What makes flight recorders harder to find than tagged sharks?

Question: It really bothers me that we can't find planes that weigh tons with black boxes (AFAIK) technology that's almost obsolete, on the other hand shark tags (AFAIK) work great for long time and we can monitor shark movement, depth, temperature, etc., all the time. So, why?
Comment: Your question makes two unqualified assumptions - 1, that black boxes are often not found - in fact they are almost always are, and 2 - that shark tags are 100% reliable. I would suspect that some shark tags are lost, but this is not a big issue since many are tagged.
Comment: It should be noted that shark tags are as hard to detect as black boxes. They're only detected when the shark swims close to the surface. When the shark dives to deeper waters the sharks essentially disappears from our sensors. We get the depth record because the tag records them to memory and transmits them the next time the shark surfaces. So basically... black boxes would be as easy to detect as shark tags if we manage to teach crashed planes to swim like sharks (But then they'd be harder to get to because they keep moving around).
Comment: Yes, flight accidents are relatively rare and totally lost black boxes are more rare but it costs hundreds of lives and may be more if flight data that shows what had gone wrong is lost. so -black box aside- why flights depend on pilots communication for location and other flight information? what are the difficulties to send this data regularly and automatically during the flight?
Comment: Pfft, hundreds of lives? That's like e-9 size dent in human's genetic diversity, if that?
Comment: The "hundreds of lives" calculation assumes that the problem is one that can be prevented (to some degree) from recurring by obtaining knowledge of its occurence, and that such prevention will happen (it might be too expensive or politically unachievable). It also fails to consider the life analog of what economists call net present value: how far in the future would we expect to wait for the recurrence to claim lives if it is not prevented.
Answer: They're different usage cases, and have to be engineered differently. Three major points:

A shark tag doesn't have to survive a 500mph impact (#7 on the list) with the ground, and a flight recorder has to be able to do so. It adds a lot of padding and weight, and limits the kind of battery that can be used.

Sharks also don't dive to a depth much greater than 3000 feet on most occasions. A planes flight recorder is designed to survive to a much lower depth, under much larger amounts of pressure. Not to mention being designed to survive all sorts of other things.
Another point regarding depth, it is much harder to search for a signal at a depth of 15,000 ft, than it is even at a depth of 5000 ft. This article shows how big of a difference you get between even 20 meters and hundreds of meters (not thousands), it gives a good idea of what I mean.

If a shark tag fails, nobody cares. If you tag 100 sharks and 30 of the tags survive, you still have some pretty good data. But if one airplane crashes and its black box fails, it's considered unacceptable. They are required to survive 100% of the time.

All of these differences combined mean that black boxes are manufactured to much higher standards, and as a result they are bulkier, have different sorts of radios and require much more battery life (to support the larger systems) than a shark tag. All this conspires with the difficulty of getting a receiver deep into the ocean to make finding FDRs/CVRs really difficult.
That's not to say they couldn't design one that is much better, it just becomes extremely expensive (as all things are on airplanes). And you have to determine if these edge cases (like flight MH370) are worth making an airplane a few million dollars more expensive (between R&D and certification, the later being quite expensive).
I think the theory was they should be able to find any one of these within a month, and that may take some rethinking (maybe 3 months, or a year perhaps?) But they'll never be as successful as shark tags just because the requirements to be able to find one at that depth 100% of the time are quite different from the needs of a shark tag.
Comment: This answer sums up in a simple language why FDRs are designed this way, but, I was looking for one more point which is (why can't be better?) and I found it in the link you provided #8, thanks!
Comment: Moreover, found [this](http://aviation.stackexchange.com/a/2155/2156) fixes almost all the issues you mentioned in the old design.
Comment: Also, shark tags generally aren't required to survive being cooked in a pool of blazing jet fuel for hours on end.
Answer: Shark tags work by only sending the logged data when the shark resurfaces. Between those it just stores the data in memory until it can send it.
Sending underwater takes a lot of power otherwise.
Comment: Deployable black boxes make it easier to recover the black boxes but not necessarily the plane. It would be the same situation as it was with the Titanic where we knew exactly where it sank but its resting place on the ocean floor turned out to be much harder to locate.
Comment: According to [this](http://aviation.stackexchange.com/a/2155/2156) "Deployable Black Boxes" the technology exists, but the paperwork doesn't.
Comment: @slebetman The plane is gone, people aboard died, but FDRs with GPS, proper batteries and can resurface will be helpful to lessen future accidents
Answer: Because they're located in the wreckage, which can be at great depths. The only signal that can be sent at great depths is an audio signal, and that takes a lot of power (relatively speaking, the CVR and FDR are battery powered)
Sharks (or whales, they are often tagged) either remain in relatively shallow waters, or occasionally swim near the surface, where a radio signal can be detected.
The practical solution would be a realtime data feed of data now being recorded on the FDR to a remote receiver, sort of a super ACARS. In fact, ACARS data factored in determining the cause of the AF 447 crash long before the wreckage and black boxes were found - it showed a stall after loss of airspeed from frozen pitot tubes.


Has Airbus planned to build a larger version of the A380?

Question: The current Airbus A380-800 could carry over 800 people. Has Airbus planned to build a new, larger version that could carry 1000 or more passengers?
Comment: Welcome to the site! Unfortunately I'm not sure what you're asking and it looks like it will be difficult to give a precise answer because I guess no one outside Airbus knows for sure what their plans are and Airbus employees probably wouldn't discuss them anyway. I suggest that you try to ask a more specific question that can be answered clearly or, if you simply want to discuss this topic then the [chat room](http://chat.stackexchange.com/rooms/12036/the-hangar) would be a better place.
Comment: OK, that's helpful. I've edited the question to make it more specific; if you don't like the edit then you can just change it back.
Comment: thanks a lot for your response!! My quetion is about if they have planed to build more high capacity versions
Answer:
Has Airbus planned to build a larger version of the A380?

Yes,
In 2012 they planned to build a larger version of the A380.
"Airbus says 1,000 seat A380 due 2020"
However, manufacturers do change plans from time to time, sometimes in response to market conditions. "Has planned" is not necessarily the same as "is planning". Those plans are not currently (8 Jan 2015) being pursued and consequently, as time goes by without a resumption of those plans, it is increasingly likely that any target dates in those plans may no longer be attained.
If you want to know do Airbus in January 2015 have active plans to build a larger version of the A380 - that would be a new question.
Comment: That article says that the project was shelved in 2010. Given the soft sales figures since the article was written and that they are not taking orders for a -900 as of today, I'd guess than a 2020 date is unlikely.
Comment: The question was whether Airbus has planned a larger version. They have but, as you noted, plans change. @reirab. I'll update the answer to make this plain.
Answer: The answer is clearly yes: The ratio of wingspan to fuselage length is unusually large for modern transport aircraft. The A380 has a wingspan of almost 80m and a fuselage length of less than 73m, whereas in other modern transport aircraft the fuselage is longer than the wingspan is wide.
Airbus designed the A380 with lots of stretch potential. With the cooperation of engine manufacturers, the A380 may one day have a fuselage length of around 100m. This is greater than the maximum length of 80m used in current airport layouts, but Airbus is betting on operators to urge airports to accomodate a stretched A380, just like they did for the current model's wingspan, weight and height.
The A380 will be the biggest Airbus for the next 30 or maybe even 50 years, so it better offers some growth potential.
Comment: The odd proportion of wings to fuselage is also caused by the double-deck layout: due to the high weight, the A380 needs a lot of lift.
Answer: Airbus has certainly made preliminary plans for a stretched version of the A380 (the A380-900,) but no plans currently exist for that model to go into production. Demand for the A380 has been soft, leading Airbus' own CFO to suggest to investors last month that the A380 might be discontinued entirely unless they can find enough customers willing to buy a re-engined version of it soon.
Orders for large, quad-engine airliners, including the A380, have been light lately. Since taking the first order 14 years ago and over 7 years since the first delivery, only 318 A380s have been ordered, nearly half of which were from Emirates, and many of the A380's orders will likely be cancelled. While the Boeing 747 has had over 1,500 deliveries over its long lifespan, it, too, currently has a small order book with only 16 net new orders since 2008. In contrast, twin-engine wide-bodies have been selling very well lately. The A350 just delivered its first aircraft and already has 778 orders. Similarly, the first 787 was delivered a little over 3 years ago and it has 1,055 total orders, so far. The 777X, currently scheduled for production in 2020, was first offered for order a little over a year ago and already has 286 orders. Total 777 orders so far number a whooping 1,807. The long-haul wide-body market has been trending very strongly towards twin-engine aircraft like the 777, A330, 787, and A350 lately rather than mammoth quad-engine aircraft like the 747 and A380. As such, it seems unlikely that Airbus is going to be sinking billions of dollars into a stretched A380 any time soon.
Answer: Actually I think they don´t have any plans for a stretched version of A380.
Tim Clark, CEO of Emirates, wants a larger A380 but Airbus said (last time when this topic came up) that they would rather improve the current A380 and increase the performance.
They are making a change by increase the lower floor height to add extra seat in each row
on economy but thats it.
Now Tim Clark is pressuring to make a neo-version af A380 and and Airbus is considering
that option. Emirates say that they would order up to 70 A380neo if that plane will be launched but Airbus has to calculate the cost and if it´s will be profitable for them.
Comment: Welcome to aviation.SE Ingdor (sorry, my keyboard doesn't support Icelandic :-)) "I think" doesn't really qualify as an answer here. We'd like to see your thoughts supported by evidence. Any links perhaps that support your claims?
Comment: Hi, Delta Lima

Airbus talked about strecthing the A380 back in 2012 with seats for 100 more passengers but
because of poor demands Airbus said in june 2013 that they would improve the current version instead

Here´s link to a story I wrote on my website (sorry it´s in icelandic but google translate should do the trick)

http://www.alltumflug.is/flugfrettir/4108/Ekki_%C3%AD_myndinni_a%C3%B0_lengja_A380
But it´s interesting maybe to know the status if there are any plans to make A380-900. I´ll contact Airbus spokesman
after the weekend and get the lates info on that
Comment: Of course they have plans to stretch the A-380! They had them before starting the project. That they now claim not to have any is probably to make airlines buy the current model.
Comment: If you have a reference for a quote from Tim Clark and/or Airbus that corroborates your answer, please provide it in your answer
Answer: Yes, and in the short-term they're also talking about re-engining the existing A380 with engines based on those on the A320neo as outlined here.
Comment: That link just says that they're considering an neo A380, not that the new engines would be based on the A320neo engines (CFM LEAPs.) It's extremely unlikely that they'd be using anything remotely like a LEAP on an A380 variant. Even with 4 of them rather than 2, it would be ridiculously underpowered. 4 similar engines (CFM56s) do power A340s, though.


Why don't lens mount adapters have the same effect as extension tubes?

Question: I use a Metabones adapter for Canon lenses on a Sony body. Why doesn't the lens adapter, which sets the lens further from the sensor, have the same effect as using extension tubes, allowing closer focus?
Comment: @twalberg No, something like [this](https://www.kentfaith.com/KF06.069_canon-eos-to-sony-nex-e-mount-adapter) - a glassless adapter. The Metabones ones are *optically* the same, just add some clever electronics for autofocus, aperture control, IS etc.
Comment: If by "lens adapter" you mean what is essentially an extension tube with optical elements in it, then they don't do the same thing because of what the optical elements add to the total lens equation.
Comment: If it allows for closer focus, then you won't be able to focus to infinity. Most people prefer being able to focus to infinity so adapters are designed like that. However, there are adapters that has adjustable length to allow both close and infinity focus.
Comment: It should. What in the results differs?
Answer: Because the Canon EF mount lens "expects" to be further from the sensor than a Sony E mount lens; this is known as the flange focal distance or the registration distance - a Canon EF lens focuses the incoming light on a plane 44mm behind the lens, while a Sony E lens focuses it on a plane 18mm behind the lens.
If you somehow bodged it horribly so that a Canon lens was mounted in the same place as the Sony lens, it would be focusing everything on a point 26mm behind the sensor and it would all be a bit of a disaster really. The EF to E lens mount adapter ensures that the Canon lens is mounted 44mm from the sensor so that the incoming light is focused in the correct place.
Comment: Indeed. If I recall correctly, that's also the reason why you can mount nikon F lenses on canon EF but not the other way around. And it's also the reason why it will be possible to mount any full frame lens on the Nikon Z.
Answer:
Why don't lens mount adapters have the same effect as extension tubes?

They do. But whether it limits far-focus capability depends on one factor: the difference in distances from the image plane to the back of the lens mount flange between the two systems.
If the adapted lens's mount is deeper than the camera's mount, the adapter tube can make up the difference so that the lens sits exactly where it needs to in order to have full range of focus.
If the adapted lens's mount is shallower than the camera's mount, then the adapter is working exactly like an extension tube and will reduce far-focusing capabilities, if there's no glass element. If there is a glass element in the adapter, the adapter no longer acts like an extension tube, but is now acting like a converter lens, where the added glass has changed the apparent focal length to regain focus-to-infinity. The Speedbooster acts like a wide converter, which decreases the focal length (and increases the DoF and max. aperture).  But other adapters often use a teleconverter lens to increase the focal length (which decreases the max. aperture).
See also: Can I use lens brand X on interchangeable lens camera brand Y?
Answer: The Metabone adapter is an optical accessory that mounts between the camera body and the camera lens. Such a mounting relocates the lens further forward. Such repositioning corresponds precisely like the action of extension rings or tubes in common use. However rings and tubes are void of lenses whereas the Metabone adapter contains lenses that modify the focal length of attached lens.
Supplemental optics similar to this device has been in use almost from the beginnings camera / lens design. We can mount such devices before or after the camera lens. These devices alter close focusing distance or they modify the lens, converting it to a telephoto or a wide-angle.
Many such supplemental lenses have been or are currently being marketed. The Metabone adapter revises the focal length of the attached lens, it shortens it about 70%. In other words, say a 50mm lens is combined with a Metabone adapter. The 50mm focal length is altered, it converts to become35mm. This action is analogous to add-on wide-angle converters commonly available. However, most such devices mount before the camera lens whereas the Metabone adapter mounts after the camera lens. Again, not a new idea.
How does the Metabone adapter realize a lens speed increase?  The photographic industry uses the f-number system to specify the relative speed of a lens. The camera lens acts like a funnel in that it gathers light. The greater the working diameter of the lens (aperture) the brighter the projected image (speed of the lens). Entwined with aperture is focal length. Both are contributors as to how bright the projected image will be.  Say the aperture diameter is untouched and the focal length doubled the projected image dims to 25% of its original brightness (2 f-stops). Conversely, if the focal length cut in half, the image brightens 2 f-stops.
The Math: 50mm lens 12.5mm aperture = f/4  --- 100mm lens 12.5mm aperture = f/8 --- 25mm 12.5mm aperture = f/2
Suppose you set your 50mm to f/8 achieved with a 6.25mm aperture.  Now you mount a Metabone that shortens the focal length 70%. The revised focal length is35mm. The aperture remains unchanged at 6.25mm, the revised f-number is 35 ÷ 6.25 = 5.6 (written f.5.6). Simply stated, the Metabone shortened the focal length, this act increased the angle-of-view (more wide-angle), the image brightened as a result, the revised f-stop is f/5.6 = 1 f-stop speed gain.
The cleverness of the Metabone is, it shortens the focal length, this gives rise to a speed gain plus it adapts a lens designed for a larger format camera to operate on smaller format cameras mitigating the crop factor that would normally charge.  Remarkable is the fact that back-focus distance (flange focus distance) of the lenses is corrected taken into account allowing lens interchangeability.
Also, Meabone is credited with suppressing some aberrations normally realized when a supplemental lens is added.   (If all true, hats off to the optician
Comment: You're confusing the Metabones adapter (glassless) with the Speedbooster (glass). The question is about the *adapter*.
Answer: Extension tubes don't have any lens elements; they're completely hollow. Metabones adapters do have lens elements.
Comment: The Speedbooster does, but not the T Smart Adapter


What is fruition in Buddhism?

Question: I see it everywhere in my book on jhana. but don't truly understand it's meaning or even find a definition.
Comment: And path. The two are often mentioned together, and I'm still not completely sure what they each mean.
Comment: @DeusIIXII, this is an important question that you asked. I am going to be hard pressed for time, the coming three months. But I cannot ignore when a good question is asked. So I will expand on the earlier answer given. Do give me some time to formulate an answer.
Answer: Fruition is more related to the 4 stages of sainthood. This is realising of the fruit (Pala) of practice. What his means is you realized the path.
Comment: They happen very closely. This is why they are mentioned together. But path happens 1st followed by fruition.
Comment: But, Suminda, the two concepts are often mentioned together -- path and fruition -- suggesting that the latter is more than just realizing the former, no? I mean, can one have path without fruition, or fruition without path?
Comment: Thank you kind sir.. Once again you have helped me a lot.
Comment: You are welcome.
Answer: Fruition is more related to the stages of Attainment. These levels of attainment are described as including four or eight kinds of individuals. There are four [groups of noble disciples] when path and fruit are taken as pairs, and eight groups of individuals, when each path and fruit are taken separately:

•  (1) the path to stream-entry; (2) the fruition of stream-entry;
  •   (3) the path to once-returning; (4) the fruition of once-returning;
  •   (5) the path to non-returning; (6) the fruition of non-returning;
  •   (7) the path to arahantship; (8) the fruition of arahantship.

So, Fruition simply means "Coming to Fruition". It is the moment of the fruition of their path (magga-phala) – be it the stream-entry path, the once-returning path, the non-returning path, or the path to arahantship.
The moment of fruition is the understood experience and results in a turned-around vision of existence. The new understanding at the culmination of the stream-entry path recognises and go beyond the first three fetters (saŋyojana) that bind a being to rebirth, namely self-view (sakkāya-ditthi), clinging to rites and rituals (sīlabbata-parāmāsa), and skeptical indecision (Vicikicca).
The new understanding at the coming to fruition of the Sakadāgāmi or "once-returner," stage is first three fetters (saŋyojana) are fully cut off and that s/he has  significantly weakened the fourth and fifth saŋyojana.
The new understanding at the coming to fruition of the anāgāmi or "non-returning" stage is that s/he is free from Kāma-rāga (Sensuous craving) and Vyāpāda (ill will).
A key principle in Buddha Dhamma is cause and effect; nothing happens without a cause or a reason. The word "FRUITION" can be used here in this way: Even if root causes are there, we can stop them from bringing their results by blocking the conditions for them to come to FRUITION (a seed has the potential to bring about a tree, but for that to happen the seed must be given a fertile soil, water, and sunlight). In the same way, kamma vipaka (result of a past kamma) can come to FRUITION only when right conditions for the corresponding kamma seed to germinate are realized.  This is why we can prevent many bad kamma vipaka from come to FRUITION by acting with yoniso manasikara or by "being mindful" in seeing life through the 'Dhamma Eye".
Answer: As the venerable appearing as @Saptha Visuddhi has given a detailed answer, I will give a simple one. Fruition is a significant milestone in the practice of Dhamma. The final fruit is the Arhathhood which is the elimination of suffering. A dhamma practitioner practices all the components of the Eightfold noble path, which includes development of wisdom until he/she reaches each of the 4 fruitions and finally the Arhanthood (or Buddhahood).

It is said that at each fruition, a taste of nibbana can be experienced. And once that it's experienced, a normal person would no longer have doubt about the Buddha, Dhamma or Sangha. And that person is bound for nibbana. The practice of vipassana removes mental defilements step by step, increasing wisdom, until a person achieves each of these states.
Answer: Once one achieved stream-entry, one will know what is what. The same applied to once returner, non-returner etc. In layman term to make clear, if one go to a retreat home/dwelling, the entrance to the dwelling is the path(magga) and the dwelling where one(stream-enterer) stay is fruition(phala). But magga is very very short just like passing by the entrance while phala is the stage where one (stream-enterer or once returner or non-returner or arahant) can be in this stage for long enough depend on the concentration achieved just like dwelling in a retreat home. If pre-determined before meditation session, can stay in the specific fruition stage for a definite period of time.
Answer: Eradicating all craving and realizing nibbäna

What is fruition in Buddhism?


What lenses are must-have yet affordable for a Canon T2i camera?

Question: I have a canon T2i camera. I am beginner looking for some tips on the best lenses to carry around.
Comment: 50mm 1.8 is your best bet. It's cheap too.
Comment: What kind of photography are you interested in? General, portrait, landscape, etc. That will dictate what kind of lenses you get in answer.
Comment: portrait and landscape
Answer: The 50 1.8, for sure. It's a good lens for portraits and general usage. I even recommend people to just skip the kit lens all together and start with the 50 1.8 when buying a Rebel. It's also a good lens for shooting video because it's lightweight.
Since you're into landscapes, you'd enjoy Canon's 10-22. It's a great lens for the smaller sensor and isn't terrible expensive. Sharpness and color is good. It shows a little bit of CA, but offers good image quality overall.
As far as telephotos, you can't go wrong with Canon's 70-200 f/4L. These can be had for around $500 used. 70-200 is a "must have" focal length in my opinion. There are some other options in that focal length, like the 70-300 or 55-250, but you'll really appreciate the colors and contrast from a L-series lens.
For a little over $1,000 total, those are three great lenses that will go a long way and you'll pretty much be equipped for anything.
Comment: What? The 10-22 is specifically designed for the smaller sensor. It's effectively a 16-35 on 35mm. The horizontal viewing angle is near 100°! That's the widest option Canon offers for a 1.6x sensor.
Comment: "... Canon's 10-22. It's a great lens for the smaller sensor" - I'm not sure I agree with this.  With a 1.6 sensor, *no* wide angle is a good option, as the sensor pushes them all up in focal length.  I think I missed your intent?
Comment: Guys, thanks for your comments. I currently own the following 18-55 mm Kit lens + I now bought f/1.8 50mm. Now tell me what other lenses are useful.
Comment: I have to agree that the 10-22 is a great lens for the smaller sensor.  I've rented one on numerous occasions and it is really a great wide angle for the small sensor cameras.
Comment: If you can find an 80-200 2.8L, I would definatly buy that over the 70-200 f4L. It's sharper, in my experience and has a larger aperture. You can find them for around $600-800. It's built like a tank too.
Answer: I stretched my budget to the Canon 15-85 3.5-5.6 IS USM when I upgraded my camera a month or so ago, and I'm very happy with it. The 15mm wide end is great for landscapes and the lens is impressively sharp at all focal lengths. The image quality and 15-85mm range has kept me from changing to another lens at all since I got it.
I can't say it's great value as it costs a pretty penny and it's not compatible with full-format bodies should I want to upgrade later, but as a general purpose lens for a crop-sensor canon I think it's about as good as it gets.
Answer: One of the most popular lenses in in the Canon arsenal is the nifty 50 - a 50mm, f/1.8 lens.  Its prime so it won't zoom, but it's aperture opens WAAAAY up so that you can use it in those low light situations without uglying everything up with the on camera flash.  Check it here.
Answer: Something I found helpful with my T2i was a good collection of fast primes.  Indoors with less light you'll find many of the Canon lenses to be very slow and hard to work with.  The T2i's sensor starts getting pretty noisy around 1600 ISO so you'll want all the light you can get.
I highly recommend grabbing a nice M42 (screw mount) adapter for 5 bucks or so off Amazon/E-bay and buying a bunch of cheap, fast M42 primes.  Most of these older lenses can be had for under 100$ easy. Since you already have the nifty fifty you can look at some other focal lengths and see what suits you.
The best thing about these old primes is that they're built like tanks--rarely any plastic like the Canon lenses. Just remember that you're on a 1.6x crop sensor so multiply the listed focal length of the lenses by 1.6 to get an idea of actual zoom factor.
Comment: can you point me to some really good m42 primes that are less than 100 bucks? Where should I find them and what adapter should I buy?
Comment: M42 lenses are great fun but bit tricky to focus quickly, even with a AF confirm adapter.
Comment: They can be tricky but the price is certainly right.
Comment: Definitely get a focus confirm adapter if you can swing it.  They have an electronic connection to the camera that will show you when the picture is focused in the viewfinder.  Some nice primes to look for in M42 are the Vivitar 28mm/2.8, Takumar 50mm/1.4, and the Vivitar 70-210mm/3.5 (Kiron).  Honestly some of these lenses are cheap enough (~15-20 bucks) that you can do some experimenting and see what you like.
Answer: While the 50mm 1.8 is a great lens for a great price, keep in mind that 50mm on your camera is fairly zoomed in. The 50mm became popular on full frame cameras - on those cameras, 50mm is a great focal length because it is similar to your own visual field. On cropped sensor cameras like yours, everything is zoomed in ~60%, so you'll have to step further away to capture everything your eyes see.
If you have the kit lens, set it to 50mm (almost all the way zoomed in) and walk around taking photos without changing the zoom at all. While the 50mm lens is much nicer than the kit lens, you will get a chance to determine if the zoom level works for you. It was too zoomed in for me, especially because I wanted the lens for indoor shots, so I went with the 35mm f2 instead.
Answer: As deciding on a lens is generally a personal choice, rather than offering my own subjective opinions, I'll direct you towards my favorite lens review site: The Digital Picture. This site has excellent, hands-on reviews of a multitude of brand and off-brand lenses for Canon gear. You should be able to find the information you need here.
That said, here are some of the reviews I recommend:

Canon EF 50mm f/1.8 II Lens Review (Landscape, maybe portrait)
Canon EF-S 10-22mm f/3.5-4.5 USM Lens Review (Landscape, limited to crop-sensor)
Canon EF 28-135mm f/3.5-5.6 IS USM Lens Review (General purpose)
Canon EF 24-105mm f/4 L IS USM Lens Review (Landscape/Portrait, high quality)
Canon EF 135mm f/2.8 With Softfocus Lens Review (Portrait, general quality)
Canon EF 135mm f/2.0 L USM Lens Review (Portrait, very high quality)
Answer: Having used both the 10-22 EF-S and the 70-200 F4 EF L I have to agree with the earlier answers that included these lenses.
I've also enjoyed the 24-105 EF L for a high quality walk-around lens.
I would like to recommend that you try renting a few of the lenses that you are thinking about purchasing.  It is relatively inexpensive to do so and you can really find out if they are what you want to buy or not.  Just search for "canon lens rental" and you'll find a lot of options.
Answer: I've bought a 50mm 1.8; Tamron 17-50 2.8 VC and Tamron 18-270 VC, for my 450D (the model before the T1i)
All three have been fantastic so far. I'd recommend all three.
Though, if you don't mind changing lenses more often, then get a dedicated telephoto zoom instead of the 18-270, like the 70-200 f/4 as suggested above.
Answer: I'm a real amataur, but I upgraded to the t2i from the original digital rebel.  I've got the t2i kit lens, the Canon EF 50mm II and Canon EF 75-300mm 1:4-5.6 III.  I stuggled to get any kind of indoor sports picture with the old rebel, but with the higher iso of the t2i I'm able to use any of the lens for decent shots.  Definitely the 50mm is worthwhile,  for a cheaper zoom i've been happy with the EF 75-300.


Not exactly a question: whoopsie problems during dist-upgrade in saucy

Question: It's not a question but I think it can be useful ...
While dist-upgrading a saucy custom DVD, I've got an error about whoopsie:
invoke-rc.d: unknown initscript, /etc/init.d/whoopsie not found.
dpkg: error processing /var/cache/apt/archives/whoopsie_0.2.24.1ubuntu1_i386.deb (--unpack):
 subprocess new pre-removal script returned error exit status 100
invoke-rc.d: unknown initscript, /etc/init.d/whoopsie not found.
...
Errors were encountered while processing:
 /var/cache/apt/archives/whoopsie_0.2.24.1ubuntu1_i386.deb
E: Sub-process /usr/bin/dpkg returned an error code (1)

Investigating a little, I've found that on my other pc, running precise, /etc/init.d/whoopsie, was a symlink:
whoopsie -> /lib/init/upstart-job*

while in chrooted saucy looking for /etc/init.d/whoopsie I've got cannot access /etc/init.d/whoopsie: No such file or directory
So I've created the above symlink and finally dist-upgrade worked fine.
Silvia
Answer: I'm running Ubuntu 13.10 (i.e. Saucy) and have Whoopsie installed but don't have /etc/init.d/whoopsie OR /lib/init/upstart-job.
I'm also trying to create a custom Ubuntu 13.10 LiveCD and can confirm the above fix works when I run it in the chroot.


How high to climb before clipping on a sport climb?

Question: The guy who taught me to lead sport in the gym suggested that when I'm going for a clip, I position my body so that the clip is somewhere between my hips and my chest. He claimed it was a bad thing when most people reached up high to clip. This question is about whether this advice is right, and if so, why. I've written up what I was able to figure out about this in my own answer, but I'm not sure if my analysis is right, and I'd be interested in other people's answers or criticisms of my own answer.
Answer: Petzl does recommend this for the second bolt:

Clip the second bolt at waist level; this reduces the amount of rope
  out and thus helps prevent the climber hitting the ground in case of a
  fall  before making the clip.

(Section F, second panel.)
I think that's generally good advice for clipping the second bolt (and sometimes for the third bolt if it's far from the second).  For all other bolts, an important thing to remember is that a quality, well-bolted route will have logical stances from which the equipper intended the clip to be made. Bolts are (generally) not uniformly distributed throughout the route, so it's impossible to make blanket statements as to where you should clip from.
Climbing past a perfectly good stance to clip from an awkward stance above doesn't make sense, even though it could potentially minimize a few feet of falling.  Keep in mind the huge mental boost (for most climbers) of being one foot below a bolt instead of several feet above it.
As I've gained more and more experience, I've gotten better and better at judging those "clipping stances" from the climb (or even from the ground).  This makes the climbing more efficient.  The only way to get better at this is to get new pitches of climbing under your belt and recognize when you clipped from an awkward stance where a better stance existed nearby.
Answer: The pragmatic answer has already been given, but in my own words:

Clip from the most solid stance available
Clip with your harness as close to the rope-end carabiner as possible
Sometimes the old mantra "the leader must not fall" still applies

There is a "trick" I'll share at the end of this post, but first:
The Analysis
I'll use a simplified schematic to illustrate several scenarios.  In each:

The left side of the graphic represents the arrangement before the fall while the right side is after.
The black dot represents an anchored belayer
The blue dots represent points of protection
The red dot represents the climber's waist.

Scenario 1a:

We have one bolt at 3 meters and a second at 5 meters.  The climber attempts to clip with his harness at 4 meters but falls a moment before clipping.  Because additional slack was introduced the climber decks.
Scenario 1b:

The same setup, but this time the climber exercises discipline and doesn't attempt to clip until his harness is level with the protection, but he still falls.  The fall factor is slightly higher but the rope arrests the fall at 1 meter and all is well.  Or is it?  First you may have realized that if the red dot is the harness there should be legs (or if inverted a torso) below that point.  Okay, so his feet touch but all is well?  No.  This didn't account for any stretch in the rope, movement of the belayer, or rope slip in the belay device.  Precisely accounting for stretch would be complicated as it will be a function of the fall itself, and the other factors are even harder to pin down.  However if we add only 20 percent rope stretch the climber falls another meter and decks:
Scenario 1c:

(Note that in my calculation of fall factor I am including the additional distance fallen due to rope stretch.  I don't know if this is accepted practice but since it represents a release of potential energy it seems appropriate.)
(All illustrations hereafter will include the 20% stretch factor.)
How might this situation be addressed?

The climber can accept that he is basically highball bouldering until the 2nd bolt is clipped (don't forget the pads!)
The belayer can attempt to run backward if he sees the climber fall (good luck!)
The second bolt could be placed one meter lower (Scenario 2a)

Scenario 2a:

Here even with 20% rope stretch the belay catches the fall.  But how can that help on existing bolts with no opportunities for natural protection?  Here's the "trick" I mentioned at the beginning:  effectively lower the position of the bolt by using an extended draw.  You can reach above your head to clip the upper carabiner without putting any slack in the climbing rope, then clip the rope into the hanging carabiner at waist level.  To make it even more slick you can pre-clip that carabiner to the rope and attach the rest of the extended draw to your harness with velcro; now you can grab, rip, and clip in one fluid motion.  Decking averted!  Well there's one more issue.  Suppose the next bolt is at 7 meters.
Scenario 2b:

(The first bolt is omitted from this drawing as it is now inactive in the system.)
Remember the extended draw effectively lowered the second bolt to 4 meters so even if the climber is patient about clipping the third bolt he still risks decking if he falls.  The solution is to re-clip the second bolt with a short draw, moving the effective point back to its original 5 meters:
Scenario 2c:

Here the climber clips the third draw at chest height.  If he fails he is still caught at 1 meter.
That's a lot of faff that will rarely be used but it's nice to have in your bag of tricks, along with stick-clipping etc., especially if you are not a bold climber.
Please remember that these drawings are only a rough first-order approximation of the real world and that the combined elasticity factor of 20 percent was merely a guess.  Nevertheless I hope that these figures help others to think about the processes and risks involved.
Comment: @Mr.Wizard Once again a great answer, very demonstrative. You should go for more climbing lessons!
Comment: @Roflo A second quickdraw.  Most bolt hangers should handle two carabiners, and the loops on cams do easily.
Comment: Your 20% guess is actually on the low side...Many Ropes made for sport climbing actually have Dynamic Elongation of up to 30% such as Maxim Equinox, Mammut Eternity and Edelrid Boa.  Petzl Contact is even 35%!  All these ropes are 9.8mm no dry treatment.  You can almost see the elongation when you catch a huge fall and the rope is secure in your ATC and brake hand but your climber is still in a downward motion...it's pretty cool!
Comment: @AM_Hawk Yes, but those figures are elongation during the severe UIAA test drop with a rigid 80kg mass and a 1.78 fall factor.  I don't have data for elongation at lower factors; do you?
Comment: How would you _safely_ reclip?
Comment: Of course! That makes sense. First thing that came to my mind was re-clipping the _same_ quickdraw.
Answer: negative points to consider when clipping way above your head as opposed to clipping around chest height:

you have to drag out a load more rope, which will slow you down, wasting energy
the rope may be running over/ in the way of your next hold
extending your arm to its maximum length and doing work with it, is awkward/ uncomfortable
you may not be in the best position for holding on with only one arm. in terms of balance, posture, wait on feet, quality of holds

There's probably a few more. With regard to fall factor, it's less of an issue with sport climbing indoors since your unlikely to be doing a multi-pitch.
The likelihood is that people clip way above their heads because they fear falling above the last clip. I do it myself sometimes. Don't be scared, theres little reason to be.
rock n ice article
http://www.rockandice.com/lates-news/tnb-clip-like-pro-5-tips-from-sasha-digiulian-and-sean-mccoll
Comment: There's another point to consider: if you fall while clipping, you will for sure cling to the rope as you are already holding it. If you were about to clip in a position that required to reach high above you, you hold the rope at a position far enough from your harness that it can either wrap around your hand while falling or that you will partially catch your fall with your hand. In both cases, serious injury may be the consequence.
Comment: But here's a nice example of how it looks like from a climber's perspective when falling with the rope in hand: http://www.rockandice.com/video-gallery/weekend-whipper-bad-clipping-technique-causes-big-fall
Comment: The relevant part of the video seems to start at 2:55.
Comment: @BenediktBauer i appreciate the possibility of this happening. are you aware of any actual instances?
Comment: I did some searching but couldn't find any definitive answer to your question. The only thing I found was some statistics that stated some incidents with the climber gripping the rope during fall but they did not distinguish between this happening while clipping or while already in air. Also it could be difficult to tell in many cases unless someone was thoroughly watching the climber in exact that moment where they where clipping and starting to fall.
Answer: You certainly don't want to climb so high that your hips are above the clip before you do the clip. Your arms aren't long enough to reach down that far.
When leading trad, I would typically prefer to place the piece right in front of my face, so that I can carefully look at the placement and get it right so it will hold. In sport climbing, however, this isn't a concern.
All other things being equal, we would like to minimize:

the fall
the fall factor
the chances of hitting the deck

I had never actually done the math until today, but here's how #1 and #2 seem to work out. Let's say the distance between clips is 1 unit. You climb past your most recent clip until your hips are x units above it, and then you reach for the next clip. As you reach for that next clip, the amount of rope you have out past the last clip is 1+(1-x)=2-x. If you miss the clip and fall, you're going to fall x until your hips are at the last clip, and then another 2-x, plus rope stretch, so the total is 2. In other words the length of the fall is exactly the same regardless of x. In the gym, where the quickdraws are evenly spaced, every fall that you make while attempting to clip is a fall of twice the distance between quickdraws (not counting rope stretch).
If your last clip was at a height h above the ground, then the fall factor is 2/(h+2-x). This is actually bigger (worse) if you climb higher before clipping.
When the rope first comes up taut at the bottom of your fall, you're at a height h-(2-x)=h-2+x. This is higher if you climb higher before clipping, and that makes you less likely to hit the deck with rope stretch.
So it sounds like:
(1) If you're in doubt about hitting the deck, it's safer to clip from a position as high as possible.
(2) If you're in doubt about your belayer's ability to hold a high-fall-factor fall (or if you're climbing trad and in doubt about whether your last piece will hold), it's safer to clip from a position as low as possible.
Does this make sense? Are there factors I'm leaving out?
Comment: From a technical and mathematical point of view I think you are right. Although I think that in normal (non-multi-pitch) sports climbing fall factor isn't a critical factor and one does not need to care too much about it in this setting.
Comment: In most cases when sport climbing, #3 (hitting the deck) is the only thing we really care about. Many exceptions exist.
Comment: One thing you are leaving out is the difficulty of the moves and the clipping stance. If your choices are either a great clipping stance prior to the crux move but with a chance of a ground fall or making the clip in the middle of the crux, I might be willing to expose myself to a ground fall (or more likely backing off the route and complaining about the jerk who bolted it).


Spawn process that run in parallel in R

Question: I am writing a script that needs to be running continuously storing information on a MySQL database.
However, at some point of the day I will like to produce some summary of the data being colected, but writing this in the same script will stop collecting data while doing these summaries. Here's a sketch of the problem:
while (1==1) {
    # get data and store it on the relational database

    # At some point of the day (or time interval) do some summaries
    if (time == certain_time) {
        source("analyze_data.R")
    }
}

The problem is that I'll like the data collection not to stop, being executed by another core of the computer.
I have seen references to packages parallel and multicore but my impression is that they are useful to repetitive tasks applied over vectors or lists.
Answer: You can use parallel to fork a process but you are right that the program will wait eternally for all the forked processes to come back together before proceeding (that is kind of the use case of parallel).
Why not run two separate R programs, one that collects the data and one that grabs it? Then, you simply run one continuously in the background and the other at set times. The problem then becomes one of getting the data out of the continuous data gathering program and into the summary program.
Answer: Do the logic outside of R:
Write 2 scripts; 1 with a while loop storing data, the other with a check. Run the while loop with one process and just leave it running.
Meanwhile, run your other (checking script) on demand to crunch the data. Or, put it in a cron job.
There are robust tools outside of R to handle this kind of thing; why do it inside R?
Comment: I wanted to avoid this, and write it in a single R script. The reason I'm doing it in R is because I'm familiar with it, and I'm doing some plots on it.
Comment: would [Rscript](https://stat.ethz.ch/R-manual/R-devel/library/utils/html/Rscript.html) be suitable?

Spawn process that run in parallel in R


How to reverse engineer the SEO on a website?

Question: I have read this question. My question is a bit different from it. I want to know how can I reverse engineer another website that is ranking the best for some keywords. For example some website called example.com is there and it ranks high for many keywords and I want to learn from it how can my website be of the same authority and get the same ranking (or probably better ranking if I found something that they are missing). Can anyone enlist it as a procedure, how to reverse engineer a website?
Answer: Use alexa.com. Does your competitor have 7,000 quality links? Then that's why they rank. Otherwise, you'll just have to guess based on the keywords on the page. Use those keywords too and use good SEO practice in general. Be Warned: Copying their website (including a paragraph or 2) will greatly reduce your ranking. Google penalizes duplicate content.
Also the length of time a website has been online matters. Did your competitor get a head start? Then it's gonna be hard to unseat them without many more quality links.
Answer: Use SEOmoz's Open Site Explorer to analyze how your site is faring against a competitor on multiple parameters.
Answer: Use http://www.majesticseo.com/ to check all the targeted website links, and the new links timeline. Then optimize yours to beat him. (Caution, aged domain always get a special boost in rankings)


Memory is not released after the execution stored procedure followed by a process end

Question: I am running a stored procedure in query builder and closing query builder. However, the memory allocated doesn't get released. The stored procedure uses temp tables and drops them immediately after its use. These tables get created in a loop, get truncated, and dropped immediately. Any table that is created gets dropped immediately. The purpose of the stored procedure is only to make updates after a calculation using these temp tables.
After each execution, about 1.4 GB memory increases and never get released.
QUESTIONS

What factors should be considered when creating temp tables in a stored procedure ?
How can I claim memory after the stored procedure gets executed ?
Comment: Which database platform is this question for?
Comment: SQL Server 2008 R2
Answer: SQL Server doesn't release the memory it consumes unless it gets an order from the operating system to do so.
If you need, you can set the maximum amount of memory SQL Server will consume.


What is the difference between the Yarkovsky effect and YORP effect?

Question: As far as I understand, both the Yarkovsky effect and the Yarkovsky–O'Keefe–Radzievskii–Paddack (YORP) effect exert forces upon bodies as a result of thermal photon radiation. How do both effects differ from one another?
Comment: As Rob's answer shows, it's a rather arbitrary. The Yarkovsky was described first, in terms of affecting translational behavior. The YORP effect was described later, in terms of affecting rotational behavior. In truth, they're one and the same. An applied force whose action does not go through the center of mass results in both translational and rotational acceleration.
Answer: The Yarkovsky effect is the thrust on a small object in space that has been heated by sunlight, created from radiant energy. The YORP effect is when the thrust produces rotation, likely due to uneven heating or differences in surface projections (IE: A mountain acts as a better solar collector than a flatter portion of a spherical object on the opposite side).
See: "The Yarkovsky and YORP Effects" (Feb 4 2015), by
D. Vokrouhlicky, W. F. Bottke, S. R. Chesley, D. J. Scheeres, and T. S. Statler:

"The Yarkovsky effect describes a small but significant force that affects the orbital motion of meteoroids and asteroids smaller than 30 − 40 kilometers in diameter. It is caused by sunlight; when these bodies heat
  up in the Sun, they eventually re-radiate the energy away in the thermal waveband, which in turn creates a tiny thrust. This recoil acceleration is much weaker than solar and planetary gravitational forces, but it can
  produce measurable orbital changes over decades and substantial orbital effects over millions to billions of years.
The same physical phenomenon also creates a thermal torque that, complemented by a torque produced by scattered sunlight, can modify the rotation rates and obliquities of small bodies as well. This rotational variant has been coined the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect. During the past decade or so, the Yarkovsky and YORP effects have been used to explore and potentially resolve a number of unsolved mysteries in planetary science dealing with small bodies.".
Answer: Both effects are the result of sunlight being absorbed and re-radiated as heat. As this re-radiation (cooling) is not uniform, it results in kinematic effects (unbalanced recoil). However, the defining physical difference boils down to the Yarkovsky effect being a force and YORP effect being a torque. The former is applied to the objects barycenter, whilst the latter is applied to the object at some distance r from its center. So we may view Yarkovsky as a push destabilizing the orbit and YORP as a spin destabilizing the structure of the body itself.


How large should the active menu area be?

Question: Here are two similar examples of a typical menu bar.
What would you expect as an active hover area for click?
Should it be the same or different in these two examples?
Does the device matter?
What do you think?
Answer: As a general rule, you want to make the interaction area as large as possible to aid with touch interfaces. The counterbalance to this is that you need to make the button area visually cohesive, so it affords the interaction.
Given this principle, I would suggest you go for option A in both examples.

It is worth noting, however, that A only holds in example 1 because the container constrains the area that could be a link - in a larger area or an area where the container isn't distinct from the background a user might expect the interactive area to only expand to cover the single line of links/dividers.
In the following example there is no obvious vertical constraint so users might expect only to be able to interact with the element as its height is visually defined by the vertical bars:

download bmml source – Wireframes created with Balsamiq Mockups
Answer: Definitely A.
This style of menu bar is emulating a basic button and a button includes the padding.
Also, the bigger the hit area the easier it is for the user.
Answer: There was a study that was conducted which determined 13px x 13px minimum optimum touch-point.
Didn't find the doc. But a potential google hit.
Hope that helps.
All the best!
Nash


Find the number of pairs of positive integers $(a, b)$ such that $a!+b! = a^b$

Question: How many pairs of positive integers $(a, b)$ such that $a!+b! = a^b$?
A straight forward brute-force reveals that $(2,2)$ and $(2,3)$ are solutions and this seems to be the only possible solutions, I was just wondering how could we prove this.
Answer: We first show that $a \leq b$.
Assume by contradiction that $a >b$. Then
$$a^b=b!( a(a-1)...(a-b+1) +1) \,.$$
Thus $a(a-1)...(a-b+1) +1 | a^b$. But $gcd(a,a(a-1)...(a-b+1) +1)=1$ thus  $gcd(a^b,a(a-1)...(a-b+1) +1)=1$. This shows that $a(a-1)...(a-b+1) +1=1$ which is not possible since $a>b$.

We now prove that $a \leq 2$.
Since $a \leq b$ than $a!| a!+b!=a^b$.
Assume by contradiction that $a > 2$. Then, by Bertrand Postulate, there exists a prime $p$ so that $p|a!$ and $p$ doesn't divide $a$. Hence $p|a!$ but $p$ doesn't divide $a^b$, contradiction.
We proved that $a=2$, now the rest is easy.
Answer: It is clear that there are no solutions if $a=1$ or $b=1$. Any solution must be such that $a\ge2$ and $b\ge2$; this implies in particular that $a$ must be even.
Fact 1 . If $a=2$, there exist solutions with $b=2$ and $b=3$; there are no solutions with $b\ge4$.
Proof. If $2+b!=2^b$ with $b\ge4$, then $4$ divdes $b!$ and $2^b$, but not $2$.
Fact 2. If $b=2$, the only solution is $a=2$.
Proof. If $a!+2=a^2$ with $a\ge3$, then $a^2\equiv2\pmod3$, but $2$ is not a quadratic residue modulo $3$.
From now on we assume that $a\ge4$ is even, $b\ge3$ and $a!+b!=a^b$.
For a positive integer $a$ define
$$
\nu(a)=\min\{p\text{ prime}:p\le a,\ p\not\mid a\}.
$$
For instance $\nu(6)=5$ and $\nu(10)=3$.
Fact 3. $b<\nu(a)$.
Proof. If $b\ge\nu(a)$, then $\nu(a)\mid a!$, $\nu(a)\mid b!$ and $\nu(a)\mid a!+b!=a^b$, in contradiction with the definition of $\nu(a)$.
Fact 4. $6\mid a$.
Proof. If $3\not\mid a$, then $\nu(a)=3$, so that $b\le2$. But there are no solutions with $b=2$ other than $a=2$.
Fact 5. There are no solutions with $a=6$.
Proof. It is an easy calculation, since we have to check only $3\le b<5$.
From now on we assume that $6\mid a$, $a\ge12$, $b\ge3$ and $a!+b!=a^b$.
Fact 6. $b>0.59\,a$.
Proof. We know from Stirling's formula that $\log a!>a\log a-a$. Taking logarithms in the equation $a!+b!=a^b$ we get $b<(1-1/\log a)a$. Since $a\ge12$, $1-1/\log a\ge0.59$.
Up to now we have shown that $0.59\,a<b<\nu(a)$. All is left is
Fact 7. $\nu(a)\le a/2$.
Proof. Let $p$ be the largest prime dividing $a$. If $p=3$, then $\nu(a)=5<a/2$. If $p>3$, then $a\ge12\,p$. Let $q$ be the smallest prime larger than $p$. Then $\nu(a)\le q<2\,p\le a/6$.
Fact 8. There must be a simpler way.
Proof. ?
Answer: Given:
$1\cdot2\cdot3\cdot...a + 1\cdot2\cdot3\cdot...b = a\cdot a\cdot a...$
Case $b>=a$:
$= a! + a!\cdot \frac {b!}{a!} = a!\cdot(1+\frac {b!}{a!})$
Case $a>=b$:
$= b! + b!\cdot \frac {a!}{b!} = b!\cdot(1+\frac {a!}{b!})$
Prime factorization shows the need for $a$ to be less than 5.
That is, given that $a!$ or $b!$ is a factor of $a$, and that $x!$ has every prime factor less than or equal to $x$, $a$ contains every prime factor less than or equal to $a$ or $b$. If $b>=a$ then the only case for which $a$ contains all the prime factors of $a!$ is $a=a!$.
In the latter case, $a!$ diverges far too quickly for $a^b$  to even be in the same ballpark. For example, $b=5$ gives $a>=30$ which implies $a!$ is more than 25 orders of magnitude larger than $a^b$.
Comment: Can you please elaborate on "Prime factorization clearly shows the need for a to be equal to either a! or b!" ?
Comment: But what if that largest prime factor of $b!$ also divides $1+\frac{a!}{b!}$? For example, when $b=3$ and $a=5$, then $3$ is the largest prime factor of $3!$ and it also divides $1+\frac{5!}{3!}$.....
Comment: Hat eaten. Thank you sir and would you care to critique my corrections?
Answer: I am hoping to prove the $a\le2$ part of the accepted solution without Bertrand's Postulate .  Let
$a>2$ , then $a-1>1$ , so $a-1$ is either prime or composite , in any case , there is a prime $p$ such
that $p|a-1$ so that $p\le a-1<a$ , hence $p|a!$ ,  and since g.c.d.$(a,a-1)=1$ so $p$ does not divide $a$
Now since
 $a\le b$ , so from $a!\Big(1+ \dfrac{b!}{a!}\Big)=a!+b!=a^b$ we get , as $p|a!$ , so the left hand side is
divisible by $p$ , hence we should also have $p|a^b \implies p|a$ , contradiction ! So $a\le 2$


Is there a difference between Marvel and DC Comics' philosophy?

Question: Marvel and DC Comics are obviously the two major comic publishers.  Are there any differences in their philosophies on comics published?  Marvel seems to have much more fantastic superheroes than DC, for example.  Is there a conscious segregation between the two?
Comment: They both run the gamut of fantasy. Superman's an alien being who can pass for human when he's not flying or melting stuff with his eyes, but Batman and Robin are ordinary humans who do what they do with a combination of training and technology. On the Marvel side, you have a character like Iron Man (pretty much Batman's counterpart in the Marvel universe; rich genius playboy uses his technology to fight evil) right alongside Thor (ripped right out of Norse mythology and played as a demigod) and the Hulk (genetic experiment gone horribly wrong).
Comment: Marvel writes families, DC writes Pantheons.
Comment: Hey, don't say, Marvel has more fantastic superheroes... In terms of popularity, Even wolverine is nothing in front of Batman. And, I am just not including Superman.
Comment: Really I actually think of it as the other way around DC is more fantasy and Marvel is more real. However it has been a few years since I've read current comics maybe they changed.
Comment: I was speaking in terms of their powers - DC seems (to a comic newbie) to have more realistic superheroes, as far as that oxymoron goes, whereas Marvel tends to have powers less tied to reality.
Comment: @OghmaOsiris that's basically what I was curious about.  Can you put that into an answer please? :)
Answer: The discussion of the difference between the philosophy of DC's comic creations and Marvel's isn't nearly as wide as it once was. The main difference is the approach to the characters and their perspectives. Unfortunately, both mythologies have become a bit tarnished and it is more about a profit motive than maintaining their previous ideologies.
Since most of the previous creators of those mythologies have died or choose to remain silent, the two groups appear more and more alike as new talents and leaderships take over how the characters, look, behavior and thinking. So I will be looking at them more historically (as a long-time reader) than as a modern comic consumer who may not see any appreciable difference between the two groups. (And they wouldn't be wrong...)
The DC Way

DC started its hero-making defining its heroes as mythic beings who worked as paragons of Humanity, literally the best of what a Man could be. Superman, Batman, Wonder Woman were all paragons of virtue; strength, will-power or personal fortitude.

DC's Batman shows the indomitable spirit of Man, Wonder Woman shows that peace is desirable but may often have to be fought for. Superman shows the innate goodness of hard work, moderation in all things, restraint and humility even when blessed with phenomenal power. He is a god aspiring for humanity.

Their heroes covered every elemental region and often replicated gods of myth. Aquaman (Posidon), the Flash (Hermes), the Martian Manhunter (Proteus), each of these heroes had mythic counterparts though you may not recognize them immediately. Even their non-powered heroes were legendary in their abilities, e.g. Green Arrow or Batman both physical specimens whose skills allowed them to hang with the gods as legendary heroes like Hercules and Perseus.

DC's heroes can be likened unto gods who have come to Earth (in some cases literally e.g. Superman). They exist to be the exemplars of how great humanity can be when we work together toward common goals and their heroes promote the future of Humanity.

This same mythic nature works against DC when they try to create new heroes who are not as mythic and this may explain why most of their new creations simply never gain the ground their iconic originals did.
The Marvel Way

Marvel's approach was somewhat different. Where DC showed gods in men's clothing, Marvel wanted to elevate Men (and Women) to a god-like stature.

Frail mortals such as Peter Parker and Dr. Banner were suddenly endowed with god-like capacities but with all-too human frailties. Anger, rage, indifference, contempt, mortal weaknesses which gave Marvel's heroes a more human, more understandable every-man quality.

Marvel tried to create heroes who often acquired superheroic capacities, the Fantastic Four being the perfect example. Astronauts, scientists, pilots, stuntmen the F.F. were already some of the best at what they did, so when they were bathed in the cosmic storm which gives them their powers, they simply experienced an apotheosis, an extending of their heroic status into a god-like state.

Marvel further expounds on that god-like state when they have the Mighty Thor (who is believed to be a god) come to Earth to battle the Fantastic Four early in their career. Though they are beaten, Thor admits they were far more than mere mortals. This is the evolution of most of Marvel's early character designs, including Daredevil (enhanced senses liked to extraordinary fighting capacity), Luke Cage (superhuman strength and steel hard skin) and Doctor Strange (accomplished surgeon turned Sorcerer Supreme).

Marvel also played with the other half of the human equation, the desire for normality. For those beings who were born with capacities that made them more than Human, Humanity is cruel and unforgiving. Two examples of groups seeking acceptance and never finding it are the Inhumans and the mutant (also known as Homo Superior).

The Inhumans, subjects of experimentation from millennia ago,  each member was different on the outside than any other member, but they were a warm and loving people (for the most part) extraordinary beings simply wanting what ordinary people wanted, acceptance and respect.

The X-men and other mutants blessed with superhuman abilities were not revered but reviled, by humanity who feared this embedded potential for change right within their very DNA. Marvel also paid homage to the self-made men such as Hank Pym and Tony Stark whose genius allowed them to supersede their humanity using technology.

Marvel's most iconic heroes have been consistently able to be related to by a wider audience because their primary issues are very human, seasoned with a superhuman sauce. Tony Stark has translated well to the silver screen as a wise-cracking, know-it-all, ever so technically smart and yet in some ways so socially inept. Spider-Man for all of his ability still is a young man trying to find himself and adjust to the idea of great power and its inherent responsibility.
Despite their differences, both companies have successfully managed to tread the ground where most humans find themselves needing guidance and looking to mythology to find the answers. What do I do when I find myself in a position of power and authority? How do I conduct myself? How do I lead effectively? How do I set a good example? Is this the best I can be?
Comment: I've been waiting for a Thaddeus input on this question for ages!
Comment: The one thing that's always really bugged me about the whole X-Men "we fear them because they're going to out-compete us and eradicate us like we did to the Neanderthals" hook is that that's not what happened to the Neanderthals.  Genetic research has shown that modern humanity, and particularly the Caucasian race, has a non-trivial percentage of Neanderthal DNA in their genome.  It's believed to be responsible for several fairly common traits, most notably red hair.  *We didn't exterminate the Neanderthals; we assimilated them.*  Why wouldn't the same happen again with humans and mutants?
Comment: Thank you. I'm sorry I was so late to the conversation. This is the kind of thing I usually get to in a timely fashion...
Comment: Of course, there are exceptions to these trends. To me, [Squirrel Girl](https://en.wikipedia.org/wiki/Squirrel_Girl) always felt like a DC character who wandered into a Marvel comic.
Answer: You say that DC has more plausible characters, but actually, Marvel Comics has tried to make most of their superheroes more realistic than DC. Stan Lee has said in a few interviews that when he created most of his comics, he wanted his fans to think that it could happen to them, so he made situations more realistic. Like a radio active spider bite, or an accidental dose of gamma rays, or they were all just born that way, etc. DC comics are far more far fetched because half of their heroes are aliens or all the superheroes are super geniuses like Batman, Atom or Mr Terrific.
But, because the origin stories are more plausible, the writers have already gained your trust and can create more elaborate or fantastical stories and you'd still think they could happen. With DC comics, once we accept that the superheroes are super because they aren't from this planet or they are richer than God, then the stories stay at that level of fantasy and the reader never really sees how fantastic the characters are, when in comparison to other comics, are much more elaborate or fictitious.
Comment: I don't understand well your answer. Are you basically saying "Marvel has realistic heroes/unrealistic situations and DC has unrealistic heroes/realistic situations ?"
Comment: I guess you could simplify that. But it really comes down to the characters and their origins.
Answer: Stan Lee himself answered this: he grew up with DC characters like Superman and didnt like the fact their "powers" came from no where. Superman just jumps up and flies, etc. His idea was to create characters who had a plausible reason (albeit based in fantasy) for gaining these powers. The idea of extreme genetic mutation (X-men), bitten by radioactive spider (Peter Parker), etc.
DC characters are basically nut cases with strange fetishes and illogical powers.
Answer: It is not too much, but the philosophies of Marvel and DC comics are simple. However, the weight behind them carries more than one would think. When you say "Fantastic Heroes" I am guessing you mean the way the Marvel Heroes achieve their objectives without casualty and/or sacrifice. As both a fan of both franchises I can speculate that DC has more realism than Marvel. Although the heroes in DC are more far-fetched as to obtaining their powers and gifts, they encounter mid-life crises and tragedy as much as the average Police Officer, Fire Fighter, and Military Personnel, or in other words: to incur the wrath and hate of others just by indulging and following your beliefs. However, DC shows the full extent of the consequences for fighting for what you believe in, both in terms of philosophy and mental stability. Marvel on the contrary, takes a different approach. When seeing tragedy or an impossible situation approaching, Marvel Heroes always "Try to find a better way" as to avoid the oncoming event, prompting that no matter the situation may be, it can always work out or there's a solution without needed sacrifice. In conclusion, both Comic Franchise's philosophies have their pros and cons. For Marvel: Always believing that heroes can prevent every disaster is foolish. As individuals who shoulder the burden of billions, they must realize the reality of saving everyone is impossible. For DC: The grim reality of being a hero can be devastating, even for the  most adamant. But despite the difficulty of being a hero, people will always be hoping and building towards a better future with or without the help of heroes. And that's all I can say, hope it helps
Comment: I may not agree entirely with this, but I must say, it is extremely well written. Kudos.
Answer: At heart, it's an issue of identity.
DC heroes are superheroes with secret identities. It's not that Clark Kent is Superman---it's that Superman disguises himself as Clark Kent. Green Lantern disguises himself as Hal Jordan (or John Stewart, etc.). This isn't necessarily bad, just think Batman: Batman has become the identity, and Bruce Wayne has become the disguise (a concept that has generated some of the greatest stories in comic history, with layers of psychological complexity). To me Batman will always be the greatest hero DC has to offer precisely b/c the character is delves deepest with identity issues. It's yet another reason why Batman/Joker is the greatest DC rivalry: Joker's original identity, too, has all but disappeared. They are two people who have transferred their identities over to the characters, or the legends, if you will.
In Marvel, people with real lives sometimes have to put on their tights and be heroes. Perhaps the greatest example here is Peter Parker, who's girl troubles, family issues, bullying issues at school, social rejections, pure nerdliness, etc., were traditionally foregrounded just as much as the hero stuff.
Finally, it's worth saying that I'm painting in broad strokes here, and possibly talking about the "olden days of yore" for both companies. Clearly DC has opened up the personal lives of its heroes the last couple decades, while Marvel has moved some of its characters towards more of an iconic status. I think part of what made "Man of Steel" work this past summer is precisely that the main character is Clark more than he is Superman (of course, I seem to like this movie more than most of my friends, so what do I know? lol).
Answer: One of the differences I note is that DC superheroes are in fictional cities (Superman lives in Metropolis, Batman in Gotham City...), while Marvel has stories located in real cities (e.g. Spiderman/DareDevil/F4 lives in New York).
Answer: I Think that the major difference between Marvel and DC is that Marvel is more about science and experiments than DC but I dont know the DC Universe as well as Marvel's ... But both Universe have Grown so big now that this point could be irrevelant now ...
Comment: Some examples to support that position would be nice.


Singing with allergies and asthma?

Question: Save your voice while being sick but it gets blurry with allergies and asthma. I can hear an allergic reaction from my voice before I can feel anything, like playing Singstar and a pet visiting. The volume of lungs can greatly vary during allergic season from more normal. So how should you train singing with allergies and asthma?
Comment: I hope someone has some good ideas.  That's a challenge to say the least.  Many allergy medicines designed to relive the symptoms have the effect of drying the mucous membranes which is very bad for singers.  So one thing I would suggest is that the type of allergy drugs that are antihistamines or otherwise dry up mucous membranes or have a dehydrating effect should not be used for several days prior to singing.
Answer: I believe practicing or singing during an allergy or any infection is very dangerous as it gives a lot of strain to the already strained muscles of the throat. A proper medication is really required to recover. Yoga, meditation and breathing exercises really help for singing. Either ways, a good exercise and a good balanced diet is required to maintain a good voice and good health. A humidifier is required since it helps keeping the air moist. You'll definitely bounce back once you regularly practice after the recovery of asthma or allergy.
Happy Singing :)
Comment: +1 for nice suggestions. Many allergy/astmma medicines make things dry and sound very different. Is a humidifier a portable machine?
Comment: Yes few are portable, "evaporative", "cool moisture", or "wick humidifier", consists of just a few basic parts: a reservoir, wick and fan. Sorry for the late reply.

Singing with allergies and asthma?


Few events that I failed to understand in The House That Bled to Death

Question: In the Hammer House of Horror TV series episode The House That Bled to Death I did not understand why the girl Sophie killed his father? Also how the cat was killed, was there any ghost/sprit of the old women?
Answer: There are multiple ways to interpret the ending, and ultimately I don't think we can point to one of them and say "That is the right ending; the other one is just wrong."  I think the screenwriter was happy to leave that uncertainty, because horror flourishes better in an atmosphere where things are uncertain.
To start with what's relatively certain...  It seems pretty certain that William was the one who killed Sophie's cat.  From William and Emma's conversation in the pool, it seems obvious that he was the one who made most of the frightening events happen.  If the cat had really died by cutting itself on a broken window (which is what supposedly happened) he might have remarked about what an extraordinary stroke of luck it was, since it was one of the most frightening of the events...  but he says no such thing, so the natural conclusion is that it is one more thing that he engineered to bolster the "haunted murder house" story.
Notice that after the animal's death, William refers to it more than once as "the stupid cat" or "a stupid cat", which no one else does - it may be that he's trying to dismiss its importance out of guilt for killing it.  Or, it's also possible that he never liked the cat, perhaps because his daughter seems fonder of the cat than of her parents (Emma makes that statement, early in the episode.)
So it seems unlikely that any of the "haunting" events which happen in the house were actually supernatural.  If there was any part of those events which was not actually engineered by William, he likely would have mentioned what a good stroke of luck it was.
So, the other question is:  is any part of the ending, after they've left the house, supernatural?
Well, it doesn't have to be.  When Sophie leaves the pool and goes upstairs, she reads the book that the estate agent wrote about the "hauntings" in the house.  She sees the photo of Timmy, the cat she loved, and she flashes back to Timmy's bloody corpse.  She then opens one of the suitcases they took from the house, and finds some of the props that were used to frighten the neighbor Jean earlier - the bloodied knitting, and the eyeglasses, which William denied ever seeing.
She now has all the pieces to put together the truth:  that every terrifying, traumatizing thing which happened to her in that house, including the death of her beloved pet, all the things that are still giving her nightmares three years later, were all just a hoax perpetrated by her own father.
She might be killing him just for revenge - revenge for her trauma, revenge for her murdered cat.  The whole narrative makes sense that way, and there's no need to invoke anything actually supernatural.
But horror and irony go very, very well together, so it's tempting to ask:  what if Sophie's murder was prompted by supernatural influence?  What if it wasn't just her own anger at her father, but some influence from the house?  There's nothing in the episode that proves such an influence, but there's an intriguing line which leads to some speculation:  when William sees the distinctive sword in Sophie's hand, and asks "Where did you get that?" he might mean "I had those swords packed away in a place I never expected you to go looking; why did you go poking into that stuff?"
Or, he might have meant "How on Earth did you get those?  I thought I got rid of them entirely when we had finished giving Mr. Peters the 'haunted house' story he was selling!"  Earlier, the swords were supposedly reappearing by supernatural means, despite having been taken away by the police and later thrown away (supposedly) by William.  If they really did come to Sophie's possession by supernatural means, it would be deeply ironic - all the more so because it would be those who tried to profit by exploiting a tragedy, and the supernatural, meeting their own tragedy from the supernatural.
So, ultimately, you can take either interpretation, depending on which you like.  There is no "proof" that anything supernatural occurred, but believing that it did adds an extra layer of closure to the scene.


Why did Lord Rama ask mother Sita for Agni Pariksha?

Question: What is the reason for Lord Rama to ask Mother Sita to give Agni Pariksha? What do the scriptures say about this?
Answer: In this chapter of the Yuddha Kanda of the Ramayana, Rama explains why he made Sita walk through fire, despite having complete trust in her:

Seetha certainly deserves this pure factory ordeal in the eyes of the people in as much as this blessed woman had resided for a long time indeed in the gynaecium of Ravana. The world would chatter against me, saying that Rama, the son of Dasaratha, was really foolish and that his mind was dominated by lust, if I accept Seetha without examining her with regard to her chastity.
I also know that Seetha, the daughter of Janaka, who ever revolves in my mind, is undivided in her affection to me. Ravana could not violate this wide-eyed woman, protected as she was by her own splendour, any more than an ocean would transgress its bounds.
In order to convince the three worlds, I, whose refugee is truth, ignored Seetha while she was entering the fire. The evil-minded Ravana was not able to lay his violent hands, even in thought, o the unobtainable Seetha, who was blazing like a flaming tongue of fire.  This auspicious woman could not give way to the sovereignty, existing in the gynaecium of Ravana, in as much as Seetha is not different from me, even as sunlight is not different from the sun. Seetha, the daughter of Janaka, is completely pure in her character, in all the three worlds and can no longer be renounced by me, as a good name cannot be cast aside by a prudent man. The salutary advice of you all, the affectionate guardians of the world, who are saying what is conducive to our good, must be certainly carried out by me.

So it was done in order to demonstrate to the rest of the world that Rama wasn't taking in an unfaithful wife, even though Rama personally knew she was faithful.
Of course, this still wasn't enough to make the people of Ayodhya believe that Sita had been faithful, which is what ultimately led to Sita's exile.
By the way, on a side note according to the Skanda Purana, it is Vedavati, not the real Sita who goes into the fire, as I discuss in my answer here.
Comment: There is also a thing of Maya Sita who was conjured for the sole purpose of playing out the Leela, written in the Kurma Purana. But you obviously knew it.
Comment: @ArkaprabhaMajumdar Yeah, I alluded to it in the end of my answer.
Answer: Seeta parityaga (Disowning) episode - a character assassination
The Seeta parityaga (Disowning of Seeta), Seeta Agnipravesha, arrival of all GODs and Sri Rama accepting Seeta  episodes were described in the Sargas 115 to 118 of Yuddha Kanda of Srimad Ramayana.
Sri Rama sends Vibhishana to bring Seetha to his presence. Vibhishana brings Seetha to Sri Rama's presence.
Sri Rama informs Seetha that the dishonour meted out to him and the wrong done to her by Ravana have been wiped off, by his victory over the enemy with the assistance of Sri Hanuma, Sugreeva and Vibhishana.
However, regarding with suspicion on the character of Seetha, Sri Rama disowns her and asks her to seek shelter elsewhere.
Seetha gives a taunting reply to Sri Rama, saying that why she was not abandoned by the latter, even at the time when Sri Hanuma came to see her in Lanka.
Then, Seetha requests Lakshmana to prepare a pile of fire for her to enter. When Lakshmana prepares a pyre, Seetha prays the fire-god and enters into it, in order to prove her conjugal fidelity.

Lord Brahma, Lord Shiva and other gods reach that place and eulogise Sri Rama as the incarnation of Lord Vishnu and Seeta as Adilakshmi.

ततो वैश्रवणो राजा यमश्च पृभिः सह | सहस्राक्षश्च देवेशो वरुणश्च
  जलेश्वरः ||  षड्र्धनयनः श्रीमान् महादेवो वृषध्वजः | कर्ता सर्वस्य
  लोकस्य ब्रह्मा ब्रह्मविदां वरः ||  एते सर्वे समागम्य विमानैः
  सूर्यसंनिभैः | आगम्य नगरीं लङ्कामभिजग्मुश्च राघवम् ||  (Yuddha Kanda
  117 Sarga 2 - 4 Slokas)
"Thereupon, Kubera the King of Yakshas, Yama the lord of death
  together with the deceased ancestors, Indra the lord of celestials
  Varuna the lord of waters, the illustrious Shiva the great deity who
  bears the device of a bull as his banner and having three eyes, Brahma
  the creator of all the worlds and the best among the knowers of sacred
  knowledge all these together reaching the City of Lanka in aerial
  cars, shining like the sun approached Rama."

After lengthy dialogue, Lord Brahma requests Sri Rama to take back Sita.

विशुद्धभावां निष्पापां प्रतिगृह्णीष्व मैथिलीम् | न किंचिरभिधातव्या
  अहमाज्ञापयामि ते ||   (Yuddha Kanda 118 Sarga 10 Sloka)
"Take back Seetha, who is sinless, with a pure character. She should
  not be told anything harsh. I hereby command you."

Then Sri Rama accepts Seeta since her chastity was confirmed by AGNIPARIKSHA.

अनन्यहृदयां भक्तां मचत्तपरिवर्तिनीम् | अहमप्यवगच्छामि मैथिलीं
  जनकात्मजाम् ||   (Yuddha Kanda 118 Sarga 15 Sloka)
"I also know that Seetha, the daughter of Janaka, who ever revolves in
  my mind, is undivided in her affection to me."
प्रत्ययार्थं तु लोकानां त्रयाणाम् सत्यसंश्रयः | उपेक्षे चापि वैदेहीं
  प्रविशन्तीं हुताशनम् ||   (Yuddha Kanda 118 Sarga 17 Sloka)
"In order to convince the three worlds, I, whose refugee is truth,
  ignored Seetha while she was entering the fire."

The episode of Seeta parityaga (disowning) was, in my view, not written down by Sage Valmiki but a PRAKSHIPTA (an insertion made by somebody with a view to elevating the status of Lord Vishnu to that of SARVA LOKADHIPATI at a later date) for the following reasons.

According to Srimad Ramayana, Lord Brahma was the ultimate God and the place of Vishnu was only next to Lord Indra.  Shiva was only an ex-Senadhipathi
As Putrakamesthi episode was inserted to make believe the readers that Sri Rama was in fact the incarnation of Lord Vishnu, Seeta parityaga (Disowning of Seeta), Seeta Agnipravesha,  episodes were inserted consciously  to pave way for the arrival of all GODs and Sri Rama accepting Seeta  episodes.
Hence, eulogising Sri Rama as the incarnation of Lord Vishnu and Seeta as Adilakshmi by Lord Brahma and Lord Shiva WAS DONE to elevate the status of Lord Vishnu and did not fit into Srimad Ramayana
Sri Rama always expressed his great eagerness in getting back his dear wife Seeta at the earliest. At no point of time, till his meeting with Seeta after the death of Ravana, he was depicted expressing his desire to give up Seeta as she was residing in Ravana's house.
If Sri Rama already had a doubt of Seeta's conjugal fidelity or he already decided to disown Seeta after killing of Ravana, he would have felt relieved with the news of death of Seeta.  Instead, his immediate reaction to the news of Indrajit chopping off the head of illusionary Seeta was to faint away.

This episode alongwith the episode of abandonment of Sita in Uttara Kanda, (interpolations) left a long lasting negative impression on the character of Sri Rama as male chauvinist.
Whoever inserted Seeta parityaga (Disowning) episode" in Ramayana,  for elevating the status of Vishnu, which was an epithet in Veda, as SUPREME LORD, forgot that it led to a character assassination of Sri Rama.
Comment: Lord Rama never doubted Sita. The Agni Pravesha was an attempt by Lord Rama to prove to the world that Sita is pure.
Answer: Technically Rama didn't ask Sita to go into the fire. It was Sita herself who wanted this ordeal.

chitaaM me kuru saumitre vyasanasyaasya bheShajam |
  mithyaapavaadopahataa naahaM jiivitumutsahe
"O Lakshmana! Create a pile of fire for me, which is a remedy for this
  disaster. I no longer wish to survive with false blames."

The Agnipariksha was never an intention of Rama, albeit that had to be done because the Sita who was kidnapped by Ravana was no other than an illusory form of Sita called Maya Sita. This story, retold in Caitanya caritamrta 2.9.200 - 212, appears in Kurma Purana 2.34.111 - 140.

A chaste woman devoted to piety (dharma) shall always attain welfare
  and happiness. No man can, by any means, create discomfiture for
  her.  Just as in the case of Sita,1 well-known in the three
  worlds, as the charming and beloved wife of Rama, the son of
  Dasaratha, she conquered the king of Raksasas.
  Urged by Kala (Death), Ravana, the king of Raksasas, desired Sita, the wide-eyed beautiful wife of Rama.
 It is reported that by means of his Maya, he disguised himself (as) an ascetic and determined to abduct that beautiful lady
  while she was strolling (solitarily) in the tenantless forest.
 The lady of pure smiles realised his intention. Remembering her husband, the son of Dasaratha, she sought refuge in
  the Avasathya (household) fire.
 With her palms joined in devotion, Rama's wife worshipped the great Yogi (the fire-god), the destroyer (scorcher) of the worlds,
  as if he was her husband Rama incarnate (and prayed): Eulogy of the
  Fire-god.
 I bow unto Krsanu (fire) of the form of Kala, of great Yogic power, the greatest riddle, the destroyer of all living
  beings.
 I take shelter in lord Pavaka (the purifying deity), the eternal deity of universal forms, the Yogin who wears the (elephant)
  hide, the lord of the goblins, the Supreme god.
 I resort unto the Atman of radiant blazing body abiding in the hearts of all living beings. I seek refuge in the Lord whose
  form is the universe, the source of all that fiery, brilliant. I
  resort to the fire-god, the Lord of great Yogins, the sun, the supreme
  god. I seek refuge in Rudra, the great swallower (destroyer), the
  trident-bearing Lord, the fire of the Universal destruction, the Lord
  of Yogins, the dispenser of fruits (in the form) of enjoyment and
  liberation.
 I resort unto you the diverse-eyed deity with the forms of Bhuh, Bhuvah and Svah}, one who is lying hidden in the golden
  abode, the great one of unmeasured splendour.
 I resort to Vaisvanara abiding in all living beings, the lord who conveys Havyas and Kavyas (i.e. offerings) (to gods and
  Pitrs). I resort to Lord Vahni.
 I resort to that Supreme reality, the excellent and auspicious principle of the sun. I resort to the Agni ascending to
  heaven, the greatest splendour, the imperishable conveyor of oblations
  to gods.
 After repeating (the prayer in) these eight (?) verses on Vahni, the famous wife of Rama mentally meditated on Rama and remained
  silent with her eyes closed.
 Then out of the Avasathya (household) fire, Lord Mahesvara (the great god), the bearer of sacrificial oblations, of
  resplendent soul manifested himself as if burning with his own
  refulgence.
 Desirous of getting Ravana killed he created an illusory Sita. Taking the real Sita, the beloved of Rama, the fire-god vanished
  there.
 On seeing such a Sita (i.e. the illusory one) Ravana the lord of Raksasas, took her and went to Lanka, situated within the
  ocean.
 After killing Ravana, Rama took Sita and (came back) accompanied by Laksmana. His mind became agitated due to
  suspicion.
 For convincing the living beings, the illusory Sita entered the fire; immediately she was consumed by the fire.
 After burning the illusory Sita, the lord fire-god of hot rays, showed the real Sita to Rama. The fire-god (the purifier) became
  a beloved of Devas.
 Catching hold of the feet of her husband, the daughter of Janaka, the lady of beautiful middle, made obeisance to Rama on the
  ground.
 On seeing it Rama was delighted in mind. Surprise was evident in his eyes. After bowing to the Vahni with bent head, Raghava
  propitiated him.
 The lord spoke to Vahni: Was this fair-complexioned lady burned by you before, as she has been seen come to my side again?
 Lord Fire-god, the scorcher of the worlds, spoke to the son of Dasaratha, telling him everything as it had happened in the
  presence of all living beings.
 "This beloved of yours is highly chaste as goddess Parvati. She is the greatest favourite of the goddess whom she had
  propitiated by means of penance
 This chaste lady of good conduct is endowed with the readiness to serve her husband like Bhavani in regard to Isvara. She
  was protected by me because she was desired by Ravana.
 But Sita who was abducted by the lord of Raksasas was the illusory Sita created by me with a desire to get Ravana killed.
 On that account, Ravana, the wicked king of the Raksasas and the destroyer of the worlds, had been killed. The Maya has also
  been withdrawn.
 "Accept this pure Janaki at my instance. See lord Narayana your own self the source of origin and the place of
  everything".
 After saying this, the fierce lord fire-god whose flames spread everywhere and who had faces on all sides was duly honoured by
  Raghava and the other people and he vanished.

Thus we see that Maya Sita was just an illusion who went back to Agnidev through the Agnipariksha while Agnidev himself brought out the real Sita to Rama. At that moment Rama (who definitely knew everything) was (just for a show to the common public) very happy and elated. The Agnipariksha was done for 2 major reasons. 1> Return of Maya Sita back to Agnidev, and 2> A foolproof convincing of the common public that Sita was not unchaste, as a disgruntled public would not be beneficial for Ram Rajya. This was a risk which Rama had taken on his own honour. While its true that people were speaking ill about Sita, they all stopped in their tracks when they witnessed the apparently "cruel" act of Rama. Everyone's emotions are running high. They know what they have witnessed. By this time they knew Sita was pure, even purer than fire itself. Rama had achieved his motive.
It was not possible for Ravana to even touch the lotus feet of mother Sita. Sita is the mother of the universe and the supreme goddess of fortune. Nobody can touch mother Sita. In fact, a person with material senses cannot even see her. When Ravana kidnapped her, he took only her material illusionary form.
Lord Rama is the Supreme Personality and He knew everything. He was just playing the role of a human. After the agni-pariksha, He accepted the real mother Sita. He took her back to Ayodhya, where He was coronated, King. Lord Rama set very high standards for human conduct and behavior with His exemplary qualities.
See another comprehensive answer of mine about the same topic, here.
Answer: Sita was actually the daughter of Lord Agni and Mandodari. Mondodari was very beautiful and Agni got  thrilled saying her beauty . In the union Sita was born However Agni promised that Sita was born to destroy Ravanas dynasty . However you will remin as virgin only . She was asked to put Sita somewhere. Manodari filled all necessary things for the child including ornaments and asked the servants to Dispose off the child at a far away place. She was thus buried in a casket at Jankas plouging field. As Janaka had no issue he was asked to plough the field . During the act the casket was retrieved and Sitha came into the hands of Janaka. As he came ploughing field which is also called Sita , she was named thus.
Later she was married to Rama.
When Rama went to exile in forest Lord agni came and told Rama that I will take away Sita and give you Mayua Sita, Original Sita will be returned durting Agni Pravesh.
In order to get back the Original Sita the Agni Pariksha was conducted.
Comment: You should cite sources.
Comment: Source-In the Malyalm book called Adhyatma ramayan written by Ezuthachan  in the aranya kand  there is a chapter called Ravana mareecha samvad whrein Rama is aking sita to hide hereself in Vanhimandal and keep Maya seeta inplac  till the killing of RAvan .