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Hadn't heard about John Dee before, seems like a pretty cool dude like Alberti was. I've been wondering if your current society prevents "polymaths"/Renaissance men like him to exist. I know there probably are some, and that in Tudor times most people stayed in the same line of work forever (peasants), but it's an interesting question.

Either way, it's interesting to see how geniuses used to think, read, and learn.

Fun fact: John Dee would sign his secret correspondence with Queen Elizabeth with a special symbol: two circles with a line above them that angles sharply to their right. This symbolized his service as "the Queen's eyes". In more modern times the symbol would be adapted into a form still synonymous with espionage: 007, James Bond's code number.
"Athanasius Kircher: the Last Man Who Knew Everything" by Paula Findlen, a history professor at Stanford, is a good book that touches on this:

https://books.google.com/books?id=C0iGO0Hr95UC

One way of thinking about it is that polymaths like Kircher and Dee simply can't exist anymore because the sheer amount of data encompassed in science and the humanities have expanded beyond the capacities of any single human mind. It's worth keeping in mind that early modern polymaths still generally believed that the age of the world could be measured in thousands rather than billions of years, and that the sum total of all human knowledge could fit in a few hundred feet of library bookshelves. No one in a position to be a polymath now holds those illusions anymore.