Why can't the Schrödinger equation be derived?

Question: Honestly, I don't get it. People say it's because it's a postulate. But, I mean, I see people deriving the Schrödinger equation with the help of the wave function, $T+U$ and partial differentials in three space coordinates and one time coordinate. How is that not a derivation? And why can't the Schrödinger equation be derived?
Comment: I thought you could derive an exact equation, just not for systems with more than two particles.
Comment: Related: https://physics.stackexchange.com/q/142169/55751
Answer: A derivation means a series of logical steps that starts with some assumptions, and ends up at the result you want. Just about anything can be "derived", as long as you vary what the assumptions are. So when people say "X can't be derived", they mean "at your current level of understanding, there's no way to derive X that sheds more light on why X is true, over just assuming it is".
For example, can you "derive" that momentum is $p = mv$? There are several possible answers.

You ask this as a student in introductory physics. Some might say yes. For example, you can start from the kinetic energy $K = mv^2/2$, and then assume $K = p^2/2m$. Combining these equations and solving for $p$ gives $p = mv$, so this is a derivation.
You ask this as a student in introductory physics. Some might say no. The above derivation is just nonsense. Starting from $K = p^2/2m$ is basically the same thing as assuming the final result, and if you're allowed to do that, it's no better than just taking $p = mv$ by definition. It's like "deriving" $1 + 1 = 2$ by defining $2$ to be $1 + 1$.
You ask this as a student in advanced mechanics. Most would say yes. You start from the deeper idea that symmetries are related to conserved quantities, along with the definition that momentum should be the conserved quantity associated with translational symmetry. Putting these together gives the result.

The point is, you can make up a derivation for anything -- but you might not be at a stage in your education where such a derivation is useful at all. If the derivation only works by making up ad-hoc assumptions that are basically as unmotivated as what you're trying to prove, then it doesn't aid understanding. Some people feel this is true for the Schrodinger equation, though I personally think its elementary derivations are quite useful. (The classic one is explained in a later answer here.)

There is often confusion here because derivations in physics work very differently than proofs in mathematics.
For example, in physics, you can often run derivations in both directions: you can use X to derive Y, and also Y to derive X. That isn't circular reasoning, because the real support for X (or Y) isn't that it can be derived from Y (or X), but that it is supported by some experimental data D. This two-way derivation then tells you that if you have data D supporting X (or Y), then it also supports Y (or X).
Once you finish putting high school math on a rigorous foundation, undergraduate math generally builds upward. For example, you can't use Stokes' theorem to prove the fundamental theorem of calculus, even though it technically subsumes it as a special case, because its proof depends on the fundamental theorem of calculus in the first place. In other words, as long as your classes are being rigorous at all, it would be very strange to hear "we can't derive this important result now, but we'll derive it next year" -- that would be in danger of logical circularity.
This isn't the case in physics: undergraduate physics generally builds downward. Every year, you learn a new theory that subsumes everything you previously learned as a special case, which is completely logically independent of those earlier theories. You don't actually need any results from classical mechanics to completely define quantum mechanics: it is a new layer constructed below classical mechanics rather than above it. That's why definitions now can turn into derived things later, once you learn the lower level. And it means that in practice, physicists have to guess the lower level given only access to the higher level; that's the fundamental reason why science is hard!
Comment: @Cell Certainly. The point is that as you go deeper in the physics, the deeper layers are logically independent of the shallower ones (since you can use them to derive the shallower ones), but they're not conceptually independent (since they're not intuitive if you don't understand the shallower layers first).
Comment: @Cell having prior knowledge of something is not the same as using it as a formal axiom in a logical derivation.
Comment: For one thing, in glosses over the changing roles of definitions. I think that most intro students would actually say that you can't derive that momentum is $mv$ because that's a *definition*, not a postulate. Then later, a "better" (i.e. more general or "elegant") definition of momentum gets introduced. But the layering is not always unique - even among equal experts, you'll often have two equivalent statements, and the experts will disagree which is best thought of as the definition and which is best thought of as the corollary to that definition.
Comment: @Cell all of which has nothing to do with what a "derivation" is.
Comment: In fact, in my opinion the biggest conceptual shift from high-school/pre-med physics to "real" physics is that the former just focuses on conveying true facts, while the latter is also concerned with the logical relations between those facts - clearly distinguishing between definitions, postulates, and theorems. That's why a first mechanics course rarely clearly answers the question https://physics.stackexchange.com/questions/70186/are-newtons-laws-of-motion-laws-or-definitions-of-force-and-mass.
Comment: @tparker Yes, I would agree with all that! My example was too short to clearly display separate definitions, postulates, and theorems, but the distinction should definitely be made.
Comment: I'm mostly on board with this answer, but I would quibble with one thing. You seem to be implying (perhaps unintentionally) that's there's a unique "best" way of layering facts together such that the facts in any layer can be derived from the deeper layers, and the progress of one's physics education consists of understanding the more advanced/abstract ideas at ever-deeper layers. But this is kind of an oversimplification.
Comment: @Cell This means precisely that if you know both layers, you can usefully and rigorously derive the shallower layer from the deeper one -- but if you only know the shallower layer, looking at a derivation from the deeper layer will just lead to more confusion.
Comment: "Deeper" in the physics sense normally means more general/abstract, moving in the direction of becoming a concept. So while the momentum being defined as mass*velocity makes perfect sense at one level the concept that the word "momentum" tries to capture (in advanced discussions) is different and therefore a different quantity that captures this essence or plays this role can take the name. Like "crystal momentum", or even "angular momentum". So in physics the mathematical definition of a thing is open to revision when we find a good reason to change it. Completely unlike mathematics.
Comment: @OrangeDog That's what mathematicians say. But I've never heard of anyone who learned set theory that never learned to count as a child first. They can say they redefined it, but I'm not convinced one can understand intuitively what a a set or even an "object" or "item" is in physical space without some prior experience of enumeration.
Comment: Are you saying that it's possible to use a set of ideas/theorems up to advanced physics such that none of them depend on accepting p=mv before deriving it?
Comment: I'm not knowledgeable enough to know if that's true in physics, but it sounds misleading to me. In the same way when mathematicians will say 1+1 is 'defined' to be equal to 2 by some fancy axiom. But to learn the advanced set theory or whatever one must learn basic arithmetic and accept 1+1=2 as a fundamental truth. Otherwise you are cutting off the branch on which you're standing.
Comment: @Cell the opposite is true. Set theory starts without any assumptions of arithmetic.
Comment: @OrangeDog That's why I used the word "intuitively" which I used to mean informal/implicitly. For example I looked up the definition of addition in set theory on MathSE: mathSE/15869/how-is-addition-defined . Both answer use the union symbol. So I look up the definition of union in set theory on wikipedia: wiki/Union_(set_theory) . There's a nice example of the union of two sets with a picture. But wait a minute I only understand the pictoral example because I understand that "1" set is "an object", "a circle" and 1+1=2 so there are 2 sets. Now I use this see how 1+1 is defined to be 2.
Comment: Yes because derivations always implicitly use the end result to show how to get to the end result.
Comment: Somewhat related is this (part) of the interview with Richard Feynman: https://www.youtube.com/watch?v=P1ww1IXRfTA&t=14m56s
Answer: A bit of a different perspective than other answers:
I was once in a strange physics class as an undergraduate, where an old 90 year old professor would mumble to himself while drawing terribly on a tablet connected to a projector. Everyone would get A's by default so no one would pay attention, in fact some days I would be the only one to show up, but this was "Modern Physics", and I wanted to be a physicist so I paid attention, trying to learn whatever I could.
One thing I'll never forget:
the old professor said that everyone says that Schrodinger's Equation is an axiom, but you actually can derive it!
If you imagine yourself in the shoes of Schrodinger. Experiments are showing up that things with matter have wavelike properties. Are there equations of motion that describe "wavelike behavior"?
We know how some waves operate in classical mechanics. Now typically in classical E&M, we throw out the imaginary part of $e^{i k - \omega t}$ to work with $\cos(\omega t)$, but what happens if you simply keep the imaginary part of the plane wave?
If you start off with a plane wave:
$$\Psi = e^{i (k z - \omega t)}$$
and you find its derivative
$$\frac{d\Psi}{dt} = -i \omega e^{i (k z + \omega t)}$$
if you use the Einstein's idea that energy is quantized into packets of energy (that is that E = h f $\implies f = E/h \implies \omega = E/\hbar $) this becomes:
$$\frac{d\Psi}{dt} = -i \frac{E}{\hbar} e^{i (k z - \omega t)}$$
this immediately becomes
$$i \hbar \frac{d\Psi}{dt} = E \Psi$$
and since the Hamiltonian represents the total energy operator, we can make this:
$$i \hbar \frac{d\Psi}{dt} = H \Psi$$
Which is exactly the Schrodinger's equation!
Now this contradicts what even Feyman says:
"Where did we get that (equation) from? Nowhere. It is not possible to derive it from anything you know. It came out of the mind of Schrödinger."
I was curious after class and I asked him some questions about this. No matter what isn't there always needs to be an axiom! He responded saying that yes, there needs to be a starting point, but this is how he imagines Schrodinger came up with it, since this is a very simple and a natural way of obtaining it using knowledge at the time.
To me what's remarkable about this "derivation", is that you only need to start with two things:

The state your observing has the form of a plane wave: $\Psi = e^{i (k z - \omega t)}$
And that energy is quantized in packets: $ E = h f$

And that's it! You don't even need the de Broglie's hypothesis!

EDIT: Some people are curious why the Hamiltonian for the Schrodinger equation has such a strange form:
$$H = \nabla^2/2 + V(x)$$
This is also very simple, you just need to plug in the definition of the momentum operator into the equation for the Hamiltonian (which classically is just kinetic energy + potential energy)
$$H = \frac{p^2}{2m} + V(x)$$
$$p = -i \hbar \frac{\partial}{\partial x}$$
$$H = -\frac{\nabla^2}{2m} + V(x)$$
It's that simple!
Now if you are also curious where $p = -i \hbar \frac{\partial}{\partial x}$ comes from, this is also simple. For classical waves, the value "k" is considered to be the momentum. So if we do what we did before, but now find the derivative with respect to position instead of time:
$$\frac{d\Psi}{dz} = i \frac{p}{\hbar} e^{i (k z - \omega t)}$$
$$\frac{d\Psi}{dz} = i \frac{p}{\hbar} \Psi$$
$$-i\frac{d\Psi}{dz} =  \frac{p}{\hbar} \Psi$$
$$p \Psi = (-i\hbar\frac{d}{dz}) \Psi $$
This suggests that any time you use $p \Psi$ you can swap it out with $(-i\hbar\frac{d}{dz}) \Psi$, and this is why people say "The momentum operator is $(-i\hbar\frac{d}{dz}) $ in the position basis."
Comment: You said: "*You don't even need the de Broglie's hypothesis!*"
Then you write, the momentum operator is $p = -i \hbar \frac{\partial}{\partial x}$.
But postulating this definition of momentum operator
actually *is* postulating de Broglie's hypothesis $p=\hbar k$,
because $-i\frac{\partial}{\partial x}$ is nothing but the wave number $k$.
Comment: This is exactly how Schiff starts out.
Comment: But then the question is why the Hamilton operator represents the energy in a system and why for a particle in a potential (which is the original Schrödinger equation) it should take the rather strange form $\frac{\Delta^2}{2m}-V(x)I$.
Comment: Actually Feynman spends a significant amount of Volume 3 on making the Schrödinger equation 'plausible' (for me it is a derivation)
Comment: You don't need the de Broglie's hypothesis to get $i \hbar \frac{d \psi}{dt} = H \psi$. I edited it to make that step more clear
Comment: You associate a wave function to the motion of a particle but you don't  use de Broglie's hypothesis? We grew up with the quantum ideas and take them as granted.  But at that time there was no reason to even think about using waves to describe a particle.  Well,  before de Brollies.
Comment: de Broglie's hypothesis is specifically that $p = \frac{\hbar}{\lambda}$ not that $\psi = e^{i kz - \omega t}$. You don't need to use the "de Broglie's hypothesis" to arrive at Shrodinger's equation if you suppose a different "wavelike" supposition (that your solution is a plane wave $\psi = e^{i kz - \omega t}$).
Answer: Although knzhou's answer makes a good point stressing the possibility that what is taken as a starting point at the introductory level could become a consequence of a more fundamental principle, I think that there is a key point that should be stressed more clearly.
In physics, whatever conceptual tool we develop has to be rooted in, and its motivation comes from the need to describe and predict what happens in the real world.
Every theory we have, is not just an equation but it is based on some definitions (always conventional; definitions can be useful or not, but never true or false), on some formal apparatus, and on a set of principles which are a convenient way to summarize a lot of experimental activity.
An equation like $\vec F = m \vec a$, within classical mechanics, can be taken as a principle (Newton), or it could be "derived" from a more geometric point of view by referring to groups of transformations on symplectic manifolds. But the important thing that shouldn't be forgotten is that it is an equation within a theory describing the dynamical behavior of macroscopic bodies under a certain set of conditions.
Beyond the range of applicability of classical mechanics, some new physics enters the game. New physics means that some experimental findings are not described anymore by Newton's equations (independently if assumed as principles or derived within a  more general approach), and one has to find a new theory.
This change from a theory (or better from a set of equivalent theories) to another set is the irreducible step that justifies the statement that Schrödinger's equation cannot be derived. To be more precise, Schrödinger's equation can be derived, if one assumes as a starting point an equivalent equation. But it cannot be derived from starting points that are not consistent with quantum mechanics. For example, there is no way to deduce Schrödinger's equation from classical mechanics. The best one can do is to recast classical mechanics in the form the closest to quantum mechanics. Still, at some point, a key conceptual difference justified by experiments has to appear. Without that, Physics would be a branch of Mathematics.
Answer: Equations aren't 'derived' in a fully rigorous way in physics as the derivation always uses physics in some or all of its key steps.  Also physicists have access to tools which mathematicians do not have access to because they do not require full rigour in their derivation: Feyman path integrals are a prime example.
As an example, in the derivation of the Klein-Gordon equation a key step is to take the square root and then only keep the positive root even though the square root function is multi-valued, but this is physically reasonable as the negative square root would represent a negative energy solution. This is why I am not really sure how I feel about attempts to take physical theories and reduce them to a fully axiomatic form, as that might not always be possible or even useful.
The question also depends on what you mean by a derivation.  The derivation of the Einstein equations from the differential Bianchi identity involves some key physical assumptions and so is presumably not a 'real' derivation in your eyes, but those same equations can be derived by taking a variation of the Einstein-Hilbert action and you could argue that this derivation is legitimate as it relies on standard calculus of variations.  This type of derivation is key in modern theoretical physics and traces back to Noether (maybe the most important concept in theoretical physics).
Answer: Start with the classical nonrelativistic energy expression. Make the De Broglie assumption that matter, not just light, can be described by waves. As a consequence identify E with $\frac{\hbar} {i} \partial_t $ and similar for P. There you have the Schrödinger equation.
Answer: You could look at Schrödinger's original paper where he introduces the equation. It's actually very nicely written.
E.Schrödinger, An Undulatory Theory of the Mechanics of Atoms and Molecules, Physical Review (1926) Vol. 28, No. 6 pp. 1049-1070
As people have pointed out, you need to make some assumptions to derive the equation. Schrödinger's approach was to say: in optics we can model light by waves (wave optics) or by light rays (geometric optics); geometric optics can be obtained as a short-wavelength approximation of the underlying wave theory. Hamilton's formulation of geometric optics is actually very similar to his later formulation of classical mechanics, so Schrödinger was looking for an underlying (dispersive) wave theory that would produce classical mechanics as the short wavelength limit.
In Hamiltonian/Lagrangian mechanics, there is a quantity called the principal action W: fix a basepoint x, then for any y, W(y) is the integral of the Lagrangian along an action-minimising trajectory from x to y. This function satisfies the Hamilton-Jacobi equation $\partial W/\partial t = -H$. If your system is autonomous (H is independent of t) then you get $\partial^2 W/\partial t^2=0$ so $W=-Ct+S(x,y,z)$ for some constant C and some function S.
In wave optics, waves satisfy the wave equation (possibly dispersive). To get to geometric optics, you end up looking at waves $e^{iW}$, where W is the "eikonal", a function in geometric optics that plays the same role as the principal action in Hamiltonian mechanics. So Schrödinger guessed that the wave equation of quantum mechanics should be the dispersive wave equation with the dispersion relation chosen to ensure that $e^{iW}$ is a solution, where W is the principal action. The identification of the constant C with $E/\hbar$ is then made for consistency with Einstein/Planck/de Broglie.
I wrote a more detailed blog post about this back in 2012:
http://jde27.uk/blog/why-schrodinger.html
but I recommend reading Schrödinger's paper instead!
Comment: Thanks for your blog. It's eminently illuminating. I was looking for such an explanation for years.
Comment: I think it'll take a lot of time for me to understand your blog post, but it's very interesting to see how Schrodinger came up with it. I couldn't follow everything with a simple read through, but it's looks pretty interesting. Thanks for the contribution.
Answer: Partial differential equations are derived from basic principles of physics, such as conservation of energy or quantization of energy. They are not axioms. I prefer starting with the Hamiltonian and the principle of least action via calculus of variations, which is indeed axiomatic.
PDE have an infinite number of solutions. The physically reasonable ones are picked out by assuming boundary and initial conditions. For the Schrodinger equation, these are usually assumptions about the far-field behavior, and these assumptions have to be physically reasonable, that is, they can't violate what we know from experiments.
Are physical assumptions axioms? This is the key difference between pure and applied mathematics or mathematical physics - the latter recognizes that physical assumptions can't be ignored and are in a sense axioms. I would argue that physical assumptions can be used in proofs as axioms and do not compromise rigor. Pure mathematicians would likely disagree with me.
The plane wave derivation above is an assumption about the far-field behavior of solutions of the Schrodinger equation. And given the assertion "...since this is a very simple and a natural way of obtaining it using knowledge at the time", the professor's assertion answers Feyman's objection quite naturally. Plane waves were very well known in Schrodinger's time from the well-studied wave equation. The key is that Schrodinger realized that the equation described phenomena other than plane waves. It neatly answers the "where did the equation come from".
Answer: Suppose you concluded after seeing the double slit experiment that the position of a particle is in a (linear) superposition of all positions:
$$|{\psi}\rangle = \sum_i \psi_i |x_i\rangle \xrightarrow[\text{cont. limit}]{} \int \mathrm{dx}\ \psi(x) |x\rangle$$
such that the absolute square of $\psi(x)$ gives the probability distribution of finding the particle at $x$ (the Born rule):
$$\rho(x) \equiv \psi^*(x)\psi(x) = |\psi(x)|^2$$
Indeed, if the coefficients $\psi(x)$ are complex, you get interference terms that are in agreement with experiment ($|\psi(x) + \phi(x)|^2 = |\psi(x)|^2 + |\phi(x)|^2 + 2 \Re{(\psi^*(x)\phi(x)})$). Probability distributions need to be normalised, which means the state vectors need to be normalised:
$$\quad \||\psi\rangle\| = \langle\psi|\psi\rangle = \int \mathrm{dx}\ \mathrm{dx'}\ \psi^*(x)\psi(x') \underbrace{\langle x|x'\rangle}_{\delta_{x',x}} = \int \mathrm{dx}\ \rho(x) = 1$$
To define the dynamics, there's an operation that evolves the system in time:
$$|\psi\rangle(t_1) \xrightarrow{U} |\psi\rangle(t_2)$$
Since states are now vectors, this operation must respect the vector space structure; i.e. $U$ must be a linear operator. Furthermore, it must respect that $\rho(x)$ is a probability distribution:
$$|\psi\rangle(t_2) = U|\psi\rangle(t_1), \quad \langle\psi|U^*U|\psi\rangle \overset{!}{=} \langle\psi|\psi\rangle = 1 \iff U^*U = \mathbb{1}$$
i.e. no matter what $t_1$ and $t_2$ are, $U$ should be unitary. In general, a unitary operator can be written in the form:
$$U = e^{A}$$
where $A$ is an anti-hermitian operator:
$$A^* = -A$$
Indeed, $U^*U = e^{A^* + A} = e^0 = \mathbb{1}$. An anti-hermitian operator is the imaginary unit times a hermitian operator: $A = i K$. Now:
\begin{align*}|\psi\rangle(t) &= U|\psi\rangle(t_0)\\ &= e^{iK}|\psi\rangle(t_0)\\ \frac{\partial}{\partial t}|\psi\rangle(t) &= \frac{\partial}{\partial t}e^{iK}|\psi\rangle(t_0) = i\frac{dK}{dt} e^{iK}|\psi\rangle(t_0) = i\frac{dK}{dt}  |\psi\rangle(t)\\
\implies -i\frac{\partial}{\partial t}|\psi\rangle(t) &= \frac{dK}{dt} |\psi\rangle(t)\end{align*}
Identifying the hermitian operator $H \equiv \frac{1}{\hbar}\frac{dK}{dt}$ with the Hamiltonian, you get the Schrödinger equation.
In fancy words, the equations and mathematics of QM can be derived naturally if one admits that symmetry groups in nature (Poincaré group) should be treated through a unitary representation (S.E. equation from time translations, as we have seen above). Woit's addresses this beautifully in his book "Quantum Theory, Groups and Representations" (available for free)".
Comment: the evolution operator is $e^{iH\color{red}{t}}$.
Comment: There was an error, but that's not what I intended to write (evolution operator is $\mathrm{T} e^{i\int \mathrm{dt} H}$).
Comment: I don't really get the point of this. Isn't $\frac{dK}{dt}$ in this case is arbitrary? There's no justification that this is the hamiltonian or that it has any structure for that matter. (maybe it's a very complicated time dependent matrix, for example) Is this part answered?
Comment: Also something else I don't get with this derivation with unitary matrices, is that I don't understand how this can't apply to normal probability distributions - the "quantum interference" aspect isn't exactly covered, and it just seems like this could be applied to any probabilty theory.
Comment: $\frac{dK}{dt}$ is what we would call in physics the generator of time translations. This is the Hamiltonian by definition. Concerning the second question: the point is that we take for granted the Born rule (which can be deduced from experiment); namely that the probability distribution is the norm square of some complex vector  $\rho = |\psi|^2$.
Answer:
I see people deriving the Schrödinger equation with the help of the wave function, T+U and partial differentials in three space coordinates and one time coordinate.

Indeed, there are various "derivations" of varying complexity like the process often encountered, using de Broglie ideas about matter waves to guess or arrive at the new equation for the wave. This is quite close to but not exactly the same way that Schroedinger used to discover the thing.
These are not derivations in the strict sense of the word (like in mathematics). Such derivation could assume only known things and derive the Schroedinger equation as a necessary consequence. Such derivation at the level of knowledge/skill of 3-5 year physics study programmes at a university does not exist, because there is not enough simpler things known that would necessarily imply the Schroedinger equation.
Historically, we have Schroedinger equation not because somebody derived it, but because Schroedinger discovered it, as he was thinking of ways to describe atomic systems in terms of a wave in agreement with the Einstein-Planck relation $\Delta E = h\nu$ and de Broglie ideas about matter particles having frequency and wavelength. He based his discovery, or got inspired by, Hamilton's and Jacobi's theories on classical mechanics and their similarity to geometrical optics.
There are some derivations on the level of quantum field theory or some other formal framework of theoretical physics, but as far as I have seen they lack in clarity and usefulness to a person on the level of undergraduate physics student - in these derivations one needs to assume things that are equally or more incomprehensible than the Schroedinger equation itself, such as quantized theory of field (infinitely many degrees of freedom), more difficult mathematics of distributions and operators, for more than 1 particle there are interactions that are hard to describe exactly, there are infinity cancellations or spurious removals needed to get results etc.
Maybe there is a deeper theory than quantum theory, that is easy to understand and the Schroedinger equation for atoms and molecules comes out of some specialized assumptions there, similarly to how scalar wave optics in small gradient medium can be explained as a simplified inaccurate model of full electromagnetic theory of light and matter (Maxwell's equations and some constitutive relations). But so far nobody has found such more general theory with explicative power (like the EM theory is in case of simple wave optics), and thus the best we can do when teaching Schroedinger's equation and related things is to use combination of:

heuristic or formal "arrivals" at Schr. Eq. from other knowledge of atomic/molecule physics and quantum theory
the origin story of Schr. Eq.
examples of how to use the equations and examples of its successes when when compared to measured data (such as atomic spectra) or other results of experiments (such as diffraction patterns or detector counts)
Answer: As others have said, a derivation means a derivation from postulates or axioms. Postulates can be motivated (as for example in Schrödinger's original treatment), but they cannot be derived. So, the question is really "what axioms are needed for a mathematical treatment of quantum mechanics; is Schrödinger's equation an axiom, or is it a theorem?"
Text books are usually more concerned with practical application than with mathematical structure, and generally treat Schrödinger's as a postulate, but it is in fact a theorem and can be derived from the Dirac–von Neumann axioms. An outline of the derivation is given at Derivation of the Schrödinger equation. I have given a detailed derivations in The Hilbert Space of Conditional Clauses and in A Construction of Full QED Using Finite Dimensional Hilbert Space
The key postulate is that probabilities are given by the Born rule (or expectations given by the inner product). One also requires that the fundamental physical behaviour of matter does not change. This enables one to show that the probability interpretation requires unitary time evolution satisfying the conditions of Stone's theorem, and the general form of the Schrödinger equation follows as a simple corollary.
The Schrödinger equation is also constrained by relativistic considerations, from which one finds the Dirac equation, and the form of the interaction density which must be composed of field operators obeying the Locality (or microcausality) condition, that (anti-)commutators vanish outside the light cone. Non-relativistic forms of the Schrödinger equation are seen as semi-classical approximations in which the photon field operator is replaced by its expectation.


Why we see Goddess Durga sometimes sitting on a tiger and sometimes on a lion?

Question: I don't know why we see Goddess Durga sometimes sitting on a lion and sometimes on a tiger? Which animal was actually Durga's mount (vahana)? Is it Tiger or Lion?
Comment: Both. The form that rides the tiger is the more ferocious one and the simhavahini is the more beatific form. One of the weapons wielded by the tiger-mounted Durga is just the tarjani (i.e. forefinger raised in warning/threat). Just her tarjani is sufficient to detract evil-doers.
Comment: @moonstar2001 Do you know any scriptures that describe the "ferocious' one riding on a tiger?
Comment: Goddess Durga actually has two Vahans. One is tiger and another is lion. She was sometimes used tiger and sometimes her lion. When she had killed Mahishasur,she used the lion,she had killed many demons with her tiger. When she had took the form of Kushmanda who was one of the Navdurgas,that time she was sitting on her tiger.So,this means that Goddess Durga's two vahans were a tiger and a lion.
Comment: People confuse the tiger and the lion. She has only one vahan and that is the lion.
Answer: Durga rides on a lion. The story is told in this chapter of the Devi Mahatmya of the Skanda Purana.  Durga was created out of the combined energies of Brahma, Vishnu, Shiva, and other gods.  And after she was created, the gods have her a variety of weapons and other ornaments:

The bearer of Pinaka (Siva) drawing forth a trident from his own trident presented it to her; and Visnu bringing forth a discuss out of his own discuss gave her. Varuna gave her a conch, Agni a spear; and Maruta gave a bow as well as two quivers full of arrows. Indra, lord of devas, bringing forth a thunderbolt out of (his own) thunderbolt and a bell from that of his elephant Airavata, gave her. Yama gave a staff from his own staff of Death and Varuna, the lord of waters, a noose ; and Brahma, the lord of beings, gave a string of beads and a water-pot. Surya bestowed his own rays on all the pores of her skin and Kala gave a spotless sword and a shield. The milk-ocean gave a pure necklace, a pair of undecaying garments, a divine crest-jewel, a pair of ear-rings, bracelets, a brilliant half-moon (ornaments), armlets on all arms, a pair of shining anklets, a unique necklace and excellent rings on all the fingers. Visvakarman gave her a very brilliant axe, weapons of various forms and also an impenetrable armour. The ocean gave her a garland of unfading lotuses for her head and another for her breast, besides a very beautiful lotus in her hand. The (mountain) Himavat gave her a lion to ride on and various jewels. The lord of wealth (Kubera) gave her a drinking cup, ever full of wine. Sesa, the lord of all serpents, who supports this earth, gave her a serpent-necklace bedecked with best jewels. Honoured likewise by other devas also with ornaments and weapons, she gave out a loud roar with a defying laugh again and again. By her unending, exceedingly great, terrible roar the entire sky was filled, and there was great reverberation. All worlds shook, the seas trembled.

So Himavat, the god of the Himalayas and father of Shiva's wife Parvati, is the one who gave Durga her lion.
Comment: But Goddess Durga is also seen sometimes with Tiger.
Comment: I think Goddess Durga have two vahans.
Comment: @Keshav Where is **white** lion mentioned?
Comment: @Surya Hmm, I must have gotten the white part from some other source, but I don't remember.  In any case I'm taking it out for the time being.
Answer: I would definitely say that given the scriptural sources, the goddess has only the lion as her mount. But please note that iconographical instructions often give descriptions which are not strictly consistent with the stories. Again, sometimes painters and iconographers take liberties. While the Devimahatmya categorically mentions the lion as the goddess's only vehicle, there are beautiful Pahari paintings where she is fighting Mahishasura while riding on a tiger. Famous Sanskrit scholar Alf Hiltebeitel has also remarked that if one goes by the actual representations of the goddess over the centuries, then the lion and the tiger seem interchangeable as her vehicle. Moreover, scholars have also argued that a half-tiger and half-woman figure inscribed on an Indus seal is actually a prototype of the goddess riding on a tiger, thus hinting that the goddess's association with the tiger predates her association with the lion, and dates back to prehistoric times when Hindu mythology didn't exist in its Classical form.
Comment: Welcome to Hinduism SE! You should cite sources.
Answer: The various manifestations of Bhagavatî Durgâ(Mahâdurgâ, Jayadurgâ, Vanadurgâ, Shûlinîdurgâ, Chandikâ, Mahishamardinî) have the lion as their vâhana. There is no mention of Her riding a tiger in any scriptural text (Devîmâhâtmya, Devîbhâgavata Purâna, Kâlikâ Purâna, Mahâbhâgavata Upapurâna, Tripurârahasya, Shâkta sections of Skanda Purâna; Vâmana Purâna; Brahmavaivarta Purâna; Varaha Purâna; Shiva Purana, Lalitopakhâyanam). While worshipping, the lion is offered as Her seat by means of the Simhamantra. Even in some abhichâra prayogas She is depicted to be dancing on a buffalo or lion head. Even the Agni Purâna, which describes the procedure of depicting deities in icons, states the presence of lion as Her vâhana.
As per the Pûrvakhanda of Vâyavîya Samhitâ of Shiva Purâna, the tiger named Somanandî is the vâhana of Bhagavatî Pârvatî. And since many people outside the Shâkta circle assume that the wife of Bhagavâna Shiva & the mother of Bhagavâna Shiva are the same person; the tiger got superimposed over the lion in North India.
Answer: There is a huge confusion about devi riding tiger due to probably,
Shiv Purana, Section 7.1 - Vāyavīya-saṃhitā, Chapter 26 - The attainment of higher status by the tiger (vyāghra)
The goddess said:—

Is this tiger that has resorted to me seen by you? He has guarded my penance grove from wicked animals.
Dedicating his mind to me he worships me without thinking of anything else. There is nothing more pleasing to me than his protection.
He shall be appointed as an official in my harem. Out of pleasure Śiva will grant him the post of Ganeśvara.

Chapter 27-  Gaurī's embellishment

He was named Somanandin because Soma means Śiva and this tiger pleased Soma as well as Nandin.

Thus, now we know that Somanandi became the Gana of devi.
But does that mean she rides over it?
Let's take this example, Andhaka, Banasur, Tripurasura are all Ganas of Mahadeva. So, does that implies that Mahadeva rides over them? Atleast non of us could have seen that vigrahas.
Thus, Devi rides Simha. And this can be found in enumerated citations.
3rd Skandha, chapter 23, Shloka 21,

They began to argue "Who in this Lady, mounted on a lion? Whence has She so suddenly come?"

5th Skandha, chapter 9,

The mountain Himālyā gladly offered Her various gems and a beautiful lion, of a golden colour for Her conveyance.

Such examples that the lion aids devi is too found in Durga Saptashati in Madhyam and Uttam Charitras.
Lets take a look at some dhyan mantras-
Navdurga katyayani dyanam-

चन्द्रहासोज्ज्वलकरा शार्दूलवरवाहना ।
कात्यायनी शुभं दद्याद् देवी दानवघातिनी ॥
Here शार्दूल means lion.

Shodashbhuja Bhadrakali -

घण्टां परशुं मुशलं विभ्रतो वामपाणिभिः ।
सिंहस्था नयनै रक्तवर्णैस्त्रिभिरभिज्ज्वला ॥

Ashtadashbbuja bhadrakali dhyan-

सिंहोस्योपरि तिष्ठन्ती व्याघ्रचर्मणि कौशिकी ।
विभ्रती रूपममतुलं ससुरासुर मोहनम् ॥

Chandraghanta dhyanam-

वन्दे वांछित लाभाय चन्द्रार्धकृत शेखरम्।
सिंहारूढा चंद्रघंटा यशस्वनीम्॥

Durga dhyan-

विद्युद्दामसमप्रभां मृगपतिस्कन्धस्थितां भीषणां
कन्याभिः करवालखेटविलसद्धस्ताभिरासेविताम्।
Here मृगपति means Lion, स्कंध means shoulders, thus the one sitting on shoulders of lion.

Since, I can't cite so many dhyana mantras over here, lets take look at paintings which are indeed made from Shastrokat dhyaan mantras-

Left to right-
1.Ashtabhuja Durga, 2.Angala Parmeshwari, 3.Lalita devi riding koti koti simhas in war against Bhanda(as per Lalitopkhyanam), 4.Jataveda Durga, 5.Shoolini Durga, 6.Adya devi, 7.Manonmani, 8.Kolhapur Mahalaxmi(mula prakriti of Saptashati), 9.Banashankari (Shakambhari), 10. Shodashbhuja Bhadrakali, 11.Ashtadashbhuja Ugrachanda, 12.Dashbhuja Katyayani.

Left to right-
1.Vimala devi of Puri Shaktipeeth, 2.Ashtadashbhuja Mahalaxmi, 3.Vanadurga, 4.Dhakeshwari(now in WB), 5.Kamakhya, 6.Tuljabhavani(Tuljapur), 7.Kanakdurga(Vijaywada), 8.Shiv Kutumba, 9.Vindhyavasini, 10.Jagadhatri, 11.Pratyangira, 12.Raksha Kali.
So, the motto to show all these images was that in all these 24 images none of the deities ride a tiger. All are seen with a lion indeed.
You can also add to this list, Saptashrungi, Ambaji, Kushmanda, Vaishnodevi(Rudra sundri/ Agni durga), Tara, Varahi, even folk deities such as Karni maa rides lion, and such many more to go.
Thus, concluding devi indeed as Vyagra as her gana, but that doeChapter plies that she rides it.
(Ps- credits to respective artists for the arts used as reference here.)
कालिकार्पणमास्तु ।
Answer: In Durgasaptashati depicted in Dhyana like:

singhahskandadhirudham trivhubanmakhilam teja puryanti dhyayed Durga Jayakhyam tridasprivritam sevitam sidhikamam.

Singhastha shashisekhara etc.


Difference between "novel" and "fiction"

Question: Both novel and fiction refer to a book in which the story is just imaginary. But what's the difference between them and what are the scenarios to use them right?
Comment: What about the dictionary definitions of these words was unclear?
Comment: in essence, Fiction is about content: "not true." Novel is a form factor: a story of considerable plot complexity and length. A historical novel may describe true events, a fictional screenplay is fiction, but not a novel.
Answer: Fiction is  a literary genre that includes novels, but it also includes other forms such as short stories.
Comment: And poems, humour books, my excuses for not delivering on time. All literary work is either Fiction or Non-fiction. Novels are only a part of the Fiction type.
Answer: "Fiction" refers to any made-up story, anything presented as not being true but purely for entertainment, education, etc.
Within the broad category of fiction, we divide stories up by length. The shortest are "short stories". A "novel" means a book-length story. In between is the "novella": you might fit 3 or 4 novellas into a reasonable-length book. If a story takes more than one book, it becomes a "series". If there are exactly three books in the series, it's called a "trilogy". (I'm not aware of specific names for a series with four or five books or any number but three. I'm not sure why that gets a specific name.)
Sometimes people attach specific word-counts to these names. Like they will say that a novel is a story of 40,000 words or more, a novella is 20,000 to 40,000 words, and anything shorter is a short story. As far as I know there's no standard in the publishing business, though. These are just ballpark numbers.
These terms all imply prose, as opposed to poetry.
Comment: "40,000 words" is the description in English, I wonder what they say in other languages?
Comment: @GEdgar Sure, in languages where the average word length is longer or shorter, I imagine they'd use different numbers. The "real" definition is that a novel is "book-length".
Answer: Fiction is the act of writing something that isn't true:

A literary work whose content is produced by the imagination and is not necessarily based on fact.

The word fiction can also as a label refer to longer works of imaginative prose.

The category of literature comprising works of this kind, including novels and short stories.

A  novel on the other hand, is a bound written work of length:

A fictional prose narrative of considerable length, typically having a
  plot that is unfolded by the actions, speech, and thoughts of the
  characters.

There are two additional things to keep in mind about novel versus fiction.
While several novels are fiction, they do not necessarily have to be fiction to be novels. Truman Capote's In Cold Blood is one example of a non-fiction novel.
Also, imaginative works of fiction can be of just about any length, from a few hundred to tens or even hundreds of thousands of words.
To define and market these written works, the publishing industry has a loose set of guidelines that define writing based on length:

Micro-Fiction: Under 100 words
Flash Fiction: 100-1,000 words
Short Story: 1,000-7,500 words
Novelette: 7,500 - 20,000 words
Novella: 20,000 - 50,000 words
Novel: 50,000-100,000 words
Epic: 110,000+ words

(Note: This is just one definition of length, but it is generally accepted that a novel is at least 50,000 words, with 70,000 words being the average length of a modern novel.)
Comment: I remember learning the difference between Novel and Novelette/Novella is that Novelette has strictly one explicit thread (any side threads may only appear as simple cameo events seen from the main thread). Novel drives multiple threads at once.
Comment: Re: "they do not necessarily have to be fiction," my understanding is that a "non-fiction novel" is actually a *combination* of fact and fiction and that the term "novel" would not apply to any work that was purely factual.
Answer: Fiction works can be classified based on their style and length of the writing. Fiction is writing based on the author's imagination and invention of a story, characters and/or backdrop.
Novels
Novels, novelettes (also known as "novelet") and novellas all contain the same subject matter but exist along a spectrum in terms of word length. Novels, at the far end of the spectrum, may have numerous conflicts, story lines, and chapters, and generally have 40,000+ words.
Fiction refers to a story containing imaginary or made up events. A novel refers to the length of a work of fiction. It's usually considered the longest form of literary prose. Shorter works of fiction would be a novella or a short story. Also, fiction can refer to things outside of writing. Movies and plays, would be considered works of fiction
Answer: As against imaginative or fictional, the novel is a realistic form. It represents that segment of life and society, in more or less approximate terms,which has been seen and experienced by actual men and women of a particular period.
While reading a novel, we may feel that we have been transported to a different world with its own rules.Towns and villages etc holds out as actual places with their distinct colouring and feel.Yes,the emphasis is on actuality.
Fiction on the other hand denotes an unreal thing, a 'creation' of the mind of a person gifted with an unusually inventive with powerful  imagination. It denotes that the account presented in a work bears no relation with the reality of life as we know it- it is imaginative and more, it is fictional.


Looking for words with a similar meaning to Pocket-veto

Question: I am currently looking for words that mean, "To nullify an event or call, by ignoring the event or call, until the event or call has passed". I know Pocket-veto fits the bill (I apologize in advance for this pun), however I'm looking for a more informal word, as I can best describe it. Thanks.
Answer: In US English, you can use to table

Postpone consideration of:
I'd like the issue to be tabled for the next few months

(Oxford dictionary)
By tabling a bill, either literally or figuratively, the president effectively pocket  vetoes it if it's less than ten days before Congress adjourns.
Comment: Be aware, in Australian English (not sure about British) this means the exact opposite, to table an issue means to discuss it right now. I assume the interpretation stems from putting sth on the table. I learned this the hard way... ;)
Answer: If you want very informal:
blow off

to ignore, evade, or treat as unimportant ("I mentioned his insulting remark, and he just blew the whole thing off"); to not go to or participate in ("He blew off his first-period class three times that week"); to fail to meet (someone) as planned without alerting the person beforehand ("I waited 20 minutes before I realized my sister had blown me off").

(dictionary.com)
Answer: Perhaps this, which implies that missing the opportunity is not intentional:

miss the boat - (informal) to lose an opportunity to do something by being slow to act

If there is full intent, you might just pass on it, or take a pass on it.

pass on something - to refuse an opportunity

(Cambridge Dictionary)


The difference between 245/70r16. Instead of a 265/70r16

Question: I have a 2004 Chevrolet Avalanche with the tow package ,would it be alright to use 245/70r16 tire instead of  265/70r16?
Answer: If you think your Avalanche is getting okay mileage now (most likely between 15-18 highway), you're going to hurt it worse by using those tires. The ones you want to use are shorter overall. Secondly, since they are skinnier tires, by two centimeters, you won't have as much grip and possibly stability as you do now. The speedometer will be off by a bit, reading faster than you're actually going.
You can use them, but there's some large tradeoffs for doing so. Personally, it's not something I'd do.
Comment: @teresa this is a useful link, showing revolutions per mile ie how it will affect the fuel consumption : https://www.tacomaworld.com/tirecalc?tires=245-75r16-265-75r16
Comment: Another consideration if the vehicle is used for towing is the load rating of the new tires. A tire with a lower load rating may have difficulties towing, up to and including tire failure. If you don't tow, or tow exclusively light loads, it won't matter.


Why don't cameras have automatic eyepiece covers?

Question: The question is clear and I am not sure how to further explain it. Why don't cameras have internal automatic eyepiece covers?
Answer: Because it would add expense and complexity, and most consumers don't request it.
Answer: By "internal automatic eyepiece cover" I assume you mean something to block the light instead of something to protect the eyepiece glass from scratches.
There are no cameras with an "Automatic Eyepiece Cover" but some Pro level cameras have a manual eyepiece shutter to block off light during long exposures when your eye is not covering the viewfinder.  This prevents exposure errors due to light entering the viewfinder.
Canon EOS-1Dx

Canon A-1

Other Cameras use a rubber piece that snaps onto the viewfinder to block the light.
Comment: All good info, but doesn't really address the question, which is *why* an automatic cover doesn't exist.
Comment: What is your idea of an " internal automatic eyepiece cover" ?  Is it a simple user activated eyepiece shutter like some cameras already have?  Or is it a fully automatic device that activates anytime you remove your eye from the viewfinder?
Comment: It's not really automatic if the user has to activate it. I expect OP means a cover that moves into position when the shutter is released.
Comment: Thanks Mike, I've accepted your answer because it shows they existed. I meant something like the Canon A-1 above. or something which activates automatically when face/eye is not close to the eyepiece. there are sensors for turning off the display when face is close, why not this?


[Titles] Should the most relevant tag be included in the title?

Question: Suppose I have a fairly generic question (like about the use of global variables or something like that) but I'm looking for an answer related to PHP, should I include that requirement in the title? I know that it's what tags are for, but maybe it helps visibility and relevance in external engine (google) searches?
Comment: It's ironic that the [original](http://meta.stackexchange.com/questions/10647/howto-writing-good-titles) has a *terrible* title. lol
Comment: Stack Exchange does this automatically nowadays to the HTML title.
Comment: It helps in indicating context!
Comment: I like how this Title is clear, because it has a tag at the beginning. But it is the *most important* tag, not the *most popular*! Can I do this in my questions also (outside of Meta)?
Answer: Just don't pseudo tag the title. Please.

How can I frob my whatsis in PHP?

is good, but

[PHP] I want to frob my whatsit.

is bad.
Answer: I only do this when I'm asking the type of question that's liable to get answered by people who haven't actually read the question or the tags.
For example, I asked "Is SQL Server DRI slow?" and actually got a very good answer, but I suspect that if I hadn't added the "SQL Server" part then a bunch of people might have given irrelevant answers for other DBMSes (and the specific DBMS was the issue there).  If I had just asked "Is DRI slow?" then the title would have suggested a product-agnostic question; aside from including the product name, there was no way to reword it to be more specific.
On the other hand, I also asked about "Approaches for generic, compile-time safe lazy-load methods", and even though the verbiage does not suggest a specific language, I think it's obvious to any reader that the language matters.
Honestly, it can't hurt to include the product name, but as dmckee says, just don't make it a "pseudo-tag" at the beginning of the question; make your title a coherent sentence that includes the product name in its proper place (i.e. "Is there an XYZ library available for .NET?").
Answer: Keep tags in the tags, please.
You don't need the additional visibility. People interested in PHP likely already have that in their interesting tags.
People interested in not seeing PHP questions likely already have that in their ignored tags list.
Neither group will be served by you placing the tag in the title.
If you start to get answers from people who didn't notice the tag, then maybe you should consider editing the title to include the tag (without the brackets).
Still, I hope you won't need to change the title from "How do I Consume a WCF Service using nuSOAP" to "How do I Consume a WCF Service using nuSOAP in PHP".
Answer: If PHP is a requirement, you can certainly mention it in the title, but nobody can force you to do so. You can use any title you wish. If people think that it's not sufficiently precise, it will get edited anyway. That being said, some people do overlook tags, so the more precise your question title (and body) is, the better.
Comment: @Tomalak: I am not arguing in favor of titles such as "[PHP] [CSS] [float] problem"; I am arguing in favor of precise descriptive titles such as "Problem with CSS floats in PHP" vs. "Halp needed". How is a precise title inferior to an imprecise one? I'm not following. And "let's train people not to overlook tags" is nothing but empty words. *How* do *you* train people not to overlook something? That is, other than saying "please don't overlook it" in a comment, which they then overlook.
Comment: Then let's train people _not_ to overlook tags, instead of pandering to their laziness/ignorance with something inferior.
Comment: That title is neither precise nor descriptive. _What_ problem?
Answer: Please keep the tag in the title if it's not obvious! (as per dmckee's post) The questions shown in the sidebar in StackExchange sites do not include the tags, and it can be very frustrating to check question one after another just to find out if it applies to your situation.
Comment: The correct fix is for the SE templates to be modified show tags in these scenarios, not to move that information into the title where it cannot be indexed, or otherwise stored & represented in a useful semantic manner.


My writing analysis came back with a report of "Straight forward writing style". What does this mean?

Question: I am curious if this is a positive, negative, or neither here nor there. The analysis was done by Wattpad and it also included that fact that I write more like a journalist above anything else. The analysis was done by taking the first 3,000 words from my YA/Teen fiction novel and analyzing it. It's a new Wattpad feature.
Comment: [Hemmingway Style](https://www.cliffsnotes.com/literature/f/for-whom-the-bell-tolls/critical-essays/hemingways-writing-style)
Answer: There's a certain amount of subjectivity to this, but on the whole a straightforward style is viewed largely positively in current trend. Especially where you are writing for a YA/Teen audience who may not have as fully-developed a comprehension ability as older audiences.
I'm not hugely familiar with Wattpad - and I've never tried their analysis tools so I can't comment on their efficacy or accuracy, but if your beta readers (if you've had any read it yet) are saying similar things then that would be an encouraging sign.
Answer: To find out what

Straight forward writing style

means in Wattpad you might try asking its opinion on other books in the YA/Teen genre.
My first impression of "straight forward writing style" was that it'd be good for a report but that I might want something more imaginative for YA/Teen. But "imaginative"  may not be one of their categories.
Answer: IMHO it is very good.  I hate oblique confusing writing trying to be artsycraftsy but which only slows me down and confuses me.  Some English profs may disagree which is their right.
Answer: Take it as a piece of positive feedback from whatever algorithms the Wattpad engineers have cooked up. In today's hyper-competitive publishing world (especially in teen/YA genres) being "straight-forward" is a plus. Most readers won't bother wading through confusing text when there is so much other content available to them.
If you're looking for another fun writing analysis tool, check out the Writing Style Comparison -- it lets you submit a sample and will tell you what famous author you most resemble. I just ran it against the text in this post ... and apparently George Bernard Shaw would have been a hit on StackExchange.


Surface Area of Intersection with Skull

Question: I was wondering if anyone can help me. I pretty much need to know the amount of surface area there is on a plane lying tangent to a human skull. I would GREATLY appreciate any help with this. Thanks in advance.
Answer: First cut the part of the skull that is sticking through the plane using the bisect tool:
Then delete the rest of the faces so you're left with only the part you need to measure:
Join up all the edges to get a plane, and then delete everything else so only the plane you made is left.
Lastly go to user preferences and activate the 3d printing addon (found under mesh) and it will tell you the area of your plane. I would add more screenshots, but i can only post 2 since i dont have enough reputation.

Surface Area of Intersection with Skull


Thymeleaf: Login user via sign up page instead of /login

Question: So far I know that it works automatically,

but don't know how to use it if i had created a new user via some sign page. Now instead of taking the user to log in page again.
Is there any way to log in user automatically on sign up.
Answer: As part of where you register your user, you can manually stuff a new  authentication object into the SecurityContextHolder. This will keep the user from having to log in manually.
<code>
// build authentication token based on the username and password provided
Collection authorities = new ArrayList<>();
authorities.add(new SimpleGrantedAuthority("user"));
Authentication auth = new UsernamePasswordAuthenticationToken(email, password, authorities);
// set authentication in context
SecurityContextHolder.getContext().setAuthentication(auth);
</code>


Self-organizing maps: fuzzy input?

Question: I would like to know if there are SOM implementations (preferably R) available that accept fuzzy input. That is, I have data in which some nominal features are spread out between a number of categories. For example: feature 1 has 5 categories and an observation might have the values (which are actually probabilities) [0, 0.5, 0.25, 0.25, 0].
Comment: Why wouldn't you just treat the 5 categories as 5 separate features?
Comment: This does sound as a good and simple option, thank you. Is this good/best practice? I suppose there is no real way of avoiding the increased number of inputs? I ask because my sample size is quite small.
Answer: There are a few papers which propose fuzzy SOM.
Petri Vuorimaa, "Fuzzy self-organizing map", Fuzzy Sets and Systems
Volume 66, Issue 2, 9 September 1994, Pages 223-231.

Kohonen's Self-Organizing Map is one of the best-known neural network models. In this paper, we introduce a fuzzy version of the model called: Fuzzy Self-Organizing Map. We replace the neurons of the original model by fuzzy rules, which are composed of fuzzy sets. The fuzzy sets define an area in the input space, where each fuzzy rule fires. The output of each rule is a singleton. The outputs are combined together by a weighted average, where the firing strengths of the fuzzy rules act as the weights. The weighted average gives a continuous valued output for the system. Thus the Fuzzy Self-Organizing Map performs a mapping from a n-dimensional input space to one-dimensional output space. The learning capability of the Fuzzy Self-Organizing Map enables it to model a continuous valued function to an arbitrary accuracy. The learning is done by first self-organizing the centers of the fuzzy sets according to Kohonen's Self-Organizing Map learning laws. After that, the fuzzy sets and the outputs of the fuzzy rules are initialized. Finally, in the last phase of the new learning method, the fuzzy sets are tuned by an algorithm similar to Kohonen's Learning Vector Quantization 2.1. Simulation results of a two-dimensional sinc function show good accuracy and fast convergence.

Janos Abonyi, Sandor Migaly and Ferenc Szeifer, "Fuzzy Self-Organizing Map based on Regularized Fuzzy $c$-means Clustering"

This paper presents a new fuzzy clustering algorithm for the clustering and visualization of high-dimensional data. The cluster centers are arranged on a grid defined on a small dimensional space that can be easily visualized. The smoothness of this mapping is achieved by adding a regularization term to the fuzzy $c$-means (FCM) functional. The measure of the smoothness is expressed as the sum of the second order partial derivatives of the cluster centers. Coding the values of the cluster centers with colors, regions with different colors evolve on the map and the hidden relation between the variables reveal. Comparison to the existing modifications of the fuzzy $c$-means algorithm and several application examples are given.

Self-organizing maps: fuzzy input?


How do you say "fruits of darkness" in Latin?

Question: I am writing a text where this phrase is on a big part. It will be the title, so it's important to me to got it right. Thank you. :)
Answer: There's a few ways to translate this. I am ignorant of the nuances, but here's my best understanding based off of minor Googling and Whitaker's Words.
Fructus Tenebrarum = The fruit/benefit/reward of darkness.
Fructus Obscuritatis = The fruit/benefit/reward of blindness/darkness/lack of understanding.
Fructus Crepesculi = The fruit/benefit/reward of twilight/darkness.

If you want to decline this properly in your work (I don't know your intentions) these are the ways you want to decline it.
Subject of sentence: Fructus Tenebrarum/Fructus Obscuritatis/Fructus Crepesculi
Object of sentence: Fructum Tenebrarum/Fructum Obscuritatis/Fructum Crepesculi
Indirect Object: Fructui Tenebrarum/Fructui Obscuritatis/Fructui Crepesculi
Within Prepositional Phrase: Fructu Tenebrarum/Fructu Obscuritatis/Fructu Crepesculi
Comment: Thank you very much! The nuances are that "fruits" mean the rewards which will appear from the darkness, and "darkness" will literally be the night (but also dark powers). So I think "Fructus Tenebrarum" will be right. So does your translation mean plural even thought you wrote "fruit"?
Answer: In addition to Nickimite's fine examples, there is also:

fructus caliginis "fruits of darkness" (deep darkness, with a vague connotation of being in a dark nebula; gloom, blindness, calamity)
fructus obscuri "fruits of darkness" (the dark, with a vague connotation of darkness covering the world from one's vision; the hidden, unknown)

I think obscuri is more common than obscuritatis.
Tenebrarum is excellent. It also has the advantage of being grammatically plural (even though it is just "(the) darkness" semantically), so perhaps a suggestion of powers of darkness is most easily made. It is not seldom used with ominous connotations, like the underworld.
Crepesculi is probably uncommon.
Lewis & Short say this:

tenebrae is stronger than obscuritas, and weaker than caligo

As to the form fructus, that can be either plural or singular (one with a final u pronounced long, the other short). Nickimite has given the declension of the singular. Fructus has a connotation of fruit one enjoys, from fruor "to enjoy, profit from". There is also frux "fruit", plural fruges, which is from the same root, but I believe it rather has a connotation of "usefulness".


Why did gods follow rule of Hinduism?

Question: There is a main rule in Hinduism with the idea that everybody is born, everybody lives and then  dies. This was the case for humans. My question is: Why did Brahma, Vishnu and Shiva follow this rule? What would be the point of following this rule when they are all seeing, all powerful and all knowing. What is the significance of following this rule?
Comment: Which rule in particular? Gods actually follow their rules- rules of the Gods.
Comment: _" rule in Hinduism with the idea that everyone is born, live and then die"_ It is not rule of hinduism. It is rule set by Lord himself for us. He gives us life for limited time period only. Whoever has born, he has to be die one day, this rule has nothing to do with hinduism.
Comment: @Rickross This rule means "There is a main rule in hinduism with the idea that everyone is born, lives and then dies. This was the case for humans." The question is that why do Devatas take birth, live and die. Not about the rules of Devatas.
Answer: The Gods have their own rules, their own Laws. Such rules are not the ones we humans are required to follow.
This is mentioned in the Vedas as follows:

DevA devAnAm anu hi vratA guh.
..........
The Gods move according to the law of workings of the Gods.
Rig Veda 3.7.7

The Commentary on this mantra:

Even the Gods observe a law and that law is the law of Truth. For the
  Gods are themselves born of Truth, grow in Truth and live in Truth.
  They are emanated from the vast Being of the Supreme to carry out its
  Truth-Will in the manifestation. They uphold and follow the workings
  of this Will, its law of effectuation. They are both the guardians and
  functionaries of this Law.
Adapted from Sri Aurobindo.
Answer: I think you are mixed up in the definition of omnipotent and  omniscient. The main religious concept of whole vedic thought was rta which is a moral order or cosmic force which governs spiritual motion of human beings. Even Gods can not escape rta, violators are severely punished.
Consider a powerful rocket like Saturn V that made lunar exploration possible it would produce a thrust of > 100 KN. That said the rocket still has  to follow laws of gravty. So being able to overcome gravity does not mean the law of gravity cease to exist. Same thing is hold true for Gods. As mentioned by Rickross that Gods follows rule of Gods. Rule of karma does not apply on them as that is applicable for people who born on earth. However killing someone (brahmin/bystander) is a sin even for Gods and they have to atone the sins
Comment: What is "rta"? An abbreviation?

Why did gods follow rule of Hinduism?


Navigo at Orly airport

Question: I am arriving at Orly airport.
1- Can anyone tell me if i can get the carte decouverte there and charge it for the week ( mon-sun)
. If yes can you please precise where .
Thx in advance.
Comment: I want to buy the Nd and use it on Orly bus. Orlyval isn't covered with ND. I just want to make sure that i can buy it upon my arrival and use it
Answer: You can buy a Navigo Découverte pass at any RER station and most Métro stations (those that have a ticket window). At Orly, use the Orlyval shuttle to the Antony train station (RER B line, which also connects with the Métro).

Navigo at Orly airport


DNA Inheritance- Math vs. Biology

Question: After doing some statistical analysis of the raw math involved in DNA contributions, I would like to understand the scale of the biological factors.  I know that 99% of the human genome is identical in all human beings, so genetic recombination and gene conversion should be irrelevant in those areas.  I know that recombination occurs at different rates depending on the chromosomes and loci.  But what is the average order of magnitude?  That is, if I know that a chromosome mainly came from Grandma, how much of it is likely to be from Grandpa?  .1%, 1%, 10% ?  And, does the age of the male affect the rate of recombination to a measurable degree (in spermatozoa only, as body cells would not affect inheritance).
Comment: What do you mean by "the scale of the biological factors"? And what do you mean by "the average order of magnitude"? As you just said, differences are tiny between any two randomly drawn humans (in DNA sequence), so if this is your 'metric' there can't be any differences in 'orders of magnitude'. If you only ask about the fraction of the particular DNA (in chromosomes) that was copied into your own genome from your ancestors, then it is roughly half from your parents, a quarter from your grandparents, and so on.
Comment: DNA tests are done only on the variable segments:  It would be pointless to say "you're a 99% match to this other sample, it must be your identical twin."  Using the "average" of the actual distribution is misleading.  Only 32.24% of people inherit between 23.91% to 26.09% from a grandparent while 90.69% inherit somewhere in a range of 17.39% to 32.61%.
Comment: Agree, so, what is that you are asking then?
Comment: DNA testing is in its infancy, and different labs use different protocols for their tests and different models to report results.  2 samples from ME will not show a 100% match to MYSELF.  The zygote that turned into my mother, say, had 23 intact chromosomes from each of her parents.  When my zygote was formed, recombination may have occurred in the specific ovum that made me.  Take chromosome 1- the main body of which came from her father.  Is it likely to be 99.9% grandpa with .1% recombined from grandma, or more in the 90% grandpa 10% grandma range?
Answer: So, at core (it seems) you are interested in the rate of recombination events and the magnitud of their occurrences. This would be the only source I can think of that would give you information about the 'composition' of one chromosome (other than brute-force sequencing).
As you seem to know, recombination is an important factor that 'shuffles' some specific areas of the chromosomal DNA during meiosis (process needed to produce gametes). There is a technique developed by T. H. Morgan almost a century ago, that measures the rate of this 'recombination' events by comparing how two (or/and more) particular loci co-ocurr across generations (when recombination occurs, it is more likely to break co-occurrences of distant loci, as opposed to close loci). Thus, we can use this distance measure as a measure of recombination. In fact, in honor of Morgan, the units used to measure recombination rates are called 'centiMorgans', and abbreviated cM. A cM is the probability for a particular loci (it can be a gene or a smaller sequence) to co-occurr with another loci (to be 'linked' to). Thus, is a relational measure: every particular sequence is related to another, and by transitivity (if A and B are close, and B and C are also close, then A and C will probably be close -this is a generalization-). When done in chromosomal or genomic scale, we can build linkage maps.
In modern times, there's quite more resolution, from whole genome studies at gene/chromosome resolution, and even higher resolutions (remember that a 'loci' can be any unit of your interest in the DNA).
Being all that said, recombination rates, and thus the probability of inheriting certain DNA features from parents/ancestors based on recombination, vary quite a lot. There are many 'hot-spots' and other regions seem to be 'protected' from recombination (for instance, regulatory DNA). According to the work I cite here, the probabilities of recombination can vary within about an order of magnitude (the most likely recombination occurring at 10 times higher probability than the less likely), but this varies a lot.
I hope this helps a bit. I am still not sure what do you mean by "biological factors", but for sure recombination is one of the important factors influencing the identity of each chromosome across generations (others are, of course, point and chromosomal mutations).
Comment: I reviewed my understanding of centiMorgans.  It appears to be the measurement of a rate, but the units used are a distance.  To me, this is like estimating travel time by considering only the distance, with no regard as to terrain, weather or traffic.  As you said, there are known hot-spots in the genome.  With a cM being a .01 probability, and rounding to about 7,000 cMs in a human, that would be an average of 70 instances of genetic recombination in a single generation, and that's a non-directional switch, as opposed to conversion.  With variables you point out, only general ranges matter.
Comment: It gives a rate because the probability of 'linkage' between any loci can only be in the [0,1] range. So, even though it is thought of as a 'distance', in reality (both as conceived by Morgan, and in real 'physical' terms) it reflects the frequency of recombination events. So, to me, it is a bit like the inverse of your metaphor: we get traveling times, yet we like to talk about it as a 'distance traveled'; the weather, traffic, etc, are implicit to the traveling times observed (the linkage).

DNA Inheritance- Math vs. Biology


Will the retina iPad Mini charge with non-certified cables?

Question: I just bought a retina iPad Mini. Tried 3 different cheap lightning cables, none will charge it. Tried with 12W and 5W USB chargers. It will only charge with the Apple cable that came with it. But these Chinese cables charge my iPhone 5 and old iPad Mini just fine. Did something change in the new iPad's lightning chip? I wonder if is is a widespread problem or just me.
Answer: See this question for more info. In short, you're taking your device's life in your hands when you don't use legit products. You have a multi-hundred-dollar device, do not cheap out on the thing that's directing nontrivial amounts of electricity into it!
Authorized products aren't that expensive and you can be sure that you won't have strange things happen.
Newer devices will straight up refuse to work without the authentication chip in the cable. Previous devices (and maybe iOS versions) would still charge, but display the error, or do so at a reduced rate.
Answer: Yes, you have to use certified cables.


How do I best clean the cog wheels?

Question: Would it be best to take it off first then soak it in soap, or should I use petrol to get the grease off first?
Comment: Possible duplicate of [What to use to clean your chain (and cogs)?](https://bicycles.stackexchange.com/questions/692/what-to-use-to-clean-your-chain-and-cogs)
Comment: A toothbrush is all you need.  You can spray on a bit of WD-40 if you wish, to speed things along.  (Do keep the WD-40 and other solvents off the tires and brakes.)
Comment: Never use petrol - use kerosene if you want a cheap readily available material to remove grease/oil etc. Petrol is toxic and flammable. kerosene is less so in both counts.But citrus cleaner is still safer and nicer to use
Answer: You don't need to take the cassette (cogs) off to clean it.
Use a citrus degreaser fluid. Clean the chain and chainrings at the same time. You can use a rag pulled taut to get between the cogs, or there are a number of specialized cassette and chain cleaning tools available.
There are many instructional videos out there with tips on cassette and chain cleaning also.
Answer: If you've got the tools (chain whip, lockring tool, wrench), it is easier and more thorough to remove the cassette and soak it in a degreaser than it is to clean it in situ.
I remove the chain and cassette, drop them in a wide-mouthed jar, cover with Simple Green (a non-toxic cleaner, possibly not available where you are), and let it sit for a few hours, agitating occasionally. Then rinse, let dry, and re-lube the chain.
Comment: I am not clear on the reason down votes. Cleaning The cassette on the wheel with the greaser is a good way to damage the seals and potential he encouraged debris into the free hub body.
Comment: EXACTLY! Only way to safely clean it really, unless you make certain your hubs are designed perfectly to avoid this (which none are) is to take it off.
Answer: Same as the others - I leave it on the bike to clean.
I use a combination of an old screwdriver to break up and pick off any compacted dirt from between cogs.  Too much of that and the chain doesn't sit right.  Then I use a cassette cleaning brush tool to brush off the loose and powdery dirt.

Last is a wipe with an old rag to restore some shine to the sides of the cassette, but I don't degrease it.
The chain I clean in a similar way - I pick off larger blobs of dirt that live on the outside of the inner plates.  Then I use a chain cleaning machine with degreaser in it, either turps or proper fluid.  Petrol tends to upset the tool's plastic.

Then I let that dry, and apply a wet or dry lube after an hour or so.
Comment: @Carel dirt can definitely get inside the links, it's not like they are sealed, that's easy to see if you take a chain apart. That being said: it is indeed not straightforward to estimate what the best is: a little bit of dirt on the factory-applied grease/wax, or removing that by submerging the chain and then trying to get new lubricant inside again. Depends on chain type/age/number of kilometers/weather type/...
Comment: Those chain cleaning devices do more harm than good. The bath tends to remove the grease inside of the links (where no dirt sits) and once the grease is removed it will be difficult to put back and grit will get inside. A chain is cleaned best with an oily rag and if necessary with a hard brush, like a pan-scrubbing brush.
Answer: I've found out that those cotton strings or ropes from paper shopping bags are a rather practical tool for cleaning cassettes.
Remove the wheel, sit down and put it against your shins, cassette facing away. Then engage one of these strings between two cogs and move it left/right/left/right. The freewheel helps and for increased efficiency the string can be soaked with detergent or solvent. It may be washed and re-used quite a number of times.
Answer: You don't need to take the cassette off the bike. Spray/squirt a concentrated degreaser and use cloth strips (I recommend 1 inch wide and 3 inch long) to get in between the cogs, clean them nicely and free the surface of all the tough muck. Better yet, if you've got a specialized cassette cleaning claw,  give it a go: they work pretty well.
Hope this helps you.
Answer: Depends on what is meant by "best".
The most thorough approach would be to remove the cassette from the wheel and clean it in an ultrasonic cleaner. Probably excessive.
Second best it to remove the cassette and use a mild solvent (e.g. WD40) and a rag to clean the sprockets. This is a good time to examine sprockets for cog wear (the smaller ones in particular).
It is also possible to clean in situ with a wipe, a rag or some kind of floss.
Whatever you do, do not flood a mounted cassette with solvent. You might inadvertently remove lubricant from the freehub and/or wheel hub.

I personally remove, clean and examine my cassette once a year. If your chain is well maintained you are unlikely to have to clean your cassette more frequently.
Answer: I personally do a full bike overhaul every six months, though I absolutely torture my road bike doing off-roading on places I wouldn't even put a mountain bike....
My chain is cleaned thoroughly after every ride, and then stored in a small vat of chain oil to keep it from rusting. (Bad practice, I know, but I'm lazy and like to make sure the chain is ready for every ride. Pull it out, attach it, run it through the cogs a couple of times and then wipe off the excess oil from the chain and cogs and derailleur before the ride.)
I'd first remove the wheel, get my cassette lock-ring removal tool and a chain whip and remove the cassette, taking a note of all the positions of the rings. Then, on my cassette, there are little holes that were probably put in for weight reduction; I'd nail each cog onto a big board of ply-board, soak in a strong degreaser and agitate with a brass wire brush, then pressure-washing off everything, then repeat on the other side. (As I said, this bike is tortured, and as such, everything needs a very heavy cleaning...)
The free-hub itself I would also replace, too. Every year or so, I replace my chain, chain-rings and cassette, bottom bracket, headset and hub axles/bearings. I personally disagree with using a degreaser on the cassette whilst it's still on the wheel as the degreaser can get into the wheel hub, and much worse, into the free-hub mechanism itself.
A more basic way would be to just remove the cassette, degrease it in a plastic tub and leave it to soak for a couple of minutes then brush off with a plastic brush, rinse off and then re-assemble. Place your (I'm assuming) freshly-cleaned chain back on, lubricate the chain and then ride on! If possible, avoid getting oil on the chainrings; only the insides of the chain need lubrication.
There is no extreme heat happening on the chain and cassette, so lubrication is not a requirement, and if anything, would hinder the efficiency of your chain by something hilarious like 0.0005 percent because of the layer of oil there. A pathetic number, but another good reason is it'll turn any road dust and brake dust into a grinding paste for your chain.
Answer: Best way is to take it off and clean them individually.
A quick hack that works for me is wrapping a rag around a CD and working it in between each cog. See below.

I find that by regularly using this method, I do not have much build up between services versus if I use a brush alone it just moves the dirt around without removing it.
Hope that helps.

How do I best clean the cog wheels?


Are Polypropylene training weapons safe for LARP?

Question:
Cold Steel (as pictured above) and other companies make polypropylene training weapons. Are these safe to use when LARPing?
Comment: Comments are not for extended discussion; this conversation has been [moved to chat](https://chat.stackexchange.com/rooms/77073/discussion-on-question-by-christopher-albertson-are-polypropylene-training-weapo).
Answer: When in doubt, check with the person responsible for weapon checks at your LARP, but training weapons like this are considered NOT safe for most non-historical LARPs.
Always check with your Herald/Reeve/Rules Guy before bringing a new weapon onto the field.  They'll be happy to help.  Usually, they'll be checking for a few things.  I'll break these up by categories, since the answer varies a bit by what you're doing:
Historical LARPs like SCA generally have very strict safety standards, but since everyone is wearing armor they break down to require that weapons be dulled and metal.  There may be restrictions on chain length for hinged weapons as well.  Again, this varies from organization to organization and even chapter to chapter.
Fantasy Combat LARPs with No Player Contact like Amtgard or Hiraeth will generally be much more towards the pool noodle end of things.  There is a minimum diameter for weapons and no minimum weight.  This helps keep everyone safe, and cores out of people's eyes.  Speaking of, these kinds of larps don't allow metal weapons of any stripe, so without knowing the core material (the rigid shaft in the center of most foam weapons) it will probably be tossed.
Fantasy Combat LARPs with Player Contact like Dagohir allow for minimum weights and diameters for their weapons, but allow contact between players.  These sorts of Larps will also find metal cores unacceptable.  In general due ot the player contact, Contact larps like this require cloth covers on non-shield equipment, since that prevents jagged edges that can occur sometimes on plastic-coated weapons.
Sci-Fi/Apocalypse NERF LARPs are actually the most welcoming of this kind of weapon, but it will varies.  The new-ish Fall of Man LARP would allow this weapon since it is similar to the hand-held weapons that NERF produces.  This is probably the only one outside a Historical LARP that would allow this on the field, but you'd need to be very careful with it.
Answer: Answering your question from the perspective or Russian LARP culture, there are two main systems:

Where only foam weapons are allowed and armour is usually aesthetical, not really protective. This thing is rather new to our scene.
Where weapons actually hit hard and people are expected to have real armour made of real steel, a trauma is usually believed to be the consequence of badly constructed armour rather than the attacker hitting too hard, unless they have hit a completely unarmoured body part or an unarmoured player.

Of course, polypropylene weapons are banned in the case of point 1, besides some really short knives that are sometimes allowed. For point 2, it depends, the safety standards usually regulate weapon weight and the minimum width of the blade.
In any case, at each event we usually have one guy responsible for censuring weapons. He is to decide which weapons are allowed and which are not. Ask your weapons guy when in doubt. :)
Comment: From the point of view of a weapons checker in one of the larger UK systems, no, for pretty much the same reasons that Baskakov_Dmitriy gives above. Most UK systems will have a page on their website either containing or allowing download of their weapons check guidelines to give you an idea of the acceptable equipment for that system.


How should I control my sexual impulses when I can't medically fast?

Question: I take multiple pharmaceutical drugs, and so fasting is unhealthy for me. Yes, I've tried taking it before fajr and after maghrib, but the way it works is that when I fast it messes with my health because of the way the medications affect my body. The Prophet (SAWS) advised young men such as myself to marry or fast. Unfortunately, I can not marry because for one, I am in school, and too physically weak to enter a trade (though perhaps exercise should help, but my mother who I live with has threatened to kick me out if I leave college, and I have no job, so I fear homelessness or sudden change and I have autism and dislike change). and for two, i am not mentally mature, in part because i suffer from borderline personality disorder and anxiety issues, and fear i would be an oppressor to whomever i marry or whatever children i have with them. i am 19. what should i do? keep in mind, my mother (and there is no father figure), encourages me to "date, so as long as it's not girls from our jamaat, date an american if you want, or meet in groups"
Answer: First : I just want to point out that almost every Muslim young man has been through the sexual desires you are feeling , you are by no means alone in that , so when you attempt to compare yourself to someone , do compare yourself to your fellow Muslims , that will spare you much of the pain you'll feel when you compare yourself to your American friends many of which , by no sin of their own but by their cultural standards, have no restrictions on adultery , dating , mixing and all these sinful actions whatsoever .
You are a Muslim , so you are different , you have obligations and a faith in the God that created you , so always keep that in mind .
I have no right to say anything about your mother's suggestion , but the entire previous part is dealing with it implicitly , so do with that what you will .
Now : For the question itself , I want to say that if you can't fast , you can still pray , and make dua that Allah would remove the intensity of what you are feeling , you can get up , make wudu and pray whenever you feel the urges overwhelming you , it will only take a couple of minutes but a world of difference , also  you are free to follow any human method not mentioned in the quran , it is completely okay . There are actually many movements in America encouraging abstainment and self-control , they also offer incredibly good advice , about certain techniques and changes in diet and many more , that is another good supplement you can use in order to overcome these feelings , and I believe that a mix of these two approaches (Islamic and psychological) would really go a long way with you , and I really wish you all the best brother !


Data Import Wizard : - Lookup Relations Issue

Question: I am not sure but I am wondering if there was a recent change in the Data Import Wizard tool as now it requires the Id of all the lookup relations from a particular object whilst before was working with only specifying the name of the record and was able fetch the required id based on the name you input.
Comment: Can you give a bit more detail please @Marc Zaharescu - is this a custom object or standard and which other objects does it have the lookup relationships to?
Comment: I have tried to import a set of Accounts which have lookup relations to different Custom Objects. Before I was able to only specify the name of the records in the lookup and it would match the id automatically, but now I need to specify the id of the record.
Comment: You could try dataloader.io which can do the same thing.
Answer: we've also encountered this problem, but unfortunately it is due to a change in the Data Import Wizard which now requires salesforce IDs for all look up fields. The error message generated is:'Your import failed: Import for object Account did not succeed. Error received - null'
I've had several lengthy conversations with salesforce help with this (and apparently they've had a lot of complaints about it), as it is completely impractical for us to enter salesforce IDs instead of recognisable names/titles, and unfortunately no way to solve without entering IDs until Salesforce change back to the old system. We are trying to get Salesforce to change, I've posted this as an 'Idea', so if you are having problems with this, please vote on my idea: https://success.salesforce.com/ideaView?id=0873A0000003OryQAE
Answer: Solution-

Use data loader to update record, via data loader you will see the account look up fields. If you use data import wizard you will not see the look up fields.
Use account name to account Id so will update as account name


Saturn Headlight Problem

Question: I have a 2001 Saturn SL2 that is having a problem with one of its headlights. When I turn on the headlights, frequently one is not lighting. If I go to the front and give the lens a quick knock, it turns on and stays on until I turn the headlights off.  It doesn't flicker or show signs of a loose connection. I have cleaned the connector and that hasn't helped. I'm out of ideas at this point and hope someone can suggest a next step.
Comment: Have you tried replacing the bulb itself? It could be that the filament is loose and reconnects with the little bump.
Comment: I hadn't thought of that since it appeared to turn on and stay on. I'll give it a try and let you know how it turns out.
Comment: Thank you! I did change out the bulb and that appears to have fixed it. I did look at the filament under a magnifying glass and still didn't see where it was failing. Thank you again for your help!
Comment: There is also something attached to the rear of the headlight called a calibrator or something it looks like a battery pack. There's usually a headlight frame too accessible from underneath the car to take the headlight out.
Answer: My suggestion is that the filament inside of the bulb is loose. When you rap on it, it reconnect briefly, which lights the bulb. It will continue to do this until it completely burns out. This will probably require a replacement bulb to fix.

Saturn Headlight Problem


Adsorption and distribution chromatography difference?

Question: Well, yes, that is the question. What is the difference between the absorption chromatography and distribution chromatography?
Answer: Adsorption Chromatography = Utilizes a mobile liquid or gaseous phase that is adsorbed onto the surface of a stationary solid phase. The equilibriation between the mobile and stationary phase accounts for the separation of different solutes.
Distribution Chromatography (aka Liquid-Liquid extraction) = Due to its liquid stationary phase, the ingredients are only separated by their respective polarity, i.e. according to their distribution coefficient KD. Distribution chromatography is also ideal for the concentration of trace quantities. This is more closely related to Flash, Column, and Gas Chromatography.
Comment: Basically, the first is solid-liquid, the second liquid-liquid?
And if it is so, why does RP-chromatography belong to distribution chromatography and not to adsorption chromatography?


How to correct for small p-value due to very large sample size

Question: I am running into a problem where an independent variable, which should have no predictive power on the dependent variable based on domain knowledge, comes out with very small p-value because the sample size is very large(~100,000). If I only use < 5000 data points, then the p-value becomes large enough to support the prior that the variable is insignificant. However, I don't think tweaking the sample size to get to the desired conclusion is a good practice. Is there any procedure to adjust for small p-value simply due to huge sample size?
Comment: When the p-value is small, chance is not a good explanation for the estimated relationship. That's it, period: no adjustment is needed. Perhaps you should be focusing on *effect size* or measures of *importance* in your application rather than p-value.  See [this related question](http://stats.stackexchange.com/questions/7815), too.
Comment: The problem is I am working with economic models, where a R^2 of 0.01 is considered "very" high. Is there an effect size analysis that would be appropriate for such low signal-to-noise ratio problems?
Comment: It's the one you do when reviewing literature and the effects you found.  Maybe this effect is in the range of meaningful sizes, maybe not.  You have to assess that.  Maybe your prediction of no effect was based on the fact that it was just really small.  If it's actually a meaningful amount then you've got an explanation for why others didn't find it.
Answer: You're valuing the p-value far too highly.  Report the magnitude of the statistically significant effect.  It should be such a small value that statistically significant is pretty irrelevant.  In terms of something like Cohen's d, it takes an effect size of about 0.006 to need N's that large to be found.  Talk about the effect size reasonably.  That's what you should be doing for all of your effects, significant or not, expected or not.
Comment: Cohen's D works well for tests that look at means, but if you're running nonparametric tests, say Wilcoxon rank sum, there is no (equivalent) effect size measure. How would you then treat that situation?
Comment: I crafted a response but as it got more involved I decided the better thing to do is suggest you direct this to SE after a careful look at the current questions on effect size and nonparametric tests. I only will say here that Cohen's D is only mentioned for convenience sake as the questioner gives no information on what the actual measures are.
Comment: Well, for general nonparametric methods, there seems to be a lack of effect size measures. I've resulted to using Cohen's D or a bootstrapped Cohen's D. There have been other threads that have attempted at this as well http://stats.stackexchange.com/questions/133077/effect-size-to-wilcoxon-signed-rank-test
Answer: A few years later... The paper by Naaman (2016) Almost sure hypothesis testing and a resolution of the Jeffreys-Lindley paradox seems relevant. From the abstract:

A new method of hypothesis testing is proposed ensuring that as the sample size grows, the probability of a type I error will become arbitrarily small by allowing the significance level to decrease with the number of observations in the study.

see also the Wikipedia entry for Almost sure hypothesis testing.
Answer: Keep in mind the truth that "correlation is not causation".  That is, while you might not see WHY there should be a predictive relationship, there nonetheless is a strong enough correlation that you receive a small p-value.

As an example: I could perform a health & fitness study on kids who weigh between 75 - 100 lbs.  If I also write down their ages & their heights, I would find correlations between both age & height to health as well as weight to health.  Why?  Well, if I grab a 4 year old who weighs 75 pounds, s/he is likely unhealthy.  Similarly if I grab a boy 6'2" who is 100 lbs.  This makes sense to you because it is intuitive.  The effects in the case you're studying are likely less intuitive.

Why did this occur?  Because I put a constraint on one correlated variable which inherently creates relationships with the others.  (If I took all weights, then the 6'2" 100 lb boy would be drown out by other 6'2" kids who weigh much more.)

Lastly, keep in mind that the p-value you are calculating is against the null hypothesis (or so I presume).  The null hypothesis is merely testing against absolutely no effect.  So if you have a mild effect that is so trivial you think is uninteresting, it will still have a low p-value.  So as others said, p-value alone is not the end-all-be-all.  It is merely a good filter & starting point.
Answer: If the p-value indicates a relationship, then it is likely that the relationship does exist.  However, I wholeheartedly agree with the previous response, that you should be focussing on a measure of the effect of the relationship.
Comment: The "it is likely" statement is incorrect in general. If, for example, one was working in a field in which large numbers of false positive signals were generated, chance might be at least as good an explanation for a small p-value as a real relationship. We cannot trust $p$-values to be the sole arbiters of truth.