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Computation, Proof, Machine

Dynkin, E. Library Catalog Record Errera, A.

Computational Knowledge and the Future of Pure Mathematics

Periodico di Matematiche. Library Catalog Record Franklin, P. The Four Color Problem. Franklin, P. The four color problem. Baltimore, MD: s. Library Catalog Record Fritsch, R. Der Vierfarbensatz: Geschichte, topologische Grundlagen, und Beweisidee. Gonthier, G. Guthrie, F.

Note on the Colouring of Maps. Hadwiger, H. Library Catalog Record Haken, W.

Computational Knowledge and the Future of Pure Mathematics—Stephen Wolfram Writings

An attempt to understand the four color problem. Haken, W. Combinatorial aspects of some mathematical problems. In Proceedings of the International Congress of Mathematicians pp. Library Catalog Record Heawood, P. Map-colour theorem. Heesch, H. Library Catalog Record Hitotsumatsu, S.

Library Catalog Record Hudson, H. Four Colors Do Not Suffice. Kauffman, L. Spin networks, topology and discrete physics. In Yang, C.

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Library Catalog Record Kempe, A. On the Geographical Problem of the Four Colours. Koch, J. Computation of four color irreducibility. MacKenzie, D. Library Catalog Record May, K. The Origin of the Four-Color Conjecture. Mayer, J. Infinite graphs — A survey. Nelson, R.

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Graph colourings. The four-color problem. New York-London: Academic Press. Osgood, T. University of Illinois at Urbana-Champaign.

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Robertson, N. The Four-Colour Theorem. Enveloped in precarious, casual and fast decisions and enclosed in a bubble of self-satisfaction, this subject has no consciousness. The only option left here is to exit the cybernetic condition, to step away from the vortex of data proliferation and reject the automatisms of the self.

This demands a full distrust in the system and a break from the cybernetic spell of social media so that a veritable social rhythm can enter collectivities. In other words, only a messianic promise, a call forth for a faceless, unconnected, impersonal and indifferent subject can oppose the predictive analytics of computable, classifiable and forever interchangeable data. To further understand the implications of this proposition, one could turn to the use of tactics of invisibility in contemporary post-internet aesthetics. For instance, Adam Harvey project CV Dazzle Look 5 offers an instance of these micropolitical tactics of excess that focus on how to develop tactics to thwart facial recognition algorithms.

These efforts to break from the cybernetic hypothesis of a unified subject in the image of networked data by calling forth for a impersonal and invisible politics however more profoundly coincide with a reactive response to the crisis of political possibilities to think, act and live beyond the cybernetic script. More importantly, this view seems to foreclose the possibility of critique from within the becoming intelligent of the instrument of reason, whereby the dystopic view of control society is counter-acted by a messiac call for a world outside instrumentality, relegating machine thinking to the sheer efficiency of tasks.

From this standpoint, the cybernetic hypothesis seems to overlook what Paul Virilio already anticipated in The Vision Machine , arguing that the profound transformation of optical media into the sightless thought of the computer exposed a speed in time processing that decoupled machine thinking from the transcendental model of optical perception. This implies that machines will learn to recognise what is invisible now as much as branches of computer vision are already creating adversarial images designed to thwart automated recognition systems.

Four Color Theorem (4CT) – Resources

It can be then suggested that not only the claim that the subject needs to exit its networked condition remains an unconvincing sceptical proposition that seems to reify the image of the self-determining modern subject thinking, acting and living autonomously from the instruments he uses foreclosing the possibility of reinventing what an instrumental subject can be beyond the dominance of the servo-mechanic model of machines. In what follows, this article will attempt to argue that an instrumental alienness of machine thinking must be accounted for to re-invent a critical theory of automation.

But, how is it possible to break away from techno-governance and techno-politics and yet offer an alternative critique of automation? In the next section, I will turn to the hypothesis of accelerationism. Although there are many versions of this view, I will refer to it as generally proposing a rather nuanced materialist approach and not an idealist rejection of instrumentality. The Accelerationist hypothesis in particular can be understood as addressing the self-limiting tendency of capital, manifested in its surplus value investment in the technical machine and the form of fixed capital , as activating an internal critique of capital in the form of a machine desire—or instrumentality—running away from its own transcendental determination.

This hypothesis already starts from the possibility of techno-sciences not to coincide with a self-determining subject and with its automation in sheer efficient functions. Instead, within the accelerating machine of capital, whose deterritorialising tendencies, according to Deleuze and Guattari, could break open capital monopoly, this hypothesis addresses possibilities to construct perspectives for what is and how is the task of critical thinking in the age of automated decision.

However, how to describe an apparatus of capture that runs away from itself, how to understand the dominance of algorithmic forms of subsumption that challenge both the law of the subject and its crisis today? From this standpoint, it can be suggested that here the critique of technology is above all a critique of power and of the unleashing of the colonial war in and against populations by the war machine of capital. Here the condition of real subsumption is not simply a question of techno-scientific knowledge, of mathematics or computation, but is mainly a question of how power operates within the automated matrix.

The computerised social world is not equivalent to power, but is in itself re-organised and automatised according to non-hierarchical criteria that enable the management of society and of the labour market in terms of information networks.

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Negri argues that informatisation—and not only physical assets such as buildings, vehicles, plants, equipment—is the most valuable form of fixed capital, because it is socially generalised through cognitive work and social knowledge. Automation incorporates information technology within itself, because it is able to integrate informatics and society within capitalist organisations.

Here, automation coincides with a higher level of real subsumption, namely the networked command of algorithmic capital. This rule-based machinery both centralises and commands an increasingly fragmented and complex system of knowledge, corresponding to an alien configuration of the General Intellect now animated by the automated cognition of machine learning.

Attuned to the post-operaist spirit, Negri urges us to invent new modes of re-appropriation of this fixed capital in both practical and theoretical dimensions.

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  5. To embrace the political potential of information technology for Negri means to positively address computable capacities that could augment productivity while directly reducing labour time disciplined and controlled by machines , increase salaries and grant social income to everyone. Instead of rejecting inductive data retrieval and transmission, Negri calls for the re-claiming of quantification, economic modelling, big data analysis, and abstract cognitive models through educational and scientific practices.

    For Negri, mathematical and computational models can be politically repurposed beyond the limits imparted by capital on the function of automated cognition. By overcoming the negative critique of instrumentality, Negri rehabilitates the political dimension of technical means.