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Feb. 21st, 2006 07:37 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
anafema_deviceО как... Какие загадки принесла френдлента - гравюра Дюрера, которую столь любезно представил нашему вниманию manon_gabrielle сподвигла прочитать вот такую статью:
Plato's abandoned search for the beautiful
Основная мысль статьи заключается в том, что главной темой гравюры была не меланхолия, а красота. Дюрер искал объяснения понятию красоты и поиски эти привели его к Платону ("Большой Гиппий" о прекрасном) и Луке Пачоли ("Божественная пропорция"). В статье доказывается, что создавая гравюру, Дюрер опирался на текст Палтона - диалога Сократа и Гиппия. Суть диалога в том, что Сократ неоднократно спрашивает у Гиппия, что есть красота и Гиппий дает ряд ответов, которые Сократ легко опровергает. Заканчивается диалог тем, что оба философа не могут найти ответ на этот вопрос и признаются в собственном невежестве. Именно это состояние осознания собственного бессилия и визуализировал Дюрер, я бы даже сказала антропоморфно персонофицировал, в виде Меланхолии. В статье отвергается связь образа Меланхолии с идеями Марсилио Фичино, флорентийского неоплатоника.
Маленькие выдержки из статьи:
We return to the key passage in Plato's dialogue, quoted above, when Socrates is exasperated with Hippias: "... I asked for the beautiful itself, by which everything to which it is added has the property of being beautiful, both stone and stick and man and god and every act and every learning." By "stone and stick and man and god and every act" Socrates may be referring to Hippias's previous answers. The word mathemati, here rendered as "learning," will become the modern "mathematics," but it had a broader and looser meaning in Greek. The word is a cognate of manthano, "I learn," so the Loeb edition of the dialogue translates the phrase used by Socrates as "every acquisition of knowledge." Ficino translated it correctly as "disciplina," but that Latin word would obscure the "mathematics" from Durer and Pirckheimer, which was to be vital to Durer's interpretation of the text.
For instruction in the meaning of mathemati, it seems that Durer turned to "De divina proportione" Pacioli.
This second chapter of De divina proportione, a panegyric on mathematics, gave Durer at least seven loosely mathematical themes that reappear in Melencolia I (an eighth became the subject of his third treatise (66)). We shall examine them in the sequence adopted by Pacioli.
Pacioli began his second chapter by quoting "the master of those who know" (Aristotle) that there is nothing in the intellect that has not in some way first passed through the senses: "... and of the senses, the wise conclude that the most noble is sight." "This art of painting is made for the eyes, for the sight is the noblest sense of man," echo Durer's notes in 1513. (67) Pacioli goes on to assure his patron, Lodovico Sforza, that while the mathematical disciplines may have been restricted to scholars in the past, in future they will reach a much larger public, for "they are the foundation and ladder that gives access to every other science [sieno fondamento e scala de pervenire a la notitia de ciascun altra scientia]."
Leaning against a wall in the center of Melencolia is a ladder, silhouetted against the distant landscape. If it gives access to "every other science," as Pacioli maintained, we would expect it to rise from a mathematical foundation. Indeed, it stands on a raised platform supporting the geometric solid, in a space full of mathematical symbols.
In 1512 Durer wrote, "The measurements of the earth, the waters, and the stars have come to be understood through painting and many more things will become known to men by means of painting." (73) Durer viewed painting as the means for representing the world, not as "fine art."...
Perhaps the distant sea and coastline in Melencolia I, under the "rainbow" and "comet," refer to "the universe below and above" that in Pacioli's words (quoted above) "must necessarily be subject to number, weight and measure." (74)...
Pacioli continued his second chapter by declaring that he would omit other "practical and speculative" sciences dependent on mathematics, including "all the mechanical arts," in order to be less tiresome to the reader. (75) The mechanical arts may be represented by the tools and instruments in Melencolia I, but Durer linked these objects more directly to the text of Greater Hippias, as we shall see.
We return to Greater Hippias... "the useful we call beautiful, and beautiful in the
way in which it is useful, and for the purposes for which it is
useful, and at the time when it is useful; and that which is in all
these aspects useless we say is ugly. "...
Durer also accepted the last suggestion, for in his notes of 1512 he wrote, "Usefulness is a part of beauty. Therefore what is useless in a man, is not beautiful." (78) In the engraving, the passage finds its first parallel in the whites of Geometry's eyes, which gleam against her dark face, their penetrating stare contrasting with those of the putto on the millstone, which are perhaps "unable to see" (Fig. 6). The beauty of Durer's sleeping dog lies not in its unprepossessing appearance but in its usefulness as a hunter...
In Greater Hippias, Socrates returned to his theme. That which has power to accomplish anything is useful, while that which is powerless is useless (295e). Power then, is beautiful ("Dunamis men ara kalon"); the want of power ugly (Ficino: "Potentia ergo pulchrum, impotentia turpe"). Hippias agrees. We recall Durer's notes on his drawing with the quadrant and plumb line: "Keys mean power; purse means wealth" (Fig. 7). If the keys hanging from Geometry's belt are a reference to Socrates' claim that "Power is beautiful," we should find a further allusion in Plato's text to the purse/wealth...
If Durer had expected an answer to the question, "What is the beautiful?" Plato has disabused him of that hope. As with all Plato's dialogues, the assumption remains that it is better to travel well than to arrive...
In Melencolia I, the most conspicuous object for which we have still to find an explanation is the large irregular polyhedron. In Greater Hippias, the subject most frequently evoked by Socrates and Hippias, which we have yet to find illustrated in the engraving, is the beautiful itself. Could these two lacunae be mutually dependent, so that they vanish when conjoined?
...The four elements of earth, air, fire, and water were each formed of the four most beautiful bodies (the regular polyhedra, 53e), which in turn were formed from the most beautiful triangle (54a). The fifth regular polyhedron, the dodecahedron, was left over... Aristotle reasoned that this fifth element, the "quintessence" to later generations, was ungenerated, indestructible, and unchanging. (93) Pacioli, without referring to Aristotle, conflated the two traditions and claimed that Plato had associated the dodecahedron with the quintessence...
The dodecahedron is made up of twelve pentagons, each of which...
If Durer's problem had been to find a visual equivalent for the beautiful itself, the dodecahedron was the most obvious solution at his disposal. In Plato's dialogue. Socrates and Hippias did not find the beautiful. They remained in a state of ignorance, unclear whether they were better off alive or dead, a condition Durer made visible as melancholy. The engraving shows that Geometry/Melancholy has not succeeded in fashioning a regular dodecahedron. As far as we can see, she has managed just three pentagons, but on a solid so irregular that it can be read as a partially truncated cube (Plato's polyhedron for earth). Is it a perfectly judged emblem for the failure of Socrates and Hippias to find the beautiful?
The following themes in Greater Hippias reappear in Melencolia I:
(a purse of) money
a beautiful maiden
(the crucible of) gold
the millstone
"all mathematics" (see below)
"whatever is useful" (dog, tools, instruments, eyes)
power (the keys)
the pleasant in sight and hearing (eyes and bell)
the condition of being ignorant of the beautiful (melancholy)
a failure to discover the beautiful (a botched dodecahedron)
These illustrations of the value of mathematics from Pacioli's De divina proportione reappear in Melencolia I:
the ladder
number, weight, and measure (panel of numbers, scales, and hourglass)
gold tested by fire
the universe below and above, subject to number, weight, and measure
geometry, in which every hidden science is to be found
Numerous references to the beautiful in Greater Hippias reappear in Durer's notes of 1512-13:
our inability to give a judgment on the beautiful
how beauty is to be judged is a matter of deliberation
beauty in some contexts is not beauty in others
a professed ignorance of the beautiful, written in the first person
(Durer adopting Socrates' voice)
usefulness is a part of the beautiful
the beautiful is hard
In addition, a direct link between Greater Hippias and Melencolia I may account for Durer's note, "Keys mean power; purse means wealth"...
By analogy to the mature form of the emblem, the legend "Melencolia I" on the wings of Durer's bat corresponds not to a title but to a motto. It offered a succinct mnemonic for the significance invested in the engraving by Durer. But to reveal the full meaning of the print required the explanatory text, which in this article we have argued was Plato's Greater Hippias.
Plato's abandoned search for the beautiful
Основная мысль статьи заключается в том, что главной темой гравюры была не меланхолия, а красота. Дюрер искал объяснения понятию красоты и поиски эти привели его к Платону ("Большой Гиппий" о прекрасном) и Луке Пачоли ("Божественная пропорция"). В статье доказывается, что создавая гравюру, Дюрер опирался на текст Палтона - диалога Сократа и Гиппия. Суть диалога в том, что Сократ неоднократно спрашивает у Гиппия, что есть красота и Гиппий дает ряд ответов, которые Сократ легко опровергает. Заканчивается диалог тем, что оба философа не могут найти ответ на этот вопрос и признаются в собственном невежестве. Именно это состояние осознания собственного бессилия и визуализировал Дюрер, я бы даже сказала антропоморфно персонофицировал, в виде Меланхолии. В статье отвергается связь образа Меланхолии с идеями Марсилио Фичино, флорентийского неоплатоника.
Маленькие выдержки из статьи:
We return to the key passage in Plato's dialogue, quoted above, when Socrates is exasperated with Hippias: "... I asked for the beautiful itself, by which everything to which it is added has the property of being beautiful, both stone and stick and man and god and every act and every learning." By "stone and stick and man and god and every act" Socrates may be referring to Hippias's previous answers. The word mathemati, here rendered as "learning," will become the modern "mathematics," but it had a broader and looser meaning in Greek. The word is a cognate of manthano, "I learn," so the Loeb edition of the dialogue translates the phrase used by Socrates as "every acquisition of knowledge." Ficino translated it correctly as "disciplina," but that Latin word would obscure the "mathematics" from Durer and Pirckheimer, which was to be vital to Durer's interpretation of the text.
For instruction in the meaning of mathemati, it seems that Durer turned to "De divina proportione" Pacioli.
This second chapter of De divina proportione, a panegyric on mathematics, gave Durer at least seven loosely mathematical themes that reappear in Melencolia I (an eighth became the subject of his third treatise (66)). We shall examine them in the sequence adopted by Pacioli.
Pacioli began his second chapter by quoting "the master of those who know" (Aristotle) that there is nothing in the intellect that has not in some way first passed through the senses: "... and of the senses, the wise conclude that the most noble is sight." "This art of painting is made for the eyes, for the sight is the noblest sense of man," echo Durer's notes in 1513. (67) Pacioli goes on to assure his patron, Lodovico Sforza, that while the mathematical disciplines may have been restricted to scholars in the past, in future they will reach a much larger public, for "they are the foundation and ladder that gives access to every other science [sieno fondamento e scala de pervenire a la notitia de ciascun altra scientia]."
Leaning against a wall in the center of Melencolia is a ladder, silhouetted against the distant landscape. If it gives access to "every other science," as Pacioli maintained, we would expect it to rise from a mathematical foundation. Indeed, it stands on a raised platform supporting the geometric solid, in a space full of mathematical symbols.
In 1512 Durer wrote, "The measurements of the earth, the waters, and the stars have come to be understood through painting and many more things will become known to men by means of painting." (73) Durer viewed painting as the means for representing the world, not as "fine art."...
Perhaps the distant sea and coastline in Melencolia I, under the "rainbow" and "comet," refer to "the universe below and above" that in Pacioli's words (quoted above) "must necessarily be subject to number, weight and measure." (74)...
Pacioli continued his second chapter by declaring that he would omit other "practical and speculative" sciences dependent on mathematics, including "all the mechanical arts," in order to be less tiresome to the reader. (75) The mechanical arts may be represented by the tools and instruments in Melencolia I, but Durer linked these objects more directly to the text of Greater Hippias, as we shall see.
We return to Greater Hippias... "the useful we call beautiful, and beautiful in the
way in which it is useful, and for the purposes for which it is
useful, and at the time when it is useful; and that which is in all
these aspects useless we say is ugly. "...
Durer also accepted the last suggestion, for in his notes of 1512 he wrote, "Usefulness is a part of beauty. Therefore what is useless in a man, is not beautiful." (78) In the engraving, the passage finds its first parallel in the whites of Geometry's eyes, which gleam against her dark face, their penetrating stare contrasting with those of the putto on the millstone, which are perhaps "unable to see" (Fig. 6). The beauty of Durer's sleeping dog lies not in its unprepossessing appearance but in its usefulness as a hunter...
In Greater Hippias, Socrates returned to his theme. That which has power to accomplish anything is useful, while that which is powerless is useless (295e). Power then, is beautiful ("Dunamis men ara kalon"); the want of power ugly (Ficino: "Potentia ergo pulchrum, impotentia turpe"). Hippias agrees. We recall Durer's notes on his drawing with the quadrant and plumb line: "Keys mean power; purse means wealth" (Fig. 7). If the keys hanging from Geometry's belt are a reference to Socrates' claim that "Power is beautiful," we should find a further allusion in Plato's text to the purse/wealth...
If Durer had expected an answer to the question, "What is the beautiful?" Plato has disabused him of that hope. As with all Plato's dialogues, the assumption remains that it is better to travel well than to arrive...
In Melencolia I, the most conspicuous object for which we have still to find an explanation is the large irregular polyhedron. In Greater Hippias, the subject most frequently evoked by Socrates and Hippias, which we have yet to find illustrated in the engraving, is the beautiful itself. Could these two lacunae be mutually dependent, so that they vanish when conjoined?
...The four elements of earth, air, fire, and water were each formed of the four most beautiful bodies (the regular polyhedra, 53e), which in turn were formed from the most beautiful triangle (54a). The fifth regular polyhedron, the dodecahedron, was left over... Aristotle reasoned that this fifth element, the "quintessence" to later generations, was ungenerated, indestructible, and unchanging. (93) Pacioli, without referring to Aristotle, conflated the two traditions and claimed that Plato had associated the dodecahedron with the quintessence...
The dodecahedron is made up of twelve pentagons, each of which...
If Durer's problem had been to find a visual equivalent for the beautiful itself, the dodecahedron was the most obvious solution at his disposal. In Plato's dialogue. Socrates and Hippias did not find the beautiful. They remained in a state of ignorance, unclear whether they were better off alive or dead, a condition Durer made visible as melancholy. The engraving shows that Geometry/Melancholy has not succeeded in fashioning a regular dodecahedron. As far as we can see, she has managed just three pentagons, but on a solid so irregular that it can be read as a partially truncated cube (Plato's polyhedron for earth). Is it a perfectly judged emblem for the failure of Socrates and Hippias to find the beautiful?
The following themes in Greater Hippias reappear in Melencolia I:
(a purse of) money
a beautiful maiden
(the crucible of) gold
the millstone
"all mathematics" (see below)
"whatever is useful" (dog, tools, instruments, eyes)
power (the keys)
the pleasant in sight and hearing (eyes and bell)
the condition of being ignorant of the beautiful (melancholy)
a failure to discover the beautiful (a botched dodecahedron)
These illustrations of the value of mathematics from Pacioli's De divina proportione reappear in Melencolia I:
the ladder
number, weight, and measure (panel of numbers, scales, and hourglass)
gold tested by fire
the universe below and above, subject to number, weight, and measure
geometry, in which every hidden science is to be found
Numerous references to the beautiful in Greater Hippias reappear in Durer's notes of 1512-13:
our inability to give a judgment on the beautiful
how beauty is to be judged is a matter of deliberation
beauty in some contexts is not beauty in others
a professed ignorance of the beautiful, written in the first person
(Durer adopting Socrates' voice)
usefulness is a part of the beautiful
the beautiful is hard
In addition, a direct link between Greater Hippias and Melencolia I may account for Durer's note, "Keys mean power; purse means wealth"...
By analogy to the mature form of the emblem, the legend "Melencolia I" on the wings of Durer's bat corresponds not to a title but to a motto. It offered a succinct mnemonic for the significance invested in the engraving by Durer. But to reveal the full meaning of the print required the explanatory text, which in this article we have argued was Plato's Greater Hippias.
