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Episode #187 – The Shannon Trap
In 1948 Claude Shannon formalised information theory by excluding meaning from the math, a move that was correct for his engineering problem and costly once the field adopted his m
Episode #192 – The Universe Demands Horns
A persistent knowledge structure can only take one shape. Information is physical, verification is asymmetric, and those two facts force a Gabriel's horn topology on anything th
Episode #191 – Why The Search Has To Be Expensive
P versus NP is the unproven conjecture that finding solutions is genuinely harder than checking them. This episode argues the same cost asymmetry runs through every act of knowl
Episode #189 – Gabriel’s Horn: The Shape of Everything
In 1641, Evangelista Torricelli, a student of Galileo, rotated the curve y = 1/x around the horizontal axis and obtained a shape whose interior volume converges to π while its sur
Episode #188 – The Exhaust Principle
In 1973, Jacob Bekenstein showed that a black hole’s entropy is proportional to its surface area. The result has been treated as a paradox for fifty years. This episode pr
