Paper. I limiti della singolarità, i buchi neri dell’evoluzione tecnologica e il rallentamento della crescita esponenziale

Ci vuole un po’ di tempo a leggere questo paper, zeppo di formule e grafici. Il titolo è: On Singularities and Black Holes in Combination-Driven Models of Technological Innovation Networks. Gli autori sono: Ricard Solé, Daniel R. Amor, Sergi Valverde. Si trova su Plos.

Parla dell’evoluzione della tecnologia. La domanda di fondo è questa: la tecnologia evolve seguendo uno schema esponenziale? Oppure va in modo lineare? O addirittura rallenta? Gli autori hanno i dati secolari dei brevetti. E una teoria da verificare: la tecnologia evolve con la generazione di innovazioni che avvengono prevalentemente attraverso la ricombinazione di tecnologie precedenti. Se questo è vero, con tutte le nuove tecnologie che si accumulano a disposizione di chi le deve ricombinare è probabile che la crescita sia esponenziale. All’atto pratico non è sempre così. Perché gli autori si rendono conto che occorre tener presente l’obsolescenza di alcune tecnologie del passato che non possono più essere ricombinate. Il che riduce le probabilità di crescita esponenziale. E alla fine si aprono diversi scenari. Ovviamente in attesa di ulteriori indagini, come sempre nella scienza.

Mi porto a casa qualche conseguenza da queste considerazioni che discutono l’accelerazione dell’innovazione per via di ricombinazione:
1. l’esplosione esponenziale della fioritura di innovazioni fondata sulle tecnologie attuali è un’ipotesi ma non una certezza
2. è più probabile l’accelerazione delle innovazioni in un contesto in cui le tecnologie vengono escluse meno dalla possibilità di ricombinazione, cioè sono riusabili
3. è più probabile un rallentamento delle innovazioni in un contesto in cui le tecnologie diventano obsolete per chiusura della piattaforma, copyright, obsolescenza programmata, ridotta standardizzazione, ecc

Conseguenza supersintetica: su internet c’è più innovazione. Su una piattaforma proprietaria c’è meno innovazione. Perché molte più tecnologie finiscono nel buco nero dell’obsolescenza o della non riutilizzabilità.

Ma a parte queste considerazioni, questo è l’abstract del paper:

It has been suggested that innovations occur mainly by combination: the more inventions accumulate, the higher the probability that new inventions are obtained from previous designs. Additionally, it has been conjectured that the combinatorial nature of innovations naturally leads to a singularity: at some finite time, the number of innovations should diverge. Although these ideas are certainly appealing, no general models have been yet developed to test the conditions under which combinatorial technology should become explosive. Here we present a generalised model of technological evolution that takes into account two major properties: the number of previous technologies needed to create a novel one and how rapidly technology ages. Two different models of combinatorial growth are considered, involving different forms of ageing. When long-range memory is used and thus old inventions are available for novel innovations, singularities can emerge under some conditions with two phases separated by a critical boundary. If the ageing has a characteristic time scale, it is shown that no singularities will be observed. Instead, a “black hole” of old innovations appears and expands in time, making the rate of invention creation slow down into a linear regime.

E questo è il finale:

The nature and tempo of innovation is a difficult and timely topic. It has been the focus of attention from evolutionary biologists, economists and physicists alike. Inventors get inspiration from previous, existing designs, while they push forward the boundaries of invention. In searching for a theory of technological change, the combinatorial nature of technology seems to be an essential component of human creativity. By combining previous designs into novel ones, there is a potential for an explosion of novelties, which could eventually move towards a singularity. How can we test such possibility? Patent files are a privileged window into such process, since they provide a first approximation to both the growth of inventions and their interactions over time. The accelerated pattern of patent growth suggests that a super linear process of innovation is taking place and available evidence indicates that this is at least partially associated to combinatorial processes [21].

In this paper we have explored a simple class of models that include both the richness of combinations and how rapidly the relevance of previous inventions fades with time. These two features can be seen as two opposing forces: the diversity of potential previous inventions to be combined powers combinatorial design, while the obsolescence of the same inventions makes them less likely to contribute to combinations. Our goal was not as much as to fit data than understand the basic scenarios where singularities might emerge when both features are included.

We have shown that long-memory kernels permit the presence of singularities under some conditions, while kernels involving a characteristic time scale of ageing forbid divergences to occur. The first class predicts two different phases, which reminds us of a picture of innovation defining a phase transition between sub-critical and super-critical phases [33]. The second provides a plausible reason why singularities might fail to be observed, while the transient dynamics of innovation appears hyperbolic. Further investigations should analyse other temporal trends (including the patterns of fluctuations) associated to these class of models and a more detailed analysis of available time series. Existing models of evolution of innovations [34, 35] can provide very useful tests to the ideas outlined here. Other factors have not been considered here, such as the limited resources effectively available for developing new technologies. Nevertheless, our models suggests that some generic trends can be defined that pervade the ways in which innovation evolves.