There is extensive evidence that many regions of the mammalian brain code for compressed representations of the past. ``Time cells'' implementing this representation have been observed in hippocampus, various frontal regions, and striatum.  My students and I proposed a theoretical framework by which the brain could represent functions over the past (and space, and other continuous variables as well) using a scale-invariant form compression. We've argued that this compression is optimal under various assumptions.  The theory (coupled with reasonable constraints on neural computation) requires that the brain compute the Laplace transform of the to-be-estimated functions as an intermediate step.  Recent evidence has shown evidence for the Laplace transform of time in the entorhinal cortex of rats and monkeys.  The implications of this dual space for cognitive computation will be discussed.