# Wikipedia:Reference desk/Archives/Science/2011 April 8

Science desk
< April 7 << Mar | April | May >> April 9 >
Welcome to the Wikipedia Science Reference Desk Archives
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.

# April 8

## Delay in Nobel awards

Why there is a delay in some Nobel awards, such as for Luc Montagnier, who was awarded the award for HIV discovery only in 2008?--89.76.224.253 (talk) 03:19, 8 April 2011 (UTC)

The delay is to avoid problems with giving awards to "discoveries" that later wind up being discredited, as happened with some of the early awards. See Nobel Prize#Recognition time lag. Red Act (talk) 03:41, 8 April 2011 (UTC)
I think also sometimes the discoveries take a while to realize their full potential, and sometimes it's such a "slow" incline that it's hard for anyone to notice. The 2009 physics prize was won by the two guys who invented the Charge-coupled device in the late 60s / early 70s. It's not like that was going to be "disproved". Back then it was a fantastic discovery, but no one could have imagined just HOW much difference it would eventually make to the world. I think it's just a case of it sort of creeping up slowly, becoming so ubiquitous until someone thinks: "Wow the guys who invented the CCD don't have a nobel prize for it? Better give them one while we still can." Vespine (talk) 06:27, 8 April 2011 (UTC)
The Nobel system is not a perfect one. Sometimes it takes awhile to recognize the importance of something. Sometimes they want to make sure it is correct. Sometimes it is because the people who can nominate Nobel Prizes are the "old guard" of science in many cases. Sometimes it is because there are political stakes involved. Some are awarded quite immediately; some take decades to award. Long after the fact (50 years or something like that) the records are opened and you can actually find out why a given prize took a long time, who nominated it, what the stakes were, etc. There is really interesting historical work done on Einstein's 1923 award, for example, which has aspects of all of the above issues involved with it (wanting to make sure he's right, old guard, politics, etc.). The Nobel Prizes should not be taken as some kind of objective, straightforward recognition — it's based on the votes and deliberations of scientists, who are just as prone to mundane concerns as politicians. --Mr.98 (talk) 13:49, 8 April 2011 (UTC)
Maybe also worth noting that the Nobel Prize is never awarded posthumously, so if you are unfortunate enough to die before being recognized, you miss your chance. Vespine (talk) 03:15, 11 April 2011 (UTC)

## Iodine-131

How do we know that the half-life of Iodine-131 is about 8 days? Did the scientists back then prove that the half-life of Iodine-131 is 8 days by waiting and measuring the Iodine-131 after 8 days or did they just write down as a theoretical 8 days? 174.114.236.41 (talk) 04:29, 8 April 2011 (UTC)

8 days isn't long to wait. Of course, they could wait any period, determine how much has decayed, then use that to mathematically calculate the half life. However, they wouldn't want to wait so little that almost none had decayed or so long that almost all of it did, or the accuracy would go way down. So, if they can wait for (what they expect to be) the half-life, that's the way to get the most accurate results. StuRat (talk) 04:51, 8 April 2011 (UTC)
I suspect it's more practical to measure the radioactivity and work it out from that. Measure the flux of beta particles coming out of a known mass (therefore a known number of atoms). Divide the number of betas per second by the number of atoms, and that's the probability that a given atom will disintegrate in one second. Divide log(2) by that number, and that's the half-life in seconds. --Trovatore (talk) 04:57, 8 April 2011 (UTC)
I don't think that would work, because you never measure every decay, and the percentage you measure will differ for any given isotope. Surely they measured the change in radioactive decay over time, thus getting an accurate half-life. Wnt (talk) 05:37, 8 April 2011 (UTC)
You don't have to measure every decay. You can measure, say, the flux through a pinhole (depending on the intensity), and scale it up.
But on reflection I do suppose it's probably easier, in the range of half-lives under discussion, to look at the rate at which the intensity declines, because you don't have to know exactly how much you started with or what fraction you're observing of decays. The downside is that it can be confounded by daughter nuclides.
For much longer half-lives, I'm reasonably sure it's done by measuring radioactivity. Let's say it's been 150 years since the discovery of, say, U-238, whose radioactivity is so modest that it takes four billion years for half of it to decay. If you could have isolated a pure sample at that time, and watched it till now, its radioactivity due to U-238 would have declined by only about a part in forty million, if I did that right in my head. Measurable now, probably, but not if you had to compare with records made then. (Moreover, I'm not sure the total alpha flux wouldn't have increased, because its daughter products are shorter-lived and therefore more radioactive — too lazy to figure that out right now.) --Trovatore (talk) 09:38, 8 April 2011 (UTC)
See http://ie.lbl.gov/radioactivedecay/ Ariel. (talk) 07:18, 8 April 2011 (UTC)

## Jaw mobility

Riddle me this. I presume I'm typical, and I can move my lower jaw not just up and down, but about two teeth left and right, and a small distance forward and back. So why can't I (even if pushing on it) make my lower jaw rotate left or right relative to the upper one? (I understand that there's a good reason for it not to do so, but the mechanics mystify me) Wnt (talk) 04:32, 8 April 2011 (UTC)

Tie two sticks loosely together with some string. You can move the sticks relative to each other in almost any direction - except that you can't make them separate. In order to rotate the jaw, one side would have to separate from its socket, and it can't do that, despite being able to move in most other directions. Ariel. (talk) 05:16, 8 April 2011 (UTC)
But there must be a fair amount of sliding possible on the "socket", or else how would the other motions be possible? Wnt (talk) 05:33, 8 April 2011 (UTC)
Our article Temporomandibular joint may give some useful basic concepts. --Cookatoo.ergo.ZooM (talk) 11:25, 8 April 2011 (UTC)
You state that your lower jaw will not rotate with respect to your upper jaw. I find it possible to selectively make the left or right molars touch, or to simultaneously make both sides touch, which implies a bit of rotation, besides the translations you described. Edison (talk) 14:06, 8 April 2011 (UTC)
In the meanwhile, I went over that article again, and I realize I made a simple error in deduction: my jaw can slide somewhat forward and back in place, but moves up and down only by rotation. Neither pivot point actually moves up and down (superior/inferior that is), so there's no way for it to rotate about the anterior/posterior (dorsoventral) axis. But then someone goes and says that theirs can! That's what I love about biology... it takes all your logic and folds origami out of it. Wnt (talk) 20:49, 8 April 2011 (UTC)
That's actually a very accurate analogy when it comes to protein folding... All the kings horses and all the kings men can't make head or tails of how proteins fold. ManishEarthTalkStalk 10:51, 9 April 2011 (UTC)

## How many people have ever lived?

I heard a claim recently that there are more people alive today than the total number of people that have ever lived before. I'm having a little difficulty wrapping my head around that idea so I'm asking can that be true? For this question let us limit the definition of "people" to Homo sapiens sapiens only. Roger (talk) 08:53, 8 April 2011 (UTC)

See Number of humans who have ever lived. The simple answer to the question is no - it was estimated in 2002 that about 6% of all people who had ever existed were alive then. Ghmyrtle (talk) 09:09, 8 April 2011 (UTC)
Thanks! It seems the joking claim that "Wikipedia has an article about everything" is not too far off the mark. Roger (talk) 09:27, 8 April 2011 (UTC)
Wikipedia has an article on everything.  ;-) Dragons flight (talk) 10:02, 8 April 2011 (UTC)
Wikipedia does have an article on everything ! SpinningSpark 11:39, 9 April 2011 (UTC)
As for the more general question of whether more of any species are alive than have ever lived, for that to be the case, you'd need a rapid population increase with each generation from the origin of the species. If the old generation died immediately when a new one was born, then we'd need to double the population with each generation. If old generations stay alive for several more generations, then that complicates matters. Doubling with each generation isn't impossible, for many species, for a few generations, but keeping it up for long is. Perhaps if a species which evolved on a small island moves to a much larger habitat with no natural predators, they might be able to have many generations of rapid increase and reach the "more alive now than have ever lived" status, briefly. StuRat (talk) 17:30, 8 April 2011 (UTC)
Might it have been true at the point where population started to exponentially grow at the beginning of the 20th century? SpinningSpark 11:45, 9 April 2011 (UTC)
Wikipedia has a graph on everything!
The lowest point on this graph is about 40 years. Average age of a parent (which is essentially what we mean by the length of a generation) is significantly less than that. --Tango (talk) 14:22, 9 April 2011 (UTC)
The definition of a generation I was taught at university is the time it takes the women in a population to replace themselves, in other terms, the average age at which X number of women produce X number of daughters. Roger (talk) 14:38, 9 April 2011 (UTC)
The table Estimated world population at various dates in the above linked article (scroll half way down) indicates that only in the era of the Neolithic revolution the population may have increased sufficiently fast to balance the living and the dead. --Cookatoo.ergo.ZooM (talk) 17:30, 9 April 2011 (UTC)
<factoid barf-up mode> While I*'m aware that this comment is nothing more than a miscellaneous unconfirmed memory floating somewhere in my noggin', I remember reading in the Guinness Book of World Records some 15 years ago that it was estimated (somewhere) that approx. 75,000,000,000 humans had ever lived on the Earth. </end factoid barf-up mode>
Best regards: Cliff L. Knickerbocker, MS (talk) 11:06, 13 April 2011 (UTC)

## Singing stars

How exactly is the sound created that is described here: http://www.bbc.co.uk/news/science-environment-13009718 ? I am already aware that that there's no sound in the vacuum of space. I think its a deficiency in that article not to explain how the sound is sourced. I presume it is either from measuring some vibration in the surface of the star, which I did not think telescopes could do, or measuring fluctations in brightness. Thanks 92.24.184.41 (talk) 10:53, 8 April 2011 (UTC)

This seems to be a more detailed BBC article describing the same thing. We have an article on Asteroseismology. 130.88.134.38 (talk) 11:02, 8 April 2011 (UTC)
The sound wave is the fluctuation in brightness, either in visible or infra-red range. The Movietone sound system works this way. Cuddlyable3 (talk) 14:11, 8 April 2011 (UTC)
I think the most important fact from the second article is that the sounds are actually thousands of times lower than what "we" can hear, as they put it. One of the basic theorems of astronomy is that when you look at a whole star's light output at once, you shouldn't see (or hear) variations in it that are faster than the time it takes light to cross it. Wnt (talk) 21:44, 8 April 2011 (UTC)

## Name this flower?

I found this http://img715.imageshack.us/i/unknownflower.jpg/ flower in SE england, where it was only about three inches high. It is very likely to be a garden flower rather than a wild flower. Thanks 92.24.184.41 (talk) 11:53, 8 April 2011 (UTC)

It's a periwinkle. Mikenorton (talk) 12:00, 8 April 2011 (UTC)
Vinca major, in fact. Ghmyrtle (talk) 12:01, 8 April 2011 (UTC)
Looks to me more like Vinca minor; the "squared off" petals on the flowers seem to be more indicative of that species. The Vinca majors have more pointed petals... --Jayron32 12:10, 8 April 2011 (UTC)
Yes, definitely the lesser periwinkle (vinca minor). I've just picked one from my garden to check against the image and they are almost identical except the leaves on my variegated variety are slightly more pointed. The plant is sold in England as a garden plant suitable for shaded areas. Dbfirs 16:22, 8 April 2011 (UTC)

## Stalactites and coal dust

How could decades old hardened lignite dust be removed from stalactites? SpinningSpark 16:58, 8 April 2011 (UTC)

Is that the result of coal mining in the vicinity of already existing stalactites? If so, what probably caused the lignite to adhere? I'm just curious—how thick is the coating of lignite? Bus stop (talk) 17:06, 8 April 2011 (UTC)
I suspect that you'd need to wash them each individually, probably with a solution of dish-washing detergent (be sure to use fragrance-free, as a "lemony fresh" smelling cave is just wrong). If needed, you could use abrasives, such as steel wool (be sure to rinse thoroughly, as bits of steel wool can then rust.) A labor-intensive operation, no doubt, but perhaps worth it, if they are pretty under the dust, and if a cave full of them would then become a tourist attraction. StuRat (talk) 17:18, 8 April 2011 (UTC)
We don't know if they are in their natural setting or have already been removed to a home, laboratory etc. Bus stop (talk) 17:32, 8 April 2011 (UTC)
Frequently, you can't. If it is an active cave, the dust may actually be part of the formation, mixed in with the limestone. In which case, leave it alone. As time passes, a new surface will cover the old. Tdjewell (talk) 18:05, 8 April 2011 (UTC)
Maybe you can degrade it with bacteria.PMID 16521578 Wnt (talk) 20:52, 8 April 2011 (UTC)

To answer some of the questions on context: a family member has purchased a run-down "mansion" in East Germany in the grounds of which is a semicircular building forming the entrance to a grotto in which are very many stalactites and a local talking point. During the communist era the building was used as a coal store and this is the source of the discolouration on the stalactites. The condition is described as similar to the blackening of concrete on buildings in polluted cites. I could also mention that there is a safety issue - someone came close to being injured when a large stalactite detached from the ceiling while he was doing some work with a hammer in the building. I like the leave-it-alone-to-resurface-itself answer best. Any ideas how long that would take? SpinningSpark 00:53, 9 April 2011 (UTC)

That would be depend on both the rate of deposition of the material and how opaque it is. What type of stalactites are they ? Are there any signs of the coal being covered up ? How long since coal was stored there ? At a minimum it would probably takes decades, and at a maximum centuries or millenia. Another approach might be to paint them. Anything would probably look better than they look now. You could either attempt to match their original color or perhaps go with bright colors to be "artistic". You could also take the fallen one away and work on it someplace safer, to determine just what it would take to clean it. StuRat (talk) 08:39, 9 April 2011 (UTC)
That reminds me, is it true that you shouldn't touch the stalactites with a bare hand because the grease layer left there would stop them growing? Or is that just a cautionary tale they told to us when we were kids so we don't break everything in the cave? – b_jonas 17:56, 9 April 2011 (UTC)
That sounds legit to me. If you put a finger print on a bathroom mirror then take a shower, you may see water droplets go around the print. The same could be true of the water carrying the minerals that deposit to form a stalactite. I would still expect that they would continue to form, but in a somewhat altered shape. StuRat (talk) 22:21, 9 April 2011 (UTC)

## Cells Removal

Just wanted to get an opinion or thoughts not medical advice- going back to cells. If it is possible to add cells with gene therapy is it also possible to remove cells from our bodies, besides the dead cells (like dead skin cells)? —Preceding unsigned comment added by 70.136.157.40 (talk) 17:19, 8 April 2011 (UTC)

Sure you can remove living cells. Cut your finger. See that drop of blood on the floor? There's cells from inside your body there. Cut your finger off. See that finger lying on the floor? That's cells too. --Jayron32 18:33, 8 April 2011 (UTC)
Bone marrow transplantion involves first destroying the patient's bone marrow then completely replacing it. It is then possible to replace the orginal bone marrow with a compatible but genetically advantageous one.[1] Rmhermen (talk) 19:05, 8 April 2011 (UTC)
Technically speaking, gene therapy does not really have anything to do with adding cells to the body. You might be thinking about stem cell therapy, which purports to do this (though not with anywhere near as much success as you might imagine given the hype surrounding stem cells). Another form of "adding cells" to the body would be "good old-fashioned" organ transplantation, of which bone marrow transplantation is a subset (and in a way the first type of stem cell transplant). Removal of cells within tissues of the body can be performed with "good old-fashioned" surgery, or phlebotomy in the case of blood cells, but if what you are referring to is some kind of targeted means of only removing certain types of cells from the body, then no. There is no such thing at present. --- Medical geneticist (talk) 19:39, 8 April 2011 (UTC)
Although I can imagine it, not too far in the future, for certain types of cells. For example, for cancer cells in the blood, something similar to dialysis could be done, where blood is removed, each cell examined by a computer which identifies and discards the cancerous ones (say due to a "disorganized nucleus"), and returns the rest. This probably wouldn't cure the cancer in a single shot, since some cancer cells would remain in the spleen or other places. However, it might help enough, especially with multiple treatments, to eventually cure the disease, or at least prevent metastasis. StuRat (talk) 20:03, 8 April 2011 (UTC)
It is possible to remove specific cell types using drugs, e.g. streptozocin or MPTP. And incredibly, the former actually has a medical use (didn't know that until I read the article). Wnt (talk) 21:35, 8 April 2011 (UTC)
Also, would adding some bacteria count? – b_jonas 17:45, 9 April 2011 (UTC)

## Panderian organ in Trilobites

Does this adjective commemorate Heinz Christian Pander? Is there a reference somewhere? Finding a definition is also not straightforward.... Androstachys (talk) 17:35, 8 April 2011 (UTC)

This page of the Geological Magazine seems to be the first appearance of the term in the literature; you can draw your own conclusions from it. Looie496 (talk) 18:42, 8 April 2011 (UTC)
Thank you - just what I was looking for! Androstachys (talk) 20:27, 8 April 2011 (UTC)

## quantum numbers for a multi-electron system

I'm really having trouble with this, and none of the Wikipedia articles are clear on distinguishing vectors from numbers and the like at an elementary level. How do I calculate the total spin S = S1 + S2 for a system of two electrons? The formulas they gave me in my textbook makes it seem that S is a constant (sqrt 3)/(h-bar), but shouldn't S be free to take a up a range of values from opposite spins to coupled spins? (i.e. S = S1 + S2 should have three different values?)

With this in mind, how do I determine J = L + S for a two electron system if both have l=1? 128.143.102.160 (talk) 20:00, 8 April 2011 (UTC)

By "total spin", they mean the magnitide of the total spin here and there are two possibilities when you add two spin 1/2: Total spin 1 and total spin 0. If the total spin is 1 then you have 3 possible z-components: 1, 0 and, -1, and if the total spin is 0 then there is only a z-component of 0, so there are 4 states in total, which is obvious because each spin 1/2 particle can have a z-component of 1/2 or -1/2, so 2 times 2 = 4. Count Iblis (talk) 20:46, 8 April 2011 (UTC)
I'm confused at the difference between quantum numbers and their vectors. Sometimes they appear to be the same. For example, from L=L1+L2 and S=S1+S2 I'm supposed to derive the possible values of quantum numbers j which is related to J=L+S (does this equal (L1+L2) + S1+S2)?). I'm reallllly confused. By another means, I've found out for two electrons l=1, s=1/2, that the possible values of j are j1+j2...j1-j2, etc. giving 0,1,2 and 3. However I'm supposed to use another route using the total L and total S of the system. help? 128.143.102.160 (talk) 20:53, 8 April 2011 (UTC)
To understand the angular momentum quantum numbers it may be helpful to look at the hydrogen atom orbitals. You don't need the radial part of the orbitals, just the angular part, also known as the spherical harmonics. Any smooth complex-valued function on a sphere can be written as a weighted sum of the spherical harmonic functions. They are grouped by ℓ values: there's one function with ℓ=0 (used for the S orbitals of the hydrogen atom), there are three with ℓ=1 (the P orbitals), five with ℓ=2 (D orbitals), and so on. Why this grouping? The reason is that rotating the sphere turns functions with a given ℓ value into sums of functions with the same ℓ value only. Since the sphere is symmetric, functions that can be rotated into each other are "all the same" in some sense, and it makes sense to group them together. These constant-ℓ groups are irreducible, meaning that they can't be subdivided into smaller groups while preserving the property that functions in each group rotate only into functions of the same group. Professional physicists say that they are irreducible representations (irreps for short) of the rotational symmetry.
The grouping by ℓ is imposed on you by the symmetry of the sphere, but within each ℓ you can choose whatever basis you like for the functions. The ℓ=0 case is trivial, since there's only one function (up to a constant factor). For the ℓ=1 case, the Wikipedia article gives you this orthogonal basis:
${\displaystyle {\begin{array}{lcl}Y_{1}^{+1}(\theta ,\phi )&=&e^{i\phi }\sin \theta \\Y_{1}^{0}(\theta ,\phi )&=&\cos \theta \\Y_{1}^{-1}(\theta ,\phi )&=&e^{-i\phi }\sin \theta \end{array}}}$
It's worth trying to visualize these functions. θ is the latitude and runs from 0 (north pole) to π (south pole). φ is the longitude and runs from 0 to 2π. ${\displaystyle Y_{1}^{0}}$ is +1 at the north pole, −1 at the south pole, and zero at the equator. In the particle interpretation of quantum mechanics, this represents back-and-forth motion along the north-south axis. ${\displaystyle Y_{1}^{\pm 1}}$ are zero at the poles and maximal in magnitude at the equator, but they rotate in the complex plane in opposite directions as you go around the equator. These represent rotation about the north-south axis in opposite directions.
Naturally, any other "north-south" axis is just as good as this one, and will give you a different basis for the function space.
Another interesting basis is
${\displaystyle {\begin{array}{lclcl}f_{x}(\theta ,\phi )&=&{\tfrac {1}{2}}(Y_{1}^{+1}(\theta ,\phi )+Y_{1}^{-1}(\theta ,\phi ))&=&\cos \phi \sin \theta \\f_{y}(\theta ,\phi )&=&{\tfrac {1}{2i}}(Y_{1}^{+1}(\theta ,\phi )-Y_{1}^{-1}(\theta ,\phi ))&=&\sin \phi \sin \theta \\f_{z}(\theta ,\phi )&=&Y_{1}^{0}(\theta ,\phi )&=&\cos \theta \end{array}}}$
These functions are all −1 at one pole, +1 at the opposite pole, and 0 at the equator, but with respect to three different axes through the sphere that are at right angles to each other. If you reparametrize the sphere with Cartesian coordinates x, y, and z where ${\displaystyle {\sqrt {x^{2}+y^{2}+z^{2}}}=1}$, these functions are just ${\displaystyle f_{x}(x,y,z)=x,f_{y}(x,y,z)=y,f_{z}(x,y,z)=z\!}$. Any ℓ=1 harmonic can be written as a sum of these three functions. To put it another way, any ℓ=1 harmonic can be written as ${\displaystyle f_{\vec {v}}}$ where ${\displaystyle f_{\vec {v}}({\vec {w}})={\vec {v}}\cdot {\vec {w}}}$. Note that ${\displaystyle {\vec {v}}}$ rotates as an ordinary 3D vector if you rotate the sphere, so every ℓ=1 harmonic can be said to point in a certain direction, represented by ${\displaystyle {\vec {v}}}$. But ${\displaystyle {\vec {v}}}$ is a complex vector, so this is a somewhat abstract kind of "pointing". For example, ${\displaystyle Y_{1}^{+1}}$, which represents rotation in the xy plane, equals ${\displaystyle f_{x}+if_{y}\!}$. In the particle interpretation, ${\displaystyle f_{\vec {v}}}$ represents back-and-forth motion along the ${\displaystyle {\vec {v}}}$ axis. ${\displaystyle f_{x}+if_{y}\!}$ represents back-and-forth motions along the x and y axes that are out of phase by 90° (a factor of i), which is the same as circular motion in the xy plane.
So, depending on which basis you use, you can think of a P harmonic as pointing in a direction represented by a (complex) spatial vector, or as a superposition of three discrete momentum values around a single axis (represented by another complex vector, but not a spatial one).
Every quantum measurement selects a preferred orthogonal basis for the function space, and the components in that basis become probabilities according to the Born rule. In a Stern–Gerlach apparatus, the measured quantity is the angular momentum around a particular axis, and so the ${\displaystyle Y_{1}^{0,\pm 1}}$ basis is the measurement basis. In principle you could set up a lab experiment in which the ${\displaystyle f_{x},f_{y},f_{z}\!}$ basis was the measurement basis, though I'm not sure what it would be.
When dealing with spin instead of orbital angular momentum, the most important change is that, in addition to the groups of 1, 3, 5… associated functions, there are also groups of 2, 4, 6… associated functions that are assigned half-integer values of ℓ. They don't have an obvious model as harmonics on a sphere, but abstractly they behave very much the same. The ℓ=½ "harmonics" are simpler than the ℓ=1 harmonics. They are all equivalent under spatial rotation (not true of the ℓ=1 harmonics—you can't rotate back-and-forth motion into circular motion) and they all represent circular motion in some plane. This means that every ℓ=½ harmonic can be associated with a real spatial vector, giving the rotational axis. Also, all orthogonal bases for ℓ=½ look the same: they consist of two harmonics representing opposite circular rotations in the same plane (spin "up" and spin "down").
In a system of two particles the angular momentum is represented by a smooth function of two points on the sphere, ${\displaystyle f({\vec {w}}_{1},{\vec {w}}_{2})}$ instead of ${\displaystyle f({\vec {w}})}$. As before, we'd like to find irreducible subspaces of this space of functions. One basis for this space of functions is the functions ${\displaystyle Y_{\ell _{1}\ell _{2}}^{m_{1}m_{2}}({\vec {w}}_{1},{\vec {w}}_{2})=Y_{\ell _{1}}^{m_{1}}({\vec {w}}_{1})Y_{\ell _{2}}^{m_{2}}({\vec {w}}_{2})}$. Rotations of the sphere will preserve ℓ1 and ℓ2, so this carves up the function space into a bunch of independent finite-dimensional subspaces. For example, ℓ1 = 1 and ℓ2 = ½ gives you a 3×2=6 dimensional subspace that rotates into itself. But most of these spaces can be further subdivided (they are reducible). The rules for doing this are the rules you're learning about adding spins. When ℓ1 = ℓ2, there is always a 1-dimensional subspace that rotates into itself, called the "singlet". When ℓ1 = ℓ2 = ½, the 2×2−1 = 3 other dimensions (besides the singlet) turn out to be irreducible, and are called the "triplet". I could go on, but maybe that's enough... -- BenRG (talk) 02:59, 9 April 2011 (UTC)

## Does this seem right to you?

So, I'm cruising home on the freeway, and noting that the tach says the engine speed is 2400 rpm. It finally occurs to me that that's 40 revolutions per SECOND. I can't shake my finger between two stops two inches apart at 40 cycles per second, and we're talking throwing a half-kilo weight back and forth faster than that?

• Does that seem right to you?

Perhaps RPM measures something other than the obvious. In a four-cylinder engine, one rev of the crankshaft = 1 rev of 4 pistons; I wonder if somebody in marketing decided that 600 crankshaft revs per second was going to be called "2400 RPM"?

• That can't be right -- can it?

I followed that confusing thought with how much gas is burned per cycle. Just to make the math simpler, lets say I get 32 miles per gallon -- which is 128 oz, or 4 oz per mile. At 60 mph, I'm doing 1 mile per minute, or 4 ounces of gas to turn the crankshaft 2400 revs.

Now, gas is only injected every second rev, and there are about 600 drops in an ounce, so now we're at 2400 drops to fuel 1200 injections, or two drops per cycle.

• Does that seem right to you?

I realize there are more important problems in the world, but this has been bugging me for a while. Thanks to anyone who doesn't write me off as a crank! DaHorsesMouth (talk) 21:45, 8 April 2011 (UTC)

Our articles, gear ratio, and ignition timing, may help you conceptualize the innards of the internal combustion engine and the rest of the drive train. Yes, mechanical components inside your engine are moving very fast. Gasoline engines are incredibly powerful machines. Nimur (talk) 22:18, 8 April 2011 (UTC)
Also, Gearbox#Automotive basics. Nimur (talk) 22:25, 8 April 2011 (UTC)
As a non-American I find the mixture of non-metric measurements of miles, ounces and gallons bad enough for practical calculations (even though I once used them), but to try to work this out with some assumed precise size of a drop seems ridiculous. Please share that size with us. HiLo48 (talk) 22:42, 8 April 2011 (UTC)
Please note I used "half-kilo" in the opening paragraph :-) ~DHM — Preceding unsigned comment added by DaHorsesMouth (talkcontribs) 01:46, 9 April 2011 (UTC)
He said "about 600 drops in an ounce", so he already told you. One definition of the US drop is 1/576 of a US fluid ounce (which makes a drop equal to about 0.05 ml). Dragons flight (talk) 22:52, 8 April 2011 (UTC)
2 drops doesn't sound unreasonable. Those drops are vaporized prior to ignition. StuRat (talk) 22:55, 8 April 2011 (UTC)
Ah, my apologies. Yes, the drop was defined - "1/576 of a US fluid ounce". Does anyone have any idea where that definition came from? Does it have any official standing? HiLo48 (talk) 23:00, 8 April 2011 (UTC)
Resolved: and Nimur gets credit for "the understatement of the thread:" Yes, mechanical components inside your engine are moving very fast.

Thanks!