Rembrandt and two circles

Rembrandt uses the minimum amount of visual information required to tell a story. In his later years he practiced abbreviation and omission so successfully that one sometimes imagines elements of the painting that aren’t there. In the beautifully blurred Self-Portrait With Two Circles, for example, one thinks one sees Rembrandt’s hand holding the palette and brushes. The circles on the wall behind Rembrandt are a mystery but may allude to a Renaissance theory that the ability to draw a perfect circle freehand was the mark of a great artist.

There are many theories surrounding the meaning of the circles. One is that they are mystical symbols representing the perfection of God, while another suggests they are symbols of theory and practice, with Rembrandt himself as the link between thought and execution. There is also the theory that the circles reflect a double-hemisphere world map – a map that depicts the eastern and western hemispheres as two globes. Others believe they were simply added to balance the off-centre composition.

The most popular theory focuses on a story about the great Italian painter Giotto (d.1337), who reputedly proved his artistic skill by drawing a perfect circle freehand. Although Rembrandt paints two incomplete circles rather than one perfect circle, scholars have suggested that he is associating himself with Giotto’s legendary genius, using his own distinctive, virtuoso style.

. composition of two circles in the 2nd dimension.

. then there is the study of completion of the 3rd dimensional shape.

. today there is the embodiment of the 4th dimension structure , which this website is helping me to complete..


mathematicians had to resort to plaster moulds or carving wood if they wanted a physical representation of a shape. “Mathematicians tend to think about objects that can be difficult to visualize, that are in more than two dimensions, and whose physical structure, arrangement, and symmetries are really vital to the understanding of the object,”
Another of his popular objects, called Grid, explores how to do four dimensional math without actually being able to perceive the fourth dimension. He explains it like this: If we lived in the second dimension, we wouldn’t be able to see objects in 3-D space—but we could make out their shadows cast onto a 2-D plane, however distorted. Grid is basically a map projection (technically called a stereographic projection)—a light source placed above the sphere projects the curved surface onto a flat plane. A 2-D person could see that grid, even if they weren’t able to perceive the sphere. Similarly, we 3-D people can theoretically perceive the shadow of an object in 4-D space squished down into our dimension.
Much of our understanding of the biological mechanisms that underlie cellular functions, such as migration, differentiation and force-sensing has been garnered from studying cells cultured on two-dimensional (2D) glass or plastic surfaces. However, more recently the cell biology field has come to appreciate the dissimilarity between these flat surfaces and the topographically complex, three-dimensional (3D) extracellular environments in which cells routinely operate in vivo. This has spurred substantial efforts towards the development of in vitro 3D bio mimetic environments and has encouraged much cross-disciplinary work among biologists, material scientists and tissue engineers. As we move towards more-physiological culture systems for studying fundamental cellular processes, it is crucial to define exactly which factors are operative in 3D microenvironments. Thus, the focus of this Commentary will be on identifying and describing the fundamental features of 3D cell culture systems that influence cell structure, adhesion, mechanotransduction and signalling in response to soluble factors, which – in turn – regulate overall cellular function in ways that depart dramatically from traditional 2D culture formats. Additionally, we will describe experimental scenarios in which 3D culture is particularly relevant, highlight recent advances in materials engineering for studying cell biology, and discuss examples where studying cells in a 3D context provided insights that would not have been observed in traditional 2D systems.

A turban is a kind of head-wear based on cloth winding. Featuring many variations, it is worn as customary head-wear, usually by men. Communities with prominent turban-wearing traditions can be found in South Asia, Southeast Asia, the Near East, the Arabian Peninsula, North Africa, the Horn of Africa, and parts of the Swahili Coast. Turbans worn in South Asia are known as Pagri.

Wearing turbans is common among Sikhs, who refer to it as a Dastar. In certain other faith communities, the headgear also serves as a religious observance, including among Muslims, who regard turban-wearing as Sunnah Mu’akkadah (confirmed tradition).

Additionally, turbans have often been worn by nobility, regardless of religious background. They are also sometimes donned to protect hair or as a headwrap for women following cancer treatments.

The turban is known as a very religious millinery hat. Though turbans have been around for thousands of years, the first mentioning of them was in the fourteenth century at the end of the Moorish rule in Spain. The Prophet Muhammad is believed to have worn a turban in white, the most holy colour. Many Muslim men choose to wear green, because it represents paradise, especially among followers of Sufism. In parts of North Africa, where blue is common, the shade of a turban can signify the tribe of the wearer. There have been over sixty-six types of Turbans. Hindus tend to reserve their turbans for ceremonies and significant occasions, whereas Sikh men wear them all the time. In Islamic countries, the headgear is regarded as Sunnah Mu’akkadah (Confirmed Tradition).

The origins of the turban is uncertain. Early Persians wore a conical cap encircled by bands of cloth, which historians have suggested was developed to become the modern turban, but other theories suggest it was first widely worn in Egypt. Sikh men commonly wear a peaked turban that serves for the purpose of covering their long hair, which in respect for God’s creation is never cut. Devout Sikhs do not cut their beards either, so many instead twist them and tuck them up into their turbans. A style of turban called a phakeolis was also worn by soldiers of the Byzantine army.