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One of the limitations of conventional thinking in computation is that computable functions proceed in a sequential manner, one independent step after another. When computer scientists talk of parallelism, they usually mean carrying out more than one of these independent linear computations at the same time.
In the biological world, things are more complex because steps in biological computations may not be independent. Each feedback loop is part of a hugely complex biochemical network and is affected by many factors simultaneously, not least of which is the presence or absence of light and the state of the network with which it is most closely linked, which themselves may be interdependent feedback loops.
Process algebra is a form of computation that can handle multiple simultaneous interdependent steps and this makes it perfect for modelling these tricky biochemical networks and the feedback loops that drive them.
An often overlooked property of process algebra is that it is not equivalent to a standard sequential Turing machine. Because process algebra encompasses concurrent processes and the communication between them, it is subtly different and potentially more powerful.
Several orders of magnitude separate the efficiency of biological computation from what is possible with silicon.
More:
In computer science, the process calculi (or process algebras) are a diverse family of related approaches to formally modelling concurrent systems. Process calculi provide a tool for the high-level description of interactions, communications, and synchronizations between a collection of independent agents or processes.
An algebraic approach to the study of concurrent processes. Its tools are algebraical languages for the specification of processes and the formulation of statements about them, together with calculi for the verification of these statements.
PEPA
Tags: Bio-PEPA, calculus, computation, math, programming, stochastic process algebra
The term “Mind Projection Fallacy” was coined by the late great Bayesian Master, E. T. Jaynes, as part of his long and hard-fought battle against the accursed frequentists. Jaynes was of the opinion that probabilities were in the mind, not in the environment – that probabilities express ignorance, states of partial information; and if I am ignorant of a phenomenon, that is a fact about my state of mind, not a fact about the phenomenon.
I remember (dimly, as human memories go) the first time I self-identified as a “Bayesian”. Someone had just asked a malformed version of an old probability puzzle…
You’ve probably seen the word ‘Bayesian’ used a lot on this site, but may be a bit uncertain of what exactly we mean by that.
Bayes’ theorem was the subject of a detailed article. The essay is good, but over 15,000 words long — here’s the condensed version for Bayesian newcomers like myself.
Bayes’ Theorem for the curious and bewildered; an excruciatingly gentle introduction.
Eliezer Yudkowsky’s T-Shirt
This post is elementary: it introduces a simple method of visualizing Bayesian calculations. In my defense, we’ve had other elementary posts before, and they’ve been found useful; plus, I’d really like this to be online somewhere, and it might as well be here.
Everyday use of a mathematical concept.
I recently came up with what I think is an intuitive way to explain Bayes’ Theorem…
A law of probability that describes the proper way to incorporate new evidence into prior probabilities to form an updated probability estimate. Bayesian rationality takes its name from this theorem, as it is regarded as the foundation of consistent rational reasoning under uncertainty. A.k.a. “Bayes’s Theorem” or “Bayes’s Rule”.
Eliezer Yudkowsky is on bloggingheads.tv with the statistician Andrew Gelman.
Several different points of fascination about Bayes…
When looking further, there is however a whole crowd on the blogs that seems to see more in Bayes’s theorem than a mere probability inversion…
Bayesian statistics is a system for describing epistemological uncertainty using the mathematical language of
probability.
Bayesian probability is one of the most popular interpretations of the concept of
probability.
Edwin T. Jaynes was one of the first people to realize that probability theory, as originated by Laplace, is a generalization of Aristotelian logic that reduces to deductive logic in the special case that our hypotheses are either true or false. This web site has been established to help promote this interpretation of probability theory by distributing articles, books and related material. As Ed Jaynes originated this interpretation of probability theory we have a large selection of his articles, as well as articles by a number of other people who use probability theory in this way…
Bayesian statistics is so closely linked with induction that one often hears it called “Bayesian induction.” What could be more inductive than taking a prior, gathering data, updating the prior with Bayes Law, and limiting to the true distribution of some parameter?
Gelman (of the popular statistics blog) and Shalizi point that, in practice, Bayesian statistics should actually be seen as Popper-style hypothesis-based deduction. The problem is intricately linked to the “taking a prior” above.
Or, how to recognize
Bayes’ theorem when you meet one making small talk at a cocktail party.
Still, I’m sure Blogger won’t mind me using their resources instead. The basic idea is that there’s a distinction between true values x and measured values y. You start off with a prior probability distribution over the true values. You then have a likelihood function, which gives you the probability P(y|x) of measuring any value y given a hypothetical true value x.
In other words, What is so special about starting with a human-generated hypothesis? Bayesian methods suggest what I think is the right answer: To get from probabilistic evidence to the probability of something requires combining the evidence with a prior expectation, a “prior probability”, and human hypothesis generation enables this requirement to be ignored with considerable practical success.
Andrew Gelman recently responded to a commenter on the Yudkowsky/Gelman diavlog; the commenter complained that Bayesian statistics were too subjective and lacked rigor. I shall explain why this is unbelievably ironic…
Maybe this kind of Bayesian method for “proving the null” could be used to achieve a better balance.
Bayesian brain is a term that is used to refer to the ability of the nervous system to operate in situations of uncertainty in a fashion that is close to the optimal prescribed by Bayesian statistics.
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Tags: Bayes' Theorem, bayesian, bayesianism, Eliezer Yudkowsky, guide, introduction, lesswrong, math, mathematics, probability, statistics
A lot to read up on. Will take some time to read and even longer to actually understand everything. I have a lot of catching up to do.
Tags: Books, Clifford A. Pickover, complexity, Der Gödelsche Beweis, education, Ego Tunnel, From Eternity to Here, Gary L. Drescher, Gödel, Good and Real, Greg Egan, history, Incandescence, Len Fisher, Ludwig Wittgenstein, math, Müsli, Phillip J. Davis, Philosophische Untersuchungen, Reuben Hersh, science, science fiction, Sean Carroll, Steven E. Landburg, Stories of your Life and Others, Ted Chiang, The Big Questions, the math book, The Mathematical Experience, the perfect swam, Thomas Metzinger, Tractatus logico-philosophicus, Wittgenstein und das Unendliche
Led by University of Tsukuba professor Daisuke Takahashi, the research team performed the calculation using a massive parallel processing (MPP) supercomputer called the T2K Tsukuba System, which consists of 640 high-performance computers clustered together to achieve processing speeds of 95 teraflops (95 trillion floating-point operations per second). The supercomputer calculated pi to 2,576,980,377,524 decimal places in 73 hours 36 minutes.
Pi
By comparison, it took the previous record holders about 600 hours to perform their calculation (over 8 times longer than it took the T2K Tsukuba System).
Link: pinktentacle.com
Tags: computing, math, pi, trillion, world record
I’m a 26 year old German 