's grim looks, and shiver As I swing here upon the cross, Then, through the blood and weeping, stretches My dying sight to space remote; I see upon the river’s reaches Christ sailing to me in a boat."

"Grip your gun like a man, brother! Let's have a crack at Holy Russia, Mother Russia with her big, fat arse! Freedom, freedom! Down with the cross!"

"My spirit is old; and some black lot awaits me On my long road. Some dream accurst, inveterate, suffocates me Still with its load. So young – yet hosts of dreadful thoughts appal me, Sick and opprest. Come! and from shadowy phantoms disenthral me, Friend."

"Abstract art.. searches for new ways to achieve harmony and equilibrium."

"Alexander, were you looking for me?"

"That’s the saddest loss of all, to go on for a few weeks, a few days, a night, a minute, and think everything is still all right when the structure you’ve built your life on has crumbled. We should have been mourning you, but instead we made plans, went to work, dreamed, loved, not knowing you were already behind us.”"

"Ask yourself three questions and you will know who you are. Ask 'What do you believe in? What do you hope for? But most important - ask what do you love?"

"(Tatiana nervously looked down at the present.) "Thank you". Gifts were not something she was used to. Wrapped gifts? Unheard of, even when they came wrapped only in plain brown paper."

"There will be only one standard, the standard of survival at all cost, and it will be up to you to say at what price survival.Hold your head high, and if you are going to go down, go down knowing you have not in any way compromised your soul."

"After being relegated to an obscure mid-tier university, blocked from leading journals and openly mocked by his peers, including his former mentor, the late 19th century German mathematician found refuge for his groundbreaking work on infinities in, of all places, the Roman Catholic Church … Catholic theologians welcomed Cantor's ideas, which provided a workable way of understanding mathematical infinities, as evidence that humans could grasp the infinite and could also, therefore, have a greater understanding of God, himself infinite. What a welcome relief this must have been to the chronically depressed Cantor! As John D. Barrow writes in The Infinite Book: A Short Guide to the Boundless, Timeless and Endless, Cantor "started to tell his friends that he had not been the inventor of the ideas about infinity that he had published. He was merely a mouthpiece, inspired by God to communicate parts of the mind of God to everyone else.""

"Why was Cantor so vehemently opposed to infinitesimals? In his valuable essay, "The Metaphysics of the Calculus," Abraham Robinson suggests that Cantor already had enough problems trying to defend transfinite numbers. It seems likely that, consciously or otherwise, Cantor deemed it politically wise to go along with orthodox mathematicians on the question of infinitesimals. Cantor's stance might be compared to that of a pro-marijuana Congressional candidate who advocates harsh penalties for the sale or use of heroin."

"I discovered the works of Euler and my perception of the nature of mathematics underwent a dramatic transformation. I was de-Bourbakized, stopped believing in sets, and was expelled from the Cantorian paradise."

"[T]here exist no other sets than finite and denumerably infinite sets and continua... [I]n mathematics we can create only finite sequences, further by means of... 'and so on' the order type ω, but only consisting of equal elements... but no other sets. Cantor and his disciples... think they have knowledge of all sorts of further sets; their fundamental principle... comes to about the same as the axiomaticians. ...[T]his principle is unjustified and... we assert that the several paradoxes of the 'Mengenlehre'... have no right to exist... [I]t would have been the duty of Cantorians, immediately to reject a notion which gives rise to contradictions, because it is... not built... mathematically."

"Mathematics is in its development entirely free and is only bound in the self-evident respect that its concepts must both be consistent with each other, and also stand in exact relationships, ordered by definitions, to those concepts which have previously been introduced and are already at hand and established. In particular, in the introduction of new numbers, it is only obligated to give definitions of them which will bestow such a determinacy and, in certain circumstances, such a relationship to the other numbers that they can in any given instance be precisely distinguished. As soon as a number satisfies all these conditions, it can and must be regarded in mathematics as existent and real."

"No one shall expel us from the Paradise that Cantor has created."

"As for the mathematical infinite, to the extent that it has found a justified application in science and contributed to its usefulness, it seems to me that it has hitherto appeared principally in the role of a variable quantity, which either grows beyond all bounds or diminishes to any desired minuteness, but always remains finite. I call this the improper infinite [das Uneigentlich-unendliche]."

"What I assert and believe to have demonstrated in this and earlier works is that following the finite there is a transfinite (which one could also call the supra-finite), that is an unbounded ascending ladder of definite modes, which by their nature are not finite but infinite, but which just like the finite can be determined by well-defined and distinguishable numbers."

"Infinity, in its first form (the improper-infinite) presents itself as a variable finite [veranderliches Endliches]; in the other form (which I call the proper infinite [Eigentlich-unendliche]) it appears as a thoroughly determinate [bestimmtes] infinite."

"In 1874 the German mathematician Georg Cantor made the startling discovery that there are more irrational numbers than rational ones, and more transcendental numbers than algebraic ones. In other words, rather than being oddities, most real numbers are irrational; and among irrational numbers, most are transcendental."

"A set is a Many that allows itself to be thought of as a One."

"I have never proceeded from any Genus supremum of the actual infinite. Quite the contrary, I have rigorously proved that there is absolutely no Genus supremum of the actual infinite. What surpasses all that is finite and transfinite is no Genus; it is the single, completely individual unity in which everything is included, which includes the Absolute, incomprehensible to the human understanding. This is the Actus Purissimus, which by many is called God. I am so in favor of the actual infinite that instead of admitting that Nature abhors it, as is commonly said, I hold that Nature makes frequent use of it everywhere, in order to show more effectively the perfections of its Author. Thus I believe that there is no part of matter which is not — I do not say divisible — but actually divisible; and consequently the least particle ought to be considered as a world full of an infinity of different creatures."

"The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it in its highest form has created and sustains us, and in its secondary transfinite forms occurs all around us and even inhabits our minds."

"The totality of all alephs cannot be conceived as a determinate, well-defined, and also a finished set. This is the punctum saliens, and I venture to say that this completely certain theorem, provable rigorously from the definition of the totality of all alephs, is the most important and noblest theorem of set theory. One must only understand the expression "finished" correctly. I say of a set that it can be thought of as finished (and call such a set, if it contains infinitely many elements, "transfinite" or "suprafinite") if it is possible without contradiction (as can be done with finite sets) to think of all its elements as existing together, and to think of the set itself as a compounded thing for itself; or (in other words) if it is possible to imagine the set as actually existing with the totality of its elements."

"This view [of the infinite], which I consider to be the sole correct one, is held by only a few. While possibly I am the very first in history to take this position so explicitly, with all of its logical consequences, I know for sure that I shall not be the last!"

"My theory stands as firm as a rock; every arrow directed against it will return quickly to its archer. How do I know this? Because I have studied it from all sides for many years; because I have examined all objections which have ever been made against the infinite numbers; and above all because I have followed its roots, so to speak, to the first infallible cause of all created things."

"The transfinite numbers are in a certain sense themselves new irrationalities and in fact in my opinion the best method of defining the finite irrational numbers is wholly dissimilar to, and I might even say in principle the same as, my method described above of introducing transfinite numbers. One can say unconditionally: the transfinite numbers stand or fall with the finite irrational numbers; they are like each other in their innermost being; for the former like the latter are definite delimited forms or modifications of the actual infinite."

"I entertain no doubts as to the truths of the transfinites, which I recognized with God’s help and which, in their diversity, I have studied for more than twenty years; every year, and almost every day brings me further in this science."

"What I declare and believe to have demonstrated in this work as well as in earlier papers is that following the finite there is a transfinite (transfinitum)--which might also be called supra-finite (suprafinitum), that is, there is an unlimited ascending ladder of modes, which in its nature is not finite but infinite, but which can be determined as can the finite by determinate, well-defined and distinguishable numbers."

"Mathematics, in the development of its ideas, has only to take account of the immanent reality of its concepts and has absolutely no obligation to examine their transient reality."

"The essence of mathematics lies entirely in its freedom."

"If there is some determinate succession of defined whole real numbers, among which there exists no greatest, on the basis of this second principle of generation a new number is obtained which is regarded as the limit of those numbers, i.e. is defined as the next greater number than all of them."

"Er ist aber in Kopenhagen geboren, von israelitischen Eltern, die der dortigen portugisischen Judengemeinde."

"Every transfinite consistent multiplicity, that is, every transfinite set, must have a definite aleph as its cardinal number."

"The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent otherworldly being, in Deo, where I call it the Absolute Infinite or simply Absolute; second when it occurs in the contingent, created world; third when the mind grasps it in abstracto as a mathematical magnitude, number or order type."

"There is no doubt that we cannot do without variable quantities in the sense of the potential infinite. But from this very fact the necessity of the actual infinite can be demonstrated."

"The old and oft-repeated proposition "Totum est majus sua parte" [the whole is larger than the part] may be applied without proof only in the case of entities that are based upon whole and part; then and only then is it an undeniable consequence of the concepts "totum" and "pars". Unfortunately, however, this "axiom" is used innumerably often without any basis and in neglect of the necessary distinction between "reality" and "quantity", on the one hand, and "number" and "set", on the other, precisely in the sense in which it is generally false."

"In order for there to be a variable quantity in some mathematical study, the domain of its variability must strictly speaking be known beforehand through a definition. However, this domain cannot itself be something variable, since otherwise each fixed support for the study would collapse. Thus this domain is a definite, actually infinite set of values. Hence each potential infinite, if it is rigorously applicable mathematically, presupposes an actual infinite."

"I realize that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers."

"In re mathematica ars proponendi quaestionem pluris facienda est quam solvendi."