[jacb]

Ha! Certainly none of us will get anywhere close to this bound, no matter how much time we log in Anki. But the OP asked "Would an infinitely-long-lived, but forgetful person be able to recall an infinite number of facts using this method?", and the answer is a surprising "no, you turn into a black hole".

[ben_w]

Sometimes even just one piece of knowledge can turn you into a black hole. It’s why nobody remembers every digit of Graham’s (phone) number.

;)

[jquery]

his phone number is highly compressible though, it’s the decompression/serialization step that turns you into a black hole

[jrussino]

I know we're all playing around here, but surely the answer must be that there's a limit rooted in the specific biological/chemical implementation of memory in the brain that our hypothetical "infinitely-long-lived, but forgetful person" would hit before the Bekenstein bound (probably long before) and therefore it's impossible to turn a brain into a black hole via that mechanism.