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Calculus without limits

Hyperreal numbers: infinities and infinitesimals - "In 1976, Jerome Keisler, a student of the famous logician Tarski, published this elementary textbook that teaches calculus using hyperreal numbers. Now it's free, with a Creative Commons copyright!" (pdf—25mb :) [more inside]
posted by kliuless on Sep 17, 2014 - 28 comments

Selected Lectures on Science and Engineering in the Boston Area

If you live in the Boston area and would like to attend science, technology, math, or engineering lectures, you'll find Fred Hapgood's exhaustive and continually-updated list of Selected Lectures on Science and Engineering in the Boston Area very useful. (Here's his list of sources.) Perhaps you know of a list like this for lectures in your locality or field of preference?
posted by not_on_display on Sep 15, 2014 - 6 comments

Math and equations are fun.

The power of math: 17 Equations That Changed the World - a one table summary of the book by Ian Stewart FRS. Business Insider gives its interpretation of the importance of each equation. Brain pickings (2012) on this book and equations, and another extract from the book. [more inside]
posted by Wordshore on Aug 10, 2014 - 36 comments

The Foehr Reef

The Foehr Reef is part of the worldwide Crochet Coral Reef Project. It was made by over 700 women and combines more than 4000 individual pieces of marine wonder. A short video shows its beauty [alternating English and German audio]. PDFs with pictures. "The Crochet Coral Reef is a woolly celebration of the intersection of higher geometry and feminine handicraft, and a testimony to the disappearing wonders of the marine world." It originated out of a desire to increase awareness of environmental threats to the world's reefs and is a conjunction of art, environmentalism, and geometry. [more inside]
posted by travelwithcats on Aug 10, 2014 - 7 comments

21st Century Wiener

Norbert Wiener: The Eccentric Genius Whose Time May Have Finally Come (Again) - "The most direct reason for Wiener's fall to relative obscurity was the breakthrough of a young mathematician and engineer named Claude Shannon." [more inside]
posted by kliuless on Jul 11, 2014 - 12 comments

The Quest for Randomness

Can you ever be reasonably sure that something is random, in the same sense you can be reasonably sure something is not random (for example, because it consists of endless nines)? Even if a sequence looked random, how could you ever rule out the possibility that it had a hidden deterministic pattern? And what exactly do we mean by “random,” anyway?
posted by empath on Apr 24, 2014 - 48 comments

A SAT Attack on the Erdos Discrepancy Conjecture

Computers are providing solutions to math problems that we can't check - "A computer has solved the longstanding Erdős discrepancy problem! Trouble is, we have no idea what it's talking about — because the solution, which is as long as all of Wikipedia's pages combined, is far too voluminous for us puny humans to confirm." (via; previously ;)
posted by kliuless on Apr 12, 2014 - 24 comments

"I really like polyhedra."

Polyhedra and the Media - On the new polyhedra of Schein and Gayed, and mathematical journalism.
posted by Wolfdog on Mar 11, 2014 - 20 comments

there is no soundtrack

Finite time blowup for an averaged three-dimensional Navier-Stokes equation - "[Terence Tao] has shown that in an alternative abstract universe closely related to the one described by the Navier-Stokes equations, it is possible for a body of fluid to form a sort of computer, which can build a self-replicating fluid robot that, like the Cat in the Hat, keeps transferring its energy to smaller and smaller copies of itself until the fluid 'blows up.' " [1,2,3] (previously)
posted by kliuless on Mar 9, 2014 - 15 comments

John Baez on the maths of connecting everyone (and everything) on earth

Network Theory Overview - "The idea: nature and the world of human technology are full of networks! People like to draw diagrams of networks. Mathematical physicists know that in principle these diagrams can be understood using category theory. But why should physicists have all the fun? This is the century of understanding living systems and adapting to life on a finite planet. Math isn't the main thing we need, but it's got to be part of the solution... so one thing we should do is develop a unified and powerful theory of networks." (via ;)
posted by kliuless on Mar 2, 2014 - 17 comments

Scale invariant art

Astroblast and Overstepping Artifacts are music videos by the project Musicians with Guns, which take the viewer through detailed tours of some beauty. Relax and enjoy.
posted by Blazecock Pileon on Feb 27, 2014 - 9 comments

Network Nonsense

Open warfare erupts in the world of mathematical biology, as Lior Pachter of UC-Berkeley writes three blog posts attacking two papers in Nature Bioscience, accusing one of them of being "dishonest and fraudulent": The Network Nonsense of Albert-Laszlo Barabasi, The Network Nonsense of Manolo Kellis, and Why I Read the Network Nonsense Papers. Kellis (MIT) and his co-authors respond (.pdf.)
posted by escabeche on Feb 12, 2014 - 53 comments

I Was Told There Would Be No Math

M.I.T. professor Max Tegmark explores the possibility that math does not just describe the universe, but makes the universe.
posted by COD on Jan 14, 2014 - 111 comments

ipython notebook - a web-based interactive computational environment

"The IPython Notebook is a web-based interactive computational environment where you can combine code execution, text, mathematics, plots and rich media into a single document". It can be installed faily easily with anaconda or on Amazon EC2. Various interesting notebooks are to be found at the official Notebook Viewer site Another collection of interesting notebooks on many topics. [more inside]
posted by meta87 on Jan 5, 2014 - 56 comments

Intuitive Guide to Principles of Communications

Charan Langton (blog) hosts Complex To Real: which "...offers tutorials I have written on various topics in analog and digital communications that will help you cut through this complexity." [more inside]
posted by Confess, Fletch on Dec 21, 2013 - 8 comments

Where My Ladies At?

Recently Emily Graslie, of the fantastic natural history tumblr and youtube series TheBrainScoop, was asked a question about whether she had personally experienced sexism in her field. Her response is fucking amazing.
Inside is her goldmine of awesome female science educators online with channels that focus on Science Technology Engineering and Math. My work day is fucked.
[more inside]
posted by Blasdelb on Dec 6, 2013 - 37 comments

Math with Bad Drawings

Headlines from a Mathematically Literate World [more inside]
posted by Blasdelb on Dec 4, 2013 - 32 comments

binding the andat

Closing in on the twin prime conjecture (Quanta) - "Just months after Zhang announced his result, Maynard has presented an independent proof that pushes the gap down to 600. A new Polymath project is in the planning stages, to try to combine the collaboration's techniques with Maynard's approach to push this bound even lower." [more inside]
posted by kliuless on Dec 1, 2013 - 16 comments

My God, it's full of... everything

Revelations in the field of quantum physics have resulted in the discovery of the Amplituhedron, a jewel-like higher dimensional object whose volume elegantly predicts fundamental physical processes that took the brilliant Dr. Richard Feynman hundreds of pages of abstruse mathematics to describe. The theoretical manifold not only enables simple pen-and-paper calculation of physics that would normally require supercomputers to work out, but also challenges basic assumptions about the nature of reality -- forgoing the core concepts of locality and unitarity and suggesting that space and time are merely emergent properties of a timeless, infinitely-sided "master amplituhedron," whose geometry represents the sum total of all physical interactions. More: The 152-page source paper on arXiv [PDF] - Lead author Nima Arkani-Hamed's hour-long lecture at SUSY 2013 - Scans of Arkani-Hamed's handwritten lecture notes - A far more detailed lecture series "Scattering Without Space Time": one, two, three - Arkani-Hamed previously on MeFi - A hot-off-the-presses Wikipedia page (watch this space)
posted by Rhaomi on Sep 18, 2013 - 128 comments

Assume A Cylindrical Cow

The Mathematics of the Manhattan Project
posted by empath on Jul 10, 2013 - 40 comments

Why Philosophers Should Care About Computational Complexity

"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 - 31 comments

Great Scientist ≠ Good at Math?

Do you need to know math to do science? Harvard professor emeritus E. O. Wilson says, "no." Jeremy Fox, an Associate Professor of Population Ecology at the University of Calgary disagrees.
posted by Obscure Reference on Apr 8, 2013 - 74 comments

Computerized Math, Formal Proofs and Alternative Logic

Using computer systems for doing mathematical proofs - "With the proliferation of computer-assisted proofs that are all but impossible to check by hand, Hales thinks computers must become the judge." [more inside]
posted by kliuless on Mar 16, 2013 - 25 comments

Aspiring Animators & Game Designers, Study Your Calculus & Combinatorics

Every film Pixar has produced has landed in the top fifty highest-grossing animated films of all time. What's their secret? Mathematics. Oh, and 22 Rules of Storytelling. [more inside]
posted by zarq on Mar 8, 2013 - 40 comments

Oliver Heaviside

Surely you've heard of the physicist Maxwell, but what about Oliver Heaviside? Oliver Heaviside: A first-rate oddity.
posted by Evernix on Feb 14, 2013 - 14 comments

OMG SCIENCE!

Henry Reich of Minute Physics shares his favorite science blogs, video channels, and other resources on the web. (Minute Physics previously) [more inside]
posted by ocherdraco on Feb 8, 2013 - 5 comments

the power and beauty of mathematics

An eternity of infinities (via) [more inside]
posted by kliuless on Feb 2, 2013 - 23 comments

Teaching Computers to Hear Emotions

New research can detect five different emotions with 81 percent accuracy. [Additional project information].
posted by Evernix on Jan 8, 2013 - 21 comments

direct realism

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 - 19 comments

weee eigenvectors

Eigenfaces for facial recognition. (This post assumes familiarity with the terminology and notation of linear algebra, particularly inner product spaces.)
posted by Evernix on Oct 6, 2012 - 18 comments

noncommutative balls in boxes

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 - 78 comments

The Art of π, φ and e

The Art of π, φ and e [more inside]
posted by Blazecock Pileon on Jun 26, 2012 - 24 comments

Ice

Ice
posted by jjray on Apr 15, 2012 - 33 comments

How to quantify all aspects of society

"Samuel Arbesman is a senior scholar at the Ewing Marion Kauffman Foundation and author of the forthcoming book 'The Half-Life of Facts'. His research and essays explore how to quantify all aspects of society." [more inside]
posted by knile on Apr 10, 2012 - 4 comments

A Shory Biography of Emmy Noether

Amalie Noether: The Mighty Mathematician You’ve Never Heard Of
posted by jjray on Mar 27, 2012 - 49 comments

Monte Carlo

The year was 1945. Two earthshaking events took place: the successful test at Alamogordo and the building of the first electronic computer. Their combined impact was to modify qualitatively the nature of global interactions between Russia and the West. No less perturbative were the changes wrought in all of academic research and in applied science. On a less grand scale these events brought about a [renaissance] of a mathematical technique known to the old guard as statistical sampling; in its new surroundings and owing to its nature, there was no denying its new name of the Monte Carlo method (PDF). -N. Metropolis
Conceptually talked about on MeFi previously, some basic Monte Carlo methods include the Inverse Transform Method (PDF) mentioned in the quoted paper, Acceptance-Rejection Sampling (PDFs 1,2), and integration with and without importance sampling (PDF).
posted by JoeXIII007 on Dec 17, 2011 - 13 comments

That which does not kill us makes us stronger

> comp.basilisk - Frequently Asked Questions :: Is it just an urban legend that the first basilisk destroyed its creator?
Almost everything about the incident at the Cambridge IV supercomputer facility where Berryman conducted his last experiments has been suppressed and classified as highly undesirable knowledge. It's generally believed that Berryman and most of the facility staff died. Subsequently, copies of basilisk B-1 leaked out. This image is famously known as the Parrot for its shape when blurred enough to allow safe viewing. B-1 remains the favorite choice of urban terrorists who use aerosols and stencils to spray basilisk images on walls by night. But others were at work on Berryman's speculations...
[more inside]
posted by Rhaomi on Nov 6, 2011 - 88 comments

Knotty Problems

Science through yarn: Wooly Thoughts. The Home of Mathematical Knitting, including knitted klein bottles and hyperbolic planes. The Museum of Scientifically Accurate Fabric Brain Art (previously). Much, much, more on knitting, crochet and quilting used to visualize complex theories in topology, probability, chaos and fractals. [more inside]
posted by Bora Horza Gobuchul on Nov 6, 2011 - 8 comments

C is still for Cookie, and that's good enough for me

Science! (autoplaying video) The 42nd season of "Sesame Street," which premiered today, will be including a few new educational categories for preschoolers in its usual mix of lessons and parodies: STEM skills — Science, Technology, Engineering and Mathematics. In addition to more scientifically accurate slapstick, characters will try experiments, build bridges and boats, launch rockets and think through problems that require trial and error, observation and data -- all problem areas for America's students. [more inside]
posted by zarq on Sep 27, 2011 - 34 comments

The Earth Is Flat (to a certain approximation)

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 - 16 comments

The Cartoon Guide to Life, the Universe, and Everything

Larry Gonick 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-by-way-of-Pogo 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 (previously), 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 - 29 comments

What is reality?

Horizon asks "What is reality?" -- youtube for links for those outside the UK: 1, 2, 3, 4. It's a hard question. To help you answer it, Stanford has a set of free courses available on line by Leonard Susskind: General Relativity, Cosmology, 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 - 67 comments

Schrödinger's Ratio

If you look around, you'll see that the ratio of 1.618:1 appears in architecture, nature, and artistic works (such as music, previously). Studied by the Greeks, the Golden Ratio is pretty much everywhere and is common accepted as aesthetically pleasing, and now it has been found to exist down into the nanoscale level, as a byproduct of investigating the Heisenberg Uncertainty Principle. We may not be able to nail down both position and speed, but it appears the macro ratio is an echo of the micro one. [more inside]
posted by Old'n'Busted on Oct 29, 2010 - 31 comments

Arthur's Classic Novels, his Love of Mankind and the Internet

Arthur's Classic Novels has 4000 free ebooks, no registration, nicely organized by author and topics: great old Science Fiction magazines l plentiful online education with 650 books for doctors l a vast collection of famous novels l short stories l by women l Buddhist Scriptures, including The Buddhist Bible, a fave of Jack Kerouac l magazines online l stories by Robert Sheckley l The Autobiography of Charles Darwin l huge collection of fairy tales l philosophy l P. G. Wodehouse l vintage technology l Oscar Wilde l Mark Twain l Rudyard Kipling l George MacDonald l the Koran l a collection of eText resource links. About Arthur Wendover. [more inside]
posted by nickyskye on Sep 16, 2010 - 33 comments

Q to the E to the D

Futurama has always been a haven for geek humor, but last week's episode "The Prisoner of Benda" pushed things to the next level. First hinted at in an American Physical Society interview with showrunner David X. Cohen (previously), staff writer and mathematics Ph.D. Ken Keeler devised a novel mathematical proof based on group theory to resolve the logic puzzle spawned by the episode's brain-swapping (but no backsies!) conceit. Curious how it works? Read the proof (in the show or in plain text), then see it in action using this handy chart. Too much math for a lazy Sunday? Then entertain your brain with lengthy clips from the episode -- including two of the funniest moments in the series in the span of two minutes.
posted by Rhaomi on Aug 22, 2010 - 130 comments

How to operate the first digital computer.

Learn how to operate the world's first fully electronic digital computer in this helpful instructional video. No, not ENIAC - the Atanasoff Berry Computer. Here's an operator's manual. More information about the reconstruction.
posted by loquacious on Aug 13, 2010 - 24 comments

Pixel Pickle

Editors of the pop-culture magazine Wired provided the title "iPhone 4’s ‘Retina’ Display Claims Are False Marketing" to a highly critical article about the new iPhone's high-resolution "Retina" display, so-called as the human eye cannot resolve individual pixels when viewing it. A technician who worked on the Hubble telescope disagreed with the Wired editors' choice of rhetoric in very strong technical terms and issued less stringent disagreement with Raymond Soneira, the writer of the piece. Neuroscientist and photographer Bryan Jones published his own highly readable technical analysis of the display's pixel arrangement, that helped him decide whether Apple's claims were truthful or not.
posted by Blazecock Pileon on Jun 26, 2010 - 64 comments

magnetic sculptures

Robert Hodgin'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 - 11 comments

A glorified geometry with superimposed computational torture

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 - 18 comments

Contact is the secret, is the moment, when everything happens. Contact....

From 1980 - 1988, a science education series called 3-2-1 Contact ran on PBS. Produced by Children's Television Workshop, the series was geared toward an older audience than other popular CTW offerings Sesame Street and The Electric Company, and focused on teaching kids about science, math and the world around them. [more inside]
posted by zarq on Jan 25, 2010 - 79 comments

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