"This is a story of how the impossible became possible. How, for centuries, scientists were absolutely sure that solids (as well as decorative patterns like tiling and quilts) could only have certain symmetries - such as square, hexagonal and triangular - and that most symmetries, including five-fold symmetry in the plane and icosahedral symmetry in three dimensions (the symmetry of a soccer ball), were strictly forbidden. Then, about twenty years ago, a new kind of pattern, known as a "quasicrystal," was envisaged that shatters the symmetry restrictions and allows for an infinite number of new patterns and structures that had never been seen before, suggesting a whole new class of materials...."
Physicist Paul J. Steinhardt delivers a fascinating lecture
(WMV) on tilings
. However, it turns out science was beaten to the punch: a recent paper
Islamic architecture developed similar tilings centuries earlier.
posted by parudox
on Mar 18, 2007 -
Dr James Anderson, from the University of Reading's computer science department, claims to have defined what it means to divide by zero. It's so simple, he claims, that he's even taught it to high school students
[via Digg]. You just have to work with a new number he calls Nullity
(RealPlayer video). According to Anderson's site The Book of Paragon
, the creation, innovation, or discovery of nullity is a step toward describing a "perspective simplex, or perspex [ . . . ] a simple physical thing that is both a mind and a body." Anderson claims that Nullity permits the definition of transreal arithmetic
(pdf), a "total arithmetic . . . with no arithmetical exceptions," thus removing what the fictional dialogue No Zombies, Only Feelies?
identifies as the "homunculus problem" in mathematics: the need for human intervention to sort out "corner cases" which are not defined.
posted by treepour
on Dec 7, 2006 -
Raft to the Future:
An article about the weirdness of physical models of the universe, how that weirdness correlates to the inherent incompleteness
of mathematical systems, and how time itself can emerge
at the fringes of these incomplete models.
posted by knave
on Nov 6, 2006 -
Grigory Perelman, awarded the Fields Medal for his work on the Poincare Conjecture, talks
to the New Yorker.
posted by Gyan
on Aug 29, 2006 -
The Zero Saga
contains a great deal of information about the concept of zero, and its relation to other numbers and concepts in mathematics. It was linked in Good Math, Bad Math
; which contains a variety of other informative articles on the numbers
that capture our imaginations
. (Note: You may want to skip past part 4 of the Zero Saga, as it contains replies to the site, and as such should probably be at the bottom of the page. But, to compensate, the comments on Good Math are better than most blogs I've read.)
posted by Eideteker
on Aug 3, 2006 -
Mapping the StarMaze
A tale of mathematical obsession: "Before I can explain my decades-long quest to map the starmaze I must acquaint you with a small puzzle...I have a habit of seeing everything (cities, organizations, computers, networks, brains) as a maze, so I named this puzzle the starmaze....The first problem I ran into was that there were a lot of rooms...I invented wacky names
for each room...But something funny happened...In that instant I finally grasped that the starmaze was arranged on the edges of a nine-dimensional hypercube
posted by vacapinta
on Jun 4, 2006 -
Gregory Chaitin's Meta Math! The Quest For Omega
"Okay, what I was able to find, or construct, is a funny area of pure mathematics where things are true for no reason, they're true by accident... It's a place where God plays dice with mathematical truth. It consists of mathematical facts which are so delicately balanced between being true or false that we're never going to know, and so you might as well toss a coin." From Paradoxes of Randomness
"In my opinion, Omega suggests that even though maths and physics are different, perhaps they are not as different as most people think. To put it bluntly, if the incompleteness phenomenon discovered by Gödel in 1931 is really serious — and I believe that Turing's work and my own work suggest that incompleteness is much more serious than people think — then perhaps mathematics should be pursued somewhat more in the spirit of experimental science rather than always demanding proofs for everything." From Omega and why maths has no Theory Of Everythings
, see also
posted by MetaMonkey
on Apr 13, 2006 -
of Algebra: "Gabriela, sooner or later someone's going to tell you that algebra teaches reasoning. This is a lie propagated by, among others, algebra teachers.
posted by daksya
on Feb 16, 2006 -
Significance of numbers.
Not to be confused with the concept of "significant figures," this page lists the significance of numbers 0 through 1000.
"2 is the only even prime."
"24 is the largest number divisible by all numbers less than its square root."
"3367 is the smallest number which can be written as the difference of 2 cubes in 3 ways." Whoa!
posted by scarabic
on Nov 11, 2005 -
Norman Wildberger's New Trigonometry
Dr Norman Wildberger has rewritten the arcane rules of trigonometry and eliminated sines, cosines and tangents from the trigonometric toolkit. The First chapter of his new book, Divine Proportions, is online (.pdf
posted by Kwantsar
on Sep 25, 2005 -