How do I train myself to sing pure vowels?

Question: When singing in languages like Italian or Latin (which don't run to diphthongs the way English does), I sometimes find it hard to sing pure vowels, particularly when holding a note for a while.  Should I attack this as an "ear" problem (and I need to listen to more music in these languages), or is there some vocal technique I can apply that will help?
Comment: Interesting. It seems so strange that pronouncing only one vowel could be harder than pronouncing two (diphthong), to a non-native english speaker.
Comment: Trust me. Being a native speaker of English makes it extremely hard to learn to voice the five pure vowels (as in Latin, Spanish and Italian) consistently. English has about 16 vowel sounds, and we English speakers find it very hard to banish our dipthongs and extraneous vowels from our myriad regional English accents when we sing certain other languages.
Comment: http://www.youtube.com/watch?v=FQt-h753jHI&feature=related Is this you?(;
Comment: @mrbuxley: nope. :-)  @Gauthier: I suspect that we tend to imitate the sounds we hear and speak every day, which are probably different for the two of us.
Comment: @WheatWilliams yeah, hence the question -- since I can't change my native language, what else can I do to improve this?  Yet another area where English adds complexity. :-)
Answer: It may be helpful to take out all of the consonants and sing through a song in Latin or Italian with only the vowels. For instance Dona nobis pacem would become oa oi ae. That will allow you to focus more specifically on the vowel sounds without the consonants getting in the way or encouraging you to run to dipthongs.
Comment: My choir director loves to tell us about his voice teacher who made him do this perfectly before dropping in consonants.  Luckily, he never made us do that!
Answer: Interesting question! The only tip that springs to mind is to think of constantly renewing the vowel, so rather than thinking "I'm singing a long oo, here I go, ooooooooooooooooo" it can be helpful to think of lots of tiny, pure oo's strung together. ("oo-oo-oo-oo-oo-oo-oo-oo")
You may also want to be aware of what your lips and tongue are doing during a long note, as if they change shape they will necessarily affect the vowel sound.
Comment: Thanks.  Paying more attention to what my lips and tongue are doing over the course of a vowel sound was quite informative. :-)
Answer: The easiest way to hold a pure vowel sound is to maintain mouth position. Take, for instance, the 'O' sound of wrote. It is easy to close the jaw slightly to form the 't' and create a diphthong of the 'O' as in the phonetic o-oot. Instead keep the jaw relaxed on the O sound and instead of closing the mouth, reach up with the tongue to softly lick the t sound from the top of the mouth. Most deviations from pure vowel sounds occur when encountering the following consonant sound. Emphasis on consonants can be avoided - even when we should have a diphthong. Try the word wild --- most people triphthong this to ooWah-eeeee-ald because of jaw position. Instead, sing "hhhhWahhhhhhhhh- eeld" with very little movement of the jaw and just a small eeld with the tongue against the roof of the mouth. Start breathing before engaging the vocal chords to prevent a loud start that falls back in volume. We need not have the ooWah begin words that begin with W.
Answer: IMO, this is practice, practice, practice. Go over the song phonetically, and speak each word on a single tone or in a speaking voice, properly pronouncing each vowel. Always remember that note transitions are where your dipthongs and consonants should be placed, and it should happen as fast as still sounds natural.
Now, that said, you imply that "pure" vowels equal "Latin" vowels. This is not necessarily the case; you can sing unelisioned vowels, and be consistent across an entire choir as to the color of each vowel, without the vowels having to be "ah", "eh", "ee", "aw", "ooh". The Latin pronunciation is simply an easy, natural, dialect-neutral set of vowels that works for classical music in most languages.
Answer: There are many techniques, and the answers so far are great, but I'll add another suggestion that works great for some folks:
Modify the words mentally. Instead of singing a-bout (which can lead to funny dipthongs), think of it phonetically as uh-bah-oot. The vowel you're holding for a long time is close to "ah", and the "oo" from the u is more part of the final t sound than part of the previous vowel.
Eventually, you learn to make these kinds of modifications automatically.
Answer: It is all about becoming conscious, with each syllable you sing, of the different positions and shapes of all the parts of your vocal apparatus: lips, tongue, soft pallate, and the placement of the tone in your head. And whether or not these positions are moving or changing during the production of the vowel. (if they move or change while you make one vowel sound, this is what creates a dipthong.)
The best way to learn this is to take lessons from a voice teacher or sing with a choir director who gives you feedback on your vowel production and shows you what you are doing wrong.
The good news is that, with continued practice of good habits, this meticulous and constant self-examination and self-awareness of the changing positions of your lips and tongue, etc., eventually become second-nature and you no longer have to think about them constantly as you sing.


How to keep track of abilities for D&D 4e?

Question: What are some effective ways to keep track of my character's various abilities?  I would prefer cheap or free tools.
Answer: I print out my power cards as shown in character builder (9 per page), and then use a marker (candy, pennies, beads) and just place it on the sheet when it's used.  For special powers (like dailies that can be used 2x per day or something) I just put multiple markers on them.  Keeps things very simple.  At the end of the day, I just eat... er... remove all the markers.
Answer: Transparent file folders.  Slide your character sheet in, grab yourself a dry-erase marker and just mark off abilities as you use them. Wipe clean after a rest.  I like this method because it persists through the week when you end a gaming night mid-encounter.
Answer: Cards are very useful. You might also check out weem's combat sheet, which gives you room to list all your abilities organized by what they do -- i.e., you have a place to list defensive abilities, a place to list reactive abilities, and so on. This is really handy when you're trying to remember that, oh yeah, I can do this really cool thing when someone hits me.
Answer: I have a character sheet modeled off the one at the back of the PHB. It includes hit points, equipment, feats I've taken, languages and the master list of my powers.
As for using the powers in combat, I use handmade 3x5 cards. I write all the details about it (pretty much copy text from the book), and include my attack bonus and damage dice with any bonuses from feats or equipment added. I also include entries for circumstantial situations ( like "Combat Advantage: +1d8 sneak attack damage" ). I write the name color coded for Daily(Black) vs Encounter(Red) vs At-Will(Green) vs Free(Orange). For things that can be used 2x a day/encounter I make two cards. I make a card for other standard things I want to remember I can do as well: Second Wind and Use Action Point (and any class features).
During combat I'm always shuffling through my cards as the situation changes, keeping the ones I'm planning to use at the top. When I use the power or action, it gets flipped over into the used pile. If its a sustained power, it stay face up in front of me until it ends. After the party has a short rest, I can grab all the encounter/free actions (red and orange) from the used pile and I'm ready to go again... well, once I make sure my healing has been taken care of!
Answer: I find cards can be useful if I want a reference for the exact wording of a power, but I find them too cumbersome to use in actual combat, especially as you get to higher levels and start getting more and more powers and items and especially if you don't have a big space to play in.
Instead, I use a master list on a single sheet of paper that lists all the character powers with a bare minimum summary of what each power does written beside it.  I find it makes it easier to decide what to do by scanning down a single page rather than shuffling through a stack of cards, but that's just my preference :)
I also find it handy to put my magic item powers (especially the encounter ones) in the list with all my other powers as I forget them otherwise.
Anyway, it ends up looking something like this...

<code>[blah blah initiative, defenses, saving throws, etc. etc.]

+3 Feyslaughter Longsword
MBA: +24 vs AC, 1d8+15. Crit: 23 + 3d6 (or 3d10 vs. Fey)
OA: +29 vs AC, 1d8+15.
Burst: +24 vs. Def, 1d8+11. Crit: 19 + 3d6 (3d10 vs. Fey)

At-Will
-------
Tide of Iron.  Str vs AC. Hit: 1[W]+Str mod dmg, push target 1 sq, shift 1 into vacated space
Footwork Lure. Str vs AC. Hit: 1[W]+Str mod dmg, shift 1, slide target into space left.
Knockdown Assault. Str vs Fort. Hit: Str mod dmg, knock prone

Encounter
---------
Come and Get It. Close Burst 3, pull 2. Secondary atk: Close Burst 1, Str vs. AC. 1[W]+Str mod dmg. (1d8+11)
...
Strikebacks (item).  Imm. Reaction when hit with melee attack, make MBA vs. that enemy

Daily
---------
Rain of Blows (stance). Deal 1[W] (1d8+5) dmg vs. enemies that start turn adjacent
Unyielding Avalanche (stance). Gain regen Con mod (1), +1 power bonus to AC/saves, Deal 1[W] (1d8+5) damage and slowed until EoNT vs. enemies that start turn adj.

Grimlock Helm (Item). Minor Action, Gain Blindsight 5 & become blind until EoE
...

Utility
-------
Pass Forward (At-Will). Move Action, Move speed & don't provoke from 1 enemy if you end adjacent to that enemy.
...
</code>
Answer: Use a spreadsheet. I personally use a custom character sheet I created in OpenOffice.org Calc.  My abilities are condensed into brief descriptions and I can just check them off as I use them.  I use conditional formatting on the checkbox cell to grey out the line. I also have short rest and extended rest macros to go through and clear them out. Being a psion, the augments are in the cell comments.
Answer: Note: By "various abilties" I assume you mean abilities the English word as opposed to the DnD concept of abilities.
I knew a group who printed up playing cards representing their powers; when they used the power they'd turn the card upside down or sideways. (on the other side would be the same description of the power, but kind of grayed out)
Answer: If you have an iPhone or laptop, you could use iplay4e.com - it imports characters built with character builder, and then lets you track pretty much everything you could on a character sheet. If you have the infrastructure, there's no additional cost.
Answer: I use a version of Weem's sheet, but one created by myself. It's functionally a checklist of "Stuff that happens on my turn" and "out of turn actions" with all of the decision trees roughed out.
Because the fuctional creation of a cheet-sheat pre-articulates most strategies, I don't have to spend time in combat figuring out what my options actually are, just how to apply them.


Review tests first

Question: I am going to adopt TDD in our team and one of the ideas I have is to review tests first. So one would write interfaces, mocks, and tests first, submit them for a code review and once interfaces and tests (think specification) are approved an actual implementation can be written (theoretically, can be done by another developer). I wonder how viable this idea is?
Answer: IMHO it sounds a lot like a waterfall development model, where the specifications of the 1980's have been replaced with Tests. i.e. "Must complete step X before you can start step Y". "Dev writes design and any other dev can implement" ... I am almost certain that in the real world it will fail to deliver good product and productivity. Too much time will be wasted making "perfect" tests, leaving not enough time to write robust, quality code. As soon as you set the expectation that developers are interchangeable like Construction site laborers (no disrespect), your management team will believe it, and tasks will be scheduled accordingly.
Waterfall is out of favor and is considered last centuries methodology, however there is nothing wrong with it if that is what you are trying to achieve, and in a few situations TDD combined with Waterfall might be a preferable approach (I am thinking outsourcing to sweat shops where the job goes to the lowest bidder....).
Developing by starting with tests is a great approach, however, requiring the completion of tests before code starts is likely to reproduce the entire class of problems that Waterfall and "design before code" created, and these are easily avoided.
I would suggest you look towards a more flexible approach - such as "Tests should be first reviewed at 30% of allocated task time, and final review at the 80%." This allows the code and tests to evolve together, but clearly sets the expectations that the tests are at least as important than the code.
Final acceptance then requires both code and tests to be complete and reviewed.
Comment: @JustinC: That mindset comes from purists, who conveniently completely ignores that fact the most developers don't know enough at the start, and improve knowledge as they progress. If you insist all tests are completed before code starts, you are saying "Write tests to test things that you do not know". To me complete means finished, no more changes, that is it, done.... If "Finished" means "just one more tweak here and a tidy up there, and I'll fix up the todo when i know what needs doing" then the model can be made to work - sort of.
Comment: If it is not red green refactor, it is hard to call it TDD.  That being said, adding a review phase every few hours isn't a bad approach, especially if not paired.
Comment: Maybe that came out wrong, but I agree with the compromise to the process.  Especially if as it sounds, and they are coming from a more traditional approach that is big design upfront.
Answer: I would strongly suggest you DO NOT take this approach.
Writing unit tests on top of production code is a lot of overhead for many people.  No matter how you slice it, with unit tests, you end up writing double if not triple the amount of code you would have had otherwise.
Unit tests are great and they have a huge number of benefits, but a lot of those benefits are long term and they don't start paying back until later (when people need to reference on how to use API, when next co-op breaks existing code... etc).
However, unit tests have huge short term benefit in that, when people write code (with or without TDD), people need to exercise that code at least once before checking it in.  In non-TDD environment, they would try to run the code within the context of a larger application, or they might write some throw-away utilities just to invoke the functions they just wrote.  Unit tests are awesome because while you are writing them, you get to see your code run and fix it on the spot.
When a person gets into the flow (what is referred to as red/green/refactor cycle), TDD overhead, IMO based on very limited experience (but a lot of research) becomes much smaller than 2x because even though you are producing more code, that code is instantly helping you write your production software that much faster by providing feedback on an order of magnitude sooner than with manual testing.
So ideally to get the benefit with TDD with least amount of overhead, you want to think about next function you want to add to production, write a test, write the function, make sure it passes, cleanup, go on to the next function.... ship it.
What you are proposing will directly kill that short-term benefit I just described. Instead of writing one test and then functionality, you'll end up writing many tests and feedback is much slower since between reviews/approvals it could take hours if not days.  And instead of writing the test for exactly the next piece of production code you will work on, you'll end up writing preemptive tests for things you "might" introduce in production.
Answer: The TDD cycle is all about quick feedback - post-commit asynchronous reviews will break your pace.
If you want unit tests to be approved by another developer, pair programming is IMO a much better idea.
Answer: Personally, I would be afraid to write tests first. The question is, what if the tests passed?
Let's say I spent a lot of effort up front to write good test codes.
After I completed the main code, it is very hard to resist to immediately try these tests.
Now what if the tests passed? Does it mean my code is correct to my best knowledge? Probably not, but I'll probably take the passing of the tests as the excuse to conclude the task.
If I don't have the tests up front, I'll spend a lot of efforts to review the code to "prove" it's correct.
When a problem is complicated enough, one's brain power is strained, and waning through time; I would rather budget the earlier time to reason about the main problems.
Comment: I understand your concern, and it is therefor the test should never pass the first time. A TDD cycle goes like this: 1) Write the minimal, sane, test needed for the tests to fail. 2) Write only the production code you need to pass that test. 3) Refactor 4) goto 1. Clearly, you should try your test before even starting writing production code, to verify that your test will catch that bug/missing feature. Then you should implement enough of the feature to make the test pass, refactor, and then write a new minimal test.
Comment: You shouldn't be afraid to write the tests first, as long as the scope of what it's doing is clear.  It's also the case that you'd want to hit the code from more than just the happy path, too.
Answer: This idea doesn't sound viable at all.  It seems that more focus is spent on verifying the tests as opposed to the actual code - which doesn't make sense.  Tests can pass, but at the same time, the code it's testing may run for 12 hours in production, which makes the code review on the tests worthless.
It's also the case that the programmer just doesn't know everything about the requirements of the code.  It's tough to write tests for something that you're not entirely sure how it should behave, so "happy path" tests are a bit of smoke and mirrors, too.
Adhere more to fail/pass/refactor instead - let your developers write smaller bites of the code, code review the quality of the production-caliber code, then let them continue with the smaller bites of code.  Do feel encouraged to review the tests to see if they're actually testing anything, but don't let it interrupt the TDD flow.

Review tests first


How to Maintain the Balance of Power on Risk?

Question: How can I stay strong enough to avoid being eliminated while at the same time avoid being too strong and making myself a target?
Answer: Hold a medium-to-small sized continent (like South America or Africa) and avoid aggression while you build up.  Attempting to take Asia, Europe, or North America will raise a lot of red flags, and Australia's defensibility makes it suspicious too.
RISK is defined in the later game by the ridiculous armies you get when trading in cards, so your main task is to be in the position to trade in for a lot, then bust out of your home and take another continent.
Answer: Don't underestimate the importance of visual cues or psychological warfare;  in games like Risk and Diplomacy, these are the very underpinnings of your negotiation platform.  For example, if you are playing one of the game sets that features little men and cannons, then arrange them on your spaces facing away from one enemy, and massed on the 'border' with another enemy.  It has no in-game effect whatsoever, but sends a very definite visual message, which is interpreted on a subconscious level.  When it comes to your turn to attack, mull over your options, or pretend to be doing some dice-math in your head, while staring down intently at a given enemy.  Even if you don't actually attack, you've conveyed to the rest of the table that you WOULD attack that enemy, if only you COULD, which leads to the "He must be doing too well" syndrome from everyone else.
Answer: There are two sides to Risk, one of them being the actual armies, countries and cards you hold. As lilserf correctly points out, you usually aren't allowed to hold any major continents. I don't quite agree with Australia. It's easy to defend, but it's usually not near the tension and there's the danger that you get isolated, so I don't find it superior over South America or Africa.
Now the other side of risk that you shouldn't underestimate is your mouth. Making deals, persuading etc, can have a huge impact on how the other players react. The most dangerous thing is often a player getting a lot of armies without really having a plan of what to do. Here the weapon is not what's on the board, but what's in your mouth.
Comment: Maybe it's just the people I play with - Australia seems to be way overvalued for its defensibility :)
Comment: @lilserf: Each group tend to form a consensus on what's okay and not, which can differ a lot. Another important point is the number of players.
Answer: I enjoyed reading the answers to this quintessential question that defines the game of Risk. I find Risk to be a game of balance of power & playing your position is important.  What you do when you are the dominating player is different than when you are the mid-player or the week player.  When playing on line in real time you must also consider who are the reliable players in relation to connectivity as to who will drop next.  In addition to the other answers posted here I would add the isolating method.  If your opponent controls Australia or South America early on, you choose as position on the map far from theses continents & eliminate all soldiers of that player that are near yours thus forcing the incremental strength of that player to attack your opponents as opposed to you.


Etymology of "topological sorting"

Question: This may be a dumb question, but what's "topological" about topological sorting in graph theory?
I thought topology was related to geometry and deformations.
Comment: Introducing a complete order on a set endows it with [order topology](http://en.wikipedia.org/wiki/Order_topology)...
Comment: @Sasha Is the order topology not only defined for total orders? And according to [this math SE post](http://math.stackexchange.com/questions/422893/partial-order-induced-topology) there is no canonical induced topolgy for partial orders?
Answer: Graph theory was originally (and still sometimes is, depending on who you ask) considered a branch of topology.
This may sound strange to people with a modern education, where "topology" means more or less "the part of mathematics that deals abstractly with continuity and limits, without using real numbers" -- or at least without giving the real numbers any central position in the theory. However, earlier on, "topology" appears to have been a catch-all term for "the part of mathematics that isn't about numbers or geometric magnitudes". (This was before algebraists stopped pretending that algebra is necessarily about numbers). Only later did a distinction between what we now call topology and discrete mathematics become common.
In this old usage, "topological sorting" simply means "the kind of sorting you can define without reference to comparison of numbers".
Answer: The use of "topological" in "topological sorting" and "topological order" appears to stem from the use of the word "topology" to describe the structure of networks in computer science literature. Indeed, if you look at the early papers on topological sorting (Lassser, CACM, 1961; Kahn, CACM, 1962) you will see they are motivated by topological sorting of PERT charts (project management). A quick google books search shows even earlier analogous uses of "topology" in computer science, e.g. to describe the structure of electrical circuit networks.
Most likely the terminology became widely known after it was employed in Knuth's influential book The art of Computer Programming, vol. 1, 1967. Of course the phrase "network topology" is still in wide use today.
More general mathematical results go back to at least to 1930, see the Szpilrajn extension theorem.
Answer: I can only guess, but knowing that topos means place in Greek, I imagine it is because we are sorting elements based on their place in a partial order, rather than on magnitude. If I am right, there is no connection at all with topology in the mathematical sense.

Etymology of "topological sorting"


Parameters in arithmetic induction axiom schemas

Question: The induction schema of Peano Arithmetic is standardly given as the universal closure of $\phi(0)\land \forall x (\phi(x)\rightarrow \phi(x+1)) \rightarrow \forall x\phi(x)$.  However, since the language of arithmetic has a name for every standard number, it is not obvious (to a beginner like me) why parameters are necessary in the induction schema; why not restrict to the case where $x$ is the only free variable in $\phi$?

Does having parameters in the induction schema really make the system stronger, and, if so, how is that proven?
Are there natural theorems that can only or most easily be proven using the stronger system?
Is the weaker system of any interest?
Answer: $\def\fii{\varphi}$While the other answers resolve the question, a simple way of deriving induction for a formula $\fii(x,\vec p)$ with parameters $\vec p$ is to use parameter-free induction on the formula
$$\psi(x)=\forall\vec p\,[\fii(0,\vec p)\land\forall y\,(\fii(y,\vec p)\to\fii(y+1,\vec p))\to\fii(x,\vec p)].$$
In fact, this derives the induction schema with parameters from the (parameter-free) induction rule, since $\psi(0)$ and $\psi(x)\to\psi(x+1)$ are provable in Q without any assumptions on $\fii$.
Comment: That's pretty tricky!
Comment: Thanks for the clear answer. I always wonder why logicians don't answer in a more formal way. This is clear positive exception.
Comment: You're welcome.
Answer: The two theories are equivalent. To see this, let's assume that we have the parameter-free induction, and suppose that $\phi(x,y)$ is a formula with two free variables. Suppose we have a model $M$, satisfying the parameter-free induction, and there is a $b\in M$ such that $\phi(x,b)$ obeys the hypothesis of the induction scheme with parameter $b$, but not the conclusion. I claim that there is a least such $b$ in $M$. The reason is that the collection of such $b$ violating the induction scheme for $\phi(x,b)$ with parameter $b$ is a parameter-free definable subset of $M$, since this property is expressible, but the parameter-free induction scheme proves that every nonempty definable set $B$ has a least member, because otherwise the assertion $\psi(x)$ expressing that $x$ is below all members of $B$ would be inductive and hence universal, contrary to $B$ being nonempty. So there is a least such $b$.
In particular, the least such $b$ is actually definable, and so we do not actually need it as a parameter after all, and so the induction scheme for $\phi(x,b)$ follows by the parameter-free induction scheme. So there can be no such $b$ for which the parameter-induction scheme fails.
Thus, the theory of parameter-free induction implies the full theory you mention.
Answer: While parameter-free induction and parameterized induction are equivalent, there is an important subtlety which often justifies the addition of parameters.
Suppose that $\phi(x,p)$ is such that $$\exists p(\phi(0,p) \land \forall x(\phi(x,p) \to \phi(x+1,p)) \land \lnot \forall x \phi(x,p)).$$ Joel's trick is that $$p_0 = \min\lbrace p : \phi(0,p) \land \forall x(\phi(x,p) \to \phi(x+1,p)) \land \lnot\forall x\phi(x,p)\rbrace$$ is definable without parameters. However, the existence of $p_0$ is another instance of induction (in the guise of the least element principle).
The complexity of a formula in arithmetic is often measured by counting the number of quantifier alternations when put into prenex form (often ignoring bounded quantifiers). With this measure, the complexity of the induction that justifies the existence of $p_0$ is strictly greater than that of the original formula $\phi(x,p)$. So there is a price to pay for removing parameters.
Therefore, when considering atithmetical theories with limited forms of induction ($EFA$, $PRA$, $IOpen$, $I\Delta_n$, $I\Sigma_n$) it is necessary to include parameters. It is also natural to think of $PA$ as the union of these restricted theories, which leads to the inclusion of parameters when formulating the induction scheme.
Answer: You can prove that the two theories are, in fact, equivalent. By induction (NB: 'meta-induction') on the number of parameters, we can reduce the claim to the case where you have a theory $T$ with the usual induction schema and a theory $T'$ that is an extension of $T$ by a one-parameter induction schema.
So assume $T$ and $T'$ are not equivalent. This implies that there is a model $\mathcal{M} \vDash T'$ and a two-place open sentence $\phi(x,y)$ such that
$$\mathcal{M} \vDash \phi(0,\beta) \wedge (\forall x (\phi(x,\beta) \rightarrow \phi(x+1,\beta))) $$
but  also,
$$\mathcal{M} \nvDash \forall x \phi(x,\beta)$$
for some $\beta \in \mathcal{M}$. But note now that the above is equivalent to
$$ \mathcal{M} \vDash \exists y (\phi(0,y) \wedge (\forall z (\phi(z,y) \rightarrow \phi(z+1,y))) \wedge \neg \forall z \phi(z,y) $$
and if you call this last sentence $S$ then you get that $S \wedge \phi ' (x)$ violates the usual induction-schema, where $\phi ' (x)$ is the one-place open sentence we get by by closing $y$ under the existential quantifier in $S$. That is to say we have $S \wedge \phi ' (0)$ and $ \forall x (S \wedge \phi ' (x) \rightarrow S \wedge \phi ' (x+1))$ but not $\forall x S \wedge \phi ' (x)$. But that is a contradiction since $\mathcal{M}$ is a model of $T$. Hence the two theories are equivalent.
Comment: Are some of your $b$'s supposed to be $\beta$'s?
Comment: corrected - - -


Tool for Virtual machine Test Orchestration

Question: What would be a good Orchestration tool for Triggering tests in Virtual Machine? Basically I want to trigger multiple parallel VM's to run automated tests. The tool should also have queuing mechanism.
Comment: Do you believe this problem is specific to virtual machines, or is it equally applicable to physical machines?  Can you describe what you mean by "triggering tests in virtual machine"?  For example, should triggering include starting and provisioning the virtual machine?
Answer: Microsoft Visual Studio's Lab Manager can do this, I keep meaning to play around with it myself because I am in need of the same thing.  Since I have not had a chance to play around with it yet, I can't tell you how well it works, but here is a link to the main page with a bunch of other training and documentation links on it: http://msdn.microsoft.com/en-us/vstudio/ee712698
This is likely a pretty expensive option, however my company already has licenses for Visual Studio Ultimate and TFS, so for us it should be pretty easy and inexpensive.
If I get a chance to play with it, I will update this thread with additional pertinent information.
Comment: yep - Lab Manager is meant to do this. +1
Answer: Your continuous integration server should be able to handle this, if you use one. For example, Jenkins and TeamCity are capable of launching generic jobs, and both have "VM" plugins to abstract away the fact that the system on which you are starting your job is even a VM. We use TeamCity + VMWare Fusion in our work and it is effective.


Motherboard / RAM compatibility

Question: With standard PCs, does any modern RAM generally work with any modern motherboard, so long as they can physically interconnect?
If not, is there a table I can consult?
Answer: Not quite, and don't waste your time looking at manuals and such. Your head will explode.
Crucial has a Windows app you can just download and run on your PC so you buy the right kind of memory. Purchasing is then a one click operation. In my experience they are cheap and delivery is fast.
You can also run an app called CPU-Z which will tell you what kind of memory is in your motherboard, how many free slots you have etc.
Comment: That Crucial app sounds cool -- except I don't yet have the motherboard I'll be plugging the RAM into, and even if I did, I wouldn't be able to run the app because... I don't have any RAM. :)
Comment: In that case, grab the specs for the motherboard ram and then punch them into Crucial or Newegg's webiste and you should find plenty of results.
Answer: Well generally things won't explode, you'll be safe there. However you'll need to consult the motherboard manual to find out the clock speeds it supports, only memory with a matching clock speed (or higher, it will just run at the speed of the motherboard) will work.
Answer: Despite the warnings above, most of the time, any memory of the proper type and speed will work.  The people above are correct -- if you don't want to throw money away, consult the OEM, manufacturer, or use an application such as the one provided by Crucial.
Most of the RAM problems I've had were problems of mixing RAM purchased at different times. One machine I had would work with either 512 Meg stick of RAM that I had, but it just would not work with both at the same time.  I never figured this out.
In my experience, you're much more likely to have a problem mixing RAM sticks purchased at different times than you are if you totally replace all of the RAM in the computer with matched memory sticks.  So far, I've never bought memory and had it fail to work -- unless I was mixing memory sticks of different types.
I know that it is absolutely possible to buy memory and have it fail to work.  This appears to be much more true (in what I have seen) for systems that take special memory, such as parity memory.  If you want to ensure that you don't throw money away, consult the right experts.  Otherwise you are taking a (usually small) chance that the memory will not work.
Note that at least in what I have seen, trying incompatible memory in a motherboard has never damaged anything.  It just failed to POST or failed ot boot or failed to be reliable.  In every case I have personally experienced, incompatible memory has not caused any damage to other hardware.
Answer: No, just because the RAM fits in the slot doesn't mean it will work.
The best place to start is usually to check out the support web site, Manual or Specs sheet for the motherboard.
If you have a system from a one of the major manufactures (Dell, HP, etc) you can usually look up exactly what by using the search tools on a RAM manufactures site.

http://www.crucial.com/
http://www.kingston.com/
Answer: Once I've installed 2 memory modules in the mainboard and all worked nice. After some hours using Windows, the computer shows the BSOD...
The reason was the 2nd memory module was problematic (each module have 2gb - just when Windows used more than 2Gb the computer crashed. I noticed that then I ever use a memory test program like MemTest.

Motherboard / RAM compatibility


SQL Server restore from transaction log

Question: In SQL Server 2005, if you have a database with no backup - but it is running in full recovery mode - is it possible to "roll back" some deletes?
If yes - how?
Answer: No. The recover process always starts from a full database backup and then it applies the log backups.
If your database has no backups then it is not in full recovery mode. Untill you actually take a backup it will always run in simple, no matter the intented recovery mode (aka 'pseudo simple', see New script: is that database REALLY in the FULL recovery mode?)
If your database really is in FULL recovery mode, then a backup was tacken and the recovery can start with that.
There are third party tools that can analyze the log and recover stuff, but they work only if the log was not recycled, so is back to the discussion whether the recovery model is really full or simple.
Answer: For future reference: ApexSQL was actually able to recover the deleted data from the log. Pretty amazing.
Answer: Not with standard tools. You'd normally restore.
Some 3rd party log analyzer might be able to help to pick out what you want, but you've lost your data most likely.
Answer: I would say no, even if a database is in full recovery mode, until the first full backup is taken it is actually running in a pseudo full mode and not the true full recovery mode.
This causes you a problem since without the first backup to replay the logs upon, you will not be able to replay the log.

SQL Server restore from transaction log


Recycle Bin Timer Job

Question: The recycle bin timerjob is configured to run daily at 1.00 am . The CPU utilization of the database was nearly 90 %. When i checked the recycle job status it was initialized at 12.00 noon. Now the status has changed to failed. How do i debug what went wrong at what are the possible reasons and how to rectify it
Answer: Check how much content is in the recycle bin. If you're dealing with alot of big files, try restoring some to the original library and manually executing the recycle bin clean up job. Continue deleting a small number of files at a time and running the clean up job until all files have been purged.
Alternatively, turn the second level recycle bin off, then on again (this will delete everything from the second level recycle bin for that web application, regardless of when it was added).
Here's a good reference on dealing with recycle bin clean up issues: http://blogs.msdn.com/b/ajithas/archive/2009/09/08/deleting-very-large-objects-from-the-second-stage-recycle-bin.aspx.

Recycle Bin Timer Job


How to find and fix a bad smell of moisture?

Question: We just bought a 3-year old house and there is an odd smell of moisture in the master bedroom and attached bathroom.  It smells like someone just took a shower although the house has not been used in 10 days.  During those 10 days, the central air conditioning was set at 80 degrees.  We can't locate the source of the smell as you get used to the smell pretty quickly.  We noticed the smell during our visits before buying the home, but it seemed like it could easily be coming from their items or having just showered.  The master bedroom and bathroom are on the 2nd floor of a 3-story townhouse.
Comment: Did they do a mold inspection as part of your purchase and sales aggrement?
Comment: @mikes - no they did not
Comment: You have mold/mildew somewhere. That's likely what you are smelling. Are there carpets? Peeling paint? Enclosed rooms/cupboards? Keep snooping.
Answer: It sounds likely that you might have a minor leak somewhere perhaps. You haven't really mentioned where you live as that can have a big impact on the expected environment in the home. If you in a low lying area and have a basement it could be related to ground water in the area seeping into your basement.
More than likely though you simply have a leak somewhere. I've seen thermal imaging solutions advertised as a great solution to this but have not personally used a service like this. Here is a link to a site that details the process pretty well so you can get an idea of how it works. You'll have to call around your local area and find a company that offers these services though.
Once you've fixed the source of the problem and know the extent of the area affected your best option for clearing up related problems is going to be a dehumidifier. In most cases you want to aim for 40-50% humidity at most.
If you live in a humid environment and the ambient humidity is upwards of 60% inside the house regularly than that may be the sole cause of your problem. Either way your first step is going to be finding the source of the problem.
Answer: Maybe you could better describe the smell. Is it the smell of soap, cosmetics or just a musty wet odor? Regardless, I'd be checking the bathroom exhaust fan to see that it is properly vented to the out of doors and not into the attic or some other indoor space.  I would also check the AC filters and clean the air ducts, both feed and return. Carefully check the adjacent areas, attic, basement, air ductwork to try to find a source of the strongest odors.
Also check the drains/traps as a source of your smell.


Is randomness deterministic?

Question: Is randomness based on lack of knowledge or behavior of universe is true random?
Or in other words,
are the allegation by EPR about hidden variable in the QM theory justifiable? What evidence can disprove/prove EPR?
Comment: The question is very vast and more philosophical than physical in nature. It also mixes some concepts through each other like randomness, probability and determinism. It needs a clear exposition of the various terms and a narrowing down of the question like "Are current models of the universe deterministic?" otherwise the question is too broad and not really about physics specifically. In the meantime, I advise reading [this text](http://www.scribd.com/doc/11328575/Jean-Bricmont-Determinism-Chaos-and-Quantum-Mechanics) to clear up ideas a bit.
Comment: The question body doesn't quite make sense... besides, is this asking about randomness in general, or non-determinism in quantum mechanics specifically? In the former case it's off topic and in the latter case it really needs to be reworded.
Comment: Does the sun rise in the east? Do eggs harden when boiled? You have to be a little more precise in your question. Otherwise you're just being poetic.
Comment: has relationship  knowledge with randomness ? is predictability no  randomness ? lack of determinism randomness ?
Answer: This is a very general question, and can be answered from several perspectives. I shall try to give an overview so you can perhaps research the areas that interest you a bit more.
Firstly, the most fundamental interpretation of probability (as considered by most mathematicians) is Bayesian probability. This effectively states that probability measures state of knowledge of an observer.
This view has interesting ties with physics, in particular quantum mechanics. One could consider the random outcome of a QM measurement (wavefunction collapse) from a frequentist approach, but it is often more appealing philosophically to consider it as a state of knowledge. (The famous thought experiment of Schrodinger's cat is a good example - until one opens the box, we can only say it is an "alive-dead" cat!)
Interestingly, Bayesian probability does not explicitly preclude determinism (or non-determinism). Our current understanding of quantum mechanics does however. In other words, even knowing perfectly the state of a system at a given time, we cannot predict the state of the system at a future time. This most famous upset Albert Einstein, who spent many years of his life looking for a more fundamental deterministic theory - a so-called hidden-variables theory. Since then, however, we have learnt of Bell's theorem, which implies the non-existence of local hidden variables, suggesting that there is no more fundamental theory that "explains away" the non-determinism of QM. This is however a very contentious issue, and in any case does not rule out the existence of non-local hidden variable theories - the most famous of which is Bohm's interpretation.
In summary, this issue is far from settled, and creates a lot of contention between different groups of physicists as well as philosophers today.
Comment: The "local" weasel in Bell's theorem leaves open the possibility that everything is predestined, but makes it in principle impossible to every know all the underling data needed to resolve any given "random" event (because it might be stored in some location outside your historical lightcone and still matter. Grrrr...). So there is a metaphysical escape for those who don't like God throwing dice, but us mere mortals are stuck with randomness in our lives.
Comment: @mbq:  The Schrödinger equation might be deterministic, but wavefunction collapse is not.  The operators representing quantum observables project onto a single eigenvalue of the observable.  The information about the rest of the unobserved state is lost, and the loss happens randomly.
Comment: @Jerry This is because (as always) measurement ruins isolation -- yet the larger system composed of measured system and measuring system stays deterministic.
Comment: @Sklivvz Sure, but there is no contradiction here.
Comment: @dmckee: The local objection is not usually interpreted to mean QM should be replaced by nonlocal outside the lightcone stuff, because outside the past lightcone is meaningless. Instead you intepret it as nonlocal holographic stuff on the cosmological boundaries. I believe this is what t'Hooft is suggesting. There is no point in introducing truly unobservable hidden variables.
Comment: Well, Shroedinger equation is deterministic, so the whole QM is a nonlocal hidden variable theory.
Comment: @Jerry: Thanks - I was going to make precisely that comment, except the site was broken for me!
Comment: @mbq I have to side with Jerry here, as measurement is only well defined mathematically, but the exact physical interpretation of it is an unresolved problem of QM.
Answer: There is a fundamental randomness in the universe but we can often treat things as deterministic. For example, we can accurately predict the path of a projectile provided we know the initial velocity and the gravitational acceleration. However, every measurement has uncertainty due to the accuracy and precision of the instruments used to make the measurements. From these measurements, our predictions also have uncertainty.
Uncertainty becomes a fundamental problem at extremely small scales. You should read up on the Uncertainty Principle for a detailed explanation of this but I will attempt to put it simply. To make a measurement, you actually have to interact with the object. For example, to see in the dark you may use a torch. This will shine light at objects, which will be scattered and reflected and your eyes will detect the reflected light. Here light interacts with the object you are observing. At a large scale this doesn't change much, but at extremely small scales the energy carried by light is enough to change the system significantly. So the action of observing necessarily implies that you are changing the system so that you can never measure something exactly. It is important to realise that this is a fundamental law of the universe, not just that our equipment is not good enough. I recommend searching for Dr Quantum videos - it is an animated series that explains these concepts. Due to these limitations, we have to model things like the position of a particle as a probability distribution.
Another important thing with regards to determinism is radioactive decay. We can predict very well how much of a radioactive substance will decay in a certain time. It is simply an exponential decay. However, if we extract a single atom, we have no idea when it will decay. This is completely random - the decay of an atom is indeterministic and not at all affected by environmental factors. Again, our models are reduced to probability.
Answer: I think there is another level at which this question is being asked.  Randomness of a symbol string means there is no formal data compression algorithm that reduces the string to some small form.  The shortest description of a string is the level at which its complexity is reduced to an extremum, and that it can be executed by a Turing machine which halts.  This is the Kolmogoroff complexity of a symbol string.  So to emulate the string there exists some Turing machine which has a "tape" and a stack, where the complexity of the string can't be significantly more (longer length, more bits etc) than the Turing machine to guarantee a halting condition.  A set of $n$ coin tosses will produce $N~=~2^n$ possible binary configurations.  For $n$ large a smaller percentage of the $N$ binary strings are likely to satisfy this condition.  The Kolmogoroff complexity is then a form of the Chaitan halting probability, which is itself not computable in general, which does give a bound on the number of strings which are "halting."
This leads to the indefinability of randomness.  To define randomness you need some algorithm which can compute that a string is random.  So given a string $S$ there must exist a Turning machine which determines $Rand(S)~=~T\vee F$.  However, that is not mathematically possible.  This means randomness is not computable.
Answer: Ok, what if we were to use some sort of metaphysical observation (no measurement) and then use this observation to choose when to measure thus perhaps partially aligning the colapse with some higher order?  I would assume the waveform would collapse according to the same 'random' order but perhaps because of the partial alignment we could somehow influence the outcome of said measurement.

Is randomness deterministic?


Installation of custom ubuntu livecd

Question: I'm following the guides at https://help.ubuntu.com/community/LiveCDCustomization and https://help.ubuntu.com/community/Installation/FromImageLoadedOnHardDrive in order to make a custom ubuntu cd to send to a family member. It appears to me that if i make a custom image that when i chose the Install option from the boot menu it will actually install that custom image with all of the packages that I chose and not the default ubuntu installation. But I wanted to make sure that is the case because if I cannot create an installable custom cd then its useless for what I want to do. Can anybody clarify this for me? Thank you.
Answer: When you customize a CD in this manner (creating usually a DVD sized image), it will be in essence an image of an installed system squashed into a compressed image.
When you install on a new system, all the programs you installed (and changes made to the underlying system) will be carried over.
Answer: What you see on the newly created custom live cd, is what you get...
Comment: you don't have to dumb it down for me!
Comment: How do you suggest that I dumbed it down? All I did was answer your question.

Installation of custom ubuntu livecd


How can a pre-schooler improve her handwriting skills?

Question: My brother's daughter is 6 years old. She is very smart and picks up things very easily. But when it comes to handwriting, she is not doing good.
What techniques or tools can we give her in order to improve her handwriting?
Comment: pencils and paper. but I wouldn't sweat it that much. handwriting isn't all that critical of a skill anymore and most people bad at handwriting grow up to be successful doctors anyways.
Comment: Start her typing, that's the only way I've ever been able to write anything presentable :)
Answer: Techniques and tools to improve handwriting:
Knowing how to form the letters is important so that they aren't stopping and starting. Training the muscles to make smooth movements takes practice and, of course, time for development. My kids are Lego fiends, who enjoy using the tiniest of pieces and their hand-writing is atrocious unless they concentrate and focus on forming the letters correctly. Here are my suggestions:

Some say use larger pencils because they are easier to hold. As a grade 1 teacher, it helped some but not all.
With my own children I used pencil grips that encourage proper grasp.
Sometimes just using a better pen made all the difference. (Perhaps because they were more careful?)
We have a whiteboard in our kitchen where we model writing (messages and lists) and encourage our children to write too (they take turns adding to the lists and leaving messages). Drawing with markers seems to be easier than with crayons or pencils or some pens.
Teach cursive first. It's more fluid. (Montessori schools often do this.)
Tracing exercises:

Kumon worksheets have a number of tracing exercises that get
progressively more difficult. You can buy their workbooks from most
bookstores.
Another way is to lightly write the letters in dashed lines. Here are some worksheets for practice printing and writing.
A faster way is to write things with a yellow marker so that she can write overtop (trace).
Drawing curves and circles is important.

Use chopsticks. These use the same muscles and have a built in reward system (food)! This is something the whole family can learn to use together. Smaller sets are available (usually in Chinatown), or find some wooden ones that you can modify. You can also get what we call "cheater chopsticks" that have the same movement but require less coordination.
Use lined paper and be firm about them doing their best work and staying in the lines. Erase work that is not their best until they do it properly. This sounds severe, just be pleasant about it and matter-of-fact. 7-year-olds may have messy letters but this one thing, staying in the lines, will have the most impact. Praise good work!
Practice discrimination. Have them circle their best work. For rows of practice letters, circle the 3 that they think are the best. Then you circle the 3 that you think are the best and say why. Sometimes you won't choose the same letters but eventually your criteria will converge.
Comment: 200 bounty awarded for being very specific. That's gotta be helpful to the asker!
Answer: While i agree with Pierre and Péter, sometimes parents feel like "you're either getting better or you're getting worse"; that if you're not doing anything to make it good, that you're letting it get bad.
In that spirit, one thing you could do would be to ask the niece, daily, to write something general about her day: what play time was like, what they had for lunch, thinks like that. This would probably be best timed right after school and will allow THE CHILD to make it better thru practice, as opposed to YOU making it better for them thru whatever method.
But there are several caveats here... Simple encouragement may be enough to get them started but if it isn't, then you can't force the issue in the slightest. Ask, but don't "make time for their daily journal". They have to want to do it on their own or it turns into a frustrating chore. Frustration leads to anger, anger leads to hate, hate leads to... well nevermind that, but you don't want her hating anything.
On the other hand, I'm not a fan of pushing children along a derived path which kind of goes with what the other guys said. All things being equal, children's bodies will develop all the appropriate skills in time.
One of my favorite comedians (Louis CK) had a bit that applies here. He talked about people fumbling with their phones and becoming frustrated with impatience. then he hollers

"GIVE IT A SECOND. Will you give it a second? it's going to SPACE
  can you give it a second to get back from space?"

The point is that in the era of instant total gratification, sometimes it takes real effort to be patient. This is one of those times where I think the payoff from patience and diligence (watching to see if it becomes a long term issue) is worth more than the downside of immediate action.

Louis CK bit on patiences: http://www.youtube.com/watch?feature=player_detailpage&v=8r1CZTLk-Gk#t=85s
Answer: 6 to 7 years old kids are still too young to learn how to write. That's because the myelin sheaths that increase the efficiency of neurons are still being build till age of 12. The myelination level can be more advanced for some kids which explain why some are advanced.
The children can still learn to read and write, but often in pain. The main problem I see with this is that in societies where performance is legion, we often want our children to walk upon one year of age and speak fluently in two years. Since it's biologically difficult or even impossible, parents create a frustration in children who can not achieve what they are expected to do. You can disgust the child to learn in these conditions and make it a procrastinator in power: a real time bomb.
We must therefore remain cautious and follow the stages of child development. Instead of worrying about performance, worrying about his well being.
My 2 cents.
Comment: Thank you for the info. I second your opinion on following child developments. we are also not pushing her to do better. we are not even comparing. But going further, are there any ways to improve handwriting? Peter mentioned one good method of writing big with bigger pen. Btw, our handwriting is not that great and hence we want to do what ever to get hers better.
Comment: @Pierre I am skeptical of your myelin reference and basically citing a __physical limitation__ which prevents a child's handwriting from improving.  See this video of [Sungha Jung playing guitar](http://www.youtube.com/watch?v=rjAFtX_Ywg4) -- although he is probably an anomoly, the video shows just what is possible for a child with his hands who practices with discipline.  (This video is dated 2006 and he was born in 1996, so he is _at most_ 10 here.)  Anyway, I agree with the sentiment that says "don't rush it", but I _disagree_ with the idea that there is a _physical limitation_ there.
Comment: Yes he is very special, which is not the case of the vast majority of us.
Answer: I fully agree with @Pierre's answer. Don't try to "improve" her handwriting. That may seem to work in the short term, and do much damage in the long term. At this age, there can be huge differences in physical development between individual children, which have nothing to do with "intelligence" or "skills" or anything, and which - under normal circumstances - are bound to even up in a couple of years.
Namely, a lot of children aren't yet capable of controlling the small, delicate movements which are required for writing with a "normal" pen in "normal" size. Try giving her a bigger, thicker pen, and let her write big letters - that way she can practice the movements in large scale, which may be more comfortable to her, and less stressing for her muscles and nervous system.
Btw who says she is "not doing good"? Teacher? You? Other relatives? ... And based on / compared to what? As you say, she is a preschooler so there shouldn't be any pressure on this issue even from the school (or so I imagine).
Comment: +1 for encouraging big letters, and for "no pressure in preschool".
Answer: As a parent, I agree with giving it time as handwriting is a skill that does take time to develop. as an occupational therapist, handwriting is usually a symptom of something else: weakness, low muscle tone, decreased hand eye coordination , etc. I don't intend on diagnosing or worrying anybody but I usually recommend the patients I see to begin general strengthening. Luckily for kids that means playing , wheelbarrow walking, carrying some'heavy' grocery items to develop good shoulder strength. A lot of children use their shoulders due to weakness and one can imagine those are big muscles for sUch a precise task like handwriting.
You can also try different board games to help her develop more precise fine motor skills, smaller pegs, manipulating different items etc.
You can hide small items in play dough to help with hand strengthening.
It is a good idea to try different pencils and paper to work on 'handwriting' but there are many other ways too to work on the skills needed for handwriting that can be fun for her and even good family activities.
Answer: Speaking from personal experience, I had a lot of trouble learning to write. I found it awkward and frustrating making the tiny movements, and because the results always looked poor, I didn't enjoy it.
When I was an older teenager my parents arranged for me to see a handwriting specialist. She analysed exactly which specific movements were difficult for me. In my case it was the bottom half of clockwise curves, so lower case g, f, j, and o in particular were painful and awkward.
The solution was incredibly simple, write in copperplate. My handwriting went from slow and illegible to quite reasonable in that one day.
This is just an answer from personal experience, but if I was trying to help a child, I would be looking closely for specific movements that the child finds difficult, and then working out a way to change the handwriting style to avoid those movements.
Answer: You need to remind her every time she is trying to write or color to hold her pencil properly.  If she doesn't develop proper skills now she will have trouble working out of them (like any habit). I found with my daughter who had the same problem that she loved the triangle pencil grip (harder to find then the circle ones which do nothing.)  Just encourage, not force and she will slowly incorporate the write hold into her life.
As well, writing is a fine motor skill, so try to work on other fine motor skills aside from writing.
Answer: As others have mentioned, writing is a complex and difficult skill that children are often not ready for at 5-6 years of age. It is a fine motor skill which are generally developed later than gross motor skills. I would suggest having her engage in other fine motor activities, one example is building with Legos. Also, coloring, or even playing with a Barbie doll, particularly dressing and undressing it are all good fine motor skills. An increase in fine motor skills will most likely increase her writing skills as well.
Answer: NGenius gave a very good and specific answer about how to improve her handwriting, from a teacher's perspective this would be the usual answer.
However, you say that she "picks things up very quickly".  There is a relationship between gifted kids, left-handedness, and delays in fine motor coordination in both lefties and righties.  It has been pretty well established that their brains typically develop differently than the brains of non-gifted kids.  When I taught in a 2e classroom (kids that are gifted but that also have a learning or emotional disability that makes a regular classroom too difficult for them to excel in), most of my students had a lap top on which they did all their work, took all their notes etc.
It is possible that she is not yet ready to get her letters perfect or even legible.
We've had quite a struggle with this one in our house, so I've written about it a few times on my blog.  There is an article about prewriting skills activities in preschool and learning to write the alphabet already on the blog as well as one about the typing program I recently purchased and introduced to her.  I did this so she could type most of her work and only have to write when we are specifically working on handwriting (This year that will be for about 20 minutes, 2 times/week) or she is writing in her History Journal or Science log.  Both subjects are ones she really enjoys, so she is more willing to struggle through the writing aspects for these two subjects than she is some of the "more boring" subjects.  She LOVES the typing program and often ASKS if she can work on learning her typing.
I think this system tells my child that I love her as she is and I support her strengths and exploring those strengths.  We don't get bogged down in worrying too much about getting her handwriting perfected, but she isn't getting out of that work entirely which lets her know that working on building up our weaknesses is important too - its just about keeping it all in balance.


How can I compete against the unit armies tactic in Risk?

Question: How to I avoid one player getting too strong by playing just to defend a small area or continent and only gaining territories just to obtain Risk cards to trade in for more armies.
Answer: Convince the other players of the power of his tactics and the need to 'break his continent' before he 'runs away with the game'.  Lead the coalition against his evil ways.  Use this coalition to mask your own strategy, as you set yourself up to emerge most powerful from the ashes.
Risk is all about controlling the perceptions of the rest of the table.
Answer: Box him in and attack him elsewhere.
If he's boxed in, he can't gain territories around his base except by suffering heavy losses. Now he has to gain his Risk Card Territory elsewhere, where he's vulnerable. Whittle down the number of his territories, and soon he'll have to place some of his new armies outside his base to have a good chance of gaining a territory, which means those armies are not strengthening his base.
Comment: Often not practical.
Answer: Play with the rules variant (which is in the manual in at least some versions of RISK) that tones down the trade-ins for armies.  Instead of the trade-ins escalating by 5 in the endgame, they simply go up by two every time (4, 6, 8, 10, 12, 14, 16...).
This makes the other ways of obtaining armies more relatively important and downplays the importance of the cards.
Comment: I don't see any reason why this should tend to disfavour a player who's turtling in a small continent. Indeed, I'd think that it just makes their continent bonus relatively more valuable, and so *favours* them.
Answer: Force him to come towards you and leave the safety of his base.  Then he's either forced to attack territory outside of his base if he hopes to continue to gain Risk Cards and grow his armies, or stop collecting risk cards altogether.  Also, if you can gain and hold choke points on the map against him, you force him to seek those cards in other parts of the map.  If he continues to become to powerful, seek an alliance with the other players to cut him down to size.


Numeric integration with unknowns

Question: The problem I have is a system of three non-linear equations with three unknowns. Each equation has a integration term. But the integration term has all the three unknowns in there. Some suggested to discretize. So I need to discretize all three unknowns. And solving the system become looping over the three variables and find when the equations hold at certain combination of the values.  I am not sure if this is the right way to go or there are better options
The three equations are
\begin{equation}
L=N_a \int_S l(s)dF(s)
\end{equation}
where $l(s)=(\gamma(1-\theta)Ak\frac{P_a}{q})^{\frac{1}{1-\gamma}}[\theta((\frac{\theta}{1-\theta})\frac{q}{r})^{\frac{\rho}{1-\rho}}+(1-\theta)s^{\frac{\theta}{1-\theta}}]^{\frac{\gamma-\rho}{\rho(1-\gamma)}}s^{\frac{\rho}{1-\rho}}$
\begin{equation}
K_a+K_n=K
\end{equation}
, where $K_a$ is determined by a similar integral as above $K_a=N_a \int_S k(s)dF(s)$, and $k(s)$ has a similar function as $l(s)$
There a similar third equation.The three unknowns are $q$, $N_a$ and $K_n$. But the problem is the integrand $l(s)$ has $q$ in there.
Answer: Without seeing your equations, one can offer nothing more than hypothetical advice.
One possible approach would be to differentiate the equation on both sides, obtaining, instead, a differential equation, which can then be solved using many methods. This, however, may not be possible, and you might be stuck with an integro-differential equation.
Alternatively, you could restrict the domain of your independent variables (either naturally, through restrictions invoked during the derivation of the problem, or heuristically based on some extrinsic expertise). Then, you could treat each integral as just some function, $F(x,y,z)$. Writing a numerical integration routine that allows you to compute $F(x,y,z)$ with sufficient accuracy is the same as computing the value $F(x,y,z)$ -- you can then use a standard root-finding method (e.g. Newton's method) to compute the solution. (This would be slow).
Without seeing the equations, however, it is impossible to advise you on what the best approach would be.
Comment: I put the equations in there. I hope the question is clear now.
Answer: Perhaps you could differentiate relevant equations to convert them to a system of ODE instead, and then use standard methods?

Numeric integration with unknowns


בישול Versus שולק

Question: The Shulchan Aruch and the Gemara use two words that to me seem to mean the same thing: "Cooking". My question is what is the difference between שולק (Sholek) and בישול (Bishul)? Please provide sources.
Answer: Rashi in Pesachim 39a says that shaluk is extensively cooked, and Tosafos there 39b agrees. That's pretty much the standard pshat. However, Ran in Nedarim 49a translates it there as undercooked.
Answer: Shaluk means "stewed" for a very long time. It's a subcase of bashul, "cooked."
Yes I know, need to provide source ...
(I have a bad feeling someone could be using this site to cheat on their homework ...)

בישול Versus שולק


Can I change the flour type of my sourdough starter?

Question: I started my sourdough starter with rye flour.
But after some months I continued feeding it with wheat flour. I feel like there is less life inside than before.
Might it be due to the change in flour or must there be some other reason?
Answer: Robert Cartaino's answer hits a main point: sourdough cultures are adapted to what they are typically fed.  When switching flours, it may take a while for the culture to adjust.  The starter may seem a bit sluggish at first.
That said, I would NOT recommend trying to start a wheat culture if you already have a healthy starter that began with rye.  There are two main reasons.
First, rye is particularly rich in certain sugars and food that natural yeasts tend to like, so rye starters naturally tend to look more "lively" than wheat starters, especially in the early stages of a starter.  Part of what you may be seeing in your transition to wheat is simply less activity produced because the food source is less rich in nutrients, not necessarily because the yeast and bacteria can't digest it.
Second, a lot of recipes to generate new starters recommend using rye at the beginning, regardless of what you ultimately plan to feed the starter.  Because it provides a strong food source for young cultures, it's usually a lot easier to begin with rye (perhaps this is why you did).  In my experience, it tends to take new wheat starters at least twice as long to get strongly established compared to rye, and there's a higher chance of failure if you don't use a good recipe.
For both of these reasons, some people even recommend always feeding your starter with rye flour, even if you tend to make wheat-based bread.  Since many people have success doing that (and I have personally), I don't think you need to begin a whole new culture with wheat alone.
If your starter really is sluggish (and not just a little less active than it was with rye), you can help your starter to adapt to the new food.  I'm not sure what your typical feeding routine is or what the hydration level of your starter is.  But the general thing to do in these circumstances is to dilute your starter and feed it large quantities of the new food.  For example, if you maintain 200 grams of your starter normally, I would discard all but maybe 40-50 grams and then add enough new flour and water to get back to 200 grams in whatever your usual proportion is.  (Some people would be even more extreme in diluting the starter and cut the starter proportion even further.)
Within a few days of feedings like this, you will have strongly selected the yeast and bacteria that thrive on whole wheat and your starter should be strong again.  After a week of feedings like this, I doubt you could distinguish the performance of your starter from one that was begun on wheat.  (Note that the specific microorganisms may still be slightly different, but your starter should do a fine job raising dough and providing flavor.)
Comment: Fair enough. My suggestion to "start over" was based on an assumption that the author switched for good reason and wished to continue with the wheat flour. My rye starter always seemed to *sour* better anyway.
Comment: @RobertCartaino, absolutely. I didn't mean to be argumentative or to undermine anything else you said. It's a complex question. When I first began trying to make starters from scratch, I tried the method of beginning with whatever flour I planned to use it for (rye, whole wheat, white, etc.). After a few trials, I found that rye just was easier to begin, and I didn't see a major difference in performance/taste when I switched flours.  I later found that others have had similar experiences. The one time recently I made a whole wheat starter, it took FOREVER to get strong (compared to rye).
Answer: Different flours contain different varieties of naturally-occurring yeasts and bacteria. When you create a sourdough culture, these yeasts and bacteria compete and eventually stabilize to balance out into a favorable equilibrium. Natural selection. Unfortunately, when you changed the type of flour you fed to that culture, you dramatically changed the environment the yeasts optimized for.
It's entirely possible that your rye-based culture simply will not do as well in the wheat flour. Unfortunately, since that culture is already dominant in your starter, it may be competing with the naturally-occurring organisms present in the new flour.
It may balance itself out eventually, but it may simply be better to start a new culture with the type of flour you wish to use in the longer term.


How to efficiently hit an index in a query that uses IN (mysql)

Question: I have a table like this where people can subscribe to certain feeds and the query fetches from the subscription.
Here is a sample table:
+--------+-----------------+-------------------+---------------------+-----------+
| by     | subscription_id | subscription_type | feed_created_time   | content   |
+--------+-----------------+-------------------+---------------------+-----------+
| Peter  |              12 |                 1 | 2012-12-30 10:00:00 | asdf      |
| George |              34 |                 2 | 2012-12-21 00:19:00 | qwerty    |
+--------+-----------------+-------------------+---------------------+-----------+

and its full detail
CREATE TABLE `table` (
  `by` varchar(20) NOT NULL,
  `subscription_id` int(11) NOT NULL,
  `subscription_type` int(11) NOT NULL,
  `feed_created_time` datetime NOT NULL,
  `content` text NOT NULL,
  PRIMARY KEY (`subscription_id`,`subscription_type`,`feed_created_time`),
  KEY `subscription` (`subscription_id`,`subscription_type`)
) ENGINE=InnoDB DEFAULT CHARSET=utf8;

I've created the primary key like so to create a cluster which would allow most likely types of pulls to be most efficient. So the "next applicable" is immediately following.
And here is how I'm making the query right now:
SELECT * FROM table
WHERE subscription_id IN (12,34) AND subscription_type=1
ORDER BY feed_created_time DESC;

I would also like to make a more complicated queries like...
SELECT * FROM table
WHERE (subscription_id IN (12,34) AND subscription_type=1 )
   OR (subscription_id IN (34) AND subscription_type=2 )
   ...
ORDER BY feed_created_time DESC;

It works fine, but I noticed that when I do an explain, it's unable to use any indexes. Or, it at least reports that it hasn't chosen to use any indexes despite the primary and subscription key being available. It just creates a temporary table and sorts them.
It has no problem selecting keys when making queries like subscription_id = 12 AND subscription_type=1 but the IN in the query seems to make all keys unusable. How can I make the queries use the indexes?
Comment: Using temporary and/or Using filesort would be necessary because your `WHERE` and `ORDER BY` do not reference the same columns.  But `KEY` is NULL?  Consider posting the output of `EXPLAIN SELECT`.
Comment: A similar question with answers: http://stackoverflow.com/questions/586381/mysql-not-using-indexes-with-where-in-clause
Answer: Reverse the 'subscription' index. As it is, MySQL will probably use the PRIMARY KEY for lookups by a single subscription_id.
Once MySQL hits a RANGE query, which an IN clause is, it doesn't use the rest of the index.
CREATE TABLE `table` (
  `by` varchar(20) NOT NULL,
  `subscription_id` int(11) NOT NULL,
  `subscription_type` int(11) NOT NULL,
  `feed_created_time` datetime NOT NULL,
  `content` text NOT NULL,
  PRIMARY KEY (`subscription_id`,`subscription_type`,`feed_created_time`),
  KEY `subscription` (`subscription_type`,`subscription_id`)
) ENGINE=InnoDB DEFAULT CHARSET=utf8;


General Equilibrium for Mathematicians

Question: I've been reading up a lot on the recent financial crisis, and central to the story is the existence of general equilibrium models in economics, say, as proven by Arrow and Debreu (and MacKenzie?). Regardless of the real-world validity of these models (they're not looking so hot these days), I'm interested in them as a purely mathematical exercise. So, that said, does anyone know of a good (preferably available online) exposition of the existence of a general equilibrium aimed at mathematicians?
Answer: It would be hard to beat Debreu's Theory of Value
http://cowles.econ.yale.edu/P/cm/m17/index.htm
a masterpiece of economic and economical exposition.
Answer: I think it is worth pointing out that, from a purely mathematical point of view, economic general equilibrium theory is an exercise in fixed point theory.
The same may be said of the theory of non-cooperative games. John Nash invented the solution concept now known as the Nash equilibrium in his thesis. VonNeumann dismissed Nash's result as "just a fixed point theorem" but Nash eventually received the nobel prize in economics for this work.
The mathematical setup for economic general equilibrium theory focuses on constructing what is called the "excess demand correspondence". This is derived from assumptions about how consumers and producers formulate their plans to take best advantage of the prices they observe in the market place. The excess demand correspondence associates to any vector of market prices (one price for each commodity) the convex set of vectors of aggregate excess demands (one excess demand- possibly negative -for each commodity) that will arise when consumers and producers respond to that specified price vector.
The main idea of the proof is then to find another convex set of price vectors, each of which can be interpreted as a supporting hyperplane to the given convex set of excess demands, and each of which maximizes the market value of the excess demand.
This construction then can be shown to yield an upper semi-continuous, convex set valued function from the convex set of allowable vectors of market prices to the space of is convex subsets. One then applies an appropriate fixed point theory to deduce the existence of a price vector which, because of the structure of the excess demand correspondence, has the property that the value of excess demand in each market is zero. This is the market equilibrium price vector.
Comment: ...''just a fixed point theorem.''  I don't find this criticism very trenchant.  One of the fundamental problems of mathematics is to solve equations (of various sorts).  A result that proves that a system of equations has at least one solution is a good result.  How good depends on how non-obvious the existence of the solution is.  Maybe von Neumann's criticism was somewhat more detailed?  How non-obvious was Nash's result at the time?
Answer: One mathematically interesting development in general equilibrium theory is the application of tools from differential topology such as Sard's Lemma. Look at Balasko's The Equilibrium Manifold (Amazon) or Mas-Colell's Theory of General Economic Equilibrium. You can get a flavour of this approach by looking at this online paper by Geanakoplos and Polemarchakis.
Answer: Kim Border has lots of excellent lecture notes related to mathematical economics, including some on general equilibrium theory. The lecture notes on general equilibrium theory  by Nicholas Yannelis are very extensive and introduce a lot of the related mathematics.
The original paper by Arrow and Debreu, probably the most famous paper on the existence of an general equilibrium, can be found here. It is based on a result by Debreu to be found here. Ted Bergstrom has a nice survey on how to weaken several assumptions used in many existence proofs. In particular, how to substantially weaken the rationality requirements.
Mathematicians might be interested that existence of equilibrium has also proven for some infinite dimensional models that are important for finance, growth theory and various other fields. This literature makes much use of functional analysis, especially Riesz spaces. A good survey by Mas-Colell and Zame can be found here.
Answer: A short paper I've been wrestling with, providing a perspective on how do intertemporal equilibria relate to the information that economic agents need to make decisions?
Fortnow, Killian & Pennock (2006), Betting Boolean-style: A Framework for Trading in Securities based on Logical Formulas, provides a characterisation of what a market-maker must do, information-theoretically, in order to provide a coherent pricing if they offer what the authors call Arrow-Debreu secuirties, which are bets about future prices.  The authors admit in their conclusions that they don't know whether equilibria in their model matches the Arrow-Debreu notion of equilibria.
The reswitching problem that was a central focus in the Cambridge Capital Controversy (CCC) led the anti-neoclassicals to claim that paradoxes in the valuation of assets with varying interest rates meant that there was no unitary notion of value of goods used in production, and hence "capital" was an incoherent notion in mainstream economics.  The mathematics of basic reswitching examples is pleasingly simple, if the interpretation is not: Vienneau (2006) A Model For Exploring Manifestations of Capital-Theoretic 'Paradoxes' in Temporary Equilibria introduces a two-goods, three-processes reswitching example, and shows how the model has no single long-term equilibrium due to capital reversing.  The author briefly mentions the defences of general equilibrium models in the CCC of Debreu and Samuelson, and doesn't reach any conclusions, except to argue that he has provided a useful model for looking at the effect of reswitching and capital reversing on the dynamics of equilibria.
Answer: I recommend the paper " An elementary core equivalence theorem" by Robert M. Anderson. It is a very short paper that contains a fairly self contained description of the basic models and concepts. You can then try to guess how to prove the existence of equilibrium based on some fixed point theorems or look at papers that Anderson quote.
There are various more advanced models including models with incomplete informations
("rational expectation is a useful buzz word). There are also plenty of examples of market failure.
(I do not see why the recent financial crisis has anything to do with these models being less hot...)
Answer: To answer your request, you could start from a master: Smale S., ``Dynamics in General Equilibrium Theory'', American Economic Review, Vol.66, No.2, 1976.
Answer: Debreu is certainly a superb exposition, but I think a better choice is McKenzie, for two reasons:
1)  Debreu's model assumes a fixed number of firms, which means that it's implicitly a model only of short-run equilibrium.  McKenzie's model (which was contemporaneous with Debreu's) allows the number of firms to vary (at the cost of assuming constant returns to scale) and is therefore a better introduction to the kind of models you seem to be interested in.
2)  Debreu's book, well written as it is, dates from the 1950s.  Because McKenzie's book is much more recent, it's able to offer some historical perspective that I think will be helpful to you, as well as incorporating a lot of material (e.g. uncertainty) that wasn't well worked out until more recently.
Like Debreu, McKenzie was a good and careful expositor.
Answer: Acemoglu's new textbook Introduction to Modern Economic Growth includes a very thorough and rigorous exposition of the foundations of macroeconomic theory including general equilibrium and so on.
Comment: Just a remark, but the general equilibrium theory is considered
to be a part of microeconomics, not macro, even if in a sense it
is about the economy as a whole.
Comment: Well, not exactly. It's true that general equilibrium theory is first encountered by students on microeconomic courses. But most modern academic and policy-oriented macro is done within some kind of general equilibrium framework.

General Equilibrium for Mathematicians


How can I grow cold weather crops in a hot climate?

Question: I would really like to grow brocolli, potatoes, blueberries, and/or spinach in Oklahoma (zone 6). But all my previous attempts have failed miserably. Does anyone have pointers on how to do this, or should I just give up? Even tomatoes are difficult to grow down here, because the summer heat can be brutal.
Comment: Like Ed Staub, I'm in NH, so I can't give much advice for your climate from my own experience. I will say that spinach can survive a NH (Z5 and 4-5' of snow) winter, so you may want to try overwintering greens like spinach and kale, possibly with some simple protection like row covers. Don't start them until the worst of the summer heat is over. winwaed's suggestion of growing in the fall seems like a good strategy to me.
Answer: I grew up in Eastern Kansas(hardiness zone 5b).
I had the most success with tomatoes when I bought them as seedlings and selected heat loving varieties. Late frosts were also a problem. I also found they needed to be in the sun but did poorly if the area did not also receive shade(especially during the hottest part of the day.
I also found that spinach did not do well after June. Early Spring or late winter was a good time to plant it.
I have not personally grown blueberries in Kansas but I have a friend that successfully grew them after many years of trying out different plants and soil combinations. She built a netted shelter around them that keeps creatures away from them. As I am not familiar with the type of blueberries that grow well in Oklahoma I suggest this article. I used a similar site when I started growing blueberries where I currently live on the West coast.
A couple things I have learned is that you need to plant more than one bush. I am trying several varieties that are supposed to do well in my region. I tried to choose a well drained protected location. I mulched around them during the winter to try and protect the roots from the cold.  The birds always seem to get my blueberries so netting or some other type of protection is necessary.
Answer: Haven't tried spinach or blueberries, but I've grown potatoes and tried broccoli here in N.Texas (similar climate to OK but our frosts are not as bad).
Your growing season for these plants are limited to spring (or possibly autumn), so there's a race from when growth starts (or last frost) until it gets too hot. As Ed says, watering is important. For the potatoes, I've found they do best on a north facing wall and with good watering later in spring when the rains are less frequent.
In order to lengthen the growing season my first attempt to grow broccoli was with grow lamps but became a failure due to aphids on the seedlings. Will try again in autumn or next year.
Answer: For tomatoes, you'll need to get the soil to hold enough moisture between waterings, and to not dry out too deep in the heat of the day.  So you need lots of humus, and lots of mulch.
If your garden's small and dollars aren't tight (or you can get it cheap), my favorite quick-and-easy source of humus is composted cow manure.  But there are many other options.
For mulch, I prefer one that's a grass of some kind - but be sure not to use too much that's too green (which will burn).  Some folks also worry about introducing weed seeds, but it hasn't been a problem for me.
Of course, you must keep an eye on it.  You'll probably still have to water heavily daily in the heat of the summer.  You're best off watering in the morning, to avoid molds.  For a small garden, consider use of a simple sprinkler that just has holes for the water to squirt out of.  These put out big droplets, so you lose less to evaporation.  Just don't spray hard directly at the leaves - it should "falleth as the gentle rain, upon the place beneath".
You also should try to use seed varieties that are heat-tolerant.
I live in New Hampshire, so take this with a grain of salt.  You may need to do more than this - but it's a good start.  For the other plants besides tomatoes, I think I'd better defer to folks who have experience with your climate.


Camping in (US) national forests

Question: Is it legal to camp in unmarked areas in United States national forests? I'm specifically thinking of Utah/Idaho if state makes any difference.
Comment: Welcome to travel.SE.  State and a particular forest might make a difference.  Can you be a little more specific?
Comment: this would likely be in Uintah-Wasatch-Cache National Forest.
Comment: I discussed this in [my answer here](http://travel.stackexchange.com/questions/8805/how-can-i-find-free-camping-locations-in-the-u-s/8806#8806).
Comment: See also [this post](http://outdoors.stackexchange.com/q/1819/566).
Answer: Backcountry camping in US national forests is free. There is the option of using a fee based campground as well. If you end up going backcountry camping, set up a good distance from established hiking trails and water sources(for animals). Bury human waste 6 inches below and pack out all trash.
Answer: For the US national forests you can find most of what you will need on the US Forest Service website.
Specifically for Uintah-Wasatch-Cache you can use this link and it will have the information about the various camping possibilities.  From Cabins, Group, RV as well as wilderness camping including the required information on camping regulations.
Answer: Camping regulations will vary according to area and land designation (wilderness, travel restricted, winter closures, etc...). Always check with the local Ranger District to get the details.
That being said, there are a few general principles:
Vehicle Camping:
For the most part, you are allowed to "dispersed camp" in any United States National Forest unless there is a specific regulation prohibiting it (special use area, conservation area, etc.)
What this means is, you can pull your car off a forest service wherever there is an established turn-out and camp. You can not, however, drive off into an undisturbed area and set up camp.
Camping is usually limited to 14 days, after which you are required to move at least 2 miles away.
Dispersed camping is free.
Back-country (foot) Camping
If you are hiking in, you have even more options. Again, in general, you are free to set up wherever you like, however some areas might have regulations in effect encouraging visitors to practice "Leave No Trace". For example, while it is ALWAYS a bad idea to camp within 100 feet of a stream or lake, in some forests it may be illegal.
Also, as good practice, it is better to camp in areas that already impacted -- unless that impact is minor, and stands a chance of full recovery if you do not camp there. See this discussion for more information.
For more discussion about the different public lands and what is allowed, see this question.
Comment: Can you elaborate on the "bad idea to camp near a stream or a lake". I suspect flooding or wildlife is a primary concern, but I was curious if there was more I should know.
Comment: @JoshuaEnfield All the national forest sites I've looked at require some minimum distance from water sources because of potential human impact on it (e.g. contamination from waste).
Answer: Camping regulations vary significantly between different national forests.  The only way to know what is allowed is to ask each forest you plan to visit.
For example, in the White Mountain National Forest of NH, car camping is highly restricted.  It is only allowed in designated areas and along a very limited few roads.  The designated sites are mostly in fee-based camps where you get a parking spot, grill, flat place for the tent, trash cans and restrooms nearby, etc.  There are a limited number of free spots along a mostly obscure dead-end road that are just a place to pull out.  These are termed "undeveloped" and are strictly first-come first-served.  Don't show up Friday or Saturday evening during the summer or fall and expect to find a spot.
Backcountry camping is allowed in the WMNF more freely, but there are restrictions, like you must be 1/4 mile from the trail, group limits in the wilderness areas, and various exclusion zones.  Penalties for getting caught where you're not supposed to be can be stiff.
Part of the reason the WMNF has to be so restrictive is because they get a lot of visitors relative to the land area.  It's only 2-3 hours drive from Boston and other populated areas, and the only area for a long ways with tall enough mountains for the tops to be above tree line.  There are also a lot of roads thru the area that people have to use for ordinary purposes having nothing to do with the forest.  The restrictive rules are to give people access but to keep the place from getting destroyed.  In my opinion, they do a pretty good job of ballancing the demands, which also include commercial ski and lumber operations.
In contrast, the much larger national forests in much less densly populated areas can afford to be more liberal.  The first time I visited the Apache-Sitgreaves National Forest in AZ, I went to the ranger station to ask about camping regulations as my first order of business.  They looked at me kindof funny and it took a while for them to comprehend the question, since you are pretty much allowed to camp anywhere and nobody ever asks them.  Eventually one of them actually said "just don't camp in the middle of a road".
The combined contiguous area of the Kaibab, Coconino, Apach-Sitgreaves, Tonto, and Gila National Forests exceeds that of Massachusetts, but far fewer people live in the vicinity.  The rules are lax because they can afford to be.  Everyone can camp mostly where they want to and it's not causing a problem, so no need to regulate.
I don't have experience with the forests you mention in ID.  But, what I'm trying to point out is that you shouldn't assume anything.  Ask.  Probably the rules will be more on the lax side considering size, remoteness, and nearby population, but unless you ask you can't be sure.  There will probably be some local specific restrictions that you need to know about, even if most areas are generally open.  Some restrictions can also vary be season, weather, and perceived threat of fire, so can change on the fly.  Again, you have to ask.

Camping in (US) national forests