Quote from: Alana Arden on August 25, 2024, 03:56:54 PM

Each node in a Bitcoin network has no physical address in the mempool or Bitcoin blockchain, only scripts.

The nodes in the network do have a physical address and that is their IP address and port which is the way we can find other peers/nodes and connect to each other.

The rest of your statement is a bit strange. Perhaps by "node" you mean the person who is sending a transaction and the output they create doesn't contain an actual address, it only has a script.

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A Bitcoin address represents just a number, and the number that the address represents is a simple way of talking about transferring control over value to us humans.

As it was mentioned it is also not just a number. It is more complex than that. Each output script is like a smart contract that holds the locking mechanism that is "locking" the coins in that output and can be "unlocked" by the spender when they provide the other half of the smart contract which will be executed by the nodes.

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Within the wider Bitcoin network, I can display the addresses used by my transactions by converting transaction output scripts into an address representation of how to represent that information as a number via standard rules.

Technically you can only do that if the output script is one of the standard scripts that has a corresponding address format (like P2PKH, P2WSH, etc.). Otherwise if it doesn't (like the standard P2PK or OP_RETURN or P2MS scripts) or is non-standard, you can not convert it to an address.