"One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In particular, I argue that computational complexity theory---the field that studies the resources (such as time, space, and randomness) needed to solve computational problems---leads to new perspectives on the nature of mathematical knowledge, the strong AI debate, computationalism, the problem of logical omniscience, Hume's problem of induction, Goodman's grue riddle, the foundations of quantum mechanics, economic rationality, closed timelike curves, and several other topics of philosophical interest. I end by discussing aspects of complexity theory itself that could benefit from philosophical analysis."
posted by cthuljew
on May 5, 2013 -
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 -
Old Theories As Limits of New Ones
-- Theoretical physicist, Lubos Motl, takes a brief tour through the history of physics, and explains the simple mathematical relationship of old theories to the theories that replace them.
posted by empath
on Aug 5, 2011 -
is a veteran American cartoonist best known for his delightful comic-book guides to science and history, many of which have previews online. Chief among them is his long-running Cartoon History of the Universe
(later The Cartoon History of the Modern World
), a sprawling multi-volume opus documenting everything from the Big Bang to the Bush administration. Published over the course of three decades, it takes a truly global view -- its time-traveling Professor thoroughly explores not only familiar topics like Rome and World War II but the oft-neglected stories of Asia and Africa, blending caricature and myth with careful scholarship (cited by fun illustrated bibliographies
) and tackling even the most obscure events with intelligence and wit
. This savvy satire carried over to Gonick's Zinn
chronicle The Cartoon History of the United States
, along with a bevy of Cartoon Guides
to other topics, including Genetics, Computer Science, Chemistry, Physics, Statistics, The Environment
, and (yes!) Sex
. Gonick has also maintained a few sideprojects, such as a webcomic look at Chinese invention
, assorted math comics
), the Muse magazine
mainstay Kokopelli & Co.
(featuring the shenanigans of his "New Muses"
), and more
. See also these lengthy interview snippets
, linked previously
. Want more? Amazon links to the complete oeuvre inside! [more inside]
posted by Rhaomi
on Jun 6, 2011 -
Horizon asks "What is reality?"
-- youtube for links for those outside the UK: 1
. It's a hard question. To help you answer it, Stanford has a set of free courses available on line by Leonard Susskind:
, New Revolutions in Particle Physics
, Quantum Entanglement
, Special Relativity
, Classical Mechanics
, Statistical Mechanics
, The Standard Model
. (Each link is to lecture 1 of a full college course of a dozen or so lectures.) If you need help with the math, the Khan Academy
should help get you up to speed.
posted by empath
on Jan 23, 2011 -
's Magnetic sculptures
: "These forms are created with cylinder magnets, spherical magnets, and ball bearings. Magnetism is the only thing holding the forms together. They are fairly fragile and picking them up will likely crush them. All of the forms I created were variations of the 12 sided dodecahedron. This particular platonic solid seems to be the form the magnets are happiest with." [via
posted by dhruva
on Apr 14, 2010 -
Trigonometric Delights. This book is neither a textbook of trigonometry—of which there are many—nor a comprehensive history of the subject, of which there is almost none. It is an attempt to present selected topics in trigonometry from a historic point of view and to show their relevance to other sciences. It grew out of my love affair with the subject, but also out of my frustration at the way it is being taught in our colleges.
posted by Wolfdog
on Mar 24, 2010 -
-- or as O'Reilly might term the Social Graph
-- sort of mirrors the debate on 'brute force' algorithmic proofs
(that are "true for no reason
.) in which "computers can extract patterns in this ocean of data that no human could ever possibly detect. These patterns are correlations. They may or may not be causative
, but we can learn new things. Therefore they accomplish what science does, although not in the traditional manner... In this part of science, we may get answers that work, but which we don't understand. Is this partial understanding? Or a different kind
?" Of course, say some in the scientific community: hogwash
; it's just a fabrication of scientifically/statistically illiterate pundits, like whilst new techniques in data analysis
are being developed to help keep ahead of the deluge...
posted by kliuless
on Jul 21, 2008 -
A new study in Science claims that teaching math is better done by teaching the abstract concepts rather than using concrete examples
. From an article
by the study authors in Science Mag (requires subscription):
If a goal of teaching mathematics is to produce knowledge that students can apply to multiple situations, then presenting mathematical concepts through generic instantiations, such as traditional symbolic notation, may be more effective than a series of "good examples." This is not to say that educational design should not incorporate contextualized examples. What we are suggesting is that grounding mathematics deeply in concrete contexts can potentially limit its applicability. Students might be better able to generalize mathematical concepts to various situations if the concepts have been introduced with the use of generic instantiations.
posted by peacheater
on Apr 26, 2008 -
"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 -