Big news‚ everyone: the sausage catastrophe has been reproduced with tiny balls.Look. It’s a little-known fact in mathematics‚ but the more difficult your theorem is to prove‚ the sillier its name has to be. Take‚ for example‚ the fact that there is no nonvanishing continuous tangent vector field on even-dimensional n-spheres – or to use its common name‚ the hairy ball theorem. Or‚ hey‚ need an algorithm to determine whether a set of sections provides a basis for the Mordell–Weil abelian group of a given elliptic surface? Why not try the Cox-Zucker machine! And let’s not even start on all the theorems and concepts named after Tits.We tell you this only to make it clear that despite sounding like the kind of weird punk band your parents used to listen to in 1976‚ Sphere Packing and the Sausage Catastrophe are actually a big deal in math circles – and a recent paper confirming a long-suspected result on the problem is genuinely impressive and important.Indeed‚ “the theory of infinite packings of convex bodies‚ in particular‚ lattice packings of spheres is a fundamental and classical topic in mathematics‚” wrote mathematicians Martin Henk and Jörg Wills‚ who were not involved in this new result‚ back in 2020. “[It] plays a role in various branches of mathematics [such] as number theory‚ group theory‚ geometry of numbers‚ algebra‚ and [it] has numerous applications to coding theory‚ cryptography‚ crystallography and more‚” they noted.So‚ what exactly is this problem that has such wide applicability? Well‚ in a word: balls.More specifically‚ it’s this: what is the most efficient way to pack balls? It sounds like an easy question – all the hardest ones do – but it has evaded a definite answer for centuries. Even the solutions we do have seem weirdly overcomplicated: for instance‚ we’ve known since 2005‚ and been pretty sure since 1611‚ that the best way in three dimensions is to use the “cannonball” method – yes‚ like how pirates used to do – but only if you have an infinite number of them. Which‚ let’s face it‚ even the saltiest of seadogs did not.Unfortunately‚ that’s the kind of nonsense you end up with when you let mathematicians tackle a simple problem – which is why this new result came from a group of physicists‚ instead. “In reality‚ however‚ all packings are inherently finite‚ which means that their extension is limited in space‚” the researchers write (classic non-mathematical starting point there). “This raises the question of what is the most efficient way to pack equally-sized spheres in either a container with a predefined shape‚ or inside a flexible container like the smallest convex hull that encloses the spheres.”And unlike Kepler’s clusters of cannonballs‚ the answer is totally unintuitive: it’s a sausage. At least‚ at first.“One of my students observed a linear packing‚ but it was quite puzzling‚” Hanumantha Rao Vutukuri‚ assistant professor in experimental physics at the University of Twente‚ told New Scientist. His team hadn’t even been thinking about this Keplerian puzzler at the time; they were experimenting with putting spherical nanoscale particles inside microscopic containers known as vesicles.“We thought that there was some fluke‚ so he repeated it a couple of times and every time he observed similar results‚” Vutukuri said. “I was wondering‚ ‘why is this happening?’”Now‚ was it unexpected? Yes. But was it completely unpredictable? No – and in fact‚ it was predicted‚ by mathematician Fejes Tóth all the way back in 1975. Proving it‚ however‚ was a different story – and the team ran up against some challenges pretty early on in their experiments.“The vesicles kept rupturing with more than nine particles‚” said Marjolein Dijkstra‚ Professor of Soft Condensed Matter at Utrecht University‚ in a statement. “This prevented us from testing how the stacking of particles would change if we added more than nine.”Luckily‚ we have something Kepler never had: computers. Faced with these burst vesicles‚ the researchers moved instead to computer simulations of the problem‚ investigating the most efficient way to pack now up to 150 balls.And it’s a good thing they went so high. Had they stopped at 55‚ they would only have obtained half an answer – because at 56‚ something catastrophic happened.Literally. It’s called the “sausage catastrophe.” It’s when “a sudden transition in the packing density occurs from a linear to a cluster arrangement‚ where the coordinates of the particles extend in all three dimensions‚” the paper explains – in other words‚ all of a sudden‚ it becomes more efficient to make a smush of balls‚ like Kepler did‚ than a line.That‚ ultimately‚ is why we should care about this weird problem. Not just because it’s fun and provides closure to Kepler’s pirate friends‚ but because it shows that experiments really can have an important place in math.“Our systematic investigation of these clusters with various shapes has allowed us to directly prove‚ with a practical approach inspired by the physics of colloids‚ the existence of previously unidentified clusters that exhibit a packing efficiency that is superior to the sausage configuration‚” the team writes. “Nevertheless‚ it remains to be determined whether mathematical proofs can be developed for the packing of these clusters and for the entire Fejes Tóth conjecture.” “Finite sphere packing is still an open and intriguing problem‚” they conclude. “We believe that our work can serve as a catalyst for further research in this direction.”The paper is published in the journal Nature Communications.

If you grab a jar of honey out of the kitchen cupboard (or your jar of royal honey out of the bedside table)‚ you’ll be able to see an expiration date stamped across the packaging. But does honey ever really “expire”? And if not‚ why?The components that make up honey are‚ crucially‚ nothing to do with bee vomit. In fact‚ despite being made up of at least 181 substances‚ honey is essentially just mostly sugar and water. While its exact composition differs depending on bee species‚ plants‚ and even weather‚ the inclusion of gluconic acid and other organic acids makes honey – you guessed it – acidic. As well as being mildly acidic‚ honey also has antibacterial properties which help prevent the growth of bacteria. So‚ the answer to the question “does honey ever go bad?” is no‚ not really. As long as you store your honey in the right conditions‚ it can remain delicious for a very very long time. Honey’s unique ability to stand the test of time has made it a popular ingredient for centuries‚ with records of it being used as far back as 5500 BCE.What makes honey last?Honey is produced in the bee’s honey sac‚ or honey stomach‚ and it gets its flavor from the type of flower the nectar is collected from. The honey sac is a specialized organ that works as a store for nectar or water‚ enabling the bee to safely transport it back to the hive. Once home‚ the bee will regurgitate the nectar in a process called trophallaxis‚ and begin adding sugar-inverting enzymes to the nectar to create honey. As bees add the enzyme glucose oxidase to the nectar‚ which converts sugar into gluconic acid‚ hydrogen peroxide is also produced. The presence of hydrogen peroxide – a chemical that is also used to clean wounds‚ although that is no longer recommended – contributes to the antibacterial properties of honey. Today‚ medical-grade honey is even used to treat drug-resistant bacterial infections.This unique composition‚ and comparatively low water content‚ is what makes honey impervious to the growth of bacteria and fungi. Its high sugar content (honey has a carbohydrate content of around 80 percent) increases the osmotic pressure of honey‚ causing water to be drawn out of microbe cells‚ halting their growth and reproduction. Additionally‚ the low water content prevents fermentation and breakdown of the honey.While it has been thought that honey’s acidity‚ with an average pH of 3.9‚ contributed to its longevity‚ studies comparing honey with low and high acidity levels found no significant difference in antimicrobial activity.Can honey ever go off?While the expiration date you see on the packaging of honey is largely there as a manufacturing requirement and to help keep track of produce‚ there are still a few ways honey can turn against you.Avoiding moisture is the key to keeping your honey in good shape. Always store it in an air-tight container in a dry area to prevent contact with moisture that could allow microorganisms to multiply.Additionally‚ as honey is a natural product‚ there is always a slight risk of contamination from dust‚ dirt‚ and the bees’ digestive tract. However‚ these contaminants are generally found in very low quantities and the composition of honey should prevent any growth of bacteria from contaminants.Honey can also be considered toxic if the pollen has been collected from flowers containing plant toxins. “Mad honey” is made from the nectar of rhododendrons and‚ despite claims of having medicinal properties‚ can cause nausea‚ hallucinations‚ and even death if consumed in high quantities.But while the risk factors surrounding consuming old honey remain very low‚ it’s likely you will see your honey crystalize at some point. Crystallization in honey happens as the sugar and water separate‚ and the process is sped up when the honey is kept at colder temperatures. Crystalized honey will appear paler‚ opaque‚ and harder than regular honey. It also releases more water during the crystallization process‚ slightly increasing the risk of fermentation.So‚ as long as you take good care of your honey‚ it could potentially outlive you – so better start considering who gets the honey inheritance.All “explainer” articles are confirmed by fact checkers to be correct at time of publishing. Text‚ images‚ and links may be edited‚ removed‚ or added to at a later date to keep information current.  The content of this article is not intended to be a substitute for professional medical advice‚ diagnosis‚ or treatment. Always seek the advice of qualified health providers with questions you may have regarding medical conditions.  

Palworld‚ the new survival and crafting game which has surpassed Counter-Strike 2‚ Lost Ark‚ Dota 2‚ and myriad others in terms of Steam player count records‚ will be investigated by The Pokemon Company amid ongoing discussions regarding potential copyright infringement. Palworld‚ affectionately known as ‘Pokemon with guns‚’ allows players to capture creatures and use them for a variety of tasks and battles. Players and critics have observed possible similarities between the designs of Palworld’s creatures‚ called Pals‚ and fan-favorite Pokemon. The Pokemon Company‚ established by Nintendo‚ Game Freak‚ and Creatures‚ says it will take “appropriate measures” regarding any infringement on Pokemon's intellectual property. Continue reading Palworld is going to be investigated by The Pokemon Company MORE FROM PCGAMESN: Palworld pals‚ Palworld review‚ Palworld system requirements

What is the Homeworld 3 release date? Homeworld is back and this time Blackbird Interactive and Gearbox Publishing are at the helm of the project and aiming to deliver the long-awaited experience that meets fans’ expectations. What have we seen so far from the game and what can you expect from it once it releases? Announced at PAX West 2019‚ Homeworld 3 quickly met its crowdfunding goal by one hundred million percent after Gearbox Publishing only asked for $1. With fans of the series waiting patiently for so long for their backer rewards and the next entry in the series‚ the game has seen some quiet periods and a delay‚ which has stalled excitement somewhat over the last year or so. But‚ with the release date finally on the horizon‚ expect to see a lot more on top of what we already know about what will hopefully be one of the best PC games of 2024. Continue reading Homeworld 3 release date‚ gameplay‚ trailers‚ and more MORE FROM PCGAMESN: Homeworld 3 release date‚ Best strategy games‚ Homeworld 3 system requirements

Diablo 4 Season 3 isn’t off to the best start‚ with Blizzard already responding to widespread complaints with its new offering just days after launch. As even its biggest and most enthusiastic streamers‚ and its wider player base as a whole‚ express disappointment with the trap-filled Season of the Construct‚ game director Joe Shely says the team is already planning improvements. Continue reading Blizzard admits Diablo 4 Season 3 “can be improved” after a bad start MORE FROM PCGAMESN: Diablo 4 builds‚ Diablo 4 review‚ Diablo 4 classes

Can You Smell What the Rock Is Cooking? Dwayne Johnson Has Had a Great Week and He's Cooking Up SUCCESS

Nintendo has released several special edition Joy-Con controllers to pair with specific fandoms in the past‚ including Pokemon‚ Animal Crossing: New Horizons‚ and The Legend of Zelda exclusive variants. Now‚ the Super Mario Brothers are taking a backseat as Princess Peach steals the spotlight for a Joy-Con colorway.

Pocketpair’s ‘Pokemon with Guns’ game has taken off much how you might expect a Pokemon with Guns game to. It’s a roaring success‚ at this moment the most-played game on Steam‚ according to SteamCharts‚ and it seems that people are digging its curious combination of base-building‚ combat‚ and exploration.

California Crazy: Woman Who Stabbed Date 108 Times—Killing Him—Gets Only 100 Hours of Community Service

The British Museum has released the latest annual report of the Portable Antiquities Scheme (PAS) which marks that 2022 had the highest number of Treasure cases (1‚378) ever reported in a single year. The report highlights some of the most stand-out Treasure finds in 2022‚ including an intriguing Iron Age hoard of gold coins found inside a hollow flint globule. The hoard was discovered on New Year’s Day 2023 in East Garston‚ West Berkshire. It consists of 26 Iron Age gold staters found inside a naturally-occurring hollow flint ball. The staters are of the “Savernake Wreaths” type‚ produced in East Wiltshire in the late Iron Age (50-20 B.C.). They feature a stylized design of crossed wreaths on one side and a horse at gallop facing right with a spiral above it and a wheel below. Hollow nodules of flint are commonly found in the upper strata of the Chalk‚ a limestone geological layer in southern and eastern England formed between 90 million and 66 million years ago. Before it hardened‚ the Chalk was mud on the sea floor. Dissolved silica filled gaps in the compacting mud‚ forming nodules sometimes around sea creatures like urchins and cockles that left hollows inside the nodules once they decayed. This is not the first coin hoard found in a flint nodule. Iron Age coins cached inside nodules have been found in Kent‚ Oxfordshire and Wiltshire. Using hollow flint balls as containers for gold coins appears to have been an established practice in Iron Age England. The nodules often have natural holes and openings making them handy piggy banks even unmodified. Sometimes a hole would be enlarged to fit the coins more easily. The East Garston flint nodule had no natural hole; a piece deliberately broken to create the opening. The staters and flint ball were declared Treasure‚ as all coins hoards have been since the Treasure Act was passed in 1996. Under the terms of that legislation‚ the definition of Treasure in the UK has been two or more prehistoric objects made of metal‚ any metallic object composed of at least 10% silver or gold by weight that is at least 300 years old and coins in hoard 300 years or older. Once an object is determined by a coroner’s court to be Treasure‚ it becomes property of the crown and is offered to a local museum for the amount of its assessed value. The money is then split between the finder and landowner. This definition has allowed exceptionally unique and important archaeological artifacts like the Ryedale Hoard‚ the Crosby Garret helmet‚ the Roman licking dog and the Allectus aureus to fall through the cracks. Despite being undisputed and irreplaceable archaeological treasures‚ they were not Treasure according to the short-sighted legal definition and were therefore returned to the finders who then sold them to the highest bidder. In 2019‚ the UK’s Department for Digital‚ Culture‚ Media and Sport announced a plan to revise the Treasure Act to plug the loophole. The updated language would define Treasure as any object that is at least partially metal‚ at least 200 years old and is deemed to provide “exceptional insight” into British or regional history because of its rarity‚ location or connection to a historical personage or event. After five long years‚ the revision is finally about to take effect. The new criteria will apply to all objects found after July 30th‚ 2023.