Mathematicians develop model for how new ideas emerge

January 24, 2018, Queen Mary, University of London
Edge-reinforced random walks produce a co-evolution of the network with the dynamics of the walkers. At time t the walker is on the red node and has already visited the grey nodes, while the shaded nodes are still unexplored. The widths of edges are proportional to their weights. At time t + 1 the walker has moved to a neighboring node (red), and the weight of the used edge has been reinforced by δw. At this point, the walker will preferentially go back, although it can also access the set of 'adjacent possible' (green). Credit: Iacopo Iacopini

Researchers from Queen Mary University of London have developed a mathematical model for the emergence of innovations.

Studying creative processes and understanding how innovations arise and how novelties can trigger further discoveries could lead to effective interventions to nurture the success and sustainable growth of society.

Empirical findings have shown that the way in which novelties are discovered follows similar patterns in a variety of different contexts including science, arts, and technology.

The study, published in Physical Review Letters, introduces a new mathematical framework that correctly reproduces the rate at which novelties emerge in real systems, known as Heaps' law, and can explain why discoveries are strongly correlated and often come in clusters.

It does this by translating the theory of the 'adjacent possible', initially formulated by Stuart Kauffman in the context of biological systems, into the language of complex networks. The adjacent possible is the set of all novel opportunities that open up when a is made. Networks have emerged as a powerful way to both investigate real world systems, by capturing the essential relations between the components, and to model the hidden structure behind many complex social phenomena.

Growth of knowledge in science. (a) An empirical sequence of scientific concepts S is extracted from a temporally ordered sequence of papers by concatenating, for each scientific field, the relevant concepts present in the abstracts. (b) The network of relations among concepts is constructed by linking all the concepts appearing in the same abstract. The network is then used as an underlying structure for running our edge- reinforced random walk model. (c) The model is then tuned to the empirical data by selecting the amount of reinforcement δw that reproduces the Heaps' exponent β obtained by fitting the Heaps' curve extracted from S as a power law. Credit: Iacopo Iacopini

In this work, networks are used to model the underlying space of relations among concepts.

Lead author Professor Vito Latora, from Queen Mary's School of Mathematical Sciences, said: "This research opens up new directions for the modelling of innovation, together with a new framework that could become important in the investigation of technological, biological, artistic, and commercial systems."

He added: "Studying the processes through which innovations arise can help understanding the main ingredients behind a winning idea, a breakthrough technology or a successful commercial activity, and is fundamental to devise effective data-informed decisions, strategies, and interventions to nurture the success and sustainable growth of our society."

In the study, the discovery process is modelled as a particular class of random walks, named 'reinforced' walks, on an underlying network of relations among concepts and ideas. An innovation corresponds to the first visit of a site of the network, and every time a walker moves from a concept to another, such association (an edge in the network) is reinforced so that it will be used more frequently in the future. The researchers named this the 'edge-reinforced random walk' model.

To show how the model works in a real case, they also constructed a dataset of 20 years of scientific publications in different disciplines, such as astronomy, ecology, economics and mathematics to analyse the appearance of new concepts. This showed that, despite its simplicity, the edge-reinforced random walk model is able to reproduce how knowledge grows in modern science.

Professor Vito Latora added: "The framework we present constitutes a new approach for the study of discovery processes, in particular those for which the underlying network can be directly reconstructed from empirical data, for example users listening to music over a similarity between songs. We are already working on this idea, together with an extended version of our , where we study the collective exploration of these networked spaces by considering multiple walkers at the same time."

Explore further: New tipping point prediction model offers insights to diminishing bee colonies

More information: Iacopo Iacopini et al. Network Dynamics of Innovation Processes, Physical Review Letters (2018). DOI: 10.1103/PhysRevLett.120.048301

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mackita
not rated yet Jan 25, 2018
In dense aether model the ideas emerge like shortcuts between facts in similar way, like the density fluctuations inside gas or filaments of dark matter between massive objects inside our Universe. The leading mechanism here is principle of least action: the handling too many facts is time and energy expensive, so that the people gradually develop mental shortcuts for their more effective handling: ideas and theories. New theories condense from gradually growing pile of new facts and exceptions around established rules and theories, which leads into layered "brane" structure, described by Thomas Kuhn in his famous article and book: "The Structure of Scientific Revolutions". The similarity goes even deeper, as theories often develop in condensed phase dualities (quantum mechanics and relativity, string theory and loop quantum gravity, lamarckian and Darwinian evolution and so on...
mackita
not rated yet Jan 25, 2018
We introduce a model for the emergence of innovations, in which cognitive processes are described as random walks on the network of links among ideas or concepts, and an innovation corresponds to the first visit of a node. The transition matrix of the random walk depends on the network weights, while in turn the weight of an edge is reinforced by the passage of a walker.
This model isn't quite different from my theory of human consciousness, in which the random neural spikes travel across weighted nodes (synapses) between neurons and the neurons get opened once multiple spikes travel across single neuron at the same moment. From this moment such a neuron switches and it becomes a preferred route for propagation of further spikes, i.e. it becomes a part of hardwired solution ("engram").
mackita
not rated yet Jan 25, 2018
In dense aether model a conceptually similar process runs during formation of new fluctuations inside the quantum foam of existing fluctuations forming the vacuum. The foam behaves like soap foam during shaking: it gets more thick temporarily and once two or more signals pass the same place at the same moment, the foam becomes so dense in this particular place, it "switches" : the waves passing through it become trapped inside the resulting dense node of foam by total reflection mechanism and node of foam changes into localized particle. From this moment the further waves become mediated by newly formed particle preferably instead of choosing random path across the foam. The human brain therefore serves like simulator of quantum foam. Not quite accidentally the structure of human neurons resembles the foamy structure of dark matter between galaxies, this structure should be also similar to structure of quantum foam forming the vacuum (holographically dual by AdS/CFT correspondence)
mackita
not rated yet Jan 25, 2018
Human society also behaves like dynamically condensing foam i.e. network sharing ideas randomly. Once some ideas gain sufficient profit for its proponents their density will increase around it and once critical density will be reached, the ideas will condense into a new theory. From this moment the newly formed theory will starts its independent life like a meme propagating independently across human society, i.e. like the particle. The successful theories attract another ideas, which are preferably routed between them: for example most of effort in theoretical physics gets routed across two main established theories (quantum gravity) - only limited volume of new ideas remains developed independently of them. The new ideas condense preferably along connection line of established theories in process which can be described like Gregory-Laflamme instability or causual dynamical triangulation.

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