Talk:2694: Königsberg

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Why would aluminum foil be valuable? I can see how it would be hard to produce at the time. But how would it be used and why would people of the time see a lot of value in it? 03:42, 5 November 2022 (UTC)

Good question, but I'm persuaded the novelty and scarcity of metallic aluminium would have made it plenty valuable among those already wealthy enough to recognize what it was. Prussia was wealthy and Königsberg was its largest port city back then, so probably the mayor would have been able. 03:49, 5 November 2022 (UTC)
Aluminium was very valuable - methods for its extraction from ore didn't exist in any useful form until much later. 03:55, 5 November 2022 (UTC)
Would scarcity be enough to make it valuable? Since nobody had this material back then, there wouldn't be any known applications for it. Compared to bringing e.g. a simple pocket calculator, a flashlight, a solar-powered e-book reader, etc. If an alien landed in my house and brought me some weird, shiny material that would be unable to build on earth, I wouldn't be too interested. But if they had some cool gadget or books full of alien information, I would immediately see its value. 04:05, 5 November 2022 (UTC)
At the time, there were few chemists who could have recognized what it was, but the Mayor of Königsberg would plausibly have been able to commission one. It likely would have taken months if not years, though. I guess if you have a time machine such details don't matter. 04:11, 5 November 2022 (UTC)
Bear in mind that platinum was once 'an inferior substance that got in the way of accumulating silver', and cobalt was the stuff that the underground spirits mischievously put in the way of those seeking copper. To different degrees, their attractiveness has increased since those times they were considered less than desirable.
But, for aluminium foil, I suspect it would have been like pineapples in English(/European?) stately circles... Not to be used for anything practical, but shown off (as long as it did not deteriote beyond a certain point), possibly there'd be money to be made in 'hiring it out' to decorate tables at fancy dinners (in carefully handled fragments, after the first few tearing incidents). L
“Not to be used for anything practical”: Well they could wrap their leftovers in it…
Before they put them in the fridge?  ;o)
Perhaps BBQing vegitables? 20:37, 5 November 2022 (UTC)
No doubt a natural philosopher or somesuch would give his eyeteeth to analyse the substance, but being so far beyond the ability to recreate (assuming they discovered what they might even need to do) it would take the bankrolling of an extremely rich patron to obtain permanent posession of some without obligation to return it to the social circuit situations. So easily destructed (I wonder if they'd discover thermite a hundred and more years early, before they ran out of potentially finely shredded aluminium?) or at least aesthetically denatured.
I suppose a screwed up ball of foil (carefully glued together internally, of all fragments still reobtainable) could be the end-game for the original roll, and a wonder it could still be (again, taking the "pineapple place" on the tables of the high and mighty, relatively untarnishing as it would be and gingerly some lucky few would be allowed to hold it and marvel at its sharp fragility and metallic lightness.
...or, in another destiny, perhaps it would be given to a master tailor, in order to (try to?) create some sartorial masterpiece for one or other monarch of the age. Not that I'm sure they'd be able to accomplish that properly (limited pre-offcut trials on how to attach it to underfelts/whatever and to somehow exploit its flexibility without exceeding its very low tolerance for shear-force damage). It'd be a story and a half, whatever happened to it! 05:38, 5 November 2022 (UTC)
"Aim for brevity while avoiding jargon." —Edsger Dijkstra 06:33, 5 November 2022 (UTC)
Re: wealth signaling via aluminum - When aluminum was first extracted, one of its main early uses was in jewelry. Victorian examples are still around and are not terribly rare. Miamiclay (talk) 20:33, 5 November 2022 (UTC)

Noting that "the citizens' old coffeehouse problem" (c.f. linked reference), originally of how to cross the bridges was never solved but instead proven by Euler to be insoluble. He did give a proof to satisfy those who had henceforth decided there perhaps could be no solution, but that necessarily postdates the initial issue that could not originally be solved, and which Euler (in turn) also did not solve. But how to rewrite this to everyone's satisfaction? I see a bit of a tussle of interpretation in the edit history over this. 13:50, 5 November 2022 (UTC)

Proving that a problem has no solution is still called solving it in math and logic. 15:34, 5 November 2022 (UTC)
That's solving the issue of the solution (if you've proved there is none), at the meta- level. It is described as a "negative resolution" in the primary wikilink, which adds another semantic complexity but at least points to what was proven. Right in its first paragraph. For the everyday reader that hasn't yet burrowed into the wikilink, and without in-depth knowledge of terminological scope, they shouldn't be given the wrong idea about what question was actually answered. And "We've solved it: there's no solution!" is not a particularly helpful reduction of this kind of outcome. 16:53, 5 November 2022 (UTC)
Ordinary usage by mathematicians and laypersons alike is that e.g. Wiles "solved" Fermat's last theorem, by proving no solutions exist. The AMS source has the same usage. 22:56, 5 November 2022 (UTC)
...ok, so looking at it myself, maybe this change removes both parties' objections. (Probably not, but perhaps a way towards a final rapprochement.) 17:02, 5 November 2022 (UTC)
Sure. That's fine. 22:56, 5 November 2022 (UTC)

I read somewhere (maybe some Martin Gardner book?) that nowadays in Koenigsberg (or Kaliningrad as it is called today) there IS an eight bridge. But I couldn't confirm it.-- 17:26, 5 November 2022 (UTC)

There's a link to the Google Maps aerial view in the map caption. 20:31, 5 November 2022 (UTC)

As the comic at face value is about city planning of Königsberg and features the Mayor of Königsberg and a map of Königsberg, I very much think that an explanation of what Königsberg is should be a part of an explanation of the comic. So I disagree with this edit and its summary. Also, what I have been taught about image captions is that they should explain what is seen in the image. The information that two bridges has been destroyed is already present in the comic explanation. —While False (museum | talk | contributions | logs | rights | printable version | page information | what links there | related changes | Google search | current time: 12:16) 17:46, 7 November 2022 (UTC)

(While you were writing that, I was writing this. Copied up from the "my text" bit of an edit-conflict verbatim as it definitely is stil relevent.)
About that... I agree with some editors that the caption isn't really where 'current status' geopolitical and infrastructure information should be. I also agree with other editors that it isn't nececessary for the Explanation (of which the image and its caption is technically part). So, how about... a Trivia section? Can be less cramped as well as heing auxiliarily informative about these things in a few (relatively) short points.
  • "Today, K. is known as ..., and is located in the modern-day...", plus
  • "Since that time <x> bridges were destroyed/removed, <detailed thus>, and <y> bridges have been built, <also detailed>", and maybe also
  • "Currently <...pedestrians can do this, vehicles can (only?) do that...>"..?
...but perhaps leave the map-link and add a tiny bit more, "...also see <maplink> or <Trivia-anchor>", in the caption itself.
For consideration, anyway. 18:02, 7 November 2022 (UTC)
Sure —While False (museum | talk | contributions | logs | rights | printable version | page information | what links there | related changes | Google search | current time: 12:16) 18:37, 7 November 2022 (UTC)