An article in the November-December 2017 issue of American Scientist on pictorial mathematical languages features the Quon Language created by Harvard mathematicians Zhengwei Liu, Alex Wozniakowski, and Arthur M. Jaffe. The Quon project includes the study of two-dimensional, three-dimensional, and higher-dimensional languages. "This pictorial language for mathematics can give you insights and a way of thinking that you don’t see in the usual, algebraic way of approaching mathematics," says Jaffe.
Fig. 2. Inverse design of vegetable, animal, and mineral surfaces.*
Nature has a way of making complex shapes from a set of simple growth rules. The curve of a petal, the swoop of a branch, even the contours of our face are shaped by these processes. What if we could unlock those rules and reverse engineer nature's ability to grow an infinitely diverse array of shapes?
Top images (A): Illustrates the development of stem cells on hydrogel, a soft substrate, to pre-bone cells after the removal of water. Bottom images (B): Depicts the development of stem cells on glass, a hard substrate, to pre-fat cells after the addition of water.*
Adding or removing water from a stem cell can change the destiny of the cell, researchers have discovered in a new study published in the Proceedings of the National Academy of Sciences of the United States of America (PNAS).
Waves of vertebrae-building signals pulse outward in mouse cells mimicking a developing embryo.
Like a string of pearls, the spine is made of a series of similar vertebrae. A so-called segmentation clock creates this repetitive arrangement in developing embryos: Each time the clock ticks, a vertebra starts to form.