Unification

Posts

On the shoulder of giants

(Jul 23, 2019)

I have been deeply inspired by many giants in the scientific community. I hold them in the highest regard for either their thoughts well resonate with mine or their propositions fuel my neural engines. While unification has been the holy grail for too long, I find clues lurking in the works of these great men.

  • Alan Turing - Turing machine, Turing test
  • John von Neumann - Self-replicating machines, automata theory, stored program
  • Kurt Gödel - Incompleteness theorem
  • Ray Solomonoff - Algorithmic probability, universal prior
  • Andrey Kolmogorov - Algorithmic complexity
  • Benoit Mandelbrot - Fractals
  • Albert Einstein - General relativity
  • John Archbald Wheeler - It from bit
  • Max Plank - Plank units
  • Werner Heisenberg - Uncertainty principle
  • Claude Shannon - Information theory
  • Richard Feynman - Quantum computation, Feynman diagrams
  • Alonso Church - Lambda calculus
  • Erwin Schrödinger - Schrödinger equation, Schrödinger cat, quantum biology
  • De Bröglie - Wave-particle duality
  • Marvin Minsky - Artificial intelligence
  • Neils Bohr - Atomic model
  • Erwin Schrodinger - Wavefunction
  • James Maxwell - Maxwell’s demon
  • Stephen Hawkins - Hawkings radiation

…and among those who are still around

  • Gregory Chaitin - Algorithmic complexity, omega number
  • Hector Zenil - Algorithmic complexity
  • Stephen Wolfram - Cellular automata types
  • David Deutsch - Constructor theory
  • Jürgen Schmidhuber - Low complexity art, Gödel machines
  • Marcus Hutter - AIXItl
  • Roger Penrose - Quantum mind, Penrose tilings
  • Leonard Susskind - String theory, loop quantum gravity
  • Scott Aaronson - Quantum complexity theory
  • Cristian S. Calude - Algorithmic information theory, quantum computing
  • Ken Thompson - Regular expressions, Unix, B
  • Edward Witten - M-Theory

… the list keeps growing as the horizon of my knowledge widens.

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(A)daitva

(Jul 23, 2019)

When you are into the topic of emergence, you can’t help but wonder about the phase transitions where different laws take over at different scales. Quoting Douglas R. Hofstadter (from the book I am a strange loop), “thinkodynamics is explained by statistical mentalics”, sometimes knowing everything about individual components of a system (e.g. neuron) tell us very little of how the components behave as a whole (e.g. consciousness). It is not sorcery that the usual scientific method of reductionism does not work here. It is simply that many laws of the overall system is embedded in the interaction behaviour of the components, rather than the components themselves. In physics, we call this coupling. In quantum computing, perhaps, a similar notion is of entanglement. Following the ideas of Juan M. Maldacena (in his ER = EPR paper with Leonard Susskind), in classical mechanics, they are wormholes.

A question that perhaps keeps popping up is, are gravity (general relativity) and quantum mechanics one and the same - two different ways (even mutually conflicting at times) of interpreting the same thing? They work extremely well in their own niche scale - GR for galactic scales, QM for atomic scales. The obviously problems arise when there is both, mass concentrated in small space, as in the early Universe or blackholes. One way of approaching this problem is called the Holographic Principle, where two very different interpretations, a bulk theory in n-dimensions and a boundary theory in (n-1)-dimensions, describe a single reality.

However, grand unified theory (GUT) and consciousness are not the only places where scientists have trouble going from two views of reality to one. It is very much a problem within the basic postulates of quantum mechanics itself; where normally a closed system evolves unitarily (which is invertible, deterministic and continuous), while any interaction with an observer (nothing to do with consciousness), results in a measurement (which in irreversible, probabilistic and instantaneous).

What is more interesting as a computer scientist is to wonder, is this duality true for computability and complexity as well? For complexity, Shannon and Kolmogorov metrics converge asymptotically for true randomness. For computability, what is the difference between the state machine and the tape in the Turing Machine. For languages, what is the difference between syntax and semantics? Why does the explaination capability of a neural network inversely proportional to it computation expressibility - is that the Godel’s incompleteness theorem in action?

Are there more such dualities?

  • the idea and the meta
  • the syntax and semantics
  • the body and the soul
  • the particle and the wave
  • the observer and the object
  • the theorems and the axioms
  • the first and the zeroth
  • the natural and the supernatural
  • the known and the unknown
  • the knowable and the unknowable
  • the statistics and the probability
  • the output and the program
  • the program and the compiler
  • the tape and the state machine
  • the system and the environment
  • the continuum and the quanta
  • the memory and the processor
  • the cardinals and the ordinals
  • the nodes and the network
  • the position and the momentum
  • the energy and the duration
  • the entanglement and the coherence
  • value of a field and its change at a certain position
  • spin on 2 different axis

Does generalization take you only as far as indentifying 2 fundamental ideas working in a symphony? We can either call it a single coin, or we can call them two opposite faces, or acknowledge only the face facing us, or the entire set of possibilities while they/it are/is spinning.

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The Grand (Un-)unified Theory

(Jul 23, 2019)

While theoretical physicists are lamenting over the differences and compatibility of two of the most fundamental physical laws, a more birds eye view of the landscape of the universal design reveals some very important structures, that are so deeply embedded around us, we need to ask, why? Here I ponder over some of those structures that I find particularly interesting.

  • Godel’s Incompleteness Theorems
  • Kolmogorov Complexity
  • Quines
  • Fractals
  • Chaos
  • Shannon Entropy
  • Holographic Universe
  • Quantum Entanglement
  • Golden Mean
  • Neural Network
  • DNA
  • Thermodynamics
  • Standard Model
  • Brainwaves
  • Plank Units
  • Cellular Automata
  • Church-Turing Thesis

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