Latest news with #ChristopherMoore
Yahoo
11-07-2025
- Yahoo
Mathematicians Say There's a Number So Big, It's Literally the Edge of Human Knowledge
"Hearst Magazines and Yahoo may earn commission or revenue on some items through these links." Here's what you'll learn when you read this story: The Busy Beaver number, or BB(n), represents a mathematical problem that tries to calculate the longest possible run-time of a Turing machine recording 1s and 0s on an infinitely long tape for various sets of instructions called states. While the first three BB(n)s equal 1, 6, and 21, respectively, it takes 107 steps to get to BB(4), and BB(5) produces a staggering 17 trillion possible Turing machines with a 47,176,870 steps being the answer. Now, as mathematicians attempt to wrap their minds around answer BB(6), they're beginning to realize that even expressing the unfathomably large number, likely bigger than the number of atoms in the universe, is itself a problem. For most people, the term 'busy beaver' brings to mind a tireless worker or (for the biologists among us) an absolutely vital ecosystem engineer. However, for mathematicians, 'busy beaver' takes on a similar-yet-unique meaning. True to the moniker's original intent, the idea represents a lot of work, but it's work pointed at a question. As computer scientists Christopher Moore puts it in a video for Quanta Magazine, 'What's the longest, most-complicated thing [a computer] can do, and then stop?' In other words, what's the longest function a computer can run that does not just run forever, stuck in an infinite loop? The solution to this question is called the Busy Beaver number, or BB(n), where the n represents a number of instructions called 'states' that a set of computers—specifically, a type of simple computer called a Turing machine—has to follow. Each state produces a certain number of programs, and each program gets its own Turing machine, so things get complicated fast. BB(1), which has just 1 state, necessitates the use of 25 Turing machines. For decades, many mathematicians believed that solving the Busy Beaver number to four states was the upper limit, but a group of experts managed to confirmed the BB(5) solution in 2024 (on Discord, of all places). Now, participants in that same Busy Beaver Challenge are learning fascinating truths about the next frontier—BB(6)—and how it just might represent the very edge of mathematics, according to a new report by New Scientist. First, a brief explanation. The aforementioned BB(1), which is the simplest version of the BB(n) problem, uses just one set of rules and produces only two outcomes—infinitely moving across the tape, or stopping at the first number. Because 1 is the most amount of steps that any of the 25 Turing machines of BB(1) will complete before finishing its program (known as halting), the answer to BB(1) is 1. As the number of states increases, so do the steps and the number of Turing machines needed to run the programs, meaning that each subsequent BB(n) is exponentially more taxing to solve. BB(2) and BB(3) are 6 and 21 respectively, but BB(4) is 107 and takes seven billion different Turing machines to solve. Granted, many of these machines continue on indefinitely and can be discarded, but many do not. The Busy Beaver number was first formulated by the Hungarian mathematician Tiber Radó in 1962, and 12 years passed before computer scientist Allen Brady determined that BB(4) runs for 107 steps before halting. For decades, this seemed like the absolute limit of what was discernible, but then mathematicians solved BB(5) in 2024 after sifting through 17 trillion (with a t) possible Turing machines. The answer? An astounding 47,176,870 steps. Quanta Magazine has an excellent explainer about how this was achieved. But finally solving BB(5) presented the next obvious question: What about BB(6)? Of course, adding just one more rule makes the problem beyond super exponentially harder, as BB(6) is estimated to require 60 quadrillion Turing machines. 'The Busy Beaver problem gives you a very concrete scale for pondering the frontier of mathematical knowledge,' computer scientist Tristan Stérin, who helped start the Busy Beaver Challenge in 2022, told New Scientist. In a new post, anonymous user 'mxdys'—who was instrumental in finally confirming BB(5)—wrote that the answer to BB(6) is likely so unfathomably large that the number itself likely needs its own explanation, as it's likely too big to describe via exponentiation. Instead, it relies on tetration (written as, say, yx, as opposed to exponentiation's xy) in which where the exponent is also iterated, creating a tower of exponents. As Scott Aaronson, an American computer scientist who helped define BB(5), notes on his blog, that means 1510 can be thought of as '10 to the 10 to the 10 and so on 15 times.' As mxdys notes, BB(6) is at least 2 tetrated to the 2 tetrated to the 2 tetrated to the 9. One mathematician speaking with New Scientist said that it's likely that the number of all atoms in the universe would look 'puny' by comparison. While these large numbers boggle the mind, they also tell mathematicians about the limitations of the foundation of modern mathematics—known as Zermelo–Fraenkel set theory (ZFC)—as well slippery mathematical concepts like the Collatz conjecture. It's unlikely that mathematicians will ever solve BB(6), but if the Busy Beaver Challenge is any evidence, that fact likely won't stop them from trying. You Might Also Like The Do's and Don'ts of Using Painter's Tape The Best Portable BBQ Grills for Cooking Anywhere Can a Smart Watch Prolong Your Life?
News.com.au
30-06-2025
- News.com.au
Camper found alive after desperate three-day day search
A hiker who went missing on the NSW South Coast has been found safe after a large-scale three-day search. Christopher Moore, 38, was last seen about 10.30am on June 25 when he was dropped off on Twelve Mile Rd in Jerrawangala, about 32km south of Nowra, to begin a camping trip. He was expected to be picked up at the same location two days later but failed to arrive, prompting a large-scale search effort. Search teams had been scouring bushland in the Jerrawangala and Wandandian areas since Mr Moore was reported missing. The search resumed about 8.30am on Monday. Police confirmed Mr Moore was located in dense shrub off Twelve Mile Rd about 11.50am. Emergency crews assisted him in walking to safety. NSW Ambulance paramedics assessed Mr Moore at the scene and determined he was uninjured. He was taken to Shoalhaven Base Hospital for further monitoring.
Daily Mail
30-06-2025
- Daily Mail
BREAKING NEWS Desperate search for missing camper at Jerrawangala continues as authorities race against the clock
A desperate search for a missing camper who disappeared in NSW bushland has entered its third day. Christopher Moore, 38, failed to return home from a camping trip at Jerrawangala, about 32km south of Nowra, on Friday. He had been dropped off on Wednesday and did not arrive at his pick-up spot two days later. An urgent search was launched with authorities focusing their efforts around the Jerrawangala and Wandandian regions. South Coast Police, Police Rescue, and members of the SES, Polair, and NSW Rural Fire Service have all joined in on the search. Fears have been raised a low-pressure system could bring heavy rain and gale force winds and hamper the search on Tuesday. more to come
The Guardian
30-06-2025
- Climate
- The Guardian
Police expand search for missing hiker on NSW south coast ahead of forecast severe weather
Police and emergency services have expanded their search for a hiker missing on the New South Wales south coast after the Bureau of Meteorology issued a severe weather warning for the region. Christopher Moore was last seen on Wednesday at about 10.30am when he was dropped off for a solo camping trip at Twelve Mile Road in Jerrawangala about 30km south of Nowra. He was due to be picked up at the same location on Friday but when he did not arrive, his family contacted police, who began a search for the 38-year-old. 'All of the services SES, RFS, national parks, police rescue are all involved again today as they were yesterday,' the spokesperson said on Monday. 'We have additional resources today because the weather is supposed to turn a little bit for the next couple of days, so we have additional crews working to try and locate him'. The BoM warned that large parts of the NSW coast would be hit by gale-force winds and dangerous surf conditions from Tuesday evening. ⚠️Coastal Hazard Warning for Tues 1 force winds will produce large and powerful surf conditions from Seal Rocks to Batemans Bay, from Tues evening. Beach conditions will be dangerous, with possible erosion and damage. Other warnings current. Police and his family hold concerns for Moore's welfare. Moore was described as being of Caucasian appearance, about 180cm tall, of thin build with short light brown hair, a beard and a moustache. He was last seen wearing khaki and black pants and a khaki-coloured hooded jumper. Sign up to Afternoon Update Our Australian afternoon update breaks down the key stories of the day, telling you what's happening and why it matters after newsletter promotion Anyone with information was urged to contact Nowra police or Crime Stoppers on 1800 333 000.
ABC News
29-06-2025
- Climate
- ABC News
Search continues for missing hiker Christopher Moore in bushland near Nowra
Authorities are ramping up search efforts to find a missing bushwalker on the NSW south coast in "difficult terrain" ahead of forecast rainy conditions. Christopher Moore has not been seen since Wednesday morning after he was dropped off for a solo camping trip on Twelve Mile Road at Jerrawangala, south of Nowra. Mr Moore's family alerted police to his disappearance on Friday, after the 38-year-old failed to return to the same road to be picked up around midday. Chief Inspector David Cockram said the hiker was "experienced" and was believed to have adequate supplies with him, including thermal clothing, food and boots. "Despite that, we've had some cold conditions and we've definitely got concerns for his welfare." Search efforts to find Mr Moore started on Friday afternoon, with extensive multi-agency efforts continuing across the weekend. NSW Police has been aided by a helicopter, the Rural Fire Service and State Emergency Service, with many crews searching through the thick bushland on trail bikes. "We're doing anything we can provide to that search capacity to try and find this fellow," Chief Inspector Cockram said. The search has been conducted in a large area across difficult terrain in Jerrawangala National Park and around bushland near Wandandian. "You'd have to have some sort of experience, good provisions and good equipment to try and navigate through that area, particularly as a solo person," Chief Inspector Cockram said. "I think [Mr Moore] had intentions to go off track as well, which provides some further complications for us. Chief Inspector Cockram said authorities would put "more boots on the ground" on Monday morning ahead of expected wet weather in the region. The Bureau of Meteorology has forecast a medium chance of showers for Nowra, located 30km north of the search ground, on Monday evening, before more rainfall is expected from Tuesday to Friday. "If we're looking at a large amount of rain, that's definitely going to impact our ability to be on the ground," Chief Inspector Cockram said. "We're going to rip in [on Monday] and see what we can do with some additional resources."
