Bremermann's Limit
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Image from DALLE3 AI and Avengium
The maximum limit allowed for computation under the laws of physics.

Bremermann's Limit derives from the Old Earth pre-singularity physics discoveries of Heisenberg's Uncertainty Principle and Einstein's principle of mass-energy equivalency. It is the maximum theoretical computational speed allowed by the laws of physics - 2E47 bits per second per gram of computing substrate. Together with the Bekenstein Bound, which imposes a fundamental limit on information density, Bremermann's Limit represents the limits of physical computation, and the fundamental limit to how densely-packed and fast ultratech computronium nodes can be. Past a point, archailects and hyperfast high-toposophic civilizations can only grow physically larger, but not more densely-packed or faster per gram of computing substrate. This is the reason why there are no proton-sized Archailects, although myths and legends still persist, especially among the less educated. Even so there are still tiny intelligences with smaller amounts of processing power.

This doesn't prevent miniaturization in high transapientech civilizations and archailects. A proton masses on the order of E-24 grams. Thus even with the Bremermann Limit a proton-sized computronium node has a theoretical maximum processing density of E23 bps, 7 or 8 orders of magnitude greater than a baseline human brain, although in practice this is only attained with very advanced civilizations. Even so this allows a low to middle level transapient mind to be based on the mass of a nuclear particle.
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Development Notes
Text by Mike Parisi
Steve Bowers
Initially published on 31 December 2007.

AI image added march 2024