From John o' Groats to Land's End (1) – that proverbial phrase covers the entire island of Great Britain. Here is a novel one: from the Bells But & Ben in Yell to the Witchball in The Lizard. That's the northernmost and southernmost pub in Britain, respectively. This map shows the shortest route between both – and every other pub in the UK, all 24,725 of them. That is one massive pub crawl.
But why? Computational mathematics, is why. This monster of a map is a solution to a cartographic conundrum called the Travelling Salesman Problem (2).
Suppose you are a salesman presenting your wares at several locations today. The problem: work out the shortest route between all, taking into account that you need to start from home and arrive back there at the end of the day. For a small number of locations, the solution to that problem usually is self-evident. Add enough locations, and the solution becomes more difficult. Difficult enough for a manual to be published in 1832 called Der Handlungsreisende, proposing a number of routes for salesmen travelling through Germany and Switzerland.
The solutions it proposed were based on experience, but the Travelling Salesman Problem (TSP) tantalised scientists, who sought to formulate a universal answer. The first to come to grips with the problem was the 19th-century Irish mathematician W.R. Hamilton, who developed the icosian game, the purpose of which is to find a Hamiltonian cycle in a dodecahedron (cf. inf.): a circuit that starts and ends at the same point, and visits all other points only once (3).
Another important TSP theorist was Viennese mathematician Karl Menger, who in the 1930s conceded that
“of course, this problem is solvable by finitely many trials, but rules which would push the number of trials below the number of permutations of the given points are not known. The rule that one first should go from the starting point to the closest point, then to the point closest to this, etc., in general does not yield the shortest route”.
As Menger states, the easiest solution to the TSP is to simply to try all options. But even for a relatively low number of locations, the number of variables is enormous – for just 10 cities there are over 180,000 combinations, for example.
But a systematic solution remains elusive even today, as computers are currently able to calculate solutions for millions of points only to within 2% to 3% of the optimal result (4).
The TSP has many useful applications, from finding the shortest mailman routes to devising the optimal sequence to drill holes in circuit boards, and even calculating the easiest way for Santa to complete his annual one-night tour of all the chimneys in the world. Perhaps the most important consequence of the TSP is that there are no known algorithms to crack the codes on which we rely to keep our data secure.
Finding the shortest route between all pubs in Great Britain may not have figured high on the list of TSP issues to be solved, but solved it now has been, thanks to the Faculty of Mathematics at the University of Waterloo in Canada.
They attacked the TSP by mapping out the shortest-possible walking tour through the pubs of the United Kingdom, or as they so scientifically called the project: UK24727, after the number of pubs (5) involved. Some stats:
This line drawing conveys the route of the tour, which also includes ferry excursions off the British mainland for pub tours in the Hebrides, Orkney and Shetland islands, the isle of Man and Northern Ireland.
The entire map, with a Google Maps markers for each of the pubs, gives the impression that most of Britain is covered by an unbroken canopy of red balloons – darker areas indicating a concentration of balloon ridges, where the greater density of pubs suggests the presence of large cities.
Apart from solving a mathematical problem, the map also has an obvious practical use, for planning your next pub crawl. Attempting the entire route is not recommended, but zoom in to certain areas or the cities listed in the menu on the right, and plot your next excursion.
Like this drinking trip of the Hebrides: arrive by ferry from Oban, slake your thirst at the Am Politician in South Uist, wet your whistle at the Langass Lodge in Loch Eport, polish your pint at Harmersay House in Lochmaddy and get one for the road in the Carlton at Stornoway, before jumping on the ferry back to the mainland at Ullapool (where you can continue indulging at the Ceilidh Place).
Or why not find the watering holes closest to the UK's other two extremities: have a session the Black Cat in Belleek, the westernmost pub in the realm, and take in spirits at the Royal Falcon in Lowestoft, probably the easternmost pub – there are quite a few bunched together in that area, so you might have to visit a few more.
Visit the legendary watering holes of London in the time-saving succession devised by these thirsty mathematicians: make your way from De Hems to the French House via the Golden Lion and then on to... wait, weren't we going in the other direction? Doesn't matter: thanks to this Hamiltonian cycle, we'll end up here again eventually.
Having devised the world’s longest pub crawl, the TSP team at Waterloo University is gearing up for the next challenge: sending their putative salesman on the shortest possible tour past all 49,603 places listed in the U.S. National Register of Historic Places. “This problem is quite a beast”, they admit.
“We currently have a tour of length 350,201,525 meters. That is a little less than the distance to the moon. But we don't know if this is actually the shortest tour. There might possibly be a tour that is 196 meters shorter than our tour. Ouch! Close is just not good enough”.
Find the entire map here. Warning: loads slowly! For more information on the UK pub crawl, and other road-TSP projects covering 120 German cities, 50 U.S. landmarks and others, see the TSP page at the University of Waterloo’s Mathematics Faculty. Many thanks to Joel Winten and Folkard Wohlgemuth for sending in this map.
Strange Maps #818
Got a strange map? Let me know at strangemaps@gmail.com.
(1) John o' Groats, in Scottish Gaelic Taigh Iain Ghròt, is a village of 300 at the northern tip of the Scottish mainland. It is the northernmost inhabited place in Great Britain. Dunnet Head, about fifteen miles (24 km) to the east, is the northernmost place per se. John o' Groats was named after Jan de Groot, a Dutchman who operated a ferry from here to Orkney around the year 1500.
Land's End, in Cornish Penn an Wlas, is a headland and holiday resort at the western tip of Britain (7), on the Penwith peninsula in Cornwall. It is about 33 miles (53 km) east of Lizard Point, Britain's southernmost extremity. The 838 miles (1,349 km) trip between John o' Groats and Land's End is the longest one possible between two inhabited places in Britain.
(2) Or in this case, the Travelling Alesman Problem.
(3) Related to the Seven Bridges of Königsberg problem, proven by Euler to be unsolvable. More on that at #536.
(4) For actual travelling salesmen, not the theoretical ones dreamt up by Hamilton, Menger e.a., the TSP is even more complex, for distance is only one of the variables; the more important ones are time and money: How long does it take to get anywhere, and how much does it cost? For example, is it worth it to take the plane instead of the car to get from A to B and C and back to A again? That depends on whether the value of the time saved outweighs the value of the extra money spent.
(5) Since the exact number of pubs fluctuates due to closures and openings of various establishments, the study was based on the 24,727 pubs as listed in on the Pubs Galore website.
(6) I.c. the route connecting the 200 Tesla superchargers in the United States, a road-TSP problem solved by Mortada Meyhar. Below his map of the Travelling Tesla Salesman.
(7) Actually, the westernmost point of England, but not of Britain. As reader Kevin Jones points out, "the most westerly point of mainland island of Great Britain is Corrachadh Mòr, only 0.5 degree further west than Land's End. If you are ever in Scotland, it is wonderful place to visit, with its views over the islands of the Inner Hebrides. The geology is very interesting, it being a remnant of an igneous complex from the splitting of the North Atlantic about 60 million years ago".
U.S. Navy ships
The U.S. Navy controls patents for some futuristic and outlandish technologies, some of which, dubbed "the UFO patents," came to light recently. Of particular note are inventions by the somewhat mysterious Dr. Salvatore Cezar Pais, whose tech claims to be able to "engineer reality." His slate of highly-ambitious, borderline sci-fi designs meant for use by the U.S. government range from gravitational wave generators and compact fusion reactors to next-gen hybrid aerospace-underwater crafts with revolutionary propulsion systems, and beyond.
Of course, the existence of patents does not mean these technologies have actually been created, but there is evidence that some demonstrations of operability have been successfully carried out. As investigated and reported by The War Zone, a possible reason why some of the patents may have been taken on by the Navy is that the Chinese military may also be developing similar advanced gadgets.
Among Dr. Pais's patents are designs, approved in 2018, for an aerospace-underwater craft of incredible speed and maneuverability. This cone-shaped vehicle can potentially fly just as well anywhere it may be, whether air, water or space, without leaving any heat signatures. It can achieve this by creating a quantum vacuum around itself with a very dense polarized energy field. This vacuum would allow it to repel any molecule the craft comes in contact with, no matter the medium. Manipulating "quantum field fluctuations in the local vacuum energy state," would help reduce the craft's inertia. The polarized vacuum would dramatically decrease any elemental resistance and lead to "extreme speeds," claims the paper.
Not only that, if the vacuum-creating technology can be engineered, we'd also be able to "engineer the fabric of our reality at the most fundamental level," states the patent. This would lead to major advancements in aerospace propulsion and generating power. Not to mention other reality-changing outcomes that come to mind.
Among Pais's other patents are inventions that stem from similar thinking, outlining pieces of technology necessary to make his creations come to fruition. His paper presented in 2019, titled "Room Temperature Superconducting System for Use on a Hybrid Aerospace Undersea Craft," proposes a system that can achieve superconductivity at room temperatures. This would become "a highly disruptive technology, capable of a total paradigm change in Science and Technology," conveys Pais.
High frequency gravitational wave generator.
Credit: Dr. Salvatore Pais
Another invention devised by Pais is an electromagnetic field generator that could generate "an impenetrable defensive shield to sea and land as well as space-based military and civilian assets." This shield could protect from threats like anti-ship ballistic missiles, cruise missiles that evade radar, coronal mass ejections, military satellites, and even asteroids.
Dr. Pais's ideas center around the phenomenon he dubbed "The Pais Effect". He referred to it in his writings as the "controlled motion of electrically charged matter (from solid to plasma) via accelerated spin and/or accelerated vibration under rapid (yet smooth) acceleration-deceleration-acceleration transients." In less jargon-heavy terms, Pais claims to have figured out how to spin electromagnetic fields in order to contain a fusion reaction – an accomplishment that would lead to a tremendous change in power consumption and an abundance of energy.
According to his bio in a recently published paper on a new Plasma Compression Fusion Device, which could transform energy production, Dr. Pais is a mechanical and aerospace engineer working at the Naval Air Warfare Center Aircraft Division (NAWCAD), which is headquartered in Patuxent River, Maryland. Holding a Ph.D. from Case Western Reserve University in Cleveland, Ohio, Pais was a NASA Research Fellow and worked with Northrop Grumman Aerospace Systems. His current Department of Defense work involves his "advanced knowledge of theory, analysis, and modern experimental and computational methods in aerodynamics, along with an understanding of air-vehicle and missile design, especially in the domain of hypersonic power plant and vehicle design." He also has expert knowledge of electrooptics, emerging quantum technologies (laser power generation in particular), high-energy electromagnetic field generation, and the "breakthrough field of room temperature superconductivity, as related to advanced field propulsion."
Suffice it to say, with such a list of research credentials that would make Nikola Tesla proud, Dr. Pais seems well-positioned to carry out groundbreaking work.
A craft using an inertial mass reduction device.
Credit: Salvatore Pais
The patents won't necessarily lead to these technologies ever seeing the light of day. The research has its share of detractors and nonbelievers among other scientists, who think the amount of energy required for the fields described by Pais and his ideas on electromagnetic propulsions are well beyond the scope of current tech and are nearly impossible. Yet investigators at The War Zone found comments from Navy officials that indicate the inventions are being looked at seriously enough, and some tests are taking place.
If you'd like to read through Pais's patents yourself, check them out here.
Laser Augmented Turbojet Propulsion System
Credit: Dr. Salvatore Pais
More than half of 18 to 25 year-olds in the workforce are considering quitting their job. And they're not the only ones.
In a report called The Next Great Disruption Is Hybrid Work – Are We Ready?, Microsoft found that as well as 54% of Generation Z workers, 41% of the entire global workforce could be considering handing in their resignation.
Similarly, a UK and Ireland survey found that 38% of employees were planning to leave their jobs in the next six months to a year, while a US survey reported that 42% of employees would quit if their company didn't offer remote working options long term.
New work trends
Based on surveys with over 30,000 workers in 31 countries, the Microsoft report – which is the latest in the company's annual Work Trend Index series – pulled in data from applications including Teams, Outlook and Office 365, to gauge productivity and activity levels. It highlighted seven major trends, which show the world of work has been profoundly reshaped by the pandemic:
- Flexible work is here to stay
- Leaders are out of touch with employees and need a wake-up call
- High productivity is masking an exhausted workforce
- Gen Z is at risk and will need to be re-energized
- Shrinking networks are endangering innovation
- Authenticity will spur productivity and wellbeing
- Talent is everywhere in a hybrid world
"Over the past year, no area has undergone more rapid transformation than the way we work," Microsoft CEO Satya Nadella says in the report. "Employee expectations are changing, and we will need to define productivity much more broadly – inclusive of collaboration, learning and wellbeing to drive career advancement for every worker, including frontline and knowledge workers, as well as for new graduates and those who are in the workforce today. All this needs to be done with flexibility in, when, where and how people work."
Organizations have become more siloed
While the report highlights the opportunities created by increased flexible and remote working patterns, it warns that some people are experiencing digital exhaustion and that remote working could foster siloed thinking. With the shift to remote working, much of the spontaneous sharing of ideas that can take place within a workplace was lost. In its place are scheduled calls, regular catch-ups and virtual hangouts. The loss of in-person interaction means individual team members are more likely to only interact with their closest coworkers.
"At the onset of the pandemic, our analysis shows interactions with our close networks at work increased while interactions with our distant network diminished," the report says. "This suggests that as we shifted into lockdown, we clung to our immediate teams for support and let our broader network fall to the wayside. Simply put, companies became more siloed than they were pre-pandemic."
Burnout or drop out
One of the other consequences of the shift to remote and the reliance on tech-based communications has been the phenomenon of digital burnout. And for those who have most recently joined the workforce, this has been a significant challenge.
The excitement of joining a new employer, maybe even securing a job for the first time, usually comes with meeting lots of new people, becoming familiar with a new environment and adapting to new situations. But for many, the pandemic turned that into a daily routine of working from home while isolated from co-workers.
"Our findings have shown that for Gen Z and people just starting in their careers, this has been a very disruptive time," says LinkedIn Senior Editor-at-Large, George Anders, quoted in the report. "It's very hard to find their footing since they're not experiencing the in-person onboarding, networking and training that they would have expected in a normal year."
But it is perhaps the data around quitting that is one of the starkest indications that change is now the new normal. Being able to work remotely has opened up new possibilities for many workers, the report found. If you no longer need to be physically present in an office, your employer could, theoretically, be located anywhere. Perhaps that's why the research found that "41% of employees are considering leaving their current employer this year".
In addition to that, 46% of the people surveyed for the Microsoft report said they might relocate their home because of the flexibility of remote working.
A hybrid future
In looking for ways to navigate their way through all this change, employers should hold fast to one word, the report says – hybrid. An inflexible, location-centred approach to work is likely to encourage those 41% of people to leave and find somewhere more to their tastes. Those who are thinking of going to live somewhere else, while maintaining their current job, might also find themselves thinking of quitting if their plans are scuppered.
But remote working is not a panacea for all workforce ills. "We can no longer rely solely on offices to collaborate, connect, and build social capital. But physical space will still be important," the report says. "We're social animals and we want to get together, bounce ideas off one another, and experience the energy of in-person events. Moving forward, office space needs to bridge the physical and digital worlds to meet the unique needs of every team – and even specific roles."
Bosses must meet challenges head on
Although the majority of business leaders have indicated they will incorporate elements of the hybrid working model, the report also found many are out of touch with workforce concerns more widely.
For, while many workers say they are struggling (Gen Z – 60%; new starters – 64%), and 54% of the general workforce feels overworked, business leaders are having a much better experience. Some 61% said they were 'thriving', which is in stark contrast to employees who are further down the chain of command.
Jared Spataro, corporate vice president at Microsoft 365, writes in the report: "Those impromptu encounters at the office help keep leaders honest. With remote work, there are fewer chances to ask employees, 'Hey, how are you?' and then pick up on important cues as they respond. But the data is clear: our people are struggling. And we need to find new ways to help them."
Reprinted with permission of the World Economic Forum. Read the original article.
