While anglers fishing during the winter season on Upper Red Lake will continue to have a four walleye bag limit with only one walleye allowed longer than 17 inches. The same regulation has been in place since the May 2017 fishing opener. From December 2017 through November 2018, anglers harvested about 235,000 pounds. That's a record high for annual harvest since walleye fishing resumed on the lake in 2006. Do you and our officials say eventually there may be a need to make some adjustments to size or bag limits if spawning stock declines and needs more protection, but for now they say the opportunity to harvest some fish over 17 inches is popular with anglers and it meets the harvest plan objectives by spreading harvest over a wide range of sizes and removing some of the surplus spawning stock. If you enjoyed this segment of Lakeland News, please consider making a tax-deductible contribution to Lakeland PBS.


So we finished yesterday with this little application of Ehrenfest's theorem, which showed that on the understanding that the Hamiltonian operator is p squared over 2m plus v, the potential energy inspired by classical physics. And on the understanding that p is the operator that I claimed that it is, which is defined by the relation p hat on a psi is equal to, right. So this is, I'm claiming that the operator defined by this equation p hat is the momentum operator. It seems reasonable to take this to be the energy operator, the Hamiltonian. That being so, when we use Ehrenfest's theorem to find the rate of change of the expectation value of x, which in classical physics would be the actual value of x, we find that it's in fact equals the expectation value of the momentum divided by m, which is in a classical sense what we would call the velocity. So that's one good thing. It's obvious now that we should move forward and calculate the rate of change, use Ehrenfest's theorem to calculate the rate of change of the momentum's expectation value, and live in hope that this becomes the force. Anyway, this is going to be, maybe we'll leave the ih bar, put it over here, same as that. So this is going to be p comma h expectation value of Ehrenfest's theorem over ih bar, because I haven't put the ih bar here now on second thoughts. So we need to calculate p comma h. p comma h is p comma p squared over 2m plus v, comma there. Obviously, p commutes with itself, so to forget that. So therefore, this is p comma v. And when we discussed commutators, we showed that if you take the commutator of an operator with a function of an operator, this is a function of x, then what you end up with is the derivative of this operator. Well, you do end up with that in the event that the commutator, so do you remember we expanded, what we did was we expanded v of x as v0 plus v1 x hat plus v2 x hat squared over 2 factorial, et cetera, et cetera, et cetera. And then when we calculated p hat v, what did we get? We got v0 plus v1 p hat, et cetera, plus, and here we would have v2 over 2. This would be, because we're taking the commutator of p with x squared, which is p with x with the other x standing idly by plus x p comma the other x from our basic rule for doing the commutator with products. Because this thing is only a number, it's minus i h bar in fact, we can take this number outside. It doesn't matter the fact that this number is in front of x and this number is behind, here it's behind x. Because it's a number, we can just pull it out. This becomes 2x hat, which cancels this. And at the end of the day, we are looking at p comma x, a common factor in all these things plus, sorry, brackets, v1 plus v2x plus v3x squared over 3, et cetera, et cetera, et cetera, sorry, over 2, which is the Taylor series for dv by dx. And this one here is minus i h bar. So we have minus i h bar dv by dx. So our equation of motion, so putting this commutator back in up there, we discover that d by dt, the rate of change of the expectation value of the momentum, is, oops, we pick up a minus sign from here because we have a minus i h bar here and we want to find the commutator over i h bar, so we get minus the expectation value of dv by dx. So lo and behold, we have Newton's law of motion. We have the rate of change of momentum is equal to force. But in this expectation value sense, it's expectation value of the rate of change. The rate of change of the expectation value of the momentum is equal to the expectation value of the force because, in some sense, the force has to be thought of as something that's, well, it is. It's something that has quantum uncertainty because it has uncertainty because the position is uncertain. Different positions will give rise to different forces, et cetera. So I think that makes a pretty convincing case that the momentum operator is as advertised because we're able to recover on that understanding Newton's laws of motion. So now let's look at state's very important topic. Let me do it here, in fact. States of well-defined momentum. That is to say, we want to know what are the wave functions? What do the states look like in which you're certain to the measurement of the momentum is certain to produce a given number? So we're interested in the eigenstates of the momentum operator. The operator p on an eigenstate labeled by p, this is a number, is equal to that number times p. So this is the definition. This defines these states. If we want to know what these things look like in terms of in real space, we want to bra through with an x. And then we're looking at x. p hat p is equal to p xp. This is the wave function of our state of well-defined momentum. Let's introduce a newfangled notation and declare that this is u sub p of x. This is just the definition, the wave function. p equals up of x. And this left side, by the definition of the p operator, is minus ih bar dup by the x. So here we have one of these trivial differential equations, which we know how to solve. It tells us that up of x is equal to a constant times p to the i p over h bar x. If we put e to the i p over h bar x in for u, when we do this differentiation, we get down an i p over h bar. The h bars cancel. The minus i and the i together make a 1. And the p sticks around is what we want. So that's it. So a state of well-defined momentum, the states in which you are certain to measure a given value of the momentum is a plane wave, is a wave like this. So it's a wave. And we have that the wave number, usually called k, is the momentum divided by h bar. Because h bar is incredibly small, typically this wave number is extremely large. And the wavelength, of course, lambda being 2 pi over k is 2 pi h bar over p is h over p is going to be very small. And the bigger the momentum, the smaller the wavelength. That's obviously crucial for physical applications. What else can we say? We can say that there's complete, if you know the momentum, then so if we're in a state of well-defined momentum, the result of measuring momentum is certain, so you do know the momentum, then your wave function looks like this, which means that the probability density is independent of space. So the probability density, which is up squared, is equal to some constant, which is independent x.  It's as likely to be here as on the other side of the universe. So from that it follows, you already got it's like these states of well-defined energy, these states of well-defined momentum do not, in practice, occur. They are mathematical idealizations, because you would never see a particle which had totally uncertain position because it would spend all of its time not in your laboratory. Your laboratory is such a negligible part of the universe. So that's something to be a bit clearer about. What else do I want to say about this? Oh yeah, we should address this wavelength. Yep, I should mention this, of course, is called the de Broglie wavelength. De Broglie was thinking about relativity curiously in 1924, whatever in his thesis, for which he won the Nobel Prize in 1929. And he came up with the idea that there was this relationship between the particles would be associated with a wavelength. So that's called the de Broglie wavelength in his honor. And as regards numbers, well, we'll look at some numbers later on. But the general idea is that the size of an atom is determined by the de Broglie wavelength of the electrons that are in, you know, that make up atoms. So if you have a hydrogen atom in its ground state, its characteristic size is given by the de Broglie wavelength of the electron that's in there. And the electron that's in there is in orbit around the proton with a certain momentum. Right, so this de Broglie wavelength is setting the size of atoms. I think that's a point worth making. But we'll look at some numbers later on. So if you have an electron, so an electron in hydrogen, right, is moving around. It has the binding energy of hydrogen is 13.6EV. It has a kinetic energy, which is half that, because of the virial theorem, which we'll have all these results later on. But they're already in classical physics. So it has a kinetic energy of order 6 electron volts. And that gives you a de Broglie wavelength, which is a 10th of a nanometer. That gives you some kind of sense of scale. OK, what about normalization? So we've deduced that the wave function of a state of well-defined momentum should be some constant times this exponential.  We usually normalize our wave functions. So usually we like to have the integral dx of psi mod squared is 1, because that's the total probability to find it somewhere. But this normalization isn't going to work, because if psi is proportional to e to the i kx, psi mod squared is going to be 1. The integral from minus infinity to infinity of 1 is just infinite, and no constant in front is going to normalize it successfully. So we don't use that normalization. The normalization that we use is this normalization Do you remember yesterday we agreed that x primed x should be delta of x minus x primed? So this thing here is the amplitude to be at x primed if you're certainly at x, which is why it's nothing unless x primed is equal to x. And this amplitude becomes very large when x equals x prime, so that when you integrate over this, you get 1. So that's what we should do in this case. P is an operator with a continuous spectrum, same as x. So we want to choose the normalization constant, choose the constant such that p primed p equals 1. Sorry, not 1, delta p minus p primed by precise analogy with that. So that's something that's fairly straightforward to do. We write this. We put an identity operator into here made up of x's. So this implies that, well, this thing here is equal to p primed x, x, p. That's just sticking in an identity operator. So we're going to say that xp is equal to some normalizing constant times e to the i p on h bar x. And the name of the game is to find the value of this, because we know that this thing is this. The nice thing is that this is the complex conjugate of that. So what we have is that this is equal to a mod squared, because we get an a from here and an a star from here. The integral dx of e to the minus i p primed over h bar x, that's from here. The complex conjugate of that with p made into p primed. And from this, we simply have an e to the i p over h bar x. And that can be written just to clean it up a little bit. p minus p primed x over h bar dx over h bar h bar, all right? So this h bar was always present. This one I've put in, I've divided the x by h bar and multiplied by compensating h bar here. So the variable of integration is now x over h bar, which is still running from minus infinity to plus infinity. And now this is a standard integral, which I hope you will recognize from Professor Esler's course from Fourier analysis. From Fourier analysis, we know that this integral is 2 pi times delta p minus p primed. So what we're concluding is, going right back up to the top, that that original delta p minus p primed right up there is equal through these integrals to mod a squared times 2 pi h bar, 2 pi h bar delta p minus p primed. And that clearly tells us that a mod squared is equal to 2 pi h bar is just h is equal to 1 over h. The phase of a is unimportant. So we're entitled to take it to be real. So what we do is we choose a to be 1 over the square root of h, not h bar but h. So that means that the correctly normalized thing, x wave function, xp, is e to the i p over h bar x over the square root of h. So this is an important result. It tells us something else that's of interest if we take its complex conjugate. Because its complex conjugate says that p x is equal to e to the minus i p over h bar x over root h. And what does this mean? This means the amplitude to find that you have momentum p, given that you're definitely at the place x. So if you have an electron that's localized at the place x, its wave function is a delta function essentially, right? It's localized at x. You can ask, what's the amplitude for this to have various momenta? The answer is given by this complex number here. The modulus of this complex number here is independent of p. So what does that mean? It implies that the probability of having p given x is some constant. All values of momentum are equally likely. From a momentum which is nothing very much, or 0 even, up to a momentum which is associated with some relativistic gamma, some large value of gamma. All momenta are equally likely, including extremely high ones. So that's clearly unphysical. And what that tells you is, you will never succeed in localizing a particle precisely to an exact x. The state of being definitely at x is unrealizable, because it would imply that there was enough energy somehow in the system that there was a non-negotiable probability of finding the momentum to have some extraordinary large values, right? So there we are. So what we've discovered so far is if x is certain, p is totally uncertain. And conversely, if p is certain, x is totally uncertain. Let's, therefore, investigate, both of these situations are clearly unphysical. So let's try and discuss something which is physical. And let's suppose that we're dealing with a probability distribution in x, which is a Gaussian, e to the minus x squared, whoops, x squared over 2 sigma squared over the square root 2 pi sigma squared, right? So this is a Gaussian distribution of probability in x, which is our generic model of where we've got this thing localized at the origin to within plus or minus sigma, more or less, right? We can ask, what wave function yields this probability? Well, the answer is essentially it's a wave function, which is the square root of this. So a suitable wave function. There are many possible wave functions because phase information isn't conveyed by the probability. But let's write down this wave function, which is e to the minus x squared over 4 sigma squared over 2 pi sigma squared to the quarter power. So if you take the mod square of this wave function, you get the probability and the probability you get to that one there. So I could multiply this by all kinds of complex, all kinds of numbers of modulus 1 and arbitrary phase. And I would still get that. But this real wave function is the simplest one that we can write down. And now let's calculate for this. So this is a well-defined wave function, which we know localizes our particle to the origin plus or minus sigma. Let's ask, so what is the probability distribution for this psi of measuring a particular value of p, right? So what we want to discover for this is, so what's p of psi? Well, that's the integral dx of p x, x of psi. We know what this is because we've just been working it out. This is a state of well-defined momentum. So this is 1. This is the integral dx of e to the minus i p upon h bar x, I believe. I hope I've got that minus sign right somewhere up there. Over the square root of h times this, which is the wave function we just wrote down, e to the minus x squared over 4 sigma squared over 2 pi sigma squared to the quarter power. So this is a, and we have to integrate this from minus infinity to infinity. Now physics is full of integrals of this sort, and there's a box in the book explaining how to do them. I don't want to take the time to go into the sorted details now, but all you do is you gather all these exponents of the exponential together, and what we've got here is an integral dx of e to the i quadratic, right? If you gather this together, there's a linear term and there's a quadratic term, so you can express that. I mean, that is e to the i quadratic expression in x. And what you do is complete the square of the quadratic, change your variable of integration, and use a standard result that the integral dx e to the minus x squared from minus infinity to infinity is equal to the square root of pi. We use this standard result. And that's how we evaluate these integrals here. I would recommend learning how to check in the box out, making sure you understand how that goes, and doing this integral yourself as an example after the lecture. But I don't want to take time to do it now, because it's just algebra. Let's just write down the answer and discuss its physical implications. So this turns out to be that p of psi is equal to e to the minus sigma squared p squared over h bar squared over, and there's a normalizing constant, which is 2 pi h bar squared over 4 sigma squared to the quarter power. So if we square this up, we get the probability of measuring various momenta, which is clearly going to be e to the minus 2 sigma squared p squared over h bar squared over 2 pi h bar squared over 4 sigma squared to the quarter. So our probability in position in real space, we have the particle localized in a Gaussian distribution with a width sigma, it turns out from this calculation that the possible values of the momentum, the probabilities associated with different momenta, is also a Gaussian distribution centered on 0 in momentum. And the width of this distribution, the spread in momentum. So in order to find what that is, you'd have to express this as e to the minus p squared over 2 sigma p squared. So the dispersion in momentum is h bar over 2 sigma. So the dispersion in momentum is small when the uncertainty in real position is large and conversely. So we have a result that for this particular model, the dispersion in x times the dispersion in momentum is h bar over 2. Yes? You are worried about this, too? Oops, thank you. It should be a half. Yes, of course, because I've squared the quarter. Thank you very much. I've squared the quarter, and it's become a half. So this is the classical statement of the uncertainty principle. It's really only an order of magnitude. In this particular model, it is an exact mathematical statement. It's a statement about the widths of two Gaussians. But in a generic case, if you know your probability distribution is like this, just some curve that's got a natural width and a location in x, then the corresponding probability distribution in p will have a width which is broadly related to the width in x here by a relationship of this type. But it won't be exactly h bar over 2 in the generic case. It's exactly h bar over 2 just for these Gaussian distributions. But the really key idea is that the product of the uncertainties in these two things will be on the order of h bar. So there are two important points to make here. We need to be clear what we're saying. We are not saying that if you measure the position of an electron and then you measure its momentum, you will find results which scatter in this way. This is not the uncertainty of a measurement in x and then the uncertainty of the following measurement, the following momentum measurement. This is a statement about if I have a large supply of electrons, different electrons, set up so that they're pretty much in the same wave function. And I choose to measure the momenta of half of them and I'll get a dispersion of sigma p. And if I measure the positions of the other half of them, I'll get an uncertainty sigma x, which satisfies this relationship. Because this uncertainty in momentum is the uncertainty associated with the original wave function x of psi. And if I would measure the position of that electron, I would change the wave function into something near to a delta function centered on whatever answer I got. So when you make a measurement, you change the wave function. And we've calculated the dispersions for measurements using the same wave function, not an initial wave function and then the wave function that we get when we make the measurement. And the reason we've done this partly is that we do not know what the wave function is we get when we make the measurement. That's in the lap of the gods. You make a measurement. So remember the basic dogma. If we have, let's go back to the discrete case because it's simpler. If I have my wave function is sum sum a n e n, some linear combination of stationary states. This is a well-defined wave function. If I measure the energy, then this thing collapses to psi is equal to e k for sum k. And which k is in the lap of the gods? The apparition does not tell us. It's just a wheel is, the roulette wheel is spun. And one of the k's is chosen. So it is up here. If you measure the position, you will find some value. And after you've made that measurement, your wave function will be different. It'll be more or less the delta function associated with that x, not the wave function we're working with here. And the uncertainty on a subsequent measurement of p will be larger, will be large. The other thing to say is how do we understand this physically, this uncertainty relationship? We say to ourselves, well, if the wave function is highly localized in space, if you think about that wave function as made up as an interference pattern between states, between plane waves, which are states of well-defined momentum, then in order to have the interference pattern highly localized so that the sum of all these waves cancels to high precision everywhere, except in some narrow region, you will need to use waves with a very large range in wave numbers. And that's why the momentum is very uncertain if the position is rather certain. So it's because of this basic quantum, the basic principle of adding amplitudes, a highly localized electron. We're entitled to think about a highly localized electron as an interference pattern between states of different momenta. And we will need to have a very large range of possible momenta if we want to have a highly localized electron. And tightly defined confined interference pattern. Let us now talk about the dynamics of a free particle. So we've just got a particle whose energy is not there's no potential energy, it's just free to roam. So the Hamiltonian operator is going to be p squared over 2m. We drop the plus v of x, it's a free particle. And what we're going to do now is talk about the time evolution of this particle. So imagine that you've got the particle at t equals naught, you've got it localized around the origin. And let's zazz this up a little bit by saying it's localized around the origin, but it's moving with some, we've got some idea what its velocity is. So we're going to say it's initially, we're going to write down an appropriate expression for its momentum. So this is the wave function in, well, it's the complete set of amplitudes with respect to momentum of a particle which is localized at the origin and has no, the mean momentum is nothing. Suppose we start from p of psi is e to the minus sigma squared over h bar squared p squared minus p naught squared. Sorry, p minus p naught. Sorry, what do I want to do?  So it would be reasonable to conjecture that we'll find out whether this is true or not when we do the calculation. But the conjecture is, the reasonable conjecture is that this complete set of amplitudes characterizes a state of the particle where it is moving with momentum p0. p0 is a constant, right? This is the momentum eigenvalue. This is just some constant. So it has a velocity which is on the order of p0 over m. And it's localized at the origin to plus or minus sigma. We'll find out whether this is true or not, but that's the conjecture. Now let's ask ourselves what is the wave function in real space that corresponds to that at different times as a function of time? Why can we do this? Because we have a free particle, the Hamiltonian is just p squared over m, which means that a state of well-defined energy is going to be a state of well-defined momentum. The Hamiltonian is a function of the momentum, so it has the same eigenstates as the momentum. So a state of well-defined momentum is going to be an eigenstate also of the energy. Now we know how to evolve in time states once we, so remember our basic equation, which is that time t is equal to the sum an e to the minus i en t over h bar times en at naught. Remember, this was why we were excited by the states, why these states of well-defined energy, the stationary states are so important, is because they enable us to evolve in time a system where an is equal to en naught upside. These things set the initial condition for the calculation, and the time evolution is given by these exponentials. So we want to use this formula in this other context here. We know what this is. This is a state of well-defined momentum. We know what this is. This is just some exponential with the relevant energy going in there. And this is the amplitude to have momentum p. So this transforms, this is the discrete case, this transforms in our case into psi is equal to an integral over all possible momentum. That's the analog of the summing over the energies. When you sum over momentum, you are summing over energy because different momentum, all right? e to the minus i, what's this? This is the energy associated with momentum p. I called it e p up there, but we can be more definite. It's p squared over 2m h bar t, sorry, t over h bar, excuse me, t over h bar, right? That's the exponential thingy there. What's this got to be? This has got to be a state of well-defined p. And let's, we wanted to know what this looked like in real space, so let's bra through with x. And then this, sorry, sorry, sorry, I'm missing something altogether, excuse me, excuse me. Let's leave that out, I've missed something out. I missed out the a n's, didn't I? What are the a n's? It's the amplitude to have, at the time t equals naught is the amplitude to have energy en, which in our case is the amplitude at t equals naught to have momentum p, right? And then now we have the state p. And now if we want the wave function information, we should bra through with x. Then everything over here becomes a function of momentum and a known function of momentum. This is a function of momentum, also time. This is a function of momentum, we just put it down by conjecture, it's that thing there. This is a function of momentum, it's the, this is a plane wave, this is e to the i p upon h bar x within a sign, no it is exactly that. So let's just see what we get here. So this is a dirty grade integral dp e to the minus i p squared t over 2m h bar. Let's put this one, no let's keep it to the right order, e. Then here we have e, what we said it was going to be, e to the minus sigma squared over h bar squared p minus p0 squared over a horrible 2 pi h bar squared over 4 sigma squared to the 1 quarter power if I've got that right. And this thing is our wave function for a state of well-defined momentum, which is e to the i p over h bar, sorry, px over h bar over the square root of just h. So what do we have here? We have an integral of an exponential of a quadratic expression in p, right? Because here we have a p squared. When you square this thing up, you're going to have a p squared and a minus 2 p p, and a linear part in p, and here's a linear part in p. So it's another of these integrals of a exponential of a quadratic expression in p, which can be solved by the methods described in the box that we used just before. Now, the algebra in this case is a little bit weirisome. It's absolutely straightforward. It's absolutely straightforward, but it's just a bit weirisome. And the answer, in fact, that this comes to is quite a complicated expression, because what we're going to arrive at is something which has both phase information and amplitude information. But we only want to know what the probability is of finding the particle at this place or the other place. And that probability, the mod square of the answer to this calculation, is much simpler. And I'm going to write it down. So what follows now is a very straightforward calculation. I would urge you. There's box doing it in the book. I would urge you afterwards to look through this and make sure you understand it. But it is just algebra. And what's interesting is to understand the physical implication of this. So we're going to extract the mod square of the resulting of the answer when you've done all this integration. And what apparently it is is sigma over root 2 pi h bar squared mod b squared e to the minus x minus p0 t over m squared. I need to tell you what b squared is, don't I? And here, b squared is a complex animal. It's sigma squared over h bar squared plus i t over 2m h bar. So what have we got? This is a Gaussian distribution in x. At any fixed time, it's a Gaussian distribution in x. The center of the Gaussian is at p of p0 of m times time, which means that it's centered on what one would call v times time, because p0 over m, we said this was the mean momentum of the expectation value of the momentum of our original wave function. So it's the mean, if you thought of this as many different particles, it's really only one particle. If I thought it as many different particles, it would be the mean momentum. So this is essentially the mean velocity. So that's what you would expect. The probability distribution is moving in space with a speed v0 equal to p0 over m as we would expect. And the dispersion associated with this Gaussian is determined by that stuff. So we have a sigma as a function of time, which is going to be given by, so what should this be? This should be 2 sigma squared. So sigma is going to be given by the square root of those two, which is going to be from this, sigma squared plus t squared. I better write this down. It's too hard to do it in one's head. Plus h bar t over 2m sigma. Yeah, sorry, this should be another sigma. What should we call this? This should be called, well, let's just call this the dispersion. Well, we can call it sigma sub t. Whereas this other sigma is the original sigma. So we've got a Gaussian distribution. And that has a dispersion given by this. Sorry, sorry, sorry, there's something wrong here, isn't there? Because on dimensional grounds, yeah, yeah. Did I write down the right integral? No, I didn't. That's exactly what's gone wrong. Sorry, we're missing from here a sigma squared on top. That's crucial. So when I say what the dispersion should be, we should arrange this as 2 pi dispersion squared. So dispersion squared is equal to this divided by that. Sorry, then I have to square root it. So it's divided by that, which makes it that. And this I've copied out of my notes. And I expect it's still right. But I was trying to do some of this in my head, which was dangerous. So what do we got? We've got that the dispersion at time t is equal to the original dispersion at time t0, plus this extra bit here. And what is this extra bit here? What was the original uncertainty, the original uncertainty in momentum from the uncertainty principle here? The uncertainty momentum was equal to h bar over 2 sigma. So the uncertainty in the velocity was equal to h bar over 2 m sigma. So what's this? This is equal to sigma, plus the uncertainty in the velocity times time. I shouldn't be squaring this, should I? I think we might need to take a square root of square, actually. Let's not chase that down in the moment, because this is the basic idea. The basic idea is the uncertainty in position is growing like the uncertainty in position times velocity. But that's what you would expect, because what do we have? We have a bunch of particles originally at the origin and moving to the right with v0 plus or minus delta v. Some are going faster, some are going slower. At some later time, this is moved over by an amount v0 times time. And this width of the, there was a width sigma here. But the ones that were going slower than the average will have slipped behind. They were already, some of them will already been sigma behind, but then they've slipped behind extra by an amount delta v times t. And some of the ones which were in front have got even more in front, because they have, they had bigger velocities by delta v. So that the total width is equal to the original width plus this extra width, and I think probably we should be taking some squares and square rooting. But you see that what we're getting from this calculation makes perfectly good sense physically. Let me just remind you how we've done this calculation, because it's the methodology which is, in many ways, well, it's good to see. It's crucial to see that what emerges from this makes sense physically, but it's also good to remind yourself, how do you actually calculate these things in this damn theory? The way we've done this is we've used this central expression. We've said that states, I can evolve something in time so long as I can express my original state as a linear combination of states of well-defined energy. In this particular case of a free particle, a state of well-defined energy is exactly the same as a state of well-defined momentum. So we wrote that sum expression in the integral form that's appropriate, because momentum has a continuous spectrum.  I think we're probably pretty much ready to finish. Again, I want to stress, I think I should stress, that we've obtained this perfectly sensible physical picture through an orgy of quantum interference, because in order to get what we wanted, we took a perfectly well-defined spatial distribution and expressed it as an interference pattern between states of well-defined momentum, which we then evolved each state of well-defined momentum in time in its trivial way, just that exponential. And then we allowed them to interfere at this later time in their evolved form to find out what the distribution was in real space. So that's what I mean by it's an orgy of quantum interference. We've taken something, we've decomposed it into an infinite number of other things. We've taken something physical. We've decomposed it into an infinite number of things which are not really very physical, namely states of well-defined momentum. We've evolved each one of those independently in time because they are states of well-defined energy. And then we've interfered the evolved momentum states. We've allowed, by working out this integral, was working out the results of the corresponding interference. We were adding up an infinite number of amplitudes and allowing them to interfere and out comes something that makes sense, which is a wave packet that's traveling and spreading and behaves in a way which does make perfect sense from a physical point of view, from a classical physical point of view. Okay, we'll finish with that.


Greetings, aspirants. I welcome you all to another video of Frequently Asked Questions series. This video is brought to you by Shankar IAS Academy. As you all know, in this particular series of FAQ session, we try to address the common queries among UPSC aspirants regarding this UPSC examination. So, in that line, today I have a wonderful question to discuss. Let me read out the question for you. Does Shankar IAS Academy recommend some non-academic books for UPSC aspirants? Yes, we obviously do recommend you to read some non-academic books and I am here to tell you about the top 5 picks that an UPSC aspirant must read. Let me read out the book list for you. The first book is PAX INDICA written by Shashitaroor. The second book I would recommend is 21 Lessons for 21st century written by and the third book I would recommend is India Unbound written by and the fourth book I would recommend is argumentative Indian written by and the final book I have to recommend you is a brief history of time written by Stephen Hawking. So, now let me tell you why you should read PAX INDICA written by Shashitaroor is a person who does not require an introduction. So, just look at the title given by him to this book PAX INDICA. Here PAX means a period of peace that has been forced on a larger area like an empire or even the whole world by the most powerful nation at that time and here INDICA is the Greek word for India. See every country has their own PAX time. Yes, for example, the world-witnessed PAX Britannica during the 17th, 18th and 19th century British Empire was the most strongest and the largest of all empires. Later, Suez Canal crisis of 1956 marked the end of PAX Britannica. The 28th century was dominated by USA which can be indicated as PAX Americana and through this title PAX INDICA India and the world in 21st century the author is signaling that this is the time for India to foster peace in the world by overseeing the state of affairs in the world. So, the term is an aspirational word and the term reflects our global aspiration and this is the exact reason why you should read this book. As an aspirant, you can understand the geopolitical situation in various regions of the world and its relationship with India. You can get a hold on numerous disputes, conflicts and solutions to such disputes, especially in Indian context. Since it is a simple primer on India's foreign policy by one of the most popular writer, explained with ease, this is a must-read book. So, now let's move on to the next book 21 Lessons for 21 Century written by Yuval Noah Harari. Now, he also does not require any introduction because he is an author of one of the best-selling book titled Sapens, A Brief History of Humankind. So, now coming to the title of this book, as the name itself suggests, this book actually gives 21 lessons for the 21st century. The book tries to give some clarity to the readers about the current events and the immediate future of the human societies. That way, this book helps in leveling the global playing field. Answers to questions like, what is happening right now? What are today's greatest challenges and choices? What should we pay attention to? What should we teach our kids or some of its highlights? So, this book read, writes, in a world deluged with irrelevant information, clarity is power. So, as a UPSC aspirant, you can learn how to present a topic wonderfully from this gem of Yuval Noah Harari, a simple and the easy-read book. The next book I'm going to talk about is India Unbound written by Gurcharan Das. See, this book talks about the transformation of India from the birth of the writer in 1942 to 1999. The author mainly speaks about the politics in India and the economy in India during that period of time. Since the author classifies the entire timeline into three major sections, the book is a great mixture of memory, economic analysis, social investigation, political scrutiny and managerial outlook being thrown into the understanding of India. See, though the book looks a little bit outdated, the core concepts of the book have passed the test of time. So, as a aspirant, you can learn and understand what liberalization has done to India. So, now moving on to the next book. The next book is The Argumentative Indian written by Amitya Sen. We all know about Amitya Sen for his key contributions to the research on fundamental problems in welfare economics. In this book, Sen argues that understanding and applying argumentative tradition is crucial for the success of India's democracy, the difference of its secular politics, the elimination of inequality based on class, cast, gender and community and the pursuit of the subcontinental peace. See, it is an excellent book but not in the simplest of language. So, I would not recommend this book to the persons who are going to give their first attempt and for those persons who does not have and knowledge about Indian society and their past. But those who have a basic idea of India along with the command of English, this book is a gem. And the final book in the recommendation is A Brief History of Time which is written by Stephen Hawking. In this book, A Brief History of Time, Hawking writes a non-technical term about the structure, origin, development and eventual fate of the universe which is the object of study of astronomy and modern physics. Apart from this, the author writes about cosmological phenomena like the big bang and the black holes and he discusses two major theories. One is general relativity and the other is quantum mechanics. Since this book has so many takeaway points, reading this book will take you to enlightenment. So, here we are nearing to the end of the video. So far, I gave you recommendations what to do. Now, I will tell you what not to do. Please don't go and buy all the books and become a Sudanku. Sudanku is a person who owns a lot of unread literature. So, if you are asking me what I should do, I would recommend you to choose one book at a time. Just go through the book, write down some catchy codes or interesting examples and illustrations. You can use all of them in your main examination wherever it is required. See, we recommend all these books just to help you to expand your horizon and give a wide intellectual thinking. So, don't waste time in reading these books alone. Just read these books whenever you get time in between your preparation. I hope you loved this video. To know more videos like these, just subscribe to Shankara Ayes Academy YouTube channel. Now, very, very thank you for listening.


I thought we were a little sharper this morning to tell you the truth. I was very, very pleased with how we played against Catholic. I felt like we were really hitting on all cylinders. The defense was really good, and I was real pleased with the way we played against Catholic. St. Mary's, I thought, are serving. We were really sharp as far as our serving goes. We were a little bit off, I think, hitting, but it wasn't terrible. Our defense again was good because I think they hit OOO, so defensively we did a pretty good job, and I thought we did a good job sealing the net with lots of blocks. Yeah, that was because we jumped off to that big lead immediately. We were up 9-2 and we were blocking, and I'm having a good old time. I mean, they're not going to give up, and I think we just kind of let down our guard a little bit, and they got back in the game, and St. Mary's a good team. So they were able to put some balls down against us and got a little bit of momentum, and of course they're playing Steven since they kind of got excited.  No, no, we're definitely gearing up for our big match on Tuesday, and I thought we had some really good, we had a whole week of practice. We didn't have any matches this week, so I think that's why one of the reasons we were so sharp against Catholic today.


What's going on everybody this is Giovanni from the options training channel the inevitable Finally happened with me in it on the right side of the market Finally, it's about two minutes until the opening bell for the markets here And the cues have gapped up over a dollar from yesterday's close. I am still holding on to one Option one call option of the 223 50 calls. They closed at 286 by 293 yesterday Let's see up. Let's see where they open up today. Let's see where I end up selling Alrighty markets have opened here. Look at that trading 3 19 markets Let's see what happens here where we go from here and I went ahead and 320 320 I sold I'm happy for that. We are good. We are good That's awesome. We're we're completely out of that one Fill 320 awesome awesome trade there Absolutely without a doubt happy about that my original by order was 264 My highest sell order was 320 and it's gonna go up from here But I can't sit here and watch it all day. So I sold and I'm happy with this new all-time highs For the markets here this morning Really happy about it already guys. Well, I'm gonna head to work gotta go back to reality 2000 years later What's up everybody? I am so sorry that I haven't been able to get this video out to you Quicker I've been feeling under the weather and I just wasn't up to finishing this video yesterday And so it's about 1134 my time in the morning And I'm just now getting around to feeling a tad bit better enough to finish this video So let's talk about this last trade that I made but I bought two of the 223 50 calls that expired at the time in eight days at 264 put in a limit order at 290 it executed after hours that day and in the very next day the Markets capped up and I was able to sell for 320 this sell right here at 320 was for a 20% gain Altogether I was able to make 15% Let's talk about it really quick I'll make a video at a later date Explaining just a couple of key things about this particular Strategy the MOBO band strategy You can see here the middle chart This is the one hour chart on the cues off to the right This is the daily chart on the cues and off to the left is the intraday one minute chart of the calls that I traded You can see here that the Particular strategy this particular strategy has actually counted this trade as a losing trade a bad trade This comes to show you guys that with great money management skills You can turn a bad signal into a good signal now. It's not gonna happen all the time But this is a prime example of that This particular strategy you just you can't account for that You can't tell the strategy to you know sell at X gain and So on and so on so you just have to get better at managing those trades Prime example great example here And you can see that the high of the day of those options got up to three twenty three thirty five excuse me and Man, I mean they plummeted Completely down to as low as what's that low a dollar forty five went back up and then back down But check out the five minute charts on the cues Look at that ginormous drop there Huge drop you can made a lot of money to the downside, but of course we don't trade Fighting the trend and if we go back to the daily chart You can still see that we're still in an uptrend You got fairly close close than it has been in quite some time This was back on the 6th of January when we got really close and almost touched that lower Bollinger ban But you can see that we've been in an uptrend boy since December 6th Huge rally in the markets here, but we'll see what happens Basically in a nutshell really quick. We only trade in the direction of the daily charts That's the only direction that we trade and we trade the one hour charts, but thank you so much everybody for watching again I'm so sorry that I couldn't get this video out to you quicker. Just not feeling very good I think it caught a cold so hopefully the next trade is a green trade. Let's keep this going Let's make 2020 the best year yet guys. Thank you so much everybody for watching. I will talk to you guys later


is terrible. He wrote Oz for us. He wrote Wonderland for adults. He wrote Neverland for grown-ups, and why I don't think it's that good. Neverwhere is less than most of its parts. Neverwhere by Neil Gaiman is a very, very popular book. It's one of his best known, one of his most beloved books, and I like it. I've read it three, I've read it as many times as I have copies, which is not on purpose. But yeah, Neverwhere. It's um, I've read it several times, and it is so light. And I found myself, you're wondering why it doesn't really work for me that well, and because I've read it now so many times, I think with each time that I've read it, I've narrowed it down more, why it is that this book is so popular, but why it doesn't really work for me, and why I don't think it's that good. I'm going to make an argument for it being objectively less good than some of his other books, but of course, reading is subjective, art is subjective, so if it's your favorite book, nothing I say can really invalidate that. So basically, I've come to the conclusion that Neverwhere is less than the sum of its parts, because there's a lot of individual things about Neverwhere that are really, really great and are the very things that I love Neil Gaiman for, but the way that it all comes together or doesn't is what keeps it from being a favorite of mine and what keeps it from being what in my opinion would be more objectively one of his better works. So Neil Gaiman's prose is one of the things that I love him best for, that's why he's my favorite writer. It's not necessarily that the stories he tells are always my favorite stories, they very often are not, but I am always impressed with his writing. I don't think I've ever read a game in a book where I wasn't impressed with the writing, with the prose itself, and that remains true in Neverwhere. Neverwhere, there's some really excellent bits of writing. I often praised him for the way that he zeroes in on very specific things about characters, situations, people, like people at large, what it is to be adult, what it is to be a child, all these kinds of things. He really, he pinpoints very specific things about them to where he does not have to tell you paragraphs and paragraphs, pages and pages about displays or this character or this situation. He can get away with being very brief, very concise, and just telling you this like one thing about this character and you now have an image in your mind.  So I do have some examples, like the way that he describes Mr. Vandimar and Mr. Krupp. There are four simple ways for the observant to tell Mr. Krupp and Mr. Vandimar apart. First, Mr. Vandimar is two and a half heads taller than Mr. Krupp. Second, Mr. Krupp has eyes of a faded china blue, while Mr. Vandimar's eyes are brown. Third, while Mr. Vandimar fashioned the rings he wears on his right hand out of the skulls of four ravens, Mr. Krupp has no obvious jewelry. Fourth, Mr. Krupp likes words while Mr. Vandimar is always hungry. Also, they look nothing at all alike. And then further still about Mr. Vandimar and Mr. Krupp. They were the kind of suits that might have been made by a tailor 200 years ago who had had a modern suit described to him but had never actually seen one. The lines were wrong and so were the grace notes. Now Mr. Vandimar and Mr. Krupp are these sort of like sinister antagonist henchmen type figures that appear throughout and everywhere. Those are just two examples of how they are described. They are described that way in that style throughout the entire book. So you don't need a ton of elaborate specificity. It's in the absurdity of the descriptions and in the inherent sort of irrationality to how they look and also how the narrator is describing them that gives you a sense of their vibe beyond just their clothes. I mean in essence those were just descriptions of their physical appearances and yet I bet you have a sense of their vibe and the the tone and the the impression you should have of them as characters not just of what they're wearing. The next example isn't as good. It's about the lady door. She looked Richard thought as if she'd done a midnight raid on the history of fashion section of the Victoria and Albert Museum and was still wearing everything she'd taken. So I mean here again like the the brevity is insane. Like he a different author would have said oh she was wearing this which was from this era and this which was from this era and this which looked like it was from this era and this was shabby so it looked like it was genuinely actually old and and this here looked like it was a little bit newer but also like it probably had been worn and none of it matched and you could just go on and on and on and on or you could be Neil Gaiman say it looks like she raided the history of fashion section of the museum and is still wearing everything and bam you have an image in your mind of what that is and also the type of person that would look like that. Then my example of his description of Jessica is actually a description of Richard I guess who's our main character but in this way he is describing to you who Jessica is as a person and Jessica saw in Richard an enormous amount of potential which properly harnessed by the right woman would have made him the perfect matrimonial accessory which I just feel tells you so much about Jessica as a person like I personally have an image in my mind immediately of the type of person that Jessica is even though ostensibly that's a description of Richard here's another example where like we are sort of describing Jessica incidentally so this example is from Richard meeting Jessica for the first time and he's in a museum in France he'd tried to apologize to her in French which he did not speak gave up and began to apologize in English then tried to apologize in French for having to apologize in English until he noticed that Jessica was about as English as it was possible for any one person to be like just this short sentence I feel like if you've never read Neverwhere you still have a pretty good image in your mind right now of what Richard is like and what Jessica are like and you've just had like a few sentences so like I said I'm ceaselessly amazed by Neil Gaiman's ability to just very concisely convey so much to you beyond what he is on the face of it actually telling you and that is true in Neverwhere uh next his approach to magic and the inexplicable is again I very much like his approach to that in general and I like his approach to it in Neverwhere magic is inherently illogical and I like that Neil Gaiman unlike many other writers of speculative fiction he leans into that he fully embraces the fact that magic by its very nature cannot and should not be made sense though so he leans into making it make even less sense so rather than coming up with like wordy explanations for how this thing that is to be magical it has to be impossible uh at least as far as our natural own real world is concerned so instead of going jumping through trying to explain this impossible thing and how the rules of this universe make it possible he instead draws attention to the inherent impossibility of it and is like yeah and it's and you know what it's happening this thing is completely impossible let me remind you how ridiculously impossible this is and you know what else this thing is currently happening so for example when it comes to angels Richard did not believe in angels he never had he was damned if he was going to start now still it was much easier not to believe in something when it was not actually looking directly at you and saying your name likewise when we're talking about a library that is to be found in London below another character is saying he's meeting us in the library Richard was almost proud of the way he didn't say what library or point out that you couldn't put a library on a train instead he followed door towards the Earl's empty throne round the back of it and through the connecting door behind it and into the library here again like another author might have gone on and on about how this tiny tiny train impossibly it's bigger on the inside fits an entire library in it and when you went through this tiny door then you opened into this expanse that is way bigger than it should be because this fits an entire library into it but the train on the outside looks like a normal so you could go on and on and on and on about that and you and it would be you know possibly immersive and imaginative but Neil Gaiman simply has his main character say you know what I'm not going to say that that's impossible you know what I'm just gonna accept that this impossible thing is about to happen to me and then all of us in the audience can also imagine the utter impossibility of a library fitting in a train no perhaps I should have started with this in case you've never read Neverwhere um but the concept of Neverwhere I also think is very very cool so the concept of Neverwhere if you've never heard of it never seen it I say seen it it was originally television show and we'll get to that as well Neverwhere even though it's called Neverwhere the actual place in his portal fantasy is not called Neverwhere it's called London Below and in essence Neil Gaiman was like so there's all these great portal fantasies right for kids there's Oz there's Wonderland there's Neverland and so he wrote Oz for us he wrote Wonderland for adults he wrote Neverland for grown-ups that's what London Below is supposed to do and be and as a concept you know that's I love it because I love those kinds of stories and there is he's right something inherently magical about that kind of a story that's why we have so many but London Below is terrible the fun of those other portal fantasies is that however dangerous and sinister and macabre some aspects of them are and they put you know their protagonists into some alarming situations that realistically you probably wouldn't want to experience nevertheless they are wondrous places that like a theme park would happily recreate for you and that you would kind of like to imagine going there like flying to Neverland I certainly dreamed about that when I was a kid I was less of a fan of Wonderland but again Wonderland is like pretty kooky and crazy and cool and bizarre and like you'd want to see all these crazy wonderful things that Lewis Carroll describes and going to Disneyland in a place that makes you feel like you're in Wonderland is something you would desire to do similarly the Wizard of Oz like the Emerald City and Munchkin Land like these are places that like the Wicked Witch is pretty scary and realistically you would not want to be confronted with the Wicked Witch but going to Oz sounds fantastical and fun and imagining that you could do that is something that you'd like to imagine the world of London below in Neverwhere is it's horrifying it is a place of nightmares it's not like kind of terrifying but mostly wondrous it's mostly terrifying and not not really wondrous it's just like absurdly terrifying and I don't I mean reading Neverwares it's not that scary a book I wouldn't say but it's just it's really deeply unpleasant the idea of being in London below if you visited the London Underground or really any subway station it's it's like what if that was magical but was still grimy and dirty and and filled with rats and filled with like smelly people and close confines and strangeness and rudeness and death and danger and no one is very nice and everything is awful and dingy and dirty and awful and scary and nightmarish and the rats are in charge you have to not only encounter rats but you have to like obey the rats which again I mean if he's going for topsy-turvy sure obeying the rats is pretty topsy-turvy but I don't think that's fun to imagine that like the initial impression of like oh how funny the rats are actually in charge down below like I get it but also like get me out of here so in these other portal fantasies like Alice in Wonderland like Wizard of Oz like like Neverland or Peter Pan with Neverland in it there is this kind of sense of like we're gonna have to go home at the end but like oh what a shame that we have to go home what a shame that we can't live forever in Wonderland in Oz in Neverland like that you'd want to be there that you'd want to go back that you're sad to leave it and leaving London below is like the sooner the better so um my own spoilers but like when we're reaching towards when we're getting near the end of Neverwhere and we are presented with the possibility of leaving London below forever like I don't I feel like the book wants you to have this feeling of like oh what a shame that is and wouldn't it be nice to stay in London below but like no it would not be nice to stay in London below I would never ever want to be in London below again like whose dream is this if Universal Studios or or Disneyland was gonna recreate the London below experience as a an area of the park or as a theme park attraction I'd be like no no one wants this next Richard the main character the problem with Richard is that he's not much of a character in a lot of these portal fantasies you know Dorothy or Alice or or even Harry Potter and the the portal fantasy that is the wizarding world they are often audience surrogates to take you on this adventure to be your way to get into this wondrous world this portal fantasy but they still usually have a want they still usually have something that they're trying to do or that they're specifically trying to run away from or whatever it is I mean like Dorothy in the wizard of us she is trying to find the wizard so that he could send her home like she has a stated goal and desire and now she's going on this adventure and it takes her off course but like she's trying to get to the wizard so he can send her home like she has a goal and so that like gives drive and purpose to the story Richard things happen to Richard things happen around Richard Richard reacts to stuff that's happening near and around him and the lady door who he is with she does have a stated goal and a want but it gets not one that Richard fully understands or would have any real reason to be invested in seeing done because she's kind of nobody to him so it's almost like um if instead of following Dorothy you're following like the scarecrow who's like decided to help Dorothy but like it's Dorothy's quest so like Richard is like along for like doors quest but so then door should be the protagonist but door is already part of London below so like she can't be our intro to this like portal into this other world that's Richard the normal guy you get swept into this other world but he doesn't have a stated goal a stated purpose I mean I guess he vaguely is like I would like to go home kind of like Dorothy but like no one is really giving him an ability like a a way to do that and so he's not like trying to like go see the wizard so he can go home or something he's just he's just kind of helping door because door needs help so I guess that's what we're doing cool and this works a little bit better on television where one a charismatic actor can kind of make up for that lack by just kind of like being a dynamic personality this can make for an an effective surrogate for a reader if you are you know a reader can and see themselves as this average person that gets swept away into this world but because he has no stated goal or purpose there's just like a lack of tension and stakes like there's like what are we doing like what are we trying to do what are we trying to prevent like there's nothing we are vicariously striving towards alongside Richard we're just like we become just as passive as Richard is in this story and a passive reading experience is not an engaging one which is why I think the world of London below and this story like I don't feel sucked in by it because I'm not swept away on this quest I'm not engaged in this quest I don't feel any stakes for this quest like I okay Richard is in the an awful magical subway that does sound yikes like I wish him the best I don't I don't feel any investment in that or enticement to go on or see how this unfolds so lastly Neverwhere was actually originally written for television and that I think shows and I think that is part of why it doesn't work as well because when you're writing for television certain principles about storytelling remain true no matter what the medium is but there are certain things about storytelling that your your priorities will shift depending on the media and in visual mediums like film television or stage basically almost any medium but books some part of your priority is having something be visually appealing or visually enticing or visually exciting and in a book unless it's a comic book it's harder to do things that are just purely visually appealing certainly there are writers that are famous for their sort of lyrical beautiful prose in lush worlds they describe Leni Taylor which I personally love I don't like Aaron Morgenstern but I know that's what people get out of Aragon and Morgenstern's books action scenes are this way I often don't like action scenes in books because like it's again like okay it's fun to watch an action scene in a movie because you're actually watching two people do something that's really impressive to look at you know it's it's like watching gymnastics in the Olympics it's seeing them actually perform this feat that's impressive if I read a book where it says like they're able to do a handstand I'm like cool they're able to do a handstand great but like it's I'm not seeing it so like it's not that engaging whereas in a film it would be so there's a lot of stuff in Neverwhere that feels like it was written for the screen in that way that like this was this scene was written the way that it is because this would make for an interesting visual a cool action sequence a cool moment on screen and that certainly should be your priority if you're writing a story for television but when Neverwhere became a book that's less effective likewise the story feels very episodic and it was written as a television show so having Richard just be kind of this like baseline character that's just like your average dude who's in this strange situation but we're kind of like episode to episode kind of just seeing different weird parts of London below and different weird stuff is happening that like works better as a TV show where we don't have to have this like driving narrative like in a book where Richard is just kind of our eyes our reason for the audience to like be seeing this scene but we're not seeing a scene in a book we're like living this scene through Richard if Richard is not interesting then we're not gonna have an interesting time and I mean Richard is not the only one lacking in this regard I did give examples of his descriptions of characters which I do think are very effective and if it wasn't for that this truly would be a snooze fest because despite that I mean like the other characters they they're even less characters than Richard is and he's not much of one I mean like who is door she's like both an inciting incident and a plot convenience and plot device wrapped up into one person she's not a person or a character that you really like feel you know or have a reason to root for or like has layers and complexity like she comes into Richard's life is the inciting incident is the reason that he ends up in London below and then because she has magical powers then she's also the like the way that magical plot convenience has happened she's the exposition because she can go around explaining London below to Richard she's just like she like is a functional piece of the story more than a character and Richard he's an audience surrogate and the rest of the characters are even less than Richard and door they're literally just in each individual scene or in each individual episode of this television show this would be the episode in which we meet this weird quirky character this weird quirky place this weird quirky thing and that's kind of what we do in this episode then we move on to the next thing which in a show works a lot better than in a book now there are some truly poignant moments and thought provoking moments in the book which is why I still do give it four stars so a moment that comes to mind is Richard's or deal with the friars that is quite a weighty moment but the reason that it's weighty has almost nothing to do with the story the story itself has no meat to it when this story manages to when we're in this book manages to get an emotional reaction out of you it's almost 100 percent down to Neil Gaiman's ability to employ a turn of phrase that in itself is something that strikes you that resonates with you that hits you in some way it's it's the sentence itself it's not this moment in the story doing it to you the moment with the talk of the incident with the friars the ordeal that's a little bit more of the story doing it for you but even then it's more this the specific ways in which he phrases things in that scene that hit home and so that's why the book is good it's Neil Gaiman's writing but it's specifically like his prose and him being a wordsmith and him just constantly just serving truth is about life in every sentence but the story itself doesn't do anything doesn't have anything doesn't there's there's nothing to pull and hook and mesmerize and transport film and so that's why i feel that it is less than the sum of its parts you have an excellent writer who has some of the best prose around you have a really cool concept in this this portal fantasy for adults a very creative handling of how magic would work in this scenario to make it very creative and bizarre and and witty and and it just kind of feels like a collection of things rather than a story so even though i would give high marks for all of these things again i gave high marks for the descriptions of characters but the characters themselves aren't much to write home about give high marks for prose but the writing of the story isn't much to write home about i give high marks for where the world is the world building is done and described and how magic is described but it's like a horrifying place to be so like i don't want to be transported there so it's it's a very mixed experience in that sense what it does very well it does exceedingly well because it's game and doing it but it's so flawed and so held back by both the origin of how it was created and just like generally some issues with how it's structured that it will never be a favorite for me for these reasons but i get why it could be for others if you do feel transported and excited to be transported to the world of London below i do not understand you but like if that's true for you i get why you like never wear if for some reason something about Richard really resonates with you because there's not that much there but if what is there just really does work for you and you really latch on to Richard like i get why then this book might work better for you if you really resonate with Richard but yeah i don't really get why anyone would super love this book and other people do so maybe you can tell me why you're one of them so let me know in the comments down below your thoughts and feelings about never wear if you have read it if you want to read it if you've never read it if i'm convinced you never to read it i hope not because i do think it's a good book and i do think it's in it it it's quality but i just i don't think it's nearly as good as it could or should be based on the list of what's in it and frankly because the tv show is so old i find myself thinking never wear would make a really good adaptation which feels weird to say because it's a it was adapted from a tv show into a book but now that we have the technology i think we should re-adapt it into a tv show but you know better so as i say let me know in the comments down below your thoughts and feelings whatever you want me to know i post videos on saturdays at the random times as well definitely saturdays so like and subscribe join my patreon if you feel so inclined and i'll see you when i see


But then we started the formal part of the test which is to have somebody else come into the room while you're out of there and by a random means by choosing a counter out of a bag which is what we used. We used poker chips numbered from 1 to 10 but then place it in the appropriate cup, turn the cups all down and then leave the room and we would come in and he would and so I wouldn't know where it was. I couldn't give any clues subconsciously or consciously and he got one right out of ten which is exactly what you would expect by chance alone and of course he was the most astonished of everybody because he'd never really tried it in a double blind test like that and then he said of course oh I see what it is this encyclopedia on the shelf here has gold stamping on the cover and that's what distracted the stick I said wait a minute but you did 20 of them and you got 20 out of 20 when you knew where the gold was and he said oh yes well that's because we were a little further away from the encyclopedia I said no that encyclopedia that is not gold it's gold color but it's not gold believe me and he said well there must be some gold behind it in the wall we haven't turned our wall down to see if there's any gold in there well you better do that yes I have a rush home and do that by the way well just amazing now then we moved to sort of another group of people who are out there sort of well I guess there's no sort of about it they're out there actually fleecing people and and you wrote a book about it called the faith healers yes and boy there's a lot of them out there there were a lot and there's a lot that have come along in recent years to replace those that have gone oh yes and I want to hear a little bit about well first of all WV Grant from a few years ago who was one of these healers if I have my notes right I think he was the one that referred to a Dr. Jesus or was that well most of them use the expression Dr. Jesus but he was very big on Dr. Jesus hallelujah but he was one of the people I mentioned my book the faith healers which is currently on sale and available at your bookstores the faith it is the book itself didn't make much of a stir because people who want to believe in this thing won't buy the book they don't want to see the evidence and people who don't believe it by the book and they say yes exactly what I expected there's nothing there the faith here's don't feel a thing that they don't heal anybody pardon me the faith here's don't heal anybody they have lots of faith but they don't heal anybody and I think I've never met one that is not an outright conscious crook because they use gimmicks to make it appear as if they've healed people such things as telling you to stand up and walk out of a wheelchair which they'd never been in before in their lives there was seated in the wheelchair that they didn't need to sit in and when they stand up the audience thinks wow that person is healed that person knows that he or she isn't healed but they don't give away the actor they do that part of the tape reverting is not used on the air you see they're they're crooks and they deserve to be locked up in my opinion WV Grant was very big on this sort of thing and he used all kinds of the standard gimmicks that have been used for a couple of generations now by the faith faith leaders to make people believe that they really can do what they say they can do and there was Peter Popoff and such you saw that I demonstrated him at the lecture the other night and I put Peter Popoff out of business he declared bankruptcy went out of business for a short time but now he's back on television again because people forget they want and they need to believe that it's true you see so they forget all the negative evidence and WV Grant actually did get locked up for income tax evasion perhaps because I brought the attention of the IRS to him I don't know but in any case he got locked up he's now out and I'm sure he'll be back at it anytime at all because it's the only talent he has so he wasn't locked up for conning people he was locked up for yeah it's like Al Capone they got him for the wrong thing you see but they got him now the Peter Popoff case was very interesting because this was a national story it broke on the the tonight show with Johnny Carson and millions of people saw that and which was a great thing it put put pop off out of business almost immediately tell us a little bit about sort of how that operation worked I know you went in and had to do a little bit of investigation to find out exactly what technique he was using yeah we it was pretty evident to us from the beginning we saw that he was using the usual interview techniques which is hours before they start the video taping on the actual services they call it I call it a show what they call it a service they have people wandering around the audience interviewing people what is your problem and he what is your address you live where and this kind of thing this is all being picked up backstage and stored and then being fed back to him when he gets out on the floor through a concealed hearing aid you see so that was the gimmick that he was using it's supposed to be the voice of God it was the voice of his wife backstage residing this whole thing to as you saw from the videotape that I used for the Carson show and by the way Carson remembers that very well I spoke to on the phone several months ago and the first thing he brought up and she says I'll never forget the pop-up episode I said you remember that no you said oh do I remember that I'm still talking about it it's the most amazing piece of footage when you when you see the original well just a clip of it that aired and then you see that same clip overlaid yeah with the soundtrack in the background of what he was hearing yes through his ear it is astonishing isn't that because at first you could say wow that must be a miracle he couldn't know these things yeah God must be speaking to him but God sounded like his wife to me and moving and unfortunately he's back on television is there anything that can be done to get these people off the air yeah get smart and don't tune in and don't buy the products and whatnot don't send money to yes there is something it could be done but you can't get the government to do it because as the Attorney General of California at the time many years ago told me I'll never get reelected if I come out against minister anybody reverend anybody I don't care whether he's a real reverend or not and I asked him I said is it your job to get reelected or to do what you were elected to do in the first place and that that made me pay the lunch field because he got up and left in the Huff so but no it's very difficult Tony to get the government to do something about it they'd rather just ignore that and say okay sure it's not disturb that whole situation they'll get them on income tax but they won't get them for being crooks and taking money dishonestly yeah I have to admit this subject really fascinates me because I was brought up in the fundamentalist atmosphere as a youngster and and to see this perpetuated and new generations falling for the same things that have been happening for years it's just too bad well don't don't assume that all religious people are crooked not by any means of course but there are people in the in the trade the most prominently known ones and such who are and that should be stopped by by legal processes and we should have that protection from our government and we haven't got it now one of the current ones on television is a fellow by the name of Benny Hinn oh yes and I want to talk a little bit about his technique I've done a little bit of reading research I know there's some folks out there who believes that he uses a type of hypnotism or mesmerism to get these people to fall over and I want to talk a little bit about that and your opinion on that well it's known as slaying in the spirit it's very common in charismatic movements and such and people who go to these services know what's expected of them when he gestures at them they're supposed to fall over and you'll sometimes see them look behind and make sure there's someone there to catch them sometimes they're not too sure but Benny Hinn's people are rehearsed on the staircase on the way up onto the stage where the cameras don't show them when the rest of the audience can't see them that's way below that level and they're told what to do and when to do it and how to do it and when by the time they get up on stage all he has to do is turn to them ago like this and they fall over all mass that there was a time when the evangelist used to do it to one person alone be healed hallelujah and whatever they'd fall over but Hinn just goes out there and goes whoops like this and four or five of them fall over at one time and the people standing behind them if you are up close enough to hear as we were on many occasions they'll say no just now kind of thing so they know that they're supposed to fall over and they know they'll be caught and laid out on the stage and slaying in the spirit it's called it's strictly a gimmick it's choreography and it's very effective for the people at the front who don't know what the gimmick is yeah and the people watching at home on television oh yes of course that's the main thing of course yeah because those tapes sometimes they'll go for two and a half hours just to get 30 minutes of tape that they can use now I've heard you talk a little bit about sort of a an expose or I guess you were on a documentary


Fire is the visible effect of a chemical reaction called combustion. Combustion produces heat and light through oxidation, which is the rapid combination of a specific substance with oxygen. We can see oxidation every day. The browning of the inside of an apple is an example of slow oxidation, as is the green color on copper. The Statue of Liberty was originally copper-colored, but oxidation turned the brownish metal to the green we recognize today. Rapid oxidation has much more immediate results. Fire occurs when oxidation is combined with combustible materials and high temperatures. When this process is particularly fast and violent, an explosion can be the result. Even so, combustion only occurs when the right conditions are present. Three components are required for combustion to take place. Air with at least 16% oxygen, fuel or combustible material, and a high temperature. These three components make up the fire triangle. Combustion cannot occur if one component is missing. So why is the fire triangle important? Fire can sometimes be dangerous and devastating to nature, wildlife and humans. When a forest is dry and surrounding air has little humidity, a large fire, such as the Los Conchus Fire of 2011, can grow very quickly and be difficult to stop. Firefighters can use the fire triangle to help extinguish fires. They can remove oxygen by smothering the fire with flame retardant, such as slurry dropped from planes. They can remove heat by cooling the fire with water, and they can remove fuel by digging a fire line or starting a backfire to starve the fire of fuel. While uncontrolled fires can be dangerous, natural fires are an important part of nature and can contribute to the Earth's natural life cycle. As more people move to wooded areas, understanding fire and combustion can help us prevent fire disasters.


Welcome back. Here is another morphological tree I want to generate with you using Liz Selkirk's proposals concerning a compositional structure of words. This has turned out to be very helpful for the analysis of present-day English derivatives. So here is another derivative for you. It is overgeneralization and this will be the result of our analysis. But how do we arrive at such a result? Well, let us again build the morphological tree step by step. As usual, you should start using an empty sheet with the word you have to analyze written down at the bottom so that you have enough space on top of it. Because we are generating a tree structure right here. Step one, as usual in such morphological analysis, exercises is you provide a morphological analysis. A simple analysis that is the analysis of the derivative into its base form and into its affixes. For reasons of readability, let us normalize all morphs orthographically or phonologically. That is, we use the defaults, if possible. For example, ION for, in this case, realization, generalization. So instead of the alomorphation, we are using the default morph ION. The next step is we assign word classes to all the morphs. General is an adjective. I's turns adjectives into verbs. So the inherent word class is verb and ION is nominal is a noun. Well, it is not really a noun, but it turns verbs into nouns. The problem is over. Over has, as we will see in a second, no real constant or permanent or inherent word class. Okay, let's now start generating the tree structure. We start with the base form and combine it with the suitable affix to the left and right. And of course, the affix we can combine, we can take for the combination with general is I's. Over general is not a word. You wouldn't find it in the corpora such as the British National Corpus. So we have to combine I's with general. And now we can ask the question, what is the result? What is the category that has to be associated with the mother node? Well, to do this, we have to take the percolation conventions that were defined in the 1980s by Selkirk. Now, here they are again. And in this case, we can simply apply rule number one, which passes the features of the affix up to the first branching node. So we have this situation generalize is clearly a verb. Now we take this new base form generalize and combine it with another suitable affix. The problem here is that both affixes are suitable. There's a verb such as over generalize. There is also a noun like generalization. Well, what can we do? Well, we could perhaps quickly look the resulting word forms up in the British National Corpus. And then we will find that over generalization is more frequent than over generalize, which, by the way, is spelled without a hyphen. So let's take generalization next. And this is then the new branching situation. And again, we need syntactic features for the new mother node. And we can simply pass the features of the affix up to the new branching node. So generalization is a noun. OK. And now we have to combine the prefix over with this new word form, with this new derivative generalization. And it is, of course, this structure. And again, we have to assign syntactic features to the new mother node. That is, OK, let's apply rule number one of the percolation conventions, which looks like this. The problem, however, is that the prefix over, as I've already said, has no real features. It can be attached to all sorts of base forms, such as overdue, overkill, overoptimistic, and so on and so forth. Hence, the mother node fails to obtain syntactic features. So we cannot really apply rule number one. It doesn't work. So what can we do now? Well, we take rule number two. If a branching node fails to obtain features, well, then we take the feature of the second daughter, which is in this case the noun. And we then have this new situation where rule number two of the percolation conventions now can be applied. And the final result is that overgeneralization is a noun. OK, that's it. The print version of the solution is available in the VLC e-lecture library. Well, and if you want to see more trees, you have to join us and take part in our practicals or look more solutions up in our practicals, in our practical sheets, where we have more than 50 trees with structures of this kind. Thanks and see you again.


Hey guys, it's Jess and welcome back to my channel. I hope you're all having a very happy and productive week. And of course, being Friday, today means it's time for my Question of the Week video. So if you guys do have any study-related questions, then make sure to leave them in the comment box below. You can actually also send them through on my other social media accounts too at Study with Jess for Instagram and Twitter. So if you guys aren't following me, make sure you go follow me there as well. But today's Question of the Week I'm really excited to address because I feel like no matter how old you are, it's going to apply and be beneficial for all of us. So I'm really excited to get into it. So if you guys enjoyed today's video, then thumbs up to let me know. And also comment below. I'd love to read all of your thoughts and comments as well on today's topic. So today's Question of the Week comes from Jade and Jade asked the following. Jade says, Hey Jess, love your Q of the Week videos. I want to be successful in life and I work really hard, especially because I'm in my last year at university. How can I become successful after I finish studying? Love Jade. So Jade, I think the most important thing when talking about being successful in life is to actually define what does success mean for you. And I feel like all of us are going to have slightly different definitions and that's totally fine. That's normal. And if anything, there's no right or wrong answer or definition for success. It's just depending on what you feel is important to you and what you want to accomplish and get out of your life. So in my opinion, I think if you want to attain success in your life, you have to define it and give yourself something to focus on so that you can inch yourself closer towards achieving that goal. And I think personally, I like to have everything written down. I feel that being able to read over something, it just gives me a bit more direction on what it is that I want to achieve and get out of my life. So I really encourage you guys to write down your definitions of success and I thought I'd even share with you my definition of success a little bit later in today's video. And if you do happen to have some trouble working out your definition of success, then something that worked really well for me was to actually think back to a time when I felt really successful in life and I felt like I had accomplished something, I achieved something, I was really proud of myself. So personally, I thought I'd just share this with you so you can get a bit of an idea on what to do or what to think about. For me, a time when I felt really successful in life was when I was working on my study skills book, The High School Survival Guide. And no, I'm not trying to endorse my book here and I'm not trying to say that I felt really good because I got to write 36,000 words or I get to call myself a published author. It's really not about that. What it was for me was actually that I was able to sit down for a long amount of time and work really hard on something that was really rewarding. I got to create something that never existed before and I love that. I love creating things and bringing new things into the world that are going to benefit others. And I like that it challenged me as well because writing a book, it's a long process. It's hard. It's hard to come up with all of the content. It's hard to think of everything that you want to put down on paper and make sure that it comes across the right way. So it really challenged me. But at the same time, I was also so grateful for this opportunity that I know not many people get to have especially in their 20s and I got to work with some fantastic people. I got to learn from experts in their field that knew so much more about publishing and design and production and manufacturing and marketing, you name it. So for me, being successful was actually about being able to work on exciting projects that brought about new opportunities for self growth. Now apart from thinking about your definition of success another thing I really advise you guys to do is actually turn it into a positive affirmation that you can get to read over regularly. So having it as an affirmation rather than just a definition personally I find that to be a lot more empowering and it really helps you to feel like you are moving closer and closer towards achieving what it is that you want out of life. So I wrote down my definition of success along with an affirmation of being successful and I thought I would share it with you guys now. So I hope you guys can appreciate it and that it does give you guys some inspiration on how to write yours out and if you guys have a vision board this would be the perfect place to display it as well. But anyways, here is my definition of success along with my affirmation as well. So I wrote, and I have this on my phone because I was doing this earlier this week I actually do have it pinned on my vision board too though but I like to have it on my phone purely because I don't know, you want to display it everywhere that you possibly can. So I wrote this, I wrote success means working with people who are experts in their field. I work on exciting new projects that allow me to attain new skills and form fantastic and memorable experiences. I grow and I feel I'm not limited by what I do. My work gives me financial freedom and peace of mind. I feel a sense of purpose and my hunger to accomplish and enjoy more opportunities and projects grow. So as you can see my affirmation and idea of success doesn't really relate directly to financial gain at all and the reason I wanted to also make this video and address this question is because I feel like so many people commonly associate the idea of success with money and I don't think that that's the case because if I were to win the lottery tomorrow which would be great, not saying I don't want to but if I did win the lottery tomorrow and millions of dollars just fell into my lap yes, I would be very grateful I'd feel very fortunate or blessed and lucky but I wouldn't really feel successful in life because I didn't really accomplish anything I didn't achieve anything I didn't grow, I didn't learn anything I don't really have anything to show for all of my efforts so I wanted to make this video because I want you guys to realize that being successful, it's not about the money it's actually about finding a sense of purpose in what you do in life and I feel like I'm finally at this place in my life where I genuinely love what I do it makes me feel so fulfilled I'm able to be creative I'm able to still use my academic skills I'm able to teach, I'm able to learn I'm constantly learning from other people and I just find that to be so rewarding so it doesn't matter how much money I make I feel like even at my age I feel like I am a successful person because I've jumped, I've taken a leap of faith and I work really hard at what I do and I feel like there is a greater good to what I do as well I'm not just doing it for myself I'm doing it for you guys too I hope you enjoy today's video and Jade, thank you so much for sending in your question I hope that I have given you some guidance on how you can be successful in your life too and if you guys did enjoy today's video then like I said, show me some love and thumbs up and if you guys aren't subscribed also make sure to click the subscribe button down below and I'll see you guys on Monday for Brain Food but until then, have a very happy and productive weekend bye


How do you make smart decisions on health risks? A couple of months ago, RiskBytes described risk as the probability of a specific, bad thing happening. To avoid a risk, we need to know how likely something is, and we need to know just how bad it is. And how do you feel about that? I'm sorry? How do you feel about that? The bad thing? Well, I suppose I just don't want it to happen. Of course. We never want bad things to happen to us, but I meant how do you feel about the risk? The risk? That's just a number, surely. We don't just think about risk numbers. We feel them too. There is a feeling of being at risk. Come again? Have you ever had someone cough on you, and worried that you would get sick? Or have you ever been running so late that you feared you might miss your bus or plane? Those feelings are the feeling of risk too. We have feelings any time there is uncertainty about what will happen to us. Okay, so I get the feelings bad, but surely it's the number that's important. Definitely. Numbers are important. And sometimes risk numbers and risk feelings agree, but sometimes they don't. Sometimes your brain may say, this risk number is really small, at exact same time that you feel really scared. So which should we listen to, our brain or our feelings? It depends. Sometimes we should listen to our brains, and sometimes we should listen to our feelings. But both are important. I'll be back to talk more about risk and feelings on risk bites over the next few months. But until then, stay safe, and feel safe too.