I, AIXI

A new cool eprint has appeared:

J. Veness, et al. A Monte Carlo AIXI Approximation. eprint: 0909.0801

The question that defines the context for this article is: How should probabilities be assigned? One way, with much to recommend itself, is take them to be algorithmic probabilities or universal priors. Suppose one has observed the first N values of a discrete time series, maybe a byte stream, and wishes to predict or make a bet about the next value. Is there a general probability measure appropriate for all cases that fit this abstract setting and, if so, which one?

A priori bias in the Dembski-Marks representation

Dembski and Marks (2009b) recently published a minimalistic (and simplistic) representation of a search problem consisting of a search space and a distinguished target set (blogger reactions: 1, 2, 3, 4, 5, 7). From the discussion in the paper and two other articles it is clear that the authors’ object of study is related to, though not equivalent to, the issues raised by Wolpert and Macready’s No Free Lunch theorems. Despite its minimalistic character, the Dembski-Marks representation is not less restrictive than the Wolpert-Macready representation of a search/optimization problem. The Dembski-Marks representation, i.e., a distinguished target in a search space, can easily be introduced as an extra feature in the Wolpert-Macready representation. However, it is not possible to introduce the full Wolpert-Macready representation within the Dembski-Marks representation. Indeed, the absence of a constant, distinguished target set is a prerequisite for all No Free Lunch theorems. It is therefore interesting to estimate how much of a restriction it is to make the Wolpert-Macready representation conform to the Dembski-Marks representation.

Clusters and tree structure from genealogical data

Modern biology provides a wealth of interesting mathematical challenges in the modeling and reconstruction of evolution. A new eprint explores the theoretical prospects for defining a phylogenetic tree structure, despite complications like lateral gene transfer, hybdridization and the difference between gene and species trees:

A. Dress, et al. Species, Clusters and the ‘Tree of Life’: A graph-theoretic perspective. eprint: 0908.2885

Entropy decrease results in memory loss

I found a fun arrow-of-time paper in PRL, arguing that dynamical decreases in the entropy of an isolated system are not at all impossible, just impossible to remember!

L. Maccone. Quantum Solution to the Arrow-of-Time Dilemma, Phys. Rev. Lett. 103:080401 (2009), arXiv:0802.0438

Abstract: The arrow-of-time dilemma states that the laws of physics are invariant for time inversion, whereas the familiar phenomena we see everyday are not (i.e., entropy increases). I show that, within a quantum mechanical framework, all phenomena which leave a trail of information behind (and hence can be studied by physics) are those where entropy necessarily increases or remains constant. All phenomena where the entropy decreases must not leave any information of their having happened. This situation is completely indistinguishable from their not having happened at all. In the light of this observation, the second law of thermodynamics is reduced to a mere tautology: physics cannot study those processes where entropy has decreased, even if they were commonplace.

While interesting, I wonder if this approach is really promising. Basically, the author proves his Eq. (2), stating that the sum of entropy changes in a system A containing the observer and another system C equals the entropy change in a reservoir plus the change in the total amount of correlations (i.e., mutual information) between A and C. In the most interesting case when the entropy of the reservoir is constant, any entropy decreases in A and C must come at the expense of decreasing the amount/strength of correlation between A and C. This, according to the author, means that an entropy decrease in C automatically results in the observer in system A losing any memories or records (a memory/record is a kind of correlation) of C’s previous higher entropy state. However, very little correlation (a very small memory/record) is needed to retain, say, just the numerical values of C’s entropy at different times. Entropy decreases in C could, for all we know, come at the expense of other, more detailed, correlations between A and C, while leaving memories of measured entropies intact. Thus, it seems that much more work is needed to actually establish that entropy decreases are unobservable (due to being impossible to remember). The Phys. Rev. Focus commentary also hints at this problem.

Dembski and Marks publish trivial ID paper

Pseudoscientists in the Intelligent Design (ID) movement have long desired a track record of ID-related publications in peer-reviewed journals. Now Dembski and Marks are touting a new publication as a step in this direction. Reading the paper will be a disappointment to everyone who had hoped for any non-trivial results. The three things offered are:

Global warming contrarians gain new ally

I’ve been meaning to write a little note on a talk by Naomi Oreskes, available on YouTube, ever since it came to my attention via the comments on a blog (probably The Intersection or Pharyngula, though I regrettably don’t remember). Now the perfect excuse to do so has come up.

Two recent posts (one, two) at The Panda’s Thumb discuss contrarian views regarding global warming. The most interesting aspect is not the details of those views. No, the most interesting aspect is the person who holds those views: the intelligent design creationist William Dembski.

New law suit against The Pirate Bay

A new law suit against The Pirate Bay is reported in the news. Major movie studios have teamed up to stop TPB from providing torrents. Though TPB lost the previous court battle, the old torrents remain available and new ones are added every day. There’s also some bad news for the planned sale of TPB, as one player pulls out due to doubts about funding.

ZDnet even says the new law suit will block the sale of TPB to the dubious Global Gaming Factory, though no one else seems to have reported that. If true it would be a bit ironic since the new owner says it is negotiating deals with Hollywood studies to turn TPB into a legal file sharing site. Is this Hollywood’s answer to GGF? I guess it makes some sense to try to get TPB to cease activity as a torrent tracker, especially since GGF’s take over is still a bit unclear, but TPB is just one of several torrent trackers and users are already shifting attention to other trackers.

Jimmy Carter meets Prof. Steve Steve

This picture at Panda’s Thumb will make waves in the blogosphere. Prof. Steve, the world’s most educated science education mascot, met with none other than former President Jimmy Carter (or vice versa).

Is information, or constraints on inference, all there is?

“What is information? Is it physical? We argue that in a Bayesian theory the notion of information must be defined in terms of its effects on the beliefs of rational agents. Information is whatever constrains rational beliefs and therefore it is the force that induces us to change our minds.” — Ariel Caticha (eprint: 0710.1068)

“Perhaps physics is nothing but inference after all.” — Ariel Caticha (eprint: 0808.1260)

“Physics is the ability to win a bet.” — Attributed to J. R. Buck by C. A. Fuchs (eprint: quant-ph/0105039, p. 125)

Some theories present us with intruiging conceptual puzzles. This is the case with probability theory and statistics. Originally the notion of ‘probability’ was introduced in the study of games of chance, where players who are uncertain about outcomes in a game need to decide on a strategy.

Please stand up during take off and landing

Upright seating is again being considered for short passenger flights, this time by Ryanair. The same Ryanair that previously has considered charging extra for fat people and is currently mulling over a toilet charge. With the current financial crisis these ideas may have greater probability of being taken seriously by customers. I just hope the airline companies won’t start charging me for not losing my luggage… Or is that what travel insurance is for?