Wikipedia:Reference Desk archive 2

Wikipedia:Reference Desk -- Archive

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I have a question about NP-complete problems. (There are a couple of small articles on this, but their names seem to be rapidly mobile lately, try searching.) OK, so 3-SAT is NP-complete. That's where you have to satisfy clauses that are the OR of three different variables, each possibly negated. How about if the clauses are the XOR of three variables. How about if the clauses are Majority function of three variables, each possibly negated. (That is 2 or 3 out of 3 must be true). How about if exactly one must be true, etc. added August 20. This problem is left as an exercise by the reader :) Seriously, most of them are probably NP-complete, some aren't. To prove a particular problem as NP-complete, you need to prove it's in NP (which should be trivial as they are restricted instances of SAT and thus in NP), and then transform another NP-complete problem into that problem (so, for instance, show that you can transform any instance of OR 3-SAT into XOR 3-SAT). --Robert Merkel

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What are the largest moons in the solar system? A few are larger than Mercury, no? (Posted Sept. 4.) -- See moon for a list of those bigger than Pluto.

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What exactly is going on on the floor of the New York Stock Exchange? Stock exchange and New York Stock Exchange do not yet contain an answer. (Posted Sept. 17.)

Today, a lot of moaning, gnashing of teeth, and beating of breasts.

Doesn't that happen every day?

I've added a little more of a description of the trading floor to New York Stock Exchange. It'd be nice if someone could clarify some other things, though, e.g: 1) What powers the NYSE employee has over the stock she's managing, and 2) How the traders actually on the NYSE floor connect back to people that invest without physically going to NYSE. --Ryguasu 08:56 Dec 26, 2002 (UTC)

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I would like to know what kind of work the prisonsers in Auschwitz II Birkenau (those that were not gassed on arrival) had to do on a daily basis. AxelBoldt 11:54 Sep 2, 2002 (PDT)

Axel, I can recommend that you read Primo Levi's first hand accounts in The Truce (Published in the US as Survival in Auschwitz). user:sjc

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20020912 I would like the history behind the Canadian expression "Canuck". I'm also interesed in the etymology behind the word itself, Cheers, Lars.

The ultimate origin of the word is disputed, but some of the more likely possibilities are explained on this web page: http://www.comnet.ca/~dmarchak/candef.htm. Having read several web pages on the subject, I chose this one as being the most convincing. --Heron

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Here's a question that any encyclopedia worth its salt must answer: why do dogs eat other dogs' poop? This has been bothering me for a long time. As an exercise to the reader (writer!): you must find an appropriate place to answer this question in the encyclopedia. Cuisine? Most people don't consider dog poop cuisine, though some dogs might. Dog? Too general. Dog cuisine[?]? Too easily confused with certain East Asian dishes. Perhaps canine ethology[?], but I don't even know if that is regarded as a field. So! Creativity and research are needed! (Posted Jan. 11, 2001.) Because dogs are morons. Next question? (Indeed! :-) But what explains this moronic behavior?) The real answer is apparently "several possible reasons, including copying their mother, copying their owner, or just because they like the taste". Full study of the issue at Coprophagia in the Canine (http://www.vetmed.wsu.edu/pets/study.htm) Wasn't Coprophagia an album by The Who? I found the study, now someone else can write the damned article! :) (Grand, so now we know where to put the article: coprophagia!) Because some dog owners like to let their dogs lick their face!

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What is potential difference? All I remember from school is something about electricity being compared to the height of rivers & speed of water flow, which (as I recall) left everyone more confused than ever. -- Tarquin 01:36 Aug 27, 2002 (PDT)

Potential difference is a pedantic term for what normal people call a voltage. Since a voltage can only be measured across two points, the statement that "the voltage of point X is Y volts" is meaningless unless you know what point the measurement was relative to. As an engineer I was taught that it is better to say "the potential difference between point X and point Z is Y volts".

In normal parlance, people say things like "the mains voltage in the UK is (nominally) 240 volts", which everybody understands to mean that, if you put an ac voltmeter across the live and neutral wires, the meter will read (nominally) 240 volts. The context makes it clear that points X and Z are the live and neutral wires.

Another reason to distinguish "potential difference" from "voltage" is that the latter term implies that we are using the SI unit of volts. If somebody one day replaced the SI system with another, then the volt would become obsolete, and "potential difference" would be measured in fnuts or whatever.

A similar contrast exists between "current" and "amperage". Physicists and pedants prefer the term "current" because it's general, but engineers and real people sometimes talk about "amperage" because amperes are what appear on most current-measuring instruments. If amperes were one day replaced by gzorts then ammeters would have to be renamed gzortmeters, but the word "current" could still be used.

If this isn't clear then please complain, and I'll have another go.

-- user:Heron

I agree, with you, Heron. I prefer the Sino-Japanese term for voltage, which, I believe literally means "electricity pressure".

--Juuitchan

Thank you :-) I'd better rephrase the question: why is voltage / PD or fnuttage ;-) measured across two points? What does voltage actually measure, in real terms?

It's the energy per electron. If you have a battery which gives you a higher voltage, then every electron moving between the poles of the battery will be able to do more work (like giving you a brighter lamp). If you multiply the number of electrons per second that flow (that is the current = amperage) with the voltage (= energy per electron), you get the energy per second, which we call power or wattage.

If you think of electric circuits as flowing water, then voltage is akin to the pressure difference between two points. In the case of a water circuit, you could measure it by connecting the two points with a pipe which has an elastic membrane in its middle, so that no water can actually flow through. The extend to which the membrane is stretched by the water is a measure for the "voltage". AxelBoldt 11:53 Sep 2, 2002 (PDT)

Thank you Axel. I didn't know the amount of work per electron could change. -- Tarquin

Another electricity question for the voltage page: when a battery runs down, which measurable quantities decrease? Does a household battery which is labelled, say 5 volts actually produce less once it has been used -- Tarquin

A battery can be modelled as a perfect voltage source (i.e. one that can supply infinite current) in series with a resistor. The voltage source depends on the chemistry of the battery, not on whether it is empty or full. When a battery runs down, the value of the fictional resistor, called the internal resistance, increases (ask a chemist why: it's something to do with electrolysis). When the battery is connected to a load (e.g. a light bulb), which has its own resistance, the resulting voltage across the load depends on the ratio of the battery's internal resistance to the resistance of the load. When the battery is fresh, its internal resistance is low, so the voltage across the load is almost equal to that of the battery's internal voltage source. As the battery runs down and its internal resistance increases, the proportion of its internal voltage that gets through the internal resistance to appear at the load gets smaller, so the battery's ability to deliver power to the load decreases. Eventually, the battery's resistance gets higher than even the very high resistance of a voltmeter, so the meter reads a voltage lower than the battery's internal voltage.

To answer your question, the directly measurable quantity that decreases is the voltage across a given load. If you connect a fixed load, say a 100 ohm resistor, across a battery, then you can calculate, using ratios, the internal resistance of the battery. You could then compare this with the internal resistance of a fresh battery. Measuring the voltage of a battery with no load (called its open-circuit voltage) tells you very little about its state of charge. If your household battery is labelled 5V, then when new it should produce 5V whether on-load or open-circuit. As it runs down, its on-load voltage will decrease, but its open-circuit voltage will stay at 5V until the battery is completely knackered. At this point the voltage will appear to drop suddenly, because the battery is no longer able to drive the tiny current that your voltmeter needs to make its measurement.

By the way, wouldn't this be more appropriate to the "battery" article than the "voltage" article?

--Heron

Probably better on battery, yes. Thank you. -- Tarquin