Wikipedia:Reference desk/Archives/Science/2017 February 3

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February 3

Feynman Lectures. Lecture 46. Ch.46-4, Ch.46-5 [1]

...

For instance, if we expand the volume by a factor of 2, the entropy change is Nkln2.

— Feynman • Leighton • Sands, The Feynman Lectures on Physics, Volume I

...

So we now have to talk about what we mean by disorder and what we mean by order. It is not a question of pleasant order or unpleasant disorder. What is different in our mixed and unmixed cases is the following. Suppose we divide the space into little volume elements. If we have white and black molecules, how many ways could we distribute them among the volume elements so that white is on one side, and black on the other? On the other hand, how many ways could we distribute them with no restriction on which goes where? Clearly, there are many more ways to arrange them in the latter case. We measure “disorder” by the number of ways that the insides can be arranged, so that from the outside it looks the same. The logarithm of that number of ways is the entropy. The number of ways in the separated case is less, so the entropy is less, or the “disorder” is less.

— Feynman • Leighton • Sands, The Feynman Lectures on Physics, Volume I

If the natural logarithm is the entropy, then I assume next. Suppose we have a box with room for certain molecules (half are black and half are white). Then the number of ways of obtaining the separated state is $({\text{number of white m.}})!\cdot ({\text{number of black m.}})!$. For 4 molecules we have $2!\cdot 2!=4$. For 6 molecules we have $3!\cdot 3!=36$.
The ways of obtaining non-separated state are $({\text{total states number}})-({\text{separated states number}})=({\text{number of molecules}})!-({\tfrac {\text{number of molecules}}{2}})!^{2}$. For 4 molecules we have $4!-2!^{2}=24-4=20$. For 6 molecules we have $6!-3!^{2}=720-36=684$.
Now, the entropy difference from going from separated to the mixed state will be $\Delta S_{4}=\ln {(20/4)}=1.61$ and $\Delta S_{6}=\ln {(684/36)}=2.94$. But according the first quote we should get always $\ln {(2)}=0.69.$ Can someone explain this please?

Username160611000000 (talk) 05:36, 3 February 2017 (UTC)

Or should we consider a limited number of states? E.g. as separated:
$|\circ \circ \circ |\bullet \bullet \bullet |$ no. of ways = 36
$|\bullet \bullet \bullet |\circ \circ \circ |$ no. of ways = 36

and as mixed:
$|\circ \bullet \circ \bullet \circ \bullet |$ no. of ways = 36
$|\bullet \circ \bullet \circ \bullet \circ |$ no. of ways = 36
$|\circ \bullet \circ \circ \bullet \bullet |$ no. of ways = 36
$|\bullet \circ \bullet \bullet \circ \circ |$ no. of ways = 36

In 3rd and 4th mixed arrangements we see some degree of order, so I'm not sure does it satisfy the Feynman's requirement that from the outside a box looks the same. Besides 2nd arrangement of separated state also looks different.

Username160611000000 (talk) 06:57, 4 February 2017 (UTC)

@Username160611000000: I haven't looked at this in depth, but I'm thinking it is not factorials at all. There is no real force by which molecules of gas expel others from their vicinity - they rebound of course, but where they are is random. It is merely maximization of entropy that disperses the molecules. So if you have four molecules of black and white, then looking at them one-side-or-the-other you have precisely one way they can exist before the barrier is pulled up, but 16 ways afterward (each might be on either side). So... (now I have no idea really) I'd guess one binary bit of data (one molecule/atom left or right) is a factor of 2 entropy, and you take the ln of all those binary bits to get an entropy figure??? Wnt (talk) 02:50, 5 February 2017 (UTC)

@Wnt: 16 ways afterward (each might be on either side) - 2⁴ = 16. Yes, having 4 binary slots we can transfer 16 different messages, i.e. 0000, 0001, 0010, 0011, 0100, 0101, 0110, 0111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111. But I don't think Feynman meant that the black molecule transforms to the white. So we have the state 0011 and can rearrange it to 0011, 0101, 0110, 1001, 1010, 1100 (agrees with $W={\tfrac {N!}{\prod \limits _{i}{}N_{i}!}}$ Boltzmann's entropy formula ). Also, information theory is irrelevant, because Feynman did not explain it. Username160611000000 (talk) 09:15, 5 February 2017 (UTC)

@Username160611000000: I wasn't saying that the black transforms to white, only that all four molecules (black and white) might be on the same side. This would separate the chamber into "pressurized" and "vacuum" areas by chance, but there is not actually any force to prohibit that - the four gas molecules have plenty of room to slide past each other while staying all on one side, if they should happen to be there. It's only chance that makes the pressure. One consequence of this though is that as we look at large numbers of molecules, such states become extremely unlikely - so I think your formula has to converge to the other as some kind of limit. But I don't know how to work with that products-of-factorials formula, and while the article seems to hint at that I don't know it is saying it. Wnt (talk) 16:48, 5 February 2017 (UTC)

I have simplified the example by saying "box with room for certain molecules". So the box size allows the mixing but doesn't allow two molecules to stay in (1/N) part of the volume. Username160611000000 (talk) 18:39, 5 February 2017 (UTC)

What is nerve discharge?

I could not find an article on nerve discharge in Wikipedia. Here it is mentioned that "Properly known as piloerection, horripliation or pilomotor reflex, the bumps we get are stimulated by fear and cold and they are essentially just a temporary change in the skin. These stimulants cause a nerve discharge from the sympathetic nervous system (which is an involuntary portion of nerves we have) and the nerve discharges create muscle contractions called arrrectores pilorum that raise the hair follicles in our skin."

Is nerve discharge the same as nerve impulse? --IEditEncyclopedia (talk) 05:38, 3 February 2017 (UTC)

Yes it is. 2601:646:8E01:7E0B:6C71:C0BE:6D28:E33B (talk) 07:29, 3 February 2017 (UTC)

More or less. A nerve impulse is a signal generated by a single cell. A writer who uses the term "nerve discharge" will usually be thinking about a substantial number of nerve impulses organized into some sort of pattern. Looie496 (talk) 14:38, 3 February 2017 (UTC)

What is the name of this disease?

Two men in my neighbourhood died for the same reason within six months. The cause of their death is "water deposited in their stomach"(English translation). As their family members were crying, I didn't ask the details to them. — Preceding unsigned comment added by 42.110.138.197 (talk) 06:12, 3 February 2017 (UTC)

Ascites. --IEditEncyclopedia (talk) 06:44, 3 February 2017 (UTC)

Could also have been Water intoxication. --Jayron32 11:32, 3 February 2017 (UTC)

Ascites is rarely terminal in and of itself. As our article on the subject relates, it can be caused by cirrhosis, other severe liver diseases, metastatic cancer, Budd–Chiari syndrome, constrictive pericarditis, nephrotic syndrome, angioedema or other conditions involving the liver or circulation of blood to and from the liver. Complications of ascites such as spontaneous bacterial peritonitis, hepatorenal syndrome and thrombosis of the portal vein and splenic vein can also cause death.

Ascites can be treated by removing the fluid directly through a needle inserted through the skin and abdominal wall (paracentesis) or through the kidneys with medicines called diuretics until the underlying cause can be treated.

For ascites to cause death in and of itself, it'd have not to be treatable by those two methods or to have resulted in severe complications, which would be the actual cause of death. loupgarous (talk) 02:14, 8 February 2017 (UTC)

Automatic envelope-opening machines?

Do major organizations that receive tons of checks have machinery to open envelopes? Or do envelopes containing checks have to be opened by hand? Let us say a health insurance company receives payment in the form of a check sent to cover a monthly premium. Those checks might be sent by individuals or by banks, using online "Bill-Pay". Such checks can be sent by United States Postal Service (in the United States). I am interested to know how the checks are removed from the envelopes. My guess is that the envelopes have to be opened by hand. I would imagine a high degree of automation sets in at the point at which the checks, freed from their envelopes, are fed into a machine. I have a hard time imagining a machine opening an envelope without occasionally damaging the contents (the checks). Anybody know anything about this? Bus stop (talk) 07:14, 3 February 2017 (UTC)

Wikipedia doesn't seem to have an article on them, but a simple Google search on envelope, opening, and machine produces numerous results. --76.71.6.254 (talk) 09:14, 3 February 2017 (UTC)

This [2] has some discussion of such machines and mentions some that can semi-automatically scan items. It seems to imply (to me anyway) machines which still need a fair amount of operator involvement in the extraction or scanning process. However if you search for the company mentioned, you can find machines like [3] [4] [5] [6] and can get an idea of the level of operator involvement and it can be minimal. Some of these include videos and there are also others e.g. [7] [8] [9] [10] to give a better idea. Note that the first source suggests the machines are called extractors not openers or opening machines. Mail openers just open the mail for an operator to remove the contents. Although the fancier machines for payments by Opex seem to be called things like 'Remittance Processor' or 'Retail Payment Automation' (but these still talk about extractors). Nil Einne (talk) 09:36, 3 February 2017 (UTC)

Thank you for that input. Let me ask a followup question. What does this mean: "Cutting Method - Basic units will just slice the bottom off the piece where higher end machines will mill the edge off. This may sound petty but the big difference is paper cuts. The milled versions will have a softer edge which is important when pulling the contents out of hundreds or thousands of envelopes per day."[11] What is the difference between "slicing" paper and "milling" paper? Bus stop (talk) 19:20, 4 February 2017 (UTC)

• They usually operate with a roller guillotine device close to one edge. The roller stays in place, the envelopes are passed through it on a belt. This cuts off a mm or so from the edge - not usually enough to hit the letter inside. Cheques also have printing standards so that there's nothing important right next to their edges - a slightly tapered cheque is still both valid and machine readable. Andy Dingley (talk) 10:45, 3 February 2017 (UTC)

Thank you to everyone. I guess it's not as complicated as I thought. It occurs to me that it could be easier if all factors were made uniform—if all envelopes were a standard size/type and all checks were a standard size/type. Bus stop (talk) 14:15, 3 February 2017 (UTC)

Arrector pili muscle and the term 'arrectores pilorum'

Our article describe the plural form as Arrector pili muscles ("The arrector pili muscles are small muscles..."). But this article uses the term "arrectores pilorum". Is arrectores pilorum plural form of arrector pili? Then why do Wikipedia article says it arrector pili muscles, not arrectores pilorum? --IEditEncyclopedia (talk) 08:09, 3 February 2017 (UTC)

It seems to me that the Wikipedia article is correctly using the singular. Compare the usage with, for example "the face muscles are small..." - face is singular.--Phil Holmes (talk) 08:48, 3 February 2017 (UTC)

First as to the linguistics: arrector is not classical Latin (it's not in my Cassell's New Latin Dictionary from 1959), but is obviously derived from ad and rector (in this context, "driver"), and some web sites translated it as "raiser", which makes sense. Pilus means a hair, which becomes pili in the genitive singular, so arrector pili means "raiser of the hair" (in the sense of a single hair) or "raiser of a hair". Each muscle only raises one hair, but when we speak of multiple muscles they would be "raisers of the hairs"—hence arrectores piliorum pilorum, with the second word in the genitive plural. However, that's if we're speaking Latin. In English we can say "the arrector pili muscles", treating the Latin phrase as simply a name and therefore not pluralizing it.

To get a handle on actual medical usage, I went to Google Scholar and searched for the two phrases. I found exactly one hit on a search for the exact phrase "arrectores piliorum", but on searching for the exact phrase "arrector pili muscles", I got an estimated 1,590 hits. Conclusion: the first one may not be wrong, but the second one is what most medical people use. --76.71.6.254 (talk) 09:36, 3 February 2017 (UTC)

Whoops, I tricked myself by misspelling the genitive plural there. If the word was pilius, then the genitive plural would be piliorum, but the genitive singular would be pilii. In fact the second I isn't there—it's pilus, hence pili and, as the original poster said, pilorum. And if I correct the search to look for "arrectores pilorum", then I get about 1,830 results.

Correct conclusion: Both versions are correct and about equally common in actual medical use. Sorry about that. --76.71.6.254 (talk) 09:45, 3 February 2017 (UTC)

Exploding Pyrex

I was doing some research on Exploding Pyrex,[12][13][14] and I was wondering, is there any test a consumer can do to differentiate between dishes made of Borosilicate glass and Soda-lime glass? Density? Index of refraction? The coefficients of thermal expansion seem to differ, but how to measure that? --Guy Macon (talk) 13:37, 3 February 2017 (UTC)

• According to the linked articles, the difference of density (2.23 vs 2.52) is relatively large (>10%). Density is fairly easily measurable: weight with a kitchen scale; measure volume by placing the dish in a recipient, filling water to the top, removing the dish, and use a measuring cup to fill to completion. I guesstimate this should be precise to 5% (if you are sufficiently careful not to spill to much when removing the dish from the recipient), in which case you have the answer... unless there is a possibility of intermediary results (there are probably kinds of glass with density around 2.4).

CTE has relatively small values: expansion is less than 3‰ for a 300°C heating (which is about the max usual ovens can heat). I guess it would probably be extremely hard to measure the length variation with non-specialized material. Maybe a clever protocol could allow to compare two different materials and deduce which one has the largest CTE, though (random idea: align objects in the oven, use a lamp and check if the shadow of the front object moves over the background one as you heat). Tigraan^{Click here to contact me} 14:36, 3 February 2017 (UTC)

• I'm a laser engraver. My rule is simple: if it has a Pyrex brand mark on it, and it wasn't my mother's or otherwise known to be ancient, then I assume it's soda glass and don't touch it.

The problem is that the soda glass is now tempered to give it strength and that tempered glass is a risk for engraving. Release the tension in the surface layer and it will shatter spontaneously, possibly a long time after engraving. Also the original borosilicate, having a lower CoTE, doesn't laser engrave terribly well either - you can't win!

Looking at it with crossed polarisers would be interesting. The soda glass also has a slightly visible greenish tint to it. Andy Dingley (talk) 15:04, 3 February 2017 (UTC)

Industrial production of breast milk

Are there ways to produce breast milk in large volumes for consumers (including synthesis)? Specifically, on a country level, is it technologically possible to partially or completely supersede cow milk production with breast milk? Thanks.--93.174.25.12 (talk) 15:21, 3 February 2017 (UTC)

Human milk bank. --IEditEncyclopedia (talk) 15:29, 3 February 2017 (UTC)

As a side note, I don't understand why you want to replace cow milk with human milk. Cow milk contains more protein and less saturated fat compared to breast milk. --IEditEncyclopedia (talk) 15:29, 3 February 2017 (UTC)

Infant formula is a rough approximation of breast milk and is manufactured on a very large scale. Richerman (talk) 15:44, 3 February 2017 (UTC)

Some are trying to make milk proteins in genetically modified yeast. This includes human proteins, but also possibly exotic milk like armadillo. Graeme Bartlett (talk) 00:28, 4 February 2017 (UTC)

What is the reason that products with fructose are for diabetic people?

I saw in the supermarket a specific area for 'diabetic people' (in fact a lot of non diabetic people use these products because they don't want be diabetic...), and I've seen there that a lot of the products contains fructose instead of glucose. Then my question is what is the difference for the body in the end of the day? here is in the end of the day fructose it's sugar as well, so why does fructose it's considered to be healthier? 93.126.88.30 (talk) 15:36, 3 February 2017 (UTC)

"... the European Food Safety Authority stated that fructose is preferred over sucrose and glucose in sugar-sweetened foods and beverages because of its lower effect on postprandial blood sugar levels.", from Fructose, though apparently there is also evidence suggesting excessive fructose intake can cause Diabetes_mellitus. Diabetic diet has a sentence about fructose, but it's not supported by a reference. Also "Fructose, by contrast, has a low glycemic index, but can have a high glycemic load if a large quantity is consumed."

It seems that there are many reasons that some diabetics and some doctors may think fructose is a good sweetener for diabetics, but the issue is not simple, nor is it fully understood. SemanticMantis (talk) 16:10, 3 February 2017 (UTC)

I think the reason is reasonably simple: fructose basically tastes sweeter than glucose. In other words, if you take amounts of fructose, glucose and sucrose that all produce the same rise in blood sugar, the fructose will have the strongest sweetening effect. Thus fructose allows people to get the level of sweetness they are looking for with the least effect on blood sugar. For more detail see our article on fructose. Looie496 (talk) 16:27, 3 February 2017 (UTC)

See also Fructolysis, which (as I understand it) says that fructose can only be processed through the liver (which takes time) and not all the fructose is turned into usable glucose. Alansplodge (talk) 17:06, 3 February 2017 (UTC)

…fructose it's sugar as well… That doesn't mean what you think it does; there are sizable differences between different sugars in how they are handled by the body. Diabetes is the body's inability to control blood glucose levels. You commonly hear about "blood sugar level", but what's really meant is blood glucose level. Diabetics have to watch their glucose intake so they don't develop hyperglycemia. Hence, diabetics are advised to consume other sweeteners like fructose. --47.138.163.230 (talk) 01:41, 4 February 2017 (UTC)

• This advice is still based on quite old studies, that suggested fructose is considered to be healthier. They were of short duration that just looked at the immediate effect of fructose vis cane sugar upon insulin levels. So, very possibly, a premature conclusion was assumed. Correlation can not always be taken as proof of causation. Yet, in the last decade much comparison has been done to track down the rise and rise and rise of Type 2. Diabetes and Kidney Disease in American Indians: Potential Role of Sugar-Sweetened Beverages, Added Fructose: A Principal Driver of Type 2 Diabetes Mellitus and Its Consequences, etc. Researcher are now beginning to unravel the reasons why high levels of fructose in our modern diet is prime suspect number one. ( low levels are OK since as primates we have evolved to usefully metabolize small amounts to our benefit). However, it is very difficult for them to get funding for this 'unpopular' research. Remember too, that many a healthcare professional left med school many years ago and his/her knowledge is rapidly becoming out-of-date. There is also, that little question that must be asked. Heath care providers may not want to lose their share of the $2,500 each 'Type 2' has to spend on medication each year, when a cost-free change in diet would suffice and be more efficacious ! Upton Sinclair wrote: "It is difficult to get a man to understand something when his salary depends on his not understanding it." There are many 'anecdotal' reference by people that have found (or come to believe) this to be true and in my personal experience I know people who have eventually been able to throw away their pills. -Aspro (talk) 14:51, 4 February 2017 (UTC)

Magnets and compasses terminology

At school we learned that William Gilbert was first to describe magnetic declination, the angle at which the compass needle "dips" downward, thus proving the existence of the Earth's magnetic field; see Representing Space in the Scientific Revolution p. 75 and Beyond the Mechanical Universe: From Electricity to Modern Physics p. 161. However, our magnetic declination article is talking about what the Ordnance Survey call "magnetic variation", and according to Wikipedia, Gilbert's "magnetic declination" is actually magnetic inclination. Neither article mentions "magnetic variation" which is widely used in the UK, see Understanding Magnetic Variation and Compass - Magnetic Variation. I'm now a bit confused. Alansplodge (talk) 16:58, 3 February 2017 (UTC)

Yes, you and I must have been brought up with the same curriculum. However, I would tend to say "dip" rather than declination. I suspect for declination/variation there may be a US/UK difference. Thincat (talk) 17:30, 3 February 2017 (UTC)

"Magnetic variation" does redirect to Magnetic declination, though. Deor (talk) 23:04, 3 February 2017 (UTC)

Why do humans live in one location year-round instead of following the food supply?

Humans don't have much body hair. Counterintuitively, they shave off their body hair too instead of keeping it for warmth. Also counterintuitively, the weather may be at water's freezing temperature, but humans still walk outside with winter coats. Why don't humans just migrate to warmer weather or live in the tropics year-round? Other animals migrate for food and water, but humans just stay put. 66.213.29.17 (talk) 18:49, 3 February 2017 (UTC)

Good question, but there's a lot going on here! For starters, you may want to read up on Nomadic people, and migrant workers - some of us still do move around to follow the food! But most of us don't. We've grown attached to staying mostly in one area so that we can have nice things like houses with heat and indoor plumbing. There's a lot of related factors, you may enjoy reading about the history of the agricultural revolution, city#history, civilization, and maybe public infrastructure and social contract. SemanticMantis (talk) 19:17, 3 February 2017 (UTC)

(edit conflict) We used to before we invented agriculture, and some still do, see Why and How Far Hunter Gatherer Groups Migrate. However, that article notes that "the distance humans can travel on foot is limited by body size", so it's a bit tricky to actually migrate into a different climate zone. Some modern humans do have the means to do this - see Snowbird (person). Alansplodge (talk) 19:21, 3 February 2017 (UTC)

• Also see transhumance. Humans did once live this lifestyle. Humans evolved to be more efficient, events like the Neolithic revolution and the agricultural revolution and domestication of animals allowed for division of labor because people could be employed by something other than subsistence farming or hunting-gathering. People had leisure time now to not spend their whole lives gathering food. The settled life style was better for more people, so that's why we do it. --Jayron32 19:25, 3 February 2017 (UTC)

There is some reason to believe that some hunter-gatherer societies had plenty of leisure time, maybe more than we do. This is discussed, with references and criticism, at Original_affluent_society#The_Three_to_Five_Hour_Working_Day. SemanticMantis (talk) 19:39, 3 February 2017 (UTC)

It depends how one defines leisure and how one defines survival. I don't spend much time gathering food. I mostly spend my day telling other people how atoms work, and the rest of my time playing strategy video games and displaying my smugness on an online encyclopedia as one of the resident polymaths. As compared to hunter-gatherer societies, I personally spend approximately zero hours working for my direct survival; as do most people in the developed world. If survival requires merely enough food to not starve, which is how these things are often defined from the point of view of the people who define these things, I spend about $200 dollars per week buying food for a family of four; the two incomes in my family make about $1600 dollars per week, thus we spend about a bout 1/8th of our 80ish combined work hours per week on actual survival, so 10 hours out of the 168 hours per week, or about 6 percent of my life working enough to not starve to death. Considering we eat a gross overabundance of calories compared to subsistence living, this is probably rediculously high as well; i'd estimate that if we were only buying enough food to not starve to death, I'm overbuying by a factor of 5 or so. So, I spend about 1% of my time to not die of starvation. The rest, as defined by those who are looking at the context of the earliest civilizations is "leisure time", i.e. time not spent starving to death. Pretty fucking good if you ask me, and still far better than hunter-gatherer society. Remember, that 3-5 hour workday was 3-5 hours spent working to not die. I spend about 15 minutes per day doing that. The rest of my "work", while still labor, is entirely excess to my survival, and is this "leisure time". --Jayron32 04:27, 4 February 2017 (UTC)

• I do live near my food supply - a supermarket. My wife prefers me with shorter hair. Dmcq (talk) 19:33, 3 February 2017 (UTC)

• Note that there's another reason to migrate towards the equator in winter, if it gets too cold for you, then. Many people still do this type of yearly migration. Of course, it's not possible for most, who are tied down to their work and school locations, unless you count vacations. StuRat (talk) 20:56, 3 February 2017 (UTC)

The switch from hunting and gathering to farming allowed the population to grow from about 50,000 10 thousand years ago to 7.500,000.000 today, an increase of 150,000 times. It would be difficult to switch back now, especially considering border controls. TFD (talk) 21:58, 3 February 2017 (UTC)

• Migration implies following desirable conditions, but it requires (approximately; at a guess) that those who move and come back can drive those who stay and try to adapt out of existence. Bear in mind that an ecological niche, such as Bangladesh, tends to have a maximum stable population, and over a period of generations those in excess tend to be deleted. So spreading to another niche, however undesirable, still increases the total population and leaves some struggling to adapt to it. Bear in mind, while it is controversial, it is thought that human ancestors were present in Diring Yuriakh (we need an article) hundreds of thousands of years ago. [15] The Denisova Cave after which Denisovans are named is also in Siberia though relatively south in it, still by no means warm. These were humans who could not hop on a jet and fly away - but they could hunker in caves and presumably other dwellings and stay warm with fires. And simply because someone could... someone did. Wnt (talk) 00:27, 4 February 2017 (UTC)

• The question makes a false assumption. Most of the inland Paleosiberian peoples such as the Yukaghir people and the reindeer herders spent the summer in the far north and the winter hundreds of miles to the south. This pattern is thousands of years old. μηδείς (talk) 03:50, 4 February 2017 (UTC)

That's an excellent point. And even hunter-gatherers who don't follow migrating species often moved from one type of terrain to another as the seasons changed. That said, it's not a move to the tropics to avoid wearing clothes, just a move I think from one biome to another depending on which is more hospitable at that time of year. Wnt (talk) 02:39, 5 February 2017 (UTC)

Our technological development has enabled us to make our food come to us instead of us going after it. Roger (Dodger67) (talk) 19:09, 5 February 2017 (UTC)