Wikipedia:Reference desk/Archives/Science/2012 April 6

= April 6 =

Virtual work
Here's something I don't understand about virtual work.

By definition, $$\delta W=\vec{F}\cdot\delta\vec{r}$$. Normally, we write $$\vec{F}\cdot\delta\vec{r}= \dot{\vec{p}}\cdot\delta\vec{r}= \frac{\mathrm{d}(\vec{p}\cdot\delta\vec{r})}{\mathrm{d}t}-\vec{p} \cdot\delta\dot{\vec{r}}$$ and solve from there.

But couldn't we just say that $$\delta W=\delta T=\sum_k \frac{\partial T}{\partial q_k}\delta q_k,\ \mathrm{where} \ q_k=\mathrm{k^{th}} \ \mathrm{degree} \ \mathrm{of} \ \mathrm{freedom}$$? It doesn't give the right answers, but physically I don't see why this shouldn't work. 65.92.5.132 (talk) 02:19, 6 April 2012 (UTC)


 * Hello, if T is kinetic energy then surely $$\frac{\partial T}{\partial q_k}$$ is zero? For example, a point particle has $$T = \frac{1}{2} m \dot{q}^2$$ which isn't a function of $$q_k$$.
 * Perhaps we need:

$$\delta W=\delta T=\sum_k \frac{\partial T}{\partial \dot{q_k}}\delta \dot{q_k} $$ and then connect this to $$\delta\vec{r}$$ ? Sorry I get confused with generatised coords. 94.72.209.210 (talk) 13:07, 6 April 2012 (UTC)
 * There are situations where T can depend on $$q$$ as well as $$\dot{q}$$. For example, if a point mass is attached to a rigid rod which is pivoted at the origin and rotating in the xy plane w/ angular speed $$\omega$$ (the point mass is allowed to slide up and down the rod), then $$\vec{r}=q\cos{\omega t}\hat{x}+q\sin{\omega t}\hat{y}$$ (q is the distance from the point mass to the origin) and so $$T=\frac{1}{2}m(\dot{q}^2+\omega^2q^2)$$. And besides, $$\delta\dot{q}_k=0$$ by the definition of a virtual displacement. 65.92.5.132 (talk) 15:09, 6 April 2012 (UTC)


 * You aren't defining your terms, but it looks like you're using standard notation, where T is kinetic energy. If so, you forgot U (potential energy).  Even when working in generalized coordinates, you must still use total energy.  And, as pointed out above, kinetic and potential energy can both vary as functions of q, dq/dt, or any other generalized coordinate.  Nimur (talk) 00:41, 7 April 2012 (UTC)
 * Sorry for not stating it, but I'm defining $$\delta W$$ to be the total work done, including work done by any conservative force. Also, why would dependence on $$\dot{q}$$ matter? Isn't $$\delta\dot{q}=0$$? 65.92.5.132 (talk) 02:34, 7 April 2012 (UTC)

Dreams: maker versus watcher
I am often struck by the disconnection between what things in dreams appear as and what they are interpreted as. In a dream, I can know that what I see as a tiger is 'really' a lion. Sometimes I've thought that the concept was real and its graphic rendition was fouled up, but this time it appears otherwise...

A dream I had last night involved the story of a little girl living out on the streets who was taken in by a caring family. After she told a social worker how much she loved it there and hoped she'd be adopted, her would-be parents took her up to an even nicer bedroom to stay. There's a sudden heavy thump on the ceiling that makes the hanging light in the room sway, and they tell her that's "their daughter Grace". Then they hurriedly lock the door leaving the girl inside, and as Grace comes down into the room she screams and runs over to a tiny window which she manages to get open and slide out through. As a fast-tempo musical theme from The Nutcracker (I think) starts up I see Grace, who is a giant snake with glowing eyes that follows the girl out the window and chases her around the manor's rooftop.

Now what was odd, though, is that all the while I'm watching this giant snake slither out the window and around the dormer windows this little girl was so desperately skirting, (eventually devouring a Garfield-like "pet cat" the girl had with her the whole time after she slammed a far door on it) I never once believed that what I saw as a giant snake was anything other than an older girl. I was still thinking, this is the cannibal freak daughter that was locked up in their attic chasing her. But the set-up - the thump on the ceiling, even the family adopting street urchins so that when they disappear nobody notices so that their "daughter" can have its preferred human meat - it all points to the person creating the dream knowing it was a giant snake the whole time.

Is there any term for this? Who makes the dream? Who watches the dream? Where are these people located in the brain? What mechanism notices incongruities between what we see and what we think we see, and how is it deactivated?

I suppose what perplexes me the most is, if one part of me had the ability to cobble together such an elaborate plot, why is a different and seemingly unconnected part able to watch it? Why isn't there just one place in the brain capable of conceptualizing the idea of "snake" and "little girl"? Wnt (talk) 13:24, 6 April 2012 (UTC)
 * (...crickets...) I don't think you'll get any refs for this one :). Dreams are so subjective, and you can easily appreciate how hard this would be to study scientifically. Anecdotally, I think I know what you mean, but I don't think it implies a "dream maker" vs. "dream watcher" dichotomy. Rather, I think it points toward the differences between what you "see" in a dream v.s what you "know" in a dream. Example: I've had dreams about people I know where (to borrow acting terms) the "part" of person X is "played" by person Y. Often, person Y is indeed a famous actor/actress, maybe because my brain is more inundated with images of the famous person, so their face fills in, even when the dream is about someone I know personally. This, to me, sounds similar to what you describe. You "knew" it was a cannibal human, but it was "played" by a giant snake. Does that make any sense? SemanticMantis (talk) 22:00, 6 April 2012 (UTC)
 * It sounds like we're observing very close to the same thing - which means there's something reproducible to it. But it sounds like in the case you describe the known version was indeed more fundamental than the seen version, which is interesting.  I can't believe there isn't data on it though, at least, psychological anecdotal data, given how many shrinks tried to infer Freudian things from dreams - surely some must have taken a general interest in how they work, and come up with some such observations.  (Actually, as I was fairly consciously aware while having it, this dream was rooted in a certain Commons thread where for a time I played the part of the social worker, but the less said there the better) Wnt (talk) 04:24, 7 April 2012 (UTC)
 * Just to pick up on SemanticMantis's point, the meaning of your dream will be apparent to you if you think hard enough about it. Dreams, as they are currently perceived by the psychological community, are a way of making sense of memories, and as memories are derived from your own experience, nobody else can tell you what a dream means. So the maker of the dream, the watcher of the dream, are all you. --TammyMoet (talk) 08:11, 7 April 2012 (UTC)
 * The idea that YOU are one "consciousness" experiencing it self and reality in real time is an illusion. Reality and perception are CREATED in the brain by many "modular" components which play disparate roles. I'm having a hard time finding references in Wikipedia, possibly split brain and Dissociative disorder could be taken as references, maybe even Alien hand syndrome. There is a term I've come across called "reality testing" which I can't find in wiki but would be relevant. Reality testing is something your brain does continuously in parallel and subconsciously. While you are asleep, your reality testing "process" is greatly diminished which is why when you are dreaming, very unusual scenarios might not seem out of the ordinary at the time. Vespine (talk) 00:34, 10 April 2012 (UTC)

Middle East climate
Why is the Middle East so dry even though it directly borders parts of Europe and Asia that aren't? --204.184.214.187 (talk) 14:43, 6 April 2012 (UTC)


 * Not all of the Middle East is very dry; Israel, Lebanon and parts of Jordan and Syria have a more moderate climate. Also, the Middle East is not a unique dry part, but part of a much larger dry area spanning from northwest Africa to parts of west India. At Köppen climate classification, you can view a world climate map illustrating this. What exactly the cause of the drought is, may be complicated and is probably related to wind patterns, but I don't know much about that. -- Lindert (talk) 15:19, 6 April 2012 (UTC)


 * In a nutshell, it seems you don't get much rain around the Persian Gulf and the Red Sea because the atmospheric circulation known as the Hadley cell carries water away from the Middle East, and the mountains around the Iranian plateau (mostly, I think, the Zagros Mountains) trap what rain does blow in. This paper has more details, though it's rather dry and technical. Smurrayinchester 15:51, 6 April 2012 (UTC)


 * It's part of a dry subtropical lattitude band that stretches from the Sahara to the Gobi and also includes the US Southwest and adjoining northen part of Mexico. It's southern hemisphere counterpart includes the Namib and Kalahari in Africa, the Atacama in South America and the Central dessert in Australia. Roger (talk) 20:42, 7 April 2012 (UTC)
 * The answer is the Hadley cell, but not the reason given above. The reason the subtropical latitudes are so dry is that air rises in thunderstorms near the equator, it then must sink at some point. These desert regions are areas where there is a net subsidence, or sinking of the air, which in general suppresses the rising motions that contribute to rain. This is a very general, averaged effect, so local effects such as the Indian monsoon cause areas at similar latitudes to be quite moist.- Running On Brains (talk) 21:57, 7 April 2012 (UTC)

Vitamin B12 absorption
I've read that vitamin B12 absorption from low dose supplements (less than about 50 micrograms) is limited to a maximum of about 1.5 micrograms, presumably because the limiting factor is the availability of enzymes needed for absorption.

How long does it take after taking one supplement before the body is able to absorp 1.5 micrograms from the next supplement? Count Iblis (talk) 15:58, 6 April 2012 (UTC)

Uniqueness of the attractor for Earth's climate
Earth's climate tendencies can be viewed as an attractor within which the actual climate evolves. For example, in the above discussion of the Middle East's climate, the Hadley cell carries water away from the Middle East, giving it a mostly dry climate; the Jet Stream over the US follows a time path that, while not precisely repeating itself annually, stays within certain limits; etc.

But is it known whether the observed global climate attractor is unique? In other words, if we held constant the locations of the continents and oceans and the orbit of the Earth, but started from initial conditions of say zero wind velocity everywhere (or started with new initial conditions after some massive external disruption), would we eventually return to the attractor that we are familiar with? Or are there multiple attractors, each with a different basin of attraction in the space of initial conditions? Duoduoduo (talk) 17:38, 6 April 2012 (UTC)


 * It partly depends on the timescale you look at. There is, I believe, a pretty strong case that Snowball Earth is also an attractor -- if the entire Earth were covered with ice, it would reflect so much sunlight that it would never warm enough to melt the ice.  It is widely believed that the Earth has been in such a state several times, but that it eventually escaped because over the course of a few hundred million years so much CO2 accumulated in the atmosphere that it eventually produced enough global warming to melt the ice.  That account isn't universally accepted, though. Looie496 (talk) 17:46, 6 April 2012 (UTC)


 * One big effect seems to be the motion of the continents. When they move they change ocean currents, and, to a lesser extent, air currents, causing massive changes in the climate.  So, you would have to stop plate tectonics, among other things, to get a constant climate.  The "snowball Earth", for example, might be caused by plate motions.  So, I would argue there would be a single equilibrium point if none of the inputs changed, but, since they do, we end up with multiple equilibrium points, depending on the current inputs to the system. StuRat (talk) 17:58, 6 April 2012 (UTC)


 * My gut feeling is that the Ice Ages approximate such an attractor (I know the orbit is supposed to be involved, but have you looked at the comparison? It's not very convincing looking).  In any case, the transition back and forth from Ice Age to not is so extreme, I think it would have a good chance to kick us out of any smaller attractors if they exist.  Of course, climate has changed on that time scale in many places, e.g. North Africa which in Carthaginian times was better suited for horses than camels. Wnt (talk) 20:32, 6 April 2012 (UTC)


 * As Looie said, it depends on the timescale you are looking at. We will never reach a true attractor in climate (even if one might exist locally), because the solar and geophysical inputs are constantly changing: on short scales we have seasons, on intermediate scales we have the Milankovitch cycles, on longer scales we have drifting continents, and on even longer scales we have ever-increasing solar luminosity, and decreasing tides and increasing length of day due to the tidal acceleration of the earth-moon system. This is not to mention the occasional high-impact events such as supervolcanoes and impact events, and other bizarre occurrences (Messinian salinity crisis, megafloods) which can affect the earth for thousands of years, or human activities such as deforestation and anthropogenic emissions causing photochemical smog, ozone depletion, and global warming.- Running On Brains (talk) 20:56, 7 April 2012 (UTC)

Explaining light
Some years ago I received from an aquaintance by e-mail a curious physics explanation. I need some help to provide a serious point-by-point answer. The following is the exact text as I received it, with no attempt to correct typos e.g. Cerb to Cerne, paricles to particles, degenartion to degeneration.

(text starts)That collider at Cerb, Switzerland is another non-starter. They are using something ( electrons/magnetism throigh a material conductor) to find out what conditions were like when there was nothing. It's a dead end. All you ever get when dividing matter into ever smaller paricles is another surface. No one has yet considered that there may be a dimension where light can not go less than 186k/sec., and that this dimension ( the big bang) ocurred when an anomaly, or time warp, retarded light and as it descended from super light, time came with it and the release of supercharged energy created heat, which when it expanded created matter. Desension of superlight from hyperspace couldn't dispell itself fast enough resulting in a dense coagulation, or degenartion of energy, into more solid form.

I've never understood why if the speed of light is a constant, its speed can become squared; as in E= Mc2. But if the speed of light can be squared ( in fact) there should be a universe, or dimension, where this is the standard. (text ends) 84.209.89.214 (talk) 23:52, 6 April 2012 (UTC)


 * Technobabble like this example can sound quite serious, but it is pure gibberish. A point-by-point explanation would be useless, because this text excerpt is absolutely meaningless.  It name-drops several interesting topics in physics, and it misspells CERN, among other errors; but it doesn't actually say anything.  Nimur (talk) 00:44, 7 April 2012 (UTC)


 * Perhaps you should reply in technobabble too ? "The light-force emanations vibrate into crystalline astral projection planes in non-isotropic Euclidean parallel multi-verses, thus ensuring the isotope strings of an invariant cosmology." StuRat (talk) 00:54, 7 April 2012 (UTC)


 * One fairly big problem is that there was not "nothing" at the Big Bang, there was an incredible amount of energy contained in an infinitely small space. The idea of the Large Hadron Collider is not to create "nothing from something", but to create as large an amount of energy in as small a space as possible. The rest is basically gibberish. Speed squared is not a speed, any more than distance squared is a distance (for instance, 5 inches squared is not 25 inches, but 25 square inches, which is a measurement of area). Smurrayinchester 09:05, 7 April 2012 (UTC)

just one easy to contradict point. Let's say a typical rat is 5-6 inches. If a person is 5-6 feet, that means that the length of a person in terms of rats is 12 * ratlength. But if 12 * ratlength is meaningful, then there must be a rat the size of a person. We just have to find it and put it on television. (this is the same argument used about the fact that you can 'square the speed of light' in e=mc^2, exactly the same as multiplying the length of a rat by 12. it doesn't have any bearing on the speed of light!) 188.156.106.2 (talk) 08:39, 7 April 2012 (UTC)


 * There are rats the size of people (infants, at least). See nutria. StuRat (talk) 16:43, 7 April 2012 (UTC)
 * Nutrias are nothing! Check out these guys. Evanh2008 (talk) (contribs) 21:23, 7 April 2012 (UTC)


 * Yep. Tecnobabble, and not even good technobabble. In addition, heat could not have existed before matter since heat is a property of matter. Evanh2008 (talk) (contribs) 09:03, 7 April 2012 (UTC)

Escape velocity
Is the escape velocity of the Earth's gravitational field in m.p.h. is equal to the length of the circumference in miles? 84.209.89.214 (talk) 23:53, 6 April 2012 (UTC)


 * No. Why would it be?  That the numerical values, expressed in different units, are similar is merely a coincidence.  Dragons flight (talk) 00:01, 7 April 2012 (UTC)


 * Earth's circumference in cubits is 8.8×107 while Earth's escape velocity is 8.8×107 cubits per hour. Lord! it's a miracle!
 * For any spherical body, the ratio between its circumference and its escape velocity is given by the following expression: $$\frac{\sqrt{2} \pi r^\frac{3}{2}}{\sqrt{GM}}$$
 * Subbing in Earth's dimensions gives us 3575 seconds, which is coincidently very close to the 3600 seconds in each hour. Thus it's pure coincidence that an object travelling at escape velocity around Earth would take approximately one hour. Anonymous.translator (talk) 02:16, 7 April 2012 (UTC)


 * As a side note, "Eight Eights" (88888888) is probably the shortest mnemonic possible for memorizing both Earth's equatorial circumference and Earth's escape velocity. For someone living in ancient Egypt at least.Anonymous.translator (talk) 02:24, 7 April 2012 (UTC)


 * Escape Velocity = the speed at which a prisoner is pardoned after making a generous contribution to a retiring US President, or governor of a US state. StuRat (talk) 02:36, 7 April 2012 (UTC)