Category: Physics

Entanglement and Information

Mark DavisLeave a comment

shannons-formula-smallResearch can flow into interesting little eddies that cohere into larger circulations that become transformative phase shifts. That happened to me this morning between a morning drive in the Northern California hills and departing for lunch at one of our favorite restaurants in Danville.

The topic I’ve been working on since my retirement is whether there are preferential representations for optimal automated inference methods. We have this grab-bag of machine learning techniques that use differing data structures but that all implement some variation on fitting functions to data exemplars; at the most general they all look like some kind of gradient descent on an error surface. Getting the right mix of parameters, nodes, etc. falls to some kind of statistical regularization or bottlenecking for the algorithms. Or maybe you perform a grid search in the hyperparameter space, narrowing down the right mix. Or you can throw up your hands and try to evolve your way to a solution, suspecting that there may be local optima that are distracting the algorithms from global success.

Yet, algorithmic information theory (AIT) gives us, via Solomonoff, a framework for balancing parameterization of an inference algorithm against the error rate on the training set. But, first, it’s all uncomputable and, second, the AIT framework just uses strings of binary as the coded Turing machines, so I would have to flip 2^N bits and test each representation to get anywhere with the theory. Yet, I and many others have had incremental success at using variations on this framework, whether via Minimum Description Length (MDL) principles, it’s first cousin Minimum Message Length (MML), and other statistical regularization approaches that are somewhat proxies for these techniques.… Read the rest

A, B, C time!

Mark DavisLeave a comment

time-flows-awayThis might get technical, despite the vaguely Sesame Street quality to the title. You see, philosophers have long worried over time and causality, and rightly so, going back to the Greeks like Heraclitus and Parmenides, as well as their documenters many years later. Is time a series of events one after another or is that a perceptual mistake? For if everything comes from some cascade of events that precede it, it is illogical to presume that something might emerge from nothing (Parmenides). And, contra, perhaps all things are in a state of permanent change and all such perceptions are confused (Heraclitus). The latter has some opaque formulations in the appreciation of the Einsteinian relativistic form of combining space and time together while still preserving the symmetry of time in the basic equations, allowing for the rolling forward and backward of the space-time picture without much in the way of consequences.

So Lee Smolin’s re-injection of time as a real phenomena in Time Reborn takes us from A and B theories of time to something slightly new, which might be called a C theory. This theory builds on Smolin’s previous work where he proposed an evolutionary model of cosmology to explain how the precarious constants of our observed universe might have come into being. In Smolin’s super-cosmology, many universes come to be and not be at an alarming rate. Indeed, perhaps in every little black hole is another one. But many of these universes are not very viable because they lack the physical constants needed to last a long time and for entities like us to evolve to try to comprehend them. This does away with any mysteries about the Anthropic Principle: we are just survivors.… Read the rest

Cosmologies and Theories of Everything

Mark Davis1 Comment

Zach, fictional though he is, is not the only one interested in cosmological theories. But what form do these theories take? A Theory of Everything or TOE is a theory that intends to explain the entire observable universe using a compact specification of equations and the conceptual arguments that support them. In the modern sense, a TOE is a physical explanation of the large-scale structure of the universe. Later, we can start to expand the TOE to look for “bridging laws” that help justify other phenomena that approach the human scale.

What are our alternatives? The previous post mentioned the Catholic Church’s embrace of Big Bang cosmology as justifying Genesis. Apologist and philosopher of religion William Lane Craig also elaborately evaluates Big Bang theories as substantiating theism by supporting creation at the singularity event.

But do these notions change the underlying TOEs? No, in general. The best that they can do is accept the TOE as an input and make a deductive argument based on assumptions that are not excluded by the TOE. For apologists, that means that the singularity event provides a divide between a non-temporal pre-universe and the current universe–effectively between non-existence and existence. But that is not the only TOE available to us. There are a range of TOEs that have been devised.  The following is derived from Marcus Hutter’s A Complete Theory of Everything (Will Be Subjective):

  1. (G) Geocentric model: Ancient notion that the Earth is at the center of the known universe.
  2. (H) Heliocentric model: Evolution of the model to centralize on the Sun.
  3. (E) Effective theories: General relativity, quantum electrodynamics, and Newtonian mechanics, but without a unifying architecture.
  4. (P) Standard model of particle physics: Beginning of unification that contains numerous arbitrary parameters and has yet to unify gravity.
… Read the rest