# More really is different

@article{Gu2009MoreRI, title={More really is different}, author={Mile Gu and Christian Weedbrook and Alvaro Perales and Michael A. Nielsen}, journal={Physica D: Nonlinear Phenomena}, year={2009}, volume={238}, pages={835-839} }

Abstract In 1972, P.W. Anderson suggested that ‘More is Different’, meaning that complex physical systems may exhibit behavior that cannot be understood only in terms of the laws governing their microscopic constituents. We strengthen this claim by proving that many macroscopic observable properties of a simple class of physical systems (the infinite periodic Ising lattice) cannot in general be derived from a microscopic description. This provides evidence that emergent behavior occurs in such…

## 39 Citations

More is Different…Sometimes: Ising Models, Emergence, and Undecidability

- Mathematics
- 2015

Philip Anderson’s seminal paper `More Is Different’ is explicit in its arguments for the failure of construction methods in some areas of physics and inexplicit about the consequences of those…

The Case for Strong Emergence

- Political ScienceThe Frontiers Collection
- 2019

As everyone knows, physicists have proved that free will doesn’t exist. That’s because we are made of tiny particles which follow strict laws, and human behavior is really just a consequence of these…

Thermodynamics of emergence: Langton's ant meets Boltzmann

- Computer Science2011 IEEE Symposium on Artificial Life (ALIFE)
- 2011

This paper develops and discusses five hypotheses that are not meant to be irrevocable but rather thought-provoking about the nature of emergence, and introduces two modeling approaches for Langton's ant to clarify these hypotheses.

Sensitivity of Complex Networks

- Computer Science, MathematicsArXiv
- 2016

This work characterize necessary and sufficient conditions for the emergence of new macroscopic dynamic behavior in the thermodynamic limit and proves that these conditions are satisfied only for architectures with power-law degree distributions.

A frontier of knowledge

- Physics
- 2010

At any time, there are areas of science where we are standing at the frontier of knowledge, and can wonder whether we have reached a fundamental limit to human understanding. What is ultimately…

On perception and some consequences: The world, the brain and infinity

- Sociology
- 2014

This paper presents a new type of perception that consists of adding something to the sensory data that is not present in any of the brain states or in sensory data of the past or present, not even…

Chapter 1 – Complex Systems

- Computer Science, Mathematics
- 2017

A range of topics pertinent to complexity, such as self-organization, self-organized criticality, power law distributions, computational irreducibility, and quantitative characterization of complexity are covered.

Undecidability of the Spectral Gap in One Dimension

- Physics, MathematicsPhysical Review X
- 2020

The spectral gap problem - determining whether the energy spectrum of a system has an energy gap above ground state, or if there is a continuous range of low-energy excitations - pervades quantum…

Emergence, Reduction and Supervenience: A Varied Landscape

- Mathematics, Physics
- 2011

This is one of two papers about emergence, reduction and supervenience. It expounds these notions and analyses the general relations between them. The companion paper analyses the situation in…

Ground State Spin Calculus

- Physics
- 2010

We present an intuitive compositional theory from which one is able to predict and also to control the ground state manifold (and higher energy excitations) of interacting spin systems governed by…

## References

SHOWING 1-10 OF 26 REFERENCES

Unpredictability and undecidability in dynamical systems.

- Physics, MedicinePhysical review letters
- 1990

It is shown that motion with as few as three degrees of freedom can be equivalent to a Turing machine, and so be capable of universal computation.

Conservative logic

- 1982

Conservative logic is a comprehensive model of computation which explicitly reflects a number of fundamental principles of physics, such as the reversibility of the dynamical laws and the…

Gödel's theorem and information

- Mathematics
- 1982

Gödel's theorem may be demonstrated using arguments having an informationtheoretic flavor. In such an approach it is possible to argue that if a theorem contains more information than a given set of…

Tiling problems and undecidability in the cluster variation method

- Mathematics
- 1988

In cluster approximations for lattice systems the thermodynamic behavior of the infinite system is inferred from that of a relatively small, finite subsystem (cluster), approximations being made for…

Long-Range Order in a Two-Dimensional Dynamical XY Model: How Birds Fly Together.

- Physics, MedicinePhysical review letters
- 1995

A nonequilibrium continuum dynamical model for the collective motion of large groups of biological organisms and describes a large universality class of microscopic rules, including those recently simulated by Vicsek et al.

Universality in Elementary Cellular Automata

- Mathematics, Computer ScienceComplex Syst.
- 2004

The purpose of this paper is to prove that one of the simplest one dimensional cellular automata is computationally universal, implying that many questions concerning its behavior, such as whether a…

Life Without Death is P-complete

- Mathematics, Computer ScienceComplex Syst.
- 1996

It is shown that if a cellular automaton in two or more dimensions supports growing "ladders" which can turn or block each other, then it can express arbitrary Boolean circuits, including the "Life without Death" rule.

On the computational complexity of Ising spin glass models

- Mathematics
- 1982

In a spin glass with Ising spins, the problems of computing the magnetic partition function and finding a ground state are studied. In a finite two-dimensional lattice these problems can be solved by…

Renormalization group theory: Its basis and formulation in statistical physics

- Physics
- 1998

The nature and origins of renormalization group ideas in statistical physics and condensed matter theory are recounted informally, emphasizing those features of prime importance in these areas of…

Undecidability and intractability in theoretical physics.

- Computer Science, MedicinePhysical review letters
- 1985

Cellular automata are used to provide explicit examples of various formally undecidable and computationally intractable problems and it is suggested that such problems are common in physical models, and some other potential examples are discussed.