Artificial Neural Networks has struggled to devise a way to incorporate working memory into neural networks. While the ``long term'' memory can be seen as the learned weights, the working memory consists likely more of dynamical activity, that is missing from feed-forward models. Current state of the art models such as transformers tend to ``solve'' this by ignoring working memory entirely and simply process the sequence as an entire piece of data; however this means the network cannot process the sequence in an online fashion, and leads to an immense explosion in memory requirements. Here, inspired by a combination of controls, reservoir computing, deep learning, and recurrent neural networks, we offer an alternative paradigm that combines the strength of recurrent networks, with the pattern matching capability of feed-forward neural networks, which we call the \textit{Maelstrom Networks} paradigm. This paradigm leaves the recurrent component - the \textit{Maelstrom} - unlearned, and offloads the learning to a powerful feed-forward network. This allows the network to leverage the strength of feed-forward training without unrolling the network, and allows for the memory to be implemented in new neuromorphic hardware. It endows a neural network with a sequential memory that takes advantage of the inductive bias that data is organized causally in the temporal domain, and imbues the network with a state that represents the agent's ``self'', moving through the environment. This could also lead the way to continual learning, with the network modularized and ``'protected'' from overwrites that come with new data. In addition to aiding in solving these performance problems that plague current non-temporal deep networks, this also could finally lead towards endowing artificial networks with a sense of ``self''.