BSc (UNAM), PGCert (Oxon), MPhil (ENS), PhD CompSci (Lille), PhD Phil (Sorbonne). Elected member of the London Mathematical Society, Fellow of the British Royal Society of Medicine, member of the Canadian College of Health Leaders.

At Westminster interviewed for St James’ Houses of Parliament History Project on the 75th anniversary of the NHS and how our discoveries and deep technology will help the NHS continue delivering on its mission. September 2023.

Latest two books published by Springer Nature (2022) and Cambridge University Press (2023)

Methods and Applications of Algorithmic Complexity offers an alternative approach to algorithmic complexity rooted in and motivated by the theory of algorithmic probability.  It explores the relaxation of the necessary and sufficient conditions that make for the numerical applicability of algorithmic complexity better rooted in the true first principles of the theory and what distinguishes it from computable or statistical measures, including those based on (lossless) compression schemes, such as LZW and cognates, that are in truth more related to traditional Shannon entropy and demonstrably inadequate to characterising causal mechanistic principles. 

Algorithmic Information Dynamics (AID), is a type of digital calculus for causal discovery and causal analysis in software space, the result of combining perturbation and counterfactual analysis with algorithmic information theory. It is the means to navigate software space, like in the Matrix movie. Watch the video below for more information or read the Scholarpedia page on AID for more technical details.

Algorithmic Information Dynamics

As Featured in Nature

Nature, the world’s top journal in science, produced a video (by their own initiative and not paid for) to explain our research based on algorithmic probability, an Artificial General Intelligence approach to causal discovery, after our article on causal deconvolution, ​a type of AGI able to understand cause & effect.

  • Reddit and PLOS Science invited me to an Ask Me Anything session​ that was in the top 10 all time Reddit/PLOS Science ​AMAs in 2018

  • Quanta produced a podcast to explain our research (published by the Royal Society) on the computational basis of the emergence genes

  • I was invited to write an essay to imagine how Computing will look like in the year 2065 published by Springer Nature (ed. Prof. A. Adamatzky): Reprogramming Matter, Life, and Purpose.

Short Bio

I serve as a board director for several startups in the areas of healthcare and fintech in the UK, Canada, and Sweden. I am the sole Founder and Chief Visionary Officer of Oxford Immune Algorithmics, an AI spinout from the University of Oxford. I am a mentor at the CDL Oxford Saïd Business School, graduated from the CDL Toronto Rotman School of Management and from the SpinLab program at HHL Leipzig Graduate School of Management.

Trained as a mathematician, computer scientist, and epistemologist (Ph.D. Lille, Ph.D. Sorbonne, MPhil ENS, PGCert Oxon), I have held industry and academic senior staff and faculty positions in different institutions across several countries in cities ranging from Mexico City to Boston, Pittsburgh, Paris, Stockholm, London, Dubai/Abu Dhabi, Toronto, and Tokyo running the gamut from Assistant Professor, Senior Researcher, Principal Investigator, to Lab Leader and Policy Advisor on AI for Scientific Discovery (for institutions such as the U.S. Navy or the OECD). 

In the last 10 years, I have been associated with Oxbridge and the Golden Triangle in the UK, affiliated with the Universities of Oxford and Cambridge as a faculty member and senior researcher, and at the Alan Turing Institute in London at the British Library. Before that, I was Assistant Professor at the Unit of Computational Medicine and later Lab leader at the Algorithmic Dynamics Lab at the Center for Molecular Medicine, Karolinska Institute (the institution that award the Nobel Prize in Physiology or Medicine).

In the U.S., I was a visiting scholar at Carnegie Mellon and a member of the NASA Payload team for the Mars Biosatellite project at MIT, where I was in charge of the development of the tracking software to study the effects of microgravity on small living organisms.

More recently, I have been working on the formalisation and mathematisation of the field I call Semantical SETI that has for a long time lacked proper attention and my team and I are transforming. See video below and publications.

Also in the U.S., as part of the then small Wolfram|Alpha team (about only 5 people back then, today 200+) based in Boston led by Stephen Wolfram, I contributed to the code behind the A.I. engine of Apple’s Siri, Amazon’s Alexa and other systems that enables these computational linguistics’ systems to understand and answer factual questions. These functions were also incorporated also to ChatGPT as an option to make them answer factual questions and reduce hallucinations.

I am an expert in reversible large recursive language models, or RLLMs. RLLMs are invertible inference computable models that, unlike traditional LLMs, like ChatGPT, can be truly traceable and explainable because they are mechanistically and causally connected through a chain of cause and effect hence avoiding the kind of problems regular LLMs (and some humans) get into such as hallucinations (making up ‘facts’).

I introduced the field of Algorithmic Information Dynamics (AID), a new and exciting field devoted to the study of dynamical systems in software space using the power of Artificial General Intelligence methods. Gregory Chaitin, one of the founders of modern computer science and complexity theory, described me as a “new kind of practical theoretician“.


I have been awarded several grants from the Swedish Research Council (VR), the Foundational Questions Institute (FQXi), and the Silicon Valley Foundation and won several awards from The Kroto Institute, University of Sheffield to representing the future of healthcare in the UK at the Dubai Expo 2020 to winning the Etihad AI first prize against companies like Microsoft and Accenture.

I am also the Managing Editor of Complex Systems, the first journal in the field of complexity founded by Stephen Wolfram in 1987.  I serve as Editor for several journals including Entropy, Information, Frontiers in AI, and Complexity; and for book series such as Springer’s on Complexity. 

A formal approach to the Semantics of SETI and techno-signature detection

For too long scientists and thinkers have made rather simplistic assumptions about how zero-knowledge messaging could be interpreted or deciphered when exchanging information between intelligent beings with no common language. From the Arecibo message to the Voyager’s discs. How can we speak to diverse minds on Earth and beyond? The same rules can help understand immune cells that have produced their own cytokine-based grammar to understand threats and diseases to intelligent animal species that are capable of sophisticated individual and social language.

Proving the use and abuse of Shannon Entropy and statistical lossless compression wrong

Because of its extreme simplicity but high expressivity at demonstrating a key point in causality and complexity, my proudest piece of code I have written to this date is this highly-nested recursive function written in the Wolfram Language running in Mathematica while travelling on a train after attending a Nobel Prize event in Gothenburg back to Stockholm in about an hour while discussing a new paper idea to be written with my friend and colleague Dr. Narsis Kiani. The paper was published as part of a paper of ours in the peer-reviewed journal Physical Review E published by the American Physical Society:

The single line of code shows how a super-compact fully deterministic algorithm can fool any statistical inspection including Shannon Entropy-based methods (comprising popular compression algorithms like LZW usually abused in complexity science) believing that the resulting object may be random to a.

The resulting evolving object is always a directed connected graph that can grow to any size with Entropy-divergent properties.  Its degree sequences grow with (almost) maximal entropy rate (from which it can be fully reconstructed) but its adjacency matrix (from which it can also be fully reconstructed) grows with (almost) lowest entropy values. 

ZK[graph_] := EdgeAdd[graph,Rule @@@ Distribute[{Max[VertexDegree[graph]] + 1, Table[i, {i, (Max[VertexDegree[graph]] + 2), (Max[VertexDegree[graph]] + 1) +(Max[VertexDegree[graph]] + 1) – VertexDegree[graph, Max[VertexDegree[graph]] + 1]}]}, List]]

With its generating code NestList[ZK, Graph[{1 -> 2}], n] where n is the number of iterations determining the graph size and 1->2 is a 2-node single-edge graph to begin with.  The algorithm keeps adding nodes and edges to keep the connected graph growing and diverging with an apparent maximal entropy degree sequence.

This is one of the foundations to understanding our research, based on underlying possible generating mechanisms beyond statistical methods that have dominated science for decades or centuries and can go beyond, or combine, methods from statistical mechanics but is based and motivated in the principles of algorithmic probability, a powerful form of Artificial General Intelligence.

The most important discovery in science according to Minsky

Marvin Minsky, widely considered the founding father of Artificial Intelligence, made the following astonishing claim related to algorithmic complexity and algorithmic probability describing what turns out to be exactly the description of my own research in a closing statement months before passing away:

“It seems to me that the most important discovery since Gödel was the discovery by Chaitin, Solomonoff and Kolmogorov of the concept called Algorithmic Probability which is a fundamental new theory of how to make predictions given a collection of experiences and this is a beautiful theory, everybody should learn it, but it’s got one problem, that is, that you cannot actually calculate what this theory predicts because it is too hard, it requires an infinite amount of work. However, it should be possible to make practical approximations to the Chaitin, Kolmogorov, Solomonoff theory that would make better predictions than anything we have today. Everybody should learn all about that and spend the rest of their lives working on it.

The Pervasiveness of Universal Computation

I got interested in neural networks from the standpoint of computability and complexity theories in my early 20s when I was writing my final year memoir for my BSc degree in math​​ at UNAM. Today, I am helping revolutionise the field by reintroducing the theories of computability and algorithmic complexity back into AI and neural networks.

​On the right, an image showing how a deep neural network trained with a large set of fine art paintings ‘sees’ me. My current research consists of helping machine and deep learning see beyond these statistical patterns in more clever ways than simple pattern matching. By introducing algorithmic probability to Artificial Intelligence I help the field to reincorporate abstract reasoning and causation in current AI trends.

Known to underperform in tasks requiring abstraction and logical inference, current approaches in deep and machine learning are very limited. An example of our research in this direction is our paper published in Nature Machine Intelligence which can be read here for free (no paywall).

These CAs that we have proven to be Turing-universal using novel methods, and thus are able to run any computable function, are the result of combining the power of extremely simple computer programs (ECAs):

Composition of ECA rules 50 ◦ 37 with colour remapping leading to a 4-colour Turing universal CA emulating rule 110.

Composition of ECA rules 170 ◦ 15 ◦ 118 with colour re-mapping mapping leading to a 4-colour Turing universal CA emulating rule 110.

As reported in our paper published in the journal of Cellular Automata, we proved that these two 4-colour cellular automata are Turing universal, found by exploration of rule composition. This means that these CAs can, in principle, run MS Windows and any other piece of software (even if very inefficiently).

These new CAs helped us show how the Boolean composition of two and three ECA rules can emulate rule 110.

This also means that these new CAs can be decomposed into simpler rules and thus illustrates the process of causal composition and decomposition.

The methods also constitute a form of sophisticated causal coarse-graining learning that we have explored in other papers such as this one. In the same paper, we also introduced a minimal set of ECA rules that can generate all others by Boolean composition.

In this other paper, we also found strong evidence of pervasive universal computation in software space

Other authored and edited books

‘Lo que cabe en el espacio’ a short book I prepared right after my BSc degree, is available for Kindle and for free in mobi and pdf.

As contributor

I contributed to the final materialization of the Leibniz-Chaitin medallion after Leibniz’ original design 300 years ago to celebrate his discovery of binary arithmetic

Histograms of number of cities visited (with at least 4 cities) and continents:

The Leibniz-Chaitin medallion story in celebration of the works of Greg Chaitin and the discovery of binary arithmetic from which, according to Leibniz, everything can be created

Around the globe

I have been to more than 400 cities in more than 50 countries giving talks related to my
work in about half of them ​and as an invited speaker in about 18: