### Wu on place value

[T]he rules of place value are logical consequences of the way we choose to count. By choosing to use 10 symbols (0 to 9), we are forced to use no more than [sic] one position (place) to be able to count to large numbers.

### What i think he’s saying

I have never heard of Roman numerals.

Hmmm, I’m not sure how Roman numerals contradict Wu’s argument. Roman numerals certainly have place value, although the rules are different. Either way, you’ve piqued my curiosity in this article. How does Wu plan to fold this into an argument on how Common Core standards are phoenixes? The suspense is killing me.

Roman numerals are positional, not based on place value. “I” is always equal to 1, no matter where it appears. Sometimes it means “subtract 1” and sometimes it means “add 1”, but it’s never anything but 1. The rules of place value value, though, require that 1 sometimes means 1 unit, sometimes 1 group; but which depends on where it is in the number.

Plus, you can do Roman numerals without that positional requirement. No need to write 4 as IV; you could just as easily write IIII.

The point is that place value is actually a very, very complex system. It is not just the “logical consequence” of a choice made in advance; it is the result of many thousands of years of human development. There are other assumptions you have to build into the model before place value pops out as a consequence (some degree of compactness of numeration, for instance, and of ease of arithmetic-Roman numerals fail on both of these, but they don’t fail the test of

number of digits required to represent any counting number).As for the other question? Gotta read the article. Link to free pdf in previous post.

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