Stationary eye with moving pupil, is it possible?

Question: I am making a sci-fi web-comic set on an alien world and I thought up an idea for an eye that works much like an eye from a mammal, but instead of moving the whole eye, only the pupil moves. This idea sprouted from the eyes of mantis, though their moving pupil is possible because of their compound eyes, I would like to know if my idea could be physically possible in a structural sense.
Comment: Welcome don't be shy your pupil is dilated!
Answer: My first thought is of the "windsock" eye design of the anterior median eyes of a spider.

(Emphasis mine)

As the lens is attached to the carapace, the eye's scanning movements are restricted to its retina through a complicated pattern of translations and rotations. This dynamic adjustment is a means of compensation for the narrowness of the static field of vision. It is analogous to the way most primates move their eyes to focus images of interest onto the fovea centralis. Such movements within the jumping spider's eyes are visible from outside when the attention of the spider is directed to various targets.

This is actually the opposite of what you ask, but the same thing: the eye does not rotate as a whole object.  If the pupil moved and the retina stayed fixed, how would that look any different from moving the whole thing?
There are good reasons why the eye would not be a moving ball like ours. For example, birds have better resolution and for larger imaging area and stability of same has a flat back (not round; more like a camera film plane) and fixed to bone so it stays stable.  An animal might evolve a way to pivot the primary lens, like a view camea's front board, which has the added benefit of doing what a view camera can do with perspective and focusing on planes like a cliff face, all in focus at the same time.  Landscape photographers use a tilting lens to allow more of the ground (at different distances) to be in focus — shouldn't that be useful to an animal watching for dangers or dinner, just as well?

Now this is what you describe exactly. Look at why cameras do that,  and design evolutionary pressures to exploit these same advantages.  The independent motion of the lens and sensor plane gives abilities that are not present through moving the camera as a rigid unit.  So, it may be selected for even if the lack of swiveling of the eye can be dealt with in a different way or the non-round rigid back was no longer a priority.
Comment: +1 for an excellent answer, -1 for making an arachnophobe look at a close-up photo of a spider -- and one of the most horrifying of all, in fact: a spider capable of *jumping 50 times its body length!!* It's bad enough when they can crawl at you, but when they can do that *and* jump, it's game over, man!
(In reality I wouldn't downvote any answer for that, but I seriously cannot scroll back up to upvote you either, so it works out the same in the end...)
Comment: +1 for exposing completely different optical system to me.  Thank you very much.
Comment: Yay for thinking outside the normal bounds!  Science is still learning a lot from the other optics available in nature.  [This](http://www.sciencedaily.com/releases/2006/04/060404194138.htm) telescope is modelled off the [eye structure](https://www.osapublishing.org/view_article.cfm?gotourl=https%3A%2F%2Fwww.osapublishing.org%2FDirectPDFAccess%2F2CBE553E-DE9C-87EC-10E986E723BBA4E6_184257%2Foe-17-16-14156.pdf%3Fda%3D1%26id%3D184257%26seq%3D0%26mobile%3Dno&org=) of a lobster.
Comment: Earlier this week my wife got caught in a spider web that was strong enough to pull her head back and she had to tear herself out of it.
Answer: Sure it's possible but why would you do that?
You want to meld this:

to this:

Making a stationary retina is certainly possible.  Making a moving pupil may be possible too.  The trick is getting them to work together.  The control structures required to move a pupil around while maintaining focus on an immovable retina is far more complex than maintaining focus on a retina that moves along with the pupil.  I don't know of any optical structure, natural or man-made that forces the pupil to move independently of the retina.  The physics governing optics are very unforgiving.  Getting them wrong means that your creature won't be able to see properly and thus won't survive as well as creatures with simpler eyes closer in design to our own.
From an evolutionary perspective, it doesn't make much sense.  A more complex eye is more prone to errors in development and less resilient to damage. A simpler, more robust eye (like our eyes or an insectoid compound eye) would do much better.
Comment: I have examples in my Answer for both natural and mechanical systems where they move independently.   Knowing about them, it *does* make sense.
Comment: Well dang, that's new stuff to me. Thank you for sharing that.
Comment: "I don't know of any optical structure, natural or man-made..."  I am reminded of the way a cathode ray tube works to focus a beam onto each part of a phosphorescent screen.  In reverse, the stationary part would be the retina, and wherever the beam was focused would be the pupil.  There's one optical system.  It isn't exactly the same, but the foundation is there.
Comment: I must say, it's great to see alien design breaking mamal-centric shovenism.  Most people don't even realize how alien *birds* are, let alone non-vertibrets.
Answer: It took me a while to figure a way to this could happen and make some 'logical' sense.  What I came up with is is the eye (rods cones or what ever sensors they have) are just on an immovable sheet some distance behind a lens like a movie screen. similar to how our eye works, but instead of the Iris and pupil being apart of the eye, the eye is set like the bones in the body, but the eyelid is the pupil opening and closing for more light, moving focus kind of like a telescope.  They could also help 'flex' the lens to give a wider range of focus for the eye, looking real close and seeing very far away.


Do electrons experience wind resistance?

Question: Electrons have a mass, as a particle with mass, they experience most effects of objects with a mass. So do they experience any sort of wind resistance? Or is that simply explained by their cross section interaction probability with a given particle?
Comment: Wind resistance has nothing to do with mass.
Comment: could you maybe specify the physical situation that you have in mind? For example, electron from cosmic rays traveling in the atmosphere? Electrons in solids?
Comment: @sintetico I would mostly be talking about electrons allowed to "freely roam". I.e electrons who would not be confined to the cloud around an atomic nucleus. But perhaps that situation would be insightful in some way as well.
Answer: If we speak of electrons, then it is appropriate to speak of "wind* as a flow of atoms. Electrons are usually confined to atoms or materials, inside of which the wind atoms do not penetrate, so the collision of electrons with wind are very unlikely.
One place where one does encounter a stream of unbound electrons is electron microscope. In this case one always assures that the measurement takes place in vacuum, since otherwise electrons will indeed get scattered by air.
Finally, in particle colliders streams of particles are routinely scattered against each other. One could think of it as electrons experience resistance of, e.g., a wind of protons.
Comment: In radiation oncology, electron beams sometimes are used to treat skin cancer. The beam exits from the vacuum environment of a linear accelerator through a thin-but-solid metal "window," and it it may have to pass through ten centimeters or more of room air before interacting with the patient's skin. I don't know how or how often the electrons, which have a kinetic energy on the order of several MeV, interact with the air molecules.
Comment: @SolomonSlow This is very interesting! I imagine one could calculate collision frequency between electrons and the air to see, whether there is an important effect.
Answer: If one imagines a macroscopic object moving through air, one can very well approximate air resistance as the action of a continuous fluid. At low speeds, this situation can be described by viscous friction, which is a force proportional to the speed of the object, and with direction opposite to its direction of motion (I neglect here the effect of turbulence).
If you have electrons moving in a medium, for example, cosmic rays moving through air, or electrons moving in a solid or in a liquid due to the effect of an electric potential, the above approximations cannot be valid. One cannot approximate the action of the medium on the electron as the action of a continuous entity. From the point of view of an electron, air, fluids, or a solid, are made of individual atoms. Therefore, one has to consider the statistical average of all possible collisions (scattering) of the electron with atoms. The situation is better described as individual collisions, Brown motion in fluids, or Drude theory of solids, depending on the context. All these approaches consider the statistical average of the medium on the electron trajectory. In practice, the electron will move freely for an average distance $l$, which is called the mean free path. Surprisingly, or maybe not, in the Drude theory of electron in solids, the average effect of collisions is proportional to the electron velocity, analogously to the case of viscous friction.
Answer: Electrons do have a mass ($9.10938356 \times 10^{-31}\,\mathrm{kg}$). The effects of this mass in your particular situation are likely immeasurable though.
I partially agree to Vadims answer, collision of electrons with wind are very unlikely indeed.
There is another kind of resistance electrons would experience in this case. The air that typically makes up wind consists of more than just regular oxygen molecules (O2). There will likely be ionized particles, some may even be caused by the aforementioned stream of electrons. Ionized air will interact with electrons and thus provide some kind of resistance.
I wouldn't really consider it wind resistance though.
Answer: I think maybe the most common event in which electrons might encounter 'wind resistance' would be during the initiation of a lightening strike, where leaders ionize a path to ground.  That process does not move from point to point at the speed of light, but at the speed with which atoms can be ionized in the general direction of the lowest resistance path.  The act of ionizing is accomplished by free electrons produced by the potential difference between cloud and ground.  Something else to think about; electrons, like photons move from one atom to the next in a chaotic way that is determined by the availability of a place in the orbit structure of the receiving atom, thus an individual electron moving in a wire may take aeons to go inches, while the effect of the electron being introduced at one end will be measured at the other end at the speed of light.
Answer: A high voltage electric arc between two vertical wires, whose separation increases with height, tends to move up (even though the separation is increasing).  I assume this motion is caused by the convection of heated air.  (This situation does include ionized atoms.)
Answer: Short answer: NO
Medium answer: The electron will not be slowed or pushed by wind or air, it will either hit a single atom or it won't.
Longer answer:
Wind resistance (drag) deals with objects on a macro scale.  It is a simplification dealing with many, many atoms in both a gas and an object moving through the gas.  Take for example a .177 steel BB.  There are about 3 million million million million atoms.  When moving through the air these atoms displace the air in a certain way and this slows the BB down (wind resistance).  The wind resistance or drag depends on the item's size and shape because it deals with how the atoms in the BB push the atoms in the air out of the way.
Contrast this with a single electron.  The tiny electron is not going to push heavy atoms out of the way to create drag.  Instead, the electron will be absorbed if slow enough and create a negative ion, or bounce off the atom.  The atom itself has electrons and much heavier protons and neutrons.  As a very rough example it would be like that BB hitting a cinder block.  The BB is not going to go through a sea of cinder blocks and push them out of the way to create drag.  It might knock off a chunk of one cinder block and slow down (like an electron dislodging another electron in the atom to create a positive ion), but it will be bounced off in a different direction at a slower speed.


Is cosmological constant some kind of field that permeates all of space?

Question: One simplest candidate for dark energy is a cosmological constant.
Is cosmological constant some kind of field that permeates all of space, or is it just some kind of energy stored in space?
Answer: @Forge Cosmological constant is not a candidate for dark energy, it is the quantity which denotes dark energy.
And yes it is believed that dark energy fills up all of spacetime but the theoretical calculation of vacuum energy density vs Experimental measured value have largest disagreement ever with respect to any disagreement in science. Theoretical calculations predicts about 10^(108) order of discrepancy. This is called Vacuum Catastrophe.
Also it's more preferred to look at dark energy as a antigravity force field without any dark energy particle content. But not a single one interpretation is more accurate than other because we don't yet know what dark energy force field is or even if it made of dark energy-particles or not.
Answer: The cosmological constant has the same effect as an intrinsic energy density. Although it was introduced as a constant, and intended to be positive, you can build the theory with a negative cosmological constant, or one that varies in time in some preferred frame (and so is not constant) or one that varies in space and time the right way and as such becomes a scalar density field. All of these variants are mathematically natural, but evidence for it is controversial.
Although I feel that @Aman_Pawar's comment that it is the quantity that denotes dark energy is misleading in being a bit incomplete - the point is that it is not a separate entity, such as some kind of quantum particle, that would, when combined with relativity require inclusion as an adjustment to the cosmological constant, it is literally the way in which the energy density is expressed in Einstein's equations.
I expanded on this because of the part of your question in which you asked - is it some kind of field. And the answer to that is that it would be mathematically natural and make physical sense for it to be interpreted as a measure of some density. The next question is whether this field is observed empirically.


Will point-and-shoot cameras be able to compete with camera phones?

Question: As camera phones become more and more sophisticated, will they ultimately replace point-and-shoot cameras?
Comment: The real question is when do we stop calling these things phones?  They're computers that just happen to make phone calls as well...
Comment: I would like to point out also that this is really a discussion, unless somebody's got a crystal ball, there is no *right* answer.
Comment: @rfusca - I agree, the concept of phone is meaningless, it's a network with devices that interact.
Comment: @rfusca, @John, We will go on on calling them phones, regardless of added capabilities, because that is their central purpose. We are born to communicate, see http://en.wikipedia.org/wiki/Social_intelligence. Danial Goleman's book 'Social Intelligence' is particularly relevant, see http://www.amazon.com/Social-Intelligence-Science-Human-Relationships/dp/0553803522
Answer: I don't believe that camera phones will replace true P&S cameras. The limitations of the phone form factor will be the barrier conditions. having the flush lens and small size requirements limit the image quality. It is not to say that camera phones will not continue to advance, it is more that the requirements of being a "phone" will outweigh the requirements for being a camera.  Just from looking at my phone with the small flash, the flush small lens, and the battery life of a gnat when shooting pictures I think it is not well suited to being used as a camera.
People will be willing to carry a camera for taking pictures on vacations and other events that provide more control than what the phone can do. It is not a question of the electronics being capable it is just how the technology is packaged and if it will be pleasing to the consumer.
I still have separate music player and telephone as I find that a device can typically do one thing very well, or many things mediocre. I would prefer to have one device that does one thing very well.
Comment: +1 - The question is highly subjective and speculative, but you did well in response and I tend to agree. Cell phones are trying to be jacks of all trades and thus are becoming masters of none.
Comment: Its a matter of time before P&S are no more, see my answer below. Goodbye P&S and hello super new gadgets!
Comment: @kacalapy - Time will tell, but at this point, cell phones are actually quite a ways behind the point and shoot market and it's not a market that is standing still. Yes, there will be some that go to the cell phone as the option, but I'm not convinced it's a large enough market to kill the other. The same kind of claims have been made for many a decades, especially around SLRs and, well, they're still here.
Comment: Can someone hit fast forward so we can know now... and enjoy the cool new toys sooner.
Comment: +1 The problem is that my phone is already my MP3 player, calendar, email, text machine and... erm.. phone. The biggest problem with this is using it for many of these functions at once and battery life!
Answer: I don't think there's any question that camera phones will take over mass-market point & shoot cameras. The question isn't really if, but when.
The iPhone uses a 1/3.2"-format sensor (using the weird standard where 1" = 16mm, so 15.5mm²). This is smaller than what's used in most point & shoot cameras (especially the good ones), but isn't so far off.
In fact, take a look at the specs for the Canon Powershot A200, announced June, 2002. Sensor the same size as the iPhone, and a fixed-focal-length lens of around the same range. But, only 2Mpix, and ISO from 50 to 400 (and we can bet that 400 was pretty bad).
And the iPhone isn't even state-of-the-art for camera phones — for that, look at the Nokia N8, which has a 1/1.8" (36.8mm²) sensor with max ISO of 1200 and apparently very nice optics to boot. This clearly competes with a lot of point&shoot cameras now, at least on some levels.
So, it's pretty clear that the best current camera phones handily beat at least some of the P&S digicam field from a decade ago, and I think it's reasonable to assume that in much less than another decade, phone cameras will beat today's crop.
A larger form-factor may always have room for a level of quality that literally can't be squeezed into a camera phone, but from that direction, there's pressure from low-end dSLRs and especially mirrorless interchangeable-lens cameras. Right now, there's a pretty impressive bunch of high-end P&S cameras (more than I would have predicted), but I think it really can't last. Camera phones have two major advantages: 1) people have them already, and 2) the fact that they phones are now software platforms makes them so superior in many ways. Not only can one fundamentally change the camera uesr interface, one can post-process in the field, and instantly share the results.
So yeah: it'll happen. In fact, it is happening. When is an open question, but mostly the discussion over which value of "soon" to pick.

Update as of April, 2011: TechCrunch ran an article yesterday titled iPhone 4 About To Be Flickr's Top Camera. Point & Shoots? Pretty Much The Opposite. The title pretty much says it all. Of course, Flickr has an inherent bias, since the iPhone can automatically upload pictures with no extra steps, but still, I think it's plenty illustrative of future trends. As TechCrunch puts it:

Six months ago, the data looked bad for point & shoots. Now it looks downright frightening. If the trend continues (and it's actually speeding up), the point & shoot is finished.
Comment: @lindes: again, I don't think *cameras* are going away, just mass-market point-and-shoots. People who want do do post processing *at all* are already at the edge of that. Right now, being at the edge is okay, because you benefit from the economy-of-scale, but the mass market moves on, P&S cameras will be split into very-cheap-crappier-than-phone-cam models (which already exist) and more expensive enthusiast and super-zoom models. These, in turn, will get squeezed by cheap dslrs and mirrorless cameras, making them very niche indeed.
Comment: +1  The phone as a software platform is a very good point.  This is one area where camera manufacturers are going to have to pick up their game.
Comment: Manufacturers like Motorola will be picking things up in the mobile arena, not canon or nikon. This should help put out better dslr models faster though, I hope.
Comment: Micro 4/3rds have made similar claims over the dSLR, but I'm not seeing it. Unless there's a massive sea change in the technology, cell phones will be limited compared to dedicated hardware. Now, for a lot of people, that's enough, but not enough, I think, to kill the P&S market as we know it.
Comment: Which claims does micro 4/3rds have? They're not a device people are already carrying nor are they general-purpose software platforms. The mirrorless category really can't compete with dSLRs until the electronic viewfinders are on par with or exceed optics (which will happen, but maybe not in five years). I don't think camera phones are going to replace _cameras in general_; there's still plenty of room for larger devices. And the super-zoom P&S still has some breathing room, but the general I-just-want-a-camera-to-put-in-my-pocket/purse mass market just won't be there.
Comment: It's worth adding that the A200 I reference received very good reviews.
Comment: The "software platform" argument is an interesting one, and certainly holds some merit.  However, I see two things to argue that dedicated point&shoot cameras may persist, even so: (1) point-and-shoot cameras *are* doing at least some post-processing stuff -- As just one example: automatic HDR and "slide panoramas" in the Casio EX-ZR100: http://exilim.casio.com/products_exzr100.shtml; (2) I think some people will always prefer to do post-processing on a bigger screen than could ever fit in these devices (e.g. a 20" or bigger display), and will thus prefer better optics over built-in software.
Comment: @mattdm: Perhaps, but I carry my G9 around with me all the time, as an in-between for my phone camera (which I use for some stuff) and my SLR(s) (which I only bring with me when I expect specifically to be shooting), and use it for those images that the phone cam doesn't do a good job of.  It also has a hot-shoe, which I don't expect to see on a phone... though perhaps bluetooth would someday be able to trigger a pocketwizard or something?
Comment: @lindes: probably your SLR is too big. :) But seriously, I don't think having image quality approaching the G9 is an unreasonable expectation for five years from now. The lenses will have a little more compromise, but it'll be in the ballpark. And from the other side, there will be micro 4/3rds (and similar) in the ballpark size, price, and weight as the G9, but with all the advantages of a large sensor and interchangeable lenses.
Comment: Now, in all of this, I'm not considering large-sensor fixed-lens cameras like the Fujifilm X100 or the Leica X1. Those are, as awesome as they look to be, niche products. It's _possible_ that things like the G9's successors will stay around as niche products, but I think as the mass market falls away, there just won't be the sales to justify them.
Comment: @mattdm: I can't agree with you on this. By the time phone cameras will come to speed of today's P&S cameras, the later will be ahead yet again. Phone isn't supposed to replace P&S. It never was and it never will. Phone is a phone. P&S Camera is a P&S camera. Putting decent optics in a phone will make it unusable as phone. Optics isn't electronics that evolves in density and capabilities. The higher resolution sensor and their small size will require much much better optics which is a big limitation. So phone cameras won't replace P&S cameras. Sorry mate. Won't happen.
Comment: @mattdm: But it's a completely different question whether phone cameras will start satisfying non-demanding users (which most are). Evolving phone camera quality may produce this effect. But quality will still be behind P&S. But since people aren't demanding they may settle with phone camera instead.
Answer: Contrary to looking at the problem from a "when phones cameras will be comparable to P&S", which is inevitable advancement of the technology (although I won't commit to a 5 years time frame), there is another path - P&S cameras will become cellular enabled! I see no reason why a camera like the Digital Elph can't include a mobile phone chipset (kind of what MODU's vision was all about). Then, the above question will become meaningless, as now you have a cell phone with P&S camera quality.
At the bottom line, it does not matter what way you look at it - phones become cameras or cameras become phones. It is all about convergence and there is no doubt that this is the way of the consumer market future.
Answer: I'm going to take a different tact from the other posters... I don't think it matters. There are some certain facts in all of this that are relevant:

Cell phones and P&S cameras will improve.
Some percentage of the population will be happy with the cell phone, some will not.
World population is approaching 7 billion.

Given the above, both formats will, I think, do very well for any forseeable future. They compete, in a sense, but not entirely. However, I agree with ysap, the convergence is clear, but I do think that there will always be a segment of the population that wants the advantages of the dedicated hardware and, hence, P&S will persevere.
Answer: There are point-and-shoot cameras that already have many features of a phone - microphone, speaker, touch screen, WiFi connectivity, similar form factor. I see no reason why there would not be a model in  near future that is fully capable of mobile networking, including making phone calls. The network rates are already cheap enough to afford this. After all, easy instant sharing seems to be a buzzword for selling P&S cameras.
Answer: Camera phones will largely replace point and shoots in the consumer and hobbyist markets. However for the prosumer, true professionals and enthusiasts markets, I seriously doubt this will be the case.
Camera phones tend to have the ability to implement many features in software to compensate lack of physical space for some features. On the other hand, cameras may change shape and size drastically to accomadate features while at the same time being capable of any amount of soft-features.
Lenses, sensor size, compression circuitry, real time enhancement circuits such as light and color balance, anti-blur and many similar features are very different implemented as hardware or cannot be simulated effectively.
As I see it, this means there is a need for cameras in general that camera phones cannot fill due to restrictions inherent to the product.
Someone could come out with a phone that had interchangeable lenses or one or two extra features. Perhaps even a phone for photographers, but they still would not have the same depth of features or quality as high-end point and shoot cameras.
Answer: Actually, the prediction is that within 5 years point and shoot cameras will start to fade in favor of camera's built into mobile devices (they will be less phone and more... well who knows whats going to be packed into them in 5 years). Personally, I think this may take a little longer but is inevitable with the amount of money the mobile market commands today and more importantly the growth it has seen in the past few months and years.
After a fast search it would seem I am not alone in thinking this. See this article title The future of the point-and-shoot (there isn't one) for more.
Comment: I don't buy it. Cell phones are not up to par in image quality to kill the P&S market in any forseeable timeframe. The same sentiments were expressed with micro 4/3rds versus the APS-C dSLR, and with FF dSLR versus medium format. There's no question that a huge number of consumers will go cell phone, but is it enough to kill point and shoot? Not convinced. They're a long way off in my opinion.
Answer: To take it in a larger context, the phones are starting to be called "hand-held devices".  They are Turing complete and have specs that leave '90s desktop computers in the dust.  How long will it be until I come home, plug my phone/handheld/whatever-it-will-be-called into a a dock that has a power source, keyboard, speakers and monitor and use the processor on it to my web browsing and programming?
I said that so I could say this, low end point n shoots for simple snapshots will be integrated into that and the demand for cheap cameras will drop off, especially as the devices get smarter.  But I expect that major camera manufacturers will partner with handheld manufacturers to make a decent enough product.
I don't see the entire compact camera market going away though.  I like my 12x zoom.  I don't know if that can be out into a the same space as something I want to talk to pull out and start talking on.
But then, I go out with the specific goal of getting a few good pictures to show off.  I bought my compact for the specs of picture clarity at large sizes and lower light, the zoom, and the full manual settings.
One final thought:
If I made handhelds, I'd figure out a way to make is easy to mount the thing on a tripod for group photos.  The typical screw on the bottom might be too costly in precious handheld device space.  ...maybe a special clamp?
Answer: There has been a trend towards multi-function phones that do everything possible. The thing is, people are starting to look towards "appliances", which are devices designed to do one thing well, with the most simplistic controls.
A point-and-shoot camera is simple. You switch it on. Point it at someone and press the big button.
On a multi-purpose devices, the workflow cannot be this simple as you have to tell the device what function you want it to perform and then use one of the multi-purpose buttons to take the picture.
Ergonomically the multi-purpose device has to make similar compromises. People want slim phones, but it is easier to hold a chunky camera that gives you a steady grip.
Answer: Most of the photographers here are being photographers, and are answering "No," because even compact cameras will continue to enjoy image quality and handling benefits over phones, at least as far as we can predict.
But that wasn't the question. The question was will they ultimately replace point-and-shoot cameras, and in the marketplace, I think the answer is mostly "Yes." Most people aren't that picky about image quality, and don't want to carry around a bunch of different devices. Already, the iPhone 4 will soon be the most popular camera on Flickr, and some have attributed the death of Flip compact video cameras to the smartphones. That's not to say that the compact segment will disappear entirely; there will always be something like the S95 and G12 for people who want a more serious compact camera, but I think you'll see more and more people foregoing the P&S for their phone.
Answer: The answer is much larger than a debate about cameras.
The technology is advancing quickly and the cell phone is acquiring a number of capabilities that are giving it a unique place in our lives.
- a phone (obviously).
- a computing device with downloadable 'Apps'.
- a video camera.
- a conventional still camera.
- a credit card.
- a bus/airline/theater, etc ticket
- a navigation device.
- a security access device.
- a payment transfer system.
- an information resource - Internet.
- a book reader.
- a music player.
- a video player.
- a navigation device.
- a personal organiser.
It is thus becoming an essential device that all people must have with them at all times.
So does this mean it will displace the P&S camera?
No, not really. It is extending photography to the vast number of people who were not photographers in the first place. So many more people are becoming photographers, in the limited sense of everyday snapshots.
Some of these people, through exposure, will aspire to better photographs and migrate upwards to more capable cameras. These will be P&S cameras because their experience with cell phones will condition them to expect nearly the same convenience.
Some of the existing owners of P&S cameras will instead use their new cell phones simply because they are conveniently always available and the quality in any case is good enough for them.
And still others will have multiple devices for multiple purposes just as today many DSLR owners also have a P&S camera.
So the market will be layered with cell phones owning a vast proportion. P&S cameras will have lost somewhat to this while it will also gain some of the new converts to photography.
My cloudy crystal ball says that the cell phone will have brought so many new converts to photography that enough of them will upgrade to P&S cameras to offset any losses to the cell phone.
And for many people it is not a case of either/or but rather using different tools for different circumstances.
Photography, as a hobby, will be the winner.
Answer: lol no... P&Ss like G12 (bigger sensor), SX30 (35X zoom!) will always be better than any camera phones. And, I agree that camera phone are getting better with every new release, but so are the P&Ss!
If ever, any phone company can incorporate a DSLR within a phone, only that day they will overcome P&Ss :D


Why does my 3rd method not show me that power = force dotted with velocity?

Question: I have derived 3 expressions for the power that a force, $\vec{F}$, transfers to a body. (A) and (B) are consistent, but (C) isn't. Where have I gone wrong with (C)? EDIT: THE MISTAKE HAS NOW BEEN SPOTTED. (Explained below.)
(A.) The infinitesimal work done on a body by a variable force, $\vec{F}$, on a body as it moves over an infinitesimal displacement, $\delta \vec{r}$, in an infinitesimal time period, $\delta t$, is given by $$\delta W = \vec{F} \cdot \delta \vec{r}.$$
(This is only exactly true for when the path the body follows over the time interval, $\delta t$, is a straight path, and when the force, $\vec{F}$, is constant over this time interval and over its displacement. But as $\delta t \to 0$, this becomes a better and more accurate approximation.)
And dividing both sides through by $\delta t$, and applying the linearity of the dot product: $$\frac{\delta W} {\delta t} = \frac{\vec{F} \cdot \delta \vec{r}} {\delta t} = \vec{F} \cdot \frac{\delta \vec{r}} {\delta t}$$
And as $\delta t \to 0$, $\frac{\delta W} {\delta t} \to P$, the instantaneous power the force delivers to the body, and $\frac{\delta \vec{r}} {\delta t} \to \vec{v}$, the body's instantaneous velocity.
$$\therefore P = \vec{F} \cdot \vec{v}$$
(B.) Generally, the work done on a body by a force, $\vec{F}$, is $$W = \int \vec{F} \cdot d\vec{r} = \int \vec{F} \cdot \frac{d\vec{r}}{dt}\, dt = \int \vec{F} \cdot \vec{v}\, dt$$
(I have had to assume the 2nd equality holds. I've seen an explanation as to why $\int f \frac{dx}{dt}\, dt = \int f \, dx$ but I haven't seen why it holds even when we have a vector $d\vec{x}$ and it is dotted with the integrand.)
The time derivative of the work the force does on the body is the power it transfers to it,
$$P = \frac{dW}{dt} = \frac{d}{dt} \left( \int \vec{F} \cdot \vec{v}\, dt \right) = \vec{F} \cdot \vec{v}$$
The last equality holds because of the fundamental theorem of calculus.
(C.) In the specific case where a body follows a straight-line path, the work done by a force, $\vec{F}$, on it, over a displacement, $\vec{s}$, is given by $$W = \vec{F} \cdot \vec{s}$$
And the time derivative of the work that the force does is the power it transfers to the body:
$$P = \frac{dW}{dt} = \frac{d}{dt} \left( \vec{F} \cdot \vec{s} \right) = \frac{d\vec{F}}{dt} \cdot \vec{s} + \vec{F} \cdot \frac{d\vec{s}}{dt} = \frac{d\vec{F}}{dt} \cdot \vec{s} + \vec{F} \cdot \vec{v}$$
In the 2nd equality we have applied the product rule for differentiating the dot product of two vectors. And notice that the time derivative of displacement from some fixed initial position is just the body's velocity, $\vec{v}$.
However, my problem is with the $\frac{d\vec{F}}{dt} \cdot \vec{s}$ term. It doesn't feel right because there is no reason why the instantaneous power a force transfers to a body could necessarily depend on it's displacement from some arbitrary chosen initial position.
I cannot explain why this term would be zero in order for it to agree with the other results: the force, $\vec{F}$ doesn't necessarily need to be constant; the displacement from the initial position obviously won't always be zero and there is no reason for the vectors $\frac{d\vec{F}}{dt}$ and $\vec{s}$ to be necessarily perpendicular!
So I think I've made an error in (C). Can anyone see where I've gone wrong?
EDIT:
THE MISTAKE HAS BEEN SPOTTED NOW! As Puk has pointed out, for (C) to be correct - for $W = \vec{F} \cdot \vec{s}$ to really give you the work done by a force, $\vec{F}$, on a body following a straight-line path while it is displaced by $\vec{s}$, you need $\vec{F}$ to be constant!
(Not because otherwise the body can't follow a straight line path - even if $\vec{F}$ varies there can be other variable forces acting on the body to ensure there is no component of net force on it in any direction - other than parallel to the path - which will ensure it won't deviate from the straight-line path!) The reason $\vec{F}$ has to be constant is because this is how work done is defined: it is the dot product of a force acting on a body that stays constant for some time and the displacement it moves over that time. Think about it - because if $\vec{F}$ didn't have to be constant then how would you know which time to evaluate $\vec{F}$, in $W = \vec{F} \cdot \vec{s}$? There would be no reason to choose any specific time (e.g. at the start or end or middle of the 'journey' - or at any other time!) to evaluate $\vec{F}$ because it isn't mentioned in the definition!
Having $\vec(F)$ as constant resolves the inconsistency because then $\frac{d\vec{F}}{dt} = 0$ and the $\frac{d\vec{F}}{dt} \cdot \vec{s}$ term disappears.
Comment: There is no error, but the time derivative of a vector is the time derivative of it's components. As such, given that we know the trajectory is linear the derivative of each component will be null and so the whole term becomes 0.
Answer: $W = \vec F\cdot\vec s$ is only true if the force $\vec F$ is constant through the whole displacement $\vec s$. If it is constant, then $d\vec F/dt$ vanishes and there is no discrepancy. If it is not constant, the formulation of work as $W = \int\vec F\cdot d\vec r$ as in (B) is the correct approach and yields the correct power.
A straight line trajectory does not mean we can dispense with the integral. It doesn't make much sense for the work done between time $t = 0$ and time $t = T$ to depend only on the force at $t=T$, and at no prior time. The integral serves to correctly "average" the force in time/distance.
Comment: This makes so much sense! Of course F has to be constant throughout the whole displacement for (C) to be true! (Or else which value of F would you choose to plug into W =F.s to find the work done over the displacement!) And that obviously leads to dF/dt = 0. Thank you!!!


Recommendable Hot Backup System for MySQL?

Question: I am looking for a hot backup system for mysql databases? I like to ask you for experiences and expertise.
Answer: So the place you want to look for good solutions to MySQL issues is Mysql Performance Blog/Percona. Specifically, what you want to do is use their XtraBackup, which fixes a number of issues that occur with InnoDBs hot backup. You'd be well served to use their patched server with their InnoDB replacement XtraDB.
They integrate a number of third party patches for MySQL, including their own and Google's, and have enhanced the InnoDB storage engine with fixes, enhancements and better logging. Additionally, Percona sponsors a fantastic toolbox for MySQL called Maatkit, which gives some components to help you with backups and integrity checks.
Answer: I know InnoDB hot backup but works just for InnoDB
http://www.innodb.com/products/hot-backup/
Comment: @Hugues - It is not free though... Back to searching... thanks.
Answer: I use the MySQL GUI Administrator Tool. It has a backup tool, which you can use to schedule daily backups through windows. You can create different backup projects, schedule the backups, and control how the backup runs and the type of output file it creates.
I've always found it reliable, and the other tools bundled with it are also useful for basic database administration.


What are the math topics involved in FRM 1

Question: Is there a way to get the math curriculum for FRM level 1 without purchasing the Exam? I wish to take a look at the math topics and see if I have any chance of cracking it. But  I could not find an online resource that lists the math topics required for FRM 1.
Answer: See below. You can find out more here at the GARP website. You may need to register, but it's free. Download the study guide. The bullets below are from it.

Discrete and continuous probability distributions
Population and sample statistics
Statistical inference and hypothesis testing
Estimating the parameters of distributions
Graphical representation of statistical relationships
Linear regression with single and multiple regressors
The Ordinary Least Squares (OLS) method
Interpreting and using regression coefficients, the t-statistic, and
other output
Hypothesis testing and confidence intervals
Heteroskedasticity and multicollinearity
Simulation methods
Estimating correlation and volatility using EWMA and GARCH models
Volatility term structures
Comment: Thanks. Matrix algebra is not explicitly mentioned...but I suppose good knowledge of matrix algebra is expected anyway?
Comment: These topics are covered in curriculum, detailed knowledge going in isn't required, but would definitely be beneficial. Having sat for, and passed part 1 (in 2013), I can say that a good grasp of basic statistics and basic algebra is a minimum requirement.


Good resource for chrooting Apache2 on Debian

Question: I need a better resource than this or this on how to secure Apache2 using chroot on a Debian system. It seems most articles deal with Apache1. I tried to follow them and adapt to Apache2, but it only had bad results.
Comment: afaik, you do not secure apache by chrooting, but rather _try_ to contain the damage to the rest of the system in case of a breach.
Answer: You can use mod_security to do this for you very easily.
The documentation is here.
Just install libapache-mod-security and add the following line to your apache.conf.
<code>SecChrootDir /chroot
</code>
Answer: Since you are running Debian, my advice would be to just use makejail, which creates old-style (external) jails with ease. I've used it many times without any trouble. I originally came up with the internal chroot idea implemented in ModSecurity (I am the author), which was subsequently implemented by mod_chroot and is now available in Apache itself. Had I known about makejail at the time, I would have never bothered with anything else. Having said that, the internal chroot facility is generally very easy to use if your requirements are not complex. It is very important to choose the correct directory structure. For example, put your jail in /chroot/opt/apache, then create a symlink /opt/apache to /chroot/opt/apache. (It's been a while since I chrooted the stock Debian Apache and I don't remember where exactly the Apache is installed at.) That would make the paths inside and outside the jail identical, which is critical.
Also, Chapter 2 of Apache Security (which I wrote) is available online from http://www.apachesecurity.net. It contains a detailed discussion about chroot and step-by-step instructions. It starts on page 40.
--
Ivan Ristić
ModSecurity Handbook & SSL Labs
Answer: This seems like an easy way, but is it really secure?


Could the mobile emitter in Voyager be used by any program created on the holodeck?

Question: In the Star Trek: Voyager episode, "Future's End, Part II", Voyager's EMH, the Doctor, was able to leave sickbay or the holodeck and roam freely with the help of a mobile emitter (the technology originating in the 29th century). Could this be used by any hologram created on the holodeck?
Comment: I hope so! Let's get that Irish bartender wandering around, occasionally making longing looks at Janeway in the cafeteria.
Comment: Oh, wait, [they did that](https://scifi.stackexchange.com/a/255400/440)
Comment: I'm thinking my very own holographic  coffee cup. I suppose you could stick a butler onto the coffee cup too.
Answer: The mobile emitter was evidently compatible with other holodeck characters, as it enabled the USS Voyager's Leonardo da Vinci hologram to walk around on a planet's surface, far from any other holoemitters, in the Voyager Season 4 episode, "Concerning Flight".

The mobile emitter also proved compatible with the USS Equinox's EMH (VOY: "Equinox"), the Michael Sullivan hologram (VOY: "Spirit Folk"), the Reginald Barclay hologram (VOY: "Inside Man"), and Iden, a hologram created by the Hirogen, using Starfleet holographic technology (VOY: "Flesh and Blood").
Comment: Not recalling those other instances but a notable distinction is the EMH program can self activate and shutdown the hologram.  The nonplayer character holograms in theory should not have the ability, knowledge, or desire to prefer an emitter or prefer to be activated.
Comment: And presumably a mere character should be a vastly smaller program vs something as sophisticated as an EMH regardless of the sentient vs non-sentient issues.
Comment: Also Marayna (a holographic character controlled by an alien) was able to briefly use the emitter in Alter Ego, to visit Tuvok in his quarters after her program was "deleted".


Is inconsistent charging bad for batteries?

Question: I am designing a generator for a bench press that generates electricity when you work out, but it would charge the battery inconsistently and I don't know if that would be bad for a battery.
Comment: To some extent the answer depends on the battery chemistry you use, and what you plan on doing with the charge in the battery. You need to share more detail.
Comment: Note that you will expend power, not generate it, if you use electricity to simulate gravity.  You can make a useful exercise machine where you have to push upwards with force equivalent to what would lift a certain weight to generate power as the bar moved upwards, but when it stops moving you will feel only the weight of the real bar, not the simulated one, so you will lose almost all of the benefit of the muscle control part of the exercise but safety will be greatly increased.  Obviously a mechanism to pull the bar down capable of pulling equivalent to many kg would be dangerous.
Answer: For most cell chemistries, deep discharge, overcharge, or very rapid (high current) charge or discharge are damaging. Simply irregular use, as long as it does not completely deplete the battery during disuse, is harmless.
If you use a charge regulator designed for the battery, there should be no harm in inconsistent charging -- in fact, some chemistries benefit from occasional charge/discharge, rather than floating at full potential.


List of Stablecoins built on Ethereum

Question: What are some stablecoin projects built on Ethereum and how do they distinct between each other?
Answer: Stablecoins - regardless of the platform on which they've been implemented - generally fall into three broad categories:

Centralised / IOU : A centralised controller holds an asset and creates IOUs that can be traded back in for the asset at a later date.
Collateralised: Coin is issued in response to collateral being pledged. Value is kept stable by various means.
Algorithmic (also called Seigniorage Shares ): Value of the coin is kept stable by algorithmically expanding or contracting the supply of coins in circulation.

For details on how each of these types work, see a general overview, such as this CoinMarketCap blog post.
Below are few examples of each type in the Ethereum ecosystem. (The list isn't exhastive - this is just what I have in my notes.)

Centralised / IOU

TrueUSD (ERC-20)
DGX Token (don't think this is ERC-20)
Gemini Dollar (ERC-20)

Collateralised

DAI
Synthetix

Algorithmic

Terra
Ampleforth
Basis

List of Stablecoins built on Ethereum


Ubuntu's default Firefox does not play videos on after Ubuntu upgrade

Question: A few days ago Ubuntu (22.04 LTS) showed me a message saying I can upgrade my OS (or something along those lines). I click on agree (any button that would let me proceed) and the upgrade took place (without restarting). Along with the upgrade Firefox was also updated to its latest version at the time (119.0). Since then, videos on Twitter play but without sound. On some other websites also none of the videos play. On YouTube, Firefox shows me a message saying "To play video, you may need to install the required video codecs" but the videos play fine; I haven't tried other websites but I assume all would have some issues. Google Chrome however doesn't have this issue and all videos play without any issues.
Note that I restarted my computer after the upgrade but this didn't resolve the issue either.
I did the followings and restarted Firefox but none have worked so far for Twitter and some other random websites that I come across, but they resolved the issue for YouTube and now YouTube videos play, although I still get that codec message at the top of the tab:
sudo apt-get install ffmpeg
sudo apt install ubuntu-restricted-extras
sudo apt install libavcodec-extra

Until today I didn't know you can install things on Ubuntu 22 as a snap package and that by default, Firefox is a "snap" package on Ubuntu 22. So I also did the following and installed ffmpeg as a snap package but still have the same issue after restarting Firefox.
sudo snap install ffmpeg

Could you help me figure out what I should do to fix this issue?
Answer: Since you already have ffmpeg installed, install the libavcodec package.


How can I tie my laces so they don't come undone?

Question: This might seem like a silly question but this is a constant issue for me when hiking or even in general. I have "double" looped my laces but I actually really hate it because it's a pain to untie. Is there a way I can tie my laces so they don't come undone AND so they can be undone by pulling the two laces like normal?
Comment: Ian's Shoelace Site: Surgeon's knot http://www.fieggen.com/shoelace/surgeonknot.htm
Comment: Have you tried the [heel lock](https://www.google.com.mx/search?q=heel+lock)? It's not as easy to untie as your _normal_ knot but it stays tight even if the _top knot_ comes loose.
Comment: @BenCrowell Hmm, i believe the knot I am currently using is the slipped square knot.
Comment: Are you currently tying a slipped square knot (which is usually pretty secure), or a slipped granny (which isn't)?
Answer: First of all if you are really interested in tying your shoes, check out Ian's Shoelace Site. All credit for the imagery used here and most of the information given goes to the author Ian Fieggen.
For me the requirements to my shoelace knot are the same as yours (and probably most of everyone's): Secure but still quick to tie and untie.
The Double Shoelace Knot you mentioned is very common but in my opinion completely useless. It is not more secure than a simple knot. It is just a simple knot done twice, so it has the get undone twice. Plus it is cumbersome to open.
The one knot I use is a slight variation from the Better Bow Shoelace Knot. Until the following step you do it the same way:

Instead of going through the first yellow loop as originally shown in the picture below you bypass the yellow loop and go directly through the middle (shown in red, added by myself). So this variation is essentially a standard knot with an extra loop.

This is much less fiddly than the original version and is still secure enough (at least I never noticed one getting loose). Untying is very simple, just poll on a loose end.
Comment: I used the content from Ian's Shoelace Site according to his statement "Generally, I'm pretty agreeable to others passing on this knowledge by using portions of the content of this website provided that you simply credit Ian's Shoelace Site as the source or myself (Ian Fieggen) as the author." in the section "Website Content" of http://www.fieggen.com/shoelace/info.htm.
Comment: [Ian Fleming](https://en.wikipedia.org/wiki/Ian_Fleming)?! :O
Comment: @Liam The mind of humans is a curious thing - they share in common just the first letter of their surname... Thanks for the hint!
Answer: Instead of a knot, how about a shoelace buckle?
Simply pull the laces through with the button pushed in, and then release and let it hold them. To take the shoes off, push the button and pull the laces through to create enough slack to remove.
Comment: This would be great for hiking but I don't think it would go well with my business casual clothes during the week. It would definitely work but probably not very "stylish". This is mainly why I'm interested in a knot.


What makes a question 'community wiki'?

Question: The following question was asked by 'Community Wiki'. What does it take to mark question as community wiki'?
Tab Panel Error
Answer: Anybody with the right privileges (including the asker/answerer) can mark a question as community wiki.
The idea being that it is a question/answer that would particularly benefit from being kept up to date by everybody then marking it as a wiki entry makes it easier for others to edit, i.e. they don't require the usual level of reputation needed for an edit. It also means that no points are awarded as it's supposed to be a community effort rather than one person leaching points from everybody.
As for this particular question, I think it was automatically marked as a community wiki by the system because of the number of edits made to it. I've now removed that status as this question does not really fit the criteria for being a wiki page.
Comment: You are correct about why the system made it wiki (and correct to remove it). But the Community Wiki function has been largely deprecated and **users can no longer make their questions wiki.** See **[The Future of Community Wiki](http://blog.stackoverflow.com/2011/08/the-future-of-community-wiki/)**. The 'suggested edit' feature has largely replaced Community Wiki as a way of broadening participation.
Comment: @robert any way to disable to automatic conversion to wiki if it's use is discouraged?

What makes a question 'community wiki'?


Multiple boards blinking at same time

Question: I want to make two or more boards to blink an LED at the same time (within 1 ms difference) The boards cannot be connected with wires to each other and will be located in different rooms. How can I do this? What components do I need?
Comment: <1ms difference in 60 seconds, means around 17ppm. The crystals on the arduinos have a much higher deviation. So syncing every minute would not be enough, or you have to take the time-difference between 2 syncs and adjust your delays accordingly. Alternatively you could use the internal 8mhz oscillator on the atmega, instead of the crystal. The internal oscillator can be adjusted relatively easy. That way all the boards run at around the same frequency, and every minute any accumulated deviation is reset.
Comment: Could you tell us WHY you want them to blink simultaneously in different locations? If we know we can help you better.
Comment: What is the cycle time? Is it okay if they sync every second or so? Or do they have the have the same value returned for `millis()`? In the first situation you can just send a "pulse" every second. In the latter you'd need to send some actual data, which makes it slightly more complicated. Definitely go with RF. There are some very cheap 433Mhz transmitters and receivers on the market. One arduino will be the master and send. The other boards will have a receiver.
Comment: @Gerben I want the LEDs to blink in a fixed time interval (say every minute interval). If the time difference between multiple boards blinking remains within 1ms, then the sync cycle can be every minute or more.
Comment: @Tom It is for synchronization of multiple devices
Comment: Can both arduinos be connected to mains power?
Comment: @bigjosh They are in different rooms, powered by battery. Cannot to be wired together.
Answer: Have both sync to a master clock using GSM shields. These shields are getting very cheap (as low as $14 on ebay).
The shields receive the time wirelessly from the cellular network and this time base is extremely accurate. Here is some example code to read the current time from the shield...
http://forum.arduino.cc/index.php?topic=163155.msg2102141#msg2102141
Note that you will need a SIM card to get the time, but you should not need an active cellular account.
Answer: You can also use real time clock (RTC) modules to syncronize arduinos. These are cheaper than other solutions like GPS or WiFi.
Answer: You could certainly do it with multiple Arduinos, each with a WiFi shield, but that would cost a lot of money.
Instead I would suggest building a low power radio transmitter that sends simple morse code clicks, and then building amplifier boards that use the clicks to trigger LED blinks. You'd need to use a frequency that is open for low power use in your country, like the range for garage door openers.
I've seen circuits in old electronics kits for building morse code transmitters, but they might not meet current FCC regulations.
Comment: Ultimately, some of the simple SPI-interfaced 2.4 GHz RF chips/modules probably could provide a solution - nrf24L01 type stuff - which is cheaper, easier, and less likely to false trigger in the presence of interference than a DIY RF link.  Either a software PLL, or a series of "count down" messages could be used to bridge missed messages.
Comment: 1ms synchronization with WIFI is by no means "certain".  It may be possible, but having tried to do that, it's actually rather tricky - especially if there is a router in between, packet latency can vary widely.  Nor is a simple on-off-keying demodulator likely to yield nice results, as it will be very subject to interference.  However it could possible be used as input to a software phase locked loop - a local timer which would over time speed up or slow down if it found that the radio pulses it did detect tended on average to be a little earlier or later than expected.
Comment: @ChrisStratton, those are cool, and cheap too! (voted). Point taken about the home brew radio transceiver. You'd need to make an FM transmitter and receiver using PLLs, and that would take quite a few components. Why not post you suggestion as an answer? Seems like the best solution.
Comment: Although I was suggesting building one Arduino-based transmitter and a bunch of analog radio receiver based LED flashers. The nrf24L01 solution would require an Arduino per flasher, so the total cost per receiver would be fairly high. Could you rig those up with an ARTiny?
Comment: With efficient programming, yes, it should be able to be done with an ATtiny85.  And even an ATmega328p isn't that expensive, nor does it require more support components.  Much of what you pay for in an "Arduino" is the USB interface, PCB, power circuitry, connectors, etc.

Multiple boards blinking at same time


Mac mini running Catalina has no sound input

Question: I have my Blue Snowball plugged directly into a USB on the back of my Mac Mini. The light indicating power to my mic is showing. I didn't find any input devices in preferences, even the built-in mic. I did an NVRAM reset and nothing happened. I tried going into safe mode and creating another administrator account to find a sound input device, that didn't work.
Comment: Where are you looking for sound input?
Answer: Apple Menu > System Preferences > Sound is the place to look for Input Sources:
I've selected the Internal Microphone in the screenshot below for legibility. To use the Snowball mic (an amazing mic, BTW,) just select it. You can adjust the input volume, too.


What is a stress fracture and how can you avoid it when training for a marathon?

Question: When I trained for my first marathon, I began feeling pain in my lower legs. My doctor said that this could be due to stress fractures in my bone from overworking my body. So my questions are, what is a stress fracture and how can you avoid one while training? Does a stress fracture mean you should stop running altogether until it goes away?
Comment: stress fracture http://orthoinfo.aaos.org/topic.cfm?topic=a00112
Comment: I think you should better discuss with the doctor who diagnosed you. We don't know the details, and when it comes to pain and injury, doctors are the best person to help. They can answer if you can train further or stop.
Answer: While this could indeed be due to a stress fracture, there are actually a number of things that could be causing you pain. First, a stress fracture is a small crack in the bone typically due to overuse. It cannot be 100% diagnosed without some imagery (bone scan, xray etc), but if you have a tuning fork, you can try placing it near the site of pain. While not the best test, if the vibrations reproduce the pain you may very well have a stress fracture and you would have a good case for your doctor to refer you for xray. If you do in fact have a stress fracture, you would have to stop running and wait for it to heal. A couple of other issues that could cause pain, but are not a stress fracture could be shin splints (very common) or compartment syndrome (not as common). Shin splints happen when the muscle attaching to you anterior tibialis (shin bone) are overworked and become tight. The muscles pull on the shin and cause pain. Consistently stretching and strengthening your calf muscles is the best way to deal with this issue. Compartment syndrome is when blood flow becomes so great in the calf muscles that pain results. Both compartment syndrome and shin splints can be treated conservatively with stretching, strengthening, rest and possibly anti-inflammatories (ibuprofen). You could also try massage or other manual therapy. In both cases you can continue to run if you can deal with the pain, but realize it may delay healing. Slowly building up your mileage is the key to avoiding these issues. Also, make sure you give yourself time in between runs to fully recover from the previous run. A general rule of thumb is to not increase your weekly mileage from week to week by more than 10%. I hope this helps. Good luck.


topdown bottomup approach in complex systems

Question: In continuation to question Topdown bottom up reductionism emergentism my second question is ; in complex system, like the economy, which are highly complex systems where it is often impossible to explain macro
phenomena by a simple summation of micro processes or events. It's hard to predict the results of actions in the system and sometimes impossible to find the causes of large abnormalities, or even to single out factors that influenced an event. So does top-down bottom-up approach does not work in complex systems ?
Comment: The title of this question is very strange to me. Normally "top down" and "bottom up" are contrasted as two different approaches to understanding something. This question is the first time I've ever seen it phrased as if "top down bottom up" is one single approach.
Comment: Edison tried 1600 options before lucking into carbonized bamboo as a filament material  Bottoms up.  In contrast, Nuclear bomb #1 (trinity), worked impressively well, first try.  Top-down,  The top-down approach to light-bulb filaments wasn't panning out.  Edison took a circuitous "shortcut".
Comment: It is never possible to explain macro phenomena by a "simple summation" of micro processes or events, one has to account for their interactions. And it is hard to deduce non-trivial mathematical theorems generally, it does not mean that deductive approach does not work. Causes of large abnormalities and factors that influence an event may be too numerous to survey, without one or few dominant ones, but that is not the approach's fault. It is convenient for us when there is a single major cause we can focus on, but the world does not always oblige.
Answer: The topic of Complexity targets not a precise domain (here you have an example of past answer of mine). Complexity refers mostly to a set of tools that serve to address systemic complexity (yes, it is circular). Consider here that complex means difficult to understand. If you try to address Complexity as a formal system, you will get lost in its contradictions.
The Complex Systems discipline is an attempt to differentiate "complex" systems from all the rest, that is, "simple" systems. However, the General Systems Theory born in fact to address the problem of complexity: to divide a complex problem in simple parts, so that solutions to parts can be found (a.k.a. Systemic Thinking in pop/mainstream jargon). If you don't understand a complex system, you can understand the simple components and even if you can't comprehend the totality (it is normal, we are limited beings), you can anyway manage it. The hardest part of the Systemic approach is the division of complex parts into simple parts: it requires a lot of experience and knowledge, it is not just turning the Systemic Thinking belly button switch on.
The top-down or bottom up approaches apply indistinctly to simple or complex systems (whatever that means). In both cases, the whole is divided in parts and it is not the whole who is addressed, but moreover the parts. But the core of the problem lies here: the parts MUST be simple.
Comment: complex adaptive system has to have diverse connectedness interdependent adaptation
Answer: If you want to solve a set of differential equations do you need to understand the equations describing the local interactions or do you just need the boundary conditions (representing the global, outside conditions)? Obviously you need both. So it is rarely a "either/or" but often both: The rules that govern a system at the bottom and the outside constraints on the top, even in these extremely simple cases.
And then for more complex systems in order to understand them or have a chance to simulate them you need multiple levels in between. E.g. think of the task of understanding a complex biological system just from the basic equations of physics.
As for the economy you will have lots of things that are outside of what a narrow view on economics can predict. Global politics, new technical and scientific discoveries that significantly change some fundamental rules of the game...


What hotshoe flashes are compatible with my Canon EF film camera?

Question: I'm looking for a hot shoe flash for my old Canon EF analog film camera from the 70s.
Any ideas? Is there anything I should specifically look at to make sure it's compatible?
1973 Canon EF film camera
Comment: @Michael C I am pretty sure the OP meant analog EF film camera so I edited the original post to show that.
Comment: There were no EF systems in the 1970s. Canon introduced the EOS system and the EF lens mount in 1987. In the 1970s most Canon SLRs used the FD mount.
Comment: Ok, the EF model, rather than the EF system. I'd forgotten about that one. I was lusting for the A-series at the time.
Answer: The Canon EF film camera did have a dedicated flash called the Speedlite 133D but it was very low powered and difficult to use. It was called "The CAT System" (Canon Auto Tuning) and needed a ring installed on the front of the lens in order to transmit focus distance information to the flash.

Instead, I would recommend any film era Thyristor flash from the late 1970s and early 1980s. Get one with a bounce head for more natural looking light.
Two Canon examples would be the Canon 199A and the 299T. They would both work very nicely with your Canon EF film camera.

A more modern option would be the Canon 580EX II or 600EX RT. These modern Speedlites are fully compatible with modern digital ETTL flash, but both also have an option to use "External Auto" mode that uses the old Thyristor system of the film era.
With any of these Thyristor flashes, you just set the camera aperture and ISO to match what is set on the flash, and the flash uses the external light meter at the front of the flash to automatically adjust the light output for proper exposure.
Answer: Any single pin flash will work.  Do not use a modern unit.   It is a waste of $.  If you want period relevant equipment, Vivitar made excellent basic strobes back in the day.  I've also had good luck with Starblitz/Hanimex strobes.  Units with tilt/swivel heads and twin strobes are the most useful, in my opinion.


Removing old 531 frame bottom bracket. Where to source a pin spanner etc

Question: I've been riding a vintage 531 frame bike which I've stripped and rebuilt. However, I'm having problems with extracting the bottom bracket. This has some play in it, so I really need to remove, regrease and replace the bearings. I've managed to free up the lock ring with the help of a chisel and lump hammer (to give you an idea of how frozen it was) but I cannot now remove the bearing cup as I need the correct pin wrench tool. Has anyone any idea where I might buy a tool for such an old bike in the UK? There are 4 pin holes approximately 2cm (13/16ths)apart. The pin holes are approximately 2mm in diameter. The ones I've found that are readily visible on amazon etc are adjustable, but are for larger pin holes.
Answer: Non-cycling-specific pin spanners do indeed tend to have fatter pins, but in the cycling section you should find something.
Park Tools SPA-2, for example, has pins just over 2mm diameter (so you should check), and the spacing is adjustable over a small range about what you need because its a little springy. I bought mine for working on a 90s Raleigh; they're not needed so often on modern bikes.
Hopefully you'll need less force than to remove the lock ring, as it's not a massive tool.
Alternatively it's possible to measure the spacing of an opposite pair of pin holes and make something from scrap metal using M2 screws as pins. That's only worth it if you've got all the tools and materials to hand
Comment: @Criggie good point. That Park one, if you tried hammering it, would probably get its own back by springing into your face at the first hit, but the pins will snap easily
Comment: Might be worth mentioning that if they're going to repack the BB anyway, there's no harm in putting penetrating oil on the threads to maybe make it a bit easier to move the cup with a pin spanner
Comment: Additionally - pin spanners will not survive hammering, so just don't.
Answer: In the end I resorted to the "brute force and ignorance" solution. Drastic I know, but the bike was unusable as it was, so I really had nothing to lose! I used a lump hammer and a small cold chisel to shift the locking ring by inserting the tip of the chisel in one of the lock ring grooves. I then used the lump hammer and a 1/16" punch to loosen the cup by holding the punch tip in one of the four pin holes. This took some effort, so I expect a pin spanner would not have been up to the task! Fortunately the bearings were in racers so I didn't need to hunt around for errant bearings. I tried to loosen the drive side cup but this seemed beyond any reasonable force! Anyhow, I managed to clean it all using a rag liberally soaked in wd40. Bearings regreased and replaced. From the effort this took I'm expecting that the part of the internal thread might have been a little stripped! However,the play in the bracket has now been rectified and all feels much smoother!


How do I create and use a custom hook?

Question: I posted a question here, which had one suggestion, but no answer. Does anyone have any advise on how to implement a custom hook in Drupal 8 which will allow other modules to update a table of contents which is created by a parent module? The table of contents will be an unordered list.
Comment: Have a look at the section under "To define a hook:" [here](https://api.drupal.org/api/drupal/core%21core.api.php/group/hooks/8.2.x), does that help?
Comment: @KevinNowaczyk it depends on the purpose of the hook. A hook is not specific for rendering, but can be used for it. If you want to create a custom hook to provide content and you invoke the hook at the place you need the content, it will work. And because the hook is custom and new to your function, you have to define how the hook should provide its results. Then if you invoke the hook during your parent render function you can receive the results in a usable format.
Comment: Only partially. This explains how to create a hook for the child function to use, but nothing on how the parent module renders the content. Does the parent use a controller to add content to, say, $output['table_of_contents'] and then the parent's hook appends the data that is returned from the child, to this array?
Answer: Just for simplicity sake if you want to create and use a custom hook in drupal 8
for other developers to use
first to help others define the use of your hook in mymodule.api.php file
this hook can act on anything required.
example:
 // my hook
 function hook_mymodule_alter_something(array &$data) {
   // here others will make a module that will call this to alter "$data"
 }

then when needed in your module.
 \Drupal::moduleHandler()->invokeAll('mymodule_alter_something', [&$data]);

then the other developer can then make use of this by calling
function MYOTHERMODULE_mymodule_alter_something($data) {

Answer: This section resides in a controller in the parent module:
$plugin_items = [];
// Call modules that implement the hook, and let them add items.
\Drupal::moduleHandler()->alter('flot_examples_toc', $plugin_items);
if (count($plugin_items > 0)) {
  $output['plugins'] = [
    '#title' => 'Plugins',
    '#theme' => 'item_list',
    '#items' => $plugin_items,
  ];
}

And this resides in the child [module].module file.
use Drupal\Core\Url;

function mymodule_flot_examples_toc_alter(&$item_list) {
  $options = [
    ':one' => Url::fromRoute('flot_spider_examples.example')->toString(),
  ];
  $item_list[] = t('Spider Chart (with spider plugin)', $options);
}

The parent creates an array and passes it to the children by reference. They can alter the array by adding elements to it. The parent then adds it to the render array.
Answer: You need to implement two hooks 1. hook_token_info() & 2. hook_tokens() in your module file
Below i have given code to create my custom token "query-param-all" and used that token in views- Textarea field.....
/**
* Implements hook_token_info().
*/
function mycustom_token_info() {
  $type = [
      'name' => ('Custom Token'),
      'description' => ('Tokens for custom things.'),
  ];
  $node['query-param-all'] = [
      'name' => ("Get all URL query string"),
      'description' => ('Get all URL query string'),
  ];
  return [
      'types' => ['customtoken' => $type],
      'tokens' => ['customtoken' => $node],
  ];
}

/**
* Implements hook_tokens().
*/
function mycustom_tokens($type, $tokens, array $data, array $options, \Drupal\Core\Render\BubbleableMetadata $bubbleable_metadata) {
  $replacements = [];
  //print '
'; print_r($data);exit;
  $current_path = \Drupal::request()->query->all();
  $query_param = '';
  if( count($current_path) > 0) {
    $amper = '';
    $query_param = '?';
    foreach($current_path as $key => $value){
      $query_param .= $amper.$key.'='.$value;
      $amper = '&';
    }
  }

  if ($type == 'customtoken') {
      foreach ($tokens as $name => $original) {
          switch ($name) {
              case 'query-param-all':
                  $replacements[$original] = $query_param;
              break;
          }
      }
  }
  return $replacements;
}

Comment: As it's currently written, your answer is unclear. Please [edit] to add additional details that will help others understand how this addresses the question asked. You can find more information on how to write good answers [in the help center](/help/how-to-answer).

How do I create and use a custom hook?


What does the "machine" in "support vector machine" and "restricted Boltzmann machine" mean?

Question: Why are they called "machines"? Is there an origin to the word "machine" used in this context? (Like the name "linear programming" can be confusing but we know why it is called "programming.")
Comment: I once was told that "machine" means "algorithm", but I didn't ask about the origin.
Comment: @dontloo Could be, as in "Turing machine." Hopefully someone can provide information on the historical contexts.
Answer: I think this article sums it up.
Basically, machine comes from machine learning, a term that was coined in 1959 by Arthur Samuel, way before the final developments that led to the soft marging kernel SVM in the 90's and the Boltzmann Machines in the 80's. Vapnik and Lerner called their algorithm the Generalized Portrait algorithm back in 1963, see more here.
A machine in this context would be the output function, or as the article puts for historical reasons, the hypothesis, built from the learned parameters.
Answer: Possibly because some of the earliest machine learning algorithms were implemented as actual physical machines. From Wikipedia:

The perceptron was intended to be a machine, rather than a program,
  and while its first implementation was in software for the IBM 704, it
  was subsequently implemented in custom-built hardware as the "Mark 1
  perceptron".

(Picture from Cornell Library via Wikipedia)

ADALINE (Adaptive Lineardi Neuron or later Adaptive Linear Element) is
  an early single-layer artificial neural network and the name of the
  physical device that implemented this network.

A source for more information about these machines is the book Talking Nets.
Comment: While the hypothesis raised in this answer is sound, it could benefit from sources. Indeed, as my answer points out, Arthur Samuel coined the term, and he worked at IBM at the time, and his paper was published at an IBM journal.
Answer: Meriam-Webster defines the word as "a literary device or contrivance introduced for dramatic effect." It certainly does the job of increasing the dramatic effect. "Support vector algorithm/approach/equation/function/..." just doesn't sound as good as "support vector MACHINE!"
I would also suggest "kernel density machine" and "maximum likelihood machine." Actually, I'm going to call all my algorithms "machines" from now on.


How does Google Maps Navigation know you are in a tunnel when it switches to night mode?

Question: I suppose this isn't exactly a new feature but it is new to me since I don't travel through tunnels very often.  What exactly is the software using when it decides to switch over to night mode when in a tunnel?  GPS Location? A light sensor? A combination of both?
Comment: simply from rich google map data.
Comment: I don't think the map data on its own explains it--I travel all the time on the roads directly above without it switching.  But yes, you couldn't do it with poor map data...just ask Apple!
Comment: So, I think it uses also altitude value from GPS to determine whether you are in the tunnel or the road above it! As in its new feature, In-door navigation through some buildings, It uses altitude to determine in which floor you are (I'm not sure!).
Comment: The last time I used the in-building navigation, you had to manually select the floor.  I don't think it is using altitude, either that or I never have a lock on enough sats to derive an altitude value.  I park below I-95 and I'm always being routed directly from I-95 instead of the city streets that are underneath it (where I start).  I guess thats why I initially assumed altitude wasn't used.
Answer: Hard to say without knowing which device and firmware version we're talking about, so what follows is my speculation.
I have a Garmin Nuvi which continues navigating in a tunnel, turns and all, despite losing its satellite reception.  Mine doesn't switch to night mode, but it clearly knows it is in a tunnel from the map data. Since loss of reception is a given in a tunnel, the device must be dead-reckoning while it's in there. (Re-broadcasting is out because it would affect the signal timing which is key to calculating a fix).  In fact, I have tested this by entering a tunnel fast and decelerating once inside it.  The device alerted that it had lost reception and continued to display my entry speed, "passing" turnouts and the tunnel exit before I did.
From that, I inferred that the firmware was using map information, possibly cross-checked with loss of satellite lock, to know when I've entered a tunnel.
Comment: Hadn't thought about the satellite lock.  So would it switch to night mode even if the tunnel was lit (I don't have a lighted nearby)?  I guess I could put a flashlight on it.
Answer: Recently I was driving in Italy and I realized that this Google Maps feature works more precise in Italy than in my home country Germany.
I tested it a little bit in Italy and I found the following:

it does not matter if the tunnel is lighted or not, it always goes into night mode
drive into a tunnel and keep the speed constant through the whole tunnel and it will work perfectly
accelerate in the tunnel, then it will turn off the night mode too late
reduce the speed in the tunnel, then it will turn off the night mode too early
stop in the tunnel for several minutes, then it will turn off night mode after a while and won't turn it on again

From these observations I conclude that in Italy it relies entirely on map data and approximates when you leave the tunnel only by the speed you drove before the tunnel.
Answer: Perhaps it uses the ambient light sensor in your phone and changes to night mode when there is less ambient light.
Comment: AFAIK, Google Maps doesn't use light sensors for tunnels and night mode. Sometimes I put my phone inside a bag or car compartment and it doesn't turn to night mode despite the darkness.
Answer: Easy solution to force night mode that I found.

go to settings
go to date and time
disable automatic date and time.
set your time to 7pm or later.

That should set the app to night mode you can change the time back when you're done traveling
(Galaxy S7. Version 7.0)
Comment: This doesn't answer how Google Maps detects when the user is inside a tunnel though.


Dark Souls 2 Compatibility Question

Question: I own a copy of the original release of Dark Souls 2 on Steam, but my friend was wondering of getting the Scholar of the First Sin edition on Steam. If I want to be able to summon him in my game, would it be possible considering we have different versions?
Comment: @UniKitty Maybe the decision of getting the game depends on the answer. If his friend does not want the game unless they play together, it is a perfectly viable question, and not really testable by himself.
Comment: Why not do the testing instead of asking?
Answer: It depends
If your friend is buying the DX 11 version, you will not be able to summon him, because the DX 11 Version has a different server.
If he is upgrading from Dark Souls 2 (DX 9) to Scholars of the first sin (DX 9) you will be able to summon him because you are on the same server.
Here's a picture that has a full comparison of the different versions:
Answer: "Dark Souls 2" and "Dark Souls 2: Scholar of the First Sin" edition are not compatible with each other, the DX11 version has some items and enemies that the DX9 version does not. As such, co-op does not work between the two versions.
If you're still in doubt about the versions, here are links to the two different versions on the steam store. Dark Souls II and Dark Souls II SotFS. There is a 40% discount for people that own the DX9 version.

Dark Souls 2 Compatibility Question


How does a pinch of salt make a difference to a recipe?

Question: Many recipes ask for a pinch of salt. How can such a small amount of salt make any difference to the taste of the recipe?
Answer: The simple answer is: people can taste (and smell, when the substance in question has a smell) substances in very low concentrations. A pinch of salt is not a small amount at all, it is a sufficient amount to be tasted.
Comment: I added 100mg salt to 100, 200 and 300ml of water and compared the taste to fresh water. I could easily detect the salty taste in both the 100 and 200ml samples. I _fancy_ I could taste it in the 300ml sample, but it would require a blind tasting to be sure. Anyhow, 100mg is the smallest amount I'm willing to call a "pinch". The largest two-finger pinch I could muster was 900mg which is enough to alter the taste of 1.8l water. A three-finger pinch (people do that right?) measured at 1.8g would be noticeable in 3.6l water.
Comment: @ChrisSteinbach Yeah, I don't think it's usually meant to be a tiny two-finger pinch. And plenty of people just have a salt shaker so they never pinch, they just shake what seems like the right amount in.


Error in Rails Best Practices

Question: I have installed RailsBestPractices by gem install rails_best_practices and then I went to a Rails project home directory, when I want to execute it I get this:
$ rails_best_practices -g
Invalid gemspec in [/usr/lib/ruby/gems/1.8/specifications/rails_best_practices-1.4.0.gemspec]: invalid date format in specification: "2011-11-20 00:00:00.000000000Z"
/usr/lib/ruby/site_ruby/1.8/rubygems.rb:926:in `report_activate_error': Could not find RubyGem rails_best_practices (>= 0) (Gem::LoadError)
    from /usr/lib/ruby/site_ruby/1.8/rubygems.rb:244:in `activate_dep'
    from /usr/lib/ruby/site_ruby/1.8/rubygems.rb:236:in `activate'
    from /usr/lib/ruby/site_ruby/1.8/rubygems.rb:1307:in `gem'
    from /usr/bin/rails_best_practices:18

What is wrong? and How can I fix it?
This issue was alse reported in developer's code repository.
Thank you very much.
Answer: In the root of the project:
$ rails_best_practices .

Error in Rails Best Practices


How do I charge an AGM battery?

Question: Not a one that's completely dead, but say an AGM battery that's at 75% and I want to top it off before trying to use it again.  Can I use a regular lead acid battery charger?  Do I have to worry about if the charger has a desulfation circuit (which they ALL seem to now, I couldn't find one without, I know they're death to Li-Po batteries)?
Answer: You don't need to worry about the desulfation circuit, although there are mixed reviews about how effective they are.
However, AGMs are more sensitive to overcharging than a standard SLA (sealed lead-acid) batteries.  Actually, it's not the main charging cycle that is harmful, but the float-charge cycle that is used to top them off.  If you are getting a new charger, make sure it has a setting for AGM batteries.
More detailed information can be found here.
Good luck!
Answer: AGMs only charge to 12.8 volts. Most lead acid battery chargers go to 13.5 Volts. This will damage an AGM battery. You need a charge controller that allows you to control the maximum level.
Comment: That doesn't make a lot of sense as that means you couldn't use an AGM in any standard car as they charge at 14 volts...
Comment: According to Australian 4WD Action magazine the answer is to use a DC to DC convertor that matches voltage to the battery type. It has the advantage that you can add solar panels later as well.

How do I charge an AGM battery?


How did the scientists know two black holes collided 1.3 billion years ago?

Question: I saw a TEDx talk the previous day about the LIGO experiment and in that video he said they are waiting for the day Jan 1st 2017 for the Ripple in Gravity caused by two black holes colliding each other to reach us. But how could they make such an estimation? How the scientist knew about some incident happened 1.3 billion years ago?
Comment: Please give the exact tine in the video where this erroneous claim is made.
Comment: The waveform detected by LIGO depends on the masses of the black holes, which determines the total energy release in form of gravitational waves. When they compare that with the strength of the signal that was received they can estimate how far the event had to be away... assuming that the theory is correct. The claim about future signals is completely nonsensical, though.
Comment: @RobJeffries around 14:20
Answer: Right so what you have misunderstood is that this was a statistical prediction about when the first detection might be made, based on assumptions about the number of possible sources in the universe and their distance from us.
It is mildly surprising that (advanced) LIGO found such a big signal so soon after it began operations.
Detecting a few more will start to tell us a lot about how many large black holes there are in the universe as a function of cosmic time. Because the signal strength scales as 1/distance and binary mass to the power of 5, whilst the number of massive stars scales as $M^{-2.3}$ I think one expects most detections to be from distant very massive objects if their density is uniform in time.
The latter can be inferred because the signal strength and frequency from binary mergers tells you how far away they are, and GWs travel at the speed of light.
Comment: LIGO was commissioned in 2002, so the "first light" was quite some time ago. They had something like four runs in the original configuration, then runs as "enhanced LIGO" and this, I believe, is the second major upgrade "Advanced LIGO". Since the new design is going to be ten times more sensitive than the original LIGO, the detection volume has increased 1000 fold. One can wonder, though, if this was a "pure luck" mega-event that could have been detected by the original design or if the non-detection in previous runs indicates a problem with the earlier experiment.
Comment: I *think* the prediction refers to advanced LIGO. If I've got it right the signal was at 35-250 Hz with a peak strain of $10^{-21}$ and a "characteristic strain" of about half that. I can't find a zoomed-in plot to make sure but it looks like LIGO would certainly not have detected this.
Comment: I don't think so, either, but the less sensitive detector may have detected smaller events that were closer. I don't know what power law the  distribution follows (or if there is even such a distribution, since the black hole masses are limited from below), so maybe there aren't more smaller events closer to us... in which case the non-detection would have been consistent with this event.
Comment: @CuriousOne If the mass function is say $N(m) \propto m^{-2.5}$ and assuming a uniform density and production rate in time and ignoring cosmological complications, then I think the number of detectable events as a function of distance $r$ and mass $m$ should scale as $m^{+2.5} r$, so you expect fewer detectable events at small distances and far fewer from lower mass objects even though they are more common (we know that much less massive black holes and neutron stars exist).
Comment: I know all about the spectrum problem (from neutrinos and cosmic rays), what I don't know is what the predicted spectrum looks like. Is the exponent -2.5? Is there even a spectrum? There are, for sure, no 0.5 solar mass black holes if we trust general relativity.
Comment: @CuriousOne The lowest mass black holes/candidates are $\sim 5M_{\odot}$ - all are in binary systems! The frequency with which high mass stars are born goes as $\sim M^{-2.5}$. I simply extrapolated from this (assuming a linear relationship between stellar mass and BH mass!) to get my detectable signal dependence on mass and distance. A second order effect is that the chirps have a mass-dependent frequency.
Comment: Yes, that is exactly what I was looking for and that pretty much clears up the "why now" for me. Having said that, it's still a beautiful signal!
Comment: @CuriousOne It's in the nature of these things that they must (should!) have many more signals at 4-5 sigma significance that they have not yet presented.
Comment: Let us [continue this discussion in chat](http://chat.stackexchange.com/rooms/35683/discussion-between-curiousone-and-rob-jeffries).