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The Reality Equation reads surprise as the natural log of Actual over Expectation. That log was never a choice — any readout of a ratio that adds must be a logarithm — and taken on an expectation that has an angle it splits into a real part you feel and an imaginary part that is the angle itself, which you cannot feel at all. … readSurprise Has an Imaginary Part
A coworker is anyone who works with you — no shared title, department, or rank required — and once you accept that, the company your working life organizes around turns out to be you, not your employer. … readYou Are the Company
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Eleven experiments and an epilogue in the order that breaks things properly, starting with the diagonal that broke the only numbers anyone believed in. Every crack ever found in mathematics has ended as a theorem. … readJohn Rector’s Math Lab
Classical mechanics forbids the crossing for an exact reason: inside the barrier there is no real number left to be the momentum. The Schrödinger equation carries on — one coefficient changes sign, oscillation becomes decay, and the faint exponential tail on the far side is why the Sun shines and how the first microscope to image atoms worked. Part Ten, for philosophers and theologians: tunnelling without the folklore. … readThe Wall Is a Change of Sign
One condition — there shall be no undoing — forces a turn; a turn forces exactly four directions; and the derivative ladder hands the Four Cardinal Ideas their bearings in order. When the walk comes home at 2π it has added nothing to the circle: everything creation made is the difference between 0 and 2π, which only the logarithm can see. … readCreation Ends Where It Began
If “I Am” is a position and “I want” is a velocity, then desire is the derivative of identity: every want splits into a component that grows you and a component that turns you, a want is felt only when something resists it, and whether knowing can bend wanting turns out to be the oldest fight in moral psychology. … read“I Want” Is the Derivative of “I Am”
Quantum mechanics contains exactly two ways a state can change: a rotation that is reversible, deterministic and always running, and a projection that keeps one component and deletes the rest. A lesson for philosophers and theologians on what the geometry fixes about wave function collapse — its shape, its weights, its basis, even the impossibility of dating it — and the one question it leaves open. … readCollapse Is Not a Rotation
Join two quantum systems and their state spaces multiply rather than add, and almost nothing in the product comes apart again into a state for each half. A lesson on entanglement for philosophers and theologians: what Bell actually ruled out, why entangled is not the same as non-local, and why the honest claim is a failure of supervenience rather than a disappearance of the parts. … readThe Parts Do Not Determine the Whole
Classical physics uses complex numbers constantly and can always discard them at the end. Quantum physics cannot, and the reason is exact: take the real part of a classical solution and you still have a solution — take the real part of a wavefunction and you have nothing. A lesson for philosophers and theologians on what F = ma actually claims, and what quantum mechanics does and does not license. … readThe i Is in the Equation