Creative Thought as a Darwinian Process

(http://arxiv.org/html/nlin.AO/0411057)
This is the kind of nonsense that I (prejudicially) expect out of the humanities.
Admittedly, the authors are arguing against an even more extreme position.
On the other hand, I suspect that the extreme position they are arguing against (that ideas replicate and compete in a Darwinian way for brain space within a single brain) is a paper tiger - Nobody holds that position in an non-nuanced way.

Nitpicky details:
"It has been proven that the mathematical description of contextual change of state introduces a non-Kolmogorovian probability distribution, and a classical formalism such as selection theory cannot be used." That's a pretty exotic claim. Who proved it? I browsed through the references without finding something that is obviously "The proof of ... non-Kolmogorovian ...".

"Campbell would argue that we are unaware of generating and selecting amongst multiple possibilities because it happens subconsciously. [...] One argument against this is simply that there are times when one is aware of selecting amongst alternate possibilities, which suggests that if it happens, one is aware of it. But there are other times when it does not feel like one is selecting amongst alternate possibilities." Did you hear? The introspectionists (Wundt, Titchener) have been thoroughly discredited. Your counterargument has no force at all.

"Note that whereas Darwinian variation-selection is quite an elaborate affair, CAP [context-driven actualization of potential] is simply change of state in response to a context. CAP subsumes variation-selection, which is one process through change of state can occur." You may believe that there is a more careful description of what "context-driven actualization of potential" consists of elsewhere in the paper. This is as much of a definition as they give.

As far as I can tell, the theory is:

There is a state of mind.
It changes.
How it changes depends in some way on the previous state of mind.

And this "subsumes" selection theory in the sense that, in both theories, there is a state, and it changes.

Compare this paper to "Stability and Diversity in Collective Adaptation" (http://arxiv.org/abs/nlin.AO/0408039), which I wrote a little about recently. They both mention evolution (adaptation of populations) and events within one individual's lifetime.

The "Creative Thought" paper gives no mathematical model, neither for it's opposition (selection theory/replicator equations), nor for its own "CAP". The "Collective Adaptation" paper has lots of math.

The "Creative Thought" paper claims that if you have sequential states, you cannot have selection pressures between the states. The "Collective Adaptation" paper explains that you can move from a discrete time (with one action per time) to a continuous-time model if adaptation is slow compared to action selection. That is, the frequency of visiting a particular action/state can be analogous to the size of the population of a replicator.

Overall, I disrecommend this paper.

Quantum Lambda Calculus

(http://arxiv.org/abs/cs/0404056)
Quantum programming languages are apparently Peter Selinger's thing, and Benoit Valiron is his student.

I think that if you're familiar with affine linear types and have even a little knowledge of quantum computation, this paper will seem straightforward. (I'm not saying it was easy for the authors to write, but there are not big surprises.)

I'm not sure how useful this will be after quantum computers are built (reality always makes things new and difficult), but it might be useful for assessing the impact of, say, a 15-qbit peripheral with such-and-so operations that it can perform. Knowing the impact (a vague guess at the efficiency gains one might expect), could affect development of such a peripheral- which operations are important to support and which are inessential.

The Zhang model of Self-Organized Criticality

(http://arxiv.org/abs/math/0411590)
Though it really shouldn't, the phrase "Self-Organized Criticality" seems to mean "avalanches".

I presume that you, dear reader, are familiar with the sandpile cellular automaton. If not, visit:
http://www.cmth.bnl.gov/~maslov/soc.htm

The Zhang model is a slight variant, where the height/energy at each site is a smooth number (I hate to say "real number", they could be rationals), rather than a small integer.

This paper is the first I've seen that use IFSs (iterated function system - a method for producing fractals) for a real purpose- I thought that people only used them to make pictures of ferns and unrealistic claims of image compression.

It seems like they spend a lot of time analyzing avalanches in a two-site lattice, (sortof like saying you're studying chains of dominoes falling with two dominoes) but I suppose that's where one can draw pictures of the state space. Overall, I recommend this paper.

Brownian Loop Soup

(http://arxiv.org/abs/math.PR/0304419)
I discovered another interesting-sounding phrase "brownian loop soup". I don't understand it well. What I sortof know is:

1. Some things (certain kinds of fractals) have exact self-similarity, meaning that you can zoom in on a section and have the zoomed-in version look exactly the same as the original image.
2. Some things (other kinds of fractals) have statistical self-similarity, meaning that you can zoom in on a section and have the zoomed-in version look similar to the original image.
3. Sometimes there are numbers (fractal dimensions, for example) that say something about these very corrugated and random objects.
4. Random walks in the plane diffuse outward in a gaussian way. A walk with finite memory also diffuses outward in a gaussian. Self-avoiding walks (they never visit the same place twice - a physical example might be a polymer) require potentially infinite memory, and they're difficult to Monte Carlo simulate (you get stuck). There are easy-to-simulate approximations of self-avoiding walks (loop-erased random walk, "Schramm-Loewner Evolution"?).
5. Random walks and self-avoiding walks display statistical self-similarity.

I presume that "brownian loop soup" is in this tradition - proving probabilistic claims about statistically self-similar paths.

Winning the Hand of the Princess Saralinda

Suitors come to the castle in order to try to win the hand of the Princess Saralinda. The first suitor to perform n amazing feats will succeed. If the number n of feats is large and the times to perform the feats are all i.i.d., then how long is it before a suitor will win the hand of the Princess? We develop asymptotics describing the distribution of this random time as the number of feats gets large; e.g., we show that this time is of order n m - s sqrt(n log(n)), where m and s are the mean and standard deviation of the time to perform a single feat.
(http://citeseer.ist.psu.edu/431343.html)

Truly, an excellent first paragraph.

Queueing theory has always confused me.

If I understand correctly, it is entirely possible to perform Monte Carlo simulations of the queueing scenario and obtain this result empirically. Possibly it was first obtained empirically. However, the body of the paper contains no reference to any simulations, and derives the result entirely analytically. Which is impressive, no doubt, but I worry that there might be a disproportionate emphasis within mathematical culture on analytical results.

The nightmare scenario is when mathematics becomes a field like athletics, where the participating requires (and demonstrates) enormous talents, the participants undergo fantastic gyrations, and the end results are of no particular value.

Modern Military Mathematics

(http://www.nada.kth.se/~hedvig/publications/fusion_03a.pdf)
This is a paper funded by an institute for "Data Fusion". That is, you have various surveillance techniques, like satellite images and humans on the ground calling in reports, and you want to provide the bosses with reliable information.

This is called "Filtering" - which sounds reasonable if you're saying "I'm going to put a bandpass filter on this telephone so that you don't get that hissing"; but sounds odd to my ear if you're saying "I'm going to put a filter on the reports from the field to track where the target is going".

About particle filters: Do not think of coffee filters keeping particles from going through. One can represent a probability distribution by parameters (mean and standard deviation, perhaps). However, what if the correct distribution is not normal? Perhaps a weighted sum of normal distributions would be better? "Particle Filter" is a codeword meaning "we are going to represent a probability distribution by a set of samples from that distribution".

I imagine particle filters as similar to the representation of the population in genetic algorithms. In an infinite-population case, the population moves across the fitness landscape like a cloud. We approximate that (smooth) cloud by a list of individual samples from that cloud. We want to do two things to the population- one is replication (parts of the cloud get more dense according to the fitness landscape), and the other is mutation and crossover (which makes the cloud spread out in a certain way.

In the paper, the cloud is the "probability hypothesis distribution" (a function whose integral over a given region is the approximate number of targets (cars? tanks?) we expect in that region). There are two operations that one wants to do with the cloud- one is update it with new information (which pulls the cloud together into spikes), and one is evolve it forward in time (which makes the cloud spread out in a certain way).

I recommend this paper. There's a footnote which points to movies that might be entertaining even if you don't read the paper: http://www.foi.se/fusion/mpg/FUSION03

Chaitin's "How Real are Real Numbers?"

Chaitin's a bright guy and worth reading.
Unfortunately, this (http://arxiv.org/pdf/math.HO/0411418) paper is merely a rehash of what he (and other people) have said already.

If you're familiar with:
the distinction between countable and uncountable sets,
Cantor's diagonalization argument that the set of reals is uncountable,
the fact that the set of nameable numbers is countable,
and that the halting problem is unsolvable,
then I don't recommend that you read this paper.

If you don't want to read the paper,
here's my version:

Pat pointed to something on the screen and asked Dana "Is that a real number?"
Dana said "Um" and pointed to something on the desk and said "Is that a hunk of metal?"
Pat said "Well, yes. But I see your point- it's also a fork."
Dana said "You can imagine a physical object where the best description of it is 'hunk of metal'. However, a real number inside a computer is never a plain vanilla real number. There's always a more appropriate description."
"In fact it's a rational number between 0 and 1 represented as a rho-shaped linked list of bits."

testing testing, three two one.