I cannot look at a 16-digit credit card number and tell whether I've mistyped it or not. And neither can anyone else. I can, however, easily examine four separate four-digit numbers and spot typos.
1341329913245890 or 1341 3299 1324 5890? The choice is obvious. Yet most websites will not accept anything but the 16-digit string. It's a trivial matter to strip the spaces and normalize the credit card number, and it speaks to the incompetence of many website developers that they don't do this. The cognitive burden should be pushed onto the programmer, not the user.
On a related note, Irish people write phone numbers as a seven-digit string. I can't parse 6274986 at a glance either, but I can parse the US-style form, 627-4986.