Michael Nielsen (with Andy Matuschak) also wrote about how Hindu-Arabic numerals enabled more powerful kinds of thinking (compared with Roman numerals.)
> ...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 distributivity
I think that is partly why LLMs are bad at math and often fail at counting subsequences. Play with the tokenizer and you see long numbers are split into groups of 2 or 3 numbers.
The main advantage of Arabic numerals on paper have is that operations are non destructive and you can restarts a calculation if you lose your place. The main disadvantage is memorising the times table and the amount of scratch paper you need.
https://numinous.productions/ttft/#how-to-invent-hindu-arabi...
> ...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 distributivity