Wikipedia:Reference desk/Archives/Science/2018 November 2

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November 2

Can 2 people eat the same food, and 1 gets diarrhea, the other does not?

So I recently found out about the 2 types of diarrheas: the ones caused by viruses (food not cooked enough), and the others with excess water to the bowels (such as too many solutes, such as too much magnesium or vitamin C). So my question is, what are other factors, besides immunology? For immunology, I imagine such a case where 1 got immune from eating the same contaminated or undercooked food. The only other variable I can think of is allergies, I wonder if eating food 1 has allergies to, can cause diarrhea. Thanks. 67.175.224.138 (talk) 00:09, 2 November 2018 (UTC).

Yes - 1 might not. I've traveled to some far-off places with what I consider dodgy hygiene practices. Fast food from a market stall in Jerusalem gave me problems but the locals ate it with impunity. After a few weeks I was able to do so too. I did not become immune to anything. My gut flora adapted. 196.213.35.147 (talk) 06:00, 2 November 2018 (UTC)

Actually a big percentage of Foodborne illness is caused by bacteria not viruses. Our article says albeit without a source that "one third of cases of food poisoning in developed countries". It also mentions there tends to have been an overestimation of bacterial causes in the past due to a lack of sufficient testing for viruses, and it's of course true that not all foodborne illness results in diarrhea, but definitely a lot of bacterial causes do and I don't think many epidemiologists or medical doctors will ignore bacteria as a cause. The phenomena describe by the other IP is well known, see Traveler's diarrhea for information. It's also sometimes called "Montezuma's revenge" and "Delhi belly". Nil Einne (talk) 07:21, 2 November 2018 (UTC)

I wonder if other countries have different types of bacteria, so if you eat an apple that has different bacteria, that your body has never made contact before, it can have problems. But I think you're implying more amounts of bacteria, on the same food. I heard for some 3rd world countries, when you fly in, you get to take a shot to get exposed to some bacteria/viruses beforehand. But for older people with weaker immune system, sometimes that shot makes them more sick to begin with, you have to wait until you fully recover from the shot. 67.175.224.138 (talk) 01:45, 3 November 2018 (UTC).

BTW Coeliac disease is an example of a disease which can have diarrhea as a symptom, which can develop in some individuals depending on several factors including genetics. For people with the disease, a Gluten-free diet is the only accepted treatment which will generally improve, but may not eliminate symptoms. However as mentioned in our article, it's not an allergy. Wheat allergy is something else. While there may be others who will benefit from a gluten-free diet, as our article mentions it's also very common as a fad diet and for a lot of people there's little evidence it has any real benefit, for example in reducing diarrhea. Irritable bowel syndrome can also have diarrhea as a symptom and as our article says, the cause of IBS is still not well understood but diet appears to help management for some people. Nil Einne (talk) 07:45, 2 November 2018 (UTC)

Lactose intolerance springs to mind. Wnt (talk) 11:17, 3 November 2018 (UTC)

Poisonous snakes and frogs question.

Are poisonous snakes and frogs immune to their own poison. And if so - are they immune to the poison from other snakes/frogs of the same species, but different breeds? Or of different species of snakes/frogs. Note I'm not asking about snake biting frog or frog poisoning snake, but snake on snake vs. frog on frog. The venom that they secrete. Would the same breed or same species be immune to itself. Thanks. 67.175.224.138 (talk) 00:16, 2 November 2018 (UTC).

Apparently they are at least immune to their own venom.[1] ←Baseball Bugs ^{What's up, Doc?} carrots→ 00:56, 2 November 2018 (UTC)

Golden poison frog indicates the species members cannot poison each other. ←Baseball Bugs ^{What's up, Doc?} carrots→ 01:01, 2 November 2018 (UTC)

According to this article,[2] venomous snakes are resistant to snake venom, but not necessarily immune to it. ←Baseball Bugs ^{What's up, Doc?} carrots→ 01:04, 2 November 2018 (UTC)

This article on snake cannibalism raises some interesting questions. [3] I would imagine the snake being eaten has been bitten by the larger snake thus killing/neutralizing it. 196.213.35.147 (talk) 06:21, 2 November 2018 (UTC)

Some interesting stuff at kingsnake (so-called due to their penchant for eating other snakes, including venomous ones). They themselves are not venomous, but they're immune to many venomous snakes suggesting that venom creation and immunity are distinct adaptations. Matt Deres (talk) 12:16, 2 November 2018 (UTC)

Original poster, please be aware of the difference between poisonous and venomous, they are not the same thing.RichYPE (talk) 19:09, 3 November 2018 (UTC)

"Sentient" life on land vs in the seas

Given that 70% of the earth is covered by water, one might reasonably expect that sentient life (and thus civilizations) would develop there rather than on the land. I would suggest that there are likely some significant advantages to a water environment over a land-based one. Are there any theories as to why sentient life and civilizations developed on land but not in the seas (as the largest bodies of water)? What is it about the land that gave the edge to sentience developing there? 76.71.159.5 (talk) 02:08, 2 November 2018 (UTC)

How will the dolphins use tools? Flippers aren't very good at tool use or holding things. And who knows maybe dolphins are sentient, at least a little. If they are sentient then they're raping bastards, still like wild animals. Sagittarian Milky Way (talk) 02:37, 2 November 2018 (UTC)

Maybe the octopi have the potential for civilization but farming started civilization on land, not sure how that'd work with a carnivorous creature. Sagittarian Milky Way (talk) 02:42, 2 November 2018 (UTC)

Let me use the word "evolve" instead of "develop." Evolution allows for the development of tool manipulating appendages. The octopus can use tools. Why could a sentient aquatic creature not farm in the ocean? 76.71.159.5 (talk) 02:47, 2 November 2018 (UTC)

What would they farm? ←Baseball Bugs ^{What's up, Doc?} carrots→ 03:10, 2 November 2018 (UTC)

Being non-fully carnivorous and missing some abilities actually helps IQ, our closest living relatives can easily convert live prey into skeletons or live off leaves both without tools, and are much stronger and harder to knock out than men, prehumans lost the ability to do that and compensated by inventing tools like weapons, grinding shit with rocks and cooking. Thus the ones that did that progressed to hydrogen bombs and interstellar travel while the ones that didn't are still eating without farming and have the smarts of a 3 year old. A flying animal might also have less incentive to human level intelligence. For one, birds have very low fuel economy and IQ costs calories. Sagittarian Milky Way (talk) 03:20, 2 November 2018 (UTC)

In effect, animals are what humans once were: hunters and gatherers. ←Baseball Bugs ^{What's up, Doc?} carrots→ 04:08, 2 November 2018 (UTC)

Humans still are hunter gatherers in many contexts, for example in the ocean most of the time. People resort to agriculture when high population forces the issue (even in and near the ocean, where this is now happening). But animals also farm, e.g. leafcutter ants. Gray squirrels farm trees with considerably more foresight than humans [4] though you can argue it is perhaps not "deliberate". Wnt (talk) 11:15, 3 November 2018 (UTC)

Question about the derivation of dy/dx?

Derivatives show us how fast something is changing at any point. For example; the gradient of the graph of y = x² at any point is twice the value of x thereat. The process of finding the derivation of a gradient / slope of a function y=f(x) or y = x² is as follow.

Pick any two points A and B close to each other on the curve of y =x². The coordinates of A on the curve are (x, y) or (x, x²). Add Δx at A as usual. When x increases by Δx, then y increases by Δy. The x changes from x to (x +Δx) while y changes from y to (y + Δy) or f(x) to (x+Δx)². Thus the x and y coordinates of B on the curve are (x + Δx, y + Δy) or ([x+Δx, (x+Δx)²]. Now the instantaneous rate of change is given by

Δy/ Δx = [(x + Δx)² – x²] / [x + Δx - x]

Δy/ Δx = [x² + Δx²+2xΔx − x2] / Δx

Δy/ Δx = [2x + Δx] / 1

Reduce Δx close to zero by taking limit (Δx to dx and Δy to dy)

dy /dx = 2x + dx

dy /dx = 2x------Eq1 OR

dy = 2x.dx --Eq2

ABC is an infinitesimal triangle made by dx, dy, and hypotenuse or slope of tangent where point A and C are always on the curve. Length of AB = Base = dx, Length of BC = Perpendicular= dy and Length of Hypotenuse = AC. Angle CAB or BAC is the slope of a tangent

According to the aforementioned Eq1 or Eq2-

• dy/dx is directly proportional to x or angle CAB is directly proportional to x.

• dx is indirectly proportional to x OR x is inversely proportional to dx

• dy is directly proportional to x.dx or dx

The length of dx > dy when Angle CAB < 45 degrees

The length of dx = dy when Angle CAB = 45 degrees

The length of dx < dy when Angle CAB > 45 degrees

The proportionality of both the angle CAB and dy with x are in contradiction with the proportionality of x and dx in the triangle ABC after probing the equation of dy/dx = 2x beyond its derivation on a graph of y = x2. When x increases; dx decreases, dy increases, and angle CAB increases. This means AC also increases and ultimately SECANT when x increases. Our goal is to bring dx, dy and AC to zero (not away from zero either positively or negatively - Point C has to be on the curve) or secant to tangent by reducing them close to zero but here dx heads toward zero but dy and AC increases when x increases on axis mathematically.

Although the difference in the length of dx and dy can be noticeable clearly on the graph if we examine the triangle ABC at two different points for a gradient (dy/dx), say when an angle BAC = 0.1 degrees and 89.9 degrees on the curve but UNIT CIRCLE is the best example for observing the change in an angle CAB (say 0.1 and 89.9 degrees) of a triangle ABC for dy and dx and the comparison of their lengths.

RISE = dy = 2x and RUN = dx = 1 (always constant) in a GRADIENT of 1 in 2x which we obtained from the Eq1 of dy/dx=2x /1 at any point on the curve when there is no difference between secant and tangent – No idea how do we get dy/dx = 2x.dx but above said contradiction may be due to the introduction of another curve of y =(x+dx)² at a point where we seize x or y=x² deliberately and introduce delta x OR when function y = f(x) changed to y=f(x+Δx)². The value of x has reached to its maximum value instead of unlimited when a curve y=x² doesn’t continue anymore at a point where we introduce delta x or dx as y=x² and y =(x+dx)² are two different types of curve (two diffrent functions).

Further, integration is the reverse process of differentiation. Although delta x or dx is ignored during the process of derivation of dy/dx becaue of their small values but we can’t ignore them in the process of integration which makes a lot of difference in summation. They can’t be disappeared forever and should resurface during the process of integration or summation.

Similarly, dy is the small vertical change in y, therefore, we take the sum of all the small vertical lengths [dy(s)] not the whole slice or y-coordinate(s) from zero to its value on the curve when we integrate both sides of the equation of dy = 2xdx but it turns into function of x² or area under the graph – no idea how but summation of vertical lengths on a graph gives vertical length only not curve?

Is the derivation of the natural relationship of a gradient of 1 in 2x at any point with y=x² or dy/dx=2x still unbeknownst to illuminates?Eclectic Eccentric Kamikaze (talk) 06:08, 2 November 2018 (UTC)eek

I'm not certain that I've understood your problem with the standard derivation, but your erroneous conclusion that "dx is indirectly proportional to x OR x is inversely proportional to dx" seems to be where your confusion starts. Also, it's the tangent of the angle that is proportional to x. For integration, it's the vertical slices of width delta x that are summed to give a total area. See our article Trapezoidal rule. Dbfirs 07:52, 2 November 2018 (UTC)

I believe our OP is confused by the specific case of the calculation of the derivative for a parabola (with a function y(x) ≝ x ²), and the general case of the calculation of the derivative for any other function.

To be very clear: the derivative is only equal to "2x" in the case of the simplest form of the quadratic equation. The derivative for other curves is equal to some other value or expression. Many methods exist to simplify the calculation for standard curves; many more difficult methods exist to formally calculate or to estimate the derivative for very complex functions.

A few good calculus books should help. Stewart's Calculus is $240 well spent. It presents the rigorous theoretical bits in a manner that is both acceptable to proper mathematicians, and also palatable to introductory students. If that's too expensive, you can find it in any good university library.

We can also point you to many free resources, like Wikipedia's List of calculus topics - but most students need a lot more structure (in the form of a good textbook and a good instructor) if they wish to really learn these difficult mathematical methods.

Nimur (talk) 14:54, 2 November 2018 (UTC)

I'd also highly recommend the YouTube channel 3Blue1Brown, his explanations of calculus are very visual and intuitive in a way that most written texts and class lectures are not. He has a series on there called "The Essence of Calculus" that is just fantastic, and could clear up many of the OPs problems. Here is a link to the playlist. --Jayron32 15:05, 2 November 2018 (UTC)

Both dx and dy are dependent on x as explained above. The mathematics is very simple and self-explanatory. If the tangent of the angle is proportional to x then doesn’t it mean both dy and dx also changes when x increases or decrease.

The difference in the lengths of dx and dy can be seen clearly if dy/dx is found at four different points of 1, 2, 3 and 4 on a curve of y =x². Assume point 1 ia at where angle CAB is small say 0.00001 degrees and point 4 is at where angel CAB is say 89.0009 degrees.

Find dy/dx at point 1, 2, 3 and 4 as shown on a curve

Now integrate the final result of the standard derivation which is equal to dy = 2x.dx wrt x

Where does it say in the standard derivation of dy/dx that Δy is equal to the whole vertical slice of width equal to Δx on the graph which we use for standard derivation of dy/dx? - readers confuse here

Here, on L.H.S dy is infinitesimal vertical length (2x.dx) on the graph which we use for the standard derivation not the whole vertical slice of width equal to Δx as thought. The sign of delta means small not whole. its delta y not y therefore shouldn't the sum of all infinitesimal vertical lengths be one vertical length but we get y= x² as per power rule, but how? — Preceding unsigned comment added by Eclectic Eccentric Kamikaze (talk • contribs) 06:06, 3 November 2018 (UTC)

There is an awful lot of confusion in what you say. Lets start at the beginning. The 1,2,3 and 4 in your diagram - what are they? They look more like distances along the curve than x values. Getting from lengths along a curve to x or y values is a lot more complicated. Also the angle BAC is not proportional to dy/dx, it is the tangent of BAC which is proportional to dy/dx. Δx can be anything you choose when calculating Δy, it is their ratio and what the ratio tends to as Δx tends to 0 that is interesting. Anyway start by putting the numbers along the x axis to make things straightforward. Dmcq (talk) 08:41, 3 November 2018 (UTC)

If you have three points on a curve close enough to be looking at "infinitesimals" between them, then they are essentially in a straight line. (Assuming a continuous function, which we are) I assume the points you would really want would be in a right triangle, always 90 degrees at lower right. One at the lower left left on the plot in your little segment (x1, y1), one at the lower right (x2, y1) not on the curve, and one at the upper right on the curve (x2, y2). I speak assuming we're on the right side of the parabola with values increasing when I say that. Then the tangent of the angle at the left point is (y2-y1)/(x2-x1). We could figure out the angle itself (arc tangent) but there is no reason to; there's nothing I think you would do with it except see if it has the right tangent, which it does by definition. Note it cannot exceed 90 where the tangent is infinity. Note "delta x" = x2-x1 and "delta y" = y2-y1. In the limit that delta x and delta y approach 0, you can say they are dx and dy. Wnt (talk) 11:07, 3 November 2018 (UTC)

I can't claim to understand your question (too long and complicated for me) but it may help to think of infinitesimals like dx as "nilpotent", i.e. they live in a special number system where dx²=0 even though dx≠0. So all the higher powers of dx vanish right away. You can actually rigorously reconstruct calculus that way (smooth infinitesimal analysis) but that's probably not good for beginners. Note that there is a calculus textbook on Wikipedia's sister project Wikibooks, at b:Calculus, if you don't want to buy a traditional book. 173.228.123.166 (talk) 02:19, 4 November 2018 (UTC)

I understand this notion in approximations, but how do you make nilpotent rigorous? Is dx^5/4 still equal to zero? Wnt (talk) 14:19, 4 November 2018 (UTC)

Wnt, I've got a specific book recommendation for you: A Transition to Advanced Mathematics. I've previously recommended this book during our discussions on an unrelated question - also, coincidentally, about exponentiation. The way we hold ourselves to mathematical rigor is through the use of the constructive proof. This is a concept that is extremely important in modern mathematics; surprisingly, this way of thinking is not usually taught to users outside of the core math disciplines. It requires you to think very much like a mathematician - or a very good computer-programmer - by strictly defining your premises and then accepting the steps that necessarily follow from those premises. It's very much aligned with the core idea presented in the video series linked earlier by Jayron - you have to start thinking about math as if you were inventing it from scratch, and you follow through every detail.

Among the many ways we can sustain a "nilpotent" operator are the construction of modular arithmetics; or, through the use of nonlinear operators (in the sense of relaxing constraints about additivity, commutativity, homogeneity - including the use of quantization;,... and surely there are more esoteric methods that are probably of great interest to specialist applications and to general mathematical theorists.

If you're like most readers - including most actual mathematicians! - you've encountered a lot of difficult words in there. Every one of these words is excruciatingly important, and you cannot ignore them, because they describe consequences to the mathematics. This is why a great textbook can help: you need to learn at least a few things before you even begin attacking this specific task. First, you need a good reference (because you'll want to frequently refer back to the core definitions of such difficult words, at least until you've committed them to memory). More importantly, you need to learn the method of mental gymnastics that mathematicians actually use: their step-by-step process allows you to use the entire capacity of your brain to prove sub-steps using excruciating rigor such that you can later accept the consequences and free up your mental resources regarding the intervening details. In advanced mathematics, this is important - because in general, those details would occupy the entire capacity of even a very powerful brain, leaving no surplus capacity to proceed to the next step. You have to become familiar with this procedural approach, else you will have to just take some of mathematics on faith: in other words, if you can't grok an existence proof, then we tell you by argument from authority that there do exist numbers that exponentiate to exactly zero without approximation. This is less satisfying, philosophically.

Meanwhile - in a note for our readers other than Wnt: I can't emphasize strongly enough that the idea of nilpotency is not part of a standard introductory treatment of infinitesimals - so I would caution the OP against applying this idea to the differentials unless they're prepared to study it in excruciating detail.

Nimur (talk) 17:00, 4 November 2018 (UTC)

I tried to get you all beyond the final conclusion of the standard derivation of dy/dx =2x where dx is not equal to zero but tends to zero but I think my approach was too direct.

Eq 2 is the standard or general derivation of dy/dx at any point on the curve of y=x². Although its very clear from the Eq2 that dx, dy, hypotenuse and angle CAB changes when x changes but lets derive the standard derivation of dy/dx at point 1, 2,3 and 4 on the graph of y=x² as shown.

POINT 1 ON THE GRAPH: Let A1 is a fixed point at point 1. B1 is nearby point. The coordinates of A1 on the curve are (x, y) or (x, x²). Add Δx at A1 as usual. When x increases by Δx, then y increases by Δy. The x changes from x to (x +Δx) while y changes from y to (y + Δy) or f(x) to (x+Δx)². Thus the x and y coordinates of B1 on the curve are (x + Δx, y + Δy) or ([x+Δx, (x+Δx)²]. Now the instantaneous rate of change is given by

Δy/ Δx = [(x + Δx)² – x²] / [x + Δx - x]

Δy/ Δx = [x² + Δx²+2xΔx − x2] / Δx

Δy/ Δx = [2x + Δx] / 1

Reduce Δx close to zero by taking the limit (Δx to dx and Δy to dy)

dy /dx = 2x + dx

dy /dx = 2x------Eq1 OR

dy = 2x.dx --Eq2

Now, if there is a dx (base) then there are dy (perpendicular) and hypotenuse also which form a tiny triangle A₁B₁C₁ at POINT 1 on the curve where the slope of the tangent has to be determined.

The three sides of the aforementioned tiny triangle are

Base = dx, Perpendicular = dy, Hypotenuse= (dx^2 + dy^2)^0.5

Now when x increases in the general equation of dy = 2xdx [dy/dx= 2x], then all of the following also increase due to the trigonometric reasons.

1- Perpendicular = dy 2- Hypotenuse= (dx^2 + dy^2)^0.5 3- Angle of the slop of dy/dx = angel C₁A₁B₁

But the Base =dx decrease.

Repeat the same for point 2 and 3 on the graph.

Length of both dy and dx changes when x increases or decreases and the slope of the tangent as well

POINT 4 ON A GRAPH: Let A4 is a fixed point at point 4 on a graph. B4 is a nearby point. The coordinates of A4 on the curve are (x, y) or (x, x²). Add Δx at A4 as usual. When x increases by Δx, then y increases by Δy. The x changes from x to (x +Δx) while y changes from y to (y + Δy) or f(x) to (x+Δx)². Thus the x and y coordinates of B4 on the curve are (x + Δx, y + Δy) or ([x+Δx, (x+Δx)²]. Now the instantaneous rate of change is given by

Δy/ Δx = [(x + Δx)² – x²] / [x + Δx - x]

Δy/ Δx = [x² + Δx²+2xΔx − x2] / Δx

Δy/ Δx = [2x + Δx] / 1

Reduce Δx close to zero by taking the limit (Δx to dx and Δy to dy)

dy /dx = 2x + dx

dy /dx = 2x------Eq1 OR

dy = 2x.dx --Eq2

Now again, if there is a dx (base) then there are dy (perpendicular) and hypotenuse also which form a tiny triangle A₄B₄C₄ at POINT 4 on the curve where the slope of the tangent has to be determined.

The three sides of the aforementioned tiny triangle are

Base = dx, Perpendicular = dy, Hypotenuse= (dx^2 + dy^2)^0.5

Now when x increases in the general equation of dy = 2xdx [dy/dx= 2x], then all of the following also increase due to the trigonometric reasons.

1- Perpendicular = dy 2- Hypotenuse= (dx^2 + dy^2)^0.5 3- Angle of the slop of dy/dx = angle C₄A₄B₄

But the Base =dx decrease.

So would the length of dx, dy and hypotenuse at POINT 1, 2, 3 AND 4 be constant or varies as said. And the same is applied to angle C₁A₁B₁ and C₄A₄B₄. — Preceding unsigned comment added by Eclectic Eccentric Kamikaze (talk • contribs) 07:20, 5 November 2018 (UTC)

The values of dx, dy, and any length you compute using them, are differentials. They all have very small values that are close to zero. The only meaningful way to compare such values is using the methods of calculus - like the equations presented as L'Hôpital's rule.

When you try to apply conventional arithmetic manipulations to differential elements, you frequently find non-sensible results. This is because somewhere in your calculation, you are dividing by zero, or otherwise breaking a similar rule, that causes the result to be incorrect.

You can't even compare two differential quantities to see which one is larger unless you correctly apply l'Hôpital's rule! The little tiny triangles you've drawn have special properties as the length of their legs tends toward zero, and if you care about correct answers, you must learn and respect these special properties!

These exact conundrums are the reason why you are learning calculus. You are finding new methods that yield more correct results to such difficult problems. If you keep trying to apply simple trigonometry and triangle-geometry equations, you will compute wrong answers.

Try to find a good calculus book and follow the textbook presentation. These mathematical ideas are new to most students, and they are difficult. Don't make them more difficult by inventing your own methods that we already know won't work! After you've mastered the concepts and have new analytical tools in your toolkit, you can go back and play with the same problems - and you'll be able to see exactly why your geometric equations do not apply in these problems.

Nimur (talk) 15:44, 5 November 2018 (UTC)

As said earlier, our goal is to reduce these differentials of the subject to zero, not away from the zero either positively or negatively but dy increases when x increases. Anyway, I appreciate your replies. Thank you. — Preceding unsigned comment added by Eclectic Eccentric Kamikaze (talk • contribs) 19:27, 5 November 2018 (UTC)

Southern skies

The "Daily Telegraph" of 20 October reports the results of an evaluation by the National Physical Laboratory of the blueness of the sky around the world. The top three locations – Rio de Janeiro, Bay of Islands (New Zealand) and Ayers Rock (Australia) are all in the southern hemisphere. Cornwall came bottom. I can vouch for this – the sky in Perth, Western Australia is a deeper blue than it is here – but why the geographical bias? Is it something to do with the amount of moisture in the atmosphere? — Preceding unsigned comment added by 2A00:23C1:CD83:1F01:B1DD:854C:CF46:CA19 (talk) 09:58, 2 November 2018 (UTC)

I found National Physics Laboratory - Blue Sky Science which links to Expedia’s Best Blue Sky: Experiments and Results but am none the wiser. Alansplodge (talk) 11:29, 2 November 2018 (UTC)

The Wikipedia article about the color of the sky is at Diffuse sky radiation and the answer is that the color of the sky is a complex melange of factors, including specific kinds and amounts of gases and particulate matter in the air, air pressure, angle at which the sunlight strikes the sky on that particular day at that particular latitude, etc. etc. It isn't just one simple thing. --Jayron32 11:42, 2 November 2018 (UTC)

Speculation is that it is due to nitrogen oxides in the air, these add a brown colour. Smoke and dust would also degrade sky colour. All these substances are less in the air in the Southern Hemisphere due to less pollution and unvegetated deserts. It may also be affected by clouds, and so actually fluctuate wildly from time to time. (on p 28) Graeme Bartlett (talk) 11:45, 2 November 2018 (UTC)

Hypothesis: there is less land in the southern hemisphere, and so likely less dust and pollution produced there. Winds tend to flow west to east, so southern hemisphere dust and pollutants will mostly stay in the south, while those from the north will mostly stay in the north. Therefore the air the south will be clearer. A quick Google search for "global air pollution map" does seem to support my theory that there will be more pollution produced in the northern hemisphere. Iapetus (talk) 12:09, 2 November 2018 (UTC)

"The atmosphere is much more polluted in the northern hemisphere than in the southern hemisphere. This is because, while the southern hemisphere mainly consists of oceans, the northern hemisphere includes the large continents of Asia, Europe and North America and their industry and traffic." [5] Alansplodge (talk) 18:31, 2 November 2018 (UTC)

From space you actually have the most perfect view on the atmospheric layer surrounding the earth. You can look right thru it, against a deep black background with almost no distraction, around the edge of the planet. Its the same blue all around. On earth its simply a question of local weather or "perfect day"(for photography) to see an unusual deep blue sky. I remember one day in Germany just some years ago on a beautiful summer day with absolute no clouds. I believe this can happen anywhere on earth - even in the middle of a Jungle. There is even a specific Term for it in the German language! Its called de:Kaiserwetter (Redensart). --Kharon (talk) 23:28, 2 November 2018 (UTC)

Siblings procreating

In the TV show Game of Thrones, two characters, Cersei and Jaimie, are twins involved in an incestuous relationship. They have also produced three children (the oldest was a sadist and psychopath). My question is: what are the genetic implications of twins having children together and is there more risk (genetically) for the children having developmental problems when compared to non-twin siblings procreating? 142.46.150.122 (talk) 12:53, 2 November 2018 (UTC)

We have an article on Incest between twins which may help in your research. It's mostly from a social point of view, but some of the references may lead to productive areas (no pun intended). Matt Deres (talk) 13:16, 2 November 2018 (UTC)

Despite cases like those described here [6], among humans you can pretty much assume that if they are able to reproduce with one another they must be fraternal twins. This means that genetically, they can be pretty much treated the same as full siblings. Edit: Actually I see our article mentions Twin#Semi-identical twins have been observed and it would seem opposite-sex semi-identical twins (where both are fertile) would occur. For that case, there would likely be a greater risk of problems due to homozygosity than with normal full sibling pairings. That said, while I'm fairly sure it's not the case in GoT, heteropaternal superfecundation with fraternal twins is another possibility and I wonder if more likely. Edit2: I probably should link to sibling incest, incest and inbreeding as these discuss the issues surrounding full sibling incest. Really only the later 2 for the issues which you're interested in. Nil Einne (talk) 13:54, 2 November 2018 (UTC)

If the above answer confuses you, in simple terms: For nearly every case where human twins are able to produce a child together, you can pretty much treat them as full siblings in genetic terms and so likewise problems that arise due to genetic similarity. You can come up with possibilities where this isn't the case, but these are going to be very rare. This does refer to the real world, not fantasy worlds with dragons, people resistant to fire etc where you could come up with different rules. Nil Einne (talk) 14:35, 2 November 2018 (UTC)

Just to make sure I am understanding: the child would be (genetically) the same as a sibling of the parents? If, so, then genetic "problems" and "anomalies" would be the same as non-twin siblings producing a child? 142.46.150.122 (talk) 18:24, 2 November 2018 (UTC)

Yes, with the usual caveats of "never say never", identical twins are basically always the same sex. So, the only way for twin-based incest to produce children is to have fraternal twins of opposite sex, and fraternal twins are no different from any other brother and sister (genetically), they just happen to be brother and sister gestated in the same womb at the same time. The genetic relationship of fraternal twins is the same as the genetic relationship between a brother and sister born years apart. Also, the "genetic problems and anomalies" you note are largely overblown. The greatest threat, genetically speaking, for children born of close relations is the concentration of harmful, recessive traits, but these sorts of things are rare enough. Basically, if a family has a harmful recessive trait, it will tend to be somewhat more likely to express itself in cases where there is close genetic relationships, but that presumes those traits are there. It doesn't create those problems out of whole cloth, and the famous cases where it happened (the Blue Fugates, King Charles II of Spain who only had something like 8 great-great-great-grandparents where he should have had 32) are famous because they are so extreme; there are a multitude of other similarly close families without any history of problems but you never hear about them because they are normal. --Jayron32 19:03, 2 November 2018 (UTC)

[I]f a family has a harmful recessive trait – based on [7], most individuals carry a recessive autosomal allele that would cause sterility or death by adolescence in homozygotes. Adrian J. Hunter^{(talk•contribs)} 03:01, 3 November 2018 (UTC)

Facinating. Thank you for that. --Jayron32 03:02, 3 November 2018 (UTC)

Which is why evolution made sexy time with twins you grew up with icky. Sagittarian Milky Way (talk) 03:39, 3 November 2018 (UTC)

Indeed: Westermarck effect. Matt Deres (talk) 14:36, 3 November 2018 (UTC)

It is conceivable that a zygote could be produced with Klinefelter syndrome, leading to two identical twins, one of which loses the Y chromosome (chromosome loss) to become a normal female, at least in the germline. The XXY male has reduced fertility on average, but they are not always infertile. Because genetic mosaicism is common within single individuals, and hence also I would assume in identical twins, I would still say that the twins in this case are identical, even if of opposite sexes. As it involves three somewhat unlikely events (Klinefelter, homozygotic twins, and chromosome loss) I don't know if this has actually happened; it is also conceivable that it happened but has not been noticed because any idiot knows a man and a woman are not identical. Our article twins actually describes similar very rare cases, but those are X and XY -- just the chromosome loss. But Turner syndrome has a very high rate of infertility, though it is not assured. If mating and fertilization did occur in either case, the progeny would be 50% homozygous for one or other copy of the parent's chromosomes, which is an extreme test of whether any lethal or harmful recessive alleles are present, so the child could have serious medical problems. However, looking it up [8] the rate of alleles causing death before reproductive age is thought to be 0.29 per haploid genome and remarkably constant between species; if the children had half haploid genomes that means an 85% chance of not suffering genetic lethality before puberty, at least. As for sadistic or psychopathic behavior, I am so far unaware of any convincing claim of a genetic basis for evil, and certainly not any single gene for it. (Somehow I suspect that if a single gene were identified, those without the psychopath allele would nonetheless find themselves quite capable of rounding up and exterminating the carriers in the name of a healthy society...) Wnt (talk) 10:50, 3 November 2018 (UTC)

I'm curious how you arrived at the 85% chance. I don't see how one gets from an average number of (harmful) genes to a probability. Also, what do you mean by 'half haploid genomes'? That sounds like 1/4th of a complete human genome. Thanks - Lindert (talk) 17:19, 4 November 2018 (UTC)

@Lindert: If the entire genome is haploid (or rather homozygous, made from two identical haploid genomes, given that the haploid is inviable), the risk is 0.29 = 29%. In a mating of identical individuals, half the alleles get matched up with themselves; the other half get matched with the other copy in the parental genome, which may or may not be the same allele. I.e. breeding Aa x Aa yields 50% AA or aa, 50% Aa, where A may or may not be the same as a. However, if A was a, then if that allele were lethal, the parents would not have lived to begin with. So I ignored that chance and just took 29%/2 = 15% chance of matching up lethals, with the caveat that the risk might be less since you aren't actually making half of all the genes homozygous. Wnt (talk) 09:27, 6 November 2018 (UTC)

@Wnt: I had to read that a few times, but now I get what you mean I think. However, it still seems to me that you're improperly equating an expected value with a probability. 0.29 harmful alleles per haploid genomes does not mean that 29% of haploid genomes have a harmful allele. If you had a group of 100 women who have a total of 29 children (0.29 per woman), then it would not follow that 29% of the women are mothers, because that assumes no woman has more than one child, and this reasoning would lead to absurdities if there were 1.2 children per woman. The same goes for the '15%', which is not a probability, but an average number of alleles. - Lindert (talk) 10:18, 6 November 2018 (UTC)

@Lindert: OK, that's true, but I ignored it as an approximation. If there are 0.29 alleles per genome, a self-fertilizing sperm would have something like a 29%*29% = 8% chance of having two lethal alleles. Three would be 29%*29%*29% = 2.4%. Now to be sure, that's not a grand approximation either; what I really want is a Poisson distribution where lambda = 0.29, which gives me e^-0.29 = 0.748926 chance of no events (1 minus that = 25.17363%), 0.29*e^-0.29 chance of one event = 0.2169965, chance of two events = 0.3146449. So if I were saying a 29% frequency I'd actually have a 25.2% chance of seeing a lethal phenotype ... but actually, in this case I was dealing with a 14.5% chance to start, and doing the same thing (1-e^-0.145) gets 13.49776%. In mathematics that may be really different but in biology an approximation that is 7.4% too high is practically the same number. ;) Wnt (talk) 01:22, 7 November 2018 (UTC)

Yes. In other words, if we ignore any personal details, in genetic terms Cersei having kids with Jaimie is actually no different from her having kids with Tyrion. Nil Einne (talk) 11:32, 3 November 2018 (UTC)

Thanks everyone. This was a very interesting read and answered my question! 76.71.159.5 (talk) 01:20, 5 November 2018 (UTC)

"As for sadistic or psychopathic behavior, I am so far unaware of any convincing claim of a genetic basis for evil, and certainly not any single gene for it. "

I happen to be a fan of the novel series A Song of Ice and Fire since the mid-2000s. It does not attribute Joffrey Baratheon's mental issues to his ancestry, and his siblings do not exhibit similar traits. On the other hand, it gives some hints on what was going on with him.:

• Bouts of anger which he could never control. Impulsive nature, and a lack of foresight that tended to be self-destructive. Superficial charm and feigned politeness, lack of empathy, and a sense of entitlement. Most character do not seem to consider him to be particularly intelligent.
• Of his three parents:
  • 1) Robert Baratheon (his legal father) actively disliked Joffrey, showed him little affection, and was described as physically abusive to his son (he had knocked out two of Joffrey's teeth when angry with the boy). Several of Joffrey's early schemes were suggested to be failed attempts to emulate his ruthless father (a famous warrior who gained the throne in a civil war), and to gain Robert's respect and approval. In Jaime's words, Joffrey was "A child hungry for a pat on the head from that sot you let him believe was his father."
  • 2) Jaime Lannister (his biological father) took little part in his upbringing and formed no emotional bond with him. Once seeing the corpse of Joffrey in the novels, Jaime realizes (to his surprise) that he does not feel sorrow. He proceeds to have sex next to the corpse (because he was celibate for quite some time.) He later claims that Joffrey deserved to die.
  • 3) Cersei Lannister (his mother) supposedly loved him, but could neither control his behavior, nor instruct him. Joffrey in fact orders the first execution of his reign (Eddard Stark) as an act of defiance towards his mother, disregarding Cersei's plans about Stark and breaking an agreement. Cersei at some point bonds with Tyrion Lannister (the brother which she dislikes), over their mutual frustration at Joffrey's special talent to alienate anyone previously loyal to him.
• As a little kid, Joffrey tortured animals, and at some point cut open a pregnant cat to get her kittens. An ambiguous scene in the novels implies that Joffrey habitually bullied (or molested) his younger brother Tommen Baratheon.
• Joffrey's grandfather Tywin Lannister (and other characters), pointed at times similarities in behavior between Joffrey and former king Aerys II Targaryen, who had a series of mental issues. Though Joffrey had no known biological relation to Aerys, the novels leave it unclear whether the similarities were coincidental, an act of conscious emulation on Joffrey's part, or an implication that Joffrey had Targaryen ancestry (the Targaryens had the reputation that madness runs in the family). A long-standing fan theory is that Tywin may not be the biological father of Cersei and Jaime, and that their true father was Aerys II (Tywin's closest ally, turned into an enemy for unclear reasons.) Cersei at some point exhbitits pyromania, one of Aerys II's main traits.
• As Joffrey got older, he seemed to get sexual gratification from having women stripped and beaten in front of him. Suggesting some developing sexual vices at least. And he was more of a voyuer than an active torturer. Dimadick (talk) 13:06, 6 November 2018 (UTC)

Mixture dilution math

Hydrogen peroxide is useful for household purposes. It is typically sold in brown bottles with 3% concentration ie. 97% water. This is wasteful packaging and shipping from Amazon.com so I found a dealer that sells 12% concentrate (max Amazon allows to ship - it becomes dangerous at high concentrations ie. rocket fuel). I would like to dilute the 12% concentrate to 3%. How many parts water to 12% hydrogen peroxide to achieve 3%? If helpful in verifying, this provides a ratio when using 35% concentrate: 11 water to 1 hydrogen peroxide to achieve 3%. -- GreenC 13:47, 2 November 2018 (UTC)

See here for a nice explanation. It's a simple calculation: C1 x V1 = C2 x V2; that is the concentration x volume for any solution is constant. (that video uses "M" for molarity as a measure of concentration, but it's basically generalizable to any concentration unit, including %, at least to the accuracy you're seeking here). Strictly speaking, this only works if the volumes of the mixtures are additive; they may not be in your case, but it will be close enough to get you down to the tolerances you care about (that is, you want a 3% solution, not a 3.0000000% solution). Figure out the final volume you want to mix up, and multiply that times the fraction of the concentrations, and that's the initial volume of your concentrate you measure out. So, in your case, if you want, say 1000 mL (1 L) of final solution, you would measure 3/12 (1000) = 250 mL of concentrate, and pour that into your destination container, then add enough water to bring the final volume up to 1000 mL. --Jayron32 13:56, 2 November 2018 (UTC)

And just a bit of clarification: for volumetric dilutions, you DON'T measure out the volumes separately and then combine, you first add your concentrated solution to your final (measured) container, and then fill that container with solvent until it reaches the volume mark. That is, get a container that has 1 liter marked on it, add 250 mL of your 12% solution to the container, then fill it to the 1 liter line with water. That sounds like an unimportant detail, but it isn't: volumes are not necessarily additive, and adding 250 mL of your concentrate to 750 mL of water will not necessarily give you 1000 mL of final solution. This video has an excellent demonstration and explanation as to why not; it uses ethanol and water, but similar explanations work for any mixture of different things. --Jayron32 15:14, 2 November 2018 (UTC)

User:Jayron32 ok this is good. Using imperial units.. a gallon contains 128 ounces so (3/12)*128 = 32oz of hydrogen peroxide + 96 ounces of water. Or simply a ratio of 3:1 water to hydrogen peroxide. Is that right? (understood re: how to combine the mixtures). I can more easily remember 3:1 or does the ratio change based on amounts of liquid? -- GreenC 15:20, 2 November 2018 (UTC)

• Point of detail: You mean American units there. Using Imperial units, a gallon contains 160 fluid ounces. The 128 is correct for American gallons. --76.69.46.228 (talk) 20:31, 2 November 2018 (UTC)

The ratios hold regardless. a 3:1 water:concentrate ratio (or more properly a 1:4 concentrate:final volume ratio) will give you the right concentration for a 12% -> 3% dilution. --Jayron32 15:22, 2 November 2018 (UTC)

Also, pour it slowly; letting the additional fluid slide down the side of the container with minimum turbulence. Disturbing hydrogen peroxide solution tends to release some of the oxygen. --Guy Macon (talk) 16:03, 2 November 2018 (UTC)

When I was younger I went to the chemist to buy some sodium hydroxide (NaOH). The pharmacist asked me what it was for, and I said to isolate sodium by electrolysis. My mother saw it, said the chemist should never have sold it to me and put it on top of the wardrobe. She later disposed of it. 94.192.183.95 (talk) 19:19, 2 November 2018 (UTC)

Got it thanks, Jayron3. And Guy Macon I also learned hydrogen peroxide deteriorates about 10x as fast at room temp versus in the refrigerator, or about 10% oxygen lost per year vs 0.1% 1% if kept cold. -- GreenC 20:04, 2 November 2018 (UTC)

Er, that's a 100x difference, not 10x. Matt Deres (talk) 19:50, 3 November 2018 (UTC)

Fixed. -- GreenC 13:33, 4 November 2018 (UTC)

Label on Streetlamp

Is this label on this a Wattage rating? Context is a US street lamp? ShakespeareFan00 (talk) 21:04, 2 November 2018 (UTC)

It might be a Colour Rendering Index (CRI) rating. [9] 97 is pretty good, 80 is typical, 100 is best. Why that would matter of a streetlamp is a good question other than I've seen complaints about how they cause everything to appear yellow, or concerns about too much blue light etc.. so a natural-color streetlamp would be better than some others. -- GreenC 21:43, 2 November 2018 (UTC)

That sticker said 15 when it was 150 watts high pressure sodium. At least in New York City. 25 for 250 which was way too bright (HPS was an order of magnitude more light per watt than 100 watt incandescent). Sagittarian Milky Way (talk) 23:01, 2 November 2018 (UTC)

If you walk along the street, do all the street lamps have that same label? --76.69.46.228 (talk) 08:00, 3 November 2018 (UTC)

Oh, I had another idea. I googled on the keywords "97 led" and "street light|lamp". Unfortunately the results were varied. On this page 97 clearly was the CRI rating as GreenC suggests (but I didn't see any street lights on that page). On this page 97 was apparently the wattage rating as the original poster suggests. And on this page (http://www.sensor-lux.com/97-led) the 97 appears in the URL, but if you click on either of the two models shown to get specifications, 97 does not appear in the specifications (or in the model number either). Still another possibility is that 97 is the number of LEDs in the fixture, as you might see on an LED flashlight package; but from the given photo, that doesn't look right.

I think to really answer the question it might be necessary to identify the brand of LED fixture. Probably it would be easier to contact the office that installed the street light and ask them the question. --76.69.46.228 (talk) 08:15, 3 November 2018 (UTC)

I think the IP might have been on the right track. Most obvious reason for this prominent label is to make it easier to report which ones are burned out. Please confirm others have the same number. Wnt (talk) 10:28, 3 November 2018 (UTC)

On the subject of "concerns about too much blue light" see these comments:

LED illumination is a serious health hazard.[10].

- 146.199.251.221 10:54, 18 August 2018

Apparently LEDs are blue [11].

- 86.132.186.138 15:21, 19 August 2018

Some streetlights have letters/numbers on them which are nothing to do with the equipment. They're location indicators, so that engineers can get to them quickly when a fault is reported. 2.25.226.253 (talk) 17:04, 3 November 2018 (UTC)

The label on street light is called a NEMA tag. It provides linemen on the ground information about the wattage, and what type of lamp is currently in the fixture. Red = Probe Start Metal Halide Red/White = Pulse Start Metal Halide Yellow = High Pressure Sodium Green or White (depending on the manufacturer) = LED

As for the wattage

3, 5, 7 = Equal 35w, 50w, and 70w HPS 10, 15, 20, 25, 31, 40, X1 = 100w, 150w, 200w, 250w, 310w, 400w, 1,000w (HPS) 17, 25, 40 = 175w, 250w, 400w.