One might suppose that reality must be held to at all costs. However, though that may be the moral thing to do, it is not necessarily the most useful thing to do. The Greeks themselves chose the ideal over the real in their geometry and demonstrated very well that far more could be achieved by consideration of abstract line and form than by a study of the real lines and forms of the world; the greater understanding achieved through abstraction could be applied most usefully to the very reality that was ignored in the process of gaining knowledge.

Summary

This quote suggests that focusing solely on reality may not always be the most advantageous approach. The Greeks' emphasis on ideal concepts rather than real-world observations, as evidenced by their study of geometry, demonstrated the power of abstraction. By delving into abstract ideas of lines and forms, they gained a deeper understanding that could be applied effectively to the real world. This implies that exploring beyond reality, through abstract thinking and concepts, can often lead to a greater understanding and more practical knowledge in relation to the actual reality being studied.

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