Antoni Gaudi and learning algorithms from Nature

Happy holidays.

A few days ago, I was exploring Barcelona. This means that I saw a lot of architecture by Antoni Gaudi. His works have a very distinct style; their fluid lines, bright colours, myriad materials, and interface of design and function make for very naturesque buildings. They are unique and stand in sharp contrast to the other — often Gothic revival and Catalan Modernisme — architecture around them. The contrast is conscious; when starting out, Gaudi learned the patterns of the neo-Gothic architecture then in vogue and later commented on it:

Gothic art is imperfect, only half resolved; it is a style created by the compasses, a formulaic industrial repetition. Its stability depends on constant propping up by the buttresses: it is a defective body held up on crutches. … The proof that Gothic works are of deficient plasticity is that they produce their greatest emotional effect when they are mutilated, covered in ivy and lit by the moon.

His buildings, however, do not need to be overgrown by ivy, for Gaudi already incorporates nature in their design. I felt this connection most viscerally when touring the attic of Casa Mila. The building was commissioned as an apartment for local bourgeois to live comfortably on the ground floor off the rents they collected from the upper floors. And although some of the building is still inhabited by businesses and private residence, large parts of it have been converted into a museum. The most famous part among tourists is probably the uneven organic roof with its intricate smoke stacks, ventilation shafts, and archways for framing other prominent parts of Barcelona.

This uneven roof is supported by an attic that houses an exhibit on Gaudi’s method. Here, I could see Gaudi’s inspiration. On display was a snake’s skeleton and around me were the uneven arches of the attic — the similarity was palpable (see below). The questions for me were: was Gaudi inspired by nature or did he learn from it? Is there even much of a difference between ‘inspired’ and ‘learned’? And can this inform thought on the correspondence between nature and algorithms more generally?


I spend a lot of time writing about how we can use algorithmic thinking to understand aspects of biology. It is much less common for me to write about how we can use biology or nature to understand and inspire algorithms. In fact, I feel surprisingly strong skepticism towards the whole field of natural algorithms, even when I do write about it. I suspect that this stems from my belief that we cannot learn algorithms from nature. A belief that was shaken, but not overturned, when I saw the snake’s skeleton in Gaudi’s attic. In this post, I will try to substantiate the statement that we cannot learn algorithms from nature. My hope is that someone, or maybe just the act of writing, will convince me otherwise. I’ll sketch my own position on algorithms & nature, and strip the opposing we-learn-algorithms-from-nature position of some of its authority by pulling on a historic thread that traces this belief from Plato through Galileo to now. I’ll close with a discussion of some practical consequences of this metaphysical disagreement and try to make sense of Gaudi’s work from my perspective.

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Fusion and sex in protocells & the start of evolution

In 1864, five years after reading Darwin’s On the Origin of Species, Pyotr Kropotkin — the anarchist prince of mutual aid — was leading a geographic survey expedition aboard a dog-sleigh — a distinctly Siberian variant of the HMS Beagle. In the harsh Manchurian climate, Kropotkin did not see competition ‘red in tooth and claw’, but a flourishing of cooperation as animals banded together to survive their environment. From this, he built a theory of mutual aid as a driving factor of evolution. Among his countless observations, he noted that no matter how selfish an animal was, it still had to come together with others of its species, at least to reproduce. In this, he saw both sex and cooperation as primary evolutionary forces.

Now, Martin A. Nowak has taken up the challenge of putting cooperation as a central driver of evolution. With his colleagues, he has tracked the problem from myriad angles, and it is not surprising that recently he has turned to sex. In a paper released at the start of this month, Sam Sinai, Jason Olejarz, Iulia A. Neagu, & Nowak (2016) argue that sex is primary. We need sex just to kick start the evolution of a primordial cell.

In this post, I want to sketch Sinai et al.’s (2016) main argument, discuss prior work on the primacy of sex, a similar model by Wilf & Ewens, the puzzle over emergence of higher levels of organization, and the difference between the protocell fusion studied by Sinai et al. (2016) and sex as it is normally understood. My goal is to introduce this fascinating new field that Sinai et al. (2016) are opening to you, dear reader; to provide them with some feedback on their preprint; and, to sketch some preliminary ideas for future extensions of their work.

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