Using Plastic Water Jugs as Fermenters

Question: I asked this on Twitter a while back, but I thought I might get some other thoughts on it. I have one of those 5g Poland Spring water jugs. If I get a bung that fits it, is there any reason I couldn't use it as a fermenter (either primary or secondary?). Some people have said it should be fine, others have said that "chemicals in the plastic" will leech into my beer and produce off-flavors. I find this latter argument difficult to accept given that those same chemicals don't leech into the water that the jugs held. Thoughts one way or the other?
Answer: The consensus answer is that the only thing safe to put food with non-neutral PH into is #1 Polyethylene terephthalate or #2 High-density polyethylene.  The big blue jugs you get with water in them are made from #7 polycarbonate.  Polycarbonate has some potential health issues as it can leach, even in water at room temperature, a substance known as Bisphenol A which can have detrimental health effects.  There is a movement going on to discontinue use of #7 polycarbonate plastics in the bottled water industry and replace them with #1 or #2. It is my understanding that the company that makes Better Bottles is benefiting from this.  I know people will argue up and down that they haven't seen any health effects, but I simply wouldn't bother risking it.  Better bottles and bucket fermenters are cheap.
I have fermented in plastic carboys can I cannot recommend it.  You CAN get them clean with Oxy-Clean, but they are a PITA.  Glass fermenters where you can use a carboy brush or plastic bucket fermenters are superior, in my opinion.
As to the oxygen permeability issue, unless you are going to leave the product in the plastic for years, it should be a negligible effect. #1 or #2 plastics have a very low oxygen permeability.
Answer: In short: you'll probably be fine.
To explain, the primary danger is oxygen leaching through the plastic and oxidizing your beer. This is a real risk however you can minimize it.  I believe it will take months at the rate of diffusion. Your beer will come out tasting like stale crackers or wet cardboard.
The reason chemicals in the plastic may leech into your beer and not the water is because beer is acidic while water is fairly neutral in pH.  A few hours in the sun may drive off those chemicals. There is probably some food-safety regulation governing water jug composition guarding you from harmful chemicals.
Try it out.  If you don't have a problem, relax & don't worry.
Answer: I often used plastic jugs when first starting out, probably because they were cheaper and available. One thing I recall is the relative difficulty in removing krausen scum from the inside - perhaps the plastic isn't as smooth as glass; I'm not sure. But this was also years ago and I'm not sure I tried as hard as I would now. So perhaps with a good soak in the right chemicals - Oxyclean, bleach, what have you - it would be no problem.
Answer: I don't think you can taste bpa, but certainly microwaving food and eating it from bpa plastic will raise bpa levels in your blood stream. However, it appears that ceasing the behavior also drops the levels back down, so I'm not convinced it's a great health risk and unless you put hot wort into the jug, it shouldn't cause this effect.
The other issue with any plastic is the permeability; they simply let more air in than glass. PET seems to be much better than polycarb, but glass is 0. Having said that, I've switched over to plastic Big Mouth Bubblers for my primaries, but more for the convenience and price than anything else.
Answer: I use a #7 five gallon jug to transport brewing water from the RO machine in front of the market to my house... but I ferment in glass carboys.  I had two batches spoiled by a hairline crack on the bottom of a better bottle.  When I moved it, I smelled sour spoiled beer, and when I tasted it, it was awful.  I noticed it just after I had brewed a batch, and the local homebrew shop had closed 10 minutes earlier.  I put the new batch on top of a platter filled with starsan, but the bugs in the scratch ruined both batches.
Answer: I ran out of bottles and threw some of the last beer into a Poland spring bottle with a screw cap. It blew up like a bomb and became highly pressurized. I did it more for an experiment to find a secondary fermentation potential. I added priming sugar and maple syrup to the full batch and for this experiment I added a lot more extra maple syrup,  maybe table spoon for about one beers worth, so it explains the high pressure bottle bomb. I degassed it and tasted a drop. It's amazing. I feel as though I need to pour it down the drain. I wonder if it is safe to do a natural carbonation in a plastic bottle like that. Any input would be appreciated. The main batch is all in glass bottles but this plastic test bottle came out incredible.
Answer: What about the alcohol in the beer?
It's a solvent so might it leech chemicals from the plastic?
Lots of studies show that #1 and #2 are okay with water but has anyone studied if it is good with alcohol?
Since PH and Alcohol each provide the possibility of leeching, and since cleaning and micro-cracks are an issue with plastic, personally, I will stick to glass.
Answer: Tangential topic- but I have found to remove trub from plastic fermenters (or any fermenter), add hot water, PBW, and invert to cover the caked on trub. Come back 5-10 mins later, and the trub is dissolved.  WOOP WOOP! Cheers!
Answer: As one is only fermenting for 14 days in a pre-used plastic container I would argue that it is safe to ferment in a plastic food grade container. In fact one might argue that the more one used it for fermenting the safer it would be as there is only a limited and very small amount of "objectionable" chemicals in the plastic to begin with. I presume the original water was consumed without complaint so one might wonder why any beer brewed in it would be "bad". Yes there may be better things to use but I don't think it would be deleterious per se to use this item.

Using Plastic Water Jugs as Fermenters


How can I wrap fish for freezing if you don't have a vacuum seal?

Question: I know the ideal way to store fish in the freezer is to use a vacuum seal, but does anyone have any tips on what to do if you don't have one handy?
Answer: If you wrap the fish (or any meat you're freezing) with a layer of plastic wrap and a layer of aluminum foil, it will keep out air out and moisture in as much as possible without vacuum sealing.
Make sure you wrap with plastic wrap first, then aluminum foil.  The taste of aluminum can leech into the food and supposedly there are health risks associated with aluminum/meat contact as well, though I haven't heavily researched them.  Better safe than sorry, though.
Then I also recommend using a straw to suck out as much air as possible, as chris suggests.
This article has some great guidelines on freezing meat and minimizing freezer burn.  While it only calls out meat and poultry, I use the same methods for fish with great success.
Comment: That's what I do now. Plastic, then foil, then ziploc.
Answer: You can also place the fish in a plastic bag and use a bowl of water to push the air out of the bag.  Just make sure to seal the bag while the end is still out of the water so you don't get any water in the bag.
Answer: If you're portioning it, you can store it in freezer bags, and suck the air out with a straw.  It's not perfect, but it is an improvement.
Answer: We portion our fresh fish into what we would eat at a meal, place in a ziplock bag and fill with water, squeeze out as much air as possible, zip shut and then freeze.  If we have company, we take out 2 or 3 bags.  Usually the fish are cleaned and filleted.  This keeps the fish from freezer burn.  Has worked great for us for many years.


Are any writings of the Apostles non-Canonical?

Question: Do we have any writings that are reasonably likely to be written by Apostles, but are not included in the Bible?
Answer: One of the closest examples would be Paul's Letter to the Laodiceans.  Scholarship is divided about the authorship, whether it is Paul or a Marcionite forgery - but the point is that at the time, when canonization was occurring, it was not accepted as such.
Most everything else (Gospel of Peter, Gospel of Thomas, etc...) was pretty much rejected even at the time as being inauthentic.
Oddly, Hebrews was often ascribed to Paul, but not universally.  Still, that was its reason for inclusion.
At this point, even if we could authenticate a new work, that would not automatically make it scripture, however.  Canonization was often supported by apostolic authorship, but it was cemented by common concurrence.  At this point, the canon is closed, by consensus.
*P.S.  I've walked through Laodecia, and seen the place on the picture.  It's an amazing place!
Comment: Fascinating - great answer, as always.
Answer: There is another example: Epistle of Barnabas, which suffers from some of the same questions of date and authorship that the letter to the Laodiceans.


How to learn gemara independently

Question: Is there an organized path that a Ba'al Teshuva can follow to learn Gemara and prepare the Daf by himself?
I mean after he is able to learn with Artscroll.
Comment: See also: http://judaism.stackexchange.com/questions/299/talmud-study-where-to-start/300#300
Comment: rony, welcome to Judaism.SE, and thanks very much for posting your question here! I look forward to seeing you around.
Comment: Rabbi Simcha Wasserman zt'l (son of Rabbi Elchanan Wasserman Hy'd) answers this http://dafyomireview.com/article.php?docid=57
Comment: Read the Gemara mnukad, Read the Amud, Do Rashi, then look up all words you don't know, now read it.... think think think, then..... look at artscroll for a pshat you didn't know... then..... Listen to a Shuir to complete the cake
Answer: Sit with Jastrow's Aramaic dictionary and Frank's Practical Talmud Dictionary and look up every word and phrase until you start recognising you've looked this up before. This is the way I did it, but unlike every other person I know I enjoy finding words in the dictionary.
If you have the opportunity then full-time learning in a Yeshivah would obviously be best.
Otherwise, regular learning with a partner (or a group) on the same sort of level as you will keep you making progress and provide motivation to continue. A chavrusa with a patient partner on a higher level will also help correct your inadvertent misconceptions.
Personally, I only felt I was able to learn Gemara competently on my own after two years of full-time Yeshivah, starting from scratch.
Finally, the hashkafah I have been taught discourages exploring Acharonim until you are well able to extract the pshat from the Daf, and even then its far from the focus of your learning.
Answer: There is a basic way of analyzing the text that should get you "in" to some degree.
Identify every statement in the shakle ve tarye according to one of these seven categories.

Difficulty
Resolution of difficulty.
Disproof
Proof
Question
Answer
Statement.

II. Understand how each move is achieving its goal.
    E.g. How did the proof achieve its goal.
III.Make sure each move is relating to the next move.
E.g. Is the resolution addressing the difficulty.
Always check the language of each statement for the following:
Ι. Superfluous  language i.e. wordiness.
ΙΙ.Repetition of the same concept.
ΙΙΙ. Inconsistency in language.
Ιν. Is there a  chiddush being stated ? (i..e new idea.)
ν. Change in language or change in law.
I have a blogsite where I go into detail in these steps of analysis.
http://www.howtolearngemara.com
There is a phenomenal set of audio shiurs that go through the following sefarim
Way of the Talmud i.e. Darchei Hatalmud by Rabbi Yitzchak
       Ways of reason i.e.Derech tevunot by the Ramchal
       Book of Logic i.e.Sefer Higayon By the Ramchal
       Book of Rhetoric
Here is the link
http://learntalmud.org/
Comment: +1. My ninth-grade _rebbe_, Rabbi _Baruch_ Rabinowitz, who should be well, taught us to identify KTRM: kasha/terutz/raya/memra, which was a simplified version of the system in this answer (he included IIRC _sh'elos_ as _kushyos_, and the like, presumably for simplicity). He also made us analyze flow, much as this answer advocates. By the end of ninth or, at most, tenth grade, any of us in the class could open a _g'mara_ we'd never seen before and do a passable job of figuring it out (without ArtScroll!). I owe the man a good deal.
Answer: According to Rabbi Pogrow, the following method works to remember what one learns:

Learn the material once. Either through a Shiur, Artscroll, whatever it takes to know Pshat. One should focus on the structure, where are questions, what are answers, which questions do the answers answer, etc. One should also take note of names (who said what).
Review it inside four times. For this one should need only a normal Gemara, because one should already have learned the translations in step one. If one still doesn't remember them, one could look them up. By the end of this session, one should know the Amud.
Spend the same amount of time one learned in Shiur in review of material learned in the past week.
Spend two days out of the week (he suggests Shabbos and Sunday) as review days. On these two days, do not go ahead. Spend that time reviewing ALL the material one has learned in this program.

There are some more tips over there, but this system does work.
Comment: Related: http://judaism.stackexchange.com/q/68864
Answer: When I was younger I used to sit, as the top answer suggests, with a Jastrow, looking up every word I was uncertain of. I found this approach slow and frustrating, and after doing it for a couple of years, I still hadn't progressed to the point of being able to open up a random gemara and read it.
What really enabled me to get really good really quickly was having a chavruta in yeshiva who went really quickly, and translated nothing unless I asked him to. I literally only had too options: sink or swim. We would learn a daf and a half every afternoon, and after we finished I would review it by myself. And then in night seder, I'd review the previous daf. And then in lunch break I would review the daf we studied a week before.
Counter-intuitively, it wasn't fighting to understand the daf that taught me how to learn. It was seeing sheer volume of page after page of gemara, and with each iteration and page, becoming familiar with the constructs and logical paradigms used by the tana'im.
I suggest learning lots of gemara with lots of chazara bekiut, just to get a feel for the style and language usage. Write translations you don't understand down in a little notebook in the first reading, and try to use that notebook as little as possible in revisions. Also try to use nothing other than your notebook for translation when  you're reviewing.
Be careful that your revisions are extremely precise. You must understand exactly how each word fits into the overall picture. Don't just accept that you got it right the first time. Recalculate everything in your brain every time. Slowly reworking everything will get easier. I used to take an hour to review a daf, and do so in around 20 mins now.
Try to think in the language of the gemara rather than translating it in your mind first. The extra step of translation is a real handicap that you should deal with as soon as possible.
Ditch the Jastrow if it's too frustrating, and just use an artscroll for a first read. If you don't remember it from the first read, you will become intuitively familiar with the style from the artscroll-less revisions.
Oh, and if you can find yourself a chavruta who pushes you to your breaking point, that is a valuable chavruta. You should keep 'em.
Answer: Organized path, eh? I didn't find anything like that. In my experience I found very few systematic guides on how to actually approach sugyos, including all the assumptions of the Gemara, Talmudic logic, etc. The Ramchal has a couple works which have been translated into English (Feldheim), but they are extremely dry and technical, and relate to the component logic rather than overall approach. There is a famous work by Yitzchak Kampanton (Darchei ha-Gemara) in Hebrew, but I did not find a particularly well-defined derech there. Could be I wasn't patient enough to analyse the Hebrew text.
In retrospect, if you have an analytical mind, get this book and learn up your sugyos with that. Ditto to Michael Sandler on the Frank, but I see it more as a reference - Big Blue (the Feldheim) is more streamlined and good for learning the ropes.
I used Soncino before I was competent in the actual Talmudic language in the original, which is good inasmuch as it gives you the words whilst leaving the logic up to you, as opposed to ArtScroll.
My personal advice: hammer away (long-term) until you understand the standard devices of Talmudic argumentation, and understand the framework of your sugya before you set your eyes to any commentaries. If some piece of the framework eludes you, that's okay; but IMO the Gemara speaks to us on its own without commentaries, even if you/I don't understand all of a particular sugya.
Comment: There are audio shiurs that clearly explain the sefarim you mentioned
http://www.koltora.com/english.php
Answer: Try to do as much as you can on your own, and only look at Artscroll when you can't understand something. Then make sure to read it again in the gemara on its own. This way, you'll be able to get through gemara, and be able to read it without Artscroll. Using a dictionary will probably take too long. If you want to remember the words, you can always write them down from Artscroll's translation.
(Not that there's anything wrong with learning with Artscroll, but you want to be able to view the gemara on it's own, and anyways, Artscroll is kind of long.)
Answer: advice: dont learn on your own you are bound to make mistakes. Chavrusa learning is there to prevent mistakes and also be challeneged. Learning gemorah is less about pshat and more about sharpening your midn to think through Torah lense.
In fact the Gemorah in Makkos states that there is an issur to learn alone. It is disputed what this means and where it applies (e.g. some dont hold of it in Eretz Yisroel as the air there sharpens one's mind) however one who learns alonge is boudn to make mistakes.
Learning with an Artscroll is called b;'chavrusa - except it takes away your training to think.
www.dafyomi.co.il is a good resource they also have quizzes that you can use to test yourself on every daf.
Answer: There are two programs that are available in many cities, in the U.S., Canada, and England (and probably some other places too).
The first is called Fundamentals of Talmud, or in some cities Yesodei HaTorah.  This is their website.  It is designed to be systematic and break the gemara down in a way in which you can build skills on your own.  The program is possible to do individually, they have material and audio shiurim which enable complete independence, but some cities also have Yesodei HaTorah classes.
PBM is another program.  It started in London, but has spread to many other cities and countries.  There website is here, although you can look around the web to find other websites associated with them.  They also have a systematic program, and their system has multiple tracks, and seems to be more thoroughly developed.  I have limited exposure to it, but they seem to be more based on live shiurim than Fundamentals of Talmud is, and it is harder to track down where you can find them.
Both of these programs are designed to foster independent study skills and are very organized.
Personally, when I learned to learn gemara (post high-school), I took a chunk of 10 daf (happened to be the first 10 of Shabbos) and learned them until I knew them cold - I knew all the steps of the discussion, I knew every word, I knew how each phrase was used and which phrases indicated what.  I found that within 10 folio pages, you will find a significant volume of critical vocabulary, Talmud logic-structures, and concepts to be able to get a basic idea of a Gemara.  But my experience has been that everyone works differently.
Comment: I think the real answer to the question which is really a most important one is that one should not learn a gemoro daf after daf. One should start with easy ones and carry on from there. There ought to be a list of 'easy' ones and children should also be learning this way. No one seems to have mentioned looking at the mishnayot first. One should remember that artscroll is quite advanced. The chumash with targum also helps to get a feel of aramaic. A lot of the answers here are for advanced students and wont help the beginners. One should also make a kind of flow chart when learning.
Comment: I should also add the way I learn a gemoro is first the easy parts. A rule of thumb can be where there is less than a page of gemoro on a mishna. There is absolutely no need or gain to doing it in order.
Comment: @preferred I don't know what makes an answer real or fake, but I didn't pick a particularly easy one - some yeshivos learn those as the yeshiva masechta in morning seder, they aren't particularly simple.  The method I used, and I was a beginner (first time learning a gemara), was as I explained.  Although, the programs I referenced do pick out the gemaras they choose with careful selection criteria.
Answer:
Reading

The Gemara is written in a mixture of Hebrew and Aramaic. Rashi and Tosafot use a mixture of Hebrew and Aramaic. To learn Gemara independently, the student must reach the level where the commentaries, starting with Rashi, start to anticipate the difficulty of understanding the words. This does not always happen, but in general the Gemara is not "flat" in terms of "difficulty," and even on a pure peshat textual level, this is a feature of the text. A student will recognize that a particular section is easy or difficult, and see this reflected in the commentaries. If you think it is hard, and Rashi is explaining every word, you are probably right.

Thinking

The most basic difficulty people have with Gemara is that the entire discussion assumes a familiarity with the contents of Chumash and the Mishnayot. There are a few parshiot, like Mishpatim or Shofetim, which will cover many of the laws in the Gemara, but also areas like Kodashim and Tuma an Tahara, which come out of Vayikra, and those Sedarim of the Mishna, are extremely difficult if one has not taken the "introductory course" of the Mishna. Learning a single Seder of Mishna, or two, with a commentary like Kehati would familiarize someone with the concepts of the Gemara, which would provide a basic level of bekiut necessary to follow the discussions and think about the issues in an intelligent way.

Weighing

Using specific knowledge of how the issue plays out in Torah She B'al Peh - Mishna, Yerushalmi, Tosefta, and Bavli - we might try to understand the flow of an argument, by looking at parallel passages and details that Tosafot might mention, or issues that Rashi is not directly mentioning. To do this requires very serious Torah knowledge, which is why people who can do this well are usually giving shiur.

Pursuit

Something might jump out at the learner. They have to be able to go into the Rishonim and Achronim and track the different shitot and assumptions about the Gemara, along with how those shitot come out from the lashon of the Gemara or other sources on the same topic of the Gemara. This is what most people consider to be iyun.
None of this is learning as if someone can read through the Artscroll Gemara, like Gemara is some book in a language you don't understand, that if only you could understand the language, you would be able to read it like Harry Potter or the newspaper. Gemara requires serious intellectual effort, but this is the highest form of serving God.
One of best Rebbeim said, as we were learning a difficult Gemara, that he doesn't understand how people learn Daf Yomi. A beginner might find this difficult to understand. After all, how can the Rebbe, who is an expert, not understand how to learn Daf Yomi?
The answer is that Gemara is like a mountain range, and you can't go very far at all without reaching a very high mountain. The mountain is bigger and more difficult the more you understand the complexities of the Gemara.
So, learning independently can be more like mountain climbing, or walking at the feet of the mountains at a faster pace. If you know that topics are deep like the ocean, then it is okay to keep moving on, even though I would not recommend that as the major form of learning in a person's life, which would not be in such depth. Rav Ovadya Yosef zt"l used to say that he doesn't understand why people with one hour a day to learn would do Daf Yomi, they should learn Halakhot of Shabbat. But later, I heard that he said that by learning Daf Yomi, a Jew can learn every area of Torah She B'al Peh, and through that exposure to all areas of Torah achieve much. So really, there are different ways you can do it, and no limit to the depth that can be reached, although reaching the level of someone who can walk though, and recognize, the easier parts - that only comes through learning. L'fum Tzara, Agra - according to the pain, so too the reward.
Answer: There is an easier way, that will give you guaranteed results.  I do the daf yomi using the English Armaic Steinsaltz Gemora.  I do the 1/2 daf on the audio (Rabbi Grossman), which takes a about 20-25 minutes, in the morning, and the other 1/2 in the night.  After doing the audio I review the Gemora entirely on my mine own, gradually adding on the different meforshim.  Doing it this way, you will pick up the language and begin to master Gemora, eventually on your own. Good Luck!
Comment: The Steinsaltz gemara [is now online](https://blog.sefaria.org/2017/02/07/setting-the-talmud-free/)
Answer: Following a link from idaven.com, there's a website dafyomi.org. They have an audio track in English you can listen to for each daf. Be warned that the quality is not 100%, and the Rabbi may sometimes go a bit fast (especially if you're not from a Yeshiva background), but it's a good way to listen to someone talk about the daf each day, from your computer (you can also download the MP3 files and listen to them at your convenience on your music player).
Hatzlacha!
Comment: I recommend Rabbi Eli Mansour's because it goes a lot slower and is in my opinion probably more understandable. DAILYGEMARA.COM
Answer: Once you have the basics down and understand the simple daf, (or even beforehand, depending on the type of learner you are), I find that it is helpful to constantly ask the question 'why?'
Why did the gemarah start here? Why did the Gemara give 2 answers to this question, is there a flaw in the first answer, or the second, or both? What is the reasoning behind this particular question?
If you start to read rishonim, like rashi and tosafos, do the same thing. Are rashi and tosafos arguing? If they are, what is their reasoning? Why did rashi describe something that seems obvious, or use extra words to make what seems like a simple point? (I have been taught that rashi in particular amongst rishonim was very very careful with every one of his words.) Why did this rishon say things in this way?
This can take a lot of time and cover very little ground, depending on how deeply you want to delve. If you still want to cover ground, you can write down these questions as you learn, and then designate a time, a different time of day, or once a week, or the beginning of your session, where you work on answering one of your questions. I learn by myself often, and I find that this method helps keep my mind sharp while still allowing me to progress through a Gemara.
Hatzlacha to you!
Answer: Since the time this question was asked (2011) and since the last time there was activity on it (2017), several incredible online resources have sprung up: (expanding on my previous answer from MY Meta)

1) Sefaria- quite literally "A Living Library of Jewish Texts." Sefaria has pretty much all of Shas translated into English, as well as most of the accompanying Rishonim/ pertinent Halacha seforim right next to whatever Gemara one is learning.
2) Mercava- similar concept to Sefaria-- ie translating Shas-- however the main difference is that Mercava has the Tzuras HaDaf (original form of the page).
3) Google Search in Hebrew- wonderful for searching any phrase/ concept. Upon finding a page that is difficult to understand, one can also toggle it back to English.

HebrewBooks.org is another.
Are all superb resources to help with one's Gemara learning!

How to learn gemara independently


Is it acceptable to contact a potential customer who has accessed your site, using their IP?

Question: We run ad campaigns to attract potential customers to our website. Sometimes customers click, but don't make contact. Is it acceptable to reach out to these customers, based on the public info available from their IP?
Comment: From a consumer-friendliness standpoint, it's never ever acceptable to contact me unless I contact you first.
Comment: Interesting that you would already have their contact info. And not everyone is on a static IP address.
Answer: If I get spammed because I was "foolish" enough to leave my e-mail address, then stupid me.
If I get spammed just for visiting a website, then - how can I put this politely? I'd be pretty darn peeved.
If I knew a site's owners were employing such practices, I'd avoid them like the plague.
If I found out I was contacted because I just happened to visit a website, I'd scream hell and bloody murder.
Bear in mind that my visit may not have been intentional, but the result of a mis-click, somebody's url shortener, misleading link title, ... whatever. Even if my visit was intentional, I'd still not want to be contacted just because I visited the site. After all, when I visit a physical store, I can just come in look around and go and I know I won't be bothered by mail from the owner addressed to me personally.
That you may have the means to find out my contact information using my IP-address doesn't mean you should use those means.
Spam is spam no matter how you obtained my e-mail address (or telephone number or whatever).
Comment: Indeed.  I'd work on the basis that if potential customers wanted to hear from you - they'd leave a means of being contacted.
Answer: No.
However, I assume that you're considering this not with people who visit the site once and leave, but with people who visit it more than once without making a purchase or visiting the part of the site that you want them to see.
A technique that I do consider ethical would be to track visitors and after a certain number of repeat visits, pop something up that says "Answer our 5 question poll about our product / website! One person who answers the survey will receive [insert prize related to product or service here]!" (Assuming you actually follow through on your promise and give respondents prizes, of course.) You'll then have a legitimate reason to request their contact information and an opportunity to ask them whether it's okay for you to email them about other things.
In the survey, you can ask questions about whether they found the information they were looking for, what they think about the product / service / price / whatever, etc. That might help you figure out why potential customers are leaving the site without doing what you want.
It can also be helpful to look at analytics. Specifically, in addition to watching how they got to the page, you can watch the path they take through the site. That can help identify issues with the navigation or the content that might be preventing them from continuing through the desired path. Google analytics is free and has some of those features, although there are more extensive paid tools available.
If you find design or content issues that seem like they could be contributing to the problem, you can then try techniques like displaying a slightly different version of the website to repeat visitors and seeing whether that one performs better.


Can determinant of liquidity risk be used as a dimension or measure of liquidity risk

Question: Can I take liquidity risk determinant as a dimension of it in order to examine the impact of liquidity risk on performance of banks? For example in a literature, Tangibility i.e., ratio of fixed assets to total assets was used as a determinant of liquidity risk and results found to have significant relationship of this tangibility ratio with liquidity risk. So based on these findings can i take this tangibility ratio as a measure or dimension of liquidity risk in order to examine the impact of liquidity risk on performance of banks?
Comment: just rushed back from holidays because the SE emergency pager beeped like nuts. Thanks for ruining my holidays...;-)
Comment: If someone knows answer of this question then please answer it as soon as possible. Thanks
Answer: Friend, take a step back and think what you really want to measure. During normal times you should never care about liquidity risk or credit risk of banks, EVER, at least what concerns the text book definitions of liquidity and credit risk. During times of stress you want to throw all accounting gimmicks and monkey numbers aboard and focus on one single number. CASH available to pay off short-term liabilities. NOTHING ELSE. Walk me through one single bank run or bank blowup scenario where any other numbers mattered. So, if accounting numbers during stressed times and accounting numbers during regular market cycles do not matter then why do you want to focus on those? I understand if you want to become an accountant but if you truly show interest in understanding solvency then forget each and every last one concept of what CFA or other accounting related sources teach you regarding liquidity or credit risk of banks.
Believe it or not, but before Lehman went belly up none of the analysts who evaluated the solvency of LEH cared about the inputs to measuring credit or liquidity risk. They all cared about whether LEH can satisfy today's and tomorrow's margin calls and expected redemptions as well as the probabilities of having further credit lines pulled. Those who sat on the other end of the table did not evaluate LEH's credit in any traditional sense. Those decision makers had all ears on T.S. Paulson and also what the FED had up its sleeve, the probability of a bailout, in summary, political decisions where all that mattered. Same with Bear Sterns, same with every other bank prior to having gone belly up.
By the way, even if you looked at liquidity and credit risk way earlier before the last days of LEH' life may I remind you that their liquidity numbers (however faked they were) did not point to a default within days. Lights went out when JPM pulled their lines (for debatable but completely legitimate reasons). Sure, liquidity and credit risk numbers deteriorated over months prior to the crisis but so did everything else. Its like saying that "hey, I told you my 'economic-feel-good-index' went down the river since October 2007, so you have to watch that each time you care about evaluating bank risk". As long as any metric is anchored to a mix of economic, market, sentiment numbers then obviously you observe the higher correlation between such metric and market risk the more overall market stress feeds into the ingredients of such metric.
//beginning of rant(please stop here if not interested)//
I recommend you diligently study this "stuff" to get your As in your MBA courses and CFA exams. However, keep in mind that most of the accounting numbers are there for one reason: To feed a whole industry of people who would not exist without this construct and to provide CFOs and CEOs with ever more ways to mask their real numbers. Nobody trading CDSs cares about traditional credit risk evaluations. It is generally those who continuously emphasize the importance WHO DO NOT HAVE A SKIN IN THE GAME, such as accountants, analysts, fund managers, educators, the media. Why I include fund managers? Because I cannot take someone seriously who comes out in 2008 and arrogantly tells the world that his fund performed 5% better than the benchmarks....it is "only" down 37%. //end of rant//


How do you get the bag of hops into the carboy and then remove it?

Question: I always have a difficult time getting the hops in the carboy and then removing it when dry-hopping. What's the trick?
Answer: The easy answer is don't use a bag.  I usually use whole flowers when dryhopping.  They float on top and then I rack to another carboy when done w/ the dryhop.
I used a bag 2x and it was a royal pain in the butt.  Getting it out was always the hard part, brute force was my method.  It always made me worry about contamination.
Comment: Agreed. When I dry-hopped with a bag the leaves absorbed so much wort that I had to wait until they were dry to remove the bag. Some narrow tongs would help you make the bag in to a carboy-hole-shape.
Answer: It's easier using pellet hops in the bag. What I do is place the hops in the bag along with a weight of some sort (a stainless butter knife or something thin) to get the bag to sink. Tie a length of dental floss to the top of the bag and lower the bag into the carboy keeping a length of the floss outside the carboy. Lower bag halfway down and then push the stopper/airlock back into the top of the carboy cinching the dental floss in place so that you can pull the bag back up later. I would recommend racking the beer out of the carboy before trying to retrieve the bag because it will expand and need to be worked out of the carboy opening.
mark
www.backyardbrewer.blogspot.com
www.thebackyardbrewer.com
Answer: Thanks Mark, I've wrestled with this for awhile.  Funny, 20 years brewing in a vacuum... the simple concept of a weight and dental floss never occurred to me... I suppose that says something about my intellect....  I think I love this website.  No more loose pellets in my secondary carboy.


Confusion over a point in basic category theory

Question: "Let Top be the category of topological spaces." If I see a definition like this, in which homeomorphic (isomorphic in the category) spaces are not identified together, then for each given topological space, how many times does it show up as an object in Top? Once? Countably many times? Uncountably many times? Is there a semantic crisis if we don't identify all homeomorphic topological spaces to the same object?
Answer: Well, such categories are actually proper classes.  For instance, spaces that are homeomorphic to $\mathbb{R}$ will be given on ANY set of the same cardinality.  So how many there are, depends on how many such sets there are...but there are quite a lot of sets.  In fact, more than any individual set worth. (Though on the details there, I'm not sure about what happens for fixed cardinality)
We CAN identify them, and we get a skeleton.  However, we usually don't do this, because there's no natural way to pick one object in each class, and one of the important catch phrases for category theory is "never make a choice." (Naturally, this is a vast oversimplification, but it's a good rule of thumb)
Comment: I like the motto "don't be evil" for the rule of thumb. http://ncatlab.org/nlab/show/evil
Comment: Charles, about your parenthetical remark: even the class of sets with only one element is already a proper class, and it is clearly bijective with the class of all sets. So it doesn't matter if you fix a particular cardinality or not.
Comment: Regarding the question of whether moving to skeleta simplifies anything (and why it probably doesn't), see http://mathoverflow.net/questions/11674/can-skeleta-simplify-category-theory
Comment: @François - Precisely my point, and that is a good motto, I should link to that page more often.
Comment: Good point.  Hadn't thought much about it.
Answer: If what you mean by "the category of topological spaces" is the category whose objects are pairs $(S,T)$
where $S$ is a set and $T$ is a topology on $S$ and by topological space you mean a pair $(S,T)$ where $S$
is a set and $T$ is a topology on $S$, then clearly each topological space appears exactly once.
Comment: +1 : I suggest thinking about this response until you realise your original question was the wrong one to ask!
Comment: That's true, but I can see the usefulness of formulating things this precisely. Part of the problem is that my intuition is a little loose.
Comment: I think what the OP intended to say is "how many times does an isomorphism class of topological spaces occur?"
Answer: It would be best to talk about the category of sets first, I think.  Any isomorphism class of sets shows up so many times that a given isomorphism class doesn't itself form a set - for example, $\{ 1, 2, 3 \}$ or $\{ 4, 5, 6 \}$ or $\{ \text{Cat}, \text{Dog}, \text{Monkey} \}$ are all elements of the isomorphism class of sets of cardinality $3$, and more generally so is any set whose elements are three different sets, so there are at least as many sets of cardinality $3$ as there are sets.
The same occurs in any category where you insist on representing the objects as sets, but one of the nice things about category theory is that it more or less doesn't matter what "machine language" you use to describe a category.
Comment: Wait a minute, isn't $\mathrm{Cat}$ -the 2-category of small categories- a proper class?  ;P
Comment: A universe where {Cat, Dog, Monkey} isn't a set isn't very useful, is it?  In all seriousness, you can interpret them as strings, hence as the sets in ZF corresponding to the numbers that make up their ASCII representations.  But again, the "implementation details" are totally unimportant.
Comment: So I suppose then that we don't really need "Pet Axiom 1) Your favorite pet is a set."
Comment: Unless I misunderstand something, {Cat, Dog, Monkey} isn't a set, is it? I suppose it depends on what you mean by the category of all sets, but I'm pretty sure cats don't show up in ZF...
Answer: This is not essentially different from what everyone else has said, but for some reason I feel like saying it anyway.
The number of times that a given topological space appears in the category of topological spaces is exactly once.  That's the definition of the class of objects of Top.
As for isomorphism classes: there is exactly one object in Top which is isomorphic to the empty set $\varnothing$ with its unique topology: namely $\varnothing$.  For any nonempty topological space $X$, the subclass of Top consisting of spaces $X'$ which are homeomorphic to $X$ forms a proper class: i.e., they are more numerous than any set.  This is true because the class of all sets is a proper class, and if $(X,\tau)$ is any nonempty topological space and $S$ is any set, then $X \times \{S\}$ is a set which is different from $X$ but in bijection with it: $x \mapsto (x,S)$, and the image of $\tau$ under this bijection gives a topological space which is homeomorphic to $(X,\tau)$ but with a different underlying set.
So, except for one, the homeomorphism classes in Top are "unsetically" huge.  Nevertheless, the modern perspective is that this is fine (or, perhaps, harmlessly irrelevant) whereas it is a bad idea to work with the homeomorphism class of the space instead of the space itself.  One way to think about this is that a given topological space $X$ is a relatively simple object, but the class of all topological spaces homeomorphic to $X$ is a ridiculously complicated object.  (This has not always been the received wisdom: notably Bertrand Russell's definition of the number $2$ was the class of all sets which can be put in bijection with, say, $\{\emptyset, \{ \emptyset\} \}$.)  From a less philosophical perspective, one wants to speak about sets of maps between two topological spaces $X$ and $Y$, and if $X$ and $Y$ are only well-defined up to a homeomorphism, these sets are themselves not so well defined.  As soon as one studies commutative diagrams of morphisms of objects in a category (or more generally, functorial constructions), one recognizes that the concept of "topological space up to a homeomorphism" is a painfully awkward one.
It is also simply against the spirit of category theory to pass to isomorphism classes: many would say that this overemphasizes the somewhat quaintly philosophical notion of equality of objects.  Instead of saying "the topological space $X$ is equal to the topological space $Y$", many mathematicians now think it is both simpler and more useful to say "$\Phi: X \rightarrow Y$ is a homeomorphism".  For more on this point, I highly recommend Barry Mazur's article When is one thing equal to some other thing?
Answer: (Expanding on Yuan's point about the irrelevance of "machine language" and JT's about "the wrong question to ask":)
In a sense, one oughtn't even be able to ask whether two topological spaces (i.e., objects of Top) are equal, only whether they are isomorphic; if one can't ask about equality, then one certainly can't speak of cardinality (with respect to such equality), and so there is no notion of the cardinality of the collection of objects isomorphic to a given one.
However, if you construe every topological space as implicitly carrying extra non-topological information via which such a non-topological notion of equality is defined (e.g., if you take the points of topological spaces to furthermore be elements of the cumulative hierarchy of well-founded sets of sets of sets..., allowing one to ask whether points in distinct spaces are equal by appeal to this extra structure, and accordingly whether spaces themselves are equal by virtue of an isomorphism sending points to equal points), then, of course, the question can be answered (in the given example, as noted above, the answer will be that the isomorphism classes form proper classes). But this is not really a question about the category of topological spaces, as such; this is a question about the particular manner in which one may choose to realize the intuitive theory of topological spaces within the ontology of another (meta)theory/implement the structure of the category of topological spaces within a context imposing further structure as well.
If one avoids selecting such "implementation details", then the question is meaningless, in precisely the same way as questions such as "Is the integer 9 an element of the rational -3/5?" are meaningless in the abstract.


Can I export View NX2 Custom Settings?

Question: Is there a way to export the Custom Settings for Adjustments Palette that I used in the editor view of NX2?
Answer: With all 3 Develop edit panes, and the Adjust edit pane, closed, control-click in the space beneath the closed Adjust pane.  You will see a contextual menu appear, where you can save (and load) settings.
This copies settings from all Develop and Adjust panes, but you can save/copy after editing only those settings that you want to apply later.
Answer: The previous answer seems to be for Capture NX2 which does not answer the original question which appears to be for View NX2 a different program.  So, the answer as far as I know is, NO you cannot save anything in View NX2 related to edits except Picture Control profiles.
Answer: Maybe some of my scripts for copying adjustments might help you to export to other images.
Edit: The one batch allows to copy the nikon adjustments to a cache file. The another batch copies back to a bunch of files and adjust nikon settings. So it is an export like you might want, It depends where you want to export..
Comment: Can you elaborate? What do your scripts do exactly, and how might they help?

Can I export View NX2 Custom Settings?


Is Use of keyword instead of preposition good?

Question: i would like to know if we write articles using the fixed keyword instead of using the preposition for it good for SEO keyword density?
Answer: While it may be a good idea to write for humans or for search engines, it's a great idea to consider writing for both. The first rule of great writing is this:
Don't write to be understood; write so that you cannot be misunderstood.
Always assume that a sentence will be taken out of context or be used by itself to represent the whole of paragraph. If you use too many "he/she/it/them/those/us/thing/stuff/do", you will not be understood.
Which is the better sentence?  Which one appeals to both humans and search engines? Which one is most likely to be understood out of context?
1) He gave her the stuff to make more things.
2) John gave Sarah the AC/DC albums to create additional wall photos.
Answer: Write the article so it makes sense to human beings. If you start writing content so it reads like what you think the search engines are looking for you're going to end up with bad content. Bad content makes getting links much more difficult to do. It also makes people leave your website which is also against your goals.
Anyway, search engines are smart enough to know synonyms, prepositions, etc, for words and phrases so I would be worrying about this anyway.
Comment: Also, Google is starting to crack down on "overoptimization", which is just another word for making spammy sites that are designed for SEO, not for creating value for users.
Answer: Many people suggest that the search engines are all knowing of synonyms, plurals, etc. of the same word stem. I agree that it's largely true, but I have found many situations where it just is not so, and because of that, I do feel like a little variation in the usage of your keyword stem is probably a good idea.
So, my answer would be to suggest that you do actually vary the way you use your keyword, but as you do that, it's quite important, like John Conde suggested, to write your content to make sense to human beings.


Why are functional equations important?

Question: People who talk about things like modular forms and zeta functions put a lot of emphasis on the existence and form of functional equations, but I've never seen them used as anything other than a technical tool.  Is there a conceptual reason we want these functional equations around?  Have I just not seen enough of the theory?
Answer: The simplest reason functional equations have importance, for someone learning this stuff for the first time (not knowing about modular forms, automorphic representations, etc.) is that they can be used to verify the Riemann hypothesis numerically up to some height!
To explain this, let's start off with a limitation of methods of complex analysis in detecting zeros of functions. There are theorems in complex analysis which tell you how to count zeros of an analytic function $f(s)$ inside a region by integrating $f'(s)/f(s)$ around the boundary (this is the argument principle).  So we could integrate around the boundary of a box surrounding the critical strip up to some height and see there are, say, 10 zeros of the Riemann zeta-function up to that height (yeah, there's a pole on the boundary at $s = 1$ which messes up the argument principle integration, but don't worry about that right now).  How can we prove the 10 zeros in the critical strip up to that height are on the critical line?  Complex analysis provides no theorems that assure you an analytic function has zeros on a line!
The functional equation comes to the rescue here.  I'll illustrate for the Riemann zeta-function $\zeta(s)$.  Its functional equation is most cleanly expressed in terms of
$$Z(s) = \pi^{-s/2}\Gamma(s/2)\zeta(s)$$
and is the following:
$$Z(1-s) = Z(s).$$
We also need another "symmetry": $Z(s^*)^* = Z(s)$, where ${}^*$ means complex conjugation.
Where does this come from?  For an entire function $f(s)$, the function $f(s^*)^*$ is also entire: in fact its local power series expansion at any point a is the one whose coefficients are complex conjugate to the coefficients of $f(s)$ at $a^*$.  Or you could directly prove $f(s^*)^*$ is complex-differentiable when $f(s)$ is.  The significance of this is that if $f(s)$ is real-valued for some interval of real numbers then $f(s^*)^* = f(s)$ on that interval, so by the rigidity of analytic functions we must have $f(s^*)^* = f(s)$ everywhere when it is true on a real interval (not one point intervals, obviously). Lesson: an entire function $f(s)$ that is real-valued on some interval of the real line satisfies the formula $f(s^*)^* = f(s)$ for all complex numbers $s$.  By the way, this also applies to meromorphic functions on $\mathbf C$ too (rigidity of meromorphic functions).
Let's now return to the zeta-function. Because $\zeta(s), \pi^{-s/2}$, and $\Gamma(s/2)$ are real-valued for real $s > 1$, their product $Z(s)$ is real for $s > 1$, so $Z(s^*)^* = Z(s)$ for all complex $s$. In particular, for a number $s = \frac12 + it$ on the critical line (here $t$ is real),
we have the key calculation
$$Z(s)^* = Z(1/2 + it)^* = Z(1 - (1/2 + it))^* = Z(1/2 - it)^* = Z((1/2 + it)^* )^* = Z(1/2 + it) = Z(s),$$
where we used $Z(s) = Z(1-s)$ in the second equation and $Z(s^*)^* = Z(s)$ in the second to last equation.
This tells us the function $Z(s)$ is real-valued on the critical line.  The Riemann zeta-function is not real-valued on the critical line, but this modified (completed) zeta-function $Z(s)$ is.  Moreover, because $Z(s)$ differs from $\zeta(s)$ by factors that are finite and nonzero inside the critical strip ($\pi^{-s/2}$ is a nowhere-vanishing entire function and $\Gamma(s/2)$ is meromorphic with no zeros and only has poles at $s = 0, -2, -4, \dots$), the zeros of $\zeta(s)$ and $Z(s)$ inside the critical strip are the same thing.  (In fact, nontrivial zeros of $\zeta(s)$ are exactly the same thing as all zeros of $Z(s)$, which is one reason $Z(s)$ is a nicer object that $\zeta(s)$: the Riemann hypothesis is a statement about all zeros of $Z(s)$!)  So what?  Well, we just showed in the key calculation above that the function $Z(1/2 + it)$ is real when $t$ is real, so by computing we can provably detect zeros of $Z(s)$ on the critical line Re($s$) = $\frac12$ by looking for sign changes of $Z(1/2 + it)$ as t runs through the real numbers.
So here is a two-step procedure for proving the RH numerically up to height $ T$ (i.e., in the box in the critical strip from the real axis up to height $T$):

Use complex analysis (the argument principle) to count how many zeros $Z(s)$ has in the critical strip up to height $T$ by integrating $Z'(s)/Z(s)$ around a box surrounding that region. (If the poles of $Z(s)$ at $s = 0$ and $s = 1 $ bother you, recall the argument principle can account for poles or you might prefer to use $s(1-s)Z(s)$ in place of $Z(s)$ to be working with an entire function which satisfies the same functional equation as $Z(s)$ and is also real-valued on the critical line.)
Count sign changes for $Z(1/2 + it)$ when $0 \le t \le T$.  There is a zero between any two sign changes, so $Z(s)$ has at least as many zeros on the critical line as the number of sign changes that were found.  (Finding a sign change is a computable thing: if a function value at a point is approximately positive or negative then it is provably so by checking the error in your computation well enough, whereas proving a function value at a point is exactly zero with a computer is basically impossible.)

If the counts in steps 1 and 2 match, then voila: all zeros of $Z(s)$ up to height $T$ in the critical strip are on the critical line, which confirms the Riemann hypothesis up to height $T$.
This method will not work if there are any multiple zeros on the critical line: the argument principle counts each zero with its multiplicity, so if for instance there is a double zero then the argument principle may tell us $Z(s)$ has 10 zeros (with multiplicity!) up to some height while we find only 9 sign changes because one zero is a double zero so it doesn't give us a sign change.  (Or if there were a triple zero we get 10 zeros with multiplicity from the argument principle but we find only 8 sign changes.)  A graph may suggest that the mismatch in the numbers in the two steps is coming from a multiple zero, but it doesn't rigorously prove anything.  Fortunately, this has never happened in practice with the Riemann zeta-function: the two counts always match.  In fact the conjecture is that all nontrivial zeros of $\zeta(s)$ are simple zeros.
What about more general L-functions $L(s)$? By multiplying $L(s)$ by suitable exponential and Gamma functions, you get a function $\Lambda(s)$ whose functional equation is
$$\Lambda(1-s^*)^* = w\Lambda(s),$$
where $w$ is a constant with absolute value 1. (For the Riemann zeta-function, $\Lambda(s) = Z(s)$ and $w = 1$. For Dirichlet L-functions, $w$ is usually not equal to 1.)  Let $u$ be one of the square roots of $w$, so $w = u^2$. Then using the above functional equation, the function
$$\frac1u \Lambda(s)$$
is real-valued on the critical line ($s = 1/2 + it$ for real $t$), so we can detect its zeros there by looking for sign changes.  The same method described above for detecting zeros of $\zeta(s)$ in the critical strip by using $Z(s)$ and its functional equation can be applied also to $L(s)$. This is basically the way all variants on the Riemann hypothesis are checked numerically (modulo important details of practical calculation that I don't get into), and the functional equation is an essential ingredient in justifying the method.
What is crucial here is not just the idea of sign changes, but also the expectation that the zeros are all simple (so we can find all the zeros by sign changes and the argument principle).  As with the Riemann zeta-function, it is expected that the nontrivial zeros of Dirichlet $L$-functions are all simple.  But there are examples of $L$-functions with a multiple zero on its critical line, thanks to ideas from the Birch and Swinnerton-Dyer conjecture.  This does not wreck this approach to verifying the Riemann hypothesis for such L-functions, because such multiple zeros are supposed to happen only at one (known) point which we think we understand.
Comment: This answer is still very helpful, though; thank you!
Comment: Oy, I see now that I looked only at the question in its short title form and didn't notice the question in its full form was asking for a *conceptual* reason for the importance of functional equations.  Boy, did I waste my time writing that non-conceptual answer...
Answer: There are many reasons that functional equations are important. Some background: To most varieties/schemes occurring in arithmetic geometry, you can associate a zeta function/L-function. There are two main ways of constructing these, either from l-adic cohomology, or from counting solutions in various finite fields. Usually the word L-function is used for functions associated to varieties over number fields, constructed from l-adic cohomology, and the word zeta function is used for functions associated to schemes over Z or some other ring of integers, or over a finite field. However, there is some confusion about the terminology, and there is also some overlap between the two, since there is a close relation between the L-function of a variety and the zeta function of an integral model for the variety.
Over finite fields, the functional equation is part of the famous Weil conjectures, proved by Deligne. One reason that the functional equation is cool is that it reflects Poincare duality in the etale cohomology of the variety, so it is in some sense a deep geometric statement. For background on the Weil conjectures, see for example Freitag and Kiehl: Etale cohomology and the Weil conjectures, and the survey of Mazur: Eigenvalues of Frobenius acting on algebraic varieties over finite fields, in some conference proceedings.
For the definition of L-functions and zeta functions and lots of other background, see Manin and Panchishkin: Introduction to modern number theory, chapter 6. There are at least two deep reasons for being interested in the functional equations for these functions. Firstly, the existence of a functional equation seems to always be directly related to the L-function coming from an automorphic representation, and the idea that "every L-function from algebraic geometry (aka motivic L-function) also comes from an automorphic representation" is in some sense the number-theoretic incarnation of the global Langlands program. See for example Bump et al: An introduction to the Langlands program. The most famous cases where this has been proved is (1) Tate's thesis, which treats Hecke L-functions, and where the corresponding automorphic representation is one-dimensional, i.e. a character on the ideles, and (2) the work by Wiles and others related to Fermat's last theorem, where they show that the L-function associated to an elliptic curve over Q also comes from a modular form, and hence satisfies the expected functional equation. See the book of Diamond and Shurman on modular forms.
The other deep reason for thinking about the functional equation is that some optimistic people dream of an "arithmetic cohomology theory", which would allow us to mimick the proof of the Weil conjectures, but for zeta functions over Z or L-functions over Q. Then the functional equation should be related to Poincare duality for this cohomology. All this is related to the Riemann hypothesis, noncommutative geometry, and the field with one element. See for example Deninger's Motivic L-functions and regularized determinants (pdf), his more recent survey Arithmetic Geometry and Analysis on Foliated Spaces, some slides of Paugamlink broken on the functional equation, and also the later chapters of Manin-Panchishkin. Some of the key names if you want to find more references: Deninger, Connes, Consani, Marcolli; most of them have lots of stuff on their webpages and on the arXiv.
Answer: As was mentioned in other answers, the functional equations are related to duality. In general, however, the "dual" object need not be the original object. It just so happens that the objects that give the Riemann zeta function and L-functions of modular forms are self-dual (up to a twist). For a general motive, M, for example, the functional equation (conjecturally) relates values of the L-function of M to values of the L-function of M*, the dual of M (see for example an article of Panchishkin's link text). For automorphic representations, its the contragredient (see section 14 of Borel's article on L-functions in Corvallis link text). So, conceptually, the functional equation is just an expression of this duality.
As Andreas Holmstrom alluded to above, the functional equation is (conjecturally) related to which L-functions are automorphic. The type of result is called a "Converse theorem". A famous "classical" one is Weil's converse theorem which basically says that if you have two Dirichlet series such that for infinitely many Dirichlet characters, the twisted Dirichlet series have analytic continuation, are bounded in vertical strips AND are related by a functional equation, then they are Dirichlet series coming from a modular form (see Bump's book, theorem 1.5.1). For GL(n) see Cogdell's "L-functions and Converse theorems for GL(n)" link text).
To add to the above paragraph, the existence of a functional equation is thought to be one of the characterizing properties of L-functions as expressed by the notion of the "Selberg class" (link text)
Answer: It seems worth mentioning another application of the functional equations.  To fix ideas, I will suppose that $E$ is an elliptic curve over ${\mathbb Q}$, and let $L(E,s)$ be the $L$-function of $E$.  There is then a functional equation relating $L(E,s)$ and $L(E,2-s)$;
one feature of this functional equation is that it has a sign, i.e. has the form
$L(E,s-2) = \pm (\text{ a positive constant })L(E,s),$ where $\pm$ is some fixed sign, depending on $E$, and easily computed (say using the modular form corresponding to $E$).
Thus one find that the order of vanishing of $L(E,s)$ at $s = 1$ is odd (even) precisely
if the sign is $-1$ ($+1$).
Since the order of vanishing is conjectured to coincide with the rank of $E({\mathbb Q})$
(the BSD conjecture), this is pretty important arithmetic information which is obtained pretty easily from the functional equation.  In particular, if the sign is $-1$, we always expect there to be a rational point of infinite order, and arranging things so that the sign is $-1$ (by twisting by a well-chosen character, say) is a common way of forcing the existence of rational points in various situations.  (There is a large body of research focused around this expected relationship between signs of functional equations and the
existence of rational points on elliptic curves; for example, it lies at the heart of the study of Heegner points by Gross and Zagier and Kolyvagin. Some important recent contributions are by Nekovar, Mazur and Rubin, and T. and V. Dokchitser.)
Answer: I am surprised no-one seems to have mentioned one key use for functional equations: they are a key input in converse theorems. If you have a power series in q that you're trying to show is a modular form of level 1, then one strategy is to show that the associated L-function has the right kind of functional equation (and a couple of other nice properties). The functional equation can translate into a relation between f(z) and f(-1/z), and the right kind of functional equation translates into the right kind of translation property for f, which is what you needed to show it was modular (the fact that it was a power series in q gives you the boundedness at infinity and f(z)=f(z+1)).
This idea was generalsed by Weil, who proved that sufficiently many functional equations for your L-function and its twists will imply that it's the L-function of a modular form. Hence elliptic curves with complex multiplication are modular! (because their L-functions are L-functions of grossencharacters). That's an algebraic statement whose proof I outlined above makes essential use of the functional equation of the L-function.
Comment: Actually the relation to converse theorems was mentioned in my answer. Though the specific case of CM elliptic curves is a nice illustration.
Answer: Hi Qiaochu,
I would say that functional equations of zeta-like function are popular
because it is one of the simplest non trivial example of functions having
a symmetry only when analytically continued. But in itself the impact
of such a functional equation is quite limited, even though some people
are convinced that this equation is a key for solving the Riemann Hypothesis,
which is misleading (this feeling is supported also by the Hamburger theorem
that states that any Dirichlet function having an analytic continuation like
zeta and obeying the same functional equation is proportional to zeta, but when
considering L-functions it becomes false and the Davenport-Heilbronn L-function
is an example of Dirichlet function with a L-function-like functional equation
but also with infinitely many zeroes in any vertical strip included in the critical
strip, therefore failing to obey a Reimann hypothesis).
However, as for me these functional equations hide a much deeper phenomenon.
The functional equation is an artefact of the action of the Fourier transform
on zeta functions. What's more, the same symmetry which can be proved in a
simple manner for local zeta functions extends to global ones, which is
a highly non-trivial result (proved for general Hecke zeta functions by John Tate
in his thesis).
In addition, you can see the Fourier transform as the image of a particular
linear operator by the Weil representation. And looking at the action of the
Weil representation in a more general context leads to some generalized
Poisson Formulas, and most probably there is still some unexplored stuff to
discover in this field (but that's a personal point of view...).
Best regards,
Eric
Answer: Apart from their conceptual significance, functional equations are useful when doing concrete estimates in analytic number theory. The usual textbook proof by the method of contour integrals for the bound \vartheta \leq 1/3 in the Dirichlet divisor problem relies on the functional equation of the Riemann zeta function.
Answer: Sometimes you get very concrete algebro-geometric facts from functional equations:
Example 1: The functional equation relating Weierstrass P (for a lattice L in C) and it's derivative is the equation representing the elliptic curve C/L in Weierstrass form.
Example 2: if F is a modular form on the Siegel upper half plane (the universal cover of the moduli of Abelian varieties Ag) with weight W, then the class of (F)_0 in Pic(Ag) is W times the Hodge class.
Answer: It was my understanding that, in some cases, the functional equation is the only known way to prove that the analytic continuation of one of these number theoretic functions is entire. Even in the case of zeta, I don't know another argument that zeta continues past Re(s)=0. (I can get into the critical strip by writing
zeta(s) = 1/(s-1) + \sum [ n^{-s} - (n^{-s+1} - (n+1)^{-s+1})/(s-1) ],
the sum now converges uniformly for Re(s)>epsilon>0.)
So maybe the question should be "do we care about the values of zeta (and other L-functions) to the left of the critical strip?"
Comment: "do we care about the values of zeta (and other L-functions) to the left of the critical strip?" Absolutely! The values of the zeta function at negative integers are rationals, and hence make sense as p-adic numbers. Furthermore, for n negative, the map sending n to zeta(n) is p-adically continuous (for n in a fixed congruence class mod p-1) and so we can define a p-adic zeta function! p-adic L-functions have been used to e.g. prove Leopoldt's conjecture for abelian extensions of the rationals. However pi isn't a p-adic number and so this trick wouldn't work if we only restricted to +ve vals.
Comment: You can easily get the analytic continuation to the whole complex plane, strip by strip, by repeatedly integrating by parts in the representation obtained from the Euler-Maclaurin formula.
Comment: Tate's thesis gives a nice explanation of the prime factors and the Gamma function in the functional equation for Dedekind zeta functions. We wouldn't have that nice explanation without a functional equation.
Comment: This technique is originally due to Euler in his paper on the functional equation of the zeta function (note no notion of complex analysis yet!).
Answer: Functional equations are useful to understand the "symmetries" of a given function, pretty much as periodicity. For example, they may be used in the continuation of functions to the complex plane. The functional equation for the Gamma function, Gamma(z+1) = zGamma(z), for instance, let us understand the continuation of this function to the left of the line Re(z)=0.

Why are functional equations important?


Is this patent expired?

Question: Is the
USD388287 S
patent expired? I am looking to design something similar to this.
Answer: Design patents filed before Dec 18, 2013 have a patent term of 14 years from the date of grant. See http://www.uspto.gov/web/offices/pac/mpep/s2701.html#sect2701.
The design patent you listed was granted on Dec 30, 1997 and so it expired Dec 30, 2011.
Answer: Patents are typically granted for 20 years, which for this patents still have a few years to go.
The patent is a design patent, and it looks to me that the what is patented is the exact liking -- so you may be Ok to design something similar as long as it is not exactly the same.

Is this patent expired?


Is it alright to use mockups to build a portfolio?

Question: I graduated with a B.S in Information Science. As I went through university, I realized that I was interested in HCI and usability. However, I did not have much material that would be relevant to building a portfolio to demonstrate UX work. I feel that my current one (www.ctrlaltm.com) is quite bare to be frank and I want to redesign it to make it more appealing to myself and to anyone who views it. I have participated in an open-source project but I did not have much experience in UX at the time so I felt that I was not able to contribute as well as I could have. So I'm thinking of making mockups to put on the redesign of my site.
Answer: Anything that could represent your knowledge in Information Architecture and User Experience is perfectly valid portfolio material. It doesn't really matter what's in the portfolio as long as the consumer of the content understand how great you are, and why it would be a loss NOT to hire you. So, yes, Wireframes, Mockups, Use cases, Requirement analysis, Personas and everything else which is the outcome of what we do is perfect for a portfolio.
Answer: Mockups, etc. are fine. In fact they're good.
When I look at a portfolio I'm looking to understand how a person works - now what the final results look like. The final results are - in any non-trivial project - down to many people. I need to understand how the person helped do that. Mocks, wireframes, pencil sketches, etc. are all good.
One thing though. Be very clear what the status of the work is.
Having mocks and sketches from student projects or personal work is completely fine. Making student or personal work look like client work will get you binned. Since we'll ask about the clients in any interview you get ;-)
Answer: One of the things I would like to add to Bennys answer is to "show your work". Often UX architects or UI Designers will show the nice pretty completed work. That's ok but the person hiring you wants to know how you got to the end work. Most of my portfolio is of hand sketched wire frames, thought concepts, information architecture etc. Just showing the pretty stuff doesnt cut it anymore.
Answer: A portfolio should contain mockups as well as initial sketches and discarded options.
It is there to give other people insight into what you are able to do.  A great way of handling this is to not just show finished products, but also intermediate steps which usually make up the bulk of the work.
Answer: I use anything and everything I can think of in my portfolio -- and in fact, I've been dinged by other folks for NOT having mockups and not "showing enough of my work", because it's that showing of your work that separates you from a mere web designer and makes it clear you actually know what you're taking about.
They want to see a lot of things, but because a UX Designer works as part of a team communicating with other folks and justifying your choices in a corporate setting, you should show them your process, which includes:

Mockups
Wireframes
Rationale for doing things one way vs. another
Findings and evaluations of previously / currently existing systems (e.g. fantasy redesigns of Amazon or another site)
Personas
Mental Models

This said, make it clear what you did, who you did it for, and when you were working for someone else / a class vs. your own fooling around. Having a project that your professor eventually pulled the plug on is fine. It doesn't have to be complete, it doesn't have to have made it into production, but you do need to be honest about it.


How are internal nodes in a innodb b-tree physically stored?

Question: How are non-leaf b-tree nodes physically represented in innodb?
Recall that a b-tree (more specifically a b+tree) has both leaf nodes and non-leaf nodes. In a b+tree all the leaf nodes sit below a tree of non-leaf or "internal" nodes and point to the pages that actually contain row data.
I know that non-leaf nodes are stored in the non-leaf node segment and use pages sort of like data pages. I have found ample documentation on how data pages are physically stored, but I haven't been able to find anything on what the non-leaf index pages look like.
Answer: In On learning InnoDB: A journey to the core, I introduced the innodb_diagrams project to document the InnoDB internals, which provides the diagrams used in this post. Later on in A quick introduction to innodb_ruby I walked through installation and a few quick demos of the innodb_space command-line tool.
The physical structure of InnoDB's INDEX pages was described in The physical structure of InnoDB index pages. We'll now look into how InnoDB logically structures its indexes, using some practical examples.
An aside on terminology: B+Tree, root, leaf, and level
InnoDB uses a B+Tree structure for its indexes. A B+Tree is particularly efficient when data doesn't fit in memory and must be read from the disk, as it ensures that a fixed maximum number of reads would be required to access any data requested, based only on the depth of the tree, which scales nicely.
An index tree starts at a "root" page, whose location is fixed (and permanently stored in the InnoDB's data dictionary) as a starting point for accessing the tree. The tree may be as small as the single root page, or as large as many millions of pages in a multi-level tree.
Pages are referred to as being "leaf" pages or "non-leaf" pages (also called "internal" or "node" pages in some contexts). Leaf pages contain actual row data. Non-leaf pages contain only pointers to other non-leaf pages, or to leaf pages. The tree is balanced, so all branches of the tree have the same depth.
InnoDB assigns each page in the tree a "level": leaf pages are assigned level 0, and the level increments going up the tree. The root page level is based on the depth of the tree. All pages that are neither leaf pages nor the root page can also be called "internal" pages, if a distinction is important.
Leaf and non-leaf pages
For both leaf and non-leaf pages, each record (including the infimum and supremum system records) contain a "next record" pointer, which stores an offset (within the page) to the next record. The linked list starts at infimum and links all records in ascending order by key, terminating at supremum. The records are not physically ordered within the page (they take whatever space is available at the time of insertion); their only order comes from their position in the linked list.
Leaf pages contain the non-key values as part of the "data" contained in each record:

Non-leaf pages have an identical structure, but instead of non-key fields, their "data" is the page number of the child page, and instead of an exact key, they represent the minimum key on the child page they point to:

Pages at the same level
Most indexes contain more than one page, so multiple pages are linked together in ascending and descending order:

Each page contains pointers (in the FIL header) for "previous page" and "next page", which for INDEX pages are used to form a doubly-linked list of pages at the same level (e.g. leaf pages, at level 0 form one list, level 1 pages form a separate list, etc.).
A detailed look at a single-page table
Let's take a look at most of what's B+Tree related in a single index page:

Create and populate the table
The test table in use in the illustration above can be created and populated with (make sure you're using innodb_file_per_table and using Barracuda file format):
 CREATE TABLE t_btree (
  i INT NOT NULL,
  s CHAR(10) NOT NULL,
  PRIMARY KEY(i)
) ENGINE=InnoDB;

INSERT INTO t_btree (i, s)
  VALUES (0, "A"), (1, "B"), (2, "C");

While this table is quite small and not realistic, it does demonstrate nicely how records and record traversal works.
Verify the basic structure of the space file
The table should match what we've examined before, with the three standard overhead pages (FSP_HDR, IBUF_BITMAP, and INODE) followed by a single INDEX page for the root of the index, and in this case two unused ALLOCATED pages.

$ innodb_space -f t_btree.ibd space-page-type-regions

start       end         count       type
0           0           1           FSP_HDR
1           1           1           IBUF_BITMAP
2           2           1           INODE
3           3           1           INDEX
4           5           2           FREE (ALLOCATED)

The space-index-pages-summary mode will give us a count of records in each page, and is showing the expected 3 records:

$ innodb_space -f t_btree.ibd space-index-pages-summary

page        index   level   data    free    records
3           18      0       96      16156   3
4           0       0       0       16384   0
5           0       0       0       16384   0

(Note that space-index-pages-summary also shows the empty ALLOCATED pages as empty pages with zero records, since that's often what you're interested in for plotting purposes.)
The space-indexes mode will show the stats about our PRIMARY KEY index, which is consuming a single page on its internal file segment:

$ innodb_space -f t_btree.ibd space-indexes

id          root        fseg        used        allocated   fill_factor
18          3           internal    1           1           100.00%
18          3           leaf        0           0           0.00%

Set up a record describer
In order for innodb_ruby to parse the contents of records, we need to provide a record describer, which is just a Ruby class providing a method that returns a description of an index:
class SimpleTBTreeDescriber < Innodb::RecordDescriber
type :clustered
key "i", :INT, :NOT_NULL
row "s", "CHAR(10)", :NOT_NULL
end
We need to note that this is the clustered key, provide the column descriptions for the key, and the column descriptions for the non-key ("row") fields. It's necessary to ask innodb_space to load this class with the following additional arguments:

-r -r ./simple_t_btree_describer.rb -d SimpleTBTreeDescriber

Look at the record contents
The root page (which is a leaf page) in this example can be dumped using the page-dump mode and providing the page number for the root page:

$ innodb_space -f t_btree.ibd -r ./simple_t_btree_describer.rb -d
SimpleTBTreeDescriber -p 3 page-dump

Aside from some parts of this output we've looked at before, it will now print a "records:" section with the following structure per record:
{:format=>:compact,
 :offset=>125,
 :header=>
  {:next=>157,
   :type=>:conventional,
   :heap_number=>2,
   :n_owned=>0,
   :min_rec=>false,
   :deleted=>false,
   :field_nulls=>nil,
   :field_lengths=>[0, 0, 0, 0],
   :field_externs=>[false, false, false, false]},
 :next=>157,
 :type=>:clustered,
 :key=>[{:name=>"i", :type=>"INT", :value=>0, :extern=>nil}],
 :transaction_id=>"0000000f4745",
 :roll_pointer=>
  {:is_insert=>true, :rseg_id=>8, :undo_log=>{:page=>312, :offset=>272}},
 :row=>[{:name=>"s", :type=>"CHAR(10)", :value=>"A", :extern=>nil}]}

This should align with the above detailed illustration perfectly, as I've copied most of the information from this example for accuracy. Note the following aspects:
The :format being :compact indicates that the record is the new "compact" format in Barracuda format tables (as opposed to "redundant" in Antelope tables).
The :key listed in the output is an array of key fields for the index, and :row is an array of non-key fields.
The :transaction_id and :roll_pointer fields are internal fields for MVCC included in each record, since this is a clustered key (the PRIMARY KEY).
The :next field within the :header hash is a relative offset (32) which must be added to the current record offset (125) to yield the actual offset of the next record (157). For convenience this calculated offset is included as :next in the record hash.
Recurse the index
A nice and simple output of recursing the entire index can be achieved with the index-recurse mode, but since this is still a single-page index, the output will be very short:

$ innodb_space -f t_btree.ibd -r ./simple_t_btree_describer.rb -d
SimpleTBTreeDescriber -p 3 index-recurse

ROOT NODE #3: 3 records, 96 bytes
RECORD: (i=0) -> (s=A)
RECORD: (i=1) -> (s=B)
RECORD: (i=2) -> (s=C)

Building a non-trivial index tree
A multi-level index tree (overly simplified) in InnoDB looks like:

As previously described, all pages at each level are doubly-linked to each other, and within each page, records are singly-linked in ascending order. Non-leaf pages contain "pointers" (containing the child page number) rather than non-key row data.
If we use the simpler table schema with 1 million rows created in A quick introduction to innodb_ruby, the tree structure looks a little more interesting:

$ innodb_space -f t.ibd -r ./simple_t_describer.rb -d SimpleTDescriber
  -p 3 index-recurse

ROOT NODE #3: 2 records, 26 bytes
NODE POINTER RECORD >= (i=252) -> #36
INTERNAL NODE #36: 1117 records, 14521 bytes
NODE POINTER RECORD >= (i=252) -> #4
LEAF NODE #4: 446 records, 9812 bytes
RECORD: (i=1) -> ()
RECORD: (i=2) -> ()
RECORD: (i=3) -> ()
RECORD: (i=4) -> ()

NODE POINTER RECORD >= (i=447) -> #1676
LEAF NODE #1676: 444 records, 9768 bytes
RECORD: (i=447) -> ()
RECORD: (i=448) -> ()
RECORD: (i=449) -> ()
RECORD: (i=450) -> ()

NODE POINTER RECORD >= (i=891) -> #771
LEAF NODE #771: 512 records, 11264 bytes
RECORD: (i=891) -> ()
RECORD: (i=892) -> ()
RECORD: (i=893) -> ()
RECORD: (i=894) -> ()

This is a three-level index tree, which can be seen by the ROOT, INTERNAL, LEAF lines above. We can see that some pages are completely full, with 468 records consuming almost 15 KiB of the 16 KiB page.
Looking at a non-leaf page (page 36, in the above output) using the page-dump mode, records look slightly different than the leaf pages shown previously:

$ innodb_space -f t.ibd -r ./simple_t_describer.rb -d SimpleTDescriber
  -p 36 page-dump

{:format=>:compact,
 :offset=>125,
 :header=>
  {:next=>11877,
   :type=>:node_pointer,
   :heap_number=>2,
   :n_owned=>0,
   :min_rec=>true,
   :deleted=>false,
   :field_nulls=>nil,
   :field_lengths=>[0],
   :field_externs=>[false]},
 :next=>11877,
 :type=>:clustered,
 :key=>[{:name=>"i", :type=>"INT UNSIGNED", :value=>252, :extern=>nil}],
 :child_page_number=>4}

The :key array is present, although it represents the minimum key rather than an exact key, and no :row is present, as a :child_page_number takes its place.
The root page is a bit special
Since the root page is allocated when the index is first created, and that page number is stored in the data dictionary, the root page can never relocated or removed. Once the root page fills up, it will need to be split, forming a small tree of a root page plus two leaf pages.
However, the root page itself can't actually be split, since it cannot be relocated. Instead, a new, empty page is allocated, the records in the root are moved there (the root is "raised" a level), and that new page is split into two. The root page then does not need to be split again until the level immediately below it has enough pages that the root becomes full of child page pointers (called "node pointers"), which in practice often means several hundred to more than a thousand.
B+Tree levels and increasing tree depth
As an example of the efficiency of B+Tree indexes, assume perfect record packing (every page full, which will never quite happen in practice, but is useful for discussion). A B+Tree index in InnoDB for the simple table in the examples above will be able to store 468 records per leaf page, or 1203 records per non-leaf page. The index tree can then be a maximum of the following sizes at the given tree heights:
Height  Non-leaf pages  Leaf pages  Rows    Size in bytes
1   0   1   468 16.0 KiB
2   1   1203    > 563 thousand  18.8 MiB
3   1204    1447209 > 677 million   22.1 GiB
4   1448413 1740992427  > 814 billion   25.9 TiB

As you can imagine, most tables with sensible PRIMARY KEY definitions are 2-3 levels, with some achieving 4 levels. Using an excessively large PRIMARY KEY can cause the B+Tree to be much less efficient, however, since primary key values must be stored in the non-leaf pages. This can drastically inflate the size of the records in non-leaf pages, meaning many fewer of those records fit in each non-leaf page, making the whole structure less efficient.


Real World Mythic Setting Material

Question: Can you recommend setting material for roleplaying games (books, websites, etc.) that presents places in the real world but with supernatural overtones based upon a locale's myths, fairytales, and legends?
Answer: Ars Magica has a bunch of sourcebooks with mythic real world location.
Answer: GURPS Places of Mystery might be good for this. Despite being a GURPS book, it's not very system-specific at all. It's more oriented towards human constructions that have mythic overtones than towards completely natural places, though. I can't find any reviews other than the one I wrote a long time ago, here, which is oriented towards Feng Shui.
Answer: King Arthur Pendragon for Arthurian Fantasy. LOADS of information, and really well done. Greg's a bit of a scholarly type, on top of it.
4th Ed has the most comprehensive rules; it's the only edition with magic available for PC's.
It also has a setting sourcebook for Beowulf era Scandinavia.
Comment: Not only is there tons of resource material; but, the game system really is a masterpiece. I prefer v5; but, your milage may vary.
Answer: Robert Grave's "Poetry" being his Greek Myths and White Goddess advance a full mythic system (a modern poetic reinterpretation of various Greek stories), with the interesting side effect that all Male Heros Must Die.
Graves hypothesises that neo-lithic European culture shared a single cultural basis in a myth about a Mother Goddess and a Sacred Sacrificial King.
Graves hypothesises that this became myth as various tribes rejected the concept of sacrificial Kings.  Graves claims that Kings were either half-year Kings, with the summer and winter Kings murdering each other; or that there was a singular King with his "inverse".  Eventually Kings resisted being killed, using boy substitutes, "one day" adult male substitutes who die on the day they're made king, extending "King for a year" to three or seven years.  Graves claims that Greek myths are reinterpretations of wall cartoons of the actual myth, and that a singular mother goddess is reread as a sequence of repressed various female goddesses.
Graves links this with the ages of man, and ideas about pre-agricultural and agricultural myths—these concepts are often used (via Tolkien) for the generation of fantasy races.  So Graves' myths are compatible to the standard fantasy world via this method, or via the "multiple ages of the world, multiple races" system.
Graves is batshit insane, but his mythology is more detailed that Lovecrafts, and just as creepy when it comes to burning children alive because the King doesn't want to stop being a King.
Answer: You might be interested in mythic fiction and urban fantasy fiction. I particularly enjoy Robert Holdstock, Charles de Lint, and Neil Gaiman.
Answer: Just a few off the top of my head:
Qin has a lot about China before the Empire. Exceptionally good.
Tibet has a lot about, not a shock, Tibet. Exceptionally good.
Hoodoo Blues has a lot about Voodoo.
Northern Crown is set in "a colonial New World where the legends of North America come alive".
Answer: D20 Modern's Urban Arcana setting might be what you're looking for, but I found it a little cumbersome as a system.
Answer: The Palladium system has a number of sourcebooks for various implementations of their "meta" roleplaying system, include such books as "Mystic China" (Ninjas and Superspies), and their Rifts system had a number of books for real-world settings that fit into the SF/Fantasy setting from which you could pick and choose elements.
Answer: Some of the Cthulhu books do this, although it of course translates it into the mythos.  The example that came to my mind is that in Cthulhu Invictus the Vestal Virgins remain virginal in order to keep out some evil beasty.
Comment: Cthulhu mythos is hardly *locale's myths, fairytales, and legends*.
Answer: I always found this an advantage of the old GURPS 3e setting books. Many of these are still available as pdf or can be acquired cheaply used.
Answer: I also recommend the Palladium system- Integral to my current game is their Dragons & Gods books, which introduce many mythical religions.

Real World Mythic Setting Material


Which unit should be used in web design to define space (margin, padding, etc.)?

Question: In the CSS of a website is it better, for human readability, define margin and padding units in px, em or pt?
Answer: Is white space difficult to read when specified as pixels?
An EM is a variable unit and is useful when you want to scale something based upon the (variable) size of something else. It is common when specifying type to set the line height relative to the type size and this is what EMs are for. 10pt with 1em line height is classic 10/10 or "solid" type, and 1.2em (or 120%) and 2em are probably the 2 most common line heights.
For CSS, ems are useful when you want to set type in a container and want the container to scale up or down if one later changes the type size. This means that one only needs to set the type size in one location and everything else cascades from there (it is an ease of editing feature). It is up to the designer to decide if scaling up the box is a good idea (or if it will break the design, should the box get too large). edit: there is also the problem of client-side letter scaling, so ems have a use with respect to accessibility.
Regarding pt and px, since pt is an inches measurement and inches do not really exist in the computer monitor context, I tend to use px.
In summation: ems are a useful variable unit for ease of design, and have no bearing on readability.
Answer: Margins and padding for text (p, h1, h2, etc.) should always be defined in ems if your text is defined in ems, so they stay proportional as the user scales text up and down. Even if you spec your text in px, ems are good units for padding and margins, because the user can still override the basic text size.
The rest of the layout's m+p should be in px if you have a fixed-width layout, ems if it's % or em based ("liquid" or "elastic"). These shouldn't normally affect readability, unless column widths are allowed to become so narrow that there's only one word per line, or something similar.
To maintain proportionality and best appearance, margins around an image that's floated in text is best defined in ems, otherwise images look terrifically cramped when text is scaled up (or lonely and unloved in the rare case that it's scaled down).
Answer: It doesn't really matter what unit of measure you choose as long as your consistant throughout.
em measures depend on the fixed size of a parent element and can change.  On the other hand you can always rely on px to control your layout.
Users should be able to modify to some degree but you don't have to turn over too much control to them.
For text I like to set defaults then increase or decrease depending on the use.
<code>body {  /* I actually eliminated the body tag from my layouts since switching to HTML5 */
font:12px/100%;
}
.content p {
font-size: 1.1em;
}
</code>
For fixed width layouts use px for structure and em for padding and margins around text.


I'm baking an acorn squash. How long should I bake it for?

Question: I'm baking an acorn squash. How long should it bake for and at what temperature? I also noticed on the spaghetti squash question that those are baked sliced face down. Should acorn squash bake face down too?
Answer: To roast acorn squash, set your oven to 350 and roast for about 30-35 minutes.  I normally roast cut side up, unless I am using some kind of sauce to go with it.  I find that the squash cooks to a more even color than when you place it directly against a metal pan which can develop diffrent temps across the surface.
You can also baste with some butter as long as it is face up, which is pretty good.
Answer: Lately I have been microwaving my squash and it has been coming out incredibly well.
Cut the squash in half, scoop out the seeds, put it face down on a bowl or plate with a little water, stab it with a fork a few times and do it for the same amount of time as you would a baked potato (I actually have an auto-sensing baked potato setting, which has worked perfectly).
The squash is done when a fork pierces smoothly from the outside, so you might need to add more minutes.
Or, when it is nearly done, flip it over, add a pat of butter, maybe some brown sugar, and then finish.
But we've just been eating it straight, adding butter at the table and it has been easy and exquisite.
Comment: Its good to see that there are others doing this too. I think it depends on the application though. I make this mac and cheese that uses acorn squash as a healthy additive and alternative to so much cream and cheese and microwaving works really well.
Answer: I cut the acorn squash In half, Scoop out the seeds and put them in a baking dish or deep casserole. Drop one and a half  to 2 tablespoons of brown sugar in the well of the squash, Along with 1 tablespoon of butter.  Lay a medium Porkchop on top of the squash covering the brown sugar and butter.  Cover the casserole, and bake at 350° for one hour.
Answer: I cut the squash up into single serving pieces - cut it in half, then take the seeds out and keeping halving all you have until the pieces are the size someone would likely eat. Brush with butter, sprinkle with nutmeg, then microwave for 3 or 4 minutes (poke to see if it's soft.) This has the advantage of not competing for limited oven space.
Comment: Kate, do you notice a flavor difference in the squash when microwaved instead of baked?
Comment: No I don't - as a result the only time I bake a squash in the oven is when I have almost nothing else in there. Since baked/roasted squash is more of a Thanksgiving thing for us, the oven is always jammed full.
Answer: One of the things to keep in mind when microwaving squash or any food for that matter is to make sure that you let it sit for about 5 minutes or so after your done cooking it before eating. Because of the way microwaves work to heat up the food they continue to heat for that period of time. Something consumed may not feel too hot, however if it continues to heat after you ingest it your run the risk of causing burns to your esophagus and or stomach.
I think that for oven cooking 350 degrees for about 30-40 minutes would work well. This does depend on your oven slightly. As for cooking them face down it depends on how you are preparing them. If you have them in pieces for serving ( like watermelon slices ) and they are seasoned with sugar and nutmeg or whatnot I would do them face up to get some caramelizing  on the sugar. Another way to do them is season them add a little liquid to the pan and cover them. That works as well. Hope it helps.
Comment: Microwaves heat by directly exciting polar molecules into vibrating, which is heat.  The heating stops instantly when the microwaves are stopped.   There may be carry-over heat, as heat from one part of the food conducts into another part of the food, but the increase of heat energy in the food stops immediately with the cessation of microwaves.
Answer: I cut the acorn squash In half, Scoop out the seeds and put the squash on a baking try cut side up. Drop one and a half to 2 tablespoons of brown sugar in the well of the squash, Along with 1 tablespoon of butter, some times I add dried cranberries and apples with a sprinkle of walnuts inside for a change. Bake for about an hour at 350. Should be able to stick a fork into it easily when done. We are having it this way tonight for supper.
 Oh it also helps when baking it on a tray to cut a little off the bottom so they don't roll around on the tray while putting them into the oven.