The Springer Online Mathematical Encyclopedia is really very interesting. The quality is amazing.

The Online Encyclopaedia of Mathematics is the most up-to-date and comprehensive English-language graduate-level reference work in the field of mathematics today. This online edition comprises more than 8,000 entries and illuminates nearly 50,000 notions in mathematics. The Encyclopaedia of Mathematics is updated on a regular basis to remain a quick, precise source of reference to mathematical definitions, concepts, explanations, surveys, examples, terminology and methods, which will prove useful for all mathematicians and other scientists who encounter mathematics in their work.

Just read Doron Zeilberger’s 72nd Opinion. The man is quite a bit pretentious (“mathematician is really another species, higher than homo sapiens”) though he doesn’t lose one bit of respect from me.

Back in 2002, I had a discussion, in a café in the old town of Saint Malo, where I basically tried to convey the following message, but not as well put:

(…) most of human mathematics is completely useless. It was developed by humans for human consumption. In order for humans to understand it, it had to proceed in tiny steps, each comprehensible to a human. But if we take the “mesh size” of each step, dA, to be larger, one can do potentially much bigger and better things, and the computer’s dA is much larger, so we can (potentially) reach a mountain-top much faster, and conquer new mountain-tops where no humans will ever tread with their naked brains.

So this activity of computer-generated mathematics is the future. Unfortunately, many human mathematicians still don’t realize the importance of this activity, and dismiss it as “just a computer program” and “no new mathematics”.

At the time, the mathematician I was talking to, a man I greatly respect, objected that nobody could predict what could be useful, so to claim that non-computable math. is worth less than computable math., was just foolish. It managed to silence me. Indeed, while I believe that algorithms are a higher form of mathematics, I cannot prove that it is, and neither can Zeilberger, but he makes a great case for it:

[computable math] is a methodology that will make all computer-free math obsolete very soon.

I didn’t see this pass by, but ACM has launched several new journals. At least some of these will be top tier. Here are some titles I like:

• Transactions on Knowledge Discovery in Data
  
• Transactions on the Web
  
• Transactions on Storage
  

This can only be a good thing.

PyX is a Python package for the creation of PostScript and PDF files. It combines an abstraction of the PostScript drawing model with a TeX/LaTeX interface. Complex tasks like 2d and 3d plots in publication-ready quality are built out of these primitives.

Here is the type of things you can do:

Naturally, the code is a bit hairy:


from math import pi, cos
from pyx import *
from pyx.deco import barrow, earrow
from pyx.style import linewidth, linestyle
from pyx.graph import graphxy
from pyx.graph.axis import linear
from pyx.graph.axis.painter import regular
from pyx.graph.style import line
from pyx.graph.data import function
mypainter = regular(basepathattrs=[earrow.normal], titlepos=1)
def mycos(x): return -cos(x)+.10*x
g = graphxy(height=5, x2=None, y2=None,
x=linear(min=-2.5*pi, max=3.3*pi, parter=None,
painter=mypainter, title=r"$\delta\phi$"),
y=linear(min=-2.3, max=2, painter=None))
g.plot(function("y(x)=mycos(x)", context=locals()),
[line(lineattrs=[linewidth.Thick])])
g.finish()
x1, y1 = g.pos(-pi+.1, mycos(-pi+.1))
x2, y2 = g.pos(-.1, mycos(-.1))
x3, y3 = g.pos(pi+.1, mycos(pi+.1))
g.stroke(path.line(x1-.5, y1, x1+.5, y1), [linestyle.dashed])
g.stroke(path.line(x1-.5, y3, x3+.5, y3), [linestyle.dashed])
g.stroke(path.line(x2-.5, y2, x3+.5, y2), [linestyle.dashed])
g.stroke(path.line(x1, y1, x1, y3), [barrow.normal, earrow.normal])
g.stroke(path.line(x3, y2, x3, y3), [barrow.normal, earrow.normal])
g.text(x1+.2, 0.5*(y1+y3), r"$2\pi\gamma k\Omega$", [text.vshift.middlezero])
g.text(x1-.6, y1-.1, r"$E_{\rm b}$", [text.halign.right])
g.text(x3+.15, y2+.20, r"$2J_k(\varepsilon/\Omega)+\pi\gamma k\Omega$")
g.writeEPSfile("washboard")
g.writePDFfile("washboard")


(Source: 0xDE)

The Canadian Semantic Web Working Symposium was held yesterday in Quebec City and it was a great success. Of particular interest was the keynote speaker, Michael Huhns who argued that web services ought to be thought of as agents. The best paper award was given out to Jie Zhang and Robin Cohen for their paper “A Trust Model for Sharing Ratings of Information Providers on the Semantic Web” which I thought was really well thought out. You can buy the proceedings on amazon.