Carr opens with a history of how memory and thoughts about memories have changed over time. Then he discusses the biology of how memories form.
Finally he gets to the impact of technology on memory. Calculators helped students learn deeper mathematics concepts because they freed up a student’s working memory to learn the concepts. The internet on the other hand forces a user to make many choices and offers many distractions. So, looking up a fact on the internet taxes working memory and makes it harder to learn something since the cerebral cortex has less resources to devote to memory formation.
Further, many have said that the internet frees up brain space for higher thought since facts can be looked up instead of memorized. Instead, less practice memorizing leads to weaker memories. Humans don’t have a practical limit on the number of memories they can form so no space is really saved by not memorizing something. And as mentioned above when you look things up you expend part of your working memory on that task.
There is therefore something to be said for memorizing commonly used facts, formulas and processes. This fits nicely with what I have read before about becoming an expert in a subject. You need a base of information that you can recall easily. You also need to know the commonly used processes in that field.