Lifeboat Foundation

When a legendary mathematician found a mistake in his own work, he embarked on a computer-aided quest to eliminate human error. To succeed, he has to rewrite the century-old rules underlying all of mathematics.

Music for the game is ‘procedurally’ generated as players move through its universe.

The Defense Advanced Research Projects Agency has demonstrated a new mathematical framework that works to help researchers discover patterns in complex scientific and engineering systems. DARPA said Thursday researchers at Stanford University created algorithms designed to explore patterns in data in order to gain insights into network structure and function under the Simplifying Complexity in Scientific Discovery [ ].

A new mathematical model aims to track the activity of Islamic State sympathizers online and determine when groups will turn from talk to action.

Nice.

Networks are mathematical representations to explore and understand diverse, complex systems—everything from military logistics and global finance to air traffic, social media, and the biological processes within our bodies. In each of those systems, a hierarchy of recurring, meaningful internal patterns—such as molecules and proteins interacting inside cells, and capacitors and resistors operating within integrated circuits—determines the functions or behaviors of those systems. The larger and more intricate a system is, however, the harder it is for current network modeling techniques to uncover these patterns and represent them in organized, easy-to-understand ways.

Researchers at Stanford University, funded by DARPA’s Simplifying Complexity in Scientific Discovery (SIMPLEX) program, have made progress in overcoming these challenges through a framework they have developed for identifying and clustering what mathematicians call “motifs”: essential but often obscure patterns within systems that are the building blocks of mathematical modeling and that facilitate the computational representation of complex systems.

Continue reading “Mathematical framework that prioritizes key patterns in networks aims to accelerate scientific discovery” »

Thomas Aquinas and other ludicrous pseudo-philosophers (in contradistinction with real philosophers such as Abelard) used to ponder questions about angels, such as whether they can interpenetrate (as bosons do).

Are today’s mathematicians just as ridiculous? The assumption of infinity has been “proven” by the simplest reasoning ever: if n is the largest number, clearly, (n+1) is larger. I have long disagreed with that hare-brained sort of certainty, and it’s not a matter of shooting the breeze. (My point of view has been spreading in recent years!) Just saying something exists, does not make it so (or then one would believe Hitler and Brexiters). If I say:” I am emperor of the galaxy known as the Milky Way!” that has a nice ring to it, but it does not make it so (too bad, that would be fun).

Given n symbols, each labelled by something, can one always find a new something to label (n+1) with? I say: no. Why? Because reality prevents it. Somebody (see below) objected that I confused “map” and “territory”. But I am a differential geometer, and the essential idea there, from the genius B. Riemann, is that maps allow to define “territory”:

Continue reading “MND: Your Daily Dose of Counter-Theory” »

A transistor, conceived of in digital terms, has two states: on and off, which can represent the 1s and 0s of binary arithmetic.

But in analog terms, the transistor has an infinite number of states, which could, in principle, represent an infinite range of mathematical values. Digital computing, for all its advantages, leaves most of transistors’ informational capacity on the table.

In recent years, analog computers have proven to be much more efficient at simulating biological systems than digital computers. But existing analog computers have to be programmed by hand, a complex process that would be prohibitively time consuming for large-scale simulations.

In 2009, President Obama pledged to “restore science to its rightful place.” He said, “We will not just meet, but we will exceed the level achieved at the height of the space race, through policies that invest in basic and applied research, create new incentives for private innovation, promote breakthroughs in energy and medicine, and improve education in math and science.”

Today, the White House released an Impact Report listing 100 things that Obama has made happen with the support of many people across research, policy, education, and, yes, maker culture. Here’s the full Impact Report. A few examples from the list:

When an astronomical observatory detected two black holes colliding in deep space, scientists celebrated confirmation of Einstein’s prediction of gravitational waves. A team of astrophysicists wondered something else: Had the experiment found the “dark matter” that makes up most of the mass of the universe?

The eight scientists from the Johns Hopkins Henry A. Rowland Department of Physics and Astronomy had already started making calculations when the discovery by the Laser Interferometer Gravitational-Wave Observatory (LIGO) was announced in February. Their results, published recently in Physical Review Letters, unfold as a hypothesis suggesting a solution for an abiding mystery in astrophysics.

“We consider the possibility that the black hole binary detected by LIGO may be a signature of dark matter,” wrote the scientists in their summary, referring to the black hole pair as a “binary.” What follows are five pages of annotated mathematical equations showing how the researchers considered the mass of the two objects LIGO detected as a point of departure, suggesting that these objects could be part of the mysterious substance known to make up about 85 percent of the mass of the universe.