Without a computer how are you turning that seed phrase into addresses or signatures that allow spending from owned utxos? You can do the math on paper but it takes a long time. You can put your seed phrase into a general purpose, internet connected computer but that is dangerous due to the large attack surface. Signing devices or hardware wallets, are just calculators with all the right math pre-programmed in and a reduced attack surface.
Discussion
Yes.
But...
If they are just offline (in terms of internet connection) calculators, how do the keys and seed phrase get generated and then used online to correctly approve transaction? I am not seeing how those two things work.
keys are generated offline in a one way process. you can for example install Electrum on a PC without internet and create a whole set of new keys. An address generated offline is then unknown to the blockchain until you transact with it. This also means that you can sign a transaction on an offline device to then broadcast it from an online device. The tx is already signed and cannot be tampered with.
