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June 23

Random chance, probability, and predictability

In chemistry, I once learned that the exact locations of the electrons are not known (and probably not important anyway), but the probability of finding the electron at a particular point can explain why something bonds with another. Then in statistics, I learned about probabilities, which then made me think of randomness. In a realistic setting, what is randomness? While in theory "random" means "everything is equally likely", how is this practically possible? If one writes a personal name on an index card and repeats the process for 50 index cards, each having an unique name, and then puts all the cards in a Black Box and shakes the Black Box, then it may seem random that a random card will be drawn, but in reality, the card at the top may be more likely to be drawn than the card at the bottom. Maybe "randomness" is the "unknown"? If one doesn't know or expect something, then it's "random"? Another case is when a teacher lists the students "randomly". Practically, the students may race to the teacher and line up. Whoever's first in line may just happen to be closest to the teacher to begin with or be the fastest person in the room. The last student in line may be the slowest person, or because he/she can't find any open spots, may be forced to be the last in line. At what point is something "random"? At what point is something "biased" or has some sort of tendency/correlation? 50.4.236.254 (talk) 00:37, 23 June 2017 (UTC)[reply]

This is trickier than it may appear. Probability and statistics of discrete events (i.e. probability of a 2 dice roll being a seven (1 in 6) verses a 2 (1 in 36)) is different than quantum location where the distribution is a fundamental construct of the particle. Temperature of a gas is the mean of the temperature of individual particles and processes like evaporative cooling and sublimation work on the principle that particles are discrete. An electron in the orbital is a completely different construct that is described in models as a distribution and probability but lacks discrete components that can be separated to define the distribution. It is not a collection of random individuals but the distribution is a fundamental part of the particle. --DHeyward (talk) 01:05, 23 June 2017 (UTC)[reply]

Randomness doesn't mean all results are equally likely. It means the next result can't be predicted from the previous result. Iapetus (talk) 11:59, 23 June 2017 (UTC)[reply]

There several definition of randomness, yours is one of them. "all results are equally likely" is another definition, perfectly legit provided (big caveat!) you have a correct definition of "result" (ie: equal chance for a dice to produce 1-6, which is correct, vs equal chance for a dice to produce 1 or not, which is not). Unfortunately those 2 definition do not means exactly the same. Gem fr (talk) 14:00, 23 June 2017 (UTC)[reply]

Your question is hard, and not solved. There are different definitions of randomness, that do not exactly overlap. A system perfectly deterministic, but chaotic and hence unpredictable ( n-body problem or Double pendulum for instance), can be said random because unpredictable, or NOT random because prefectly determinist.

I would recommend determinism and Bohr–Einstein debates for the famous "god don't play dice" quote and implications. Also maybe Hidden variable theory: obviously in your student example, there are hidden variables (proximity and sprinting abilities), so the order is not random, but pseudorandom. It could however be argued that those variable are themselves randomly distributed, meaning the result is random. But it is no longer, if the teacher is well aware of these abilities, meaning he actually choose the result, hence it is not random. When you think of all the things that make you shift back and forth between "it's random" and "it's not random", you end up at classical Antoine Augustin Cournot's definition of randomness (i just wonder why it is neither in his article nor randomness) « Encounter of two independent causal series ».

for instance : a first series of causes made you arrive somewhere, sometime; an other series made a bus arrive at the same place at the same time. The more common causes there are, the less random (the more biased) your encounter with the bus is. With enough knowledge of the causes, your encounter could be perfectly predicted (or explained afterward and then appear it HAD to happen), but would nonetheless stay random (according to this definition) provided they stay independent.

hope it helped, although it may rise more question than it answered Gem fr (talk) 14:00, 23 June 2017 (UTC)[reply]

Can wine and beer be used to clean stuff?

Rubbing alcohol is isopropyl alcohol. Drinking alcohol contains ethanol. What happens if flour (with added water) is left fermented on the kitchen counter for a very time and then the fermented liquid is used to make beer, which is then used to clean stuff? Will ethanol still work as effectively as isopropyl alcohol? Is it safer to use ethanol than isopropyl alcohol simply because you can ingest it safely? If you add a lemon wedge or slice to the ethanol solution, then will it smell like lemons too? 50.4.236.254 (talk) 00:53, 23 June 2017 (UTC)[reply]

Ethanol does make a good cleaner, beer and wine is usually only between 4-15% ethanol. The other stuff in beer and wine will make whatever you want to clean dirtier than before you started, defeating the purpose. Neutral spirits, such as vodka or moonshine can be used to clean things, though: [1]--Jayron 32 01:05, 23 June 2017 (UTC)[reply]

Even so, rubbing alcohol is usually 70% which is stronger than most vodkas, whiskeys, rums and so on.Sagittarian Milky Way (talk) 02:03, 23 June 2017 (UTC)[reply]

Isopropyl alcohol is more toxic to humans' central nervous system than ethanol but it's not that toxic. It'd take about a half shot to be toxic. Methanol is more toxic. Now that's some dangerous stuff. Even so, if the thing being cleaned is 50.4's mouth, using 70% isopropyl alcohol is a bad idea even if you spit it out immediately. The mouth will instantly desiccate and take days to heal. Alcoholic mouthwash is designed to not do that. Sagittarian Milky Way (talk) 02:03, 23 June 2017 (UTC)[reply]

"The mouth will instantly desiccate and take days to heal." Some people actually tried that before? 50.4.236.254 (talk) 03:50, 23 June 2017 (UTC)[reply]

Well at least the hard palate. Sagittarian Milky Way (talk) 03:55, 23 June 2017 (UTC)[reply]

"IPA causes rapid intoxication, so people sometimes drink it to get drunk. Other people use it to attempt suicide". What Is Isopropyl Alcohol Poisoning? Alansplodge (talk) 09:48, 23 June 2017 (UTC)[reply]

Some Russians told me it had been popular during Gorbachev's anti-alcohol campaign. Wnt (talk) 11:51, 23 June 2017 (UTC)[reply]

Sounds like you're describing this IPA. ←Baseball Bugs ^{What's up, Doc?} carrots→ 14:52, 23 June 2017 (UTC)[reply]

I'll stick to IPA if you don't mind. Alansplodge (talk) 09:07, 24 June 2017 (UTC)[reply]

I'm surprised no-one has mentioned Deglazing (cooking) where wine is used to dissolve the gunge off the pan after frying some meat, especially if the meat has been coated in a seasoning with flour. Dmcq (talk) 10:41, 23 June 2017 (UTC)[reply]

The ethanol I'm the wine had nothing to do with that process. You can deglaze with chicken broth or even straight water. It's simply the action of hot water the removes the brown bits. Being wine had nothing to do with the deglazing bit, you use wine because it tastes good.--Jayron 32 22:12, 23 June 2017 (UTC)[reply]

My experience is that a wine or something like it is much faster at the job than just water. Dmcq (talk) 23:31, 23 June 2017 (UTC)[reply]

And my experience is there is no difference. So we both lose.--Jayron 32 02:53, 24 June 2017 (UTC)[reply]

Well to check I have just now tried Google which knows everything with 'cleaning a pan' and the first entry it comes back with is http://www.apartmenttherapy.com/how-to-clean-burnt-pots-scorched-pans-140547 which advocates first putting water and vinegar in the pan and boiling it as the first step - so they are advocating putting something acid into the pan and wine is acid. They do say to put in baking soda after it has boiled and thats alkali, but the one thing they don't say is to just use water. Dmcq (talk) 10:47, 24 June 2017 (UTC)[reply]

Vinegar contains acetic acid, which is an acid. The difference between vinegar and wine is that vinegar is "sour wine". It has vin- in the name, which means "wine". Wine is an alcohol, which can act like an acid (donating a proton) or a base (receiving a proton). I suppose wine can be considered an "acid" if you compare it to pure water. 50.4.236.254 (talk) 14:28, 24 June 2017 (UTC)[reply]

Pinhole Camera

1. (Just to double check) Can a pinhole camera contain a lens element?

Assuming the answer is no, then:

2. Are these[2] really pinhole cameras? I can see a little glass-like reflection from little hole. And this site[3] sells what appears to be the cone-like tip of the camera, and it clearly contains a very large lens element.

Note that I'm not suggesting the seller is misrepresenting his product. Linguistically "pinhole camera" certainly covers all miniature cameras, regardless of operating principle. He has every right to sell it as a "pinhole camera". I'm just interested in learning about the operating principle behind these cameras. If they're not true (scientifically speaking) pinhole cameras then how come the front lens elements can be made so small? Is there a limit to how small the front lens elements can be before performance is unacceptably degraded? Scala Cats (talk) 01:16, 23 June 2017 (UTC)[reply]

Yes, diffraction. This is the same reason why a telescope lens has to be at least 115.8 millimeters wide to look as sharp as 20/20 vision at 60x magnification. Almost certainly not coincidentally, this is almost 60 times the width of the human pupil in the daytime. Sagittarian Milky Way (talk) 02:09, 23 June 2017 (UTC)[reply]

There are two completely different things that are called "pinhole cameras".

The first uses a pinhole instead of a lens. It is characterized by having everything in focus no matter how close or far it is, and by requiring a huge amount of light (typically full sunlight, fast film, and long exposures). Example: https://www.amazon.com/Ilford-Obscura-Pinhole-Camera-Only/dp/B00I9Z2PD8/

The second uses lenses, but configured in such a way that you can drill a pin-sized hole in a wall with a cone-shaped space behind it (there is a tool for that) and then take pictures of the inside of the room, hopefully without anyone noticing the pinhole your camera is looking through. Example: https://www.amazon.com/Vanxse-Pinhole-Security-Microphone-Surveillance/dp/B012K4VP5W/

--Guy Macon (talk) 03:10, 23 June 2017 (UTC)[reply]

It may not count as "one camera", but a Schlieren photography system includes a pinhole and at least one lens. (File:Strioscopie.jpg is clearer than the picture in en-wp, even if you do not understand French.) Tigraan^{Click here to contact me} 09:56, 23 June 2017 (UTC)[reply]

"The second uses lenses" That's what my first question is getting at. Do those tiny cameras that use lenses actually qualify, scientifically speaking, as a pinhole camera? Because the article starts off by saying "A pinhole camera is a simple camera without a lens". I not sure whether that means "A pinhole camera is commonly constrction without a lens" or "A pinhole camera is defined as a camera that uses a pinhole instead of lens" Scala Cats (talk) 17:44, 23 June 2017 (UTC)[reply]

Yes, we have dual meanings here. I have the same problem with herbal tea, which both means tea leaves plus herbs, and herbs alone (tisane). StuRat (talk) 17:55, 23 June 2017 (UTC)[reply]

Ah, gotacha. Thanks, that clarifies it. Scala Cats (talk) 18:36, 23 June 2017 (UTC)[reply]

Also note that the type of pinhole camera lacking a lens might still have a glass cover over the pinhole, to prevent dust from getting in. StuRat (talk) 17:55, 23 June 2017 (UTC)[reply]

Really? In the very unlikely circumstance of dust being a problem, wouldn't the shutter adequately serve that purpose?--Mrs Wibble-Wobble (talk) 18:37, 23 June 2017 (UTC)[reply]

No, because pinhole cameras need to keep the shutter open a long time, since very little light is let in through the pinhole, to gather enough photons for full exposure. Also, there could be a subtle breeze into the pinhole, to equalize pressure, due to temperature changes, and this could draw dust in. StuRat (talk) 18:48, 23 June 2017 (UTC)[reply]

Blocking gravity waves?

(My apologies if I missed this in the article gravitational wave.) Suppose a planet is near enough to its star that the view of a distant source of gravitational waves behind the star is completely blocked everywhere on the planet.

Is the planet affected by gravity from the distant objects?
Could detectors on the planet detect the gravitational waves from the distant objects?
If either of the answers is yes, then how? Can gravitational waves go through ~~solid~~ light-blocking objects like the nearby star?

Loraof (talk) 16:43, 23 June 2017 (UTC)[reply]

No the waves are not blocked so the waves are still detected, and I can think of a number of reasons why gravity and its waves don't interact and disperse like other interactions. But you mustn't take my word for it today though... for I looked and found this to be asserted on the APS website here: [4]. As to how, I'd would just assume that the changes in local curvatures are accrued at the speed of light regardless of the source. --Modocc (talk) 18:35, 23 June 2017 (UTC)[reply]

Note that, even assuming gravitational waves pass through stars unmolested, that doesn't automatically mean they would be detectable on the far side. This is because the signal-to-noise ratio may be too low, with all the gravitational perturbations of the nearby star (created by non-symmetric mass movements, like coronal mass ejections, solar flares, etc.), swamping the subtle gravitational waves created perhaps billions of years ago and billions of light years away. StuRat (talk) 18:44, 23 June 2017 (UTC)[reply]

The detectors would have to be really really close to the star to create any significant noise however of any kind (not by waves per se). Presently, our Sun can briefly eclipse black hole events (putting them out of telescopic view), but that would not effect our gravitational wave detection. To put this another way, the magnitude of change in curvature produced by the blackhole events are clearly on a different scale than those caused by local perturbations. -Modocc (talk) 19:22, 23 June 2017 (UTC)[reply]

Another issue might be that current gravitational wave detectors measure longitudinal:transversal length ratios and could drown in noise even if the detector is on the near side. One would have to use "grav interferometry", rather than a single receiver, to tell signal from noise if they arrive from two opposite points. I think that there might be some issues even if the detector is off to one side - but for a different reason this time: the transversal reference would get disturbed at that point, contributing to noise just as much as when crossing the axis.

There could be some second-order effect if the eclipsing object is really massive, resulting in a "gravitational Einstein ring". But I'm not 100% sure here. While emission of grav waves uses energy (>3 solar masses in the LIGO event GW150914!) it might act on too fundamental a level to get deflected by other massive objects. After all, that grav wave originated from a pair of black holes. - ¡Ouch! (^{hurt me} / _{more pain}) 09:45, 24 June 2017 (UTC)[reply]

On a side note, some articles unrelated to GW150914 show up on its "what links here" list, example HIP_41378. Not sure what's going on there. - ¡Ouch! (^{hurt me} / _{more pain}) 09:45, 24 June 2017 (UTC)[reply]

However much energy you think is involved in black hole mergers, the correct answer is much, much larger. Even after traveling billions of light years, the gravitational radiation from black hole mergers is still many orders of magnitude larger than the gravitational radiation associated with the sun or any other local source. For LIGO, noise sources are mostly normal sources of terrestrial vibrations (equipment noise, earthquakes, heavy trucks, weather, etc.). Dragons flight (talk) 14:17, 24 June 2017 (UTC)[reply]

Nice reference: https://what-if.xkcd.com/73/

I wonder how destructive the grav wave alone would be. Could it even disrupt a planet, or would it just make everything wobble? - ¡Ouch! (^{hurt me} / _{more pain}) 13:50, 25 June 2017 (UTC)[reply]

I looked for refraction of gravity waves and found some apparently relevant papers. [5][6] Thanks to Sci-Hub, Springer no longer means checkmate, but I haven't gone there because I doubt I'm going to try to make serious sense out of this anytime soon. I would *guess* that very heavy masses might be able to distort the waves away from a given viewer... Wnt (talk) 18:53, 23 June 2017 (UTC)[reply]

The effect is under normal conditions negligible, but the fact that it does exist is a simple consequence of conservation of energy. The fact that matter couples to the gravitational field (which is why you can have gravitational waves in the first place), also means that gravitational waves can interact with matter and be detected. But that means that energy can be extracted from gravitational waves (Thought experiment originally proposed by Feynman to argue that gravitational waves carry energy involves test masses that move due to a passing gravitational wave, Feynman argued that you could use masses with a hole and put a stick through the holes such that the masses would now slide with some friction against the sticks, thereby dissipating energy. Where does the energy come from if gravitational waved do not carry energy?). Then if energy is extracted from passing gravitational waves, the waves that move on will carry less energy than they would otherwise have carried. The difference is caused by the emission of gravitational waves due to extracting energy from the gravitational waves, these are opposite in phase such that the transmitted gravitational waves will have a lower amplitude. Count Iblis (talk) 19:48, 23 June 2017 (UTC)[reply]

True. But that is a big if ("if energy is extracted from passing gravitational waves") and neglected by that APS webpage. Bummer. Maybe there are sources predicting the significance/insignificance of such extractions that would be useful for the OP. --Modocc (talk) 20:28, 23 June 2017 (UTC)[reply]

Gravitational waves will be stopped by an event horizon. But that is not something that you could fabricate to any shape you like, such as a sheet. Spacetime is really stiff, and all known matter will be soft and deformable compared to space. So it is hard to couple something made from matter to moving spacetime to extract the energy and lose it. Perhaps if your gravitational wave has a tiny wavelength, such as that of an X-ray, you would stand a better chance of making it lose energy in solid matter. Graeme Bartlett (talk) 02:34, 24 June 2017 (UTC)[reply]

A common missconception (as is the choice of the term "gravitational wave" imho), these are not ripples in gravity but ripples in spacetime! If there where such ripples in gravity, as frequent and far reaching as these ripples in spacetime seem to be, the whole universe would probably be grinded down to dust and rubble by now. --Kharon (talk) 09:21, 24 June 2017 (UTC)[reply]

I'm not following you, but if this misconception is so common, do you have any citation(s) about it? Of course, the term gravitational wave always refers to any propagating ripples of the spacetime metric of General relativity which is the geometric theory of gravitation. Seems like an appropriate term actually. -Modocc (talk) 10:48, 24 June 2017 (UTC)[reply]

Can a leaning tower be built in a stable way ?

This Q comes up specifically regarding the leaning minaret in Mosul which ISIL recently destroyed, along with the rest of the mosque: [7]. I assume that at some point they would want to rebuild both, but this might also come up if the Leaning Tower of Pisa collapses, etc. So, is there a way to make a tower which appears to lean, but which is stable, as opposed to leaning further with each passing year and finally collapsing ? One thought is to give it a narrower width at the top, as this would allow one edge to slope, while the other remains vertical. Not quite "leaning" but might give that effect from certain angles:

  /    | 
 /     | 
/      |

Also, there could be a cantilevered portion, made of a lightweight material, extending past the vertical wall:

  /    |///
 /     |//
/      |/

Do we have an article on such a construction technique ? StuRat (talk) 19:11, 23 June 2017 (UTC)[reply]

Interesting. Do we have a link for the pictured structure ? Is it still standing ? Could it stand for 100 years ? 1000 ? StuRat (talk) 19:52, 23 June 2017 (UTC)[reply]

Olympic Stadium (Montreal). Sagittarian Milky Way (talk) 19:55, 23 June 2017 (UTC)[reply]

Thanks. Looks like inclined tower is the general article, but it doesn't address the stability issue. StuRat (talk) 19:58, 23 June 2017 (UTC)[reply]

Apparently the tower wasn't finished in time for the 1976 Olympics, or even 1986. Maybe it was too short to impress in summer '76 so it's not as famous as it could've been. Sagittarian Milky Way (talk) 20:12, 23 June 2017 (UTC)[reply]

A structure is stable if its center of mass lies within its "footprint" (our support polygon article refers to this). So a tower can lean arbitrarily as long as the base of the tower reaches over to cover the vertical projection of its center of mass, as can be seen in the stadium picture above. Of course in extreme cases, the material of the tower may not be strong enough to handle the stress required if the base juts out at an extreme angle. CodeTalker (talk) 20:48, 23 June 2017 (UTC)[reply]

Figuring it out in terms of center of mass gets a bit hairy when you have something leaning with a cable anchoring it from the back. Does one include the chunk of earth between where the cable is anchored to the base of the leaning object? DMacks (talk) 21:07, 23 June 2017 (UTC)[reply]

I would say yes. Talking about whether a building tips over based on its center of gravity is assuming that it's been left lying flat on the ground like a toy block. Once you start digging cables into the ground, then it depends on how much of the ground has to come out with the cables in order for it to tip. Wnt (talk) 23:09, 23 June 2017 (UTC)[reply]

Burj Al Arab is a luxury hotel located in Dubai, United Arab Emirates that takes the form of a sail, so it is essentially the world's tallest lean-to (and consistent with your first example of "leaning"). It's very stable for it doesn't have much in the way of any mass that actually leans. --Modocc (talk) 22:02, 23 June 2017 (UTC)[reply]

See Block-stacking problem, the tower can lean over as much as one likes with each layer being just as wide and heavy as any other. Dmcq (talk) 23:36, 23 June 2017 (UTC)[reply]

Obviously, there are going to be some very real lower limits to any tower's slope (total rises over runs) and length since overhangs of blocks are limited by the blocks' compressive and tensile strengths. For example, for walking on they must be stiff and not thin like cardboard.. Each uppermost block/floor can only be so long for any given thickness of material and the loads placed on them. Even really thin materials have to rise above the horizontal as they are stacked. -Modocc (talk) 02:15, 24 June 2017 (UTC)[reply]

I should clarify my Q a bit. As I'm talking about replicating ancient structures, they shouldn't rely on steel cables to keep them from toppling over. Steel beams, inside the structure, might be acceptable, so long as they could be hidden. However, I'm skeptical of how good of a building material steel is in the long term. That is, it's seems to require constant maintenance to keep it from rusting, like repainting it every few years. So, if there's a way to build an inclined tower out of stone, in a stable way, I'd have more faith in it lasting for centuries. StuRat (talk) 00:51, 24 June 2017 (UTC)[reply]

It may be harder to make a forever pure stone and mortar tower that imitates an ancient one that was never intended to lean but did anyway. The blocks of the block thing don't lean but the stones of the leaning tower of Pisa do. Also, if it leaned unintentionally the soil on that site might be crap. Sagittarian Milky Way (talk) 01:13, 24 June 2017 (UTC)[reply]

I must be clueless, but if the stones are not tilted like the ancient structure you wish to replicate, its not really a replica is it? I mean people do notice their alignments and it is near impossible to hide anything that is too substantial. I venture that carbon fiber cables might eventually be a superior alternative but that's just an educated guess. --Modocc (talk) 02:15, 24 June 2017 (UTC)[reply]

Well, you could create angled lines on the structure to make it look like each block is leaning, but you would need to do something at the top or it being level would give away the whole deception. StuRat (talk) 02:33, 24 June 2017 (UTC)[reply]

Well, fakes of just about anything anywhere can substitute for the real thing certainly, whether or not the original is preserved. Many structures can be stabilized one way or another, and the one's that can't are usually condemned and demolished. For example, our government recently relocated a tall brick lighthouse further inland away from the shoreline. --Modocc (talk) 03:12, 24 June 2017 (UTC)[reply]

Every existing building that tilted over time can and will easily be build brandnew with the help of the regular skilled work practice called Falsework. --Kharon (talk) 09:05, 24 June 2017 (UTC)[reply]

Existing buildings can be uprighted, yes, but lots of owners also like to replace or permanently rid themselves of older structures that they don't want or are failing due to rotted timbers or are otherwise unsafe due to older practices. I can understand the desire to rebuild historical structures as StuRat suggested with some or all of the tilt that they had acquired over time (upon a secure and solid foundation) in a manner that is safe and lasting. -Modocc (talk) 11:20, 24 June 2017 (UTC)[reply]

I don't see any inherent difficulty in building a new masonry at a tilt. This was actually done in the leaning tower of Pisa (though more sensibly in the opposite direction). So long as a decent foundation can be created - which is the one unique challenge - the rest is millennia-old technology.

Of course, the caveat is that there has to be a point. It won't be the real artifact for study; it is only a tourist attraction. Could not the money be spent in some better way to promote tourism? And it still stands in Iraq, subject to be destroyed again in battle in a year or five. If people want to preserve ancient artifacts, it seems like their best play is to stop spending money, especially in the Muslim world. Every site dug out is going to be destroyed by the Wahhabis in an eyeblink of history, even if it takes thirty years, even if it takes sixty. Every site surveyed will be attended by looters if it is not dug out. Apart from idle study of already open sources (Google Maps) or targeted looting expeditions (Elgin Marbles) it seems like a strict moratorium is in order, perhaps to be revisited in a century or two. Wnt (talk) 12:00, 24 June 2017 (UTC)[reply]

While I would argue that mobile artifacts should be removed to a safer part of the world (perhaps leaving cheap copies around for ISIS parts 2, 3, etc., to destroy), buildings are a bit different. Their location is itself historic, so rebuilding them in-situ is critical, for local morale, tourism, etc. If they get destroyed again, rebuild them again. StuRat (talk) 19:58, 24 June 2017 (UTC)[reply]

I concur with StuRat. Consider, for example, the rebuilding of the centre of Ypres after its almost complete levelling during the First World War. {The poster formerly known as 87.81.230.195} 94.9.80.133 (talk) 20:23, 24 June 2017 (UTC)[reply]

Something like this, perhaps? — Preceding unsigned comment added by 79.237.83.44 (talk) 03:27, 26 June 2017 (UTC)[reply]

Are those stable in the long-term, without continuous maintenance ? StuRat (talk) 21:19, 27 June 2017 (UTC)[reply]