When accountants calculate the current years income, they don't go back to when the company started and add up every income and expense item, they just add the current years results to the archived past totals. What am I missing.

The accountants won't start from the beginning, because they will have already done all of those calculations in previous years. This is similar to the function of a bitcoin node: it will node recompute the whole history to validate each new block, it will just validate each block once, and then store the network state, so that it can validate future blocks against that state.

The bottom line is, if you want to independently validate the history of the network, then you need to start from the beginning. Any other method will involve trusting that someone has supplied you with a legitimate intermediate state for you to begin your calculations from.

Note that a full node validating the chain is different than a miner working on finding new blocks. When people talk about the energy use of the bitcoin network, they are usually referring to the energy consumed by miners, not nodes.

When accountants calculate the current years income, they don't go back to when the company started and add up every income and expense item, they just add the current years results to the archived past totals. What am I missing.

The accountants won't start from the beginning, because they will have already done all of those calculations in previous years. This is similar to the function of a bitcoin node: it will not recompute the whole history to validate each new block, it will just validate each block once, and then store the network state, so that it can validate future blocks against that state.

The bottom line is, if you want to independently validate the history of the network, then you need to start from the beginning. Any other method will involve trusting that someone has supplied you with a legitimate intermediate state for you to begin your calculations from.

Note that a full node validating the chain is different than a miner working on finding new blocks. When people talk about the energy use of the bitcoin network, they are usually referring to the energy consumed by miners, not nodes.