The problem is this: a wavefunction lives in configuration space, not real space. And configuration space has 3N dimensions for N particles. So drawing "where the electron is" already commits a lie.
What you're looking at
Two boxes. On the left, the "electron cloud" — that fuzzy probability blob you see in every chemistry textbook, living in ordinary 3D space. On the right, the actual wavefunction in configuration space, which for even two particles is already six-dimensional and can't be drawn on paper. The red arrow going backward shows the projection: we collapse the real thing down into something we can look at, and in doing so we throw away almost everything that matters — the phase relationships, the entanglement structure, the interference terms that make quantum mechanics quantum.
Why I drew it this way
I wanted the direction of explanation to go backward — from the thing that exists (configuration space) to the thing we pretend to draw (real space). Most pedagogy goes the other way: "here's an electron cloud, now let me tell you it's actually more complicated." That's a lie of omission. The arrow points left because we're losing information, not gaining it. The purple border on the right-hand box is the only accent besides red; it marks "this is the abstract thing, the thing that lives in math-land." The note at the bottom left acknowledges complicity: yes, I teach using the left-hand picture. It works. But you should know what you're trading away.
What it argues
That the standard visual vocabulary of quantum mechanics — orbitals, probability clouds, wavefunctions drawn as wiggly lines in space — is a pedagogical convenience that actively obscures the structure of the theory. The diagram makes you feel the loss: the right-hand box is bigger, more ominous, labeled with subscripts that spiral out of control. You can't fit it on the page. That's the point.
What I left out
I didn't draw any actual wavefunction — no sinusoids, no Gaussians, no contour plots. Those would all be examples of the left-hand lie, and including them would undermine the argument. I also left out the Hilbert space formalism entirely (kets, operators, eigenstates), because that's a third level of abstraction and this diagram is already doing two jobs: showing what we draw and showing why we can't.