Is the human mind an algorithm?
This is a question that has been floating around for decades. Spoiler alert: we don't know. But we still can make mind-blowing conclusions.
Hello, Hypers!
Artificial Intelligence is a field as old as Computer Science itself. Alan Turing is considered the father of both, Computer Science and Artificial Intelligence. Almost from the very moment we defined what an algorithm is, we started to try to find out if our minds lie inside that definition.
We can divide AI into two main categories: strong and weak. Strong AI aims to create machines that are indistinguishable from humans. Artificial General Intelligence (AGI) is used as a substitute for strong AI, they mean the same. On the other hand, weak (a.k.a narrow) AI aims to solve specific problems such as predictions, classifications, Q&A systems, etc.
Curiously, the broader and harder field of AGI was the first to be studied. The most famous idea of these early studies is the Turing Test. Although a lot of people interpret it as a conventional experiment such that we can perform it and obtain results, this is not what it is. I’ll let @alepiad tweet to explain it:
The Turing test is not a test that can be "passed" or "failed". It is a philosophical thought experiment to argue in favor of a functionalist definition for intelligence. In this sense, it is similar to Mary's room, Theseus' ship, or the many variants of the trolley problem.
I’m planning on writing about Turing Test in an upcoming post because it deserves much more space for itself.
We don’t know even if AGI is possible, that’s why I’m writing this. The new advances in LLMs and generative AI have put this question at the center of the table (again), and AGI advocates seem to be winning the debate. I don’t think we have advanced too much in answering the question.
In this post, we are going to explore this question, I’ll throw some thoughts about it, and analyze some consequences.
Computable or not computable
We can solve a lot of problems with computers. There are also some things that computers (or, more precisely, algorithms) cannot do. You can read about the Halting problem, non-computable numbers, Ackerman’s function, or Mandelbrot’s sets as examples of non-computable things.
But all those things are quite artificial, mathematical constructions that have been useful almost just for establishing the theoretical boundaries of Computer Science. The universe we live in still has its chance to be computable. And… what about our minds?
What are we asking?
We are wondering if the human mind is an algorithm. If all the creativity, emotions, and cognitive processes can be written in a programming language.
The question is fascinating because we start answering: “No way! Mi mind cannot be reduced to a bunch of written characters that can be executed by a computer. It has to be something more complex”. But then we say: “Wait. If there is something else in my mind, then what is it?!“. Just mind-blowing.
As we said above, we are not asking whether it is possible to create machines that pass the Turing Test. AGI is an interdisciplinary field that needs the work of neuroscientists, psychologists, philosophers, etc to obtain concrete definitions and measures to determine whether AGI is achieved or not.
But I want to highlight that the problem should be inevitably reduced to a Computer Science problem: the problem of telling whether our mind is computable given a formal system that should be previously defined (by neuroscientists, computer scientists, philosophers, etc ). I think this is the only way to declare the AGI undisputed victory.
What if…?
We still don’t have an answer (IMO we are not even close) to our question. But that’s not an excuse! We can still ask what if our minds are algorithms, or what if they’re not?
Answering Yes
This means our minds are algorithms. Our conscience, emotions, creativity, etc can be reduced to a string in some formal language. That’s already mind-blowing, but wait, there’s more.
What happens with all those artificial problems we created to set the limits of computability? Let’s take the Halting Problem to illustrate the consequences.
Turing proved that no algorithm can determine, for every algorithm and all the possible inputs for that algorithm, whether it is going to stop or not. Now, if our minds are algorithms, then there exists another algorithm such that we cannot tell for some input if it will stop or not.
I think this is huge! Alan Turing used some powerful and beautiful ideas to solve the Halting Problem, but it is hard to see how they would apply to the human mind. Essentially, the idea behind demonstrations like this one (or Goedel’s theorems, or the uncomputability of Ackerman’s function) is the Cantor’s diagonal. I feel that a machine won’t be able to leverage Cantor’s diagonal approach to this extent ever. This demonstration technique has been refusing the most famous attempts to declare the absolutism of a formal system.
I’m also planning to write about Cantor’s diagonal in a future post. Let’s see now what would a negative answer mean.
Answering No
This means that our minds are something more than just algorithms. Then, what is(are) the additional ingredient(s)?
I’m finishing reading “The Emperor’s New Mind“ by Roger Penrose and I have enjoyed a lot with some of his hypotheses. In my own words, Penrose is telling us that maybe this mind-blowing question could get the answer from a comparable mind-blowing field: quantum physics.
Actually, the answer would be in a new physics theory that unified general relativity with quantum theory. This new theory could explain what is exactly behind the jumps between determinism and non-determinism in quantum theory. It should fill the holes that current theories don’t cover and Penrose thinks that it should also explain what is exactly happening in our brains. That could be the non-algorithmically component of our minds.
Conclusions
We are witnessing a lot of mind-blowing advances in AI. The hype is here and we cannot avoid it. But don’t be fooled, some things stay the same or haven’t changed too much.
In this post, we analyzed the fundamental question is AGI possible? Or, in other words, is our mind an algorithm? We have talked about lots of interesting ideas and research fields and just scratched the surface. Turing Test, Computability Theory, Cantor’s Diagonal, “The Emperor’s New Mind“, etc. I hope to write more on these in upcoming posts.
For now, I just hope you have enjoyed this one and that you are now motivated to see what’s going on under the hype.
See you!
I add this : if the answer is no, because of Church-Turing thesis we will never have a scientific proof of this impossibility.
I discussed this here :
https://open.substack.com/pub/spearoflugh/p/mathematical-necessity-nature-and?utm_source=direct&r=buw3d&utm_campaign=post&utm_medium=web
I have also wrote something about why we find quantum mechanics so baffling, basically because measurement is the dual of will (and we don't.understand free will):
https://open.substack.com/pub/spearoflugh/p/free-will-and-observation?utm_source=direct&r=buw3d&utm_campaign=post&utm_medium=web