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What is the Church-Turing Thesis?

Modern-day computers have proved to be quite powerful in what they can do. The rise of AI has made things we previously only imagined possible. And the rate at which computers are increasing their computational power certainly makes it seem like we will be able to do almost anything with them. But as we’ve seen before, there are fundamental limits to what computers can do regardless of the processors or algorithms they use. This naturally leads us to ask what computers are capable of doing at their best and what their limits are. Which requires formalizing various definitions in computing.

This is exactly what happened in the early 20th century. Logicians & mathematicians were trying to formalize the foundations of mathematics through logic. One famous challenge based on this was the Entscheidungsproblem posed by David Hilbert and Wilhelm Ackermann. The problem asked if there exists an algorithm that can verify whether any mathematical statement is true or false based on provided axioms. Such an algorithm could be used to verify if any mathematical system is internally consistent. Kurt Gödel proved in 1931 that this problem could not be answered one way or the other through his incompleteness theorems.

Years later, Alan Turing and Alonzo Church proved the same through separate, independent means. Turing did so by developing Turing machines (called automatic machines at the time) and the Halting problem. Church did so by developing lambda calculus. Later on, it was proved that Turing machines and lambda calculus are mathematically equivalent. This led many mathematicians to theorize that computability could be defined by either of these systems. That in turn caused Turing and Church to make their thesis: every effectively calculable function is a computable function. In simpler terms, it states that any computation from any model can be carried out by a Turing machine or lambda calculus. To better understand the implications of the Church-Turing thesis, we need to explore the different kinds of computational machines.

Record-Sized Collision Between Black Holes Detected by Astronomers

Two black holes have collided in a merger that could revolutionize our understanding of black hole growth.

Named GW 231,123 after the date it was recorded on 23 November 2023, it’s the most massive black hole collision we’ve seen yet, resulting in an object heavier than 225 Suns.

Previously, the most massive black hole collision produced an object 142 times the mass of the Sun.

AI Is Heading For an Energy Crisis That Has Tech Giants Scrambling

The artificial intelligence industry is scrambling to reduce its massive energy consumption through better cooling systems, more efficient computer chips, and smarter programming – all while AI usage explodes worldwide.

AI depends entirely on data centers, which could consume three percent of the world’s electricity by 2030, according to the International Energy Agency. That’s double what they use today.

Experts at McKinsey, a US consulting firm, describe a race to build enough data centers to keep up with AI’s rapid growth, while warning that the world is heading toward an electricity shortage.

Sound of Earth’s Flipping Magnetic Field Haunts Again From 780,000 Years Ago

In 2024, researchers transformed readings of an epic upheaval of Earth’s magnetic field flipping 41,000 years ago into an eerie, auditory experience.

Now a team containing some of those same scientists has sonified an even earlier flip, from epochs ago.

The resulting cacophony is an unnerving translation of geological data on the Matuyama-Brunhes reversal, a switching of the planet’s magnetic poles that took place roughly 780,000 years ago.

Extreme Conditions of Early Universe Recreated in Collider Experiment

A team of researchers have made progress in understanding how some of the Universe’s heaviest particles behave under extreme conditions similar to those that existed just after the Big Bang.

A study published in Physics Reports provides new insights into the fundamental forces that shaped our Universe and continues to guide its evolution today.

The research, conducted by an international team from the University of Barcelona, the Indian Institute of Technology, and Texas A&M University, focuses on particles containing heavy quarks, the building blocks of some of the most massive particles in existence.

Atomic swap in morphine core structure leads to safer, non-rewarding opioid alternative

One of the greatest revolutions in the field of pain medication was the isolation of morphine from the opium poppy in the 19th century. Morphine molecules act as painkillers by attaching themselves to the µ-opioid receptor (MOR) in the central nervous system and blocking the brain from sending pain signals to the rest of the body. This potent opioid analgesic also has side effects such as constipation, respiratory depression, and even serious addiction problems.

A new study published in the Proceedings of the National Academy of Sciences has found that a single heavy atom replacement in the morphine core structure can transform its pharmacological behavior, resulting in reduced and no evidence of reward behavior—a key component of addiction tendencies—even at high doses.

Based on the insight that core-atom changes to the drug molecule may exhibit biological effects distinct from the parent compound, the researchers developed a 15-step total synthesis of a morphine derivative where an oxygen atom in the E-ring is replaced with a methylene (CH2) group and called the new derivative carbamorphine.

Astronomers perform a comprehensive study of two open clusters

Using the TUBITAK National Observatory and ESA’s Gaia satellite, astronomers from the Istanbul University in Turkey and elsewhere have conducted comprehensive observations of two open clusters, namely: Czernik 41 and NGC 1342. Results of the observational campaign, published July 7 on the arXiv preprint server, deliver important insights into the properties of these clusters.

Open clusters (OCs) are groups of stars formed from the same giant molecular cloud and loosely gravitationally bound to each other. Astronomers are interested in inspecting OCs in detail as such studies could be crucial for improving our understanding of the formation and evolution of our galaxy.

That is why a group of researchers led by Istanbul University’s Burçin Tanık Öztürk decided to take a closer look at two well-known OCs—Czernik 41, discovered in 1966, and NGC 1,342, dubbed the Stingray Cluster, which was identified by William Herschel in 1799. For this purpose, they employed the T100 telescope at the TUBITAK National Observatory in Turkey and analyzed the data from the Gaia satellite.

Childhood trauma shapes adult stress appraisal and mental health outcomes, research reveals

University of Leeds psychologists report that stress appraisal and perceived stress act as key conduits linking childhood trauma to adult depression, anxiety, defeat, and entrapment.

Childhood trauma affects nearly one third of young people in the United Kingdom. Early experiences of abuse or neglect have been associated with depression, anxiety, , and substance use later in life.

Exposure to multiple types of trauma has been linked to higher rates of suicidal thoughts and . Females who experience childhood sexual abuse can face substantially elevated risks of attempting suicide compared to peers without such histories.