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Disclaimer: I have little to no background in biology, so this question is based on anecdotal evidence. I've tried to spell out all of my suppositions, but please let me know if I'm making any leaps I'm not explaining.

Some Context/My biology assumptions

There are some things I can recall very clearly and quickly, other things that are maybe a little fuzzy and take me a second to remember and others still that will feel "on the tip of my tongue" for minutes before I can recall them. And then there are things that I don't remember at all or that I know I knew but can't recall.

To me it seems there's a range of how "clear" or easy a memory is to recall. This clarity and "recallability" seem to decrease over time (assuming I don't use the memory) and it seems there's some minimum clarity/"recallability" that is required for me to recall a memory. Can the clarity and "recallability" of my memories be modeled with a continuous function? And if so...

A (maybe false) Conclusion

According to the Intermediate Value Theorem,

if a continuous function, f, with an interval, [a, b], as its domain, takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval."

So if we can model the clarity and "recallability" as continuous functions, and I can perfectly quickly recall a memory at one point and not recall it at all at another, then there should exist times with every flavor in between.

If this is true, would it be true to say that there existed a moment when my clarity/"recallibility" of a memory was high enough for me to recall it should I have chosen to and there is another moment when it wasn't (where these moments are some small distance apart)? Or is my understanding of memory incomplete to where this is all horribly wrong?

To put it in other words, how small can the time be between when you are able to recall something and when you no longer can? And following my logic, could this time be seconds or moments?

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