Imagine the human brain as a computer. (This is a somewhat controversial metaphor within neuroscience, though a serviceable analogy in the context of this argument.) Now, imagine that the human machine ran, immunized against death by hyper advanced medicine, forever. How long would it take to run out of space to store new ideas and new memories?
To answer the question pithily: Longer than you’d think, but eventually. To answer the question less pithily: It’s complicated.
ScarJo action vehicles aside, it’s a fiction that we’re not using all of our brainpower at any given moment. Our brains are made up of about a billion neurons, but as Northwestern University psychologist Paul Reber points out at Scientific American, each of those neurons takes on a fairly heavy workload — rather than acting as a simple switch (which is one reason why the brain-as-PC metaphor breaks), a single neuron connects to 1,000 other neurons. Given that, the estimated total memory is equivalent to 2.5 petabytes of data. As a bad analogy, if you could download 500-megabyte, 22-minute-long Seinfeld reruns to your brain, you’d hold a little over two centuries’ worth of sitcom.
Our brains don’t store data in the same way hard drives do — and the premise that each synaptic connection equals 1 byte is far from certain — but even at less fidelity, an immortal’s worth of memories is presumably longer than 200 years. (Just how long you can “live forever” is questionable, too, as immortality breaks down with the end of the universe itself — depending on who you ask or how you think this reality will end, that’s somewhere in the next five billion to 10^40 years, when matter decays and leaves behind lonely black holes.) The point is, if you accept that our neuronal connections could hold 2.5 petabytes, our hypothetical unkillable brain will eventually hit a limit. What happens when we’re full up no one knows, because there obviously aren’t bicentennials doddering around quoting the Soup Nazi ad nauseam.
What we do know is that we’re capable of overwriting memories. In a 2013 experiment of memory recall, 146 volunteers who watched an episode of 24, answered questions about what they’d just seen, and then listened to an erroneous recap of the show believed the errors were true. Primed by the test, the viewers’ recall was then subject to alteration. If we can alter our memories, which we do, and we forget things — which we of course also do — it doesn’t seem difficult to conclude that this immortal brain will take advantage of these systems to overwrite long-ago memories. Barring a breakdown of the brain’s neuroplasticity due to dementia, Parkinson’s, or other diseases, why couldn’t a brain re-write parts of itself? George Costanza forever.