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January 17

Three objects rearranged

We stack three ceramic pieces in the washroom and put a bar of soap on top. They are constantly being rearranged. Each piece can be upside down or not, and in any position (top, middle, bottom). How many different configurations are there? Many thanks to anyone who can help. :) Anna Frodesiak (talk) 00:29, 17 January 2017 (UTC) Can't you just tell your family to leave things alone so you don't have to come here and give me a headache before going to bed - hee hee. DrChrissy ^(talk) 00:55, 17 January 2017 (UTC)[reply]

DrChrissy, you can't tell them anything. They talk back. :) Anna Frodesiak (talk) 08:43, 17 January 2017 (UTC)[reply]

Think I will stick to my cats then! The only things they move around is the food in their bowls! DrChrissy ^(talk) 19:33, 17 January 2017 (UTC)[reply]

Anna, if the bar of soap is also considered in this calculation and considered to be placeable upside-down or right side-up, then there are 2x2x2x2 or 16 possible combinations. If you're considering only the ceramic pieces depicted in the graphic, those can be organised in 2x2x2 or 8 possible combinations. loupgarous (talk) 00:36, 17 January 2017 (UTC)[reply]

Hi loupgarous. No soap in the problem. Eight? That doesn't seem possible. Again, each can be upside down, and each can be in any position (top, middle, bottom). Are you absolutely sure? Best, Anna Frodesiak (talk) 00:45, 17 January 2017 (UTC)[reply]

48. Six orders (3×2), multiplied by 8 (2³) inversions. Andy Dingley (talk) 00:47, 17 January 2017 (UTC)[reply]

E/C :I'm not considering the soap. Each object can be in 2 orientations (upsidedown or right side up) and there are three pieces so there are 2³ orientations = 8. The pieces can be in 3 places so the number of places combinations is 3² =9. 8x9 = 72 total combinations. DrChrissy ^(talk) 00:49, 17 January 2017 (UTC)[reply]

Looks like Andy and I agree about the inversions, but disagree about the orders. DrChrissy ^(talk) 00:51, 17 January 2017 (UTC)[reply]

Pick a piece. One of three. Put it in a pile.

Pick another piece. One of two remaining. Put it on the pile.

Put the remaining piece on the pile.

Six. Andy Dingley (talk) 00:58, 17 January 2017 (UTC)[reply]

Good catch on places, Andy, Chrissy and Anna. There are 6 possible orders and 2x2x2=8 possible upside down/right side-up orientations in the array, giving a total of 6x8=72 different permutations of order x spatial orientation. loupgarous (talk) 01:14, 17 January 2017 (UTC)[reply]

6×8 = 48, not 72. StuRat (talk) 02:01, 17 January 2017 (UTC)[reply]

So, 72? That's the final number? No wonder it never looks the same. I must say, 72 really surprised me for only 3 objects stacked up. Thank you all! Anna Frodesiak (talk) 01:21, 17 January 2017 (UTC)[reply]

E/C I think I see why Andy and I might differ. Andy appears to be adding pieces to the pile. I have assumed that all 3 pieces are always in the pile, but only their places differ. DrChrissy ^(talk) 01:23, 17 January 2017 (UTC)[reply]

Yes, all three are always there. No more, no less. So, still 72? Anna Frodesiak (talk) 01:26, 17 January 2017 (UTC)[reply]

Nope, 48. See above. StuRat (talk) 02:01, 17 January 2017 (UTC)[reply]

Thank you, Stu, and thank you all, especially Andy who got it right first. Anna Frodesiak (talk) 02:18, 17 January 2017 (UTC)[reply]

You're welcome. (StuRat distributes multiplication tables to all concerned.) :-) StuRat (talk) 02:33, 17 January 2017 (UTC)[reply]

BTW, the number of arrangments of the 3 objects (ignoring the upside down options) can be calculated using factorial, hence

3!=3\times 2\times 1=6

. Nil Einne (talk) 04:39, 17 January 2017 (UTC)[reply]

Or...

Position	Items (removed)	Orientations	Permutations
Top	1 (two)	2	2
Middle	2 (one)	2	4
Bottom	3 (none)	2	6

Combined permutations: 2 × 4 × 6 = 48 2606:A000:4C0C:E200:8097:8662:1582:8D5D (talk) 06:12, 17 January 2017 (UTC)[reply]

Thank you all again. Anna Frodesiak (talk) 08:43, 17 January 2017 (UTC)[reply]

The number of permutations (the ordering) for 2-out-of-3 is (perhaps surprisingly) the same as for 3-out-of-3.

Build a pile of three. 6 permutations. Build a pile of two and "put the last one in an opaque box" - still 6, because putting the last one "on the top of the pile" or "back in the cupboard" is topologically the same thing. Andy Dingley (talk) 10:34, 17 January 2017 (UTC)[reply]

Right. Without the "orientations" multiplier (2x) in the table above, the top permutations would be 1 ... and one times whatever is whatever. 2606:A000:4C0C:E200:C196:3184:5BEE:2C53 (talk) 17:35, 17 January 2017 (UTC)[reply]

You all seem to be missing ht point that 8 X 6 = 42. μηδείς (talk) 15:18, 17 January 2017 (UTC)[reply]

I hope that's a joke. StuRat (talk) 15:53, 17 January 2017 (UTC) [reply]

If it's a Douglas Adams joke, that should be 6 x 9. See here. Matt Deres (talk) 16:18, 17 January 2017 (UTC) [reply]

The way to keep that 'joke', such as it is, straight is to remember the third line by an anonymous author, the base is thirteen. Wnt (talk) 16:58, 17 January 2017 (UTC)[reply]

Thanks. And to think, for all these years I have been preaching heresy. This even came up last weekend. My dad asked me for help with the Sunday crossword; "What was the first error of THGttG, 8 letters?" I said fortytwo, and insisted on it, even when he said it was causing all sorts of problems. Turned out he was asking "what was the first airer of THGttG, which was BBCRadio. μηδείς (talk) 20:59, 17 January 2017 (UTC)[reply]

Surely 42₁₃ is not read "forty-two", but "four-two base thirteen". Double sharp (talk) 10:51, 19 January 2017 (UTC)[reply]

Inverse of pressure

I know that the inverse of speed is "pace" and the inverse of density is "specific volume". I was searching on Google for inverse of pressure but I can't find a term for that. I'm curious for what the term could be called; I can figure it out but it could take a bit of time and effort. Then I just found that the inverse of pressure is "specific surface area" which has units in m²/kg, while inversely kg/m² is the unit of pressure. I figured that out based from density differ in pressure only in power in the denominator part of the unit (kg/m² for pressure and kg/m³ in density) and 'volume' in specific volume downgrading to 'area' to make "specific area" and then I googled that and found the answer on myself. Planet Star 05:35, 17 January 2017 (UTC)[reply]

So first of all I'm not sure that "pace" is really standard for "reciprocal speed". It's true that runners might say they're running at a "six-minute pace" (meaning six minutes per mile, i.e. 10 mph) but generalizing that into "pace = 1/speed" has the ring of WP:OR to me.

More important, pressure is not (properly) measured in kg/m^2. Pressure is force divided by area, not mass divided by area. You can measure pressure as kgf/m^2, where kgf is a rather nonstandard unit, "kilograms force", meaning the force needed to accelerate a one-kilogram mass at 1g.

The specific surface area article does not, unless I missed it, talk about 1/pressure. --Trovatore (talk) 06:04, 17 January 2017 (UTC)[reply]

I seen it on Google that pace can be the reciprocal of a speed in the context of running such as seen in the top result in that page. As kg and lbs are units of weight, the units of weight can be used in units of pressure, like pounds per square inch or psi, therefore they can be flipped to make square inch per pound or sip which is an imperial unit of specific area. And I don't see that it said that it is inverse of pressure in that article either, though in my opinion specific area is the inverse of pressure. Planet Star 06:23, 17 January 2017 (UTC)[reply]

So the shibboleth I've been trying to avoid here is that you're confusing weight and mass. The reason I've been trying to avoid it is that people are a little too insistent on it, in a linguistic sense — in fact one of the meanings of "weight" in English is actually "mass", and there's nothing wrong with that.

But in any case kilograms, according to standard usage, are a measure of weight-in-the-sense-of-mass, not weight-in-the-sense-of-force, and kg/m^2 is not a unit of pressure, although kgf/m^2 is. --Trovatore (talk) 06:31, 17 January 2017 (UTC)[reply]

To expand on Trovatore's point, in strict, modern scientific use, mass (the amount of "stuff") is measured in kilograms, while weight (the force exerted by a mass due to gravity) is measured in Newtons. (Named after Sir Isaac Newton, rather than being a new, modern version of the ton). Imperial/customary units are more complicated, as a "pound" can be a unit of mass, or of weight, and other units of mass such as the slug. Iapetus (talk) 14:03, 17 January 2017 (UTC)[reply]

If a car was taken to the Moon where gravity is one-sixth that on Earth, the car would be easier to jack up to change a flat tyre because its weight would be one-sixth. Push starting the car would take the same effort that it takes on Earth, neglecting air and wind resistance and tyre rolling resistance, because the car has the same number of atoms (the same mass) that it has on Earth. Weight and mass are not interchangeable. Akld guy (talk) 18:55, 17 January 2017 (UTC)[reply]

The original question is sort of curious. Look up "square meters per newton" and there are a lot of weird answers. Like, a "brewster" is one trillionth of a m²/N, "a unit used in optics to measure stress-induced birefringence."^[1] Piezoresistivity tensors have units of reciprocal stress, i.e. this.^[2] Aquifer compressibility of fractured rock has the same.^[3] Ditto kinematic viscosity.^[4] And shear mode compliance.^[5] There are only a small number of actual hits for the phrase, but every one is inventive. My guess is that most folks invented a way to write these things in terms of pressure, but this is not physics as I've ever worked through it. Wnt (talk) 15:24, 17 January 2017 (UTC)[reply]

I googled "square meters per newton" and found one result that said is a unit of "pressure-viscosity coefficient" and then I googled that and found this page especially seen in Table 1. The page uses mm²/N. Planet Star 23:16, 17 January 2017 (UTC)[reply]

I know for a long time that mass and weight are not interchangeable in terms of definitions, but some of the units like pounds can be used for both weight and mass. Pound would be an imperial unit of mass/weight while kilogram is a metric unit of mass/weight. One kilogram is 2.2046 pounds. But if we weigh an object on another world that has different gravity, they're weight would change but mass would stay the same. On the moon, one kilogram would equal to 0.37 pounds. Planet Star 23:07, 17 January 2017 (UTC)[reply]

Let's avoid the confusing term "weight" altogether. Let's say "force", which is unambiguous.

It is not correct to say that pounds are a unit of both force and mass.

Rather, there are two different units, pounds-force (lbf) and pounds-mass (lbm). Pounds-force are a unit of force; pounds-mass are a unit of mass.

Either of them may, when context is sufficient to disambiguate, be referred to as "pounds". But that does not make them the same thing!

As for kilograms, by nearly universal agreement, they are a unit of mass, not force. There is a legacy unit, kilograms-force (kgf), which is still used in some niches. But that does not make specific surface area the reciprocal of pressure, because it is measured in m^2/kg, not m^2/kgf. --Trovatore (talk) 23:19, 17 January 2017 (UTC)[reply]

Do small children have more nerve endings per unit skin area than grown ups?

Small children seem to feel more pain during injections than grown ups, is that because they have more nerve endings per unit skin area? Count Iblis (talk) 08:33, 17 January 2017 (UTC)[reply]

That could be the case, but the more likely explanation is that grown-ups have simply built up more pain tolerance from all those small injuries in childhood and adolescence. 2601:646:8E01:7E0B:F88D:DE34:7772:8E5B (talk) 09:40, 17 January 2017 (UTC)[reply]

The articles Pain and Pain in babies (and their references) might be good places to start. We do not (as yet) have an article Pain in children. Also Nociceptor and Nociception. {The poster formerly known as 87.81.230.195} 2.122.62.241 (talk) 11:06, 17 January 2017 (UTC)[reply]

The answer is surely to be found here (PubMed), but you need some additional terms for an inspired search. So far, I haven't thought of what they are. Certainly I agree this is the case, though - I remember that as a kid if I went up to climb the stairs normally and I banged my shin on it (even with carpet around the edge of the step!), I would fall to the ground screaming, and that was no act! I remember once it left a tiny little bruise and I thought my leg was going rotten, but usually it didn't. Now I find bruises on my shins and I have no idea how it happened. (It is possible that the biology of bone growth had something to do with this, but still, the middle of the shin is far from the epiphyseal plate) Wnt (talk) 14:34, 17 January 2017 (UTC)[reply]

There is also Psychogenic pain, to wit, "physical pain that is caused, increased, or prolonged by mental, emotional, or behavioral factors." (emphasis mine). A person's attitude towards the event, or internal mental state at the time of the event, can effect in a very real way how much pain they perceive. People who are fearful of the shot may report higher pain levels than those who are not. This article reports that "...distraction ... significantly reduced pain perception. There were no interaction effects of either age or gender. Fear was a significant covariate, but distraction was effective even when fear was not held constant." That is, age was not necessarily a factor, but both attentiveness (or distraction) and fear were correlated to pain perception. --Jayron 32 15:38, 17 January 2017 (UTC)[reply]

I'm still pretty fearful of shots (it's a hard habit to break) but they don't hurt any more. This reminds me of one of the old tests for a witch, where an old woman would be unable to feel a pinprick that any of the young amateur Inquisitioners could not imagine failing to object to, proving her in league with the Devil. Wnt (talk) 19:50, 19 January 2017 (UTC)[reply]

If the number of nerve endings doesn't increase as we grow, then logically, we have fewer nerve endings per surface area (skin) as we expand (grow). 107.15.152.93 (talk) 17:20, 17 January 2017 (UTC)[reply]

On average, sure, but do keep in mind e.g. Allometric Growth. An infant's head is far larger, proportionally, than an adult's [6]. It is entirely logically possible that nerves would remain equally dense in some areas (e.g. finger tips), but become far less dense in others (e.g. back). SemanticMantis (talk) 18:57, 17 January 2017 (UTC)[reply]

Yes, a little bit, if I'm reading this study correctly [7]. The abstract says:

“

Significantly higher intraepidermal fiber densities were seen in the youngest group

”

Note that "significant" does not mean the difference is large. If you look at Fig. 3, you'll see the difference is actually very small. The youngest cohort analyzed was age 10-19, so it's entirely possible that there are bigger differences in younger children. I found this paper with this search of google scholar [8], I suspect adding in other terms (e.g. child, infant, etc) or looking further down the list may get you something more clear and substantive. SemanticMantis (talk) 19:14, 17 January 2017 (UTC)[reply]

A fun trick related to this is the following: Get a "victim" to hold out their arm in front of them with the palm facing upwards. Tell them to keep their arm straight and close their eyes. Start very, very slowly to trace one of your fingers from the wrist towards the elbow joint. Then instruct the victim to tell you when they think your finger has reached the elbow joint. I won't spoil the surprise! DrChrissy ^(talk) 20:07, 17 January 2017 (UTC)[reply]

Thanks everyone for their input here! Count Iblis (talk) 08:13, 20 January 2017 (UTC)[reply]

Do humans ever crave romaine lettuces and tomatoes?

For some reason, humans often say they crave sweets. But then when they go into specifics, they mean colorful baked pastries and candies and soda pop. I've never encountered one who has a fruit craving. "I want to eat a banana right now. I need potassium!!!" When it's a fat craving, they eat hamburgers and French fries, not "I need an avocado. Must have an avocado." Or let's say a person needs something to munch on constantly, but then eats a whole pack of cookies. If the cookies were swapped for a whole head of washed Romaine lettuce, then it'd probably take the same amount of time to munch on, and the person may absorb in water and usable nutrients. Why are fruits and vegetables not attractive? Do they ever induce cravings? 66.213.29.17 (talk) 17:58, 17 January 2017 (UTC)[reply]

Our Food craving article should be of interest. --107.15.152.93 (talk) 18:21, 17 January 2017 (UTC)[reply]

"Why are fruits and vegetables not attractive? Do they ever induce cravings?" Sorry, that's just not true. For example right now I'm really craving an apple.

We have articles on food addiction and Sugar#Addiction.

You also may enjoy reading about comfort food, Essential_nutrients, and recall that salt is essential for life. Lots of people eat lots of different things, and have lots of different preferences. We do have a nice Index_of_sociology_of_food_articles, many of which discuss how certain foods get treated differently in different cultures. SemanticMantis (talk) 18:52, 17 January 2017 (UTC)[reply]

I crave orange juice, pasta, and pickles. That's why I am having bariatric surgery on Friday. μηδείς (talk) 20:50, 17 January 2017 (UTC)[reply]

"I want to eat chocolate right now. I need phytonutrients!!!"

2606:A000:4C0C:E200:C196:3184:5BEE:2C53 (talk) 20:55, 17 January 2017 (UTC)[reply]

The answer likely has to do with our evolutionary history. When our cravings evolved, we were getting way too much fiber, fruit, and veggies and found it quite difficult to get enough protein, fat, carbs, salt, and sugar (fruit of that era had just a tiny bit of sugar). So, there was no need to develop cravings for things we already had too much of. Fruits and veggies just became what they had to eat when there was "nothing better to eat", which was most of the time. But when they were lucky enough to kill something, they needed to eat all they could, and not fill up on fruits and veggies. StuRat (talk) 22:27, 17 January 2017 (UTC)[reply]

Our ancestors lived in a World where there were no supermarkets and fast food restaurants, also before the invention of agriculture, you had to spend a lot of time finding edible fruits and vegetables, and what you would find didn't look like what we're used to eating today. The craving we have today for junk food evolved to allow us to select the very specific edible and nutritious foods out of everything that grows in Nature. This leads today to a very strong attraction to modern fast foods containing an unnatural amount of salt, sugar, and fat, which is going to be the cause of death for most of us.

The sense of taste we have for salt sugar and fat gets less sensitive the more you eat of foods containing a large amounts of them. If you start to eat only healthy foods and stop adding sugar and salt to your food, your sense of taste will recover and you'll be able to sense the taste of vegetables and fruits much better. You can then find eating a banana just as tasteful as what eating a candy used to be like when you were still eating junkfoods. Count Iblis (talk) 23:33, 17 January 2017 (UTC)[reply]

Yes, I've mostly stopped eating beef, and now it tastes like blood, whenever I do eat it. StuRat (talk) 00:26, 18 January 2017 (UTC)[reply]

People who go on long backpacking trips often come out with tremendous cravings for fruits and vegetables, to such a degree that "all you can eat" salad bars are not viable in places that host large numbers of backpackers. I have also myself experienced strong cravings for fruits and vegetables while recovering from a cold. My personal belief is that these are basically potassium cravings, but that's really just speculation -- there is no doubt about the reality of the cravings, though. Looie496 (talk) 15:48, 18 January 2017 (UTC)[reply]

Pica can be caused by a nutrient deficiency. Also, see specific appetite. StuRat (talk) 22:49, 18 January 2017 (UTC)[reply]

- Many Inuit will have a craving for traditional foods if they have been without them for some time. Especially caribou mipku (dried meat), piffi (dried fish), tunnuq (caribou fat) and quaq (frozen caribou or fish). I would think that in other places where seals are more common they would crave that too. Of course most Inuit seem to crave the same junk foods as the rest of the world. CambridgeBayWeather, Uqaqtuq (talk), Sunasuttuq 07:40, 19 January 2017 (UTC)[reply]

- - Surely what you're describing is a form of comfort food or food craving. If they ate mipku as children, they'd probably crave it as adults, just as anyone else would crave their mom's specialty, regardless of how good it actually was. Matt Deres (talk) 20:10, 20 January 2017 (UTC)[reply]

Were moonwalkers allowed to keep any pieces of it?

Were they given/allowed to keep a small souvenir? Sagittarian Milky Way (talk) 22:16, 17 January 2017 (UTC)[reply]

Apparently not. [9] The things are apparently absurdly valuable - $50,800 per gram! There are a lot of stories about NASA trying to track down rocks they gave to every state and most countries that apparently have turned into the tokens of some preposterous international financial board game. Wnt (talk) 23:57, 17 January 2017 (UTC)[reply]

Yes. Apollo astronauts were allowed to keep a few rocks as lunar souvenirs, under the condition that they would never be sold but instead passed down from generation to generation. [10] In 2012 Barack Obama signed a bill into law granting NASA's Mercury, Gemini, and Apollo crew members "full ownership rights" to the artifacts they received and retained more than 40 years ago. The legislation (H.R. 4158) was authored in response to recent challenges raised by NASA's General Counsel and Office of Inspector General (OIG) over the attempted sale by several astronauts of their mementos.[11] --Hillbillyholiday ^talk 00:51, 18 January 2017 (UTC)[reply]

Reading that article, it says "The bill doesn't apply to the mementos astronauts brought from Earth to fly as souvenirs in their personal preference kits, and it explicitly excludes "lunar rocks and other lunar material." - so you're wrong.

The short answer seems to depend on the minimum mass of a "piece" of the Moon - if you're an Apollo astronaut, you get to keep dust sticking to your gear during your mission, and even incorporate it in privately-owned works of art. Our article on Apollo 12 astronaut Alan Bean refers to Bean's paintings of scenes from the Apollo missions; Paul D. Spudis, a senior staff scientist at the Lunar and Planetary Institute, Houston, Texas, USA (writing in "Can You Legally Own a Piece of the Moon?", an article in Air and Space Magazine) says that Bean is said to mix lunar dust which had stuck to his space suit and been recovered after the mission in the paints used in some of those paintings. NASA doesn't seem to have asked for the remaining dust, the paintings incorporating them, or a cut of Bean's profits from sales of those paintings.

Anything larger than that is held to be US Federal government property and cannot be owned by anyone as private property. American space writer James Oberg reported in "Astronauts, Cronkite To Get Moon Rock Plaques", a short article on the NBC News website that "The federal government forbids private ownership of any Apollo sample," and that the lunar samples included in commemorative plaques presented to astronauts active from Projects Mercury to Apollo, and the CBS News anchorman Walter Cronkite (who was on the air for 27 of the 30 hours the Apollo 11 astronauts were on the lunar surface) remained the property of the US National Aeronautics and Space Administration ( NASA). Oberg elaborated "...the honorees or their families will select in coordination with NASA a museum or some other educational institution where the awards will be on display in their name." So these are loans of lunar rock to various museums made by NASA in the names of the various honorees. loupgarous (talk) 00:55, 18 January 2017 (UTC)[reply]

Ah, I missed that bit at the end. But if the Time article is to be believed, it seems they were given souvenir samples, though they may not be true "owners". I definitely read somewhere that Armstrong managed to smuggle back a few moon-pebbles up his arse, discarding them in disgust after it was conclusively proved to him that the Apollo missions were indeed fake. --Hillbillyholiday ^talk 01:08, 18 January 2017 (UTC)[reply]

That fringe theory was debunked years ago by several successful reflections of laser light from reflectors left by Apollo missions to enable precise seismographic measurements as well as measurement of the distance between the Earth and Moon. Several researchers with no connection to NASA or the US federal government have conducted these experiments successfully. loupgarous (talk) 01:54, 18 January 2017 (UTC)[reply]

You're saying they used lasers to prove Armstrong didn't actually put moon-rocks up his bottom? --Hillbillyholiday ^talk 02:06, 18 January 2017 (UTC)[reply]

If you really believe the Apollo missions were faked, you should sue your educational system for fraud. ←Baseball Bugs ^{What's up, Doc?} carrots→ 08:31, 18 January 2017 (UTC)[reply]

If you really believe I really believe the Apollo missions were faked, you're plain nuts. --Hillbillyholiday ^talk 09:11, 18 January 2017 (UTC) (Do you also believe I missed the logical incompatibility between these two propositions: a) Armstrong returned from the moon with rocks up his arse; b) Armstrong thought the moon landings were faked? Hint: deliberately self-contradictory statements are often used in jokes.)[reply]

Well, your humor is too subtle for my feeble brain. But it's good to know that even a hillbilly is smarter than the presumably educated individuals who've convinced themselves that the moon landings didn't happen. ←Baseball Bugs ^{What's up, Doc?} carrots→ 12:21, 18 January 2017 (UTC)[reply]

Poe's law. Tigraan^{Click here to contact me} 17:36, 19 January 2017 (UTC)[reply]

The only moonwalker I can think of who was always looking for a small piece to take home was Michael Jackson. StuRat (talk) 22:29, 17 January 2017 (UTC) [reply]

If he were still alive, that would be a serious BLP violation. ←Baseball Bugs ^{What's up, Doc?} carrots→ 11:07, 20 January 2017 (UTC)[reply]