We must therefore not be discouraged by the difficulty of interpreting life by the ordinary laws of physics... We must also be prepared to find a new type of physical law prevailing in it. Schrodinger - Nobel Laureate 1933 Schrodinger Can this law be derived (in principle) from fundamental physics alone? `Theory of Everything’ on Fundamental Particles Candidate Law Yes/No Ultra-Powerful Computer Nearby 747s

Fundamental Particles Flock of Birds Flocks of Birds are made out of Fundamental Particles

Single Bird Dynamics Dynamics Particle Physics Atomic Physics ChemistryChemistry BiologyBiology Laws of Flocking The Laws of Particle Physics imply the Laws of Flocking

“At each stage, entirely new laws are necessary, new laws, concepts and generalisations are necessary, requiring inspiration and creativity.” "The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe.” – ”More is Different” Science 1972 AndersenAndersen ” “Everything is either Physics or Stamp Collecting” Rutherfor d

Quantum Mechanics Continuum Mechanics Additional Law Density Stress Viscosit y Friction Defined only on the Infinite limit. Defined only on the Infinite limit. The axioms of any mathematical system is `known’, yet there exists many propositions of such systems that are formally undecidable. Gödel's Incompleteness Theorem:

Quantum Mechanics Continuum Mechanics Additional Law without Reverse Causality Additional Law without Reverse Causality InspirationInspiration Experiment s

b 1,3 = 1 b 2,3 = 0

b 1,3 = 1 Introduce Hamiltonian b 2,3 = 0 c 1,1 = 3 EXAMPL E: H = = 4

Introduce Hamiltonian b 1,3 = 1 b 2,3 = 0 c 11 = M 11,21 = 4 EXAMPL E: H = – 4 = 0 Interaction Single Body

The Ising Lattice is crude model of a range of biological systems. k = 3 Protein Folding FlockingFlocking Magnetis m Neural Networks

FlockingFlocking The Direct Approach: Simulate everything from first principles. Computationally Infeasible for even systems of modest size Even if we could simulate something, we may still not understand it without appealing to macroscopic concepts. Magnetis m

FlockingFlocking Magnetizatio n Group Velocity Proportion of Spins in `1’ State Reductionism contends that these macroscopic observables can always be logically deduced from a fundamental description of the system. Any Macroscopi c Property Enter Macroscopic Principles: The existence of a biological law indicates that the system can be understood in terms of macroscopic observables, and the macroscopic principles that govern them Magnetis m

FlockingFlocking What we show: Any averaging macroscopic property of the lowest energy state of such Ising Lattices are formally undecidable. Proportion of Spins in `1’ State Magnetizatio n Group Velocity Any laws that govern such properties cannot be derived from fundamental principles. X Proportion of Spins in `1’ State Magnetis m

There exists no way to determined whether a given Turing machine (Computer) will Halt, or run forever. The Halting Problem: Does the program square its inputs? Does the program halt? Does the program destroy your computer? Does the program square its inputs? Does the program halt? Does the program destroy your computer? EXAMPLE: TURING MACHINE

Rice’s Theorem Any Black Box Property of a Turing Machine is undecidable. x T(x) P = 0 P = 1 Property P A function P that maps the configuration space of the system to a real number.

Rice’s Theorem Any Black Box Property of a Turing Machine is undecidable. x T(x) P = 0 P = 1 A function P that maps the configuration space of the system to a real number. Property P Rice’s Theorem (Physical) P is dependent on T(x) for some universal encoding, then P is undecidable.

Input Output There exists many `Universal System’, systems capable of simulating Turing Machines. EXAMPLE: CELLULAR AUTOMOTAS Rule 110 Game of Life EXAMPLE: TURING MACHINE

EXAMPLE: CELLULAR AUTOMOTAS Rule 110 Game of Life f EXAMPLE: TURING MACHINE

`0’ and `1’ Encoded by Gliders EXAMPLE: CELLULAR AUTOMOTAS Rule 110 Game of Life EXAMPLE: TURING MACHINE Prosperity (Average Number of Alive Cells) is Undecidible. Rice’s Theorem (Physical)

EXAMPLE: CELLULAR AUTOMOTAS Rule 110 Game of Life 1.Show the Periodic Ising Lattice can encode an arbitrary CA, and hence is universal. Prosperity (Average Number of Alive Cells) is Undecidible.

EXAMPLE: CELLULAR AUTOMOTAS Rule 110 Game of Life 1.Show the Ising Lattice can encode an arbitrary CA, and hence is universal. 2. Show that knowledge of a given Macroscopic Property of the ground state implies knowledge of the Prosperity of the underlying CA. Prosperity (Average Number of Alive Cells) is Undecidible.

EXAMPLE: CELLULAR AUTOMOTAS Rule 110 Game of Life 1.Show the Ising Lattice can encode an arbitrary CA, and hence is universal. 2. Show that knowledge of a given Macroscopic Property of the ground state implies knowledge of the Prosperity of the underlying CA. Prosperity (Average Number of Alive Cells) is Undecidible. Knowledge of the Property Solves the Halting Problem.

Any Boolean Function f, can be simulated by a finite Ising Block.

WireWire NOTNOT FANOUTFANOUT NANDNAND XORXOR Observe that there exists a Designer Ising Block for each basic logical operation: ProofProof

f Any Cellular Automata.... Automata.... With Update Rule f... FANOUTFANOUT SWA P HfHfHfHf HfHfHfHf Can be simulated be a periodic tessellation of Designer Ising Blocks.. 1.Show the Ising Lattice can encode an arbitrary CA, and hence is universal. 2. Show that knowledge of a given Macroscopic Property of the ground state implies knowledge of the Prosperity of the underlying CA.

Prosperity (Average Number of Alive Cells) is Undecideble. Magnifier Block L STRATEG Y: Engineer a CA Encoding so that a given physical property is highly dependent on the Prosperity of the underlying encoding. or Input 0 Input 1 Degeneracy Magnifier or Input 0 Input 1 Correlations Magnifier Knowledge of these properties lead to knowledge of Prosperity or Input 0 Input 1 Magnetization Magnifier:

Any averaging Macroscopic Properties of the Periodic Ising Lattice at Ground State are in general, undecidable. k = 3

We must therefore not be discouraged by the difficulty of interpreting life by the ordinary laws of physics... We must also be prepared to find a new type of physical law prevailing in it. Schrodinger - Nobel Laureate 1933 Schrodinger The observable quantities of Biological Systems generally makes some continuity assumption at some stage. Bird Density Bird Species Wind Speed Magnetic Fields

We must therefore not be discouraged by the difficulty of interpreting life by the ordinary laws of physics... We must also be prepared to find a new type of physical law prevailing in it. Schrodinger - Nobel Laureate 1933 Schrodinger Fundamental Laws Biological Laws InspirationInspiration Biological Laws potentially contain additional knowledge over fundamental physics... Even if a `Law of Everything’ was found and a super-computer readily available, it is unlikely that biological laws can be systematically derived. The observable quantities of Biological Systems generally makes some continuity assumption at some stage. Bird Density Bird Species Wind Speed Magnetic Fields