Boltzmann machines can be used to obtain solutions to problems for which direct mathematical calculation of a solution is not possible or would take too long. The range of problems for which such a machine might be useful is very broad, and inversion of a linear equation is described as one example. A method is described that allows time-intensive operations on a computer to be replaced with a highly parallel optical system that can be incorporated in such a way as to let the computer take full advantage of the speed of the optics without sacrificing the precision possible in the computer. A tie is made between Boltzmann machines and neural networks, and it is shown how a Boltzmann machine may perform functions demonstrated by other neural network architectures.