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78 posts tagged with Mathematics *and* science.

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## The golden ratio has spawned a beautiful new curve: the Harriss spiral

## Islamic Astropolitik

Despite Western anxieties over Muslim conquest, traditions of Islamic astronomy and the portability of ritual space in Islam find Muslims at home among the stars. [more inside]

## 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]

## 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]

## 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]

## I'm leaving my body to science, not medical but physics

Let's Talk About Science is a blog devoted to discussing the world of science and technology communication with clear, beginner-friendly language, written and compiled by nanoscientist/physicist Jessamyn Fairfield and science educator ErinDubitably. [more inside]

## 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 ;)

## 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)

## 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 ;)## 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.)

## One pill makes you nano, and one pill makes you giga...

The pressure of a human bite is about 1/9th of the atmospheric pressure on Venus. The fastest bacterium on earth is just outstripping the fastest glacier. A square meter of sunshine in the spring imparts about 1 horsepower. [more inside]

## Math with Bad Drawings

## 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]

## ASCII fluid simulator

## Card tricks...

...to leave a smile on your face, by Helder Guimarães: Individual vs Crowd | Chaos | Freedom | Trick [more inside]

## Evolved design

Unleashing Genetic Algorithms on the iOS 7 Icon - In the pursuit of something just a bit tighter than Marc Edwards' superellipse approximation, Mike Swanson applies genetic algorithms to the task of making a better button-making script.

## 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)## "Topics galore."

## Assume A Cylindrical Cow

## 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]

## 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]

## 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]

## the power and beauty of mathematics

## 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]

## Skill-Luck Continuum

"We have little trouble recognizing that a chess grandmaster’s victory over a novice is skill, as well as assuming that Paul the octopus’s ability to predict World Cup games is due to chance. But what about everything else?" [Luck and Skill Untangled: The Science of Success]

## 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]

## The Art of π, φ and e

## Because Print Is Not Yet Dead

Free online graph paper generators: variations of squares, triangle, rhombus, and hexagonal, circular and polar, for drawing, gaming, writing, note-taking and much more. Blank Sheet Music (Flash) for all arrangements (PDF). Create and edit your own grids, probability and logarithmic graphs, petri-dish inserts and storyboards. Also, multilingual monthly and yearly calendars. Plus, more than you ever wanted to know about ISO paper dimensions and printable paper models of polyhedra. Prev-ious-ly.

## A Shory Biography of Emmy Noether

## The Hacker Shelf

The Hacker Shelf is nice crowd-sourced guide to (legally) free books on various computational and mathematical subjects. The topics page gives you an idea of the breadth of material available.

## Monte Carlo

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).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

## That which does not kill us makes us stronger

`> comp.basilisk - Frequently Asked Questions ::`

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]

**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...

## 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]

## Creating the Future of Education and Work

In February 2011, every teacher in Providence, Rhode Island was pink slipped. Not all 1,926 of them got fired, of course, but with the district facing a $40 million deficit, anything is possible. The district says it needs flexibility, just in case. Every school district in the United States faces its own version of what’s happening in Providence. However, “IMAGINATION: Creating the Future of Education and Work” is focused not on how we got here but rather how we can move forward from here immediately even as the education system continues to struggle. [more inside]

## Technically elegant but nearly forgotten

Ron Doerfler's Dead Reckonings - Lost Art in the Mathematical Sciences is a collection of essays, in weblog format, on historical techniques in mathematical sciences, antique scientific instruments and other related topics. [more inside]

## i + e = δ

144 sites for online education. Categories include science and health, business and money, history and culture, law, computer science, mathematics, and languages. [more inside]

## Not a cryptic FPP

Vortex-based mathematics is the most advanced ever known to mankind. Don't have time for a time cube? Time need no longer limit us. Here, Marco Rodin (inventor of the Rodin Coil) gives us the background.

## Dear NASA, Your Mom thought I was big enough. Love, Pluto

Following in the footsteps of prestigious publications like the Annals of Improbable Research, NCBI ROFL, Rejecta Mathematica, the Journal of Universal Rejection, and the Journal of Unpublished Results, comes the Journal of Are You Fucking Kidding. Previous, previously, and previouslier.
h/t to Retraction Watch

## 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.

## Complex matters for the millenium

*I am pleased to announce a proof that P is not equal to NP.*In this paper, Vinay Deolalikar (HP Labs) proposes a proof to answer the most important problem in its field of mathematics. [more inside]

## 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.## The Unreasonable Effectiveness of Mathematics in the Natural Sciences

The Unreasonable Effectiveness of Mathematics in the Natural Sciences is a 1960 essay by Eugene Wigner. Via Steve Strogatz.

## cosmic spiral visuals

The Anatomy of Spiral Arms,

*shows how galaxies naturally evolve to form grand-design two-arm spirals.*The Hubble Ultra Deep Field in 3D. [more inside]## Figure 3. Basic model outbreak scenario. Susceptibles are quickly eradicated and zombies take over, infecting everyone.

## 3D Mapping

Durango Bill's Home Page. With topics that include: 3D end-to-end tour of the Grand Canyon, the origin and formation of the Colorado River, and examples of river systems that cut through mountain ranges instead of taking easier routes around them in Ancestral Rivers of the World. [more inside]

## Computable data* (conceivably knowable) about people

Stephen Wolfram discusses Wolfram|Alpha: Computational Knowledge Engine - at the same time Google Adds Search to Public Data, viz: "Nobody really paid attention to the two hour snorecast" -- like a cross between designing for big data and a glossary of game theory terms -- on Wolfram|Alpha (previously), yet the veil is being lifted nonetheless: "[on] a platonic search engine, unearthing eternal truths that may never have been written down before," cf. hunch & cyc (and in other startup news...) [via] [more inside]

## Does Your Answer Seem Right?

NYT Guesstimation Quiz. Enrico Fermi estimated the yield of the Trinity A-bomb test by dropping some shredded paper. He also asked his students to estimate unusual quantities like the number of piano tuners in Chicago - to show that just about anything can be estimated without detailed knowledge.

## Homework Helper

World of Science contains budding encyclopedias of astronomy, scientific biography, chemistry, and physics. This resource has been assembled over more than a decade by internet encyclopedist Eric Weisstein with assistance from the internet community. MeFi visited Weisstein's Mathworld a couple years ago.

## You and Your Research

You and Your Research was a talk given by Richard Hamming in 1986. Read it if you have an interest in doing first-class work.

## Reality

The Reality Tests. "A team of physicists in Vienna has devised experiments that may answer one of the enduring riddles of science: Do we create the world just by looking at it?"

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