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Although a complete novice in brain science, I have been curious. My question might appear to be similar to this previously asked question, but I believe I am addressing a different case.

The brain's storage capacity is said to be something closer to around 2.5 petabytes (a million GB).
An article on ScientificAmerican.Com says:

...neurons combine so that each one helps with many memories at a time, exponentially increasing the brain’s memory storage capacity to something closer to around 2.5 petabytes (or a million gigabytes). For comparison, if your brain worked like a digital video recorder in a television, 2.5 petabytes would be enough to hold three million hours of TV shows. You would have to leave the TV running continuously for more than 300 years to use up all that storage.

I think that's a lot of storage space, and someone like me may never utilize even 20 percent of it. But a vast portion of that storage space can get filled up over a long period of time if we indulge in a lot of study, research or learning, can't it?

In that case, is it possible that all or part of the information that has been acquired and stored gets jumbled and becomes irretrievable; or worse, irrational? I have never heard about such a case, but I am wondering if a brain malfunction like that can ever happen.

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Did you read the answer on the question you linked explaining how the hard-drive analogy is misguided? Thus "2.5 petabytes" doesn't really mean anything. Also, have you ever tried remembering a dream? What about what you had for breakfast 537 days ago? Presumably you remembered that 536 days ago. –  Artem Kaznatcheev Mar 9 '14 at 19:39
Despite @Artem's point, I'll overextend the metaphor just a little further. Have you heard of computer storage getting corrupted just because the free space got used up? Probably some other cause occurred in most instances, like physical damage or interruption of power during some important process. Hard drives can become fragmented, but this only slows retrieval. Somewhat like defragmentation, the cognitive process of drawing connections among ideas and combining them into more abstract, coherent wholes improves neurological storage and retrieval. I'd say learning usually helps connect ideas. –  Nick Stauner Mar 9 '14 at 23:24
Some kinds of learning may not work like this though. I imagine that focusing and ruminating on a particularly narrow aspect of experience would produce a less functional sort of learning. Superstitious belief seems to exemplify the irrational products of excessive focus on limited information. In such cases, one might draw invalid inferences about the focal object or phenomenon ("thing") from incidental circumstances. Due to overly exclusive focus on the thing one is trying to understand, one could fail to consider more valid explanations of the incidental circumstances that form superstition –  Nick Stauner Mar 9 '14 at 23:35
@NickStauner - Right. Nevertheless, people keep thinking of how much information the brain can hold and that is often analogously expressed in terms of digital storage. But yes, I can now see that such comparison doesn't fulfill its own purpose. Does that also mean that we are yet to discover how to express how much information the brain can store? –  Elzee Mar 10 '14 at 3:52
I don't know; it probably suits some less-than-overambitious purposes sufficiently. People use analogies like these for all sorts of reasons, yourself included. It is interesting to consider whether cognition would malfunction at the limits of information storage capacity, but @Artem's point makes that a very challenging hypothesis to test. IMHO, I've described more available and likely scenarios that lead to irrationality through imbalanced attention and information representation, rather than simply too much info. However, some disorder theories might offer better examples than superstition. –  Nick Stauner Mar 10 '14 at 4:12

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