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Is it possible that the length of the existing block chain will one day become unwieldy to compute? Would it make more sense that the chain would somehow be rolled up like normal bank ledgers do with opening balance for every account every year?

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Is it possible that the length of the existing block chain will one day become unwieldy to compute?

A fully validating node, on first startup, will sync to the network by downloading and verifying the entire blockchain history. Doing so means validating every block and transaction in the blockchain history (but a node does not necessarily need store the entire history, it can opt to 'prune' old transactions that are not relevant to it, once they have been validated locally).

Right now, your 'average' PC will probably take a few days to sync. As the blockchain grows, it will take more computational time to validate the entire chain. Much work is being done to optimize these validation steps, with the goal being to maintain a low barrier of entry in terms of computational power.

Many of the important properties of Bitcoin (censorship resistance, immutability, etc) are born of it's decentralized network of nodes, so working to ensure the largest number of users are able to run a full node is very important for maintaining a healthy network. The blockchain will continue to grow in size, so balancing this against computational resources is an important part of scaling bitcoin efficiently.

Would it make more sense that the chain would somehow be rolled up like normal bank ledgers do with opening balance for every account every year?

Bitcoin does not use 'account balances', instead it uses an 'unspent transaction output' (UTXO) system under the hood. If I understand correctly, what you are suggesting would be to implement a 'checkpoint' that new nodes can start from.

This would mean that a new node has to place trust in the checkpoint they have received, since they will not be able to verify the authenticity of the UTXOs as being 'real bitcoins' themselves. Bitcoin is designed to be a system that can be engaged with without having to trust any other user on the network, so doing so is somewhat antithetical to its design.

If you search for 'checkpoint' on this site, you'll find some answers such as this one, which contain more info.

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