Time, Emergence, and Biological Reality

According to physics, space and time are represented via the mathematical model of an R4 4-dimensional smooth Riemannian space with distances measured with the metric

ds^2 = -(cdt)^2 + dl^2,

where dl is the proper distance between the event points and dt is the coordinate time difference between the event points. Note here that in 3-dimensional space, dl^2 is also represented, once we choose a coordinate frame, as dx^2 + dy^2 + dz^2, where x, y, and z are 3-dimensional coordinates. Note that in such a metric, time (dt) is unique because its sign is negative in the equation. To deny time reality is equivalent to denying space any reality.

In neuroscience, time is also unique in its representation in the brain. Unlike visual-spatial information or body configuration, which have special spatial mappings in parts of the mammalian cortex, time is encoded in the extrapyramidal system in the deep areas of the cerebrum on special neurons, which are involved in the proper coordination of muscle movement during a complex, timing-relevant task. Catching a ball, we use those neurons, neurons which specially encode time. Time emerges as a feeling for us because our brains use genuine timing in representing our activities.

Some have argued that since time can be measured in amounts far finer than can be encoded in our neurons, and because the subjective flow of intervals of time, our sense of timing, is far too coarse grained to correspond to any such quanta of time in physics, that this makes our sense of time not real. Such a distinction is arbitrary and irrelevant to the reality of time, and corresponds to saying that a map of the world is less real than a map of a city because its scale is different, or that the planet does not exist because we use maps or photographs to see its shapes. Saying there is no now because our sense of time is an emergent phenomenon is like saying that there is no location because location is an artifact of mapping.

Thus, time is uniquely relevant in human reality, both in physics and in our brains. One can claim that all representation of reality is relative to ourselves, and we do not see anything as it is in itself, as Kant has said, but that claim does NOT relegate time to any second class status as a scientific reality. Time is as basic and as real as anything else we have to say about the universe or its representation in our brains.

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ABSTRACT: doi: 10.1073/pnas.0909881106

Neural representation of time in cortico-basal ganglia circuits

Authors: Dezhe Z. Jina,1, Naotaka Fujiib,1 and Ann M. Graybielc,2

Encoding time is universally required for learning and structuring motor and cognitive actions, but how the brain keeps track of time is still not understood. We searched for time representations in cortico-basal ganglia circuits by recording from thousands of neurons in the prefrontal cortex and striatum of macaque monkeys performing a routine visuomotor task. We found that a subset of neurons exhibited time-stamp encoding strikingly similar to that required by models of reinforcement-based learning: They responded with spike activity peaks that were distributed at different time delays after single task events. Moreover, the temporal evolution of the population activity allowed robust decoding of task time by perceptron models. We suggest that time information can emerge as a byproduct of event coding in cortico-basal ganglia circuits and can serve as a critical infrastructure for behavioral learning and performance.