WING IV · VIVARIUM
Biology is the only science whose subject matter is trying to become something else while you measure it. Nothing in this wing is a recording of a living thing: every stage runs the rule and lets the behaviour be whatever the rule produces. Twice in five exhibits a result arrives that nobody put there — a swimming stroke, and a threshold — and both are named only once they have turned up.
EXHIBIT I · NATURAL SELECTION
At the scale of a bacterium, water behaves like syrup and inertia does not exist. The equations of motion lose their sense of time, so any stroke retraced exactly in reverse gives back exactly the distance it won. A scallop — one hinge, open and shut — therefore cannot go anywhere at all. Purcell called this the scallop theorem in 1977 and answered it with three rods and two hinges.
This creature is told none of that. Its genome is ten numbers describing how its two joints move, and its fitness is nothing but net displacement after three strokes. Watch the gait diagram on the right: a stroke that draws a line goes nowhere, and evolution finds the loop on its own, usually within a few hundred generations. It keeps going while you read the rest of the wing.
it runs in a worker · pause stops it · set drag to 1.00 and nothing can swim
EXHIBIT II · THE GENETIC CODE
Sixty-four codons name twenty amino acids and one full stop, so the code is redundant — and the redundancy is not scattered at random. It sits almost entirely in the third base. That is why changing a base at the end of a codon usually changes nothing at all, and why the same substitution one place to the left usually changes everything. Click any base and the readout says which of the two just happened.
Underneath, the protein folds. Each residue is scored hydrophobic or polar by its Kyte–Doolittle value and dropped onto a square lattice, where the only rule is that two hydrophobic residues touching are worth −1. That is the whole model, and it is a caricature on purpose: one term, two letters, and a hydrophobic core still assembles in the middle without anyone asking for one.
click a base to change it · edit opens the sequence · fold anneals
EXHIBIT III · MORPHOGENESIS
Two chemicals. One converts the other into more of itself; one diffuses twice as fast as the other. That is the entire mechanism, and it is enough for spots, stripes, labyrinths and cells that divide — with no template, no plan and no gene that says spot here. Turing published it in 1952, two years before he died, and biology took forty years to agree with him.
The plane on the left of the controls is the parameter space: feed rate F across, kill rate k down. Every pattern this exhibit can make is somewhere on that little rectangle, and moving a few thousandths turns coral into mitosis. Set the two diffusion rates equal and the pattern does not simply weaken — it never forms.
drag on the stage to paint · click the F/k plane to move · reseed
EXHIBIT IV · EPIDEMIC THRESHOLD
Herd immunity is not a policy and not a number anybody chose. Immunise a fraction v of a population and every infection now meets only (1−v) of the susceptible contacts it would have met, so the reproduction number falls to R₀(1−v). Growth stops the moment that drops below one. Nobody in the crowd became any more immune than they already were; the arithmetic of who-meets-whom simply ran out.
The threshold is not drawn on the chart, and it is not drawn anywhere. Push the vaccinated fraction up a percent at a time and watch where the outbreak stops travelling. Only once it has died out on its own does the readout name what happened and print 1 − 1/R₀ next to the fraction you chose.
click a node to start it there · 50 trials for the distribution
EXHIBIT V · THE ACTION POTENTIAL
There is no threshold in the Hodgkin–Huxley equations. Nowhere in them does it say if the voltage exceeds −55 mV, fire. There are four coupled differential equations describing what fraction of each kind of gate is open, and the threshold is only the place where sodium's positive feedback outruns potassium's negative one. A hair more current does not give a slightly larger answer. It gives the whole spike.
The gates are plotted underneath, and they are where the refractory period stops being a rule and becomes a fact: fire it twice in quick succession and the second pulse fails, because h has not come back yet. The integrator and its step size are controls, too — set Euler at 0.5 ms and watch a model that has stood since 1952 produce nonsense, because of arithmetic rather than biology.
drag on the trace to inject current · paired fires it twice