The ugly duckling theorem is an argument showing that classification is not really possible without some sort of bias. More particularly, it assumes finitely many properties combinable by logical connectives, and finitely many objects; it asserts that any two different objects share the same number of (extensional) properties. The theorem is named after Hans Christian Andersen's 1843 story "The Ugly Duckling", because it shows that a duckling is just as similar to a swan as two swans are to each other. It was derived by Satosi Watanabe in 1969.
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| - Ugly-Duckling-Theorem (de)
- Teorema del brutto anatroccolo (it)
- Twierdzenie o Brzydkim Kaczątku (pl)
- Ugly duckling theorem (en)
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| - Das Ugly-Duckling-Theorem (zu deutsch Hässliches-Entlein-Theorem) ist ein Satz über Ähnlichkeiten verschiedener Merkmale und damit verbundene Aussagen für die Mustererkennung. Es wurde von Satoshi Watanabe bewiesen und trägt seinen Namen nach dem Kunstmärchen Das hässliche Entlein. (de)
- The ugly duckling theorem is an argument showing that classification is not really possible without some sort of bias. More particularly, it assumes finitely many properties combinable by logical connectives, and finitely many objects; it asserts that any two different objects share the same number of (extensional) properties. The theorem is named after Hans Christian Andersen's 1843 story "The Ugly Duckling", because it shows that a duckling is just as similar to a swan as two swans are to each other. It was derived by Satosi Watanabe in 1969. (en)
- Il teorema del brutto anatroccolo (orig. Ugly duckling theorem) dimostrerebbe secondo Satoshi Watanabe come sia impossibile classificare senza un qualche criterio di preferenza (o bias). Esso è così chiamato per via dell'omonima famosa favola di Hans Christian Andersen, in quanto mostra che, se tutto quanto fosse uguale, un brutto anatroccolo sarebbe tanto simile ad un cigno quanto i cigni lo sono tra loro. È stato proposto da Satoshi Watanabe nel 1969. (it)
- Twierdzenie o brzydkim kaczątku (ang. the Ugly duckling theorem) – twierdzenie mówiące, że żadna klasyfikacja nie jest możliwa bez stronniczości: dowolne dwa obiekty, o ile tylko są odróżnialne, są do siebie równie podobne. Udowodnił je w 1969 r. Nazwa twierdzenia wiąże się z bajką Hansa Christiana Andersena z 1843 r. pt. „Brzydkie kaczątko”, ponieważ twierdzenie to wykazuje, że kaczątko jest tak samo podobne do łabędzia, jak dwa łabędzie podobne są do siebie. (pl)
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| - Das Ugly-Duckling-Theorem (zu deutsch Hässliches-Entlein-Theorem) ist ein Satz über Ähnlichkeiten verschiedener Merkmale und damit verbundene Aussagen für die Mustererkennung. Es wurde von Satoshi Watanabe bewiesen und trägt seinen Namen nach dem Kunstmärchen Das hässliche Entlein. (de)
- The ugly duckling theorem is an argument showing that classification is not really possible without some sort of bias. More particularly, it assumes finitely many properties combinable by logical connectives, and finitely many objects; it asserts that any two different objects share the same number of (extensional) properties. The theorem is named after Hans Christian Andersen's 1843 story "The Ugly Duckling", because it shows that a duckling is just as similar to a swan as two swans are to each other. It was derived by Satosi Watanabe in 1969. (en)
- Il teorema del brutto anatroccolo (orig. Ugly duckling theorem) dimostrerebbe secondo Satoshi Watanabe come sia impossibile classificare senza un qualche criterio di preferenza (o bias). Esso è così chiamato per via dell'omonima famosa favola di Hans Christian Andersen, in quanto mostra che, se tutto quanto fosse uguale, un brutto anatroccolo sarebbe tanto simile ad un cigno quanto i cigni lo sono tra loro. È stato proposto da Satoshi Watanabe nel 1969. (it)
- Twierdzenie o brzydkim kaczątku (ang. the Ugly duckling theorem) – twierdzenie mówiące, że żadna klasyfikacja nie jest możliwa bez stronniczości: dowolne dwa obiekty, o ile tylko są odróżnialne, są do siebie równie podobne. Udowodnił je w 1969 r. Nazwa twierdzenia wiąże się z bajką Hansa Christiana Andersena z 1843 r. pt. „Brzydkie kaczątko”, ponieważ twierdzenie to wykazuje, że kaczątko jest tak samo podobne do łabędzia, jak dwa łabędzie podobne są do siebie. (pl)
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