What is the concept behind being able to continuously pour iced tea while rolling an airplane?

Question: I recently saw Bob Hoover's famous video in which he is pouring tea while he is rolling the plane. Can you explain the physics that allow the tea to flow "up" when the plane is upside-down? Why doesn't the tea fall out of the pitcher like it would normally if turned upside-down?
Comment: You're better off asking on SE.Physics, but what happens when you tie something to the end of a piece of string and whirl it around your head?  [Centripetal force](https://en.wikipedia.org/wiki/Centripetal_force) you seek.
Comment: I'm voting to close this question as off-topic because it belongs to [physics.se](http://physics.stackexchange.com/).
Comment: See here for the solution: http://aviation.stackexchange.com/questions/489/is-it-safe-to-roll-an-airplane-that-isnt-approved-for-it
Comment: Hi.  Welcome to SE.Aviation!  Please post a link to the video.  My guess is that he performs a [barrel roll](https://en.wikipedia.org/wiki/Barrel_roll) in which case, the force you feel is always towards the floor of the aircraft.  If you closed your eyes, you would not even know that you were rolling.
Comment: Can u please explain how the force is always towards the floor?@simon
Comment: Have you ever been in a rollercoaster, or a fast-maneuvering car?
Comment: Also: [Does centrifugal force exist?](http://physics.stackexchange.com/questions/109500/does-centrifugal-force-exist)
Answer: The maneuver Bob Hoover is performing is a specific kind of roll called a barrel roll.  If you look at the path traced by this maneuver it is a corkscrew rather than a linear path that you might be imagining.  Because the airplane is rotating about a longitudinal axis as it translates forward there is centripetal acceleration toward the axis of rotation, or "up" in the reference frame of the person in the airplane.
To the observer in the reference frame of the airplane (e.g. the pilot or a passenger), the centripetal acceleration is interpreted as the fictitious centrifugal force.  This is exactly the same mechanism that you experience when driving around tight curves, though the force is in a different direction.  The end result in the airplane is that for a properly executed barrel roll, the centripetal acceleration causes the net force you experience inside the airplane to remain constant throughout the roll (in your reference frame, with the net force pointed "down").
If you were to close your eyes you would not know the plane rolled.  Likewise, the iced tea does not "know" it is upside down.  For a less dramatic demonstration, next time you are on a commercial airplane pay attention to when the plane is banking and turning and note that a cup of water on the tray doesn't notice the turn.  The cup stays in place and the fluid remains level (with reference to the airplane).
You can also demonstrate this with a small bucket and some rope.  Put some water in the bucket, tie the rope to the bucket and swing it in a circle vertically (be careful).  The water stays in the bucket if you swing it fast enough, and this is the same mechanism you see in Bob Hoover's video except it is the whole airplane being swung around in a circle like the bucket.
Comment: so we can say that the G force applied by aircraft's floor is more than that of earth's
Comment: @RocK. Gravity is stil pulling you, in exactly the same direction with exactly the same force.  The floor exerts a force opposite to the centripetal force.  So gravity is pulling you down with +1g, centrifugal force is applying a force on you to push you away from the centre of the roll.
Comment: You must fly different airlines to me... The last plane I was on, the cup certainly didn't stay still! Hopefully it was just the copilot practicing his coordinated turns
Comment: For the net force to be constant, would not the centripetal acceleration have to be 2g higher at the top of the roll than at entry and exit? I think that would lead to either a noticeably pear-shaped barrel ( narrow end up) or require an airplane capable of accelerating significantly from entry to the top, and correspondingly able to lose all the excess speed on the way down. From the film I have seen, Bob Hoover's 707 roll appears to be somewhat pear-shaped, though it is hard to tell if the camera is panning.


Squid access.log export to excel

Question: Is there a way to export the contents of access.log to excel spreadsheet so as to manipulate the data from there?
Answer: The squid native log format is :
time elapsed remotehost code/status bytes method URL rfc931 peerstatus/peerhost type
In the fact, you can develop a simple parser using awk or maybe with perl or python, ... and delimit the data with a delimiter of your choice to get a CSV file.
Somethink like this:

 awk '{ print $1","$2","$3","$4","$5","$6","$7","$8","$9","10 }' /var/log/squid/access.log

For more information, please find here a small squid log viewer using python.
http://github.com/mezgani/sqview
Answer: Easy enough with Perl, which has modules for working with Excel, but wouldn't a database be a more appropriate tool? Excel really seems like the wrong tool for this job. Sort of like using a lawnmower to pick flowers. Sure it will work but there are better ways.
Comment: Best. Analogy. Ever.
Answer: Yeah, Excel can read CSV files, so your best bet would be to alter the log format such that it's comma separated (or perhaps some other delineation token).  You can then open your CSV-formatted Squid log using Excel.
See: http://wiki.squid-cache.org/Features/LogFormat
Alternatively, if you don't care to alter the format, you can toss a script together to reformat to include the fields you need.

Squid access.log export to excel


Is the muslim allowed to "waste" his time?

Question: Is the believer allowed to use his time sometimes in activities that don't have many benefits or any benefits for him, such as videogames, watching movies, and the like,
Question: what is the ruling on "wasting" your time?
Answer: In the name of Allah, the Beneficent, Most Merciful
All praise and thanks are due to Allah, the Lord of the worlds. We cannot find words to praise Him, as He only sees fit how laudation should be addressed to Him. We seek refuge in Allah from the evils within ourselves and the evils of our bad deeds. Whosoever Allah guides will never be led astray, and whosoever He leads astray will never find guidance. We bear witness that there is no god but Allah, the One without any associate, and We bear witness that Muhammad is His Messenger and bondman, peace and blessings be upon him, his kith and kin, his Companions and all those who follow their guidance until the Day of Judgment.

Your Question: What is the ruling on "wasting" your time?
Answer The basic principle is that, it is sinful to waste time, because you are doing things that does not benefit you. A Muslim should engage a lot in dhikr.
The Prophet said:

"Take advantage of five matters before five other matters: your youth, before you become old; and your health, before you fall sick; and your richness, before you become poor; and your free time before you become busy; and your life, before your death."

Allah Says:

"O ye who believe! Obey Allah, and obey the messenger, and make not vain your deeds! Qur'an" (47:33)

Both the Quran and the Sunnah emphasize the importance of time in the life of a Muslim. Allah swears at the beginning of many Chapters by time or moments in time, for example, Allah Says (what means): "By the dawn and the ten nights (i.e. the first ten days of the month of Thul-Hijjah)..."[Quran 89: 1-2]
Allah also Says (what means): "By the night when it covers, and by the day when it appears..." [Quran 92:1]
Another verse reads (what means): "By the morning brightness and by the night when it covers with darkness..." [Quran 93:1]
Also, Allah Says (what means): "By the time..." [Quran 103:1]
The whole of mankind is in great loss, except those who fulfill the four qualities or characteristics mentioned in the Surah. Why is the whole of humanity in great loss?-simply because they have lost the meaning and the use of time. And whoever loses these days, these months, these years; whoever loses time, he is in loss; because this is your capital. Any trade that you do, you must have a capital. And our capital in life is our 'Time.'
When Allah swears by something of His creation, it is evidence of its importance, and this directs our attention to the benefit of that thing.
For example, Mu'aath bin Jabal, may Allah be pleased with him, narrated that the Prophet (may Allah exalt his mention ) said: "A person will not move on (on the Day of Judgment) until he has been asked about four things: his life and in what he spent it, his knowledge and what he did with it, his wealth, from where he acquired it and on what he spent it, and his body and how he wore it out."
Ibn Al-Qayyim, may Allah have mercy on his soul, said:

"Wasting time is worse than death, for wasting time severs one from Allah and the hereafter, whereas death severs one from the present world and the people living in it." Whoever wastes his time will inevitably regret losing every single moment of it; and whoever spends a day in his life without discharging a duty, fulfilling a religious obligation, or acquiring some useful knowledge, has indeed wasted that day can squander his whole life in this way.

One's time is the period for work, either to achieve eternal happiness in the hereafter or to cause oneself destruction and misery. Due to the importance of time, Allah has sworn by some of its parts. He has even sworn by the entire time including its nights and days.
Imam Ibn al-Qayyim offers a wonderful metaphor for the year (al-sana) as a sprawling tree and highlights the worse consequences of wasting time that leads to the disobedience of Allah:

"A year is like a tree: the months are its branches; the days are its limbs; the hours are its leaves and breaths are its fruits. He whose every breath was spent in the worship of Allah has reaped the fruits of the tree but he whose every breath was spent in disobedience to Allah, his fruits are poison".

References:

Do Not Waste Your Time!
WASTING TIME
"Beware of Wasting Time"
Wasting Time
List Hadith on wasting time is a sin/haram?
Answer: "Wasting time cuts you off from Allah and the hereafter, whereas death cuts you off from worldly life and its people." - Imam Ibn Al-Qayyim
If the video games or movies don't boost your spirituality but include inappropriate scenes and language then this can affect your spirituality and perhaps take away focus in prayer.


ISP 5 Device Limit ... again

Question: Sorry for the delay in responding to the suggestions that were posted in my first question (ISP 5 Device Limit - double NAT the solution?). I've been travelling and have not been able to try anything. Below is what I've tried and where I have not been successful. Any more help gratefully appreciated.
I figure I need to give a more comprehensive overview of what I've got and how it's set up.
First of all - I am using all Apple products here. I am iMac, iPad, iPhone, Apple TV, Airport Express and Time Capsule. I used to like the way that it 'just worked'. Now I find that it requires a bit of encouragement before it 'just works'.
So, as I stated in my original question; my ISP has a router in my building that is limiting me to 5 devices. I am hard wired into this router and I can neither access it physically nor logically (they won't let me access it). Also, I only appear to be able to connect to it through the LAN ports on my Time Capsule. Any device I connect appears to be on a rolling IP list with the following settings:
Router  188.8.131.52
Devices then get assigned IPv4 addresses in the range (as far as I can see) from 220.127.116.11 onwards.
SubNet Mask  255.255.255.0
DNS Servers 18.104.22.168, 126.96.36.199
I have my Time Capsule / Router in Bridge-Mode which means I am limited to the 5 devices and cannot use Guest Networks etc.
What I've tried today.

Static IPs:
On all devices, I went from DHCP to Static and put in the same information when they had connected using DHCP. Somewhat surprisingly this did not work. None of the devices enjoyed any  connection to the router and certainly no internet connection.

Intentional Double-NAT - Time Capsule to 'DHCP and NAT':
By selecting DHCP and NAT on my Router I was able to connect devices to my Time Capsule in the range 10.0.1.2 to 10.0.1.200. This offered no internet connectivity and didn't really help the situation. In this mode, however, I was able to force the devices - individually and laboriously - to look for the Router and previously listed DNSs by inputting the numbers from 'Bridge-mode' into the STATIC settings and then resetting the connection. The Router then appeared to assign a distinct IP address to the device and it worked on the network. I had this working for more than 5 devices. However, this is not a great solution because as soon as one of the mobile devices left the building it needed repointing to the Router. The connections were also not very stable. Especially when trying to hold onto a VPN.

Spoofing a few MAC addresses:
I'm afraid I don't really know what this would achieve, nor how to do it on an Apple device…

So … I'm almost back at Square One. I have had to withdraw to the Bridge-Mode position again with the 5 device limit to see if there's a better course of action to follow.
ANY help would be much appreciated. I am positive that I cannot be the only one suffering under this 5 device limit!
Answer: Fixed it.
In the end, I did two things.
1.Connecting the Ethernet cable into the WAN (rather than LAN) port of the TC.
2.Resetting to TC to factory defaults and setting it up again. The only discernible difference being that IPv6 went from Automatic to Link-Local only.
Regardless, it now just works. I think I was thrown by the '5 Device Limit' that I was told about which led me to try and get around that limit and trying to be too clever about it all!

ISP 5 Device Limit ... again


Why is green considered a toxic color in movies?

Question: In movies I often see green used to color dangerous and/or poisonous substances colored green, like green clouds of gas considered poisonous, and green acid considered dangerous. Can anyone explain this, or explain where this came from?
Comment: Because the people invoved don't like Broccoli? (Unless they are doin a James Bond movie, that is)
Comment: Related question on Chemistry.SE: [Why are acids usually depicted in fiction as green?](https://chemistry.stackexchange.com/q/43989/7951)
Comment: Or the Pepto Bismol color of Klingon blood whom were considered "evil" at times. I always thought pink blood was rather an odd choice for such a hearty warrior race.
Comment: Ha, I made a reference to this question in a world building question a couple days ago. Nice to see the answers (I didn't know arsenic was green), so thanks for asking!
Comment: This is a really great question (with great answers), but at the same time I do not think it can be on-topic, since it does not ask about a specifically SFF trope. I am thus voting to close.
Comment: Well holy crap, I did not expect such a simple question to get so much attention! But I want more answers, as they are quite intriguing and entertaining to read.
Comment: If it's not appropriate here, could this question be migrated to a more appropriate SE site?
Answer: Because it was forever linked to poison by Radium and Green pigments in the 1800's. Paris Green and Scheeles Green in particular helped cement this association early on.
Radium Poisoning

It was clear from the beginning large doses of Radium was dangerous, the Curies made it clear early on, but it was commonly held that in small doses Radium was beneficial.
Those who painted radium watches suffered from drastic Radium poisoning, and would glow green. The radium girls destroyed the reputation of Radium, giving us the classic radioactive green glow association

https://en.wikipedia.org/wiki/Radium_Girls
https://www.spectator.co.uk/2016/06/the-radium-girls-still-glowing-in-their-coffins/

What Made Green Pigments So Toxic?
Both were arsenic compounds that produced popular shades of green, known for their brilliance. They were excessively used

Paris green (copper(II) acetate triarsenite or copper(II) acetoarsenite) is an inorganic compound. It is a highly toxic emerald-green crystalline powder3 that has been used as a rodenticide and insecticide,[4] and also as a pigment, despite its toxicity.

https://en.wikipedia.org/wiki/Paris_green
So much so that Paris Green was later used as an insecticide. It was used to kill mosquitos, and in the Paris sewers to kill rats.
https://en.wikipedia.org/wiki/Paris_green#Insecticide
How Did They Respond in the 19th Century?
Green gained an ominous reputation, with tales of women in green dresses collapsing, newspaper printers being overcome by fumes, and children wasting away in bright green rooms

https://en.wikipedia.org/wiki/Scheele%27s_Green#Toxicity
Famous Deaths
It's widely implied that these green pigments contributed to Napoleons death due to the lavish green suite he slept in.
There are also reports it caused health issues with famous artists who used the pigment, such as blinding Monet
Other Dangerous Colours
There are other colours with similar associations, I would recommend this Ted Ed video
Comment: I was reading your answer, and was going to link to that Ted Ed video if you didn't. Very nice answer! :)
Comment: Well, there is always absinthe.
Comment: Thanks @Shokhet ! If you know any more references I can add let me know :)
Answer: This comes from Real Life; see Why is green the color of poison? for example.

Have you ever wondered why poison is so often associated with the color green? Take movies or video games, for example: even the vials containing poison would frequently be made of a green glass. Sure, there are poisonous plants and all, but look no further than the 18th century, when some toxic green pigments forever ruined the reputation of the color.
...
The beloved pigments of Cézanne and Monet, who excessively used them in paintings, Scheele's and Paris green were so toxic that they were routinely used to kill the rats. So toxic, in fact, that Monet's blindness, Cézanne's diabetes, and even Napoleon's death are still blamed on them.
Answer: Chlorine gas, used as a chemical weapon in WWI, killing thousands of people, is green. Since then, green gas is associated with poison in popular media, including sci-fi and fantasy.

quote from Wikipedia on Chlorine discovery
Scheele observed several of the properties of chlorine: the bleaching effect on litmus, the deadly effect on insects, the yellow-green color, and the smell similar to aqua regia.
Comment: Do you have a source showing that this is not simply a coincidence?
Comment: @armflare it is hard to provide a concrete source to such a widely used concept. I remember reading a historical novel on WWI (do not remember the title) and it was stated that survivors of that particular gas attack only remembered green gas and dead bodies of their fallen comrades. Also, since school chemistry classes, everyone should remember that green gas is a deadly poison. It became common knowledge so far.
Comment: This strikes me as unlikely since so few people would see chlorine gas (only the particular soldiers and scientists that encountered it). However many people would've seen green wallpaper (mentioned in Tom Nowell's answer) which could let it enter people's heads easier as 'toxic color'.


Remote Garage Door Opener

Question: I live in a condo, we have a shared garage but our own automatic garage door openers.  My garage door opens and closes with the button inside the garage hard wired on the wall.  But, my remote opener stopped working.  I just had a new battery put in hoping that was the issue.  It's still not opening the garage door.  Is it possible to get the circuit board inside replaced?
Comment: I would suggest trying to re-pair the remote with the opener before replacing anything; if it's a modern one that automatically learns the code from the opener, it probably forgot it when you replaced the battery.
Comment: Have you talked to your condo association?  Since the garage door is shared, there's certainly an expert who knows all about this door system, and has seen this problem before.
Answer: You might not have to replace the door opener circuit. Genie, for instance, sells a conversion kit that sits inline with your wall panel. The unit has its own radio receiver and works with any Genie compatible remote (which are easy to find). I've used these on some off-brand openers where the remotes died and replacements were impossible to find. They work great.

Remote Garage Door Opener


Question considered off-topic

Question: Why is this question considered off-topic?
Answer: Because trying to use a non-powershell command line on a 17 year old, unsupported Windows server is the poster child for the reasonable information technology management practices close reason.
Answer: This is a case where Stack Exchange's desire to be nicer leads to confusion.  I forget the explanation of why it's nicer, but details of why a question was closed are hidden from anyone with less than 3000 reputation.  You see this short explanation:

Closed. This question is off-topic. It is not currently accepting answers.

Want to improve this question? Update the question so it's on-topic for Server Fault.

A longer explanation of why it's closed is shown to people who are able to cast close and re-open votes and would have answered your question:

Closed. This question is off-topic. It is not currently accepting answers.

Questions should demonstrate reasonable information technology management practices. Questions that relate to unsupported hardware or software platforms or unmaintained environments may not be suitable for Server Fault.

Closed 3 days ago by Greg Askew, Swisstone, Dave M, womble♦.

(Viewable by the post author and users with the close/reopen votes privilege)
Comment: Actually, [the off-topic reasons have been upgraded](https://serverfault.com/admin/flags/site-specific-close-reasons) and some mods have initiated a discussion on their meta sites to personalize the messages, though the public-to-all "close description" is empty by default since the migration to the new design, and mods also need to deactivate the current reason to modify it...

Question considered off-topic


Can you only read the al-Fatihah in any prayer and rakaat?

Question: So,sometimes I want to do a sunnah prayer but the problem is that I have no time. Even if I do,it's not very long. So,I always think to myself "Can I do it without reading the extra surah after the al-Fatihah? Is it allowed? Will Allah accept it?". Finally,I've found this website and I hope this will help me.
Comment: Praying is a duty for every Muslim saying you don't have time for that already is sinful because prayer is the most important worship as it is a daily duty with specific timings that one is ordered to respect. Anything else in this life is compared to that of no value, as nothing should hinder you from obeying Allah. See also https://islam.stackexchange.com/q/51361/13438 and https://islam.stackexchange.com/questions/49489/can-you-read-sura-fatihah-after-the-fatihah-in-salaah
Answer: You need to recite an extra surah other than Fathihah for prayers. But you dont need to do a long surah, why not a single verse from Ikhlaas or Naas.
We can recite verse 2:255 but not 112:1? Both are single verse but only size differs. So if you dont have time, just recite a single line of a surah and that will be enough.
Answer: According to some scholars, if you choose to read a surah after Surat al Fatihah, you must read at least 3 verses, or 1 verse which is equivalent to 3 verses.
You may read only surah Fatihah, then move on to rukoo, but ask yourself this:
Do you love Allah enough to omit 1 surah, after al Fatihah, when, from my experience, a very few amount of Muslims omit reading a surah after reciting al Fatihah?
Be a good example to all Muslims.
Proof from Sunnah:
https://sunnah.com/muslim/4/45
https://sunnah.com/muslim/4/46
Assalam u Alaykum WaramatUllahi Wabarakatuhu
Comment: Try to bring on more evidence to back up your answer


$\sum_{n=0}^{\infty}(-1)^n a_n = \pi$, $a_n\in \mathbb Q$ and not $a_n$ not monotonic

Question: How can I construct a sequence $\{a_n\}$ of positive rational numbers, which is not monotonic such that $$\sum_{n=0}^{\infty}(-1)^n a_n = \pi$$
I thought a lot on this question but I always come up with a monotonic sequence. Any help will be appreciated.
Comment: pick your favorite monotonic sequence such that $\sum (-1)^n a_n = \pi$, and then swith $a_0$ with $a_2$.
Comment: Take your favorite sequence $(a_i)$ of rationals such that your sum converges to $\pi$. Form a new series as follows: after the $a_i$ become less than $1/10$, insert terms $1/10$ and $- 1/10$ as appropriate.  After the $a_i$ become less than $1/100$, insert terms $1/100$ and $-1/100$ as appropriate ...
Answer: From Madhava formula, we have
$$\pi = 4 - \dfrac43 + \dfrac45 - \dfrac47 \pm = \sum_{n=0}^{\infty}\dfrac{(-1)^n 4}{(2n+1)}$$
We can write $\dfrac1{2n+1} = \dfrac{k\sqrt{n}+1}{2n+1} - \dfrac{k\sqrt{n}}{2n+1}$. Hence, we have
$$\pi = \sum_{n=0}^{\infty} \left( (-1)^n\dfrac{\sqrt{n}+4}{2n+1} + (-1)^{n+1}\dfrac{\sqrt{n}}{2n+1}\right) = \sum_{n=0}^{\infty}(-1)^n a_n$$
Writing it out, we see
$$\pi = \dfrac{\sqrt{0} + 4}{2 \cdot 0 + 1} - \dfrac{\sqrt{0}}{2 \cdot 0 + 1} + \dfrac{\sqrt{1}}{2 \cdot 1 + 1} - \dfrac{\sqrt{1} + 4}{2 \cdot 1 + 1} + \dfrac{\sqrt{2} + 4}{2 \cdot 2 + 1} - \dfrac{\sqrt{2}}{2 \cdot 2 + 1} + \dfrac{\sqrt{3}}{2 \cdot 3 + 1} - \dfrac{\sqrt{3} + 4}{2 \cdot 3 + 1} + \cdots$$
where $a_n$'s are as desired, i.e.,
$$a_n = \begin{cases} \dfrac{\sqrt{2k}+4}{2 \cdot (2k)+1} & \text{ if $n = 4k$}\\ \dfrac{\sqrt{2k}}{2 \cdot (2k)+1} &\text{ if $n=4k+1$}\\ \dfrac{\sqrt{2k+1}}{2 \cdot(2k+1)+1} & \text{ if $n=4k+2$}\\ \dfrac{\sqrt{2k+1}+4}{2 \cdot(2k+1)+1} & \text{ if $n=4k+3$}\end{cases}$$
Below is the pictorial representation of the sequence $a_n$. The first $44$ values of this sequence are plotted. As you can see from the figure below, the sequence oscillates up and down and is not monotonic.

Below is the convergence of the partial sum $\displaystyle \sum_{n=0}^N a_n$ to $\pi$. The $\color{red}{\text{red line}}$ is the value of $\pi$ for reference. You can see how the partial sums converge to $\pi$.

I didn't see $a_n \in \mathbb{Q}$. Here is the answer if you want $a_n \in \mathbb{Q}$. $$\dfrac1{2n+1} = \dfrac2{2n+1} - \dfrac1{2n+1}$$
Hence,
$$\pi = \sum_{n=0}^{\infty} \left({(-1)}^n\dfrac{8}{2n+1} + (-1)^{n+1} \dfrac4{2n+1}\right)$$
$$\pi = \dfrac81 - \dfrac41 + \dfrac43 - \dfrac83 + \dfrac85 - \dfrac45 \pm \cdots$$
Now choose $a_n$'s as follows.
$$a_n = \begin{cases}\dfrac{8}{4k+1} & \text{ if $n=4k$}\\ \dfrac4{4k+1} & \text{ if $n=4k+1$}\\ \dfrac4{4k+3} & \text{ if $n=4k+2$}\\ \dfrac8{4k+3} & \text{ if $n=4k+3$}\end{cases}$$
Comment: I see how you solved it and loved the way you justified it. Thanks a ton. I really appreciate it..
Answer: There are a few methods possible for achieving this. One is to make use of Newton's method as it applies to $\sin(x)$ (which will repeatedly overestimate the step by a small amount). That is,
$$
\Delta x = -\frac{\sin(x)}{\cos(x)} = -\tan(x)
$$
Choose a starting value slightly above $\pi$, say $a_0=3.5$. Then let $a_n=-\tan(\sum_{i=0}^{n-1} a_i)$. Each term will then be of opposing sign relative to the one before it, and it will converge rapidly to $\pi$.

EDIT:
Oh, just noticed the "$a_n\in\mathbb{Q}$" condition. This can be enforced by simply using a rational approximation to $\tan$ for each step, simply requiring that it be, for instance, $\frac1m$ for the integer $m$ that makes it nearest to the value of $\tan$ that is a longer step than $\tan$ itself. For instance, the first iteration has $a_1=-\tan(3.5)\approx -0.374$. The nearest value of $m$ is thus $3$, but that makes it a smaller step, so choose $2$, and you have $a_1=-\frac12$.
Then, $-\tan(3)\approx 0.142$, which is nearest to $\frac17$, but that's too short a step, so we take $\frac16$. Now $-\tan(3+1/6)\approx -0.0251$, so the nearest is $\frac1{40}$, but again, too big a step, so use $m=39$. And so on. The sequence of values of $m$ is thus (in absolute value, for each step):
$$
2, 6, 39, 1763...
$$
Comment: Thanks for taking time to look at my question. I appreciate it
Answer: As a conditionally convergent series can be rearranged to give any value at will, use your favorite of those series (mine happens to be $\sum_{n \ge 1} \frac{(-1)^n}{n}$). The trick is to pick positive terms until the sum is larger than your target $\pi$ (there is $a_0$), then pick enough negative terms to fall bellow (your $a_1$), and keep going.
No, not exactly a nice set of terms, and it can be considered cheating as you need to know your target beforehand.
Answer: if $\sum_{n=0}^{\infty}(-1)^n a_n $ is absolutely convergent then all rearrangement will still converge to the same value.
So take any sum $\sum_{n=0}^{\infty}(-1)^n a_n = \pi$ that is absolutely convergent and rearrange them in a way that are not monotonic.
Comment: I needed that statement to understand the question. Thanks


401(k) distribution tax calculation

Question: Wanting to receive $25k distribution from my fully vested 401k w/former employer.  Figuring required 20% withdrawal penalty to be $5k (25,000 x20%), so my account balance would be reduced by a total of $30k.  However, they are telling me it will be a $31,250 deduction (25,000 / .80).  Is this right?  Im paying tax on the tax penalty?   Plus then I'll owe the IRS another 10% penalty at time of filing on which figure, $25k or $31,250?
Answer:
I'm paying tax on the tax penalty?

No, you're paying tax on the amount withdrawn to cover the tax. If you withdraw $31,250, you'll pay a tax of $31,250 * 20% = $6,250, netting $25,000.  This process is typically called "grossing up".
You could withdraw $30,000 and pay the other $1,000 of the $6,000 tax (plus the $3,000 penalty) out of pocket.

Plus then I'll owe the IRS another 10% penalty at time of filing on which figure, $25k or $31,250?

You'll owe a 10% penalty on whatever is withdrawn, so if you can't cover any tax out of pocket, you'll have to withdraw a total of 25,000 / (1 - 0.2 - 0.1) = 35,714.  You'll pay a 20% tax of 7,143 and a 10% penalty of 3,571 for total tax/penalty of 10,714, netting you $25,000.
So you're effectively paying 43% in tax and penalty.  Still want to make that distribution?
Comment: @Ben true, it would be taxed at the marginal rate when filed. But 20% is withheld and is still considered a withdrawal that is also taxed.
Comment: Where's this "20% tax" coming from?  20% is taken off the distribution as a forced payment of estimated tax, but **there is no actual 20% tax**, at the end of the year the income tax and penalty will be calculated and reconciled against the advance payment, with the difference due (or refunded).
Comment: I wasn't familiar with the grossing up method to calc. the 20% penalty. Thx.for all your detailed responses.
Answer: If this acct has a balance you are not disclosing, and you requested $25K in a way that specified 'net', then yes, a $31,250 distribution with $7500 withholding, will net you $25,000.
You then still owe $3,125 penalty if under 59-1/2, and still reconcile taxes at year end.
Is the need to withdraw urgent? Best to avoid it, if not.
In response to Ben's comment to D Stanley's answer, I'd like to add an important point/clarification.

A retired couple (with zero other income/no social security payments, etc, but over 55, so no penalty on 401(k) withdrawal), withdraws $100K. $20K is withheld.
$76K is taxable after standard deduction. Tax due is $8739. The mandatory 20% withholding is far more than would be needed to cover the tax for most taxpayers. Note: The top 10% of all earners is $120K or so. For the OP of this question it implies he needs to do the math to understand the actual tax due vs the 20% withheld. For others, it means a strategy of regularly transferring funds from one's 401(k) to an IRA to be able to fine tune the percent withheld.

401(k) distribution tax calculation


Describe geometrically the elements of the equivalence classes

Question: After showing that the relation $R$ defined on $\mathbb R\times \mathbb R$ by $((a,b), (c,d))\in R$ if $|a|+|b|=|c|+|d|$ is an equivalence relation (I already did), how can I describe geometrically the elements of the equivalence classes $[(1,2)]$, respectively $[(3,0)]$?
Answer: The equivalence class is the set of points in  $(x,y)\in \mathbb{R}^2$ such that $|x|+|y|=3.$ Try picking some various branches of the $| \cdot |$ and plot those lines to see what it looks like.
Answer: HINT: A pair $\langle x,y\rangle$ belongs to $[\langle 3,0\rangle]$ if and only if $|x|+|y|=|3|+|0|=3$; what's the graph of the equation $|x|+|y|=3$? More generally, for each $c\ge 0$ you have an equivalence class consisting of all $\langle x,y\rangle$ such that $|x|+|y|=c$; what does the graph of that equation look like?
Answer: Do you know any important properties of equivalence classes. One is, as it pertains to this example:
$$\bigcup_{[(x,y)]\in R}^{} [(x,y)] = \mathbb{R} \times \mathbb{R}$$ This should give tell you that $[(1,2)] = [(3,0)]$ for starters. To get an idea behind the geometry, try starting from the point $(1,2)$ and begin moving parallel to one of the axes and think about how you need to adjust the other coordinate to find other members of $[(1,2)]$.


What does market cap (or market capitalization) mean?

Question: When I look at my Google finance page, and I look at a company, lets say Citigroup for example, and I see that the market cap is 83.45 billion, what does that mean?  Does that mean Stock Price X Number of shares outstanding?  Because if so, that doesn't add up.  Also, by issuing more shares of a stock, does a company affect their market cap?
Answer: Market cap is basically the amount of money that it would cost to buy all of the shares of public stock in a company.  Or  share cost * number of outstanding shares.
It is a measure of how much a company is worth.
http://en.wikipedia.org/wiki/Market_capitalization
Comment: Welcome, harmanjd!  I'll add: anybody wanting to actually buy all of the shares of public stock in a company would realize it's impossible to do without their buying activity driving the market price up. So, market cap is more a theoretical figure for valuation.
Comment: It is actually a measure of how much capital the company has in secondary markets. The company's worth will also include any long term debt obligations it has, private shares, and its realizable assets --none of which appear directly in the market cap (unless of course the share price reflects that information).
Answer: Market cap is the current value of a company's equity and is defined as the current share price multiplied by the number of shares. Please check also "enterprise value" for another definition of a company`s total value (enterprise value = market cap adjusted for net nebt).
Regarding the second part of your question: Issuing new shares usually does not affect market cap in a significant way because the newly issued shares often result in lower share prices and dilution of the existing share holders shares.
Answer: Market Capitalization: Market Capitalization also known as the market cap, it is the total value of a company. The market cap helps in knowing how big or small a particular company is according to its share capital. The market capitalization is affected by the fluctuation in the share price of the company.
Calculation of Market Capitalization:
Market capitalization is calculated by multiplying the company's outstanding share capital with the current share price of the company.
Market Capitalization= Total  No. of Outstanding Share × Current Share Price
Outstanding Share: Outstanding shares are those shares which are issued by the company and available for trade on the stock exchange. As well as the promoters, investors and restricted shares also known as the outstanding share. Outstanding shares are those which are issued by the company, but not repurchase.
Free Float Market Capitalization: Free Market Capitalization means using only the share price of that shares which are on trade in the market for calculating market capitalization.
Free Float Market Capitalization = No. of tradeable shares  × Current price of shares
The number of trade-able shares is available on the website of NSE and BSE. Trade-able shares do not include the shares of shareholders or promoters.
Mainly there are three types of Stocks:

Large Cap Stock: Large Cap Stocks are those whose capitalization value is more than 1000 crore. These type of stocks are low risk-taking than mid cap and small cap. Which means these stocks are more secured.
Mid Cap Stock: Mid Cap Stocks are those whose capitalization value is between 500 crores to 1000 crore. These stocks are neither more risk-taking nor less risk-taking.
Small Cap Stock: Small Cap Stocks are those whose capitalization value is less than 500 crore. These stocks are more risk-taking as it is for less time.
Comment: What's a crore?


Renewing US driving license while living in UK (I still have a US address BUT no UK license)

Question: I have been living in the UK on a long-term basis (married to a Brit) but regularly return to Connecticut to visit family, etc. My license is up for renewal next month--I was told I could do this online or my mail but everything I've googled suggests I need to do it in person at the DMV/AAA location. A) Is this the case and B) I've seen elsewhere on this site that this may not be legal?? I still have an address in the States (the house I grew up in, stay in while visiting, and will inherit when my parents pass) and get bank statements for my US accounts sent to it.  I NEED to be able to drive in the US since everything is so far apart and public transport non-existent where I'm from. Using a British license is not an option since I don't have one.  I've always used public transport or walking since I arrived here, so have never needed a car or license.  What are my options here?
Comment: I think your best option is to go through the hassle and expense of getting a full UK license. Once done, that license is valid for driving for any of your visits to Connecticut for up to 90 days. I know this doesn't answer your question and may seem daunting (been there myself), but once done, everything becomes much much simpler. If local ID is an issue, you should consider applying for a Connecticut State ID https://www.dmv.com/ct/connecticut/apply-id-card, which from your description, and the vagueness of the rules of state residency, shouldn't be too much trouble for you to acquire.
Comment: Sorry, I've since discovered that I can in fact renew by mail, but the 2nd question still bothers me.
Comment: You could edit your question to take out the part you've already figured out, or to post (inside the question) an update with the new information you found.  (I agree that it can be done remotely.) // You could phone a DMV office and ask.  I doubt it's illegal, but if you're concerned, you could ask in general terms, without giving your name.  I don't think they would ask you for it. // I suppose one option would be to get a UK license; however, renewing the NY license sounds viable.
Comment: Related: https://expatriates.stackexchange.com/q/15829/11369
Comment: In principle you're supposed to *get* a UK license because that is where you actually reside.  But since you maintain an address in Connecticut you might be able to maintain your license there, too. Be careful to consider whether this has implications for your income tax liability in Connecticut.
Comment: Hmmm...it does seem a bit much to pay for driving lessons, learn the rules of the road and pass a test to drive in a country I have no need or intention of driving in, just to be able to drive back in the States!  Why is there no provision for expats? I also don't think I'd have time to do this before our next visit which means I'd be stranded at my parents' house for the whole visit. Surely this also means that when I do move back to the States, I would need to pass a test there all over again as well?
Comment: @ouflak why 90 days? In general as long as the driver does not establish residence in Connecticut the foreign license should be accepted for at least a year.  The problem is that the continued use of the Connecticut address might be seen as maintaining residence there (in which case, of course, renewing the Connecticut license is the correct course of action). The worst situation would be for both jurisdictions to consider that Bethany is a resident and therefore needs a license issued by that jurisdiction.
Comment: @phoog If considered resident by both jurisdictions, Bethany would only need a Connecticut license. There is no problem being resident in the UK without a UK driver's license if you don't drive in the UK.
Comment: @PatriciaShanahan of course.  I forgot that Bethany isn't driving in the UK.  It would only be problematic for someone who wanted to drive in both places.
Answer: If I understand your problem correctly it is to retain a valid license apon return to your home country and not to actually drive while in the UK.
As a general rule a driver's license is residence based.
When you move, often longer than 6 months (UK 12 months), you must convert your existing license to a local license if you want to drive there

the converted license will contain the information about your original license

It would seem that US licenses cannot be converted and that a theory and practical tests are needed.
When returning from the UK, with a valid UK license, as a visitor to the US you can use that license and convert it back to the original license should you one day return permanently to the US.
Answer: I can't find a definition for "residence" or "resident" in Connecticut law that applies to driver licensing. I found a definition for purposes of Connecticut income tax:

You are a resident for the taxable year if:

Connecticut was your domicile (permanent legal residence) for the    entire taxable year; or
You maintained a permanent place of abode in Connecticut during the entire taxable year and spent a total of more than 183 days in Connecticut during the taxable year.

So if you claim to be a resident for driving purposes, you might have a hard time claiming you are not a resident for income tax purposes. Maybe a CPA could offer suggestions.
Comment: @Bethany What about your driving insurance?
Comment: The challenge with insurance, however, is that while permissive users are covered, they're only covered *if they're properly licensed to drive.* If you have a CT license which you obtained by asserting that you live in CT, it's possible that an insurance claim would be denied if the insurance company discovered you're actually resident in the UK, and therefore obtained the CT license by misrepresentation.
Comment: It is also insurance fraud to claim you are a resident if you are in fact not a resident.
Comment: Thanks--would you mind clarifying this?  As far as I know, I don't have any insurance policies in the States.
Comment: @Martin Bonner, in the US the auto insurance is usually arranged by the vehicle owner, not the driver. There are some exceptions, but usually the insurance obtained by the vehicle owner covers any driver the owner lends the vehicle to. So someone spending most of his/her time abroad is probably borrowing a vehicle while in the US. (Or using public transport, and just wanting to keep the license to avoid the need to take the road test over again upon permanent return to the US.)


Asher Yotzar before or after Bracha Achronah

Question: I read in a Sefer about a situation where a person uses the facilities before making a Bracha Achronah . My question is , do you make an Asher Yotzar first and then the Bracha Achronah or vice versa ?
Comment: Did the *sefer* provide an answer or just the question?
Comment: what does the sefer say and what would be your reason for questioning the order it gives? If it doesn't give the order what was the purpose of the scenario?
Comment: related http://judaism.stackexchange.com/q/55150/759
Answer: Since the bathroom usage had just occurred and needs to be handled, and a bracha should be made as close as possible to the action that requires it, logic would indicate that it should be done first. Additionally, one becomes obligated immediatel upon using the bathroom no matter how minimal the usage. One is not necessarily obligated to say the bracha acharona as one could still continue eating. This is based on logic only. However, as seen below, the logic is not completely true. It would depend on whether of not one intends to eat or drink more.
Halachipedia  states
:

Asher Yatzar vs. Other Berachot
If one uses the bathroom and additionally needs to recite boreh
  nefashot on food that he ate, asher yatzar should be recited first.
  [20]
If one uses the bathroom and then needs to recite asher yatzar as well
  as birkat hamazon or al hamichya, birkat hamazon or al hamichya take
  precedence. [21]
One may recite asher yatzar after the beracha of hamapil if he uses
  the bathroom.[22]
If one left the bathroom and then heard thunder or saw lightning
  before reciting asher yatzar, he should recite the beracha on the
  thunder or lightning because the time for those passes quickly. [23]
[20] Mishna Brura 7:2 says this based on tadir visheayno tadir, tadir
  kodem.  Yalkut Yosef Kitzur Shulchan Aruch 7:9
[21] Yalkut Yosef Kitzur Shulchan Aruch 7:9
[22] Halichot Shlomo 20:44, Sh"t Yechave data 4:21, Sh"t Tzitz Eliezer
  7:27, Sh"t beer Moshe 1:63
[23]Mishna Brura 227:12


Possible marble color combinations.

Question: I have 23 marbles of 7 different colors.  I want to know how many different color combinations there could there be?
Comment: Are the marbles indistinguishable apart from their color?
Comment: Yes, color is the only distinguishable attribute.
Answer: I assume you consider the colors to be distinct and the marbles to be otherwise identical. (If the marbles were distinct before being colored, then you would have $7^{23}$ possibilities.)
This is a classic stars and bars question. We are essentially placing 23 objects into 7 distinct categories. To do this, we order the 23 marbles along with 6 "dividers" any way we like. All those marbles that occur before any dividers are given color #1, those between the first and second divider get color #2, etc. So there are $\binom{23+6}{6}$ color combinations.
If you want at least one marble of each color, simply set aside one marble for each color and arrange the others along with the dividers. There are $\binom{(23-7)+6}{6}$ ways to do this.
If you wanted to have at least 2 or at least 3 of each color, or if you wanted to have at least a certain number of marbles in a specific color, you just set those aside and arrange the rest the same manner.
Answer: Call the colours $1$, $2$, and so on up to $7$.  Line up $23$ uncoloured marbles in a row.
This creates $22$ "gaps."
Choose $6$ of these gaps to put separators into.
This can be done in $\dbinom{22}{6}$ ways.
Paint all the marbles up to first separator with colour $1$, then the ones between the first separator and the second with colour $2$, and so on. That will create all possible colour combinations in which there is at least one marble of each colour.
If you allow the possibility that some colours might not occur, a similar analysis holds. Add $7$ marbles to your collection. So now you have $30$ marbles. Do the painting as described above. It can be done in $\dbinom{29}{6}$ ways.
So now you have $30$ marbles, with at least one of each colour. Give away $7$ marbles, one of each colour. You are left with $23$ marbles. Every colour combination of $7$ colours (including the combinations where some colours may be missing) is uniquely produced in this way.
Thus the answers are:
$\dbinom{22}{6}$ if there must be at least one of each colour, and
$\dbinom{29}{6}$ if one or more colours could be absent.
For more about the idea used above, please see the Wikipedia entry Stars and Bars.
Comment: @Brett: If you do not insist on at least one marble of each colour, I would expect the questions to say "I have 23 marbles of *up to* 7 different colors"
Comment: This is the solution if you insist on having at least one marble of each color.
Comment: @Henry: I think you're right, but it isn't 100% unambiguous to me, so I thought a clarifying comment was in order. +1.

Possible marble color combinations.


Public Upload into a Picasa Album

Question: Is there any way to Create a Public Upload Page to a picasa Album  so that whom ever I give the link to can upload images to my picasa Album ?
Answer: You can enable the upload by email feature of Picasa.
This will allow you to setup an email address to which you send an email with pictures that will be posted directly in a Picasa Album. More info here.
Comment: Thanks but that is not an option.

Public Upload into a Picasa Album


Is there a way to draw LEGO figures using Blender?

Question: I have some basic experience in Blender. Is there any way to insert pre-drawn LEGO pieces into Blender?
Comment: Will it blend, in other words?
Answer: First note that this question is a possible duplicate of Do any programs exist that allow you to build your own LEGO manuals?  With that, here is the answer:

(optional) Create a model in LEGO digital designer or LDraw and export it as a LDraw (*.ldr) file.
Install LeoCAD, and either open the model that you made in LDD/LDraw (recommended) or create your model directly in LeoCAD.
Export your model in LeoCAD as a 3D studio (*.3ds) file and import that in Bender.

I learned this technique from this very site less than a week ago and have already tried it out.  So far, it works great and has given me loads of ideas.
Edit: The Linux version of LeoCAD currently does not export to the *.3ds file format, so you can not set up a pipeline that way; I know this from experience.
Comment: You can also use the Lightwave (.obj) exporter from LeoCAD and import that into Blender - note also that LeoCAD has the "Minifig Wizard" allowing you to create your Minifigs directly in there.
Comment: I just did a video using the same method as InkBlend. It worked well for me and here is the link https://youtu.be/kIbvFUuAoLU
Answer: For a general introduction to Lego characters (humanoid figures) modeled directly in Blender you might like to view http://www.youtube.com/watch?v=jWfS82EOa4A&list=EC3F4C5FF0451A92D9 which is a tutorial on modeling a Lego man. I have just begun to analyse this tutorial to see if I can make an expanded PDF version that will incorporate the correct proportions for this figure but when I will complete this task and if I will publish it depends on too many factors to predict.
Answer: I would start to model the lego-head.
It is pretty simple, because u can use only one cylinder and then extrude/move and scale faces.
Here is a nice tutorial with an attached blend file.
http://infofreund.de/modelling-lego-head-blender/


Standardizing variables with negative values in R

Question: Because my dependent variables in a multiple linear regression model are in different units, some coefficients are > 10,000 and others less than 0. I need to standardize them by using the scale function on R, but because some of my data is negative, it's impossible to take log of some of the variables which I need to do before standardizing. Is there any other step I can take? Can I standardize without log transformation first?
Comment: I suggest visually inspecting scatterplots of each independent variable versus the dependent variable to see if there is any obvious transformation such as exp or log that would help in the regression. This is usually fast and easy to do.
Comment: @AdamWheeler thank you!! I just have a quick question—If I were to transform one dependent variable with negative values in this way, would I do the exact same transformation to the other dependent variables and independent variable?
Comment: I'm not clear on the motivation for a log transformation. I also wonder if you mean "standardize them" or simply "rescale them". Rescaling and standardizing are two different operations. But unless I'm failing to miss the point, I think the answer is yes. You can definitely standardize variables without ever log transforming them.
Comment: @BrentHutto I'm not sure if I understand the difference between the two. Is rescaling the same as the scale function in R? If so, then my understanding is that log transformation is necessary beforehand (i.e. #6 on https://stats.stackexchange.com/questions/156791/standardized-vs-centered-variables)
Answer: Sometimes people take the natural log (or better yet, the base-two-log!) of a dependent variable because they feel the distribution of the log-transformed variable has better properties than the distribution of the untransformed variable, relative to whatever model they are estimating. One drawback is your regression parameter can not be interpreted in terms of the original variable, only in terms of the log of the DV. And don't be tricked into "back transforming" regression parameters with an inverse log (exponential) function, that is NOT valid.
The explanation you linked to is saying IF you are going to log-transform a variable then you ought to do that before standardization. It is not saying you should always log-transform, in my opinion sometimes people getting into the habit of log-transforming when it isn't even strictly necessary.
Whether on a plain old dependent variable or a log-transformed dependent variable, the R function scale() will let you alter the centering or the scale of a variable. And if you use some estimate of the variables mean and variability to the rescaling then you're said to have standardized the variable (i.e. made it into a de facto Z-score).
Sometimes you only center a variable. Subtract the variable's overall mean from each value and get a centered version that has mean zero. If you center only, the standard deviation will be unaffected. This is not "standardized".
Other times you may or may not center a variable but you don't like the units it is expressed in for some reason. Maybe your DV values are like 15,000g or 12,800g because that's expressed in grams and you'd rather work in kilograms. So you use the scale() function to divide each value by 1,000 and give you numbers like 15.0kg or 12.8kg. Again, this is not standardization. It is just rescaling.
So you can mix and match centering (or not) rescaling (or not) and you can do it with or without converting to a standardized scale. And all of those choices you can do with or without a log-transform. It all depends on what you're trying to accomplish and why.
Comment: P.S. I myself have not used the scale() function. It is a general-purpose utility that can do all sorts of interesting things, not just the very simple operations I've described. For instance I center variables all the time but do it by simply using "cDV=DV-mean(DV)" to create a centered version very simply and quickly. So I may have misrepresented something about the scale() function...but I hope not!
Answer:
... because some of my data is negative, it's impossible to take log of some of the variables which I need to do before standardizing.

Your question is similar to an other question here, so I'll give the same advice.  Before you worry about the mechanics of using logarithms, you need to step back and think about the coherence of the underlying measurement you are asking for.  The logarithmic transformation takes positive rate values and puts them on a scale where multiplicative changes become additive changes.  It can be extended to deal with negative numbers, but the logarithm of a negative number is a complex value (i.e., with an "imaginary" part).  It is extremely unlikely that you will need to take a logarithmic transformation of negative data values (and therefore move your data into complex analysis) in any standard statistical practice.
I suggest you start by looking at this dependent variable and asking what the negative values actually represent, and how they were formed.  You will want to ask two questions: (1) why do I have negative values; and (2) why do the values have such heavy positive skew.  If the values were formed by subtracting a constant $y_* >0$ from some underlying positive set of values that could reasonably be presented on a log-scale, then a natural transformation might be to take $\tilde{y}_i = \ln (y_i + y_*)$.  If something else happened then a different transformation might be appropriate.


Can I digitally buy and download the first Diablo game?

Question: Does Blizzard allow people to buy and download the first diablo game online? Or do I need to purchase a physical copy?
Comment: I'm voting to close again because abandonware doesn't give any additional rights to downloading games you have not purchased. Blizzard still owns the IP, and downloading it is still piracy. Whether Blizzard is currently, or will in the future, sell the game is immaterial. Its theirs.
Comment: A discussion exists on meta: [Should we allow links to "abandonware" game sites?](https://gaming.meta.stackexchange.com/questions/266)
Comment: @Frank True, not sure what the site's policy on abandonware is. I'm nearly certain that StackOverflow will have one, though Arqade might not. We'll see!
Answer: The original Diablo game is now available digitaly on GOG, DRM-free and supported on Windows 7, 8, and 10.
https://www.gog.com/game/diablo
You can try searching on Amazon for either the PC or PlayStation physical copy. If not, look for other releases or bundle. In 1998 there was a re-release bundle called Diablo + Hellfire. Blizzard also released a Game of the Year Collection in 1998 that contains the original Diablo. The Blizzard Anthology, released in 2000, also contains the original Diablo game. The Diablo Gift Pack contained the first two Diablo games but no expansions. In 2001, a Diablo: Battle Chest was available which contained the original Diablo, Diablo II, and the Lord of Destruction expansion.
Diablo II, however, is still available from Blizzard's online store. The original Diablo II game, Lord of Destruction expansion, and the Diablo II Battle Chest (which includes the Diablo II, its expansion, and strategy guides for each) are all there. However, the Battle Chest for Diablo II does not include the original Diablo game, but Diablo II and its expansion are available for digital download.
Answer: Situation changed just a few days ago.
gog.com offers it now.
https://www.gog.com/game/diablo
Answer: The Diablo 2 Battle Chest comes with Diablo 1 game.
Comment: Only the original release of the Diablo Battle Chest comes with the original Diablo. The newer version, which is easier to find, only comes with D2, LoD, and a strategy guide.
Comment: Correction to the - "The Diablo 2 Battle Chest comes with Diablo 1 game." The picture shows that it does before u click the page on the store. However once u click it it shows the diablo 2 battle chest w/o diablo 1
Answer: Diablo 1 is now treated as abandonware and can be downloaded online from archive.org.

First, download the game here. You can mount this .iso file (right click --> Mount on Windows 10, slightly harder before), and then install Diablo by launching AUTORUN.EXE from the newly mounted Diablo drive.
Then, download the 1.09 patch from here to the same folder that you installed Diablo, and launch it in order to update the game. This is the only official patch from Blizzard you'll need.
Finally, install the third party patch from here as well, which fixes a lot of startup and graphical issues and allows you to play at various resolutions, in windowed mode, and etc.

If you want to play with friends, you can utilize GameRanger or Hamachi to play multiplayer games on simulated local networks nowadays, despite Battle.net discontinuing support for the game early in 2018.
Comment: Abandonware is not technically legal to download. There is no LEGAL means of obtaining the game from a download. Look for it in shops. (I still see copies on Game racks in discount stores)
Comment: @Stese We do make an exception for abandon ware: https://gaming.meta.stackexchange.com/questions/266/should-we-allow-links-to-abandonware-game-sites
Comment: an exception or not, it's misleading to state that abandonware is 'freely downloadable' I've made a comment on that question with that intent.
Comment: @Stese Free as in beer, not as in speech. :D


The Pope is resigning. How does a living pope confer his authority?

Question: I read that Pope Benedict XVI is resigning. I don't know much about Catholic/papal authority as it relates to leading the Church, but as far as I can remember, a pope dies before another one takes the reigns. Apparently, this has happened before, but how does the living pope confer that authority to a successor, since he's still alive? Since he resigned, is his authority to lead the Catholic church removed from him, or how does that work?
Answer: Yes, as the Pope said in his resignation speech, he gave up the office and it is for those whose duty is to convoke the conclave and elect a successor — just as it would be if he had died.
As a cardinal, he's entitled to attend the conclave (he probably won't) but he can't vote because he's over eighty.
Comment: Additionally, his papal ring will be destroyed, just as if he had died. I forget the source, but the analogy of death while still breathing is wholly correct.
Comment: Yes, after he abdicates he has no say whatsoever in where authority passes thereafter.
Answer: Jimmy Akin stated on his blog:

Pope Benedict may follow the pattern of previously resigned popes and
  spend the rest of his days in a monastery. Alternately, he may live
  quietly with his brother. Either way, he will do his best to stay out
  of the public eye so as to give his successor the freest hand
  possible. (This is the same thing that usually happens when a U.S.
  president leaves office; it's traditional for him to more-or-less
  vanish, at least for a time.)

The papal authority is removed completely from the ex-pope. From wikipedia, I understood that his ring, seal etc. are destroyed as though he died, though it's not clearly stated there.
As Andrew Leach wrote, as a cardinal the ex-pope can attend conclave, but even if he was younger than eighty, he would be expected not to be very active in the election of his successor (part of the tradition of vanishing from public).
EDIT: according to what I found while researching answer for a related question, there is an aspect of the pope's role he maintains after resignation, or even after death: the obligation and authority to pray for the Church.
Another EDIT: as Cardinal Lombardi said, Joseph Ratzinger won't participate in the conclave. In Czech version the Vatican Radio goes to more details, such as that Ratzinger will no longer be a Cardinal, but I didn't find it in English.
Comment: It's on [Vatican Insider](http://vaticaninsider.lastampa.it/en/inquiries-and-interviews/detail/articolo/papa-el-papa-pope-rinuncia-appointment-22203/) Because this is entirely new -- the circumstances are rather different from Gregory XII -- I rather think that no-one, including the Curia, knows precisely what the procedures and protocols are.


Using a newer JQuery version

Question: The Drupal 6 version of jQuery is too old (1.26). Could I delete, and replace it with a newer version?
Answer: No, that would not be advisable; instead, use the jQuery Update module.
Comment: it's not unheard of to make Drupal 6 work with jQuery 1.4+ but it takes a lot of core hacking and patience, I wouldn't recommend it for anything other than a personal project.  For most other stuff use jQuery Update and get used to 1.3.2 :)
Answer: Deleting the jQuery library used by Drupal 6 and replacing it with a newer version (especially if the new version is 1.3.x, or 1.4.x) is not a good idea because Drupal core JavaScript code (but also JavaScript code used by third-party modules) would stop working.
Some versions of jQuery comes with a compatibility file that allows to code though for the previous version of the library to work with the new version; sometimes, that single compatibility file is not enough for Drupal, as it is shown by the jQuery Update project, which replaces some of the JavaScript files used by Drupal, including ahah.js, tabledrag.js, and teaser.js.
As of 14 August 2011, the jQuery library used by the latest Drupal 6 version of jQuery Update is 1.3.2; jQuery 1.2.6 is the version used by the latest Drupal 5 version.
Answer: There's nothing wrong with using a newer version of jQuery alongside Drupal's core version of jQuery. The function noConflict() is made for running a jQuery library alongside another javascript library, even if it's just another version of jQuery (http://api.jquery.com/jQuery.noConflict/).
I wrote a post about using noConflict + your custom jQuery version and scripts here: http://drupal.org/node/1058168
Answer: For what it's worth:

Drupal 5: jQuery 1.2.6
Drupal 6: jQuery 1.3.2
Drupal 7: jQuery 1.5.1 and jQuery UI 1.8.11

With the release of IE9 imminent, and jQuery 1.5.1 release was made to fix all bugs related to IE9, does it make sense to put this release into D7? Their changelog suggests many IE related bugs were fixed.
"jQuery now supports Internet Explorer 9 as a top level browser. All known bugs have been fixed and/or been reported to the IE team for resolution in the final release."

Using a newer JQuery version


deriving a bayesian statistics equation

Question: can someone give me some pointers on deriving p(alpha|rest) on page 4 of http://www.stat.cmu.edu/~brian/724/week06/lec15-mcmc2.pdf (pdf warning)?  I'm having trouble separating it out from beta.  This isn't homework, but it seems substantially similar, so I'll mark it as such.
Comment: Post the question here because future readers will understand nothing if the PDF is removed.
Comment: what exactly are you asking for?
Answer: You have an expression $$p(y,\theta,\alpha,\beta)= \prod_{i=1}^{N} {n_i \choose y_i} \theta_i^{y_i} (1-\theta_i)^{n_i-y_i} \prod_{i=1}^{N} \frac{\Gamma(\alpha+\beta)}{\Gamma(\alpha)\Gamma(\beta)}\theta_i^{\alpha} (1-\theta_i)^{\beta} p(\alpha,\beta).$$
The proportionate expression for $p(\alpha | y,\theta,\beta)$ treats  $y$, $\theta$ and $\beta$ as known constants, and so removes any multiplicative term which does not depend on $\alpha$, including all of the lefthand product and part of the righthand product to give $$p(\alpha | y,\theta,\beta) \propto \prod_{i=1}^{N} \frac{\Gamma(\alpha+\beta)}{\Gamma(\alpha)}\theta_i^{\alpha} p(\alpha,\beta).$$  The next stage is to notice for example that $\prod_{i=1}^N k = k^N$ and similarly for the terms in the product not depending on $i$. That gives the stated result of $$p(\alpha | y,\theta,\beta) \propto \left[\frac{\Gamma(\alpha+\beta)}{\Gamma(\alpha)}\right]^N \prod_{i=1}^{N} \theta_i^{\alpha} p(\alpha,\beta).$$  [This "key observation" also applies to the conditional expressions for $\theta_i$ and $\beta$.]
If you want to turn the proportionate expression into an exact expression, you then need to divide by the integral over $\alpha$ of the proportionate expression.

deriving a bayesian statistics equation


How was digital sound playback achieved on the Commodore 64?

Question: The Commodore 64 did not have any hardware dedicated to digital audio playback, so how were some games and songs able to achieve this on an unmodified and unextended Commodore 64?  Did these techniques require specific hardware revisions?
Answer: No hardware revisions are necessary.  The digitization playback is achieved by bit-banging the volume register of the SID chip to simulate a digital playback device.  Essentially, the SID can be used as a 4-bit digital playback device.  What's amazing is that the thing sounds as good as it does playing back digital data.
A great article about digis on the C64 can be found here: http://sid.kubarth.com/articles/the_c64_digi.txt
Comment: Actually, 4 bits. The volume register is 4 bit wide, and it happened that any change to the volume register produced a "clic" sound with the new volume (hence a 16 level volume). Changing the volume register value very quickly allowed the "clic" sound to follow the instant values of a 4 bit digital signal.
Comment: This does not really answer the question. Changing the volume on my PC does not make it possible to play samples. You need to incorporate the comment by @mcleod_ideafix for it to make sense.
Comment: Would be good if the answer would be edited to correct the bit-depth, in line with the document it cites.
Comment: It was the same technique used on all machines with a AY-3-8910 sound chip  (Atari ST, MSX, Amstrad CPC, etc); On the ST it was typical to use the Timer B to generate a scanline interrupt to change the volume at that time, at around 15khz, allowing sounds of up to 7.5khz, the lack of filter made the result quite harsh. The three channels were playing a carrier signal like what Stavr00 described below.
Comment: The same can be done with a disk drive! [YouTube](https://www.youtube.com/watch?v=5gnMgmlKi_o)
Answer: The best audio quality was obtained with pulse width modulation using the square wave voice.  The oscillator was set to 0 and the pulse width was set by flipping the pulse width from 0 to maximum.
With the CPU speed at 1mHz the fastest pulse switch rate achievable is around 15kHz, producing a sound wave of 7.5 kHz or less. Setting the low pass filter help smooth the sound.

Source: https://en.wikipedia.org/wiki/Pulse-width_modulation
https://www.c64-wiki.com/index.php/SID
Comment: Pulse-width modulation needs a carrier greater than 4KHz to get good results; even with a perfect reconstruction filter, an A440 (not a particularly high note) would need to have all harmonics beyond the fourth filtered out; an A880 would only get to have the fundamental and octave harmonic.  Most sounds need at least the fifth harmonic before they even start to get "interesting", so a 4KHz PWM rate isn't going to cut it except when trying to produce very low notes.
Comment: I re-read the digi article in the original answer, and it explains a different way of doing PWM. Will rewrite.
Answer: There were also some more recent creative alternatives taking advantage of filters and undocumented test bits as well.  Check out the Cubase64 demo by Mahoney: http://www.livet.se/mahoney/cubase64  You can also find versions of it playing on the real thing on YouTube, naturally.  (spoiler alert: your face will melt -- it's that awesome.)
Comment: You need to actually write how that works, in this answer, otherwise it's just a comment.
Comment: Noticed your comment -- I could have copy/pasted the article body of the page I linked to and just credit the author but it was rather long and honestly I didn't want to take credit for someone else's work.  Instead I linked to the article that explains it better than I ever could.  I'm not sure how your nit-picky response was any more helpful, suppose you were better off not having someone show you an awesome demo?  Sheesh!  If what I wrote was just a comment I can only imagine how others would classify your reply.
Comment: I came back to post this after re-moulding my face back on. That was insane!
Answer: It seems that all the earlier posts only give partial answers to the question. The below extract of the relevant parts of my doc
https://bitbucket.org/wothke/websid/src/master/docs/digi-samples.txt
should remedy that situation and give a more comprehensive overview of all the respective techniques:

There are basically 4 general approaches [that are used to play digi
samples on the C64]:
[..]

$d418 "volume register" based

This is probably the oldest technique: The SID's audio output is
directly  modulated by changing the master volume. The result of this
approach  primarily depends on the original output available for
modulation, i.e.  ideally the original output would need to be at a
constant maximum which  would then allow the technique to modulate it
to "anything"  between 0 and that maximum. A flaw in the old 6581 SIDs
made them particularly suceptible to this exploit: respective chips
always produce  a relatively large DC voltage offset on the master
volume D/A which means  that there is always "some" kind of original
signal that can be modulated  via the master volume - even when there
is no regular voice output.
[..]
However this technique usually works poorly on the newer 8580 SID
chips, since those no longer produce the flawed DC voltage offset,
meaning  that there may be very little original signal avilable for
modulation  (depending on what other regular output the SID's voices
are producing).
[The technique can still work on the 8580, provided that there is
suitable output from the SID's regular voices that can be modulated.]
[..]
Mahoney's "8-bit samples"
There is a more recent "turbo charged" variant of the $d418 approach
[..] Here the trick is to carefully setup the regular voice output
such that  not only the volume but also different filter activation
will influence  the modulated result. [..]
Due to the fact that the "carrier signal" has been specifically set
up, the approach runs fine also on newer 8580 models. [i.e it runs on
all  SID models but a specific implementation is always optimized for
a particular  SID model's filter and D/A converter characteristics and
will not  yield optimum results when used on other models] [..]

frequency modulation based

This technique probably produces the highest-quality sample playback,
allowing for actual 8-bit samples. [Respective players typically only
use the high-byte of the frequency register to control the "step
width" - see below.]
The underlying principle is to use one of the waveforms that linearly
transition from 0x0 to 0xfff (i.e sawtooth or triangle), to start it
at 0  and then let it go up for a fixed number of clock cycles until
it has  reached the desired output level and then output that level
for the  duration of a sample.
The sample playback rate of this type of player is fixed, e.g. the
player might play a new sample every 129 cycles. This means the SID
will always "step up" the waveform output for exactly 129 cycles
and it is then just a matter of finding suitable frequency settings
[i.e. the size of each step] that will result in the desired  output
levels after 129 clock cycles [aka steps].
[This technique works on all SID models.] [..]

pulse waveform based

An early/primitive form of pulse-waveform based sample output can be
found in Slapshot_1987.sid. Here a 7kHz 1-bit signal is generated by
manually turning the test-bit on/off and thereby toggling betweeen
the 0x0 and 0xfff output level. [This works on all SID models but the
audio quality is generally abysmal.]
More sophisticated later players use what might be be called a "pulse
width modulation" approach. [..]
Their principle is to use a high frequency pulse-waveform and then
manipulate the "average" output signal by shifting the pulse-width one
way or another to get any average level between 0x0 and 0xfff.
[This approach works on all SID models eventhough the audio quality
oftentimes suffers due to the used carrier signal.] [..]

waveform toggling based

Finally there is an approach that tries to let one voice create
different output levels by toggling between different waveforms. The
respective frequency and pulse-width settings of that voice are
previously configured in such a way that the respective waveforms
result in the desired output levels.
[This works on all SID models but the resolution available for  each
audio sample is usually small.. due to the limited amount of
different waveforms available.] [..]

PS: for some hands on experience you might use my below playlist
to try out respective digi-songs online and see what technique these are actually using: https://deepsid.chordian.net/?file=/$TinyRSid%27s%20Digi%20Favourites/
Comment: Link-only answers are generally frowned upon here.
Comment: I appreciate that the linked article is quite lengthy, but quoting the (most) relevant parts would make this answer useful in the future, even a dystopian future where the BitBucket website is no longer accessible.
Comment: I updated the response and inlined the relevant parts directly


What determines rocket height/width?

Question: I was wondering what determines the height/width ratio of a rocket? What are factors that influence the choice between a tall skinny rocket like Falcon 9 or a wider shorter (in ratio) like Ariane 5 or GSLV?
Comment: If there would be no atmosphere, the optimal shape of the tanks of the rocket would be a sphere.
Comment: @Uwe If it wasn't under high thrust...
There's a reason rockets are usually arranged in a stack.
Comment: @AntiElonGuy high thrust or high drag? A stack with less drag is essential in air but not in vacuum.
Comment: Structurally speaking, a stack is better becuase you don't have torque forces acting on the main axis of the craft due to mass around it.
Answer:
What determines rocket height/width?

If there had to be a concise answer, it would definitely be @JCRM's answer that it's an optimization of a series of compromises. But there'd have to be a caveat for the smallest rockets.
Those are a mix of design, budget, and schedule compromises.
Rocket designs often (but certainly not always) evolve from previous designs, and inherit working and proven subsystems and states. This answer to Why does PSLV use four stages to get to LEO, and why do they alternate solid, liquid, solid, liquid? explains one example of heritage nicely.
But there is no question that for atmospheric rockets the size has something to do with it. Aerodynamics and especially drag kicks in at the low end of size. For a fixed height/diameter ratio rocket, as the size goes down, the drag decreases as only mass to the 2/3 power whereas thrust may decreases roughly linearly, and drag slowly overcomes thrust.
The only way you can deal with this is by making the rockets inordinately long and skinny to minimize the drag associated with the cross section. Strength, and drag along the sides of the rocket limit the practicality of this. Also note that even with the extreme ratio, it's rare for a sounding rocket to achieve orbit. See this answer to the question Will JAXA try again to launch TRICOM-1 with the "world's smallest orbital rocket" SS-520-4 again? as well as answers to How small could an orbital rocket be?.

The best way to get at all of this is to look at the extremes, so I'll compare sounding rockets to the Saturn V, and a few points in between, and one notable, pasta-based exception.
Sounding rockets have the most extreme aspect ratio. The Black Brant series shown below makes a good example. According to Wikipedia the Black Brant 10 is 14.5 meters tall and 0.44 meters in diameter (at the base) which is a height/diameter ratio of about 33:1 and has a mass of 2.6 mt.
Towards the other end of the spectrum, and even ignoring any side-mounted boosters the Delta IV Medium has a height/diameter of 62.5/5.0 = 12.5:1 and a mass of 283 mt, and the Ariane 5 ES has a height/diameter of 50.5/5.4 = 9.4:1 and a mass of 773 mt.
And for the largest flown rocket, the Saturn V at 110.6m tall and 10.1 meters in diameter at the base, the height/diameter 11:1 and mass was about 2970 mt.
Wikipedia says F9 FT is 70 meters high and 3.7 meters in diameter, **a height/diameter ratio of nearly 19:1 and a mass of 549 mt.
Except for the sounding rockets, most rockets fall in the 9:1 to 15:1 range, with a slight but noisy trend to smaller ratios for the most massive rockets.
However, the question If not constrained by underpasses, etc., would Falcon 9 have been less of a flying noodle? addresses the unusually extreme aspect ratio of the Falcon 9 and links and asks if it would be shorter/fatter if not for the requirement to travel by US highways and through tunnels.
It links to the question Why is Falcon 9's shape so tall and skinny?.
@geoffc's answer says in part:

SpaceX manufactures their booster in Hawthorne, CA. They then truck it on the highways to McGregor, TX for test firing with all 9 engines.

Then it is back on a truck for the drive to Florida to LC-40 at the Air Force station for launch.

The diameter of the booster at 12 feet/3.6 meters is the largest they could go and still be road transportable.

So the F9 is a flier from the cluster in the 9 to 15 range only for a particular bit of rocket heritage, the F9 was born on the road.

Script for plot: https://pastebin.com/Sz26Jz8K makes it easier to add more rockets in edits.
<code>rocket         mass (mt)      height(m)    diam(m)   h/d
Saturn V         2970           110.6       10.1     11.0
Ariane 5 ES       773            50.5        5.4      9.4
Falcon 9 FT       549            70.0        3.7     18.9 'flying noodle'
Delta IV medium   283            62.5        5.0     12.5
Electron           12.5          17.0        1.2     14.2
Black Brant 10      2.6          14.5        0.44    33.0  sounding rocket
</code>

Source: Magellan Aero; Black Brant Rockets

Source: Gunter's Space Page: Black Brant left: Black Brant-9 (SOAREX 8) [NASA], right: Black Brant-10 (NASA 12.073) [NASA]

below: GIF of Falcon 9 faster than normal speed to make the noodle-moniker evoking motion more visible, from the YouTube video SpaceX B1021: The First Rocket to Fly Twice (a supercut of highlights
Comment: I've included a link to the plotting script in case there's need to add a few more examples. Feel free to add responsibly, or to just make recommendations in comments.

What determines rocket height/width?


Morality of Forgiveness in Islam

Question: Say in a scenario, someone as bad as Hitler or Hitler himself had converted to Islam on his death bed, He would be forgiven for ALL his sins and therefore not punished for the sins that he did. This sounds disgusting and unjust to let a man like Hitler not receive any punishment for his actions. So why does Islam have such a concept and allows this?
Comment: Salam and welcome to IslamSE the Q&A site about Islam. For further information on our site and the stack exchange model consider taking the [tour] and checking our [help].
Answer: Obviously, forgiveness has some conditions and requirements. Islam doesn't state every sinner will be forgiven upon his repentance or as soon as conversion to Islam. Quran explicitly says in 4:1

But repentance is not accepted of those who continue to do evil deeds
  up until, when death comes to one of them, he says, "Indeed, I have
  repented now," or of those who die while they are disbelievers. For
  them we have prepared a painful punishment.

Thus, this idea is not from Islam.
Comment: Well if you do convert to islam you are forgiven for all your sins, and don't try and bend what the Quran says; be blunt and answer. If Hitler STOPPED doing horrible things and converted, He WOULD be forgiven in Islam ; NO QUESTION. But I am asking how can you still be muslim believe such an immoral concept such as forgiveness? Shouldn't he be punished? This is common sense, if he Hitler was in a court and asked for forgiveness that wouldn't be sufficient at all and would be put in jail for lifetime.
Comment: Look at [this link](http://www.islamquest.net/en/archive/question/fa850) for more clarification.
Answer: There's a difference of opinion about this matter:

Soms scholars say that only converting to Islam is cleaning your waistcoat based on the long hadith saying:

... Islam wipes out all the previous (misdeeds)? ... (Sahih Muslim)

Note that the person who converted in this hadith  'Amr ibn al-'Aass prior to Muhammad's () answer displayed above actually had the following conversation with our prophet ():

He (the Holy Prophet) said: What has happened to you, O 'Amr?
  (I) replied: I intend to lay down some condition. He asked: What condition do you intend to put forward? I said: should be granted pardon.

so the person was aware of his misdeeds. 'Amr indeed fought, killed and tortured Muslims before converting, but he became a good Muslim afterwards.
Other scholars say that only those misdeeds from which one has repented after conversion are forgiven based on:

Say to those who have disbelieved [that] if they cease, what has previously occurred will be forgiven for them. But if they return [to hostility] - then the precedent of the former [rebellious] peoples has already taken place. (8:38)

There's also a hadith saying:

Allah's Messenger (ﷺ) said, "If a person embraces Islam sincerely, then Allah shall forgive all his past sins, and after that starts the settlement of accounts, the reward of his good deeds will be ten times to seven hundred times for each good deed and one evil deed will be recorded as it is unless Allah forgives it." (Sahih al-Bukhari)

And another one saying:

A man said, "O Allah's Messenger (ﷺ)! Shall we be punished for what we did in the Pre-Islamic Period of ignorance?" The Prophet (ﷺ) said, "Whoever does good in Islam will not be punished for what he did in the Pre-lslamic Period of ignorance and whoever does evil in Islam will be punished for his former and later (bad deeds).
  (Sahih al-Bukhari and Sahih Muslim)

This view is held by a majority of scholars.

Also note that this might also only apply to misdeeds on the rights of Allah worship matters, monotheism (oneness etc.) or doing something which is haram, but doesn't harm any person, as for the case that it harms a person there seem to be a second difference of opinion, while some scholars consider a general amnesty others even consider applying the hudud (punishments) for example in Radd al-Mohtar  رد المحتار a book on hanafi jurisprudence you may read:

وإذا كان وقت الشرب غير موجب للحد لا يحد بعد الإسلام بخلاف ما إذا زنا أو سرق ثم أسلم فإنه يحد لوجوبه قبل
  So if a person was not subject for hadd punishment while drinking (alcohol) they wouldn't be subject of punishment after converting to Islam in opposite to the case of a person committing adultery or robbery who converted afterwards they would be subject of had punishment as they were before.
  (Source fatwa islamweb #32104)

Drinking alcohol is a sin one may perform, but not harm anybody else, while adultery or robbery is one were another person is involved! The same would apply -by analogy- to killing if all conditions of applying hadd are met.
This actually is in opposite to a fatwa given by imam a-Shafi'i on an adulterer who converted to Islam.
Finally the hadith of the killer of 100 people shows that the morality of forgiveness you are condemning was present in former religions (Judaism and Christianism too):

The Prophet (ﷺ) said, "Amongst the men of Bani Israel there was a man who had murdered ninety-nine persons. Then he set out asking (whether his repentance could be accepted or not). He came upon a monk and asked him if his repentance could be accepted. The monk replied in the negative and so the man killed him. He kept on asking till a man advised to go to such and such village. (So he left for it) but death overtook him on the way. While dying, he turned his chest towards that village (where he had hoped his repentance would be accepted), and so the angels of mercy and the angels of punishment quarrelled amongst themselves regarding him. Allah ordered the village (towards which he was going) to come closer to him, and ordered the village (whence he had come), to go far away, and then He ordered the angels to measure the distances between his body and the two villages. So he was found to be one span closer to the village (he was going to). So he was forgiven."
  (See for example in Sahih al-Bukhari and Sahih Muslim)

Commentators of this hadith ended by the statement that the punishment or forgiveness in the hereafter is by Allah as he said:

Indeed, Allah does not forgive association with Him, but He forgives what is less than that for whom He wills. ... (4:48 and 4:116)

See also Why these mostly identical verses in surat an-Nisa' have a different ending?.

Allah's Messenger (ﷺ) said to us while we were in a gathering, "Give me the oath (Pledge of allegiance for: (1) Not to join anything in worship along with Allah, (2) Not to steal, (3) Not to commit illegal sexual intercourse, (4) Not to kill your children, (5) Not to accuse an innocent person (to spread such an accusation among people), (6) Not to be disobedient (when ordered) to do good deeds. The Prophet (ﷺ) added: Whoever amongst you fulfill his pledge, his reward will be with Allah, and whoever commits any of those sins and receives the legal punishment in this world for that sin, then that punishment will be an expiation for that sin, and whoever commits any of those sins and Allah does not expose him, then it is up to Allah if He wishes He will punish him or if He wishes, He will forgive him." So we gave the Pledge for that.
  (See for example in Sahih al-Bukhari and Sahih Muslim)

We only know that a punishment in this life replaces that in the hereafter Does punishment in the worldly life replace punishment in the hereafter?.

Morality of Forgiveness in Islam


How to format author information in research papers?

Question: Is there any standard style for adding author information in research papers? I see different papers use different styles. Some have affiliation and contact address only. Some have affiliation, email, contact address in full. Some include designation also. So what is the best style one should follow? I am preparing a paper for a Springer Conference.
Comment: The conference probably has a website with all this information. If not, look for how papers in this conference in previous years, or in other Springer conferences, were formatted.
Comment: @Anthony: Springer's templates and documentation do not really answer the question (and the conference web site usually just refers to Springer's documentation). For example, if you decide to include your email address, Springer's templates provide commands that you can use to *format* it properly. However, *whether* you include your email address is entirely up to you.
Comment: I agree with Peter. Moreover, Springer provides you with a set of files which take care of the formatting properly. And if your paper is accepted, it will be edited again anyway to make sure it conforms to their format.
Comment: @Kaveh: Sounds like a good idea.
Comment: @Jukka, I just noticed that migration does not work for questions older than 60 days anymore.
Answer: I think you should keep in mind how people are going to use this information and for what purpose.

You use it to advertise yourself and your identity. You hope that little by little, people learn to recognise your name and know what kind of work you do.
Other researchers will use the information to find more information about you and your work. If they find a relevant paper written by you, they might want to find your home page and see if you have done more recent research on the same topic. Or they might want to contact you and ask more about your work.
Various organisations will use it to construct bibliography databases (DBLP, ACM Portal, MathSciNet, etc.) and to come up with all kinds of statistics (how many papers were published by university X). The editors of the bibliography databases typically want to figure out which papers are written by the same person (far from trivial, as the names are not unique).

Some advice based on the above use cases:

Please try to include your full name. Do not abbreviate your first name. Use the same version of your name in all research papers, and use the same version on your home page. For example, if you decide to use middle initials, do it consistently.
An email address might be a good idea (at least if you are not worried about spam email). Not that I would ever send email blindly to an address that I see in a paper, but googling for the email address might be much faster than googling for your name if you happen to have lots of namesakes.
Affiliations (the names of the universities, departments, institutes, and/or companies) are a must to keep your employers happy... They also help with disambiguation if you happen to have lots of namesakes. (Unfortunately people change universities often or have double-affiliations, and this will also create some confusion in the bibliography databases.)

I have no idea who would ever use your full postal address for anything nowadays – if they need it, they can google for up-to-date information. However, it might be nice to include the town and country, especially if your university does not happen to be named after (a well-known) city.
Comment: Instead of saying that you have to use your full name, I would say that decide what your name is in your first paper (including whether you want to use foreign accents, how to transcribe non-latin alphabets, married names etc.) and then stick to it for the rest of your career.
Comment: Good point about using your full name. Definitely use a middle initial and always stick to it. This will be important for all sorts of reasons, including when your university assesses you for promotion by doing all sorts of bean-counting, such as counting citation.
Comment: I agree with Daniel. Formatting your name the same way every time, and separating yourself from other people with similar names, are more important than providing your full legal passport name. If you want to use a shortened form of your name (Dan, say, instead of Daniel) or first initial and spelled-out middle name, or only the first part of a Spanish double surname, that's ok, but then you should use that form forever. Not using my middle initial hasn't caused me problems, but I have an unusually-spelled last name. If your name is common, middle initials are a good way to be different.


What food pairs well with an IPA?

Question: Consider your average american IPA.  What food would go well with it?
Comment: may i ask what is IPA ?
Comment: @NullPoiиteя http://beer.stackexchange.com/questions/28/what-are-the-differences-between-an-ipa-and-its-variants
Comment: I would also like to ask what an IPA is in case the question has not been thought to be edited for the comment above.
Answer: As a complete novice to food pairings with beer, I've been looking at this nifty pairing chart on http://www.craftbeer.com [PDF] whenever pairing questions have come up on Beer.SE. According to it, the suggested pairing for an IPA is

Strong, spicy food (classic with curry!); bold, sweet desserts like carrot cake

and for a Double/Imperial IPA is

Smoked beef brisket, grilled lamb; Southern chicken-fried steak.

I found a great little summary by Michael Agnew (2012) that explains some of the rationale behind these pairings (emphasis mine hereon):

When pairing IPA with food you have three basic flavor hooks at your disposal; bitterness, hop flavor (spicy, grassy, herbal, earthy, and citrus), and caramel. Hop flavors have a great affinity for spices and light fruits. Bitterness has a cooling affect. Paired with spicy dishes, IPA will fan the flames at first, but douse them in the end. Bitterness also amplifies salty and umami flavors. The caramel flavors in the beer will latch onto the sweeter side of a dish, tying into things like caramelized onion or the crispy skins of roast poultry. And the hop acids and carbonation make IPAs great palate cleansers to take on even the fattiest deep-fried delights.

Samuel Adams has a "Pair with Sam" tool, and looking at its suggested pairings for their Whitewater IPA (hoppier than their Latitude 48 IPA), pork appears to be the meat of choice: pulled pork, barbeque ribs, chorizo, roasted pork tenderloin, and sweet sausage; and the rest of its suggestions align with the salty-and-spicy pattern we've  seen.
We seem to have found strong consensus already, but just one more to make sure. In Blue Point Brewing Company's words, its IPA pairings are meant to complement

intensely flavorful, highly spiced dishes, such as curry, and bold, sweet desserts like flourless chocolate cake and crème brulée

or

rich, aromatic, spicy and smoked foods such as chili, BBQ ribs, grilled chicken, and beef.

Actually, I think they stole those words from Wegmans' Guide to Beer and Food Pairing.
Comment: I was just going by my gut (literally!) on what I've found works. Nice to see some evidence about why!
Comment: This answer makes my mouth water.
Comment: @mdma - Nice—I hope one day I'll develop that sense!
Answer: CHEESE! Extremely sharp cheddar is best. A sharp Vermont or New York white cheddar will do as well.
My personal favorite is Tillamook Special Reserve Extra Sharp.
Answer: Cured meats - the saltiness of the meat and bitterness in the IPA play well together.
Comment: Agreed, although I was tending towards sausage.
Answer: Spicy foods. My personal favorite is stir fry. Something that isn't heavy on carbs is ideal, so with stir fry I go light on the noodles (or rice) and heavy on peppers, onions, and meat (usually chicken or beef). Again, don't use the milder sauces like teriyaki, use something with some kick.
Answer: Be mindful of the variety of IPA on the US market -- the average New England IPA is a different beast than the average west coast IPA. I'll call out a few excerpts from the serious eats article Andrew Cheong quotes above:

IPAs that lean extra-heavily on bitterness can be a bit tricky to match with food, which can make the beer seem astringent.

...

...IPAs that emphasize hop flavor and aroma over bitterness...I especially like these beers when served with Indian food. Hop flavor melds wonderfully with common Indian spices like tamarind, coriander, and cardamom.

...

Mexican food mixes light and dark flavors like cilantro and refried beans, lime and roasted chilies. Those combinations make great partners for IPA with its own caramel/citrus combo. Stick with lighter-bodied beers here, since bigger brews can easily overwhelm.

My personal experience -- I predominantly drink IPA these days -- is that I haven't had a memorably bad pairing, save for once where an overly sweet cupcake clashed with the bitterness of the IPA. But that was likely an exceptionally high-IBU beer. (I suddenly feel the need to gather more data).

What food pairs well with an IPA?