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This important distinction is both applied in the context of environmental as well as social sustainability. However, further elaboration is necessary to capture the complexities of sustainability assessments in the context of AI. To this end, our analysis of the ends and means of \u201csustainable AI\u201d in social and environmental contexts leads to a matrix of four dimensions reflecting its social and its environmental impact and costs. This matrix avoids overly narrow, one-dimensional assessments that too quickly label some AI-based technology as sustainable. While a selective assessment can, at best, warrant the narrower verdict of \u201cthin\u201d sustainability, only such a comprehensive assessment can warrant the verdict of what we call \u201cthick\u201d sustainability. In consequence, we recommend to broaden the normative scope in considering the ethics and justice of AI and to use the notion \u201csustainability\u201d more carefully and sparingly, and to pursue the more ambitious goal of \u201cthick\u201d sustainability of AI-based technologies to meaningfully contribute to actual improvements of human lives and living together. Current conditions of an economy oriented towards permanent growth, however, may make it difficult or even impossible to realise sustainable AI.<\/jats:p>","DOI":"10.1007\/s43681-023-00259-8","type":"journal-article","created":{"date-parts":[[2023,2,2]],"date-time":"2023-02-02T09:12:24Z","timestamp":1675329144000},"page":"201-212","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":30,"title":["Beware of sustainable AI! 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