Gizmodo offers a challenging but rather intriguing primer on the nature of infinity—which is not a number itself or some threshold, unless posited as the point at which parallel lines verge together, and the idea that infinity is amenable to being doubled or tripled through a quantum mechanical demonstration that makes a classic thought experiment seem not so rarefied or cheeky.
In 1925, mathematician David Hilbert pondered the following brain-teaser: supposing there is a grand hotel with an infinite number of rooms which is always booked and has no vacancies, but a guest desperately begs in the lobby for a room for the night. The hotel staff can still oblige, despite the occupancy and the infinite inconvenience, since in a countable infinity, there is always a +1, by have the guest in room number one move into room number two, and so on. By a countable infinity, and there are several different types of infinities, Hilbert means an enumerated set, that one could walk the corridors counting off room after room—though one might never reach the end—and also room-service is not logically bamboozled as they know the new whereabouts of every visitor and N+1. Then suppose an infinitely large tour bus with an infinite number of guests pulls up in the parking lot. No problem still, says management, as everyone in an odd numbered could move to an even numbered one and the vacated rooms—bogglingly, free up accommodations for the infinite number of new arrivals. This shifting works, logically and in quantum states where vacancies are created, because the countable infinity—once taking on more guests, while still assigned to a numbered room, Hilbert’s Hotel becomes another sort of infinity—the kind that is innumerable, something that can’t be counted in a discrete way because there always room in between—like the number of points on a line—being infinite and a point being that which has no part, something dimensionless. Paradoxical things may appear only academic when first puzzled to their conclusions but it is pretty astounding and reassuring to find that there is potentially real application for these concepts.
Thursday, 5 November 2015
bellhop or to infinity and beyond
Wednesday, 4 November 2015
peacock throne
5x5
steckdose: a comprehensive overview of the world’s plugs and electrical sockets with some interesting historical background
swedish fish: arcade veteran Activison scoops up Candy-Crush maker
the adventures of harry mudd: Star Trek spin-offs that were never produced, via Neatorama
sequential hermaphroditism: one of the oldest trees in Europe is in parts changing genders
Tuesday, 3 November 2015
squadron 40 – diiiive!
catagories: ๐ฌ, holidays and observances, lifestyle
Monday, 2 November 2015
marrakesh express
There is a strange and tense notice being placed on the official announcement that Afghanistan stands ready to accept back all those newly-arrived deported from Germany, helping to alleviate a system already overburdened by deferring to refugees from more eminently dangerous war-zones.
The press seems to be deriding the declaration as if it were mock- charitableness and a mock-decision, citing past examples of the Afghan government extorting monies from Britain and Scandinavian countries in the form of a fund for reintegration—otherwise refusing to allow back its citizens whose asylum claims were denied, as if they had been radicalised by their abroad. Afghanistan, however, has offered no resistance and only caution that migrants should not be compelled into a second exile and careful measures should be instituted to those ends—with the additional burden of proof of country of origin, who’s posing as a Syrian hoping to garner more favourable treatment—and the whole discussion significantly began over a week hence when the Chancellor made a side trip during her visit to China and both governments implored Afghans not to undertake the journey, as their manpower and political will were needed back at home in order for the country to thrive. Obviously draining the ablest (since it takes some motivation and means to coordinate passage) is ultimately a disservice to one’s homeland. What do you think? Does this accord signal a shift in Germany’s welcome-policy, a refinement of responsibility or both?