Proto-World Languagelanguages descend. A famous example stating this has been the Biblical story about the Tower of Babel.
The American linguist Joseph H. Greenberg claimed that long-distance relationships can be shown by applying an approach he called mass comparison. The languages are compared by using a limited set of words (including function words and affixes) simply by means of counting cognates. He used this method to establish a classification of African Languages. His work has generated considerable interest outside the linguistic community. It is still much debated.
Traditional historical linguistics state that so far it has been impossible to show that all the world's languages are genetically related. Critics say that from the purely statistical point of view, among any two unrelated languages, there would be more than 40% of words sharing a roughly similar sound and meaning. Therefore, the concept of comparing languages basing only on general comparisons between their vocabularies is considered flawed.
Hans Henrich Hock and Brian D. Joseph, Language History, Language Change, and Language Relationship: An Introduction to Historical and Comparative Linguistics. Mouton de Gruyter, Berlin 1996; chapter 17