Wash sales + restricted stock in USA: grant date or vesting date?

Question: I have restricted stock from my employer. When determining wash sale rules, what is the appropriate date to use for when the stock is "acquired"? Is it the grant date or the vesting date? (and if you know the answer, could you please link to the relevant IRS documentation? I've looked at IRS Pub 550 and can't make heads or tails of it.)
Answer: The vesting date. Look at publication 525, under stock options, where they talk about ESPP:

Your basis is equal to the option price at the time you exercised
  your option and acquired the stock. The timing and amount of pay
  period deductions do not affect your basis.
Comment: hmmm... that talks about basis, not wash sales... but it's a start.
Answer: For restricted stock, I think the vesting date meets the requirements of the second wash sale trigger from IRS Pub 550: Wash Sales:

Acquire substantially identical stock or securities in a fully taxable trade

I base this on these two quotes from IRS Pub 525: Restricted Property:

any income from the property, or the right to use the property, is included in your income as additional compensation in the year you receive the income or have the right to use the property.

-

Until the property becomes substantially vested, it is owned by the person who makes the transfer to you, usually your employer.

So on the vest date:

The transfer is taxable
Ownership is transferred to you

That seems close enough to "a fully taxable trade" for me.
Maybe this changes if you pay the tax on the stock on the grant date. See Pub 525: Restricted Property: Choosing to include in income for year of transfer. Obviously, if this is important you should consult your tax advisor.
Technicalities aside, I don't think it passes the sniff test. You're getting salable shares when the restricted stock vests. If you're selling other shares at a loss within 30 days of the vesting date, that smells like a wash sale to me.


Can I take recommendation from someone I met at a conference?

Question: I met a faculty (from a university in the UK) at a conference. She liked and praised my work and we are in touch after conference. She has an impressive profile and her research work is similar to mine. Is it okay to take a recommendation letter from her to seek postdoctoral position overseas? Will it help?
Comment: What's this recommendation letter for? Applying to grad school or "something else"?
Comment: Comments on some answers seem to indicate this may vary by field. You may want to add that detail to your question. It's also recommended to wait at least 24 hours before accepting an answer as best answer, open questions encourage more answers to be posted.
Comment: Its for a post-doctoral position.
Answer: There's nothing stopping you asking for one. However, you need to consider what would be written in such a letter.
In short, you can ask for a letter, but be careful how you use it. What could the person say on your behalf if a potential employer contacts them to get more information about their assessment of you?
For instance, it doesn't seem that you have a professional relationship - you haven't co-authored papers, nor have you worked together in the same institution, nor have you served on the same committees, etc. Any of these things is not necessary, of course, but these are the sort of things a referee would cite as evidence that they are in a position to recommend you or your work.
However, it sounds like your contact does know of your work. However, are they a world-leader in your field? Do they have the respect of your community? When they say good things about you or anyone else, do others pay attention?
How will a reader interpret a reference letter that is based only on a familiarity of your published work, and a single meeting at a conference?
Comment: _How will a reader interpret a reference letter that is based only on a familiarity of your published work_ — At least in my field, the fact that someone knows and is willing to praise your work _despite_ having no professional relationship makes the evaluation significantly more credible, and therefore more useful. For faculty hiring, letters from people with existing professional relationships are viewed with suspicion; for tenure and promotion cases, such letters are simply forbidden.
Comment: @JeffE For tenure and promotion the situation is fundamentally different; one would expect a tenure applicant to have developed a research program beyond what was done at the PhD level, and that the work of the candidate would have received enough accolades to be recognized by colleagues who are not current or recent collaborators.  I'm not sure this higher threshold is realistic for postdocs.  Asking people who do not know you well for reference letters is dangerous.
Comment: @ZeroTheHero In my subfield (theoretical computer science) the best postdoc candidates _have_ developed independent research reputations.  Of course, that can't be "beyond the PhD level"—by definition!—but that's a red herring, as is "receiving enough accolades".  The right benchmark is _whether they have done enough high-quality, high-visibility, high-impact work_ to be recognized by independent, arms-length colleagues.  The best postdoc candidates in my field most certainly have.
Comment: Yes @jeffe that's fair enough, hence it is a question for the poster to try and determine the value of such a letter in context. One concern for example is the suitability of a candidate for a teaching or supervision role. It is hard to assess someone for this based on research outputs alone.
Comment: If the position requires teaching then they will ask for a letter that specifically addresses teaching.  The research letters are not expected to address teaching.
Comment: The paragraph starting "However" is really good and important.  Graduate students usually err by asking people who know them well but are insufficiently famous, when a letter from someone more prominent (even if it had less personal detail) would be more effective (provided that person can speak to your work).
Answer: It's best for people applying for postdocs to have at least one letter from a well-known researcher in the field who is not at their school.  It is quite typical that this person has only seen you talk once or twice and has read your work.  Of course your advisor's letter will have more detail and first-hand experience, but an outside perspective on the value of your research is a valuable addition.  You should definitely ask for a letter from this professor!
Answer: You can definitely ask her for a letter of recommendation. It cannot hurt I assume.
However, considering that the person does not know you much, the letter might not have much weight in the eyes of whoever reads it.
Since there is not much to lose, ask for the letter. If you receive it, use it as you see fit. There is no guarantee whether it will help or will be useless.
Comment: Well, there is a small risk that it hurts your relationship with the acquaintance and that interviewers particular remember a let-down moment when they first see you have a recommendation from someone important but then see it's very superficial / based on low insight. I'd feel at least a bit weirded out if someone I spoke to once during a conference and maybe exchanged a mail or two asked for a reference letter. An application that includes a reference from someone famous which then turns out very weak content-wise, might also look like aiming at the stars without any substance.
Comment: So while I agree that, given a good CV otherwise, it can be an added benefit, I would see some risks as well. Also depends on the circumstances, if the position matches a lot with the discussions one had, it might come off more as, "look you want to fill a position in that area, which is exactly where this young person wants to go and has apparently some knowledge in, Research in that direction makes sense", then it's more a reference for the research proposal and less for the candidate.
Comment: @FrankHopkins: I totally agree, there is always some associated risk in any endeavor (including drinking some water ;) ). I thought I need not explain that to someone searching post-doc anything.
Answer: Most reference requests come, implicitly or explicitly, with the expectation that the referee will describe in what capacity and for how long she/he has known the candidate.  As a result, references from people you've met recently or only have passing acquaintance usually do not carry much weight.
Ask yourself how you would start a reference letter if the situation were reversed.

Dear Selection Committee,
  I write supporting the application of [candidate].  We met once at [this conference] a few weeks ago and exchanged emails afterwards.  He seems quite reasonable and full of good ideas but I've never seen him in a lab, I have no idea of his academic performance, cannot comment on how well he works in a team etc.

and how you would react receiving such a letter.
It might make a difference in a post-doc application if the position is offered by a colleague of that person, so that this person can supply a final supporting opinion to other strong reference letters.
The situation would become different if you were to have conversations with this person over an extended period of several months, were invited to her lab for some sort of visit or internship, started a project or co-applied for some grant, and generally develop your initial meeting into something much more substantive.
Comment: JeffE seems to be saying CS is similar.  What field is your advice coming from?  Have you been involved with postdoc hiring?
Comment: This is not really true of research letters in math, which aren't mostly focused on how well they know the applicant but instead on how well they know the applicant's *work*.
Comment: @NoahSnyder Yes of course and my field is physics, though I've interacted with chemists.  Words from people who don't know a candidate are cheap.  Maybe I'm reading this differently than you but whenever I am asked for a reference or I see reference letter, how well the referee knows the candidate is crucial to provide context beyond the CV.   Nobody wants to hire a bright but socially abrasive candidate.  Granted former thesis directors may have a vested interest but someone you meet at a conference would be very suspicious, and indeed people would see this as desperation.
Comment: @NoahSnyder I  will grant you that math is different, and in more than one way.
Comment: @NoahSnyder I can only claim that _theoretical_ CS is similar.  But I do claim that.
Answer: All the answers here assumed that this recommendation letter is for graduate school and if someone doesn't know you very well, its weight maybe is less than someone that know you very well such as your adviser. But, I want to look at this situation from other views, which is not very familiar for all academic people. I believe if that professor will be convinced to sign off on a recommendation letter for you, it means you have a really good scientific reputation that resulted to that someone as an independent researcher endorse your scientific work in a recommendation letter and I think it has even more weight than a recommendation letter from a dependent person (e.g. your advisor). But be cautious cause this is not the generally accepted view in routine academia specially for applying to graduate school but it may have some advantages for other purposes. This other purposes could be convincing someone outside of academia to understand your research and be convinced that it has substantial merit. But again it depends pretty much on your special purpose from getting this recommendation letter, which is not specified explicitly in your question.
Comment: _First of all, these days nobody will write a recommendation letter from scratch for someone else even your advisor._ — **This is simply false.** I write at least 20 recommendation letters every year, mostly for graduate admissions, but also for postdoc searches, faculty searches, tenure, promotions, and various awards/honors. And yes, I write them myself. This is a normal and expected part of my job. At least in US academia, any letter that smells like it was written _or even read_ by the applicant immediately poisons the application.
Comment: That's exactly opposite to my purpose... First of all, these days nobody will write a recommendation letter from scratch for someone else even your advisor. At least, it's rare I think, so people, if they accept to sign off on a letter, will tell you to prepare a draft letter and they will review it. The important point here is that if you prepared a draft for someone he or she sign it off without changing it otherwise I would not use it at all.
Comment: Only 20+ years of reading and evaluating graduate-school and faculty applications. Faculty writing recommendation letters themselves is not rare (in the US); it's completely normal, expected, common behavior (in the US).  Applicant-written letters are relatively easy to detect, and even when they're not, they tend to be badly written, because people who don't regularly _read_ recommendation letters don't know how to _write_ good recommendation letters.
Comment: _I believe if that professor will be convinced to sign off on a recommendation letter_  — If a professor merely "signed off" on a recommendation letter, that letter is almost certainly worthless.  But if you can convince a professor to **actually write** a strong recommendation letter, you're in business.
Comment: @JeffE Exactly! That's my main argument here. When I'm saying "singing off on a recommendation letter", I mean a strong recommendation letter otherwise you should put it in trash...
Comment: You missed my point: "Signing off" is not sufficient.  They must actually write the letter themselves, in their own words.
Comment: @JeffE I said: "at least, it's rare". I didn't say nobody will do that but it's rare. "At least in US academia, any letter that smells like it was written or even read by the applicant immediately poisons the application." any evidence or example?


Attending job talks when you are leaving the department

Question: I am leaving my current department in the next few weeks. We are currently in the mist of our hiring season and have 12 job talks and campus visits schedule before I leave. None of the positions we are currently trying to fill are explicitly the replacement position to mine and the areas of expertise of the candidates are pretty far removed from mine. We are a large enough department, that there will still be a reasonable sized audience and enough people for the candidates to talk to. Is it inappropriate to skip the job talks and not meet the candidates, unless they specifically ask to meet with me?
Comment: Among other things, I think it depends on why you're leaving. This depends on your department's culture of course, but if were mine: If you're leaving for a department which is obviously much stronger, or to be closer to family, or to solve a two-body problem (or any other reason which does not reflect badly on your current position), I'd be inclined to introduce yourself and freely answer any questions; if you don't much care for your department or the town in which you live, it might be good manners to absent yourself.
Answer: Impossible to answer well without knowing more and I don't think it is appropirate to post more on a public forum!
I think it really depends on your relationships with your colleagues who you are leaving behind. In some situations it is better to absent yourself from situations where people are looking forward to the future of your old department. In other situations your experience may be helpful and it may be supportive to your colleagues who you will leave, but I guess who you want to stay on good terms with and continue to support. (I have not exactly been in this situation before, but similarish ones)
Answer: You do not need to attend all 12!  If anyone questions your absences -- which I doubt they will (people may well not even notice) -- you can say you are up against some deadlines, and also mention needing time for packing and such.
Perhaps you could pick out a small handful of talks that you are sincerely interested in attending.


IDA Pro Debugging Window Closes in a Second!

Question: Starting my RE adventures with IDA Pro, I'm opening a windows .exe file in it. While debugging the file, the debugger runs fine and exits with a return 1 value:
Debugger: process has exited (exit code 1).
The problem is all this happens in a second! Before feeding the .exe to IDA Pro, I have tried to open it with double-clicking. The windows console shows itself and fades away in a glimpse; The only way I can get the .exe running with the console remaining open, is by the cmd. I guess IDA Pro debugger is simply exiting for the same reason the console fades in normal running the .exe! So I'm stuck with a .exe file running fine but I don't get the chance to debug it and monitor the flow of the program!
Answer: Seems like you did not add any breakpoints. By default no breakpoints are applied.
You can add a breakpoint on program entry (among other events) in the Debugger Options. In Debugger Options, check the box that says "Suspend on process entry point", or any of the other events available. Read more here:
https://www.hex-rays.com/products/ida/support/idadoc/1413.shtml
Alternately, you can find a line of assembly and add a breakpoint on that line and the program will break once execution reaches that instruction.
Once a breakpoint is hit, you can step over each instruction, etc.
Comment: actually the problem is not the breakpoints! The interesting part is that the debugger won't exit for specific breakpoints while it does for other ones. I didn't have the issue with Ollydbg. However, I find it much more easier to navigate through IDA Pro GUI. I have tried the events too but they basically are not worth the effort. Even when the debugger suspends and I move to the breakpoint, the debugger again exits
Comment: Does the binary have anti debugging? Maybe it works in Olly because you have plugins which hide debugging. For Ida look into Ida stealth, Scylla Hide, or Titan hide. Probably others but these are the plugins which I know of that can help you get by anti debugging.
Answer: Are you opening a 32 or 64 bit .exe (cannot add this as a comment due to no enough reputation points)? If you are opening on 64 bit file with a 32 bit instance of IDA, you may encounter issues. If you're using the free version,there are limitations on what can be opened as stated here: https://www.hex-rays.com/products/ida/support/download_freeware.shtml
This question is similar to this other posting: IDA cannot launch debugger for 64-bit exe files
Comment: I tried another .exe which prompted for an input. Since the console remains open for an input, the debugger also won't exit when you open the .exe in IDA Pro. So, I guess it's initially a matter of the .exe file itself.
Answer: So I went through the assembly and found an exit subroutine. Evidently the debugger used to exit once reaching the command. I simply avoided the exit section since all that was supposed to occur, happened before the exit command.


Hello! Can someone please translate: 'My Little Ghost' to Chinese?

Question: I'm creating a story with this title and the setting I'm supposed to have is in ancient China. It would be helpful if you can show me how it is spelled and if the translated version sounds more like an endearment from an older boy to a younger boy. Thank you!
Comment: 我之小鬼, as far as sounding like an endearment from an older boy to one younger, i don't even think the English form firs that description
Comment: Quote:- "...an endearment from an older boy to a younger boy ".  小鬼" is suitable only if the younger boy, in your story, is "naughty, crafty, mischievous", like, for example, constantly playing pranks.
Answer:
My Little Ghost: 我的小鬼:
Wǒ de xiǎoguǐ
Answer: Since your story background is in ancient China, expressions such as 我的小鬼 seems to be inappropriate.
If you're considering making the story in Classical Chinese, the following words may be helpful:

Calling a younger brother: When both are young, the older can call the younger by his nickname/infant name; When grown up, the older should call his younger brother by Zi (a certain nickname used to refer to someone respectfully).
Offensive expressions used for cursing: 竖子, 小子, etc.

If you still want to use modern Chinese, you can simply use:

弟弟, 老弟, 小屁孩 (contemptuous/joking)

I finished this in a hurry so I didn't have time to provide the words' pronunciations. Type those words in Google Translate and you'll get corresponding Pinyins, mostly accurate.
Answer: 小鬼 is used to refer to little kids.
There is a phrase:
人小鬼大
literally: small person big demon
mischievous (and clever) kid
Maybe you could use:
亲爱的小幽灵
dear little ghostie


Best knives that don't need regular sharpening

Question: I'm looking for a knife that doesn't need to be regularly sharpened. The knife is for someone who has damaged wrists, and they find it difficult to have to continuously sharpen their knife.
Comment: Hello Joey, choosing knives that don't dull easily is a good question. Unfortunately, we don't do brand recommendations here, basically if we did, everyone voting would need direct knowledge about the relative quality of all mentioned brands, and that's not the case, so the voting tends to reflect how widespread a brand is rather than its quality. So the question will have to be about getting generic answers on which features to look for, but you will have to pick your own brand.
Answer: Ceramic knives will hold their edge 'forever', but are brittle. As long as they don't fall, they should be fine.
I googled "ergonomic ceramic knife" and a number of items popped up.
Answer: IF ceramic and/or serrated knives do not work as a solution, here are the points for choosing a steel knife that will need less frequent sharpening.
A good starting point is choosing a knife made from a relatively hard (60-62 HRC) AND high wear resistance steel - VG-10 (not bargain basement grade VG-10 though: there seems to be much that can go wrong in making a knife from that steel), or Aritsugu's A-type steel, are well known to be good choices for that purpose.
The key is who eventually sharpens it (can be another person, maybe a professional) has to sharpen it properly - no wire edge. no overheating. intelligent choice of sharpening angles to match knife and user. advising the user on what to do and do not do with it.
Also, sharpening it when it is new can be advisable: Very few knives come with an optimal edge when they are new.
Alternatively, a knife that integrates well with a sharpening aid made or endorsed by the same manufacturer (Wusthof and Global do offer such) could work - the sharpening by these devices is not ideal but acceptable for some.
Answer: Don't believe the marketing - any knife will dull after some use.
But... You don't need to sharpen knives every time! You don't need to shave with your cooking knives. For real cooking work to be done it's enough just to hone (to fine the cutting edge) with sharpening steel. Look at https://www.youtube.com/watch?v=Nd7r-3RGpJA
And best of all: 3-5 strokes is enough.
Answer: For the average knife and user, stay away from "high carbon steel," as they tend to need sharpening and "touching up" relatively more frequently.  Standard stainless steel tends to be relatively more brittle.  A blade made from what used to be called "chromalloy" (chromium/molybdenum/vanadium steel) is most likely your best option, holding an edge better than high carbon steel and being less brittle than stainless.
What will the knife be used for?  Cooking/prep work?  Self defense?  Daily carry?  Hunting?  All need to factor into blade choice.
One parting observation: Use of a ceramic "steele" to touch up the blade might be a better choice if the user has limited mobility.  Just use a lighter touch than with a steel Steele.
Just my $0.02
Answer: As others have pointed out, harder steels will be better at holding an edge, as will ceramic knives. May I suggest though: let the knive be sharpened by a professional? Most week markets or similar have a "knife guy" who will sharpen your knives for a few dollars/euros a piece. And you don't need to do this every month. Every quarter of half year is probably way more than a home cook would need. Inbetween, use a honing rod to keep the edge sharp.
Answer: For more than 30 years I have made forged stainless steel knives that hold an edge far longer than other stainless knives and will out-cut carbon steel knives forged or otherwise, and sharpen easily. Of course knife manufacturers and knife makers have tried to keep this information hidden, gee I wonder why? They're not cheap, not made in china. But in the words of many o my customers, "Worth every penny." I have published my edge testing results on my website- seanmcwilliamsforge.com and yes, I do make kitchen knives.
Comment: I'd hesitate to flag this as spam, as the affiliation is clearly stated, but it does feel a bit too much of an advert, especially as a first post from a new member.


Is there a theory of computation that takes failure and decay of the computation substrate into account?

Question: There are obvious differences between a Turing machine and a real computer. Not only is the latter finite in size, it is also prone to failures and it is made from decaying matter. The kind of framework I have in mind is this (but please excuse the handwavy vagueness): In some sense, (quasi)particles that constitute matter can be thought to perform computation: They have state that persists at least for some time (properties such as position, spin, charge, momentum) and they can change their state in feedback loops by interacting with other particles. The more elementary particles locally affect each other, the more complex the state and feedback loops can be. What kinds of computation we can perform on such a substrate depends on the configurations and rules that govern the particles, in particular, how many feedback loops they allow to simultaneously affect a local arrangement of particles. In this sense I'm looking for a framework that is analogous to the Chomsky hierarchy, i.e. in which the complexity of the system is successively extended to eventually build up to a notion of general computation. Is there something similar to this in the literature?
Comment: A Turing machine is finite in size, but its size is potentially unbounded. At no point in the execution of a Turing machine is an actual infinite tape needed – when people say that a Turing machine is equiped with an infinite tape that is a bit sloppy: it actually needs a finite but arbitrarily extensible tape. A bit like when you buy a new hard disk when you run out of space.
Comment: See also http://cstheory.stackexchange.com/questions/4565/what-is-known-about-the-effectiveness-of-reliable-computing and http://cstheory.stackexchange.com/questions/17914/does-a-noisy-version-of-conways-game-of-life-support-universal-computation/18213#18213. You might be interested in studying how cellular automata can withstand noise (http://dl.acm.org/citation.cfm?id=808730, http://link.springer.com/article/10.1023/A:1004823720305).
Comment: tricky question but try [spintronics](https://en.wikipedia.org/wiki/Spintronics) which encompasses QM computing and more (eg error correction in QM computing which has much research). but note most CS research is the opposite, a noiseless model is assumed, and a lot of very advanced engineering/ technology goes into "correcting/ rejecting noise". one other area to look in is the influence/ measureable/ quantifiable effect of cosmic rays on RAM and hamming codes used to correct it in high-reliability memory systems.
Answer: I'm not 100% sure what the question is about, but the title seems to ask about computation that allows failure. There is a lot of work on noisy (erroneous) computation in the sense that I think you are asking about. I don't have time to give a complete overview, but here are some pointers that may be of interest.

Distributed systems. This is probably by far the most developed field because the very definition of a distributed system is based on the possibility of (partial) faults. There are elaborate theories of DS depending on the chosen fault model, e.g. fail/stop or byzantine failure. See also the work on failure detectors.
Cryptography. This may seem a bit bizarre, but I think much of the field of cryptography can be seen as a form of extreme failure, with the adversary trying to undermine (in a general sense) the working of the system. You can think of the usual polynomially bound attacker as an case of failure model. This lead to things like secure multi-party computation as an algorithmic tool in the face of extreme adversity.
π-calculus: see (1) for a generalisation of Shannon-style information theory to interacting processes. I think the error model in (1) is unrealistic, because it does not cater for the situation where an error converts a free into a bound name or vice versa.
Turing machines: see (2, 3, 4).
Cellular automata: various researchers have added failure models, sorry no references at the moment, maybe look at work by  P. Gacs.
λ-calculus: see (6).
Assembly language: see (5, 7).
Quantum computation: is all about error correction, I'm not qualified to say more on this.
An increasingly important subfield of computation is the use of probabilistic process calculi to model chemical reactions. Have a look at Luca Cardelli's recent work.

Note also that this line of thinking is very old: J. von Neumann wrote about this in 1956 [8]. Maybe even more impressive C.-A. Petri invented Petri-nets in August 1939 at the age of 13 for the purpose of describing chemical processes.

M. Ying, Pi-Calculus With Noisy Channels.
I. Capuni, P. Gacs, A Turing Machine Resisting Isolated Bursts Of Faults.
I. Capuni, Fault-tolerant Turing Machine.
E. Asarin, P. Collins, Noisy Turing Machines.
J. Chang, G. A. Reis, D. I. August, Automatic Instruction-Level Software-Only Recovery.
D. Walker, L. Mackey, J. Ligatti, G. A. Reis, D. I. August, Static Typing for a Faulty Lambda Calculus.
F. Perry, L. Mackey, G. Reis, J. Ligatti, D. I. August, D. Walker, Fault-tolerant Typed Assembly Language.
J. von Neumann, Lectures on Probabilistic Logics and the Synthesis of Reliable Organisms From Unreliable Components.
Comment: "**Quantum computation**: is all about error correction, I'm not qualified to say more on this." If you are not qualified to say more (or provide references), then it seems a bit misplaced in your list. For all other items, you provided at least references. I guess error correction in QC is more comparable to noisy Turing machines than to byzantine failure, i.e. classical computation can guard itself even against extremely adversarial fault scenarios (in theory), while QC can at least deal well with unavoidable noise and imperfections (in theory).
Comment: I think the techniques available in fault tolerant quantum computation basically allow you to correct any type of error that you can treat classically. If you care about adversaries that is a whole different story, but I do not see why we need to consider adversaries in the OP's question.
Comment: This week I am overworked but if no one has expanded on that comment in about a week I can try to write an answer about quantum computing.
Answer: Rabie introduced the model of "Rusted Turing Machines" in his thesis: The Power of Weaknesses:What can be computed with Populations, Protocols and Machines (Chapter 7).
The idea is that there is a restriction on the number of time the TM can change its internal state because of decay. Rabie introduced the class $Piv(f(n))$, the class of Turing Machines that change their internal state $O(f(n))$ times. An RTM is then an element of $Piv(1)$.
In this model, Rabie

gave some results on different languages that can be computed;
showed that he halting problem of RTM is decidable;
provided upper bound for the busy beaver problem with RTM.
Answer: the question is challenging in its broadness & disclaimer of vagueness however some areas of research can be cited that impinge on it. roughly the 1st half of the question is about unreliable models of computation and the 2nd half is asking about a "hierarchy" built out of such unreliable systems.
a general trend in CS and computer engineering is that "noise is the enemy" and many auxiliary systems are built to reduce/ minimize/ suppress it, even with new models of computation eg quantum computing. the theme that "reliable systems can be built out of unreliable ones" via many techniques is a broad theme in CS & its related engineering. so a "hierarchy" does indeed exist in the sense that larger systems are built out of subsystems but the general idea is to remove noise/ error in the subsystems.

spintronics (eg found in recent Nature articles) is a new general term and area of investigation given for harnessing sub-electronic effects such as electron spin for computation, and also encompasses quantum computation. electron spins are extremely delicate to manipulate, nearly an analog phenomenon, and subject to the Heisenberg uncertainty principle in measurement. by the way one of the leading systems for minimizing noise in QM computation cited by experts is the Martinis lab approaches, recently acquired by Google & published in Nature: State preservation by repetitive error detection in a superconducting quantum circuit, Kelly et al
error correction in RAM has been used for many decades. it was discovered that some chip packaging was slightly radioactive and caused RAM to be unreliable by altering bits (aka, literally, as asked, "decay"). Hamming codes were used to correct this (in one of the early applications of them). some fraction of the RAM is dedicated to the error correction. this can be seen as a sort of hierarchy where the low-level RAM is unreliable but the overall system/ abstraction improves reliability to a high degree. the same technique is used in modern Flash memory. survey/ refs can be found in this paper: Error correction in Flash memory / Worley
TCP/IP and many other network protocols are an example where noisy subsystems are "fixed" with error correction. packets have "checksums" and are rebroadcast if consistency errors are detected by the receiver. the so-called network protocol "stack" is also a hierarchy-like construction.


When a source node sends a packet to a unicast destination, what will be the entry in the frame destination address(layer2 mac address)?

Question: When a source node sends a packet to  a unicast destination, what will be the entry in the frame destination address(layer2 mac address)? will it be default router's mac address?
Comment: possible duplicate of [ping reply arp table](http://networkengineering.stackexchange.com/questions/16013/ping-reply-arp-table)
Comment: Did any answer help you? if so, you should accept the answer so that the question doesn't keep popping up forever, looking for an answer. Alternatively, you could provide and accept your own answer.
Answer: It's depends whether the destination is within the subnet or not. If it's within the subnet, it'll put the destination device's MAC itself (assuming ARP has already done it's job). If the device is outside the network, then packet will be forwarded to the default gateway, hence, the MAC address of the default gateway.
Comment: This is not completely correct. This router does not need to be the default gateway, it's the next hop towards the destination. Also, due to asymmetric routing the router delivering the packet to the destination doesn't need to be the best router towards the original source. So to be precise: it's the MAC address of the router delivering the packet to the destination.
Comment: The term 'default' is incorrect here. A host needs a next-hop for the networks it needs to reach, a default gateway to connect to the entire internet is not required. Also, a host can have multiple routes via various routers.
Comment: Hi, I just re-checked the post from my computer and I am confused about what you just said.
Could you please elaborate this statement?
**This router does not need to be the default gateway, it's the next hop towards the destination.**

As far as I know, a host NEEDS to have a default gateway to communicate outside its network.
Answer: When a node wants to send a packet it will look up the destination address in it's routing table. Based on that table it will determine the IP address and interface for the next hop. If the destination is on one of the local subnets then the next hop IP address will simply be the destination. Otherwise it will be the IP address of a router (most likely the default gateway).
The MAC address (if applicable) for the next hop IP address will be determined by arp (for IPv4) or neighbour discovery (for IPv6)


Scientists who made a mark in the world despite their disabilities

Question: Stephen Hawking is a famous scientist who despite being disabled made a big contribution to the scientific world. I want to know other such scientists who have a big influence on us.
Comment: I don't know if he qualifies as a big scientist but I'm gonna say Burkhard Heim, blind, death and with no hands.
Answer: Leonard Euler, whom many consider the greatest mathematician of all times, and also the most prolific one, was partially or completely blind during most of his career. His sight began to deteriorate at the age of 31 and he lost his sight completely at 59. He died at 76 and continued to work hard until his death.
(At the age of 68 he published a paper every week in the average!)
Some other famous mathematicians who were blind were:
Lev Pontryagin (from his childhood, as a result of an accident).
Anatoli Vitushkin (from his youth, as a result of an accident).
Mathematician Andre Bloch can be probably also considered as handicapped: he spent all his mathematical career in a mental asylum (after having murdered several people). His mental disorder was apparently the result of severe wound during WWI. (This was the reason of confining him rather than executing).
Another mathematician who was severely wounded in WWI was Gaston Julia (he lost his nose).
Answer: I am not sure if you count pure mathematics as having a big influence on you, but Solomon Lefschetz did a lot of important work after he lost both his hands in an accident. See also this question.
Answer: These are some of the scientists whom I know about:

Thomas Edison
Thomas Alva Edison, an American inventor and businessman, has been described as America's greatest inventor. A bout of scarlet fever as a youth had left him almost entirely deaf in both ears.

Temple Grandin
Animal behaviourist and autism activist Grandin was diagnosed with autism as a child. Grandin's work on animal behaviour has been cited as an inspiration for multiple changes to the livestock industry, including how animals are cared for at meat processing plants.

Gustav Kirchoff
Physicist Kirchhoff's work in the 1800s is still relevant to our understanding of electricity today. He made headway into the still-young field despite an unknown disability that restricted his movement to a wheelchair or crutches for most of his life.

Edwin Krebs
Krebs was hearing-impaired but made a sensational discovery in the 1950s about cellular activity in the human body that led to greater understanding about hormones, cell life spans, and even how the body can reject transplanted organs. He won the 1992 Nobel Prize for medicine for this commendable feat.
Comment: While I can see that the OP's question is not well-stated,  I don't think these examples are particularly relevant.   Partial deafness, for example,  has no effect on someone's ability to research biology (or for that matter, to compose a great 9th Symphony).   Grandin's condition actually **helped** her understand animals.


RHEL 7, GNOME shell - decrease desktop icon size

Question: Question: I recently installed RHEL 7.2 and.. the icons on the desktop are HUGE. How can I decrease their size?
Answer: Run this in a terminal :
gsettings set org.gnome.nautilus.icon-view default-zoom-level small

Comment: Additionally, on Centos 7 (the current release 7.4.1708 while typing this comment), this gives the list of all icon size options: `gsettings range org.gnome.nautilus.icon-view default-zoom-level`.
Answer:
Just go to "dconf-editor", then org -> gnome -> nautilus -> icon-view, and set the default-zoom-level small
Comment: Also note that nautilus now has this option built in
Answer: One more way how to change the size of desktop icons is directly from Nautilus:

Open nautilus
change the way of displayed icons to icon view NOT detailed view!
zoom icons using Ctrl + mouse wheel

While zooming the icon view the icons are changed on the desktop at the same time.
Zooming is not reflected while using detailed view!
Edit: If you're on a laptop without scroll wheel, use Ctrl + +, or Ctrl + -, to increase or decrease icon size.
Comment: This answer is highly useful - especially because it shows how "accidentally" the icons on the desktop got too big in the first place. It's not that uncommon to change the icon-size in Nautilus (especially since for some file-types Nautilus shows a preview) and if the desktop was not visible at the same time, one would never realise why or when it changed.
Comment: the most simple solution here.
Answer: Going below 48px requires changing the Nautilus source code and recompiling. (Yes, they hard-coded icons sizes.)
**** INSTRUCTIONS FOR NAUTILUS 3.20.4 ON UBUNTU-GNOME 17.04 ****

Install the following dependencies:

libgd-dev
autotools-dev
libexif-dev
libexempi-dev
libselinux1-dev
libtracker-sparql-1.0-dev
libext-dev
libxml2-dev
libgnome-desktop-3-dev

Each one installs a bunch of other stuff, so hopefully I've given you the correct parent package name. I apologize for not recalling with 100% accuracy exactly what I installed, but this looks fairly correct to me immediately after my install. (Notify me if I'm inaccurate anywhere.)

Download the version of Nautilus that you are currently using from the Nautilus snapshots website. To find that out, run nautilus --version from the terminal. After downloading the archive, unzip it to whatever directory you want to work from.
From within the unzipped package, open the file nautilus-icon-info.h. Within the first several lines you will see various sizes designated for the particular scroll-setting options. For instance, within the file for version 3.20.4 the icon sizes start on line 36. Change each of those levels to whatever you want to use so that you can make the icons much smaller (or larger).
After editing and saving the file, it's time to configure, compile, and install. Run the following commands from the terminal from within the base directory of the version of nautilus that you have downloaded and unzipped. Make sure that you are within the base of the folder structure of the nautilus directories!
./configure
make
sudo make install

This can be run altogether with the command ./configure && make && make install.
If the ./configure command fails, it's because you are missing some other dependencies. I apologize if my list of dependencies above was incomplete. Google (or whatever search engine you want) to find what package it is that you need. You can use Synaptic to search for what you need if you're unsure even after Googling.
Once installed, I suggest a reboot just to make sure that every single thing is reloaded properly. You can now tweak with your icon sizes as you wish.
Have fun!
Answer: This solution was design to address the issue in rhel 7.4 but might also be relevent here.
There seem to be a design decision regarding icons size acroding to this link. but that looks to me like a bug: https://bugzilla.redhat.com/show_bug.cgi?id=1478153
there is also a solution sugested here: https://access.redhat.com/solutions/3138541
But eventually what i did to address this is as followed:
sed -i '/default-zoom-level/{n; s/large/standard/} '  /usr/share/glib-2.0/schemas/org.gnome.nautilus.gschema.xml && glib-compile-schemas /usr/share/glib-2.0/schemas/ >/dev/null 2>&1


How many Matrixes were there?

Question: In this scene

 of The Matrix Agent Smith tells Morpheus that there were multiple Matrixes, the first one being "perfect". There is reference to this throughout the trilogy and in the Animatrix and it is revealed that there was more than one "failed Matrix". So how many Matrixes were there? I'm aware that an exact number probably isn't divulged but what conclusion can we draw from the evidence given?
Comment: Actually to me "Matrixes" *feels* wrong.
Comment: Am I alone in thinking it should be "Matrixes" unless we're on [Math SE](http://math.stackexchange.com/)? I realise both are acceptable plural forms but it just *feels* wrong.
Comment: Possible dupe of ["Is there good evidence for the Nightmare Matrix?"](http://scifi.stackexchange.com/questions/95790/is-there-good-canon-evidence-for-the-nightmare-matrix?s=1|2.2424)
Comment: @Lilienthal:   You're right.   Using 'Matrices' as the plural for a proper noun without any evidence that's the proper plural, and when 'matrixes' and 'matrices' are both correct for the general usage, isn't right.    This is like assuming that someone likes to use the plural '-men' for their last name ending in '-man'.   It could be whatever the designee says it is, but you wouldn't assume it without having some canon basis.
Comment: @JimConant:   What's the plural of the mutant [Cycplos](https://en.wikipedia.org/wiki/Cyclops_(comics))?   Obviously it is either *Cyclops* or *Cyclopses*, not [*Cyclopes*](http://www.oxforddictionaries.com/us/definition/american_english/cyclops)
Comment: At least three, A "paradise" matrix, a "nightmare" matrix and the Matrix we see.
Comment: Should that be "matrices"?
Comment: Considering what @ThePopMachine said I will change it to Matrixes.
Answer: There were the two Beta Matrixes and then Neo lives in the 6th cycle of the Matrix 1.0.
Now it depends if you count those as one Matrix or as 6, making the answer either 3 or 8.

The Architect explains that, in addition to two unstable versions of
  the Matrix, there have been five iterations, or cycles, of the Matrix.
  In each stable iteration, an incarnation of The One has appeared. Neo
  is the sixth One to appear in this sixth Matrix iteration.

Matrix Wiki
Comment: I'd count them as one; they were 6 iterations within a living cycle of a single system. If a server crashes and reboots, is that a new system or the same one?
Comment: The Matrix is the software not the hardware and it was redone like from paradise to nightmare just with really small changes so the question is more like you change from xp to win 7 then to win 8 and then you go for win 8.1. For some that counts as a new OS for some it doesn´t, it is still worth noting in any way though.
Answer: Three. Or four including the pre-Matrix beta
We know about the Pre-Matrix Beta 1:

After the Machine war ended, the remaining surviving humans were taken to be studied and plugged into an initial first power plant matrix without their awareness of being plugged into that matrix.

Which was followed by the Paradise Matrix:

The Paradise Matrix was the first prototype Matrix, which was designed by The Architect to control humanity by putting their minds into a constructed virtual reality. Unlike later versions, it simulated a perfect world with no suffering to try to pacify their minds, but the human minds did not accept this version. Many of those connected died, and a Nightmare Matrix was designed in its place that tried to correct its flaws.

Which was followed by the Nightmare Matrix:

The Nightmare Matrix was the second prototype Matrix, designed by The Architect after the massive failure of the Paradise Matrix in the hope that human minds would more readily accept an imperfect world with suffering. Unlike the first version, this Matrix instituted a basic cause-and-effect programming and forcibly made those connected to it accept the program.

And finally the Modern Matrix, which is the one we see in the movies:

The solution was ultimately stumbled upon by an intuitive program, originally intended to study aspects of the human psyche: The Oracle. She discovered that if humans were given a choice, even at a subconscious level, to accept the reality of the world around them, ninety-nine percent of humans would accept the virtual world.
Comment: Or five, if we include the one we're currently in... dun dun dunnnnnn
Comment: Why that few? Those are just _kinds_ of matrix. There could be more than one Modern Matrix or Paradise Matrix running side by side, each with subtle differences in order to test and improve for future iterations, and in order to support more than 7 billion-ish human batteries at a time. "Endless fields" could provide for enough hosts to populate multiple simultaneous matrices.
Comment: @JoelCoehoorn, these are just the ones explicitly mentioned. Personally, I'd say that there certainly has to be far more. Surely the machines would want to also to experiment with other ideas on the side. After all, the modern matrix is rather flawed and has room for improvement. And of course, there's the whole thing that you described. Presumably that if they want to use humans as batteries, they're going to reproduce humans like mad, yet the matrix has a limited population if they don't want to rewrite history.

How many Matrixes were there?


Android Google map to provide alternative route

Question: Google Map web version can provide 3 alternative routes when routing directions. However, it seems Android Google map can only provide 1 route and have no option to choose alternative routes. Is there any way to get the alternative routes?
Answer: To see alternate routes, you need to use Navigation as opposed to Maps.
If you already have Maps open, click the blue arrowhead in the upper right to switch to Navigation, then click the context button on your phone, then select Route Info, then click the third button to the right along the bottom which will have both a dashed and solid line going to a map pin.  Alternate routes will appear, and you can select them along the top of the route info map.
Answer: I have observed that in navigation mode the routes displayed are from the current location and not between the two locations selected.


An averages problem

Question: The average salary of the workers in a workshop is RS.8500. If the average monthly salary of 7 technicians is RS 10000 and the average monthly salary of the rest is RS 7800. Then the total number of the workers in the workshop is?
Answer: What do we know?

We know that $\dfrac{\text{Total salary earned}}{\text{number of workers}} = 8500$.
And we know that $\dfrac{\text{salary earned by technicians}}{7 = \{\text{the number of tecnhicias} \}} = 10000$.
Finally, we know that $\dfrac{\text{salary earned by workers besides the technicians}}{\text{number of workers}-\text{number of technicians}} = 7800$.

From 2. we know the total salary earned by the technicians. We can use this to combine 1. and 3. into a system of equations with two unknowns: the total salary earned and the total number of workers.
Can you handle it from there?
Answer: Let $n$ be the number of workers among the "rest."  Then the total number of workers is $n+7$.
The overall average wage is is $8500$. So the total wage bill for all the workers is
$$(8500)(n+7).\tag{$1$}$$
We find the total wage bill in another way. The $n$ "other" workers between them earn $(7800)(n)$. The $7$ technicians between them earn $(10000)(7)$.  So the total wage bill is
$$(7800)(n)+(10000)(7).\tag{$2$}$$
The two expressions $(1)$ and $(2)$ for the total wage bill must give equal results. From this you should be able to get a nice linear equation, which is not difficult to solve for $n$.
Remark: There is a more informal way to solve the problem. It substitutes thinking for the algebra. The $7$ technicians each earn $1500$ more than the average salary of $8500$.  So between them, they get a total of $(1500)(7)$ more than they would if they got average salary.
This $(1500)(7)$ must come out of the hides of the poor "other workers," whose individual earnings are $700$ below average. So each of the poor other workers contributes $700$ to the wealth of the technicians. Since the total contribution is $(1500)(7)$, the number of "other workers" must be
$$\frac{(1500)(7)}{700}.$$
That is more or less how this type of problem was solved before "algebra" came into widespread use. People learned "rules" to partly automate the process, and bypass thinking.
Answer: Let $n$ represents the total number of workers. Total salary of $n$ workers=$8500n$.$$$$ Total Salary of $7$ technicians $=70000$ and total salary of the rest $n-7$ workers $=7800(n-7)$ $$\implies 70000+7800(n-7)=8500n$$ $$\implies 70000-7800*7=(8500-7800)n$$ $$\implies 15400=700n$$ $$\implies n=22$$ Thus, total number of workers $=22.$

An averages problem


What is the significance of Sauron never having a physical presence in the Lord of the Rings?

Question: So I noticed that in Lord of the Rings Sauron acts as a very interesting villain. He never makes a corporeal appearance, nor does he have any acting dialogue. He's mentioned plenty of times through other characters, history, and lore, but never makes an appearance himself. I know the canon mythology is that Sauron doesn't have a physical body from his rebirth, but what is significant about that?
Comment: Wild guess, probably not true but would be awesome: someone at an Inklings gathering claimed that any main antagonist must always appear onstage in the story, and Tolkien was like "challenge accepted".
Comment: If I recall correctly, Gollum comments that Sauron is missing a finger, and I think that Gollum had been taken as a prisoner into Sauron's presence.
Comment: Slush book is not an expression I had encountered before.
Comment: Indeed,  if he didn't have physical body he wouldn't be back - that's pretty much the point - as long as maia doesn't have material body they can't do anything.
Comment: I seem to recall from the slush books that each time he was defeated and returned he had less power. After the fall of Númenor, he was still powerful, but diminished to the point where he could no longer hold a physical form.
Comment: @mikado You have a "slush file," which is where you keep all the bits you aren't using just in case you might have a need for them later. JRR Tolkien had a file cabinet full of these, plus early drafts which were handwritten, later typewritten, hand-edited, etc. His son Christopher assembled all this unused and mid-edit material into 12 books which are the history of the creation of Middle-Earth. I use the term "slush books" loosely, but that's what they are: books made of the unused or edited material, slush.
Answer: Tolkien never explained the choice to leave Sauron off-stage, or at least he did not do so in the published letters. But I can see three ways in which the decision makes sense.
First, The Lord of the Rings is written largely from the down-to-earth point of view of the hobbit characters, a narrative strategy that Tolkien recognized was necessary to reach a large audience. Discussing the possible publication of the Silmarillion, he wrote:

But I am afraid that all the matter of the First and Second Ages is very 'high-mythical' or Elvish and heroic, and there is no 'hobbitry' at all: an ingredient that seems to have made the present mixture [that is, The Lord of the Rings] more generally palatable.
J. R. R. Tolkien (1955). Letter to Lord Halsbury. Number 174 in Humphrey Carpenter, ed. (1981). The Letters of J. R. R. Tolkien. London: George Allen & Unwin.

It would have been difficult for Tolkien to reconcile the rural-comical tone of 'hobbitry' with the representation of a mythic figure like Sauron. For an example of how this could have gone wrong, consider the one scene of Sauron's dialogue that made it into the novel. For although the question says that he does not "have any acting dialogue", this is not quite true. Pippin speaks with him using the Palantir of Orthanc, and reports the conversation thus:

'"So you have come back? Why have you neglected to report for so long?"
'I did not answer. He said: "Who are you?" I still did not answer, but it hurt me horribly; and he pressed me, so I said: "A hobbit."
'Then suddenly he seemed to see me, and he laughed at me. It was cruel. It was like being stabbed with knives. I struggled. But he said: "Wait a moment! We shall meet again soon. Tell Saruman that this dainty is not for him. I will send for it at once. Do you understand? Say just that!"
J. R. R. Tolkien (1954). The Lord of the Rings: The Two Towers III.11. London: George Allen & Unwin.

In this passage, Sauron is at risk of coming across as a pantomime villain rather than a mythic figure of evil, and it was surely a wise decision to include no more of his dialogue than this.
Second, the distance of Sauron from the events of the narrative conforms to the pattern of military leadership in The Lord of the Rings. The captains whom Tolkien approves (Aragorn, Theoden) have a heroic style of leadership, fighting in the first rank of battle and inspiring their armies with their personal bravery; while the captains whom Tolkien disapproves (Sauron, Saruman, Denethor) have a modern style of leadership, directing strategy from a safe distance in their fortresses. Denethor draws our attention to this in a conversation with Pippin:

'Not—the Dark Lord?' cried Pippin, forgetting his place in his terror.
Denethor laughed bitterly. 'Nay, not yet, Master Peregrin! He will not come save only to triumph over me when all is won. He uses others as his weapons. So do all great lords, if they are wise, Master Halfling. Or why should I sit here in my tower and think, and watch, and wait, spending even my sons? For I can still wield a brand.'
J. R. R. Tolkien (1955). The Lord of the Rings: The Return of the King V.4. London: George Allen & Unwin.

This is one of several passages in which Tolkien uses the word 'wise' ironically to describe conduct so prudent as to become self-defeating. Saruman says that "it would be wise" (II.2) for Gandalf to join him in an alliance with Sauron; Gandalf describes Sauron as a "wise fool" (III.5) for thinking that his enemies are "seeking to cast him down and take his place"; and Saruman's enchanted voice "seemed wise and reasonable" (III.10).
The image of Denethor sitting in his tower and "spending even his sons" ought to remind us of the situation on the Western Front of World War I. Tolkien had fought at Thiepval Ridge on the Somme in September 1916, while General Haig directed the battle from the Château de Beaurepaire near Montreuil-sur-Mer, a hundred kilometres away.
Third, the physical absence of Sauron corresponds to the way that evil is conceptualized in The Lord of the Rings. In Tolkien's world, goodness corresponds to light, and evil flourishes in darkness. Evil beings are hidden from the world in underground lairs: barrow-wights in the barrow-downs; the Balrog in Moria, Shelob in Torech Ungol. Sauron's army advances under the darkness of "a great cloud [that] streamed slowly westward from the Black Land, devouring light" (V.4), and the turning point of the siege of Gondor is when a wind blows the cloud away "and the darkness was removed" (V.5).
Tolkien described the power of the Nazgûl as presiding in the fear of their victims, which is magnified in darkness:

Their peril is almost entirely due to the unreasoning fear which they inspire (like ghosts). They have no great physical power against the fearless; but what they have, and the fear that they inspire, is enormously increased in darkness.
J. R. R. Tolkien (1958). Letter to Forrest J. Ackerman. Number 210 in Carpenter (1981).

It is well known that the most frightening monsters in movies are those that are not shown in detail: nothing that the special-effects department can contrive is as fearsome as the viewer's own imagination. Thus, Sauron's threat would be diminished if he were brought into the light of the narrative.
Comment: 1) Listing Denethor with Sauron and Saruman as "bad captains" seems a mite unfair. He was overly proud, and flew entirely off the handle near the end, but Gondor was almost single-handedly holding back the dark for a long time, sitting on the western border of Mordor while others ignored the danger. 2) "spending even my sons" - I'd never thought of that in terms of WWI, but wow, it [works really well](https://www.poets.org/poetsorg/poem/parable-old-man-and-young). 3) Very good point in the last paragraph; I wrote about this at more length [here](https://literature.stackexchange.com/a/6170/17).
Comment: Wow. This is such a good answer. I'm going to wait a little bit before accepting and awarding the bounty. Thank you!


How to collaborate on a document without SharePoint?

Question: Five of us are working on a proposal together in Microsoft Word. Unfortunately, we don't have SharePoint at work. Is there another (better) way to contribute to the content than incessantly emailing Microsoft Word documents back and forth? We are sick of dealing with versioning problems! Help!!
Answer: You could use Microsoft SharePoint Workspace, previously known as Microsoft Office Groove.
It is a desktop application designed for document collaboration in teams with members who are regularly off-line or who do not share the same network security clearance.
It does not provide you with SharePoint like versioning but it is still very nice collaboration tool. It does not require SharePoint or any other server to be installed*. It is part of Microsoft Office 2010 Professional Plus suite.
Learn more: Official Site | Wikipedia.
Note: * For some advanced stuff you will need a server but I do not think you have such a case.
Answer: You can synchronise a document library with Microsoft Outlook.
With this, everytime you hook up to the network, Outlook will synchronise the documents from the library to your computer. When you go offline, you can work on the documents, and your changes are uploaded back to the library when you reconnect.
You probably will get conflict issues, so break the document down into smallest sections possible, and use a master document to string them all together.
Link
http://office.microsoft.com/en-us/word-help/create-a-master-document-and-subdocuments-HP005187002.aspx
Answer: It is possible to do some collaboration using Office Live.  While this is mostly used for individuals, I have seen some small teams use it with success.
Answer: Also notice that Windows SharePoint Services 3.0 and the new SharePoint 2010 Foundation is free. Those editions include alot of functionality for team work, like the Team Site template.
Download SharePoint 2010 Foundation here
Answer: There are some of third party tools out there that let's you collaborate directly in Word.
DocVerse (non-free www.docverse.com ) and CodoxWord (free www.codoxware.com ) are two of them that comes to mind. I'm not sure if you can get DocVerse now they are being bought by GOOG.
In comparison to SharePoint, these tools often let you work in the same document WITHOUT having to break up the document into a Master and subsections (which is the cause of some major versioning woes).  DocVerse tracks the changes you and your collaborators make in a way similar to Word's Track Change feature, though you will need to manually merge the changes together. CodoxWord will actually merge the changes for you automatically like in Google Docs, so for us that was a BIG plus. Both of these tools have their own document sharing services. CodoxWord has a way of letting you share a document directly with people without uploading it, if security or confidentiality is an issue for you (as it was for us).
We also use SharePoint at work, but only as a way of hosting documents. We check out the document from SharePoint and use CodoxWord to do the collaborative authoring part, then check the document back into SharePoint.
Hope this helps.


Is it possible to learn a language just by being exposed to media and books?

Question: Say I want to learn to speak Chinese.
Could it be possible to learn Chinese just by watching subtitled Chinese movies/tv and reading books made for children?
Comment: What do you mean by "learn"? Ability to comprehend? It is possible. Ability to converse? More difficult. What is your intention?
Comment: Possibly change the question to address what are the effects of trying to learn from exposure or the difficulties/challenges that come from this approach to make it less vague.
Comment: @callyalater I don't intend anything. I just remember my high school Spanish teacher who assigned us at once to read any book in Spanish. I was wondering if I could have learned the entire language by myself just by reading (so, I guess, my intent would be to comprehend). After all, immersion is a great way to learn.
Comment: It is not clear whether "for children" only applies to "books" or also to subtitled Chinese movies/tv. In addition, it is not clear whether you mean subtitles in Chinese or in your native language. If the question can be made more specific, I would be willing to vote to reopen it, because there are SLA theories (or at least one such theory) that are relevant to this question.
Comment: The question should also be narrowed down by specifying whether it is about learning languages from the same [language family](https://en.wikipedia.org/wiki/Language_family) as one's native language or a from a different language family, e.g. learning Chinese when your native language is a Indo-European language.
Answer: The short answer is, yes. You could learn (to comprehend) a language just by being exposed to media and books.
The longer answer is, yes, but...
Books (and other language learning kits) provide a basis for language comprehension. They have rules and exercises to test your grammar and other non-interactive linguistic devices. However, this is a very limited scope of language and trains you only to that particular author's style and literary interpretation.
Media (movies, tv, music, &c.) add more for your understanding of a language, but is still one directional (the movies can not verify if what you heard was correct or not) and tends to be very informal and slurred.
In your example of Chinese (which I speak), many characters have the same pronunciation which can lead to written passages that make sense when written, but not spoken (see the famous Lion Eating Poet in the Stone Den Poem for an example). In spoken, colloquial Chinese, many people will draw characters on their hands or give a phrase where the character occurs to clarify the spoken meaning. These may or may not be presented in books and media.
There are also the non-verbal linguistic cues (body language) that cannot be fully communicated in writing. For example, in Chinese, rather than say "death" or that someone "passed", many people (especially the older generation) will just stop speaking and curl their index finger in front of you to indicated that someone has died.
With all of this said, books and media provide a good foundation for comprehension, but true fluency is improbable with just those resources.
Answer: It depends on the language, but for most languages, not completely.
Especially with a language such as Chinese and Japanese, which has many complex features, you need to get a good learning book for the grammar and you need to get support for learning the pronunciation properly. The pronunciation is quite important in Chinese, since pronouncing a character a bit differently can result in a radically different meaning. Also, when just listening to movies and reading books, you won't see the Pin Yin system, which is very useful.
For languages such as English and French, it would also be hard to completely master the verbs and tenses, since there are lots of forms and they are already hard with good explanation.
Also, you must make sure that you are not learning a dialect. This can be especially harmful when you are learning two completely different dialects and mix them up. That will also be confusing for the learner.
Answer: Yes
This is a purely anecdotal answer.
The first time I travelled to Romania a few years ago I made a local friend who was quite surprised to find that he was able to speak English. He'd never studied it at school or in self-study, and said he must've picked it up by watching the Cartoon Network as a kid! He's never been to an English speaking country. I'm not sure he's been out of Romania.
I think he's in his early-to-mid forties. He has a typical Romanian accent, not heavy, everyone can understand him. We can converse on just about any topic. He doesn't have to ponder before speaking, he's fluent.
I'm sure others I met on that trip also claimed they learned English from watching TV.
This surely won't work for arbitrary language pairs. A lot of "big words" in English have Romance origins in common with Romanian and this must be a big help. It will surely also work best when learning as a child.
Answer: No.
At least it very much depend on your definition of learning.
Being exposed to media and books, you'll get more familiar with the sound of a language, and get to learn a few words. Even more words, if you persist for some time. However, grammar isn't something to be picked on the flight.
So sure, you'll be able to communicate given enough time. But you'll stop where a higher proficiency is required. A structure studying of grammar is really necessary at some point of a language learning process.


When one should use spacing line \quad or \,

Question: In general, in most places, it is said that using TeX defaults is the best. However, TeX does provide things like \, and \quad etc. When one should use them? Both in general and in math mode in particular.
Comment: Although this does not answer the question, [this post](http://tex.stackexchange.com/questions/25262/space-on-the-right-hand-side-of-an-unary-math-operator/25278#25278) gives some insight into the respective whitespace distances (both positive and negative) which may shed light on some of their uses - thanks @Herbert.
Answer: The classic Mathematics into Type, by Ellen Swanson (the AMS has made a PDF copy available here), gives a good explanation (Section 3.1 SPACING BETWEEN SYMBOLS IN MATHEMATICS) of when to use no space, thin space, thick space, em quad and two-em quad in math mode. A brief summary:
No space

Between two symbols and between a number and the symbol it
multiplies.

Before and after subscripts, superscripts, parentheses, braces,
brackets, and vertical rules.

In expressions in the subscript or superscript.

Thin space

Before and after symbols used as verbs.

Before and after symbols used as conjunctions.

After, but not before +, -, \pm, \mp used as an adjective.

After the commas in sets of symbols, sequences of fractions, and coordinates of points.

Before and after the symbols of integration, summation, product, and
union.

Before and after functions set in roman type. Exceptions: If any of these functions are preceded or followed by parentheses, braces, brackets, or bars, then the space is eliminated.

Before and after vertical rules appearing singly rather than in pairs; the
same rule holds for a colon that is used as a mathematical symbol rather
than as punctuation.

Before back subscripts.

Before and after ds, dx, and similar combinations of d and another symbol following.

Thick space

Before the parenthesis in congruences in text.

Before a mathematical condition in text.

Em quad

Between a symbolic statement and a verbal expression in displayed expressions.

Around conjunctions.

Two-em quad

Between two separate equations or inequalities in the same line.

Between a symbolic statement and a condition on the statement.

TeX has built-in spacing, and most of the times it does an excellent job, so (most of the times) you don't need to add space manually.
The following document contains the summary of the rules given by Swanson and some examples; these examples also contain some cases which are not built-in and which require manual attention.
\documentclass{article}
\usepackage{amsmath}

\setlength\parindent{0pt}
\begin{document}

\textbf{No space}\\
Between two symbols and between a number and the symbol it multiplies:
\[
  ab\qquad xy\qquad 2a\qquad 2xz\qquad 4aC
\]

Before and after subscripts, superscripts, parentheses, braces, brackets,
and vertical rules:
\[
  2x^2y_3z (x)y\qquad a\{b\}\qquad y[a]\qquad a\lvert x\rvert\qquad b\lVert y\rVert
\]

In expressions in the subscript or superscript:
\[
  \lim_{0\to a}\qquad a^{n-1}
\]

\textbf{Thin space}\\
Before and after symbols used as verbs:
\[
  a \subseteq 2
\]

Before and after symbols used as conjunctions:
\[
  a +2
\]

After, but not before $+$, $-$, $\pm$, $\mp$ used as an adjective
\[
  a= -2
\]

After the commas in sets of symbols, sequences of fractions, and
coordinates of points:
  \[ (a,b,c) \]

Before and after the symbols of integration, summation, product, and
union:
\[
  a\int x\,\mathrm{d}y
\]
The thin space between $x$ and $\mathrm{d}y$ in the expression above is \emph{not} built
into \TeX.

Before and after functions set in roman type:
\[
a \sin x \qquad \log 2.
\]
Exceptions: If any of these functions are preceded or followed by parentheses, braces, brackets, or bars, then the space is eliminated:
\[
a \sin \lvert x \rvert.
\]

Before and after vertical rules appearing singly rather than in pairs; the
same rule holds for a colon that is used as a mathematical symbol rather
than as punctuation:
\[
  a \mid b
\]

Before back subscripts:
\[
a\,_2T_3
\]
The thin space between $a$ and the following back subscript on $T$ in this example is not built into \TeX.

Before and after $\mathrm{d}s$, $\mathrm{d}x$, and similar combinations of $d$ and another
symbol following:
\[
  \int f(x)\,\mathrm{d}x\qquad \iiint f(x)\,\mathrm{d}r\,\mathrm{d}\theta\,\mathrm{d}\phi
\]

\textbf{Thick space}\\
Before the parenthesis in congruences in text: $z= a\pmod x$

Before a mathematical condition in text: $t_n\ (n=1,2,\ldots, p)$

\textbf{Em quad}\\
Between a symbolic statement and a verbal expression in displayed expressions
\[
  E_n(t) \to e^{-t}\quad\text{as }t\to\infty.
\]

Around conjunctions:
\[
x(a+b)\quad\text{or}\quad y(a-b).
\]

\textbf{Two-em quad}\\
Between two separate equations or inequalities in the same line
\[
x^2 + y^2 = a^2,\qquad x-y=b.
\]

Between a symbolic statement and a condition on the statement
\[
x^n + y^n = a^n\qquad (n = 1,2,\ldots p).
\]

\end{document}

The compiled code looks like :
Comment: For those interested, two more books dealing with math spacing: **[1]** Chaundy, Barrett and Batey, *The Printing of Mathematics*, Oxford University Press, 1957, p. 86-91 (more complete than Swanson); **[2]** Wick, *Rules for Type-setting Mathematics*, 1965, p. 52-59 (not as interesting).
Comment: @Gonzalo: At the end of your answer as well as in the example, you mentioned that sometimes manual spacing should be done. Is there a complete list of the two cases, namely when thin space is need and implemented in TeX, and when it has to be added manually?
Comment: TeX spaces symbols more exactly than some of Ellen Swanson's rules above would imply. For instance, in `$a=b$` it puts a thick space (created manually with `\;`) on either side of the = (a verb symbol), in `$a+b$` it puts a medium space (created manually with `\>`) on either side of the + (a conjunction symbol), and in `$a\sin b$` it puts a thin space (created manually with `\,`) on either side of "sin" (a function set in roman type).
Comment: @Gonzalo -- a pdf copy of "[math into type](ftp://ftp.ams.org/pub/author-info/documentation/howto/mit-2.pdf)" has just been posted on-line at ams.  this edition isn't perfect, but the consensus here is that it's more useful to post it now than to wait for it to be updated.  (it's still under copyright.  redistribution is discouraged, but linking is okay.)
Comment: @barbarabeeton those are good news! I've updated my answer providing the link. Thank you!
Comment: @Gonzalo -- I believe you implemented a thick space in your example with `\ ` (the control space), rather than with `\;` (the thick space).
Answer: Addressing why, the table in the AMS' Short Math Guide for LaTeX, discussing spacing in math mode, provides a helpful approach. If we use the elements as intended then TeX will provide good (arguably, best) spacing. However, if the elements are used like an member of another class then adjustments to spacing may be needed:
Class     Mnemonic    Description                Examples
number             (Parts of speech)
0         Ord      simple / ordinary ("noun")    A 0 Φ ∞
1         Op       prefix operator               \sum
2         Bin      binary operator (conjunction) + ∪ ∧
3         Rel      relation/comparison (verb)    = < ⊂
4         Open     left/opening delimiter        ( [ {
5         Close    right/closing delimiter       ) ] }
6         Pun      postfix/punctuation           . , ; !

Some of these adjustments are made automatically by TeX, e.g.

symbols of class  Bin, notably the minus sign −, are automatically
  coerced to class 0 (no space)  if they do not have a suitable left
  operand.
The spacing for a few symbols follows tradition instead of the general
  rule: although / is (semantically speaking) of class 2, we write k/2
  with no space around the slash rather than k / 2. And compare p|q p|q
  (no space) with p\mid q p | q (class-3 spacing).

As others have pointed out, there are views on what changes to spacing improve the look, or ease of comprehension, of a document. Often an author will have to follow a house style but changes to the default should be considered carefully when a symbol is being used as TeX would expect. It should be noted, too, that best typographic practice varies between languages and over time.
Answer: One common case (in math mode) is with integrals:
\int f(x)\,dx

is much better with \, (even better is \int f(x)\,\textup{d}x, by the way).
Another common case is with factorials: compare 2!3!4! to 2!\,3!\,4!.
Also, some people might argue that \sqrt{\,\log 2} look better than without a \,.
Another interesting case is with : - \{x:x^2-1>0\}, but f\colon X\to Y.  Formally, you don't use \, or similar macros, but \colon is similar: it is hand-made tuning of spacing.
On the other hand, sometimes \! (a negative thin space) is also needed, although I can't recall the exact example.
(These examples are what I remember from The TeXbook, which I don't have at home; as far as I remember there are more of them there.)
In general, since both semantics and typesetting of math is so complex, it is actually quite often that you need fine-tuning like that.
And \quad and \qquad is another story – e.g., spacing between two formulas in display mode.
Comment: Knuth gives, inter alia, the following two examples for using *negative* thin spaces to fine-tune TeX's output: \(\ \int!\int dx\,dy \) and \[ \int\!\!\!\int dx\,dy \] , i.e., double integrals in text- and display-style math.
Comment: @Mico: more on `\!` in http://tex.stackexchange.com/q/9091
Answer:
in math mode never, except for very special cases. For a differential operator like dx it is better to define \newcommand*\diff{\mathop{}\!\mathrm{d}} and then use \diff x in math
in text mode for e.\,g. or in german z.\,B. or titles like
Dr.\,med.
\quad can be used whenever you need some space in text mode, same for \qquad
Comment: I use `\` after every acronym that has `.` at the end, this way the `.`won't be followed by a larger space (which is what TeX dos because it thinks the `.` is the end of a sentence). e.g.: `the e.m.k.\ for this chain is...`
Comment: Is `\,`, as in `e.\,g.`, the canonical way of handling spacing in abbreviations?
Comment: from typographers view it is the canonical way


How to poke or ask a community member to answer the question?

Question: Under the place where you post questions, there is a textbox where you can enter email of someone who you think might know the answer to your question. I wonder if there is a way to mention a member of this site in that textbox to politely ask him/her to involve. I'm asking this since I cann't find some member's email address. If there is not such a thing, they could add it as an new feature.
Comment: Have you tried commenting in other answers of his to make him know about your wish? If someone asked me that way I would have tried to assist.
Comment: @Royi , yes it is a good idea actually, back then I was not probably aware of usage at sign
Comment: Nothing like experience. You're welcome :-).
Answer: Other than contacting the person in chat there is no way of "targeting" users in this way.
If your question is interesting and tagged correctly then, assuming that they are interested in those tags, then it's highly likely they'll see the question anyway, and if it's a good question they may well answer.
Questions are, by definition public, and open to anyone to answer, whether they have a registered account here or not. Also as the focus of the site is on questions and answers it's highly unlikely ever to be implemented.
If a user has edited a post you can "ping" them in the comments using the "@username" syntax, but using that to ask them to answer would be considered rude and the comment is highly likely to be deleted.

Some discussion as to why this won't be considered is here.
Comment: Thanks for the tips, I am seeking a way to "politely" ask. Sometimes, people are too busy to check out the site, so it would be great if some sort of connection is established. To prevent issues discussed in the "http://meta.stackexchange.com/questions/431/any-way-to-send-a-personal-message-to-another-user/433#433", we can prevent user from typing a letter and just provide him with multiple choices as predefined requests.


Time as a physical dimension

Question: What is the intuition behind time being a physical dimension? I read the phrase "in cosmology terms, far away means long ago" somewhere and I got to thinking what if time is an emergent property of the interaction between matter and gravity. How can we think of time outside of space and matter? Or does it not need to be?
Or am I just confusing matter and physical dimensions?
Comment: "Spacetime" per Minkowski. Check out "Raum und Zeit" ("[Space and Time](http://www.minkowskiinstitute.org/mip/MinkowskiFreemiumMIP2012.pdf)")
Comment: This [secondary source](http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters_2017_Jan_1/spacetime/index.html) might aid in your understanding of Minkowski spacetime
Comment: Wow. Thanks. That clarifies a lot. Atleast as a foundation for understanding relativity
Comment: @Mr.Kennedy just finished reading  the space and time chapter from the link. What part of the Mathematics of it all, prohibits the existence of t < 0? And if it doesn't, isn't the mathematical approach ill suited for our intuitive thinking of time (where we can't wrap our heads around t < 0)? First let me know if my question makes logical sense, and then go ahead with any thoughts on it. Because I'm not sure I totally understood minkowski after the past light cone and the future light Cone part. No prior background in advanced geometry
Answer: The intuition behind time being a physical dimension is in the experience of being able to "travel" through it. However, in daily life we only seem to be able to move in one direction and at one speed. In theory, we enter the realm of traveling through time forward, backward, and at different speeds. Thus it has traits of physical dimensions. The phrase, "in cosmology terms, far away means long ago", can at least refer to what we see. Because light takes a specific amount of time to reach us, we are actually seeing an image of something which existed in the past. The farther away it appears to be, the older the image which we see. One way we can think of time outside of space and matter is by thinking of space and matter being inside time. Time does not necessarily need space or matter to exist. If space and matter exist, they do so for a length of time. Matter exists in the physical dimensions. The physical dimensions describe matter. Thus, there are two uses of the term "physical dimensions". The first is the name of a place, the second is a measurement.
Comment: Welcome to philosophySE! Good answer :) Do we know that time does not necessarily need space or matter to exist? Are space and time indistinguishable from [spacetime](http://www.minkowskiinstitute.org/mip/MinkowskiFreemiumMIP2012.pdf) (and this no matter how many dimensional aspects we may describe them with)? Per [Max Tegmark](http://space.mit.edu/home/tegmark/dimensions.gif), time without space is at the very least completely unpredictable.
Comment: Thank you! Conceptually, time could exist by itself. Time would only need itself to exist because existence occurs for an amount of time. Already a new concept, existence, is introduced. If there were matter in existence, which then ceased to exist for a certain amount of time, then new matter came into existence, time would exist by itself during this period. It may very well be that time is simply a unit of measure of the occurrence and existence of things, rather than an entity unto itself. In trying to stay within philosophy, I can't say much more without going into physics.
Comment: Certainly epistemic considerations of time are inadequate as Minkowski demonstrates with spacetime, and ontologically it is conceivable that time could exist independently of time, however, how would we know that we knew that time existed so? As for physics - use whichever tools are adequate to the occasion of resolving your query! :) If you haven't, do read Minkowski's "Raum und Zeit" - he's great!
Comment: @takintoolong Can time not be thought of as the rate of change of existence? Because we can calculate the age of the universe only due to the "changes" (expansion of space) that we observed. If the universe was static (nothing ever changed) , so as to speak, would time be an entity then?
Comment: Mr. Kennedy and Ravi Shankar, you are both assuming our own existence. For us to "know", "calculate", or "observe", we must exist for some period of time. I think time is a measurement of change. I think the universe always has been changing, always is changing, and always will change.
Comment: What does moving through time with "speed" mean? To the extent that we say "time flies" or "slows to a crawl" I guess it moves at different "speeds", but that is based on comparing "subjective" time perceptions to the motion of clocks. To talk about "speed" of "moving through time" one needs to measure it against some other... time, it seems.
Comment: Conifold, it would be our own time compared to the world time as we traveled. If we were traveling through time our body would exist in the speed we are used to while the rest of the world appeared to be in fast forward or rewind. What comes to mind for me is "The Time Machine" by H.G. Wells.
Answer: There are various theories whereby spacetime (the whole ball of wax) is emergent, e.g., https://arxiv.org/abs/1504.00464 Reading between the lines of your question, I'd guess the best way for you to think about it intuitively is as follows. What's more fundamental: "objects" or "events"? To best interpret time as just another dimension, instantaneous "events" would be the better answer. Then, say, "eating breakfast" and "eating lunch" are two events, separated not only by the distance between the two restaurants you ate at, but by the several hours difference when you ate the meals. In this kind of view, "objects" are just highly-correlated (and kind-of-continuous) sequences of events.
Comment: From my understanding of your answer, events are "objects" +"that moment in time". But objects can be percieved independently of all "monents of time". Can "a moment in time" be perceived independent of all objects existing "then"? Or is that just a limitation of my thought?
Comment: @RaviShankar Your remark, "objects can be percieved independently of all 'monents of time'" would be wrong under this interpretation. See, e.g., "Events as Fundamental Entities in Physics", http://link.springer.com/article/10.1007/BF02724247 (though, sorry, I'm not seeing a free pdf offhand). And, no, the observation of an event >>defines<< a "moment in time", and objects pretty much correspond to sequences of events (though the word "sequence" itself pretty much implies a pre-existing/pre-defined time notion, so I'm playing too fast-and-loose with ideas that require a paper-length discussion)
Comment: @RaviShankar re-reading your comment, your remark "events are 'objects' + 'that moment in time'" seems to suggest you're thinking of objects as fundamental. In this interpretation, that's backwards. Events are fundamental, objects are "just in your head", essentially emergent, a convenient way of organizing events so your mind/brain can make sense of them as simply as possible. Of course, this is only possible because nature, in the classical regime, exhibits events that can be organized as "highly correlated 'sequences'" in the first place.
Comment: So, what would the length of a moment in time be?
Comment: @takintoolong Seriously? No such thing. And that's regardless of whether or not we're considering (space)time as "emergent". Typically, given two events, say e1 and e2, there'd be a time t(e1,e2) between them which, in most interpretations, would be observer-dependent (an invariant observer-independent interval between events involves both space and time). But "length of a moment" is meaningless, at least to me.
Comment: Yes, I was serious. I figured it out later though. The length is zero.
Answer: 19th Century proponents of Time as a fourth physical dimension included Gustav Fechner (under the pseudonym of Dr. Wises) and C.H. Hinton. The idea was popularised by H.G. Wells in his 1895 novel The Time Machine. Hermann Minkowski and Albert Einstein soon gave it its modern formulation. It is motivated by the idea of a "block Universe", of a mathematical description of spacetime spread out like a four-dimensional map on which we can trace our timelines, in much the same way we can trace a journey on an ordinary map.
Of course, the Minkowski metric of Time's imaginary multiplier and Einstein's shape-shifting relativistic coordinates provide a rather more sophisticated model of the block universe, but from the perspective of Time as a fourth dimension, that is all they do.
As for time, space and matter, the quartet of mass, energy, space and time are welded together by Relativity into a recursive and inseparable whole sometimes referred to as MEST. None makes any existential sense without all the others. For example, as Einstein explained, "Spacetime tells matter how to move, matter tells spacetime how to bend". So having one or more as an emergent property of the remainder is an attractive proposition. Various speculative ideas have been bounced around by theoretical physicists, including wider ideas such as Time as an emergent property of quantum thermodynamic systems (whatever that is) but none has yet to make any headway.
Some nuggets do appear. In string theory there are typically six extra dimensions, of which three, like time, have an imaginary metric. Their imaginary multiplier arises from a quite different principle and they are definitely spatial dimensions. This suggests that Time in the Minkowski metric is not a spatial dimension in the same way, though it offers no help as to what it might be instead.
Then there is the Twistor theory of Roger Penrose, in which time and space are replaced by something more like frequency. Technically twistor space is a Fourier-like transform of objects in ordinary spacetime, analogous to the way a sound frequency spectrum is a Fourier transform of the physical waveform in time. It suggests that space and time are indeed closely related.
So at the moment, we can say that space and time are closely related, but we are not sure how closely or in quite what ways they differ.
Comment: Also, an important twist from Einstein's theory is the [relativity of simultaneity](https://en.wikipedia.org/wiki/Relativity_of_simultaneity), which perhaps makes [presentism](https://plato.stanford.edu/entries/presentism/) seem less appealing as a metaphysical idea (though it doesn't rule it out, one could suppose there is an objective truth about simultaneity from a metaphysical perspective even if no possible empirical experiment can distinguish which frame's definition of simultaneity is the true one).
Comment: Although simultaneity is not absolute, the remarkable thing is that the flow of cause-and-effect is never affected; different observers merely disagree on how long they have to wait for the effect. There is a similar phenomenon in some geometries, such as affine, in which order is preserved but exact distances are not. Quantum physics offers far worse challenges to presentism, but that is going off-topic.
Comment: Order is preserved for causally-related events, but not for events outside of one another's light cones which cannot causally affect one another; for a pair of such events A and B, some frames will say A happened before B, some will say B happened before A, and there'll always be a frame that says they happened simultaneously. Presentism by definition requires a single objective truth about whether any pair of events A and B happened simultaneously or not.
Comment: Exactly so. Time reversal can only occur with events which are not in a potentially causal relationship, i.e. are outside each other's time cones.
Answer: Special relativity demonstrates that time and space are related in a fundamental way.  Consider a muon created in the upper atmosphere.  These particles will travel only about 456 meters (or 2.2 microseconds) before decaying yet survive to the Earth's surface and below.  From the viewpoint of an observer on Earth the time dilation effect of special relativity results in time passing more slowly for the muon and it reaches the surface before decaying.  For an observer riding along with the muon, the muon's clock is not slowed but the distance to the Earth's surface is foreshortened, and so the distance it must travel (in its reference frame) is less than the 456 meter decay distance.  In both cases the muon survives to reach the Earth's surface, but the reason is due to time dialation (as viewed from the Earth reference frame) or distance foreshortening (muon reference frame).  This means that time and space are two sides of the same coin, so to speak.  It has an analogy in the wave-particle duality of light and matter in which an object (particle of matter or photon of light) exhibit both wave properties (e.g interference) and particle properties (e.g. photoelectric effect).  It is not intuitive to regard something as having properties that seem mutually exclusive, but it is nonetheless the nature of our universe.  It would not be correct to state that time is independent of physical dimension as theory and experiment demonstrate otherwise.

Time as a physical dimension


Trigonometric eigenvalue equation

Question: In solving an eigenvalue problem, I've come to following equation ($\lambda=1$):
$$\begin{pmatrix}
  \cos(\theta) & \sin(\theta) \\ \sin(\theta) & -\cos(\theta)
 \end{pmatrix}\begin{pmatrix}
  a \\ b
 \end{pmatrix}=\begin{pmatrix}
  a \\ b
 \end{pmatrix}$$
Now, the solution says, "This matrix equation can be reduced to a single equation":
$$a \sin(\frac{1}{2}\theta)=b\cos(\frac{1}{2}\theta)$$
I've been rotating trigonometric formulas to get to this, but I simply can't find the way. Could you help me with this, or at least give me a hint?
Answer: Since the matrix has the eigenvalue 1, it's enough to consider only the first row. Rearrange to get $(1-\cos(\theta))a = \sin(\theta)b$ which if you expand by the right formulae, give you $2(\sin(\theta/2)^2)a = 2\sin(\theta/2)\cos(\theta/2)b$. Now, if your matrix has to be non-identity, then this will give you the equation want.
Answer: $$\begin{pmatrix}
  \cos(\theta) & \sin(\theta) \\ \sin\theta & -\cos\theta
 \end{pmatrix}\begin{pmatrix}
  a \\ b
 \end{pmatrix}\\=\begin{pmatrix}
  a\cos\theta+b\sin\theta \\ a\sin\theta-b\cos\theta
 \end{pmatrix}=\begin{pmatrix}
  a \\ b
 \end{pmatrix}$$
Which gives us the following system of equations:
$$a\cos\theta+b\sin\theta=a\tag{1}$$
$$a\sin\theta-b\cos\theta=b\tag{2}$$
So from $(1)$ you have:
$$b\sin\theta=a(1-\cos\theta)$$
$$2b\sin(\frac \theta{2})\cos(\frac \theta{2})=a(2\sin^2(\frac \theta{2}))$$
$$b\cos(\frac \theta{2})=a\sin(\frac \theta{2})$$
Answer: The matrix system corresponds to the following system of equations
\begin{equation}
\cos(\theta)\,a + \sin(\theta) b = a \,,
\\
\sin(\theta)\,a - \cos(\theta) b = b \,
\end{equation}
Multiplying the first equation by $\sin(\theta)$ and the second by -$\cos(\theta)$ gives
\begin{equation}
\sin(\theta)\,\cos(\theta)\,a + \sin(\theta)^2 b = a\,,
\\
-\sin(\theta) \cos(\theta) \,a + \cos(\theta)^2 b = -b \,
\end{equation}
Add the two equations, and the simplify the resulting equation, you get
$$ b( 1+\cos(\theta) ) = a\,\sin(\theta) $$
Using the identity $ \cos(\theta) = 2\cos(\theta /2)^2 -1 $ and $\sin(\theta) = 2 \sin(\theta /2) \cos(\theta /2) $ in the above equation yields
$$ 2 b \cos(\theta /2)^2 = 2 a \sin( \theta /2 ) \cos( \theta /2 )$$
Dividing both sides of the equation by $\cos(\theta /2)$ gives the result
$$ b \cos(\theta /2) = a \sin( \theta /2 ) $$

Trigonometric eigenvalue equation