“A metaphor is not an ornament. It is an organ of perception. Through metaphors, we see the world as one thing or another.” (Neil Postman)
“[…] an idea is a feat of association, and the height of it is a good metaphor.” (Robert Frost)
“Human thinking depends on metaphor. We understand new and complex things in relation to the things we already know […] once you pick a metaphor it will guide your thinking.” (Jonathan Haidt)
“[…] key metaphors help determine what and how we perceive and how we think about our perceptions.” (Meyer H Abrams)
“Metaphor is pervasive in everyday life, not just in language but in thought and action. Our ordinary conceptual system, in terms of which we both think and act, is fundamentally metaphorical in nature.” (George Lakoff)
"Metaphor [...] may be said to be the algebra of language." (Charles C Colton, "Lacon", 1820)
“The metaphor never goes very far, anymore than a curve can long be confused with its tangent.” (Henri Bergson, “A World of Ideas”, 1989)
“The price of metaphor is eternal vigilance.” (Arturo Rosenblueth & Norbert Wiener)
“The progress of science requires more than new data; it needs novel frameworks and contexts. And where do these fundamentally new views of the world arise? They are not simply discovered by pure observation; they require new modes of thought. And where can we find them, if old modes do not even include the right metaphors? The nature of true genius must lie in the elusive capacity to construct these new modes from apparent darkness. The basic chanciness and unpredictability of science must also reside in the inherent difficulty of such a task.” (Stephen J Gould)
“Thought is metaphoric, and proceeds by comparison, and the metaphors of language derive therefrom.” (Ivor A Richards) [Link]
Quotes and Resources Related to Mathematics, (Mathematical) Sciences and Mathematicians
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