Wikipedia:Reference desk/Archives/Science/2012 October 12

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October 12

Dot product and cross product

We know "Work = Force x Displacement", where "Work" is scalar quantity and both "Force" and "Displacement" are vector quantity. This means dot product of vectors is scalar quantity. We also know that cross product of vectors is a vector quantity. Suppose, we are given "Power = Force x velocity". Here, both "Force" and "Velocity" are vector quantity and we have to find whether "Power" is scalar or vector quantity. It becomes easy if we have idea that "Force x velocity" is dot product or cross product. My question is how to recognize the given product of vectors is dot product or cross product. Please, also give me some examples where cross product of vectors is a vector quantity. Sunny Singh (DAV) (talk) 12:28, 12 October 2012 (UTC)

Any quantity is a vector if it is directionally dependent. Does a concept like "power" or "work" have a directional component? If so, it is a vector. If the value doesn't depend on the direction, it is a scalar. --Jayron32 12:44, 12 October 2012 (UTC)

Question, is there a difference between simple multiplication and the cross product? Plasmic Physics (talk) 12:51, 12 October 2012 (UTC)

Multiplication of vectors, Cross product. TenOfAllTrades(talk) 13:01, 12 October 2012 (UTC)

We don't just arbitrarily multiply vectors and then try to figure out what formula to use. We use mathematical formalism to make a simple calculation about a physical quantity we care about. A dot product of two vectors represents the physically meaningful concept of projection. Loosely stated, this calculation measures how "similar" two vectors are; or how closely aligned they are; and it is scaled by the magnitude of each vector. We can also normalize if we are concerned only with geometry, and not magnitude. We often use the scalar result of a dot product to scale another vector, if that represents some physical, useful quantity. The cross-product is a little more unusual, because its physical interpretation is somewhat less intuitive; but simply put, a cross product guarantees orthogonality. There are many situations in physics where that property of vectors has physical meaning - like when we're calculating properties in rotating reference frames; or calculating interactions with magnetic fields, spinning objects, and fluid or particle ensembles. My point is, you decide which calculation you need entirely based on the physics; not just based on arbitrary combinations of your input variables. Nimur (talk) 14:25, 12 October 2012 (UTC)

Nimur's point is what I was going after, but in less eloquent terms as he puts it. Mathematics is a tool in these cases used to elucidate the physics, not the other way around. The physics of a situation drives what mathemetics we use to help explain it. If a physical quantity has a direction, vector mathematics is used to describe it. If a physical quantity is directionless, scalar mathematics is used to describe it. The question first to be asked when trying to decide whether a quantity is scalar or vector should be "does this physical property depend on direction." --Jayron32 16:13, 12 October 2012 (UTC)

Torque is an example where the cross product is used. The result of the applied force will be a rotation around an axis perpendicular to the force and the lever. Lorentz force is another example: the force on a charged particle in a magnetic field is perpendicular to the direction of the field and to the direction it's moving in (the velocity vector). For a charged particle in an electric field on the other hand, the force will be in the direction of the field. Angular velocity can also be represented as a vector, and the cross product is used here too. One way to decide whether dot or cross product should be used is considering two cases, one with both vectors in the same direction, the other with perpendicular directions. If the result should be maximum for the first and zero for the second, then you would probably use the dot product; in the opposite case, the cross product. Ssscienccce (talk) 10:55, 13 October 2012 (UTC)

Two questions for project

Does anyone know what structural settings bending folds are most likely to be found in? What about buckling folds? This will be useful in identifying where different structures formed. Thanks.~~--- Anon — Precedingunsigned comment added by 99.146.124.35 (talk) 12:46, 12 October 2012 (UTC)

In what context, geology? Plasmic Physics (talk) 12:49, 12 October 2012 (UTC)

Yes structural geology. — Preceding unsigned comment added by99.146.124.35 (talk) 13:08, 12 October 2012 (UTC)

List of orogenies? See also Fold (geology).--Shantavira|^{feed me} 16:12, 12 October 2012 (UTC)

Malaria in Europe

From my previous question I realized that malaria was present in Europe some centuries ago, but now it has been eradicated. How could be possible that malaria mosquitoes specifically disappear but that you still get mosquitoes in Europe? What's the difference between one kind and the other?Gorgeop (talk) 14:12, 12 October 2012 (UTC)

Is genetic resistance to malaria perhaps what you are looking for? Mosquitos are not born with malaria, they need to ingest it from an infected host to be able to pass it on. If a strong resistance to malaria removes the disease from the population, then no amount of vectors will matter since there is no disease to pass on. Livewireo (talk) 14:42, 12 October 2012 (UTC)

Malaria eradication was very much intentional. We have an article National Malaria Eradication Program for the U.S. - not sure if we have the equivalent for Europe. History of malaria makes an extraordinary claim indeed, that Anopheles gambiae got loose in South America, caused the worst malaria epidemic ever seen in the New World, but was then completely exterminated by eradication efforts within a few years. Which, I have to say, seems more ambitious than programs against invasive species tend to be today, even if they had to use Paris Green (and ordinaryPyrethrum) to do it according to our article - and it was done in northeast Brazil! (Apparently this was just before DDT was discovered to be an insecticide ... not sure if it played a role; certainly it did in other efforts) Of course, those were also the days when "draining the pestilential swamps" was seen as a positive thing. Wnt (talk) 14:59, 12 October 2012 (UTC)

Generally speaking the major way to eliminate malaria was to drastically decrease mosquito populations (vector control). Historically this was achieved by drainage and later pesticides. By driving down the number of mosquitos for an extended period of time, you can decrease the amount of overall malaria in the ecosystem to basically zero levels, because the malaria parasite cannot reproduce without mosquitos. You will never really get rid of all of the mosquitos, and their populations will rebound, over time, but without the malaria parasites. Mosquito monitoring and control is no doubt still in effect (in the United States, the Centers for Disease Control and Prevention does this); if all mosquito control efforts stopped tomorrow, over time malaria would likely return to Europe and other places it has been "eradicated" from. --Mr.98 (talk) 14:59, 12 October 2012 (UTC)

See The history of malaria in England which says that locally transmitted malaria was finally eradicated from the UK in the 1950s, which is surprisingly late. We still have mosquitoes though. Alansplodge (talk) 18:03, 12 October 2012 (UTC)

Malaria is transmitted by Anopheles gambiae mosquitos and these are not like other mosquitos that are still extant in Europe. It's easier to eradicate this species, since they are not able to "hibernate", therefore, you just have to hit them hard once during the winter, when they are more prone to be eradicated. The eggs that they lay won't be dormant for months and hatch when it's hot again. Summary: it was easier to get rid from malaria transmitting mosquitos in Europe, but others are more resilient. OsmanRF34 (talk) 19:52, 12 October 2012 (UTC)

The parasite needs certain species of mosquitoes to reproduce and human or animal hosts to spread. Mosquitoes don't live long and will feed only a few times before they die. For the parasite to spread, you need infected persons (or other secondary hosts if the mosquito is a species that feeds on animals as well) in whom the parasite has had time to infect the blood cells, a mosquito of the right species has to bite him and get infected, the parasite needs time to reproduce in the mosquito and then the mosquito has to feed on another person before it dies. Infected people will eventually be diagnosed and treated, so when the infection rate is low, the number of hosts will decrease steadily. Ssscienccce (talk) 12:05, 13 October 2012 (UTC)

Volume of naphtha

How many British Thermal Units of naphtha can fit into one cubic foot or cubic meter? I have a figure with a specific number of BTUs, and I'm trying to figure out its total volume, so I went to Wolfram Alpha, but all I got was "BTU_IT (IT British thermal units) and ft³ (cubic feet) are not compatible." 2001:18E8:2:1020:749C:5B76:1D8E:3D22 (talk) 14:24, 12 October 2012 (UTC)

Well our article has a density down as "750-785 kg/m3" - with that you can work from a measure of BTU per kg, though actually a direct statement of BTU per volume might be more accurate. (This won't be perfectly accurate in any case because with that much of a density range there must be some variation in composition) Wnt (talk) 15:12, 12 October 2012 (UTC)

... and the top Google hit yields:[1]

• Petroleum naphtha "lower heating value" - 116,920 btu/gal; 19,320 btu/lb; 44.938 MJ/kg;
• Petroleum naphtha "higher heating value" - 125,080 btu/gal; 20,669 btu/lb; 48.075 MJ/kg; density 2,745 g/ft3
• NG-based FT naphtha "lower heating value" - 111,520 btu/gal; 19,081 btu/lb; 44.383 MJ/kg;
• NG-based FT naphtha "higher heating value" - 119,740 btu/gal; 20,488 btu/lb; 47.654 MJ/kg; density 2,651

"[1] The lower heating value (also known as net calorific value) of a fuel is defined as the amount of heat released by combusting a specified quantity (initially at 25°C) and returning the temperature of the combustion products to 150°C, which assumes the latent heat of vaporization of water in the reaction products is not recovered. The LHV are the useful calorific values in boiler combustion plants and are frequently used in Europe.

"The higher heating value (also known as gross calorific value or gross energy) of a fuel is defined as the amount of heat released by a specified quantity (initially at 25°C) once it is combusted and the products have returned to a temperature of 25°C, which takes into account the latent heat of vaporization of water in the combustion products. The HHV are derived only under laboratory conditions, and are frequently used in the US for solid fuels."

I'll leave it to you to double check all these numbers agree with each other. Wnt (talk) 15:20, 12 October 2012 (UTC)

Engineering and technical books usually distinguish between the LHV and HHV, as, usually but not always, the LHV is what matters to an engineer. However, it is common in college science texts to just quote a single value without stating which it is, and when they do that, it's the HHV, as it is the HHV that is measured in a simple bomb calorimeter. Ratbone124.178.45.41 (talk) 15:58, 12 October 2012 (UTC)

Actually, for the HHV / LHV question, what matters depends on the context. As an engineer who deals with this on a regular basis, HHV is what matters because that is the basis on which the fuel is supplied. It can be confusing when equipment suppliers quote performance on a LHV basis, as this gives higher efficiency numbers. --Pakaraki (talk) 06:38, 22 October 2012 (UTC)

Note that the way you asked this Q implies that a BTU is a unit of volume. Instead, I suggest that this would be a clearer Q: "How many British Thermal Units can be generated by burning the naphtha which can fit into one cubic foot or cubic meter ?". StuRat (talk) 18:45, 12 October 2012 (UTC)

Hmm, perhaps I misunderstood what a BTU is. I thought it was the amount of gas (or whatever other fuel) needed to produce a certain amount of thermal energy? 2001:18E8:2:1020:749C:5B76:1D8E:3D22 (talk) 20:41, 12 October 2012 (UTC)

Actually, a British Thermal Unit is a unit of energy. Devices having nothing to do with flammable materials, like an electrical air conditioner, are also rated in BTUs: [2]. StuRat (talk) 21:14, 12 October 2012 (UTC)

DUTASTERIDE/ASPARTAME combined side effects

many articles give detailed side effects of DUTASTERIDE and many articles give detailed side effects of ASPARTAME, but no article gives effect of both these taken together. If an article could be given on this topic of a pointer to the sites where this could be found would be good. Thanks — Preceding unsigned comment added by117.223.102.73 (talk) 16:25, 12 October 2012 (UTC)

I added a title. StuRat (talk) 18:42, 12 October 2012 (UTC)

Unless this has been studied to see if the combined side effects are worse than just the total of each, there is unlikely to be any such article. And, unfortunately, the number of combinations of two substances is too large for every combo to be studied. StuRat (talk) 19:04, 12 October 2012 (UTC)

• Don't hold your breath for such an article when this search provides zero results. -- Scray (talk) 19:59, 12 October 2012 (UTC)

dutasteride is a 5-alpha-reductase inhibitor, one could check if these enzymes are involved in aspartame metabolism. But that still wouldn't tell you much. Ssscienccce (talk) 13:21, 13 October 2012 (UTC)

Indeed you have discovered the Achilles heel of "safe chemicals" and drugs in general. One may be reliably safe in tests, but two in combination can be a different matter. The classic example of this is melamine, which is pretty much safe to contaminate/adulterate foods with ... until it meets up with cyanuric acid to form big plates of melamine cyanurate that concentrate and clog up the kidneys.

That said, the odds of any given interaction are, well, "probably very low". And because dutasteride resembles a steroid and aspartameresembles a small peptide, their interactions shouldn't be all that different from interactions of other chemicals within the body ... unless they are. Wnt (talk) 19:51, 13 October 2012 (UTC)

Well said. Chance of any interaction is low, but polypharmacy is a big challenge, and the number of potential interactionsgrows exponentially with the number of medications (our article makes this statement, and the math's pretty simple, but it would be nice to find a reliable source that shows this). Food for thought. -- Scray (talk) 20:13, 13 October 2012 (UTC)

evolution

Is it possible that someone studying our civilization 30,000 years from now differentiates caucasoid, mongoloid, and negroid the same way we differentiate neanderthal, sapien and denisavan? As different species due to the relatively narrow geneome that would exist at the future time?165.212.189.187 (talk) 18:51, 12 October 2012 (UTC)

I doubt it. A species is defined in sexually reproducing organisms as any group which can reproduce to produce fertile offspring. Clearly this is the case with all humans (even extinct Neanderthals). StuRat (talk) 18:55, 12 October 2012 (UTC)

No. While the members of a race have certain genetic similarities not shared with other races, they do not form monophyletic groups and cannot be classed as subspecies. See race and genetics for more information. Someguy1221 (talk) 18:56, 12 October 2012 (UTC)

Yes, those skeleton types are easily distinguishable, as are others. The "there is no race" POV is based on cultural and ethical, not skeletal arguments. μηδείς (talk) 20:00, 12 October 2012 (UTC)

I can differentiate tall people from short people based on skeletal morphometry, too (and height has a substantial genetic component); however, the question was about species. Differences in skeletal morphometry do not define species. -- Scray (talk) 20:13, 12 October 2012 (UTC)

Indeed. Of course there is such a thing as race. But it is not a biologically well-defined concept. I think Medeis has it backwards. The ways that we define races are cultural, and not scientific. The scientific perspective is that the concept of human races (as culturally defined) is not biologically useful or meaningful (e.g. as Someguy1221 describes), not that "there is no race." See Race_(human_classification)SemanticMantis (talk) 20:27, 12 October 2012 (UTC)

The question is whether different races could be considered to be different species, not whether different races exist. StuRat(talk) 20:19, 12 October 2012 (UTC)

I don't think the OP is arguing in a technical sense that they are separate species, he seems to be using the terms loosely. It is unlikely that future scientists would describe the races as species, since they would see unmistakable signs of interbreeding and intergradation. But the current general types will still be distinguishable to them in skeletons of our age. The differences are much more distinct than just height, white people aren't just black people with light skin. Scientists can and do distinguish negroid type skeletons from caucasoids and mongoloids and so forth all the time. Distinctions politicians and layman make may or may not correspond. Whatever it is that semanticmantis wants exactly to deny it is up to him to describe clearly. Just to say biologist, anthropologists, and other scientists don't make distinctions of race is either false, overly-vague, or a wish. μηδείς (talk) 01:47, 13 October 2012 (UTC)

Medeis, no is arguing that you can't classify people as being members of a race, nor does interbreeding and integration have anything to do with it. Rather, race simply has no meaning in cladistics, except as a geo-phenotypically defined paraphyletic grouping. Identifying a person as mongoloid carries about as much taxonomic information as pointing out that a dog is black and fluffy. Someguy1221 (talk) 02:00, 13 October 2012 (UTC)

Well, seriously, no. Telling me someone is a caucasoid tells me a lot more about what to expect about his skeleton and other statistically likely things than does telling me he's black and fluffy. Perhaps the term terrier would be more closely analogous to a "race" than black and fluffy? As for cladistics not applying to races, that will be a surprise to population geneticists and linguistic classifiers[3] for example. I am not interested in this debate, denying the reality of race is a facile way of claiming scientific sophistication. What is important is what is affirmed, not what is denied. We will see if the OP clarifies his statement.μηδείς (talk) 02:19, 13 October 2012 (UTC)

The graph doesn't refute either of us. You can take literally any group of living things and construct a phylogeny. I don't know how they constructed theirs, so I can't comment on it. I'm not saying that scientists have not worked with racial classifications in phylogeny, I'm trying to say it's not useful. In layman's terms, the group of people described as "mongoloid" does not include all living descendants of the group's most recent common ancestor, by far. In other words, there are people who genetically belong to the mongoloid classification as much as anyone who is phenotypically mongoloid does. There are even people who are phenotypically mongoloid who genetically fit in better with some other racial classification. So going back to my very first comment, the races are paraphyletic groups. If you knew any taxonomy aside from what you randomly googled, you'd know that no taxonomist would ever intentionally construct a paraphyletic group. For the most part, they only exist because many classifications were conceived before sequencing existed (some newer ones exist because species were ordered in a phylogeny before detailed sequencing was done at all). But I will give you one thing, I went too far when I said race is meaningless to cladistics. It has meaning, but I maintain that "mongoloid" is as much a species/subspecies/any-monophyletic-group as "black fluffy dog". Someguy1221 (talk) 03:38, 13 October 2012 (UTC)

It's also true that there are monophyletic groups that almost contain all of a given race. This is why cladograms like the one you showed, as well as the ones in our own article on the subject, are so easy to make. Someguy1221 (talk) 03:41, 13 October 2012 (UTC)

• Have a look at this [4] recent assessment of human phylogeny. As depicted in the first figure, human races started varying around, oh, 150,000 years ago. That's a long, long time, but it's nothing compared to the 500,000 years separating us from Neanderthals. Remember - Neanderthals persisted until very recent times (relative to that) so they were a new species. Of course, long ago, there was a time when sapiens and neanderthal were brothers in the same family, and there's a time when any two brothers today, or any two races, could be the prototype of a new species. But the races need not be the prototypes for the split - it is just as possible that a single mixed-race population subsequently divides (the nerds of all races at your local high school launch off into space...). Wnt (talk) 22:57, 12 October 2012 (UTC)

• Actually the biggest distinction among current humans is between Bushmen/Pygmies and everybody else. But even there the level of genetic similarity is much higher than between Neanderthals and Modern Man. Regarding Denisova Man, all we have from them is exactly one finger bone, one toe bone, and one tooth, so pretty much everything we can say about them comes from genetics. Looie496 (talk) 23:02, 12 October 2012 (UTC)

Despite all the pointless arguing, nobody has hit the main point. No, future scientists will not classify today's humans as separate species, because what counts as a species isn't defined based on currently-living humans. The most common definition of "species" is "a group of organisms capable of interbreeding and producing fertile offspring." There is no question that today's humans can interbreed and produce fertile offspring. Therefore, unless scientists decide to redefine species, today's humans are and forever will be the same species. --140.180.242.9 (talk) 10:38, 13 October 2012 (UTC)

Well, you usually think of the last common ancestor, and if you send some sample humans off in a flying saucer, that last common ancestor has already been born. True, it's very very unlikely, but we can't rule it out.

I am also rather curious about how much interbreeding actually occurs between the Twa or other "pygmies" and the rest of humanity. I've entertained the sci-fi speculation that these small, efficient humans await merely the development of interstellar colonization and 20 generations or so of strong selection to reveal themselves as a successor species to H. sapiens. Wnt (talk) 00:43, 15 October 2012 (UTC)

I thought Neanderthals and Sapiens could produce offspring?165.212.189.187 (talk) 12:51, 15 October 2012 (UTC)

The biological species concept is a really fuzzy concept. It's not always the case that a "mule" is sterile. For example, mallards are famous for breeding with any duck they can meet up with, and "contaminating" species in this way. There's even the odd case of ring species, which will freely interbreed along a continuum of terrain ... but act as different species at the ends! At a rough approximation, species are groups of animals that not merely can but do interbreed, or would interbreed... maybe someone else understands the philosophy here more than I do, because at some point I tend to think of the distinction as more semantic and arbitrary than deeply meaningful. I suspect for example that the incredibly rapid African cichlid adaptive radiation events have something to do with the ancestral population being made up of hybrids to begin with.

When it comes to Neanderthals, the record doesn't look like free and open mating between the two populations, but rather some very limited transfers. For example, if you backcross offspring of a rare fertile female mule back into the population, you can transfer some horse genes to the ass or vice versa (I don't know if it works both ways offhand), but it doesn't make the two the same species. Wnt (talk) 19:52, 15 October 2012 (UTC)

Couldn't that just be a result of proximity/ logistics?GeeBIGS (talk) 23:23, 16 October 2012 (UTC)

Even to the point: Can a Newfoundland breed with a Yorkshire Terrier? Would that make Dogs a "ring species"? --Jayron32 19:55, 15 October 2012 (UTC)

Sooo.... then it is "possible" or what???165.212.189.187 (talk) 14:44, 16 October 2012 (UTC)

Anything is possible, but this is extremely unlikely. StuRat (talk) 02:53, 17 October 2012 (UTC)