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Kardashev ranked civilisations by the energy they command. This paper borrows his ladder and asks how much machine cognition each rung could support. The arithmetic is deliberately simple. A civilisation has some total power. Only a fraction of that can be spared for computing, and each joule spent buys computation at whatever efficiency the hardware of the day has reached. The product of the three sets a ceiling on machine thought. To keep the resulting quantities intelligible, I express them in units of the human brain's own processing rate, as a rough yardstick rather than a claim about minds. Calibrating the ceiling against present-day supercomputers and AI accelerators led me to two conclusions I did not expect at the outset. Even today's energy supply could support far more machine cognition than humanity actually uses, so physical capacity is not what binds. 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