> Yet the only difference between a FA and a TM is that

> the TM, unlike the FA, has paper and pencil.

> Think about it.

The analogy doesn't works if you really think about it. A TM with a finite tape is equivalent to an FA. The fundamental difference between a TM and an FA is that a TM has infinite space.

(Yes, I know I missed the point and am not very fun at parties.)

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fwlr an hour ago | parent | next [-]

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.

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conqrr an hour ago | parent | prev [-]

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.

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tehjoker an hour ago | parent [-]

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.

	▲	raincole an hour ago \| parent [-]
		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 the gain from _(skill acquisition, language learning, workout, whatever) is better modeled as 1.01^365 than 1+(0.1*365).