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Recently I came across the video from Veritasium where he explains the importance of analog computers and how in specific use cases they outperform digital computers. I was wondering is it possible to design an analog computer (or maybe a hybrid analog + digital) computer that can perform hash function calculations? Just like ASIC miners.

Please let me know your thoughts on it. I am sharing the video link from that video for reference. https://youtu.be/GVsUOuSjvcg

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Analog computers can outperform digital computers in some tasks, like integrating a continuous function, matrix multiplication, signal interpolation and filtering and so on, but not in all cases. In Bitcoin, we use SHA-256 that is designed with a digital computer in mind, and will almost certainly be better done in one.
If you ignore SHA-256, you can build a PoW system optimized to analog computers, like BIP-052 OPoW, but this requires changing Bitcoin protocol.

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Analog computers have very limited precision. I believe they usually work to an accuracy of a three or four decimal digits. Hashing algorithms require higher than normal precision, accuracy and scale.

Hashing algorithms like SHA256 are designed for digital computers. If you were designing for analog computers, I suspect you would likely create a vastly different algorithm.

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