background preloader


Facebook Twitter

Video about Gödel's Incompleteness Theorem. Please Subscribe to 3QD If you would like to make a one time donation in any amount, please do so by clicking the "Pay Now" button below.

Video about Gödel's Incompleteness Theorem

You may use any credit or debit card and do NOT need to join Paypal. The editors of 3QD put in hundreds of hours of effort each month into finding the daily links and poem as well as putting out the Monday Magazine and doing all the behind-the-scenes work which goes into running the site. Fractals Explain Imagery Seen in Rorschach Ink Blots. 0 Shares It's easy to see familiar shapes in seemingly random patterns.

Fractals Explain Imagery Seen in Rorschach Ink Blots

Relatively Interesting The Map of Mathematics - Relatively Interesting. Order of operations. For example, in mathematics and most computer languages multiplication is done before addition; in the expression 2 + 3 × 4, the answer is 14.

Order of operations

Brackets, "( and ), { and }, or [ and ]", which have their own rules, may be used to avoid confusion, thus the preceding expression may also be rendered 2 + (3 × 4), but the brackets are unnecessary as multiplication still has precedence without them. The standard order of operations[edit] The order of operations used throughout mathematics, science, technology and many computer programming languages is expressed here:[2] exponents and roots addition and subtraction. Order of Operations - BODMAS. Operations.

Order of Operations - BODMAS

Triangle of Power. Earth - You decide: What is the most beautiful equation? Paradox at the heart of mathematics makes physics problem unanswerable. L: Pictorial Press Ltd/Alamy, R: Photoshot Kurt Gödel (left) demonstrated that some mathematical statements are undecidable; Alan Turing (right) connected that proof to unresolvable algorithms in computer science.

Paradox at the heart of mathematics makes physics problem unanswerable

A logical paradox at the heart of mathematics and computer science turns out to have implications for the real world, making a basic question about matter fundamentally unanswerable. Funky Chicken Walk Can Indicate a Sick Bird. Why did the chicken cross the pen?

Funky Chicken Walk Can Indicate a Sick Bird

No, seriously. That’s a legitimate scientific question. The way chickens move through a pen may tell us a lot about whether or not they’re feeling well and how many opportunities they have to spread illnesses. Now scientists are studying how chicken locomotion can reveal disease—knowledge that could help farmers do a better job of heading off certain kinds of outbreaks. Chaos Theory in Ecology Predicts Future Populations.

Sometimes ecological data just don’t make sense.

Chaos Theory in Ecology Predicts Future Populations

The sockeye salmon that spawn in British Columbia’s Fraser River offer a prime example. Scientists have tracked the fishery there since 1948, through numerous upswings and downswings. At first, population numbers seemed inversely correlated with ocean temperatures: The northern Pacific Ocean surface warms and then cools again every few decades, and in the early years of tracking, fish numbers seemed to rise when sea surface temperature fell. To biologists this seemed reasonable, since salmon thrive in cold waters. Represented as an equation, the population-temperature relationship also gave fishery managers a basis for setting catch limits so the salmon population did not crash.

But in the mid-1970s something strange happened: Ocean temperatures and fish numbers went out of sync. Edit Distance Reveals Hard Computational Problems. At first glance, the big news coming out of this summer’s conference on the theory of computing appeared to be something of a letdown.

Edit Distance Reveals Hard Computational Problems

For more than 40 years, researchers had been trying to find a better way to compare two arbitrary strings of characters, such as the long strings of chemical letters within DNA molecules. The most widely used algorithm is slow and not all that clever: It proceeds step-by-step down the two lists, comparing values at each step. If a better method to calculate this “edit distance” could be found, researchers would be able to quickly compare full genomes or large data sets, and computer scientists would have a powerful new tool with which they could attempt to solve additional problems in the field. But researchers aren’t quite ready to record the time of death. Math describes sheep herd fluctuations. View the video There’s something in the way sheep move.

Math describes sheep herd fluctuations

In a herd, Merino sheep follow a predictable pattern of spreading out and clustering together. Now scientists have developed equations that can describe those movements. The sheep’s choreography may allow them to balance their needs for food and protection, researchers report September 28 in the Proceedings of the National Academy of Sciences. “This is the first quantitative study of this kind of behavior,”says study coauthor Francesco Ginelli, a collective animal behavior and active-matter researcher at the University of Aberdeen in Scotland. Story continues after sidebar An observed group of 100 ewes slowly drifted apart while grazing, only to suddenly clump back together roughly every 15 minutes, the researchers report. Scatter plot. Waiting time between eruptions and the duration of the eruption for the Old Faithful Geyser in Yellowstone National Park, Wyoming, USA.

Scatter plot

This chart suggests there are generally two "types" of eruptions: short-wait-short-duration, and long-wait-long-duration. A 3D scatter plot allows the visualization of multivariate data. This scatter plot takes multiple scalar variables and uses them for different axes in phase space. The different variables are combined to form coordinates in the phase space and they are displayed using glyphs and colored using another scalar variable.[1] Overview[edit] New tessellating pentagonal shape discovered — Hopes&Fears — flow "Design" Mathematicians and designers are rejoicing as the 15th pentagonal tile pattern has just been discovered. Triangles and four-sided shapes can always tile a plane, meaning that they don't overlap or leave gaps in between each individual shape. Only 14 pentagonal tile patterns existed until this recent discovery, and the basic pentagon with all sides measuring the same length does not tile.

Image: Twitter German mathematician Karl Reinhardt began to experiment with pentagons in 1918 and discovered five equations for shapes that tile the plane completely. Since then, the remaining 11 tiles were discovered by R. It wasn't until just recently that Casey Mann, Jennifer McLoud, and David Von Derau of the University of Washington Bothell announced their new discovery. Image: Casey Mann. How Complex Networks Explode with Growth. Last week, United Airlines grounded nearly 5,000 flights when its computer system crashed. The culprit: a faulty network router. Later on the same morning, another computer glitch halted trading on the New York Stock Exchange for over three hours.

Some saw the sinister hand of a hacker in these outages, but they are far more likely to be a coincidence, an intrinsic feature of the system rather than a bug. Networks go down all the time, a consequence of unprecedented levels of interconnection. Disruptions can occur even in the most robust networks, whether these are power grids, global financial markets, or your favorite social network. Infinities in literature and mathematics. By Jorge Alejandro Laris Pardo During this past month, I was having a conversation with a couple of friends who study Latin-American Literature, and I noticed that they were having a hard time understanding how a literary work can have infinite critical interpretations, while at the same time not all its interpretations are critical.

Bayes' Theorem. An Intuitive Explanation of Bayes' Theorem Bayes' Theorem for the curious and bewildered; an excruciatingly gentle introduction. Your friends and colleagues are talking about something called "Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning. Unhappy Truckers and Other Algorithmic Problems - Issue 3: In Transit. Inconsistent Mathematics, Reutersvärd, and Buddhism: An Interview with Chris Mortensen.

Marty and Michael in Math Magic Land. After 400 years, mathematicians find a new class of solid shapes. 10 Paradoxes that Will Totally Surprise You. 8 math talks to blow your mind. Mathematics gets down to work in these talks, breathing life and logic into everyday problems. Touch Mathematics. One of the most abstract fields in math finds application in the 'real' world. The Philosophy of Punk Rock Mathematics – Technoccult interviews Tom Henderson. Scientists Use Math To Analyse The ‘Om’ Chant. U.S.C. Exhibit Shows Fractals Built From Paper. But what if we could experience math directly — just as we experience language by speaking it?

Some years ago I founded an organization, the Institute for Figuring, dedicated to the proposition that many ideas in math and science could be approached not just through equations and formulas but through concrete, physical activities. Tap code. Statistics Win in U.S. Election. Mathematicians at Play: 3-D Printing Enters the 4th Dimension. Fairly Simple Math Could Bridge Quantum Mechanics and General Relativity. Roll Over, Pythagoras: the "Holy Grail" of Math May Have Been Found.