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41 posts tagged with mathematics *and* physics.

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## Famous Fluid Equations Are Incomplete

The Singular Mind of Terry Tao - "Imagine, he said, that someone awfully clever could construct a machine out of pure water. It would be built not of rods and gears but from a pattern of interacting currents." (via) [more inside]

## In mathematics, you don’t understand things. You just get used to them.

Calculating the Speed of Light Using a Microwave and PEEPS (or other melty things) from National Geographic's Education Blog and NPR's Skunk Bear videos (showing some history of calculating the speed of light... with peeps as historical scientists, of course)

## Of course, everyone knows about levers...

Elementary Mechanics from a Mathematician's Viewpoint [direct link to large PDF] by Michael Spivak - notes from his eight 2004 lectures (which eventually became a book). See the quote inside to get the flavor of it. [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]

## 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 ;)## 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]

## 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

## 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)## Assume A Cylindrical Cow

## 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]

## 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 Strangest Man

*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.*[1939] [more inside]

## A Shory Biography of Emmy Noether

## I have a burning question, man.

*Before it was a website, Ask A Mathematician / Ask A Physicist was two guys sitting in the desert at Burning Man, presuming to answer (almost) any question that happened to occur to whomever happened to appear at our stand.*[more inside]

## What is up with Noises? (SLYT)

What is up with Noises? A fascinating explanation of why we hear sounds and music the way we do. It's a long video, but it's worth it!

## Nature Special Issue on the Future of the PhD

## from complexity, universality

## That Was the This Week's Finds That Was

The 300th issue of This Week's Finds in Mathematical Physics will be the last. It is not an exaggeration to say that when John Baez started publishing TWF in 1993, he invented the science blog, and an (academic) generation has now grown up reading his thoughts on higher category theory, zeta functions, quantum gravity, crazy pictures of roots of polynomials, science fiction, and everything else that can loosely be called either "mathematical" or "physics."
Baez continues to blog actively at n-category cafe and the associated nLab (an intriguingly fermented commune of mathematicians, physicists, and philosophers.) He is now starting a new blog, Azimuth, "centered around the theme of

*what scientists can do to help save the planet*."## The quantum mechanics of the waggle dance.

Mathematician Barbara Shipman speculates that a honey bee's sense of the quantum world could be as important to their perception of the world as sight, sound or smell: "the mathematics implies that bees are doing something with quarks."

## Economics and Physics Envy

"Take a little bad psychology, add a dash of bad philosophy and ethics, and liberal quantities of bad logic, and any economist can prove that the demand curve for a commodity is negatively inclined." MIT economist Andrew Lo and string theorist turned asset manager Mark Mueller on the "physics envy" that plagues economics, and how to stop worrying and love uncertainty.

## 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.

## Surely not joking, Mr. Feynman

"

*I can see the audience tonight, so I can see also from the size of it that there must many of you here who are not thoroughly familiar with physics, and also a number that are not too versed in mathematics- and I don't doubt that there are some who know neither physics nor mathematics very well. That puts a considerable challenge on a speaker who is going to speak on the relation of physics and mathematics- a challenge which I, however, will not accept: I published the title of the talk in clear and precise language, and didn't make it sound like it was something it wasn't- it's the relation of physics and mathematics - and if you find that in some spots it assumes some minor knowledge of physics or mathematics, I cannot help it. It was named."*The Feynman Messenger series at Cornell has been made available online for the first time thanks to Bill Gates.## 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.

## The Spherical Wave Structure of Matter in Space

On Truth and Reality. Despite several thousand years of failure to correctly understand physical reality (hence the current postmodern view that this is impossible) it is actually very simple to work out how matter exists and moves about in Space. The rules of Science (Occam's Razor / Simplicity) and Metaphysics (Dynamic Unity of Reality) require that reality be described from only one single source existing, as Leibniz wrote:

*"because of the interconnection of all things with one another."*[more inside]## 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?"

## Adventures in Balrog Math

## A Map of the Cat

Richard P. Feynman

**{**Information Junkie**→**PhD**→**Atomic Bomber**→**Professor/Lecturer on Physics + Mathematical Artist [DIY] + Nanotech Knowledgist**→**33.3% Nobel laureate + QEDynamic Speaker + Tiny Machinist + Challenger of Conclusions + Best-Selling Writer –**X**– Busted [outside Tuva]**→**Star Trek TNG Shuttlecraft**↓**Pepsi Black/Blue**↑**U.S. Postage Stamp**}**∞## Proofs and Pictures: The Role of Visualization in Mathematical and Scientific Reasoning

Proofs and Pictures: The Role of Visualization in Mathematical and Scientific Reasoning [video] "The picture is a telescope for looking into Plato's heaven." -- James Brown [cached]

## ...almost, but not quite, entirely unlike tea.

"...the answer to Life, the Universe, and Everything is..." "Yes? Yes!?" "...42."

via Dyson, Montgomery, Princeton, a cup of tea - as presented by Seed Magazine.

via Dyson, Montgomery, Princeton, a cup of tea - as presented by Seed Magazine.

## Math You Don't Know, and Math You Didn't Know You Didn't Know.

Jim Loy's Mathematics Page is (among other things) a collection of interesting theorems (like Napoleon's Triangle theorem), thoughtful discussions of both simple and complex math, and geometric constructions (my personal favorite); the latter of which contains surprisingly-complex discussions on the trisection of angles, or the drawing of regular pentagons.

Similarly enthralling are the pages on Billiards (and the physics of), Astronomy (and the savants of), and Physics (and the Phlogiston Theory of), all of which are rife with illustrations and diagrams. See the homepage for much more.

If you like your geometric constructions big, try Zef Damen's Crop Circle Reconstructions.

Similarly enthralling are the pages on Billiards (and the physics of), Astronomy (and the savants of), and Physics (and the Phlogiston Theory of), all of which are rife with illustrations and diagrams. See the homepage for much more.

If you like your geometric constructions big, try Zef Damen's Crop Circle Reconstructions.

## Negative knowledge (or more precisely negative information)

Know less than nothing!?

*What could negative knowledge possibly mean? In short, after I tell you negative information, you will know less...*"In this week's issue of Nature, however, Michal Horodecki and colleagues present a fresh approach to understanding quantum phenomena that cannot be grasped simply by considering their classical counterparts." [via slashdot :]## The Complexity of a Controversial Concept

The Logic of Diversity "A new book,

*The Wisdom of Crowds*[..:] by The New Yorker columnist James Surowiecki, has recently popularized the idea that groups can, in some ways, be smarter than their members, which is superficially similar to Page's results. While Surowiecki gives many examples of what one might call collective cognition, where groups out-perform isolated individuals, he really has only one explanation for this phenomenon, based on one of his examples: jelly beans [...] averaging together many independent, unbiased guesses gives a result that is probably closer to the truth than any one guess. While true — it's the central limit theorem of statistics — it's far from being the only way in which diversity can be beneficial in problem solving." (Three-Toed Sloth)## 'The Poincare Conjecture' Solved?

'The Poincare Conjecture' Solved? "Dr Grigori Perelman, of the Steklov Institute of Mathematics of the Russian Academy of Sciences, St Petersburg, claims to have proved the Poincare Conjecture, one of the most famous problems in mathematics. The Poincare Conjecture, an idea about three-dimensional objects, has haunted mathematicians for nearly a century. If it has been solved, the consequences will reverberate throughout geometry and physics."

Also of note is that Perelman's solution is only a benign side effect of his efforts toward defining all three-dimensional surfaces mathematically, which if successful would allow humanity to "produce a catalogue of all possible three-dimensional shapes in the Universe, meaning that [mankind] could ultimately describe the actual shape of the cosmos itself."

Also of note is that Perelman's solution is only a benign side effect of his efforts toward defining all three-dimensional surfaces mathematically, which if successful would allow humanity to "produce a catalogue of all possible three-dimensional shapes in the Universe, meaning that [mankind] could ultimately describe the actual shape of the cosmos itself."

## Stephen Wolfram

Stephen Wolfram has finished his book, "A New Kind of Science," which purpotedly is being espoused as a paradigm shift in many fields. But, I'm starting to see a very reductionistic attitude in many of the main theorists of complextity theory and emergent phenomena. Is the idea that the Universe is in lines of code a phallus-extension/masculine overdriven idea? Isn't math a man made mapping and can the Universe be reduced to an equation by a man? Still this book is going to be groundbreaking. Read the following exceperpt from the wired.com article:
q: "I've got to ask you," I say. "How long do you envision this rule of the universe to be?"

w: "I'm guessing it's really very short."

q: "Like how long?"

w: "I don't know. In Mathematica, for example, perhaps three, four lines of code."

link via protofunk.org, old similar thread

w: "I'm guessing it's really very short."

q: "Like how long?"

w: "I don't know. In Mathematica, for example, perhaps three, four lines of code."

link via protofunk.org, old similar thread

## Another unified theory!

Another unified theory! And this time it's not just about physics, but the eternity domain, diallel lines, sunspots, egg resonance, planetary alignment, plant dehydration and the Book of Mormon too.

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