When I was doing my PhD I was there right at the cusp of the shift towards heavy computing.
I was doing both theory and modelling work in physical chemistry and I had the benefit of being properly trained in both the new and old methods.
In the old ways, when a complex system was to be studied the first action was to develop a ‘model’ system. This was simple and well behaved experimental system – hopefully the simplest that was still within the set of behaviours of the complex system of true interest.
Then lots of experiments were performed to see how the model system behaved under different experimental conditions.
Thereafter, hypotheses were developed and translated to mathematical equations. Because easy-to-use and powerful computers didn’t exist the maths had to be solved analytically and hence the need for the simplest ‘model’ systems.
The analytical equations were used to predict how a new version of the complex system would behave. This was the goal – understanding and predictability within a wide set of pseudo-extrapolated experimental conditions.
In developing these analytical solutions, sometimes simplification were allowed, solely to allow analytical solutions to be achieved at all. This is called relaxing the requirements for an exact solution. Care was taken to keep track of these simplifications just to make sure they didn’t blow up into large errors.
Once the analytical models were developed they were tested over and over, for both improvements and errors, with further experimental data. This process would only stop when everyone decided that the models were a good enough approximation of what was really going on and moved on to more interesting things.
In the newer methods of scientific discovery the whole experiment, no matter how complex, is simply simulated numerically (usually with lots of differential equations) in a very complex software package that no one truly understands.
Having done both, in respect to modelling and understanding of the same complex experimental system, I can say that without a doubt that the old school approach provides us (the custodians of the human brain) far more learning. But the new approach is far quicker if you just want to show two lines, the experimental and the modelled, that match.
In fact the best way to get learning out of the numerical modelling approach is to drive it into unreal limiting cases hoping that something approximating a simple limiting case is observed. By aggregating limiting cases and looking at the difference between them, ‘understanding’ can be achieved.
Many of the scientists looking into how the brain works focus on the fact that there is massive neural network that represent an advanced computer of sorts. I have read articles comparing artificial intelligence to our brains, focusing on the number of processors and the interconnectivity between these.
The assumption by many is that we simply have an amazing Intel processor in our skull and the question is how do we solve all those equations so quickly. This puzzles most.
But the real question for me is, no matter how the brain-computer works, what problems are being solved and how?
I wonder if in fact our brain contains a large library of compiled ‘analytical’ solutions to ‘model’ systems, and also a simple solution solver that can apply any combination of these analytical solutions to a pertinent problem.
This would be consistent with the fact that a scientist working with analytical solutions learns so much more than the modern simulator.
An analytical solution can be a one liner in software and a handful of lines of code for inputting the data and exporting the results, just like the stuff we used to write in Basic on the Apple IIe when all this started.
I also don’t think the brain has ‘maths code’ floating around. So the analytical solutions I am talking about must be some analog of maths written in a chemical code. That is, the structure of the ‘maths’ and also the memory of the brain is stored in rules that are governed by chemical interactions.
Being a chemist I like that. Not binary, not quantum, not maths at all, but chemical. Chemistry has all sorts of rules about reaction, symmetry, interaction and transport of molecules; enough defined complexity to build a computing system capable of being us.
We humans can solve what look like intractable problems (e.g. NP problems) very quickly because we are using a collection of pre-solved and probably approximate ‘analytical’ solutions and one or more simple equation solvers. Possibly there are layers and layers of these all built on top of each other.
The brain must also have a large simulator chugging slowly away in the background looking for new analytical solutions. When found these are parsed into chemical code and then also passed down through DNA memory that encodes the chemical memory. This must be a ‘numerical’ simulator computer that looks for limiting cases that are ‘good enough’ and can be stored as analytical equations in the molecular system.
[p.s. this post is a draft; it will change]































































































