Price Elasticity of Demand for Positive Price Increases

Question: What does it mean when the price elasticity of demand  %Qd/%P is greater than one?  Typically I hear that it means the demand is elastic since if, say, the price decreases by 1% the demand for the good increases by more than 1%.  But what happens if %P is +1% and %Qd still increases by more?  Sure, this is elastic, but does it give us any more information?  I can't see why %Qd/%P > 1 makes sense in this case.
Comment: Well it appears that you forget or are unaware of a standard convention here: algebraically, the price elasticity of demand is _negative_. Economists tend to talk about it in absolute terms, considering the algebraic sign as understood. I have prepared an answer as to where elastic demand emerges, so that the concept acquires some usefulness other than descriptive.
Comment: It is not clear what you are asking. The question in your third sentence, is answered in your second sentence. "Elastic demand" is a verbal way to say that the percentage increase in quantity demanded is higher (in absolute terms) than the percentage decrease in price. In what sense, it doesn't make sense? Please edit your question to clarify, so that we can answer it.
Comment: @AlecosPapadopoulos Wait, so an increase in %P would be denoted -%P?  Why are we talking about increase in quantity and decrease in price?  To me that would imply the correct equation is %Qd/(-%P).  If this is not the correct equation the curiosity to me is that 3%/1% for example does not denote that a 1% increase in price results in a 3% increase in quantity demanded.  And if this is the case it is confusing to me that such a case would really occur very often.
Comment: @Alecos Thanks, that makes more sense then, so my revision of the equation is correct, it's just that we always consider the absolute value of Ed?
Comment: Verbally yes. Because otherwise we would have to say "the smaller the elasticity the more elastic demand is" which would obviously create more confusion. In other words, the concept of elasticity itself was conceived having absolute magnitudes in mind.
Answer: Except of the purely descriptive aspect, "elastic demand", or more accurately, regions of the demand schedule where demand elasticity with respect to price is higher than unity, in absolute terms, is linked to the basic monopoly theory, since the monopolist maximizes profits at a point of the demand schedule where "demand is elastic".
Define the demand point-elasticity with respect to price as
$$\eta = \frac {\partial Q }{ \partial P}\cdot \frac {P}{Q} \Rightarrow \frac {\partial Q }{ \partial P} = \eta \cdot \frac {Q}{P} \tag{1}$$
Note that algebraically, the elasticity is a negative number, with the sign indicating the direction of influence, since $\partial Q / \partial P <0$.
The profit function of a monopolist is
$$\pi = P\cdot Q(P) - C(Q(P)) \tag{2}$$
The first-order condition for a maximum with respect to price is
$$\frac {\partial \pi}{\partial P} = 0 \Rightarrow Q + P\frac {\partial Q }{ \partial P} - MC\cdot \frac {\partial Q }{ \partial P} = 0 \tag{3}$$
Inserting $(1)$ into $(3)$ we have
$$Q + P\cdot \eta \cdot \frac {Q}{P} - MC\cdot \eta \cdot \frac {Q}{P} = 0$$
$$\Rightarrow 1 + \eta - \eta \cdot \frac {MC}{P} =0$$
$$\Rightarrow - \eta \cdot \frac {MC}{P} = -\eta -1 $$
$$\Rightarrow  |\eta| \cdot \frac {MC}{P} = |\eta| -1$$
$$\Rightarrow P^* =  \frac {|\eta|}{|\eta|-1} MC \tag{4}$$
$(4)$ is essentially an implicit relation since $\eta$ is a function of price also, but it provides a specific insight: Since we naturally expect that price will be positive, we see that we must have $|\eta| >1$: the price will necessarily be set at a level where "demand is elastic", i.e. at a point on the demand schedule where the point price elasticity of demand is higher than unity, in absolute terms.
Answer: Yes, if elasticity is greater than one we say that demand is elastic.  This means that the percentage change in quantity demanded is greater than (in magnitude) the percentage change in price.  More generally, if elasticity is e then the percentage change in quantity demanded is e times the percentage change in price.  For example, if e=0.5, the percentage change in quantity demanded is half the percentage change in price.
Answer: If it's more than one, it means that the variation of the selled quantity is greater that the variation of the price. In other words a variation in price cause a bigger variation in production. So if price goes down, consumers will increase purchases in a bigger variation: the demand of that good is more than elastic to the price. If it's 1 it's elastic. If it's less than one, it is not very elastic or unelastic.


How to ask questions about different traditions of Buddhism?

Question: What questions can and/or shouldn't we ask about other or different traditions of Buddhism?
For example, what about the question, From the perspective of Theravada is SGI considered a cult?
Comment: SGI is an organization, not a school...
Comment: @yuttadhammo I'm confused about which word to use generally: school, tradition, lineage, sect, branch, doctrine, teaching, group, vehicle. I called it a "school" because it maybe it's teaching something. Should I use a term "organization" for SGI even if that's not a generally appropriate word (i.e. would I use "organization" for Theravada)? Is "tradition" a word I could always use?
Comment: Eh, maybe you're right... I'm thinking of the corporation that spreads the religion. I guess they use them interchangeably.
Comment: fwiw their 'About Us' says, "lay Buddhist movement" and "network".
Answer: Oh, I just wrote a few words in another thread. I guess I'll just copy it here:

I'd like to elaborate on a specific question: From the perspective of Theravada is SGI considered a cult?
.
I'll leave aside what was my initial concern: that the literal question is putting a sect against another. To this end, I'll just re-interpret it as asking if "SGI is a cult".
I'm not sure what is the general feeling of the word "cult" in a different language than english and different countries. But, in english, I fail to see this word being put to use and do any better than scream for flame wars or blur even more a blurry topic (with the added feature called "strong emotions").
Yes, it's a foggy word with a foggy meaning.  This alone is already something to personally judge the value of a question (and off we go with our up and down votes), but it's game. As far as lack of strong definitions go, we are only dealing with a foggy question whose possible answers may or may not be foggy as well, and we have instruments to work these out (comments, edits, etc).
But that's just not the case here. "cult" is not just a subjective term. And when put into context (that is, in light of how this word is socially perceived), the question comes as a simplistic ad hominem. What comes next should be hardly a surprise to anyone. After all, at this point, we don't have a harmless foggy question that may or may not harvest much value. What we have is terrain for discord, for an endless debate trying to fit in the miniature spaces of comments. I meant the endless part: someone is bound to visit it years from now, and write rants against either side.
Just to make myself clear, I have no problems with making or welcoming unconfortable questions -- quite the contrary, actually. I'm all support for those types of questions here. I also don't have any specific alergies reacting to long discussions on a question or answer -- many might be quite interesting, even if S.E. discourages this kind of use.
I have two main points to bring to attention to justify this kind of question as inappropriate (in the "flag" sense, to be closed).

The question is of divisive nature (as pointed out by @Robin111 in comments). I understand that's not good either from the buddhist perspective or S.E. perspective, very basic thing, respect...
Because of (1), its actual and potential values are undermined. At the end, what have/can we learned about SGI in this thread (other than from the singular efforts of @ChrisW, at least...)?

If one is concerned about the feel of the community around this site one might as well add to the list of reasons (after all, Buddhism S.E. have been compared to Soviet Union once...).
Probably unnecessary to bring up but, naturally, if we abandon the re-interpretation above and bring back the fact that the question is asking for a sect to judge if the other sect is bananas, I believe there is a third reason to not accept such questions.
Answer: The question From the perspective of Theravada is SGI considered a cult? is 'primarily opinion-based', and not a good question (not a question which encourages helpful answers)
It's opinion-based for two reasons:

By asking for, it justifies opinion-based answers: the "Theravada perspective" is expert about the Theravada tradition, and less likely to be knowledgeable on the practices of SGI.
It explicitly excludes more expert answers: because an expert answer about SGI, from an SGI perspective and by an SGI practitioner, would be off-topic.

Ask about their perspective
If you wanted to know more about SGI then you could ask, instead, "what is the SGI perspective"? Conversely if you have already decided, that you already know enough about SGI to make up your mind, then don't ask: you needn't disguise a statement as a question!
Assuming you're biased towards (or more knowledgeable about) any particular tradition to begin with, even so if you ask about another tradition you might prefer to phrase that question as if you were a student of (i.e. trying to learn more about or clear your misunderstandings of) that other tradition.
There are maybe, for example several other questions which could have been asked instead:

Ask what 'a true Buddha' means: in the Lotus Sutra; from the perspective of Nichiren's own writings; from the perspective of Nichiren's disciples; and from the perspective of SGI.
Ask for an explanation of any specific, genuine direct quote that interests you; for example the following sentence appears in the SGI dictionary:

Nichiren is regarded as the teacher of the true cause, and Shakyamuni as the teacher of the true effect

Questions could include:
What's meant by 'true cause' instead of 'true effect'?
What's the doctrinal/literary basis for saying this? Do we understand why its original author wrote this?
Does that affect the reasons for which and/or the ways in which Buddhism is practised?
Asking about a direct quote is better than asking about a misquote, a misunderstanding, or asking about some angry paraphrase of whatever they have and/or haven't taught you.
Ask about a practice: what explanation does SGI give for chanting? What effect is it meant to have? Is asking about an "effect" even the right question to ask?
Ask about a similar practice from the perspective of another tradition: does Theravada practice chanting? For what reason / intention / effect?

C vs Pascal type discussions are banned
I recommend what Andrei said in reply to another question, Which type of Buddhism is for me?

I'm afraid this will be like comparative-religion questions, answers coming from limited perspectives of mostly being familiar with "my" school and assuming it to be better ("truer") than others. If we assume that what type of Buddhism is better for you depends on you, then we could ask this as [etc.]

Also,

But you know that C vs Pascal type discussions are banned on all forums since 90s? :) The fact that question can be answered well, does not mean it will be answered well. A good question has an incline, so its answers naturally turn out good. A bad question is inclined toward flamewars, and takes extra effort and wisdom to answer well. Like that question about faith in B vs. C which I had to save.

In summary we should beware of asking questions which ask for direct comparisons of different traditions. We should especially beware of questions which ask for one tradition's "perspective" on another.
Part of what may have caused this question was the OP's reacting to some alleged claim by SGI that SGI's tradition is better than other traditions. I think that claim too is difficult to ask about well: and if you want to ask about you could ask for example, "What is good about SGI's doctrine?" or at least something more tactful than "Why is SGI's doctrine better than others?"

A bad question is inclined toward flamewars
I accept that this is a slightly artificial limitation. Even if Nichiren himself compared his doctrines with other earlier doctrines, for the sake of the "community" on Stack Exchange a question about comparisons should be asked carefully if at all.
FYI here are some highly-upvoted quotes from the corresponding policy of the Skeptics.SE site:

If someone wants to mock creationists, flat-earthers or vaccine-denialists he/she should just get a blog. This site should be objective and polite, as Robert explained in his excellent answer.
"Hostile or mocking responses to untenable claims" equals a failed site. It's really as simple as that.

Be nice.
Treat others with the same respect you'd want them to treat you. We're all here to learn together. Be tolerant of others who may not know everything you know.
    It's not optional or reserved for people you agree with; it is a basic tenet of the site. Any hostile behavior or ad hominem attacks should not be tolerated.

The community should reject and down-vote disproportionate, mocking behavior towards any opposing ideas or people in the guise of making a VALID argument.
[...] Otherwise, this site will fail.
Trust me on this one: Users will leave this site in droves if its primary purpose is for members to pat each other on the back and tell each other how smart they are. That type of clique-ish behavior starts when "the best quip" or "best put-down" curries favor and popularity from the community. Don't encourage those activities with your support. The best way to respond is with a polite "We don't do that here."
Let's keep the questions (and answers) canonical and authoritative. If you can resist the urge to browbeat those who hold opposing ideas (whether they're on this site or not), this site will thrive.
Well said. It's never reasonable to be hostile.

Summary
I suggest that all this is a reason why some questions could be closed:

"primarily opinion-based" is already a valid close reason
Questions can also be flagged as inappropriate for respectful discourse.

Perhaps some questions should be closed until they're made more neutral (unbiased) in tone.
A possibility is:

Put the question on hold (five closed-votes by community, or flag it for a moderator to close)
Optionally create a topic here on meta to discuss how to improve that question
Optionally if (after) it has been edited/improved, then it can be reopened (five reopen votes by community, or reopened by moderator)
Comment: "Ask about their perspective" is right. I was lazy in creating the question but I can definitely break up my conclusive, loaded question about SGI into several questions or one long, thorough one referencing their source materials...
Comment: Thank you. I don't know whether there are any SGI practioners reading the site; but there may be in the future.
Answer: I've closed the question as "off-topic", rather than opinion based. It doesn't exactly seem opinion based, since I think there could ostensibly be a set of criteria by which a specific religious movement could be reasonably labelled a cult. I don't think such labelling has anything to do with Theravada Buddhism, or any Buddhism.
A part of me is concerned with censorship - obviously censorship of hate-based content is perfectly fine, but I'd like us to keep open the potential for asking tough questions like the one asking how godless Theravadins replace god. Suppose the question in question was worded "How does SGI defend their seemingly non-Buddhist doctrines like holding Nichiren to be the true Buddha and expiating karma through chanting a specific mantra?" Would it be a reasonable question then, and thus the offense here was to try and pit two schools of Buddhism against each other? Or do we want to avoid such pointed questions all together?
Comment: The list on Wikipedia for Schools (and Movements) of Buddhism is huge. http://en.wikipedia.org/wiki/Schools_of_Buddhism. What is and isn't Buddhism is likely going to vary by whose answering that question. I think the acid test for a question for this site is if the person is actually seeking information or looking to push their own viewpoints.
Comment: An example of a question from a person looking for information: "Does the belief (or practice) of the School of X reconcile with early Buddhist teachings? Or is this a point of contention between the schools?" An example of a person pushing their own viewpoint. "Is School of X wrong because they believe Y?" Or "Is School of X a cult because they believe Y?" Skillful editing can probably turn a problematic question into one that facilitates respectful exchange.
Comment: Well, "How does SGI defend" implies that it's being attacked,  and "their seemingly non-Buddhist doctrines" implies that their doctrines seem non-Buddhist. Removing those and any similar words from the question, and just asking about "a true Buddha", "Nichiren", "karma", "mantra", would make the question more neutral. Also "pitting two schools" doesn't seem right: the "godless Theravadins" question is addressed to Theravadins, not asking for "theists' perspective on Theravadins". And "cult" is just a vague word as well as being vaguely rude, so it's unclear what it's asking.
Comment: So I think that particular question was "unclear", and "primarily opinion-based", and "inappropriate for respectful discourse".
Comment: I guess you're right... the word cult itself is too problematic.  But how do we approach the issue of what is and what is not Buddhist?
Comment: If someone answers referencing a teacher who claims to be Hindu, I point that out in a comment (or flag it); but if a question is about a Yoga teacher who says they included Buddhist influences into their meditation curriculum, I don't complain. How about allowing questions about any tradition (or culture, or literature) which self-identifies as "Buddhist": would that cause problems? If [Christians share](http://meta.christianity.stackexchange.com/q/3) a site, I'd like to think that Buddhists can as well (SGI are mentioned on Wikipedia's [Buddhism](http://en.wikipedia.org/wiki/Buddhism) page).
Comment: @ChrisW no, I suppose not.
Comment: There's an old [Robustness Principle](https://tools.ietf.org/html/rfc761#section-2.10) for computer protocols: "be conservative in what you do, be liberal in what you accept from others". So permit a wide range of questions (including other schools), but try to be careful to [stay on-topic](http://meta.buddhism.stackexchange.com/q/100/254) when answering them (i.e. answer within the context of the question).
Answer: Any question can be asked as long as it's asked respectfully and objectively and fits standard SE criteria for questions. The problem with the question we're discussing is that is was framed neither respectfully nor objectively.
People with little or no knowledge of Buddhism may come to this site for information. The tone set on a site called Buddhism.SE can shape opinions of newcomers to Buddhism. Are we practicing Right Speech? (Granted it's a site about Buddhism, not a Buddhist site; but the majority of active participants in the site indicate in one way or another that they are practicing Buddhists and as such our behavior reflects on how Buddhism is practiced in daily life.)
We have not declared some traditions of Buddhism to be valid and others invalid. That was one of the first issues discussed on this site; whether to have separate sites for separate sects and the idea was immediately discarded as impractical. Theravada and Mahayana
I did not vote to close the referenced question. My reason for this is that the OP has formed a pattern of divisive input to this site and it's something we should address and determine how we will deal with a situation where a contributor has an ax to grind and uses the site to do this. Simply closing the question without addressing the underlying "agenda" issue would only result in more questions, answers, comments in the same vein. Following are some of his contributions to the site:
From: What is meant by Namu Amida Butsu and also Nam-myoho-renge-kyo?

...not someone who is practicing to achieve one's own salvation. To practice anything after the salvation-event is to not understand that event." I don't like this. It smells of the same Christian "we are already saved, you don't have to do anything but come to church and donate" nonsense. There are so many practical Right Speech and Right Livelihood elements to the orthodox Buddhist path that are eliminated in these newer "Buddhism"s. Also, this is not a good example of Pure Land Buddhism. For a good representation I reccommend the book "The Secrets of Chinese Buddhist Meditation." –  Ahmed Jan 11 at 7:08
@Methexis How can a sect say say that the Buddhadharma is not necessary with ____? Maybe it can say that with the inclusion that one already studied and practice the other things but to have a special sect devoted to this practice... I hope the people being introduced to this practice already came from a background of heavy emphasis of Buddhist studies (cosmological, dharma, etc.) and sila and are not your typical old people scared of death and just making prayers and vows to squeeze their way into heaven... Although that still has some minor merit. –  Ahmed Jan 13 at 21:04

From: Why can't a Buddha's power just save us already? Like Jesus

@Robin111 The religion the we all practice, Shakyamuni's Buddhism has as its basic tenet self-experiment and the Four Noble Truths. Any sect, which goes against those foundational rules saying they are not necessary, is no longer defineable as Buddhism. Similarly, there are extremist sects within Islam and Christianity, which have veered far off the basic agenda that the founders established. Thus, the original religion gets blamed for the sect's idiosyncrosies, ignorance, and even pathological actions (e.g. terrorist actions). Do you see the principle? Do you see the parallel? –  Ahmed Jan 12 at 17:57
@GottfriedHelms I am over this argument. You guys are not going to get it and in the end it comes down to my "rude" style of writing doesn't it? Which by the way is perfectly precise. "Scam" is denotatively the exact word to describe these Latter-day-Religious-Sects which use the Buddhadharma's name yet being cheat you entirely of it by saying studying the rest of the Buddhadharma is not necessary, pandering to old/weak people who do not wish to study Buddhism like the science that it is. –  Ahmed Jan 14 at 16:29

I'm not trying to be Pollyanna here. But it's a slippery slope to start rudely criticizing the traditions that other people hold dear; both Buddhist traditions and religions outside of Buddhism. It's also jarring to read his comments that imply that certain schools of Buddhism are for the old, the weak, and the less intelligent.
Perhaps this should be a different thread. But this issue in it's entirety is something that should be reviewed to determine how we move forward.
Comment: If you flag these sort of comments, we can (and probably should) delete them.
Comment: Will do. Thanks. :)


Cleaning homegrown vegetables prior to consumption

Question: I grow vegetables and fruit in my backyard.  Everything is grown organically so I don't have any concerns with pesticide or chemicals on my edible fruits and vegetables.  However, they do get exposed to insects and other animals (squirrels).  I am not sure if insects lay eggs on my leafy vegetables or some of them get eaten by caterpillars.  Whatever the case may be, I would like to know what care I need to take prior to consuming these fruits and vegetables.  I am growing leaf vegetables (lettuce, kale), root vegetables (beet, carrot), tomatoes, zuccinni, cucumbers, peppers, apple, pear, grapes, etc.
Answer: Just wash them all in clean tapwater - the hardest are the leafy greens, so the way to do that is immersion in a sink full of water, then picking out the leaves and running them directly under the tap, at the same time as inspecting for eggs and caterpillars. Then a salad spinner if you've got one, or just leave them to drain down in a colander. You may need a vegetable scrubbing brush for the carrots if you're not going to peel them before cooking.
Answer: If you subscribe to the hygiene hypothesis, then there's no need to wash anything.
If you're not keen on eating insects and eggs, then a good immersion in warm salty water removes insects, and inspection is needed to remove eggs.  Insects are a good source of vitamin B12 for those who are strict vegetarians.
Comment: @JStorage I just cut off obviously damaged and/or decayed parts, and eat the rest. And I've survived 60+ years like that with no major medical problems so far! Follow basic common sense - if the parts that you intend to eat look OK, smell OK, and taste OK, they are unlikely to kill you.
Comment: I am intrigued by hygiene hypothesis.  Explains a lot of things.  BTW, how do you deal with leafy vegetables that have been partially eaten by caterpillars or squirrels. Are they safe and edible.  Same for apples, zucchini that has been bitten partially by squirrels
Comment: @JStorage we eat leaves that have been partially eaten by caterpillars.  No squirrels or other rodents here that eat our veges but I guess I wouldn't want to share my plate with them!


Why can't dry soil absorb water well?

Question: I have often heard that particularly dry soil cannot absorb water well. This was often associated with flooding after a long dry drought. I couldn't really imagine it, but yesterday I saw for myself how water that I had poured on very dry ground did not seep in but remained on the surface in a thick puddle. If the same soil was moister, it absorbed the water without any problems.
Comment: Try adding a little detergent to the water
Answer: It's due to surface tension and adsorption. If you take a beaker of water you will see how the water clings to the glass sides of the beaker in a meniscus. At a molecular level the surface is really flat and will resist any attempt to break through that surface. Take a small quantity of dry peat and toss it on the surface and surface tension will keep the pieces afloat rather like insects are able to ride on the surface without getting wet. When a tap drips, the droplets come out rounded - the surface tension is pulling the small quantities of water into a rounded form since that is the optimal response in the presence of gravity and atmospheric pressure.
Chuck a heavy stone in and of course it gets wetted pretty fast - but does it? Look closely and you can see that air bubbles can form. The stone may not be completely wetted.
One way to destroy the surface tension effect is to heat the water. When horticulturists want to wet dry peat based mixes they often do so with hot water. As the water heats up water vapour starts to rise and eventually steam which means the surface is really turbulent and cannot behave as it does when cold.
Previously wetted material allows more water penetration faster because the new water joins with the old readily. If I add more water to my beaker of cold water the two waters mix very easily.
In addition there is the effect of adsorption (as opposed to absorption). The solid materials basically refuse to be wetted and put up their own molecular surface resistance if they are really really dry. Eventually this breaks down and once wetted the phenomenon changes to hanging on very tightly to the water in its immediate presence.
Comment: Well stated! I'll add that commercially available cactus are often in a peat-based soil mix. Once it dries out it's extremely difficult to rewet. Booo peat! (as a potting media)
Comment: @Kur It's a funny concept but in general everything resists change or deviation from equilibrium. Even on the molecular level change (without energy dissipation) can only occur if the resulting bond is stronger then the previous bond. Another example would be inertia which is an objects resistance to change in motion. Even people and animals resist change, life's funny that way.
Answer: Whilst agreeing with the answer already posted, I'd add that the problem of hydrophobic soil is exacerbated if it's low in organic matter/humus content. If the soil has regular applications of composted materials (garden compost, composted manure, spent mushroom compost, leaf mould, that sort of thing) the humus content will be higher, and less prone to becoming hydrophobic during drought conditions. Heavy clay soils particularly benefit from frequent emendment with composted materials if they are likely to be in drought quite often. https://soiltosupper.com/simple-ways-to-fix-dry-garden-soil/

Why can't dry soil absorb water well?


Burnt out usb ports

Question: I accidentally burnt out my Raspberry Pi 3 Model B's 4 USB ports, and I have a touch screen that I cannot currently use because of this. The touch screen plugs into the GPIO pins, but requires a driver for it. I'd like to use the USB sticks, SD to USB adapter and the keyboard and mouse. I'd like to get a NDS emulator on it, but that requires the USB port for a SFC to USB adapter. Sorry if I'm going on too long, but I have two questions: 1. Can I replace the USB ports on it? and 2. Can I use the last 14 GPIO pins (pins 27-40) for USB, and if so, how?
Answer: Most likely when you burnt out the USB ports, you actually fried the USB circuitry on the LAN9514 combo USB+Ethernet controller.  If that is the case, then you won't be able to fix it unless you have another 9514 chip and the equipment necessary to remove and replace surface-mount electronics. (Eek!)
Regarding using GPIO pins as USB, you would need a full USB software stack with the correct drivers. Unfortunately those drivers cannot exist because the Raspberry Pi's GPIO pins are 3.3 volts, and the USB specification requires 5 volts. The amount of current supported by GPIO is also significantly smaller than needed to run USB as well.
So as much as I hate to say this, you may have to go get another Pi to solve this particular problem.  I really love your way of approaching this problem by not giving up though!  Keep up the creative questioning of how to potentially re-use things that are available to you (like the GPIO ports)!
Take care and good luck!
Comment: I'll try to plug the Pi into the ethernet on the router. If that doesn't work, oh well, if it does, why does the ethernet work but not USB?
Comment: The ethernet circuitry in the LAN9514 is isolated from the USB circuitry. It also has some overvoltage/overcurrent protection built into it to help with PoE (Power-over-Ethernet) support.  My best guess is that when you fried the USB circuitry, the Ethernet circuitry on the same chip remained uneffected because of this built-in protection  mechanism.
Comment: The Ethernet works, but the USB doesn't. So that makes sense. So it does look like I need a new Pi.
Comment: @CratStrat Sorry to hear that.  I hope your new Pi solves the problems for you!  Keep up the creative thinking!

Burnt out usb ports


403 error with nginx + passenger + rails 3

Question: I have simple application which works well on Apache but gives me error 403 after moving to Nginx.
Here is my configuration:

server {
    server_name  myapp.com;
    access_log  off;
    root /home/www/myapp/public;
    autoindex on;
    passenger_enabled on;
    rails_env production;

}

Nginx is running from www-data user which has r+x permissions to all the folders on the path to the application.
Nginx is 0.8.54 and Passenver is 3.0.5.
Any ideas what can be wrong?
Obviously no reasonable errors in nginx log file (I increased logging level to maximum) and also nothing in rails log files.
Answer: You're missing the http port:
server {
  listen 80;
   ...
}


Splitting Movement and Support

Question: In the following example from the rulebook, Tyrell attacks Blackwater using two knights from the Reach with support from a knight in King's Landing, resulting in an initial combat strength of 7. If Tyrell instead attacked with one knight from the Reach and moved the other to King's Landing, does the second knight contribute to the support order there (is the combat strength still 7)?
Answer: The key idea here is that you first resolve your march order. Then, if you march one or more of yours units "into an area containing units from another House, combat ensues" (rules, page 17).
So, you must first move all your units to the areas that you want. Then if you did move into an area that contains units from another House, you resolve combat. This means that units moved into King's Landing would be able to support the combat as if they were there in the first place.
Answer: We always move the non-combat pieces first ( knight to king's landing ) then perform the attacking move.
Combat strength stays the same.
There is no state of a piece in which it would not affect the battle, e.g. 'in transition'.

Splitting Movement and Support


Facebook photos not showing up on lock screen

Question: I want my phone to show Facebook photos on the lock screen but it just shows a blue screen with the Facebook logo. It used to work so I don't know what has changed. How can I get it working again?
Comment: have you tried reinstalling the Facebook app? have you recently installed any (OS) updates?
Comment: Yep - I think it must be some setting I've got wrong - maybe on fb. It started on my old phone - 520 - then got a new 530, restored all my settings etc from the old phone and this transferred to the new phone. Thanks for your help, this is driving me crazy!
Comment: Just a wild guess, but check your Facebook privacy settings. Sometimes apps can't get the data they request because those are too strict.
Answer: I had the same problem after Denim-upgrade. I have Lumia 820 with memory card & had transferred my Facebook there. I uninstalled it and downloaded it back to my phone memory. That solved the problem.
Answer: This can happen when Facebook is moved to the SD card. I just moved it back to phone memory and the problem was solved.
Answer: no to all that. settings-> lock screen-> set background to Facebook photos or something else. the end
Comment: How I've read the question; that's what littleskate has done, but it's not working, and your answer doesn't include any details of things to try if it doesn't work?


Should questions about non OS X specific command-line tools be allowed?

Question: The question in question is Extracting latency value from output of ping.
Should questions like this be considered off-topic? Aren't there other SE sites dedicated to these types of questions?
Answer: From https://apple.stackexchange.com/help/on-topic:

We do encourage AppleScript, Automator, and UNIX shell scripting questions as well as how to use tools like Xcode for non-language specific tasks

So yes these kind of questions are absolutely on topic here.
Now, if the question is: Should we allow them in the future? Opinions may differ, but from my point of view it's often rather difficult to differentiate between scripting questions around specific OS X features (e.g. how can I list all connected USB devices) and questions which are generic enough to belong to another site (most probably Unix & Linux). Also, if the question does require a very detailed Unix knowhow not available on AD, we still can migrate it over if it doesn't get answered in due time. In other words: I don't see a pressing need to change the policy here.
Comment: Just as an example: http://apple.stackexchange.com/questions/225026/backward-compatibility-of-shell-scripts is well-suited for both sites but on U&L it would have been not been answered at all or with an answer listing all the subtle differences of bash since before the beginning of time :-)
Comment: That makes a lot of sense. Thank you.
Answer: Just because command line tools such as these are also used in other OS, often for much longer than they have been in OS X, doesn't mean they are not a part of OS X, provided, supported, licensed and documented from Apple directly.
A lot of the time where this sort of thing could be applicable to many SE sites, it comes down to where the OP feels most comfortable asking. If someone has a question on ping or similar, but they happen to be using a Mac, then I'd feel bad pointing them at SuperUser where they might get savaged (for want of X better phrase)
Comment: Also: being BDS-based means OS X's pedigree is quite long, time-wise, as software goes.
Comment: "savaged" = treated normally on SO haha *mostly kidding*
Answer: As a Mac user who mostly "lives" on Unix & Linux stackexchange, I thought I'd provide my viewpoint on this.
Questions about command line tools (that aren't Apple-specific) are perfectly on-topic both here and on Unix & Linux.  Most such questions are also on-topic for superuser.com.  The main difference is the type of answers you're likely to receive.
Realize that a huge percentage of Unix & Linux questions relate to the command line, and frequently active users include many professional sysadmins, not to mention several people who actually write shells.  This means that a well-written question about a command line tool may get a much more in-depth answer than you're likely to find on any other site.
Now, some people (most computer users, actually) aren't interested in really learning the command line; they primarily use a GUI and if they ask a question about the command line at all, what they would actually prefer is a simple command that they can paste into their terminal, which will do what they want, and let them get back to using the GUI.  (This is fine, of course; not everyone needs to learn the command line.  We have those people at Unix & Linux also.)  This isn't the sort of answer that's considered "good" on U&L.  It's probably not considered "good" here, either!  But in-depth answers about the command line are really the norm on U&L.  So if you have a tricky, highly technical command line question, U&L is (in my opinion) the best place possible to ask.
However what goes along with this is possibly less lenience for newbie questions.  It's really hard to describe this, though, because no one is rude about it...I've rewritten this paragraph five times and I still can't quite nail it.
I suppose the closest I could come is to say: imagine the response of a bunch of (polite) doctors who were sitting and chatting if you came in and asked, "I forget, is it the ears or the eyes that are the 'sight' organs?"  They'd answer you, of course, but they would undoubtedly be amused and might even chuckle at your naiveté.  :)
So really, ask where you feel comfortable asking, and where you think you will get the best answer.  Either way it's on topic.
Answer: My two cents on this, since Mac OS/X is based on BSD there is enough subtle difference between how commands work in a OS/X Terminal vs. a Linux-derived terminal. Because of this I would recommend allowing general purpose OS/X Terminal command questions here.
Having said that, when I worked for Applecare, first-tier support advisors are NOT allowed to freelance on the command-line, they are only allowed to use terminal commands if they come from an official Apple support doc, and that's rare!
Once I graduated to tier 2 ("Senior Advisor") I thought, woohoo I can solve problems a lot faster! Well there was more freedom (and depends on your manager) but there was still a strong emphasis on solutions the customers could understand that used GUI tools. True, customers get ahead of support agents and can do some damage when they "know enough to be dangerous," so keeping them away from the command line was generally the right thing to do ... until I talked to a customer who I knew was smarter than me :)
Well I only rehash that (no longer work there) to point out that Apple culture is, as noted in other answers, generally to stay away from the command line.
But having said all that my original point stands, and there is enough difference between BSD and Linux that the content can be reasonably dissimilar. I come from SunOS and still type ps -auxww, thankfully in Linux that still works. There are whole articles written about the differences in how ping works ... on other SE sites :)
(another interesting BSD link here)


What is the difference between mathematical reasoning and philosophical reasoning?

Question:
Please see question in title.
Why isn't philosophy considered to be a branch of mathematics?
Is study of anything not a branch of mathematics, vague and imprecise?
Comment: Tried to cleanup and focus on the primary question -- please feel free to clarify your intent; it will help improve the chances of getting a great answer if you can explore a little more of the context and motivations behind your question. **What might you have been reading that's made this an important problem for you in your study of philosophy?**
Answer: Philosophical arguments are made mathematical all the time.  Its why you will see First Order Logic symbols thrown around on this Stack Exchange.
I think the big difference between mathematics and philosophy is that mathematics tends to start from something like a formal system, and see how much can be proven within it.  Philosophy approaches the question of "what formal systems are right?"  If a formal system proves something non-intuitive, Philosophers will immediately start studying the axioms of the formal system to see if they may be missing something.  Philosophers admit more shades of "color" into their arguments than mathematicians can.
There are absolutely places where they blur.  Consider the huge debate between ZF and ZFC in set theory.  If you look at the wording choices, they are hard to distinguish from a philosophical debate.  At the extreme, Proof theory and Model theory are almost more philosophical than mathematical.  A read of the consequences of Tarski's definition of Truth is really almost entirely philosophy with only a pinch of Math for seasoning.  Russel and Whitehead's "Principia Mathematica" could qualify as an attempt to make a religion out of pure math.
On the other side, philosophical issues like Xeno's paradox were deemed "insufficiently explained" until Calculus turned his philosophical argument into a mathematical argument.  Mathematical inconsistency is often used to refute a position by using the strict meanings of  FOL symbols like "AND" and "OR."  These are used to force philosophers to identify where their arguments diverge from the world of mathematics.  Turing's mathematical work strongly influences modern philosophy, especially with the development of AIs continuing as it is.
The real true difference is probably more linguistic than anything else.  There is clearly a continuous gamut from pure philosophy to pure mathematics.  However, we as humans tend to draw lines between terms because that makes them more meaningful.  Mathematics tends to be colder than philosophy.  Something is either formally proven, formally disproven, or an interesting outstanding problem.  Philosophy is more open.  Two philosophies may persist for centuries, not because nobody disproved one of the, but because people like both of them.
I think Philosophy is more willing to accept mathematics.  However, mathematics avoids associating with philosophy except under well controlled conditions (such as those needed to support the richness that explodes from Formal Systems).  This could account for the asymmetry in terminology you see.
Note: I say nothing about philosophers and mathematicians.  The people in each group are as complicated as any person.  I'm just talking about the topic described by the words.
Comment: My favorite is physicalism vs idealism, the two extremes of body vs. mind.  There are philosophies which assume everything is made of matter, and thought is just a quirk of matter; there are philosophies which assume everything is made of thought, and matter is simply an illusion.  In the middle are the dualists, which assume some things are matter, some things are thought, but the devil seems to be in the details with those theories (I particularly enjoy the philosophical debates regarding p-zombies).
Comment: Thank you for your reply. You say:_ ". Two philosophies may persist for centuries, not because nobody disproved one of the, but because people like both of them."_ Could you give me an example of any such two conflicting but simultaneously totally popular philosophies? I assume that for any two such philosophies to exist, these would need to base themselves on different formal system axioms.
Comment: Sure, but how do you define matter and thought so that they are part of the same universe? If you don't, then I don't care whether you call what things are made of: matter and thought from your sentence look just like they are used to describe the same identically equivale nt world, just that one is made out of x and the other out of y, and x and why look the same except for their name. I think I'm falling to understand.
Comment: Philosophy is bound by "us," which is intentionally ill defined, so any definition we choose must at least resemble what the native language word means.  I'd recommend looking deeper into the philosophy on your own, for there are many arguments besides those I know.  However, the classic example for using those definitions is the task of defining morality.  We find that the physical world is bound by the "laws of physics."  Objects fall at the same rate, combustibles burn, etc.  On the other side, we find concepts such as "good" and "evil."  Those words are virtually universal in humanity.
Comment: They are so prevalent that they are considered "cultural universals."  And yet, as hard as we try, we find we cannot seem to find a physical law behind "goodness."  In fact, a massive portion of the population (somewhere between 92 and 98% of the population, if Wikipedia is to be believed) belives in religions.  Religions are almost all founded on ideas of "good" and "evil" or similar issues.  How is so much of society founded on something which gives the appearance of not being bound by physics.  Philosophy digs into this question, asking more pointed questions.  One of the long standing...
Comment: ...questions regards "qualia," the measure of sensation.  How do I know the qualia I call "red" is the same qualia as you call "red?"  There's clearly more to that sensation than is captured with mere physical notations (so many pW of electromagnetic energy with X frequency), but we lack an agreed upon way to tie the physics to the thought.
Comment: These matter because, for many people, the "meaning of life" changes if the world is purely made of material, or if the world is purely made of thought.  So people seek to make sense of the gap between them, and that is where Philosophy makes its home.
Comment: @JohnSonderson Free Will v Determinism is the classic case of popular conflicting philosophies. In summary form the two arguments are as follows. 1) I am responsible for my actions but can only be so if my actions are free. Hence there is free will. 2) All actions are physical events. All physical events are caused. Therefore all actions are determined and hence not free.
Answer: I suppose it is true that there could be more activity towards taking philosophical arguments and trying to turn them into mathematics. The use of first order and modal logic in analytic philosophy is the most well-known attempt to make such a connection, and the rejection of much "continental philosophy" derives, to some extent, from the perceived impossibility of ever making any precise sense of it.
On the other hand, the mathematics traditionally considered in the spirit of analytic philosophy is typically rather simplistic compared to what practicing mathemacians care about. Maybe one might argue that making philosophical statements precise by means of first-order logic comes at the price of restricting oneself to a shallow fragment of philosophy.
However, there is a alternative proposal, which is little known, but deserves much more attention. Over the decades the mathematician William Lawvere had been proposing, more or less implicitly, that some key structures of just that Hegelian philosophy whose rejection is traditionally regarded as a prerequisite for having any precise argument at all, does have a very useful formalization -- not in first-order logic but in a richer categorical logic, in something one might call modal type theory. This subsumes modal first order logic, but is richer, in particular because there are adjunctions in this context which are not just Galois connections. Lawvere and others observed long ago that the concept of adjunctions formalizes aspects of duality that prevail through much of philosophy, see Lambek 82 "The Influence of Heraclitus on Modern Mathematics".
Lawvere has taken this to the point of concretely proposing formalization in categorical logic of the Hegelian concepts of unity of opposites and Aufhebung ("sublation"), concepts that are typically believed to defy all common sense. Turns out they do make precise sense, when regarded from a suitable perspective of mathematical foundations.
And this works rather well on both fronts: on the one hand, it does arguably capture some of the more mysterious sounding philosophical statements and illuminate them. Lawvere indicated some bits of Hegel's "Science of Logic" that are amenable to his formalization. I took the liberty of trying to elaborate on this a bit more, see on the nLab the entry Science of Logic. On the other hand, this does lead to mathematic  that is of genuine interest as mathematics. In fact this has influenced some recent research that solved solved some actual open mathematical questions. I had commented on that in another thread at Have professional philosophers contributed to other fields in the last 20 years?
In conclusion, I am thinking that there is much potential to have renewed interaction between philosophers and mathematicians. It requires passing from first-order logic to type theory (and better yet to homotopy type theory) and it turns out to have something to say about just that kind of philosophy which is traditionally being rejected as unfit for precise argument.
Comment: It seems to me I am getting genuine information out of reading Hegel under this translation. For instance this proof here http://ncatlab.org/nlab/show/Aufhebung#ExamplesBecomingFormalization that certain cohesive toposes satisfy "Aufhebung" I came to only via Hegel, under Lawvere's formalization. Also the nature of the system of modalities that I am using for "differential cohesion" somehow became clearer to me after reading Hegel, that's what the diagram here is meant to show: http://ncatlab.org/nlab/show/Science+of+Logic#Process
Comment: interesting reply, thanks... it could be clearer tho, do you mean that we could end up reading hegel in these terms, or just that it could be shown that he isn't nonsense?
Answer:
why isn't philosophy just considered to be a branch of mathematics

OK I'm going to add another answer, on a different bent.
This is at bets like asking: why isn't Hindu philosophy just a linguistics that only asks about Sanskrit?
While historical and contemporary study of Hinduism is in Sanskrit, and there is something to be said for the two being inseparable, Hinduism is a body of thought which finds expression in Sanskrit but is irreducible to a scientific study of the language.
This may leave us asking well what is philosophy then, but that's nothing to be scared of.
Indeed, I personally believe that a reduction of philosophy to formal logic would be puzzling because philosophy would cease to exist. Pure logic can only answer questions about logic, not philosophical ones.

The overt intent of Logicism is to reduce all of philosophy to
  symbolic logic

Like Russell. These founding fathers of analytic philosophy

Dewey had described the writings... which sought to reduce philosophy
  to propositional logic, as "an affront to the common-sense world of
  action, appreciation, and affection".

In effect, that reduction is nowadays a straw man, I believe. I will try and find a quote!
Answer: Actually, Even though they come from two areas, I can't see any difference in these two if they are reasoning.  Mathematics may agree with this idea; but mathematicians won't. Notations and some other things curb them from transcending their subject.
Philosophical reasoning considers all the possible factors.
If a difference is essential, I shall give you one only for the essence: "One is for 'Yours' and the other is for 'You'--the eternal 'You' also."
Now you can find out the essence from my last statement itself. But don't forget the first statement.
Answer:
why isn't philosophy just considered to be a branch of mathematics?

As Cort Ammon said in his excellent answer in the areas of logic and set theory there is considerable overlap to the extent that differences are mainly ones of emphasis.
However there are large areas of philosophy which are completely non-mathematical.
Examples would be:
1) The mind - body problem
2) Free will v determinism
3) Ethics (How should we behave? Is it possible to derive "ought" from "is"?)
4) The nature of being (What is the nature of the universe? Is there a god? What is man?)
5) Language games (Locke, Russell, Wittgenstein, Kripke, et al)
6) Epistemology
7) Causality

Is any study not a branch of mathematics vague and imprecise?

There have been many precise answers (not necessarily correct ;-) given to some of the questions above. For example (and paraphrasing for brevity):
"Knowledge is justified, true belief" (Plato)
"Ethical behavior is that which allows us to flourish" (Aristotle)
"We say A causes B if A always precedes B, A and B are proximate and there exists a convincing explanation for the connection" (Hume)


Was Fiona actually cursed to be a human?

Question: Since her mother was a human and her dad was a frog, it makes sense that Fiona was born a half-human, half-frog hybrid, which is what an ogre is. So was she cursed to be human?
Comment: @AlexDowns by that logic, Ogres are equally likely to be hybrids of human and crocodile, fern, water snake, fish, Moss, and any number of other flora and fauna that are green and live in swamps.
Comment: Welcome to SciFi.SE! This seems like idle speculation without any backing from the films: it's shown quite clearly that Fiona was born a normal human and cursed to turn into an ogre, not the other way around, and nothing in the series suggests that ogres are human-frog hybrids.
Comment: Well, ogres are green and live in swamps like frogs and talk and dress like humans.
Comment: [Discussed on meta here](https://scifi.meta.stackexchange.com/q/11930/58193).
Answer: There is no evidence in the films to support this.

The storybooks at the beginning of Shrek 1 and Shrek 2 clearly show both Fiona and King Harold to have been perfectly human at the time of Fiona's birth.
Fiona's discussion with Donkey in Shrek 1 strongly indicates that her ogre form was the result of the curse, rather than her natural state:

FIONA: When I was a girl, a witch cast a spell on me. Every night, I become this... this horrible, ugly beast.

Fiona's entire motivation for marrying Lord Farquaad in Shrek 1 was to obtain a true love's kiss from him and break the curse. If the human side was the curse, she would not - at that point - have wanted to assume that form permanently. She doesn't become comfortable with her ogre form until she realises that Shrek loves her even in that form, whereas Farquaad doesn't love her at all.
When Prince Charming arrives at Fiona's tower at the start of Shrek 2, and encounters the wolf sleeping in Fiona's bed, he seems to seriously believe for a moment that he might be Princess Fiona in her cursed form (and expresses relief that he isn't). This strongly suggests that he doesn't know what Fiona's cursed form actually looks like, which wouldn't make sense if she was cursed to be human.
King Harold's racism towards Shrek throughout most of Shrek 2 would make even less sense if Fiona had been born an ogre. Why would you father an ogre if you hated them (or alternately, why would you hate ogres if you had fathered one)?
Comment: Note that the storybooks aren't necessarily Fiona's life, just tropey books about princesses.
Comment: Wouldn't it be possible though that Fiona was *made to believe* her ogre form was the result of the curse? This would make the opposite of your last point true because if the king wanted his daughter to become human (like he had himself), then it *would make sense* that he wouldn't like Shrek, because Shrek turned his baby girl into something he didn't want her to be: her **true** ogre self.
Answer: In addition to what F1 noted, it's worth noting that in Shrek 2 we see that Fiona's diary has her pining to be "normal" again so she can be like the other princesses (she's disappointed she can't attend Sleeping Beauty's slumber party). She then practices writing "Mrs. Fiona Charming", for comedic effect

Given Charming was expecting beautiful woman to kiss, this also doesn't fit. Clearly Charming wasn't expecting to marry an ogre.


What is the relationship between image spatial domain and FFT powerspectrum?

Question: I am trying to perform contrast-transfer-function for pictures which were recorded in defocus. To do so, I have to calculate the contrast-transfer function from the Thon rings and fit the function to 1D radial average of the spectrum. Let's say that I have a picture in spatial domain where single pixel is 1.7 Angstrom size, which gives me a Nyquist Limit of resolution 2*1.7 A. So I know, that the resolution limit in my powerspectrum will be 1 / 2*1.7A. How can I connect the radial average from powerspectrum with the resolution? That is the relation of each pixel in the spectrum to resolution? I would be very grateful for some hints! Thanks!
Answer: The Contrast Transfer Function (CTF) is essentially equivalent to the frequency response of your system.
Therefore, your question is about how to read the two dimensional Discrete Fourier Transform and how to interpret its content.
To relate what is mentioned in that answer to your specific question, consider the following CTF, obtained from Wikipedia (Axis added by me):

This is a two dimensional spectrum. If you are familiar with a one dimensional spectrum, it is as if you took that one and rotated it about the centre of the image.
Therefore, low (spatial) frequencies are towards the centre of the image and high (spatial) frequencies are towards the edges of the image.
In fact, if we take a cross section of that image (along the direction of the blue line), we see something like this:

And if we shift the origin of the spectrum to its conventional position (for a 1D spectrum), we get:

So, this now describes how well each spatial frequency goes through the optical system assuming, it is symmetrical.
To relate this to physical frequency, we have to do a bit more work. Now, this is a simple grayscale image, which means that its maximum value is 255. So to normalise the "height" of this curve, we need to simply divide by 255.
The other thing we have to do is to normalise the frequency. This image is 512x512, the DC (or, constant value) is at 0, the Fs is at 512 and the Nyquist frequency is at 256. The formula is a plain simple division of $f = \frac{k}{XDim} \cdot Fs$ where $k$ is the frequency "bin" (of the discrete spectrum) and the fractional part of this we can simply represent in the graph.
Taking all of this into account gives us:

So, now, whatever your Fs turns out to be, you can put it on the diagram and work backwards to find how much each spatial frequency gets diminished as it passes through this system.
Spatial resolution is measured in "lines" per unit of length. In your case, your pixel size is 1.7Å. The "highest" frequency (in any direction) that can theoretically go through a system that is digitised at that level is one black line of width 1.7Å followed immediately by another white line of width 1.7Å and that is one cycle of period 3.4Å.
Therefore, your Nyquist frequency is 1 line per 3.4Å or $\approx 2941176471$ lines per mm.
Hope this helps.
EDIT:
All the plots in this post were created using Octave and the following code:
<code>% Load the image processing package
pkg load image
% Load the image that was downloaded from Wikipedia
I = imread("~/Downloads/CTF.jpg");
% The image is 512x512, let's take the cross section of the image to see a slice of the spectrum
plot(I(256,:));
% Now shift the origin using fftshift
plot(fftshift(I(256,:)));
% Add normalised X and Y axis, labels, grid, etc
plot((0:511)./512,double(fftshift(I(256,:)))/255.0);xlabel("Normalised Spatial Frequency");ylabel("Normalised Transfer Coefficient");grid on;
</code>
Comment: Hey! Thank you very much for this great post. I have still some questions though:
- how exactly are you changing spectrum to conventional 1D postion?
- I have some problems understanding the equation you provided for the frequency normalization: f(new frequency) = k (which I read from the raw spectrum as a distance in px?) / Xdim(is it the dimention of the whole image?) * Fs (which is what exactly?) I am missing which of the labels correspond to the Nyquist frequency. I would appreciate some additional information about it!
Comment: Doing some simulations and playing around with the equations: f is the corrected frequency, Xdim is just the size of the image in one dimension and Fs looks to be the final resolution limit. I will try to implement this approach to my fitting script and see how this will work. Thanks!
Comment: @Dawid Glad you found it helpful, please see updated post for all the code that was used to generate these plots. You might have to do a bit more reading on some basic image processing stuff (e.g. shifting the FFT origin is a standard operation). $k$ is the FFT bin, literally here the `x` position of the cross section, XDim is the dimension of the section (here 512), I am working out Fs towards the end of the post. I don't understand the question about "labels" (?).


Loud thumping sound coming from dash when turning key

Question: I have a 2010 Ford escape and just noticed this morning that when I turn the key, there is a loud thumping noise coming from the dash. It only thumps about 4 times then is done. It doesn't do it when my car is running or anything, only when I first turn the key, before even turning on the engine. It isn't battery related, it's more of a "thumping" than a "clicking" sound. I raised my hood to make sure it's not coming from the engine or anything and it is definitely coming from the dash part, by where the air comes out and hits the windshield. It makes the sound whether I have my air on or not....air still works fine. What could this possibly be? It wasnt making this sound last night.
Comment: Welcome to Motor Vehicle Maintenance & Repair!
Answer: Consider to check your dash settings for air flow and cooling or heating. Attempt to narrow down the focus by changing one setting at a time. I suspect you may be hearing duct work flaps or closures being activated without sufficient vacuum from the system.
If your dash control settings are commanding a flap movement and the vacuum necessary to create the movement is insufficient to do so, the flap may open partially and fall back.


Find the positive integral solution of indefinite equation

Question: Equation: $X^2+Y^2=Z^2+1$
How to find all positive integer solutions to this equation.

Can you find $n\in \mathbb{N}$ such that $X^2+Y^2=Z^2+n$  has no positive integers as solutions ?
Comment: Please be polite and do not post in the imperative. What have you tried?
Answer: There is no such $n$. Rewrite as $y^2-n=z^2-x^2$. Choose $y$ so left side is positive and not twice an odd number (always possible: just take $y$ of parity opposite to $n$), every such number can be written as a difference of 2 squares. Even easier: let $x=(n^2+n)/2$, $y=n+1$, $z=(n^2+n+2)/2$.
EDIT: Concerning the first question, some of the discussion at this MathOverflow question
might be of interest.
Answer: Gerry Myerson has dealt with the second question. I will say a few words about the first.
The ring of Gaussian Integers, that is $\mathbb{Z}[i],$ is the natural place to address this question. Many algebra texts use this ring to prove that a prime $p \equiv 1$ (mod 4)
is a sum of two (rational integer) squares. The ring of Gaussian integers, is a Euclidean domain, hence a unique factorization domain. Its arithmetic is complicated somewhat by the existence of the four units $\{1,-1,i,-i\},$ and uniqueness of prime factorizations is only up to reordering of terms and multiplication of terms by a unit. It has three kinds of prime: rational primes $p \equiv 3$ (mod 4) remain prime in $\mathbb{Z}[i],$ primes $p \equiv 1$ (mod 4) are expressible as a product of two different primes in $\mathbb{Z}[i],$ so when $p \equiv 1$ (mod 4), we can always write $p = (a+bi)(a-bi)$ for coprime (rational) integers $a$ and $b$ (note that also $p = (b+ai)(b-ai)$). In this case, we have ${\rm gcd}(a+bi,a-bi) = 1$ in $\mathbb{Z}[i].$ The prime $2$ is very special
in $\mathbb{Z}[i].$ We have $2 = (1+i)(1-i) = -i(1+i)^2,$ so $2$ is a unit times the square of a prime element of $\mathbb{Z}[i].$
To solve $X^2 + Y^2 = Z^2 + 1$ in rational integers, we note the following:
(*) For any even integer $Z$, the integer $Z^2 + 1$ is a product of primes which are each congruent to $1$ (mod $4$). For note that $Z^2 + 1$ is odd, so that neither $Z+i$ nor $Z -i$ can have a factor $1+i$ in $\mathbb{Z}[i]$ (if one did, taking complex conjugates shows that the other one does, since $1+i$ divides $1-i$). If $p$ were a prime congruent to $3$ (mod 4), which divided $Z^2+1$, then in $\mathbb{Z}[i],$ we have
$p$ divides $(Z+i)(Z-i),$ so since $p$ remains prime in the Euclidean domain $\mathbb{Z}[i],$  we have $p$ divides $Z+i$ or $p$ divides $Z-i.$ But, taking complex conjugates, if it divides one, then it divides the other. Then $p$ divides $Z+i -(Z-i),$ so that $p$ divides $2i$, a contradiction (this is one way that $2$ behaves differently).
(**)  For any odd integer $Z$, the integer $Z^2+1$ is divisible by $2$, but not $4,$
and its remaining (rational) primes factors are all congruent to $1$ (mod 4).
The statement about odd prime factors follows as above, and we note that $Z^2+1$ is congruent to $2$ (mod 4) when $Z$ is odd, so $Z^2+1$ is divisible by $2$, but not by $4,$
in that case.
Returning to the original question, there are two cases to consider: if $Z$ is even, we know we can factorize $Z^2 + 1$ in the form $p_1^{m_1} \ldots p_n^{m_n}$ where the $p_j$ are distinct (rational) primes, each congruent to $1$ (mod 4). For each $j,$ we may write $p_j = \pi_j \overline{\pi_{j}},$ where each $\pi_j = a_j + ib_j$ for rational integer $a_j$ and $b_j$, and each $\pi_j$ is a prime element of $\mathbb{Z}[i].$
If $Z$ is odd, we can factorize $Z^2 + 1$ in the form $2.p_1^{m_1} \ldots p_n^{m_n}$ where the $p_j$ are distinct (rational) primes, each congruent to $1$ (mod 4). For each $j,$ we may write $p_j = \pi_j \overline{\pi_{j}},$ where each $\pi_j = a_j + ib_j$ for rational integer $a_j$ and $b_j$, and each $\pi_j$ is a prime element of $\mathbb{Z}[i].$
We can also write $2 = \pi_0 \overline{\pi}_0,$ where $\pi_0 = (1+i)$.
Hence we have (in $\mathbb{Z}[i]$), a prime factorization of $(Z+i),$ which is as unique
as it can be, which , (possibly after switching $\pi_j$ and $\overline{\pi}_j$ and relabelling), has the form $Z+i = \pi_0 ^{\delta} \prod_{j=1}^{n} \pi_{j}^{m_j},$ where $\delta = 0$ if $Z$ is even, and $\delta = 1$ if $Z$ is odd.
Then a way to solve $X^2 + Y^2$ in rational integers is to write $X^2 + Y^2
= (X+iY)(X-iY)$ in $\mathbb{Z}[i].$ If we factorize $X + iY$ as a proudct of primes in $\mathbb{Z}[i],$ we get a prime factorization of $X-iY$ by complex conjugation, and then juxtaposing them gives a prime factorization of $Z^2 + 1,$ so we can exploit the uniqueness.
Up to multiplication by a unit, we must have
$X + iY = \pi_{0}^{\delta} \prod_{j = 1}^{n} \pi_{j}^{r_j}\overline{\pi}_{j}^{s_j}$,
where for each $j,$ we have $r_j \leq m_j$ and $s_j \leq m_j.$ Taking complex conjugates
gives $X-iY$ in a similar form. Now we notice that for each $j$, we must have $r_j + s_j =m_j,$ to get the right prime factorization for $Z+i.$
Then we use $2X = (X+iY) +(X-iY)$ and
$2Y= -i(X+iY) +i(X-iY)$ to calculate $X$ and $Y$.
In summary, all solutions can be found as follows: choose any positive integer $Z$, and factorize $Z+i$ in $\mathbb{Z}[i]$. This factorization will (up to multiplication by a unit) have the form $Z+i = \pi_0 \prod_{j=1}^{n} \pi_j ^{m_j}$, where $\pi_0 = i+i$
and $\delta = 0,1$ if $Z$ is even, odd respectively, and where there are $n$ distinct (rational) primes $p_j,$ each congruent to $1$ (mod 4), such that $p_j = |\pi_j|^2$ for each $j,$ each $\pi_j$ being a Gaussian integer. We may then choose $X+iY$ to be any expression of the form $\pi_0^{\delta} \prod_{j=1}^{n} \pi_{j}^{r_j} \overline{\pi_j}^{m_j - r_j}$, where $0 \leq r_j \leq m_j$ for each $j.$ Since you insist that $X$ and $Y$ be positive, it may be necessary to replace $X$ by $-X$, etc.
Comment: I imagined OP to be asking for parametric formulas giving all solutions, like the formulas $\lbrace x,y\rbrace=\lbrace2kmn,k(m^2-n^2)\rbrace$, $z=k(m^2+n^2)$ for $x^2+y^2=z^2$. I don't know if there are any.
Comment: But your link which you edited in to your answer in seems to suggest (strongly) that there is a parametrization.
Comment: There is a parametrization, but it's a bit of a cheat, as the parameters are related by $rt+su=2$, and how do you parametrize that?
Comment: That parametrization and what I am doing seem closely related, come to think of if. Factoring $z+i$ as $(r+si)(t+ui)$ in $\mathbb{Z}[i]$ amounts to writing $z = rt-us$ where $ru+st = 1.$
Comment: Yes, quite.${}$


Is there any evidence in the Roman catacombs that the Early Church had a devotion to the Virgin Mary?

Question: Is there any archeological evidence in the catacombs of Rome that the Early Church had any (particular) devotion to the Virgin Mary? If so, what are the sources that support such a devotion?
Comment: Wikipedia suggests yes. I don't have access to any of the resources, but they might worth a look if you do. https://en.wikipedia.org/wiki/Marian_art_in_the_Catholic_Church#Early_veneration
Comment: Is there any reason why you only wish to accept Roman catacombs as evidence, or are you interested in any sources from early Christianity?
Comment: @Dan I would have to ask that as a separate question , as that would modify this one greatly.
Answer: Not prior to the 2nd century, mainly since the catacombs were not developed until then.
While there are various Christian frescos in these underground tombs which demonstrate a devotion to the saints, including the Virgin Mary, the time period for their origin would be no earlier than the late 2nd century or early 3rd, for even though Christians immediately began burying their dead in the catacombs after they became available, they did not become regularly used for worship until persecution forced them underground. The frescos did not come till later, and those that are dated are probably from the late 3rd or early 4th century. By 380 A.D., the catacombs were no longer used for meeting as Christianity became legal in that year.
So even the earliest frescos would reflect practices removed by at least a century from Christ. Yet, with other historical records it is clear that devotion to the saints, including Mary, was obviously early and seems to have developed parallel with the use of the catacombs to bury the early martyrs.
Whatever the case, since the catacombs yield little empirically of the Church prior to the 2nd century and since devotion to saints seems to be of the era of the catacombs' first use by Christians, nothing found in these tombs can guarantee a connection with the Church in its most primitive and primary state.
Answer: There seems to be little  archeological evidence of any devotion of the Virgin Mary in the Early Church catacombs. But at the same token there may be glimmers of a Marian devotion amongst the faithful of the first few centuries after the Crucifixion of Our Lord Jesus Christ.

There are many Christian images concealed within the Catacombs of Priscilla, in Rome. One of these images is the first known image of the Virgin Mary, painted around the time of Christian persecution in 170 BC. The image of Mary nursing Jesus painted as a fresco high upon the walls of the catacomb was meant to refresh the persecuted Christian's spirits and give them hope as Mary's gentle gaze encourages them. Upon examining the fresco we begin to observe the intricate symbolic details that are included. For example, the clothing worn by the women within the painting reveals to us that the woman is in fact Mary the mother of Jesus. She is shown wearing a woolen garment which was most commonly worn by Roman matrons and is also wearing a short veil that was worn by dedicated virgins. We then recognize the baby on her lap as Jesus, who is glancing over his shoulder to observe another figure painted to the left. This figure is a man who is pointing up to the star of Bethlehem, he is dressed in a cloak that signifies him as a philosopher of distinction, but there is debate on who this figure was specifically. Some claim that it is depicting the prophet Isaiah who predicted that "The Lord Himself shall give you a sign. Behold a Virgin shall conceive and bear a son, and his name shall be called Emmanuel", but others claim that the man is representing the prophet Balaam who said "a star shall come forth out of Jacob, and a scepter shall rise out of Israel". Reaching out over the prophet and Mary is a blossoming tree branch that refers to the Old Testament prophecy "The Rock of Jesse has blossomed; the Virgin has brought forth Love and Man". - First Known Image of Mary, In Catacombs of Priscilla

Earliest fresco of the Virgin Mary, Catacomb of Priscilla, 2nd century

This is the oldest known image of the Virgin Mary (seen apparently nursing the infant Jesus on her lap). It is located in the Catacomb of Priscilla on the Via Salaria in Rome. It is dated circa A.D. 150. - Foundations of Marian Devotion in the Early Church

Wikipedia has this to say about the subject:

Early veneration of Mary is documented in the Catacombs of Rome. In the catacombs paintings show the Blessed Virgin with her son. More unusual and indicating the burial ground of Saint Peter, was the fact that excavations in the crypt of Saint Peter discovered a very early fresco of Mary together with Saint Peter. The Roman Priscilla catacombs contain the known oldest Marian paintings, dating from the middle of the second century. In one, Mary is shown with the infant Jesus on her lap. The Priscilla catacomb also includes the oldest known fresco of the Annunciation, dating to the 4th century. -  Marian art in the Catholic Church
Comment: The two references you have so far both claim to be the "first" or "oldest", dates differ by twenty years (is it the same image?). By all means I hope you can find more sources. Eventually, some comment about inconsistencies seems called for.
Comment: http://www.bbc.com/culture/story/20150224-the-secrets-of-the-catacombs definitely a very skeptical viewpoint. They comment on massive destruction, and claim private ownership of the Priscilla Catacomb. They do mention the same image, suggesting a date in the third century. Proposed dates so far 150, 170, and perhaps 210+ AD.
Comment: @disciple Even 210 AD is still the early church.
Comment: One from acedemia, BAR: https://www.academia.edu/31533569/Earliest_Images_of_the_Virgin_Mary  This suggests another image (not from a catacomb) precedes our picture, though they acknowledge the two are competitors. At another place, they suggest our picture has been "debunked" as Mary -- but no reference for that.


Warning about being blocked when deleting question

Question: I have a question that I would like to delete -- not a lot of details, no votes, under 1k of views. Unfortunately, it has an (incorrect) answer, so when I tried to delete it, I got warned of a question ban.  Should I just leave it, flag it or go ahead and risk the question ban?
Comment: ...and there is a bit [more detailed explanation here](http://meta.stackexchange.com/a/168835/165773): "The folks we're concerned about are the ones who ask a question, and then delete it *as soon as they get an answer* - for whatever reasons, there are folks (and used to be more of them...) who intentionally thwart the very purpose of the site - allowing answers to go on and benefit others. It's overtly abusive behavior, and doing that repeatedly is a really good way for a new user to get blocked..."
Comment: @AndrewBarber: I'm not sure what you mean by "there is an answer is not related here".
Comment: @Yannis Shog said ["It's 30 days..."](http://meta.stackexchange.com/questions/168828/require-a-minimum-rep-to-delete-your-own-question/168835#comment497853_168835) but given that asker got warning on ~2 years old question, I guess something was screwed up
Comment: found it... sort of [cross-site duplicate](http://meta.stackexchange.com/a/230660/165773): "warning folks who try to delete their own *answered* questions would be a good idea even if the q-ban didn't exist - in many cases, this is just plain *rude!* So as of right now, anyone trying to delete their own question will see this"
Comment: @gnat There should be a time element in that, there's no real reason to warn people trying to delete a two year old question.
Comment: @gnat ahhh, hmmm... I'd missed all that!
Comment: I think you are missing something here @Dronz. People cannot delete their own questions if they have upvoted answers. This whole discussion (and the question ban warning) only applies to questions that don't have any upvoted answers (or no answers at all). In the specific case we are discussing, the answer failed to gather a single upvote in over two years. That's a strong sign that nothing of real value would be lost if it gets deleted.
Comment: The fact that there is an answer is not related here. As for should you... That's up to you.
Comment: @Yannis You wrote "there's no real reason to warn people trying to delete a two year old question", but I would say there is. As the explanation in gnat's comment you were replying to said, "the very purpose of the site [is] allowing answers to go on and benefit others". Seems to me a warning would serve that, though it might be good in that case if it said, "Are you sure this question and its answers would not be of use to others?"
Comment: I think he meant that whether or not you get a warning when you try to delete your own question is not related to how many answers the question has.
Comment: @AndrewBarber I think you're wrong. Per my recollection, Shog mentioned somewhere at MSO/MSE that ban heuristics rather heavily penalizes removal of answered questions
Comment: @Qantas94Heavy: if so, I believe he is mistaken.  I deleted a zero vote, zero answer wuestion afterwords, with no warning.
Comment: @Yannis On the other hand, some two-year-old questions and answers are as valuable as recent ones.
Comment: @Dronz Not sure what that has to do with this discussion.
Comment: @Yannis It seems I am missing something. I agree that if there's been no answer in two years and someone is bothering to delete their own question, it probably doesn't need a warning. It sure looked like we were talking about questions with answers, and for example this question ( http://meta.stackoverflow.com/questions/281399/i-answered-a-question-he-accepted-it-and-then-he-deleted-the-question?cb=1 ) seems to suggest it can be done. I'm sure I'm missing something though.  Not important. Just trying to help.
Answer: If you feel the question should be deleted, then you should just go ahead and delete it. I think the warning is a bit too eager here, I doubt anyone will miss a  question - answer pair that failed to gather a single upvote in two years.
The question ban exists to stop new users from flooding the site with low quality content. It should never kick in for someone who is following the site's rules and guidelines, and has been providing quality content for years. If it does kick in, then the problem is with the question ban algorithm.
Comment: So go ahead and press that button. Never mind us, we'll be hiding under this table...
Comment: The question ban is doing a *bang up* job of keeping low quality content from flooding in.
Comment: I'm new here and still trying to figure out the "culture".  One thing is dawning on me...  Most people might think they "own" a question they post.  I know I was in shock the first time so one edited MY post; "how rude", I thought.  I know I've also deleted posts I thoght were going no where.  Maybe it needs to be clearer you don't own what you post this is one big hive.
Comment: http://meta.stackoverflow.com/questions/281464/warning-about-being-blocked-when-deleting-question#comment135706_281464
Comment: @dan-o.  As long as it isn't doing a bang up job of keeping high quality content out as well, or more realistically, keeping out FUTURE high quality content.


office outlook 2007 not receiving from a certain e-mail address

Question: Somebody that I have regularly recieved e-mails from with outlook is now unable to send me e-mails. I know this because they CC another e-mail address I have and while I receive the e-mails to my gmail account they do not show up in outlook. Nothing has changed that I know of, and the e-mails are not being rejected and sent back to her computer. I have gone into my safe list and added her e-mail address and the domain name it comes from. Any ideas what I have inadvertaly done and how to fix it? Also they are not going to the junk folder.
Comment: What type of email account do you use? (POP, IMAP or Exchange)
Comment: it is a pop/SMTP account
Answer: Check not only the "safe list" inside Outlook, but the white list from the email provider. For instance, if you're account is a GMAIL account, log into gmail and look for the Spam folder and see if the message went in there.
Often, if emails quietly dissappear and you aren't notified of it, they have been tagged as spam somewhere along the line. Think about different steps in that line - the email provider (yahoo, gmail, comcast, att.net etc.) and check out those spam settings.


Is it safe to drive this car (pics; broken shock; negative camber)

Question: Would it be safe and not cause further damage to the car if I were to drive it 1/4 mile on a dirt and somewhat bumpy road? (The towing company under my policy won't go on dirt roads.) I've been told that the issues is that the shock is broken.
Comment: Is the upper control arm broken also? If so, I don't think you will make it.
Comment: Safe is one thing. You could drive just about anything at 2mph *safely*. This, however, would probably not make it. As @cano stated ... where's the upper control arm? I see what might possibly part of it in the background behind shock, but that's some ugly damage. If you did drive it, the tire would be rubbing against the shock and what's left of the upper A-arm. Hopefully this isn't a front wheel drive vehicle (looks like a 4x4). If so, ensure you DO NOT have this in 4wd, nor that the front hubs are engaged (if you have to do so manually). This is just pure ugly.
Comment: Given the angle of the wheel and driveshaft I would not drive it. If the only thing broken is the shock absorber then why not take the new shock and the tools and a decent jack & stand and make a better than temporary repair where it is now - then take it to the shop to make sure all is correct.
Comment: What kind of tools do you have with you?
Comment: Do you have a trail jack? If so, I may have an idea for you, but it would take some ingenuity and perseverance to make it work.
Answer: Not only is the shock broken but the upper suspension control arm has collapsed too. Driving the vehicle would likely cause further damage to the tyre, CV unit & possibly front differential/bearings too as there is a lot of force being transferred through that drive shaft into the front diff with the upper control arm collapsed.
Unless you have some sort of trolly to place the front right of the vehicle on to, your only other option other than a front end lift is to put a lot of weight onto the rear left of the vehicle to help unload the right front wheel. Then perhaps an attempt at moving forward might be possible, but do it very slowly.
Answer: Is it safe? Safe is relative, but you won't be going far in that car anyway - it's broken as broken can be.
I assume you're getting the car towed to a garage for repairs. I'd suggest getting a pair of front shock absorbers online, and then paying for a mobile mechanic to come out and install them for you. That should get it moving again, and the mechanic will be able to tell you what else is broken. After those repairs, you will be safe to drive it to a garage for an alignment.


How did the Earth Dragon Balls revive everyone killed by Frieza?

Question: The Earth Dragon Balls were only capable of reviving one person at a time and that too, only once. Then how did they revive Vegeta and all the Namekians on planet Namek when the dragon was asked to revive everyone killed by Frieza?
Comment: I can understand your confusion. you would think that the huge dragonballs can do more than the small ones. But nope. Earth dragon balls(Piccolo OP) can even wish an entire planet back to life whereas the namakean ones cannot.
Comment: At the beginning of the Namek Saga they said Piccolo was one of namek's more brilliant minds and made the earth dragon balls more op than the original ones on namek.
Comment: You are mixing the powers, Namekian DBs could revive any 1 individual any number of times. But the earth dragonballs could revive any number of individuals just once.
Answer: Um... they weren't limited to only 1 person at a time.
It was the Namekian Dragon Balls that were limited to 1 at a time.  The Earth Dragon Balls had no such restriction. In fact, they were used before to revive multiple people that Piccolo killed at the end of the Piccolo saga
Further reading : Dragon Ball


What causes these white rings in images taken with Contax T2? Is there a fix?

Question:
What are these white rings that have been showing up on my film? How do I prevent them from showing up in images? How can I remove them from existing images?
Comment: Possible duplicate of [What is causing the strange lighter circles in images taken with my Canon 15-85?](https://photo.stackexchange.com/questions/46049/what-is-causing-the-strange-lighter-circles-in-images-taken-with-my-canon-15-85)
Answer: The rings may be a reflection of your lens off the back of a low-quality UV filter. (Look carefully, there are multiple rings.)  You may confirm by retaking the picture without the filter. Avoid by taking pictures without the filter or by using a multi-coated filter.
See What is causing the strange lighter circles in images taken with my Canon 15-85?
Another possibility is a type of lens flare. But I doubt it because it would be multicolored, like a rainbow, if it were flare.  Not white.
Remove from existing images using the usual photo editing techniques (cloning, healing, burning, content-aware fill, etc).
Answer: Looks like reflections off some portion of the imaging path - lens hood, filter, the part of the lens barrel that protrudes beyond the front element, maybe even something internal... Could be flare off something, too, though.
EDIT: After looking at an image of the camera (I wasn't familiar with this model), I suspect the most likely of the above is that it's a reflection off the black plastic (metal?) bevelled ring that protrudes in front of and surrounds the front lens element.
If that's the case, fixing it might require shooting with the brightest lights (the sun in your sample image) behind you, instead of, as it appears, in front and to the left, so that it can't reflect off that bevelled surface.
Removing it from existing images is probably best done by cropping. You might be able to clean it up somewhat with Photoshop, etc. but removing it completely and perfectly would be difficult.
Answer: Agree w/ Twalberg that these look like reflections. To solve in this particular image, the healing brush should take care of the lower left and lower right sides. The upper right can be done via a finessed use of the clone stamp.
To avoid in the future, if the sun is in front of you, use your left hand to shade the lens (make sure your hand isn't in the frame, but casts a shadow on the lens). This should solve your reflections issue.


Produciton of EM waves with differing wavelengths

Question: Sun is the major source of electromagnetic radiation. Then if the source is the same, how are different EM waves with differing wavelengths produced?
Comment: http://en.wikipedia.org/wiki/Black-body_radiation
Answer: Monochromatic light is only produced if the charge motion in a source has a strictly periodic motion with a fixed period. Sun has many different charges moving aperiodically, so it produces the whole spectrum of frequencies. You can imagine it as a huge set of different sources with different frequencies.


Why does Wolverine still have Adamantium claws in X-Men: Days of Future Past?

Question: On the future scenes of Days of Future Past Wolverine's adamantium claws can be seen (they even appear on the movie's poster). But towards the end of the The Wolverine, I remember those claws were cut by the Silver Samurai, and he even grows new bone claws after that. How come Wolverine has his adamantium claws again in Days of Future Past?
Comment: He cant regrow the adamatium. He can only regenerate his NATURAL body. If you saw X-Men origins you would see how he got the adamatium. So I think there's a movie missing between: The Wolverine and Days of Futures past.
Comment: i think wolverine (2013) happens after days of future past (2014) as we can see that wolverine is all alone and looks wild. maybe xmen got spilt or everyone died of old age
Answer: I haven't seen X-Men: Days of Future Past, so I can't comment on whether this was shown in the film, but this site does include quotes from the director, Bryan Singer, on the issue:

That wasn't the only tempting breadcrumb that Singer threw to Empire,
  as part of the organization's Days of Future Past marketing blitz.
  Fans who've been paying close attention to the footage and images
  released from the film thus far have observed that modern-day
  Wolverine appears to have regained his Adamantium-laced claws, despite
  the events that took place in last year's The Wolverine; when asked by
  Empire, Singer hinted at a possible explanation:
Director Bryan Singer explains that Magneto's ability to manipulate
  metal might have something to do with it. The Master Of Magnetism
  could, perhaps, "reconstitute the adamantium claws… [Wolverine] has a
  different relationship with Magneto, and perhaps Magneto could forge
  them."
Comment: Ahh...so now they are going to answer every plot-hole in interviews. Why don't they cleared it in movie? That's why i hate Singer and fox because they kills continuity every time and ignores existing work for money.
Comment: I have to admit I assumed that the facility he lost his claws in would have the ability to give them back again given they'd been working with adamantium already.
Comment: The Xmen movies are all over the place from that point of view
Comment: Confirmed [here](http://scifi.stackexchange.com/a/69026/21267).
Answer: If you watch the movie The Wolverine until the end then you can see that Wolverine meets Prof. Xavier and Magneto at the airport and they ask to regroup. Both these characters help Wolverine to his metal claws back (with major help from Magneto of course, because he controls metal) so that they can fight the Giant Mutant Destroyers in X-Men: Days of Future past because Wolverine has the power to heal.
Helping Wolverine to get back metal claws is not shown anywhere but it's understood when Magneto says, "What do I want? I want your help" (in the airport scene) and in return Magneto helps Wolverine.
Comment: I just saw that scene, and was hoping Magneto was really the key of fixing Wolverine's adamantium claws. :)
Answer: There are different types of Adamantium. The one that wolverine has is Adamantium-Beta. Wolverine possesses Regenerative Healing powers. During his exposure to Adamantium whilst having it bonded to his skeleton, his DNA was manipulated into seeing the Beta-Adamantium as his Skeleton. He can regenerate his Skeleton very quickly, but the Adamantium takes time to grow back. So he probably just had a few weeks with normal bone claws, until the Adamantium Beta grew back.
I hope this answers your question, if not please feel free to write a reply and i will get back to you as soon as possible.
Comment: He _regrows_ Adamantium? Seriously?
Comment: When did you learn that? If i am not wrong then it never appeared in any X-men movie yet.
Comment: Comic logic, love it.
Answer: Do you remember how in the x-men movies they hinted as to why his claws are adamantium?  It's because they used bone saws to inject the adamantium into his bones which would mean that just like his bone claws regrew because of his regeneration they would actually be adamantium because his bones are adamantium.  They have been making mistakes all over the series, and they are all easy to find if you watch what happens in chronological order, the only movies that have the same story line to it about the past is x-men # 1,2&3.
Comment: I can't find answer in here.
Answer: To me this is a very easy answer. After the events of the early 1970's happened,the mutants and the humans coexisted peacefully. Wolverine,up until mid 1970's happened but the events from the late 1970's at 3 mile Island never happened. Also X Men on(circa 2001) never happened.This means Everyone had no conflicts with each other. Wolverine was the only one who was completly lost when the space-time continuum finally remerged in 2001.This means Wolverine never lost his claws in Japan.
Comment: What...??? Did you even read the question?
Answer: Due to Logan altering the time line in DOFP, X-Men 1,2 and 3 never happened neither did The wolverine so he never lost his metal claws.
Comment: You are talking about the changed future. However, the future scenes the question is talking about still happen inside the old unchanged timeline, where *The Wolverine* happened very well.
Answer: There probably is a movie missing where he gets his claws back, if you look in the picture i attached you can see his bodyguard being handed  box with his clause in it at the end of The wolverine.
Comment: I have no idea what you're talking about. Do you have any evidence to support your claims?
Comment: There is no proof yet because the movie hasn't come out yet, this is just a possibility. (notice the word "probably") also i read it somewhere on the internet, but she is being handed something important, they made it too obvious even though in the background.
Answer:
Most likely magneto grafted the metal in his body to his claws. Remember the metal manipulation in x2 when he broke free?
The box being handed to the girl at the end of the wolverine is actually an original Wolverine suit she showed to him on the plane. It's in the deleted scenes. Just a tease too. It never made it to Days of Future Past.
Even if the metal became chemically bonded to his skeleton which allows for more metal to regenerate, they wouldn't allow that to be on screen. They tried to stray away from comic booky stuff as much as possible to create a real world explanation for everything that happens.
Think about it. It's an X-Men movie. As much as we love them, Havoc is still older than cyclops in the upcoming X-Men: Apocalypse movie, so what does that tell you? Deal with it!
Comment: A lot of your answer seems like mere conjecture. You bring up deleted scenes, but unless they were added back in via some kind of director's cut, they're just that: deleted and not intended to be used as canon for the story.
Comment: What does havoc has to do with it?  Did they ever made public that they will stay away from comics?