The problem with machines is they have no dynamics. For instance, in the current state of affairs, machines don't do brain waves. Instead, they use a clock that sweeps back and forth across the network, ensuring that sequential mechanisms are engaged in the proper order. In a real brain, there is no clock. Instead, neighboring systems organize themselves on the basis of mutual dynamics, and often these involve oscillatory behaviors that we can detect on the scalp in the form of brain waves.

In this section we'll highlight the importance of dynamics in brain function. One of the most promising areas of current research is the unraveling of brain electrical activity. We know though, from 100 years of research, that understanding this piece will take a lot more than putting an electrode in the brain. Invasive brain monitoring has a difficult history and there are many ethical issues associated with it, and the truth is, most scientists simply don't know enough math to make use of the results. As we've already seen on the first page of this summary, some advanced mathematical techniques are needed to understand the relationships between data and network function. One should bear in mind that the Hopfield model is only 40 years old, and the free energy formalism is only 20 years old. (That's barely enough time for some grant money ;).

In this section we'll explore an important aspect of dynamics called "criticality". Criticality occurs at the transition into chaos, and chaos is defined as "extreme sensitivity to initial conditions". Criticality is related to phase transitions, and here the word "phase" is used in a different way, it means the phase of matter like ice-water-steam, rather than the angular relationship between two sine waves. One of the important models for understanding phase transitions is the Ising model of ferromagnetism, which pertains directly to the Hopfield neural network model that was inspired by it. A careful study of Ising dynamics reveals many interesting parallels to neural network function.