Putting shit in a HDD is not the only way to store memory
There is even a way to store information using only neural networks
https://www.sciencedirect.com/science/article/pii/S0764446997824729Tl;dr an autoencoding network tends to output one of the input it was trained with if you repeatedly feed it back its output
You can continuously add new data to it by simply training it to output it back to you like a normal autoencoder, while feeding it the previous data so that it does not forget them (either you still have them around, or you get them back from the autoencoder by feeding it random vectors and inputing the output repeatedly until it converges)
The more data you add, the less likelly you will get them back during the retraining phase, so the network will naturally forget things it does not experiences often
Fun fact: it seems human memory works this way, with a short term network recalling things you did during the day, and a longer term one that is trained when you dream at night, which is why if you do not sleep for a long time, your short term memory become unreliable, while your long term one is unaffected