Why didn't Newton just propose the 2nd Law and leave it at that?

Question: Why didn't Newton just propose the 2nd Law ($F=\dot{p}$) and leave it at that? The 2nd Law implicitly contains the first, doesn't it? If so, it seems he wasn't following his own Rule #1 of Book 3 of his Principia: "We are to admit no more causes natural things than such as are both true and sufficient to explain their appearances." There are intro textbooks (e.g., this one) that study momentum first and then force $F=\dot{p}$ based on momentum. Cf. also this SE post and comments.
Comment: It doesn't contain the third.
Comment: @Geremia: If you want Ron to read your comment you have to write "at username" in your post. Also, I don't think it's good to edit a false assumption out of the question after answers have been given - the people who will come here will be confused about the answers.
Answer: Some of the problems regarding the first law are already pointed out and discussed in the question you linked to, so I'm not entirely sure where that part of your question comes from.
I understand theoretical physics as the activity of coming up with mathematical models to give a structure to the behaviour of quantities, which the consensus agrees to be part of reality. One does this to thereby "understand" reality and to be able to calculate predictions (and also to make money and/or have some fun). From that perspective it's very possible to argue that the first law is redundant. The argument is that you have to declare an explicit form for the force for every model anyway, e.g. $\boldsymbol{F}_{ab}={q_1q_2\over4\pi\varepsilon_0}{\boldsymbol{\hat{e}_{a}}\over r^2}$, and at that point the first law truly becomes just a special case. In its history, there are other ways to formulate it or read new meaning into a first law but from my perspective they don't help much in doing physics in the sense above.
The third axiom is not already captured by the second, because at the very least, if you really only take space, time, at least two point particles and Newton's equations of motion into account, then nothing would hold you from investigating a mathematical structure with $\boldsymbol{F}_{ab}\ne -\boldsymbol{F}_{ba}$. This is then not Newtonian mechanics. Moreover, having that relation guaranteed also makes it possible to conclude general results about the theory for all the systems you might consider, e.g. conservation laws.
Comment: However the third and second law could be condensed into an Only Law: $m\ddot{q} = -\nabla V(q).$
Comment: @user2617: No it can't. You need that V is equal between different objects, and only proportional to  |q_1-q_2|. This is Newton's _model_ of the world, but it contains more information than the laws.
Comment: Fair enough, although you wouldn't need to postulate the third law as a separate "law"; it would be a consequence of the symmetries of the potentials you plug in.
Comment: @user2617: If you want to answer Ron, add *at symbol + username*, otherwise he won't get a message. Also, the point is that choosing a force that can be represented as a gradient field of a scalar function $V(q)$ is a loss of generality. E.g. does the Lorentz force or friction always look like that?
Comment: "The third axiom is not already captured by the second..." Newton himself argues in the Principia that the third law is not completely logically independent of the others. See the scholium after the statement of the laws, at "In attractions, I briefly demonstrate..."
Answer: Newton wanted to sound like Aristotle. Aristotle gives physical laws in two parts--- there are the "natural tendencies" of objects, so that Earth wants to be at the center of the universe, fire wants to be on the sun, air wants to be in the middle, and water wants to be down, but above the Earth and below the air.
In order to make this happen, things go in straight lines at constant velocity. So Earth falls down, water falls down, air goes nowhere, and fire goes up. This is to make the natural tendency work.
But then there are external forces that make things deviate from their natural state. All of this is ridiculous nonsense, but this is what people called "physics" in Newton's time, and Newton had to deal.
When he is writing, he formulates the laws of motion to persuade the idiots, since he knows they won't read past page 3. So he says right up front:

Hey, bozos, there is a new notion of "natural state". The "natural state" of all things is to move with a constant motion, no matter what it is. Sorry, I mean "all objects remain in motion forever unless disturbed".
Hey, douchebags, the deviations from the natural state is by forces, which give you the time rate of change of the momentum. Sorry, I mean, "the impressed force is the magnitude of the deviation from the natural state".
Oh yeah, dipshits,  look at this amazing new thing: the forces are equal and opposite! So that in any system, as much momentum leaves one body as enters another, and this is a universal law! Ahem, I mean, "every action has an equal and opposite reaction."

So now he has stated things Aristotle style (in Latin no less), and redefines the notion of "natural state" and "deviation from the natural state" so that first and foremost, it is correct, unlike Aristotle's bullcrap, and secondly, so that it is philosophically as compelling as Aristotle idiocies, if not more so.
Remember that Aristotle's physics had things that people considered laws of nature, like

Nature abhors a vacuum: if you try to make empty space, things speed up to infinity to fill it.
Nature doesn't make jumps: everything is continuous. No atoms.
Nature proceeds in regularity: Everything moves in lines and circles

All this stuff is complete laughable nonsense, but philosophers thought it was deep. The "nature abhors a vacuum" meant that if you have a vacant position in the leadership, people clamor to fill it. Nature doesn't make jumps means you don't screw with tradition. And nature proceeds in regularity means you execute your radicals. Aristotle didn't care much about physics. He just wanted to justify the stupid politics of his time.
Anyway, Newton gives you new laws that have just as much political resonance:

Everything keeps moving of its own accord: so nature keeps changing spontaneously.
A force will change the velocity, not produce the velocity. This is resonant with the idea of "shifting the discourse slowly by political pressure".
Nothing acts without being acted upon: there are no things that can do something without changing in the process of doing it.

These philosophical points, as trite and stupid as they are, are what gave Newton's proclamations weight with the philosophers. In this way, Newton beats Aristotle, and Newtonian mechanics (aside from being correct) is a suitable replacement for the Aristotelian garbage.
The philosophical nonsense is so dated, it is hard to take it seriously. Aside from the maxim "nothing acts without being acted upon" (which is a general law of universal validity, useful for other arguments in physics), the rest is just an embarassing demonstration that Newton was a politician as well as a physicist.
Today, we can dispense with the politics, and say "Newton's laws are the statement that momentum is conserved, and angular momentum too, if you assume that action at a distance between points occurs along the line of separation of the particles". Note that Newton didn't state "the world is made of particles that attract and repel along their lines of separation" (even though he believed this), he confined himself to macroscopic laws he was sure could be justified empirically without making hypotheses regarding microscopic constituents. In this regard, he was a true scientist. As regards the three laws, remember they are the content of the first 3 pages. Read the rest of the book, that's where all the interesting stuff is.
Comment: -1. [citation needed] [POV check] Is it quite evident that Newton's personal foundational conception of physics put the convervation of momentum first, that he did not concieve of matter having a "natural state" which exhibited deviations, and that his formulation was perhaps "philosophically conservative" precisely in order to be digestible by the establishment? Even if these things are so, perhaps you might indicate what tell-tale signs there are that this is so, and do less creative anachronistic interpolation of Newton's attitudes and vernacular. This answer simply isn't very constructive.
Comment: It's all POV, of course. What isn't POV is that Newton had a model of particles pushing and pulling along their lines of separation, and asymptotically attracting--- this is because otherwise angular momentum conservation in the Newtonian model is mysterious, and he clearly believes it from his argument for angular momentum. This is not the content of his laws, however. He states these to make it clear that things move forever if they are left undisturbed, that deviations from the natural state of motion are due to forces, and the forces are such that momentum is conserved.
Comment: I don't argue that "momentum is conserved" is the bottom line of the Three Laws. But as Newton had no way of explaining **why** momentum changes *e.g.* due to gravitation (which he explicitly refused to explain, i.e. 'frame hypotheses' about), the heuristic notion of force continued to be useful, and still does today. And because so much of our prejudice about the world is friction-infused, it remains pedagogically useful even to people not immersed in Aristotle to point out Newton's First Law explicitly. But it is the revisionist angle you take which I cricitize, not the physical meaning.
Comment: @NieldeBeaudrap: What's the "revision"? That Newton was writing for people with wrong philosophy? He is obviously trying to make sure people understand that this is not Aristotle. And friction is not really the problem, it's the idea of something continuing forever _uncaused_ that is the problem. People see an effect, motion, and they want a cause. Newton is saying there is no cause.
Answer:
Why didn't Newton just propose the 2nd Law (F=p˙) and leave it at
  that? The 2nd Law implicitly contains the first, doesn't it? If so, it
  seems he wasn't following his own Rule #1 of Book 3 of his Principia:
  "We are to admit no more causes natural things than such as are both
  true and sufficient to explain their appearances."

Simply because Newton didn't write the formula $F = m * a$. This was written some time in the middle of the XIX century.
If you want to know what Newton really wrote and the historical back ground and development you can find detailed information here

Newton thought that energy is linearly proportional to velocity.  The
  second law's original formulation reads: "Mutationem motus
  proportionalem esse vi motrici impressae" = "any change of motion
  (velocity) is proportional to the motive force impressed".
This law, which nowadays is wrongly interpreted as: $F = ma$ (there
  is no reference to mass here) simply states states: $$[\delta] v
> \propto [\delta] Vis_ {motrix}$$ and in modern terms is sometimes
  (illegitimately) also interpreted as
  impulse,
  sort of : $$\delta v  \propto J [/m]$$. But mass is not at all
  mentioned in the second law (as the original text shows) but only in
  the second definition, where we can see a definition of momentum as
  'the measure of motion'

Quantitas motus est mensura ejusdem (motus) orta ex velocitate et quantite
    materiæ conjunctim = 'quantity of motion' (modern 'momentum') is the measure of the same (motion), originated conjunctly by velocity
    and 'quantity of matter' (total mass)

and, moreover 'motive force' (vis motrix) is used, like all other
  scholars of the time, referring to the yet unknown kinetic 'force'
  that made bodies move, which Galileo had called 'impeto' and Leibniz
  'motive power' . The interpretation of this formula as the
  definition of force in modern usage is an ex post facto historical
  manipulation.
It was Gottfried Leibniz, as early as 1686, one year before
  the publication of the Principia, who first affirmed that kinetic
  energy is proportional to squared velocity (or that velocity is
  proportional to the square root of energy): $$ v \propto
> \sqrt{V_{viva}} [/m]$$. He called it, a few years later, vis viva =
  'a-live' force in contrast with vis mortua = 'dead' force:
  (Cartesian) momentum (mass/weight * speed: $m *|v|$). This was
  accompanied by a first formulation of the principle of conservation
  of kinetic energy, as he noticed that in many mechanical systems of
  several masses $m_i$ each with velocity $v_i$,
$\sum_{i} m_i v_i^2$
was conserved so long as the masses did not interact. The principle
  represents an accurate statement of the approximate conservation of
  kinetic energy in situations where there is no friction or in
  elastic collisions. Many physicists at that time held that the
  conservation of momentum, which holds even in systems with friction,
  as defined by the momentum: $\,\!\sum_{i} m_i v_i$ was the conserved
  kinetic energy........
  Full post at the quoted link.

As to the rule you quote it is not his rule but the centuries old Law of parsimony better known as Occam's razor

The words attributed to Ockham, entia non sunt multiplicanda praeter
  necessitatem (entities must not be multiplied beyond necessity), are
  absent in his extant works;[21] this particular phrasing owes more to
  John Punch.[22] Indeed, Ockham's contribution seems to be to restrict
  the operation of this principle in matters pertaining to miracles and
  God's power: so, in the Eucharist, a plurality of miracles is
  possible, simply because it pleases God.[17] This principle is
  sometimes phrased as pluralitas non est ponenda sine necessitate
  ("plurality should not be posited without necessity").[23] In his
  Summa Totius Logicae, i. 12, Ockham cites the principle of economy,
  Frustra fit per plura quod potest fieri per pauciora [It is futile to
  do with more things that which can be done with fewer].

His versiom became very popular but the princple dates back to Aristotle (ibidem)

Aristotle writes in his Posterior Analytics, "we may assume the
  superiority ceteris paribus [all things being equal] of the
  demonstration which derives from fewer postulates or hypotheses

In the same wiki article you'll see that it is confirmed that Newton's rule was not original
Comment: Thanks. Also, "Occam's razor" is actually older than Occam; it was a [Scholastic axiom](http://www.catholicapologetics.info/catholicteaching/philosophy/axiomata.htm).


New caliper will not close

Question: I'm doing my first ever brake job.  Front brakes on a 2012 Kia Sedona.  New pads, rotors, and calipers.  I'm struggling on the first one because the caliper will not close with the outside pad in.  It's like it's too thick.  The pistons appear to be compressed, but I did C-Clamp them just in case, but no change.  Any suggestions?
Answer: I usually put a flat bar across the piston then put the C clamp on that, for 2 reasons:

it tends to keep the piston "square" so it does not lock or jam in the bore which means it does not go back far enough.
it makes sure that the piston goes back flush with the caliper so that it will clear the new pads.
Comment: Thanks.  It's definitely not the piston.  Even with just the outer pad, the one that doesn't touch the piston at all, I can't close it.  It's like it's almost there, but it's still about 1/4 inch from being able to screw the bolt in.

New caliper will not close


What is it like to mention Allah aloud after praying inside the mosque? (zikr o llah)

Question: Today I'm with some of my friends which belongs to very Islamic cultural background, while talking about sharia one of my friend tell us that to recite wazaif ( tasbihat) is not good. I'm surprised for a while then I think that I get guidance about this daily life matter from your people. So let me know either it is wrong or right. Thanks
Answer: The statement of your friend either is a bit blurry and needs some clarification or he is somewhat wrong.
First of all doing dhikr after the prayer actually is confirmed in the qur'an and the sunnah (I'll add or link evidences later).
What actually is the major issue is whether or not dhikr in a group and aloud is shari'a conform. And even in this we must differ between two different opinions:

It is allowed with the intention to teach the audience the wording of dhikr. However this would mean that for example the imam would recite a dhikr or a part of it and the audience would repeat it (which is rarly the case).
It is bid'ah as the prophet () nor his companions or their followers never did so.

Practically this means as long as you do dhikr on your own and in silence you are on the safe side.
See also these relevant posts:
Is loud dhikr in group allowed?
Why do some masajid ask us to read Surah Fatiha in dua?
Is it sunnah of Prophet Muhammad (peace be upon him) to do zikr in a loud voice?
Answer:
Today I'm with some of my friends which belongs to very Islamic cultural background, while talking about sharia one of my friend tell us that to recite wazaif ( tasbihat) is not good.

There's nothing wrong with doing zikr out loud so long as you are not disturbing other people; and if you are not doing this to attract attention to your own piety.

Say, "Whether you conceal what is in your breasts or reveal it, Allah knows it. And He knows that which is in the heavens and that which is on the earth. And Allah is over all things competent.
  Qu'ran 3:29


Are the nontrivial zeroes of the Riemann zeta function countable?

Question: It is known that the set of non trivial zeros is an infinite set. But is it known if it is a countable, or uncountable infinite set?
Comment: @Lucian Cantor's set is uncountable and nowhere dense.
Comment: @Lucian Ah, that makes more sense, though I would note $[0,1]\subseteq\Bbb C$ is uncountable and not dense.
Comment: @AdamHughes: I meant uncountable; sorry.
Comment: @Lucian I'm quite confused at your comment, what about $\Bbb Z\subseteq\Bbb C$, surely this is a countable, but non-dense subset.
Comment: @AdamHughes: It contains a a dense subset. Replace not dense with nowhere dense.
Comment: How can they be countable, if they're not even dense ?
Comment: @Wojowu: Very interesting; I didn't know that. :-$)$
Answer: If the set $Z$ of zeroes of $\zeta(s)$ were uncountable, then it would have an accumulation point. Now, by certain version of identity theorem, this implies that $\zeta(s)$ is identically zero on its domain, which is absurd.
Comment: Ah, perfectly simple!
Answer: The comment has left me a bit less willing to commit to the statement of my original answer, though the spirit remains, in essence, true since the two are intimately related, but as I know of no other proof of the explicit formula without zero density arguments, I think it best to avoid that as an a priori reason.
The reasons given in the other answers are my other standard go-to explanations, so I'll try and make this accepted one more developed to do justice to the status of "accepted," as the lazy approach (simple deletion) is not available to me.
The problem with uncountably many zeros is that we may cover $\Bbb C\setminus\{1\}$ by a countable number of compact sets, eg. by $A_n, K_n$ which are closed annuli centered at $1$ of inner radius $n$ and outer radius $n+1$ in the cast $A_N$. The $K_n$ are a cover of the disc
$$D=\{z\in\Bbb C | 0<|z-1|<1\}.$$
which can be taken to be
$$K_n =\left\{z\in\Bbb C : {1\over n+1}\le |z-1|\le {1\over n}\right\}.$$
But the set of zeroes, $S_0$ having no limit points would indicate that $S_0\cap K_n$ is finite (it is discrete and compact), hence $S_0$ may be written as a countable union of finite sets
$$S_0=\bigcup_{m}A_m\cap S_0\sqcup\bigcup_n K_n\cap S_0$$
and so is itself finite. This fact is not special about the $\zeta$ function, it holds for any holomorphic function on any relatively nice set, eg. $\Bbb C\setminus\{1\}$.

The original, accepted answer
The set must be countable by a simple argument. If you look at the so-called "explicit formula" it involves a sum over non-trivial zeroes of the $\zeta$ function.

$$\Psi(x)=x-\sum_{\rho}{x^\rho\over\rho}-{\zeta'(0)\over\zeta(0)}-{1\over 2}\log\left(1-{1\over x^2}\right).$$

Here the sum, $\rho$ is taken over non-trivial zeros. But we know that any infinite sum for which more than countably infinitely many terms are non-zero yields a divergent series. Since we know the explicity formula converges, it must be that the number of zeroes is countable.
Comment: This is a circular argument. The explicit formula requires a countable number of zeroes to begin with; its derivation involves the fact that $\zeta$ has a memorphic extension across $\mathbb{C}$ and a somewhat delicate treatment of its growth.
Comment: The argument based on the explicit formula may be circular, but it still shows that this fact follows quickly and elegantly from a 'known' fact.  If I were the OP, I would be immediately convinced of that the answer to my question was 'yes'.
Comment: @AdamHughes Edit the answer to reflect this fact.
Comment: @isaacg I thought of the same solution. :-)
Comment: @anomaly I retract my earlier comment:  I was able to give a modicum of improvement to help address the systematic difficulties while preserving the fundamental understanding of the course of events. Thanks again for your comment.
Answer: In short, the number of nontrivial zeroes of $\zeta(s)$ with $\lvert \text{Im}(s) \rvert < T$ is on the order of $T \log T$. So there are countably many nontrivial zeroes.


Storage check and glance options missing after factory reset of Lumia 720

Question: I reset my Lumia 720 (with the Black update), but after the reset the Storage check and Glance options are missing from settings. How do I get them back?
Comment: Have you tried SysAppPusher? (Available on the WP store)
Comment: What OS version does the Phone's about page show?
Answer: It happens because after a factory reset you need to manualy update the system apps that have been updated since the time your factory OS version was launched. Since you are in the Lumia Black version of the OS, you can't search for updates directly from the Store application, because this option are not available in the Black update. So, to search for updates you will need to use a third part app, like SysAppPusher.The app enables you to quickly check (and be notified of) updates for installed and supported system apps, as well as opening up the ability to add apps from the store you wish to track.
Answer: http://discussions.nokia.com/t5/Pool-of-Knowledge/Nokia-Windows-Phone-8-App-Updates/td-p/1640082              scan the code and you will get it..
Comment: Can you add more detail? If the link goes dead in the future, no one will be able to know what the correct actions are. It is still good to include the link so people themselves can look at the authoritative reference.


How can I get back up into flying after not flying for over 20 years?

Question: I'm a former USAF pilot and former Bonanza owner. Haven't flown private in more than 20 years, but looking to get back into it. A friend who owns a 182 and will fly with me and I know some instructors. I don't even know where my old certificate and log book is, so this is really starting from scratch. What steps do you recommend?
Comment: Welcome to aviation.SE! I'm not sure there's a definitive answer to this, but AOPA's [rusty pilot seminars](https://www.aopa.org/training-and-safety/lapsed-pilots/rusty-pilots/rusty-pilot-seminars) are intended exactly for people in your situation. You might also like to take the [tour] if you aren't familiar with this site.
Comment: The FAA just published [a safety briefing](https://www.faa.gov/news/safety_briefing/2017/media/SE_Topic_17_09.pdf) on this topic
Comment: It's like riding a bike.  A friend of mine just jumped back in to aviation cold and only needed about 10hrs to complete his commercial single add-on.  Make a few flights in a 182, get a medical (or take the BasicMed route), and do a BFR with someone who is not a friend of yours (read: will give you honest feedback).  Set aside 10hrs for that BFR.  Some of the rules have changed but all of the basics are still pretty much what existed in 1997...except now paper charts are a waste of time.  Get the Avare charting app (free, no ads) if you use Android.
Answer: I do not have a sanctioned answer, but I can give you my take on an overview of what I would plan for someone in your situation.
Your certificate duplicate can be ordered.
You will need a through review of airspace (things have changed), weather gathering (also changed), AIM stuff (changed runway markings, phraseology, etc.).  I would urge FAAST courses for various topics you might feel you can get brushed up in.
On the air side, if we were flying, we would do a "checkout" in the 182, covering the systems, cowl flap operation, targeted power settings, trim usage, etc.  A little airwork, steep turns, turning to headings, power on and off stall recoveries, emergency procedures and landings, takeoffs and go arounds.
Everyone is different, but the last guy, similar to you, flew C208 and stopped in 2003, and did not fly since then.  This summer he hit the books, watched a few videos, took a practice commercial written, and flew 3.4 hours with me.  I was real comfortable signing him off, and his wife, who was the concerned party, was real happy with the results.
Two months later we did a instrument proficiency ride, and that was a little more difficult for him, but he completed the ride in two flights and less than 4 hours.
Good luck and enjoy. Have your instructor put a new high performance endorsement in your new logbook for the 182.
Comment: Thanks, Mongo. I'm sure there are a few gremlins out there waiting for me. I plan on taking my time and listening to whomever is in charge.
Comment: Just doing a ride with a retired 757 driver who has not flown in 14 years.  He decided that he would get a Saratoga. There is slightly more complexity than in the 182, but it's not much. The biggest thing is actually accomplished studying at home.  There are simulators for much of the avionics, although the platforms for those simulators may be a pain.  (eg Garmin 430 sim runs on XP)  Have fun!
Comment: BTW, the ride with the Saratoga owner, who used to fly 757s took 3.5 dual, and 4 hours ground, and included a FR and an IPC.  The IPC took longer than the flight review. He did one flight in a glider since retiring 14 years ago.  So it can come back pretty quickly.
Answer: As long as you hold at least an FAA PPL, it should be fairly easy.  As a former military pilot you could easily obtain an FAA CPL in the category and class of aircraft you flew in the USAF per §61.73.
After that, it's just a matter of regaining currency.  You will have to undergo a flight review with a CFI and receive a logbook endorsement per §61.56 plus an Instrument Proficiency Check, if you intend to fly under IFR, as required by §91.1069 and §61.157.  It may take a few flights with an instructor, but it will all come back to you sooner or later.
I would recommend reviewing your training literature you have from the USAF or obtain copies of the FAA's Airplane Flying Handbook, The Pilot's Handbook of Aeronautical Knowledge, The Instrument Flying Handbook, and The Instrument Procedures available to you for self study.  I would also recommend that you obtain the latest copy of the FAR/AIM for 2018 and keep that on hand for reference during these flight reviews.
If you don't currently have access to your certificate, but know you possess one, contact the FAA and request an duplicate copy from them.  I'd guess the same kind of inquiry could be made with the USAF for your pilot qualifications with them.
Oh and one other thing:  did you obtain a military logbook or a civilian rating just prior to giving up flying?  You may see if you can obtain the paperwork from the FAA which you filed for these ratings.  These days everything in done on the FAA's Integrated Airman Certification and Rating Application (IACRA) database, but any Aeronautical experience you file for application for a rating can be used as an official documentation of logged flight times.  I'd check on that to rebuild your logbook on.
Answer: Apart from the flight training that other answers have covered very nicely, you may need a new medical certificate. You said you used to own a Bonanza so I'll assume you already hold an FAA private certificate (at least). Your options are:

Apply for a regular third-class medical. If you're in good health that should be straightforward, but if you have any health concerns then it would be worth talking to AOPA or an AME before you actually apply for the medical examination.
If you held any valid FAA medical between July 15, 2006 and July 15, 2016 then you could fly without a medical under BasicMed. AOPA has a lot of detailed information on it that's worth checking out (and see this question).
Fly a light-sport aircraft without any medical at all, using sport pilot privileges. (You don't need a medical for gliders or ultralights either.) You mentioned a 182 so I guess you don't plan to go this route, but it's worth including for completeness.
Answer: You may also need to obtain a new Pilot License. A rule change went into effect in 2006, that by 2010 all pilots needed a plastic license, looks kind of like a credit card, with hologram on the front, mag stripe on the back, place to sign your name. 2010 was extended to 2013.  Can request it at FAA.gov. $2 for a duplicate, free if you want your license # changed from your SSN.


Why is the range of transponder digits 0 to 7 rather than 0 to 9?

Question: As a controller on IVAO I sometimes assign codes like 0168 and find out later that the code isn't valid. For me, the range 0-9 seems more logical. Why do we have to use octal numbers and not decimal?
Comment: Possible duplicate of [Why do the transponders introduce codes instead of using aircraft registration numbers?](https://aviation.stackexchange.com/questions/30483/why-do-the-transponders-introduce-codes-instead-of-using-aircraft-registration-n)
Comment: @fooot, In which universe could this possibly be considered a duplicate?
Answer: The four-digit transponder code that is entered by a pilot is an octal number rather than a decimal number, and in the octal numbering system, only the digits 0-7 are valid.
As far as why, internally it's actually a 12-bit binary number and octal works really well since can be used as a "shortcut" for entering groups of three binary digits at a time (000 - 111, which is 0-7 in octal).
If it were designed today, with the additional computing power and software complexity available, it would be possible to use a decimal number even if it is stored as binary internally, just so that it is more familiar.  At the time that the system was created though, changing the dials directly set the code in hardware and doing the conversion would have been much more complex / difficult / expensive.
In short, it was convenient for the engineers and manufacturers, and just an oddity for the end users, so they left it that way.
Comment: In addition, even though nowadays it would be possible to use decimal encoding, with dials that allow setting 0000...4095, you would need to prevent setting 4096...4999 (or 9999 if you didn't limit the first dial to 0...4). Using octal dials, you cannot select outside the valid range of 0000...7777.
Comment: As a side note; This is the very same reason IPv4 adresses contain 4 0-255 numbers (2^8 options), MAC adresses are written down as a set of hexadecimal pairs (2^8 options in range 00 to FF). Both are used because of very easy conversion from/to binary system. Since user doesnt do any math with such addresses, there is no drawback at all.
Comment: "If it were designed today..." they would use 24 bit hexadecimal codes :)
Comment: I want to upvote this answer, but its value is exactly 2^6 and I just can't destroy this beautiful number and dare everone who upvotes it!
Comment: @Lnafziger I was referring to mode-S
Comment: Fascinating.  This also explains why the emergency codes start with 111 binary (7 decimal)...
Comment: @J.Hougaard Not necessarily, as Crowley mentioned in his comment, IP addresses are commonly referred to in decimal even though they are stored as 24 bit codes...  :)
Answer: Octal representation is a cheap way to deal with small binary numbers
Modes A and C transponders send their ID using a train of pulses of unmodulated carrier, which can be seen as a sequence of bits. Today, such transponders use 12 pulses (mode S transponders use a 24-bit address which is different):

Source
Pulses are labeled A4-A2-A1, B4-B2-B1, C4-C2-C1 and D4-D2-D1 (interleaved in the transmission). They are contained within two framing pulses for transmitter-receiver synchronization purpose, and there is an additional pulse X in the middle, always at 0 today, but used in the glory days as custom data by manufacturers (e.g. to report to ATC the position of a retractable landing gear).
The transponder must be told the value of each bit in some way. Today it wouldn't be a problem to enter the ID as a decimal number (between 0 and 4095), but when the transponder was invented, decades before the arrival of inexpensive programmable chips, a reliable converter was a costly device.
On the other hand, it was not an option to just provide the 12 values using On/Off switches:

Sample of miniature switches, source
Obviously mistakes would have been numerous, either during vocal transmission of the ID, or when entering the ID.
The simplest solution broadly used when dealing with bits is to group them, and associate a single symbol to each possible combination in the group.
It would be good to use groups with 10 combinations, we already have symbols "0" to "9" to represent them. Unfortunately when grouping bits by two, we obtain groups with 4 combinations each. If we group by three bits, the groups have 8 combinations. By four, the groups have 16 combinations, etc.
Because we are dealing with a number expressed in radix 2, the number of symbols to be used is always a power of two, never a power of 10. So engineers had no choice at the time, than to forget the decimal numbers and use an odd number of combinations. As an example, let's group by 2 bits and use Greek letters for the required 4 symbols:

We would be poor designers to produce this (except for a remake of Airplane!), but you've got the principle. To keep the system simple, we can use decimal number symbols if we need at most 10 symbols, and complete with letters if we need more. This is exactly what is done when spelling numbers in octal (groups of 3 bits) and hexadecimal radices (groups of 4 bits).
As explained in other excellent answers, the first transponders had only 6 bits for their ID, so octal was the sensible choice, and IDs were presented as 2 octal figures, e.g. "75" to represent "111 101". When the ID length was extended, the octal system remained in use.
In case your are interested by the details of how octal is used, I propose details below.

Technical specification: a 12-bit binary number and 4096 values
The transponder radio signal for the ID transmission is made of 12 pulses (modes A/C) that can be low or high, this allows 4096 ($2^{\small {12}}$) combinations.
As the pulses have only two states, low or high, we can refer them directly as a 12-bit binary number between 0 and 4095. Let's illustrate with some values:

We can add as many 0 on the left as we want (e.g. to have 12 bits), like we do in decimal: 25 = 025 = 00025.
Octal and hexadecimal representations of binary numbers
For convenience, we usually replace groups of bits by some equivalent to reduce the number of signs used. It's common to use groups of 3 and 4 bits:

Octal: A group of 3 bits can generate 8 combinations, we can easily replace this group by a single figure in radix 8 to cover these combinations. Radix 8 is named "octal" numbering.
Hexadecimal: Similarly a group of 4 bits generates 16 combinations (twice the number of combinations for a group of 3, as the two values of the additional bit can be associated with all the 3-bit combinations. We can replace the 4 bits of a group by a figure in radix 16. Such system is named "hexadecimal" numbering.

Back to our examples, replacing the bit groups by their equivalents in radix 8 and 16:

Select which radix to use
What have we got so far? We started with a 12-bit number, grouped bits either by 3 or 4, obtained the octal value (0000 to 7777) and hexadecimal value (000 to fff), two representations of the same binary number.
Which one is better in this case? The answer has been provided in other excellent posts: At the beginning there were only 6 pulses allocated for the ID. Logically, they were grouped by 3, and octal was chosen.
If there had been 7 pulses, probably the hexadecimal representation would have been selected, with values from 00 to 7f.
From radix to electromechanical switch
It is easy to design a wheel switch (thumbwheel) with 8 octal symbols that manages 3 actual switches to generate 3 on/off (low/high) electrical signals:

Source
We use the angular position of the wheel to close or open the three contacts. There are many designs to do this, one is to use brushes rotating over a disc with printed conductive tracks:

Source
The switches provides directly the binary group. By assembling four switches, we could provide the transponder the "squawk" code, that is the binary configuration for the ID pulses.
It's as easy to use 3 hexadecimal wheels with 4 contacts.
Why not 10 symbols?
We cannot group bits of a binary number into groups that can have exactly 10 combinations. This property is limited to power of 2 radix (4, 8, 16, 32...)
It was possible later, with the introduction of integrated circuits (as simple as memories) to convert quite easily decimal to binary. The 74S484 has been one such ICs. It could handle two inputs representing decimal values ("binary-coded decimal", BCD) and convert them in pure binary. The converter for 4 decimal figures (0 to 4095) would be designed like this, using 5 of these circuits:

As you see, it's more simple to use only 8 symbols ($2 ^{\small {3}}$), or 16 ($2 ^{\small {4}}$), and more generally a power of two.
It's legitimate to think we could also use a logic based on simple Boolean gates (NAND, XOR...) to manage the conversion from decimal to binary instead of a memory. This is not apparent at first sight, but it would actually requires a huge quantity of gates.
In order to be convinced, I have done the exercise for only a single bit (out of 12) and for only two decimal wheels out of 4. I removed the details of the exercise, but they can be seen in the edit history. Here is the result:

The minimization allowed to reduce the number of terms (hence gates) to 10. Still, this is only for one bit and two wheels. Sometimes it just doesn't worth the additional difficulty, specially at a time there was no ICs, to stick to decimal.
Comment: @alephzero: This is an educational answer, it needs to provide the concepts, not the state of the art. BTW a "simple keypad and micro-controller" are more expensive than you think in the aviation world, you have to make them certified. This is not a world where you can phone Apple to tell them you have a problem.
Comment: Engineer much? :) Excellent explanation!
Comment: @TylerDurden I believe that it depends on the technical level of the reader, and this answer will be better for a more technical person (like us) while my answer is better suited for less technical types. When I answer a question, I use the complexity appropriate to the original question, and the wording of his question made it seem like he didn't need this level of detail. Good info for others though, and I certainly up-voted this answer to show appreciation for the info and effort that he put into it! :)
Comment: @TylerDurden, "better" is a value judgement that requires a goal to compare against.  The goal is _always_ subjective.  Please define "better" according to what criteria.  If the criteria is "fewer words" then this answer is _objectively_ **not** better.
Comment: This is a much better answer than Lnafziger's.
Comment: Why on earth would you make a redesign now using complicated 1970s technology like that, when all you need is a simple keypad and a microcontroller - only \$10 for both, compared with at least \$50 for the parts to build this museum piece? That's assuming you can even source the parts -  the 74S484 chip is long out of production, though there are more modern equivalents.
Answer: The simple answer is that a mode A or mode C transponder allow 12 bits of identification data, and three bits can be described as an octal digit.  Therefore there are four octal digits, of which range between 0000 and 7777.
The question has changed, so I am supplementing this answer.  The convention of using octal numbers for transponder codes dates back to an earlier implementation of transponders which had 6 bits of aircraft identifying data. It was decided (I believe by some white shirted COTR) to go with octal digits. Dealing with computers, octal or hex are easier than decimal.  Later the transponder aircraft identifying field became 12 bits, and the octal convention was maintained.  It is a convention, and it has been maintained.
Supplemental: I remember a transponder which had 6 toggle switches for entering the code, prior to the 12 bit standard. The switches were marked by threes with 4-2-1 underneath them. Back prior to computer literacy of the masses, once can speculate the the selection of digits, rather than for example, hex, entered into consideration as IFF and transponder technology developed. A VFR squawk code could be entered as a 12, which would have most significant 1 switch up, and the least significant 2 switch up. I recall that secondary radar show that the same as 1200, even though it came from a transponder without the 12 bit standard. 77, or all switches up was for emergencies, and 76 and 75 all respectively mapped to modern day 7700, 7600 and 7500 codes.
Answer: Short Answer
Entering squawk codes in octal, or base-8 where allowable digits are 0 through 7, makes the human-machine interface between pilot and transponder as simple as possible.
Background
Mode A and Mode C compatible transponders use 12-bit identity or beacon codes. Each bit has two options, high or low, which works out to a total of 212 = 4,096 representable (i.e., that fit within 12 bits) identifiers, ranging from 0 to 4,095 in base-10, written 409510. Now, not all representable indentifiers are valid. For example, 75008 is reserved for specific situations, but that is not for the circuitry to worry about.
Quantities that fit exactly within some number of bits do not line up cleanly with powers of ten. Consider a hypothetical transponder that accepts four decimal digits 0000 through 9999 or 104 = 10,000 possible inputs. The pilot is more likely to handjam a bogus squawk than a representable one. This "simpler" interface now has an error condition that it must deal with: representable and unrepresentable inputs. If the pilot types or spins the dials to anything above 4095, how will the transponder reply? Should it blink an error light that the pilot may miss? How should it reply to interrogation while in a bad state? Silently clip the beacon code to all bits high (111 111 111 1112 = 409510 = 77778)? Stop replying entirely? More modes mean more testing and more expense.
Tradeoffs
'Ah,' thinks the clever old-school engineer. 'No more fancy buttons; we will give the leftmost dial only five positions, 0 through 4.' But what about the second dial that must be 0 when the first is 4 but can be any digit otherwise?
We have twelve bits to fill. Perhaps the pilot enters the binary directly. "Cessna 123AB, squawk zero-zero-one-zero-one-zero-zero-zero-…" Just imagine the frequency congestion with such long instructions, readbacks, corrections, and confirmations.
Our short-term memory is good for about seven items, give or take two. Twelve binary digits ("bits") are too unwieldy. Other factors of 12 are 6×2 and 4×3.
Factoring the twelve identity bits into six and two means squawk codes in either two 6-bit quantities (0-63) or six 2-bit (0-3) chunks. Imagine dealing with 64-position dials in the old days. Doing it with decimal buttons gets us back to the problem of unrepresentable codes. Six dials each with 0 to 3 may work, but that makes the dials smaller and forces the pilot to deal near the limit of short-term memory, both making this option error-prone and thus less desirable.
Three groups of 4-bit or hexadecimal quantities could work. Although hex values range from 0 to 1510, a common convention is to use digits 0 through 9 and then A through F for ten to fifteen. In other words, we are down to one digit per place, but in the old days, that would have meant using 16-place dials. Today, that would mean sixteen buttons on the face of the transponder. However, "Approach, Cessna tree-alpha-bravo declaring an emergency and squawking foxtrot-charlie-zero for this charlie foxtrot!" does have some mnemonic value.
The Sweet Spot
Considering it the other way, we have four groups of three bits. In binary, place values are powers of two (not powers of ten like we're used to thinking in decimal). Working with three bits each, the maximum value for any beacon code digit is
$$(1 \cdot 2^2=4) + (1 \cdot 2^1=2) + (1 \cdot 2^0=1) = 7$$
Here we find several advantages:

Squawk codes have four places — easily manageable in short-term memory.
All digits are familiar 0 through 7, so

Dial inputs have only eight positions or
Eight buttons suffice.

All four-digit pilot inputs are representable in Mode A or Mode C.
The transponder doesn't have to worry about what to do with bad inputs.
Comment: Excellent answer!
Answer: The 12 bits were set by the system timing and accuracy of pulse generation and processing technology available at the time. Having set 12 bits they could have done 0 to 4095 but that would have required special switches and/or gearing for the display. So to keep things simple they used Octal with 4 simple, 8 position switches.
Answer: In computer systems, everything is binary. This is due to the logic circuitry only having 2 states, high and low voltage. Because of this, decimal wouldn't be as simple to convert to binary as octal or hex are.
Comment: The decimal-to-binary translation is completely trivial for any computer system (even the cheapest calculator can do it!) - but the first aircraft transponders were used towards the end of WWII, well before there were any computers small enough to fit inside a plane and reliable enough to be useful for this type of application,
Comment: These systems were designed many decades ago, and the system remains unchanged for simplicity's sake. But all computers are still binary. And machine code isn't decimal because of this.
Comment: and quantum computing is going to blow your mind if you're a fan of counting possible [qu]bit states :)
Comment: @mins I've heard of analogue computers, but don't they require near constant tuning to be accurate?
Comment: @alex: We know how to have stable voltages, or stable clocks, to a given precision. We can use [operational amplifiers](https://en.wikipedia.org/wiki/Operational_amplifier), [PLL](https://en.wikipedia.org/wiki/Phase-locked_loop), etc as the base.


Forgotten Promotion

Question: My boss told me I was getting a promotion at the start of this last pay period.  My paycheck did not reflect this.  When I reached out to him he said he "forgot" to promote me.  He says I will be compensated for it on my next paycheck.  Should I reach out to his boss to ensure that this happens?
Comment: I would clarify with your boss that "compensated for it on my next paycheck" includes the previous month's extra compensation that he forgot.
Comment: Sometimes a check is a pay period behind due to payroll processing time.   Did you check to be sure the check you are looking for is actually for the pay period you think it is?  Otherwise I would have no reason to doubt his word, mistakes happen.   If you want to be sure, check with someone in your payroll/HR department.
Answer: Only if you think your boss was deliberately lying to you. It doesn't sound that way to me, so I'd leave it another month, and see what happens.
Comment: I agree, part of any job is to make your boss look good to their boss.  Give your boss a chance to fix this and see what happens.  Being too quick to escalate and making your boss look bad might make you feel better in the short run, but in the long run it could very well be career limiting.
Answer: Never attribute to malice that which is adequately explained by stupidity.
Wait and see
Your manager messed up. He admitted it, and promised to correct his mistake. If you give him the chance to correct his mistake, it will show that you trust him, and strengthen your relationship.
If, at this stage, you harass him about his mistake, it will strain your relationship. If go over his head and involve his superior, it will strain that relationship even further. The more your relationship is strained, the more your boss has reason to doubt himself about deciding to promote you in the first place.
Only act if the boss doesn't deliver
Even if you don't see that promotion next paycheck, don't involve your boss's boss. He doesn't know that your boss promised you a promotion. Speak only to your own boss, and make it clear that you expect him to do what he has promised.
Comment: I agree, I think it would be worth adding though that if it comes to that point where it doesn't happen this month Ollie make sure they have it in writing as well.
Answer: Write an email, with a request for receipt if possible. This proves you did your due diligence in asking, and provides him with a reminder come next pay period. That said, I would personally wait until next pay period to come and see if he did as asked. Give a chance for him to make good unless you have a legitimate reason to be concerned that he is lying to you.

Forgotten Promotion


steam distillation of 4-bromoaniline , why render it basic prior

Question: In the multistage synthesis of 4-bromobenzenamine, why must the solution be rendered alkaline prior to the steam distillation after the hydrolysis of 4-bromo-N-ethanoylbenzenamine?
Comment: Which compound are you distilling, the 4-bromoaniline or the 4-bromo-N-ethanoylphenylamine?
Comment: the 4-ba might be a zwitterion and in the acidic medium it may be attracted to the cation forming a salt of whatever acid was used.This would raise the boiling point of the 4-ba enough to not come over to the receiving flask. When made basic with a reagent like naoh the sodium ion will react with the cation from the 4-ba salt and the 4-ba will be left as the free base which is more volatile and can be distilled .
Answer: In principle, it is difficult to distill salts (ionic compounds). Therefore you first make sure that you have a free base in the solution. This is guaranteed in alkaline solution. For the steam distillation the compounds should be immiscible, which is another reason for having a free base. Let's compare boiling points and solubility for aniline and its salt:

Aniline b.p. 184 °C, solubility in water: 36 g/L
Anilinium chloride b.p. 245 °C, solubility in water: 1070 g/L


I need a psychologist ,i want to write him online

Question: i want to send a problem i have and to take an answer.I went to a psychologist recently but the main key of the situation was he couldnt understand my situation.I would like to write to a psychologist like an email.The reason is ,if i visit i would forget detail,i would upset my mind will not work properly.I have searched the internet but maybe i couldnt find something like that.I find only chat conversations and that i dont wanted to.Is there something to write my whole problem and after he/she will read it and he/she will obtain an aspect of view?(I want to send it only to him i dont want to be my problem public).What you have to suggested me?
Comment: I'm voting to close this question as off-topic because we can not recommend an online psychologist for you here.
Answer: Call your psychologist and ask for such option if you can get the e-mail, because you would like to explain your situation in writing.
If they don't have, you can explain your situation on the paper either handwriting or on the computer and print it before going to the appointment.
Especially when it's a private psychologist, they'll love to read what you've written to understand better your situation. In public clinic usually they've tight timeframes. But it may all depend on the specific psychologist and their approach, some of them would want to assess your situation by the direct approach.
Even when they wouldn't want to read it, it's worth to print such document just for your self (even if it's just a mind map), so you won't forget any details what you wanted to share.
If you looking just for online psychologist, I'm sure you can write to them as you like, whether via e-mail, chat or web forms. Search online for some, then send the message explaining your situation and find the most suitable for you who can understand your problems and can help you.
Comment: @e.p You need to find a private psychologist that does that. On this site we cannot recommend you any psychologist. Google it and find the email to local psychologist, send him the e-mail explaining briefly the situation and wait for the response if he's happy to cooperate in this way.
Comment: thans,but i would like to something that i cant take online help.It would better for me.Is there a site that can help me with this?
Comment: You prefer to find an online psychologist?
Comment: yes.I dont want to chat.I want first to write him my problem.It would take me to write my problem i think 30 minutes and after to read it at least 1 hour so i want  to send it to him.Its and theme from money it takes a lot.In the internet i think there are people who can help you and give you much help and they dont see your pocket.I think you know what i mean


Asymmetric keys (e.g. RSA) must be so much longer than symmetric keys (e.g. AES). Why?

Question: I have been reading that RSA has to do with math (prime numbers), while symmetric key encryption deals with blocks of data and modifying the blocks with replacements and remappings, but I still don't understand why asymmetric encryption has to have longer keys because of that, or whether that's even the reason.
Comment: Also consider ECC keys which are about as short as symmetric keys (2x or so, not 10x -20x for RSA).
Comment: Dupe https://crypto.stackexchange.com/questions/6236/why-does-the-recommended-key-size-between-symmetric-and-asymmetric-encryption-differ https://crypto.stackexchange.com/questions/8687/security-strength-of-rsa-in-relation-with-the-modulus-size https://crypto.stackexchange.com/questions/46852/why-are-key-lengths-in-asymmetric-algorithms-typically-longer-than-key-lengths-in-symmetric and more on security.SX.
Comment: @Jane Doe Consider that a symmetric key could be very long, even longer than most of the asymmetric keys you might be used to dealing with.  Here, of course, the words "long" and "short" are relative.
Comment: Actually, one could design a hash-based signature method with both private and public keys as short as the corresponding symmetric key; Gravity-Sphincs comes close...
Answer: Asymmetric algorithms
Asymmetric algorithms rely on mathematical structure. Keys for asymmetric algorithms typically have some kind of structure, as opposed to being uniformly random bit strings. This structure can be exploited to reduce the cost of breaking the system.
Additionally, with asymmetric cryptography, there is more information to work with; The public key has some known relation to the private key, and everyone has the public key. This is in addition to the usual information that you might have from what the system is used for, e.g. plaintext-ciphertext pairs or message-signature pairs.
Symmetric algorithms
Keys for symmetric algorithms do not have structure - They are simply a uniformly random block of bits.
Other than plaintext-ciphertext pairs, you typically do not have any more information about the key. The relation of the key to the bits of the plaintext/ciphertext are extremely complex with no regular or helpful structure to speak of.
Of course, you could have a cipher with a 256-bit key that is vulnerable to an attack that recovers the key in negligible time from a single ciphertext.
Key size
Key size isn't really what is relevant. What is important is the cost of the best attack to break the system.
With a strong symmetric algorithm, the best attack will be brute force guessing the key. So the size of the key more or less directly controls the cost of the best attack against the system.
The structure used by asymmetric algorithms typically results in the existence of attacks better than brute force guessing the key. So the key size has to be increased to compensate. This is visible in RSA as each prime $p, q$ is much much larger than the size required to prevent brute force guessing; Brute force guessing is not the best attack, so the keys are not scaled against the cost estimate that brute force would have.
Note
The above are generalizations that are only approximately true - it is possible to design symmetric algorithms that have structure - But those are not what people usually mean when they say "symmetric encryption".
Additionally, it's also possible to generate at random an AES key that happens to be the product of two somewhat sizable primes; But that won't tend to help cryptanalysis of AES much because that structure doesn't appear to be helpful.
Answer: Suppose you use for symmetric encryption a key of 256 bit. Any of 256-bit numbers can be used as a password. That's why there are 2^256 password candidates that an attacker has to test in a brute force attack.
Where as for RSA not every number can be used. RSA keys are based on prime numbers with special properties. In any given range only a small part of numbers fit these criteria, all others can be easily filtered out before brute force attack. For instance, out of all 256-bit numbers only 2^47 can be used for RSA. This is essentially less than in case of symmetric encryption.
That's why for RSA to get the same number of password candidates you have to use a bigger range. For instance, to get 2^256 candidates for RSA you have to use bigger range, about 13500 bits.
You can find more details here:
Security strength of RSA in relation with the modulus size
Comment: The mere number of candidate keys doesn't really explain this.  If we used 140-bit primes to make a 280-bit modulus, and used a fixed exponent like $e = 3$ so the modulus completely determines the key, the approximation $\pi(x) \approx x/\log x$ to the prime-counting function $\pi$ suggests that there are well over $2^{128}$ candidate primes and therefore well over $2^{256}$ candidate keys.  But a 280-bit modulus is hopelessly insecure for RSA—larger moduli were demonstrated to be breakable a quarter century ago!  You could probably factor a 280-bit modulus on your laptop today in hours.
Comment: (How do you get $2^{47}$ possible 256-bit primes or moduli?)


Unable to install Wine on Ubuntu 16.10 due to i386 packages

Question: I am attempting to install wine on Ubuntu 16.10 and it will not install properly due to issues with the 32 bit packages.
Using the Wine PPA, it cascades down to
wine-staging-i386:i386 : Depends: libgphoto2-6:i386 (>= 2.5.10) but it is not going to be installed

....
and so on.
Using the standard Ubuntu PPA, it fails when installing wine32:
wine32:i386 : Depends: libwine:i386 (= 1.8.5-1ubuntu1) but it is not going to be installed

And attempts to install those packages create errors about their dependencies, and so on down the line.
I have added the i386 architecture:
sudo dpkg --add-architecture i386

And attempted to use aptitude to force the issue, which didn't help.
Also, at least in the case of libwine, the amd64 version installed matches the i386 versioning exactly:
Depends: libwine:i386 (= 1.8.5-1ubuntu1) but it is not going to be installed
libwine is already the newest version (1.8.5-1ubuntu1)

I did have an old repository (xenial) installed at one point, but installed no packages from it (I ended up installing the package I needed - libpng12 - manually; installing the i386 version alongside did not fix anything)
Additionally:
I have no held packages and no pending updates.
Answer: Ubuntu 16.10 offers wine-stable (1.8.5) and wine-development (1.9.20) -- why did you use a wine ppa?  Either should install directly with a
sudo apt-get install wine-stable     (or wine-development)

Use ppa-purge (install if necessary) to get rid of the inconsistent packages you have installed
sudo ppa-purge <whatever wine ppa you used>

and try one of the standard installs.

Since Wine is community supported, you have to enable the universe software source.  Run Software Updater, click on the "Settings" buttton, and under the Ubuntu Software tab, click on the "Community maintained free and open source..." checkbox. (first box, Canonical-supported should also have been checked).

The version of libwine:386 on my fresh wine install is 1.8.5-1ubuntu2 not ...ubuntu1
   ii  libwine:i386   1.8.5-1ubuntu2   i386   Windows API implementation - library

I'd suggest you uninstall every wine package you can identify with
dpkg -l | grep wine

and reinstall wine-stable
sudo apt-get install wine-stable

Comment: I attempted the separate wine PPA after the Ubuntu 16.10 PPA builds did not work with the wine32 error above.
Comment: Universe is enabled.  The standard installs do not work, with the i386 error occurring when I try to install wine32: "Depends: libwine:i386 (= 1.8.5-1ubuntu1) but it is not going to be installed"
Comment: Hmm.  The purge / reinstall wine didn't work but it does appear that I have some package version mismatching (such as the libwine package, and some packages matching versions in yakkety/main vs yakkety/updates).  Would ppa-purge of non-main packages be worthwhile?  Upgrading to 17.10 beta and hope everything syncs better?  Thanks for your help.


Starting character alive or dead?

Question: I've been struggling with this one for a long time and it's really kept me from moving forward. My main character starts off as a queen consort, and the death of her husband and her stepson (co-kings) are supposed to serve as the inciting incident. But I'm struggling with whether to introduce her husband and stepson alive or have news of their deaths brought to my MC. My MC's husband is very important for the context of the whole story, and his past actions have consequences until the very end, and he'll be mentioned frequently throughout, but on the other hand I think it'll be a little jarring for him and his son (her stepson) to be introduced only to be killed in the same chapter. So would it be best to just have them die offscreen? I really can't decide what would be better.
Answer: What is 'better' is entirely subjective. You need to consider what your story looks like, and at what powerful point you want to begin telling it. It will affect so much about how it will ultimately come across.
There is little point describing a normal day in their lives and then kill them, because most modern readers (and editors) won't let you get to that point. If, however, you can have them add dramatic value and conflict before they die... then it may be interesting to show that.
Considering the archetype of story you seem to be trying to tell, it is not unusual to have the declaration or discovery of their death be the very first scene in the book. What this does is, for one thing, start the plot immediately while creating a whole barn full of useful questions to the author.
Ultimately, your question cannot be answered. If they are to die in the first chapter regardless, and you fail to decide -- write both versions of that chapter, and feed them to alpha readers. See which they enjoy better, and which creates the questions you need to push your story forwards.
Answer: Either way could work well. I have read novels in which a character dies inn the first chapter, even inn the opening scene, and the repercussions of that death are a major driver of the plot. David Weber's Mutineer's Moon is an example that comes to mind. Another is the killing of King Brion in the first chapter of Kurtz's novel Deryni Rising. The protagonist for the rest of the novel is the king's son and heir, Kelson.
Having news of a death start the plot is so common it is almost a cliche, but it also can work very well. Or the news od the death could be delivered at the start, but later we could see the King alive in a flashback scene. Without seeing your full story, there is no way to say what would work for that story, and you as the author must decide what will work for you and your story.

Starting character alive or dead?


How to Stop apps from waking other apps?

Question: I've been running xposed on my galaxy note 2 with 4.1.1. I have greenify enabled as well as android tuner with perms blocked.  Also,  I have everything scrambled with xprivacy. I have facebbok selected for hibernation.  Everytime I open Plume, I noticed that facebook app comes out of hibernation.  I had this same problem with "Keep" months ago,  but was able to cut the directory path through greenify. I don't see that option anymore.  I have gone through and set everything I can think of to stop this,  yet facebook still wakes when I launch Plume. Also  whenever  I use  SwiftKey (which is everytime I enter text!) it also wakes Facebook.
Answer: This is in essence working against the Google cogs' planned L app integration/cross-communication. Integration is usually good/well received.
My first guess is that you have swiftkey set to sign in with facebook and possibly have plume (twitter) linked with facebook. Try to revoke these permissions first to see if it fixes the problem.
One thing that may help you is to get rid of the android facebook account and instead either rely on using the browsers mobile facebook page, or sign in every time. I'm not sure how much this path would muck up facebooks usability.
Another option is to set up automated facebook freezing: How can I automatically freeze and thaw an app on demand?
Freezing is one step beyond hibernation and no app link or background process can thaw without deliberate action.
Comment: I don't sign in to apps with facebook, never trusted facebook in that way.  But since posting this thread,  I did uninstall facebook and go with firefox mobile sign in. That works,  it's a few extra steps, but it's been fine for the past few weeks.  I never thought of freezing with titanium though! I didn't even realize titanium's widgets were that versatile. I just tried it out on plume. I may even reinstall fb and swiftkey and "keep" now. Thanks


What are the different PC sync ports?

Question: I have 3 devices and all of them seem to have different PC sync ports. Now which is which and what are the names of these ports? What cable is needed to connect all of them? I am attaching a picture of them.
Answer: The three pictures you have included are all the same type connector, a female PC sync connector. A male PC to male PC cord will connect to any of them.
PC in the context of flash photography has nothing to do with a personal computer. It is an abbreviation of Prontor/Compur. Prontor has its origins in the Italian word pronto (quick) and was a brand of shutter produced by Alfred Gauthier in the 1950s. Compur, derived from the word compound, was the shutter brand of the Deckel Company. Both companies were based in Germany and both counted Zeiss as an influential stockholder when they introduced the standard 1/8"-inch coaxial connector for shutter/flash synchronization.
Comment: +1 for product link :). I will wait a bit more before accepting an answer
Answer: Why do you think they're different?  They all look like female PC sync ports and they'll  fit the same PC connector.  There really is only one "kind" of PC sync port; there's even an ISO standard for it: ISO 519.
The only possible difference is whether it's "screwlock"  (i.e., has threads on the outer-most side to secure the connector) or simply friction-fit, but I can't tell that from the pictures.  I just know my 5DMkII isn't screwlock, and my YN-622Cs are.  And that only matters if you have screwlock cables.  But the electrical connections are identical for both.  IIRC, it's sync on the inner post, and ground on the outside ring.
Comment: Thanks for the answer. The gap between the +ve and the -ve on the canon 7D port seems to be bigger than the rest. I will buy a male-to-male screwlock PC sync cable and report my results.
Comment: correction: I am talking about the gap between the inner post and the outside ring.
Comment: @CorruptedMyStack Possibly the difference, then, of the threads for screwlock.
Comment: I have ordered one with a screwlock hoping that it will work. There are only a few longer than 6ft on amazon. I want to experiment by putting the a pentax flash in manual that is not triggering perfectly as a optical slave.

What are the different PC sync ports?


Android app to change the name of installed apps

Question: Am looking for an Android app that has the ability to change the name of installed apps. I prefer a free app. Also the app should provide the facility to change the name back to its original(its not mandatory). Is there any ?
Comment: Are you trying to change the name in the launcher or change the name of the actual app?
Comment: @RockPaperLizard I just want to change the name in the launcher(where ever the app icon is displayed).
Answer: You can achieve this by using a different launcher. Nova Launcher allows you to change the name of each app. If you long-press an app within the app draw. Although it does not store the original name, you can modify it again to display the original app name.


If I line in the sound from a video game console, can I detect when a sound is played?

Question: The question is as the question is. It won't be this isolated sound though, it'll be a sound on top of background music. I think I can get a hold of the sound file itself from the data, but at worst I'd just make my own recording and ask for a less accurate match - if variation is possible in whatever method may be proposed.
Comment: So, that is kind of a big question.
Answer: Theoretically you could separate your desired sound by ICA method or other blind source separation methods from the background music, then design a matched filter by your separated sound. The matched filter have high response when the desired pattern (which is your desired sound) exist in the input even when it buried in noise (background music).
The matched filter has acceptable performance but i'm not sure about the ICA and other source separation methods and highly depend on your input signals (desired and background sound).


Basel II modelling vs Solvency II modelling?

Question: How do the two modelling frameworks compare? I spent some time developing PD LGD and EAD models for banking portfolios... But I never did insurance modelling project which I suspect is based on Solvency II?
Answer: There is a brief discussion of the two modelling frameworks in An Introduction to Economic Capital by Mohan Bhatia in the "Insurance Risk" chapter.  To pull a quote from the "Solvency II versus Basel II" section of that chapter:

Like the regulatory approach to internal models in Basel II, Solvency
  II aims to bring the internal modelling approaches within the
  regulatory framework by adopting the following best practices:

consistency in models being used for pricing and capital computation;
coverage of risks—all material risks to be captured, more granular assessment of risks; and
documentation of the model, covering theory, design, operation, compliance and shortcomings; and disclosure about the model to cover distribution and its variability, underlying data, calibration, appropriateness and fit.

In the same section it also states that unlike Basel II, "the correlation between risk components is explicitly recognized by Solvency II."  On p. 106 another comparison is made, saying that "Solvency II has adopted the Basel II operational risk management framework."
Some sets of presentation slides comparing the two frameworks can be found here:

Solvency II and Basel II—What can actuaries learn? (Omar Ripon and Martin Noble)
Economic Capital Models for Basel/Solvency II, Pillar II (Alexander J. McNeil)

Finally, an overview of the Solvency II framework can be found in the Deutsche Bank Research publication Solvency II and Basel III: Reciprocal effects should not be ignored.  However, the main topic of this publication is how implementation of Solvency II and Basel III will affect insurance company investment behavior and capital allocation, along with affecting banks' funding.


What is a complex phase shift?

Question: In a complex methods course I am taking, we were given an equation for a particular driven harmonic oscillator where the driving force is trigonometric. I have worked out the math and obtained an equation that tells me that the driving frequency at resonance is the natural frequency multiplied by i. My tutor tells me that this is a 90 degree phase shift, but I don't really understand why. Isn't a phase shift obtained by adding or subtracting 90 degrees? And how can a frequency, which is a measurable physical value, take on imaginary values? I would understand if we were talking about velocity. Because velocity has a direction, addition or scalar multiplication by a real value would not describe a 90 degree rotation of the vector. But frequency is a scalar quantity. What does it mean to have an imaginary frequency?
Comment: Hint: $e^{i \theta} = \cos \theta + i \sin \theta$  (Euler's formula)
Comment: I realize that, but multiplying i to a real value is not the same as adding pi/2 to the same real value. Since the natural frequency is real valued, even using Euler's identity, I can only at most add to the power. Unless the power of the frequency is the phase, that would not explain the phase shift. Even if it did, it doesn't answer the question of what an imaginary frequency means. I cannot create a driving force with a frequency of i...
Comment: Building onto K_inverse's comment, I don't know the exact context, but pertaining to $i$, this is 90 degrees (or an angle of $\pi / 2$) in the complex plane. As for the units curiosity, remember degrees, or radians, aren't really a physical unit. So if your function is rolling off of say $\omega t$, multiplying by $-1$ throws it $180$ degrees out of phase just as $i$ to $90$ degrees. Could you add the particular oscillator to the question?
Answer: If your oscillating function is of the form $e^{i\omega t}$, a phase shift looks like $e^{i(\omega t+\phi)}$, which can be rewritten as $e^{i\omega t}e^{i\phi}$.
Now, recall that $e^{i\phi}=\cos\phi + i\sin\phi$. A 90 degree phase shift corresponds to $\phi=\frac{\pi}{2}$.
Thus,
$$e^{i\frac{\pi}{2}}=\cos\frac{\pi}{2} + i\sin\frac{\pi}{2} = 0 + i = i.$$
So finally we have,
$$e^{i(\omega t+\frac{\pi}{2})}=e^{i\omega t}e^{i\frac{\pi}{2}}=ie^{i\omega t}.$$
So we see that a phase shift of 90 degrees corresponds to multiplication by $i$.
Answer: There is an article here: (the optimal driving force is shown to be $90^{\circ}$ out of phase of the motion)
Phase difference of driving frequency and oscillating frequency
Also any vector like $4j + 3i$ can be expressed in phasor form as $5 \angle 41^{\circ}$ or in complex form $4+3i$.  Adding $90^{\circ}$ is just a vector of same amplitude at $90^{\circ}$ to the original.
Answer: It is a phase shift by 90 degrees if multiplied by $i$ indeed.
Note that $i=e^{i\pi/2}$. Writing whatever driving signal in complex form, since it is sinusoidally driven, it will have an $e^{i\omega t}$ in it, multiplying by $i$ multiplies by $e^{i\pi/2}$, and when you multiply the exponentials you add the exponents to get $e^{i(\omega t+\pi/2)}$.
Taking the real part to get an answer that actually makes sense physically, you would have a $\cos(\omega t+\pi/2)$ dependency in your driving.
I think this is what you are asking, hope this helps.

What is a complex phase shift?


How do I view achievements in minecraft?

Question: I don't know how to view my achievements. I am on Minecraft bedrock edition v.1.14.60. I have actually looked up "how to find achievements in Minecraft bedrock edition 1.14.60" on Google, but even after searching that long phrase and looking everywhere the achievements were on their screens, I still can't find achievements anywhere. Here's proof!

Answer: From the Minecraft Wiki on Achievements:

Achievements are tracked per user account. They are not tracked separately per world; achievements earned in one world apply to all worlds using that edition and that user account. On most platforms that Bedrock Edition runs on, achievements are logged to an Xbox Live account, and so players have to be logged in to their Xbox Live account to earn them. On PS4, Bedrock achievements are logged as trophies to the player's console account, and if logged into a PSN account and online, they are synced with PSN but not Xbox Live (even if logged into an Xbox Live account).

This means that you can find them on your Xbox account. You can root around the Xbox website under your account until you find a page that looks like this:

Then just scroll down to view your achievements!
Comment: I don't have a minecraft account and my dad won't sign me in:(
Answer: Go to Profile in the menu and you will see the achievements button. Press on it and it will show all your lifetime achievements.
In Java Edition, press L and you will see your world achievements. Or hit esc and press the achievements button.
I hope this is useful to you.
Answer: Join a world or  go to the title screen, then just click profile, and then achievements. That is how it works for me. I hope it's useful. I use bedrock iPad


What is the plural of "equipment"?

Question: What is the plural form of the word "equipment"? Is the word "equipment" singular?
Context: for tools/objects
Comment: Equipment used as a singular is a collective noun. We do not inflect collective nouns into the plural for them to take on their collective sense. Nonetheless, equipments also exists as a word, just with a non-collective meaning. Most of the answers you have here are wrong. You have not given an example set of sentences, so there is no way to tell whether you want a singular collective sense or not.
Answer: "Equipment" is nearly always used as a mass noun, not a count noun.  There may be a few obscure exceptions, but they would be very rare.  Mass nouns don't have plurals (except when they double as count nouns).
So anything you say with "equipments" in it is more than likely to be ungrammatical.  I recommend avoiding this word.
Comment: I think I said "may be a few obscure exceptions".  In other words, there may be cases where "equipments" is OK; I just can't think of any.  However, reading the comments above, it seems that the OED has some exceptions.  I shall go and look them up, and hopefully learn something.
Comment: So, are you also suggesting that "equipments" is a wrong word?
Comment: The best answer.
Comment: David, are you telling me that there is no such relation between water, folk and equipment as I have seen it ? Besides I don't like that you have used the word ungrammatical, because you haven't told us what is grammatical for you. When you are trying to prove the opposite of one statement you have to define your statement. Simple Math.
Comment: The OED has 34 results for *equipments* across all definitions, the most recent a quotation from 1971. But it only has three as part of the *equipment* definition (1793, 1801, 1873). So "may be a few obscure exceptions" sounds fair to me.
Comment: "it is more than likely to be ungrammatical"    lol    => -1
Answer: Short answer: use 'equipment', do not use 'equipments'
Long answer: in Modern Standard English, 'equipment' is a mass or non-count noun, like 'water' or 'traffic', which describes something that is somehow implicitly plural but doesn't have a plural form. That is, it wouldn't make sense to have more than one equipment, since it describes a set of things already. 'Equipment' is already plural in the sense that it refers to a number of things together. There are instances where one has more than one set of these things, the many waters of the world.
To address some of the controversy mentioned elsewhere:

'the OED has 34 entries': if you look at what a current search for 'equipment' returns 34 of, it is 'stemming' (removing suffixes) in some arbitrary fashion. The OED search matches against the word, not any words in the definition or quotes, and the 34 words matched for 'equipments' includes 'equipment' along with 33 other words which are not 'equipments'.
'dictionaries leave out the plural': yes, they do but they also don't mark if a word is a mass noun like 'water', so you can't tell if there is no plural form as in a mass noun. A proper dictionary will give the plural form if it is mot simply '-s', e.g. 'ox, n. pl. oxen' or 'daisy, n. pl. -ies'.
'the OED has a definition for equipments': yes, it does.

2 a. concr. Anything used in equipping; furniture; outfit; warlike apparatus; necessaries for an expedition or voyage. Used in the pl. to indicate the articles  severally, in the sing. collectively.
1873   Act 36 & 37 Vict. c. 88   Sched. 1, Equipments which are primâ facie evidence of a Vessel being engaged in the Slave Trade

This definition might be used but it is a technical usage, like for hardware or military use.
'Google gives X million hits', 'Google Ngrams says that it is so': Google Search/Books/Ngrams are easy to misuse and draw several levels of unfounded conclusions from. Google (and other search engines use 'stemming' which sometimes cuts off suffixes. So you can't tell what is being counted. Google ngrams doesn't stem, but you still need to check the results. A comparison of equipment and equipments shows that the plural form does occur but at a much smaller frequency than the plural form. Even given this lesser frequency it looks like 'equipments' was more common in the past, in foreign works, and in technical works.

As a final note of relevance, as a native speaker, I find 'equipments' to sound really wrong. So if you're climbing up a mountain and have a bunch gear to put away, just 'pack your equipment', don't use the plural.
Comment: Generally agreed, but mass nouns are not really "somehow implicitly plural" -- if they were, you could put a number on them and you'd use them with "are" instead of "is". The mass/count difference is semantic, not mainly syntactic: do they come in integer amounts only? Btw, last I checked Google ngrams doesn't remove affixes unless you specially request it (though Google search does).
Answer: First of all I want to make my point the I have heard equipments, but it was really in very very rare cases. I think that both are possible although they would mean different things.
Equipment is collective noun and as such can be used in plural. Although there are a lot of collective nouns that can be used with -s or without and they mean different things.
For example what is the plural of water- water. But we can say waters when revering to different types of waters in sea, oceans, river and ect. Another example is folk and folks. Folks is collective noun for group of people, while folks referring to collection of different groups of people.
Therefore when we are speaking about different machines for fitness we can call them equipment. When we are speaking about fitness equipment and fishing equipment, we should use equipments.
Don't forget that English is something alive and in different areas in different countries even native born English folks have their own English within their own community , with different way of living, different jobs, they belong to different parts of the society and ect. English is a languages and there is nothing constant in languages it changes and evolves every day.
Comment: In my opinion, the diversity of cultures utilizing the English language in such a way that it it deviates from the mainstream establishment in a manner that is explicitly spelled out as *grammatically incorrect* is, I believe, an *abuse* of the language by those who would utilize the language as a second language. An example of this is your pluralization in "English is a languages", which is grammatically wrong, even if it is embraced by your culture. The purpose of this SE site is to support those who desire to follow the established standards, not to shrug them off.
Comment: "Water" is in no way a plural form of *water.* It's usually a mass noun, but mass nouns are grammatically singular in English.
Answer: Equipments has been in continuous use as a plural form of equipment in English for centuries, as this Ngram chart tracking instances of equipments across the years years 1700–2008 indicates:

However, the areas where equipments functions as an acceptable plural are rather narrow: as other answerers have noted, it is extremely unusual (and sounds flatly wrong in U.S. English) for someone to ask "Do you have all the equipments you need?" Microsoft Word automatically marks equipments as a misspelling because in most instances it is not the right word to use.

Historical usage of 'equipments'
Google Books search results for equipments turn up a multitude of matches for the term in publications from the period 1700–1817—something on the order of 170 unique matches. Many of these instances are associated with what most people today would refer to as "military equipment" (using equipment as a mass known). For example, from the court case of Savage v. Gulliver (March term, 1808), in Reports of Cases Argued and Determined in the Supreme Judicial Court, of the Commonwealth of Massachusetts, volume 4 (1808):

The eighteenth section of the statute of 1793. c. 14, declares what arms and equipments each private soldier shall at all times be provided with. In the nineteenth, twentieth, and twenty-fourth sections, penalties were imposed on the neglect of the soldier to appear on the parade, with his arms and equipments. If he neglected to appear, he was liable to a fine of ten shillings, and also to a fine of twenty shillings if his arms and equipments were not on the parade. If part of them were there, then to a fine of such a part of the twenty shillings, as the articles of his arms and equipments absent were in proportion to the whole articles required: which proportion, from the nature of the equipments, it must have been difficult to ascertain. But the justice was bound to exercise his discretion. If the soldier appeared with his arms and equipments not in good order, he was to be fined three shillings: and perhaps  a proportion of the twenty shillings for the articles not present. If he was absent, and his arms and equipments complete, he was then subject to a fine of ten shillings only. So that in every case, where he was liable to a fine, he was liable to more than one, except when all his arms and equipments were on the parade and in good order.

Unmistakably, equipments is not a typo here. The term also comes up in connection with outfitting a ship for a voyage, as in this example from "Naval Report," in Niles' Weekly Register (December 10, 1814):

Our ships are excellent, and all in good condition. The classes are few, and so uni form that without inconvenience the masts, spars and equipments of any one of a class will serve indifferently for any other of the same class. All the new ships. All the new ships of each rate are of the same class, and are absolutely similar in all their equipments, and in the dimensional proportions of their hulls, masts, spars &c. This strict similarity should be carefully preserved upon every principle of convenience, economy and efficiency.

'Equipments' today
A Google book search for equipments turns up more than 400 unique matches from the period 1972–2008. Clearly the plural form continues to be used—but where and by whom?
One area where equipments remains in use is in discussions of military history—as for example in the Osprey Military series "Men-at-Arms," which includes such recent titles as Artillery Equipments of the Napoleonic Wars (1979), German Combat Equipments 1939–45 (1991), and British Infantry Equipments (2), 1908–2000 (2000). Likewise army tech manuals continue to use the plural form, as in "Organizational, Direct and General Support, and Depot Maintenance Repair Parts and Special Tools Lists" (January 1968):

g. Fifteen-Day Organizational Maintenance Allowances.
...
(3) Organizational units providing maintenance for more than 100 of these equipments shall determine the total quantity of parts required by converting the equipment quantity to a decimal factor by placing a decimal point before the next to last digit of the number to indicate hundredths, and multiplying the decimal factor by the parts quantity authorized in the 51–100 allowance column. Example, authorized allowance for 51–100 equipments is 12; for 140 equipments, multiply 12 by 1.40 or 16.80 rounded off to 17 parts required.

Also disproportionately represented in the recent Google Books results are books from India. For example, from M.H. Siddiqut, Teaching of Economics (New Delhi, 1993):

CLASSROOM EQUIPMENTS
Classroom equipments constitute the following aspects:
1. The Items of Equipments:

The items in a classroom may be put into three heads which are as follows:

(a) Essential Equipments
...
(b) Desirable Equipments
...
(c) Non-Essential Equipments

And from S.K. Katiyar & H.S. Niranjan, "Topographic Mapping of Hilly Terrain Using Total Station, "in Proceedings of the National Conference on Advances in Civil Engineering: Perspectives of Developing Countries (ACEDEC-2003) (New Delhi, 2003):

Conventionally a map is prepared after doing field survey by using various equipments like chain, tape, theodolite and levels.  ... Sometimes these techniques become unsatisfactory due to non-fulfillment of certain requirements like obstruction of line of sight and steep slope of the area. In the modern age of surveying, the electronic equipments like Robotic Total Station, Digital Levels and Laser Levels can make our fieldwork tasks very easy, due to their versatile functionalities. These electronic equipments have so many advantages over the conventional instruments in terms of accuracy as well as speed. Though these equipments have much higher costs as compared to conventional surveying equipments. However if survey fieldwork cost and time is also included, then it is worth to purchase these costly equipments.

Elsewhere in modern English-language publications, however, equipments is very rare indeed.
Answer: At first, a couple of general remarks on the count/non-count dichotomy in linguistics. (Incidentally, this dichotomy is language-specific).
What is taught in school about this distinction, whether English is your L1 or L2, is a gross oversimplification. It is done for pedagogical reasons.
However, in linguistics, it has been abandoned for various reasons. On the one hand, as Allan showed in his 1980 paper in "Language", it is better to think of countability as a continuum, see the following examples (from the most countable to the least countable):
car, oak, cattle, scissors, mankind, admiration, equipment, Himalayas.
One the other hand, as Payne and Huddleston (2002) argue, "many nouns can be used with either a count or non-count interpretation". They also add that since in some cases "the existence of paired count and non-count senses is entirely predictable, so that it is not necessary for a dictionary to list both".
To make things even more complicated, some linguists have proposed up to eighteen types of concrete nouns only (e.g. Goddard 2009).
In natural languages, there is obviously a lot of variation. However, the trend is that the form "equipments" is not common. For example, I searched The Times and The Sunday Times, and "equipments" returned zero hits. Same with The Guardian. If you are an L2 learner of English, I'd recommend forgetting about the existence of that form altogether.
Some commenters suggested it might be used in cases when different types of equipment are meant. See, however, the following example from The Times:
Makro is also stronger in non-food items, such as stationery and office equipment.
Now, with The NY Times, things are a bit different.
Searching the archives from 1980 to present and manually going through the results, I got 28 hits only. Six of them were company names (Recognition Equipments Inc., Digital Equipments etc.) and one was obviously a typo:
According to Dr. P. L. Fan of the Council on Dental Materials, Instruments and Equipments, …. (1987) – see the original report here http://www.ncbi.nlm.nih.gov/pubmed/1918680
Another sentence suspiciously looks like a typo, too:
In the face of such enmity, Pakistan's armed forces stand more and more vulnerable as old, mostly American equipments wears [sic!] out, with no ready replacements. (1980)
But:
That will include $800,000 a year in grants for the groups, $100,000 a year in sports equipments, and 15,000 tickets a year to Yankee home games. (2006)
Several ski equipments are presented. (2007)
The microphone was in place, and the synthesizer and other electronic equipments were turned on. (1984)
Now, if you search the archives of the NY Times for 1851-2008, things are a bit different.
I got 9983 results, with the highest peak for 1960-1969 – 1524 results.
An important thing about those examples – it seems most of them are classified ads, e.g. "Candidates should have at least four years of maintenance experience on the above equipments" (1962).
Only the first five hits were from the other sections of the newspaper, four of them written by the same person, Burton Crane.
Oils, drugs, office equipments and a number of the high-price stocks known as … (1961)
Now about the OED examples. There are 30 occurrences in quotations (I excluded definitions).
one – 18th century
eleven – 19th century
seventeen – 20th century (most of them are used in engineering or military contexts)
one – 21th century
If you search the BNC, you can see that in British English the form "equipments" is mostly used by the military:
Total number of occurrences: 27
7 of those come from ABA Britain's defence dilemma. 1990.
6 come from JNM House of Commons Select Committee for Defence: meeting (Public/institutional). Recorded on 9 February 1994
3 come from JNN House of Commons Select Committee for Defence: meeting (Public/institutional). Recorded on 9 February 1994
etc.
With dictionaries, you need to remember one very important thing - they are a good place to start your research but you shouldn't base your answer solely on the OED (OED-thumping) or some other dictionary.
Comment: I mentioned the OED citations not as an answer, but as a comment on rudra's claim that 'there is no such word as "equipments"'.
Comment: Those who say 'there is no such word as . . .' should tell us what they mean by 'word'.
Comment: @BarrieEngland, when I see someone saying such things, I usually interpret it as "there is no such word in my dialect."
Comment: @BarrieEngland, I see. I generally avoid statements like "There is no such thing as X in English".
Answer: Well, equipment's plural is rarely used. The form that I've heard the most is "piece of equipment."
Answer: The Google Translator didn't throw any spell error while typing equipments.
But here the site, which says there is no plural form for equipment .Refer here too, to know bit more, Finally it seems both acceptable.
Comment: Try the [OED](http://www.oed.com/view/Entry/63796), which gives plural senses and copious examples. Stop playing the "hunt the net" game.
Comment: Finally you take me there, Where i exactly want to go. OED is the standard one to look for. Thanks tchrist

What is the plural of "equipment"?


How do you remove the clear section from the back of the eMac's housing?

Question: As the title states, the eMac has a clear section at the back of it's housing that forms a grill for the fan inside. This seems to be pretty good at catching dust that's impossible to get at simply by removing and washing the housing, is there a way to remove this part so I can actually get it clean?
Answer: There are take apart guides a Google search away (including the official Apple Service Source one), but from what I can see, you remove the two front feet with a #2 Phillips screwdriver while the eMac is face down on an ESD mat, then use a 2.5mm hex screwdriver to remove the three large-headed screws around the access plate on the bottom, then the six screws around the screen end of the rear housing (two each top, left and right).
Gently lift approx 5cm only so you can (gently) disconnect the power button. The rear housing should then be able to lift off completely. I highly recommend reviewing the take apart guides befor starting!
I've not found instructions for removing the grill/vent from the rear housing, but at least you should be able to clean it when the rear housing is removed without fear of wrecking the internals.
europlus
Comment: Yeah the main housing is the easy bit, unfortunately you can't get into all the nooks and crannies of the clear part and I can't find anything on removing that. I think it might be plastic-welded in :(
Comment: High pressure cleaning while outside in swimmers? If air gets there with dust, surely high pressure water will? ;)
Comment: Yeah that's pretty much all I can think of :) The machine is really well designed except for the fact that dust just accumulates and turns rock solid in there.