Really happy to see this article. This viewpoint is not new, but it is still far from being mainstream.
A big issue touched upon in this article is that the space of possible dynamical systems represented in the brain is large, and trying to collect data is not a practical way of trimming this search space. It's more useful to look at types of dynamical systems that have certain stability properties that are desirable for computation.
But the issue then becomes that these dynamical systems become mathematically intractable past a few simplified neurons. So it's really hard to make progress either by looking at data, or by studying simplified dynamical systems mathematically.
There is a third option. Evolve smart dynamical systems by large scale brute force computation. Start with guesses about neuron-like subsystems with desirable information processing properties (at the single neuron level, such properties are mathematically tractable). Play with the configurations, the rules of evolution, the reward functions, the environment, everything. This may sound a lot like witchcraft but look at how far witchcraft has taken machine learning in recent years (deep learning is just principled witchcraft). This is IMO the only way we will learn how biological intelligence works.
I think is that the question is really close to how we design a modern Processor. Certainly is important to look at the data (i.e. how behaves a real machine under actual workloads). That data might suggest design improvements (through some form of experience, art and intuition). You use simulation the test those "potentially" good ideas. Most of them are discarded...
Perhaps neuroscience should move in the same direction: how I think cortex work? Test in under (simple) working conditions. See if it makes sense. Move to more complex working conditions. Rinse an repeat.
In actual processors math is rather useless too... beyond some niches. Even in susceptible issues such as formal verification of coherence protocol design, mathematical tools are rather limited (due to state explosion).
A big issue touched upon in this article is that the space of possible dynamical systems represented in the brain is large, and trying to collect data is not a practical way of trimming this search space. It's more useful to look at types of dynamical systems that have certain stability properties that are desirable for computation.
But the issue then becomes that these dynamical systems become mathematically intractable past a few simplified neurons. So it's really hard to make progress either by looking at data, or by studying simplified dynamical systems mathematically.
There is a third option. Evolve smart dynamical systems by large scale brute force computation. Start with guesses about neuron-like subsystems with desirable information processing properties (at the single neuron level, such properties are mathematically tractable). Play with the configurations, the rules of evolution, the reward functions, the environment, everything. This may sound a lot like witchcraft but look at how far witchcraft has taken machine learning in recent years (deep learning is just principled witchcraft). This is IMO the only way we will learn how biological intelligence works.