Neural Networks with the saturated linear activation function are known to be Turing universal. The question on whether the same result holds for networks with a sigmoid activation function is a controversial one amongst the scientific community. The main aim of this talk is to shed some light into the question. It will be shown that Turing machines can be simulated by alarm clock machines, via the introduction of counter machines and adder machines. Next, a description will be given of how to substitute the alarm clocks by restless counters (which can be implemented by sigmoidal neurons). Finally, the simulation of alarm clock machines with restless counters by sigmoidal neural networks will be broken down into parts and analyzed.