Einstein once said that you should never bother memorizing what you can easily look up. The reason, I’d hazard to guess, is that humans only have so much capacity for memorization. Given the vast quantities of information that are now known by humankind, I believe it as important as ever to make careful selections with what we choose to fill our brains.
Socrates was against writing anything down. We know this both because Plato tells us and because Socrates never wrote anything down. He said that if you wrote things down to read or refer to later that you would then lose the capacity for remembering things. In the short term, this assertion may have some kernel of truth. I have heard more than one expert claim that the wandering poets of ancient Greece could recite the entirety of the Iliad and the Odyssey from memory. One way to explain this phenomenal ability is that both poems contain markers to spur memories of specific lines within them and both poems have recurring lines to reset the meter and rhythm: think, ‘rosy-fingered dawn’. The second reason poets could remember entire epic poems was in fact that memories were much more highly evolved before people could write. Everything a person learned, they had to remember or forget forever.
Regardless of how much you personally might be able to remember if you never wrote anything down and committed all things to memory, however, you would still fall behind the rest of society. Some of the greatest advances of humankind can be directly attributed to the creation of information storage and dissemination capacities. Sir Isaac Newton famously said that if he had seen a little further it was because he was standing on the shoulders of giants; a phrase he borrowed from Pascal. The giants whose shoulders we all stand on are giants who bothered to write down what they have learned so we can learn what they discovered centuries ago and can now push the envelope of knowing just that little bit more for those who will come after us.
Socrates was against a Luddite.