Causality and computation have been linked since the beginning by way of the concept of calculation.
This is an ancient Greek calculator used to predict celestial events such as eclipses.
It is known as the Antikythera mechanism
because of the island name in which it was found.
It is the first known analog computer believed to have been made by
87 BC that is more than two thousand years ago.
Possibly built by Archimedes, the device is very similar to the mechanical toys shown before
simulating the planet movements of the solar system.
These cogwheels would turn in a very precise fashion to make a prediction based on the
epicycles model that we saw in the first lesson.
Here is a computer program designed to showcase the way in which the mechanism works and what it was able to predict.
Not everything is known about this ancient device.
For example, it is not known what are the additional components needed to simulate and display planetary motions.
Turning the handle causes a sequence of interlocking gears to rotate, moving the sun and moon markers around a calendar disc.
The reason the researchers have cracked this device
with partial success getting into the mind and knowledge of the people that designed it two thousand years ago, is because it is a
mechanical device exposed in the model that it mechanistically simulates.
As we have seen before,
mechanistic models such as this one are not necessarily representing the causal
mechanism of the movements of the celestial bodies that they are attempting to simulate.
But they do capture some of their regularities.
What is most interesting is that while the mechanism was not the cause, the mechanism itself
was the cause of the numerical calculations indicating the future position of the celestial bodies.
This is literally a computer simulation performed more than
2,000 years ago
illustrating how deeply the concept of cause was taken even back the with the use of a mechanical calculator,
an analogue computer as this one.
What we will see in this course is that modern computer simulations are not very different to this one.
Simulations can be used to make optimal predictions and even try to figure out the most likely mechanistic models of natural processes.
This simple artifact actually illustrates the kind of concepts that, just as they did in the Greek island of Antikythera,
puts together computation and simulation to serve the purpose of finding possible causes for natural or astronomical phenomena.
This diagram illustrates the kind of direction in which we are pushing with algorithmic information dynamics.
The diagram shows different types of landmark approaches to the problem of causal discovery.
One can see how until very recently most approaches were mostly based on data with almost no model generation.
This was the statistics-led approach for the last decade. It's still mostly used today in the practice of research and science. In mathematics
however, we have dealt with models all the time,
mostly theoretical ones, in the area of dynamical systems that we will cover in a future module in detail.
With differential equations, for example, at the center and one of the landmarks in the area,
helping produce numerical and computer simulations.
One can also see how perturbation analysis and
related concepts such as Bayesian networks move the spectrum in the right direction of models.
Most approaches to artificial intelligence,
that we will call AI, and machine learning, that we will call ML, are statistic in nature and cannot generate models from data.
Sometimes scientists are helped by AI and ML,
but traditionally neither AI or ML can produce those models by themselves and people get confused
believing it is AI or ML who developed them.
Trends and methods in these areas, including deep learning and deep neural networks, are
black box approaches to data classification and even prediction that work amazingly well but provide
little to no understanding of generating mechanisms.
As a consequence,
they also fail to be scalable to domains for which they were not trained for and they require tons of data to be trained
before doing anything interesting, and they need training every time they are presented with even slightly different data.
I think we can expect ML an AI to hopefully get deeper into model-driven approaches,
living traditional statistics behind by incorporating
algorithmic principles.
This means pushing fundamental science rather than throwing more
computational resources to solve data-related problems as is mostly currently done in approaches with machine learning.
This is exactly what we are doing with algorithmic information dynamics.
And we will encourage you to test it on your own data for your own
purposes, as we will tell you how to do so in the last module with real-world
applications.
What we aim is to go all the way and start from the opposite end of the spectrum in the landmarks of causal discovery
diagram at the most model driven end, and from there move to the data-driven side when necessary in a feedback loop
so that a model is generated
and improved based on the data observed. And once a candidate model is produced or chosen,
it is tested again against new data
until we are left with only a handful of likely mechanistic models that we can study and exploit.
At this extreme size of model production,
generation and selection is a theory called algorithmic probability, which is going to be at the center of our
foundations methods and applications in this course.
This course is all about establishing a strong bridge between data and model-based approaches,
between observations and perturbations, and a causal calculus based on the theory of algorithmic probability
as the optimal and ultimate theory of induction.
To this end,
we will connect different areas of science such as perturbation analysis, complex networks, information theory,
dynamical systems, algorithmic complexity, and even machine learning where we think our approaches will help better
understand fundamental concepts such as deep learning and will contribute to refine tools and make them more powerful in the quest of
discovering causes.