Unification

On the shoulder of giants

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
  • 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
  • Stephen Wolfram - Cellular automata types
  • David Deutsch - Constructor theory
  • Roger Penrose - Quantum mind, Penrose tilings
  • Jürgen Schmidhuber - Low complexity art, Gödel machines
  • Leonard Susskind - String theory, loop quantum gravity
  • Ken Thompson - Regular expressions, Unix, B
  • Edward Witten - M-Theory

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

Unification vs Occam’s Razor

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?

The Grand (Un-)unified Theory

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