## 13 Citations

### A Brief Critique of Pure Hypercomputation

- Computer ScienceMinds and Machines
- 2009

Hypercomputation—the hypothesis that Turing-incomputable objects can be computed through infinitary means—is ineffective, as the unsolvability of the halting problem for Turing machines depends just…

### The Extended Turing Model as Contextual Tool

- Computer ScienceTAMC
- 2009

This work looks at ways in which computability-theoretic structure emerges in natural contexts, and how algorithmic structure does not just emerge mathematically from information, but how that emergent structure can model the emergence of very basic aspects of the real world.

### The Computational Roots of Hyper-Causality?

- Computer ScienceInt. J. Unconv. Comput.
- 2010

This work looks at ways in which computabilitytheoretic structure plays a hierarchical role in natural contexts, and how structure does not just emerge mathematically from information, but how that structure can model the emergence of very basic aspects of the real world of a non-local character.

### STUDIES IN LOGIC, GRAMMAR AND RHETORIC 9 (22) 2006

- Computer Science
- 2007

The paper will discuss methodological and cognitive premises of posing the question of decidability as well as the ideas that have been born since the appearance of the problem of decodability, and suggest a computer that could cross the barriers of the Turing machine.

### Mathematics, Metaphysics and the Multiverse

- PhilosophyComputation, Physics and Beyond
- 2012

It is argued that this depends on us selecting mathematical models which take account of the ‘thingness' of reality, and puts the mathematics in a correspondingly rich information-theoretic context, and that the task is to restore the role of embodied computation and its hierarchically arising attributes.

### Algorithmic Social Sciences Research Unit

- Computer Science
- 2010

Stephen Wolframs A New Kind of Science should have made a greater impact in economics at least in its theorising and computational modes than it seems to have. There are those who subscribe to…

### How Can Nature Help Us Compute?

- Computer ScienceSOFSEM
- 2006

Ever since Alan Turing gave us a machine model of algorithmic computation, there have been questions about how widely it is applicable (some asked by Turing himself). Although the computer on our…

## References

SHOWING 1-10 OF 45 REFERENCES

### The Myth of Hypercomputation

- Mathematics
- 2004

Under the banner of “hypercomputation” various claims are being made for the feasibility of modes of computation that go beyond what is permitted by Turing computability. In this article it will be…

### On the Possibility, or Otherwise, of Hypercomputation

- Mathematics, PhilosophyThe British Journal for the Philosophy of Science
- 2004

We claim that a recent article of P. Cotogno ([2003]) in this journal is based on an incorrect argument concerning the non-computability of diagonal functions. The point is that whilst diagonal…

### Incomputability in Nature

- Philosophy
- 2003

To what extent is incomputability relevant to the material Universe? We look at ways in which this question might be answered, and the extent to which the theory of computability, which grew out of…

### Computability and Emergence

- Computer Science
- 2006

The extent to which Turing’s approach to realworld computability is still relevant today is examined, and some fundamental questions facing those with a research interest in computability theory are pointed to.

### Non-Turing Computations Via Malament–Hogarth Space-Times

- Computer Science
- 2001

It is argued that there are several distinguished Church–Turing-type theses (not only one) and validity of some of these theses depend on the background physical theory the authors choose to use, and if they choose classical general relativity theory as their background theory, then certain forms of the Church-Turing thesis cease to be valid.

### The Incomputable Alan Turing

- Computer Science
- 2004

This paper focuses on incomputability as a powerful theme in Turing's work and personal life, and examines its role in his evolving concept of machine intelligence.

### Beyond Gödel's Theorem: Turing Nonrigidity Revisited

- PhilosophyLogic Colloquium
- 1995

In [4] it was argued that incomputability in nature dictates a mathematical model (due to Turing [39]) based on mechanical processes relative to appropriate abstractions of incomputable phenomena.…

### The Turing machine paradigm in contemporary computing

- Computer Science
- 2001

The work of Hartmanis, Stearns, Karp, Cook and others showed that the refinement of the theory to resource-bounded computations gave the means to explain the many intuitions concerning the complexity or ‘hardness’ of algorithmic problems in a precise and rigorous framework.

### Turing’s O-machines, Searle, Penrose and the brain

- Philosophy
- 1998

Analogies offered in the literature include hurricanes, the motion of the planets around the sun, and the digestion of pizza. None of these phenomena is itself computational in nature yet,…