They came up with equations to describe how the brain might in theory encode time indirectly. In their scheme, as sensory neurons fire in response to an unfolding event, the brain maps the temporal component of that activity to some intermediate representation of the experience — a Laplace transform, in mathematical terms. That representation allows the brain to preserve information about the event as a function of some variable it can encode rather than as a function of time (which it can’t). The brain can then map the intermediate representation back into other activity for a temporal experience — an inverse Laplace transform — to reconstruct a compressed record of what happened when.
Howard’s mathematics could help with that. When he heard about Tsao’s results, which were presented at a conference in 2017 and published in Nature last August, he was ecstatic: The different rates of decay Tsao had observed in the neural activity were exactly what his theory had predicted should happen in the brain’s intermediate representation of experience. “It looked like a Laplace transform of time,” Howard said — the piece of his and Shankar’s model that had been missing from empirical work.