This is false if memory's are stored physically in the brain. Unless there is an increase in brain volume, this process will eventually hit the Bekenstein bound. I don't care if the upper bound is "effectively infinite," that's not what the proof claimed.
Proofs rely on assumptions. In this case, they state outright:
> We first posit that the number of days T that a fact can be retained before it needs to be reviewed grows as a power-law in s, the number of times it’s been reviewed so far, ...
Obviously this assumption will be false in our physical universe, but that doesn't make the proof itself invalid (edited).
In logic, the soundness of a proof in fact has to do with its interpretation in some universe of discourse. To be sound, the argument has to be deductively valid, and its premises have to have true interpretations in the chosen world where it is applied.
Here we have a valid mathematical argument which is unsound in this world, where its assumptions do not hold up.
You're right. I should have said invalid rather than unsound. I still don't see the point of the criticism, however. Lots of interesting things can be learned by starting from approximations to actual reality.
This is what I have been thinking. If whatever you can remember is bigger than all experiences and lessons you could remember, then your memory is effectively infinite. I don't know if having a continuous effectively infinite memory is good or bad. As someone who play the classical guitar, having a better memory would do wonders for me.
What you're missing is that the proof only shows that memory diverges as time goes to infinity. According to the laws derived there, a finitely-lived human would have a finite memory throughout their entire lifespan. You could even use the law to derive the upper limit on how many facts can be memorized over an X year lifespan (which sounds quite antithetical to the headline, which you seem to have reacted to).
> I don't care if the upper bound is "effectively infinite," that's not what the proof claimed.
Very interesting. Do you typically process all claims as literally as you just did for this one, notably when you're interacting with people outside of the Internet? In which case, do most people react positively to your behaviour, or do they get annoyed because "you know what I meant"?
