homomorphy
Noun 1. Similarity of form: The state or quality of having the same or a similar form, shape, or structure. In biology, it refers to the resemblance in form between different organisms or parts that are not related by common ancestry. In mathematics, it relates to a mapping between two algebraic structures that preserves the operations.
- General/Biological Context:
- The homomorphy between the wings of birds and insects is a classic example of convergent evolution, not common descent.
- Scientists study the homomorphy in leaf shapes across different plant families.
- Mathematical Context:
- The concept of homomorphy is fundamental in group theory, describing structure-preserving maps between groups.
- Cryptic Homomorphy: In evolutionary biology, this refers to a superficial structural similarity that makes organisms difficult to distinguish, often as an adaptation (e.g., in mimicry).
- The cryptic homomorphy between the harmless moth and its toxic model is a defense mechanism.
- Homomorphic (adjective): Having similarity of form. Describes an object or map that exhibits homomorphy.
- The two algebraic systems are homomorphic.
- Homomorphism (noun): This is the more precise and commonly used term in mathematics for the structure-preserving map itself, rather than the abstract quality of similarity. It is often used interchangeably with "homomorphy" in technical contexts but refers specifically to the function or mapping.
- A ring homomorphism must preserve both addition and multiplication.
- Similarity
- Resemblance
- Analogy (especially in non-mathematical contexts)
- Isomorphism (specifically in mathematics for a bijective homomorphism, implying a perfect structural correspondence)
The core meaning is "similarity of form." Its application differs significantly by field: 1. Biology: Indicates a similarity in morphology (form/structure) that arises from convergent evolution or adaptation, not from shared ancestry (which is homology). 2. Mathematics: Indicates a correspondence between two algebraic structures (like groups, rings) where the operations are preserved. It is the foundational concept for a homomorphism.
- similarity of form