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Marco Fulvio Barozzi
Water, water, teach me the lesson of flowing
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De Rerum Natura: atomism and reason

Almost nothing is known of Titus Lucretius Carus (98 or 96-55 or 53 BC): in the writings of the contemporaries there is no trace, apart from a letter from Cicero, in which the great intellectual mentions the posthumous edition of De Rerum Natura that he would edit. Another source mentioning Lucretius is four centuries later: St. Jerome, in his Chronicon, argues that the poet would die suicide at 42 because of the madness induced by a love filter (poculum). To accredit his thesis, St. Jerome refers to the work of Suetonius De Viris Illustribus, considered worthy of credit. In reality, Suetonius, known as the gossip of history, was a lover of anecdotes, and does not always seem to be a reliable source. Moreover, the sources does not agree with what Elius Donatus (IV AD), master of Jerome, said, namely that Lucretius would have died when Virgil (born in 70 BC) wore the toga virilis at the age of 15, i.e. in 55 BC., at the age of forty-four. The only biographical information handed down directly from antiquity is limited to these few vague hints. Unknown is also the place of birth, which however some scholars believe to be Pompeii or Herculaneum, both for the presence of an Epicurean cenacle in the latter city, governed by Filodemus. Moreover, the gens Lucretia, of Etruscan origin, was widely represented in Pompeii, as attested by numerous inscriptions. The Lucretii of Pompeii were land owners of modest wealth, dedicated to studies, lovers of fine arts, especially devotees to those two deities, Venus and Mars, which the poet himself shows to care.

Since it is difficult to clearly trace the poet's biography, all that we can do is to draw his soul and inspiration from what reveals his work, De Rerum Natura, at the same time an illustration of the Epicurean doctrine and a true cosmogonic poetic masterpiece .

In Lucretius, the didactic purpose is deliberate. Its greatness consists precisely in having been able to compose an admirable synthesis of science and art. Such was the judgment of Cicero, also an epicurean, fascinated by the idea of ​​concluding the poem left unfinished. Virgil himself was a great admirer of Lucretius' work, defining, in Book II of the Georgics, «happy the one who could investigate the reason of things» and regretting that he could not himself write a cosmogonic poem. Another great poet, Ovid, said of Lucretius that his verses would end only with the end of the universe. Yet, in spite of the praise of the contemporaries, Lucretius' work was not widely diffused: the manuscripts received so far date back to an archetype of the 4th or 5th century, but the most notable were discovered only in the 15th century by the Italian humanist Poggio Bracciolini.

In the first two of the five books by which the work is composed, Lucretius exposes the atomic theory of Epicurus, in turn derived from that of Democritus. My article deals with these two books.

The poem opens with the invocation to Venus and Mars, followed by the first hymn to Epicurus, whose philosophical thought inspires the work. Lucretius highlights the aspect of the epicurean doctrine that he considers most important, namely that of having destroyed the superstition and terror of the gods, revealing the true nature of natural phenomena.

The life of man, in front of the eyes of all, shamefully stood
Knocked down on the ground, crushed under oppressive Religion,
That the head of the regions of the sky showed,
With a terrifying gaze, looming above the mortals:
Then first a man of Greece mortal eyes against
It dared to raise, first to stand up against;
Him, neither reputation of the gods, nor lightning, nor, with menacing
Murmur, Heaven held back, but even more aggressive
Strength of the soul excite, so that he longed to swerve,
First, the closed bars of the doors of Nature.
Therefore the vigorous strength of the soul had victory, and far away
He advanced, beyond the walls of the world that throw flames,
And all the Infinite covered with reason and with the soul:
From there he reports, victorious, what may have birth,
What cannot, for what law at last has, everything,
Determined field of action, and deep-set boundaries:
Because Religion, thrown under the feet, in turn
It is crushed, victory makes us equal to Heaven.

Lucretius claims that the Epicurean doctrine is not unholy because it nullifies the role of the gods in natural events. On the contrary, false religion is harmful, as shown by the episode of Iphigenia, the virgin sacrificed to the deities to obtain that the Greek fleet retained by the calm sea could sail from the port of Aulis. According to Epicurus, the gods may exist, but they must not care for mortal things. Resuming this concept, Lucretius affirms that the prize or the punishment does not come from the gods, but from the serenity of one's conscience or from remorse, and wisdom is the only source of happiness in life. Therefore, the men, who see in many natural manifestations the expression of a divine will that does not exist, are wrong:

_The principle of which will start for us from this:
That nothing ever comes from nothing by divine will.
Of course, fear dominates all mortals:
Because they see many phenomena occurring on earth and in heaven
Of which in no way can the causes be detected,
And they believe that they are produced by divine will.
Then, when we have seen that nothing can be created
From nothing, then from here we will penetrate more surely
What we seek, and whence everything can be created
And in what way all things occur without interventions of gods.

So Lucretius, starting from the principle that nothing is created from nothing, exposes numerous examples that are consistent with this principle.

_In fact, things taken from nothing, any of them
Would be born from every other, nor would they need germs.

The logical consequence of the principle of the eternity of matter is that things cannot vanish into nothingness, just as they cannot come from nothing. The poet prompts for the conservation of the matter that composes the universe, saying that things are constituted by aggregations of particles that can separate into the elementary constituents and then re-aggregate to give rise to different forms of nature. Thus he expresses the concept of the creative force of nature which manifest itself in a perpetual renewal of the world.

Lucretius highlights how some phenomena occur without our visual sense perceives the presence of matter, giving the wrong impression that they are produced from nothing. He shows some examples, like the wind which, although invisible, produces tangible effects, sometimes even disastrous, or smell, or heat, or cold, or the voices that produce sensations that can be revealed by our senses and therefore must be made up of material elements.

_Furthermore, we perceive the various smells of things and yet
We never discern them as they come to the nostrils,
Neither do we see the heat emanations, nor can we grasp
With the eyes the cold, nor does it happen to see the sounds;
And yet all these things need to be made
Of a corporeal nature, because they can affect the senses.
In fact, nothing can touch and be touched, if it is not a body.

After talking about the matter, the poet illustrates the concept of emptiness, which allows the movement of things and explains the different densities of matter.

_As to the whole set of things can give itself
A limit, nature forbids it; nature forces the matter
To be limited by emptiness, and what it is empty to be limited
By matter, so that, with their alternation, they make infinite
The whole, or else one or the other of the two, if is not delimited _
_By the other, with its simple nature, however, the unlimited lies.

According to the Latin poet, in the universe there is only matter and emptiness: matter is all that is detectable through the senses, while the existence of emptiness comes with reasoning. As a consequence of this principle, it is therefore absurd to resort to the existence of natures other than these, such as water, fire, air and earth. Lucretius introduces the idea of ​​ partes minimae, as a need to put an end to the subdivision of bodies and therefore to prevent their complete destruction. These primordial entities are the atoms ("non-divisible"). Matter consists of atoms, and their different aggregations give rise to different types of substances. In Lucretius’ opinion, atoms are indivisible and eternal, properties that he considers closely connected.

_It has also to be in the minute bodies, that the eye
No longer sees, an extreme point, that surely of parts
Does not result; nature it has minimal, and in itself detached
Nor did it ever live and never exist in the future
Which of the other body is only the first inseparable part,
Born to mark the beginning of the points, which, similar to it,
One following the other, in ordered series, with their
Busy gathering create the whole nature of the body;
Since they can never exist by themselves, they are forced
To pack, so to extract them is no longer given.
Atoms therefore exist of solid and simple body,
That very small parts contain in themselves mating
Tightly tightened, not in the same way
Of those atoms themselves then aggregate into the bodies,
But rather endowed with undivided and eternal essence,
And nature does not allow the slightest part to come off,
To preserve the germs of beings entire at the beginning.

It is interesting to note that Lucretius mentions the possibility that atoms are in turn composed of very small parts, but also affirms that these parts are inseparable and together form the atom entity, differently from how atoms form things, which they can change.

Lucretius also rejects the theories, advocated by Heraclitus, Thales and Anaximenes, based on the unique principles of fire, water, air and earth as primordial substances of all things. He also criticizes the pluralism of Empedocles, who also supposed the existence of four primordial elements. With regard to this theory, Lucretius condemns in particular the possibility that these principles are transformed one into another. He also refutes the atomistic theory of Anaxagoras, which has a conception different from Epicurus on the atoms, that is that the bodies, even if divided to infinity, remain identical to themselves. The basis of the refutation is essentially constituted by its conception of the atom as indestructible particles.

Passing from the atomic theory to the conception of the universe, the poet still recalls a realistic precept of the epicurean doctrine for which poetry has its value only because it makes the important mysteries of science pleasing and accessible to the mind. And this precept is introduced through the image of a sick child to whom a bitter medicine is given by moistening the rim of the glass with honey.

_But, like the doctors, when they try to give to the children
The repugnant absinthe, first the edges, all around the glass,
Sprinkle with sweet and blonde honey liqueur,
Because in the incidence of their age children are deceived,
Not beyond the lips, and meanwhile drink the bitter entirely
Absinthe drink and from deception do not receive damage,
But on the contrary, thus restored, they regain their vigor;.

Lucretius' idea of the universe was based on two fundamental cornerstones: the infinity of space and the infinity of matter. His confidence comes from the consideration that if space were not infinite, after so many centuries, life would disappear, and that the infinity of matter derives from the necessity that the number of primordial atoms, which are eternal, is not limited.

But, since I have taught that atoms are very solid
_And in perpetual they whirl, undefeated through every time, _
_Now we investigate whether their sum has or does not have _
_No limit; and likewise, the void of which we have discovered _
_The existence, or place or space, in which all things take place, _
_Let's see if everything is absolutely finished _
_Or open immense and immensely deep. _
_All that exists, therefore, is not limited to any _
_Direction; otherwise it should have one end. _
_It is evident, on the other hand, that nothing can have one end, _
_If there is not something beyond that boundary, so that it appears _
_A point beyond which nature can no longer follow. _ _

To make clear the idea of ​​infinity, Lucretius makes the example of the arrow that, even if launched from the extremes of the universe, must always go further, not being conceivable it is stopped or rebounded by the presence of new bodies. Lucretius also expresses the concept that there are no preferential points in the universe and that, because of its infinity, speaking of the center has no sense.

As for the movement of atoms, Lucretius, following Democritus and Epicurus, conceives it as a natural state, necessary to explain the formation of bodies through the aggregation of atoms, and their properties. Unlike Democritus, who attributed the weight of bodies to the motion of atoms, Epicurus and Lucretius were convinced that weight was an intrinsic quality of atoms. Democritus, then splitting the concepts of motion and force, had preceded Galileo’s principle of inertia, which says that a body can maintain its state of uniform rectilinear motion in the absence of forces. In this sense, Lucretius and Epicurus took a step back from the doctrine of Democritus, in that, by attributing the motion to the weight of the atoms, they had to postulate the existence of the _clinamen to explain the collisions of atoms and, therefore, their aggregation. According to them, atoms fall from top to bottom because of their weight, but, in a certain instant not determined, nor determinable, the atom shifts slightly from the vertical along a slight curve called clinamen. The artificial introduction of the clinamen derives from the fact that the atoms, falling perpendicularly under the action of their own weight, would never have met.

This principle of "free choice" of atoms has a physical but also a philosophical meaning: free will is in the power of every natural entity.

_In this regard, we want you to know this too: _
_That the first bodies, when in a straight line through the emptiness are thrown
Towards the bottom by their weight, in a moment undetermined at all _
_And in an indeterminate place, they deviate a little from their path
Just as long as you can call it change of movement. _
_But if they were not used to heel, all would fall down, _
_Like raindrops, through the deep emptiness, _
_Nor would a collision be born, nor strike would be produced _
_Among the first principles: so nature would never have created anything. _

The vision that Lucretius has of the nature of things is attributable to the concept by which every natural phenomenon finds its specific explanation. The only laws that regulate the motion of atoms are therefore mechanical. To the singers of feeling as the only matrix of poetry, the work of the Latin writer recalls how a rationalist could write the most beautiful poem of naturalistic argument in world literature.
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Nel 1774, Johann Wolfgang Goethe pubblicò Die Leiden des jungen Werthers (I dolori del giovane Werther), il fortunatissimo romanzo che narra di un'infatuazione romantica infelice che finisce nel suicidio. La pubblicazione del romanzo, basato sulle esperienze dell’autore, diede inizio a uno dei primi casi di merchandising intensivo. Più inquietante dello straordinario successo commerciale del Werther è tuttavia il fatto che, in vari paesi, molti giovani reduci da delusioni amorose erano così suggestionati dal romanzo che imitavano il modo di morire del protagonista, al punto che si è parlato di “effetto Werther”.
Prima, dopo e intorno al Werther
Prima, dopo e intorno al Werther
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Un classico da riproporre. Complimenti all'ignoto libraio.
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Among the various researchers who studied the atomic structure at the turn of the XX century there was a little-known Sicilian scientist, who deserves more consideration than the one received so far. He was Filippo Re Capriata, born in Licata in 1867 and died at only forty-one during the Messina earthquake of 28 December 1908. In a note presented by Becquerel in June 1903 at the Académie des Sciences of Paris, he claimed that radioactivity suggests that atoms are made up of smaller parts of unknown nature. If the particles that make up the atoms are subject to phenomena, such as radioactivity, which tend to move them away, there must have been an attractive force that initially brought them together. The Sicilian scientist thought that the radioactive atoms are those atoms in which the process of contraction is still ongoing, while those without activity would have already completed the process, and would have, therefore, extinguished, like little suns at the end of their existence.
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Tra gli anni ’80 e ‘90 dell'800 apparvero le ricerche del norvegese Sophus Lie (1842-1899), amico di Klein, che intraprese l'enorme compito di classificare tutti i possibili gruppi continui di trasformazioni geometriche e le loro applicazioni alla teoria delle equazioni differenziali, un’opera che rivelò una buona compatibilità con i tipi di geometria organizzati da Klein e che avrebbe portato a una delle principali branche della matematica del XX secolo, la teoria dei gruppi di Lie e le algebre di Lie. Un gruppo di Lie è proprio come un gruppo normale (solitamente discreto), ma opera su un insieme che sembra localmente lineare (una varietà liscia): ciò che rende i gruppi di Lie interessanti è che possono essere studiati attraverso il campo della geometria differenziale, che studia curve e superfici, cioè varietà continue.
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“A parody of mathematics”: As a description of Cantor’s work on infinity, it is surely unjust. As a description of Wallace’s, it may be taken as a tribute .+Roberto Natalini
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Nel “Saggio di interpretazione della geometria non euclidea” (1868), Eugenio Beltrami si accorse che le formule trigonometriche di Minding nei triangoli geodetici di una superficie di curvatura negativa costante erano in accordo con quelle del piano iperbolico stabilito da Lobacevskij. Egli non si proponeva di dimostrare la coerenza della geometria non euclidea o l'indipendenza dal postulato euclideo delle parallele, ma suggerì che Bolyai e Lobacevskij non avevano affatto introdotto nuovi concetti, ma avevano descritto la teoria delle geodetiche su superfici di curvatura negativa. Beltrami dimostrò che, applicando l'interpretazione dei concetti della geometria del piano ai concetti della geometria delle superfici, si trova che sulla pseudosfera è possibile una geometria che soddisfa, almeno in regioni limitate, gli assiomi della geometria iperbolica, di cui costituisce un modello.
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