Zur Farbenlehre. Vierte Abteilung - Allgemeine Ansichten nach Innen

In dieser stetigen Reihe haben wir, soviel es möglich sein wollte, die Erscheinungen zu bestimmen, zu sondern, und zu ordnen gesucht. Jetzt, da wir nicht mehr fürchten, sie zu vermischen oder zu verwirren, können wir unternehmen, erstlich das Allgemeine, was sich von diesen Erscheinungen innerhalb des geschlossenen Kreises prädizieren läßt, anzugeben, zweitens, anzudeuten, wie sich dieser besondre Kreis an die übrigen Glieder verwandter Naturerscheinungen anschließt und sich mit ihnen verkettet.
(Zur Farbenlehre. Vierte Abteilung - Allgemeine Ansichten nach Innen - Goethe)

Na medida do possível, procuramos determinar, separar e ordenar os fenômenos segundo essa série contínua. Já que agora não tememos misturá-los ou confundi-los, podemos empreender em primeiro lugar
a tarefa de julgar, no círculo, o que é universal nos fenômenos, para em seguida apontar como esse círculo particular se encadeia e se une ao resto dos fenômenos naturais afins.
(Doutrina das Cores. Quarta Seção - Goethe (tradução de Marco Giannotti))

Zur Farbenlehre. Didaktischer Teil - Einleitung

Wir betrachteten also die Farben zuerst, insofern sie dem Auge angehören und auf einer Wirkung und Gegenwirkung desselben beruhen; ferner zogen sie unsere Aufmerksamkeit an sich, indem wir sie an farblosen Mitteln oder durch deren Beihülfe gewahrten; zuletzt aber wurden sie uns merkwürdig, indem wir sie als den Gegenständen angehörig denken konnten. Die ersten nannten wir physiologische, die zweiten physische, die dritten chemische Farben. Jene sind unaufhaltsam flüchtig, die andern vorübergehend, aber allenfalls verweilend, die letzten festzuhalten bis zur spätesten Dauer.
(Zur Farbenlehre. Didaktischer Teil - Einleitung - Goethe)

Consideremos, em primeiro lugar, as cores na medida em que pertencem ao olho e dependem de sua capacidade de agir e reagir. Em seguida, despertam a atenção na medida em que as percebemos através dos meios incolores ou com o auxílio destes. Por fim, são dignas de nota na medida em que podemos pensá-las como fazendo parte do objeto. Chamamos as primeiras de fisiológicas, as segundas de físicas e as terceiras de químicas. As primeiras são constantemente fugidias, as segundas são passageiras, embora tenham uma certa permanência. As últimas têm longa duração.
(Doutrina das Cores. Esboço de uma Doutrina das Cores - Introdução - Goethe (tradução de Marco Giannotti))

Zur Farbenlehre. Didaktischer Teil - Einleitung

Die Farbe sei ein elementares Naturphänomen für den Sinn des Auges, das sich, wie die übrigen alle, durch Trennung und Gegensatz, durch Mischung und Vereinigung, durch Erhöhung und Neutralisation, durch Mitteilung und Verteilung und so weiter manifestiert und unter diesen allgemeinen Naturformeln am besten angeschaut und begriffen werden kann.
(Zur Farbenlehre. Didaktischer Teil - Einleitung - Goethe)

(...) a cor é um fenômeno elementar da natureza para sentido da visão, que, como todos os demais, se manifesta ao se dividir e opor, se misturar e fundir, se intensificar e neutralizar, ser compartilhado e repartido, podendo ser mais bem intuído e concebido nessas fórmulas gerais da natureza.
(Doutrina das Cores. Esboço de uma Doutrina das Cores - Introdução - Goethe (tradução de Marco Giannotti))

Zur Farbenlehre. Didaktischer Teil - Einleitung

Und so erbauen wir aus diesen dreien die sichtbare Welt und machen dadurch zugleich die Malerei möglich, welche auf der Tafel eine weit vollkommner sichtbare Welt, als die wirkliche sein kann, hervorzubringen vermag.
(Zur Farbenlehre. Didaktischer Teil - Einleitung - Goethe)

E assim construímos o mundo visível a partir do claro, do escuro e da cor, e com eles também tornamos possível a pintura, que é capaz de produzir, no plano, um mundo visível muito mais perfeito que o mundo real.
(Doutrina das Cores. Esboço de uma Doutrina das Cores - Introdução - Goethe (tradução de Marco Giannotti))

Zur Farbenlehre. Didaktischer Teil - Einleitung

Die Lust zum Wissen wird bei dem Menschen zuerst dadurch angeregt, daß er bedeutende Phänomene gewahr wird, die seine Aufmerksamkeit an sich ziehen. Damit nun diese dauernd bleibe, so muß sich eine innigere Teilnahme finden, die uns nach und nach mit den Gegenständen bekannter macht. Alsdann bemerken wir erst eine große Mannigfaltigkeit, die uns als Menge entgegendringt. Wir sind genötigt zu sondern, zu unterscheiden und wieder zusammenzustellen, wodurch zuletzt eine Ordnung entsteht, die sich mit mehr oder weniger Zufriedenheit übersehen läßt.
(Zur Farbenlehre. Didaktischer Teil - Einleitung - Goethe)

O homem só é levado ao desejo de conhecer se fenômenos notáveis lhe chamam a atenção. Para que esta perdure, é preciso haver um interesse mais profundo, que nos aproxime cada vez mais dos objetos. Observamos então uma grande diversidade diante de nós. Somos obrigados a separá-la, distingui-la e recompô-la, daí resultando uma ordenação que pode ser apreciada com maior ou menor satisfação.
(Doutrina das Cores. Esboço de uma Doutrina das Cores - Introdução - Goethe (tradução de Marco Giannotti))

Zur Farbenlehre. Didaktischer Teil - Vorwort

Die Farben sind Taten des Lichts, Taten und Leiden. In diesem Sinne können wir von denselben Aufschlüsse über das Licht erwarten. Farben und Licht stehen zwar untereinander in dem genausten Verhältnis, aber wir müssen uns beide als der ganzen Natur angehörig denken: denn sie ist es ganz, die sich dadurch dem Sinne des Auges besonders offenbaren will.
(Zur Farbenlehre. Didaktischer Teil - Vorwort - Goethe)

As cores são ações e paixões da luz. Nesse sentido, podemos esperar delas alguma indicação sobre a luz. Na verdade, luz e cores se relacionam perfeitamente, embora devamos pensá-las como pertencendo à natureza em seu todo: é ela inteira que assim quer se revelar ao sentido da visão.
(Doutrina das Cores. Esboço de uma Doutrina das Cores - Prefácil - Goethe (tradução de Marco Giannotti))

Zur Farbenlehre. Didaktischer Teil - Vorwort

Jedes Ansehen geht über in ein Betrachten, jedes Betrachten in ein Sinnen, jedes Sinnen in ein Verknüpfen, und so kann man sagen, daß wir schon bei jedem aufmerksamen Blick in die Welt theoretisieren. Dieses aber mit Bewußtsein, mit Selbstkenntnis, mit Freiheit, und um uns eines gewagten Wortes zu bedienen, mit Ironie zu tun und vorzunehmen, eine solche Gewandtheit ist nötig, wenn die Abstraktion, vor der wir uns fürchten, unschädlich und das Erfahrungsresultat, das wir hoffen, recht lebendig und nützlich werden soll.
(Zur Farbenlehre. Didaktischer Teil - Vorwort - Goethe)

Cada olhar envolve uma observação, cada observação uma reflexão, cada reflexão uma síntese: ao olharmos atentamente para o mundo já estamos teorizando. Devemos, porém, teorizar e proceder com consciência, autoconhecimento, liberdade e -- se for preciso usar uma palavra audaciosa -- com ironia: tal destreza é indispensável para que a abstração, que receiamos, não seja prejudicial, e o resultado empírico, que desejamos, nos seja útil e vital.
(Doutrina das Cores. Esboço de uma Doutrina das Cores - Prefácil - Goethe (tradução de Marco Giannotti))

Zur Farbenlehre

Si vera nostra sunt aus falsa, erunt talia,
licet nostra per vitam defendimus.
Post fata nostra pueri qui
nunc ludunt nostri judices erunt.

Peter Pan, James Matthew Barrie

"All children, except one, grow up. They soon know that they will grow up, and the way Wendy knew was this."

"This was all that passed between them on the subject, but henceforth Wendy knew that she must grow up. You always know after you are two. Two is the beginning of the end."

"I don't know whether you have ever seen a map of a person's mind. Doctors sometimes draw maps of other parts of you, and your own map can become intensely interesting, but catch them trying to draw a map of a child's mind, which is not only confused, but keeps going round all the time."

"Stars are beautiful, but they may not take an active part in anything, they must just look on for ever. It is a punishment put on them for something they did so long ago that no star now knows what it was. So the older ones have become glassy-eyed and seldom speak (winking is the star language), but the little ones still wonder."

"You see, Wendy, when the first baby laughed for the first time, its laugh broke into a thousand pieces, and they all went skipping about, and that was the beginning of fairies."


"`I think it's perfectly sweet of you,' she declared, `and I'll get up again,' and she sat with him on the side of the bed. She also said she would give him a kiss if he liked, but Peter did not know what she meant, and he held out his hand expectantly.

`Surely you know what a kiss is?' she asked, aghast.

`I shall know when you give it to me,' he replied stiffly, and not to hurt his feeling she gave him a thimble.

`Now,' said he, `shall I give you a kiss?' and she replied with a slight primness, `If you please.' She made herself rather cheap by inclining her face toward him, but he merely dropped an acorn button into her hand, so she slowly returned her face to where it had been before, and said nicely that she would wear his kiss on the chain
around her neck. It was lucky that she did put it on that chain, for it was afterwards to save her life."

"You see children know such a lot now, they soon don't believe in fairies, and every time a child says, `I don't believe in fairies,' there is a fairy somewhere that falls down dead."

"I don't want ever to be a man," he said with passion. "I want always to be a little boy and to have fun. So I ran away to Kensington Gardens and lived a long long time among the fairies."

"She asked where he lived.
`Second to the right,' said Peter, `and then straight on till morning.'"

"Second to the right, and straight on till morning."

"That, Peter had told Wendy, was the way to the Neverland; but even birds, carrying maps and consulting them at windy corners, could not have sighted it with these instructions."

"John said that if the worst came to the worst, all they had to do was to go straight on, for the world was round, and so in time they must come back to their own window."

"Fairies have to be one thing or the other, because being so small they unfortunately have room for one feeling only at a time. They are, however, allowed to change, only it must be a complete change."

"The difference between him and the other boys at such a time was that they knew it was make-believe, while to him make-believe and true were exactly the same thing. This sometimes troubled them, as when they had to make-believe that they had had their dinners."

"If you shut your eyes and are a lucky one, you may see at times a shapeless pool of lovely pale colours suspended in the darkness; then if you squeeze your eyes tighter, the pool begins to take shape, and the colours become so vivid that with another squeeze they must go on fire. But just before they go on fire you see the lagoon. This is the nearest you ever get to it on the mainland, just one heavenly moment; if there could be two moments you might see the surf and hear the mermaids singing."

"It was not really Saturday night, at least it may have been, for they had long lost count of the days; but always if they wanted to do anything special they said this was Saturday night, and then they did it."

"To die would be a great adventure."

Heisenberg and the Traffic Policeman

One day Herr Doktor Heisenberg is out driving. As he rounds a curve, a policeman waves him overs. The policeman leans in the windaw and asks the famous physicist "Doktor Heisenberg, do you know how fast you were going?" Heisenberg responds "No, but I do know exactly where I was!"

Latin honors

Latin honors are Latin phrases used to indicate the level of academic distinction with which an academic degree was earned.

There are typically three types of Latin honors. In order of increasing level of honor, they are:

* cum laude ("with honor")
* magna cum laude ("with great honor")
* summa cum laude ("with highest honor")

They are awarded to those undergraduate and graduate students who have achieved academic distinction. The honor is typically indicated on the diploma.

Ada's Note

In considering any new subject, there is frequently a tendency, first, to overrate what we find to be already interesting or remarkable; and, secondly, by a sort of natural reaction, to undervalue the true state of the case, when we do discover that our notions have surpassed those that were really tenable.
-- Ada Byron, Lady Lovelace --

Fita Verde no Cabelo

(João Guimarães Rosa)

Havia uma aldeia em algum lugar, nem maior nem menor, com velhos e velhas que velhavam, homens e mulheres que esperavam, e meninos e meninas que nasciam e cresciam.

Todos com juízo, suficientemente, menos uma meninazinha, a que por enquanto. Aquela, um dia, saiu de lá, com uma fita verde inventada no cabelo.

Sua mãe mandara-a, com um cesto e um pote, à avó, que a amava, a uma outra e quase igualzinha aldeia.

Fita-Verde partiu, sobre logo, ela a linda, tudo era uma vez. O pote continha um doce em calda, e o cesto estava vazio, que para buscar framboesas.

Daí, que, indo, no atravessar o bosque, viu só os lenhadores, que por lá lenhavam; mas o lobo nenhum, desconhecido nem peludo. Pois os lenhadores tinham exterminado o lobo.

Então, ela, mesma, era quem se dizia:

– Vou à vovó, com cesto e pote, e a fita verde no cabelo, o tanto que a mamãe me mandou.

A aldeia e a casa esperando-a acolá, depois daquele moinho, que a gente pensa que vê, e das horas, que a gente não vê que não são.

E ela mesma resolveu escolher tomar este caminho de cá, louco e longo, e não o outro, encurtoso. Saiu, atrás de suas asas ligeiras, sua sombra também vinha-lhe correndo, em pós.

Divertia-se com ver as avelãs do chão não voarem, com inalcançar essas borboletas nunca em buquê nem em botão, e com ignorar se cada uma em seu lugar as plebeinhas flores, princesinhas e incomuns, quando a gente tanto por elas passa.

Vinha sobejadamente.

Demorou, para dar com a avó em casa, que assim lhe respondeu, quando ela, toque, toque, bateu:

– Quem é?

– Sou eu… – e Fita-Verde descansou a voz. – Sou sua linda netinha, com cesto e pote, com a fita verde no cabelo, que a mamãe me mandou.

Vai, a avó, difícil, disse: – Puxa o ferrolho de pau da porta, entra e abre. Deus te abençoe.

Fita-Verde assim fez, e entrou e olhou.

A avó estava na cama, rebuçada e só. Devia, para falar agagado e fraco e rouco, assim, de ter apanhado um ruim defluxo. Dizendo: – Depõe o pote e o cesto na arca, e vem para perto de mim, enquanto é tempo.

Mas agora Fita-Verde se espantava, além de entristecer-se de ver que perdera em caminho sua grande fita verde no cabelo atada; e estava suada, com enorme fome de almoço. Ela perguntou:

– Vovozinha, que braços tão magros, os seus, e que mãos tão trementes!

– É porque não vou poder nunca mais te abraçar, minha neta… – a avó murmurou.

– Vovozinha, mas que lábios, aí, tão arroxeados!

– É porque não vou nunca mais poder te beijar, minha neta… – a avó suspirou.

– Vovozinha, e que olhos tão fundos e parados, nesse rosto encovado, pálido?

– É porque já não estou te vendo, nunca mais, minha netinha… – a avó ainda gemeu.

Fita-Verde mais se assustou, como se fosse ter juízo pela primeira vez. Gritou: – Vovozinha, eu tenho medo do Lobo!…

Mas a avó não estava mais lá, sendo que demasiado ausente, a não ser pelo frio, triste e tão repentino corpo.

Sapere aude!

Sapere aude is a Latin phrase meaning "Dare to know".

Dimidium facti qui coepit habet: sapere aude!
[He who has begun is half done: dare to know!]
-- Epistle II of Horace's Epistularum liber primus --

Was ist Aufklärung?

Aufklärung ist der Ausgang des Menschen aus seiner selbstverschuldeten Unmündigkeit. Unmündigkeit ist das Unvermögen, sich seines Verstandes ohne Leitung eines anderen zu bedienen. Selbstverschuldet ist diese Unmündigkeit, wenn die Ursache derselben nicht am Mangel des Verstandes, sondern der Entschließung und des Mutes liegt, sich seiner ohne Leitung eines andern zu bedienen. Sapere aude! Habe Mut, dich deines eigenen Verstandes zu bedienen! ist also der Wahlspruch der Aufklärung.
-- Immanuel Kant --

vidit

Artis monumentum, qui unum vidit,
nullum vidit,
qui mille vidit, unum vidit.
-- Eduard Gerhard --

Aufrichtig - Goethe

aufrichtig zu sein, kann ich versprechen, unparteiisch zu sein aber nicht
[posso prometer ser sincero, mas não imparcial]
-- Goethe --

Endlichen - Goethe

Willst du ins Unendliche schreiten, geh nur im Endlichen nach allen Seiten.
--GOETHE--

The Inhibition of Simultaneous Stimuli - Békésy - Sensory Inhibition

When we look at a historical section of a sense organ with a large surface, we find nerve fibers going directly to the sensory ganglion, and in addition we find a large number of lateral fibers running parallel to the surface and connecting two or more end organs with one another. It was Held (1926) who showed that in the organ of Corti there are never fibers running from every hair cell more or less direclty to the modiolus of the cochlea, and also other fibers running perpendicular to these along the basilar membrane, often connecting the hair cells over nearly a half turn of the cochlea. Unfortunately these lateral connections often seem difficult to stain. (...) The lateral fibers of the cochlea are represented in Fig. 20. At present it is still uncertain to what extent these fibers are involved in the immediate process of hearing. (...) I am unable to understand how this retinal circuitry fails to produce constant oscillation. It is difficult to imagine what type of reduction of feedback is used to avoid this oscillation. Even a simples feedback system requires many precautions to prevent its going into oscillation and to cause it to return to its original equilibrium condition after a stimulus has ceased to act upon it.

Figure 20
Figure 23

For present purposes, a simple scheme is sufficient to illustrate the problem. The small dots near the bottom of Fig. 23 represent a system of receptors on the surface of the skin. The variations of a stimulus are indicated by the lowermost graph with a maximum in the middle. There are lateral connections between the receptors and nerve fibers that run upward to the first-order ganglion cells in a row a. Alongside each of these nerve fibers is a representation of its pulse rate: the number of spikes for a certain unit of time is shown. Adrian in 1928 found that the discharge rate of a sensory nerve fiber increases with the magnitude of the stimulus acting on its end organ. In the two fibers on the far left and right sides the stimulation is minimal and the discharges represent spontaneous activity. Toward the middle the stimulus intensity increases and so also does the discharge rate.

From the first layer of ganglion cells we go to a similar level above, shown at b, and from there to still higher level, c. As far as we can now discover, the result of the lateral interconnections is to reduce or "funnel" the laterally spreading stimulation to a progressively localized section of the neural pathway, as indicated by the sketch of the sensation at the top of the figure.

This simple scheme immediately brings up the question of the kind of frequency sensation that will be produced by a stimulus whose amplitude tapers away from a central maximum as shown in this figure. It is apparent that the lateral inhibition that occurs in sense organs is not the straightforward kind that we find in muscle systems. The lateral inhibition of sense organs is actually a funneling action that inhibits the smaller stimulus effects and collects the stronger effects into a common pathway.
(...)

In a crude way we can distinguish four types of inhibitory pathways, as illustrated in Fig. 24. As A is shown the simple form of lateral inhibition that has just been described. At B is shown a forward type of inhibition, at C a backward type, and at D a form of central inhibition. In human sense organs there is an interplay of all these types of interaction.

Figure 24

The question arises whether inhibition is the correct term for this whole series of phenomena. With our limited knowledge of inhibition phenomena in single neural pathways it is difficult to decide on the proper category. In addition to inhibition we might consider the term "sensory distortion", or even "disinhibition" - because it may happen that normally the neural pathways are blocked, and the effect of a stimulus is to remove the blockage. I prefer to call the effect "funneling", because even for central inhibition there is usually an increase in the magnitude of the sensation referred to certain places.

Adaptation and Inhibition as a Means of Suppressing an Excess of Information - Békéy - Sensory Inhibition

There are many ways in which a physical activity may be so modified as to cause a human observer's perception of it to depart widely from the indications of physical apparatus. We are all aware of the existence of sensory threshold, adaptation process, and nonlinearity, all of which represent departures of perception from the regular variations of magnitude in a physical stimulus.
A further process is inhibition, whose effects are equally unexpected and often even more profound than these objects.
(...)

The important thing in a communication network is not the output level attained but the signal-to-noise ratio, for it is the ratio that determines our ability to recognize the signal a distinct from the noise. In the nervous system also it was found that "noise" is always present, in the form of general background of spontaneous activity, and a sensory effect has to be identified in the presence of this background (Hoagland, 1932). This problem is still with us.
(...)

A decade ago there was a development of communications and information theory. Already we have too much of this theory, and it is necessary to develop an inhibition theory. We shall need to discover a way of measuring the loss of information caused by a given amount of inhibition. A possible measure is the number of bits lost when the information is passed through a system divided by the number of bits introduced at the input. Such a measure I consider more important in physiology and psychology than in communications engineering.

We know that any information that we have at hand contains a number of small disturbances. These are usually eliminated by a statistical treatment. The mean value of a series of measures represents the inhibition of many small unwanted bits of information, but this procedure does not go far enough. What we are interested in is direct from of inhibition that cancels out a whole of unwanted information. The problem is of far greater scope than statisticians have ever dreamed of.

The simplest way to get rid of information is to reduce the sensitivity of the receptors. This method s used effectively in all complex living systems. For example, we know that the organ or Corti of the ear is sensitive to displacement. This sensitivity is so great that one can almost hear the Brownian movements of molecules. (...) the organ of Corti, as living tissue, requires a constant blood supply (...) hence we should expect to hear our own heartbeat with tremendous loudness. We do not so because, for one thing, there is a factor of frequency differentiating between external sound stimuli and the sound of the heartbeat. The circulatory pulsations are of low frequency, and the solution that nature made to the problem was to reduce the sensitivity of the ear to lower frequencies while leaving the sensitivity unimpaired in the range between 1000 and 4000 cycles per second (cps).
Thus it is not surprising to find that the threshold sensitivity for frequencies around 20 cps is nearly 10,000 times less than for frequencies around 1000cps. These relations may be seen in Fig.3.

Figure 3
(...)

Adaptation is a common process in living systems for the reduction of the effect of a stimulus. It is seen mainly as a progressive loss of sensitivity during a period of stimulation.
(...)

The retina seems to lose its "pattern recognition ability" quickly if the pattern is maintained on one portion of its surface. As has been proved by Riggs and others (1953) an image that is made stationary on the retina disappears partly or completely in a few seconds.
(...)

That the transients of a stimulus are of utmost importance in vision was shown in an objective way in experiments on the eye of the horseshoe crab, Limulus, by Ratliff, Hartline, and Miller (1963). Even a moderate change in the stimulus intensity, such as doubling or halving, produced an immediate change in the discharge rate of a single unit of the optic nerve, as seen in Fig. 10. This figure shows the effect of a doubling of the light stimulus, and then a return of the stimulus to its former level. The response frequency increases rapidly to more than twice its original value when the light is increased, and in about 0.5 sec returns to the base line. Then when the light intensity is dropped to its initial level, the frequency falls abruptly and soon rises to the base level once more.
Figure 10