Reductionism: to computer science from philosophy

A biologist and a mathematician walk together into their joint office to find the rubbish bin on top of the desk and on fire. The biologist rushes out, grabs a fire extinguisher, puts out the blaze, returns the bin to the floor and they both start their workday.

The next day, the same pair return to their office to find the rubbish bin in its correct place on the floor but again on fire. This time the mathematician springs to action. She takes the burning bin, puts it on the table, and starts her workday.

The biologist is confused.

Mathematician: “don’t worry, I’ve reduced the problem to a previously solved case.”

What’s the moral of the story? Clearly, it’s that reductionism is “[o]ne of the most used and abused terms in the philosophical lexicon.” At least it is abused enough for this sentiment to make the opening line of Ruse’s (2005) entry in the Oxford Companion to Philosophy.

All of this was not apparent to me.

I underestimated the extent of disagreement about the meaning of reductionism among people who are saying serious things. A disagreement that goes deeper than the opening joke or the distinction between ontological, epistemological, methodological, and theoretical reductionism. Given how much I’ve written about the relationship between reductive and effective theories, it seems important for me to sort out how people read ‘reductive’.

Let me paint the difference that I want to discuss in the broadest stroke with reference to the mind-body problem. Both of the examples I use are purely illustrative and I do not aim to endorse either. There is one sense in which reductionism uses reduce in the same way as ‘reduce, reuse, and recycle’: i.e. reduce = use less, eliminate. It is in this way that behaviourism is a reductive account of the mind, since it (aspires to) eliminate the need to refer to hidden mental, rather than just behavioural, states. There is a second sense in which reductionism uses reducere, or literally from Latin: to bring back. It is in this way that the mind can be reduced to the brain; i.e. discussions of the mind can be brought back to discussions of the brain, and the mind can be taken as fully dependent on the brain. I’ll expand more on this sense throughout the post.

In practice, the two senses above are often conflated and intertwined. For example, instead of saying that the mind is fully dependent on the brain, people will often say that the mind is nothing but the brain, or nothing over and above the brain. When doing this, they’re doing at least two different things. First, they’re claiming to have eliminated something. And second, conflating reduce and reducere. This observation of conflation is similar to my claim that Galileo conflated idealization and abstraction in his book-keeping analogy.

And just like with my distinction between idealization and abstraction, to avoid confusion, the two senses of reductionism should be kept conceptually separate. As before, I’ll make this clear by looking at how theoretical computer science handles reductions. A study in algorithmic philosophy!

In my typical arrogance, I will rename the reduce-concept as eliminativism. And based on its agreement with theoretical computer science, I will keep the reducere-concept as reductionism.
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Plato and the working mathematician on Truth and discourse

Plato’s writing and philosophy are widely studied in colleges, and often turned to as founding texts of western philosophy. But if we went out looking for people that embraced the philosophy — if we went out looking for actual Platonist — then I think we would come up empty-handed. Or maybe not?

A tempting counter-example is the mathematician.

It certainly seems that to do mathematics, it helps to imagine the objects that you’re studying as inherently real but in a realm that is separate from your desk, chair and laptop. I am certainly susceptible to this thinking. Some mathematicians might even claim that they are mathematical platonists. But there is sometimes reasons to doubt the seriousness of this claim. As Reuben Hersh wrote in Some Proposals for Reviving the Philosophy of Mathematics:

the typical “working mathematician” is a Platonist on weekdays and a formalist on Sundays. That is, when he is doing mathematics, he is convinced that he is dealing with an objective reality whose properties he is attempting to determine. But then, when challenged to give a philosophical account of this reality, he finds it easiest to pretend that he does not believe in it after all.

What explains this discrepency? Is mathematical platonism — or a general vague idealism about mathematical objects — compatible with the actual philosophy attributed to Plato? This is the jist of a question that Conifold asked on the Philosophy StackExchange almost 4 years ago.

In this post, I want to revisit and share my answer. This well let us contrast mathematical platonism with a standard reading of Plato’s thought. After, I’ll take some helpful lessons from postmodernism and consider an alternative reading of Plato. Hopefully this PoMo Plato can suggest some fun thoughts on the old debate on discovery vs invention in mathematics, and better flesh out my Kantian position on the Church-Turing thesis.

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Minimal models for explaining unbounded increase in fitness

On a prior version of my paper on computational complexity as an ultimate constraint, Hemachander Subramanian made a good comment and question:

Nice analysis Artem! If we think of the fitness as a function of genes, interactions between two genes, and interactions between three genes and so on, your analysis using epistasis takes into account only the interactions (second order and more). The presence or absence of the genes themselves (first order) can change the landscape itself, though. Evolution might be able to play the game of standing still as the landscape around it changes until a species is “stabilized” by finding itself in a peak. The question is would traversing these time-dependent landscapes for optima is still uncomputable?

And although I responded to his comment in the bioRxiv Disqus thread, it seems that comments are version locked and so you cannot see Hema’s comment anymore on the newest version. As such, I wanted to share my response on the blog and expand a bit on it.

Mostly this will be an incomplete argument for why biologists should care about worst-case analysis. I’ll have to expand on it more in the future.

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Techne and Programming as Analytic Philosophy

This week, as I was assembling furniture — my closest approach to a traditional craft — I was listening to Peter Adamson interviewing his twin brother Glenn Adamson about craft and material intelligence. Given that this interview was on the history of philosophy (without any gaps) podcast, at some point, the brothers steered the conversation to Plato. In particular, to Plato’s high regard for craft or — in its Greek form — techne.

For Peter, Plato “treats techne, or craft, as a paradigm for knowledge. And a lot of the time in the Socratic dialogues, you get the impression that what Socrates is suggesting is that we need to find a craft or tekne for virtue or ethics — like living in the world — that is more or less like the tekne that say the carpenter has.” Through this, the Adamson twins proposed a view of craft and philosophy as two sides of the same coin.

Except, unlike the carpenter and her apprentice, Plato has Socrates trying to force his interlocutors to formulate their knowledge in propositional terms and not just live it. It is on this point that I differ from Peter Adamson.

The good person practices the craft of ethics: of shaping their own life and particular circumstances into the good life. Their wood is their own existence and their chair is the good life. The philosopher, however, aims to make the implicit (or semi-implicit) knowledge of the good person into explicit terms. To uncover and specify the underlying rules and regularities. And the modern philosopher applies these same principles to other domains, not just ethics. Thus, if I had to give an incomplete definition for this post: philosophy is the art of turning implicit knowledge into propositional form. Analytic philosophy aims for that propositional form to be formal.

But this is also what programmers do.

In this post, I want to convince you that it is fruitful to think of programming as analytic philosophy. In the process, we’ll have to discuss craft and the history of its decline. Of why people (wrongly) think that a professor is ‘better’ than a carpenter.
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Hobbes on knowledge & computer simulations of evolution

Earlier this week, I was at the Second Joint Congress on Evolutionary Biology (Evol2018). It was overwhelming, but very educational.

Many of the talks were about very specific evolutionary mechanisms in very specific model organisms. This diversity of questions and approaches to answers reminded me of the importance of bouquets of heuristic models in biology. But what made this particularly overwhelming for me as a non-biologist was the lack of unifying formal framework to make sense of what was happening. Without the encyclopedic knowledge of a good naturalist, I had a very difficult time linking topics to each other. I was experiencing the pluralistic nature of biology. This was stressed by Laura Nuño De La Rosa‘s slide that contrasts the pluralism of biology with the theory reduction of physics:

That’s right, to highlight the pluralism, there were great talks from philosophers of biology along side all the experimental and theoretical biology at Evol2018.

As I’ve discussed before, I think that theoretical computer science can provide the unifying formal framework that biology needs. In particular, the cstheory approach to reductions is the more robust (compared to physics) notion of ‘theory reduction’ that a pluralistic discipline like evolutionary biology could benefit from. However, I still don’t have any idea of how such a formal framework would look in practice. Hence, throughout Evol2018 I needed refuge from the overwhelming overstimulation of organisms and mechanisms that were foreign to me.

One of the places I sought refuge was in talks on computational studies. There, I heard speakers emphasize several times that they weren’t “just simulating evolution” but that their programs were evolution (or evolving) in a computer. Not only were they looking at evolution in a computer, but this model organism gave them an advantage over other systems because of its transparency: they could track every lineage, every offspring, every mutation, and every random event. Plus, computation is cheaper and easier than culturing E.coli, brewing yeast, or raising fruit flies. And just like those model organisms, computational models could test evolutionary hypotheses and generate new ones.

This defensive emphasis surprised me. It suggested that these researchers have often been questioned on the usefulness of their simulations for the study of evolution.

In this post, I want to reflect on some reasons for such questioning.

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Labyrinth: Fitness landscapes as mazes, not mountains

Tonight, I am passing through Toulouse on my way to Montpellier for the 2nd Joint Congress on Evolutionary Biology. If you are also attending then find me on 21 August at poster P-0861 on level 2 to learn about computational complexity as an ultimate constraint on evolution.

During the flight over, I was thinking about fitness landscapes. Unsurprising — I know. A particular point that I try to make about fitness landscapes in my work is that we should imagine them as mazes, not as mountain ranges. Recently, Raoul Wadham reminded me that I haven’t written about the maze metaphor on the blog. So now is a good time to write on labyrinths.

On page 356 of The roles of mutation, inbreeding, crossbreeding, and selection in evolution, Sewall Wright tells us that evolution proceeds on a fitness landscape. We are to imagine these landscapes as mountain ranges, and natural selection as a walk uphill. What follows — signed by Dr. Jorge Lednem Beagle, former navigator of the fitness maze — throws unexpected light on this perspective. The first two pages of the record are missing.

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Darwin as an early algorithmic biologist

In his autobiography, Darwin remarked on mathematics as an extra sense that helped mathematicians see truths that were inaccessible to him. He wrote:

Darwin Turing HeadbandDuring the three years which I spent at Cambridge… I attempted mathematics… but got on very slowly. The work was repugnant to me, chiefly from my not being able to see any meaning in the early steps in algebra. This impatience was very foolish, and in after years I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics, for [people] thus endowed seem to have an extra sense. But I do not believe that I should ever have succeeded beyond a very low grade. … in my last year I worked with some earnestness for my final degree of B.A., and brushed up … a little Algebra and Euclid, which later gave me much pleasure, as it did at school.

Today, this remark has become a banner to rally mathematicians interested in biology. We use it to convince ourselves that by knowing mathematics, we have something to contribute to biology. In fact, the early mathematical biologist were able to personify the practical power of this extra sense in Gregor Mendel. From R.A. Fisher onward — including today — mathematicians have presented Mendel as one of their own. It is standard to attributed Mendel’s salvation of natural selection to his combinatorial insight into the laws of inheritance — to his alternative to Darwin’s non-mathematical blending inheritance.

But I don’t think we need wait for the rediscovery of Mendel to see fundamental mathematical insights shaping evolution. I think that Darwin did have mathematical vision, but just lacked the algorithmic lenses to focus it. In this post I want to give examples of how some of Darwin’s classic ideas can be read as anticipating important aspects of algorithmic biology. In particular, seeing the importance of asymptotic analysis and the role of algorithms in nature.
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Proximal vs ultimate constraints on evolution

For a mathematician — like John D. Cook, for example — objectives and constraints are duals of each other. But sometimes the objectives are easier to see than the constraints. This is certainly the case for evolution. Here, most students would point you to fitness as the objective to be maximized. And at least at a heuristic level — under a sufficiently nuanced definition of fitness — biologists would agree. So let’s take the objective as known.

This leaves us with the harder to see constraints.

Ever since the microscope, biologists have been expert at studying the hard to see. So, of course — as an editor at Proceedings of the Royal Society: B reminded me — they have looked at constraints on evolution. In particular, departures from an expected evolutionary equilibrium is where biologists see constraints on evolution. An evolutionary constraint is anything that prevents a population from being at a fitness peak.

Winding path in a hard semi-smooth landscape

In this post, I want to follow a bit of a winding path. First, I’ll appeal to Mayr’s ultimate-proximate distinction as a motivation for why biologists care about evolutionary constraints. Second, I’ll introduce the constraints on evolution that have been already studied, and argue that these are mostly proximal constraints. Third, I’ll introduce the notion of ultimate constraints and interpret my work on the computational complexity of evolutionary equilibria as an ultimate constraint. Finally, I’ll point at a particularly important consequence of the computational constraint of evolution: the possibility of open-ended evolution.

In a way, this post can be read as an overview of the change in focus between Kaznatcheev (2013) and (2018).
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Heuristic models as inspiration-for and falsifiers-of abstractions

Last month, I blogged about abstraction and lamented that abstract models are lacking in biology. Here, I want to return to this.

What isn’t lacking in biology — and what I also work on — is simulation and heuristic models. These can seem abstract in the colloquial sense but are not very abstract for a computer scientist. They are usually more idealizations than abstractions. And even if all I care about is abstract models — which I can reasonably be accused of at times — then heuristic models should still be important to me. Heuristics help abstractions in two ways: portfolios of heuristic models can inspire abstractions, and single heuristic models can falsify abstractions.

In this post, I want to briefly discuss these two uses for heuristic models. In the process, I will try to make it a bit more clear as to what I mean by a heuristic model. I will do this with metaphors. So I’ll produce a heuristic model of heuristic models. And I’ll use spatial structure and the evolution of cooperation as a case study.

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Algorithmic lens as Alan Turing’s wider impact

Today is Alan Turing’s birthday. He would have turned 106.

It has been too long since I last wrote about him on TheEGG. Today, I want to provide an overview of some of his most important work based on my and other’s answers on this old cstheory question. This will build slightly on a post I wrote two years ago for the Heidelberg Laureate Forum, but it will share a lot of text in common.

Turing is far from obscure. Every computer scientist and programmer has heard his name. The Nobel prize of Computer Science is named after him. He has even joined the ranks of mathematicians with feature-length films. Although a film that misrepresents much history. But even outside of film, I feel that our perceptions and representations of Turing are shaped too heavily by the current boundaries and constraints of computer science. Or at least how computer science is popularly (mis)understood.

Also, it is just easier to film the building a giant machine than about proving theorems and revolutionizing how we think about the world.

As the great breadth of his work shows, Turing would not recognize the disciplinary boundaries that confine computer science to technology. Like Abel Molina, he would see many motivations for computer science, from Science and Technology to Mathematics and Philosophy to Society. Turing viewed the whole world through the algorithmic lens. A wide ambition that is sometimes lacking in modern computer science.

In this post, I want to highlight some of the aspects of the world that Turing looked at.
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