In the Introduction, the word 'isomorphism' was defined as an information preserving transformation. We can now go into that notion a little more deeply, and see it from another perspective. The word 'isomorphism' applies when two complex structures can be mapped onto each other, in such a way that to each part of one structure there is a corresponding part in the other structure, where 'corresponding' means that the two part play similar roles in their respective structures. This usage of the word 'isomorphism' is derived from a more precise notion in mathematics. Meaning and Form in Mathematics 57 It is cause for joy when a mathematician discovers an isomorphism between two structures which he knows. It is often a 'bolt from the blue', and a source of wonderment. The perception of an isomorphism between two known structures is a significant advance in knowledge-and I claim that it is such perceptions of isomorphism which create meanings in the minds of people. A final word on the perception of isomorphisms: since they come in many shapes and sizes, figuratively speaking, it is not always totally clear when you really have found an isomorphism. Thus, 'isomorphism' is a word with all the usual vagueness of words-which is a defect but an advantage as well.

• meaning
• roles
• knowledge
• perspective
• structure
• joy
• perception
• mathematics
• transformation
• other