Lifeboat Foundation: Safeguarding Humanity
Toggle light / dark theme

Blog

Category: mathematics – Page 37

A mathematical historian at Trinity Wester University in Canada, has found use of a decimal point by a Venetian merchant 150 years before its first known use by German mathematician Christopher Clavius. In his paper published in the journal Historia Mathematica, Glen Van Brummelen describes how he found the evidence of decimal use in a volume called “Tabulae,” and its significance to the history of mathematics.

The invention of the decimal point led to the development of the decimal system, and that in turn made it easier for people working in multiple fields to calculate non-whole numbers (fractions) as easily as whole numbers. Prior to this new discovery, the earliest known use of the decimal point was by Christopher Clavius as he was creating astronomical tables—the resulting work was published in 1593.

The new discovery was made in a part of a manuscript written by Giovanni Bianchini in the 1440s—Van Brummelen was discussing a section of trigonometric tables with a colleague when he noticed some of the numbers included a dot in the middle. One example was 10.4, which Bianchini then multiplied by 8 in the same way as is done with modern mathematics. The finding shows that a decimal point to represent non-whole numbers occurred approximately 150 years earlier than previously thought by math historians.

Read more | >

Networks can represent changing systems, like the spread of an epidemic or the growth of groups in a population of people. But the structure of these networks can change, too, as links appear or vanish over time. To better understand these changes, researchers often study a series of static “snapshots” that capture the structure of the network during a short duration.

Network theorists have sought ways to combine these snapshots. In a new paper in Physical Review Letters, a trio of SFI-affiliated researchers describe a novel way to aggregate static snapshots into smaller clusters of networks while still preserving the dynamic nature of the system. Their method, inspired by an idea from quantum mechanics, involves testing successive pairs of network snapshots to find those for which a combination would result in the smallest effect on the dynamics of the system—and then combining them.

Importantly, it can determine how to simplify the history of the network’s structure as much as possible while maintaining accuracy. The math behind the method is fairly simple, says lead author Andrea Allen, now a data scientist at Children’s Hospital of Philadelphia.

Read more | >

Scientists have found that the growth patterns of trees in a forest differ significantly from the way branches expand on an individual tree.

Nature is full of surprising repetitions. In trees, the large branches often look like entire trees, while smaller branches and twigs look like the larger branches they grow from. If seen in isolation, each part of the tree could be mistaken for a miniature version of itself.

It has long been assumed that this property, called fractality, also applies to entire forests but researchers from the University of Bristol have found that this is not the case.

Read more | >

Logical reasoning is still a major challenge for language models. DeepMind has found a way to support reasoning tasks.

A study by Google’s AI division DeepMind shows that the order of the premises in a task has a significant impact on the logical reasoning performance of language models.

They work best when the premises are presented in the same order as they appear in the logical conclusions. According to the researchers, this is also true for mathematical problems. The researchers make the systematically generated tests available in the R-GSM benchmark for further investigation.

Read more | >

What is universal in natural languages? To answer that, deep connections need to be made between universal grammar, written codes, statistical patterns and Universal Turing machines.

Human language is a prime example of a complex system characterized by multiple scales of description. Understanding its origins and distinctiveness has sparked investigations with very different approaches, ranging from the Universal Grammar to statistical analyses of word usage, all of which highlight, from different angles, the potential existence of universal patterns shared by all languages. Yet, a cohesive perspective remains elusive. In this paper we address this challenge. First, we provide a basic structure of universality, and define recursion as a special case thereof. We cast generative grammars of formal languages, the Universal Grammar and the Greenberg Universals in our basic structure of universality, and compare their mathematical properties. We then define universality for writing systems and show that only those using the rebus principle are universal.

Read more | >

The technology can reconstruct a hidden scene in just minutes using advanced mathematical algorithms.

Potential use case scenarios

Law enforcement agencies could use the technology to gather critical information about a crime scene without disturbing the evidence. This could be especially useful in cases where the scene is dangerous or difficult to access. For example, the technology could be used to reconstruct the scene of a shooting or a hostage situation from a safe distance.

The technology could also have applications in the entertainment industry. For instance, it could create immersive gaming experiences that allow players to explore virtual environments in 3D. It could also be used in the film industry to create more realistic special effects.

Continue reading “New technology can reveal what’s hidden behind objects using algorithm” | >

The universe, with its myriad mysteries, has long captivated our curiosity, and among its enigmatic phenomena, black holes have held a prominent place. These collapsed cores of dead stars, known for devouring everything in their vicinity, have a cosmic counterpart that challenges our understanding – the elusive ‘white holes.’

Imagine delving into the intricacies of space-time around a black hole, subtracting the collapsed star’s mass, and unveiling the mathematical description of a white hole – a massless singularity. Unlike their gravitational counterparts, black holes, where matter disappears into an event horizon, white holes defy entry. They expel matter at an astonishing rate, akin to hitting a cosmic ‘rewind’ button.

Read more | >