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"OH WATERS, TEEM WITH MEDICINE TO KEEP MY BODY SAFE FROM HARM, SO THAT I MAY LONG SEE THE SUN." - Rig Veda
A pattern emerges: humans invent mathematical concepts by way of abstracting elements from the world around them—shapes, lines, sets, groups, and so forth—either for some specific purpose or simply for fun. They then go on to discover the connections among those concepts. Because this process of inventing and discovering is man-made—unlike the kind of discovery to which the Platonists subscribe—our mathematics is ultimately based on our perceptions and the mental pictures we can conjure. For instance, we possess an innate talent, called subitizing, for instantly recognizing quantity, which undoubtedly led to the concept of number. We are very good at perceiving the edges of individual objects and at distinguishing between straight and curved lines and between different shapes, such as circles and ellipses—abilities that probably led to the development of arithmetic and geometry. So, too, the repeated human experience of cause and effect at least partially contributed to the creation of logic and, with it, the notion that certain statements imply the validity of others.