What are computers and what are their limits? Put simply.
Episode 1 of a series on computers and Artificial Intelligence, all put simply so that most of my non-geek relatives could understand. And also, the first post on my blog!
🇫🇷 Version traduite en français ici.
Welcome, bienvenue. I may have some thought food in the fridge, please sit and take some time to read
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Dear friends, family, people on the internet reading this. As you may know already, I am starting a blog. For the later, if you don’t know me, I’m a 20-something year old passionate programmer since my teens who also studied computers, machine learning, made a bunch of small video games, worked at the European Space Agency to help detect black holes, proudly founded two postmortem-worthy tech startups in crypto and artificial intelligence (so I know very well about buzzwords), and most importantly cherishes peculiar maters such as contemporary symphonies from obscure Japanese composers, hard science-fiction novels, colorful suits, old-fashioned hats, and many other things.
I will post here from time to time in an effort to share some, hopefully surprising, valuable, thoughts on various computers-related subjects, music recommendation and vulgarized bits of knowledge (my goal being that my non-technical friends, family and even my lovely grandma could grasp it all, despite most having studied wildly different subjects). Which I hope, in this over-hyped, over-marketed, over-centralized, over-institutionalized, over-politicized world, ruled by short-form, low-risk, high-shallowness, low-value (if not even negative value) content, will give you a pool of tranquility and a cup of (eternal?) intellectual juvenility. Giving me, on the flipside, many other intellect-sharpening kind of personal benefits, which certainly can come from the act of writing for all of you. As Feynmann famously said (and got a lot of Instagram likes for) “If you want to master something, teach it. The more you teach, the better you learn. Teaching is a powerful tool to learning”. Of course before one teaches, one sits and reads. Please read, enjoy, and share with a friend, family member or random person on the internet if you may.
So yeah, computers
The subject of this series of posts is nothing less than my thoughts on computers and the future, notably the now pretty noticeable rise of all buzz-wordy Artificial Intelligence. Why start with such an ambitious, but also very well covered topic? Non-technical people in my close vicinity often come and ask me about such subjects. Most of my friends are my age and studied computing (or close), and we would all shamelessly argue for half-baked theories and somewhat obscure ideas as the free minded half-serious youngsters that we are. But as a 20-something year old in today’s world of never-ending growth to adulthood, when real 40-something (and above) adults in my family come and start wondering about such subjects, deeply concerned about them, enough so to dare ask the mere intellectual infant sitting next to them for, hopefully, optimistic insights about our future as a human society… oh well, what have I done to deserve such questions? Study? Do you mean I unintentionally made my voice matter and now I must argue with people? Oh well indeed. Anyway, I will gladly take on the challenge and give my current structured opinion on this because I find it quite fun. Needless to say, if you have a PhD in a related field or have thought deeply about such matters, you can safely skip all my vulgarization and find the music recommendation of the day at the end ;-)
Welcome to crazy land
First, it would be good to remind everyone what a computer is, in it’s purest form, so we start on solid foundations. Today’s post will be just about that, and you can come back later for the rest if you want.
A computer is a machine, so a purely mechanistic entity. By mechanistic entity I mean something predictable and understood, as much as your toaster or bicycle. If you were to know your computer well enough, you could trace all that it does step by step with high confidence and without ever having to say “Ah! Now this step is magic, I don’t know what it does!”. I don’t say it would be easy, just like it wouldn’t be so easy to trace all that your bicycle or toaster does, but it would be “possible” in theory. It’s what some bright minds like mathematician Stephen Wolfram call “reducible” processes. You can trace all that the mechanistic process does, such that if you know how all the steps will chain from the very first, you know that just by starting the process from the first step, it will reach the last one, for sure, and end in a certain way. If you start the toaster, you know it will give a toast. That’s for sure. It won’t magically decide to turn into a tennis ball. And that’s because it’s “reducible”, because what it does is mechanistic, it’s known, and it’s always predictable, as a result of us being able to trace every step with very high confidence.
As my dentist recently asked me what a “computation” was, I will also explain what I mean by that, and you’ll see it becomes interesting: A computation is the act of “reducing” a mechanistic process. By giving a first step, and a given “process”, a computation consists in deducing the result, or final step. By giving the first step “put the bread and push the lever” and giving the process “toaster” I can compute It’ll end up with a unique, predictable result: the then toasted bread. A computation is the act of “reducing” something “reducible”. The way you learn computation at school is through math of course. The first step could be “numbers 3 and 4” and the process could be “addition”, then you compute in your head, going through all the steps one by one. First, you think about your addition table, then you narrow it down to the column with 3, then you remember what’s at the line with 4 as well, and you finally visualize the answer: the result is 3+4=7. Or if you don’t know your table yet, which we all experience for some time, you run a different process, by raising 3 fingers, then 4 more, counting one by one until you get the result, and if you have learned your additions very well, the brain tends to do the work for you and it all gets reduced to just one step: remembering the result by heart. You see how doing 3+4 can be a quite complex process, but it’s “reducible”, hence you can compute it, just take the beginning and reach the end automatically.
Which ends up being quite cyclic if you think about it, and that’s the magic of computers and computations: Computers can compute, hence reduce “reducible” processes to simply “what’s at the beginning, wait, and I’ll automatically give you the end”. But they are also themselves mechanistic, they function with individual steps, hence computers are also reducible, they can be reduced with a computation. Computers can compute computers that compute computers. Take a deep breath, welcome to crazy land, it all started with Ada Lovelace in the eighteen-hundreds, oh wait maybe even Leibnitz in the seventeen-hundreds, while maybe it’s actually with Thales in 600 before Christ, anyway it’s not my fault.
Reducible vs Irreducible
Some of you may argue: “Yes but Anicet, my toaster doesn’t always give me toasted bread, sometimes it takes fire and burns my whole kitchen, nothing is reducible you’re just giving us some theoretical bullshit, stop programming, go outside and experience the real world!”. As some here may know I do experience the real world very much for a mere programmer, with all it’s uncertainty, and my life, sometimes it feels more than some others, is completely absurd, unpredictable, I can’t just “reduce it” and know what will happen. But that’s normal, life is particularly “irreducible” as a whole, just like a lot of things are. It’s all a spectrum that goes from completely reducible to completely irreducible in reality.
Some things are clearly reducible, like a lot of logical reasonings and other artificial man-made constructs such as mathematics (yet so robust they sometimes seem truly “universal” and brought upon us by the universe itself). 3+4 will always be equal to 7. When you have 3 pigs and you add 4 more you always have 7 in the end. That won’t change much. On the other hand, some things are clearly irreducible, when I roll a dice, I have no idea if I get 1 or 5, I can’t just reduce it and say I’ll get a 4 next time. Randomness is purely irreducible.
One could argue that most things actually are in-between. The toaster is giving me a toast 99.99% of the time, but 0.01% of the time, it takes fire. I can’t predict that next time it won’t take fire. I can’t just “reduce it”. Well actually, I can yes, 0.01% chance of being wrong is kind of small. I don’t care. That’s why we admit most things are “reducible”. When I have 3 pigs and add 4, I get 7. For sure, one time in the history of the entire world (I guess) a meteoroid fell on one of the pigs and the poor farmer ended up with just 6. So is it reducible?. Yes, it is by convention. Reducibility is a human construct, as much as computation or computers, but they are actually so reliable that we collectively accept them as “reducible”. And on the opposite end, some things, while being probably reducible by some computation, such as what will happen when I’ll throw that dice, are actually so complex, so hard to compute (imagine modeling all the physics involved in the dice throwing) that we accept them as “irreducible”, “random”. We simply admit that we can’t compute them.
What’s the limits of computers?
Now, it’s time for the final point of this gigantic Stephen Wolfram rip-off (hey, I gotta get the good stuff from somewhere you know, like everyone plagiarized the Greeks for most of the last 2.5 thousand years). The same way a computer can compute a computer that computes, you can make a process that’s made of subprocesses that are made of subsubprocesses right? For instance the bicycle can be seen as: 1) I move my legs, 2) the bike goes forward. But it can also be seen as 1.1) my legs moving move the pedals 1.2) the pedals transmit the motion to the dented disks 1.3) the chain is put in motion 2.1) the opposite disk is moved by the chain 2.2) the wheel is moved by the disk 2.3) the bike is pushed by the circular movement of the wheel. We can go deeper and deeper into the modeling of that process, and “unreduce” high-level steps into more and more low-level steps. But at some point we always reach irreducibility “oh I don’t know the rule of physics that explains the substeps of the motion of the bike” or if you are a physicist “oh I don’t know what will happen with that quantum effect”.
Often, some reducible sequence of step will be followed by that one step you can’t predict anymore, that one very irreducible step. And if that step has a significant impact on the end result of the whole process, it makes the whole process irreducible as well. You can’t know anymore from just the beginning what will happen in the end. For instance, if you dig the bike motion too deep you end up on the very limits of our understanding of physics, quantum theory and co., which is mostly random, but that randomness is merely the indicator that “now we don’t know anymore” (at least in my opinion) and is actually completely uneventful in the case of a bike because the randomness happens at a very tiny scale, one that definitely can’t impact the motion of the bike as a whole. So in that sense, the bike remains reducible. While, if you think of your entire trip on a bike to Bucarest from let’s say Strasbourg, then, sure you can say, I’ll go first to Munich then to Salzbourg and then to wherever until Bucarest, that makes it reducible right? But in practice a lot of unpredictable, and impactful things may happen: your bike may break, and you’re neither good enough at physics (and neither physics is good enough) to compute when and how. Or it may rain so intensely you’ll have to backtrack. Unpredictable, yet likely and impactful events, in those otherwise reducible processes, make them “irreducible”.
So that’s it, that’s the limit of computation. We can’t compute what we can’t, or don’t want to understand, model, predict, what is irreducible. Within what is overall irreducible, there are some “pockets of reducibility” some substeps that you could reduce, but the entire thing is so filled with random events that it’s irreducible from beginning to end. Otherwise everything else is computable, all the rest is reducible. And that’s a lot of things actually. That’s why computers are so useful, especially at automatizing human processes. Because the human brain is also able to do computation: our processes were made by us, therefore, for us, therefore they were mostly made reducible, devoid of indecision or unpredictability, especially the ones that were not ditched or rendered obsolete over time, and required efficiency: games, taxes, industry, education... I always find it interesting to ponder what’s reducible, what’s not, where does the convention we chose can be challenged, or how can complicated processes can be simplified in order to become reducible.
With all of these thought experiments, you now know what is a computer: it reduces the reducible in itself a reducible way. Computers are tremendously useful, they are not magic, unless we decide that they “just are” and forget, or refuse to know, about how they work, thus rendering them “irreducible” again. And they have a clear limit: irreducible processes, the limit of what’s reasonably understandable with the little time, will and knowledge we have.
The arrow of time
Generally, the future isn’t known, because irreducibility is in our way (otherwise it would be), but when something has happened in the past, it can now retroactively become reducible. We didn’t know how to cook food with a microwave before we happened to do it by mistake, resulting from some irreducible stroke of chance. Now inventing the microwave isn’t creative anymore, it has become reducible, we know how to do it, because it has happened in the past. Still, the arrow of time only goes one way. Creativity and the enlargement of the domain of the reducible can only come from past lucky irreducible events that allowed us to get confident enough to adopt a convention of reducibility on a given process, invention, form of art. (Important distinction between “enlargement” and “densification” here: “mixing”, the act of combining existing reducible things in a reducible way, doesn’t enlarge the domain, it densifies it. That’s creative, but I wonder if it is not infinitely less so.)
The painting I put as a cover for this article, Tirol by Franz Marc, is a good example. At that time it was probably quite a novel kind of art, and this composition was quite impactful (cubism wasn’t invented by the Greeks). It is, in a way, for neophytes, still a shocking and impressive composition the first time they see it. Now it would be so trivial to paint in that exact style if only you knew how to paint alright (better than I). And for AI systems such as Dall-E or Midjourney, let’s not even talk about it. It’s peanuts. But that doesn’t mean AI is super creative, the arrow of time went one way, what was irreducible before is mostly reducible now. At best, Artificial Intelligence, which is based on calculation and reducibility, "mixes" things in a reductively creative way, but not in an irreducibly creative way. It produces something new, but it doesn't truly create anything, because one could have perfectly predicted the combination it would make (not considering randomness added from outside the machine). Unless you believe all of this is black magic, in which case it will seem perfectly creative to you, as even the simplest, most understandable, predictable, and thus reducible things can always appear innovative, and therefore irreducible, in the eyes of the majority.
To make a process yield creative results, you need to add irreducibility to it, or simply put, randomness. The amount of reducibility in it doesn’t matter, could be a lot, could be a little. What matters in the end is the unexpected deviation of the whole process, which is naturally tied to the amount of irreducibility. This is what most talented artists do by following signs, gut feelings, or simply travelling, meeting an absurd amount of people, or at the contrary, meeting none for decades up to the point of taking such a unique path. And mediocre artists, just follow others, without adding anything stemming from their own irreducibility. As we will see next time, the future of work in the age of computers consists in following irreducibility: what we can’t compute.
This that we cannot compute will tend to change, as what we could not compute yesterday will become computable tomorrow. Survival favors energy minimization, or “not caring about the details if they don’t matter”. I believe our descendants will strive for that as well, of course, always as much as their survival will require, but as we know from our study of the Earth, of space, of human societies, the survival of the individual will forever be challenged. They will converge towards computing all that they can, always pushing the boundary, reducing past irreducibilities, all to remain competitive, or to take on always more life-threatening challenges. I may even ponder if they will not do so at a faster and faster rate to compensate for the constantly increasing amount of past, useful and independent irreducibilities. If that is so, will time be the same for them? Or will their experience of it lengthen, increase in density, as they will have to process more and more irreducibilities in a shorter and shorter amount of time? What will be the physical limit of the human computer?
See you next time folks
If you liked this article, see you in a week or so for the continuation of this topic: what is intelligence, what does it mean if its artificial (or if it is not), and whether that even matters.
Music recommendation of the day
Under every post, I will paste some related or random music album I like. That’s for free, that’s a bonus. Maybe you don’t give a penny. But next time you know, so at least you can activate your background neurons with something while focusing on my juvenile arguments. And that would be tremendously awesome by all means. As you’ll see I don’t know anything about music, at least not about how to play or compose it, yet I love “complex intellectual stuff that make you look smart and slightly unsettling because frankly sometimes it’s quite niche, and oh how the hell you found that album in the first place”. So I’ll just share and comment very lightly. Don’t expect deep analysis.
This Mahler symphony, the 5th, is definitely more on the “intellectual stuff that make you look smart” side than on the “how the hell you found that album in the first place” side. It’s a true classic. To me it’s the quintessential “feel it all” music, I’m never bored of it, I never feel the redundance. Tip: listen to the 2nd movement, especially between 9:00 and 11:00, that’s some godly 2 minutes of music out there, trust me. Just by listening to it, I want to sing, nuuunnnn nuun nuuuun nuuunn! It’s always interesting how such music is hard to reconstruct; to “reduce” out of the blue, but when you start listening to it, it becomes perfectly reducible for our little brains.
Learn more about me
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