You're taking that bit out of context. In that sentence he's talking about a very specific thought experiment in which we constuct a theory that certain digits

You're taking that bit out of context. In that sentence he's talking about a very specific thought experiment in which we constuct a theory that certain digits in the root of 17 and the 27th power of pi match. I think his arbitrary example is supposed to be an analogy of Godel's work. Example: let’s say that the decimal expressions of the square root of 17 and pi to the 27th power “match” just in case either they have the same digit in the tenths place, or the same two digits in the next two places, or the same three digits in the next three places, etc. The point of his example here is that the 'match' is defined in never-ending terms. If the 10th digit doesn't match, you check the next two. If they don't match, you check the next three. And so on. You can go on comparing digits forever, even though finding a 'match' becomes less and less likely.