I just saw this pic     So I got curious and logged in on physics.stack first time, is it true? I am a math major and usually wander on mathstack but I would like to understand why Bumble bee cannot fly according to physics laws but still do? I am only familiar with high school physics, no aerodynamics at all. If some one can explain it to me in easy terms, I'll be obliged.
According to some source or other (I forget which now) it is theoretically impossible for bumblebees to fly by virtue of their size/bulk/aerodynamic properties. Is this old adage apocraphyal or true? And if its true, how come they do fly?
Fix terminal after displaying a binary file I would like to search an entire MS SQL 2000 database for one value. This would be to aid development only. Keep that in mind when considering this question.   This will get all the table names and the column of the data type I'm looking for:  SELECT Columns.COLUMN_NAME, tables.TABLE_NAME FROM INFORMATION_SCHEMA.Columns as Columns  JOIN INFORMATION_SCHEMA.TABLES as tables  On Columns.TABLE_NAME = tables.TABLE_NAME WHERE Columns.DATA_TYPE = 'INT'     I was thinking something like this:  -- Vars DECLARE @COUNTER INT DECLARE @TOTAL INT DECLARE @TABLE CHAR(128) DECLARE @COLUMN CHAR(128) DECLARE @COLUMNTYPE CHAR(128) DECLARE @COLUMNVALUE INT  -- What we are looking for SET @COLUMNTYPE = 'INT' SET @COLUMNVALUE = 3 SET @COUNTER = 0  -- Find out how many possible columns exist SELECT @TOTAL = COUNT(*)   FROM INFORMATION_SCHEMA.Columns as Columns  JOIN INFORMATION_SCHEMA.TABLES as tables  On Columns.TABLE_NAME = tables.TABLE_NAME WHERE Columns.DATA_TYPE = @COLUMNTYPE PRINT CAST(@TOTAL AS CHAR) + 'possible columns' WHILE @COUNTER &lt; @TOTAL BEGIN     SET @COUNTER = @COUNTER +1     -- ADD MAGIC HERE END   Any ideas?  UPDATE I recently found this  that works quite well. What algorithm(s) are used by MoleculeModify's GenerateConformers? How can I tell if an iOS device has a GPS? I saw this keyword for the first time and I was wondering if someone could explain to me what it does.   What is the continue keyword? How does it work? When is it used? Let $\{a_n\}$ be defined as follows: $$a_1 = 2, a_{n+1}=\dfrac{1}{3-a_n}$$ $n \geq 1$.   Does $\{a_n\}$  converge?    Using the monotone convergence thereom, if the sequence is both bounded below and decreasing, $\forall n\in\mathbb{N}, n\geq 1$, then we can say the sequence converges.  I'm having trouble proving that the sequence is bounded below by induction.    Claim: The sequence is bounded below by $0$.  Base Case:  $n=1$  $a_1 = 2 \geq 0$, so this holds.  Induction Step  Suppose that $a_k \geq 0$, for some $k \in\mathbb{N}$. (IH)  Prove $a_k \geq 0\to a_{k+1} \geq 0$  I have some difficulty here.  $a_{k}=\dfrac{1}{3-a_{k-1}} \geq 0$  $a_{k+1}=\dfrac{1}{3-a_{k}}$, but we know $a_k \geq 0$, but we don't know how much bigger. It could be that $a_k = 4$, and then I have $a_{k+1}=\dfrac{1}{3-4}$, which is negative, and does not confirm with my claim of being bounded below by $0$. Have I gone somewhere wrong in my induction? Contracting with Levi-Civita (totally antisymmetric) tensor Is the gradient a surface normal vector or does it point in the direction of maximum increase of f I'm having some trouble trying to visualize and physically understand what's happening with the gradient.  I understand that the following is true:   The gradient of f (grad(f)) points in the direction of maximum increase of f   However, later on, we are told that a gradient of a surface f (grad(f)) gives us the surface normal vector (i.e pointing away). How can that be? From the first statement, I thought that the gradient must be pointing in the direction of maximum increase of f - surely the direction of maximum increase of f should be a vector pointing in some direction on f itself. How can it be pointing outward as a surface normal vector? Is there a way to separate variables between multiple notebooks? \mathbb{Z} yields undefined control sequence error How to initialize HashSet values by construction? Difference between generalized linear models & generalized linear mixed models Can't boot into Ubuntu in Windows 10 / Ubuntu dual boot I installed Ubuntu on a Dell XPS 13 laptop that had Windows 10 preinstalled on it. I installed it from a USB flash drive on a partition. When I boot my computer I can only boot into Windows 10 and Ubuntu is nowhere to be seen.  If I boot into my USB then I can see that Ubuntu is installed, but I can't get to it from the BIOS boot menu. Disabling Google Chrome Download auto numbering for existing files Transforming geometry PostGIS column with unknown geometry type? I run PostgreSQL 9.1 and PostGIS 2.0. I have a table that contains one geometry column.   But that column contains point, polygons lines, etc.   So I set it like so,   ALTER TABLE jake ADD COLUMN jake_geom geometry;  and then I setted some constraints to make it geometry enabled, but not limited on a single geometry type  ALTER TABLE jake   ADD CONSTRAINT enforce_dims_geom CHECK (st_ndims(jake_geom) = 2);  ALTER TABLE jake   ADD CONSTRAINT enforce_srid_geom CHECK (st_srid(jake_geom) = 900913);   Now, I want to reproject the geometries in that column to 4326.   According to , for the transform to work, I need to set a geometry type.  (the TYPE geometry(MultiPolygon,2163) part)  but my column does not have certain geometry type. How do I proceed?  Or I can simply do  ALTER COLUMN geom USING ST_Transform(geom,2163);  avoiding to set a type? How to add a custom icon or symbol to a flag link? I'm working on a 'sample request' implementation for a commerce site using , , sessions and a little custom code.  I'd like to add an icon or a symbol to let people know that an item they are viewing has been flagged.  I'm not sure exactly how to approach this, I can imagine perhaps adding a conditional field that displays an image or check box that is then changed by  or ajax, or perhaps something more complicated in JavaScript?  It could really be as simple as adding a checkbox that is checked or unchecked as the flag link is clicked or maybe even changing the css/html on click to be identified as marked.   Anyway, grateful for any advice here. General integral to find resistance opengl storing multiple indices into indices buffer After parsing collada files I found out that we have to load two(or more) indices each pointing to say a vertex or normal etc. like this (&lt;p>3 0 2 0 0 0&lt;/p>)  Is there a way to load (and use)these indices to indices buffer(ELEMENT_ARRAY_BUFFER) like this (vnvnvn...) ; where v is vertex pointer, n is normal pointer from the above. with vertices loaded to VBO1 like (vvvv...) and in VBO2 like (nnnn...). So that we dont have to repeat the normals in VBO2.  VBO like (vnvnvn...) is also ok. (and not something like this ), I'm not trying to use multiple indices buffer. I'm trying to put all the given indices into one index buffer and use them alternately.  (If I wasnt clear i will try for more clarification.) Why quantum mechanics? Imagine you're teaching a first course on quantum mechanics in which your students are well-versed in classical mechanics, but have never seen any quantum before.  How would you motivate the subject and convince your students that in fact classical mechanics cannot explain the real world and that quantum mechanics, given your knowledge of classical mechanics, is the most obvious alternative to try?  If you sit down and think about it, the idea that the state of a system, instead of being specified by the finitely many particles' position and momentum, is now described by an element of some abstract (rigged) Hilbert space and that the observables correspond to self-adjoint operators on the space of states is not at all obvious.  Why should this be the case, or at least, why might we expect this to be the case?   Then there is the issue of measurement which is even more difficult to motivate.  In the usual formulation of quantum mechanics, we assume that, given a state $|\psi \rangle$ and an observable $A$, the probability of measuring a value between $a$ and $a+da$ is given by $|\langle a|\psi \rangle |^2da$ (and furthermore, if $a$ is not an eigenvalue of $A$, then the probability of measuring a value in this interval is $0$).  How would you convince your students that this had to be the case?  I have thought about this question of motivation for a couple of years now, and so far, the only answers I've come up with are incomplete, not entirely satisfactory, and seem to be much more non-trivial than I feel they should be.  So, what do you guys think?  Can you motivate the usual formulation of quantum mechanics using only classical mechanics and minimal appeal to experimental results?  Note that, at some point, you will have to make reference to experiment.  After all, this is the reason why we needed to develop quantum mechanics.  In principle, we could just say "The Born Rule is true because its experimentally verified.", but I find this particularly unsatisfying.  I think we can do better.  Thus, I would ask that when you do invoke the results of an experiment, you do so to only justify fundamental truths, by which I mean something that can not itself just be explained in terms of more theory.  You might say that my conjecture is that the Born Rule is not a fundamental truth in this sense, but can instead be explained by more fundamental theory, which itself is justified via experiment.  Edit:  To clarify, I will try to make use of a much simpler example.  In an ideal gas, if you fix the volume, then the temperature is proportional to pressure.  So we may ask "Why?".  You could say "Well, because experiment.", or alternatively you could say "It is a trivial corollary of the ideal gas law.".  If you choose the latter, you can then ask why that is true.  Once again, you can just say "Because experiment." or you could try to prove it using more fundamental physical truths (using the kinetic theory of gases, for example).  The objective, then, is to come up with the most fundamental physical truths, prove everything else we know in terms of those, and then verify the fundamental physical truths via experiment.  And in this particular case, the objective is to do this with quantum mechanics. How can I use quotas in samba? I have a simple set-up with just one public share on my configuration file. How can I restrict its size?