What is translation invariance in computer vision and convolutional neural network?

Question: I don't have computer vision background, yet when I read some image processing  and convolutional neural networks related articles and papers, I constantly face the term, translation invariance, or translation invariant.
Or I read alot that the convolution operation provides translation invariance?!! what does this mean?
I myself always translated it to myself as if it means if we change an image in any shape, the actual concept of the image doesn't change.
For example if I rotate an image of a lets say tree, it's again a tree no matter what I do to that picture.
And I myself consider all operations that can happen to an image and transform it in a way (crop it, resize it, gray-scale it,color it etc...) to be this way. I have no idea  if this is true so I would be grateful if anyone could explain this to me .
Answer: You're on the right track.
Invariance means that you can recognize an object as an object, even when its appearance varies in some way. This is generally a good thing, because it preserves the object's identity, category, (etc) across changes in the specifics of the visual input, like relative positions of the viewer/camera and the object.
The image below contains many views of the same statue. You (and well-trained neural networks) can recognize that the same object appears in every picture, even though the actual pixel values are quite different.

Note that translation here has a specific meaning in vision, borrowed from geometry. It does not refer to any type of conversion, unlike say, a translation from French to English or between file formats. Instead, it means that each point/pixel in the image has been moved the same amount in the same direction. Alternately, you can think of the origin as having been shifted an equal amount in the opposite direction. For example, we can generate the 2nd and 3rd images in the first row from the first by moving each pixel 50 or 100 pixels to the right.

One can show that the convolution operator commutes with respect to translation. If you convolve $f$ with $g$, it doesn't matter if you translate the convolved output $f*g$, or if you translate $f$ or $g$ first, then convolve them. Wikipedia has a bit more.
One approach to translation-invariant object recognition is to take a "template" of the object and convolve it with every possible location of the object in the image. If you get a large response at a location, it suggests that an object resembling the template is located at that location. This approach is often called template-matching.

 Invariance vs. Equivariance
Santanu_Pattanayak's answer (here) points out that there is a difference between translation invariance and translation equivariance. Translation invariance means that the system produces exactly the same response, regardless of how its input is shifted. For example, a face-detector might report "FACE FOUND" for all three images in the top row. Equivariance means that the system works equally well across positions, but its response shifts with the position of the target. For example, a heat map of "face-iness" would have similar bumps at the left, center, and right when it processes the first row of images.
This is is sometimes an important distinction, but many people call both phenomena "invariance", especially since it is usually trivial to convert an equivariant response into an invariant one--just disregard all the position information).
Comment: Could you clarify how translation invariance is achieved with CNN? The activations of a convolutional layer in a CNN are not invariant under translations: they move around as the image moves around (i.e., they are equivariant, rather than invarianct, to translations). Those activations are usually fed into a pooling layer, which also isn't invariant to translations. And pooling layer may feed into a fully connected layer. Do the weights in a fully connected layer somehow change transalation equivariant to translation invariant behavior?
Comment: @Fredom, that might be better as a new question, but in brief--the audio signal sounds the same even when you shift it forwards in time (e.g., by adding a bunch of silence at the beginning). However, if you shift it in the frequency domain, it *sounds* different: not only is the spectrum shifted, but relationships between frequencies (e.g., harmonics) are also distorted.
Comment: @max, Pooling does increase translation invariance, especially max-pooling(!), which completely disregards spatial information within the pooling neighborhood. See Chapter 9 of Deep Learning http://www.deeplearningbook.org/contents/convnets.html (starting on p. 335). This idea is also popular in neuroscience--the HMAX model (e.g., here: http://maxlab.neuro.georgetown.edu/docs/publications/nn99.pdf) uses a combination of averaging and max-pooling to generate translation (and other kinds of ) invariance.
Comment: Oh right, pooling provides invariance over small translations (I was thinking about larger shifts, but perhaps each successive layer of pooling can handle progressively larger shifts). But what about the [fully convolutional networks](https://arxiv.org/abs/1412.6806)? Without pooling, what provides (at least approximate) invariance?
Comment: How do one explain that "speech is translational invariant only along time-axis, but not frequency axis", what does it mean?
Answer: I think there is some confusion about what is meant by translational invariance. Convolution provides translation equivariance meaning if an object in an image is at area A and through convolution a feature is detected at the output at area B, then the same feature would be detected when the object in the image is translated to A'. The position of the output feature would also be translated to a new area B' based on the filter kernel size. This is called translational equivariance and not translational invariance.
Answer: @Santanu
While your answer is correct in part and leads to confusion. It is true that Convolutional layers themselves or output feature maps are translation equivariant. What the max-pooling layers do is provide some translation invariance as @Matt points out.
That is to say, the equivariance in the feature maps combined with max-pooling layer function leads to translation invariance in the output layer (softmax) of the network. The first set of images above would still produce a prediction called "statue" even though it has been translated to the left or right. The fact that the prediction remains "statue" (i.e. the same) despite translating the input means the network has achieved some translation invariance.
Comment: Moderately it does. Remember the max pooling operator takes the maximum pixel value as its output in a given window. This mathematically necessitates some invariance since the spatial location of the maximum pixel values is irrelevant (within some tolerance).
Comment: I'm not so sure that pooling leads to translation invariance.
Comment: And why translation invariance is useful in a CNN? If we care only about detecting features, we can just remove all max pool layers and use a global max pool layer after the final convolutional layer. Why bothering with max pooling in intermediate layers?
Answer: The answer is actually trickier than it appears at first. Generally, the translational invariance means that you would recognize the object regerdless of where it appears on the frame.
In the next picture in frame A and B you would recognize the word "stressed" if your vision supports translation invariance of words.

I highlighted the term words because if your invariance is only supported on letters, then the frame C will also be equal to frames A and B: it has exactly the same letters.
In practical terms, if you trained your CNN on letters, then things like MAX POOL will help to achieve the translation invariance on letters, but may not necessarily lead to translation invariance on words. Pooling pulls out the feature (that's extracted by a corresponding layer) without relation to the location of other features, so it'll lose the knowledge of relative position of letters D and T and words STRESSED and DESSERTS will look the same.
The term itself is probably from physics, where translational symmetry means that the equations stay the same regardless of translation in space.
Comment: Couldn't we achieve translation invariance with global pooling after the final convolutional layer? Why bothering with max pool in intermediate layers?
Answer: I will answer you briefly,
translation invariant means that the algorithm will recognize the object even if you shifted its position from any place in the picture to any other place, lets say , we have a cat in photo with grass background , if you shifted the cat to the corner of the image or any other place , model still recognize , it is not affected by the translation ( shifting )


How much energy is there in 1 mol of diamond and how can you get it?

Question: Diamond is made of carbon which is during maybe 3 billion years under pressure is formed in the earth. Imagine you found a big source of diamonds such as coal...how much is the energy of the diamond compared to the coal, and how should you get the energy out of it?
Comment: Depends on quality of the coal, also it's quite hard to burn diamond.
Comment: 1. Marginally more. 2. By burning it instead of coal.
Comment: @IvanNeretin marginally more than graphite, but significantly more than coal
Answer: Diamond is just one of the allotropes of carbon. There is nothing unique about diamond that allows it to store significantly more energy than any other compound. It is true, however, that much energy is required to separate carbon atoms in a diamond lattice. This is due to the high bond dissociation energy of a carbon-carbon covalent bond.
Although bond dissociation energy in a C—C bond is relatively high, it is dwarfed by the energy predicted to be released by the mass-energy equivalence theorem.
$E = mc^2$
The nuclear mass of 1 mole diamond is about 12 grams. So the theoretical energy released in a fusion reaction involving one mole of diamond is around 1*$10^9$GJ.
I don't think this is the answer you were expecting. But this is the amount of energy in 1 mole of carbon. The method of releasing all this energy is a different story. Nuclear fusion would release a significant portion of this energy but not all of it.
Comment: I like this answer but feel it's incomplete without mention of the possibilities of (i) burning the diamond and the energy obtainable therefrom, and (ii) converting the diamond to graphite and the energy obtainable therefrom.
Answer: The trouble with the question is that is misses an important aspect of chemical energy which is the question: relative to what?
The C-C bonds in diamond are strong but this means they need a lot of energy input to break them up not that they "contain" a lot of energy. If we form diamond from gaseous carbon atoms then we release a lot of energy (though this is a theoretical idea since it isn't a practical way to make diamond).
Diamond stores slightly more energy than graphite (~2kJ/mol at normal conditions). This means that if we could convert diamond to graphite we could release a really small amount of energy. This isn't practical or desirable.
Both forms of carbon can release energy when they burn. So, in a sense, they store energy relative to carbon dioxide. This is because carbon-carbon bonds are higher in energy than carbon-oxygen double bonds so converting one to the other releases energy (this is why coal is a good energy store and fuel).
So when you talk about releasing energy from chemical, you need to specify the reaction you have in mind. Absolute energies are pretty meaningless.


Do the survivors in The Walking Dead have immunity to the zombie plague or are they just lucky?

Question: From what I recall of 28 Days Later, where the old guy gets infected and turned with a bit of infected blood, they (or at least he) didn't have immunity to the plague, unlike in Left 4 Dead.  Is this the case in The Walking Dead as well?  They don't seem to be particularly careful about how they splatter the undeads' bodily fluids all over themselves (be it a rock to the head or machete to the gut).
Comment: They probably aren't 100% sure how the infection works.
Answer: In the comics it is established that everyone already is infected, though the symptoms only show after you "die" unless the brain is damaged too much.
This was shown with

 Shane. He died by gunshot, yet turned into a zombie while laying six feet under without having endured any zombie-bites. After Rick learned of that fact, he dug him up again and killed him for good.

This also applies to the TV-show:

 There was a man, who committed suicide by hanging himself in a tree, and he turned into a zombie as well. Andrea had him killed out of mercy.
Comment: @OliverS The exact note read: "Got bit. Fever hit. World gone to shit. Might as well quit"
Comment: I think the person in your second reference got bit and *then* did what they did.
Comment: NullUserExceptionఠ_ఠ is correct, they found a note saying something like "I got infected, fever started, opting out."
Answer: The survivors have no immunity.
In both the graphic novels and the show the survivors have at least one member of their group get bitten, and start to show symptoms of the infection.
It is also mentioned that they had to take care not to get any part of the walkers, particularly the fluids, near their mouths or eyes.

 this comes up particularly when they are covering themselves in walker fluids to mask their scent.

Presumably this is to reduce chance of becoming infected by contact.
Comment: They *talk* about taking care not to get spattered in the eyes or mouth, but they almost never bother with eye protection before swinging the axe, not even in the scene you mention. And for all we know it may require blood contact anyway.
Answer: This answer is based on information up through the end of season 2 of the TV series.  In the episode Better Angels, we see two people die.  Neither die from walkers, instead they die from human on human violence.  Their dead bodies are not touched by walkers.  They both return as walkers.  Afterwards, Rick confirms to the group that Jenner told him that they're all infected.
In season 1's Vatos, one of the survivors, Jim, is bitten during a walker attack.  In the next episode, we see that he's getting very sick incredibly quickly.  We're led to believe he'll soon become a walker, an experience some of the survivors have had prior to Rick's waking up.
I think what we're seeing is that the disease that causes the walkers is dormant in living humans.  Only once a human dies does the disease become active.  Once active, it animates the brain stem and turns the body into a walker (as shown in TS-19).  Now that the disease is active in that body, biting a living person introduces the active form of the disease to the living person's system.  This disease is deadly or at least turns them into a walker quickly.
It'll be interesting to see what happens with

 Lori's

growing fetus in season 3.
Answer: Almost every interaction with the walkers ends with an inspection for cuts or bite marks. This suggests that the current survivors don't believe that they have any particular immunity to becoming zombies themselves.  It also indicates that casual contact with the walker's fluids is not sufficient for transmission.
Answer: It is said in the series that all people are already infected with the disease... This was revealed by Dr Jenner to Rick back in the first season.
Answer: TL;DR:  Neither.  Zombie blood isn't that dangerous.

Word of God:  Franchise creator, writer of the comics, and Executive Producer of both shows, Robert Kirkman:

Q:  This is a real Comic Book Guy question – but do I gather that if someone swallows a tiny bit of zombie blood they won't turn into one of the undead? There was a lot of it being sprayed around this episode [Season Three, Episode 6, Hounded].
A:  Yeah, people to a certain extent think of zombie blood as being like the blood from Alien. You know, in the Alien movies it's like, "Oh god, if it touches you, you explode!" or whatever. Whatever it is that turns these people into zombies is in them already. So the idea of getting zombie blood on your face, which happens all the time, and it turning you into a zombie is something that's just not the case.
Now, that doesn't make the zombie bite any less lethal. You know, breaking the skin, having that kind of contact with the toxicity that zombie mouths would have, would be something that causes an infection that definitely would lead to your death and then the thing that's already in you would turn you into a zombie. So there is a science to this, to a certain extent.
Q: Although, to be clear, you are not technically a scientist.
A:  No. No, no, no. But I know about everything that scientists know, I'm pretty certain! But anyway, zombie blood is not quite as deadly as a lot of people think. I wouldn't drink it in high volumes, though.
  -  Robert Kirkman, interview with Entertainment Weekly
Answer: We know everyone is infected already, but it is possible that someone is immune. With the world ending there aren't many doctors to consult on the subject.
In the TV show version, it is possible Jenner told Rick more than everyone is infected. He could have also said "but your son is immune." Rick wouldn't want to announce that. People like the Governor would cut Carl up to try and find a cure.


Allow application direct access to internet without tor

Question: I am setting up tails with crypto wallets of currencies I use. The problem is that torify does not for some reason work with them. I don't really care that much about anonymity, so I have reset iptables to defaults assuming that should do the trick. But it didn't and it seems DNS lookup is failing in the wallets. Any help?
Answer: When you "reset" (I assume you mean you flushed/cleared) iptables, you also killed the iptables rule which was redirecting traffic destined to 127.0.0.1:53 to 127.0.0.1:5353. The latter IP/Port is where Tor is actually listening and DNS requests are no longer able to reach the DNS listener and so nothing will resolve anymore.
You will either need to take a more nuanced approach to iptables reconfiguration or change the prefered DNS servers to no longer try to use Tor to resolve traffic.
Note that disabling iptables in such a manner will break many of the assumptions of Tails' security and may expose you to risks in ways that were previously mitigated against.
Answer: You can run most of the bitcoin based crypto coin wallets in tails linux without modifying iptables at all, if you specify your socks5 proxy to connect to. Here dash wallet as example:
./dash-qt --proxy=127.0.0.1:9050
This should work with most of the typical c++ qt-wallets.
In case you want to run a wallet daemon, you could use the same proxy setting, but for wallet-cli connections to it, you would then need to adjust iptables for your wallet rpc port:
sudo iptables -I OUTPUT 3 -d 127.0.0.1 -o lo -p tcp --dport 9998 --syn -m owner --uid-owner amnesia -j ACCEPT
The example above makes port 9998 (dash wallet rpc port) accessible - adjust the port for other wallets accordingly.


Closing on-topic questions as duplicates of questions closed as off-topic

Question: Regarding this question, I believe duping it to a question that was closed as off-topic is a bit disingenuous. I believe there was general consensus the question itself was on-topic. Is this really okay? Wouldn't it have been better to let the on-topic question stand on its own?
Comment: I have edited the question to provide a sample sentence.  This time around, could we please arrive at some *rules* governing closing of so-called duplicates that point to *closed* questions?  I have a vague feeling this has come up before.
Answer: Duplicates should point to a question that has at least one good answer that answers the question being closed as a dupe. In my opinion, the quality of the answers of the proposed duplicate are a bigger problem than the question being closed. The scoring of the handful of answers for the proposed dupe target seemed pretty low for EL&U, which means to me that the community wasn't that involved and the answers are suspect. If the questions are truly duplicates, the one with more community participation should be the "master" question in my opinion.
It's a simple thing for a mod to reopen a question that was closed for other reasons and re-close it as a duplicate to allow the higher quality question to thrive and attract answers that are better vetted by the community. A question that was closed for lack of research can be closed as a duplicate of a question that does have proper research without somehow tainting the well-asked question with "off-topicness".
The only hard and fast personal rule I have for choosing duplicates is that I never choose a question that has no significantly up-voted answers unless the questions are exact duplicates.
Comment: @jxh Aha. **That** suggestion may be worth working into a Meta.SE question. Do check it hasn't appeared before (but I doubt that it has).
Comment: I understand that the point of closing as duplicate is to indicate answers can be found elsewhere. However, closing a question as a duplicate of an off-topic question somehow leaves the impression that both questions are off-topic (for the same reason). I don't think the "tainting" applies in the other direction. Also, while the collection of answers on the off-topic question may contain a suitable answer to the on-topic question, the questions themselves may diverge in nuance enough where a low scored (possibly negative) answer on the dup is a match for the other. ...
Comment: ... I think this approach works well only when the highest rated answers on the older question indeed is a match for the question being closed as a duplicate of it.
Comment: It would be interesting to see if the duplicate question system was extended so that the answers on the duplicate were replicated to the new question but with 0 scores, and voting occurs anew for the old answers on the new "duplicate" question.
Comment: This is probably a close match to my suggestion: https://meta.stackexchange.com/questions/166844/show-duplicate-suggestions-as-answers
Answer: A kind golden hammer wielding participant has reopened my question.
Could we have/develop a rule or procedure for this?
The whole point of closing questions, I thought, was to make it easier to find authoritative answers to clear questions, so we wouldn't be reinventing the wheel all over the place, with some wheels coming out better/more useful than others, and the whole site looking like spaghetti code.
I don't see how closing a question with a closed question helps with that.
(However: if there's something inherently bad about the way the new question is posed, then by all means guide the OP (in this case me) toward improving the question, including closing it if necessary.)
Answer: Bear in mind that the "off-topic" close reasons include our three custom reasons, and that "off-topic" simply means "does not conform to one or more expectations".
Certainly, one of those expectations is that the question should be of a type allowed in the list in the Help pages. But other expectations are explicitly stated in the close reasons, and these appear in the banner on closed posts. You need to read the banner text.

"Questions on choosing an ideal word or phrase must include information on how it will be used in order to be answered. For help writing a good word or phrase request, see: About single word requests"

In this case, the question may well have conformed to the list in the Help, but it didn't meet the standards required for its tags.
Nevertheless, it has answers. Those answers may well suffice for other questions, such as the one you reference here. If they do not, then questions which are closed as duplicates should be edited to say why the nominated duplicate doesn't provide an answer.
It is perfectly reasonable for questions which are on-topic but lacking in detail to be nominated as duplicates, if the answers are reasonable.
There may be more of a grey area where a nominated duplicate has no answers and has been closed already. However, it's also entirely possible that closing as a duplicate of such a question is exactly the right thing to do (eg in the case where both questions are of an equal standard). In such a case, the closure serves as a pointer to question quality: "Look, here's a question just like yours which was closed."
I believe a general bar on nominating closed questions as duplicates is unsustainable. That must be permitted. (And if it were A Bad Thing, then the system would not allow it at all.)
In the case in point here, there's probably enough in the question not to close it for want of a sample sentence; and it's probably sufficiently different from the "duplicate" that reopening is reasonable.
Comment: But *your* question was closed as a duplicate of the other. The *target* was closed for lack of detail, not yours. That means that *your* question was fine in itself, just that answers had already been given elsewhere.
Comment: Yes, but one interpretation of "closed as duplicate of an off-topic question" would be "that question was closed as off-topic, so this question is too." To a casual reader just following the links, I would think that would be the impression. I understand about reading the reason the other question was closed as off-topic.
Comment: Clarification: I didn't say the rule or process for deciding needed to consist of just one step.  I can understand if the algorithm or flow chart is a bit complicated.  But I'd rather see it presented in more positive terms, as in a flow chart, than in the form you used in your answer.  I'm hoping for an algorithm that people can step through as they're evaluating a new question. // If anyone had *asked* me for a sample sentence I would have obliged.
Comment: @jxh People can believe all sorts of things, even when something stating the contrary in bold letters is right in front of them. There are plenty of folks that don't understand SE close reasons. I'm not sure that merits not linking two questions to help visitors find useful content. Regardless, the better quality question should be the one left open for more answers, but it's difficult for community members to do that without mod help if one question is already closed.


What is the difference between the official and unofficial version of a ROM?

Question: The title pretty much says it all. What is the difference between the official and unofficial version of a ROM? From what I've seen, unofficial comes before official, for ROMs like cyanogenmod.
Answer: Rahul Gopi describes the basic concept of official and unofficial, but I'd like to add some important additions.

Unofficial is not necessarily different from official in sense of code and result. One can build purely from codes supplied by the ROM team without additions, and the result will be exactly the same as Nightlies, minus some fingerprints here and there that shows who built it.
Official is not necessarily better than unofficial. For many popular devices, both exists, and the developer for unofficial versions will add tweaks to differentiate, e.g. a custom kernel, slimmed down build (i.e. removed some preinstalled apps), themed to the developer's liking. This is what I'm doing monthly as a home compiler, by the way.
Official is not always perfect. Sometimes developers have unreleased patches that aren't pushed to upstream yet, or haven't been approved in code review for various reasons, leaving long overdue bugs in official builds. Devs can push out unofficial builds with those baked in when building locally, thus fixing the bugs.
When a new Android version releases, unofficial builds almost always come first. This is due to the strict requirements (e.g. what basic features should at least work) the ROM team choose to enforce on official releases. Contrarily, devs for unofficial builds are mostly concerned about bringing the version to the mass as early as possible as a proof-of-concept.

For those reasons above, you should not assume that "who builds it doesn't matter" - look carefully at the intro of the unofficial ones (because official ones rarely offers such intro), and decide if it has an edge you need.


Installing Ubuntu on PowerBook G4

Question: I have a Mac PowerBook G4.
It has the Mac OS X Version 10.5.8 on it.
I would love to change it to Ubuntu but the last time I tried it wouldn't register the disc.
Any ideas if I need an older version or what needs to be installed in a certain way?
Comment: a start would be http://powerpcliberation.blogspot.de/2012/10/lubuntu-install-guide.html
Comment: Here's a good place to start on the installation: https://wiki.ubuntu.com/PowerPC
Answer: I'm not sure what you mean by "wouldn't register the disc" but to boot an older iBook / PowerBook from the optical drive, just hold down the C button as soon as you power on.
Another option is to boot into OpenFirmware.  This can be done by holding down Cmd-Option-O-F as you power on.  Once OpenFirmware has started (a white screen with a short message and a simpole prompt) enter the command: boot cd
I hope this helps.  I'm going from memory.
Edit for Addition:
Also, just a warning: Years ago when I used Linux on a MacBook there was no Linux driver available for the Broadcom wifi chipset that Apple used in their laptops. At the time, the only option was to use a usb attached wifi device. This may no longer be an issue.
Answer: A start would be this tutorial for Lubuntu 12.04 http://powerpcliberation.blogspot.de/2012/10/lubuntu-install-guide.html.
Lubuntu is optimized for old computers.
the latest Images you find here: http://cdimage.ubuntu.com/lubuntu/releases/ (currently 13.04)
use the "Mac (PowerPC) and IBM-PPC (POWER5) desktop image" in http://cdimage.ubuntu.com/lubuntu/releases/13.04/release/
I tried it on a PowerMac G4 and it seems to work. (although, while it's trying to install, I get the message

!! Select and install software
  Installation step failed.
  An installation step failed. You can try to run the following item again from the menu, or skip it and choose something else. The failing step is: Load installer components from CD.

But that seems to be due to an error on the old harddrive I inserted into the G4, I see some I/O errors in syslog when I change to the console with Ctrl+Alt+F1 )
Comment: I asked about this bug in the apple stack here: http://apple.stackexchange.com/questions/98190/install-linux-on-a-g4-select-and-install-software-installation-step-failed

Installing Ubuntu on PowerBook G4


Fixed Gear crank arm slips

Question: The crank arm on my fixed gear "slips" when I put large pressure on the pedals like when I take that first pedal to get the bike moving or pulling up hard on my toe straps to slow down. The slip is very smooth and feels like if your back wheel was spinning in place on wet tile/marble, however, my back wheel is not moving in situations when my crank arm slips. I've just gotten the bike from shop maintenance a few days ago too so I don't think it's an obvious issue? I've heard maybe I need it's a cog or lockring issue. Can someone tell me more? I need to be able to pedal forwards and backwards with a lot of torque safely. Thank you!!
Comment: Do you have a separate front brake?   If no, consider not riding until this problem is resolved.  Fixie with no other way to brake is a recipie for disaster should it all fail suddenly.
Comment: @Criggie From the description of the slippage as "very smooth", it seems unlikely to be the chain skipping over worn cog teeth.
Comment: For anyone who has been careless with fixie maintenance before or has had a bad lock ring this is obvious.
Comment: Some more details please - how worn is your chain, chainring, and rear cog?  Is the chain slipping over the teeth?  How much slop / deflection is there in the slack chain?
Comment: @DavidRicherby excellent point - but the only other place where slip is likely is between the tyre and road.
Comment: @steven Could you please add one or two clear, clean and well-lit photos showing the front and rear of the transmission.  This is an interesting and puzzling question.
Answer: Your lock ring is loose.
Normally the cog is quite tight from pedaling and you can do some braking with it. When you brake harder it breaks loose and unscrews until it hits the lock ring. This is what you feel as sliding. The lock ring has left hand thread to keep the cog from unscrewing completely. Now that the cog has tightened against lock ring, the process repeats when you pedal hard forward.
Now that the lock ring rattles loose, you should tighten it immediately.
Answer: Late to the party, but I had exactly the same problem. My LBS identified and resolved the problem: the chainring's teeth were worn down so the chain was slipping over the teeth when I applied heavy pressure (like skidding on a downhill or crushing it uphill). They also suggested the chain itself could've been part of the issue, since it was fairly old and stretched.
At the end of the day, I got a new chain ring, rear cog, and chain. Wasn't cheap but it solved the problem.
Answer: The crank arms have to be really tight when they are first installed. Properly installed they last indefinitely. However, if they get loose and you ride it for a while the crank arm will be ruined. You can't fix it. Just get another one. An old used one is fine. You need a crank puller to get the old one off. They are not that expensive.

Fixed Gear crank arm slips


What is Metamask?

Question: I know it's a dApp web3 browser, a wallet. But which ethereum client is used in the back end to interact with block chain? How the same account is able to connect with all networks (mainnet,testnet, private net)? If anyone know the working of Metamask/ the layer of Metamask ,please share it here.It will be very useful for all learners.
Answer: @AngeloBad is correct that, by default, Metamask uses Infura, but Metamask also allows you to use any RPC enabled Ethereum client as its Web3 provider.
Comment: I just reply to the question made with no speculation.By the way, good comment yours. I did not know it. Following the stack exchange rules, you should comment and not reply to the answer.
Answer: Metamask uses https://infura.io/ as a third party gateway.
See the docs as a source of learning: https://infura.io/docs
Answer: To elaborate on the references to the fact that Metamask uses Infura (unless you explicitly specify your own RPC endpoint), this article on their blog has a couple of useful architectural diagrams that helped me wrap my head around it: https://blog.infura.io/infura-boomerang-architecture-6dc27ef56646
Just note that it's a few years old so things may have evolved a little since then, but conceptually it's still the same.

What is Metamask?


How effective is Zumba in weight-loss and toning?

Question: I have been participating in Zumba lately and I feel more stiff after I do something else rather than Zumba. Is Zumba a good choice to working out or is it more a fun choice if it was Zumba or nothing? What does Zumba do?
Comment: How long and how intense would you be working out @Kyra?
Comment: I have been playing the Zumba for the Kinect. For a while I was doing a 45 minute class at Expert.
Answer: A big part of choosing a weight loss regiment is choosing something you are going to continue doing. Zumba appeals to a lot of people because it has a dance aspect, which makes it fun for them. (There is a stigma associated with working out in a "boring old gym.") If you are going to continue to do Zumba over other workout routines, then definitely stick with it.
As to how effective it is, that really depends on the length and intensity of your workout. There is a lot of movement to it, and if you are actually working hard (and sweating), then you are burning off calories. That means, assuming you watch your diet as well, you will lose weight and achieve muscle tone.
I would suggest that you do a combination of activities (helps mix it up, too).

Zumba - A few times a week. This is your cardio/weight loss exercise.
Weight/Strength Training - Do this once or twice a week. Doing this actually helps you burn MORE calories when you're doing your cardio portion because your muscles require more energy. It's been shown time and time again that individuals who supplement cardio with weight training maintain a healthier physique and reduced weight.
Eat Correctly - Do NOT starve yourself or go on any fad diet. Eat properly. Healthy proteins (chicken, fish, etc). Vegetables. Fruits. Don't come home from a class and gorge on ice cream or you will see no weight loss (and probably the opposite). However, it is good to reward yourself at times (at least a couple times a week) with a small treat.

Keep those three things in mind, and make sure you're working out at the proper intensity level, and you will see the changes you are looking for.
Answer: Zumba, like any physical activity will have benefit in weight-loss and toning. It just depends on how long and how hard you go at it.
The idea is to keep up your heart rate and keep moving. As long as you do this you will be burning calories.
As wikipedia says:

The best way to tone is to utilize
  aerobic exercise to reduce body fat
  and perform weight resistance exercise
  to build muscle. Performing a
  combination of such exercises can be
  referred to as toning.

With the dance exercises involved in Zumba this definitely fits in the aerobic exercise category. For best results you should combine this with some resistance training.
Answer: I do a lot of salsa and other latin dances which Zumba is based on.  Mind you I'll do about 3-4 hours of it a week.  And it does burn off a lot of calories.
If you get really good at Zumba with proper weight transfers and balance and can follow the music, then you'll really enjoy it and the weight will almost fall off on its own.  Zumba like any other dancing is all about enjoying yourself.  Pushing yourself to do more complicated dance patterns and moves.
The trick is not to set a weight loss goal, it's to set a dancing achievement goal, that way you'll get addicted and never stop enjoying. Then maybe go take real Zumba classes to challenge yourself, trade tips, etc.  Next thing you know you could become a Zumba instructor.  It's all about the right motivation.  You may not want to become an instructor, but still aim for it so you never stop.
Remember, step on toes first, strengthen the core to help with the weight transfers.


How to build a quantum computer in your house?

Question: As still quarantine is going on for some of us. I was wondering how to make a Quantum Computer in your garage. What may be the total cost for building one?
Was inspired by this youtube video.
Comment: Does this answer your question? [Building a DIY quantum computer - how to reduce a noise?](https://quantumcomputing.stackexchange.com/questions/9500/building-a-diy-quantum-computer-how-to-reduce-a-noise)
Comment: https://medium.com/qiskit/how-do-i-build-a-quantum-computer-in-my-house-1c7e9dc0c242
Comment: This article will provide a better insight.:)
Answer: A serious answer: you pretty much can't. It's not that you in particular can't, it's that no one can. Huge companies pour in huge amounts of money to try and make a proof-of-concept quantum computer (there is actually no 'proper' quantum computer yet).
A slightly less serious answer: some odd $10-100$ Million would get you started I would say. It all depends on what type of quantum bits you want to build; most of them require the need of cooling them down to single digits (or much, much less) above absolute zero. You need 'special' refrigerators for that will do this, and they are pricey.
Oh, and do you have a nanofabrication lab or a clean room adjecent to your garage? Because you're probably gonna need one of those as well:)
This is not intended to shoot you down, but more as a light joke:)
Edit:
Actually, what might be in reach for a personal investment is some very rudimentary version of a photonic quantum computer. Basically you need some glass fiber, a couple of beam splitters, a lot of attenuators and some lasers. (And a idiotically expensive single-photon detector, but we'll sweep that under the rug for now).
Comment: ...and a magical source of (N >> 1)-photon states.
Answer: With current technology, there's not much of a chance to build a true quantum computer,  but you may be able to build some interesting quantum circuits with a fairly sizable (but still on the scale of "self-funded" for the ordinary person) budget, using the optical photon model. For instance, one could use the linear optical quantum computing model. Using beamsplitters as $\hat{y}$ rotations and phase shifters as $\hat{z}$ rotations, one can construct arbitrary one-qubit quantum gates. With the addition of a nonlinear medium (like Kerr Media), one can construct some interesting circuits. For reference, here are the transformations that each of those optical tools performs:
$$
\mathrm{B}_\theta = \begin{bmatrix}
\text{cos}(\theta) & -\text{sin}(\theta) \\
\text{sin}(\theta) & \text{cos}(\theta)
\end{bmatrix}
$$
$$
\mathrm{P}_\phi = \begin{bmatrix}
e^{i \phi} & 0 \\
0 & 1
\end{bmatrix}
$$
$$
\mathrm{K}_\mathcal{E} = \begin{bmatrix}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & e^{i \mathcal{E}}
\end{bmatrix}
$$
The parametrizations on the first two matrices have to do with the properties of the materials used in creating the optical tools, and don't necessarily have anything to do with the physical angle which they are placed.
Answer: Note that while you probably can't build a quantum computer at home, you can simulate one with a classical computer, at the cost of merely an exponential slowdown. There's a rather long list of available software at https://www.quantiki.org/wiki/list-qc-simulators.
Answer: It's actually an interesting question. And the previous answers ("strictly speaking, you can't," "you can simulate quantum computers," and "photonics-based processing holds some promise") are all true.
According to a pioneer in photonics computing we won't see real quantum computing until around 2035. I've not yet seen anything to justify thinking to the contrary. Some of the downstream work of these photonic computing pioneers has yielded the fastest data interconnects that scale perfectly in parallel b/c there's no photon-electron conversion (and because there's an ingenious breakthrough at the core). There's also a really compelling set of demonstrations using these interconnects to run QC simulations , like running Grover's algorithm and QFT, fast. See https://www.datavortex.com/research/quantum-simulation/.
There's nothing wrong with simulating, there's nothing wrong with waiting 15 years, and there's nothing wrong with jumping in and trying to make it happen in one's garage. All one needs is some advanced mathematical training, some electricity, some money, and a refusal to quit.
Answer: He has basically described how to build the Cirac-Zoller quantum computer.
In the most simple approach the qubit states are electronic states of the trapped ions. Two qubit gates are possible thanks to the coupling of the qubit states to the vibrational modes of the trap -- this is cool as in superconducting architectures the two qubits that are far apart on the chip are not coupled directly.
The trapping of ions was already demonstrated a while ago e.g. here or here. As he has mentioned the next big step in his design will be placing the trap inside an ultra high vacuum (UHV) chamber i.e. less than 100nPa. This is necessary as otherwise the atoms from the air would bump into the ions and would cause decoherence.
But the really challenging step is implementation of the lasers as they do the whole job -- this might be really difficult to achieve at home, however, judging on his current progress, I hope that he will pull it off.
A real competition to his start-up is a company called ionQ that is building quantum processors with a use of this architecture. The ion trap based quantum computers are known for having qubits and gates of v high fidelity. The drawback is that they are difficult to scale up. This is the most commonly attributed to anomalous heating.
Here you can check out other architectures with their strengths and weaknesses.
Answer: All previous answers are true. I would like to contribute with a serious question and a comment.
Would it make sense to build a quantum computer in your house?
They are and will be hard to maintain. In my opinion, having them in the cloud is and will be the best solution.
Beecause of economy of scale, the cost of a home-made quantum computer will be always greater than the cost of industrial quantum devices deployed in server farms located in cold countries (e.g., Norway) and exposed as cloud services.
Comment: It probably doesn't make sense to build a quantum computer in your house if the purpose of the exercise is to execute quantum algorithms. But the purpose may be learning about quantum computer hardware, or research into its construction, for which purposes a cloud-based solution is of course useless.
Comment: Given that you need an operating temperature of around -273C, it doesn't seem plausible (at least to me) that being in a cold country will make any kind of significant difference.


Tor Path Selection using Stem to choose middle node

Question: Has anyone had luck selecting the middle node used within the path selection of tor using Stem?  I am trying to set a specific set of routers (non public, so will have a different directory server, although I could set them to use whitelisting possibly) to be chosen as the center node in order to do some latency/throughput testing but the documentation is somewhat unclear.  I know one can select the entry or exit node using the torrc file, but it is impossible to select the middle node with this mechanism since it essentially ruins privacy to have it be chosen deterministically.  Any help would be greatly appreciated.
Answer: You have to construct the entire circuit yourself, you cannot just choose the middle node alone unfortunately. To do this, you need to use the extend_circuit command in Stem's controller API.


Does this question fit ServerFault more than SuperUser?

Question: I just asked a question about Windows shell scripting in SuperUser, but I suddenly realised it may suits ServerFault better. Is this the case? How can I move it over? close/delete and re-post?
Answer: I think SU is a good place for this. It wouldn't necessarily be off-topic here, but this has an end-user vibe about it, not a system administration one (remember, SF is for professional system administration, end user/home use questions are off-topic).
But thanks for taking the time to ask this.
Comment: @Bolu The difference here is less in the activity, and more in the spirit and scope of the activity. As Sven said, it would probably fit here as well, it just fits slightly better in SU due to the context.
Comment: Make sense, I must admit I'm not a system administrator. But I was thinking that the scripts involved is more administration related rather than end-user? (I was trying to archiving service log files automatically with this script, like any sys admin will do, and how many end use will use this kind of script to move file?)
Comment: @Reaces, I see. If I add *I'm a system admin and was trying to automatically archive historical service log into another folder to free up spaces on the server* in the beginning of the question, will it fits slightly better here?
Comment: @Bolu Maybe, probably, but it is kind of irrelevant. For this kind of question you are equally likely to get an answer on SU or on ServerFault. In fact a lot of cross-over exists between the people that answer on SU and SF. So you might just get an answer from the same person on both sites.
Comment: @Reaces, that is my major concern. Many thanks!


Heatbed with zones?

Question: Waiting for a heatbed to get up to 85˚C for a relatively small part got me wondering why beds aren't hardware/G-code configurable for what area is heated? I'm sure it would be an increase in parts costs and electronics, but it seems that being able to just heat an area a little larger than the part(s) being built would save in time and energy use.
Comment: That is a *very* good question. It would require switchable sections of the PCB track, but how would those sections be configured? Differing radii of circular PCB tracks? or if in square blocks how would they be arranged, and how many (in halves, quarters, eighths etc.)? I guess the permutations for a square one are a bit more complex and numerous to be practicable. Doing it for a round heatbed seems simpler though. Also, how big would the market be, and would the added complexity in electronics (i.e. cost) and code be worth it. It seems a good idea though... Design a prototypePCB in EagleCAD?
Comment: @Greenonline RepRapFirmware already has an optional parameter (`H` for `M140`) to select heatbed, this could possibly be used for that. For Marlin it will require some extra coding as `H` is not yet a supported parameter. Nice project!
Comment: You must learn patience, grasshopper.     No, seriously: when you're printing anything that takes longer than 30 minutes to complete, the heating time is insignificant.
Comment: Well, not just all about patience ... do we really need a full 200W (~) element heating up non-used space for hours (days)?
Comment: @Jer well, Using the whole heating element the heat bed reach the printing temperature in 3 or 5 minutes, using the half heating element the time increases between 8 to 12 minutes. I don't want to wait to get roots on my feet.
Comment: I'm not sure why you are saying it will take more time to heat up. If I turn our stove's small burner on high it doesn't take longer to warm up than the large burner. Now, if there's zones each zone will also need to have its own thermistor to know when it has reached temperature.
Comment: @Jer, the reason why it takes longer is called "conduction"; heat flows to the rest of the plate that is not heated, so it takes longer. Does any of the answers helped you to get an answer on your question or helped you come to your own conclusions then please do vote and accept an answer. This helps us reduce the [unaswered questions list](https://3dprinting.stackexchange.com/unanswered). Found an other answer (then the already posted) yourself? Please add that answer (and accept after 48 hours) to share your experience with the community.
Answer: I've wondered that myself a while ago and fact is that such beds or silicone heating pads do exist. Usually these are quite large (and expensive) and usually referred to as "dual zone heat beds/pads".
As far as energy consumption; less area to heat is faster heat up times (depending on the control) and less energy consumed. For small prints this may be beneficial. The price of such beds are very high, so to break even you would have to print a lot. An alternative to buying would be to etch your own bed.
Comment: Thanks. As I've been thinking over people's answers I can see you'd want to segment the heated areas in a number of ways: ideally a bit of a heat break, some kind of switching to turn on/off zones, they'd need their own thermistor, and finally something to control/interpret all of this back to the main board. Not something you'll find any time soon on a sub-$200 printer.
Answer: The heated bed is a reasonably good thermal conductor, so the difference in energy between heating all or 10% of the bed (assuming a 3x3 grid split 1 and 8) isn't going to be that significant.
In terms of heating speed, 200W across the whole bed will heat it faster than 40W applied to the centre square, and will also be less likely to cause warming or heat cycling effects (unless PSU regulation is a problem).
If the bed is much larger, or has thermally separated zones, then there might be some justification in the increased control complexity.
As an example, although glass has a thermal conductivity around 1% of a metal, it is still 30x better conducting than air. Conductivity towards the unheated areas of even a solid glass bed will roughly match the surface loss - so best case you would reduce losses to somewhere 20%-50% of what heating the whole bed might cost (assuming the same 3x3 grid).
Comment: I had the same concerns as you about conduction, but not come to putting it in words! The only thing I can think of to dispute this is thermal silicone heating pads (on an insulated body) in conjunction with a glass bed, glass is a poor heat conductor. Nice addition!
Answer: As the etched version is very impressive (thanks 0scar for that), there are other possibilities to build zones on the bed:

Using resistance wire;
Using a etched bed with zones.

The challenge with zones is mainly down to:

When and how to switch on/off particular zone;
Temperature control needs to be added to every zone to avoid over/under heat in the particular zone.

This last point brings even more challenges as that requires a PWM channel and a temp sensor (per zone), so standard RAMPS need some extensions in the wiring.
One could overcome that using custom G-Code to set on/off zones and a double temp sensor for the main zone to follow the temperature changes.
In detail: a dedicated Arduino with PWM outputs that will read the temperature from a secondary temperature sensor in the main zone and follows it.
Comment: The commercial dual zone beds come with a controller to do that, indeed a simple Arduino should be able to do that. You could even alter the Marlin bed heating code to include an extra parameter that determines which bed to heat up. It seems that reprap firmware already has such functionality (parameter H). `Recent versions of RepRapFirmware also provide an optional 'H' parameter to set the hot bed heater number. If no heated bed is present, a negative value may be specified to disable it.`
Comment: thanks for that @0scar, I have a 500mm X 500mm  bed, so I am thinking to slice it in 100mm zones, that gives 5 zones to be controlled, and RAMPS will not handle that without extending it as that requires at last 8 extra pins and some extra computing power which we know is limited.
Comment: 100 mm squared makes 25 zones ;) What about control using i2c?
Comment: it extends by 100mm so we have 5 elements
Comment: A rotary switch can help 2P6T, also are called selectors.
Comment: @FernandoBaltazar thanks for that - great idea, but it will not be driven by G-code :-)
Comment: @profesor79 Can be driven normally the heat bed, you only select the area to be heated manually.
Answer: it is probably too late for the party but i thought about grid heated bed recently. about controlling which zone to turn on and off, i think we can treat the grid as Led matrix, the matrix led signal can be used to drive mosfets to power the heat pads.
Answer: It makes more sense to insulate "unused" areas, since the heat conduction goes with the surface area. Heating the plate at some place (instead allover the area) makes no big difference (aluminium is a very good heat conductor, this is already mentioned). But insulation will do. I would propose a downside full insulation (5-10 mm) and some "windows-shaped" square silicone (other thin material?) mats to cover the unused areas (mostly on the outer side of the bed) on the top side. Beware of collisions and auto-leveling algorithms (starting very often at corners). Side effect: you may reach much higher temperatures at the uncovered areas (might be doubled if covering half of the surface).

Heatbed with zones?


We may say that Sartre inverts Kant's moral philosophy. What does Sartre share with Kant, and how does he overturn some of his thinking?

Question: Compare and contrast Kant and Sartre. We may say that Sartre inverts Kant's moral philosophy. What does Sartre share with Kant, and how does he overturn some of his thinking?
Comment: Care to demonstrate a little work? This sounds like a homework question. Also did you search this site for questions on this very topic, there's more than one that applies to what you want to know.
Answer: ▻ THE CENTRALITY OF FREE AGENCY

In his Religion within the Limits of Reason Alone, Kant turns his attention to the problem of evil and, in doing so, develops a
  more complex picture of the human will and its moral character
  than is found in his earlier works. The discussion of radical evil -
  of how free beings can misuse their freedom ? rests on his notion
  of a freely chosen disposition. Imputability of our actions requires
  that we be the authors of this enduring aspect of the will. This
  description of our character, of our disposition, in short, of ourselves, as resulting from a free choice foreshadows existentialist themes developed by Jean-Paul Sartre; most notably, the fundamental project and the idea of radical choice. (Marcel Lieberman, 'The Limits of Comparison: Kant and Sartre on the Fundamental Project', History of Philosophy Quarterly, Vol. 14, No. 2 (Apr., 1997), pp. 207-217 : 207.)

Sartre rejects determinism, which he sees as inconsistent with radical choice and Kant rejects determinism at least as far as concerns human moral action.
▻ DIVERGENCE OVER HUMAN NATURE
Sartre famously affirms that our existence precedes our essence, by which he means that we first exist (are 'thrown into the world', as Heidegger says) and then define ourselves - acquire an essence - through and in authentic choice. In contrast Kant believes that we are essentially rational beings, bound rationally to certain rules of conduct (defined by the categorical imperative in its various formulations) to act in certain ways. Sartre holds and can hold no such idea of a blueprint of rationality by which we are defined and to which we have any obligation of any kind to conform.
▻ LEGISLATING FOR HUMANITY
Kant's ethics rests on the idea that in acting we should heed principles that can be universalised - principles on which everyone can act. Sartre holds a view not dissimilar :

When a man commits himself to anything, fully realizing that
  he is not only choosing what he will be, but is thereby at the
  same time a legislator deciding for the whole of mankind -
  in such a moment a man cannot escape from the sense of complete and
  profound responsibility. (J.-P.Sartre, Existentialism is a Humanism, in Walter Kaufmann (ed.) Existentialism from Dostoevsky to Sartre (Cleveland: Meridian Books, 1956), pp.297-8.)

REFERENCES
Marcel Lieberman, 'The Limits of Comparison: Kant and Sartre on the Fundamental Project',  History of Philosophy Quarterly, Vol. 14, No. 2 (Apr., 1997), pp. 207-217.
Thomas Baldwin, 'The Original Choice in Sartre and Kant', Proceedings of the Aristotelian Society, New Series, Vol. 80 (1979 - 1980), pp. 31-44
Wesley K. H. Teo, 'Self-Responsibility in Existentialism and Buddhism',  International Journal for Philosophy of Religion, Vol. 4, No. 2 (Summer, 1973), pp. 80-91.
Comment: Geoffrey, please do not answer such questions. You are basically writing HW essays for people who are too lazy to even google.
Comment: @Conifold. It never occurred to me that this was a HW question. You have very much greater experience of these matters than I have. It would help if a moderator flagged such questions and put them on hold. If a question has passed the controls and I see it on the page, I assume it's ok to answer. I will admit that I have come to recognise some questions as HW - to a past lecturer and setter of questions there are a few unmistakable signs. I don't answer such questions - usually because they demand impossibly much of an answer here. Your point is taken but closer moderation would help. Best -GT
Comment: @Conifold. I now note Virmaior's comment but this appeared long after I had answered the question. The real problem is that I answered the question so soon after it had been asked. Had I left it till this morning I would have heeded the comment. Best - GT
Comment: Moderators are kind of overwhelmed right now because of all the recent comment wars, and it generally often takes a while to close questions that should be closed for any reason. These HW questions usually come from new users (under 100 or low 100s rep) and have wooden phrasing characteristic of a prompt with no further elaboration. I usually vote to close for "missing context" when I spot them. We do help with HW questions if the users follow up with their own reasoning and try to explain what it is that stumbles them, but those usually say directly that the question comes from HW.

We may say that Sartre inverts Kant’s moral philosophy. What does Sartre share with Kant, and how does he overturn some of his thinking?


Double Slit Experiment: How do scientists ensure that there's only one photon?

Question: Many documentaries regarding the double slit experiment state that they only send a single photon through the slit. How is that achieved and can it really be ensured that it is a single photon?
Comment: @Qmechanic I think this is a different question.  This question is more about experimental design as far as I can tell as opposed to some conceptual difficulty with what's happening to a single photon that is fired.
Comment: @joshphysics That probably happened while you were observing something else - that's Quantum Mechanics for you :P
Comment: Tag added in keeping with @joshphysics' take on the question.
Comment: @TobiasKienzler I could have sworn it was originally a "possible duplicate" comment, but I could also be going insane.
Comment: Related: http://physics.stackexchange.com/q/70855/2451
Comment: @joshphysics That's why Qmechanic said "related" and not "possible duplicated"
Comment: Comment issue discussed in this meta post: http://meta.physics.stackexchange.com/q/4894/2451
Answer: Quantum dots. nanoscale semiconductor materials that can confine photons in 3 dimensions and release them a measurable time after. Based on material used the decay time is known empirically. frequency is also known. the latter is sufficient to calculate the energy of one photon. The former is then sufficient to calculate the rate of photon re emission from the QD. If the peaks at the detector are further apart than the decay time and each peak is measurable to one photon's worth of energy then you know you have a beam of single photons.
Comment: @user1800 The double slit experiment *with single photons* was first performed in ... **1986**, in a pioneer experiment by Aspect, Grangier and Roger, please see http://dx.doi.org/10.1209/0295-5075/1/4/004 especially Fig.4, which shows the appearance of the fringe for large number of photon counts. The gregsan answer is a modern version of the photon cascade effect that Aspect and Grangier used in the 80's for photons on demand. Studying quantum dots semi-conductor is still an active field of research for unique-photons-on-demand, too.
Comment: @gregsan To comment further about the above cited Aspect/Grangier/Roger experiment alongside the question Felicitus asked: they are sure they have only one photon because they have *two* detectors (avalanche photo-diode) which never clic at the same time. Say differently, when they clic together at the same time, you can discard the counting controllably. Thanks you for this interesting answer.
Comment: I'm sure this will work, but I doubt that anyone bothers.
Comment: The double slit experiment was performed over a century ago, there were was no nanotechnology back then. So how do you think people made sure that just one single photon was involved in the experiment, other than deducing the existence of light as quanta by the observation of experiments?
Comment: Indeed this has been our method of choice. We've been working particularly with CdS QDs. The great advantage is the ability to grow the QDs to any arbitrary size and therefore tune the photon frequency as desired.
Answer: In the double slit experiment, if you decrease the amplitude of the output light gradually, you will see a transition from continuous bright and dark fringe on the screen to a single dots at a time. If you can measure the dots very accurately, you always see there is one and only one dots there. It is the proof of the existence of the smallest unit of each measurement which is called single photon: You either get a single bright dot, or not.
So, probably you may ask why it is not a single photon composite of two "sub-photon", each of them passing through the slit separately and then interference with "itself" at the screen so that we only get one dot. However, the same thing occurs for three slits, four slits, etc... but the final results is still a single dot. It means that the photon must be able to split into infinitely many "sub-photon". If you get to this point, then congratulation, you basically discover the path-integral formalism of quantum mechanics.
Comment: I chose this answer because it explains it better to me than the highest-rated one; but thank you all for answering. I'm not a physicist, so a simple explanation like this is more clear to me than formulas. Thank you!
Answer: The practical answer (which I also wrote in a comment on the linked question) is that you turn the intensity of the light source down until the expectation value for the number of photons on the optical path is low enough to suit you.
If $\bar{n} = 0.1$ then very few of the events that are recorded on the screen will come from events where more than one photon was present on the optical path and the data will be dominated by single photon event.
Not good enough for you? Turn it down until $\bar{n} = 0.01$. Or $0.001$ or whatever suits you.
At some point the exercise becomes silly.
Comment: Unfortunately, this answer is incorrect. Turning the intensity off do not provide you're working with photon eigenstate of the light field. Coherent state with an *average* photon number *is not* a Fock state of photon. To go to single photon effect, you need matter-light interaction, as the experiments by Aspect/Grangier and Haroche/Raymond/Brune clearly shown. The first team using photon cascade effect, the second one using flux-number commutation relation on quasi-classical field (coherent) and matter (Rydberg).
Comment: @Oaoa That is not material that I'm familiar with, but I found [what looks like the slides from a graduate summer school presentation on the matter by Haroche](http://www.cqed.org/houches/haroche/), and he seem to say (lecture 1, slide 11) that for a coherent state, the distribution of fock states is Poisson, in which case very low mean occupation number *does* imply that the data is dominated by the single-photon fock state, which is what I said. Sure, there is some contamination, but you simply turn down the intensity until you are happy with the results.
Comment: Thanks a lot for the material you shared. I'm also always puzzled with this issue. Let me try to me a little bit more clear. For me, a single photon is a wave packet. Reducing (using filter of whatever) the intensity of coherent (laser, say) field will never produce wave packet: instead you will always find a continuous in time field, at rather low intensity. Maybe this is too much naive point of view. I never heard about an experiment with low intensity which results in discrete photon state. The Haroche argument is perfectly right: low occupation means 0 or 1 photon dominant (...)
Comment: (...) but 0 photon state is a coherent state (perhaps the easiest to do coherent state), and the 1 photon state is already in the queue of the Poisson distribution. Really puzzling issue. Of course the detection scheme you're using is of primary importance, too: you must detect one-photon energy per unit time for instance. My understanding of the Haroche/Brune/Raimond experiments is that you need an atom to make a Fock state. You start from a thermal field, and the atom-light interaction select the Fock mode. The atom clearly acts as an extremely precise clock, mandatory for the experiment.
Comment: @Oaoa I think the difference is that I am not worrying about being able to show that any particular count came from a single photon event, just being sure that the pattern I see is dominated by them. That kind of thing won't do for quantum computing or entanglement measurements. Or maybe I just don't get the argument. As I said, I'm a bit out of my depth with that stuff.
Answer: I'd like to add to gregsan's answer about using quantum dots by also raising diamond nanowire one photon sources or similar devices made on CVD-grown diamond waveguides in contemporary or future experiments - of course this this method was not used in the historical one-photon experiments!. See:
Mark P. Hiscocks, Kumaravelu Ganesan, Brant C. Gibson, Shane T. Huntington,
François Ladouceur, and Steven Prawer,"Diamond waveguides fabricated by reactive ion etching", Optics Express, 16, Issue 24, pp. 19512-19519 (2008) http://dx.doi.org/10.1364/OE.16.019512
This one can be freely downloaded, and I should declare my close contact with several of the authors, although I was not part of this work.
Thomas M. Babinec, Birgit J. M. Hausmann, Mughees Khan, Yinan Zhang, Jeronimo R. Maze, Philip R. Hemmer & Marko Lončar, "A diamond nanowire single-photon source", Nature Nanotechnology 5, 195 - 199 (2010)
This one is paywalled, but independent from me.
These devices might find experimental uses in more sophisticated one photon experiments both now and in the future because one can trigger them to emit lone photons almost on demand, whereas dimmed light sources simply emit photons randomly following a Poisson process and cannot be triggered. I have heard several times the opinion of several very bright (much brighter than I am) experimentalists that "no-one would bother", but I just can't shake the feeling that triggering might be useful in yet-to-be thought of experiments - I'd call myself a lousy experimentalist but once upon a time I could drive an analogue oscilloscope pretty well and triggering is surely what makes a useful piece of kit ten times more useful!
Here's how the diamond waveguide one-photon source works. One lays down a diamond waveguide by chemical vapour deposition and shapes the surrounding environment by reactive ion etching. Then a highly controlled amount of nitrogen is included into the diamond lattice. A nitrogen atom normally only makes three covalent bonds with its neighbours, whereas carbon normally makes four, so one is left with carbon atoms with one covalent bond forming electron "dangling" in the lattice wherever there is an included nitrogen. This "dangling electron" is then a fluorophore. One controls the concentration of nitrogen carefully and dices the waveguides so that there is exactly one fluorophore centre in each waveguide device: you can do this by building many devices at once then testing each and throwing out any with none or more than one fluorophores. The waveguide device can then be coupled readily to a single mode optical fibre which links the device to the outside world. The extremely high diamond to air refractive index difference (diamond $n=2.4$) and the ability to build waveguides down to below wavelength dimensions means that we can make "nanowires", which are single moded but also their strong waveguiding properties means that there is near unity probability for the photon fluoresced from the dangling electron into the single mode waveguide. So now we have something which is very readily connected to other experimental kit and doesn't need alignment.
When the time comes to use the device, a trigger signal causes an optical pump laser in the device to pulse the device with an intense beam of light, so that the lone fluorophore in the device is almost certainly raised to its metastable state. At the same time, a very high performance optical switch gates the device's optical output so no light at all escapes to the outside world. After the pumping pulse has ebbed, the output optical gate opens and the fluorophore relaxes a short time later - the fluorescence lifetime is a few nanoseconds. Although this fluorescence is governed by an exponential time-till-emission probability distribution so that, strictly speaking, it is stochastic just like the traditional dimmed light sources, the gating process means that one can control the time of photon emission to within a few nanoseconds.
Moreover, the near unity photon coupling probability into the single mode waveguide system means that there is an extremely low coupling probability for outside photons incoherent with the waveguide mode to couple in. This system is therefore extremely immune to stray light even though one photon experiments are being done: the exposure of the waveguide system to normal room light levels means that almost no photons get in - and that's before one blackens the system or puts it in a box. There is zero contamination in this device in the hands of even the most ham fisted experimentalist.
The original and main motivation for these devices is not one-photon double slit experiments, but rather as sources for quantum cryptography protocols such as the Bennett and Brassard (BB84) quantum key distribution protocol.
Comment: I suspect that triggered single photon sources *will* interest people. Perhaps interest them *a lot*. And if they become common, off-the shelf turn-key devices they *will* be used for basic interference demonstrations, but as yet such sources are a long way from that easy to use and people will only get them going for things that *matter*.
Comment: @dmckee Alas you are right that they are a long way off, owing mainly to the difficult quest for funding!


The genders of the pieces and pawns

Question: Historically, what, if any, are the genders of the pieces and pawns?  Is the king male and the queen female, etc?   What about promoted pieces?
Comment: All male. Even the queen was originally "The Advisor".
Comment: (possibly NSFW cartoon) https://i.warosu.org/data/tg/img/0301/23/1391974585894.png
Comment: Historically there was no queen. Check the history of chess, you will get the answer.
Answer: Chess originated in India and in the Indian armies of those times, it was common to have elephants, camels, horses and the like. Even now in rural India, the rook is the "elephant", the bishop is the "camel" and the knight is the "horse". The king is still the king, the queen is the "wazir" or vizier, and pawns are foot soldiers. In fact there was a recent Indian movie called Wazir, themed on chess and the Wazir was portrayed by a male character.
Traditionally, the armies fought mostly with men, however, even Indian history has had female warrior queens (for example Rani of Jhansi). The Wazir, however, is not a queen, but a powerful minister in the kingdom, maybe even the king's prime minister or right-hand-man (person?). Traditionally, this would be a male. Similarly, the elephant riders, camel riders, horse riders and foot soldiers would traditionally be male with females being the exception to the norm. The king is obviously male.
Comment: Yes, technically perfect answer.
Answer: Think about this. When pawns reach the other side they become Queens. Are the females? Or was this the first look on transgender people?
Comment: Logically, the pawns, Knights, Bishops, Rooks, and Queen are all female, but the King is male. This is why pawns can't promote into Kings.
Comment: @eyeballfrog i realised the 1st sentence a long time ago but not the 2nd sentence until now. WOW.
Answer: Depends on the language. E.g. Russian words for pawn and Rook are feminine. On the other hand, Russian words for (real life) infantry, cavalry, etc. are also feminine.
Answer: " Men are from Mars . Women are from Venus " . Quite an abstract Quote related to this Q . Isn't it ?
Ok why I say the above is because Chess originated as a game of war where there are two Kingdoms fighting against each other . In earlier days and even to this day a major portion you would see it is the men who always fights or takes part in Battle field compared to Women . True Women are somewhat competing with Men and showing good results but in medieval World this was almost prohibited .
So as Chess is as good as War so the Pieces/Pawns participating are all Males . In ancient Roman religion Mars was the god of war so men are categorised to fighting machines and that's the reason it implies the Gender is Male .

The genders of the pieces and pawns


What is the difference between perfect pitch, pitch memorization and relative pitch?

Question: I am confused by these terms. I heard perfect pitch is impossible to learn as an adult, but if you memorize all twelve notes in the chromatic scale in whichever octave, isn't that perfect pitch? If it isn't, please explain the difference between the three.
Answer: Perfect (or absolute) pitch is the ability to instantly recognize a note or to instantly produce the sound of a requested pitch. Someone with absolute pitch can immediately sing for you a D♭, or they can immediately tell that the Star Wars Theme is in B♭ without looking to the score.
Pitch memorization is exactly what it sounds like: a memorization of a pitch or pitches. But in some ways it's just another word for absolute pitch, since that's all absolute pitch is: a long-term memory for pitches. It's a bit like squares and rectangles: all absolute pitch is pitch memorization, but not all pitch memorization is necessarily absolute pitch.
Absolute pitch (or AP) is typically developed at a young age. Like foreign-language learning, it is a skill much harder to develop as someone gets older, but most literature on the subject suggests that it is possible. (Whether or not it's worth it is for someone else to decide, but I say it isn't.) At the very least, experienced musicians tend to develop some level of long-term pitch memory. After studying Mahler 8 for so long, for instance, I can always sing an E♭ thanks to the opening organ. Other research shows, for example, that when presented with the "Jeopardy" theme and a transposed version of it, the majority of listeners can determine which is the original. This suggests that even non-musicians have long-term pitch memory.
People think that absolute pitch is a magical remedy for everything, but it comes with a lot of drawbacks. Those with AP have considerably more difficulty in keys with lots of "black notes," and they often have trouble spotting transpositions and motivic relationships. Imagine you're listening to the opening of Beethoven 5—but first, try to sing the opening two pitches, and see if your pitch memory is correct!—you know all of those "da-da-da-dum" motives that are transposed at different pitch levels? Some AP listeners don't hear those relationships because their brains are so focused on the individual pitches. In contrast, those without AP tend to have less difficulty spotting the motivic connections. (This is a simplified example, because everyone knows Beethoven 5.)
Furthermore, let's say a church sings a hymn during a service, but the organist decides to transpose it down a step. Unless the AP member of the congregation has specifically practiced this skill, s/he will have an awful time singing that hymn, because they'll continue to sing the notated pitch, not the transposed pitch that the organist gave. Those without AP do this without problem.
And one other problem with AP: it changes as one gets older! Typically someone's AP slides up over time (see one source here), meaning they reach a point where what they think is A is no longer A. Yikes; no thanks!
Lastly, relative pitch is the ability to sing any pitch when explicitly given a pitch reference. For instance: this melody is in D major, and here's a D; now sing it! This skill relies not upon pitch memory, but rather the understanding of tonal function and how pitches and harmonies progress within a key. Good music educations teach such relative hearing to those with AP, but (in my humble experience) AP students often fight back, and hard.
TL;DR: (In my opinion:) You can think of absolute pitch as just the rote memorization of things. In less generous terms, it's the ability to monkey back "that's a G!" or "here's an F!" Relative pitch, however, demands a more nuanced understanding of key relationships: how does this F♯ function in the key of C? What is this D♭, and where will it resolve? And so on.
Comment: Absolutely correct; once relative pitch is developed to a certain point, it's a *much* more powerful skill than absolute pitch. I'm glad I don't have AP, even if I wished I did when I was younger!
Comment: @Tim In my experience, those with absolute pitch are typically tuned to a normative 440; a historical performance of a Baroque piece, with tonic shifted down a quarter step, really bugs them!
Comment: Nice answer, Richard. I have a friend with AP who gets headaches whenever he hears people jingling metal objects - keys / flatware / etc. Also, I'm sure you can relate - once relative pitch becomes developed enough, the distinction between the two largely doesn't matter. Last, yes, AP students always fight back hard - never had to work before at it!
Comment: In reflection, I believe my absolute pitch may be closer to what's called pitch memorization here (I figured out only Middle C in Grade 8, it took me more than one grade to finish memorizing the rest of the chromatic scale, I still find note identification faster if I hum those notes). Like other AP people, I have trouble singing transposed melodies if I've never heard them in the new key before, but I only tend to have trouble if the piece switches keys or I'm very unfamiliar with the piece--e.g. I have no trouble humming the famous Mario theme in a new key, but not the Halberd On Deck theme.
Comment: @Tim Regarding clanging metal, the precise reason was that he *couldn't* figure out the pitch. The actual frequency is so rich with overtones that his brain has a hard time "slotting" it into its "correct" pitch. Thus, headache. We also used to mess with him by playing microtones between semitones on string instruments. He'd get back at us by harmonizing m2's over us whenever we sang something. A lot of AP people "born with it" are typically pretty rigidly programmed. You can get a similar effect if you listen to a really famous piece, say, Beethoven's "Moonlight Sonata" in the "wrong key".
Comment: @jjmusicnotes - never understood that sort of thing.Why should a particular pitch/note cause a headache? When I hear any note, whatever it is, it doesn't bring on a headache. And I think if I knew what the note was wouldn't make the slightest difference. And as for hearing something in 'the wrong key'. What's that all about. I must have played xyz in 7 or 8 different keys.No idea what the 'right key' might be, but what difference would it make. I'd like to get my head around this, but need help! And would listening to Bach at 440Hz=A sound good, but not at 442Hz...? And more to the point- why?
Answer: Perfect pitch, more properly called absolute pitch, is the ability to hear a note - anything from the drone of a lorry passing, to one played on an instrument, to a buzzing bee - and be able to say what pitch and what note it is without reference to anything external. Some people have synesthesia, which manifests itself in a particular note being recognised as a colour, a taste, a feeling. Others seem to have it from birth, and can just recognise what note is being played.
Pitch memorisation is a new one on me - how anyone can memorise the 12 chromatic notes I don't understand. Yes, once a particular note is played or heard, then it's quite easy to sing other given notes, but surely that's relative pitch.
Relative pitch is relatively easy to nurture. It involves knowing the intervals, e.g. a P5. So that when a note is heard, a P5 above it can be sung or played. Thus, given a C, one can sing/play a G - the P5 of C.
Absolute pitch can be encouraged in those who don't possess it. But - it can take years of daily practice. And it's often not perfect even then! After several years, I can sing a particular note and verify it on an instrument, but at the moment, the score's only 8/10.
Answer: Relative Pitch is a recognition process based on awareness and understanding of complex pitch interrelationships from within a musical context (dynamic recognition).
Absolute Pitch is a process of pitch awareness based solely on memorization (static definition; musical context irrelevant).
'Absolute pitch' memorization is a static conception (i.e. "A"= 440 Hz) which is prized only in the area of music. It is interesting that this type of memorization is irrelevant to the visual arts (i.e. "Red"= 440 THz). I wonder if this is due to the fact that chromatic music is a 12 note system (A-G), whereas color theory encompasses hundreds of named colors, each with exponential perceptible variations of contrast, hue and saturation; and it also encompasses an awareness of the impact of the surrounding visual context on the perceived color.
The static concept of 'absolute pitch' can become meaningless at best, or an impediment at worst, in situations where A440 is not the pitch standard or in non-chromatic, non equal tempered, and micro-pitch scale systems. Because relative pitch perception is a dynamic concept and process (a practice of developing awareness of pitch interrelationships) it can be carried forward and adapted to other musical systems.
I trained with both transposing (Bb, Eb) and non-transposing musical instruments, so the concept of 'absolute pitch' has always been arbitrary in practice. However, pitch recognition is not. For example, I notice the pitches of my phone's ringtone when listening to music, wind chimes and other unrelated sounds. I don't try to memorize the pitch names. Instead, it increases my awareness of a vivid differentiation between pitch memorization and pitch recognition. Pitch recognition is a perceptual skill that can become more refined as a musician's micro-pitch (pitch color) and timbral (tone color) awareness is developed.
The development of good intonation (relative adjustments of each pitch within a harmonic context) is very different from the memorization and reproduction of the pitch definitions established in an equal temperament system.
A fundamental difficulty arises for a musician trying to develop simple, static pitch memorization when a more complex understanding and awareness of the contextual relativity of pitch has already been acquired. This difficulty is conceptual more than technical, and results from an awareness of the complex interrelationships existing between the pitches and intervals within many different musical systems and methods (i.e. Just Intonation, Raga, Maqam; micro-pitch scales). This awareness makes the concept of 'absolute' pitch seem arbitrary and not widely applicable as a musical skill.
'Absolute pitch' is dependent on a quantified reference standard, which is itself based on the conception of each chromatic pitch as a separate (discrete) entity, not affected by its musical context. With musical training and exposure to different music systems, a recognition arises that any 'absolute' conception of pitch is a reductive simplification. That is, musical pitch is a process within an integrated context (verb; relatively defined) rather than a discrete, static definition (noun; absolutely defined).
Interestingly, there is another related type of static pitch recognition which occurs, for example, when a person can begin singing a song in the correct key without knowing which key it is. Or when someone recognizes that a song is being played back in a different key from the original rendition.
Comment: Regarding "effort could be invested in memorizing the 12 note sequence of equally tempered pitches derived from A=440, but what would be the value and purpose of this effort when there are so many other systems of music beyond it to explore?", I argue that the other systems of music are quite rare (e.g. gamelan slendro's 5TET) and therefore may not be worth the effort (especially since I don't quite like gamelan music). I generally classify notes in only 12 pitch classes anyway (my only current exceptions are quarter tones); notes often don't care whether they're 12TET or justly intoned.
Comment: Another reason that it's irrelevant in art is because of the percent of the population that can do it. Anyone who isn't colorblind or blind or severely incapacitated can imagine the color "red" and get it right every time. Among musicians, the incidence of Absolute Pitch is so much less common. than the related ability in artists, memorised color recognition. Imagine if 99% of the population of Earth were colorblind. The 1 percent would then be like people with absolute pitch for music.
Comment: What's the "fundamental difficulty [that] arises for a musician trying to develop simple, static pitch memorization and recognition when a more complex understanding and awareness of the contextual relativity of pitch has already been acquired"? Based on my experience with acquiring absolute pitch, I developed relative pitch 1st, and I don't recall my relative pitch getting in the way of my nascent absolute pitch. In fact, I think my relative pitch accelerated the development of my absolute pitch--I could name other notes given my memorized Middle C until I memorized the other 11 notes.
Comment: "*Anyone who isn't colorblind or blind or severely incapacitated can imagine the color "red" and get it right every time*."
— There isn't any specific shade of 'red' that would be consistently named as a standard 'red'. In effect, the 'red' would be described subjectively as a range of relative distinctions (i.e not-orange; not-yellow). With training, additional distinctions such as reddish-orange vs orangeish-red would emerge into awareness and further extend the perceived varieties of 'red'.
Comment: The 'fundamental difficulty' for a musician who has developed an understanding of relative pitch has to do with an awareness of the relativity of pitch and interval values within many different musical systems (i.e. Just Intonation). This awareness makes the idea of 'absolute' pitch arbitrary. So yes, effort could be invested in memorizing the 12 note sequence of equally tempered pitches derived from A=440, but what would be the value and purpose of this effort when there are so many other systems of music beyond it to explore?
Comment: Your third paragraph is just wrong. Our concept of "red" is cultural so when splitting hairs like this it has the exact same issue. Different cultures that don't utilize colors like we  do and group them differently see color very differently don't make the same distinctions we do. It doesn't mean our calling something or identifying it as red is not useful, in fact it's the opposite and having 12ET and saying C4 is very similar in nature.  See https://www.sapiens.org/language/color-perception/
Comment: Great article. Identifying something as 'red' is useful for expressing perceptual distinctions in language. I am trying to point out that there is no absolute 'red' in the way that we have an absolute pitch of 'A' in music.

'A' may be defined as 440 Hz in (Western) music, but 'red' is not defined as such (in THz) in the visual arts. The establishment of a cultural standard based on an absolute numerical definition leads to circular reasoning: an absolute 'A' is 440 Hz because 440 Hz is defined as 'A'.
Comment: I don't think it's circular at all. Whether using a tuner or basing off someone else playing a note, people need to synchronize what they are playing. There were a lot of acts in the 80s that tuned either a half step lower or somewhere slightly less. Having a defined reference makes it easier to have musicians sync up rather than each be slightly off. I have a friend who has absolute pitch that can not only point them out, but they sound off to him. For this reason Absolute pitch can be a double edged sword and almost a curse to musicians where relative pitch is extremely useful.
Answer: I'm less sure of the answers than some of the others. I learned as an adult and played entirely by ear to begin with. If someone had asked me to sing an A, I wouldn't have had a clue because I'd never knowingly played one.
Over a period of years I developed a limited memory of certain notes without knowing what they were called. For instance I used to have a microwave that made a humming noise and whenever I heard it I would find myself singing a familiar classical theme that I didn't know the name of. It eventually occurred to me to track this piece down and, sure enough, the microwave was perfectly in tune with the opening bars of the piece.
I never made any active attempt to memorise the pitch and to this day I don't know what the actual name of the note was. So, do I have perfect pitch? I don't know. I couldn't sing that note on request but if I heard it I would recognise it.
I suspect that very young and prolific musicians simply pick this sort of thing up in the way we all pick up a first language. Adults find it hard to learn a new language but they will pick up a few phrases if they live in a foreign country for a while.
So there are two aspects. (1) Recognising a note when you hear it and (2) Producing a note on request. Personally I can only do (1) and only for a limited number of tunes.
I believe that although a few people are completely tone-deaf, the majority of us could have perfect pitch if we started early enough and were interested enough.
You can easily test yourself. Think of a tune that you know well (one that is always played in the same key) and find it on Youtube. Without listening first, see if you can sing or whistle the first few notes in what you believe to be the correct key. Then play the track. If you correctly get the right note without fail then you have perfect pitch.
Comment: Getting those notes correct in your last paragraph could easily be just a manifestation of the [Levitin Effect](https://en.wikipedia.org/wiki/Levitin_effect) instead of perfect pitch.
Comment: @Dekkadeci - Interesting - I hadn't heard of that. I think my point is that there are no sharp cut-offs between the different abilities. By the effect you mention, almost any musician could learn certain notes because of their common occurrence. Then, by using relative pitch quickly extrapolate to other notes. Eventually, like any memory phenomenon, this could become automatic to the point where any note could be recognised. Incidentally I wonder how people with perfect pitch coped in the days before pitch was standardised. Organists especially would have to adapt to the local standard.
Answer: Actually perfect pitch and absolute pitch are not the same thing. I read that perfect pitch is not possible to aquire in adulthood. I don't know that it has never happened to anyone. Absolute pitch unlike perfect pitch is possible to acquire in adulthood. Perfect pitch is the ability to recognize a pitch instantly when you hear it. Absolute pitch is the ability to tell what the absolute pitch of something is but not necessarily to recognize it instanty. Most people when they hear a note a few hours later don't know which note to play in their head to have it be the right note. The brain usually doesn't bother developing the ability to recall the absolute pitch of something because there's no way to describe to them what the pitch really sounds like. Until I read part of Richard's answer, I didn't know what pitch memorization was. It turns out that it's another way of saying absolute pitch. I didn't use to have absolute pitch. Later, I was sluggishly getting closer to having absolute pitch and could sense it. When season 2 of "The worst witch" came out when I was about 30, after just a few episodes, I developed some extent of absolute pitch. Now I'm quite often able to play music I heard before at the correct pitch in my head but am not always able to so it.
I believe the reason people can't develop pitch in adulthood is because actually because it works better not to have it. Once there was something going on at the roundhouse in Toronto and I bought some lemonade with tickets and they had a false memory that I didn't pay then somebody else told them I had paid and they believed that person. I believe the explanation is that the brain developed a certain method of reconstructing memories that's usually reliable but wasn't reliable in that situation. I guess the person I paid was very busy doing so many things so her brain drew less attention to my payment but she used the same method of reconstructing memories that didn't work that time. It's possible that she will eventually find a slower more reliable method of reconstructing memories and not overrely on the simpler method she was using earlier.
Similarly, instantly sensing the pitch of something is overrelying on a method of sensing the pitch that you can never be sure is actually feeding you the correct information just because it seems that way. I feel like driving is too hard for me but it's worth it. It's probably partly because I'm a slow deep thinker. Also, since I don't even have the desire to drive, I'm happier because now I don't have to put up with the stress involved in driving.