Lagrange Quotes

What is history? Any thoughts, Webster?' 'History is the lies of the victors,' I replied, a little too quickly. 'Yes, I was rather afraid you'd say that. Well, as long as you remember that it is also the self-delusions of the defeated. ... 'Finn?' '"History is that certainty produced at the point where the imperfections of memory meet the inadequacies of documentation." (quoting Patrick Lagrange)

{Comment to Delambre on chemist Antoine Lavoisier's execution during the French Revolution} Only a moment to cut off that head and a hundred years may not give us another like it.

Expansion History, and you came to the description of the triple sunrises you can see when you're hanging in Lsel Station's Lagrange point, and you thought, At last, there are words for how I feel, and they aren't even in my language―> Yes, Mahit says. Yes, she does. That ache: longing and a violent sort of self-hatred, that only made the longing sharper. We felt that way.

Newton's work on gravity led to the discovery of the Lagrange point, a place where opposing forces cancel one another out, and a body may remain at relative rest. This is where I am right now; the forces in my life confound one another. Better, for the moment, to be here and now, without history or future.

There are two classes of people who hide themselves: the criminal who flees punishment, and the saint who through humility wishes to remain unknown.

the nearer we approach to God, the more we are drawn by Him.

Let us perform all our actions with the thought that God dwells in us. We shall thus be His temples, and He Himself will be our God, dwelling in us (cf. Eph. 15: 3).

Genuine strength of will, the effect of divine grace, is drawn from humble, trusting, and persevering prayer.

Talent by itself does nothing but make a bit of noise.

A reproach given with great kindness is often well received, whereas when given with sharpness it produces no results. Thus Christ tells us: “Learn of Me, because I am meek and humble of heart.

Lagrange, in one of the later years of his life, imagined that he had overcome the difficulty (of the parallel axiom). He went so far as to write a paper, which he took with him to the Institute, and began to read it. But in the first paragraph something struck him that he had not observed: he muttered: 'Il faut que j'y songe encore', and put the paper in his pocket.' [I must think about it again].

Accordingly, we find Euler and D'Alembert devoting their talent and their patience to the establishment of the laws of rotation of the solid bodies. Lagrange has incorporated his own analysis of the problem with his general treatment of mechanics, and since his time M. Poinsot has brought the subject under the power of a more searching analysis than that of the calculus, in which ideas take the place of symbols, and intelligent propositions supersede equations.

Things are more like they are now...than they have EVER been before!

If I had inherited a fortune I should probably not have cast my lot with mathematics

The life of God is above the past, the present, and the future; it is measured by the single instant of immobile eternity.

We read in Ecclesiasticus also: “In all thy works remember thy last end, and thou shalt never sin.

With grace we can overcome it, because, as the Council of Trent says, quoting St. Augustine: “God never commands the impossible; but in giving us His precepts, He commands us to do what we can, and to ask for the grace to accomplish what we cannot do.

Happy the old people who after long experience and many trials reach this superior simplicity of true wisdom, which they had glimpsed from a distance in their childhood! With this meaning it can be said that a beautiful life is a thought of youth realized in maturity.

It is a matter for considerable regret that Fermat, who cultivated the theory of numbers with so much success, did not leave us with the proofs of the theorems he discovered. In truth, Messrs Euler and Lagrange, who have not disdained this kind of research, have proved most of these theorems, and have even substituted extensive theories for the isolated propositions of Fermat. But there are several proofs which have resisted their efforts.

There was yet another disadvantage attaching to the whole of Newton’s physical inquiries, ... the want of an appropriate notation for expressing the conditions of a dynamical problem, and the general principles by which its solution must be obtained. By the labours of LaGrange, the motions of a disturbed planet are reduced with all their complication and variety to a purely mathematical question. It then ceases to be a physical problem; the disturbed and disturbing planet are alike vanished: the ideas of time and force are at an end; the very elements of the orbit have disappeared, or only exist as arbitrary characters in a mathematical formula.

As the bee knows how to find honey in flowers, the gift of wisdom draws lessons of divine goodness from everything.

St. Augustine wrote: “Two loves have built two cities: the love of self even to the despising of God, the city of the earth; the love of God even to the despising of self, the city of God. One glorifies itself in self, and the other in the Lord. One seeks its glory from men, the other places its dearest glory in God, the witness of its conscience. The one in the pride of its glory walks with head high; the other says to its God: ‘Thou art my glory, and it is Thou who dost lift up my head.’ The former in its victories lets itself be conquered by its passion to dominate; the latter shows us its citizens united in charity, mutual servants, tutelary governors, obedient subjects. The former loves its own strength in its princes; the latter says to God: ‘Lord, Thou art my only strength, I shall love Thee.’ “968

The nearer a soul is to God, the more it deserves our esteem; the closer the ties that bit it to us, the more sensible is our love for it, and the more whole-hearted should be the devotion we show in all that concerns family, country, vocation, and friendship. Thus, instead of destroying patriotism, charity exalts it, as we see in the case of St. Joan of Arc or St. Louis.

In commenting on the Stagirite, St. Thomas discards Averroistic interpretations contrary to revealed dogma, on Providence, on creation, on the personal immortality of the human soul. Hence it can be said that he "baptizes" Aristotle's teaching, that is, he shows how the principles of Aristotle, understood as they can be and must be understood, are in harmony with revelation. Thus he builds, step by step, the foundations of a solid Christian philosophy.

However, in 1930 (published in 1931), Godel produced his bombshell, which eventually showed that the formalists' dream was unattainable! He demonstrated that there could be no formal system F, whatever, that is both consistent (in a certain 'strong' sense that I shall describe in the next section) and complete-so long as F is taken to be powerful enough to contain a formulation of the statements of ordinary arithmetic together with standard logic. Thus, Godel's theorem would apply to systems F for which arithmetical statements such as Lagrange's theorem and Goldbach's conjecture, as described in 2.3, could be formulated as mathematical statements.

Expansion History, and you came to the description of the triple sunrises you can see when you're hanging in Lsel Station's Lagrange point, and you thought, At last, there are words for how I feel, and they aren't even in my language―> Yes, Mahit says. Yes, she does. That ache: longing and a violent sort of self-hatred, that only made the longing sharper.

The genius of Laplace was a perfect sledge hammer in bursting purely mathematical obstacles; but, like that useful instrument, it gave neither finish nor beauty to the results. In truth, in truism if the reader please, Laplace was neither Lagrange nor Euler, as every student is made to feel. The second is power and symmetry, the third power and simplicity; the first is power without either symmetry or simplicity. But, nevertheless, Laplace never attempted investigation of a subject without leaving upon it the marks of difficulties conquered: sometimes clumsily, sometimes indirectly, always without minuteness of design or arrangement of detail; but still, his end is obtained and the difficulty is conquered.

The pig was soon dissected and its blood filled the bucket in the bottom of which a patch of sky was reflected darkly. It had surrendered to the vortex of life and his breathing.

We should note that mortification prepares for mental prayer, and the latter, in its turn, facilitates mortification. Therefore, prayer and mortification influence one another. Mortification and patience prepare for prayer through the purification and detachment they produce in us. They enable the person to take flight toward God, and this flight is prayer itself.

St. Thomas Aquinas deeply loved this beautiful chant thus understood. It is told of him that he could not keep back his tears when, during Compline of Lent, he chanted the antiphon: “In the midst of life we are in death: whom do we seek as our helper, but Thou, O Lord, who because of our sins art rightly incensed? Holy God, strong God, holy and merciful Savior, deliver us not up to a bitter death; abandon us not in the time of our old age, when our strength will abandon us.” This beautiful antiphon begs for the grace of final perseverance, the grace of graces, that of the predestined. How it should speak to the heart of the contemplative theologian, who has made a deep study of the tracts on Providence, predestination, and grace!

The great masters of modern analysis are Lagrange, Laplace, and Gauss, who were contemporaries. It is interesting to note the marked contrast in their styles. Lagrange is perfect both in form and matter, he is careful to explain his procedure, and though his arguments are general they are easy to follow. Laplace on the other hand explains nothing, is indifferent to style, and, if satisfied that his results are correct, is content to leave them either with no proof or with a faulty one. Gauss is as exact and elegant as Lagrange, but even more difficult to follow than Laplace, for he removes every trace of the analysis by which he reached his results, and studies to give a proof which while rigorous shall be as concise and synthetical as possible.

Napoleon:How s it that,although you say so much about the Universe,you say nothing about its Creator Laplace:No sire,I had no need of that hypotesis Lagrange:Ah,but it is such a good hypotesis:it explains so many things! Laplace:Indeed,Sire,Monsieur Lagrange has,with his usual sagacity,put his finger on he precise difficulty with the hypotesis:it explains everything,but predicts nothing

Lagrange was born in Turin (now Italy), but his family was partly French ancestry on his father's side, who was originally wealthy, managed to squander all the family's fortune in speculations, leaving his son with no inheritance. Later in life, Lagrange described this economic catastrophe as the best thing that had ever happened to him: "Had I inherited a fortune I would probably not have cast my lot with mathematics.

We could start, perhaps, with the seemingly simple question, What is History? Any thoughts, Webster?’ ‘History is the lies of the victors,’ I replied, a little too quickly. ‘Yes, I was rather afraid you’d say that. Well, as long as you remember that it is also the self-delusions of the defeated. Simpson?’ Colin was more prepared than me. ‘History is a raw onion sandwich, sir.’ ‘For what reason?’ ‘It just repeats, sir. It burps. We’ve seen it again and again this year. Same old story, same old oscillation between tyranny and rebellion, war and peace, prosperity and impoverishment.’ ‘Rather a lot for a sandwich to contain, wouldn’t you say?’ We laughed far more than was required, with an end-of-term hysteria. ‘Finn?’ ‘“History is that certainty produced at the point where the imperfections of memory meet the inadequacies of documentation.” ’ ‘Is it, indeed? Where did you find that?’ ‘Lagrange, sir. Patrick Lagrange. He’s French.

When one day Lagrange took out of his pocket a paper which he read at the Académe, and which contained a demonstration of the famous Postulatum of Euclid, relative to the theory of parallels. This demonstration rested on an obvious paralogism, which appeared as such to everybody; and probably Lagrange also recognised it such during his lecture. For, when he had finished, he put the paper back in his pocket, and spoke no more of it. A moment of universal silence followed, and one passed immediately to other concerns.

If there is no silence in our soul and the voice of the world and the passions agitate it, we cannot hear the interior word of our Master. If we habitually take pleasure in our own way of seeing things and do not wish to receive counseling from anyone, we shall hear, above all else, ourselves

St. Augustine says: “God who created you without yourself, will not sanctify you without yourself.” Our consent is needed and likewise our obedience to the precepts. God’s help is given us, he says again, not that our will should do nothing, but that it may act in a salutary and meritorious manner. Actual grace is constantly offered to us for the accomplishment of the duty of the present moment, just as air comes constantly into our lungs to permit us to breathe.

Obscure faith enlightens us somewhat like the night, which, though surrounding us with shadows, allows us to see the stars, and by them the depths of the firmament. There is here a mingling of light and shade which is extremely beautiful. That we may see the stars, the sun must hide, night must begin. Amazingly, in the obscurity of night we see to a far greater distance than in the day; we see even the distant stars, which reveal to us the immense expanse of the heavens.

Un antico scrittore disse che l'aritmetica e la geometria sono le ali della matematica; Credo si possa dire senza parlare metaforicamente che queste due scienze sono il fondamento e l'essenza di tutte le scienze che si occupano di quantità. Non solo sono le fondamenta, sono anche, per così dire, le pietre di copertura; poiché, ogni volta che si è arrivati a un risultato, per usare quel risultato, è necessario tradurlo in numeri o in righe; tradurlo in numeri richiede l'aiuto dell'aritmetica, tradurlo in linee richiede l'uso della geometria.

We must begin to detach ourselves from earthly goods in order to grasp clearly the following truth often uttered by St. Augustine and St. Thomas: ‘Contrary to spiritual goods, material goods divide men, because they cannot belong simultaneously and integrally to a number.’ A number of persons cannot possess integrally and simultaneously the same house, the same field, the same territory; whence dissensions, quarrels, lawsuits, wars. On the contrary, spiritual goods, like truth, virtue, God Himself, can belong simultaneously and integrally to a number; many may possess simultaneously the same virtue, the same truth, the same God who gives Himself wholly to each of us in Communion. Therefore, whereas the unbridled search for material goods profoundly divides men, the quest for spiritual goods unites them. It unites us so much the more closely, the more we seek these superior goods. And we even possess God so much the more, the more we give Him to others. When we give away money, we no longer possess it; when, on the contrary, we give God to souls, we do not lose Him; rather we possess Him more. And should we refuse to give Him to a person who asks for Him, we would lose Him.

Here enters a question: Does the human individual exist to serve society (communism), or does society exist to serve the individual (liberalism)? Communism and liberalism are two extremes. Between and above these extremes runs the golden middle way. The in­dividual, in temporal matters, serves society; but in eternal things he rises above civil society, since he is a fellow citizen of the saints, a member of the household of God. In defense of his country the citizen must be willing even to shed his blood. But civil authority, on the otherhand, while its proxi­mate goal is the well-being of society, has as its ultimate goal that eternal life which is the end of all human activity. Man’s active life, then, his lower and external life, is subordinated to society. But man’s contemplative life, his higher and in­ternal life, transcends civil life. Here we note the distinction between “individual” and “person.” The animal is an individual, but not a person. Man is both an individual and a person. Man, as an individual, is subordinated to society, whereas society is subordinated to man as a person. Thus in the spiritual order (as person) man is bound to provide first for himself, whereas in the temporal order (as individual) man is praiseworthy when he is generous in providing for his neighbor. Again, virginity excels matri­mony, because divine values surpass human values. And pri­vate spiritual good stands higher than common civil good. Here too lies the reason why the secrets of man’s heart are not really parts of the universe, and hence cannot naturally be known. [...] Thus in the spiritual order (as person) man is bound to provide first for himself, whereas in the temporal order (as individual) man is praiseworthy when he is generous in providing for his neighbor. […] And pri­vate spiritual good stands higher than common civil good.

In the present, in the very instant in which it is committed, venial sin deprives the soul of a precious grace. In that instant, grace was offered us to make progress in perfection, to be charitable, fervent, and industrious. If we had corresponded, our merit would have increased and for all eternity we would have contemplated God more intensely face to face. We would have loved Him more. Now this grace has been lost by our neglect, our laziness, and our limited charity. You will say, "But I can find the moment, the occasion to gain back the good that I lost." On the contrary, the answer is "no." You will not be able to revcver the quarter hour you wasted. Not even God, with all His power, would be able to restore it. This grace, a thousand times more precious than the universe, has been lost forever.

I see London, I see France I see Emily’s underpants.

It sometimes happens that mathematical methods conceived in the abstract turn out later to be so well suited to a particular application that they might have been written especially for it. When he was wrestling with the problems of general relativity, Albert Einstein came across the tensor calculus, invented 50 years earlier by Curbastro Gregorio Ricci and Tullio Levi-Civita, and saw that it was exactly what he needed. James enlisted a method that had been created in the mid-eighteenth century by Joseph-Louis Lagrange.

Lagrange points. These are gravitationally neutral positions in space.

A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P…

Luc Comtat sprach davon, dass der Nizza-Salat ein Klassiker sei, aber unverschämt oft vollkommen verdorben werde und bis zur Lächerlichkeit verhunzt. Dabei sei das Gericht so typisch französisch wie noch was. Eines der ältesten Basisrezepte reiche bis ins Jahr 1900 zurück, und es sei wohl in Paris erfunden worden, nicht an der Küste – von daher gehe es um die Sehnsucht nach dem Meer und nicht um die Küste selbst. Das erntete jede Menge Zustimmung. Albin nickte mit. Er nahm an, dass das angebracht und besser so wäre. »Ihr müsst die Seele des Salates verstehen«, predigte Comtat. »Ihr wollt die Küste schmecken, das Salz des Meeres. Ihr wollt die Erinnerung an den Sonnenbrand auf dem Rücken. Und es ist egal, wo ihr an der Riviera seid, ihr bekommt überall einen ganz anders angerichteten Niçoise. Das ist das Tolle. Ihr seid völlig frei. Aber ihr müsst an die Basics denken, die braucht es einfach.« Damit deutete er auf einige vorbereitete Zutaten und zählte auf: »Salat, Thunfisch, Tomaten, Kartoffeln, Sardellen, Basilikum, Eier, grüne Bohnen, Kapern, Oliven, Olivenöl.« Manche, erklärte der Koch, würden marinierte Artischockenherzen dazunehmen, andere wiederum schwarze Oliven aus Les Baux favorisieren oder Anchovis.

France Talk and Frogs’ Legs

The goal of society constituted in this way is consequently the common good, which is superior to the proper good of each individual, despite what individualism claims. The common good, nevertheless, ought not to absorb the proper good as communism claims. "The common good of the multitude is greater and more divine than that of an individual" (De Regno, Ch. IX). It is peace, the tranquility of order in the city or the nation.

The Church is intolerant in principle because she believes; she is tolerant in practice because she loves. The enemies of the Church are tolerant in principle, because they do not believe, and intolerant in practice because they do not love.

All we are saying, is give peas a chance.” And then she sang it again, really loud. “All we are saying, is give peas a chance.” It was a really annoying song, but the next thing I knew, all the teachers joined in. “All we are saying, is give peas a chance.” Then the whole lunchroom was singing that stupid pea song! It was totally embarrassing. It almost made me want to eat some peas just to shut them up. “I’ll tell you what,” I said to Ms. LaGrange. “If I eat a pea, will you tell me what ‘YAWYE’ means?” She was thinking it over. “Just one pea?” she asked. “Yeah, one pea.” “Okay,” she agreed. “Let’s see you eat one pea, Mister A.J.” Everybody started cheering. Ms. LaGrange picked up a pea with a spoon. She held it up to my mouth. Everybody

Lagrange’s father, once Treasurer of War for Sardinia, married Marie-Thérèse Gros, the only daughter of a wealthy physician of Cambiano, by whom he had eleven children. Of this numerous brood only the youngest, Joseph-Louis, born on January 25, 1736, survived beyond infancy.

It is the purification of the intellect which prepares for contemplation.

St. Thomas, following Aristotle, teaches that the intelligible being, the intelligible reality, existing in sense objects is the first object of the first act of our intellect, i. e.: that apprehension which precedes the act of judging. Listen to his words: “The intellect’s first act is to know being, reality, because an object is knowable only in the degree in which it is actual. Hence being, entity, reality, is the first and proper object of understanding, just as sound is the first object of hearing.

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During NASA’s first fifty years the agency’s accomplishments were admired globally. Democratic and Republican leaders were generally bipartisan on the future of American spaceflight. The blueprint for the twenty-first century called for sustaining the International Space Station and its fifteen-nation partnership until at least 2020, and for building the space shuttle’s heavy-lift rocket and deep spacecraft successor to enable astronauts to fly beyond the friendly confines of low earth orbit for the first time since Apollo. That deep space ship would fly them again around the moon, then farther out to our solar system’s LaGrange points, and then deeper into space for rendezvous with asteroids and comets, learning how to deal with radiation and other deep space hazards before reaching for Mars or landings on Saturn’s moons. It was the clearest, most reasonable and best cost-achievable goal that NASA had been given since President John F. Kennedy’s historic decision to land astronauts on the lunar surface. Then Barack Obama was elected president. The promising new chief executive gave NASA short shrift, turning the agency’s future over to middle-level bureaucrats with no dreams or vision, bent on slashing existing human spaceflight plans that had their genesis in the Kennedy, Johnson, Nixon, Ford, Carter, Reagan, Bush, Clinton, and Bush White Houses. From the starting gate, Mr. Obama’s uncaring space team rolled the dice. First they set up a presidential commission designed to find without question we couldn’t afford the already-established spaceflight plans. Thirty to sixty thousand highly skilled jobs went on the chopping block with space towns coast to coast facing 12 percent unemployment. $9.4 billion already spent on heavy-lift rockets and deep space ships was unashamedly flushed down America’s toilet. The fifty-year dream of new frontiers was replaced with the shortsighted obligations of party politics. As 2011 dawned, NASA, one of America’s great science agencies, was effectively defunct. While Congress has so far prohibited the total cancellation of the space agency’s plans to once again fly astronauts beyond low earth orbit, Obama space operatives have systematically used bureaucratic tricks to slow roll them to a crawl. Congress holds the purse strings and spent most of 2010 saying, “Wait just a minute.” Thousands of highly skilled jobs across the economic spectrum have been lost while hundreds of billions in “stimulus” have been spent. As of this writing only Congress can stop the NASA killing. Florida’s senior U.S. Senator Bill Nelson, a Democrat, a former spaceflyer himself, is leading the fight to keep Obama space advisors from walking away from fifty years of national investment, from throwing the final spade of dirt on the memory of some of America’s most admired heroes. Congressional committees have heard from expert after expert that Mr. Obama’s proposal would be devastating. Placing America’s future in space in the hands of the Russians and inexperienced commercial operatives is foolhardy. Space legend John Glenn, a retired Democratic Senator from Ohio, told president Obama that “Retiring the space shuttles before the country has another space ship is folly. It could leave Americans stranded on the International Space Station with only a Russian spacecraft, if working, to get them off.” And Neil Armstrong testified before the Senate’s Commerce, Science & Transportation Committee that “With regard to President Obama’s 2010 plan, I have yet to find a person in NASA, the Defense Department, the Air Force, the National Academies, industry, or academia that had any knowledge of the plan prior to its announcement. Rumors abound that neither the NASA Administrator nor the President’s Science and Technology Advisor were knowledgeable about the plan. Lack of review normally guarantees that there will be overlooked requirements and unwelcome consequences. How could such a chain of events happen?

Actual grace is constantly offered to us for the accomplishment of the duty of the present moment, just as air comes constantly into our lungs to permit us to breathe.

The greatest things often lie concealed in the most insignificant, as in a mustard seed, or in the tiny trickle which is the beginning of a mighty river.

St. Augustine remarked that it was more glorious for God to obtain good out of evil than to create out of nothing: it is greater to convert a sinner by giving him grace than to make a whole universe, Heaven and earth, out of nothing.

Thus trial causes hope to grow, and hope does not deceive us, for God does not abandon those who trust Him.

St. Thomas sums up all this briefly: “Now the aspect under which our neighbor is to be loved, is God, since what we ought to love in our neighbor is that he may be in God. Hence it is clear that it is specifically the same act whereby we love God, and whereby we love our neighbor. Consequently the habit of charity extends not only to the love of God, but also to the love of our neighbor.

He humbled Himself... even to the death of the cross. For which cause God also hath exalted Him, and hath given Him a name which is above all names.” Phil. 2:8 f.

a store called Emma-town. We’d tie up our horses and hang out. The wilder youths in the community would go to the LaGrange Theater. Watching movies, of course, was something that was preached against.

LaGrange County, near the town of LaGrange, Indiana. It is the second largest Amish community in the country, but to us it was always just home. The first Amish settlers moved into the Shipshewana – LaGrange County area in 1844, having moved from Pennsylvania, and their presence seeped into every part of the community. If you head in any direction you will find yourself driving along country roads dotted with Amish homes.

Cuando Lavoisier subió a la, guillotina, Lagrange expresó su indignación por la estupidez de la ejecución. "Bastará sólo un momento para que su cabeza caiga, y quizá sea necesario un centenar de años, para que se produzca otra igual".

Proneness to forget God causes our memory to be as if immersed in time, whose relation to eternity, to the benefits and promises of God, it no longer sees. This defect inclines our memory to see all things horizontally on the line of time that flees, of which the present alone is real, between the past that is gone and the future that is not yet. Forgetfulness of God prevents us from seeing that the present moment is also on a vertical line which attaches it to the single instant of immobile eternity, and that there is a divine manner of living the present moment in order that by merit it may enter into eternity. Whereas forgetfulness of God leaves us in this banal and horizontal view of things on the line of time which passes, the contemplation of God is like a vertical view of things which pass and of their bond with God who does not pass. To be immersed in time, is to forget the value of time, that is to say, its relation to eternity.

It is a famous theorem first proved by the great (Italian-) French mathematician Joseph L. Lagrange in 1770 that every number is, indeed, the sum of four squares.

To illustrate the nature of this theandric reciprocity, Thomas invokes, as an example, the physical touch of Jesus’s hand: “he wrought divine things humanly, as when he healed the leper with a touch.” The touch of a human being is not in itself miraculous, and even in Jesus this human action is not humanly healing. The miraculous fact of the healing power of this human touch, rather, as Reginald Garrigou-Lagrange puts it, “proceeds from God as the principal cause and from Christ’s human nature as the instrumental cause.” Jesus works divine things humanly. More ultimately, Jesus wills the divine will of salvation humanly. And so he wills theandrically in the sense that what he wills has an “infinite value” that “derives from the divine suppositum that is the agent which operates”. The deifying effects of the Incarnation are thus contingent on the theandric fact of the interpenetrating unity of divine-human operations.

Like the original concept, the stormrider had rectangular blades, sixteen of them radiating out from the hub, each one a flat lattice of struts twenty-five kilometers long, made from the toughest steelsilicon fibers the Commonwealth knew how to manufacture. Twenty-three kilometers of them were covered by an ultra-thin silvered foil, giving a total surface area of over one thousand eight hundred square kilometers for the solar wind to impact on. Even in an ordinary solar system environment that would have produced a considerable torque. In the Half Way system the stormrider was positioned at the Lagrange point between the red star and its neutron companion, right in the middle of the plasma current, where the ion density was orders of magnitude thicker than any normal solar wind. The power the stormrider produced when it was in the thick of the flow was enough to operate the wormhole generator. But it couldn’t simply sit at the Lagrange point producing electricity continuously; that would have been too much like perpetual motion. As the waves of plasma pushed against it, they exerted an unremitting pressure on the blades that blew the stormrider away from the Lagrange point out toward the neutron star. So for five hours the two sets of blades would turn in opposite directions, generating electricity for the Port Evergreen wormhole that was delivered via a zero-width wormhole. The stormrider also stored some of the power, so that at the end of the five hours when it was out of alignment, it had enough of a reserve to fire its onboard thrusters, moving itself even farther out of the main plasma stream where the pressure was reduced. From there it chased a simple fifteen-hour loop back around through open space to the Lagrange point, where the cycle would begin again.

True strength of will is calm; in calmness it is persevering so that it does not become discouraged by momentary lack of success or by any wounds received. No one is conquered until he has given up the struggle. And he who works for the Lord puts his confidence in God and not in himself.982

Let us remember that false prudence is tin, true acquired prudence is silver, infused prudence is gold, and the inspirations of the gift of counsel are diamonds, of the same order as the divine light. “He that followeth Me walketh not in darkness, but shall have the light of life.”1339

Thus talent sometimes wishes to correct genius, as if the eaglet wished to teach the eagle to fly.

In your patience you shall possess your souls.” Luke 21:19

Charity is patient.” I Cor. 13:4 Patience, says St. Thomas,1360 is a virtue attached to the virtue of fortitude, which hinders a man from departing from right reason illumined by faith by yielding to difficulties and to sadness. It makes him bear the evils of life with equanimity of soul, says St. Augustine,1361 without allowing himself to be troubled by vexations.

Meekness disarms the violent.

She writes: “I see nothing and I see all; certitude is obtained in the darkness;”1166 that is, I see nothing determinate, but I see all the divine perfections united, fused in an ineffable manner in the eminence of the Deity.

No one can know the true meaning of the language of spiritual writers if he is unable to explain it theologically; and, on the other hand, no one can know the sublimity of theology if he is ignorant of its relations to mysticism.

depends on the principle formulated by Aristotle and often recalled by St. Thomas: “The terms of language are the signs of our ideas, and our ideas are the similitude of realities.

It has been said that if a little learning withdraws a person from religion, great learning brings him back to it.956

St. Gregory the Great says: “Men ought by prayer to dispose themselves to receive what Almighty God from eternity has decided to give them.”1096

Mighty men of science and mighty deeds. A Newton who binds the universe together in uniform law; Lagrange, Laplace, Leibnitz with their wondrous mathematical harmonies; Coulomb measuring our electricity... Faraday, Ohm, Ampère, Joule, Maxwell, Hertz, Röntgen; and in another branch of science, Cavendish, Davy, Dalton, Dewar; and in another, Darwin, Mendel, Pasteur, Lister, Sir Ronald Ross. All these and many others, and some whose names have no memorial, form a great host of heroes, an army of soldiers – fit companions of those of whom the poets have sung... There is the great Newton at the head of this list comparing himself to a child playing on the seashore gathering pebbles, whilst he could see with prophetic vision the immense ocean of truth yet unexplored before him...

Sophie Germain’s paper, ‘Recherches sur la théorie des surfaces élastiques’, written in 1815 and published in 1821, won her a prize of a kilogram of gold from the French Academy of Sciences in 1816. The paper contained some significant errors, but became the basis for work on the subject by Lagrange, Poisson, Kirchoff, Navier and others. Sophie Germain is probably better known for having made one of the first significant breakthroughs in the study of Fermat’s last theorem. She proved that if x, y and z are integers satisfying x5 + y5 = z5, then at least one of x, y and z has to be divisible by 5. More generally, she showed that the same was true when 5 is replaced by any prime p such that 2p + 1 is also a prime.

Man will be fully a person, a per se subsistens and a per se operans, only in so far as the life of reason and liberty dominates that of the senses and passions in him; otherwise he will remain like the animal, a simple individual, the slave of events and circumstances, always led by something else, incapable of guiding himself; he will be only a part, without being able to aspire to be a whole... Personality, on the contrary, increases as the soul rises above the sensible world and by intelligence and will binds itself more closely to what makes the life of the spirit. The philosophers have caught sight of it, but the saints especially have understood, that the full development of our poor personality consists in losing it in some way in that of God, who alone possesses personality in the perfect sense of the word, for He alone is absolutely independent in His being and action.

Hello. Special Infirmary, please.’ He was surprised to hear Journe’s voice. The professor had turned out in person. ‘Have you had time to examine my customer? What do you think of him?’ A clear reply would have relieved him somewhat, but old Journe was not a man to provide clear answers. He launched into a long speech at the other end of the line, full of technical terms, the upshot of which was that it was 60 per cent likely that Lagrange was play-acting, but unless he slipped up, it might be a few weeks before they would be able to prove this scientifically. ‘Is Doctor Pardon still there?’ ‘He’s about to leave.’ ‘What’s Lagrange doing now?’ ‘He’s quite meek and mild. He allowed himself to be put to bed, and started talking to the nurse in a childish voice. He burst into tears and told her people had threatened to hit him, that everyone was against him, and it had been like this all his life.’ ‘Can I see him tomorrow?’ ‘Yes, whenever you like.’ ‘I’d just like a quick word with Pardon.’ And to the latter: ‘So, what do you think?’ ‘Nothing new to report. I’m not entirely of the same mind as the professor, but he’s more competent than me, and it’s years since I practised psychiatry.’ ‘But you have your own idea?’ ‘I’d prefer to wait a few hours before talking about it. The case is too serious to give a snap judgement. Aren’t you going home to bed now?’ ‘Not yet. I don’t think I’ll be getting any sleep tonight.

Lagrange points.

Sophie Germain had taught herself calculus at a young age. The daughter of a wealthy family, she had become entranced by mathematics after reading a book about Archimedes in her father’s library. When her parents found out that she loved mathematics and was staying up late at night to work on it, they took away her candles, left her fire unlit, and confiscated her nightgowns. Sophie persisted. She wrapped herself in quilts and worked by the light of stolen candles. Eventually her family relented and gave her their blessing. Germain, like all women of her era, was not permitted to attend university, so she continued to teach herself, in some cases by obtaining lecture notes from the courses at the nearby École Polytechnique using the name Monsieur Antoine-August Le Blanc, a student who had left the school. Unaware of his departure, academy administrators continued to print lecture notes and problem sets for him. She submitted work under his name until one of the school’s teachers, the great Lagrange, noticed the remarkable improvement in Monsieur Le Blanc’s previously abysmal performance. Lagrange requested a meeting with Le Blanc and was delighted and astonished to discover her true identity.

Like Lagrange, Michelson himself had already contributed unwittingly to the new system – in this case with an experimental result. In 1887 he and his colleague Edward Morley had observed that the speed of light relative to an observer remains constant when the observer moves.

is sweet,” he said. “You must have a favorite fruit, right?

person.

Hello, in regard to St. Catherine of Genoa, says: “In the life of the saints, and especially in the life of the contemplative saints, there is a succession of incomprehensible steps: they hesitate, they vacillate, they move ahead, they turn back, they change their paths. One has the impression that they are wasting time. It seems that the mysterious ways through which they are led never finish. God teaches them humility and makes them understand their impotence and nothingness” (Hello, Physiognomy of the Saints, p. 310).

The love of God, far from supposing lovableness in those it loves, creates it in them through pure benevolence.

Humility conceived in this manner is founded upon truth, especially on this truth, namely, that there is an infinite distance between the Creator and the creature. The more we realize this distance in a living and concrete way, the humbler we are. However elevated a creature may be, this chasm always remains infinite; and the more we elevate ourselves, the more evident this becomes. Hence, the most elevated is the humblest because he is the most illumined.

When Our Lord asked St. John of the Cross: “What do you want as a reward?” he answered: “To be despised and to suffer for your love.

St. Anselm has excellently described the levels of humility: to acknowledge that under certain aspects we are worthy of contempt; to accept being so; to confess that we are so; to wish that our neighbor believe this; to bear it patiently when this is said of us; to accept, without reserve, being treated as a person worthy of contempt; to wish to be treated in this way.

The goodness and beauty of God are infinitely superior to anything we can imagine. Thus, we can love Him more than we can know Him, and until we see Him face to face, love is more perfect than knowledge.

Man will be fully a person, a per se subsistens and a per se operans, only in so far as the life of reason and liberty dominates that of the senses and passions in him; otherwise he will remain like the animal, a simple individual, the slave of events and circumstances, always led by something else, incapable of guiding himself; he will be only a part, without being able to aspire to the whole.

To develop one’s individuality is to live the egoistical life of the passions, to make oneself the centre of everything, and end finally by being the slave of a thousand passing goods which bring us a wretched momentary joy. Personality, on the contrary, increases as the soul rises above the sensible world and by intelligence and will binds itself more closely to what makes the life of the spirit.

There will be only saints in heaven, whether they enter there immediately after death or after purification in purgatory. No one enters heaven unless he has that sanctity which consists in perfect purity of soul. Every sin though it should be venial, must be effaced, and the punishment due to sin must be borne or remitted, in order that a soul may enjoy forever the vision of God, see Him as He sees Himself, and love Him as He loves Himself.

The virtue of religion, which renders to God the worship due Him, is also inferior to the theological virtues; it is meritorious only by reason of the charity that animates it. If we should forget this, we would perhaps become more attentive to worship, to the liturgy, than to God Himself, to the figures rather than to the reality, to the manner in which we ought to say an Our Father or a Credo rather than to the sublime meaning of these prayers: the service of God would take precedence over the love of God.

that everybody has to stop talking.