If we are all Vishnu, where do the Thrimuurthulu live?

Question: The entire universe came into formation from one god - Lord Vishnu. Then how can we describe the REALM in which all the other gods like Brahma, Shiva, Indra live? Are they too a part of Lord Vishnu or separate entities?
Comment: Not all agree, entire universe came from Vishnu. See [How were the Trimurthi born?](https://hinduism.stackexchange.com/q/237/3500)
Answer: How can we describe the REALM in which all the other gods like Brahma, Shiva, Indra live?
The Trimurthis do exists in all this Universe /space- time, It is difficult to explain the nature of their existence, and their true potentialities since they belong to the very highest realms of creation.
So Trimurty's remain in their real aspect as pure energies and consciousness with dimensions / domains beyond our imagination, beyond thought, beyond sense perception, beyond mind and speech, Only handful of yogis  and Rushies envisioned them and their abode's in deep meditation.
Are they too a part of Lord Vishnu or separate entities?
I am herewith presenting some verses which are pointing at your question. Here are they -
There is a interesting story In Shreemad Bhagvatam related to your enquiry. This story is a of Shree Atri Rushi  and Anusuya . When Brahmadeva ordered Atri rushi to beget children , he performed great Tapasya (severe austerities) . And while doing that he was meditating on the supreme Creator of this universe.

शरणं तं प्रपद्येSहं य एव जगदिश्वर: | प्रजामात्मसमां मह्यं
  प्रयच्छत्विति चिन्तयन् ||20||
śaraṇaṁ taṁ prapadye 'haṁ  ya eva jagad-īśvaraḥ| prajām
  ātma-samāṁ mahyaṁ prayacchatv iti cintayan ||
He was thinking: May the Lord of the universe, of whom I have taken
  shelter, kindly be pleased to offer me a son exactly like Him.SB
  4.1.20

While Atri Muni was engaged in these severe austerities, a blazing fire came out of his head by virtue of his breathing exercise, and that fire was seen by the three principal deities of the three worlds.
That fire was perceived by the Supersoul, Viṣṇu, and thereby Lord Brahmā and Śiva also perceived it.
Then Atri rushi asked three of them O Lord Brahmā, Lord Viṣṇu and Lord Śiva, I beg to inquire whom of you three I have called by my prayer.?
The three great deities smiled, and they replied in the following sweet words.

देव उवाच – Dev Uvacha
यथा कृथस्ते सङ्कल्पो भाव्यं तेनैव नान्यथा | सतसङ्कल्प्स्य ते
  ब्रह्मन् यद्वै ध्यायति ते वयम् ||30||
yathā kṛtas te saṅkalpo bhāvyaṁ tenaiva nānyathā sat-saṅkalpasya
  te brahman yad vai dhyāyati te vayam
The three deities told Atri Muni: Dear brāhmaṇa, you are perfect in
  your determination, and therefore as you have decided, so it will
  happen; it will not happen otherwise. We are all the same person
  upon whom you were meditating, and therefore we have all come to
  you. SB 4.1.30

We can see a very another similar verse in Shreemad Bhagvatam Skanda Four –Chapter 7 –Verse 50. Which is by Supreme creator himself.

Shree Bhagvan Uvacha –
अहं ब्रह्मा च शर्वच्श्र जगत: कारणं परम् | आत्मेश्वर् उपद्रष्टा
  स्वयंदृगविशेषण ||50||
ahaṁ brahmā ca śarvaś ca jagataḥ kāraṇaṁ param  ātmeśvara upadraṣṭā
  svayan-dṛg aviśeṣaṇaḥ
**Brahmā, Lord Śiva and I are the supreme cause of the material manifestation. I am the Supersoul, the self-sufficient
  witness. But impersonally there is no difference between Brahmā, Lord
  Śiva and Me.

These verses tells us  that at the highest level Trimurty's  are the three aspects of the one and the same supreme Reality.
Your question is  whether these gods are part of  Lord Vishnu or separate entities, the answer can be in terms  both Yes and No., From human perspective they  are different because they perform different tasks, have qualities and energies that are different  widely from one another. And from high reality they are one and the same.
Note – It's is not necessary that everybody should believe in their unity .There are different views regarding this topic among different school of thoughts OR Sects .This is my attempt to answer this  questions using verses. There are various ways and total freedom in Hinduism given by supreme god himself to understand the truth and through them to  know and to reach him.


El Capitan upgrade issue

Question: I've downloaded the OS X El Capitan Installer, but when I try to put it into action, the machine refuses access to my MacIntosh HD because it says Time Machine is using the drive for backups.  How do I get Time Machine out of the way so I can upgrade the OS?
Answer: I've never known Time Machine to hold up an OS update, however…
System Prefs > Time Machine [or from the menu bar if you have set it to show there] you can tell Time Machine to halt its current backup, or switch it off completely.

A late note: if you have local snapshots enabled [which I don't, in the picture above] Time Machine changes its "Time Machine keeps:" line to
"Time Machine keeps local snapshots as space permits, and:"
Comment: This is clearly not something most people end up with. If you use Server.app to enable other Macs to use Time Machine, it doesn't place a blocking store of backups on the filesystem. About the only way I can see this is booting in target disk mode and enabling another Mac to backup or perhaps cloning a drive that had backups and then commingling it with a bootable system.
Comment: I'm a layperson but my guess is that Time Machine interfered with the installation process because Macintosh HD had been selected as the Time Machine drive.  Part of my workaround was to deselect it and replace it  in Time Machine with an external HD.
Comment: Ah, yes - that would do it. I'm not sure how it even let you select the boot volume as a Time Machine backup. It is certainly a more valuable resource on a separate physical drive.
Answer: If you're sure you don't need backups, this could be a three step process:

Turn off Time Machine
Delete the folder Macintosh HD/Backups.backupdb after making sure no other machine data will be lost.

If that works, great. If not, open terminal and type

sudo tmutil disablelocal

That might take several minutes to clear up the local storage cache of backup files. After maybe 15 minutes of no activity, reboot and try the installer again. If you have a specific error message - look in the installer logs: <code>/var/log/installer.log</code>
Answer: Thank you -- I succeeded following your first suggestion:
1) trash backups.backupdb
2) turn off Time Machine
Once the install was complete I copied backups.backupdb from the trash to Macintosh HD.  Dunno if I can access it ... Time Machine is no longer offering Macintosh HD as a backup drive candidate.

El Capitan upgrade issue


Decimating by last interpolating factor? (Multi-stage)

Question: Let's say I have a multi-stage interpolator at the transmitter, which interpolates by 2, 4 and 8 (that is, 64). When decimating (at the receiver) why should I start decimating by 8, then 4, then 2, instead of 2, 4 and 8? I mean what's the reason behind? What makes it better than doing it the other way round?
Answer: The idea is that you'll be saving computational steps in the filtering part of the decimation. Think about it, if you have 800 samples then downsample by a factor of 8, now you only have to low pass filter 100 samples for the first stage. If you instead tried to downsample by a factor of 2 first, then you'd have 400 samples to filter after the first stage. The order matters because of the number of computations taken in the filtering step.


18.04 Ubuntu Operating System does not give me a driver for Dell Mono B1160 Printer

Question: I would appreciate any help regarding installation of a working driver which will enable my Dell mono B1160 printer to operate. Too many hours I have spent trying to print from my Ubuntu computer to this Dell B1160 printer.
Thanking all who have a suggestion on the driver and installation.
Answer: I had exactly the same problem and here's the solution:

Download the driver archive from here:
Unpack it and go to ~/Downloads/B1160_B1160w_UnifiedLinuxDriver_1.01/cdroot/Linux
Execute the installation script sudo sh install.sh
Remove all printers from the system, including the one that was added during the installation.
Click Add new printer and choose Dell B1160 Mono Laser Printer in your printer driver settings
Enjoy
Answer: The Dell B1160 is actually a Samsung in disguise
https://commtechwatch.com/2012/08/the-b1160w-a-samsung-mono-laser-in-dells-clothing/
So in CUPS just choose the printer as Samsung ML2165
Worked for me on Raspbian
Answer: Before I could get the install.sh script to succeed I had to comment out the following two lines in the start_install.sh script like so:
#. "$SCRIPT_DIR/check_packages.sh"
#MISSING=`check_required_packages required_packages`

The problem is that it can't find libsane even though I installed it I guess because Ubuntu 18.04 appears to have new directory structure for so libraries that their check_packages.sh script doesn't understand.
Like the answer by @xpoback after installation completed I also had to remove the printers added by the install script and click the add button in the user interface to add it again before it started working.


Wish someone 'good luck' for an operation

Question: What is a good way of wishing someone 'good luck' for an operation? The words 'good luck' don't sound right, especially because it is a very difficult operation with lots of severe risks.
Comment: If you don't want mentioning "luck" to be misinterpreted as impugning the skill of the surgeon, or drawing attention to any inherent risk in the operation, just say what you mean: "I hope it all goes well".
Comment: Just do what you do for actors going onstage -- tell'em to break a leg.
Comment: @JohnLawler - When my wife broke her ankle earlier this year, those were my exact words as they wheeled her into surgery. :^)
Comment: Lots of severe risks would seem to make wishing the patient "good luck" *more* appropriate, not less. (Only in theatrical usage is "good luck" inappropriate--and I would hardly recommend bidding a surgical patient "break a leg"!)
Comment: Why are you trying to avoid "good luck"? Is it because you are trying to avoid having to acknowledge that the operation is risky? Or some other reason?
Comment: @AndrewLeach why not add your version as an answer?
Answer: I feel that I know what you mean by not wanting to add "luck" into the equation. It seems to me that calling luck into play would only serve to add more stress to an already stressful situation. Hoping for luck brings to my mind a feeling of more uncertainty, and questions the reliability of the surgeon and anesthesiologist. I would probably tend to want to stay as positive as possible, making a statement that is not a question as much as it is a foregone conclusion. Such as: "I will be so happy to see you in recovery after the operation" or "Things will be so much better after you're through this". Since I do not know the nature of the operation I can't give a specific answer to your question, however I do hope that you get my meaning. Best of luck to you in finding a suitable term that you're comfortable with. ☺
Answer: I happen to be a cardiologist and every week I see a lot of patients in their pre-op evaluation.  After I have seen them and my job is finished, I hand them my report and wish them good-luck.  I think what really matters is not exactly the words you use, but how it all sounds.  A warm and sincere "good-luck" when shaking hands will certainly be appreciated.


Help understanding amperage of DC motor and heat generation

Question: I am diagnosing an issue in an automotive HVAC system and have been testing the blower motor. I would expect somewhere approximately 8A to 15A of current draw. I have test wired the motor with 14AWG wire, a switch that is supposed to be rated to 30A, and a 20A fuse. It seems to blow the expected amount of air and not blowing the fuse, but the spade connectors at the switch and at the motor are getting uncomfortably warm to the touch. I measured resistance across the motor's terminals and I am seeing 5.1ohms. Wouldn't this imply that the motor should only draw 2.4A at 12v? Note, I do not currently have access to tools to directly measure the draw when running.
Comment: UPDATE: Changed out the switch for a new 35A switch, upgraded wiring to 10AWG, still have 20A fuse. Connections at the switch "sometimes" get hot now, but not all the time. Fuse still hasn't blown even if the connections stay hotter-than-comfortable-to-hold even if hot for over 20 minutes. A friend mentioned possibility of fan bearing being wonky, due to the inconsistency of the heat behavior. But if this was the case the amperage would be higher and should blow my fuse. I'm wondering if the hot switch contacts could be caused by some electromagnetic feedback?
Comment: Rather than guess, you need to measure the current when the motor is running. There may be an error in your resistance measurement (meters sometimes are defective), and also there are the issues of back EMF when the motor is running and the phase of the contacts in the motor when you measured the static resistance.
Comment: I measured the resistance with the motor off. Can it safely be measured while running?
Answer: The resistance of a DC motor determines the maximum current during starting. As soon as the rotor starts to turn, it generates a voltage called the counter electromotive force or back EMF. The back EMF opposes the supply voltage and controls the running current. Since the maximum starting current is much higher than the normal running current, measuring the resistance doesn't tell you very much unless you have other information about the motor.
Motors can safely run uncomfortably warm to the touch. If a blower motor is designed to move air over itself when properly installed, it may run warmer than normal when tested on a workbench. Here again, it is difficult to tell if the motor is running too hot without specific knowledge of the motor.
Blower motors in a car often have a speed switch that switches sections of a resistor in series with the motor for three or four operating speeds. Failure of the resistor is probably the most common failure. The resistor element can open up and cause the motor to run only on one or two speed settings or not at all. If that or a broken switch or connection is not the problem, the motor is probably bad. If the motor runs and does not make a lot of noise, it is probably ok.
Comment: The motor its self seems to be fine. The question about temperature is regarding the heat at the connection terminal on the motor and both terminals on the switch. I understand that startup current is going to be higher than running current, but my resistance measurement only shows 2A(while running current expected to be ~10A).
Comment: As suggested by @Digiproc, there may be an error in your measurement. If the motor normally draws 10 amps, the resistance can not be 5.1 ohms. Something like 0.25 ohms would be more likely. The fact that the motor seems to run properly with the blower attached indicates the motor resistance is likely what it should be. However it is impossible to properly evaluate the motor without measuring the motor current.


Cura's solution to replace corners->arcs to increase corner speed?

Question: I realized that with current Marlin I cannot use Junction Deviation with Linear Advance, see <code>[BUG] Rapid changes of acceleration break linear advance when using Junction Deviation #15473</code>.
Yet, it is very much beneficial to not stop at the corners with high acceleration but rather do a small curve. Is it possible on a G-code level?
Is there a feature or plugin in Cura which replaces sharp corners with arcs to remove need for Junction Deviation in firmware?
Comment: @R.. I am the reporter of that bug... With K=2 there issue is very serious. What board do you have? It is possible that it happens only on AVR... Anyways, it is beneficial to make corners a little less sharp.
Comment: Junction deviation does not produce round corners. It just performs the math for the allowable instantaneous change in velocity components *as if* it were going around a rounded corner with the configured deviation. See http://blog.kyneticcnc.com/2018/10/computing-junction-deviation-for-marlin.html
Comment: Short of using the arc movement commands (G2/G3), I'm not sure it would be very helpful. Doing a rounded corner with radius 0.1-0.2 mm is going to involve some utterly tiny segments, which Marlin and other firmware don't really like - they make the planner math a lot more expensive and potentially produce compounding jerk, allowing the cornering to happen *faster* than it's supposed to. The G2/G3 approach may be promising, but I've actually had to omit support for them from my builds to fit Marlin in 128k. :-(
Comment: Can you clarify whether you are actually having a problem matching the one described in the linked bug report, or just concerned that you might? I use junction deviation and linear advance, K=0.6 for regular PLA, K=3.8 for flex material, and did not observe this problem whatsoever with the former but might be encountering it with the latter.
Comment: Also, what junction deviation parameter are you using?
Comment: @R.. I am using JD=0.022
Comment: I have an Ender 3, which is an AVR-based board (ATmega 128-whatever). JD=0.022 is rather low; I use JD=0.08 (computed with [formula for converting from comparable classic jerk](https://blog.kyneticcnc.com/2018/10/computing-junction-deviation-for-marlin.html)) which isn't to say you should increase it, just that it's not a problem with your value being excessive.
Comment: Is there a reason you're not using classic jerk? I switched to JD because classic jerk seems to be the source of nasty layer shifting bugs, but if your setup isn't affected by that, classic jerk might be a solution.
Comment: @R..GitHubSTOPHELPINGICE Surely I currently live on Classic Jerk, that's the only working solution for me at the moment. But I would still be interested to try to round the corners a little bit.
Comment: And I just confirmed that I'm affected by this issue too, even with K=0.6. Uhg. Switching back to classic jerk and hoping I don't hit layer shifts again... If your bounty expires without an acceptable solution I'll run another out of my rep to follow up.
Comment: @R..GitHubSTOPHELPINGICE Yes, I understand that JD does not produce rounded corners. But I believe automatic rounded corners would be beneficial for all 3d printers (R=0.1-0.2mm)
Comment: see post processing idea here https://github.com/FormerLurker/ArcWelderLib/issues/33
Comment: @VincentAlex ArcWelderLib is awesome, It does most of what I dreamed about. But still as far as I see it does not replace corners with arcs (i.e. it does not change geometry).
Comment: @BarsMonster true, I'm also looking for something similar, the easiest would be to do it in 3D model, but that doesnt include infills, bspline fitting from CNC world would give you this, but not written for 3D gcode: https://user-images.githubusercontent.com/4163396/106666173-27fc8c80-659f-11eb-9c45-c443cbf05163.jpg
Comment: @BarsMonster an idea, draw your 2D base in dwg, use a script that rounds the corners, extend it to 3D, and slice that, a lot easier than processing gcode.
Answer: Cura's solution can be found in the "Jerk Control" settings.
Short analogy; when driving, and a corner is coming up, you basically have two options to take the corner smoothly; you can take the corner with a wide turning radius, or you can slow down. Taking a neighborhood street corner at highway speeds just doesn't work even if there's nobody else on the road; you'll very likely overshoot the corner, if you're in a RWD car you'll likely lose the back end and fishtail (or worse), and the occupants of the car, yourself included, are going to be thrown around violently, to no-one's real advantage other than to say you took that turn at 70.
Back in 3D printing land, something similar applies; as the extruder approaches a sharp corner, it will be disadvantageous all around for the extruder to try to maintain 70mm/s around what's basically an instantaneous turn. Your jerk (stopping the moving axis) and acceleration (starting the non-moving axis) settings are going to exceed the physical capabilities of your steppers and drive belts, making the corner less accurate (and in the extreme, losing steps causing layer shifts), and if your belts are not perfectly tensioned, and really even if they are, you'll get "ringing" (the 3D equivalent of fishtailing as you straighten out after the apex of a turn while driving).
The first option, cutting the corner, is your corner-to-arc replacement; rather than try for an instantaneous turn, just soften that corner by enough that you're within what's possible for the stepper motors in terms of acceleration. This keeps the speed and surface quality high, but necessarily reduces the accuracy of the print to the model.
So instead, Cura encourages the second option; slow down before the turn. Enabling Jerk Control and tweaking the associated settings lets the Cura slicer reduce head speed gradually as the extruder approaches a sharp corner, thus reducing the torque required to stop motion in one axis and start it in another, to something the steppers can actually accomplish at a rate you'd call "instantaneous". This keeps the corners sharp and avoids ringing along straight lines after a corner, at the cost of a slower overall print speed (though not as much as reducing overall print speed to the speed at which the extruder will take corners).
Now, I realize that this is the opposite of "increasing corner speed"; jerk control exists to slow the extruder near corners. However, increasing corner speed is rarely what you actually want, for the reasons stated above. If you really want nicely-rounded corners, fillet them in CAD, and then the slicer will generate a sequence of arbitrarily short linear movements (true G2/G3/G5 curve interpolation from the purely polygonal STL geometry has been experimented with, but currently more trouble than it's worth) which limit the change of velocity of the extruder as it rounds the corner, instead of making the rounding an "artifact" of printer limitations. At fine enough detail levels of conversion to an STL, the results are indistinguishable from a true curve.
Comment: I think this answer completely misunderstands/misrepresents what "jerk control" in Cura is. It simply means that Cura will issue gcode commands to set the printer firmware's jerk limits, possibly with different values for different parts of the print (outer walls, inner walls, skin, infill, etc.), rather than leaving the firmware's default setting in place. It does not mean Cura does any alteration of the movement paths or speed to reduce the physical jerk experienced by the toolhead. It's the printer's firmware that actually applies these settings to how it controls the stepper motors.
Comment: https://github.com/FormerLurker/ArcWelderLib does generate G2/G3 (arcs) from linear ones.
Comment: Please explain more about which slicer will generate G2 moves from an STL file composed completely of flat triangles.
Comment: @Davo Actually, both Slic3r and Simplify3D have experimented with exactly that. But, I will edit to clarify that what really happens is a sequence of polygonal lines of arbitrarily small length (based on a number of variables in both CAD and the slicer), where each move accomplishes the overall goal of limiting acceleration around the corner.


How to use bitcoin testnet wallet

Question: I have a simple use case.

I want to send some testnet coins to my testnet wallet and be able to
  see it in bitcoin-core in testnet mode

What I did so far: 1. Go to File-->Receiving address. Setup a new reciving address here
2. Go to website providing free testnet coins and send it the address that I set in step 1.
3. Wait until the transaction is confirmed.
Questions:
I expect to see the above transactions in the bitcoin UI. Eg. If I click on 'Overview' button, I expect to see those testnet bitcoins. Similarly, under 'Transactions', I see nothing. Could somebody point out what is going wrong here?
Comment: Can you share the transaction ID and/or receiving address you used?  Has Bitcoin Core finished synchronizing?  You are running it in testnet mode?
Comment: Thnx for checking. I did transaction more than 12 hours ago. Aahh! But I see your point, my Bitcoin core is yet far behind and thus may have not seen the transaction. Let me wait for it to finish synchronizing.
Comment: Yes, you won't see it until synchronization is finished.  I think that's the issue.  If so, could you either delete this question, or else post your own answer and accept it (click the check mark)?  This site tends to get quite cluttered by unanswered questions.
Comment: (I see you have a few other questions with answers that you haven't accepted - it would be good to either do that, or else leave a comment explaining why it doesn't resolve your issue.  The site will continually bump questions whose answers aren't upvoted or accepted.)
Comment: Thanks Nate. Yeah, I am bit of newbie on stack exchange. I see your point. I will leave this question as I think it would be helpful to somebody starting afresh with bitcoin testnet.
Answer: Thanks to Nate, the quite possible reason is that since my bitcoin core is still synchronizing, it would not have seen the transaction.
Will await for this to complete. Thanks again, Nate!

How to use bitcoin testnet wallet


How do the prizes from Conquest work?

Question: I participated in some Conquests, and in some of them, my team won. But, the prizes seemed to have no correlation with the points I put in (In one round, I had 1 point, got 2000 Coins, but in another, put 4 points, and got 1000 Coins). How does the game decide what people get for participating? Is it a set prize, or does it depend on something else?
Answer: Consider the following:
Say "Team Red" has three characters: Charizard, Mario, and Ike.  "Team Blue" also has three characters: Mega Man, Sonic, and Lucario.
Every time you play as one of those characters and you win, you add a couple of points to that character's team (you can see how many points you contribute on the results screen after the fight where you used the character, indicated by a flag). The server adds up everyone's points contributed, and it generates a percentage, which is how the server decides which team wins. For example (again):
Say you fight and win four fights: one as Ike, one as Lucario, one as Pac-Man, and one as Mario. You'll contribute (let's say) 7 points to the Red Team by winning as Ike the first time (I don't know how much exactly), 7 points to the Blue Team by winning as Lucario, no points to no team for winning as Pac-Man, and another 7 points to the Red Team for your Mario victory.
Now, if you were the ONLY person in the world who played SSB online, the Red team would win because you contributed 14 points to the Red and 7 points to the Blue.
As for the prizes, you're right. It's all random. Realistically, millions of users play SSB online, so there would be no easy way to evenly dole out prizes among everyone. It's just like random classic mode victory prizes (or pretty much anything else).
Comment: So the prizes ARE completely random?
Comment: Yes. They are random.
Comment: "Realistically, millions of users play SSB online, so there would be no easy way to evenly dole out prizes among everyone." That would only be true if prizes were somehow given out manually, since they're given out automatically by the game, it would be very easy.

How do the prizes from Conquest work?


What is the difference between WCAG 2 AAA Compliant and WCAG 2 AA Compliant

Question: I use a web app to check my site color contrast. Most of my color (Back/fore ground colors) are OK and I see YES inside textboxes except the one which refers to WCAG 2 AAA. What is it? What is the difference between WCAG 2 AAA Compliant and WCAG 2 AA Compliant?
Answer: The definition is very clear:
Level AA: For Level AA conformance, the Web page satisfies all the Level A and Level AA Success Criteria, or a Level AA conforming alternate version is provided.
Level AAA: For Level AAA conformance, the Web page satisfies all the Level A, Level AA and Level AAA Success Criteria, or a Level AAA conforming alternate version is provided.
Every single rule in the guideline has a level of conformance it belongs to. If you fulfill all requirements marked with AAA, your site has the highest compliance.
Comment: Thanks for the answer. It was helpful. If background and foreground color fail in passing Level AA, does that mean colorblind people can't see it or can see it with difficulties?
Comment: That depends on the actual contrast value. They will have at least some difficulties if it's too low, but sometimes the contrast is still enough to be readable but you are not compliant per definition. Test it with actually disabled people, they will give you good feedback whether you have to change it or it is already ok.
Comment: @MarjanVenema, what do you mean? Do you mean I should mark it as an answer plus upvoting it? Is this what you're saying?
Comment: @UX-Geek: that is exactly what I mean. Not that you _have_ to, but I can't imagine why one would want to accept but not upvote an answer.
Comment: @MarjanVenema you don't upvote because when you mark an answer you give him/her +5pt and I think there is no reason to upvote him again. upvote is there for people who wants to appreciate the answer since they can't mark it as an answer. thanks by the way for mentioning it.
Answer: To answer your comment above. The background and foreground colours pass or fail on a specific algorithm, which is different for AA and AAA. An overview is given below:
AA = Contrast ratio of at least 4.5:1 between background and foreground. 3:1 for large text (over 18 point or 14 point bold)
AAA = Contrast ratio of at least 7:1 between background and foreground. 4.5:1 for large text (over 18 point or 14 point bold)
With regards your question does it mean colour blind people have difficulties, that depends on various factors. Consider checking your site on a colour blind simulator such as http://www.vischeck.com/. Personally I think the WCAG guidelines are too limiting at the lower contrast levels. Also they have no limit for high contrast. Too much contrast can often be an issue for users with dyslexia I believe.
If accessibility is core and you have budget find a way to test with users with various disabilities, as colour contrast is only a small part of accessibility. There are companies that offer these services I believe.
Comment: I've read in the guidlines that it's not recommended to follow the exact requirement of AAA for all of your website elements. I think it would be too difficult to reach to that point, and all of you site will look so bizzare.


Ansible user ssh sudo PermitRootLogin disabled

Question: i got this working without a problem when the remote serveur doesn't have the ssh parameter :
PermitRootLogin yes
My working ansible command:
[ansible@myansible ~]$ ansible remoteserveur -a "cat /etc/sudoers"

I want to change the ssh parameter on all my servers to PermitRootLogin no for the security. When this is done, it's no more working.
UNREACHABLE! => {
    "changed": false,
    "msg": "Failed to connect to the host via ssh: Permission denied (publickey,password).",
    "unreachable": true

How could i keep my ansible's user being a normal user and having the possibility via ansible to run command as root.
Many thanks for your attention.
Answer: Are you sure you do not have "become: yes" directive in your Ansible playbook? This directive is responsible for privileged access for the Ansible agent.
https://docs.ansible.com/ansible/latest/user_guide/become.html
Answer: Many thanks Nikolay, it gave me the good way to resolve the problem.
I finaly use :
ansible-playbook permitrootlogin.yml -b -K

-b for "become" and -K "ask for privilege escalation password"
TASK [Disallow root SSH access] ******************************************************************************************************************************************************
ok: [server1]
ok: [server2]


how to flip a pixmap to draw to a texture in libgdx?

Question: So what I'm trying to do is to generate a background image for my game by drawing pixmaps to a texture. So far I can do that, but now I need to draw the pixmaps flipped in the X or Y axis to the texture. However I can't find anything to do so. The pixmap class does not provide that functionality. Then I thought I could draw a flipped texture region to a texture, but so far I haven't found how to do so. So I was wondering how can I do such a thing, would it be possible to flip a png image with other java libraries and then create a pixmap from that flipped image?
Answer: I also don't see other option except to iterate the pixels:
public Pixmap flipPixmap(Pixmap src) {
    final int width = src.getWidth();
    final int height = src.getHeight();
    Pixmap flipped = new Pixmap(width, height, src.getFormat());

    for (int x = 0; x < width; x++) {
        for (int y = 0; y < height; y++) {
            flipped.drawPixel(x, y, src.getPixel(width - x - 1, y));
        }
    }
    return flipped;
}

Comment: Thx! Btw, if you want to flip on the Y axis instead you just do `flipped.drawPixel(x, y, src.getPixel(x, height - y - 1));`.
Comment: Remember to dispose the original Pixmap
Comment: Just in case you need to rotate a pixmap by 90 degrees: I created a method to do this inspired by your idea, see http://stackoverflow.com/a/34362685/2399024
Answer: Here's a solution that doesn't require the creation of a new Pixmap. This code can also be modified to flip a Pixmap horizontally and vertically by swapping corners of a pixmap image instead of swapping pixels on opposite sides of the image.
public static void flipPixmap( Pixmap p ){
    int w = p.getWidth();
    int h = p.getHeight();
    int hold;

    //change blending to 'none' so that alpha areas will not show
      //previous orientation of image
    p.setBlending(Pixmap.Blending.None);
    for (int y = 0; y < h / 2; y++) {
        for (int x = 0; x < w / 2; x++) {
            //get color of current pixel
            hold = p.getPixel(x,y);
            //draw color of pixel from opposite side of pixmap to current position
            p.drawPixel(x,y, p.getPixel(w-x-1, y));
            //draw saved color to other side of pixmap
            p.drawPixel(w-x-1,y, hold);
            //repeat for height/width inverted pixels
            hold = p.getPixel(x, h-y-1);
            p.drawPixel(x,h-y-1, p.getPixel(w-x-1,h-y-1));
            p.drawPixel(w-x-1,h-y-1, hold);
        }
    }
    //set blending back to default
    p.setBlending(Pixmap.Blending.SourceOver);
}


Will a US visa refusal affect my UK visa application?

Question: I am applying UK standard visitor visa with family, but 2 years ago my US visa was refused. I have visited UK few years ago and Europe also. I have a good traveling history but later I tried to apply for a US visa  and it got refused. Is that going to affect my UK visa application?
Comment: US and UK are different countries. If you say you already visited the UK I don't see why the US refusal would influence the UK application.
Comment: It depends on the reason of the refusal. UK and US have different rules. But also a US visa refusal doesn't mean that now you will have an other US refusal. If you doesn't tell us the reasons, we cannot properly answer, but in any case we are not layers not immigration officers, so..
Answer: From this Travel.SE question information about visa refusals is shared between the UK and USA:

The route is a bit circuitous because the UK acts as a proxy for nations in the Common Travel Area...

The US and the UK are connected by the "Five Eyes Treaty".

Its impossible to say whether you will be accepted or not. You won't be rejected outright because of a previous refusal.
Answer all questions honestly. If you answer no to whether you have had previous visa refusals in other countries you could be refused under Paragraph 6 and could hold a UK entry ban:

This means that, if Deception is found, the instant application will be refused and (unless seeking to enter the UK on limited human rights grounds) the applicant will not be granted permission to return to the UK for at least 10 years.

If you answer honestly, you should not be refused just because of a previous refusal. You could still be refused of other factors, but you probably won't be refused outright because of the US visa refusal.


Does Wordpress have a built in message function for presenting notifications to users?

Question: Does Wordpress have something similar to Drupal's drupal_set_message function? I want to notify the user of something and was hoping there was a built in API call to do this.
Comment: Where do you want to notify the user? WordPress has nothing like this built-in, so you'll have to either find a plug-in or roll your own using something like [Toastr](https://github.com/CodeSeven/toastr) (if you want pop-ups).
Comment: A client wants us to redirect to the homepage when a contributor submits a post for review instead of back to the edit post screen. I want to let the user know that their post has been submitted.
Answer: Here's an idea: use the save_post hook to set a session containing the message you want to show the user and then redirect to the home page. In the home page template, check for the presence of that session and show the message to the user.
Something like this:
functions.php:
add_action( 'save_post', 'wpse60249_save_post' );

function wpse60249_save_post( $post_id ) {
    session_start();
    $_SESSION[ 'message' ] = __( 'Your text here...' );
}

index.php (or appropriate template):
if ( isset( $_SESSION[ 'message' ] ) :
    echo $_SESSION[ 'message' ];
    unset( $_SESSION[ 'message' ] );
endif;

Edit 10/21/2012
When I wrote this answer, I did not know that WordPress resets the $_SESSION variable but I learned that a couple of weeks ago while working on a project for a client. Thanks for the reminder about this question, @kaiser! Here is updated code using transients instead:
functions.php:
add_action( 'save_post', 'wpse60249_save_post' );

function wpse60249_save_post( $post_id ) {
    session_start();
    set_transient( 'temporary_message', __( 'Your text here...' ), 60*60*12 );
}

index.php (or appropriate template):
if ( false !== ( $temp_message = get_transient( 'temporary_message' ) ) :
    echo $temp_message;
    delete_transient( 'temporary_message' );
endif;

Comment: `$_SESSION` doesn't work properly in WP. They get unset by core during start up/request start.
Comment: That was what I was thinking...but WP doesn't support sessions so well :s I'll see what I can come up with. Thanks ;)
Comment: Check out [this article](http://devondev.com/2012/02/03/using-the-php-session-in-wordpress/).
Comment: Are transients somehow tied to the particular user viewing the page like sessions? Wouldn't the edited code using transients show the message for all users.  Although with the delete the window of time is pretty short, it still seems possible for another user to get the message instead or also.
Comment: you are missing a braked in the else
Answer: There's an update and an error message, that you can use on the admin_notices hook.
Test Plugin
/* Plugin Name: Admin Notice w test message */
function wpse60244_custom_admin_notice()
{
    return print '

Hi! Look at me! In theory I should even fade out after a short time span!

';
}
add_action( 'admin_notices', 'wpse60244_custom_admin_notice' );

You can throw this in your plugins folder and give it a test.
Sidenotes
You could - in theory also use the admin_head hook to trigger the adding of the action. If you only need it on specific admin UI screens/pages, then check for global $taxnow, $pagenow; or use the admin_head-{$hook_suffix} hook.
Comment: @Joseph Little tired today. What about `return print`?
Comment: Thanks Kaiser; I had forgotten about that. I assumed he wanted the message to show on the front end, though. Btw: `return print`?! Hehe ;-)
Comment: I guess that is valid - I thought that `print` didn't return anything but according to [the docs](http://php.net/manual/en/function.print.php), it *always* returns 1.


Dynamically resize iBooks HTML widget

Question: I want to create a dynamic widget for iBooks 2, but I can not dynamically resize the widget to match portrait or landscape mode. I found Apples documentation for resizing dashboard widgets but this doesn't seem to work within iBooks.
As an alternative it would help, if I can lock the orientation for the widget.
Is there a solution to this problem?
Answer: There is a widget object that is instantiated in dashboard and iBook contexts. It is not clear, however, if it contains any information about orientation.
It may be possible to add a listener for widget.didEnterWidgetMode, as demonstrated in this widget events demo project on github, and then read your window dimensions. This should tell you whether you are in portrait or landscape.

Dynamically resize iBooks HTML widget


What alternatives to Booking.com/Airbnb currently work in Russia?

Question: I'm looking to book an apartment in Moscow for 2 weeks this summer. What alternatives exist for Booking.com/Airbnb, which shut down their operations in Russia last year? Ideally it would be a platform that lets me put down a reservation using a Visa/Mastercard but Mir could also work as a worst case scenario.
Comment: **Comments have been [moved to chat](https://chat.stackexchange.com/rooms/145986/discussion-on-question-by-jonathanreez-what-alternatives-to-booking-com-airbnb-c); please do not continue the discussion here.** Before posting a comment below this one, please review the [purposes of comments](/help/privileges/comment). Comments that do not request clarification or suggest improvements usually belong as an [answer](/help/how-to-answer), on [meta], or in [chat]. Comments continuing discussion may be removed. And if more comment that do not ask for clarification are posted the comments get locked.
Answer: There are two obvious alternatives:

Ostrovok.ru, which is a decade old faithful clone of Booking.com with somewhat better UI, I've used it half an hour ago to book a hotel in Vytegra. Many hotels do not require paying in advance at all — you may pay in cash when you arrive.

sutochno.ru, which is more like AirBNB, but mostly targets business travellers and not party goers. Expect short term flat rentals. It would usually be sufficient to prepay a fraction of stay via Sberbank/SBP instant transfer. Most apartment rentals cannot accept cards anyway.

There are perhaps other options, e.g., try Aeroflot or RZD who will try to upsell a hotel to you.
Comment: I've certainly used onetwotrip but only with airplane tickets. I'm not sure what are their hotel options or how good they are. It's quite possible that it's robust and catered to international audience, but I just lack data.
Comment: Have you tried onetwotrip? they claim to support different payment systems depending on locale I didn't test though(I used them in EU and Russia but not recently)
Answer: I would suggest trying Avito for renting an apartment short-term. As a replacement of AirBnB.
Avito is a general classified advertisement service, so you have to switch to the real estate section. Unfortunately, the service does not have an English language version of the website, but online translation service do a decent job translating it on the fly.


Could an inflatable wing be installed on a Silent glider aircraft?

Question: Would it be technically feasible to install the Pneumagic inflatable wing on the Silent glider?
Answer: Here are some of my thoughts. I'm not fully convinced about the tradeoffs though, which would require a little more work to figure out if it was beneficial:

The wing appears a lot thicker in the article than in the silent glider, adding more drag than the solid wing which it currently uses. To get it as thin would be challenge, since the article suggests that the benefit of adding pressure is marginal for the same wing, so you could only make it thicker. In an convential design, the fabric can be a lot thinner than here were it's got to hold a lot pressure. I'm sure you have to add metal wires to maintain the shape under load, adding a weight penalty.
Using a pure air-based system, I'm also somewhat unconvinced about the 'responsiveness' at the controls, since You'd only be transferring the loads at a single point into the (flexible) structure, rather than across an area as in the article example. An analogy of this is to think of trying to apple a torque force to the center of a pool noodle in water, and to observe the ends relative to the center. You might end up having to make a rather extensive wing root structure to make this work.
The benefit would be portability, but since the silent glider has an engine, this would probably not be of a huge concern, since you could get it where you wanted it.

My verdict: It could probably be done, but I'm doubtful about the performance benefits. Then again, I'm only a first year aerospace engineering student, so you're welcome to come with thoughts and any criticism :)
Comment: "trying to apple a torque force to the center of a pool noodle in water,"....  What???  :-)
Comment: @AyanMullick I don't think so. The inflatable wing dosen't seem to have developed yet even in unpowered cases so at the moment, I don't think so. you might be able to get a wing though which detached and folded in two to fold in flat again the fuselage to save space, like can be done with many conventional (stiff) glider wings.
Comment: http://www.energykitesystems.net/Lift/2011/2011janLIFT.html

These people are trying to build a backpack-able 55lb ultra-portable glider.

These are NASA's inflatable wings.
https://www.youtube.com/watch?v=4SBi9Bffbb4#t=262

Do you thing something equally rigid could be used for gliding. And what is the difference, in material, between this and the Pneumagic.
Comment: @AyanMullick The problem which I primarily see strapping it onto the silent glider is that there is a large increase in weight by adding on an engine and fuselage, which would require it to be a thicker or faster, but I'm pretty sure it could be done, but the benefits would maybe not great. The structure dosen't seem to have a great glide ratio, since the surface isn't smooth. The main difference between the two aircraft appears to be the air pocket structure size. principle is the same.
Comment: @Manfred For the sake of portability,is there any inflatable wing available or in the making that would adequately replace the rigid wing of the Silent Glider ?
Comment: @Lnafziger. *apply* :) And a pool noodle I guess is this: https://www.google.com/search?q=pool+noodle&um


Why is $C_V$ used in adiabatic work by an ideal gas?

Question: For an ideal gas doing work in an adiabatic process, why is dU calculated by:
$$dU = C_v dT$$
The volume definitely must change in order for work to be done, so why is the specific heat that is used the one that assumes a constant volume?
Answer: This is a different definition of change in internal energy and is calculated by keeping the volume constant.
Although in adiabatic process volume has to increase or decrease in order to do some work but this definition of ∆U in terms of specific heat is intact and independent of the change in volume of a system.
In adiabatic process, say we want to find the value of ∆U, so in order to do that we find the change in temperature of the system. Then we can use a separate system in which volume in constant and use this value of ∆T and get the value of ∆U (by using the heat capacity at constant volume formula) of the initial system under observation.
This is how it made sense to me..I had the same question..I hope this clears your problem..
Answer: Internal energy of an ideal gas depends only on the temperature of the gas.
Lets suppose, internal energy is $U_1$ at $T_1$ and $U_2$ at $T_2$,then $(U_1 -U_2)$ will only depend on $(T_1-T_2)$.
The system can go from $U_1$ to $U_2$ by any process possible but you don't need to tell me what the process was,just tell me $T_1$ and $T_2$ and I will tell you  what $(U_1 -U_2)$ will be.
Example :
For a monoatomic gas ,
$$U_1= \frac32 R T_1\,.$$
And,
 $$U_2 =  \frac32 R T_2\,.$$
So,
$$U_1-U_2 = 3/2 R (T_1-T_2)$$
Now in a constant volume process from first law and definition of $C_v$ we can say that,
$$dU = C_v dT$$
The change in internal energy for a temperature change $dT$ is $C_v dT$ for a constant volume process,but as I said already  the process does not matter ,for a given change in temperature the change in internal energy will be same ,no matter what the process is.
So why don't we use the formula  $dU = C_v dT$ for an adiabatic process also ?
Ofcourse we can.
Answer: I think there are three points that deserve to be emphasized:

The internal energy is a state function, that is the difference in the internal energies of two thermodynamic states depends only on the states. It cannot depend on the process going from one state to the other.
The internal energy of the ideal gas depends only on the temperature.

Then not only for adiabatic process, but for any process the internal energy change is given by $dU=C_vdT$. To show this, choose two arbitrary points in a $pV$-diagram and join then by a composite path formed by an isochoric and an isothermal. By the first law and by the result (2) above we get $\Delta U=C_v \Delta T$. For infinitesimally different temperatures, $dU=C_vdT$. By (1), this result must be independent of the process.
The beauty of any state function (such as internal energy, potential energy, entropy...) is that we can compute it by choosing a convenient path/process.
Last but not least,

Work is not always given by $W=\int pdV$.

The above expression is true only for reversible process. It is possible to do work on the system without changing its volume, for example by stirring an incompressible fluid or by doing electrical or magnetic works.


Can briefly explain the principle behind the inversion on this power required curve?

Question: I've noticed on several graphs in the "Advanced Pilot's Flight Manual", that power available is lower for any given speed at 10,000 feet as compared to sea level flight. The power required curves intersect at the sea level best rate-of-climb (BROC) speed. Can someone briefly explain why more power is required at 10,000 feet when below this BROC speed and less power is required at 10,000 feet when above it?
Comment: Aaron, thanks for your input. I actually just finished CPL and started instructor ratings, and as I go I find there are more and more holes in my knowledge. When i was trained all I got was "more power", "more nose down". Not much theory during PPL/CPL.                                         All the questions I have are the ones he sent me to find in the books and many more, most I find in "FTGU" or "Advanced pilot" or online, but some I don't..
Comment: @leha007: Oh, I'm sorry! I thought you had just finished PPL. Even more congratulations are in order! I can totally relate to what you are saying. When I first started helicopter training years ago, I asked my CFI if a certain book would be a good source of information. He told me that he'd seen it before and it was "way too much physics and math". He suggested that I find things with simpler, more functional information... I kept the book and changed the CFI.
Comment: Aaron yeah, most CFI's are like that. I got the one that likes the theory. :)  that's good though, I like learning.
Comment: You may be interesting about sections about the powercurve of [How it flies](http://www.av8n.com/how/htm/power.html#sec-power-curve)
Comment: _"Why is that?"_ -- why is what? There are at least three factual statements in your post, depending on how one parses it. Is there one in particular you are asking about? Are you asking for a broad discussion of the whole concept of Vy? Please edit your question to clarify what it is your question actually is.
Answer: Power required is drag times speed. In essence, you ask why drag at the same lift and in 10,000 ft is growing either side of the best climb speed at sea level.
As @Kolom rightly points out, the coincidence of best climb speed at sea level being equal to lowest drag speed at 10,000 ft is just that, a coincidence. There is no causal relation.
The power required curve is shifted right due to lower density at 10,000 ft which requires the aircraft to fly faster for the same dynamic pressure. The X-axis of the plot is True Airspeed, so all polar points will shift right as altitude increases. Next, you will also note a small upward shift. This is caused by the lower Reynolds number at higher altitude which increases zero-lift drag at the same indicated speed.
The best rate of climb speed is where the local slopes of the power required and the power available curves match. Then the distance between both power curves  is greatest and leaves the highest specific excess power after the power required for steady flight has been subtracted from the available power. If the curves would be plotted over Indicated Airspeed, they would simply shift slightly up for the power required and down for the power available as density drops with increasing altitude. The author of your book chose to plot them over True Airspeed, so it might seem that the best ROC at sea level has some significance for the drag at 10,000 ft. It hasn't.
Please make sure you read the linked answers, too, because they should help to give more background. I have kept the answer short, so some things are not fully explained. For example, why there is a minimum drag point at all is explained at the target of the first link.
Answer: There is less drag on the aircraft at 10,000 feet. This means that the prop can drive the aircraft along at 120kts while moving less air than it would require at sea level. The trade-off is, when the plane is flying slowly at 10,000 feet, with a lot of drag due to the high angle of attack, the prop struggles to move enough air due to the low density of air molecules at altitude.
Comment: Thank you Aaron.


Clear Clipboard on OS X after 'n' seconds

Question: I tab a lot between tasks and would like to make sure that I do not accidentally paste something where it does not belong. Thus, is there a feature or an app that allows me to auto-clear my clipboard after n seconds or after having pasted n times?
Comment: You can use an AppleScrip _command_ `set the clipboard to ""` or from the Command Line, `printf "" | pbcopy` used in this manner will copy nothing thus overriding the general pasteboard (clipboard). Either can be used in Automator to make an App or Service, the latter of which could have a keyboard shortcut assigned. Or in an AppleScript App you could put in the Dock to click when you'd like, etc.
Comment: @Sarge Borsch, As I read the OP the goal was not to accidentally paste what was on the Clipboard to the wrong place and thus clear is to avoid an accidental paste, not hide all history, etc. So I really fail to see the point you're trying to make in your comment to me. Furthermore, I posted it as a comment and not an answer for a reason!
Comment: @user3439894 this will only _add_ empty space as the last item in the clipboard history. It is still possible to observe previously copied items.
Answer: The script below clears the clipboard every S seconds:
#!/bin/sh
# pbclear [seconds]

S=${1:-10}

while true
do
    pbcopy < /dev/null
    sleep $S
done

Save it to a file named pbclear, set executable permissions with chmod +x pbclear, and put it somewhere in your path, for instance, /usr/local/bin. Then run it in the background with  pbclear 60 & to clear the clipboard every 60 seconds.
Answer: You can use:
pbcopy < /dev/null

Answer: Here is the version that will check for clipboard changes every 10 seconds. If there is a change it will clear the clipboard after 10 minutes, but only if there were no new changes in the last 10 minutes.
The reason for this is that a simple solution from https://apple.stackexchange.com/a/331203/41513 may clear the clipboard between you copy something and try to paste it.
#!/bin/bash

clipboard=""
counter=0

while true; do
  # Get the current clipboard content
  new_clipboard=$(pbpaste)

  # Compare the new clipboard content with the previous one
  if [ "$new_clipboard" != "$clipboard" ]; then
    # Clipboard content has changed
    clipboard="$new_clipboard"
    counter=0
  else
    # Clipboard content has not changed
    counter=$((counter+10))

    # If 10 minutes have passed without any changes, clear the clipboard
    if [ $counter -ge 600 ]; then
      echo "Clipboard cleared"
      pbcopy < /dev/null
      clipboard=""
      counter=0
    fi
  fi

  # Wait for 10 seconds before checking the clipboard again
  sleep 10
done


Constants class that should implement an interface

Question: I need to create a class/classes in C# that will contain constants for paper sizes properties like dimensions, aspect ratio, horizontal and vertical resolution etc. for various paper sizes like A4, Letter and so on. The first idea was to create an interface(or abstract class) IPaperSize from which we would have inherited classes A4Paper, LetterPaper etc. with the values stored inside. It also makes sense to make the classes static since it only stores constants, but with the current design I am unable to make it static because of inheriting from interface. What's the best approach here?
Comment: What purpose the interface or abstract class? Don't create one if you don't use it outside of inheritance. If you use it, you can't use static classes either.
Comment: Terminology: one inherits from a class, but implements an interface.
Comment: just use an enum and export an "encode" that maps string names to constants, and "decode" that maps constants to strings. this way your class instances can be used to encode/decode constants in a binary compatible language agonistic way that works everywhere from jscript to assembly. use ifs for small encode/decodes, hash tables for large ones.
Comment: @radarbob Changed, my bad.
Answer:
I need to create a class/classes in C#...

No, you need to create a set of fixed values. Don't instantly therefore think of classes. Leave that decision until later.
So, you need a collection of values, grouped by paper type. The structure that comes to mind therefore is a dictionary. The paper size is the key, the aspects of that size are the value.
Now at this point, we need to make a decision. You talk about many properties of each paper size. But in reality, only two are needed: the width and height. From that, the aspect ratio etc can all be calculated. So do you manually calculate them once and and define multiple properties, or just set the width and height and calculate the other values at runtime? Let's go with calculating them just once at runtime, at startup.
So with that, we now know we need a class (or struct, if you prefer, since we are using C# here. But I'll stick with a class):
public sealed class PaperDetails
{
    public PaperDetails(double width, double height)
    {
        Width = width;
        Height = height;
        AspectRatio = width/height;
        ...
    }

    public double Width {get;}
    public double Height {get;}
    public double AspectRatio {get;}
    ...
}

Then, we need to identify paper types. An enum seems the ideal choice here:
public enum PaperSizes
{
    A4,
    Letter,
    ...
}

Then we can create our dictionary:
private static readonly Dictionary<PaperSizes, PaperDetails> _paperTypes =
    new Dictionary<PaperSizes, PaperDetails>
    {
        [PaperSizes.A4] = new  PaperDetails(297, 420),
        [PaperSizes.Letter] = new PaperDetails(270, 200),
        ...
    };

Finally, we just need a static class to encapsulate that dictionary and to provide read-only access to it:
public static class PaperDetailsPerSize
{
    private static readonly Dictionary<PaperSizes, PaperDetails> _paperTypes =
        new Dictionary<PaperSizes, PaperDetails>
        {
            [PaperSizes.A4] = new  PaperDetails(297, 420),
            [PaperSizes.Letter] = new PaperDetails(270, 200),
            ...
        };

    public static PaperDetails GetPaperDetails(PaperSizes size) => _paperTypes[size];
}

Job done and no need to worry about static classes not be able to implement interfaces. We didn't use constants (other than the width and height values, which are value, not named, constants). If that's a concern, then create a bunch of named constants to define those values and populate the dictionary with them.
Comment: I would probably need to avoid calculation and enter the values manually because of some messed-up API that uses those values, but this is very much what I'm looking for. I already use that enum, forgot to mention it.
Answer: Rather then going with constants, you could create an immutable non-static class (with get-only properties), and provide a bunch of predefined instances. It doesn't really have to inherit anything, or implement any interface, especially if it only stores these values and doesn't have any behavior. If the class is fairy small, consider making it a struct (see this), and providing a custom implementation for GetHashCode and Equals.
As for how to provide these predefined values - you could make another class with a bunch of static factory methods (or properties - A4, Letter, etc.) that return the appropriate instance (creating it on the fly; alternatively, you could instantiate all in advance, and just return existing instances).
Comment: Another way to provide the values to clients is to use an enum and a dictionary - see David Arno's answer. That's probably less work, and possibly more flexible then a class with static properties I mentioned above.


How to make a group of polygons larger?

Question: I need to edit the vertices of about 30 polygons in an equal way, how would I go about this? Alternatively is there some method to just increase the size of a group of polygons 200%?
Comment: Good question.  I hadn't heard of scaling before - it should be part of the buffer tool in my opinion.
Answer: I believe this is possible using the scale tool:
http://webhelp.esri.com/arcgisdesktop/9.3/index.cfm?TopicName=Scaling_features
It might not be enabled by default, so you can turn it on.
Here's a tutorial of how it works:
http://webhelp.esri.com/arcgisdesktop/9.3/tutorials/editor/Editor_Ex4_5.htm
Failing this you could always do a buffer and then union the output with the original file, although this a bit of a 'dirty fix'
Comment: 10:
To use the Scale tool, you must first add it to an ArcMap toolbar from the Commands tab of the Customize dialog box. The Scale tool  is found in the Editor category.
Click the Edit tool  on the Editor toolbar.
Click the feature that you want to scale.
Click the Scale tool  on the toolbar to which you added it.
Move the selection anchor (the x), if necessary, since the feature is scaled based on the selection anchor's location.
Drag the pointer over the feature to scale it, or press the F key to set a scale factor.
Release the mouse button when you are finished scaling the feature.
Comment: I can't find scale in 10?
Comment: I think one way I can get around it - not preffered though - is as I am using data driven pages I can change the extent of my grids..I think
Comment: I can't seem to add it? nothing happens when I click the scale button and check my editor box

How to make a group of polygons larger?


Outlook email and my ip address

Question: If I send someone an email using Outlook online, can the recipient know my IP?
I knew before that it was possible but I was wondering if the email providers like Outlook, Gmail had added some sort of security for that?
Comment: Why are you worried about someone knowing your IP address?
Comment: When using a webclient, the IP of the device accessing the webclient is not part of the email sending process, so your IP is not passed on.
Answer: An e-mail is nothing but text conforming to the SMTP (Simple Mail Transfer Protocol). When accessed through a web client, it appears formatted, but the its source (underlying raw text) can be displayed (in Outlook Web you can click on the three dots on the right side of an e-mail message and then on View message source).
One of the headers present in the source is the Received header, which says where the e-mail was received from. In theory, this could be your personal IP (or domain, if applicable). However, close inspection of the message source will reveal that with most e-mail sending services (Outlook Web itself for example), the Received headers only mention Microsoft server IPs.
If you were to send it yourself however (e.g. by opening a Telnet session to an Outlook SMTP server and sending an e-mail), your IP would indeed be visible by viewing the message source.

Outlook email and my ip address


What is the evidence for the authenticity of St. Paul's writings?

Question: Muslims and even some atheists claim that St. Paul's writings are forgeries, but what is the evidence that the writings of St. Paul are authentic?
Comment: It requires faith to recognise, receive and believe the words that they are holy and come from the Holy Spirit. Many have not that faith. Faith is the _evidence_ (you seek) - the substance of things hoped for, the ***evidence** of things not seen . . . . . as the writer to the Hebrews tells us (who may, or may not, be Paul), Hebrews 11:1.
Comment: There are even many "Christians"  who make the same claim.  "Jesus' words only" adherents are one example (https://jesuswordsonly.github.io/).  This is an important question. +1
Answer: All of Paul's writings, save Titus & Philemon, are quoted within a generation of Paul's lifetime, by people who were in a position to know who wrote them. Many of Paul's letters are quoted by Clement of Rome, who knew Paul personally.
All of Paul's writings, save Philemon, are quoted within 2 generations of Paul's lifetime, by well-informed scholarly writers.
(for Philemon--which is short enough there's not much material to quote =)--we have to wait for Tertullian for our first surviving scholarly citation).
Additionally, every surviving manuscript of the 13 Pauline letters (Hebrews excluded) is attributed to Paul.
Our evidence that Paul wrote these letters is not 2000 years removed from the composition of these documents; in almost all cases it is within a few decades of when the documents were written, and some of this evidence comes from people who knew Paul personally.

Appendix
For a chart of citations of Paul's work by early scholars, see here.
The Pastorals (1 Timothy, 2 Timothy, Titus) are the works attributed to Paul that are most often accused of being forgeries. For a brief, critical review of these accusations, and the assumptions upon which they rest, see my work here and here.
Comment: It's worth noting that the idea Paul wrote Hebrews is still heavily disputed among scholars from what I've seen.
Comment: @LukeHill yes I excluded Hebrews for this reason; it is unclear who wrote it and the best we can do is speculate.
Answer: What is the evidence for the legitimacy of St. Paul's writings?
Hold To The Rod has demonstrated quite well the legitimacy of St. Paul's writings. I simply wish to add a few points here.
To me the best criteria to show their authenticity would be the the Early Church in no form or fashion would have accepted the Epistles of St. Paul if they were deemed forgeries.
Some have made the claim that there are forgeries amongst them because the style, wording, language, etc. Are different between some letters.
For that matter, I have done that in many of the posts I have written here on Christianity SE. Some posts are more personal, while others are a more matter of fact like. The differences do not prove that I did not write those different posts. People, including St. Paul, can freely write in a various manners according to their inspiration, insights and the intended target audience. No problem in my books here.

The Critics' Arguments
The critics' arguments that someone else wrote Paul's three Pastoral letters to Timothy and Titus are based on five main issues.
Historical references in Paul's letters are not consistent with the account of Paul's life in the book of Acts.
The false teaching described in his letters was a clear reflection of the Gnosticism of the second century.
His descriptions of the church's structure better describe the church of the second century and not of his time, the first century.
His letters don't contain the themes of his theology.
The Greek vocabulary in his letters contains words not found in Paul's other letters, nor in the rest of the New Testament.
These arguments are unequivocally and absolutely dismissed by theologians as we'll see.
Theological Refute
Argument #1: The incompatibility of the timeline is because the narrative of Acts ends with Paul's first imprisonment in Rome, not with his death. The argument could only be true if Paul was never released from jail, but we know he eventually was. He even knew he was going to be released (Philippians 1:19, 25–26; 2:24; Philemon 22), and his death did not occur for many years.
Argument #2: Theologians agree there are some similarities between Paul's dissent in his three letters and second-century Gnosticism. However, unlike Gnosticism, false teachers, who based their teachings on Judaist legalism, were still in the church (Colossians 1:7; Titus 1:10,14; 3:9).
Argument #3: The church's organizational structure is quite consistent with Paul's writings such as in Acts 14:23 and Philippians 1:1.
Argument #4: Paul's Pastoral letters do mention the central themes of his theology: the divine inspiration of Scripture (2 Timothy 3:115–17), election (2 Timothy 1:9; Titus 1:1–2), salvation (Titus 3:5–7), the deity of Christ (Titus 2:13), his personal calling by Jesus (Titus 2:5); and substitutionary punishment by Jesus for our sins (Titus 2:6).
Argument #5: The Greek vocabulary and subject matter were necessary because of the audience it was written for. The Pastoral letters were personal letters to Timothy and Titus, who were both Greek.
More Counterarguments
Theologians further point out…

The early church never would have tolerated forged letters as part of Scripture.

If they were forged, why weren't the changes made so everything was consistent with Paul's other writings?

If the letters were written by dictation, does that still count Paul out as the original author?

Finally, why would Paul warn us about deceivers (2 Timothy 3:13; Titus 1:10) if he was one himself? That doesn't make sense. He would have blown his own cover, in a sense.

We can only conclude, then, that Paul's three supposedly forged Pastoral letters were indeed written by him shortly after his release from his first Roman imprisonment. The only exception is 2 Timothy. That letter — his last letter — was written after his fifth and final missionary journey and during his second Roman imprisonment just before his martyred death in 67 A.D.
One interesting side note is that Jerusalem's second temple (sometimes called Herod's temple) was burned to the ground just three years after Paul's death. The third temple won't be built until the days when Jesus returns during Tribulation. - Who Wrote Paul's Letters in the New Testament?

What is the evidence for the authenticity of St. Paul’s writings?


Why was the plane empty in The Impossible

Question: As part of the final scene of the 2012 drama The Impossible, we can observe that the plane that was picking up the injured family has plenty of empty seats and no one else on board aside from some personnel. Given the situation and many people desperately requiring medical help at the airport, why wasn't anyone else put on board?
Comment: Because this is likely paid by their insurance etc.
Comment: Indeed, the plane was provided by Zurich Insurance who would not take on anyone who was not their client.
Answer: Because it was a private plane (deigned for medical transports) that was chartered by the insurance of the injured family, Zurich Insurance. And as such it was only available to their clients.
Arguably, that final scene is another one that hammers home the vast gap between the Thai population and the Westerners: this family can get on this plane and leave the devastation behind and get "proper" medical care in Singapore (and don't share this privilege with other victims), whereas previously in the movie the locals are shown over and over again to share what few resources they have left with anyone needing help.


When did the Pharisees stop being afraid to arrest Jesus?

Question: In the beginning of Jesus's ministry, the Pharisees were angered at Jesus but were afraid of what the crowd thought if they were to arrest Jesus. "They looked for a way to arrest him, but they were afraid of the crowd because the people held that he was a prophet." Matthew 21:46. So, it makes me wonder how they mustered up the courage to arrest Jesus if he became more and more popular. How did they know that if they were to arrest Jesus, the crowd wouldn't turn against them after the display of the crowd just laying down palm trees when Jesus arrived in Jerusalem singing "Hosanna to the Son of David!"?
Comment: I think one factor is that it wasn't just one group that was against Jesus. Both the Pharisees and the Sadducee's were against him. The latter were associated with the priesthood of the day if I'm not mistaken, and were highly involved in the process of arresting and trying Jesus falsely, and getting him crucified.
Comment: They also were very afraid that if the people rebelled against the Romans under Jesus (they misunderstood his ministry), that the Romans would crush the rebellion and destroy the nation. Whereas the Pharisees seemed mostly to just be jealous of Jesus's popularity and upset that he didn't join in with them but rather publicly rebuked them. I'm not a historian—just a history enthusiast.
Answer: As you rightly point out, the Jewish religious leaders were afraid to arrest Jesus in case the crowds turned against them and caused a riot.  Two days before the Passover and the Feast of Unleavened Bread, the teachers of the law were looking for some sly way to arrest Jesus and kill him.

But not during the Feast," they said, "or the people may riot" (Mark 14:1-2).

My NIV Study Bible notes remark that the population of Jerusalem increased from about 50,000 to several hundred thousand.  It would have been too risky to apprehend Jesus with so large and excitable a crowd present.
However, while Jesus was in Bethany, eating at the table of Simon the Leper, Jesus was anointed with very expensive perfume.  This displeased many, but none more so than Judas Iscariot, who was entrusted with the money that was given to Jesus and the disciples.
It was at this point that Judas Iscariot went to the chief priests to offer to betray Jesus to them (Mark 14:10).  This was the unexpected opportunity the chief priests were looking for.  Judas would betray Jesus with a kiss on the evening of the 14th day of Nisan, when the Passover lamb would be sacrificed.   After partaking of the meal with Jesus and the other disciples, Judas slipped out to inform the Jewish religious leaders that he would identify Jesus at the place called Gethsemane.  Now they could make the arrest under the cover of darkness, far from any curious eyes.
The arrest of Jesus was pre-meditated.  The warrant for Jesus' arrest had been hastily issued by the Sanhedrin.  A crowd, armed with swords and clubs, sent from the chief priests, the teachers of the law and the elders, accompanied Judas.  They had lost their fear the moment Judas enabled them to arrest Jesus in total darkness, and without any crowds present.
As a matter of interest, the betrayal of Jesus was prophesied hundreds of years before its fulfilment (Psalm 41:9):

Even my close friend in whom I trusted, who ate my bread, has lifted his heel against me.

I found an interesting article on the six parts to Jesus' trial, three stages were in a religious court and three stages were in a Roman court.  https://www.gotquestions.org/trials-of-Jesus.html
Comment: Up-voted +1. Yes, indeed. It is John who reports Jesus saying _Have not I chosen you twelve, and one of you is a devil?_ John 6:70. And it is John who also tells us of Judas' thieving. Once Judas offers to betray Jesus to the Council, the way is clear for a fake trial and a false execution . . . . .
Comment: Note also: Jesus' popularity took a downswing shortly before his arrest that might've also emboldened the Pharisees. Jesus did two things that annoyed the average Jewish person who considered He might be the messiah: He entered Jerusalem to their praise, but then, to their shock, didn't turn to go to the Roman fortress to kick out the Romans, as they thought the (non-divine) messiah must do, but instead turned to the Temple and whipped the money changers and upturned tables. That confused many.
Comment: The second was a prior to entering Jerusalem, He made the unclean and uncomfortable statement that people following Him must eat His flesh and drink His blood (John 6:66; John 7:12). In both situations, He didn't fit the mould they expected a messiah to, as His first coming wasn't as the fulfillment of messiah (that'd be His second coming), but as the 'suffering servant' of Isaiah, and sacrificial lamb. The people wanted a conquering king to kick out the Romans and save them physically, but Jesus came first to save them spiritually, with the conquering king of physical salvation still to come.
Comment: As the people cottoned on to Him not being interested in kicking out the Romans, they weren't as keen on Him as they were prior. Actions and statements of His led to dampening of public support for Him, including His "Give unto Caesar what is Caesar's" tax comment, Him actually paying the Roman taxes (or sending Peter to on His behalf), and befriending tax collectors and centurions.
Comment: @JaminGrey - Whilst I appreciate your input, comments are there to seek further information in response to what has been posted.  You present an interesting point of view, although I can't agree with your third paragraph. However, this is not the place to pursue the matter and conversations on comments are discouraged.
Answer: When did the Pharisees stop being afraid to arrest Jesus?
If the truth be known, they never stopped fearing the outcome of arresting and putting Jesus to death.
Their hatred of Jesus and his teaching overrode all the fear they may have had about arresting Jesus.
This is bore out in just before Jesus was arrested, when Caiaphas was in council with the leaders and priests of the Jewish nation.

3 Then assembled together the chief priests, and the scribes, and the elders of the people, unto the palace of the high priest, who was called Caiaphas,
4 And consulted that they might take Jesus by subtilty, and kill him.
5 But they said, Not on the feast day, lest there be an uproar among the people.- Matthew 26:3-5

Again they showed their fear of Jesus and his teachings after his death on the Cross.

The Guard at the Tomb
62 The next day, the one after Preparation Day, the chief priests and the Pharisees went to Pilate. 63 "Sir," they said, "we remember that while he was still alive that deceiver said, 'After three days I will rise again.' 64 So give the order for the tomb to be made secure until the third day. Otherwise, his disciples may come and steal the body and tell the people that he has been raised from the dead. This last deception will be worse than the first."
65 "Take a guard," Pilate answered. "Go, make the tomb as secure as you know how." 66 So they went and made the tomb secure by putting a seal on the stone and posting the guard. - Matthew 27:62-66

The incident that ultimately lead the Scribes and Pharisees to overlook their fear about arresting Jesus was when Jesus raised Lazarus from the dead.

According to the Gospel of John, the news that Jesus raised Lazarus from the dead spread like wild fire. Caiaphas the high priest and the Jewish council of the Sanhedrin were enraged. This kind of miracle would surely seduce the people to follow Jesus into rebellion. The fear was that such a rebellion would provoke a clampdown by the Romans.
Then the chief priests and the Pharisees called a meeting of the Sanhedrin.

"What are we accomplishing?" they asked. "Here is this man performing many signs. If we let him go on like this, everyone will believe in him, and then the Romans will come and take away both our temple and our nation."

Then one of them, named Caiaphas, who was high priest that year, spoke up, "You know nothing at all! You do not realize that it is better for you that one man die for the people than that the whole nation perish." (John 11:47-50)

"I am the resurrection and the life. The one who believes in me will live, even though they die; and whoever lives by believing in me will never die. Do you believe this?"

Protecting power and public order was now the real priority and Caiaphas the high priest knew that Jesus must die. - Caiaphas the High Priest - Jesus Considered a Threat
Comment: Some important insights here (+1)
Answer: The crowds did welcome Jesus when He entered Jerusalem less than a week before His death — and yes, they did turn against Him only a few days later. The Bible says they shouted to Pilate (the Roman governor), "Take him away! Take him away! Crucify him!" (John 19:15).
The Pharisees didn't have the courage to arrest Jesus in the daytime because the crowds were going to protest if they do so. So they came to arrest Jesus in the night.

Every day I sat in the temple courts teaching, and you did not arrest me - Matthew 26:55

Jesus Christ was arrested and beaten by the Roman soldiers in the night before Peter denied Him three times. Rather than Him overthrowing the Roman government, the news of Jesus beaten by them was the reason. The reason was expectation was quite contrary to the reality that is happening right in front of them on the next day morning, thereby the disappointment has taken place. On top of this, Judas himself who is one of the twelve disciples deceived Jesus which is again a good excuse for the Pharisees and chief priests to convince some of the gullible audience.

But the chief priests and the elders persuaded the crowd to ask
for Barabbas and to have Jesus executed - Matthew 27:20

Many expected Jesus would declare Himself to be their king, and would lead a revolt against the Romans who were occupying the Jewish nation. In other words, they hoped Jesus would become a political leader. This is the same reason why the disciples were downcast when Jesus Christ was crucified. (cf. Luke 24:13-35)
But Jesus didn't come to set up a new political system. He came instead to change our hearts and save us from our sins by His death and resurrection. He declared during that last week,

"My kingdom is not of this world. If my kingdom were
of this world, my servants would have been fighting, that I might not
be delivered over to the Jews. But my kingdom is not from the world. -
John 18:36.

This deeply disappointed those who hoped He would overthrow the hated Roman occupiers. These reasons have convinced the audience enough to be on the side of Pharisees.
Comment: It is important to note that "the crowds" are not necessarily all the same people. Just as in our society we have many groups with different interests, so did that ancient society. That and I think it very likely that the "crowds" appearing before Pilate were likely packed by Pharisee supporters of one kind or another.
Answer: <OP: When did the Pharisees stop being afraid to arrest Jesus?
It is clear that Jesus ministered from about His age 30 to 33 1/2.  During this time, He performed many miracles.  The Gospel of John identifies seven of them, the last of which is the raising of Lazarus.  By this time, some of the Pharisees believed, but others had been opposed.  It was a sequence of events culminating in His arrest.
Here is one earlier event that references John 10:22-42.

"But Rabbi," they said, "a short while ago the Jews there tried to stone you, and yet you are going back?"  John 11:8

Thomas puts it this way when they are called to Bethany, a mere two miles from Jerusalem, about Lazarus.

Then Thomas (also known as Didymus[fn]) said to the rest of the disciples, "Let us also go, that we may die with him." John 11:16

By this stage, there was opposition, even a failed, half-hearted attempt to stone Him.  But it was this last recorded miracle that some decided it was time to end His ministry.

If we let him go on like this, everyone will believe in him, and then the Romans will come and take away both our temple and our nation." So from that day on they plotted to take his life. John 11:48, 53

Lazarus was the final straw in the decision to arrest Jesus, but when exactly was this?  We know times from what follows, which was the six days before the Passover (John 12:1), but as to precise timing before this, we do not know.  We can, however, narrow it down to between the Feast of Dedication and six days before Passover when the Triumphal Entry took place on the fifth day before.  There is also this mention.

When it was almost time for the Jewish Passover, many went up from the country to Jerusalem for their ceremonial cleansing before the Passover.  John 11:55

This was after Lazarus' and before the six days.

Six days before the Passover, Jesus came to Bethany, where Lazarus lived, whom Jesus had raised from the dead. John 12:1

On the next day, Jesus made the Triumphal Entry.  The Pharisees react again.

So the Pharisees said to one another, "See, this is getting us nowhere. Look how the whole world has gone after him!" John 12:19

Four days later on Thursday they would arrest Him before the Feast of Unleavened Bread.
So, when did the Pharisees stop being afraid to arrest Jesus?  Once they realized the "whole world" was believing Him.  They saw He was a threat to their prestige, power, and pocketbook.  This was sometime between the "six days prior to Passover" and the "raising of Lazarus".  Basically, even perhaps ironically, it may have been about the time of Purim, the commemoration of the deliverance of Israel from Haman in the last month of their year or about 30 days prior to Passover in the first month.


Is Two hours of transit at Atlanta airport enough to catch the other flight?

Question: Its my first time traveling in USA, and i will be transit in Atlanta airport for two hours.
I am afraid to lose the next plane to Florida.
Could you please give me any advice what should I do?
Comment: Please add more details about your itinerary. Where are you flying from and to? Which terminals? Which airlines?
Answer: Provided that all parts of your journey are booked onto the same ticket, the best advice that can be given is: Relax!
Airports and airlines have minimum connection times, and you would not have been able to buy the ticket if the minimum connection time would not be met for your connection. If because of a delay in your incoming flight or long queues at immigration (if you arrive with a non-domestic flight from a non-pre-clearance place), you will miss your outgoing flight, you will be re-booked free of charge by the airline. Obviously you will arrive later then, but at least it doesn't cost anything extra. Also note that before departure of your first flight, that flight is announced to be delayed significantly, you can approach the staff of the airline before departure to already ask for a re-booking.
As already written, if your flight legs are on separate tickets, this does not apply. In fact, 2 hours is rather short unless you are travelling with hand luggage only.
Comment: Don't trust the ticket seller to leave enough time for connections.  Sometimes they do not.  If you are flying into Atlanta (which does not get snow) from a city that does get snow, 2 hours might not be enough.  Check to see if the carrier has a later flight out of Atlanta, in case you miss yours.  Atlanta is somewhat spread out.  But if you walk quickly, you should be fine with 1 hour.  Two hours should be more than enough, no matter if you are switching carriers.  BUT, if you are arriving or departing on an international flight, you probably will need more than two hours.


What would be non-ergodic physics processes?

Question: As the title says, what would be non-ergodic processes that occur in statistical physics?
Many textbooks do not really cover ergodicity really well so I ask this question. I can't suddenly remember any non-ergodic process in physics..
Answer: A process is ergodic if you get the same statistical momenta

considering a single realization for a sufficiently long time,

and by

considering a sufficiently big number of realizations at a precise moment.

In other word you can extract all the information on a process by looking at a single realization for some time. Having said that is clear that any non-stationary process cannot be ergodic (different realizations will behave differently as time goes), but we can have non ergodic stationary processes. Let's see some examples:

Every second you flip a coin and you sample the result: this is a stationary process and also ergodic. If you had flipped $N$ coins at $t=0$ you would have got the same result.
You flip a coin once at $t=0$ and then you sample the result every second: this is a stationary process, but not ergodic. If you had flipped $N$ coins and sampled at $t=0$ you would have got a different mean with respect to the one that you get in time.
You keep flipping the coin and sampling every second until you get head, then stop flipping, but go on sampling. This process is not stationary and not ergodic as well, although both the properties are approached going to big times.
Comment: Could you clarify $3$? The trajectory eventually becomes heads while sampling at $0$ varies.
Comment: @A.S. I do not understand what is not clear...
Comment: In what sense does a process $(3)$ approach stationarity and ergodicity going to "big times"? It becomes constant (head) eventually - so do you stop comparing to the first flip and compare to some other "distant" flip?
Comment: @A.S. Then it's quite a matter of definition. In the definition that I used the sampling of multiple realizations doesn't need to be taken at $t=0$ but at a generic *precise moment*. You could take it at $t\rightarrow+\infty$, then you have a constant process. In a stronger definition you may require that for any time, then this wouldn't work.
Answer: Motion of integrable systems, which are confined to their KAM tori. They don't sample all of phase space, and in fact if they have rational tunes they don't even sample "all of the KAM torus".


Can Alpha Centauri be observed from Eilat Israel, and if so when and for how long?

Question: Wikipedia states that Alpha Centauri is the third brightest star, outshone by only Sirius and Canopus, and can be observed from latitudes south of ABOUT 29°N. With Eilat listed at 29°33′25″N, are the 33′25″ within the range covered by the word 'ABOUT' such that Alpha Centauri would be observable for a short time during the year?
Comment: This would seem to be a trivial question as the maximum altitude (ignoring refraction (but that is also easily known)) is easily calculated by hand. Isn't there a canonical question for this?
Comment: @PeterMortensen based on the answer, it seems this is quite an edge case, and so if there was a canonical answer for it one would have to work hard to find it.
Answer: Mnyah… perhaps, depending on your definition of observable, and the lengths to which you are willing to go.
tl;dr You need refraction and altitude.
Refraction
The 33'25" is, coincidentally, roughly equal to the diameter of the full Moon, meaning that, when α Cen culminates, it is a Moon diameter below the horizon. It is, also coincidentally, roughly equal to the angle of atmospheric refraction toward the horizon, as seen in this parametrization:

Plot of atmospheric refraction vs. apparent altitude, using G.G. Bennett's 1982 formula. Author: Jeff Conrad.
That means that α Cen should juuust graze the horizon. According to Stellarium, tonight it will happen at 5:30 in the morning:

Position of α Cen — here called "Rigel Kent" — at culmination on 19 January 2024, as seen from Eilat. It will reach roughly 30' below the horizon, but refraction should take it roughly 30' closer to the horizon. Created using the free software Stellarium.
Refraction may vary quite a lot. Especially in the spring time, if you have a view over the sea, the heating air can increase quite a lot.
Altitude
Rather than relying on refraction, you could increase your altitude. Stellarium in principle allows you to type in altitude, but (my version of) this feature seems to be broken. So let's calculate:
Using standard trigonometry, you will find that the distance $d$ to the horizon seen from an altitude $h$ is $d = \sqrt{2hR}$, where $R$ is the radius of the Earth. The angle $\theta$ below the horizon that you can see is given by $\tan\theta = d/R$. I've plotted this relation below, from which you can see that you need to increase your height to 200–300 meters (not taking into account refraction).

Google tells me you don't have many tall buildings in Eilat, but the nearby Mt. Shahmon may help you, if you can get a clear view toward the horizon.
Good luck!
Comment: The declination is -60 deg 50', so you can be as far north as 29.17 degrees latitude and have alpha Centauri graze the horizon (in theory).
Comment: @C.Burns But I can really recommend Stellarium. It's easy to use (once you've googled your way to a keyboard shortcut cheat sheet), it's beautiful, and you learn a lot about how the night sky works :)
Comment: Wow great answers...still WHICH DAY of the year would one maximize one's chances of getting a glimpse?
Comment: @C.Burns That depends on your preferred time of the night. With each month, the star culminates two hours earlier (because there's 24 hours/day, while there's 12 months/year). At the moment, you'd have to get up early (5:30). Going forward in time from now, α Cen will culminate earlier and earlier, so e.g. on 21 March, it culminates around 1:30 at night, while on 21 June it culminates at 20:30 (not 19:30 because summertime). I'm in Denmark, so I can't see any stars at 20:30 in the summer, but I suppose you can in Eilat.