The Nature of Computation
- Intellects Vast and Warm and Sympathetic
: "I hand you a network or graph, and ask whether there is a path through the network that crosses each edge exactly once, returning to its starting point. (That is, I ask whether there is a 'Eulerian' cycle.) Then I hand you another network, and ask whether there is a path which visits each node exactly once. (That is, I ask whether there is a 'Hamiltonian' cycle.) How hard is it to answer me?" (via
) [more inside]
posted by kliuless
on Dec 1, 2012 -
Morton and Vicary on the Categorified Heisenberg Algebra
- "In quantum mechanics, position times momentum does not equal momentum times position! This sounds weird, but it's connected to a very simple fact. Suppose you have a box with some balls in it, and you have the magical ability to create and annihilate balls. Then there's one more way to create a ball and then annihilate one, than to annihilate one and then create one. Huh? Yes: if there are, say, 3 balls in the box to start with, there are 4 balls you can choose to annihilate after you've created one but only 3 before you create one..." [more inside]
posted by kliuless
on Jul 21, 2012 -
The trend of mathematics and physics towards unification provides the physicist with a powerful new method of research into the foundations of his subject, a method which has not yet been applied successfully, but which I feel confident will prove its value in the future. The method is to begin by choosing that branch of mathematics which one thinks will form the basis of the new theory. One should be influenced very much in this choice by considerations of mathematical beauty.
 [more inside]
posted by smcg
on Apr 28, 2012 -
"Perhaps twenty or thirty people in England may be expected to read this book."
G.H. Hardy's review of Whitehead and Russell's Principia Mathematica
, published in the Times Literary Supplement 100 years ago last week. "The time has passed when a philosopher can afford to be ignorant of mathematics, and a little perseverance will be well rewarded. It will be something to learn how many of the spectres that have haunted philosophers modern mathematics has finally laid to rest."
posted by escabeche
on Sep 12, 2011 -
Fate, Absolute Life and Death, the Aleph, the Zeitgeist, the sinking of the Atlantis, the World Trade Center
, the formation of the universe...what more could you want from art? There's probably already been a been a post on this guy, Paul Laffoley, but I should hope more people could get a glance at some of this man's work
. Crazy or brilliant, you make your decision. A video
from his website.
posted by moonbizcut
on Aug 31, 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 -
The Meaning of Life
according to various rather famous people (Dennett, Fukuyama, etc). I'm watching the Dennett video at the moment and it starts rather weakly, but, by midway through, is rolling along nicely. With topics like "being good without god" and "the anthropic principle" it struck me as relevant to a couple of recent askmefi threads
Dennett: [pause] i guess i'll say it again, more slowly...
(oh, and the player interface is rather delicate - give it time to load and click play a few times...)
posted by andrew cooke
on Oct 1, 2004 -
Laws of Form
In 1969, George Spencer-Brown published a mathematical book called Laws of Form
, which has inspired explorations in philosophy, cybernetics, art, spirituality, and computation. The work is powerful and has established a passionate following as well as harsh critics. This web site explores these people, their ideas and history, and provides references for further exploration. I read this then, didn't understand much of the math due to my innumeracy, but was struck by a passage in passing... I especially am curious to see what the numerate in MetaFilter have to say.
posted by y2karl
on Nov 11, 2001 -