"Every perception is to some degree an act of creation, and every act of memory is to some degree an act of imagination."

-- Gerald Edelman, Second Nature: Brain Science and Human Knowledge
1 How to invent Hindu-Arabic numerals?3 How to invent Hindu-Arabic numerals?How to invent Hindu-Arabic numerals?How can we develop transformative tools for thought?2020-10-18JournalWe can't know the answer to this question for sure. But it's worth pointing out that the Hindu-Arabic numerals aren't just an extraordinary piece of design. They're also an extraordinary mathematical insight. They involve many non-obvious ideas, if all you know is Roman numerals. Perhaps most remarkably, the meaning of a numeral actually changes, depending on its position within a number. Also remarkable, consider that when we add the numbers 72 and 83 we at some point will likely use 2+3=5; similarly, when we add 27 and 38 we will also use 2+3=5, despite the fact that the meaning of 2 and 3 in the second sum is completely different than in the first sum. In modern user interface terms, the numerals have the same affordances, despite their meaning being very different in the two cases. We take this for granted, but this similarity in behavior is a consequence of deep facts about the number system: commutativity, associativity, and distributivityThe same phenomenon occurs in the conventional grade-school algorithms for multiplication and division. One of us has spun a short piece of discovery fiction discussing in more detail the way a hypothetical designer might have arrived at these ideas.. All these properties (and many more) point to the design and mathematical insights being inextricably entangled: the mathematical insights are, in some sense, design insights, and vice versa. Continue reading…