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The Boltzmann brain gained new relevance around 2002, when some cosmologists started to become concerned that, in many theories about the universe, human brains are vastly more likely to arise from random fluctuations; this leads to the conclusion that, statistically, humans are likely to be wrong about their memories of the past and in fact ...
Diagram of a restricted Boltzmann machine with three visible units and four hidden units (no bias units) A restricted Boltzmann machine (RBM) (also called a restricted Sherrington–Kirkpatrick model with external field or restricted stochastic Ising–Lenz–Little model) is a generative stochastic artificial neural network that can learn a probability distribution over its set of inputs.
A Boltzmann machine, like a Sherrington–Kirkpatrick model, is a network of units with a total "energy" (Hamiltonian) defined for the overall network. Its units produce binary results. Boltzmann machine weights are stochastic. The global energy in a Boltzmann machine is identical in form to that of Hopfield networks and Ising models:
The measure problem in cosmology concerns how to compute the ratios of universes of different types within a multiverse. It typically arises in the context of eternal inflation . The problem arises because different approaches to calculating these ratios yield different results, and it is not clear which approach (if any) is correct.
It is more transparent to just avoid such terms. The reworked content is avoiding using these loaded terms altogether and using instead meaningful terms like "Boltzmann brain" and "non-Boltzmann brain" and "other spontaneously formed entities" which are plain and precise terms for the subject matter.
Boltzmann was born in Erdberg, a suburb of Vienna into a Catholic family. His father, Ludwig Georg Boltzmann, was a revenue official. His grandfather, who had moved to Vienna from Berlin, was a clock manufacturer, and Boltzmann's mother, Katharina Pauernfeind, was originally from Salzburg.
The general equation can then be written as [6] = + + (),. where the "force" term corresponds to the forces exerted on the particles by an external influence (not by the particles themselves), the "diff" term represents the diffusion of particles, and "coll" is the collision term – accounting for the forces acting between particles in collisions.
Boltzmann's distribution is an exponential distribution. Boltzmann factor (vertical axis) as a function of temperature T for several energy differences ε i − ε j.. In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution [1]) is a probability distribution or probability measure that gives the probability that a system will be in a certain ...