Obviously currently this doesn’t happen, but assuming there would be some techniques or devices for learning more – would there be a limit to how much our neural networks in the brain can store?
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This is a very difficult question to answer in an eli5 manner, however there is something called the “Bekenstein bound”. This bound describes how much information is needed to recreate the state of a finite region of space, which is the same thing as saying how much information can “fit” in a finite region of space. If you force that finite region of space to contain more information than its Bekenstein bound, that region of space will collapse into a black hole!
So you can see that the idea of a Bekenstein bound was derived using black hole thermodynamics and that is a topic that is definitely not eli5-friendly. However, it can be used to give a back-of-the-envelope calculation as to how many bits of information a human brain can possibly contain before it can collapse into a black hole.
[Here](https://en.m.wikipedia.org/wiki/Bekenstein_bound) is a wikipedia article about the topic and its calculations for a human brain.
According to this article, if you could somehow represent a human brain as a computer, then you would need 10^(7.8*10^41) bits to recreate the human brain. By the Bekenstein bound theorem, this is the same thing as saying that that many number of bits is the maximum number of bits a digitized human brain can contain before it collapses into a black hole. This number is so big that it’s really hard to describe.
Related to the idea of a Bekenstein bound and how much information our brain can store, there are natural numbers (i.e. 0, 1, 2, 3, 4, etc) that are so large that if you tried to imagine it, your head would collapse into a black hole. One such number is Graham’s number. Yet, even a number as large as Graham’s number is just as far away from infinity as the number 0 is from infinity.
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