Wikipedia:Reference desk/Archives/Science/2016 June 7

Science desk
< June 6	<< May | June | Jul >>	June 8 >

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.

June 7

Logarithm of a dimensioned quantity

From Moment magnitude scale:

$M_{\mathrm {w} }$ is a dimensionless number defined by Hiroo Kanamori as

$M_{\mathrm {w} }={\frac {2}{3}}\log _{10}(M_{0})-10.7,$

where $M_{0}$ is the seismic moment in dyne⋅cm (10⁻⁷ N⋅m).

How does it make sense to take the logarithm of a dimensioned quantity and end up with a dimensionless one? 86.171.42.219 (talk) 00:19, 7 June 2016 (UTC)

It makes sense in three cases. The first case is when you are looking not at the value of the logarithm, but at the changes (differences) of that value as a function of something else. For example, a logarithm of signal power is not very useful, but a change in a logarithm of signal power is a measure of the signal attenuation, see decibel. Indeed, difference of logarithms is the same as a logarithm of a ratio, and a ratio of two values of the same quantity (e.g. power) is dimensionless. The second case is when you have a scale, or a fixed standard unit, of a quantity that you take a logarithm of; as in your own example above. In that case you are really taking a logarithm not of a dimensional quantity, but of that quantity divided by that standard unit, which in your case is (10⁻⁷ N⋅m). --Dr Dima (talk) 01:10, 7 June 2016 (UTC) Oops I forgot explain the third case. The third case is when an additive constant is unimportant. For example, entropy is a logarithm of the number of microscopic states availavle to the system at or near its total energy value. "At or near" means that you count the states within a certain (small) energy range, so it is a dimensional quantity, depending on how narrow this energy range is. However, this multiplicative factor of the number of available states becomes an additive constant once you take a logarithm; and that additive constant is not important as it does not affect any of the thermodynamical propoerties of the system. Hope this helps. --Dr Dima (talk) 01:16, 7 June 2016 (UTC)

Thanks. Do you mean to say that "$M_{0}$ is the seismic moment in dyne⋅cm" does not mean that $M_{0}$ is a dimensioned quantity, having units of dyne⋅cm, but is a dimensionless quantity because it has been divided by the reference level of 1 dyne⋅cm? That would make sense with the logarithm (like in decibels), but that is not, to me, what it seems to say. 86.171.42.219 (talk) 01:51, 7 June 2016 (UTC)

Yes, that sort of usage "in dyne⋅cm" means that the variable itself is considered dimensionless. --69.159.60.83 (talk) 05:37, 7 June 2016 (UTC)

I will note that other logarithms of quantities are dimensionless; for example pH is the negative logarithm of H⁺ concentration. Concentration has a measurement of mol/L, but pH is dimensionless. In chemistry, the way that this is worked around is that some measurements are specifically defined as relationships of Thermodynamic activity, which is a) defined as unitless and b) quite literally not directly measurable, so impossible to determine directly. Concentration is used as a sort of "surrogate measurement" in calculations involving the impossible-to-measure concept of "activity", such as both pH and equilibrium constant. So, we say that pH is the negative logarithm of activity, which is unitless but unmeasurable, and so we use molar concentration as a "stand in" for the calculation, since we can measure that, and at low enough concentrations, activity and concentration are proportional anyways. I'm not sure how this works with moment magnitude, but that's the sort of hand-waving we use in chemistry. --Jayron32 05:41, 7 June 2016 (UTC)

Personally, I would tend to write:

$M_{\mathrm {w} }={\frac {2}{3}}\log _{10}\left({M_{0} \over 1\,{\text{dyne-cm}}}\right)-10.7$

or even:

$M_{\mathrm {w} }={\frac {2}{3}}\log _{10}\left({M_{0} \over 10^{16.05}\,{\text{dyne-cm}}}\right)={\frac {2}{3}}\log _{10}\left({M_{0} \over 10^{9.05}\,{\text{N-m}}}\right)$

Which are all ways to describe the moment magnitude, if one treats $M_{0}$ as a dimensioned quantity rather than treating it as dimensionless. However, it isn't uncommon to see formulas presented in such a way that you are expected to take some variable as its dimensionless value in some units (especially in engineering), but personally I find those presentations rather annoying and suboptimal. Dragons flight (talk) 06:27, 7 June 2016 (UTC)

In physics, one doesn't specify in which units quantities have to be filled in in a formula. As long as one uses the basic units of a consistent system of units, the result comes out of the formula in basic units of the same system, whether that be SI or cgs or any other system. Imperial or American customary units are not so consistent, so that becomes very messy and those are avoided in science. If there is a logarithm in the formula, one has to make sure one takes the logarithm of a dimensionless quantity. If it's not dimensionless already, one has to divide by some constant of the same dimensions to make it dimensionless. For sound levels, one divides by a standard flux of $10^{-12}\mathrm {W} /\mathrm {m} ^{2}=10^{-9}\mathrm {erg} /\mathrm {cm} ^{2}$ to calculate decibels, for stellar magnitudes one divides by the flux of Vega. From a theoretical point of view it would make more sense to use some constant of nature, but that's not always practical.

In this case, the explanation going along with the formula suggests a particular unit. This is an implicit way of stating that one should divide by a standard quantity equal to unity when expressed in this particular unit. I would write:

$M_{\mathrm {w} }={\frac {2}{3}}\log _{10}\left({\frac {M_{0}}{M_{\mathrm {std} }}}\right)-10.7$

with $M_{\mathrm {std} }=1\,\mathrm {dyne} \cdot \mathrm {cm} =10^{-7}\,\mathrm {N} \cdot \mathrm {m} =0.08856\,\mathrm {firkin} \cdot \mathrm {furlong} ^{2}/\mathrm {fortnight} ^{2}$ a standard seismic moment. Or I could absorb the 10.7 term into the logarithm and use a different standard moment:

$M_{\mathrm {w} }={\frac {2}{3}}\log _{10}\left({\frac {M_{0}}{M_{\mathrm {std} }^{\prime }}}\right)$

with $M_{\mathrm {std} }^{\prime }=1.122\cdot 10^{16}\,\mathrm {dyne} \cdot \mathrm {cm} =1.122\cdot 10^{9}\,\mathrm {N} \cdot \mathrm {m} =9.937\cdot 10^{14}\,\mathrm {fir} \cdot \mathrm {fur} ^{2}/\mathrm {ftn} ^{2}=0.5736\,E_{\mathrm {Planck} }$. That's not a nice value in any system (although it's quite close to unity on the Planck scale), but that quantity was chosen to keep close to an earlier seismic scale, developed before seismic moments were properly understood. PiusImpavidus (talk) 10:58, 7 June 2016 (UTC)

Unless anyone can cite Hiroo Kanamori calling $M_{\mathrm {w} }$ dimensionless the gentleman is being misrepresented, because it does not make sense at all. AllBestFaith (talk) 11:32, 7 June 2016 (UTC)

It looks like the original author didn't worry about units - you see that surprisingly often; many people just want to plug numbers into formulas without thinking about them as carrying units with them. What gets interesting is that I would think you can actually carry unit analysis into the realm of logarithms (even though that article explicitly states that they are undefined!) For example, you might say (assuming base 10 for the moment) that log (10 N m) = 1 + log N + log m. You could write something like log m = 2 + log cm or log N = log kg + log m - 2 log s, I think. In which case we could "fix" the above formula by adding "- log N - log m" at the end of it. Note: don't do this! Use Dragons flight's second formula instead, as it has the minor advantage of being sane. But you should be able to, I think. Wnt (talk) 12:58, 7 June 2016 (UTC)

Is "10 N m" really 10 multiplied by "N" multiplied by "m"? Anyway, I find it hard to see what meaning could be ascribed to "1 + log N + log m"! 86.171.42.219 (talk) 21:57, 7 June 2016 (UTC)

I would say yes, at least in the sense that if you keep track of them you can tot them all up to 0. Now to come up with a meaning for a value of "2 + log m" on its own would be harder; yet it seems like it would be a dead giveaway that your pre-log value should have been divided by some reference value - in meters. I suppose it means it's 100 relative to the comparable exponent value for 1 meter. Wnt (talk) 00:11, 8 June 2016 (UTC)

Yes, you can think of N and m as constants equal to the ratios between those units and the "true units" (Planck units, if you like, but it doesn't matter). Then log m is simply the logarithm of the ratio, and represents a shift of the zero point from "true zero". It's not common, but there's nothing insane about it; it's an internally consistent approach. -- BenRG (talk) 02:28, 8 June 2016 (UTC)

Rate of genetic similarities

Modern academia put the DNA similarity between humans and chimps at 95%-99%, as per Human_evolution#Evidence_from_molecular_biology. And in cats, for example, it's reportedly a whooping 90% of homologous genes shared with humans. That seems quite high, as at around 90% of genetic similarities I'd expect some stronger resemblance, such as between modern humans and Neanderthals, and in cats I'd expect around 65-70%. Is it some sort of non-coding DNA that is not responsible for morphological and physiological features? Brandmeister^talk 14:02, 7 June 2016 (UTC)

All the studies make lots of suppositions - including the ones that a "minor difference" is, in fact, of little concern, and that all species have similar rates of change in DNA as their similar species have. Also, the fact is that their is apparently quite substantial variability within human DNA - vide the recent studies that a significant proportion of modern human DNA is likely inherited from "extinct pre-Homo Sapiens species". (Many people appear to have up to about 4% Neanderthal DNA, many have up to about 5% Denisovan DNA, and there is a really good chance that several other "extinct species" also have DNA found in modern human populations, and totally dwarfing the chimp DNA position). Using an analog - the difference between the Davenport electric car's "MNA (Motor Nucleic Acid)" and the Tesla Model S's MNA is extremely small indeed. Yet one might find it not that difficult to spot differences. Collect (talk) 14:20, 7 June 2016 (UTC)

• The genes that make up our appearance are only a small fraction of the total genome. Most of the enzymes and structural proteins are largely similar between all mammals, and in some cases all species. And are cats and humans really that different? Two eyes, four limbs, same internal organs etc. We have about 24% genetic homology with grapes.... (many other species here) Fgf10 (talk) 15:06, 7 June 2016 (UTC)

Trying to spell that out a little more: so many genes have to do with biochemical machinery, and this machinery is/has been broadly conserved via stabilizing selection. How to cells transport things? How do cells metabolize? Then there are many genes that have ontogenetic roles and are related to tissue and organ formation. But cats have skin, and fat, and muscle, and hair... and though those things are a little different in cats, they have most of the same tissue types and organs that work in mostly the same way. Also, homology is not identity. Finally, OP may be interested in reading up on Evolutionary_developmental_biology, aka "Evo-devo", a field that makes much of the similarities (and differences) between a fetal human and a fetal cat. SemanticMantis (talk) 15:24, 7 June 2016 (UTC)

This appears to be a handy overview of nearly all differences between cats and humans, from skeletal system to muscular, nervous, digestive, etc. If the 90% assertion on human similarity is true, are the remaining 10% able to encode all those anatomical and physiological differences? Brandmeister^talk 21:02, 7 June 2016 (UTC)

Hey that's a pretty cool slide set- thanks! My understanding is that there are two sources of differences between a cat and human. One source is that 10% of genes that occur in humans but have no analog in cats. But the other source is that the genes we "share" are not 100% identical, they are merely homologous forms. So while cats and humans have many similar genes, a given shared gene will not be identical. See here [1] for some specific examples of how homologous genes are similar different. I'm not sure which of these sources is more responsible for the differences, nor to if that question even makes sense. Also consider that by this reckoning, you and I have 100% of our genes (i.e. loci) in common, yet we have differences, due to having different alleles. I'm now past my point of expertise. Perhaps User:Fgf10 or User:Wnt can expand on this or tell me if I said anything incorrect :) SemanticMantis (talk) 15:12, 8 June 2016 (UTC)

That is a cool slide set. But it's worth adding that while "the" human and "the" cat are different, individuals may be less so. A particular human may lack a vermiform appendix, or have the left common carotid artery arise somewhere other than the aorta, thus resembling the case for the cat. But of course, all this anatomy is very roughly 100 times more ancient than the unique features of modern human beings. The truth is, we still have no idea what features make humans so unusual in their behavior, nor is any existing theory truly sufficient to rule out qualia in a rock or a computer keyboard, let alone a cat. Wnt (talk) 22:02, 8 June 2016 (UTC)

Surnames dying out

I think we have an article on this, if I could only remember what it is called. In a society where family names descend by patrilineality, at some point rarer names will die out, because sooner or later all the children in a given generation will be girls, and will not pass the name on to their children. (Ignore sexism, single mothers, and volitional name changes - this is a thought experiment.) The model that shows how this works can be applied to other things transmitted by descent such as genes. Am I mis-remembering? What is this phenomenon called, and what application does it have in current research of any fields? Carbon Caryatid (talk) 17:36, 7 June 2016 (UTC)

Galton–Watson process. --Jayron32 17:44, 7 June 2016 (UTC)

Elementary, my dear Galton! Thanks. Carbon Caryatid (talk) 18:21, 7 June 2016 (UTC)

Colloquially called "daughtering-out". - Nunh-huh 00:21, 8 June 2016 (UTC)

Does this mean that eventually everyone will be named Smith? ←Baseball Bugs ^{What's up, Doc?} carrots→ 18:50, 7 June 2016 (UTC)

I'm Brian! DMacks (talk) 18:57, 7 June 2016 (UTC)

No. Read sections 2 and 3 of the linked article, which give conditions for extinction of a name. Note that extinction in finite time is always possible, so persistence of a name for all time is necessarily a probabilistic notion. As explained in the "examples" section, real-world names seldom conform exactly to this model. And if one name was likely to increase while others diminish, smart money is on Wáng/Wong over Smith, which is actually a fairly uncommon name. SemanticMantis (talk) 19:41, 7 June 2016 (UTC)

Smith is the most common surname in America, though obviously there are a lot more Chinese than Americans. ←Baseball Bugs ^{What's up, Doc?} carrots→ 23:52, 8 June 2016 (UTC)

The article Y-chromosomal Adam says we are all patrilineally descended from a common male ancestor who lived 200,000 to 300,000 years ago. So equating the Y chromsome lineage to surnames, this implies that all other surnames that coexisted with his died out at some point (with no changing of surnames allowed). Is that right? (Also the same applies to Mitochondrial Eve). Loraof (talk) 21:27, 7 June 2016 (UTC)

That common ancestor lived hundreds of thousands of years before there were surnames. But no other man with a Y-chromosome at that time has any male descendants alive with that chromosome. - Nunh-huh 00:20, 8 June 2016 (UTC)

Sure, and in that case, the other haplogroups/surnames had a positive chance for extinction in finite time. The fact that they did die out doesn't mean they had to, and none of this means we should a priori expect one surname to eventually exclude the others. It's always possible for everyone not named Hernandez to die tomorrow, right? So we cannot ever say with certainty that a haplogroup/surname will persist indefinitely. Under the model assumptions, we can sometimes say that a given lineage will almost surely go extinct. SemanticMantis (talk) 15:02, 8 June 2016 (UTC)

What is the term for stoppage or accumulation of blood in the lower part of the body?

What is the term for stoppage or accumulation of blood or fluid in the lower part of the body or other organs? (under influence of gravity. for example by bad blood circulation or even after death). There is a word that should start with the prefix hypo-xxx 93.126.88.30 (talk) 20:07, 7 June 2016 (UTC)

After death: Livor mortis. --NorwegianBlue ^talk 20:15, 7 June 2016 (UTC)

Indeed, it is hypostasis as mentioned in the article that you linked. Thank you! 93.126.88.30 (talk) 20:34, 7 June 2016 (UTC)

Edema is accumulation of fluid (mostly water). It's commonly in the lower part of the body, due to gravity, in people who are upright most of the day. For those who are bedridden, the accumulation may be more towards the back, depending to the position of the patient. It's common to rotate the patient to even it out. Compression stockings are used to limit accumulation in the feet, but unless they have a graduated reduction in compression near the top, the patient can get the "muffin top" effect where all the accumulation pools right above the stockings. Phlebitis, an inflamation of the veins, often in the legs, is also related. StuRat (talk) 17:14, 8 June 2016 (UTC)

You might also look at Ascites. DrChrissy ^(talk) 17:25, 8 June 2016 (UTC)

I thought I might find it in g-suit but it's not there. DrChrissy ^(talk) 17:23, 8 June 2016 (UTC)

Wacom share holding stock

Would you buy a piece of the company? Is it worth - or did they stopped to built interesting things and the company was years ago more interesting for investment? --Ip80.123 (talk) 23:53, 7 June 2016 (UTC)

The Refdesk doesn't give advice, especially not professional advice. It also doesn't make unsourced predictions, especially when assuming a perfect market the existing price would be assumed to approximate the best rational estimate, within some unknown and doubtless financially interesting margin of error. If you go to Humanities and ask where to look up stock predictions they might help you though. Wnt (talk) 00:14, 8 June 2016 (UTC)

Here's some general advice about the stock market, from Will Rogers: "Buy only good stock. Wait till the price goes up, then sell it. If it don't go up... don't buy it!" ←Baseball Bugs ^{What's up, Doc?} carrots→ 00:38, 8 June 2016 (UTC)