I do not want to poison this forum with politics. But I want to understand, precisely, what is meant by the bolded statement. It is made by a physicist who used to work at Harvard regarding the relationship between pure math and physics.
A physics-oriented question appears at the end of Chapter 3: Are we really talking about continuous objects themselves or about finite sequences of symbols that talk about continuum?
That's a good question and I am inclined to say the latter. If we talk about specific things, these specific things are always countable because they must be describable by a finite sequence of symbols. Even when we talk about intervals of real numbers that arguably contain an uncountably infinite number of real numbers, we must still specify the endpoints of the interval by a finite sequence of words or symbols – and such sequences are "discrete" i.e. "countable".
This is why I tend to consider the very fact that real numbers are uncountable to be nothing else than a linguistic curiosity: the actual, well-defined real numbers you may ever encounter form a countable set! This is why the uncountability of the real numbers – and the whole discipline of maths based on this formally provable claim and similar claims – doesn't have implications for "talking about physics".
Here is the link to the full blog. If you want more context, I would suggest to start reading from the "Chapter 2 talks about sets, their elements..." part.
It appears he is talking about the symbols and notation we write down to describe the real numbers. But the bolded part is explicitly referring to the set of real numbers.