148 The Phenomena of Morphogenesis 



pressions are in soft and watery structures which seem to be a direct 

 expression of protoplasmic configuration. Even though protoplasm is seem- 

 ingly an amorphous and semiliquid material, these structures that it builds 

 are far from formless, and the beautiful symmetries that they display 

 seem clearly to be manifestations of the fundamentally symmetrical char- 

 acter of living stuff itself. Organic symmetry presents a basic problem for 

 students of morphogenesis. 



INORGANIC AND ORGANIC SYMMETRIES 



There are many examples of symmetry among inorganic objects. These 

 often resemble the symmetries of living things, but there are certain 

 fundamental differences between them. What the relation between these 

 two types may be and whether organic symmetries have their origin in 

 those of the inorganic world are problems that have long been discussed 

 but are still far from solution. 



The arrangement of iron filings around the two poles of a magnet is a 

 familiar example of symmetry, as are the lines of force in an electrostatic 

 field. The least-surface configurations shown by liquids and especially by 

 liquid film systems provide beautiful examples of symmetry. The resem- 

 blance of such systems to multicellular structures in plants and animals, 

 particularly the more minute ones, has been observed by many biologists 

 and is discussed at length by D'Arcy Thompson ( 1942), who has analyzed 

 the various forms possible in a film system. The molecular forces that 

 operate here, however, are probably not important in determining the 

 symmetry of large organic bodies. 



Much is now known, from X-ray studies and other sources, of the actual 

 structure of molecules, and these are found to display symmetries, often 

 very complex and specific ones. Whether such molecular forms have any 

 relation to the bodily forms of plants and animals is a problem which has 

 aroused much speculation but on which little evidence is available. Harri- 

 son ( 1945 ) has discussed some of the possibilities here. 



Crystals provide the most familiar and remarkable examples of sym- 

 metry in the inorganic world. Their very specific forms are the reflection 

 of the forms and relationships of the molecules that compose them. The 

 study of crystal symmetry is a complex science in itself and has intimate 

 relationship to geometry, chemistry, and mineralogy. Crystals possess 

 axes and planes of symmetry, as do organic structures, but crystalline sym- 

 metry is a much more formalized and rigid phenomenon than organic. 

 Many biologists have endeavored to find a relation between crystals and 

 organisms in their form and symmetry, but this search, in general, has 

 been a rather fruitless one. Organic symmetries can be described in the 

 same geometrical language that we use for crystals, but whether there is 



