Memory for the past makes use of a record of what happened when-a function over past time. Time cells in the hippocampus and temporal context cells in the entorhinal cortex both code for events as a function of past time, but with very different receptive fields. Time cells in the hippocampus can be understood as a compressed estimate of events as a function of the past. Temporal context cells in the entorhinal cortex can be understood as the Laplace transform of that function, respectively. Other functional cell types in the hippocampus and related regions, including border cells, place cells, trajectory coding, splitter cells, can be understood as coding for functions over space or past movements or their Laplace transforms. More abstract quantities, like distance in an abstract conceptual space or numerosity could also be mapped onto populations of neurons coding for the Laplace transform of functions over those variables. Quantitative cognitive models of memory and evidence accumulation can also be specified in this framework allowing constraints from both behavior and neurophysiology. More generally, the computational power of the Laplace domain could be important for efficiently implementing data-independent operators, which could serve as a basis for neural models of a very broad range of cognitive computations.Connectionist models have had astounding success in recent years in describing increasingly sophisticated behaviors using a large number of simple processing elements (LeCun, Bengio, & Hinton, 2015;Graves, Wayne, & Danihelka, 2014). However, the native ability to perform symbolic computations has long been noted as a key problem in developing a theory of cognition (Fodor & Pylyshyn, 1988;Gallistel & King, 2011;Marcus, 2018). Among other things, symbolic processing requires operators that are independent of the data on which they operate. For instance, a computer program can add any pair of integers whether they are familiar or not. Human cognition also has a powerful symbolic capability that allows us to perform many data-independent operations. To take a concrete situation, after focusing on Figure 1 one could close one's eyes and implement a huge number of operations on the contents of memory. For instance, one could choose to imagine Moe Howard's