Alright, we were doing the actual beam deflections from last Friday. This is where given some of our standard loads we were able to figure out just not just standard loads but also standard supports. We looked at a couple but whatever those loads happened to be and we're going to show today that we can handle just about anything, whatever those loads happen to be we're going to be able to figure out what the deflection is and that's actually finding out this deflection, the amount the beam actually moves due to the elastic response of the material itself. We were able to, for some simple loadings, figure out just what that equation was, remember that was called the elastic curve. Elastic meaning a couple things to us, one is the beam will, if not pushed too far will return to its unloaded state if the loading is removed but elastic also had to do with the fact that the curve was, this curve is continuous. Remember that term from calculus, well actually pre-calc I guess you would even do continuous where there's of course no step change in the position of the beam. The only way that could happen is of course we had beam failure and we're not stressing any of these beams to the point of failure but it also meant that the slope was also continuous meaning there was no abrupt change in the slope of the elastic curve itself. This meant that the beam had no sharp corners in it, even if the beam itself was continuous it can't maintain any sharp corners. There is a way we could do that, I can't remember off hand if our book has any of these type of problems but there were some in several other books where there are actually two beams joined together by a smooth pin joint, the very type we'd see in statics last fall and these beams can, well depending on whatever the load is, these beams can have a rather abrupt change in the slope of the elastic curve itself. I don't know if it does something like that but it's the deal where there's a continuity in the beam itself but a discontinuity in the slope of the beam because of this hinge joint but like I said I can't remember off hand if our book had any of those. So we worked through this and it was usually a matter of figuring out the moment as a function of x and then integrating backwards to this curve using the shear moment, the load shear moment, slope and displacement curve all related by their integration. Now all of these, not all of these, some very simple loads of these are all done in this appendix C here, slopes and deflections of beams and you can see some of the ones we actually even did in class and what's available here is the slope usually as a function of the maximum slope, the maximum angle made by the beam under that particular load or possibly the two different slopes of the different ends depending upon what the load is. What you have to do though is be very, very careful. Don't use one of these solutions just because the problem kind of looks like the picture. It has to look exactly like the picture. It has to be precisely this case. The last column is usually the beam curve itself, this curve that we were actually working on coming up with last Friday. Also available though are the deflection at a certain point. This is not the point of maximum deflection, it's just the deflection where the load happens to be. That may be what you need. If this was a floor beam and this was a wall on that beam, you'd want to know the deflection right there because it could deflect enough that the wall separates from its own ceiling above. You don't necessarily care what the maximum deflection is when it's more critical what the deflection is actually under that beam, under that particular point load. If you did need the maximum deflection, you can take this curve here, differentiate it, set it equal to zero and find out where the maximum deflection is. There's some other possibilities. All the ones on this first page are those with simple supports, the pinned end and the roller end. Again, be careful that the loading is exactly as shown here, otherwise you can't use this. And all this is a matter of the author doing for these problems exactly what we did on Friday and then just giving you the results. You remember every time we need a moment of inertia, there's some very standard shapes available in the tables, pre-done for us, that's exactly what this is. Some standard loadings, pre-done for us with the answers right here. On the second page were several examples of cantilever supports with different types of loadings on them. Again, you need exactly the loadings shown in the picture to use this solution. Like a test problem right there. Oh, it gets even better because there are lots of problems available that are not on here but are relatively easy problems to do and we'll talk about how we do those right now. So imagine we've got a simply supported beam with a uniform load and remember that could be nothing more than the weight of the beam itself. That's exactly how the weight of the beam would show itself in one of these problems as a uniform distribution of a load per unit length of beam. But then imagine we've also got a point load at about a quarter. So this is not replacing the distributed load with an equivalent single load. This is a separate load to that shown by the uniform distribution. So it's an 8 meter beam and that load is one quarter of the way along. You'll remember one of the terms that appears very often in these and you can see it all over the place on the chart here, this EI. That's the modulus of elasticity, whatever the material of the beam is determines that and then I is the cross sectional moment of inertia of the beam itself. So it's often worth it in these problems that it's either just given or it's something if you have the separate parts to it that you go ahead and calculate it separately so that it's available for all the other times you need it. Sometimes this is termed the flexural rigidity of the beam, these two together. So we've got a beam with that already established. The first thing you should do is look in the tables and see if this solution's already available and then you can determine what it is. We want to find the slope and the deflection at certain places. None of those are available. We're kind of close, but kind of close isn't good enough. If we tried to solve it with just this one, it wouldn't work. If we tried to solve it with just this one, it wouldn't work either. However, we can use superposition. We'll do an equivalent situation of two solutions superimposed over each other. That being the solution of just the single load added to the solution of the uniform load. Both of these are available separately in the tables. We'll get a solution of the two of them together by combining these two solutions as we go through these. So we can figure out the deflection due to the first loading, add it directly to the deflection of the second loading. We'll have the deflection of the two together. So we'll look at these. This one is the second one in table C. In fact, it's the one we did on Friday. We actually did a beam where the point load was one-quarter of the way along the beam. We actually did that on Friday. So we don't need to redo it because it's either right there available in your notes. The numbers might change slightly or we can just take it right out of the table. So we're looking for the general beam deflection. I'm going to make sure I slip over to the right one. Be careful that you pay attention to what A and B stand for. So we have V equals minus P BX over 6 EIL where L is the length of the beam and P is the magnitude of the point load itself. And then, which one am I looking at? L squared minus V squared minus X squared. And so we can put all of those values in where for our particular setup we have A equals 2 meters, B equals 6 meters, and L equals 8 meters. Oh, and P equals 150 kilonewtons. So you put all those values in. We even have the EI. We can put everything in and this all reduces down to minus 187.5 times 10 to the minus 6. 28 minus X squared. That's just reducing everything. Putting all the values in and collecting terms and simplifying. It all comes down to that. And that's the particular solution for just this sub part of the problem. And if we put in, let's pick a value for example, right at X equals A. I think that's the value I put, right at where P is. This comes out to be minus 9 millimeters. So we would know from this particular loading that that distance there is minus 9 millimeters. And if you remember, we do need them to be very careful with the minus signs because there are loadings where the beam could actually go above the neutral position rather than below. For the second loading, I'll have to bring it over here. Just, I don't have a lot of room there. The second loading is also in the book. It's the fourth one down in our book as long as they didn't change the order between the versions. And so if we go over to this particular solution here, and then again, we just fill in the pieces. W, X, remember X is the position, but W is that uniformly distributed load. The value of the linear part of the distributed load over 384. Let me make sure I'm looking at the right one. Oh, I had actually slipped down. 24EI. It's hard when you can't see the whole picture on the screen. X cubed minus 2LX squared plus L cubed. And of course, we just set our values to what we were given as a problem. W is the 20 kilonewtons per meter. EI, we've got. L, of course, is 8. For that one, that's all we need to know. And then that, actually, you don't have it. Well, yeah, I do have it reduced just for simplification here. Not a bad idea. Oftentimes in problems, we need to look at a couple different points of these. And so it's nice to have it in a very simplified form. X cubed minus 16X squared plus 12. That's just all of the values we've got put in. Simplified, reduced, cleaned up a little bit. And then at the very same place where X equals A, right under the load P, the value A doesn't have a specific importance in this loading we're doing now, but it relates to the original problem so it's somewhat useful. So at X equals A, again the 2 meters in, we get a value of minus 7.6 millimeters. And so as this beam deflects at a point 2 millimeters in, we get a deflection of minus 7.66 for that separate problem. We add the 2 together. So V is the minus 9, minus the 7.6 millimeters. It is minus 16.6 millimeters for that entire problem.  So we know this beam's going to deflect in some way. And at a particular point now, we know that the deflection will be minus 16.6. And we can also figure it out at any other place along there. If it was also important to figure out what these angles are, then we simply figure out the 2 angles on the separate sub-problems and then add them together. So rather straightforward, rather quick, as long as the sub-problems you need are available on the table, then you can save yourself a lot of trouble. If they're not, then you have to go through and figure out what the moment is as a function of X, integrate it to the deflection and finish the problem that way just like we did on Friday when we first set these up. And if you go back to Friday's problem, you'll see that this specific solution is just like we came up with. Sorry? Here? Oh, what's missing is I had an X pulled out. And I didn't see it. I had it in there. So yeah, that would be there. It would be 28X minus X cubed. Good point. You've got to be really careful with these subscripts, superscripts, and all the different factors and variables as part of it. Just for your own interest, you can notice that you'll get this very same 9 millimeters if you do it from the other end of the beam where A now is 6, B is 2, L is still 8. You'll still get the minus 9 millimeters now at a point 6 meters from 0 just to show you that you can use that from either end, but you have to be very careful which end and that you make sure that the values you put in match the pictures there precisely. Okay, so we'll do a couple more. These work well with some examples. Here's a model of a hairbrush design. So it's a long plastic beam that the users are going to hold on one end with a fist and then pull down using yellow. There's your hair. Pulling the hairbrush down through the blonde here. We're going to make a model out of that as a beam like this where we'll model that end as cantilever as it would be as the users holding it then with a uniform load and we'll take it to about halfway. So that'll be our model and then we'll put some values to it. Let me check out. Okay, so the entire length is 120 millimeters. This is half of it. It goes half the length. So this is 60 millimeters across there and the load is something like... I'm going to stop doing these things late at night. The load is 50 newtons per meter with a proposed cross-section of the hairbrush. Make it out of plastic, some kind of unreinforced plastic so we'll have an E for it. And I said 10 millimeters by 25 millimeters. Plastic has a modulus of elasticity of 2 gigapascals. So E times I is something like... Oh, I didn't do it separately. So you can do it separately. Remember to watch your units. I for a rectangular shape is just 112 BHQ. So we know we're going to need that. I just didn't have it on my paper. The first thing to do is check to see if the solution is in the tables. If not, we've got to come up with a solution that represents it. So looking at the cantilever solutions... Well there's a uniform load. There's a uniform load halfway across the beam but it's at the cantilevered end, not at the free end. So we can't use that solution. So we don't have a available solution in there but we can make an equivalent picture of it that will suffice. So here's our original model out of it of the one that is in the picture which is this one here that is in the table and the uniformly distributed load goes to the halfway point which is sort of like what we've got and then we'll add to it the uniform distribution that's also in the tables of the same magnitude going in the opposite direction. That way this first portion here will cancel that portion there to leave the first part of the beam unloaded which is like in our model for the hairbrush and then we'll have a load here it'll be in the opposite direction but we'll just have to be careful remember the hairbrush it doesn't matter where you're going you have to do it both ways we just have to make sure we get it so it makes sense for the picture we've got here so I guess let's make it so it is better so it does a better match we should put this one upside down that makes more sense right David? I can see it frowning we'll make this one then like that that'll match our model precisely again these two ends will negate each other leaving it unloaded then this adds to the unloaded end and gives us just exactly what our model is so you can do that let's step through it find the deflection and the maximum angle we know it's going to do something like that the maximum we expect to be down there and we also expect that's where the maximum deflection will be as well so practice opening up if you have your book that'll help if not I'll put up the relevant ones right here yeah I can just barely get them both on the screen okay so we'll leave this one and then the first and the third here on the pages that we've got so you set those up, see what we get with them the third you just make positive sorry? yeah well for this one positive yeah you'll have to make it well W remember is positive one down put in W as negative or just change these to positive and put in the magnitudes either way all the same same with the deflection these are all assuming downward loads so all of these deflections are negative and the angles are the negative too as shown alright so see what you can do with putting those two together just so I don't get sidetracked from my notes we'll number this one two and that one one as we refer to this visually perhaps V1 and V2 as symbols and we can also figure out the elastic curve as well so there's the two solutions we need in the table let's practice and see if we all get the same thing and if the same ones looks like you're the international nation too I'll have to remember that set up the curves with the appropriate values and then just add them together for the two superimposed solutions we've done this superposition thing before and you can imagine some of them can evolve three four more of the simple models to add it together if it looks okay put some hands on the airbrush point the thumb now the thumb is along the backside there okay like that is that okay? are you happy with that? much better now now you can finish the problem I guess we can argue whether the cantilever should have started right back here but we didn't have a solution that would work for that we need to simplify a little bit but would you decide? what I've called number two here remember we're looking for the deflection at the far end they're going to be different there's different equations there because there's different loadings there so we're looking for the loading at the far end so v2 if we're looking for the maximum deflection out here at the free end that's the second of these two equations it's inverted so we take off the minus sign w over lq we said minus w over lq 192 eI 4x minus l over 2 I believe we've got all those values what do you get for eI then? I don't have an eI out separately I do have I what do you say? not 26 even 0.04 0.04 22 times 10 to the 6th Newton's per meter squared and for 112th bh q I've got 1.28 and it's 10 to the minus 8th meters to the fourth 10 to the 6th 9 to the 9 you have gpn oh yeah yeah I was doing megapascals the last time 10 to the 9th so whatever that comes up eI just don't have it calculated separately then the maximum deflection again take out the minus lq and remember all these units should work out did the units work out? I hope so since you didn't track them you better do them and then for the second one we can use the loading just as shown minus wx squared 24 eI x squared minus 4lx plus 6l squared and the maximum expected deflection the angle the slope again at the end and again the model and the solution match each other so we can use just the x picture x is no x is wherever along the beam you're interested in this so if we want to know what the maximum deflection is you'd want to x at l if you want to know it anywhere else in between reduce everything check your units make sure everything's in meters if that's what you're doing all those distances in you've got some numbers you've got some numbers the units the units is always right you too no units how can I tell if your number is right so what? radius intermediate values written down with x equal to l on all of these a lot of it simplifies you can really get it reduced down to a single piece there once you get all the numbers put in so see if we all agree you can imagine if hairbrush was too flexible it would be a little flexible yeah a little bit flexible especially if you're worried about losing hair which you are yet but you will be I'll see you guys at the 50th reunion yeah I'll be laughing at how bald fat we are you'll be laughing unless you're laughing at this already it's just going to get worse alright everybody's coming along who's got some values if you think you got them ask somebody else who does you can prepare them so we get this in radius yeah remember this is all based upon the angles being very small the tangent theta equals theta we had to use f from the very first almost the very first fold when we started going on we forgot to go on right there so yeah these are not typically very big deflections plus this is not a very large object anyway so it doesn't have a whole lot of length the flex both the angle and the absolute expansion are going to be small get your plus and minus signs right because these two deflections are in opposite directions the minus sign in there has to do with a positive load which we have always taken to be a downward load as positive small is that meters millimeters he's got 0.02 millimeters but that's minus yeah so one was down two was even downer yeah something something didn't quite work there we expect there to be a negative displacement as pictured Newton meter squared over Newton meter squared which is no units but remember that's when Newton's applies yeah well that's got to be 10 to 6 Newton's Tom got anything yet both positive plus you because that's a positive deflection this is a negative deflection and on a model we'd expect it to be oh I only have one okay yeah number two we expect to have should be positive one should be negative hopefully if they work out the total deflection is negative is that negative you want to be positive I guess brush me to pull down we'll give it an upward load on our original model but this is not Australia negative 0.0 oh I get what you mean for what? yeah she's pulling it down load would be up Phil what are you at negative 0.77 millimeters but it is negative for the total and you got 0.77 millimeters 0.012 0.004 0.004 oh that's closer to what I had I had 0.004 I had 0.04 that's meters millimeters 0.004 you have the individual number centimeters no I don't have that in the individual numbers one or the others may have slipped a power of 10 what do you have David? 10 times probably almost exactly 10 times what you had but it was negative negative yes so did you have the same thing then the traffic had but not negative all right well well that's details the physics is there just perhaps the sixth grade algebra is for either one of us I was kind of rushing through this last night did this last night? yeah which is the tail end of the long weekend easy all right so we'll double check those numbers when you've got a couple minutes to down but the basic idea is there I want to have time to get on this to the other application of this as we've seen before as long as your physics are there there's a search that a simple superposition works very well in lots of different applications all right we also have used this type of thing for those problems that are statically indeterminate we did this for torsion we did it for the strain simple elongation and we can do it now so imagine we have an over constrained beam what that means is a beam for the simple statics equations we've used before are insufficient if we have a beam like this our typical static solution from last fall will not suffice there's just too many problems for the number of equations we've got but we've now got this idea of superposition to add on as another possible or actually counts as another equation another equation actually comes into it so we can make this into two models this one of course is not on the solution so we can take it as two models that will superimpose and use that as a way for us to then get to a solution that we do have this solution is available it's the one we just looked at that will cause a deflection of something like that we expect the beam to deflect something like that remember a cantilever support the slope is zero and then there's zero displacement over here so we'd expect something as a displacement like that so we can't clearly get it with the solution we've got there but we can add to it another solution that we do have available and that's then a simple load at the end that brings the beam back up to where it would have been such that those two together we would expect to give us the solution we have there and that will give us the reaction at both walls so maybe we'd say something like this we have a v1 down and then with the second model the same magnitude deflection only would be up such that the two added together means no deflection at the simply supported end the zero slope for both will guarantee zero slope for the other solution and we'll then be able to find the full solution so let's put that together and from appendix c we have vmax as minus wl fourth 8 over ei so that's going to be our v1 and the minus is appropriate because our model matches that in the book so we know that we expect a maximum deflection at the end of that particular model of minus wl adi and we don't have to have values for these we're just doing them in absolute variables and then we add to it the inverse of that top logic so again we're using the first and the third but we've got to flip the first one over because it's in the opposite direction that we're using it here so that will take out the minus sign pl cubed over 3i that's this deflection here the maximum deflection of a single point load at the end of a can the free end of a cantilever beam and then we're saying that maybe I'll call this a 2 here would make more sense we're saying that v1 plus v2 equals 0 that as simple as it is is the extra equation we need to solve the original problem and so we can then use that to solve for p which is equivalent to the reaction at that point which is 3 eighths wl as simple as that when you put v1 plus v2 equals 0 put those two together the unknown is p that we're using to represent the reaction at that end you're not done because we don't have the reaction at the wall we also need that so that is going to take a separate model to find the reaction at the wall so we'll split that into two models as well one of them will be a simply supported beam actually we're going to have to to model this twice so a simply supported beam however we know that this one would have a slope at the left end which we don't want so we'll have to find what moment is there that will bring that back up so that's actually itself two models both of which we can do to get the original anticipated deflection not in any particular order we can do a uniform low distribution that will give us a deflection like that add to it simple moment as calculated by that and then we can use the two together to give us zero angle at the wall such that theta one and theta two are equal and opposite we need those two to find out what the reaction at the wall is for this for any of our static solutions when we find the reactions it's not just at the simple at the wall supports but also at the wall support so you know P on the far right so why do you need two separate models there because we don't have any simple model we can use to illustrate that one well I guess we could we could have made this as another solution we could have done it as this well actually it's the same two we've got there well no it wouldn't be because yeah what needed if we did this we're not going to get the moment at the wall so this isn't going to suffice we had to bring the moment into it so we we had to remodel it and then split that into this superposition so now we're back on the other page we're using this load here plus this load here only done from a different end with the moment running in a different direction so we again have to be very careful with this we're using these two middle loads and we're using the angle ones so there's the ones we're using there so we have to be a little bit careful we'll call that one that two just to stay consistent with my notes so the first one we have to be careful with the subscripts we're doing the angle over at the end where the moment is so we want this particular picture m I have listed as m a m a l over 3 e i and as pictured that will be positive so if the moment is positive then this will be in the correct direction because the sides are swapped and the moment is swapped that's like two negatives so we can use the same equation we don't want this as theta max theta just theta 2 and theta 1 it doesn't matter which end we use because it's symmetric so it's minus l cubed over 25 24 e i minus wl cubed over 24 e i minus wl cubed yeah yeah I want to change these numbers are right so I want one here two there one here two there so one's on the bottom it's arbitrary the way I have to do it in notes and so we put that together we should get m a equal to minus wl squared over 8 remember every time we did this superposition thing that do statically indeterminate problems the material itself didn't matter so we ended up cancelling out and that again is the case when we put these two things together theta 1 plus theta 2 equals 0 solve for m a the not only the material but the cross section of the beam cancels out theta 1 plus theta 2 yeah that's a negative no no that's our negative convention so does it not come out in the algebra we got m a l over 3 e i minus because I have a minus here wl cubed over 24 e i and those two have got to add to 0 okay oh this yeah you're right because we don't need this in the negative since we've already got the proper sense to it so this would be a positive then all we need is the magnitude we already know the direction we already know the direction of a moment at a cantilever wall now the question might be we use two different models here we use this model first where we have the uniform load with a point load back up on a cantilever beam then we use this model a simply supported uniform load and a simply supported beam with a moment the question might be we use those for two separate purposes we use this for the right end reaction we use that for the left end reaction the question might be do two models give the same elastic curve we have an elastic curve that we'll get from this solution we'll have an elastic curve we'll get from this solution the question is do they each give the same elastic curve if they don't then it might not be appropriate to choose two separate models so let's let's let u3 find the elastic curve for this model and u4 find the elastic curve for this model and we'll see if they're equal if they're not then you either have to decide is one the better model than the other or perhaps neither model is good and it may not be obvious which is which so do the same thing just use p and w for the loads that's w that's p actually we just need w find the elastic curve for the two which is a matter of for the one that's pictured up there which is the second one we did you've got this elastic curve over here you just need to add those two together taking into account one of them that's upside down and then for the other one we use those two cantilever solutions there those elastic curves we use this in some place either group needs to see the elastic curves people doing the left hand one your elastic curves are up there don't forget that we've got the simply the simple load at the end of a cantilever beam upside down we can go for your two beams that's these two right here you've got this load with this elastic curve and then this load with that elastic curve be careful that this is at the opposite end from which x is this one three people where the moment is actually in there use the use the one we solved that M equals WL squared over 8 because we now know that we have to pick out the minus sign yep the first and the third write out the equation for the elastic curve and put them together put them together minus x squared minus is okay, we're in the same way 24EI the EI is not going to cancel in this case adding these together but they don't add together to equal zero they add together to equal whatever they equal x squared minus 4L x plus 6L squared is the first part yep, that looks good and when we add to it this one where we now know the load we're just going to have to narrow it down yeah we know the load P as well, that's got P in it but we know what P is we know that it's three 8's one of the three 8's so we can put that in but it's upside down where P equals what we found before I don't have it in there it's three 8's WL so that will give you a low curve I'm sorry, an elastic curve for one of them and then for the other one we have to go to this one the second one where this one is at this the uniform one here it's in a proper orientation x cubed minus 2Lx squared plus L cubed and then V2 the second one with the moment this is upside down so we have to turn this over we know the magnitude of M zero I had an MA on the board so you can figure out what that is as well using the moment that we now know no minus sign there because that one is upside down and those should give the same elastic curve do you guys have yours to compare? is it real? this is a good short little but your variables have a slider function possibly and you can imagine there are other solutions for these for example we've got this L over 2 but what if it's just L as some variable of x so other books have other solutions so hopefully this works out now add those together add those two together to give a complete elastic curve and that should equal to these the ones these two are adding together this group is adding together for this elastic curve it should give the same elastic curve assuming you've got the same you've got to hurry, we're running an overtime I'll help you now, it's 100 bucks an hour alright we're at the end there so I'll put it up as a function of x it should look like Wx squared over 24EI depending on which one you put first and what you do with your algebra 5 halves Lx minus 3 halves L squared plus no, minus x squared did you guys get that? make sure I'm reading the right one Wx squared over 24EI 5 halves Lx minus 3 halves L squared minus x squared and I got that the two did give the same model it doesn't agree, it's most likely just algebra physics is nothing more than writing down the two equations and adding them together that's all the physics is did any of you agree? you got some of the terms double check that you've got them all but they do give the same elastic curves so they're both legitimate models luckily are they close to each other? what? yeah, I don't know why they wouldn't as long as you do it right? as you said you've done well


SCP-059 is a radioactive mineral of unknown origin, superficially resembling Sheelite. A component of SCP-059 is believed to originate in an alternate universe, and to be responsible for its anomalous properties. SCP-135 is a human female, age undisclosed, that promotes rapid, uncontrolled cell growth within a radius of 2.25 meters from itself. It remains rigidly in the fetal position, and has never been observed to move. SCP-135's effect is carcinogenic to animal tissue, and induces malignant neoplasia and plant and fungal tissues in 100% of recorded exposure cases. SCP-008 is a complex prion, 100% infectiousness, 100% lethality. Research into SCP-008 is highly classified, and primarily aimed at preventing research which may lead to the synthesis of SCP-008 in the distant future.


Hi and welcome to this session. Let's discuss the following question. The question says express each of the complex number given in the exercises 1 to 10 in the form a plus iota b. The third part is iota raise to the power minus 39. For solving this question we will use the rules for powers of i. For any integer k, iota raise to the power 4k is equal to 1, iota raise to the power 4k plus 1 is equal to iota, iota raise to the power 4k plus 2 is equal to minus 1 and iota raise to the power 4k plus 3 is equal to minus iota. These rules will help us to solve the question. So this is the key idea in this question. Let's now start the solution. Given complex number is iota raise to the power minus 39 and this is equal to 1 upon iota raise to the power 39 and this is equal to 1 upon iota. We can write 39 as 4 into 9 plus 3. Now this is of the form iota raise to the power 4k plus 3 and this is equal to minus iota. So this expression is equal to 1 upon minus iota. We have to convert this in the form a plus iota b. So we will now multiply the numerator and denominator by iota and this is equal to iota upon minus iota square. Now iota square is equal to minus 1 and this implies minus iota square is equal to plus 1. So using this iota upon minus iota square is equal to iota. So our required answer is iota. So this completes the session. Have a good day.


Last week, Tory MP Owen Patterson was found to have broken MP lobbying rules by an independent standards committee. Today, our Tory government responded by overturning the ruling and abolishing that standards committee. It's all pretty brazen tonight. I'll be talking to MP Lloyd Russell Moyle about Tory sleaze and about today's events in the Commons. Also on the show, we've got an update from COP26 with Adrian Buller and then a fiery interview with Boris Johnson on CNN. Dahlia, I'm afraid, is unwell this evening so I am hosting solo today. That means I'm especially keen for your comments and your super chats so I don't get lonely here. You know the score if you haven't already do hit that subscribe button. Owen Patterson is a formatory environment secretary currently a back bench MP. Last week, Patterson was found to have a broken lobbying rules which govern MP's conduct. Specifically, he was found by an independent committee to have been paid substantial sums by two private companies and then use his position as an MP to work in their interests. The companies in question were Randox, which is a clinical diagnostics firm and Lin's Country Foods, a processor and distributor of meat products. These gigs were pretty lucrative so Randox paid him £8,333 per month. That's only for 16 hours work a month and it works out as £100,000 per year so nice work if you can get it. Lin's Country Foods paid him £2,000 for four hours work every month so that's £12,000 a year so in total £112,000 he was paid for 20 hours a month. Jesus Christ. I'm feeling quite bitter now. I'm not in favour of MP's having lucrative second and third jobs in the first place whatever they do whatever the rules are unfortunately you know rules are not broken by taking these side jobs. However, what's not allowed is then lobbying for the companies that are employing you according to the House of Commons Commissioner on Standards Owen Patterson had breached the rule prohibiting paid advocacy in making free approaches to the food standards agency relating to Randox and the testing of antibiotics in milk in November 2016 and November 2017 in making seven approaches to the food standards agency relating to Lin's Country Foods in November 2017 January 2018 and July 2018 and in making four approaches to ministers at the Department for International Development relating to Randox and blood testing technology in October 2016 and January 2017. Oh there he is that's Owen Patterson there he's getting paid a handsome sum to work for these firms and then he's arranging meetings with people in government because he's an MP and he has he has that access. All this meant the Commission on Standards found that Mr Patterson's approaches could clearly have conferred significant benefits on Randox and Lin's in the long term and even the short term secured meetings that were not available without Mr Patterson's involvement. Patterson's actions were an egregious case of paid advocacy that he repeatedly used his privileged position to benefit two companies for whom he was a paid consultant and that this brought the house into disrepute. There is no ambiguity there and this does indeed seem like a pretty clear cut case. The Committee on Standards which is made up of Labour and Tory MPs alongside independent lay members decided that these misdemeanours warranted a 30-day suspension for Patterson the length of the suspension would have meant that Owen Patterson could be subject to a recall petition by constituents so if 10% of his constituents voted or signed that recall petition sorry that would trigger a by-election. The catch here is that any sanction recommended by the independent committee has to be ratified in a vote by all MPs that vote happened today and whipped by Boris Johnson a majority of MPs voted against it. They voted against the findings of that independent committee. Even more brazenly MPs also chose the occasion to abolish the independent standards committee and replace it with another. Both were disgraceful moves and they meant it's been a pretty heated day in the House of Commons. This was Angela Rainer at PMQs. The independent standards process found that a member brought the rules on paid lobbying. Surely the Prime Minister accepts that this is and should be a serious offence. Yet we have seen reports that he will respond by scrapping the independent process and overturning its verdict. In no other profession in our country could someone be found guilty by an independent process and just have their mates vote them back into the job. Surely the Prime Minister and this Government are not going to do that today. No, of course we're not going to do that because a paid lobbying, paid advocacy in this House is wrong. Let me make absolutely no bones about that. Members who are found guilty of that should apologise and pay the necessary penalties. That is not the issue in this case or this vote that is before us today. It is not. The issue in this case which involved a serious family tragedy is whether a member of this House had a fair opportunity to make representations in this case and whether as a matter of natural justice our procedures in this House allow for proper appeal. That I think is something that should be of interest to members across this House and should be approached properly in a spirit of moderation and compassion. Reina was in that PMQ's covering for Keir Starmer who was self-isolating after testing positive for Covid. In that interaction there you heard Boris Johnson defending the Tories action by mentioning family tragedy. That's a reference to the tragic suicide of Owen Patterson's wife last year. That is of course horrible, really horrible that anything like that has happened. It doesn't have much to do with corruption. Johnson also criticised the independent process by which Patterson was found to have broken the rule saying it didn't allow for fair representation or appeal. On the representation front that has been denied by the committee. They in fact accepted written evidence from his supporters but didn't feel the need to hear the oral evidence as nothing they said was contested. You only really need the oral evidence if you're challenging what was said. The facts of the matter in the Owen Patterson case haven't been contested. On the issue of the appeal, I mean this could have been credible if Boris Johnson had raised it before one of his friends was found guilty by the independent commission. It doesn't stack up to make this intervention only when a decision has gone against you. On that point Angela Reina swung and she didn't miss. Mr Speaker, let me put this to him simply. If it was a police officer, a teacher, a doctor, we would expect the independent process to be followed and not changed after the verdict. It's one rule for them and one rule for the rest of us. Mr Speaker, when a Conservative member was found guilty of sexual harassment but let off on a loophole, they said the rules couldn't be changed after the event. So they can't change the rules to stop sexual harassment but they can change the rules to allow cash for access. So why is the Prime Minister making it up as he goes along? All the professions that she mentions have a right of appeal. That is what the House needs to consider. May I respectfully say to her that I believe that she needs to vote, instead of playing politics on this issue, which is what they are doing, I think that she needs to consider the procedures of this House in a spirit of fairness. On this side, instead of playing politics, we are getting on with delivering on the people's priorities. 40 more hospitals, 20,000 more police officers and wages up both up and jobs up across this country. Those are our priorities. In her question there, Angela Reina was referring to Rob Roberts. He was briefly suspended from Parliament after sexual misconduct claims were investigated but he was able to avoid a recall petition because of a technicality. So as I said, a recall petition when you can have constituents come forward, sign a petition and potentially prompt a by-election, he avoided that because of a technicality. Let's look at a write-up of the details of that particular event. This is from the independent. So they write, a loophole meant the disgraced MP who has had his Tory membership reinstated but still sits as an independent in the commons was able to avoid a recall petition because of the length of the suspension was recommended by the independent expert panel rather than a commons committee. Earlier this month, the government closed the loophole for future cases but voted down a motion from Labour to make the changes retrospective. So as you can see here, Angela Reina had a very strong point. In this case Boris Johnson said yes, the outcome was unfair but we can't change rules retrospectively. In this case, Boris Johnson has said, oh, the rules are unfair even though he doesn't have very good evidence for that and now he's very, very happy to change the rules retrospectively. It completely, completely stinks. The debate in parliament went on after PMQs. We have spoken already, as Angela Reina pointed out there, what is particularly controversial is this, the nature of overriding the judgment of a committee whilst it was in process, whilst it was investigating or in fact after it had come down with a verdict about a Tory MP. What's also controversial is what is proposed to be replacing it. So the committee which will be tasked with drawing up new regulations for MPs will be made up of nine MPs, five of them will be Conservatives. So there will be an inbuilt majority for the Tories. In a debate in the Commons this afternoon Caroline Luke has challenged Jacob Rees-Mogg on what looks like a stitch up. If you could explain why it's appropriate that this new select committee should have an inbuilt government majority where the Standards Committee doesn't with its lay members and if this is about trying to improve our processes why is he running the risk of making it look to anybody looking in from the outside that essentially it's like someone who's been found guilty of a crime but instead of actually serving a sentence what happens is that his mates come together and try to change the judicial system. It looks really bad. Sometimes to do the right thing one has to accept a degree of a premium but it is more important to do the right thing to ensure that there is a fairness. Jacob Rees-Mogg though was responding as leader of the House. Throughout the debate his answers were incredibly unconvincing. However, due to the Tories 80 seat majority ultimately the strength of anyone's arguments wasn't what determined the final result. This is the moment the vote on Ledson's amendment came in. The eyes to the right 250 the nose to the left 232. I want to read the result. The eyes to the right 250 the nose to the left 232 the eyes have it the eyes have it a lot. That was the vote on Andrea Ledson's amendment to abolish the Standards Committee MPs went on then to vote against Owen Patterson's suspension. That doesn't necessarily mean this is the end of the story because while they have voted against his suspension that doesn't mean he is completely in the clear. His fate will be decided by this nine MP committee that's just been established in this incredibly opportunistic way in the Commons today. That's supposed to be made up as I said of five Tory MPs for opposition MPs. It turns out the opposition MPs are potentially getting organised to boycott that committee which could further erode its legitimacy. To discuss a fiery day in the Commons I'm joined by Labour MP Lloyd Russell Moyle. Lloyd, welcome back to Navarra Media. Very good to see you and hear from you today. Talk me through today's events in the Commons. You were there. Did you feel as if Tory MPs who voted this through believed what they were saying or was this all just a complete farce and a facade? A charade sorry. I think most Tory MPs didn't really believe. There was a lot of agrarian faces. I mean a number of the Conservatives that I spoke to some of whom did rebel said the only person that Paterson is working for is himself. Let's remember this is a man who earned £100,000 extra a year to do corporate lobbying and I mean we spoke to one MP as we were going over and my colleague said you must be really embarrassed about this and he kind of said with despair oh I've given up I'm not embarrassed about anything anymore because it's all just too embarrassing but he still went and voted with the Conservatives. So I think that a lot of them know that this is pretty embarrassing. A lot of them know it might come back and fight them on the rear end. I think what is extraordinary is Ledson's kind of approach to this. Previously she's been seen as quite a reasonable person on these things and suddenly she's kind of pretending that she's upset that people are saying she's doing this in bad faith. It's clear she's doing bad faith. I mean I spoke to one Tory who has a 10% rebellion left.  So I think that they know it but they will all fall in line and forget it if it means them keeping their jobs and Boris Johnson if you remember was so ruthless when he first came in to people who spoke out you know he removed the whip from Clark, Ken Clark etc but I actually think that a lot of Conservatives are slightly scared. Next question to you is about Labour strategy here so as far as I understand it the Labour Party and the SNP are going to boycott this new committee which is supposed to draw up you know the new rules for standards of MPs. There'll be nine on there they're supposed to be nine on there so it could just be a committee of five Tory MPs. Do you think that will be an effective way to keep this controversy rolling on? Well I'm pleased that that has been the decision of the Labour leadership but as you pointed out at the beginning it seems like one of the things that we've listened to from the left it will help the controversy carry on for a bit. Let's remember this is a committee that is set up to review the situation and to change the way the system works. Its recommendations will have to come back to a vote in Parliament so what we will need to be doing is delegitimising that vote when it comes around. The old standards committees actually is not abolished by this process it just kind of creates a double jeopardy situation and I guess what they're trying to do is mean that if Chris Bryant's standards committee finds someone guilty they can go to this kangaroo court and find them not guilty or find it through a different process. So that's where we are at the moment and I think it's important that we just focus on the current committee and the current system. They aren't perfect either actually you know there are lots of problems with it but I think when there's votes come back and some of those votes might even have to go to the Laws there is a good argument there to say that they're delegitimised because it was only conservatives that decided it. What are the problems with the current system? So obviously you know the Boris Johnson's defenders have been going out and actually we showed a clip of him in PMQs saying that you know it doesn't allow for appeal, it doesn't allow for natural justice. Do any of those arguments stack up? I mean none of us are going to be convinced that that's why they've made this decision on this particular day, on this particular occasion when their friend has been found to have done something wrong. But sort of aside from that are there problems with the current system that need changing and what are they? Well only a month ago we had had to make an amendment to the current system because it didn't treat sex pests as if in the same way as people fiddled the money and so that means that we've got a conservative sex pest that we know and is found guilty of those things running around the corridors and they can't get rid of them. So that for example is one of the things that is wrong but that has been changed. There is some arguments that maybe you would want an independent appeal process you know kind of if this was a workplace you would have a place where you could go to the final upper tier tribunal if you felt like there had been some procedures that had been done wrong.  You know kind of there comes a point where you can't have courts and judges deciding whether an MP needs to stay it is down to the people and all this process does is trigger a potential by-election and if he thinks he's done nothing wrong if the Conservatives think he's done nothing wrong then he should be standing that by-election and the people get to decide but they want another part of the process where they can stitch it up so that's what they're wanting there. There are some other problems around you know kind of whether you're heard or not how minor offences are dealt with but that's nothing to do with this case does that make sense you know kind of you know sometimes the commissioner ends up getting caught out getting people caught up because they've gone to a free party that a media organisation might have put on one weekend and you've got to declare that and if you don't declare that you can get into trouble but in reality those are minor offences. I'm worried you've got into trouble now for going to sort of TWT Navarra conference party I hope that's not the case I'll have it be known Lloyd has never put in favours for us and we don't employ him anyway so it doesn't matter. Lloyd I want to know what you think the public will think about this lobby journalists now for some reason their sort of first response when it comes to controversy is to say well people won't care anyway they sort of put themselves in the position of a party strategist Laura Koonsberg did this this morning so she tweeted the following senior MP says they've just been ordered by whips to back the ledsome amendment this is a proper Westminster village story but it's really important if you care about how MP's actions and behaviour is monitored so this is a proper Westminster village story it's actually quite similar to the expenses scandal right it's an MP who is getting paid a handsome sum 100,000 pounds on top of his decent MP salary this isn't the kind of thing that people in the public will just think oh that's completely normal to be getting paid 112,000 pounds by two private businesses and then set up government meetings for them that shouldn't really be a Westminster village story she might have swallowed someone else's line there um Aubrey Allegretti at the Guardian disagreed so he tweeted the following despite attempts by some to paint the row over Owen Patterson as a Westminster bubble story Tory MPs say they're already getting emails from furious constituents it's starting to worry some another Tory MP admits their inbox is in meltdown over the move to avoid suspending Patterson today they said I know the usual suspects the messages I'm getting aren't from them Lloyd um I don't know if you if your inbox is full I suppose the the angry emails would presumably be targeted at people who who voted in in favour of what Boris Johnson wanted so you wouldn't be a prime target for it but do you think this is the kind of thing that's going to have Tory electoral strategists worrying do you think they've they've potentially gone a bit too far here I don't think any one instance makes uh makes a downfall of a government but what happens is if it plays into a wider narrative now let's be honest Johnson's narrative of Keir being Captain Hyanside cut through with the public and now a lot of the public in my constituency say or you just say Matt in Hyanside you're you're part of Captain Hyanside's team well equally if we can make it stick that actually the Tories are with sleaze it won't be this instance but this will be an example of an instance that will push people over um and will be part of that kind of weight of things and this of course is only one instance of Tory sleaze whether it's Hancock giving kind of dodgy deals to his pub landlord mate whether it's you know kind of the sex pest whether it's you know kind of Patterson himself and I think that it does start to cut through and we saw that into um 92 to 97 and it didn't mean that Tories switched to Labour let's not be in some kind of we didn't suddenly have blue rinse brigade turning into communists what it meant is they didn't bother turning out of the next election and actually that helps us a little slightly lower turnout actually helps the Labour party in the left because what it is it's conservatives effectively saying I just don't trust my own side and I'm not really going to support them in and get out for them so that might be a strategy and I think it will start to work but if it ends now and we have an election in two years time it will be forgotten if it dribbles on and keeps playing on and that's why not sitting on the committee is important voting against it when the next vote comes around finding more scandals because there are more scandals here there are loads of more scandals because the conservatives are in the lobbyist pockets the developers pockets we know we generate for example or whoever the next one will be they are there waiting to be exposed a quick question from Mike John Green in the super chats why did only 480 MPs vote and Mike John Green says please ask Lloyd I can see 98 conservative MPs did not vote I assume that's not that they were paired was it is that just that they they stayed actively or some will have not voted because they've sat on their hands and abstained some will be paired I mean with copies happening at the moment I'm getting about to get the night train up um but some people will have gone up already you know kind of I think Barry Gardner was already already up there for example so that's why some people would have abstained and there is no way of us knowing why personally I don't think you should have pairing oh I think pairing should be published so you know who's officially paired and then you would know who's actually abstained but the whips don't like that because they like the murkiness of it um and they like the kind of slightly backhanded channels because then they can kind of say oh well we'll we'll pretend that you were paired if you now do a favor for us later on so that's what will be happening to those conservatives that abstained and weren't paired they will be told well it wasn't as bad as breaking the whip there might be a way you can come back out of this very interesting but it's also sinister isn't it what goes on there Lloyd Russell thank you so much for joining us this evening always a pleasure to speak to you cheers um Saul with uh Fiverr says Owen Patterson described EU law making a shockingly corrupt with a lack of accountability that would make a dictator blush um that is from Buzzfeed March 2016 so he was um at one point someone who cared about corruption not anymore um let's go straight on to our next story Wednesday was finance day at cop 26 bringing together finance ministers and central bankers to discuss how to fund a green transition UK Chancellor Rishi Sunak speaking to the conference declared that the rich world would belatedly meet their decade-old pledge to provide a hundred billion dollars per year to developing countries he also spent time emphasizing the importance of private finance but public investment alone isn't enough our second action is to mobilize private finance let me pay an enormous tribute to Mark Carney for his leadership leadership that is delivering results the Glasgow financial alliance for net zero has now brought together financial organizations with assets worth over a hundred and thirty trillion dollars of capital to be deployed this is a historic wall of capital for the net zero transition around the world Mark Carney whose Sunak reference there is the former governor of the bank of England and now chair of the Glasgow financial alliance for net zero that promise of a hundred and thirty trillion dollars to achieve net zero which was blazoned on the screen behind Sunak does sound impressive but is it all just hot air to find out I'm joined by Adrian Buller who is an environmental economist at the Commonwealth think tank Adrian welcome back to Navarra hi how are you nice hair it looks great thank you very much I appreciate it um my first question she was about that a hundred and thirty trillion dollars which is apparently being made available to achieve net zero that's a lot of money so if that were the case that would be transformational is there really a hundred and thirty trillion dollars which is now committed to achieving net zero what's going on here what are they talking about yeah I mean not at all so if it sounds like an outrageously large number that's because it is to put it in context like the combined capitalization of every listed company in the entire world is a hundred and twenty trillion so less than this and it's because this number has nothing to do with money that's like actually committed to any kind of activities related to climate finance it's just the aggregate pool of assets that is controlled in some shape or form by the 450 or so financial institutions that have signed up to that so insurers asset managers banks basically anything they've got on their balance sheets counts towards that hundred and thirty trillion dollar figure that means things like my credit card debt or if you have a mortgage you know that's an asset that's technically counted in that figure but obviously that's not being mobilized in any way um towards combating the climate crisis so it's it's a kind of clever sleight of hand although it's so ridiculous that I think they almost kind of overstepped it because it becomes very obvious that it's a bit of an obscene figure the depressing bit is that even at that size it's actually still less than half of global financial assets it's about 40 percent that's even made this kind of ambiguous commitment to maybe one day sort of align themselves with net zero what is the commitment that they've they've made so they've joined this alliance which is which mark carney seems to be leading what what have they committed to what have they suggested that they will do yes my canadian breathman mark carney has basically committed everyone to sign up to this pledging voluntarily that they will align their portfolios with net zero by 2050 um the trouble is that there's no sort of agreed standard on how about actually looks for the financial system it's a complicated question you're funding things that might have lifetimes extend decades into the future so it's tricky to actually do and those kinds of things can take you know years to establish which are obviously years that we don't have um and you know they've said that they're going to create an international standards kind of board to do that but who knows how long that will really take and even then you know these are voluntary commitments and what matters is you know what happens in the next few years up to 2030 is absolutely imperative to whether or not we'll be able to reach net zero by 2050 and there's nothing in this agreement that says you can't you know continue funding new fossil fuel projects into the future even though the international energy agency has already you know it's a pretty conservative organization and it has already said you know there is no space for new fossil fuel projects um and so basically it's just kind of like a toothless exercise in PR in my opinion you know it's great that finance has decided it cares about its green image um but unfortunately it's at the moment just kind of all voluntary wishy washy fluff basically let's go back to our friend Rishi um because he did make some separate pledges which sounded to me at least like they would have some legislative force i wouldn't be entirely voluntary um here he is in that in that same speech saying he would help rewire the financial system to to funnel that cash towards a green transition let's take a look what matters now is action to invest that capital in our low carbon future to do that investors need to have as much clarity and confidence in the climate impact of their investments as they do in the traditional financial metrics of profit and loss so our third action is to rewire the entire global financial system for net zero better and more consistent climate data sovereign green bonds mandatory sustainability disclosures proper climate risk surveillance stronger global reporting standards all things we need to deliver and i'm proud that the uk is playing its part we've already made it mandatory for businesses to disclose climate-related financial information with 35 other countries signing up to do the same today i'm announcing that the uk will go further and become the first ever net zero aligned financial center this means we are going to move towards making it mandatory for firms to publish a clear deliverable plan setting out how they will decarbonize and transition to net zero with an independent task force to define what's required so rishi sunak they're talking about new transparency commitments on firms to disclose and their environmental impacts and environmental risks and also a responsibility for uk firms to demonstrate they are on track towards net zero and he's suggesting there'll be some sort of independent body to to make sure they they are doing that adrian were either of of those two or announcements or or suggestions from rishi sunak were they were they significant i mean there's a couple good things sprinkled in there you know give us some crumbs which are you know green sovereign bonds or an international reporting standard but ultimately i mean he doesn't even accurately represent his own you know new strategy in that speech so the commitments around mandating that companies disclose how they'll get to net zero is actually a lot weaker than that so you can just go on the government's own fact track website and it says you know will may or will reporting how your company will reach net zero the mandatory and the answer is no what they are mandating is that you you know disclose some information that you've thought about transition risks you've thought about the climate crisis and you know how you'll adapt to the transition in some way but there's no actual requirement for you to commit to reaching that zero by 2050 and set out plans to do that there's also no requirement around you know eliminating carbon intensive activities so again it all comes down to you know this idea that somehow with more information with enough perfect information the rational actors of the market will finally you know allocate capital appropriately when obviously you know that's not the case the financial crisis was any indication but you know we've got lots of information we know that coal plants are driving the climate crisis and yet we continue to finance them the problem is that it's you know profitable in the near term and you know the chancellor doesn't want to do anything to kind of to get in the way of that so it's all kind of about you know disclosure what this will mean for companies as opposed to you know actually kind of having any any impact on what they'll really they'll really do in the real economy you know that's a really that's a really good point transparency will only get us so far given that we we know which industries are polluting and you know that they're still doing it there was some potential good news from COP26 at least the headline that really got my attention which was that potentially the commitments made at COP26 will help limit global warming or predicted to limit global warming to below two degrees that's according to a report by scientists at the University of Melbourne they modeled that yes if if the latest commitments are all reached then warming would only be 1.9 degrees now say only 1.9 degrees obviously we need it to be 1.5 degrees to to avoid tipping points etc and for the most vulnerable countries to be okay but you know that's a it's a big advantage on what came before and we can go to from the scientists involved this is according to The Guardian the report's author Malt Meinhausen an associate professor in climate science at Melbourne and a lead author for the Intergovernmental Panel on Climate Change said the momentous shift in the projected global warming was largely triggered by recent improvements in India and China's emission targets for 2030 as well as India's commitment to net zero by 2070 he said it was the first time the combined pledges and probable emissions path of more than 190 countries had given a better than 50 chance of limiting warming to below two degrees now Adrian as I said you know we're aiming for 1.5 degrees so 1.9 is still you know it's still not what we need but it's a hell of a lot of you know it's a downside improvement from what we've been used what we've been used to hearing before COP I think we were supposed to be on track to 2.7 do you buy this do you think this is this is this is credible but that now we have we've got the deals we need to keep below two degrees yeah I mean you know I'm not a climate modeler so I'm going to assume that the science is sound um however I think you know yeah it's great to have this kind of news prior to this the same models were showing that you know based on the nationally determined contributions that had already been made before this COP we were closer to you know three degrees so that's that's a market improvement a lot of it comes down to you as you pointed out there the pledges from China India other major emitters like Nigeria and great at the end of the day it is still 50 chance of reaching a temperature that commits you know unfathomable numbers of more people to suffering every year you know drought extreme weather flooding and a lot of it comes down to two things one you know what happens in the next 10 years so up until 2030 you know it's not that we can just kind of faff around until 2040 and then be like okay now we're going to do net zero every single ton of carbon that we emit makes it harder and harder to reach net zero and makes that that curve steeper and steeper so all of it will hinge on you know what countries actually do in the near term and the other fact is that a lot of these commitments that have been incorporated into that analysis are from lower income and emerging economies that have made them and very rightfully so contingent on rich countries meeting basic commitments about you know the climate finance pledge of a hundred billion dollars a year that we've been failing to meet scaling that up and you know all sorts of kind of transfers ideally of wealth in the form of cash grants although that's perhaps wishful thinking you know from the global north to the global south so there's a lot of contingencies in there but you know those contingencies have always been there so it is you know a sliver of potential soft minute good news amidst an otherwise kind of bin fire of a conference but yeah there's still a lot of contingency and you know 1.9 as you pointed out is still not good enough I'm going to I'm going to point to maybe two more slivers of good news so a couple of developments when we when we spoke to Simon Lewis on Monday he suggested that side deals on specific areas could be a big deal at this COP26 so it's not all about what gets negotiated and signed on the final day it's also what deals get made on the side we got two of those on Tuesday one was on methane so here 103 countries have signed a deal to reduce methane emissions by 30% by the end of the decade that deal includes Britain the US the EU Indonesia Pakistan and Argentina it doesn't include China India and Russia they are free of the top five methane emitters and it also doesn't include Australia who are you know the the real laggard when it comes to climate action the other was on deforestation so here we have a nice pledge a nice promise over 100 litres of pledge to end deforestation by 2030 here the pledge includes almost 14 billion pounds of public and private funds and includes countries which cover around 85% of the world's forests so that includes Canada Brazil Russia China Indonesia the democratic Republic of Congo the US and the UK um Adrian how how significant do you think these these are these these seem like you know it is a cause for small celebration again um yeah you know the optimist in me wants the thing that they are a cause for small celebration so the methane one is interesting right because what i was talking about before in terms of what happens in the decades between now and 2050 being really important um methane is actually quite relevant to that because unlike carbon dioxide which once you've emitted it sort of sits in the atmosphere for centuries and just accumulates and continues having its effect um methane kind of goes away once you've emitted it within about a decade and so if we make these cuts that they pledge then what you do is buy yourself quite a lot of time i mean quite a lot it's probably generous but you buy yourself some time in the harder work of cutting co2 emissions because once we sort of make those cuts the methane that's already in the atmosphere which is really really potent even though there's less of it um will start to dissipate and that can kind of buy us a bit of time um you know like everything else in this these are voluntary pledges we'll see how they're met again you know the the dirty word that no one wants to say is you know also fuel production they talk about methane from agriculture and you know land use changes but a huge amount of it is just producing natural gas or fossil gas which a lot of countries are still advocating as like a clean bridge fuel which is a complete falsehood um and so unless we're doing away with that process you're still going to have a lot of methane emissions um and then on the deforestation you know the nice thing about trees is that it's hard to disagree that we should stop cutting down trees so it's much less contentious than something like ending fossil fuels um but the trouble with this is you know it's it's great I'd love to see it um again it's all voluntary there's no kind of mechanism for how it will be carried out what will happen if countries don't meet that pledge and you know we've seen very similar pledges before so uh in 2014 we had an agreement out of New York um that basically said we would have deforestation by 2020 and halted by 2030 um you know check in at 2020 and it had gone up since that point um and that didn't even really cause much of a stir so you know it's hard to know whether that will actually be met um but it's great you know to see again it will come down to something that people don't want to talk about which is you know what is the root cause of deforestation in the first place and it's industrial agriculture it's you know production in the fossil fuel industry it's massive inequality in the global economy which means that you know people in the global north are consuming so much more um than our kind of fair share and those are kind of the sticky issues that no one wants to talk about um but yes at the end of the day I think we can take a little comfort that people want to protect the trees I really like the nice thing about trees it's the beginning of a sentence everybody likes trees everyone does like trees I don't want them to be cut down um unless you're a sustainable carpenter like that guy from insulate Britain who grows them after he chops them down um Adrian thank you so much for for making sense of announcements over the past 48 hours from COP26 very insightful as always um we're gonna go on to our final story I'm told Owen Patterson um so the topic of our of the first half of our show has told Sky he wouldn't hesitate to act in the same manner tomorrow after being criticized by a standards body for breaching lobbying rules he said no question he would act the same again the background there is Owen Patterson is trying to claim that he was actually acting in the public interest because he was trying to meet up with with various government agencies to point out I think it was a sort of a danger with milk and certain things that he thought it would be in the public interest for them to know what he also did though was was when he spoke to those agencies he spoke very very positively about companies he was being employed by so if he were being an honest guy he would say oh if I were to do this tomorrow I think that it was so in the public interest that I would do it again but what I would do is I'd give up that a hundred thousand pounds they give me every year because ultimately I don't need it anyway but that's that's not what he's he said if what he wanted to be was a whistleblower talking about the safety of milk he could have done that without being paid a hundred thousand pounds a year let's go to our final story of the evening we've always known Boris Johnson doesn't like scrutiny more recently Dominic Cummings revealed he is especially hostile to scrutiny from women both of those features of the prime minister were on show in an interview Boris Johnson gave a cop 26 to CNN's Christiane Amanpour do you want to answer what's going around on social media you brought up the national treasure Sir David Attenborough and there you all were in the plenary he's 95 years old he was wearing masks and you weren't it's all over the place right I you weren't wearing a mask yesterday sitting next to 95 year old national treasure David Attenborough I've been I've been you know wearing a mask when in confined spaces with people that I don't normally meet and I think it's up to people to take a judgment about whether they're whether they're you know at a reasonable distance from from someone and whether they're with someone they don't normally meet that's what that's what that's the approach we take the way she twiddled you know her farm as well she was skewering Boris Johnson it was really the height of camp also just repeating it over and over again 95 year old national treasure David Attenborough who you sat next to without any mask you mean 95 year old national treasure David Attenborough who you sat sat next to with no mask obviously I mean it is talking about the substance of this beyond the fact that as I say Boris Johnson really didn't like being scrutinized by a woman live on TV it is kind of wild isn't it sitting next to 95 old national treasure David Attenborough without a mask on because the important thing here is David Attenborough is wearing a mask right so if David Attenborough hadn't been wearing a mask and it just seemed like you know there were four people there none of them were that fussed they all felt relatively secure I've been to many a place where no one's wearing a mask pubs nightclubs etc I'm not saying no one should ever hang out close to someone without a mask on but if you're next to someone who is more vulnerable than yourself so David Attenborough at 95 is more vulnerable than Boris Johnson and they are wearing a mask so they're clearly someone who is concerned about COVID-19 then not wearing a mask yourself you know you might say it's reckless more than that I think it's just rude right it's really rude if you are next to someone who is particularly vulnerable to COVID-19 they're clearly making an effort you could make the effort and you just decide not to no I'm gonna sit here without a mask on I find it bizarre as I often say on this show I'm a creature of I'm a social animal so I often respond to people around me I wear a mask you know as on public transport where it's where it's you know mandated when I go to my corner shop the people who work there don't wear masks most of the people going there don't wear masks so often I forget to wear a mask but what I always do is if I'm surrounded by people wearing masks and especially if I'm surrounded by people wearing masks who are more vulnerable than myself I will put on a mask it's just basic decency and it is very much basic decency that Boris Johnson is just completely incapable of embodying and and he did not like it being pointed out there um let's watch another clip from that interview again you'll see Boris Johnson getting getting really peeved at the nature of the questions can I move on to COVID because yes there's a big spike in COVID in this country and it's you know the record here is worse than it is elsewhere around Europe um well I dispute that but the facts and the figures show it the again I will dispute that shall I shall I read them uh you can read whatever you like but well first of all let me I mean just let me ask you the question yeah um you have said you're going to stick to plan A which is no mandatory mask keep the vaccines going none of the social distancing or vaccine proofs that some of the other countries are doing but the NHS confederation and the British Medical Association have just come out and said plan B should be implemented now in other words masks when it's appropriating crowded places some sort of social distancing and um and and they're saying you know maybe even maybe even vaccine proof why would you not it's a very cheap and easy and people are used to to masks why why would you not do that they say they'll be potentially yet another terrible pressure on the NHS this winter well I I'm I'm watching the data the whole time we thank you we all we're all we're all looking at the the data we've got to remain very cautious we've got to remain humble in the face of the of the of nature what the disease can do at the moment we don't see any reason to deviate from the plan that we're on my favorite part that was the thank you why did he say thank you what was he what was he saying thank you for I don't know another thing I liked about that clip was how often Boris Johnson looked to the side so he was like why is this woman asking me such difficult questions I don't know who is looking at presumably some sort of advisor but the advisor wasn't going to be able to tell him that numbers weren't worse in Europe than in Britain when it comes to COVID-19 because the numbers are a hell of a lot worse in in Britain than they are in Europe so I might have got that the wrong way around she was right the interview was right I'm kind of I'm kind of regret that she didn't get the chance to read out the numbers the the case levels the death levels that are in France Spain Germany Portugal Italy compared to the UK because they are much worse in the UK than in the rest of Western Europe I mean Boris Johnson could have been referring to some Eastern European countries where the deaths are higher that's because they have quite poor vaccination rates at this point in time and you know we know Boris Johnson does like to compare himself to those countries which are doing the worst as opposed to those countries which are most similar to us in terms of income levels and in terms of vaccination rates so again a very good skewering from that CNN host what it kind of made me think is it would be good if our political interviewers in this country were less good friends with politicians because you know if Laura Coonsburg was doing that interview I just think she knows Boris Johnson too well to talk to him like that so the fact that she has potentially never met Boris Johnson before she was just looking at him like you know any other person I think that made the interview so much more effective which is why I mean there is a strong argument to have a much thicker wall between politicians and interviewers because when they're mates you just don't get that same scrutiny you don't get that level of uncomfortableness on the part of a politician who is being made to squeal it's important for scrutiny it's also just much better TV so the bosses at the BBC when you get your next political editor to make sure they are not friends with the Prime Minister or not on friendly terms with the Prime Minister at least let's go to a couple of super chats Anna with 30 pounds great show as always thank you very much for the donation free Tory councillors knocked on my door last week and I confess I called them Tory scum they just wouldn't go away so I had no choice enough love the hair Michael thank you very much for that comment Baz cams with a fiber get the vaccine 100% agree with Baz cams get the vaccine get the booster if you're entitled to one it seems like they work really god damn well we are going to wrap up the show there thanks for everyone for joining we'll be back on Friday at 7 p.m. this time with Ash Sarkar so do make sure you hit subscribe if you haven't already for now you've been watching tisky sour on the bar media good night


Hey, it's Anafa, and yes, I haven't washed my hair in a week. Still looking pretty decent. In this short video, I want to show you something pretty crazy that I figured out, and that is how to use a sampler plugin to achieve a time warping effect that we can control very precisely. What I initially wanted to do is something a bit like wavetable synthesis, but this turned out to be pretty cool, so let me show it to you. So here is an empty Ardor session, and first thing we need is an audio clip that we want to time warp. So maybe let's try and record some singing. I am recording random vocals so we can process them later. Woo! Okay, don't pay attention to the bad performance. This is not important. This is just a test clip. Okay, so now I'm going to export this. So we can drop it into the sampler plugin.  Let's change the name of it and call this sample 01. You can also normalize it once we're at it, because it's going to make it easier to process later. Okay, so we're going to export it to 24-bit FLAC because that's pretty good. And here it is. Now you see I've created a second track here, and this is Synth V1, actually I think this is called with a smaller letter, by Rui Nuno Capella, who is also the creator of Qtractor and a few other plugins like Pad V1 or Drum K V1. So this is one of the more sophisticated sampler plugins that we have, and it has some options that are pretty unique. That is, you can, oh wait, it's a Synth V1. I need a Sample V1. Okay, so here is Sample V1. Let me load the sound we've rendered. So I can right-click, open sample, and now we have this thing, and I can just drag it here or here. Actually, I can't drag it anywhere. Okay, I can just copy this path, let's do it right here, and now. Okay, we have the sample loaded. So, now what we can do, you see there is an option to enable offset, and we can just drag these handles. Now if I... So the thing is, we can automate this switch, so we can play each note starting from a different position. And we're going to make each note very short. First, I want to disable the LFO, disable the filter, we don't need these. I'm going to turn on the volume to maximum. Effects. And I want to turn down the release. Okay, the attack is very short. That's good. All right, now we want to automate this offset start. So, you know what? I'm going to make it stay on top. So we can just have it on in here at all times. Aha! There you go. Perfect. So now I'm going to... Actually, we don't need this track at all. I'm just going to hide it. So I'm going to go to Automation, Processor Automation, Sample View 1, and then we go to Gen 1, which is the Generator, Offset Start. And this is what we need to automate. Now, if I move this thing, you can see that the offset start moves and this is the same slider here. Now, of course, we need some MIDI notes, and I would like the note that would play this in its original pitch. And because we have C4 selected here, we need to play C4 to get the original pitch. So that's the note. So you see, if I do this, we get that funny, repeating voice trying to fit everything on one screen. Not that easy. Now, if I make this automated and change this to play... You see, this is the basis of the effect that we were after. We're playing different notes. If I cut this and make it longer... You can see that the offset... the offset updates only when we hit a new note. So we need to put the notes really densely if we want to have any decent resolution of this time warping. So I'm going to duplicate this range, this MIDI region. I'm going to consolidate the range and now compress it even more. So you see, we have very densely packed notes. And now we can play with the attack and release. Maybe if we make this... So basically now we're playing back the entire sample that was loaded over the period of these four bars because we just simply automate this offset from start to finish with a straight ramp. But this ramp doesn't have to be straight. We can just do something like that. Pause for a while.  You can see this moves. We're not precisely pausing because these values are not identical. But if I do edit, Ctrl-C, now right-click here, edit, paste and we have the exact same value. Now we can do some other crazy stuff like go back. We might think now that's a bit too little time resolution. Let's consolidate these notes and time-stretch them again. Compress them four times so you have even denser notes. Now this sounds a little bit... This sounds a bit dense. Maybe we can just shorten the release because we can have these notes overlap. There is a certain polyphony here. I don't even know if it's limited by anything. Let me see effects. By the way, it has a built-in limiter which is on my default. I don't even know how it works. I don't know what's the polyphony of this sampler right now, but I think it plays everything we throw at it. Oh, we've hit a limit. We could hear that there was a limit of the played notes and we had some silence. So if we shorten this... Now, if we want to have something a bit simpler, maybe just time-warp this. Of course, this is not clean. Don't think that you can correct some vocals and get some clean time fixes.  I'm thinking about achieving some weird effects that could be useful in creative processes. Why doesn't it select? Now, where does this start? The cool thing is that if we... Okay, here is the... I want to go forward and then go back. Okay, how about we stretch that... for a longer period of time? Let's... Now, I have auto-return. Let's press 5. No, 6 on the keyboard. Okay, it's just near the end. Just need to skip some more. Yes. Now, maybe the density of the notes is too much. We can also alter that depending on where this is used. We can just have these interleaved and you don't have to have... Yeah, maybe a lower note density is a bit better. Not to mention, we can use the mod wheel to pitch shift this stuff. Sorry, pitch bend. By default, I believe this is two semitones. If we go... There's going to be 10 semitones? I don't know. Let's go Automation Bender Channel 1. I believe now we can basically pitch shift this thing up and down. As we go. Oh, yes, but it would be preferable if we just consolidated this all Whoa, that's weird. Don't want that many points. Oh, wait. It's in a discrete mode. I don't want discrete mode. Online ear mode. Yes, thank you. So we see now... I am recording. So you see the fun is we are controlling the pitch of every single slice and every single slice is a single note we are playing right here. Independently. That means we're changing the pitch independently of the timing and we are controlling the timing with this offset Automation. So we have independent control over the timing and the pitch. So this is like a manual way to do crude pitch shifting and time stretching, time warping. Why time warping? Because we can do whatever we want with this Automation Curve and just go back and forth. It's not like scratching because scratching would combine the pitch and the timing and we are like decoupling that.  Sometimes you want something interesting and you know, many great things in the music has happened because of flaws like, you know, guitar distortion. Yeah, so that's what I wanted to show you. Have fun with this Sample V1 time warping. Maybe you'll find a use for that. And if you have other ideas, share them in the comments. So yeah, that was a quickly made video. Thanks for watching. I hope you learned something. Also, big thanks to everyone who supports my work financially. I really appreciate that. And I was very surprised to see a lot of new patrons coming in during this time of self-isolation. That was surprising and I'm very grateful for your support. So if you would like to join these people and help keep this show going, please go to patreon.com.anfa or liberapay.com.anfa. Now go, grab Sample V1 and maybe make some music.