"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
3 How to invent Hindu-Arabic numerals？5 How to invent Hindu-Arabic numerals？How to invent Hindu-Arabic numerals？How can we develop transformative tools for thought？2020-10-18Journal
This is rather sobering if we compare to conventional modern design practice. In a typical practice, you'd interview domain experts (in this case, mathematicians), and read any relevant literature. You'd talk to users of existing systems, and analyze serious behavior, both individually and at scale. In short, you'd do what people in the design community refer to as immersing themselves in the target field.
This is a powerful practice. At its best it causes systems to come into existence which would otherwise be inconceivable. If applied to Roman numerals (in hypothetical ancient Rome, not todayOf course, a designer who spoke to an expert on, say, Babylonian mathematics, might well have come across some of these ideas. We'll ignore that, since it depends on the oddity that many excellent prior ideas about numeral systems had been displaced in Roman culture.) this practice would likely improve them a great deal. But it would not provide anywhere near the level of mathematical insight needed to arrive at Hindu-Arabic numerals.