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> One is to build an abstract mathematical model which you can emulate in your head

The ability to emulate your abstract or concrete programming model in your head cannot be overemphasized. I used to program the original 8-bit B&W Gameboy, which was a machine so simple and small I could literally emulate it at the clock cycle level while I was writing the code for it.

If you can fit your model into your cache (brain) you can do amazing things using just your wetware.

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