The brain catches a sea of signals (the whisper of the wind, a glint of light) but only a tiny fraction reaches consciousness. Scientists built a model where the brain's working area is described as a special 'mathematical space,' proposed by mathematician John von Neumann. In this space, sensations resemble a mist or cloud of probabilities: with weak attention, they remain diffuse, like vapor. An equation similar to Schrödinger's shows how the cloud moves until we direct our focus. Then it abruptly condenses into a single clear droplet-thought, like an instantaneous grasp of the essence.

The model revealed three stages. A too-weak stimulus — a vapor without a trace. A strong signal with scattered attention yields a droplet that evaporates at once: preconsciousness. Only when both stimulus and attention exceed the threshold does the droplet persist and enter consciousness. A computer experiment confirmed: the transition resembles a switch click, not a smooth crescendo. Consciousness turns out to be not a smooth stream but a series of momentary snapshots: each about 200 milliseconds long.

The droplet’s stability depends on the precision of the ensemble: a blurred signal leaves too many 'either-or' possibilities, and hidden alternatives spread apart. Noisy interference disrupts focusing. But when attention is sufficient, parts of the image coherently reinforce each other, casting off the excess. This whole mechanics rests on the mathematics of a unified mental landscape, where thoughts are but ripples on a common field.