How does Johannes Schmidt’s wave theory explain the spread of language changes?

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Ferdinand de Saussure seated in a formal pose, wearing a dark suit with a vest and sporting a thick mustache, circa 1900. — Linguistics Much of the foundation of 20th-century sociolinguistics was created by the Swiss linguist Ferdinand de Saussure (1857–1913).

Johannes Schmidt’s wave theory was proposed in 1872 as a critique of the "family tree" model, which incorrectly assumes that languages diverge through sharp, independent splits. Instead, Schmidt argued that linguistic evolution is characterized by both divergence and convergence.1

According to the wave theory, linguistic changes spread outward from a central point—such as a politically, commercially, or culturally influential hub—along established lines of communication. These innovations ripple through speech communities like waves.1

Key aspects of this theory include:
* Variable Reach: Successive linguistic innovations do not necessarily cover the same geographic area, meaning different changes may have different boundaries.1
* Gradual Transitions: Because changes spread across space rather than through sudden cleavage, there are no sharp, absolute distinctions between contiguous dialects.1
* Distance Correlation: In general, the theory posits that the greater the physical distance between two speech communities, the more linguistic features will distinguish them from one another.1

This model better accounts for the reality of language contact and the ongoing influence of dominant speech forms on nonstandard varieties.1