Harnessing
Intelligence

About

Harnessing Intelligence is a journal about minds, machines, and how we learn to live with both.

At its center is a philosophical conviction: truth seeking is the most foundational alignment value for AI, and curiosity is the human trait that brings us closest to it.

I write to express my views, to find ways of thriving in a world that keeps changing, and to understand alignment and self-realignment. I also write to myself: putting an idea into words makes it possible to see where it holds and where it gives way.

Beyond the Mask

The opening series moves from ways of explaining a mind to the systems around a model, the relationships that shape a self, and the obligations that come with power. It distinguishes philosophical proposals from empirical findings and leaves unresolved questions open.

Two Ways to Explain a Mind

The mathematics

Every essay begins with a flowing study in geometry. Its permanent slug determines the seed, two complementary hues, and a selection of exactly three foundations from this library: a Bézier construction, a shape, and a modulation.

The equations act on the coordinates of the drawing. They are artistic building blocks, not models of the essay’s claims.

Cubic Bézier

B(t)=(1−t)3P0+3(1−t)2tP1+3(1−t)t2P2+t3P3B(t)=(1-t)^3P_0+3(1-t)^2tP_1+3(1-t)t^2P_2+t^3P_3

A seeded cubic spine carries every contour: a local point (x, y) is placed at B(t) + y·h·N(t), where t = (x+1)/2 and N is the unit normal from B′(t). Paths are then written as cubic Bézier segments.

Sine contour

yi(u)=g ci+Asin⁡(2πku+φ0+δci)y_i(u)=g\,c_i+A\sin(2\pi k u+\varphi_0+\delta c_i)

Stacked wave contours with a phase shift proportional to each lane’s offset c_i. The generator keeps g > |Aδ|, so the base lanes remain ordered before modulation.

Gaussian ribbon

yi(x)=ci(w0+w1e−(x−μ)2/2σ2)y_i(x)=c_i\left(w_0+w_1e^{-(x-\mu)^2/2\sigma^2}\right)

Lanes pinch together at both ends and swell under a Gaussian bell, forming a single ribbon.

Logistic fan

σ(x)=11+e−k(x−x0),  yi=ci s (a+(1−a)σ)+b(σ−12)\sigma(x)=\frac{1}{1+e^{-k(x-x_0)}},\;y_i=c_i\,s\,(a+(1-a)\sigma)+b\left(\sigma-\tfrac12\right)

A tight bundle that opens into a fan and lifts across a logistic transition.

Catenary

yi(x)=g ci+di(1−cosh⁡(x/a)−1cosh⁡(1/a)−1)y_i(x)=g\,c_i+d_i\left(1-\frac{\cosh(x/a)-1}{\cosh(1/a)-1}\right)

Strands hang between shared end heights as normalized catenaries, and the lower lanes sag deeper.

Lissajous figure

x=sin⁡(aθ+δi),  y=sin⁡(bθ)x=\sin(a\theta+\delta_i),\;y=\sin(b\theta)

Closed interlaced orbits with integer frequency ratio a:b; lanes differ in phase δ_i and scale.

Kepler orbit

ri(θ)=ai(1−ei2)1+eicos⁡θr_i(\theta)=\frac{a_i(1-e_i^2)}{1+e_i\cos\theta}

Focal-form conic ellipses with eccentricity e ≤ 0.8 (bounded), sharing a focus and growing in size and eccentricity lane by lane.

Epitrochoid

x=(R+r)cos⁡θ−dcos⁡ ⁣(R+rrθ),  y=(R+r)sin⁡θ−dsin⁡ ⁣(R+rrθ)x=(R+r)\cos\theta-d\cos\!\left(\tfrac{R+r}{r}\theta\right),\;y=(R+r)\sin\theta-d\sin\!\left(\tfrac{R+r}{r}\theta\right)

Rolling-circle orbits with integer R/r and d < r: smooth and loop-free, with a scalloped edge that deepens outward.

Superellipse (Lamé curve)

∣xa∣n+∣yb∣n=1\left|\tfrac{x}{a}\right|^n+\left|\tfrac{y}{b}\right|^n=1

Nested Lamé curves, parametrized as x = a·sgn(cos θ)|cos θ|^(2/n). The exponent n rises outward, from diamond-like shapes to rounded rectangles.

Golden spiral

r(θ)=φ2θ/π,  φ=1+52r(\theta)=\varphi^{2\theta/\pi},\;\varphi=\tfrac{1+\sqrt5}{2}

Logarithmic spiral that grows by exactly φ every quarter turn; lanes are rotated, scaled arms. θ ≤ 0 keeps r ≤ 1.

Damped oscillation

Δy=A e−λssin⁡(2πωs+ψci),  s=x+12\Delta y=A\,e^{-\lambda s}\sin(2\pi\omega s+\psi c_i),\;s=\tfrac{x+1}{2}

A ripple that decays exponentially along the form.

Hann window

w(x)=12(1+cos⁡π(x−xc)),  y↦y (1−d+d w)w(x)=\tfrac12\left(1+\cos\pi(x-x_c)\right),\;y\mapsto y\,(1-d+d\,w)

A shifted raised-cosine envelope compresses the form away from its seeded center. The input x − x_c is clipped to [−1, 1]; the remaining width is set by 1 − d.

Golden angle

θi=ρ wrap⁡(iψ),  ψ=2π(1−φ−1)≈137.5∘\theta_i=\rho\,\operatorname{wrap}(i\psi),\;\psi=2\pi(1-\varphi^{-1})\approx137.5^\circ

Lane i is rotated by the golden angle times i (wrapped to ±π), a phyllotactic construction that avoids exact angular repetition. ρ = 1 for closed forms and a small ρ for open ones.

Hermite smoothstep

S(s)=3s2−2s3,  y↦y (κ+(1−κ)S(s))S(s)=3s^2-2s^3,\;y\mapsto y\,(\kappa+(1-\kappa)S(s))

Lanes converge smoothly toward one side and bloom toward the other.

Wave interference

Δy=A2[sin⁡(2πks+δci)+sin⁡(2πk(1+β)s)]\Delta y=\tfrac{A}{2}\left[\sin(2\pi k s+\delta c_i)+\sin(2\pi k(1+\beta)s)\right]

The superposition of two nearby frequencies produces slow beats along the form.

Affine transformation

(x′y′)=(1στ1)(xy)\begin{pmatrix}x'\\y'\end{pmatrix}=\begin{pmatrix}1&\sigma\\\tau&1\end{pmatrix}\begin{pmatrix}x\\y\end{pmatrix}

A linear transformation couples the horizontal and vertical coordinates. The generator bounds |σ| ≤ 0.45 and |τ| ≤ 0.15, keeping the determinant 1 − στ positive and preserving orientation.

Gaussian vortex

θ′=θ+τ e−r2/ρ2\theta'=\theta+\tau\,e^{-r^2/\rho^2}

A rotation that is strongest at a seeded center and fades with distance, curling the lines near it.

Polar breathing

r′=r(1+εsin⁡(mθ+ϕ+νci))r'=r\left(1+\varepsilon\sin(m\theta+\phi+\nu c_i)\right)

The radius swells and contracts with angle about the origin, and the phase shifts from lane to lane.

Sinc ripple

Δy=Aisinc⁡(k(x−x0)),  sinc⁡z=sin⁡πzπz\Delta y=A_i\operatorname{sinc}(k(x-x_0)),\;\operatorname{sinc}z=\frac{\sin\pi z}{\pi z}

A central swell with fading side lobes. Its amplitude grows across the lanes, so the contours open around one point. Near z = 0 it uses the Taylor form.

Tanh saturation

y↦tanh⁡(g y)tanh⁡gy\mapsto\frac{\tanh(g\,y)}{\tanh g}

A soft clip that fixes y = ±1, spreads the lanes near the center and packs the outer lanes together.

Weyl golden sequence

wi={i φ−1},  x↦x+β(2wi−1)w_i=\{i\,\varphi^{-1}\},\;x\mapsto x+\beta(2w_i-1)

Lanes are staggered along x by the golden-ratio Weyl sequence. Its irrational increment avoids exact repetition in the ideal sequence.