Wikipedia:Reference desk/Archives/Science/2013 October 30

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October 30

The term for the tendency for dominant entities to get more dominant

Like Microsoft, planets, armies, wealthy individuals, etc. Being big helps them get bigger. Is it a maths thing? It seems to be everywhere. It seems that on Earth, it's fueled by money, and people jump into exploit the phenomenon. It seems to have a runaway effect. What's the term? It there one? Anna Frodesiak (talk) 05:13, 30 October 2013 (UTC)

Oh, and thank you, by the way. :) Anna Frodesiak (talk) 05:18, 30 October 2013 (UTC)

Well, the opposite and ultimately triumphant tendency is regression to the mean. - Nunh-huh 06:27, 30 October 2013 (UTC)

The rich get richer and the poor get poorer. Clarityfiend (talk) 06:58, 30 October 2013 (UTC)

I'm not 100% certain what it is you are looking for, so here's a bunch of things that might be of interest: Matthew effect, Tipping point (sociology), Network effect, Virtuous circle and vicious circle, Positive feedback, Reflexivity (social theory), Bifurcation theory, Threshold model. Do any of these fit the bill for the type of thing you are looking for? If so, I can help you find more specific details; or if not, what is missing (so i can narrow it down)?Phoenixia1177 (talk) 07:30, 30 October 2013 (UTC)

Wow! Holy moly! Yes, it's all of those, somehow. Those are some of the most interesting articles I've ever seen. I'm just getting started on them and it will take me a while. Thank you very, very much!

Okay, I will return the favour. Here's something I made up: Tell a friend you can make a specific word come to mind. Write down "What???" on a bit of paper and fold it up. Then ask your friend: "Okay, ready? Are you sure? Okay, concentrate. Now, think of an animal between one and ten." Anna Frodesiak (talk) 08:09, 30 October 2013 (UTC)

No problem:-) I'll dig around when I get home and see if I can find something with more details. --I like your trick, I'm going to use it at work:-)Phoenixia1177 (talk) 08:15, 30 October 2013 (UTC)

Where someone might respond, "Between one and ten inclusive or exclusive?" ←Baseball Bugs ^{What's up, Doc?} carrots→ 09:48, 30 October 2013 (UTC)

Or another wise guy might say, "Three-toed sloth." ←Baseball Bugs ^{What's up, Doc?} carrots→ 09:51, 30 October 2013 (UTC)

Or they might say, "My dog." Then you say, "What?" And they say, "My dog just turned seven." ←Baseball Bugs ^{What's up, Doc?} carrots→ 09:53, 30 October 2013 (UTC)

So if you're asking this to a group, you could resort to this Casey Stengelism: "OK, everybody line up... alphabetically by height." ←Baseball Bugs ^{What's up, Doc?} carrots→ 09:53, 30 October 2013 (UTC)

At first I was confused. Then more confused. Then I finally got it. I think your friends think more than mine. Mine all just said "What???" :) Anna Frodesiak (talk) 11:16, 30 October 2013 (UTC)

Economies of scale would be a likely explanation. Ssscienccce (talk) 08:59, 30 October 2013 (UTC)

Money equates to power. Also described as, "The Golden Rule: Whoever has the gold, makes the rules." ←Baseball Bugs ^{What's up, Doc?} carrots→ 09:46, 30 October 2013 (UTC)

Ah, another good article to absorb. Thank you. Anna Frodesiak (talk) 11:16, 30 October 2013 (UTC)

See also Snowball Effect. uhhlive (talk) 13:11, 30 October 2013 (UTC)

It's important to realize that that "Golden Rule" assumes that everyone has at least some theoretical access to gold. If literally one guy had literally all the world's gold, then gold would be come worthless as money. ←Baseball Bugs ^{What's up, Doc?} carrots→ 22:50, 30 October 2013 (UTC)

Economists like to call this Natural monopoly. Jørgen (talk) 13:37, 30 October 2013 (UTC)

Another term is critical mass. Our article is strictly about the nuclear sense of the term, but it also has broader meaning similar to "tipping point". StuRat (talk) 15:07, 30 October 2013 (UTC)

And, another important concept is that all such effects only operate within a certain range. That is, we don't have one person or company that owns everything, on nation that is able to conquer the world, one animal which replaces all the rest, etc. The reason is that at some point a significant diseconomy of scale also kicks in. In the case of business, this leads to a specific ideal firm size. In another field, you also get a stable population size for a given species, even a very successful one. I don't think even black holes are expected to contain the entire universe, due to Hawking radiation and other effects. StuRat (talk) 15:07, 30 October 2013 (UTC)

And we'll throw in logistic growth for a bit more abstract mathematical fun. TenOfAllTrades(talk) 15:52, 30 October 2013 (UTC)

And I'll throw in network effect - the nature of consumers to gravitate toward the most established product/service providers (applies more to some industries than others). Someguy1221 (talk) 22:51, 30 October 2013 (UTC)

I'm going to toss Turing Patterns into the ring. Not strictly examples of this phenomenon, but interesting and related nevertheless. More generally it sounds like you would be interested in reading about pattern formation. If so I can highly recommend the series of books by Philip Ball entitled "Nature's Patterns, A Tapestry in Three Parts" Equisetum (talk | contributions) 23:50, 30 October 2013 (UTC)

I'm absolutely astonished at how much great content there is on this sort of thing. And all these articles get tons of page visits. Wikipedia builders are gooooooooooood. Anna Frodesiak (talk) 00:01, 31 October 2013 (UTC)

Heisenberg's delusion of adequately well behaved standard reality?

If you used Heisenberg's box cutter to open the impenetrable cardboard box and dump Schrödinger's cat into a region governed only by classical physics, wouldn't the poor beast die instantly in the flash of an Ultraviolet catastrophe?

I.e. what color of wallpaper is used to paper over the cracks of the run down and condemned poorhouse where classical physics has been left to die in when the physicist makes some sort of effort to separate herself from quantum reality by suggesting that the padded room she's in is not part of all that quantum weirdness "out there"? Is there a well defined "classical model" that actually works, or is it all just Heisenberg's delusion of adequately well behaved standard reality, that breaks down if you poke at any of the walls? Hcobb (talk) 13:19, 30 October 2013 (UTC)

If I not misunderstood your question, some model of a "classic" can be - The movement of the particles back and forth in time many times. Therefore statistics, Therefore possibilities, Therefore the "reality" stabilizing on part of the particles, so the "universes" are multiple . thanks Water Nosfim — Preceding unsigned comment added by 192.116.142.154 (talk) 14:06, 30 October 2013 (UTC)

I don't think you're going to get a better answer than Water Nosfim's to this one. Maybe you could rephrase the question? -- BenRG (talk) 18:14, 30 October 2013 (UTC)

The real question is how classical physics emerges as an approximation of quantum physics in a certain limit. (Just as relativistic kinematics reduce to Newtonian for low relative speeds.) This is a thorny question. The short answer is decoherence, which explains why we see an adequately well behaved standard reality in which interference effects, superposition, etc. are not obvious. It's not that some systems are fundamentally classical instead of quantum, it's just that classical physics is a good enough description of some things and not others. --Amble (talk) 19:45, 30 October 2013 (UTC)

For that matter, much of the Copenhagen interpretation is just pure nonsense, honestly, having done far more harm than good to the advancement of scientific thought. Ideas of superposition, entanglement, and collapsing wavefunctions continue to spur us on into research of fictitious "quantum computers" and the like...meanwhile we just drift further and further from, well, reality. Go figure. Sebastian Garth (talk) 07:23, 31 October 2013 (UTC)

Superposition, entanglement, and quantum computers are in no way dependent on the Copenhagen interpretation. --Amble (talk) 08:37, 31 October 2013 (UTC)

Let me rephrase that: the vast majority of Copenhagen-like interpretations are pure nonsense. More specifically, they all arise from a misinterpretation of the implications of probability with respect to physics; rather than seeing it as the mere necessity to consider all of the probabilistic "degrees of freedom" inherent in a system, they instead take the analogy too far, as it were, constructing a sort of hocus-pocus holographic multiverse of quantum weirdness in the process. Quantum computers are a direct result of such interpretations and thus nothing more than an interesting thought experiment. Sebastian Garth (talk) 15:53, 31 October 2013 (UTC)

That's quite a tangle of misconceptions. --Amble (talk) 18:12, 31 October 2013 (UTC)

You may be surprised to find that a few others agree with my assessment. But hey - what could they possibly know about all that? Sebastian Garth (talk) 19:49, 31 October 2013 (UTC)

Thanks, but I'll take modern experimental and theoretical work in quantum information over a local hidden variables interpretation that has been shown to be inadequate many decades ago. And I have no idea why you believe that quantum computers depend on any particular interpretation of quantum mechanics. They don't. --Amble (talk) 20:16, 31 October 2013 (UTC)

Bell test experiments is the relevant article, although the experiments are unlikely to convince the OP. Tevildo (talk) 21:45, 31 October 2013 (UTC)

Bell's experiments have their own set of problems and besides that don't in any way invalidate what I have said. You can use quantum equations without having to accept that they are inherently "real" (just as you can use probability in many other fields without having to draw any such conclusions). Sebastian Garth (talk) 22:34, 31 October 2013 (UTC)

They most certainly do. To quote the first line of the article, in fact:

"A quantum computer (also known as a quantum supercomputer) is a computation device that makes direct use of quantum-mechanical phenomena, such as superposition and entanglement, to perform operations on data".

Superposition and entanglement are merely (the Copenhagen-type variety of) interpretations of the possible implications posed by the equations used in quantum mechanics. Furthermore, from the first line from quantum superposition:

"Quantum superposition is a fundamental principle of quantum mechanics that holds that a physical system—such as an electron—exists partly in all its particular theoretically possible states (or, configuration of its properties) simultaneously; but when measured or observed, it gives a result corresponding to only one of the possible configurations (as described in interpretation of quantum mechanics)".

Finally, from the article on quantum entanglement:

"Quantum entanglement is a product of quantum superposition.".

So you see, all of these ideas are indeed connected. It's no wonder people like Stephen Hawking are so much more popular than Einstein in this day and age - science has become a mythological free-for-all, sadly... Sebastian Garth (talk) 21:04, 31 October 2013 (UTC)

To the extent that the theories are predictive and validated by experiment, they are valuable models. Mathematical models describe what we observe. To the extent quantum mechanics lends itself to the description of observation (and the effect observation has on the experiment), is very well documented. I think everyone realizes that a description of a thing is not the thing itself. But if it's sufficiently detailed to predict behavior of the thing, then it's a pretty good model. As far as I can tell, QM's basic premise is the observer is part of the system. Probabilities arise from the uncertainties introduced by the observer. Superposition for example, describes all the observable states for an electron. It's a useful description and model but we can't create an electron from it. We also can't observe a state not part of the superposition description nor can we violate some of the fundamental underpinnings. Until that happens, it's a pretty good model. --DHeyward (talk) 23:33, 31 October 2013 (UTC)

Yes, probability densities and the like are indeed useful and invaluable predictive tools (again, this has much more to do with the "degrees of freedom" present in a system than anything else). What I'm saying is that for whatever reason certain interpretations of QM have assigned an undue measure of "reality" to the equations. For them, probability densities are very real things that actually govern the universe. And because of this, they feel quite justified to jump to all sorts of half-baked conclusions that, frankly, have not produced any truly verified experimental results to speak of and, moreover, are not verifiable to begin with quite simply because they cannot be directly measured! That is, how can we either prove or disprove wavefunction collapse, superposition, entanglement, etc when we can't even even pin down a reasonable method to measure such things? Anyway, my views are obviously not going to be taken seriously as they are in such conflict with present accepted beliefs, so be it. In any case, I'd appreciate it if someone here would quantum teleport me a message whenever they actually get one of those quantum computers up and running. Thanks. Sebastian Garth (talk) 00:32, 1 November 2013 (UTC)

The crux of the problem is are you trying to determine the state of the cat without measuring it? --DHeyward (talk) 07:33, 31 October 2013 (UTC)

Put the cat back in the box and measure the observable O = |dead><alive| + |alive><dead|. Count Iblis (talk) 16:04, 31 October 2013 (UTC)

Division by nothing

I know that division by zero is not mathematical, but what do you get if you divide something with nothing? — Preceding unsigned comment added by 128.214.166.7 (talk) 13:22, 30 October 2013 (UTC)

By this mean insted of 5/0 trying for to do example 5/ — Preceding unsigned comment added by 128.214.166.7 (talk) 13:23, 30 October 2013 (UTC)

According to quantum physics, there is no nothing, so division is well bounded. Alternatively, you can roll up the Complex plane into the Riemann sphere by adding an infinity point, giving a result for every use of the division operator. Hcobb (talk) 13:28, 30 October 2013 (UTC)

Not sure this is a science question more a maths one. But this video has a good explination. Zero and nothing are the same thing.Dja1979 (talk) 13:59, 30 October 2013 (UTC)

• It depends on the system you are operating in. In most programming languages, "5/0" will give you a floating point exception, whereas "5/" will give a syntax error when you try to compile the program. Looie496 (talk) 14:36, 30 October 2013 (UTC)

Looie496's answer is excellent - because at the core, our original question is not well-defined. In English, we use the word "division" to refer to many related mathematical concepts, including the calculation of the multiplicative inverse and the left-multiplication by the adjoint or conjugate. In these cases, we can explicitly define a mathematical result. If you use a programming language to ask the question, you are forced to be very specific; and depending on what you ask, we can provide the result. In English, your words leave enough ambiguity about your intent that we can't answer very specifically.

Speaking of programming - I recently did battle with the innards of a mathematical representation in the C++ Standard Template Library. I was winning the battle, but I realized I had lost the war when I discovered that my predecessor had overloaded arithmetic operations, including /, as unary predicate operators so that he could divide by nothing while iterating over empty sets. I saw red-links, and knew I had crossed over the edge of reason and had reached the limit of human knowledge. Nimur (talk) 15:57, 30 October 2013 (UTC)

http://en.wikipedia.org/wiki/Division_by_zero 217.158.236.14 (talk) 14:56, 30 October 2013 (UTC)

You have lack of information about the denominator, so the outcome fo the division is not known. But what you can say is that the amount of information about the outcome will increase by 2 <Log|x|>, where you have to average over all possible inputs. Count Iblis (talk) 15:53, 30 October 2013 (UTC)

What the OP is calling "nothing" is actually the "empty set". Any computer language worth its salt will have a trap for undefined operations like that. I tried it in Oracle SQL, and 5 over null is... surprise! ...null. ←Baseball Bugs ^{What's up, Doc?} carrots→ 16:38, 30 October 2013 (UTC)

The question is not answerable. The OP admits that division by zero is not defined, but then asks what happens when you do it. It's not that it is forbidden, it's simply not defined. Some calculators/computers will raise some type of error that you could catch, like any other logical error. However, you can still approach it as much as you want OsmanRF34 (talk) 19:46, 30 October 2013 (UTC)

Division by zero is well-defined in some contexts — see our article on division by zero for a discussion, or go straight to Riemann sphere for the most important example. But what "division by nothing" is supposed to mean, I'm not sure. Zero is a thing, and the empty set is also a thing, so neither of them is "nothing". Maybe it's more of a language question? If you divide five by nothing, literally speaking, you just didn't do anything, so there is no result of this action, because there wasn't any action. --Trovatore (talk) 19:56, 30 October 2013 (UTC)

In that sense, it's no different from dividing 5 by an apple. That doesn't work either. Most computers and calculators nowadays will pre-empt division by 0 and flag it as an error. But I recall a few decades ago, a mechanical calculator. If you divided X by Y, it would compute it, apparently by figuring out what Z x Y would equate to X. All well and good, until you divided 1 by 0. Then it would start calculating the Z value mechanically. Basically it would just start counting up. The machine had maybe 15 or 20 digits, and although it seemed to be going pretty fast, each power of 10 would naturally take 10 times as long to switch to the next high-order digit as did the next lower-order digit. I figured it would have to have run for days or maybe weeks before it would hit the last digit. So I stopped that experiment, and never did learn what would have happened once it reached all 9's. ←Baseball Bugs ^{What's up, Doc?} carrots→ 22:43, 30 October 2013 (UTC)

Well, no, it is different. Dividing 5 by an apple doesn't make sense, but it could make sense if you specified what new meaning of "divide" you have in mind. Similarly with dividing by zero (though there well-established meanings already exist) or dividing by the empty set (where they don't, as far as I know) — those are both things. But the word "nothing" does not refer to a thing; it has a different linguistic function altogether. --Trovatore (talk) 22:47, 30 October 2013 (UTC)

I think the short, complex answer is infinity. Division by zero is undefined in the real number system, but in Calculus and other higher math, we can argue it is conceptually equal to infinity. Or we might say, "approaching infinity" since it cannot be reached. In other words, how many times does 0 go into some finite number? Infinite number of times. - 76.17.125.137 (talk) 01:59, 31 October 2013 (UTC)

If ∞ = 1/0, then 0 = 1/∞. Count Iblis (talk) 02:06, 31 October 2013 (UTC)

• Let me just say Hcobb's answer is no, good. Concepts are not physical objects, no more than motherhood has a molecular weight. The statement is a category error. μηδείς (talk) 02:31, 31 October 2013 (UTC)

Division by nothing produces the IP address 128.214.166.7, if you want it to. The word "nothing" in mathematics would most commonly mean "0", but not necessarily, and even what "0" means depends on the context. More importantly, the expression "5/" by itself or more generally "x/" by itself doesn't have any well-established mathematical meaning. So by talking about "x/" you're creating new mathematics (which is a perfectly legitimate thing to do), and you're free to define what you mean by "x/" without it even causing confusion due to your meaning being different from some usual meaning of that expression. In particular, you're free to define a function called "division by nothing", which is denoted by the symbol "/" using postfix notation , such that $/\colon \mathbb {R} \rightarrow \mathbb {IP}$, where $\mathbb {R}$ as usual means the set of reals and $\mathbb {IP}$ means the set of IP addresses, and for all x, x/ = 128.214.166.7 . I'm not a mathematician, so a professional mathematician might express the definition of the function a little better than I did, but my point is that you're free to define what "division by nothing" means however you want to. Red Act (talk) 03:10, 31 October 2013 (UTC)

"The word nothing in mathematics would most commonly mean 0"? No. Where do you get that? 0 is very definitely something; it is absolutely not nothing. --Trovatore (talk) 03:40, 31 October 2013 (UTC)

Well, the word "nothing" is certainly sometimes used in mathematical contexts to mean zero; here is the title of an article in Scientific American, as well as the title of book written by a mathematician, that uses "nothing" to mean "zero".[1] The word is also sometimes used to mean the empty set. The word is also sometimes used to mean neither of those things. The whole point of my sentence is that the meaning of the word "nothing" depends on the context. There is no established context I'm aware of in which "division by nothing" is defined, so creating a new context in which it is defined doesn't conflict with any existing definition. Red Act (talk) 04:51, 31 October 2013 (UTC)

The subtitle in your link is just a witticism, not a genuine use of "nothing" to mean "zero".

The thing is that nothing is used as a noun phrase, but it is not interpreted as having a referent; when it appears in a sentence, it's normally to be interpreted as the universal quantification of a negative statement. "I saw nothing" doesn't mean "I saw x, which is nothing"; rather, it means "for every x, I did not see x". So if you divide by zero, you may or may not get a definite answer, depending on the context. But if you divide by nothing, you just don't divide by anything. --Trovatore (talk) 08:26, 31 October 2013 (UTC)

Perhaps the article subtitle can be dismissed as a witticism, but the book title "The Nothing that Is: A Natural History of Zero" mentioned in the article isn't just using a witticism as far as I can tell. But I think it's all moot, because I think the term "nothing" is only used in very informal mathematical contexts, and mainstream math doesn't have a rigorous concept called "nothing". At least, Nothing#Mathematics doesn't list any possible meaning other than zero or the empty set, and I think in formal settings mathematicians would use one of those two terms instead of "nothing", when they want to talk about zero or the empty set. If you're aware of a reliable source containing a rigorous mathematical treatment of "nothing" as being defined as something other than zero or the empty set, please give a citation, so that the Nothing#Mathematics section can be updated. Red Act (talk) 09:51, 31 October 2013 (UTC)

Of course there is no "rigorous mathematical treatment of 'nothing'". That's the whole point of what I was saying — the word "nothing" looks syntactically like something that should have a referent (because it constitutes a noun phrase), but in the actual semantics of the English language, it serves a different function and does not have a referent. So there can't be a mathematical (or, indeed, any) treatment of it, because there is no "it". --Trovatore (talk) 20:26, 31 October 2013 (UTC)

I think I see your point, and to a large extent I agree with what I think your point is. The English sentence "I saw nothing" means something like "the number of objects that I saw was zero", or "the set of objects that I saw was empty", not "I saw the number zero" or "I saw the empty set". To be consistent with that usage of "nothing", the phrase "division by nothing" means something like "the number of numbers being divided by is zero", or "the set of numbers being divided by is empty", not "division by zero" or "division by the empty set". That's consistent with my treatment of the "division by nothing" function above. The function in question is a function that has one argument that's labeled as being a "numerator", and zero arguments that are labeled as being a "denominator", not a function which has one "numerator" argument and one "denominator" argument whose value is zero, or whose value is the empty set.Red Act (talk) 22:09, 31 October 2013 (UTC)

I think you are right that the above usage of "nothing" is the most common way the word is intended to be interpreted in English. However, the word is also used in ways that are inconsistent with that usage. For example, when Billy Preston sings "nothin' from nothin' leaves nothin'", he means something like "0-0=0" or perhaps "Ø∖Ø=Ø". I.e., sometimes in English, "nothing" really does mean zero itself, or the empty set itself. Natural languages are sloppy that way. In this case, the OP made it clear that his usage of "nothing" wasn't to be taken to mean "zero", so I followed the OP's specification, and didn't interpret it that way. Red Act (talk) 00:48, 1 November 2013 (UTC)

Or even better, Kris Kristofferson singing nothin' ain't worth nothin' — but it's free. (This is why I can't abide Janis's version — she ruins the bitter pathos of that line.) Sure. But this is not a mathematical usage. --Trovatore (talk) 03:39, 1 November 2013 (UTC)

It simply doesn't make sense to not have a denominator, it's a non-function. It is possible to have the denominator as undefined, but must still be something. Plasmic Physics (talk) 03:19, 31 October 2013 (UTC)

The "division by nothing" function I defined has a domain of $\mathbb {R}$, not $\mathbb {R} \times \mathbb {R}$. I.e., the "division by nothing" function doesn't have a denominator, by definition. Red Act (talk) 03:55, 31 October 2013 (UTC)

You've got it wrong, the domain is $\mathbb {R} \times$, not $\mathbb {R}$. Plasmic Physics (talk) 04:07, 31 October 2013 (UTC)

ERROR: Parsing failure (EXPECTED OPERAND). Plasmic Physics (talk) 06:16, 31 October 2013 (UTC)

It doesn't make sense for the expression "x/" to not have a denominator, if the symbol "/" in that expression is referring to the standard division function whose domain is $\mathbb {R} \times \mathbb {R}$. But that doesn't mean that somebody can't define a new function that uses the same symbol, whose domain is just $\mathbb {R}$. And if the domain is just $\mathbb {R}$, and the symbol for the new function is defined as being used after the function's argument (similar to x! for the factorial function), then the expression "x/", where $x\in \mathbb {R}$, is perfectly well defined for that new function. Red Act (talk) 06:21, 31 October 2013 (UTC)

Well, that is bit a useless answer. The OP has already defined / as division. You're basically saying, that hypothetically, if you had a million dollars, then you would have a million dollars. It is a self-evident statement, which has no real bearing on the OP's question. Plasmic Physics (talk) 07:24, 31 October 2013 (UTC)

Baseball, the empty set is no equivalent to nothing. Nothing has no mathematical definition, or any definition for that matter, the empty set is by no means equivalent to nothing - the empty set is a useful mathematical tool.

The OP most certainly has not defined "/" as being the normal division function. The normal division function is defined as a function whose domain is $\mathbb {R} \times \mathbb {R}$. But the OP has explicitly specified that the "division" function being referred to does not involve a denominator of zero. The "division" function being referred to also doesn't have a denominator that's a non-zero real, either; the expression "5/" only shows the function as having one argument, i.e., it doesn't have any kind of denominator (i.e. second argument) at all. It's possible to define a new function that meets the OP's criteria, but none of the standard functions called "division" do. Red Act (talk) 09:23, 31 October 2013 (UTC)

Where has the OP given this liberty to redefine division? Plasmic Physics (talk) 21:27, 31 October 2013 (UTC)

My first post above, at 03:10 31 October 2013, points out to the OP that if he wants to, he can take the liberty of choosing to define "division by nothing" in such a way that his question makes sense, without conflicting with existing mathematics. The function I supplied was merely an example of a function that would work for that purpose. The question is not consistent with the normal division function whose domain is $\mathbb {R} \times \mathbb {R}$. If an alternative function is not considered, then the question has no more meaning than "what is the square root of a unicorn?" Red Act (talk) 23:17, 31 October 2013 (UTC)

Then it changes nothing of what I've said. The OP has not made any indication that division has been redefined for this situation, and thus it still makes no sense to have a division with no denominator; and you're explanation is still self-evident. Plasmic Physics (talk) 03:55, 1 November 2013 (UTC)

I'd change nothing of what I've said, either. The question makes no sense with the standard division function, but if the OP should so choose, the OP is still perfectly free to define "division by nothing" in such a way that what he's written makes sense, and doesn't conflict with any existing definitions in mathematics (that I know of). And I would not at all take it for granted that it's self-evident to the OP (I don't care about you) that it's possible to do that. Red Act (talk) 04:30, 1 November 2013 (UTC)

this is more of a mathematics function. Often the answer depends not on the fixed number division, but rather whether the numerator converges faster or slower to 0 than the denominator. --DHeyward (talk) 07:18, 31 October 2013 (UTC)

We customarily use the capital Greek letter Pi ∏ to denote the product of a sequence (see Multiplication#Capital Pi notation). If we wished, we could extend and simplify the notation, defining

$x\cdot \{a_{1},a_{2},\dots a_{n}\}=x\cdot a_{1}\cdot a_{2}\cdot \dots \cdot a_{n}.$

Then $5\cdot \{2,3,4\}=5\cdot 2\cdot 3\cdot 4=120.$

The empty product is 1 (the multiplicative identity element), so $x\cdot \{\}=x$. If we chose to allow the convention of writing $x\cdot$ for $x\cdot \{\}$, then we would have $x\cdot =x$.

Likewise, we could define

$x/\{a_{1},a_{2},\dots a_{n}\}=x/(a_{1}\cdot a_{2}\cdot \dots \cdot a_{n}),$ where $a_{i}\neq 0.$

Then $120/\{2,3,4\}=120/(2\cdot 3\cdot 4)=5.$ Since the empty product is 1, $x/\{\}=x$. If we choose the similar convention of $x/$ for $x/\{\}$, then we would have $x/=x$. That is, dividing any number by nothing (in the sense of not dividing it by anything) yields that number unchanged. So in this context, $5/=5.$ -- ToE 03:45, 1 November 2013 (UTC)

Again wrong, your assumption that 'nothing' is logically equivalent to the empty set is false. Plasmic Physics (talk) 04:31, 1 November 2013 (UTC)

"Nothing" could refer to the contents of the empty set. ←Baseball Bugs ^{What's up, Doc?} carrots→ 06:37, 1 November 2013 (UTC)

OK, so you're saying that the OP's supposition is wrong? Nothing is logically equivalent to not _____, such as not 2, not pi, not i, not set, not pink unicorn. Plasmic Physics (talk) 10:49, 1 November 2013 (UTC)

Drinking Ethanol, does it makes you live longer?

I have seem to be found very contradictory claims on alcohol (as a popular beverage) where it says that drinking it will make you live longer, or have healthier life, other claims that drinking alcohol, is bad for health, and should be avoided at all costs.

There doesn't seem to be a consensus about it, so is it really true that drinking alcohol makes you live longer, or it's just a myth? Thank you. 190.60.93.218 (talk) 17:29, 30 October 2013 (UTC)

You may be interested in our articles Long-term effects of alcohol and Health effects of wine. It is true that some studies have found that regular moderate consumers of alcohol (or sometimes specifically wine) seem to live longer, or gain other health benefits. It should also be obvious from the first article that excessive alcohol consumption over a long period of time seems to be extremely bad for you. So the conclusion is less "avoid at all costs" and more "everything in moderation". But you have to keep in mind that most of these long-term studies are looking at correlation only, and correlation does not imply causation. Someguy1221 (talk) 17:57, 30 October 2013 (UTC)

Note that the studies on wine of which I am aware do not cite ethanol as the beneficial substance, but rather other compounds found in wine (see the article cited above for more information) Equisetum (talk | contributions) 23:34, 30 October 2013 (UTC)

Of course excessive consumption in bad for you, that's pretty much the definition of excessive consumption - "the amount which is bad for you" MChesterMC (talk) 09:40, 31 October 2013 (UTC)

And the big difference is what you would be drinking, otherwise. If soda, especially soda with artificial sweeteners, then a bit of alcohol is a favorable alternative. StuRat (talk) 21:55, 30 October 2013 (UTC)

Yeah, if instead of ethanol you decide to drink methanol you'll live a much shorter life. OsmanRF34 (talk) 22:02, 30 October 2013 (UTC)

"especially soda with artificial sweeteners"? Excuse me? citation please... Diet_soda#Health_concerns, mayo clinic "Artificial sweeteners and other sugar substitutes", national cancer institute - Artificial Sweeteners fact sheet Vespine (talk) 23:40, 30 October 2013 (UTC)

Well, you had a citation right in our Wikpedia article: [2]. That concluded that diet soda and regular soda are equally unhealthy. However, they made the assumption that equal quantities were consumed, ignoring the fact that many will drink more diet soda, since they aren't as worried about the calories. When you factor that in, diet sodas are worse. StuRat (talk) 01:38, 31 October 2013 (UTC)

A you say? Oh and speaking of needed citations, where's the one for the claim alcohol is preferable to soft drinks? The link you provided says nothing useful to either query. In fact it doesn't even say what you claimed it said. (It doesn't say they are equally unhealthy, it only says people who consumed diet drinks also had similar health risks and goes on to note the evidence is quite contentious and particularly mentions there are a bunch of confounding factors like people consuming diet drinks because they already had health problems, as μηδείς mentions below. I would also note since the study appears to be an observational study, it seems unlikely any 'assumptions' were made about equal consumption.)

Nil Einne (talk) 04:43, 31 October 2013 (UTC)

Try this one then: [3]. StuRat (talk) 05:01, 31 October 2013 (UTC)

Actually, an antidote to methanol poisoning is ethanol. They compete for the metabolic pathways so it becomes a rate equation as to which wins. The liver clears both but too high of the intermediate metabolites can cause blindness and death for methanol but if you can reduce the rate of methanol metabolism and spread it out through the ingestion of ethanol, you may live and also see the benefits of a beer. The liver prefers metabolizing ethanol over methanol and keeps the intermediate toxins at bay. YMMV and don't try at home. --DHeyward (talk) 08:00, 31 October 2013 (UTC)

I imagine if they catch they methanol poisoning early enough, they would induce vomiting or pump the stomach. StuRat (talk) 17:03, 31 October 2013 (UTC)

• Can you give a mechanism as to why diet soda is worse? Wouldn't it simply make sent that people who drink diet soda do so in a significant part because they are already heavy or diabetic, hence a less healthy cohort? μηδείς (talk) 02:28, 31 October 2013 (UTC)

• I believe the suspected mechanism is as follows: Your body starts to produce insulin as soon as sugar is consumed, so it will be in place as it is digested, to prevent a blood sugar spike. However, artificial sugars fool your body into thinking you consumed sugar, so the insulin is still produced, causing your blood sugar to crash. Your body then responds to this by increasing your cravings for sugar. You then eat some real sugar. You thus suffer all the consequences of consuming sugar, plus the consequences of the blood sugar crash beforehand. StuRat (talk) 04:59, 31 October 2013 (UTC)

I am highly skeptical of this explanation. There are some compounds that can activate GLP-1, but they're not in soda. (Ah, here's a ref. [4]) My own crank idea (which has no more proof than this) is that people with high blood sugar (even if not meeting the formal definition of diabetes) will find consumption of pure sugar less enjoyable or more distressing in some way, whether it is due to blood sugar spikes, the insulin response, the higher starting level of sugar at the taste receptor, etc.) In any case we should recognize it is an open mystery, despite professional attention. Wnt (talk) 16:58, 1 November 2013 (UTC)

Note that biological responses in anticipation of a future event are widespread. In digestion, we have the salivation response to food smells. There are also sexual preparations for intercourse in response to sexual stimuli, and the adrenaline release in response to perceived threats. StuRat (talk) 18:37, 1 November 2013 (UTC)

The difficulty is that the studies that show that moderate amounts of alcohol are beneficial don't present an underlying mechanism. It's perfectly possible that, for example, people who drink "socially" are getting the benefit from being social - not from the actual alcohol...or that people who are naturally more healthy are happier than people who aren't, and are therefore more likely to drink moderately. It's very difficult to disentangle cause from effect here. SteveBaker (talk) 05:59, 31 October 2013 (UTC)

I know of one abstainer who admits that the only reason he is alive is because he used to drink enormous amounts of booze, it was that or top himself. So he reckons that despite the damage it did him, at least he is alive, 30 years later. (cite: Ross Fitzgerald in The Australian) Greglocock (talk) 23:35, 31 October 2013 (UTC)

Why are we even discussing this? It clearly falls under WP:NOMEDICAL.--ukexpat (talk) 16:12, 1 November 2013 (UTC)

Because it doesn't. Rmhermen (talk) 16:58, 1 November 2013 (UTC)

Correct. Dietary advice is not medical advice. If it was, everyone who writes a diet book would be arrested for practicing medicine without a license. StuRat (talk) 17:05, 1 November 2013 (UTC)

When I come to power, many/most of them will be arrested. It's curious that a GP will routinely refer a patient to an ophthalmologist, a diabetic educator, a physiotherapist, a dietician, a neurologist, an otorhinolaryngologist, a psychiatrist, an oncologist, or various other types of specialist. We can't offer the kinds of advice that any of these people provide, because that would be contravening our No Medical Advice rule - except for the dieticians. Some people go through their entire life without ever needing any of these specialists, but the one thing that every human does every day, eat, is fair game for any and all commentators, including us, no matter how well or poorly qualified they may be to offer such advice. The only thing that threatens to outstrip the ever-increasing obesity and diabetes levels in the West, is the ever-increasing number of supposed solutions (not to mention the ever-increasing number of TV cooking shows which are usually excellent descriptions of what NOT to eat). How any one person can claim to have "the answer" when so many others also have "the answer" is totally beyond me. No wonder virtually all of this advice falls on deaf ears when it comes to their target audiences. How could they possibly believe one over another? It's all just way too horrendously confusing and contradictory for anyone to have confidence in anything anyone says about diet, and that includes so-called scientific studies. Sorry, this turned into a rant, which was not my plan. -- Jack of Oz ^{[pleasantries]} 19:29, 1 November 2013 (UTC)

Is it possible to start with "When I come to power..." without ending up in a rant ? That's like starting with "With all due respect..." without ending up insulting someone. :-) StuRat (talk) 00:45, 2 November 2013 (UTC)

Which is why I favor the phrase "with all undue respect..." FYI, when I come to power, on the first day I will immediately declare a world-wide holiday. On the second day, I will delegate all activities to others. Then I will go on holiday and leave no forwarding address. ←Baseball Bugs ^{What's up, Doc?} carrots→ 23:18, 2 November 2013 (UTC)

"With all due respect..." doesn't actually say that any respect is due. Indeed, "With all due respect, you're a jerk" implies that no respect is due. StuRat (talk) 17:12, 3 November 2013 (UTC)

Jack and Bugs, please drop me a note when the revolution starts. ;-) 220 of ^Borg 13:02, 3 November 2013 (UTC)

Practically visible universe stops growing

When will that happen? The visible universe will grow forever (and never exceed 2.36 times the space) but all but our cluster will become too redshifted to detect. What's the real ratio then? — Preceding unsigned comment added by 12.196.0.56 (talk) 20:31, 30 October 2013 (UTC)

Eventually, there will likely be nothing left to detect at all; see Heat death of the universe. For a timeline of what will happen before then, see Future of an expanding universe. And although there is a growing consensus that the universe will continue to expand forever, there are dissenting opinions; see Ultimate fate of the universe. Red Act (talk) 00:55, 31 October 2013 (UTC)

Long after you have died. You will either obtain the answer through divine intervention or simply cease to care. :) --DHeyward (talk) 08:41, 31 October 2013 (UTC)

And as you drift off into eternal oblivion, the last thing you hear will be a voice whispering, "Jackie!" ←Baseball Bugs ^{What's up, Doc?} carrots→ 06:33, 1 November 2013 (UTC)

XENON-100 project regarding dark matter detection?

Is there any short description of the XENON-100 project? or if someone cares to convert the PhD publications into an wikipedia article.. I'm particulary interested in how they physically accomplish this. Electron9 (talk) 22:00, 30 October 2013 (UTC)

You have already found the short description of the project. "XENON is a next-generation Dark Matter Direct Detection experiment, which will use liquid xenon as a sensitive detector medium to search for WIMPs (Weakly Interacting Massive Particles)." If you are not familiar with gas scintillation, the Wikipedia article may help. Nimur (talk) 22:53, 30 October 2013 (UTC)

Makes me wonder if there's other methods to detect dark matter other than scintillation or WIMP. Perhaps like interaction with a field rather than with a mass.. Electron9 (talk) 23:02, 30 October 2013 (UTC)

There are a variety of approaches to direct detection. (Note that WIMPs are a type of dark matter candidate, not a detection method.) Other channels are used to search for WIMPs: XENON-100 uses ionization and scintillation, and other projects also use phonons or heat. COUPP uses bubble nucleation. The Axion Dark Matter Experiment looks for a different candidate, axions, by searching for their interaction with the electromagnetic field in a cavity. --Amble (talk) 00:43, 31 October 2013 (UTC)

We do already have an article for the Xenon family of experiments that includes Xenon100: XENON Dark Matter Search Experiment. Funny that you ask about Xenon-100 on the day that LUX, a very similar but competing experiment, released its first results. --Amble (talk) 06:23, 31 October 2013 (UTC)