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October 6

Feynman Lectures. Lecture 27. Ch. 27–7 Resolving power [1]

Quote

It is necessary that the difference in time between the top ray and the bottom ray to the wrong focus shall exceed a certain amount, namely, approximately the period of oscillation of the light: t2−t1>1/ν,(27.17) where ν is the frequency of the light (number of oscillations per second; also speed divided by wavelength). If the distance of separation of the two points is called D, and if the opening angle of the lens is called θ, then one can demonstrate that (27.17) is exactly equivalent to the statement that D must exceed λ/nsinθ, where n is the index of refraction at P and λ is the wavelength.

I tried to derive $D>{\tfrac {\lambda }{n\sin {\theta }}}$ , but I got another answer. According to image PNG dwg we can write:
$c't_{0}-c't_{1}\approx PP_{1}=D\sin {\theta };$
$c't_{2}-c't_{0}\approx PP_{2}=D\sin {\theta };$
Where $c'=c/n$ - speed of light in medium. Adding both equations:
$c't_{0}-c't_{1}+c't_{2}-c't_{0}=2D\sin {\theta };$

$t_{2}-t_{1}={\tfrac {2D\sin {\theta }}{c'}}={\tfrac {2Dn\sin {\theta }}{c}};$
But $t_{2}-t_{1}>1/\nu ={\tfrac {\lambda }{c}}$ .

${\tfrac {2Dn\sin {\theta }}{c}}>{\tfrac {\lambda }{c}};$

$D>{\tfrac {\lambda }{2n\sin {\theta }}}.$
Where is my mistake?

I'm not sure what angle does Feynman mean by "opening angle of the lens"... May it be the angle SPR (Fig. 27–9)? Username160611000000 (talk) 03:03, 7 October 2016 (UTC)[reply]

How old are beach pebbles?

Or to put it another way, how long does it take the sea to grind pieces of rock into sand? SpinningSpark 18:17, 6 October 2016 (UTC)[reply]

Per articles like Sand and Rock there are a bewildering array of materials and methods by which rock gets turned into sand. There's no reasonable way to give even the most general answer. --Jayron 32 18:27, 6 October 2016 (UTC)[reply]

Could you have provided an answer if I had asked a more specific question? Let's say the pebbles on Brighton beach. SpinningSpark 20:39, 6 October 2016 (UTC)[reply]

Some beaches, Brighton and the UK south coast generally are good examples, have a range of ages for pebbles, sorted along the length of the beach. As the coast behaves as one long straight beach with a single Eastwards direction of motion along it (although groynes try to control this), "pebbles" begin anew as boulders from cliff erosion at one end and travel along the beach, eroding as they go, right down to cobbles, pebbles and eventually sandy beaches. By tracking their age and material, a correlation of age and size can be made.

For the South coast, the chalk cliffs erode in West Sussex and the soft chalk erodes quickly to sand. Pebbles that survive as such (and travel further East) are from the harder flint found within the chalk. This still goes on slowly today, but the bulk of them still date from the rapid erosion of the area (and so accelerated boulder deposition) at the end of the ice age and glacial meltwater erosion, maybe 10,000 years ago. The production of loose flint pebbles (flint doesn't really appear as large boulders) was so rapid in this period of great erosion that the beaches are still chewing on the remnants.

Much older though, and fascinating, are the Brighton Raised Beach structures. These are archaic pebble beaches, formed about 1/4 million years ago and now some 10m above modern sea level. They can be traced the length of the coast and for some distance inland.

Another UK pebble beach of much study is of course Chesil Beach.[2]

The classic book source (I remember it from school geology) would be Ellis, Clarence (1965). Pebbles on the Beach. Faber. ISBN 0 571 06814 6. and a more modern comparable text might be Zalasiewicz, Jan (2012). The Planet in a Pebble. OUP. ISBN 978-0199645695.

Some South coast pebbles are only a few decades old. After WWII, a lot of brick and concrete appeared on beaches, from coast defences broken up in situ (accidentally or deliberately). These were often easily trackable and helped to illustrate some beach erosion processes. Andy Dingley (talk) 13:50, 7 October 2016 (UTC)[reply]

@Andy Dingley: thanks for the informative answer. I had often wondered where the pieces of brick come from. SpinningSpark 14:59, 9 October 2016 (UTC)[reply]

This [3] paper presents what looks to be an interesting model of sand bank formation, and give some information on characteristic time scales in terms of other parameters. This [4] has tons of information about weathering of silicate minerals, and discusses an apparent disconnect between laboratory and field-derived estimates. This [5] work uses everything from cosmic ray mechanics to spall mechanics to discuss erosion and denudation at large scales, and has some interesting results for different region (Figs 3,5). The final one is pretty close to addressing the question "How many years must a mountain exist, before it is washed to the sea" :) SemanticMantis (talk) 18:42, 6 October 2016 (UTC)[reply]

Thanks, but those look like they are concerned with weathering and erosion. I'm interested in the action of waves on beach pebbles. SpinningSpark 21:48, 6 October 2016 (UTC)[reply]

It's not really guaranteed it will happen at all. For example, all along the Appalachian Mountains there is a layer of Pottsville Conglomerate that retains the pebbles of the ancient beach to this day. Wnt (talk) 12:24, 7 October 2016 (UTC)[reply]

They have only survived in that stratum because the action of the sea had stopped at some point. I believe that it is the case that pebbles that are continuosly rolled by water will always have a finite life. SpinningSpark 13:29, 7 October 2016 (UTC)[reply]

Maybe you aren't interested in those papers, but erosion is a large source of beach gravel/sand, and weathering absolutely includes wave action on beaches. I will repeat for clarity that my first ref is 100% about formation of sand on beaches. SemanticMantis (talk) 13:55, 7 October 2016 (UTC)[reply]

Thanks for explaining that. I have no access to that site so could only read the abstract and was not able to tell from that whether it would answer my question. SpinningSpark 17:45, 7 October 2016 (UTC)[reply]

Note that the title question seems to be different from what you are asking:

A) Title question: "How old are beach pebbles ?" would mean how long ago did the rock which has since been ground down to pebbles first form ?

B) Your question seems to be about how long they have been "pebbles", in which case we would need to define the range of sizes classified as pebbles. StuRat (talk) 12:43, 7 October 2016 (UTC)[reply]

According to our article pebble, "A pebble is a class of rock with a particle size of 2 to 64 millimetres based on the Krumbein phi scale of sedimentology. Pebbles are generally considered larger than granules (2 to 4 millimetres diameter) and smaller than cobbles (64 to 256 millimetres diameter)." DuncanHill (talk) 13:32, 7 October 2016 (UTC)[reply]

You have overlap on the size ranges you listed for granules and pebbles, as does the article you linked to. StuRat (talk) 19:14, 7 October 2016 (UTC)[reply]

According to the Wentworth Grain Size Scale granules are a subset of pebbles. DuncanHill (talk) 19:23, 7 October 2016 (UTC)[reply]

Looks like our article needs fixing then. Care to volunteer ? StuRat (talk) 20:16, 7 October 2016 (UTC) [reply]

Yes, that is exactly the question I am asking. Are you now able to provide an answer? For the purpose of this question, pebbles are small enough for the current to be able to roll them, but large enough that the current cannot lift them off the bed altogether. SpinningSpark 14:29, 7 October 2016 (UTC)[reply]

No, I am not qualified to answer, but by clarifying the Q, hopefully others can. StuRat (talk) 19:16, 7 October 2016 (UTC)[reply]

As an amusing semi-relevant side track, one Christopher Ball from Brighton has written a book called Reverse Theory in which he propounds that pebbles are not ground smaller, but instead built up from sand by "the process of tidemark"; claims that the whole of geological dating (including fossil evidence, plate tectonics and radioactive decay measurements) is fundamentally derived from a (therefore) illusory rate of erosion from rock to sand; and that therefore (I gather) Creationism is true and humanity has devolved from a higher to an animal state. I myself do not intend to spend either time or money reading the book, and I doubt any of this is sufficiently notable fruitloopery as to merit coverage in Wikipedia. {The poster formerly known as 87.81.230.195} 90.197.27.88 (talk) 19:33, 7 October 2016 (UTC)[reply]

Trying to identify the name of a physical scaling constant

There's a certain constant usually associated with the permeability of free space having a value of $10^{-7}$ . I've never actually seen it referred to alone anywhere and yet I've encountered it enough working with physics equations that it seems deserving of its own designation. For example, its presence (or rather its inverse) in the equation $q_{\text{P}}={\sqrt {10^{7}m_{\text{P}}\ell _{\mathrm {P} }}}$ , where $q_{\text{P}}$ is the Planck charge, $m_{\text{P}}$ is the Planck mass, and $\ell _{\mathrm {P} }$ is the Planck length. Anyway, I generally think of it as a "charge scaling constant" relating to the distance between charges used to define the coulomb (being a single meter, that is) but I'd really like to know if there is a formal definition for this value. Earl of Arundel (talk) 22:46, 6 October 2016 (UTC)[reply]

The permeability of free space or "magnetic constant" is concerned with production of a magnetic field by electric current

µ₀ = 4π×10⁻⁷ N / A² ≈ 1.2566370614...×10⁻⁶ H / m or T·m / A or Wb / (A·m) or V·s / (A·m)

It appears in the constituitive form of Ampère's circuital law

\mathbf {B} =\mu _{0}\mathbf {H} \,\!

. But I don't recognize the decimal multiplier

10^{-7}

as a physical constant. Have you read anything in the article about Planck units that leads to the equation you quote for

q_{\text{P}}

? AllBestFaith (talk) 02:25, 7 October 2016 (UTC)[reply]

Yes, and it appears in other equations as well. But to answer your question, no, I arrived at that equation myself. At some point the thought just crossed my mind that the Planck charge might not be fundamental. Consider that the gravitation constant has dimensions consisting of nothing more than length, mass, and time. Moreover, the dimensions of the resulting force (the newton) in both gravitational and electric-charge calculations also involve these sole three dimensions as well. Then it occurred to me that charges in equations always seem to appear as powers which are multiples of two. And so I just squared the Planck charge and divided that by the Planck length. The result agreed well enough with the Planck mass (after multiplying by the aforementioned scaling factor of

10^{-7}

) to convince me, at least, that the formula was correct. Wouldn't be surprised if this is already a well-known fact somewhere in the scientific community, though. If not, it probably deserves further consideration. Earl of Arundel (talk) 18:25, 7 October 2016 (UTC)[reply]

It comes from the definition of the Ampere. Greglocock (talk) 08:16, 7 October 2016 (UTC)[reply]

Basically the Ampere was defined in cgs units, which have this kind of bizarre scaling. (The odd 10^2 comes from the centimeters) There is no SI unit more unwanted and chronically confusing to me than this two-wire thing - I don't understand why we can't just use an Avogadro number of electrons instead of the Coulomb, etc. i.e. Faraday constant. Wnt (talk) 14:28, 7 October 2016 (UTC)[reply]

I imagine ^{[citation needed]} that the effort to cleanse SI units from anthropocentric concepts such as "one forty-millionth of the Earth's perimeter" was the occasion to pick definitions without weird constants in them, but the ampere was allowed to stand because the force between two wires in the vacuum was comparatively "clean". Tigraan^{Click here to contact me} 15:06, 7 October 2016 (UTC)[reply]

That's not the reason for retainng the ampere, although the fact that it had an acceptable definition certainly helped. The definitions of the amp, volt and ohm were established by international conference of electrical engineers in 1881. The international nature of the telegraph had made it essential to have a common set of units. By the time the MKS and SI sytems came along this was so well established it would have been very difficult to get the industry to change. Especially so as a set of MKS electrical units without the 10⁷ factor would be entirely impratical, either much too large (the amp and ohm) or much too small (the volt) for everyday use. Pretty much the same objection would apply to using the Faraday constant. To answer the original question, I've never heard this factor given a name, I'm pretty sure it doesn't have one, it's just a number. SpinningSpark 17:27, 7 October 2016 (UTC)[reply]

Well, instead of saying a current of 20 A you might say 207 umole/s; instead of a 110 V outlet you'd have a 10.6 MJ/mole outlet; a resistance to make 110 V flow at 20 A would not be 5.5 ohms but 51.2 GJ s/mole^2, I think; the power of 110 V at 20 A would not be 2200 W but ... oh, yeah, 2200 W. That's not an electrical unit! :) A picofarad capacitor (1E-12 C/V) would give way to 1E-12 * 1.03E-5 mole / (96485 J/mole) = 1.074e-22 mole^2/J ... I think. (I really ought to clear some cobwebs from my head and recheck that math) So OK, maybe you'd need to invent a prefix or two. But on the other hand... you'd immediately know how many actual electrons you can put into the capacitor for a certain amount of actual energy. ~~(Somehow I doubt it's actually ten, like I said, I should debug this, but can't right now)~~ oh wait, those are mole^2 so if this corresponds to a physical number of electrons it's the root of that or 1e-11 mole, which is a bit bigger. Wnt (talk) 10:52, 8 October 2016 (UTC)[reply]

Right, so there is an incongruence of sorts with the units chosen to represent electrical phenomena. And while it would be nice if we could have a more homogeneous system, it probably isn't worth the trouble. That said, in lieu of that it does seem reasonable to formally define this thing. Otherwise, we're just stuck with using an ad hoc constant to define things like Coulomb's constant (

k_{\text{e}}={\text{c}}^{2}10^{-7}

). At best, it's arcane..at the very worst, confusing. Earl of Arundel (talk) 18:25, 7 October 2016 (UTC)[reply]

Appalachian endorheic basins

As far as I can tell, there aren't any endorheic basins in the Appalachians. Why not? Or am I wrong, in which case, where are these Appalachian basins located? Nyttend (talk) 23:33, 6 October 2016 (UTC)[reply]

As can be told by looking at maps, or reading the Appalachian Mountains article, the Appalchians are low, old, and narrow. There does not appear to be any major geologic barriers to water landing in the Appalachians from reaching the ocean, the same way that there is at, say, the Basin and Range Province, which has numerous such basins due to the specific type of faulting in the region. Such faults do not exist in the Appalachians, which are mostly low rounded hills without dramatic elevation changes or significant barriers to water flow; water always has a way out. --Jayron 32 01:28, 7 October 2016 (UTC)[reply]

The thing I wonder about, in particular, is the Ridge and Valley Province. Here, you have lots of long mountains with low valleys between them, and in most cases, each mountain and each valley will be only a few miles wide. Some mountains even curve significantly, as can be seen in File:Bedford-co-air.jpg. But every valley has an outlet: very few of them lack a "normal" connection to other valleys (there don't seem to be any valleys that are blocked up at both ends), and the few exceptions, e.g. 37°5′53″N 81°20′32″W / 37.09806°N 81.34222°W all seem to have water gaps to adjacent valleys. It's not as if I'm looking for something on the scale of the Great Basin or even Devils Lake (North Dakota); something a mile wide and a few miles long would suffice. Nyttend (talk) 20:07, 7 October 2016 (UTC)[reply]

The water gap is one form of erosion I described below. That is, some water will almost always flow out, even if only drips. But, over millions of years, those drips erode a larger channel and eventually you have a water gap. StuRat (talk) 20:14, 7 October 2016 (UTC)[reply]

Two reasons, both dealing with age of the land:

1) Sedimentation, filling in any basins. Windblown particles may also settle out in the bottom of the basin.

2) Land erosion, wearing down the walls of the basins (some of which becomes sediment within the basins).

So, to have basins, you need active geological processes, such as volcanism, glaciation and tectonic uplift, to counter the above forces. StuRat (talk) 20:01, 7 October 2016 (UTC)[reply]

Appalachian geology is remarkably regular, but not perfectly so. There are weird formations like Fort Valley, Maryland where you see a ring of hills around a central region. But there are ways the water goes out. This is illustrated by Delaware Water Gap, Pennsylvania where a stream has been flowing steadily since, I assume, before the hills were first eroded out of the earth. (in other cases, like the nearby Wind Gap, Pennsylvania, you see that the stream stopped at some point and the pass gradually went up into the air as the earth eroded all around it) I don't know, but I suspect that in such a moist environment the water was always flowing and so every basin that came into being has a built-in back door for the water to get out. I always think of endorheic basins being in dry areas and I wonder if this is a reason for it? Wnt (talk) 18:58, 8 October 2016 (UTC)[reply]

October 7

Age and Height: 2 to 3 Yards Tall

How exactly does one's life expectancy decline with height, for people who are between two and three yards tall (i.e., between 1.8 and 2.7 meters) ? Or, alternately, what is the tallest human height achievable, so that the person in question might have a `very big chance` of living into their early 70s, or late 60s ?

I ask this because:

the tallest credibly-documented humans who have ever lived were less than 3 yards (~23⁄4 meters) tall.
no human above 8 feet (~21⁄2 meters) has lived more than about 55 years, with those towards the end of the spectrum dying in their 20s or 30s.
even among those (slightly) below 8 feet (21⁄2 meters), only a (significant) minority lived into their 60s or 70s.
the tallest human who did not suffer from gigantism reached a natural height of almost 72⁄3 feet (~21⁄3 meters), and lived into his early 80s.
people up to about 63⁄4 feet (2 meters) seem to have average life spans.

— See list of tallest people.

I therefore logically assume that the cut-off point for an `average` or `convenient` life span (65 to 75 years) is somewhere in between 7 and 8 feet (2.15 and 2.45 meters). But where exactly ? — 86.127.61.109 (talk) 19:46, 7 October 2016 (UTC)[reply]

See cum hoc. There may very well be a correlation between height and life expectancy, but this does not imply a causal relationship between them. Tevildo (talk) 21:10, 7 October 2016 (UTC)[reply]

The fact gigantism and acromegaly create severe health problems has already been well established. — 86.125.206.37 (talk) 23:35, 7 October 2016 (UTC)[reply]

Correlation alone may not prove causation, but we have other elements here:

1) First, the order is quite clear. The height occurs first, then the premature death (would be difficult to occur in the other order, wouldn't it ?).

2) Second, we know some of the mechanisms by which height may cause early death, such as more strain on the cardiovascular system.

Of course, we can also argue that a third factor causes both, like the genetics that lead to gigantism, but that rather seems like splitting straws. StuRat (talk) 22:17, 7 October 2016 (UTC)[reply]

Your first point is great demonstration of Post hoc ergo propter hoc. You may also be interested in learning a little about proximate and ultimate causation. SemanticMantis (talk) 22:26, 7 October 2016 (UTC) SemanticMantis (talk) 22:23, 7 October 2016 (UTC)[reply]

Again, it's only a logical error if that is the only link in the chain of causation. When the chain is complete, it's no longer a logical fallacy. StuRat (talk) 22:48, 7 October 2016 (UTC)[reply]

There is a very strong negative correlation between height and lifespan [6]. This holds true across ethnic groups and over time (at least the last 90 years). You can read that article to come some specific numbers. Someguy1221 (talk) 22:19, 7 October 2016 (UTC)[reply]

Thank you. I am already well aware of that article, as well as others in the same vein. I was hoping for something a bit more precise and substantial. — 86.125.206.37 (talk) 23:35, 7 October 2016 (UTC)[reply]

How same elements form different compounds

In a nutshell, how exactly just three chemical elements like carbon, hydrogen and oxygen and, broadly, CHON can form such a vast array of chemical substances with different properties? For example, lactose, malic acid and testosterone which are formed only by carbon, hydrogen and oxygen. Aside from different numbers in molecular formulae, is it chemical bonds that make lactose a lactose, etc or it's something else? And where do such compound-forming factors come from? --93.174.25.12 (talk) 22:15, 7 October 2016 (UTC)[reply]

Structure is a major factor. Just as you can assemble Legos to make many different things, the same is true in chemistry. For example, the same chemicals can spiral to the right or left, and this results in different properties. See levolorotary and dextrorotary. StuRat (talk) 22:22, 7 October 2016 (UTC)[reply]

You may wish to read Isomer and Chemical compound, although you may be just confused by the latter! Combinatorial chemistry give a clue as to why there are so many compounds. Graeme Bartlett (talk) 12:41, 8 October 2016 (UTC)[reply]

Already with CHON you have a great deal to work with. First, you have the basic skeleton, the arrangement of the carbon atoms, which can loop or branch. Some of these may not be C–C single bonds, but C=C double bonds or C≡C triple bonds which act as concentrated regions of negative charge that can react with electron-seeking electrophiles. Hydrogen atoms are added so that every carbon makes four bonds. But once you add O and N into the picture you can add an untold number of functional groups to give a molecule its personality, so to speak. (For this reason C=C and C≡C are also considered functional groups.) For example, you can have C=O (the carbonyl group), where the oxygen has a higher electron density, and so the carbon bears a partially positive charge and can be attacked by electron-rich nucleophiles. Or you can have hydroxyl (–OH, gives alcohols; easily forms hydrogen bonds), alkoxy (–OR, gives ethers), amino (–NH₂, gives amines, usually smelly), nitro (–NO₂, famous for exploding), carboxyl (–CO₂H, gives carboxylic acids, from which come the the sharp flavours in many fruits), amide (–CONH₂, most famously in proteins). There's more, but these cover your examples and already go beyond them. As for how all of this works, much of it boils down to the differing electronegativities of C, H, O, and N. Double sharp (talk) 14:39, 8 October 2016 (UTC)[reply]

Oh, boy, this one is a doozy. Damn decent question to ask, though. Part of it is that CHON are low-numbered common elements. Look at nucleosynthesis - they're some of the absolute top abundance elements in the cosmos. Hydrogen was around as soon as nuclei became stable; CNO are some of the lightest elements that can be fused in small and large stars. This matters because the chemistry we know is tinged by what we have available to play around with. On the other hand, some elements (like He) are common but just don't play well with others. The same is true of many alkali metals that mostly turn up in boring salts.

Very true – I forgot to mention that. Boron has an amazingly rich chemistry that rivals carbon, I daresay the richest in the inorganic realm, but stars cannot effectively produce it and so there's just not enough of it to play around with. Thus, no boron-based life. (Though there are other reasons, one among them being that boranes have a tendency to explode in an oxidising atmosphere like Earth's today.) Double sharp (talk) 14:05, 9 October 2016 (UTC)[reply]

Maybe, but the early Earth had a reducing atmosphere, not an oxidizing atmosphere as it does now, so that would not have been a barrier to boron based life if boron had been available in sufficient quantities. Given that production of oxygen was caused by changes to life itself which then evolved to cope with it there is no reason to suppose that boron based life would not do the same, or perhaps would not have created the oxygen in the first place. SpinningSpark 14:55, 9 October 2016 (UTC)[reply]

That's very interesting! Thank you! Double sharp (talk) 04:08, 10 October 2016 (UTC)[reply]

There's something to be said for the first period over the others also. I think it tends to like multiple bonds more than the others. In some ways this makes for simple-looking compounds (N2, O2) that wouldn't be formed by phosphorus or sulfur. But it also leaves us with conjugated double bonds and lots of other fun stuff.

This is actually a rather well-known observation called the double bond rule. For example, carboxyl groups (C=O) are very common, yet silanones (Si=O) are of only fleeting existence. You get restricted rotation around C=C double bonds, but not about Si=Si bonds because that pi bond is weak and easily broken. Admittedly, this is of dubious truth for P and S. Double sharp (talk) 09:50, 9 October 2016 (UTC)[reply]

Definitely electronegativity is part of it. The pure geometry of the Schroedinger equation translates into an idea that there is a "shell" of eight electrons to be added between helium and neon and that all the elements, regardless of their nuclear charge, are being pushed toward trying to get that shell filled. Yet ... CHON doesn't actually include strongly electropositive elements. C and H are sort of neutral, N and O are more electronegative but not so much as fluorine. Still, that doesn't mean you can't get a positive charge, since -NH2 can end up as -NH3+. When electronegativity is extreme (-COOH, which can be stable as just -COO^-) you can get a negative charge. It's kind of finicky - oxygen has extra electrons that could take an H+ just like a nitrogen, but it rarely will do so; -OH2+ is rarely seen even in transition structures. The extra H's are also critical for hydrogen bonds. We can make strongly hydrophilic compounds by having some components that have a partial charge on them and/or engage in hydrogen bonding, and hydrophobic compounds that are simply symmetric (CO2) or unadorned with electronegative components (CH3-CH2-CH3).

Higher order complexity is also a part of it. The difference between starch and cellulose seems to have to do mostly with how they crystallize and self-associate, AFAIK. Proteins are all about secondary structure, without which they'd just be a bunch of amino acids in a row.

Life is also a part of it. There's nothing particularly exceptional about testosterone except that most people have an androgen receptor. For those who don't, it's pretty much just another random collection of carbon rings. Wnt (talk) 18:50, 8 October 2016 (UTC)[reply]

The number-one thing is that carbon can bond in a bunch of different ways to itself and to other elements, because of its four valence electrons. Also those bonds are fairly stable. As our carbon article says, there are more compounds containing carbon than compounds of all the other elements combined (excepting hydrogen, because many hydrogen-containing compounds also contain carbon). Beyond that the different properties of organic compounds come from the overall molecular structure. The individual atoms aren't the determining factor; the important thing is that those atoms can be arranged in many different ways, similar to how you can build a bunch of different structures with the same bricks. When you get up to the size of proteins, whole amino acids can be changed often with little impact on the protein's structure or function—although not always! The article carbon-based life may be of interest. --47.138.165.200 (talk) 00:47, 9 October 2016 (UTC)[reply]

breeds of cattle and their milk

Are there breeds of cattle whose milk are known to be better tolerated by humans who are lactose-intolerant? Are there any identified strains of cattle that are much like cattle from ancient times, and has the "tolerablity", if that's a word, of their milk been studied? Thank you!144.35.45.53 (talk) 22:27, 7 October 2016 (UTC)[reply]

That would imply either a lack of lactose or the presence of lactase, the enzyme needed to digest lactose, in the lactating bovine's milk. Either seems unlikely. Here's a comparison of lactose content by each cattle breed, and, as you can see, there's little difference between them: [7]. However, the lactose content does go up the longer a pig lactates, and protein goes down. In a Meishan pig it seems to have over 2.5 times as much lactose 3 weeks into lactation than at the start. So, if the same is true of cows, that might help, especially if the object is to get your protein from milk (I calculate you would get 13.8 times as much lactose from a Meishan pig at 3 weeks into lactation, to get a given amount of protein from the milk, as you would on the first day of lactation). But just adding lactase to the milk is a simpler fix. StuRat (talk) 22:29, 7 October 2016 (UTC)[reply]

I found this while searching, but they seem to be conflating lactose intolerance with milk allergy, which is entirely different. As you're searching, be aware that the two concepts are often confused in the popular consciousness (including this). If the source starts talking about problems with proteins, they're almost certainly discussing the allergy. Incidentally, if you are interested in milk allergies, the milk of most other mammals tends not to affect sufferers as cow milk contains casein (which is the actual trigger, see references in that article). As far as the actual question goes, you might find this of interest, though it involves genetic modification rather than a breed developed the old fashioned way. Matt Deres (talk) 04:03, 8 October 2016 (UTC)[reply]

October 9

Sphere packing and alloy densities

I believe I am correct in asserting that sphere packing of unequal spheres can sometimes result in higher packing efficiency than equal sphere packing. If spheres are atoms, it seems plausible that alloys can be denser than either constituent metal. My question: does this ever happen?--Leon (talk) 17:12, 9 October 2016 (UTC)[reply]

Interesting discussion on this: http://forums.xkcd.com/viewtopic.php?t=106760 --Guy Macon (talk) 17:37, 9 October 2016 (UTC)[reply]

Yes, it can happen. See interstitial element. Note that the density differences are rather minor, but the real significance is in how the other properties of the material change. StuRat (talk) 17:48, 9 October 2016 (UTC)[reply]

See Sphere packing#Unequal sphere packing. It seems fairly obvious that after the closest possible packing of equal spheres has filled 74% of the volume, it must then be possible to add smaller spheres in the empty 26% volume. A demonstration of infinite accumulation in two dimensions of successively smaller circles is Ford circles. AllBestFaith (talk) 19:23, 9 October 2016 (UTC)[reply]

It would be interesting to see if StuRat's scenario actually occurs; in reality the addition of interstitials can cause expansion. Spot checking palladium hydride up to PdH.02 (where a phase change occurs), using a unit cell density calculation, I find that the addition of hydrogen actually reduces the density from 12.0179g/cc (Pd alone) to 11.9647g/cc (PdH.02). The expansion of the lattice parameter from 3.889 to 3.895 (from the palladium hydride article) overwhelms the additional mass of the hydrogen. Additional inputs: 4 atoms/cell and 106.42g/mol Pd, 0.08atoms/cell and 1.0079g/mol H, 6.022*10^23 atoms/mol.

Not sphere packing, but water-ethanol mixtures are somewhat well known for having a lower volume than the sum of their constituents, see Ethanol#Solvent_properties.--Wikimedes (talk) 21:24, 9 October 2016 (UTC)[reply]

There is a long list of alloys that have densities greater than the mean density of the constituents, including some rather common ones such as brass and bronze. But I don't know if there are any with a density greater than either constituent. SpinningSpark 23:14, 9 October 2016 (UTC)[reply]

Air pressure / volume graph

Hi, can anyone locate a graph of air pressure versus volume (at room temperature) that clearly shows the situation at extreme pressures when the air becomes no longer compressible? 109.148.99.203 (talk) 17:48, 9 October 2016 (UTC)[reply]

I wouldn't think you would call it air then, as at those pressures the constituents would become solid and/or liquid, unless very hot, then it would be a plasma. StuRat (talk) 17:55, 9 October 2016 (UTC)[reply]

Oh really, surely it is clear enough what I mean. 109.148.99.203 (talk) 18:59, 9 October 2016 (UTC)[reply]

What the OP seeks is a Phase diagram for air. Here is its phase diagram. Dry air is mainly (78%) Nitrogen and here is its phase diagram too. These diagrams have temperature and pressure as variables. AllBestFaith (talk) 19:06, 9 October 2016 (UTC)[reply]

Thanks but no, what I seek is, funnily enough, exactly what I asked for, which is a graph of pressure versus volume. 109.148.99.203 (talk) 19:10, 9 October 2016 (UTC)[reply]

You will see only a graph of Boyle's law that turns into a straight horizontal line at high pressure. AllBestFaith (talk) 19:30, 9 October 2016 (UTC)[reply]

It is that region that I want to see. I doubt it is exactly Boyle's law instantly turning exactly into a straight line. Also, I want to know at what pressure these effects occur at room temperature. 109.148.99.203 (talk) 19:43, 9 October 2016 (UTC)[reply]

Another thing I don't understand that someone can hopefully explain. Here it says "oxygen cannot be liquified above a temperature of -119 degrees Celsius (-182 degrees Fahrenheit), no matter how much you compress it". So what happens when you compress oxygen at room temperature until the molecules are as close together as they are in liquid oxygen? What is the essential difference between the resulting substance and actual liquid oxygen? 109.148.99.203 (talk) 00:20, 10 October 2016 (UTC)[reply]

See here and here. Neither has the exact graph you're looking for, but they do discuss non-ideal gas behavior. You may also be interested looking into the Van der Waals equation. --Jayron 32 00:28, 10 October 2016 (UTC)[reply]

October 10

What is this plant?

Please any one tell me Name of this creeper. — Preceding unsigned comment added by Sameerdubey.sbp (talk • contribs) 03:30, 10 October 2016 (UTC)[reply]

Did you mean to include an image link? --69.159.61.230 (talk) 04:03, 10 October 2016 (UTC)[reply]

What is this plant?

Please any one tell me Name of this creeper.