Mathematicians From Germany

"In 1923, when I had been a student at the 'Bauhaus' in Weimar.. ..Gropius [the director of Bauhaus] asked me to teach the basic course 'Werklehhre'. He wanted me to introduce newcomers to the principles of handicrafts. He knew that I came from that background and had appropriate practice and knowledge."

"I made true the first English sentence [Albers came from Germany] that I uttered (better stuttered) on our arrival at Black Mountain College in November 1933 [right after the closing of the Bauhaus art school in Dessau Germany, by the Nazi's] When a student asked me what I was going to teach I said: 'to open eyes'. And this has become the motto of all my teaching [famous pupils of Josef Albers at Black Mountain College were for instance the young generation starting American artists, like Robert Rauschenberg, Helen Frankenthaler, Cy Twombly, Ray Johnson and Susan Weil."

"I think it's true, as many say, I have dealt for many years with the problems that w:Op art so-called, is dealing with. For many years I have studied the logic and magic of color. And so I know what's involved when it comes to the interaction of colors, more than many who refuse to study it. But I found a way to study it, I think, that's all. And besides I refuse to be the father of a new bandwagon."

"That question is so big that there is no end [Albers refers here to the relationship between colors and the source of light]. You see, they have just you cannot participate with it if you have not lubricated your eyes very thoroughly to see the little changes produced in our eye that has another action than any optical apparatus like photography. We must know that we have two ways of seeing. For instance, when we are indoors another part of the retina is engaged compared with when we are outdoors. If we are in warm light or cool light, in higher light or lower light."

"I have not built any theory. I have only tried to build up sensitive eyes, as my book says. And I have tried to achieve that by aiming at very distinct color relationships again – like how do they influence each other? Change each other in light and in intensity, in transparency, opacity? How do they change each other in all different directions? That we make all the students aware, through experience, that color is the most relative medium in art, and that we never really see what we see. All neighboring means which occur every minute different, not only in changing light but also by our changing moods. And in the end, the study of color again is a study of ourselves."

"I say all the time, if I sell that to you, you pay me for 3 colors. And I sell you 4, I betray you. Not to cheat you, but to pet you. You see I betray you in a positive way. I make you see more than there is. And that's in all my art that way. Absolutely something else. And that's what my book is about. You never see what you see. I lead you to see something else. And therefore I direct you. That's help."

"I would say, 'My things have the look of icons.' Unconsciously they look at you not as my face is now – you see me in profile – icons are only this way. And so are my paintings."

"I have received a question I have expected, 'Don't you deal with accidents?' Yes, I deal with accidents, just as Arp admits it all the time. And I admit it, too. But I like to have them under my command and not sign them because they are accidents. If it remains only accident then sign it 'accident' or 'fate' or 'the Lord', whatever you prefer. It's not you because you have not visioned it. You see visual formulation deals with vision, visual information and visual reaction. So I speak differently from all those who deliver themselves to uncontrolled accidents."

"Duplicity in events: What happens here as new, happens somewhere else just the same way. That's so exciting. That is one of the secrets of life. Why did I sometimes build a lamp in the Bauhaus and somebody comes from Holland and says, 'Oh, somebody in Holland makes just the same lamp.' Such duplicity shows that the time is ripe for a problem and thus it is in the air, and will be solved here – and there. With this we are finding the 'creative process', for which somebody is coming to ask me about. I would say, 'I paint because I have no time not to paint.' That's my creative process."

"There science is dealing with physical facts, in art we are dealing with psychic effects. With this I come to my first statement: 'The source of art – that is, where it comes from – is the discrepancy between physical fact and psychic effect'. That's what I'm talking about. When I want to speak about why I am doing the same thing now, which is squares, for – how long? – 19 years. Because there is no final solution in any visual formulation. Although this may be just a belief on my part, I have some assurances that that is not the most stupid thing to do, through Cezanne whom I consider as one of the greatest painters. From Cézanne we have, so the historians tell us – 250 paintings of Mont St. Victoire. But we know that Cézanne has left in the fields often more than he took home because he was disappointed with his work. So we may conclude he did many more than 250 of the same problem."

"Yes it was 1949. How I came to that. That's like how one gets to know a human being. It so happens that I've always had a preference – as everyone has prejudices and preferences – for the square as a shape in preference to the circle as a shape. And I have known for a long time that a circle always fools me by not telling me whether it's standing still or not. And if a circle circulates you don't see it. The outer curve looks the same whether it moves or does not move. So the square is much more honest and tells me that it is sitting on one line of the four, usually a horizontal one, as a basis. And I have also come to the conclusion that the square is a human invention, which makes it sympathetic to me. Because you don't see it in nature. As we do not see squares in nature, I thought that it is man-made. But I have corrected myself. Because squares exist in salt crystals, our daily salt. We know this because we can see it in the microscope. On the other hand, we believe we see circles in nature. But rarely precise ones. Nature, it seems, is not a mathematician. Probably there are no straight lines either. Particularly not since Einstein says in his theory of relativity that there is no straight line, rod knows whether there are or not, I don't. I still like to believe that the square is a human invention. And that tickles me. So when I have a preference for it then I can only say excuse me."

"Art is not to be looked at. Art is looking at us. What is art to others is not necessarily art to me. Nor for the same reason and vice versa. What was art to me or was not some time ago might have lost that value or gained it in the meantime and maybe again though art is not an object but experience. To be able to perceive it we need to be receptive. Therefore art is there where art meets us now. The content of art is visual formulation of our relation to life. The measure of art, the ratio of effort to effect, the aim of art revelation and evocation of vision."

"When we are honest – that's my saying – if we are honest then we will reveal ourselves. But we do not have to make an effort to be individualistic, different from others. You see that is the nonsense of the last 15, 20 years [Albers refers here critically to American Abstract Expressionism ]. What is wrong there is that everyone wants to be different from the already different ones. And then they ended up all alike. And we are tired of that. And the youngsters feel that now. And they don't continue, you see. They see this will not last. These exaggerated performers always speak in the highest dramatic voice. And in order to achieve it get always drunk before you come to action. Sick. It's over. So I'm quite critical against many of my colleagues. It is not their self-expression. What makes me to be more than my neighbor only when I think I have to say something more than he can. That is self-disclosure. I once gave a talk in Chicago and right in the beginning I said – a lady came to me and said, 'You are against self-expression. And I am mad against you now.' 'And I'll stand upside down to demonstrate that, I said, 'Stop the sentence. You are self-disclosing; you are not self-expressing.'"

"This is what has Gropius the director made the Bauhaus famous. Not its lamps or its furniture. They are all out of fashion already. But the way of approaching formal problems or material as such, that has made it famous. And the emphasis on material, especially its capacity is my contribution. That was never cleared between us teachers. Kandinsky did what he thought should be done. Klee developed an absolutely different method. Schlemmer developed absolutely something else. Klee was my so-called form master. In the workshops there they had a crafts master and a form master. The crafts master had to direct the practical work, the mechanics of the workshop. And the form master had to develop the, formal qualities. Klee was my form master in the glass workshop. He came to me and never criticized anything. He talked about something else. Never asked about any form problem with the windows I was working on. Never a word. He was too respectful. He was the nicest master I could ask for. He talked about exhibitions. He thought I should exhibit. That's another story. We had a good relationship because we never dealt with the same problems. He didn’t attack our problems. He never brought up a problem."

"I had to go to the Bauhaus to the basic course that was given by Itten. And I submitted to that although I was a little older than Itten. But I have not the best memories of my studies there. So when that course was over everyone had to exhibit his work and then it was decided whether or not one could continue. I was accepted to continue. But I wanted to go into a workshop and I wanted to make stained glass. That was my old dream. Glass pictures. But Itten thought I was not ready for that. Certainly to delay my study in glass, Itten said, 'Glass painting is a branch of wall painting and you should go first to our wall painting workshop,' And I said, 'That's nonsense. Wall painting has to do with reflected light and glass painting with direct light.' So I said 'Sorry, I'll do my own stuff on my own.' I had no money. Just a Rucksack and a hammer. And I started these assemblages. That was in 1921, But in all books on assemblages these things are not mentioned."

"I made my examination in Berlin in 1915. And I must say also that Berlin was for me in another way very important. At the time there were all these new movements – 'Die Brücke'... ...the 'Der Blaue Reiter', Walden of the 'Storm' Gallery. Then Kassierer who bought the Chagalls, the first Chagall's that were ever seen in Europe were there. And there was 'Die Brücke'. Rottluff, Heckel, and Kirchner. You know we saw all that. Which was good. You see, Kassierer was then the man who bought the modern French painters. He had particularly Degas who I consider still today a very good painter, one of the best. But, anyway, in spite of my teaching my art was my concern. On the little money I had collected I lived in Berlin very cheaply, ate very cheaply. And already in 1920 I saved the first salaries I received to go to Munich.. .So for the first time I saw the old masters, Rubens and all at the Alte Pinakothek."

"I discovered soon that teaching has the handicap of retrospection. And that I don't believe in. So I started [at the w:Bauhaus in Dessau] instead a method of handling material with the material itself. So that was my main change. Whereas Itten before [Itten left the Bauhaus in 1923 and Albers followed him as art-teacher] had only spoken about the appearance, 'matiere' - (the French word) and I said I would turn from 'matiere' - the outside - to the inside, to the capacity of the material, before the appearance. And that changed the attitude basically I think."

"And I learned very early [Josef Albers was then ten years old] how to make imitation of wood grain. This is something I have in common with Georges Braque. Braque also learned very early from his father how to imitate marble or wood grain. So I could easily make the appearance of oak or walnut on pine. That is very easy; a very simple technique. And I learned how to imitate marble. I never made such a good joke as Braque did. When he was in the Mediterranean he fooled his friends. He painted a rowboat that had wood on one side and marble on the other side. You see, when he'd row out of the city it looked as if he were in a boat of a different material than when he came back, you see, one side was imitation wood and the other side was imitation marble."

"I helped my father who was a house painter and decorative painter. He made stage sets, he made glass paintings, he made everything. I was in the workshop and watched him. So as a child so-called art was not my view. That was, in my opinion, my father's job. But I liked to watch him; he comes, as my mother also, from a very craftsman's background. My father's parents were carpenters. They were also builders partly. They were painters. And several of them were very, active in the theater and all such nonsense, you know. On my mother's side there was much more heavy craft. They were blacksmiths. They made a specialty horse shoes and nails for them.. .So, as a child, my main fun was to watch others working. I loved to walk to the neighboring carpenter's place and up to the neighboring shoemaker in my home town."

"Kepler states expressly that he gave the name Foci to certain points related to the conic sections which had previously "no name." With their new name he associated his new views about the points themselves, and his doctrines of Continuity (under the name Analogy) and Parallelism, which would soon have become known, and would after a time have been taken up by competent mathematicians.... A letter of Henry Briggs to Kepler [dated Mar 10, 1625] suggest improvements in the Paralipomena ad Vitellionem. In this letter Briggs... comprehended and accepted Kepler's way of looking at parallels as lines to or from a point at infinity in one direction or its opposite."

"My goal is to show that the heavenly machine is not a kind of divine living being but similar to a clockwork insofar as all the manifold motions are taken care of by one single absolutely simple magnetic bodily force, as in a clockwork all motion is taken care of by a simple weight. And indeed I also show how this physical representation can be presented by calculation and geometrically."

"Nature uses as little as possible of anything."

"The die is cast; I have written my book; it will be read either in the present age or by posterity, it matters not which; it may well await a reader, since God has waited six thousand years for an interpreter of his words."

"We do not ask for what useful purpose the birds do sing, for song is their pleasure since they were created for singing. Similarly, we ought not to ask why the human mind troubles to fathom the secrets of the heavens. The diversity of the phenomena of nature is so great and the treasures hidden in the heavens so rich precisely in order that the human mind shall never be lacking in fresh nourishment."

"In Terra inest virtus, quae Lunam del."

"There is a force in the earth which causes the moon to move."

"I much prefer the sharpest criticism of a single intelligent man to the thoughtless approval of the masses."

"I used to measure the heavens, now I measure the shadows of Earth. Although my mind was heaven-bound, the shadow of my body lies here."

"Temporis filia veritas; cui me obstetricari non pudet."

"Truth is the daughter of time, and I feel no shame in being her midwife."

"The earth is the sphere, the measure of all; round it describe a dodecahedron; the sphere including this will be Mars. Round Mars describe a tetrahedron; the sphere including this will be Jupiter. Describe a cube round Jupiter; the sphere including this will be Saturn. Now, inscribe in the earth an icosahedron, the sphere inscribed in it will be Venus: inscribe an octahedron in Venus: the circle inscribed in it will be Mercury."

"Either... the moving intelligences of the planets are weakest in those that are farthest from the sun, or... there is one moving intelligence in the sun, the common center, forcing them all round, but those most violently which are nearest, and that it languishes in some sort and grows weaker at the most distant, because of the remoteness and the attenuation of the virtue."

"Geometry has two great treasures: one is the Theorem of Phythagoras, the other the division of a line in extreme and mean ratio. The first we can compare to a mass of gold; the other we may call a precious jewel."

"I propose to show that God, in creating the universe and arranging the spheres, had in view the five regular solids of geometry, and fixed by their dimensions the number, proportions and motions of the spheres. Take the sphere of the earth as a unit and circumscribe it with a regular dodecahedron. The sphere that contains this dodecahedron is the sphere of Mars."

"Vim coeli reserate viri: venit agnita ad usus: Ignotae videas commoda nulla rei."

"Discover the force of the heavens O Men: Once recognised it can be put to use: No use could be seen in unknown things."

"He who will please the crowd and for the sake of the most ephemeral renown will either proclaim those things which nature does not display or even will publish genuine miracles of nature without regard to deeper causes is a spiritually corrupt person… With the best of intentions I publicly speak to the crowd (which is eager for things new) on the subject of what is to come."

"I believe it was an act of Divine Providence that I arrived just at the time when Longomontanus [Tycho Brahe's assistant before Kepler] was occupied with Mars. For Mars alone enables us to penetrate the secrets of astronomy which otherwise would remain forever hidden from us."

"Every corporeal substance, so far forth as it is corporeal, has a natural fitness for resting in every place where it may be situated by itself beyond the sphere of influence of a body cognate with it."

"Gravity is a mutual affection between cognate bodies towards union or conjunction (similar in kind to the magnetic virtue), so that the earth attracts a stone much rather than the stone seeks the earth."

"...wheresoever the earth may be placed, or whithersoever it may be carried by its animal faculty, heavy bodies will always be carried towards it."

"If the earth were not round, heavy bodies would not tend from every side in a straight line towards the center of the earth, but to different points from different sides."

"If two stones were placed... near each other, and beyond the sphere of influence of a third cognate body, these stones, like two magnetic needles, would come together in the intermediate point, each approaching the other by a space proportional to the comparative mass of the other."

"If the moon and earth were not retained in their orbits by their animal force or some other equivalent, the earth would mount to the moon by a fifty-fourth part of their distance, and the moon fall towards the earth through the other fifty-three parts, and they would there meet, assuming, however, that the substance of both is of the same density."

"If the earth should cease to attract its waters to itself all the waters of the sea would be raised and would flow to the body of the moon."

"The sphere of the attractive virtue which is in the moon extends as far as the earth, and entices up the waters; but as the moon flies rapidly across the zenith, and the waters cannot follow so quickly, a flow of the ocean is occasioned in the torrid zone towards the westward."

"If the attractive virtue of the moon extends as far as the earth, it follows with greater reason that the attractive virtue of the earth extends as far as the moon and much farther; and, in short, nothing which consists of earthly substance anyhow constituted although thrown up to any height, can ever escape the powerful operation of this attractive virtue."

"Nothing which consists of corporeal matter is absolutely light, but that is comparatively lighter which is rarer, either by its own nature, or by accidental heat. And it is not to be thought that light bodies are escaping to the surface of the universe while they are carried upwards, or that they are not attracted by the earth. They are attracted, but in a less degree, and so are driven outwards by the heavy bodies; which being done, they stop, and are kept by the earth in their own place."

"But although the attractive virtue of the earth extends upwards, as has been said, so very far, yet if any stone should be at a distance great enough to become sensible compared with the earth’s diameter, it is true that on the motion of the earth such a stone would not follow altogether; its own force of resistance would be combined with the attractive force of the earth, and thus it would extricate itself in some degree from the motion of the earth."

"I was almost driven to madness in considering and calculating this matter. I could not find out why the planet would rather go on an elliptical orbit. Oh, ridiculous me! As the liberation in the diameter could not also be the way to the ellipse. So this notion brought me up short, that the ellipse exists because of the liberation. With reasoning derived from physical principles, agreeing with experience, there is no figure left for the orbit of the planet but a perfect ellipse."