[saulpw]

It feels like that at first glance because you haven't done the work to internalize the notation. This is like someone who uses Roman Numerals being introduced to decimal notation, and getting confused that "22" isn't just twice "2". Yet no one these days would say that decimal notation is merely syntactic shuffling.

The notation helps, but you still have to do the work.

[Diogenesian]

This is uncharitably condescending because I myself am not confused by the notation. Obviously I "did the work."

It absolutely is syntactic shuffling of scientific notation and does nothing to solve the problem of intuitive scale that scientific notation doesn't already handle. The problem is that, unlike 2 and 22, 10^16 is simply not an intuitive quantity, and pretending it is because of Knuth notation / whatever is only displacing the misunderstanding.

[saulpw]

Sorry it felt condescending. I'm sure you think it's obvious that you "did the work" because you know about scientific notation and understand the notation. I thought I had done it too, but more and more I see how my internal number line is/was still fragmented, and gets better when I think in terms of exponents first/foremost.