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April 20

Xia's five-body configuration

One of my favorite webcomics, Saturday Morning Breakfast Cereal, once made a joke about Xia's five-body configuration (comic here). I went looking for what it was talking about and found our article on the Painlevé conjecture, to which I added a redirect-with-possibilities. As an aside, the article could use some TLC; the most glaring problem is that it introduces variables without saying what they represent.

Anyway I was trying to figure out where this infinite energy was supposed to be coming from. My best guess so far is that the five bodies are idealized as point masses, which means that the gravitational energy released as you let two of them approach one another grows without bound. This of course would make them black holes in our actual universe, so that energy wouldn't be available, but in the universe of the comic, I guess this wouldn't be a problem (I've never thought very deeply about what happens to general relativity as c approaches ∞, so I'm not sure about that). But in any case there's no new energy appearing that wasn't there before, so the comic's claim that "the universe collapses" seems wrong.

No, really, I actually do have a sense of humor. I just want to know if I've understood this correctly. Does anyone have a different understanding? --Trovatore (talk) 19:50, 20 April 2024 (UTC)

O/T That article rather overeggs the pudding. The various proofs are for the 2d case ie planar. Perhaps it is obvious that if it works in 2d it'll work in 3d. Greglocock (talk) 21:22, 22 April 2024 (UTC)

I'm not too sure what it means to "overegg the pudding" but I was not interpreting the configuration as planar; if that's correct then I've misunderstood the drawing. Can you point me to why you say that? --Trovatore (talk) 21:43, 22 April 2024 (UTC)

It means exaggerating the utility of . The repeated use of the word planar is what I was getting at.Greglocock (talk) 05:45, 23 April 2024 (UTC)

The last section of the AMS article by Saari and Xia has this: "While we now know that noncollision singularities exist, several mysteries remain. Any partial listing has to include whether n = 5 is the cut-off for this surprising behavior, or whether the four-body problem can propel particles to infinity in a finite time. Can, for instance, Anosov’s suggestion be carried out? Are there planar examples with small n values?" This implies IMO that Xia's construction is non-planar. I think the sketch of the construction also implies this: the orbits of the pair of point masses m₁ and m₂ are said to be parallel to the x-y plane and highly elliptical, while m₃ moves along the z-axis. The orbits of the pair m₄ and m₅ are also orthogonal to the z-axis, with their major axes shown at an angle to those of m₁ and m₂ in the accompanying figure.  --Lambiam 12:52, 23 April 2024 (UTC)

Energy borrowed from the potential energy shed by point masses approaching each other closely but not, in the finite time, "arbitrarily closely", can only be finite. To reach infinity their distance has to become less than any positive number, which means it is zero. Doesn't that qualify as a collision? What is worse, in Jinxin Xue's 4-body solution all four bodies are said to escape to infinity in a finite time. Do they scoot off in four different directions?  --Lambiam 13:18, 23 April 2024 (UTC)

I believe the idea is this: as you approach the time of the singularity, the separation between some pairs of masses approaches zero, but the positions of those masses diverge to infinity. If you consider a collision to be when two masses have identical, finite coordinates, then that never happens in this scenario. --Amble (talk) 22:59, 23 April 2024 (UTC)

How hard would it be to construct it from satelitees? Zarnivop (talk) 22:41, 25 April 2024 (UTC)

You could put satellites in the right pattern at some starting time, but they wouldn’t actually behave as predicted by Xia’s model. That’s because the model requires perfect point masses in a Newtonian universe affected only by one another’s gravitational pull. Real satellites have other forces acting on them, have negligible influence from each other’s gravity, and are not point masses. And of course, real satellites aren’t in a Newtonian universe. —Amble (talk) 02:25, 26 April 2024 (UTC)

April 23

Fulgurite: vandalism or proper fixings?

While adding a brief historical context section to that lemma I noticed some former changes of another IP which I doubt to be correct. Please could somebody countercheck, since I have no access to the referenced Elsevier source documents from which the data has been obviously originally taken. Here the difflinks in question:

• Special:Diff/1218613828 Section or not a section?
• Special:Diff/1218613911 Greater or less than 100.000 Volts? Grounding or grounding substrate?
• Special:Diff/1218614055 Second half of a sentence was removed. Does that make sense?
• Special:Diff/1218614423 Negative or positive? Discharge or charge?
• Special:Diff/1218614559 100 million volts or only 100 volts?

I would tend to revert these unverified changes, they look illogicaly to me, but wanted to ask here first.

Many thanks! --92.117.130.94 (talk) 05:06, 23 April 2024 (UTC)

P.S.: Maybe there is a need to improve my wording or grammar in the historical section I have added, since I'm not an English language native speaker, sorry if I've used unusual or strange wording. --92.117.130.94 (talk) 05:12, 23 April 2024 (UTC)

Thanks for noticing. I've reverted these edits because they look like vandalism to me. HansVonStuttgart (talk) 08:13, 23 April 2024 (UTC)

April 26

Mass-radius relations of stars and mean molecular weight

Are there analytical expressions that describe how the radii of white dwarfs change with mean molecular weight? JoJo Eumerus mobile (main talk) 19:06, 26 April 2024 (UTC)

See White dwarf#Mass–radius relationship. The radius goes down fairly quickly as the mass increases. NadVolum (talk) 20:13, 26 April 2024 (UTC)

The radius depends on the mean molecular weight through the number of electrons per unit mass N. Ruslik_Zero 20:27, 26 April 2024 (UTC)

Thx. Is there a similar approximation for nondegenerate matter like brown dwarfs? JoJo Eumerus mobile (main talk) 13:56, 27 April 2024 (UTC)

Brown dwarfs don't really change in radius as their mass changes. Radius stays nearly constant as mass increases from the onset of significant self-compression (about Saturn's mass) to the onset of hydrogen burning (turning into a red dwarf at about 75 Jupiter masses). So they'd all more or less be one Jupiter in radius – you already see the low end of this in the Solar System, with Jupiter not being much larger in radius than Saturn. Double sharp (talk) 18:10, 27 April 2024 (UTC)

@Double sharp: Does the radius change with mean molecular mass, though? JoJo Eumerus mobile (main talk) 13:07, 28 April 2024 (UTC)

In terms of their major components, wouldn't brown dwarfs all resemble Jupiter in composition? Particularly so since many would have depleted their deuterium through fusion by the time we observed them. So I kind of doubt mean molecular mass would vary that much between them to produce noticeable changes. But admittedly I'm guessing here. Double sharp (talk) 05:46, 1 May 2024 (UTC)

Nope - brown dwarfs around Black Widow Pulsar-like pulsars may be stripped down remains of stars and thus consist mainly of helium (or carbon, oxygen etc.). Brown dwarfs formed from white dwarf debris (around black holes) or kilonova ejecta may also contain other elements. Jo-Jo Eumerus (talk) 09:08, 3 May 2024 (UTC)

Interesting: you learn something new every day, I suppose! OTOH, I guess most brown dwarfs would still be directly produced and thus indeed resemble Jupiter in composition. Anyway, it doesn't seem like the companion to the Black Widow Pulsar has a known radius, so the question may be unanswerable for now. Double sharp (talk) 10:14, 3 May 2024 (UTC)

April 29

Origin of a formula constant

I have discovered by an accurate empirical method that a constant needed in a predictive mathematical formula is 0.986093(7). In the SI metric system, the constants generally turn out to have simple origins, e.g., 2, pi, 4/3 times pi and the like, or fundamental constants such as the speed of light c, which I believe is not relevant here. Can anybody spot the components of 0.9860937 ? I have not been able to deduce it. ```` Dionne Court (talk) 14:35, 29 April 2024 (UTC)

$2^{-0.{\overline {02}}}$, or, if you like, $1/{\sqrt[{99}]{4}}$. —Amble (talk) 16:37, 29 April 2024 (UTC)

OK, I'll bite. How did you get that? Greglocock (talk) 00:36, 30 April 2024 (UTC)

Nothing too clever — I just guessed there should be good matches with $n^{-1/p}$ for some integer n and p. I tested n by brute force, and for each n, used $p=-\log(n)/\log(x)$, rounded to the nearest whole number. There are many possible answers, with n=4 as the first one. Although I took the (7) at the end to be an uncertainty level, and looking again, that may not be what OP intended. —Amble (talk) 03:51, 30 April 2024 (UTC)

I included brackets around the 7 to indicate that due to random experimental error, the value is centred around 7 but could be anything. Thus you could infer that the 3 before it is accurate (if I made no error in procedure).

The n^-p form doesn't help much because I cannot imagine any reason why it should be so. Its a bit like how we were taught in school to use 22/7 as pi - there is no reason for it, it is just a coincidence that 22/7 evaluates to equal pi to 3 places. It gives no insight into WHY pi equals 3.1416..... ```` Dionne Court (talk) 11:30, 30 April 2024 (UTC)

Right. The n^-p form is a silly example. The point is that you can produce a matching value in an infinity of ways. Without more information about the underlying process, there's no possible way to know which (if any) may be relevant. The notation I'm familiar with uses parentheses to indicate the standard uncertainty in the final digit (or digits), as shown in the NIST page here: [1]. --Amble (talk) 17:18, 30 April 2024 (UTC)

You may be interested in this inverse symbolic calculator, though it doesn't seem to recognize your constant. Staecker (talk) 23:31, 29 April 2024 (UTC)

I love that calculator. I wish I had known about it before. Thanks. ```` Dionne Court (talk) 00:56, 30 April 2024 (UTC)

I used to work with a lot of predictive formulas and nearly all of them had constants. They were calculated by using large populations and working out a best fit regression formula. The resulting constants were not based on pi or the speed of light or anything recognizable. They were based on average biological processes of humans, such as how many creatinine is cleared by the bladder on average. 12.116.29.106 (talk) 12:40, 30 April 2024 (UTC)

The problem I have been working on is not a biological process, as you may realise from the six-digit precision of the constant. It is within the realm of physics. In physics one seeks to discover why the constants are what they are and thus understand the process.

In complex biological process, the constants could be any weird thing, as dozens or hundreds of sub-processes are involved. In physics, the constants are usually very simple combinations of integers, pi, squared or rooted, trig identities, whatever. ```` Dionne Court (talk) 02:29, 1 May 2024 (UTC)

That formula above uses less symbols when printed than the given constant, I think that's pretty impressive. Too many of these approximations are worse 22/7 = 3.1428 with four symbols is only just about shorter if one says the 28 is close to 16. NadVolum (talk) 17:15, 30 April 2024 (UTC)

355/113 gets pi to six figures past the decimal point, which is eight symbols if you count the 3 and the period. The fraction is only seven characters if you write it without spaces. --Trovatore (talk) 23:23, 30 April 2024 (UTC)

Of course π itself is just one symbol.... --Trovatore (talk) 23:29, 30 April 2024 (UTC)

I think they told us in high school to use 22/7 so that we could more easily spot where algebraic cancellation could be used by dumping unnecessary precision. If it was about saving digits, they could have just told us to memorise 3.142. ```` Dionne Court (talk) 02:36, 1 May 2024 (UTC)

Yeah, I remember problems were often rigged to have a factor of 7 that you could cancel upon approximating pi as 22/7. With 3.14 that would be much harder. Double sharp (talk) 05:48, 1 May 2024 (UTC)

April 30

Tokyo Toilet smart glass defect

Hi all! I was looking through a machine translation of this press release PDF, which seems to indicate that the smart glass used for the walls of one of the toilet designs for the Tokyo Toilet project is locked into the opaque state during months where there's a drop in temperature. This document includes the word "Defects" in the URL, which I assume refers to this design only being operational during certain times of the year as a solution to some unspecified problem, but I'm struggling to find out why/how exactly the temperature affects this toilet's smart glass functionality. It's specifically tricky because trying to perform a cursory search on how temperature affects smart glass seems to mainly pull up info about passive thermochromic smart glass, but other articles and footage of the switch toggle have led me to believe that this is an active and electrically switchable smart glass setup, so unless I'm mistaken, that thermochromic info wouldn't be relevant here. Basically, I'm just looking for any leads as to what's going on here lol thanks! ~Helicopter Llama~ 16:14, 30 April 2024 (UTC)

Sounds like it's a cholesteric liquid crystal panel or something similar. These were briefly fashionable for electrically switchable opaque/transparent wall panels back in the 1990's. The company I worked for had it on one floor of their high rise head office. They were notorious for not working at low temperatures (< 10 C) and failing completely at high temperatures (> 35 C)

Another possibility is the method used in auto-switching variable darkening welding helmets - I don't know how they work, other than knowing they are battery powered and are controlled by a light sensor. ```` Dionne Court (talk) 02:12, 1 May 2024 (UTC)

May 1

Sub-brown dwarf detection (in a way)

If a copy of Jupiter (with a copy of all the moons) was a rogue planet freely floating in space, how close would it have to be to the Solar System for us to be able to detect it? And how close would it have to be for us to be able to detect the Galilean moons? Double sharp (talk) 05:58, 1 May 2024 (UTC)

There was one such search using WISE satellite. Its conclusion is that there is no Jupiter-like body closer than 82,000 au to Sun, no Saturn-like body closer than 28,000 au. Ruslik_Zero 20:40, 1 May 2024 (UTC)

It is possible of course to use a bigger telescope but they are usually have quite a narrow field of view. Ruslik_Zero 20:42, 1 May 2024 (UTC)

Exoplanets are being detected throughout our Milky Way galaxy whose center is about 27,000 lightyears distant and potentially in other galaxies using Gravitational microlensing. Some physical parameters of exoplanets can be estimated but not whether they have moons. Philvoids (talk) 23:50, 1 May 2024 (UTC)

Dinosaurs and the future

Did dinosaurs know the future? In particular, did they know that they will eventually be killed millions of years later? They probably did not know that there will be humans in the future. But perhaps, they could already know what will happen to them in the next few million years. GTrang (talk) 16:22, 1 May 2024 (UTC)

There's no evidence that dinosaurs ever developed human-like intelligence and intellect, to the point of being able to go beyond the mere needs of immediate survival (find food, hunt prey, escape from predators) and make more existential questions like that. Cambalachero (talk) 17:24, 1 May 2024 (UTC)

Gary Larson postulated the possibility:[2] ←Baseball Bugs ^{What's up, Doc?} carrots→ 17:30, 1 May 2024 (UTC)

Humans do not know what will happen to humankind in the next one hundred years.  --Lambiam 06:13, 2 May 2024 (UTC)

Lemmings do. --Cookatoo.ergo.ZooM (talk) 14:30, 2 May 2024 (UTC)

In a thousand years we might have Idiocracy or might be starting to expand to the stars. Who can say. I think this comes under crystal ball speculation. NadVolum (talk) 17:15, 2 May 2024 (UTC)

May 3

Why Bronze Age and not Brass Age?

Why was bronze so much more widely used by the ancients than brass? Was it because zinc was so much harder to come by than tin, or was it because it was so much harder to make high-quality brass than bronze, or was it because bronze had more desirable material properties than brass? 2601:646:8082:BA0:F13B:E84E:494B:CA04 (talk) 04:40, 3 May 2024 (UTC)

The principal reason is probably that stated in the lede of Brass,

"Brass is not as hard as bronze, and so is not suitable for most weapons and tools [my italics]. Nor is it suitable for marine uses, because the zinc reacts with minerals in salt water, leaving porous copper behind; marine brass, with added tin, avoids this, as does bronze."

Zinc seems to have been less familiar (and available?) than tin in the Western ancient world, but more widely used further East. However, its use even there seems to have been more often 'ornamental' that practical, probably because of its poorer mechanical properties.

My suspicion is that the fabled metal Orichalcum (Greek oreikhalkos, "mountain copper", but in Latin Aurichalcum, "gold copper") was a form of what we would now classify as brass. {The poster formerly known as 87.81.230.195} 188.220.144.58 (talk) 06:10, 3 May 2024 (UTC)

There was no 'Brass Age' because, for many years, it was not easy to make brass. Before the 18th century, zinc metal could not be made since it melts at 420ºC and boils at about 950ºC, below the temperature needed to reduce zinc oxide with charcoal. In the absence of native zinc it was necessary to make brass by mixing ground smithsonite ore (calamine) with copper and heating the mixture in a crucible. The heat was sufficient to reduce the ore to metallic state but not melt the copper. The vapor from the zinc permeated the copper to form brass, which could then be melted to give a uniform alloy.

Brief Early History of Brass. Alansplodge (talk) 16:51, 3 May 2024 (UTC)

13 year old me melted a zinc coin in a stainless spoon in a gas flame. I removed the iron the pot or pan lies on, tried to find the flame part of max spoon glow-in-the-dark (spoon incandesced orange) and waited to ensure getting very close to thermal equilibrium. Could I have boiled zinc? The copper electroplate probably didn't melt (post-'82 US pennies are this composition) so I stirred with a straightened paper clip and tried to heat a glob on the clip for a less heat-robbing zinc holder but didn't reach max temp as I didn't want it to drip on the gas holes. A whole penny in the gas ring's bowl didn't seem to boil but did puddle. Sagittarian Milky Way (talk) 22:37, 3 May 2024 (UTC)

Reflex to prevent food falling

Sometimes when a piece of food falls from my hands during eating, I have a sort of rapid reflex to prevent it from falling on floor - either by catching or deflecting it to stay on the table. Is it a sort of catching reflex in physiology? 212.180.235.46 (talk) 18:49, 3 May 2024 (UTC)

It's more than just food (as you'll find if you ever find yourself responsible for a small child), though I'm not sure it's a reflex in the technical sense. We have a List of reflexes and the closest thing I can find there is the palmar grasp reflex, which is about how babies and other infant primates grab onto things in an automatic way. This isn't quite the same thing, though. Reflex or not, the human urge to grab things that are falling can be very strong, even when the cause is hopeless or harmful; there's no shortage of videos online of people attempting to right tipping vehicles or catch falling objects they really ought not attempt. I haven't found an appropriate article on this yet, though. Matt Deres (talk) 20:10, 3 May 2024 (UTC)

I think that this does not qualify as a physiological reflex, since the pathway is not a reflex arc but involves the whole kaboodle of the visual or tactile perception of a valuable item slipping away, the ensuing cognitive recognition of impending disaster, and finally an appropriate response of fine-tuned firing of motor neurons to (hopefully) save the day, all processed in the neocortex.  --Lambiam 20:32, 3 May 2024 (UTC)

takeoff/landing distance graphs

1. I understand that weather stations don't give density as often and runway air's always close to 29g/mol but wouldn't density altitude be more accurate? A drone could fly much easier in a xenon balloon than a hydrogen balloon but a kg/m³ in Earth gravity is a kg/m³ in Earth gravity. So can I just calculate the density altitude from common weather station things like meteorological pressure/altimeter setting and geometric altitude and use that on the ISA+0°C graph? There are formulae and calculators for that online. Maybe they don't want to make the generic jetliner owners manual even longer (they're hundreds of pages) with a graph for every plausible Fahrenheit when it says it's unofficial but I don't know where to read official manual(s). It says each airline gets customized manuals. With the generic manual most temperatures don't have a graph and it doesn't have colder than standard atmosphere or very hot.

2. How do I adjust airport weather station temperature to the temperature that affects runway length used? The thermometers are in a white wood louver a bit lower than large plane wings, they're probably on grass, not significantly heated by jet engines, it should be hotter when it's hot and possibly colder when it's cold. If it's 40 or 50°C in the airport weather station in the local all-time high at 4 meters ground altitude and 40°N and 30°N respectively what's the best estimate and worst case density altitude for concrete runways and asphalt?

3. How do they make these graphs? Do they test fly them, measure the rear gear touch length (plus wheelbase if landing) and add safety factor(s)? How much? Or is it the entire distance from first penetration of a few tens of feet above ground (some precise value) with the lowest part of the plane to foremost front wheel ground touch and rearmost rear wheel ground touch to last penetration of a few tens of feet above ground (another precise value) with the lowest part of the plane or some part of the plane when a certain climb rate or slope is reached if that's later? Sagittarian Milky Way (talk) 22:39, 3 May 2024 (UTC)

Runway length corrections specified by ICAO are 7% increase in runway length for every 300m rise in elevation from the mean sea level and 1% increase in runway length for every 1°C rise in airport reference temperature (Tr) above the standard temperature at elevation (STE). Philvoids (talk) 01:00, 4 May 2024 (UTC)

May 4

HSK taper

Machine_taper#HSK_taper says:

 The shank is short (about half as long as other machine tapers), with a shallow taper (a ratio of 1:10), and slightly too large to allow the flange to seat fully in the socket.

But the drawing right beside that paragraph shows a "1:9.98". Machine_taper#/media/File:DIN_69893_hsk_63a_drawing.png

Which is correct here?

Or maybe I'm misunderstanding something and that the two values are intentionally different. OptoFidelty (talk) 02:44, 4 May 2024 (UTC)

All the refs for current standards I see are 1:9.98. For that, "1:10" seems like a simplified approximation. I agree that we shouldn't make an approximation when stating outright what a standard is. DMacks (talk) 03:45, 4 May 2024 (UTC)