No, this is a very good point - you need a supply of pen and paper, such that it feels effectively infinite. Buying a nice notebook or a nice pen is a trap because both feel finite; buying a box of decent pens and a carton of decent notepads takes you out of the scarcity mindset and unlocks the Turing machine like advantages mentioned.

I was thinking of the same. FSA can multiply within bounds. For FSA, the storage is the state itself and bounded. I agree with the sentiment but not a fan of analogies like this. We do have memory even if we don't write. Each organ adds to the memory imprint making it stronger. Visual, smell, taste, audio etc Each action adds more imprints. And this makes more sense to me than an analogy.

Another analogy which never made sense to me was improving by just 1% every day (1.01³⁶⁵).

Analogies do help explain phenomena I cannot even relate to at all, like telling me how life on Mars would be.

Ofcourse I'm not invited to parties as you can imagine, taking things literally.

Are you saying that 1.01^365 is too big? I think there are lots of things where if you are starting from near zero skill, that's not a crazy big number.

Not parent commentor, but My issue with 1.01^365 analogy is that it implies that somehow that skill multiplies itself. There is no obvious reason to believe skill acquisition is better modeled as 1.01^365 than 1+(0.1*365).

You’re welcome to my party, both of you.

A big part of understanding something is getting used to it, and analogies help with getting over a mental hang up. They may also help with deciding which areas of the new space to explore first.

But we should be examining the limits of applicability, as we do for most cognitive tools, so we know when to switch from one tool to another. It also helps to combine such tools in a complementary manner.