How does Bernoulli's principle produce wing lift? In the Ray Kurzweil's book How to create a mind is said that:      The mathematics of how Bernoulli's principle produces wing lift is still not yet fully settled among scientist [...]    What does this statement mean? I have always known that the Bernoulli equations were well known. There is something that I am missing?
How much effect does the Bernoulli effect have on lift? I understand that the Bernoulli effect is a flawed explanation for the cause of lift, and does not cause much at all, but how much?   Is there any experimental data on the force caused by the Bernoulli effect? Maybe implicitly through data of the pressure difference between the top and underside of an aeroplane's wings. After that, I assume I could (crudely approximating the pressure to be acting perpendicularly to the flight direction) use $\Delta P A$ to work out the net force on the plane.    Perhaps there is another way to quantitatively analyse the extent to which the Bernoulli effect causes lift.  Edit: see  short cartoon (content similar to Mike Dunlavey's answer).
How to reconcile the cashless human/Federation society with human traders and merchants From a variety of sources, including , we know that the Federation (or at least the humans) don't use money. This raises the problem that humans frequently visit worlds where there is currency, and, in the case of DS9, operate a station that has currency frequently in use (for example, Federation personnel frequently attend Quark's bar). Additionally, we see human traders.   My question is, how do humans get "money" (credits, latinum, etc.)? How would a human even get the resources to purchase their own merchant ship or the resources to fill its cargo holds with merchandise? If Federation personnel can simply be given money for the asking, why haven't they poured so much money down Quark's throat that he chokes on it? Connected to wifi successfully, but no internet connection I'm a relatively new macOS user. Let me try to describe the problem I'm facing as succinctly as possible  Just this morning, when I'm unable to get any internet connection even though WiFi is connected (full strength). All my other devices has no issues when connected to the same network (it's my home network)  I've logged into the router, and checked, there are no blacklisted IP/MAC addresses.  Additional information   I'm using a tMBP 15" for over a year I've had no issues with any WiFi connectivity to my home network before today. ping from terminal doesn't work as well. I'm able to connect to my phone's hotspot, and get internet from my MBP.  I have bootcamp set up. When I boot into Windows, I'm able to get internet access through my home WiFi   How can I troubleshoot this to get to the root cause of the problem? How to escape quotes in shell? Can binary data be ordinal? Binary data is often mentioned as a nominal sub-category, especially in such examples as female/male, smoker/non-smoker, etc. However, binary data with such values as pass/fail, correct/incorrect, absent/present, etc, seems to give some weight to its values. It's not like in the example of the gender, where both values are equal and differ primarily by the nominal and other context-related traits. Instead, this type of binary data clearly indicates that one value means something and the other means nothing.   In case of such distinction, can binary be considered ordinal? If yes, what are statistical tests that are usually used for such data? Also, are there any interesting books or papers on this case? Infiniteness of non-twin primes. Well, we all know the twin prime conjecture. There are infinitely many primes $p$, such that $p+2$ is also prime. Well, I actually got asked in a discrete mathematics course, to prove that there are infinitely many primes $p$ such that $p + 2$ is NOT prime. How to model the curly cable part of the phone Hello. I am a beginner in Blender. I started modeling this phone and when I got to the curly cable part it was a real challenge. Could someone guide me on this. How do I get the distance meter value between two geometries in PostGIS? I have a simple question about calculating distances in PostGIS.  I would like to get the distance between two geometries. I am using this sid : 4269 in meters what i am doing now is this : ST_Distance((a.geom,b.geom)) FROM ... but I am getting result in degrees. I think that I should work with geography but how can I cast a geom to a geography? I tried with (a.geom::geography) but i am getting an error.  What can I do to get my result in meters?   Thank You macOS app for showing external HDD usage statistics? I'm planning on selling a used external HDD on eBay.  Are there any applications for Mac out there (preferably free) that can show me statistics about the usage history for the drive so that I can let potential buyers know the condition more precisely? I have an issue which I could not solve, although I tried and I got some help on R forum.  I am trying to calculate Mahalanobis distances on a data.frame, where I have several hundreds of groups and several hundreds of variables. Whatever I do, I get the system is computationally singular: reciprocal condition number error.   It is clear that it is singular, but is there any way to get rid of it and run Mahalanobis? Should I forget solve this using another approach? If yes, then what else to use?  I have uploaded the data file to my :  It is a tab delimited txt file with no headers.  I was working with the R StatMatch Mahalanobis (also tried stats Mahalanobis) function. I have a deadline for this project (not a homework!), and I could always use this function, so I thought I will be able to keep the calculations short, but now I am lost.  Migrated . Is it safe to check floating point values for equality to 0? I know you can't rely on equality between double or decimal type values normally, but I'm wondering if 0 is a special case.  While I can understand imprecisions between 0.00000000000001 and 0.00000000000002, 0 itself seems pretty hard to mess up since it's just nothing.  If you're imprecise on nothing, it's not nothing anymore.  But I don't know much about this topic so it's not for me to say.  double x = 0.0; return (x == 0.0) ? true : false;   Will that always return true? Spaces in variable assignments in shell scripts How to use testfor with a mob with a two-word name? How can I test for mob who has a name with two words? For example villager named Grumpy Bill. For example I want to kill this villager.  This command   /kill @e[name=Bill]   would work just fine but when I try  /kill @e[name=Grumpy Bill]   it says "The entity UUID provided is in an invalid format"  What is the proper command for this action? resolv.conf not working properly with Ethernet in Ubuntu I have a Lenovo X200 laptop on which I am running Ubuntu 9.10. Recently, (I assume after some updating, but I really don't know) my ethernet port stopped working under Linux. A more tech/linux-savvy friend of mine was able to temporarily fix the problem by manually editing the resolv.conf file with the DNS servers he found through his connection. However, after rebooting, the problem came back and now I am looking for a more permanent solution. Is it still bad to use swap on a modern SSD? I have a Samsung 960 Pro SSD with Ubuntu 18.04  is it safe to put the swap file on there or would it hurt it in the long run,  I heard some people saying that new SSDs don't suffer from that issue anymore, is this true? Override route helper methods Is there a measurable set $A$ such that $m(A \cap B) = \frac12 m(B)$ for every open set $B$? Is there a measurable set $A$ such that $m(A \cap B)= \frac12 m(B)$ for every open set $B$?  Edit: (t.b.) See also  for further answers. Letter of recommendation from Post-Doc or Professor There is an image in the Wikipedia about the :    I have a rough understanding of the stress tensor: you imagine cutting out a tiny cube from the fluid and form a matrix out of the forces on each side of it: it's not hard to see that the forces that push the faces outwards so the x direction of the force on the x side, the y direction of the force on the y side, etc. is the pressure, while other forces directions are the shear stress (these can be non-zero is some jelly-like substance).  Now the first question: Why is the lower half of the spatial part is the momentum flux, while only the upper one is the shear stress on the image? Is the image wrong? Isn't the spatial part describe the classical stress tensor?   The second question is: what's the intuition behind the temporal part?  So if I have a Minkowski spacetime and cut out a cube of it, then it's quite hard to see why "pressure" on the temporal face means density, also why "shear stresses" on the temporal face translate to momentum density, not speaking of the "temporal force components" the spatial faces...  Also stresses are measured in Pascals, mass density is measured in $kg/m^3$ while momentum density is in the units of $Ns/m^3$. These units doesn't seem to be compatible, but still they are in the same matrix, why?  EDIT: It has been pointed out that momentum flux refer to the entire blue part, it indeed have a lighter frame I didn't notice. Then yet another subquestion: what's the difference between the momentum density and momentum flux? I know it existed as sort of a folder in Windows Explorer in at least Windows XP, but I just can't seem to find it in Windows 7...  How can I take a picture with my webcam in Windows 7 without using any 3rd party tools? What is a wizard that makes them non-Muggle? Or, more directly, what ancestry does the witch/wizard gene follow? Is there a patriarchal wizard (or matriarchal witch) that Muggles have no part in? Elves perhaps? Stop reading here.  Purpose of the Question/History/Don't Read There seem to be solid consequences associated with being Muggle, or Muggle-related. A dominant theme in the novels is discrimination against the non-gifted race, but, when read into, the wizard bloodline doesn't appear all that well defined. JKR indicates that wizard-ness is genetic, or inherited:  &quot;Muggle-borns will have a witch or wizard somewhere on their family tree, in some cases many, many generations back. The gene resurfaces in some unexpected places.&quot;  By the above, it stands that a family that produces a squib (non-magical born of magical parents) must be a half-blooded family in some way, since half-blooded only requires one non-magical ancestor. Of course, we are dealing in magic genetics. Any other form of genetics would make this inherited, seemingly recessive trait (or squibs couldn't exist), never appear at all. Unless they were XMen. If it is so important, what does the wizard-bloodline follow? Other Mythos In other literature a wizard can be nearly anything, but magical powers are typically inherited as well as learned. Merlin of the Arthurian Legend (also mentioned in HP) is Cambian, meaning he is born of demonic intervention; this explains his source of enchantment. Gandalf of Middle Earth is a Maiar, as are all Wizards of Middle Earth. Wizards in Harry Potter seem to follow a bloodline, and it has been mentioned (in the question Gabe linked) that genetics have a heavy play in it, meaning that squibs and parents of Muggle-born wizards should have identical genetics. This bloodline must come from somewhere. Magical Creatures In Harry Potter it is common for magical creatures to &quot;mingle&quot; with humans, these beings are typically somewhat magical. Elves have been described to have very strong magic, but are for some unreasonable reason subservient to humans. I may be mistaken, but believe it was hinted that elves and the wizarding lineage had intersected at one time. Maybe I'm imagining this. Genocidal Allusions Voldemort hates muggles, and half-bloods, and whatever else is non-wizard. The presence of this theme, suggests that this wizardly bloodline must be at least defined if the main antagonist is so obsessed with keeping that mysterious bloodline pure. Since Slytherin himself was said to be a supremacist (circa a really long time ago) it suggests that this bloodline should have existed long before he was around, especially if he founded a school with people he was not related to, but were also magical.