Wikipedia:Reference desk/Archives/Science/2010 January 21

= January 21 =

Plants
What evolutionary advantage is there for plants to taste good? It seems like this would make them more likely to be eaten by animals, and thus less favored by natural selection, but obviously this isn't the case. --75.15.162.220 (talk) 00:52, 21 January 2010 (UTC)
 * Being eaten can actually be an advantage. The biggest problem most plants face is to spread their seeds to distant locations -- setting things up so that animals scatter the seeds in the process of eating part of the plant is one way of accomplishing that. Looie496 (talk) 00:56, 21 January 2010 (UTC)


 * I think you're thinking of this situation backwards. Plants produce sugars which they use for fuel, reproduction, etc. For animals, it is an evolutionary advantage to know what is useful to eat and what is not. Extrapolate a few thousand (million?) generations and things that you should eat taste good, things you shouldn't (or needn't) tend to taste bad. As for why things that are "bad for you" taste so good - what makes them taste good is actually good for you, in smaller portions. We simply eat too much and become rubenesque. (well, not ME! ;-)) 218.25.32.210 (talk) 00:59, 21 January 2010 (UTC)
 * That makes sense for why unhealthy foods can taste good, but it doesn't explain why, to most people, at least, healthy foods taste bad. --75.15.162.220 (talk) 01:05, 21 January 2010 (UTC)
 * Your "unhealthy" foods aren't really unhealthy. This is an important realization. They're just (artificially) too rich in nutrients / we eat too much of them. 218.25.32.210 (talk) 01:58, 21 January 2010 (UTC)
 * But why do most people think that "healthy" foods (vegetables, soy, etc.) taste bad, despite their obvious health benefits? --71.153.45.189 (talk) 02:03, 21 January 2010 (UTC)
 * Cultural norms? There are approximately 1.3 billion people in China who would likely disagree with your assertion that soy (or, by implication, tofu) tastes bad. Likewise, in my experience here most Chinese cannot handle the tremendous sweetness of an American confection like a Peep. This is not an evolutionary difference, as Mr. 98 alludes to below. 218.25.32.210 (talk) 03:04, 21 January 2010 (UTC)
 * Americans are used to sugar, so tofu looks and tastes like library paste to us. But I suppose if one were raised on tofu, it might become palatable. Although that hasn't worked for lutefisk, which your typical Norwegian regards as unhealthful AND bad-tasting, yet they eat it anyway. ←Baseball Bugs What's up, Doc? carrots→ 03:20, 21 January 2010 (UTC)
 * I don't think that people think healthy foods taste bad. They just taste worse than other modern alternatives like medium rare steaks and chocolate bars - they do taste better than poison, though. Zain Ebrahim (talk) 08:20, 21 January 2010 (UTC)
 * I think steaks and chocolate bars are sickening - fruit and vegetables are much nicer. Americans have been conditioned to like fat, sugar, and salt. But it is possible to loose your taste for these too. 92.24.85.238 (talk) 21:04, 21 January 2010 (UTC)
 * Isn't antifreeze supposed to taste pretty good? Googlemeister (talk) 14:20, 21 January 2010 (UTC)
 * Indeed. As an example, the sweetness of corn has risen dramatically, leaving the original stuff tasteless at best by our standards. ~ Amory ( u  •  t  •  c ) 14:26, 21 January 2010 (UTC)
 * An issue in all of these discussions about natural selection is that 1. humans and their culture have changed a huge amount since we initially evolved food preferences, and 2. our plants have changed quite a bit as well. The vegetables that we eat in modern industrial countries bear little resemblance in many cases to their original forms. An evolutionary model can get you some places, but it can't get you all of them. Culture, history, etc. need to fill the gap. --Mr.98 (talk) 02:16, 21 January 2010 (UTC)


 * It's important to distinguish between the parts of a plant where it is advantageous for the plant species that they are eaten (the fruit) and those parts where it is disadvantageous (the leaves, etc.). Plants may evolve to have pleasant tasting fruit and unpleasant tasting leaves.  Unfortunately for them, animals are also evolving and those individuals that find the leaves palatable may do better than those that don't.  So plants might evolve bitter-tasting leaves but animals evolve which enjoy the bitter taste.  It's a war out there.--Frumpo (talk) 11:40, 21 January 2010 (UTC)


 * And animals like humans happily subvert the intentions of the plant, anyway, by learning how to cook out the bad stuff, amplify the good stuff, and even breed out the seeds. --Mr.98 (talk) 13:24, 21 January 2010 (UTC)
 * The key point here is that the vital materials of one organism will often be compatible with another. So being delicious and being healthy are more or less overlapping. Vranak (talk) 22:11, 21 January 2010 (UTC)

Numbers
This may sound foolish, but are there any numbers that don't exist, are unquantifiable, or have yet to be defined? I'm not thinking of infinity but of strange 'dark matter' numbers that we have not yet found —Preceding unsigned comment added by 86.180.35.161 (talk) 01:36, 21 January 2010 (UTC)
 * There's nothing you can do that can't be done. There's nothing you can sing that can't be sung.  There are no numbers that don't exist.  --Trovatore (talk) 01:45, 21 January 2010 (UTC)
 * Numbers are a human invention. There are the "real" numbers and the so-called "imaginary" [a.k.a. "complex"] numbers, i.e. numbers that are a function of the square root of -1. But even the "imaginary" numbers are as "real" as any other numbers in the conceptual sense. ←Baseball Bugs What's up, Doc? carrots→ 01:48, 21 January 2010 (UTC)
 * How many humans invented numbers? --Trovatore (talk) 02:18, 21 January 2010 (UTC)
 * A number of them. ←Baseball Bugs What's up, Doc? carrots→ 03:17, 21 January 2010 (UTC)
 * Numbers are by no means a human invention! They transcend the world but they also permeate it. Numbers essentially speak of relationships between things. Even without human intellect, things exist, and they are in relationships with each other, even if no one is around to take notes. Vranak (talk) 19:55, 21 January 2010 (UTC)

well not so long ago we didn't have negative numbers, fractions and exponential numbers. We do now, so therefore are there numbers we have missed in a long tradition of missing numbers? —Preceding unsigned comment added by 86.180.35.161 (talk) 02:09, 21 January 2010 (UTC)
 * And just how would we know? ←Baseball Bugs What's up, Doc? carrots→ 02:17, 21 January 2010 (UTC)


 * Ah, that's a different question. A great many structures are known whose elements are occasionally called numbers by somebody.  They don't really have much in common.  There are certainly interesting structures yet to be discovered; whether you call their elements "numbers" or not is fairly arbitrary, even if the structures themselves are not. --Trovatore (talk) 02:18, 21 January 2010 (UTC)

This question may receive more insightful answers on the math desk. I think that in earlier centuries, concepts about numbers were less well developed - as mentioned above, critical concepts about number theory had not been developed yet, so there was no human understanding about negative numbers, complex numbers, and so forth, until those ideas were first informally and later formally studied. Modern mathematical number theory is so well developed, so sufficiently abstract, that it would be very hard to conceive of a new type of number that both fits the definition of a number, and also fails to meet the criteria for inclusion in one of the existing categories. This is especially true of the very abstract set theory representations - for example, see Set-theoretic definition of natural numbers for an introduction to this methodology. If you, or anybody, could conceive a new type of number, it would probably garner a lot of attention from theoretical mathematicians. Finally, a more trivial answer to your question is that there are certainly large numbers who have never been represented in any form, ever before, by human or machine. All you have to do to generate one such number is to take the largest number which has ever been previously expressed, and add 1 to it (or multiply it by 357, and so forth). In that sense, any member of that infinite, uncountable set of specific numbers that have never been "written down" somewhere has never been discovered by humans. And this is just the integers! I won't even begin to discuss the subtlety of the real number spectrum! There's an uncountably infinite set of numbers between every two numbers that can be expressed! And so, there is an uncountably infinite number of sets, each of which contains an uncountably infinite number of numbers - have a read about degrees of infinity at the Cardinality article for more. But the significance of "discovering" a never-before-seen member of this set is moot - it doesn't surprise any mathematician (or anyone, really), because it's just another number which satisfies the properties we expect it to satisfy. Nimur (talk) 03:11, 21 January 2010 (UTC)
 * This would be a good time to reference the philosophy of mathematics article. Are numbers (or any mathematical concept) "discovered", or are they "invented"?  I'm in the "invented" camp (I identify with the Formalists), but it's not a trivial question. Buddy431 (talk) 03:23, 21 January 2010 (UTC)
 * I can't resist droning on a bit more - this time from the perspective of a computer scientist, rather than a mathematician. Every number can be thought of as the uniquely defined hash of a unique algorithm (even if we do not actually know the hash function used to generate it). And, there are plenty of algorithms that we hope to design, but do not yet know if it is theoretically possible to design. In that sense, if you could concoct a method to generate the numbers that represent the algorithms we hope to build, you might have something great - but this is more of a matter of designing a new kind of function that generates numbers. Strictly speaking, it is not a new class of numbers. Nonetheless, it's an unsolved, number-related problem at the frontier of human knowledge. Nimur (talk) 03:26, 21 January 2010 (UTC)
 * This is absolutely false, at least in the universe of the standard real numbers. Every computable number comes from an algorithm, but there are lots of others that don't. Most real numbers are not computable. Staecker (talk) 05:30, 21 January 2010 (UTC)


 * Calling composite things like imaginary complex numbers "numbers" is a weird kink that mathematicians have gotten into. I can't think why - it's an entirely illogical move.  An imaginary complex number is just a 2D vector - the operations we do on imaginary complex numbers are just regular vector operators - why make such a big deal over it?  Basically, you can do arithmetic on things like the square root of a negative number if you treat the intermediate values as vectors.  Big deal - that doesn't demand an entire new class of number.


 * A more reasonable view of what a number is would be a position on a 1D line that stretches from negative infinity to positive infinity. Every "number" is represented by a point along that line.  Integers, rational and irrational numbers are just different points along that line.  Taking that simple definition - the OP's question is answerable:


 * are there any numbers that don't exist ? - No, they are all on the line somewhere. There are no mysterious gaps.
 * are unquantifiable ? - A number is a quantity. Can a quantity be unquantifiable?  No.
 * or have yet to be defined ? - What do you mean by "defined"? A number is it's own definition...but let's come back to this one in a moment.
 * strange 'dark matter' numbers that we have not yet found ? - Can something not be 'found' when we know that (by definition) it lies somewhere on that line?


 * But you obviously seek mystery and excitement amongst numbers - and perhaps we can find some stuff like that:


 * There are numbers along that line that humans have never used - write down a number with 500 random digits and the odds are very good that nobody else will ever have written down that number - or used it for anything and that it doesn't represent anything at all in our universe - it's a brand new unused number! But it's been there on the number line for as long as we've had the number line.  It's no surprise that it's there or that it exists.  It's not really a surprise or particularly novel in any way.
 * Arguably the oddest kinds of numbers are the irrational numbers - stuff like pi and 'e'. They represent a point on the line - but pointing at that point is kinda tricky because they require an infinite number of digits.  If our questioner wants an oddity, then coming up with a 'new' irrational number would be the nearest thing to that.  Sadly, it's very easy to make a new irrational.  Just add pretty much any number to pi and you have a brand new irrational number all of your own.  But pi has a 'definition' (it's the ratio between the diameter and the circumpherence of a circle).  There are other irrational numbers that we have not yet "discovered" - and numbers like Catalan's constant that we are (so far) unable to determine whether they are irrational or not.
 * Humans haven't always known this though - plenty of people in the past didn't 'believe' in negative numbers or did not accept the concept of the number zero. Adding those concepts to our understanding is a relatively new thing.  Understanding the irrational numbers is another thing that is relative new in our history.  Perhaps there are other odd-ball classes of numbers out there that we haven't thought of yet - that would create the mystique that I think you're looking for.
 * For the notational problems associated with writing down the value of really, REALLY large numbers, see some of the last few sections of our Large numbers article.
 * You might also want to read our 0.999... article.
 * SteveBaker (talk) 04:12, 21 January 2010 (UTC)
 * I agree with everything here, except your description of imaginary numbers as "2d vectors". I can't think of how you mean that. Are you certain you're not thinking of Complex numbers? APL (talk) 04:25, 21 January 2010 (UTC)
 * Yeah - sorry - I did mean "complex" (I've fixed my response). But in my defense - until you put the imaginary part (without the 'i' - or the 'j' if you're an electrical engineer) into one element of a 2D vector and call it a "complex number" - it's really totally useless.  All discussions of the importance and value of imaginary numbers are really talking about the importance and value of complex numbers - and all of those discussions immediately jump to a little 2D image that shows the complex number is really being treated as a vector.  So all of this talk about imaginary/complex numbers could simply be boiled down to a rather simple application of vectors. SteveBaker (talk) 14:09, 21 January 2010 (UTC)
 * (ec) I'm not sure why we should insist that our fields be ordered to consider their elements to be "numbers". The complex numbers behave (in many ways) very much like the more traditional "1D line that stretches from negative infinity to positive infinity".  I, for one, appreciate the fact that I can find three solutions to the equation x3-1=0, and I don't really mind that I can't decide which solution is biggest.  To give another (weirder) example of objects known as "numbers" that Steve won't like, I refer you to the Quaternions (they're like 4D vectors!).  And since no one has yet linked to the plain old number article, I figure I can do that now. It gives some insight into when (and why) different types of numbers have been invented (that's right, invented) if anyone's curious. Buddy431 (talk) 05:18, 21 January 2010 (UTC)
 * But that same comment applies with just as much validity to (for example) 3D vectors as it does to 2D vectors and complex numbers - so is the position of an object in 3D space just a "number"? What about a description of the shape of a polynomial curve with a bunch of coefficients?  Is that a "number" too?  Where do you stop?  Is an elephant just a number?  What you do by getting excited about generalizing the concept of a number beyond a simple position on a 1D line is to turn the term into a worthless pile of mush that could be applied to anything.  That's an irresponsible thing to do.  If you need a word for numbers and vectors and matrices and other things like that - then invent a new word - don't corrupt the meaning of the original word. SteveBaker (talk) 14:09, 21 January 2010 (UTC)
 * No, my comment does not apply with "just as much validity" to 3D vectors. The 2D complex number plane truly is different from higher dimension fields, as Staecker elequently explains below.  Hamilton tried to develop a 3D version of the complex plane, but failed.  He eventually realized that he could get close with a 4D quaternion system, though even there you lose commutativity. Buddy431 (talk) 01:00, 22 January 2010 (UTC)
 * Yeah - all of the lower orders of vector have different properties and there are things like cross products that don't have meaning other than in specific numbers of dimensions. You're talking like I don't know what a quaternion is - I've been programming computer graphics applications and engines using 4D vectors that I sometimes use for representing rotations and such ("quaternions") for 20 years.  I happen to know that mathematicians want to complicate the issue with yet another special-purpose name and call them "quaternions" instead of "4D vectors" - but for me the quaternions are just another set of operations on 4D vectors. But for me, there isn't anything special about 'quaternions'.  I define operators that take a 4D vector that represents the equation of a 3D plane (Ax + By + Cz == D) and perform operations on that plane - or to store a space-time coordinate in an animation - I use the same sets of operations to perform rotations in 3D space...I don't know (or care) whether mathematicians want to give this yet another tediously painful to learn name - it's just another member of the general algorithmic toolkit that works with 4D vectors - and quaternion multiplication, rotation, spherical interpolation are others.  But splitting apart that set of operators that work on "complex numbers" from those that operate on "2D vectors" is a collosal waste of my time and a horribly complicating factor that would impede me from using these tools.  So - I have 2D vectors and some really simple rules for how to use 2D vectors to represent things like the square root of a negative number using the same vector toolkit I use to plot graphs and do plane geometry.  Imaginary (or maybe it's complex) numbers are just part of the bizarre, incomprehensible pile of vocabulary that mathematicians use to obfuscate their work form us 'mere mortals' who use this stuff every day.  Shed that stuff and vector/matrix math is easy. SteveBaker (talk) 03:53, 22 January 2010 (UTC)
 * Steve, I'm not sure if you've missed the point here, or if you're trying to slough over it. No doubt for your specific set of graphical applications, you can just remember these transformations on vectors and that's all you need.  But what you're missing is the regularities among them that are much more easily conceptualized in complex-variable language.  It's not about obfuscation, just the opposite; it's a clarifying conceptual step.  Not so much when you're doing one rotation/scaling at a time, no.  But for lots of other things.
 * The first nontrivial application is from algebra; just knowing that every polynomial can be factored all the way down to linear factors over the complex numbers. That's already very useful, and how you'd phrase it in terms of rotations and scalings I have no idea.
 * But things don't really get going until you hit analytic functions, which are simply functions that have a derivative in terms of the complex numbers. Over the reals, having a derivative is no big deal.  Over the complex numbers, it's very restrictive indeed, and tells you a lot about the function.  This information can be leveraged in all sorts of surprising ways (this is how the prime number theorem is most easily proved, for example; I imagine you care about that, given that it affects your banking security).
 * I remember a student asking me once, in a College Algebra class, why she should learn about the complex numbers. Now at some level it wasn't an unreasonable question, because frankly the whole class is useless &mdash; it's a grab-bag of algorithms that will be memorized by the students long enough to pass the final, but never understood at a level that could do the student any real good.  Just the same I was unembarrassed to tell her that she should learn about complex numbers simply because they're really really cool.
 * (What I may have left unsaid, don't remember for sure, was that unfortunately she would never get to see that coolness &mdash; in College Algebra all you see is that every polynomial can be factored down to linear factors, which is not something she'd appreciate beyond the mere formality of it, and the chance of a College Algebra student ever taking a class where analytic functions show up is negligible; by definition, College Algebra students hate mathematics, and College Algebra itself is certainly not designed to change their minds on that point. Pity that.  Still, my answer was true and honorable.) --Trovatore (talk) 08:22, 22 January 2010 (UTC)


 * (ec) FYI Steve- what makes complex numbers much much more interesting than vectors is that you can multiply and divide them. See Complex number. This fact allows you to do lots and lots of things that you can't typically do with vectors- such as define the complex derivative, which requires division. This is a very big deal, and not just in pure mathematics. Engineers and scientists have been using basic results of complex analysis for years. You might wonder whether similar multiplication operations could be defined on higher-dimensional vector spaces, and the answer is basically no. The only dimensions in which a multiplication operation can be defined which is commutative, associative, and distributive are: 1 (the real numbers) and 2 (the complex numbers). (There's also the quaternions in dimension 4 if you discard commutativity.) So you could say they're "just 2D vectors" if you like, but all the great things you can do with complex numbers are provably impossible in any higher dimensions. This is the Frobenius theorem. Staecker (talk) 05:27, 21 January 2010 (UTC)
 * But those operators that you call 'multiply' and 'divide' on complex numbers are also useful general purpose operations on 2D vectors - I use those operators in computer graphics all the time - heck they are even in the standard vector software library I wrote. If history had come out a little differently we could well have not needed to think about complex numbers at all - and just talked about 2D vectors being a handy way to work around the problem of doing math with square roots of negative numbers.  Ditto quaternions (just a bunch of handy operations on 4D vectors).  Giving these things funny names just obscures the commonality between them and other branches of math and makes the practical application of math much more complicated and jargon-laden than it needs to be. SteveBaker (talk) 14:09, 21 January 2010 (UTC)
 * Certainly if all you care about is vectors, then you'll want to emphasise the "commonality" between complex numbers and 2D vectors. But because of the multiplication and division operations (and some other things), you can do calculus with complex numbers. You can do derivatives and integrals and all the other stuff that you do in real number calculus. If calculus is what you care about, then you really should call them numbers. To insist on calling them vectors all the time "obscures the commonality" between them and numbers. Complex analysis is really much much more than some "handy operations" on 2D vectors. If you don't believe me try to formulate the Cauchy Riemann equations or Cauchy integral formula in terms of 2D vectors. You could do it, but it would be unbelievably tedious and very unnatural. And these are two of the most basic results in all of complex analysis. Take any more sophisticated recent theorems and it's absurd to think of them as vectors.
 * All that said, if all you care about in math is vectors (if, say, you're doing computer graphics), then you won't care much about fancy complex analysis, and "they're just 2D vectors" is probably OK for you. But it's not the whole story. Staecker (talk) 15:50, 21 January 2010 (UTC)
 * There is also the octonions in dimension 8 if you discard both commutativity and associativity. Dauto (talk) 05:39, 21 January 2010 (UTC)
 * Which we also have an article for, if anyone is looking for some light bedtime reading. Would it have been acceptable to go into Dauto's response and just link to the article there, or is that like the internet equivilent of telling a woman that she looks fat? Buddy431 (talk) 05:48, 21 January 2010 (UTC)
 * Please don't do that. It's considered exceedingly bad etiquette to edit other people's posts - even to insert a benign-seeming link.  The problem being that (in general) the original author might have intended a different meaning or twist on a word than you forced upon him by turning it into a link and thereby giving it a definite meaning.  If I say "Man cannot live by bread alone" and you link Man then you've changed my meaning from "People in general" to "Male human", and if you link bread you've changed the meaning from "mundane earthly things" to "food made by baking flour and water with yeast" - which is a quite different statement than the one I intended.  That probably wouldn't be an issue with a fairly obscure word like 'octonion' - but this is a point of principle.  So, no - never edit other people's posts, except perhaps in extreme circumstances to fix some piece of wiki-formatting that's disrupting the remainder of the page such as an unbalanced &lt;small&gt; tag.  You did the right thing. SteveBaker (talk) 14:18, 21 January 2010 (UTC)

Much of the above answers don't seem very mathematically informed. The original poster may be interested in computable numbers. A number is "computable" if there is an algorithm (computer program or similar strictly definable procedure) which can compute its digits. Not all numbers have this property. In fact, it can be mathematically proven that "almost all" real numbers are not computable. There's another interesting notion: definable number. A "definable" number is one which can be defined unambiguously by a simple logical sentence in set theory. Again, it can be proven that almost all real numbers are not definable.

Every number you've ever heard of (unless you're an expert in this sort of thing) is both computable and definable, even though it can be proven that the vast majority of numbers have neither of these properties. Both of these concepts may provide examples of what you are looking for if you want an "unquantifiable" or "dark matter" style number. Almost all of them are like that. Staecker (talk) 05:07, 21 January 2010 (UTC)
 * I don't think it's a matter of being "mathematically informed". The issue is that the original post can be interpreted by a mathematician, a physicist, a philosopher, a computer scientist, a linguist, etc.  Each community contains a sort of different perspective on the interpretation of the question.  Pretending that the pure theoretical mathematic approach is the only valid approach is ... well, what a theoretical mathematician would do.  But the concept of number is so broad, so vague, and is used by so many different technical and research communities, that it is silly to pretend that mathematicians have a monopoly on its interpretation.  Nimur (talk) 16:08, 21 January 2010 (UTC)
 * When "technical and research communities" use the concept of numbers, they are all using the same concept. This is because they all use standard mathematics. Computer scientists use the real numbers, not their own version of the real numbers. Same goes for physicists. So when a computer scientist says that every real number corresponds to an algorithm, he is wrong. If you want to talk about the real numbers, then "the only valid approach" is to talk about the real numbers. Staecker (talk) 18:34, 21 January 2010 (UTC)
 * Actually, no, computer scientists (except for those on the seriously hard-core theory side) don't use the real numbers at all. The real numbers are about geometry, topology, continuity; none of those concepts applies directly to computers, which have finite memories and therefore can represent only quantities with finite information.
 * The "real numbers" used in real-world computers are actually a restricted set of dyadic rationals.
 * Think of a real number as an infinite amount of information, all wrapped up in one neat little package. That has no direct application to CS (though, certainly, working with the reals conceptually is often more convenient and more powerful than working with discrete structures, and the outcome of that reasoning can be relevant to computers). --Trovatore (talk) 19:46, 21 January 2010 (UTC)
 * (Ah, on re-reading, it looks as though I may have misinterpreted you somewhat -- apologies.) --Trovatore (talk) 19:49, 21 January 2010 (UTC)
 * I think the key thing is that computer scientists use a subset of the real numbers. They don't use any numbers than aren't real numbers (or complex numbers - that's only a degree 2 extension, so doesn't make much difference). --Tango (talk) 19:51, 21 January 2010 (UTC)
 * Well, actually, I don't really agree with that. The rational numbers are not real numbers; the real numbers are sui generis.  The reals realize the intuition of a continuous line; that has little to do with the algebraic motivation behind the rationals.
 * Of course the rationals are naturally embedded in the reals. However the IEEE float and double numbers (or more precisely the operations on them) do not respect that embedding, at least not exactly.  So really the CS numbers are not even rationals; they're something a little different. --Trovatore (talk) 20:00, 21 January 2010 (UTC)
 * At the risk of sounding very brusque - yes. IEEE-754 is the formal way that engineers say "screw off" to pompous mathematical types.  We have our own definitions of numbers, operations on numbers, and consistent set of rules for working with them.  We followed the theory as far as it was useful to do so, and we don't care about the subtlety any more than that.  Now, we have to get back to programming our robots, rockets, and electric guitars - the math guys can complain all they want, but if they expect to do so using an internet-enabled computer, they are implicitly acknowledging that our system works.  Nimur (talk) 00:47, 22 January 2010 (UTC)
 * Hmm? Who's complaining?  That chip on your shoulder's pretty big, doesn't it hurt your back? --Trovatore (talk) 03:00, 22 January 2010 (UTC)
 * I think Staecker was complaining. As far as the chip on my shoulder hurting my back - you bet - my chip's huge...! : ) Nimur (talk) 03:46, 22 January 2010 (UTC)
 * I'm not sure if I was complaining.. But of course I know that computers internally don't use real numbers, they use some type of rationals. I was trying to respond to above posts which suggest that computer scientists (not computers) don't believe in the real numbers, and that rational or computable numbers are all that exist. This would be like an grocery checkout clerk saying that the number $10.054 doesn't exist, because there's no such thing as .4 cents. But I think this has gone on long enough now... Staecker (talk) 13:19, 22 January 2010 (UTC)
 * ... and if you really want to stretch your imagination with numbers that are definitely on the dark side, try our articles on Hyperreal number, surreal number and superreal number.   D b f i r s   09:02, 21 January 2010 (UTC)


 * Mathematicians invent new types of numbers by playing a game called "what if ?". "What if there were a number whose square was -1 ?" - okay, let's call it i. What if we add i to itself ? What if we add 1 to i ? What if we multiply i by itself 3 or 4 or more times ? What if we divide 1 by i ? What if we divide 2 by 1+i ? Hey presto - you have invented complex numbers. Hamilton asked "what if we could divide one 3D vector by another ?" and invented quaternions. Cantor asked "what if there were a number larger than any finite number ?" and invented transfinite numbers. George Boole asked "what if 2=0 ?" and invented Boolean algebra.
 * Physicists can play "what if ?" as well - "what if every fundamental particle were a one-dimensional vibratng loop in 11 dimensions" leads to string theory. The difference is that physicists are expected to provide experimental evidence that the results of their "what if" games bear some resemblence to the real world. Mathematicians have no such obligation - the results of their "what if" games only need to be self-consistent (in fact, even that is not essential; an inconsistent mathematical structure is possible, it is just not very interesting). Gandalf61 (talk) 10:59, 21 January 2010 (UTC)


 * OK, OK, none of you applied scientists and fundamental scientists are better than each other. Comet Tuttle (talk) 18:19, 21 January 2010 (UTC)


 * You might like the article on Illegal primes as well, number you should not use, don't even thnk about them! :) Dmcq (talk) 11:59, 21 January 2010 (UTC)


 * People constantly invent new types of numbers by taking some subset of the primes and naming them after themselves, or giving them some cute name. I generally am for deleting the articles about them as nonnotable vanity articles, since they usually lack references other than the "inventor" posting about them in some recreational math blog. Edison (talk) 19:43, 21 January 2010 (UTC)

There are well defined numbers whose values are currently unknown, such as the 48th Mersenne prime. (Calling it that is imprecise as there may still be undiscovered Mersenne primes between the 39th and what we currently call the 47th. I suppose you could say that k such that M43,112,609 is the kth Mersenne prime is unknown, although we know that it must satisfy k >= 47.)  Likewise, p, the smallest number of colors required to color any separation of a plane into contiguous regions such that no two adjacent regions have the same color, was not proven to be 4 until 1976; and n, the largest integer n such that an + bn = cn has a solution over the positive integers was not proven to be 2 until 1995. 124.157.247.221 (talk) 01:43, 22 January 2010 (UTC)
 * Those are not "new" numbers, they would simply be discovered values for a specific case in number theory. You want a "new" number? How about the one George Carlin once reported on, called "bleen". ←Baseball Bugs What's up, Doc? carrots→ 06:12, 22 January 2010 (UTC)

Could you harness the energy from an avalanche?
Hello,

Would it be possible to harness energy from the downward force of an avalanche? For example, would it be possible to install some sort of device (perhaps a turbine of some sort) at the bottom of steep mountains and generate energy from avalanches? Is there currently anything that works on these principles?

Thanks! I truly appreciate any help. --70.49.194.21 (talk) 05:40, 21 January 2010 (UTC)


 * Anytime something is moving it is theoretically possible to harness that mechanical energy and turn it into electricity. However, it is rarely practical to do so. For your avalanche power generator, you would need (at least) 3 things-


 * - some kind of ducted & self-cleaning turbine system


 * - perfect geography


 * - frequent heavy snowfall


 * Even if you found some place on earth that was sufficiently steep & snowy enough, you'd still have to build a power plant that was both avalanche-proof AND could produce cheaper electricity than whatever else is being used in the area. All of this is a moot point, however, because avalanches are singular events and power consumption is constant. Generating many kilowatts of electricity for only several seconds at your multi-million dollar plant only 2 or 3 times a year isn't going to satisfy any customers! 218.25.32.210 (talk) 07:08, 21 January 2010 (UTC)
 * Concur with 218. I Imagine that Mountainous areas also have areas of steady wind, or valleys that the wind tends to be funnelled thorough, so Wind Turbines, being an existing technnology may be a far better bet. --220.101.28.25 (talk) 07:55, 21 January 2010 (UTC)
 * Is it possible? Well, yes - as a thought-experiment you could dig a deep hole at the bottom of the mountain - hang a large basket over the top of the hole with a rope - wrap the other end of the rope around the shaft of a generator and when the snow lands in the basket, it's pushed down into the hole - pulling on the rope and thereby spinning the generator.  Or you could cover the mountainside in the path of the avalanche with piezoelectric panels and gather power as the snow lands on them.  So yeah - it's certainly possible.  But is it sensible?  Useful? Practical?  Hell no!  The capital cost of what would realistically be a hideously expensive machine would be impossible to justify.  Avalanches (by their very nature) are rare and hard to predict.  Having a big chunk of machinery sitting there completely idle for years waiting on the offchance that an avalanche might hit it is just not economically reasonable.  Also, avalanches happen in beauty spots - sticking a huge piece of industrial-scale machinery in the middle of that wouldn't be popular.   So, no, this is really a non-starter.
 * A better approach would be to wait until the snow melts and use the flow of water to turn a turbine...but we already do that - it's called hydroelectric power. SteveBaker (talk) 13:35, 21 January 2010 (UTC)


 * A minor nitpick, Steve. Avalanches don't have to be rare or particularly hard to predict.  They just seem that way becuase a) we humans know where avalanches tend to occur, and don't build stuff there; and b) when we do build, work, or play in an avalanche area, we tend to employ engineering and maintenance strategies to avoid them doing damage.  Avalanche-prone areas in developed countries regularly make use of tools ranging from mortars to helicopter-dropped explosives to trigger smaller avalanches in order to avoid building up large amounts of unstable snow.  (Neat - we have an article on avalanche control.) I fully agree with the rest of your comment, though; converting the kinetic energy of a short-term, violent event into useful amounts of electricity is a non-starter.  TenOfAllTrades(talk) 14:11, 21 January 2010 (UTC)


 * Tides have tremendous force. I've often wondered if there were a way to get power from the ocean currents or from the wave action along shores. Some reversible turbine that generates power no matter if the wave is coming in or going out. But then it has to be fish proof too... I have no idea if anything like that is even worth a darn to consider. (how much power could we get from waves?) --Neptunerover (talk) 15:38, 21 January 2010 (UTC)
 * Something like tidal power or wave power? DMacks (talk) 15:44, 21 January 2010 (UTC)
 * Well slap me silly! Somebody's way ahead of me! Thanks for pointing that out. That's really cool. --Neptunerover (talk) 16:35, 21 January 2010 (UTC)
 * It should be clarified that wave power has nothing at all to do with tides. It generates power from waves, which are produced by wind. --Tango (talk) 18:13, 21 January 2010 (UTC)


 * It is of course possible but it is highly impractical. Flowing rivers are just so much more predictable. Plus, places where avalanches occur tend to be far away from cities that need power. Power disperses as it travels long distances through the wires. Vranak (talk) 17:24, 21 January 2010 (UTC)


 * I've heard it is possible with alternating current to use transformers to step up the voltage to such that resistive losses are minimal when it is sent a long distance. But now that I think about it, direct current could also be transmitted at extremely high voltage for minimal resistive losses, now that electronic valves can be used to change it to and from AC. Edison (talk) 19:33, 21 January 2010 (UTC)


 * No doubt, but what magnitude of avalanche would it take to reach 'extremely high voltage'? The type that would occur vary rarely, I think! Vranak (talk) 19:52, 21 January 2010 (UTC)


 * Sounds like another question entirely? See alternating current, Transformer, Electric power transmission Electric power distribution, Electricity grid, Mains electricity. 2nd sentence, Yes 'extremely high voltage' conversion is possible, and is done for very long distance distribution, see Electric power transmission para. 4, SMPS (Switching Mode Power Supply), and High-voltage direct current (HVDC) --220.101.28.25 (talk) 21:14, 21 January 2010 (UTC)


 * The question can be rephrased "What voltage causes this kind of avalanche?" Cuddlyable3 (talk) 16:27, 22 January 2010 (UTC)


 * Southern California would presently be a good candidate for testing mudslide turbines. How much energy could be extracted from a 10 meter foot wall of mud, 100 m long, with a density of 1730 kg/m3 sliding down a 200 meter hillside at 10 meters/sec? Compare to  snow with a density of 160 to 481 kg/m3 but probably sliding twice as fast. Unfortunately the turbine would have to be sturdily built at great expense and would operate very rarely. Plain old water at 1000 kg/m3 has the advantage of steadier supply at greater pressure from hydroelectric dams. Edison (talk) 16:50, 22 January 2010 (UTC)

Cryogenic eutectic exergy
Which eutectic system has the most efficient exergy at cyrogenic temperatures?

On a related note, is the amount of work required to cool and recoverable from cooling a eutectic system from 3 degrees to 2 degrees Kelvin the same or less than the amount of work required to cool and recoverable from cooling it from 2 degrees to 1 degree Kelvin? If less, how much less? 76.254.70.144 (talk) 06:30, 21 January 2010 (UTC)
 * Use newtons law of cooling to determine the time taken :$$ \frac{d Q}{d t} = h \cdot A( T_{\text{env}}- T(t)) = - h \cdot A \Delta T(t)\quad $$  --123.237.193.11 (talk) 14:58, 21 January 2010 (UTC)
 * What does the time taken have to do with the relative amount of recoverable stored energy? 99.25.112.22 (talk) 05:51, 23 January 2010 (UTC)

pressure gauges
on what basis the pressure gauges are decided to mount it on the line? —Preceding unsigned comment added by Ssanthamson (talk • contribs) 08:30, 21 January 2010 (UTC)
 * What pressure do you mean: gas, oil, water, something else? Can you tell us more about thde line? Cuddlyable3 (talk) 10:06, 21 January 2010 (UTC)
 * see Pressure measurement--123.237.193.11 (talk) 14:56, 21 January 2010 (UTC)


 * If de pressure can be dangrous den the pressure gauge is mounted on de line. —Preceding unsigned comment added by 79.76.218.43 (talk) 01:00, 22 January 2010 (UTC)

driving force for sigmatropic rearrangements
What exactly are the driving forces behind sigmatropic rearrangement reactions? Are they more affected by entropy considerations than enthalpy considerations, e.g. law of mass action plays a large role here? Can I just look at bond energies? John Riemann Soong (talk) 14:59, 21 January 2010 (UTC)

A Google search for "sigmatropic driving force" throws up a few links that suggest it's generally driven by the stability of the product. Hope this helps. Brammers (talk) 20:48, 21 January 2010 (UTC)

very small question
I found this information: "The human brain has been estimated to contain 50–100 billion neurons." I'm having difficulty finding out how many neurons there are in the entire human nervous system though. Does anyone know? --Neptunerover (talk) 15:26, 21 January 2010 (UTC)
 * 50-100 billion is an enormous range. Most of the neurons in the body are in the brain (assuming that designation includes the brain stem). There are important and numerous neurons in the spinal cord, and important but less numerous neurons in the ganglions, and distributed as sensing organs in various tissues, however, they are unlikely significant in comparison to the aforementioned huge and widely distributed average. Half an order of magnitude allows for a lot of error. Tuckerekcut (talk) 16:21, 21 January 2010 (UTC)
 * Neptunerover, Neuron quotes the same number. However, Brain says "The cerebral cortex of the human brain contains roughly 15– 33 billion neurons depending on gender and age", just to complicate the issue. Note "estimated" and "roughly".
 * It certainly appears that for the brain and entire body:
 * There is great variability and
 * No one knows for certain. --220.101.28.25 (talk) 17:06, 21 January 2010 (UTC)
 * The cerebral cortex is only part of the brain, so those articles are consistent. --Tango (talk) 18:15, 21 January 2010 (UTC)
 * The indefiniteness comes from the fact that counting neurons is not easy. The numbers actually derive mainly from tiny granule cells of the cerebellum, which are estimated to number anywhere from 40 billion to 80 billion in humans.  The next largest group of neurons is pyramidal cells of the cerebral cortex, which are most commonly estimated to number around 10 billion.  All other groups of neurons are much smaller -- there is no other type that numbers even one billion.  Thus the numbers basically derive from cerebellar granule cells plus cortical pyramidal cells, plus a couple billion more for everything else. Looie496 (talk) 19:02, 21 January 2010 (UTC)

In looking up nerve cell, it goes right back to neuron. So I guess every nerve is considered to be a neuron? They're all connected in the same system with the spinal cord and everything. Into the brain then, with each hemisphere connected to its own side? Counting all the nerve cells, could 1/2 trillion be a decent ballpark figure? Thanks --Neptunerover (talk) 19:44, 21 January 2010 (UTC)


 * I will venture an inexpert opinion and say that if the human brain contains fifty to a hundred billion neurons, then the remaining somatic neurons will in no way shift that estimate significantly. For instance there likely won't be 20 billion neurons in the rest of your body put together, maybe 2 billion. But this is speculation. The brain is the seat of consciousness and the motor neurons won't likely add up to much. Correct me if I'm off the mark, anatomists! Vranak (talk) 19:49, 21 January 2010 (UTC)


 * Yes, "nerve cell" redirects to neuron because it is the same thing, the two terms are synonyms. A nerve is not a group of cells, it is a bundle of axons that are generated by neurons.  And yes, the total number of neurons outside the brain is a tiny fraction of 1% of the number inside the brain. Looie496 (talk) 19:55, 21 January 2010 (UTC)


 * Okay, if I'm understanding this better, some neurons inside the brain have axons extending throughout the body, and this is what accounts for most of the nervous system outside of the brain.(?) I was thinking there was a whole additional batch of nervous system cells with their own nuclei located throughout the body. --Neptunerover (talk) 10:06, 24 January 2010 (UTC)
 * There is. Many neurons have their nuclei elsewhere, and project their axons to the brain. For example, there are about 40 million olfactory sensory neurons that have their cell bodies in the nose, but project an axon to the olfactory bulb. Rockpock  e  t  21:17, 25 January 2010 (UTC)
 * There is a wide variation in the volume and mass of brains in normal adult humans. An old paper in Nature (1897) reported that among 50 normal adult male Scotsmen (said to be "a highly civilised and admittedly intellectual people") the cranial capacity ranged from 1240 cc to 1770 cc. Among 23 Scotswomen, the cranial capacity ranged from 1100 cc to 1625 cc, the largest 48% greater than the smallest. Why assume that there is one "correct" number for the count of neurons, when the volume varies so widely? There were also those considered mentally defective who had cranial capacity half of the normal average. The brain size and likely complexity also increases dramatically from the infant to the adult. The brain size diminishes with extreme age and senile dementia. Edison (talk) 16:38, 22 January 2010 (UTC)

dianionic copper
I don't really get transition metal bonding. Firstly, why would copper be oxidised beyond +1 -- are the spin stabilisations simply not as strong? Also, wouldn't a -2 charge make copper start a new orbital? John Riemann Soong (talk) 15:38, 21 January 2010 (UTC)

Orgasm
Is it possible for a human to orgasm without manual stimulation of the genitals (penis / clitoris)? Are there drugs that induce orgasm? Can the mind be trained to orgasm on command?
 * Yes. See the articles Nocturnal emission and Prostate massage. Some takers of Clomipramine, a drug marketed under the brand name Anafranil by Ciba Pharmaceuticals, have experienced yawn-induced orgasms as a side effect. Cuddlyable3 (talk) 20:21, 21 January 2010 (UTC)
 * Yes it is perfectly possible. If you were to break down all the orgasms ever experienced it would be but a minuscule portion, but it can and does happen. Vranak (talk) 20:22, 21 January 2010 (UTC)


 * There are porn star women who claim to have trained themselves to orgasm on demand via concentration alone (i.e. with no manual stimulus or medication, etc.). I have no direct knowledge of whether those claims are verifiable or not.  Dragons flight (talk) 21:17, 21 January 2010 (UTC)
 * It is possible to train the mind. Wired magazine has an article about fMRI studies of the brain during orgasm. The scan has to be done while the subject is lying absolutely still inside a tube, which isn't really a good setting for people to have orgasms. To get the scans they used women who could trigger orgasms using their minds alone. Staecker (talk) 21:24, 21 January 2010 (UTC)


 * Give a woman a diamond and watch what happens. :) ←Baseball Bugs What's up, Doc? carrots→ 04:10, 22 January 2010 (UTC)


 * And what is that supposed to mean I wonder? Misogyny has no home in a place of putative learning. Vranak (talk) 05:42, 22 January 2010 (UTC)
 * Women like jewelry. That's not misogynistic, it's fact. "...for when love's gone / they lustre on...Diamonds are Forever..." It reminds me of something Jay Leno said some years ago: "A polling organization paid a group of women 75 dollars each to report what turns them on. As it turned out, what turned them on was the 75 dollars!" ←Baseball Bugs What's up, Doc? carrots→ 06:06, 22 January 2010 (UTC)
 * On the more serious side, there are, in fact, women who can reach orgasm without any below-the-belt stimulation. ←Baseball Bugs What's up, Doc? carrots→ 06:07, 22 January 2010 (UTC)
 * A fact you say. Well then there's nothing more to be said then! Vranak (talk) 07:17, 22 January 2010 (UTC)
 * Try it sometime. Give your woman a nice piece of jewelry. Valentine's Day is coming up. A perfect opportunity. :) ←Baseball Bugs What's up, Doc? carrots→ 07:21, 22 January 2010 (UTC)
 * Bugs, I'm not sure if you're trying make all women look shallow and materialistic, or just yourself! :-)  Mae din \talk 07:37, 22 January 2010 (UTC)
 * Every woman I know likes jewelry, and cultural information reinforces that theory. ←Baseball Bugs What's up, Doc? carrots→ 15:31, 22 January 2010 (UTC)


 * I am OP and female and I don't like jewelry.  —Preceding unsigned comment added by 82.43.91.83 (talk) 18:00, 22 January 2010 (UTC)
 * Not arguing with that at all, it was the association. "Watch what happens" is fairly unambiguous.  And your joke forgot to mention the selfish reason the jewellery gets given in the first place, ;-)    However, please don't take my comments the wrong way, I haven't been offended or anything!   Mae din \talk 16:01, 22 January 2010 (UTC)
 * Women aren't materialistic; men just have trouble breast feeding. Bus stop (talk) 12:36, 22 January 2010 (UTC)
 * Depends whether you're talking about being on the giving or receiving end. ←Baseball Bugs What's up, Doc? carrots→ 15:32, 22 January 2010 (UTC)


 * Speaking from personal experience, the answer is yes, it's achievable, though definitely not easy. But I suppose with practice (like if I were a porn star^^) it could be done with less effort, less concentration, and in half the time!  :-)   Mae din \talk 07:46, 22 January 2010 (UTC)
 * Personally, I think that manual stimulation does not mean what the OP (and the others here, apparently) thinks it means. Deor (talk) 12:23, 22 January 2010 (UTC)
 * OK, define what you think it means. To me, it means direct contact with hands or some other object. ←Baseball Bugs What's up, Doc? carrots→ 15:31, 22 January 2010 (UTC)
 * You need hands. Cuddlyable3 (talk) 16:21, 22 January 2010 (UTC)


 * Bugs, I was trying to avoid making a snarky comment about popular conceptions of the sex lives of Wikipedians, but manual can mean only "with the hand(s)" in this context; and the original question, "Is it possible for a human to orgasm without manual stimulation of the genitals?" suggests a familiarity with one form of reaching orgasm to the exclusion of more, shall we say, interpersonal methods. Deor (talk) 17:11, 22 January 2010 (UTC)
 * I wouldn't know anything about the private lives of wikipedians, other than my own. But I see "manual" as meaning any kind of direct genital stimulation, including vibrators, intercourse, or whatever. And some women apparently can, be it from diamonds or from being stimulated somewhere else on their ample endowments. ←Baseball Bugs What's up, Doc? carrots→ 02:37, 23 January 2010 (UTC)


 * I would add that neither males or females need to use their hands to masturbate. To differing extents, fixed showerheads, fixed vibrators of various kinds, furniture which doesn't move easily and washing machines (both mentioned in masturbation for females although would also work for males to some extent) or just lying down on a soft surface (mentioned for males) could remove the need for hands. Of course manual stimulation primarily using the hands is the most common technique even more so for males and even with the others I mentioned the hands would usually be used and it would often be hard to avoid using them entirely particularly as they may get in the way (unless you're a double amputee) or you may inadvertedly use them for leverage, support etc. But I would say it's questionable if using hands to aide with these and other techniques (e.g. sex dolls) counts as manual stimulation if you don't touch an erogenous zone for stimulation, unless you also count sex as well which will often involve the use of hands by at least one partner. (And even with the aide of other things, most masturbation will I expect include some manual stimulation because there's little reason to avoid it; as I expect a fair amount of sex.) Nil Einne (talk) 02:26, 23 January 2010 (UTC)


 * I wondered about this, the original post has two elements; one is asking after the lack of manual stimiulation, and the other is "drugs that induce" and "on command", both of which imply no voluntary stimulation, physical or otherwise. It seems unlikely to me that an orgasm can be experienced just like flipping a switch, but I wouldn't say it's impossible.  I'd google it, but I don't think my employers would appreciate the content, :-)   Mae din \talk 16:34, 22 January 2010 (UTC)
 * Prozac? ~ A H  1 (TCU) 02:38, 23 January 2010 (UTC)

It possible for a female to fake an orgasm pretty convincingly. Edison (talk) 20:35, 23 January 2010 (UTC)


 * I disagree. Panting and shouting "yes!" do not an orgasm make.  There are lots of physiological responses that are not so easy to fake; the rhythmic contractions and the skin flushing, just for a start.  Being convinced by a fake orgasm somewhat depends on how "close" one is to the female who's pretending, if you get my drift, and how much experience is held by the one witnessing it.   Mae din \talk 21:34, 23 January 2010 (UTC)

Dienogest
What kind of molecule is dienogest? What is its IUPAC name? What are its effects in human and mouse females?--Mparu (talk) 20:42, 21 January 2010 (UTC)
 * Did you check out dienogest? Perhaps you can find your answers in that article and the sources from which it quotes.  DRosenbach  ( Talk 20:52, 21 January 2010 (UTC)


 * DRosenbach, you are right. I searched for dienogest using the italian version of Google, it usually displays the en.wiki article, but it did not this time. However I should have used directly the en.wiki`s search engine, sorry for this. The article shows the answers of several query asked above, thanks: I would be glad to have further hints about the side effects of dienogest in female metabolism, expecially in the field of neurology/psicology.--Mparu (talk) 09:20, 22 January 2010 (UTC)

Salt and water balance
The typical Western diet includes a lot of salt. If someone changed their diet to natural non-processed foods and thus consumed practically no salt for two or three days, would their body start urinating out excess water in an attempt to maintain the salinity of their bodies? 92.24.85.238 (talk) 21:15, 21 January 2010 (UTC)


 * NOT an expert in this area, but excess added dietary salt generally causes water retention. It seems unlikely urination would increase in the circumstance suggested, nor for the reason suggested. See Salt and also Water retention (medicine). Fluid balance may also be of interest. --220.101.28.25 (talk) 21:51, 21 January 2010 (UTC)


 * Yes. When people go on a diet, it is common to reduce salt intake (no french fries, salted nuts, saltines, potato chips, or other salty/fatty snacks). The reduction in salt intake commonly results in loss of "water weight" which gives an encouraging weight loss in the first few days. It is a reduction in retained water rather than a loss of fat deposits. It is commonly followed by a plateau, so the person decides the diet is not working and he/she goes back to overeating. If a healthy calorie restricted diet were continued, eventually the loss of body fat would show up as additional weight loss. This has always seemed like nature's way of getting us to abandon diets.

It is a pity the Unknown Person's links above are to pop books. 92.29.31.202 (talk) 21:05, 22 January 2010 (UTC)


 * On the other hand, drinking too much water at once causes a depletion of blood salt content and creates water intoxication. ~ A H  1 (TCU) 02:36, 23 January 2010 (UTC)

Pluto habitat for life in 7 billion year sun
Wow, this black blog page nearly consume 30 minutes when looking at it, but they show then way Titan and Europa might be in 5 billion years. Earler people have said at sun's expansion, Pluto can actually get nice and warm what makes people think this would happen?--209.129.85.4 (talk) 21:23, 21 January 2010 (UTC)


 * Stellar evolution is a subject that is fairly well understood by modern science. Dauto (talk) 21:46, 21 January 2010 (UTC)


 * I can't find anything relevant on that blog page (you've actually linked to a Google image search page, which doesn't help), but I can tell you this: In about 5 billion years the Sun will expand into a red giant. It will have much greater luminosity and the outer solar system will warm up. However, that will only last a few million years. After that, the sun will collapse into a white dwarf and everything will cool down again (I'm not sure what the luminosity of the white dwarf will be compared to the present sun, but it will certainly be dimmer than the red giant). During those few million years, parts of the outer solar system may well be a nice temperature for humans, but there is a problem - bodies like Titan are very small (Titan is a little under twice the mass of our moon). They can only hold on to the atmospheres that they have now because those atmospheres are very cold. If they warmed up, the atmospheres would quickly leak away. Living on Titan while the sun is a red giant would be, at best, like living on the Moon now. --Tango (talk) 23:17, 21 January 2010 (UTC)


 * It's worse than that. When the sun runs out of hydrogen fuel and starts burning helium before it does the red giant thing - it's going to emit a Helium flash during which time it could be thousands of times brighter than it is now - the solar wind will massively increase in strength - overwhelming our protective magnetosphere and bathing everything in hard radiation - and that will be fatal to life anywhere in the solar system.  So even if things somehow got survivable for humans in these normally inhospitable places, we have no way to survive the transition.  We need to be many lightyears away - settled on a planet in orbit around a much younger star long before that happens! SteveBaker (talk) 03:27, 22 January 2010 (UTC)


 * Steve, your sequence is wrong. The helium flash is at the end of the red giant phase not the beginning.  Dragons flight (talk) 04:27, 22 January 2010 (UTC)
 * Hmmm - you're right. My bad. SteveBaker (talk) 18:42, 22 January 2010 (UTC)
 * And the helium flash lasts a matter of seconds, so as long as you are on the night side of whatever body you are living on, you should be fine. The Earth will have long been abandoned as the Sun heats up over time and the seas boil in about 1 billion years so, so we'll most likely be living in airtight habits that don't really care when happens on the other side of the planet/moon. --Tango (talk) 04:47, 22 January 2010 (UTC)
 * Well, "fine" so long as you don't need the atmosphere on the other side of the planet to still be there afterwards! SteveBaker (talk) 18:42, 22 January 2010 (UTC)
 * Yes, I just said that... --Tango (talk) 20:14, 22 January 2010 (UTC)


 * Wait, Tango, Isn't Pluto cover with ice (it is methane mainly) and it have gas inside it? But Pluto is smaller than our moon. This could happen. When a ice sublimes, it can create a body of greenhouse effect to build a atmosphere, same thing could hapoen to Europa (moon), depends on what gas the white ice is made of.. Sublimation (chemistry) is changing state from ice straight to gas. Tango and Steve seem to miss a point.--209.129.85.4 (talk) 20:43, 22 January 2010 (UTC)
 * Yes, you probably would get outgassing as Pluto heated up, but you wouldn't end up with a decent atmosphere. You would have a few traces which would quickly dissipate. --Tango (talk) 23:55, 22 January 2010 (UTC)
 * This article from Space.com may be of interest. ~ A H  1 (TCU) 02:35, 23 January 2010 (UTC)
 * Yes, it is interesting. It doesn't, however, mention that, even if life can arise in a few million years, it would be extremely unlikely to reach complex multicellular levels in that time (that took billions of years on Earth, even after life arose). I'm very sceptical about the description of a "distended, puffy atmosphere" around Pluto, too. I think "distended" is supposed to mean a very high scale height, which there would, indeed, be around a planet with Pluto's gravity and Earth's temperature. The pressure would be extremely low, though - it would be trace amounts. Life would be most likely to occur in underground oceans, like those hypothesised to exist on Europa. Even finding traces of single-celled life around other stars would be a major find, of course, and would increase our estimates of the change of finding intelligent life somewhere. --Tango (talk) 19:33, 23 January 2010 (UTC)


 * Look at This what about the permafrost layers, is like white ice, except it's surface is grayish? The ices can sublime when it is warm enough, but I don't know how long it will last. If it can only maintain such a cold gas then it could be like Titan for a while, then without ultraviolet light or solar wind, the molecules just moves faster. By the way what is "outgassing"--209.129.85.4 (talk) 17:51, 25 January 2010 (UTC)


 * it means to bleed quickly. It won't just bleed away that quickly.--209.129.85.4 (talk) 17:55, 25 January 2010 (UTC)

Darwin
Wasn't Darwin racist? --70.129.184.174 (talk) 22:59, 21 January 2010 (UTC)


 * From our article Charles Darwin: "Darwin did not share the racism common at that time: a point examined by the philosopher Antony Flew, who is at pains to distance Darwin's attitudes from those later attributed to him. Darwin was strongly against slavery, against "ranking the so-called races of man as distinct species", and against ill-treatment of native people."  Comet Tuttle (talk) 23:04, 21 January 2010 (UTC)
 * But the subtitle of his book refers to "the preservation of favored races", he referred to Africans and Australians as "savages", and evolution says that Africans have changed less than Caucasians and are thus more similar to monkeys (in fact, several illustrations about human evolution would depict Africans as the evolutionary link between ape and man). --70.129.184.174 (talk) 23:07, 21 January 2010 (UTC)
 * I think the title means "race" in a more general way than just humans, as a subset of any species (the book isn't about humans, for the most part). "Savage" hasn't always had a pejorative meaning, it just means to opposite of "civilised". It is true that (sub-Saharan) Africans and Australians (before western colonisation, anyway) did not have civilisations. In modern usage, "savage" and "civilised" are used rather differently to the literal meanings used by Darwin. It is also true that Africans haven't changed as much as people that left Africa (change is hastened by new environments and small populations) so, I guess, they probably are more similar to other primates. The difference is tiny, though - they may be a few percent closer, at most. --Tango (talk) 23:28, 21 January 2010 (UTC)
 * "It is true that (sub-Saharan) Africans and Australians (before western colonisation, anyway) did not have civilisations." No, its not true. See Great Zimbabwe for example. The original inhabitants of Australia also had a culture, just different from Westetrn culture. Your comment about Africans not changing as much as people who left Africa seems unlikely when you consider their whole genotype not just appearances. 92.29.31.202 (talk) 14:10, 22 January 2010 (UTC)
 * Apparently I need to do more research into African civilisations. As for genetic change, I am confident about that - the genetic variation within people of African descent is significantly lower than between people from other continents. That suggests Africans have changed little since Homo sapiens started to leave Africa, while those that left have adapted to their environments. --Tango (talk) 15:11, 22 January 2010 (UTC)


 * " the genetic variation within people of African descent is significantly lower than between people from other continents." Citation please? I have usually seen genetic variation within Africa shown as greater than the variation between European and Arabic people, for example. There are thousands (millions?) of tribes in Africa, and the genetic differences between them can be huge. 86.178.230.208 (talk) 22:06, 23 January 2010 (UTC)
 * 86.178.230.208 is correct. Africans, as a collective, are the most genetically diverse people on earth. This is a common mistake people make, probably because of a greater number of superficial changes in non-Africans, such as diverse skin, eye or hair colours. They are not a good proxy for genetic diversity, however.  Rockpock  e  t  20:05, 24 January 2010 (UTC)
 * Note that "savage" does not necessarily have a negative connotation. See noble savage.  Also, go to http://embryology.med.unsw.edu.au/pdf/Origin_of_Species.pdf and search for the word "race".  You'll see that Darwin always uses "race" to refer to types of animals.  --Bowlhover (talk) 01:06, 22 January 2010 (UTC)
 * Darwin didn't talk about human evolution at all in Origin of Species, but he did in his later books. "The favored races" has nothing to do with human races. --Mr.98 (talk) 14:46, 22 January 2010 (UTC)
 * Just about anyone from the 19th century would be considered racist today. APL (talk) 23:39, 21 January 2010 (UTC)
 * Just about any westerner, maybe. It's best not to generalise too far. There will be a few exceptions even then, though. However, attempts to classify and judge people from history by today's standards do usually end in disaster. For example, were Ancient Greeks engaging in pederasty homosexuals? --Tango (talk) 03:34, 22 January 2010 (UTC)
 * By strict definition, yes. The question would be whether it was considered a bad thing, by the general public. ←Baseball Bugs What's up, Doc? carrots→ 04:08, 22 January 2010 (UTC)
 * Usually, Bugs, the answer is given as "no", because what we mean by "homosexual"—e.g. someone who exclusively defines their sexuality as being attracted to someone of the same gender—is a concept that would have had no meaning to the Ancient Greeks. We define a lot of our own sexuality as an act of dividing people into neat categories ("straight, gay, bisexual"), whereas the Greeks simply did not self-define in that way, and did not consider pederasty to be something that influenced questions about sexual identity. (Somewhat similar to the idea amongst prisoners that homosexual behavior while confined to an all-male facility does not in fact make one a homosexual, but is just "how things are done" there.) To take categories of the present and brute-force them onto practices of the past does not enlighten, generally speaking. It's more than just a question of whether it was condoned or not, but whether these forms of categories make any sense. An analogy that plays up the point might be trying to take medieval medical concepts and forcing them on to modern medicine... you can do it, if you want, but it doesn't make any sense and won't get you any insight, because the systems do not match up in any way, even though they are each considered to be true and natural by those who practice them. --Mr.98 (talk) 14:22, 22 January 2010 (UTC)
 * Ironically, terms like homo, hetero, and so on are Greek roots. They may not have described themselves that way, but if you went back through a time machine and defined those terms for them, they would have shrugged and said, "Yeh, I guess I am. So what?" ←Baseball Bugs What's up, Doc? carrots→ 15:28, 22 January 2010 (UTC)
 * Well, maybe. I would suspect it just wouldn't be a category they'd find acceptable. Less "so what" and more, "Wait, you can't lump me in with people who abuse children—that's not what I do." Imagine some person from a terribly politically correct future came and declared that you were a mass-murderer because you ate meat, or a slave-owner because you had a dog. You'd not only say, "wait, no I'm not," you'd say, "these categories are not correct." --Mr.98 (talk) 01:24, 23 January 2010 (UTC)
 * I intentionally didn't restrict my statement to westerners, but perhaps I'm just ignorant. I couldn't think of any society back then where most people wouldn't be considered racist by modern, western standards. APL (talk) 15:25, 22 January 2010 (UTC)


 * The book to read to find out Darwin's racial views is not Origin of Species, but Descent of Man. Approximately half of the book considers the question of race directly. (The other half considers birds, mostly.) Darwin argues what was, for Victorian Britain, a pretty liberal argument: that all people are of the same descent (different races are not different species or even subspecies), that differences between physical appearances of races are largely due to sexual selection (that is, aesthetic preferences that had been bred over time) and not natural selection, and that for the most part the difference between civilization and savagery is a matter of culture. These were extremely contradictory views when compared against the mainstream Victorian physical anthropology, who would have been Darwin's natural scientific affinity (at the time Darwin wrote, the physical anthropologists were making extremely racist arguments, going so far as to argue that Blacks were a totally different species than Whites and perhaps not really human). Stephen J. Gould has pointed out that Darwin was about as racist as Abraham Lincoln—neither of them questioned for a minute that white people, on the average, were light-years beyond the darker races in terms of intelligence and ability, but the societies they lived in gave them no opportunity to see any other alternatives. Darwin spends some great effort in Descent of Man showing how even the most apparently erudite Europeans are only a few cultural jumps from the most destitute and hopeless savages—not exactly a claim for racial superiority.
 * If someone was espousing Darwin's views from the 1960s onwards, they'd be considered racist. If they were espousing them before the 1960s in intellectual circles, they'd be considered fairly liberal-minded. Our definition of racist has radically changed in the last fifty years, and to call Darwin a racist is to completely miss that his arguments were, at the time, considered extremely anti-racist. Darwin was certainly not the most progressive thinker in all respects. But on the race question, for his time, he was pretty out there.
 * His views, of course, can be mobilized to support a variety of different positions. There are plenty who used Darwinian-style arguments to justify racism and the idea of racial superiority. But Darwin did not personally share these notions for the most part. It is a token to the robustness of the theory that it provides ammunition to so many different causes, and I don't think we can lay all that at Darwin's lap. (And lest we forget, people have used the Bible to justify all kinds of racism as well—it doesn't mean that the Bible is itself racist.) --Mr.98 (talk) 14:15, 22 January 2010 (UTC)
 * Conversely, it's equally invalid to argue "Darwin was racist, therefore Goddidit the theory of evolution is wrong". AndrewWTaylor (talk) 14:21, 22 January 2010 (UTC)
 * The argument, as I've seen it, is "Darwin was racist, Darwinism is racist, Darwinism is dangerous because it'll make your kids racist, don't teach Darwinism." Which is especially loopy given that modern teaching of evolution is usually about how it is extremely against any ideas of racial superiority. But it resonates well with a certain kind of voter, which makes it rather insidious. Unfortunately a complex explanation of the historical truth of it (as I've tried to sketch out above) is a little more complicated than such people are probably willing to listen to. --Mr.98 (talk) 14:31, 22 January 2010 (UTC)
 * By the same argument, since Newton was an alchemist who did not believe in the Trinity, gravity must be an occult heresy. Gandalf61 (talk) 14:56, 22 January 2010 (UTC)
 * Indeed, gravity is heresy, the truth is that the earth sucks. SteveBaker (talk) 18:02, 22 January 2010 (UTC)
 * And they accuse me of dredging up old jokes. :)


 * Yes, we do! SteveBaker (talk) 18:28, 22 January 2010 (UTC)
 * It's just good to see I'm not alone. :) ←Baseball Bugs What's up, Doc? carrots→ 02:29, 23 January 2010 (UTC)
 * I have a hard time believing that anyone with the radical, free-thinking ideas of Darwin would spend much time being vitriolic towards any particular race. Vranak (talk) 19:40, 22 January 2010 (UTC)
 * Racism is not necessarily about vitriol. It can be mere indifference towards any race other than one's own; or a general sense that one's own is inherently superior, while all the others are inherently inferior, so inferior it's not worth even mentioning them by name.  That sort of thing.  Indifference is a far more toxic thing than active hatred, because indifference, not hatred, is the opposite of love. --   Jack of Oz    ... speak! ...   01:59, 23 January 2010 (UTC)
 * Note that under this definition of racism, if you fight in your country's armed forces against any other country... or if you oppose foreign aid for any reason whatsoever... or even if you cheer for your own countrymen at the Aussie Open, or fly your country's flag in your back yard... or even if you feel romantically attracted only to people of your own race... you could be considered a racist based just on that! For example, I decided not to contribute to the earthquake relief effort in Haiti, does that also make me a racist? 24.23.197.43 (talk) 06:40, 23 January 2010 (UTC)
 * It depends on exactly why you decided not to contribute. And some of the examples you gave are nationalist rather than racist behaviour. Gandalf61 (talk) 09:22, 23 January 2010 (UTC)
 * I think that's an unnecessarily simplistic way of lookintg at it, Mr 24.23. We support and defend and fight for the things and people we love; that does not mean we're being racist towards the people we're not supporting or not defending or not fighting for.  If the reason you chose not to contribute to the relief effort for Haiti was solely because of the race of the people affected, and had they been "white" you would have helped out - then that would be a racist decision.  But I suspect your reasons for not contributing had nothing to do with the race of the Haitian people per se.  --   Jack of Oz    ... speak! ...   23:56, 25 January 2010 (UTC)
 * Indifference may be antithetical to love, but love is a two-way street. I will not find myself able to love a pile of dog poo that I find outside no matter how warm and tender my feelings are. Not to compare any races to fecal matter, of course, but the raw materials are the raw materials and if they are grossly unattractive then I will not be wise to insist I call my feelings towards them 'love'. Vranak (talk) 13:08, 23 January 2010 (UTC)
 * Right, but if you take the position that "I will never love a person from Race X because people of that race are generally unattractive to me", then, apart from taking a racist stance, you also close off all sorts of possibilities. "Unattractiveness" is a (subjective) quality of an individual, not of an entire race of people.  Also true of "attractiveness".  --   Jack of Oz    ... speak! ...   20:43, 23 January 2010 (UTC)
 * Hearts and minds can change contrary to what we may have sworn earlier. Vranak (talk) 05:49, 24 January 2010 (UTC)