Hello and welcome to this next lecture in the series on the subject of wavelets and multirate DSP. And in broader sense the subject that deals with joint time frequency analysis. Today's lecture is titled as towards selecting wavelets through vanishing moments. So, in this particular lecture we are going to understand the significance of vanishing moments. However, before we start our journey let us spend few minutes in recalling what we did last time. Because after all what we are going to do in this particular lecture it in a way stands on the shoulder of what we did in the last couple of lectures. So, let us quickly revisit what we did in last couple of lectures. If you remember in the last to last lecture we mentioned and we in a way expressed our belief that if last 100 years were the 100 years of Fourier transform then probably next 100 years are going to be the 100 years of wavelet transform. And this belief comes out of the fact that when it comes to dealing with non stationary type of signals Fourier transform has its own limitations. And that is where we will have to go beyond the purview of Fourier transform and start looking into the characteristics of wavelet transform. We started our journey with a basic fundamental principle that wavelet transform can decompose an underlying signal into two separate series. A single series to represent the most course version of the information and that leads us to scaling function and double series to represent the refined version or that gives us the details which are present in the underlying signal or function and that leads us to wavelet function. We further down this and then we realized that when it comes to wavelet transform scaling translation and dilation they are indeed the hallmarks of wavelet transform. And they together lead us to multi resolution analysis which is very popularly also known as MRA. The whole philosophy of multi resolution analysis is in a way based on the underlying framework. And this framework comes out of the presence of nested subsets and these nested subsets they in a way give us the entire multi resolution framework. We also looked at the two band MRA filter bank and this structure is very typical for any input signal let us say p of n. If in the analysis side I have analysis low pass filter presented by at 0 of z and analysis high pass filter given by g 0 of z and they are followed by down samplers or disseminators. This is quite essential to keep total number of samples same. For example, if I am starting off with four samples then I should be able to produce two samples here and two samples here. However, the moment you introduce decimeter or down sampler the whole structure becomes something that can be called as a multirate structure. The sampling rate is not uniform and that is why for all the unirate DSP structures we aim at designing filters digital filters. And for all multirate structures like the one shown in this particular diagram we always aim at designing filter banks. So, we have low pass filters and high pass filters their duals of each other and they together formulate filter bank and that is the whole point when it comes to design of a multirate structure. We also typically saw that if we have a given input signal p of n that belongs to v 1 then by virtue of having these disseminators we end up with projections of the same signal let us say p 0 that belongs to v 0 because we are talking about low pass filter the scaling function and correspondingly q 0 in w 0 because we are talking about the high pass filter which comes out of the wavelet function. And then if we see the ladder structure once again then we realized that I can draw this ladder structure like this v of minus 3 which is contained in v of minus 2 and this will continue. And if we are starting in v of 0 not necessarily we have to start in v of 0 this is just one example. If we start in v of 0 then by virtue of having a 2 band filter bank structure we in a way move down the ladder. And typically it is easier to move down the ladder because if I have the information and if that information is projected in a subspace v of 0 then what I can do is I can throw away the information which is w 0 and what I will be left with is v of minus 1 similarly from v of minus 1 I can throw away the information which is w of minus 1 and I can have the information projections in v of minus 2. So, when it comes to moving down the ladder you have the piece of information and just keep on losing the details and you get the approximations in the lower scales. However, we also realized that for many of the applications it is desired it is required to actually move up the ladder. And if I really want to move up the ladder for example, if I have to move from v of 0 to v of 1 then I have to have this information with me I can add these two pieces and only then I can move to v of 1. From v of 1 if I have to move to v of 2 then I have to have the corresponding projections in w of 1 and these two together can be added to produce the corresponding projections in v of 2. So, how to go about doing this and last lecture we in a way put down the framework for doing the same. And what we saw in the last lecture was this if I have some signal let us say f j of x that belongs to v of j. And for the scale of 1 upon 2 to the power j I can span the whole space whole linear space using this kind of basis function. Where 2 to the power j by 2 is the normalizing factor and by adding this factor we not only make sure that my basis functions are orthogonal, but I normalize my orthogonal basis function and such kind of basis functions are indeed orthonormal basis functions. And then phi of 2 to the power j x minus k where k is the translation parameter. So, this gives me normalization this parameter over here will give me scaling and k is obviously meant for translation. And by using this assembly then I can represent f j of x like this where all the alpha j k values are the approximated values which can be calculated using this formula. We went ahead and we also looked at the framework for finding out projections in w j subspaces. Let us say these are named as functions g j of x just for the sake of nomenclature we are talking about the same function which belongs to a subspace w j and with the scale of 1 upon 2 to the power j again I can span these linear subspaces using this kind of orthonormal basis function 2 to the power j by 2 psi which is my wavelet function 2 to the power j x minus k where k is again the translation parameter. And I can write down g j of x like this where beta of j k are indeed the details present in the underlying signal and beta j of k can be calculated like this. And then we wanted to really ensure that this assembly helps us move up the ladder. If I have projections in v 0 and w 0 and if I orthogonally add these projections then I end up with projections in v of 1. So, from v of 0 my journey takes me to v of 1. So, I have start moving up the ladder and we use this orthogonal summation formula for doing the same. If you remember last time we solved one problem the problem where we took f of x as the sample function where x f of x is equal to x for all the values of x between 0 and 3. And it is a simple straight line and then we started finding out the projections of this f of x first of all in v of 0. We know the formula and it all boils down to finding out the alpha value. So, alpha 0 0 we plugged in everything and we realized that alpha 0 0 was half. We went ahead and we also calculated alpha 0 1 and then we realized that alpha 0 1 value came out to be 3 by 2 and correspondingly alpha 0 2 value came out to be 5 by 2. And as the name suggests these are indeed the approximations which are shown in green. So, all these green values are the approximated values of the original signal it is corresponding projections in v of 0 using Haar scaling function. We then went ahead and did the similar exercise for finding out the projections in w 0 and then we realized that g 0 of x which belongs to w 0 is indeed summation over the details and the corresponding translated version of the basis function. So, the whole task was then to find out the beta values and then we did that we initially calculated beta 0 we went ahead and calculated beta 0 1 and also beta 0 2. And then we realized that all beta values were indeed minus 1 by 4 and if I have these beta values with me I can correspondingly find out g 0 of x. Then came the important task of moving from v 0 to v 1. We can go on adding up the alpha 0 and beta 0 k values to find out alpha 1 k values. We can also calculate alpha 1 k values using the normal formula and in the end we are able to tally all the different values of alpha 1 k. We solved the problem of alpha 1 0 and we realized that we do not really have to worry about this particular factor of square root of 2. Because when it comes to plugging in the value of alpha 1 0 in the formula for f 1 of x it will be taken care of and so we should focus only on 1 by 4. And then we calculated all the alpha values by adding up alpha 0 k and beta 0 k values. So, we added up all the alpha 0 k and beta 0 k values for example, in order to calculate alpha 1 0 we added up the first half of alpha 0 0 and the first half of beta 0 0 and that is how we are able to calculate the value of alpha 1 0. And then we continued for the rest of the values and that is how we are able to generate all these values of alpha 1 k. We plotted everything and then finally, all the red points all the red approximated values are indeed alpha 1 k values and they will help us find out the projections of f of x in v of 1. And we confirmed that indeed we are able to move from v 0 to v of 1 and visually graphically we can now verify that v of 1 gives us better approximation of the original signal when we compare it with the corresponding approximations given by v of 0. So, we are indeed able to add these details in w 0 and then moved on to v of 1 definitely a better approximation of the underlying signal. There is a reason as to why we revisited this entire example that we solved in the last lecture. What we are going to do in today's class is in a way based on this particular example that we solved. We are going to pose few interesting questions based on this particular example and then correspondingly try and solve these two questions and that will formulate the reminder of today's lecture. But before that let us quickly go through a MATLAB simulation of the same problem that we just solved. This is a very simple MATLAB program. CLC is meant for clearing up the command prompt. Clear all is going to clear all the variables and close all is going to close everything. Now, let us define our x axis and this could be our time axis for example. And since my signal f of x exists between 0 and 3 x of 0 is 0 and x 1 is 3. The level is selected to be 9 and this level gives us the resolution step while moving from x 0 to x 1 and that will be clear when we see the next line written over here. So, we have written that x is equal to x of 0. So, it begins with x of 0 and then it increments in a step size and this step size is 1 upon 2 to the power level. So, the step size that we have selected is dependent on the value of level variable that we select. In this step size it will start from x 0 and with this step size it will go all the way till x 1 which is 3 minus 1 of the steps that is 1 upon 2 to the power level. And the underlying function is f of x is equal to x and that is why we have written f is equal to x. And then we have saved this variable f in a MAT file which is test underscore f dot MAT. So, let me run this program and after running this program we can very clearly see the MAT file that is test underscore f dot MAT that has been generated. Now, let us invoke the wavelet toolbox and let us look at the one dimensional analysis. Now, for this analysis let us provide the signal that we have generated as the input that is test underscore f dot MAT. So, this is how our signal actually looks and let us try and analyze this signal using a simple Har wavelet and let us do the analysis till the third level. So, this is how the analysis actually looks. And now let me be interested in the different modes that can help us understand what exactly goes into the system. So, these are the separate modes of doing the analysis. And as you can absolutely clearly see as far as the approximation in a 5 is concerned it is quite crude. And as we start moving towards a 1 it gets better and better and better. And we also know the reason we add a 5 into d 5 to generate a 4 for example, and this would continue. Let me superimpose these modes to really understand it better. And instead of using 5 let me use 10 scales and then try and superimpose everything on top of one another. And now this particular plot will really help us understand what kind of things we are actually doing. And let us start one step at a time. So, instead of selecting all let me start with only the most crude level approximation. And now let us start adding up the details by which of which we will start moving up the ladder. So, you can clearly see that approximation is better now. And as you continue doing this you will get a better and better and better approximation. And then right at the end you go tantalizingly close to your real signal. So, if we just place the last value that we have obtained then this is indeed very very close in terms of representation to the underlying function or the underlying signal. Excellent. So, as can be seen from the slides this particular framework indeed gave us the power to move either down the ladder or up the ladder. And we can clearly see that the zoom in and the zoom out properties of the wavelet transform are indeed met. I can really zoom in and zoom out. And in order to be able to achieve this I have not only my scaling parameter, but also the translation parameter. The best part is this makes the entire framework extremely scalable. Scalability stems out of obviously the whole framework being multi resolution framework. And we make use of scalable systems every now and then. For example, all the images which are stored on internet they are in a way stored in a pyramidal structure. When we Google search for a particular type of image what gets retrieved back are only the thumbnails that is the uppermost slice of the pyramid. And when you select or click on that particular thumbnail then probably one of the slice from the underlying framework of the entire pyramid will get selected depending upon the resolution of the kind of hardware that you are using. Same holds true even for video analysis. Almost all the video codecs that we make use of these days they demand scalability. And that is where wavelets have started replacing many of the conventional basis structures. For example, in Zepek discrete cosine transform used to get used. In Zepek 2000 we all know we make use of 5 by 3 bi orthogonal tap which is a wavelet basis function. And so scalability is indeed the need of the time. Let us go back to slides and we have seen the framework. We have studied the framework. And this framework in a way leads us to two very important questions. Question number one how do we go about selecting the mother wavelet and the scale of analysis? So, both the questions are very important which are the sub questions of the first question. Which mother wavelet whether I should use her mother wavelet or Dobash or Shannon or mayors. There is tremendous amount of variety. And what scale of analysis I should select?  What is the stopping criteria? These are two important questions. And correspondingly there comes the second important question as well. And the second question is what is the procedure to calculate scaling and wavelet coefficients? We have been using the coefficients which are readily available to us given by Dr. Har, given by Dr. Dobash. Can we think of finding out our own wavelet? Can we think of finding out our own coefficients for doing the analysis? It is a tall order. It is a very difficult proposition altogether. However, at least we can get into the head of the scientists who in a way discovered these different mother wavelets and understand the procedure. And who knows that will lead us to finding out something of our own. However, we will do that in the next lecture. In the reminder of this particular lecture, we will try and answer the first question. And if we refer to the slides again, the first question is of great significance. The first question in a way asks us what is the significance of selecting the mother wavelet? If I have an underlying application and I know what kind of data or information I am going to deal with, then how I can appropriately select the mother wavelet in order to be able to carry out the analysis effectively and efficiently? That is the question that we will try and answer in the reminder of this lecture. And we are going to invoke one important property of wavelets which is called as vanishing moments. We are slowly and gradually move towards vanishing moments through correlation. We are very familiar with correlation and convolution. So, through correlation, we will slowly and gradually move towards moments. We will define moments, we will understand the concept of moments getting vanished and we will also try and understand why this is of great importance, great significance. In order to be able to bring out the correlation parameters in wavelet domain, let us first of all convince ourselves that in a way that is precisely what we were doing as far as the Fourier domain is concerned. In Fourier domain, we made use of this correlation to a large extent. And this particular property of correlation is of great importance. What is shown in this particular slide? These are the basis functions. So, typically the real part of the basis and the imaginary part of the basis. We know the basis function of Fourier transform is e to the power j omega. And this is the real part which is the cosine part and this is the imaginary part which is the sine part. And then if we pose this particular question that how indeed Fourier transform works, then one way of looking at Fourier transform is understanding the correlation between the underlying function and the basis function. And this can be done using simple dot product philosophy. So, what we will do is we will go back to one sample MATLAB program. So, in this particular MATLAB program as can be seen on the screen, we have generated a function. And we want to analyze this particular function, let us say y. And this function is a good looking stationary function that means all the frequencies, they are present all throughout this function. And as can be seen in fact, there are two frequencies which are present in this particular function, sine of 3 and cos of 8, x is a variable again. And you can add a 2 pi in order to make this normalized. So, this function has two frequencies sine of 3 and cos of 8. And let us find out the dot product. Well the concept of dot product is very useful particularly for engineers while doing the analysis of signals. Because in a way dot product means instantaneous product, we can look at all the instances on x axis which is time axis and carry out the multiplication as simple as that. So, keeping that in mind let us say to analyze this particular underlying signal, I invoke this particular basis in Fourier transform. Now, we have understood that Fourier basis is e to the power j which can be disintegrated into real and imaginary parts which is cosine and sine part. And let us say I am invoking this underlying signal with the basis of cos of 6 x. And if I do so, then let us see what kind of response do we get. So, this is my underlying function or a signal which is stationary signal and it contains two frequencies. This is my basis function with which I am doing my analysis. So, this is cos of 6 that is the basis I have used. And you can clearly see since cos of 6 is not present in the original signal, there is poor correlation between the signal to be analyzed which is shown in red and the basis function which is shown in blue. And as a result of that, if I do if I take the dot product between these two, then this is what I get. And if I integrate this dot product which is shown in green, then you can clearly realize that there are as much as positive parts as much as there are negative parts and they would cancel out each other. And as a result of that I will not get any peak for a frequency of 6 and it makes sense because I do not have that frequency in my original signal. So, in my original signal I have only two frequencies sine of 3 and cos of 8. So, it makes sense when these parts they would in a way cancel out each other. And that essentially indicates that the underlying signal and basis they are not correlated. Now, instead of using the basis which is not present in the original signal using a frequency which is not present in the original signal, let us invoke the underlying signal with a frequency which is present for example, sine of 3. This frequency is indeed present in the signal. So, let us try and invoke with sine of 3. And if I run this again, then this is the original signal that we are trying to analyze and this is now sine of 3. And you can clearly observe a good amount of correlation. This is positive cycle and there is lot of activity in positive area, very little activity in the negative area. This is the negative cycle and again very little activity in the positive area for the underlying signal. So, the in general correlation is much much better and that is because this frequency is actually present in the original signal. And now, if you find out the dot product, then you will realize that there are very less negative parts and the area under the positive part is much much more. So, when I integrate this dot product, I will definitely get some positive value and that will be the peak at 3, at a frequency of 3 when I am trying to plot the frequency response or the Fourier response of this underlying signal. So, that is precisely why we end up with a peak at a frequency of 3. The dot product essentially tells us that the basis of sine 3 is highly correlated with the underlying signal. This is indeed true for all different varieties of basis. Let us go back to the slides and let us run through few of the examples quickly. As can be seen in a slide, this is the same signal sine of 3 and cos of 8 when invoked with cos of 1 obviously, poor correlation and so the dot product would result into the parts that would in a way cancel out each other. Same signal when invoked with sine of 1, again this frequency is not present in the original signal. So, poor correlation and the dot product parts would cancel out each other. So, no peak will be generated at a frequency of 1. Now, if I invoke this with cos of 3, you can clearly see that cos of 3 is not present in the original signal. So, once again the dot product will have the parts that would cancel out each other. However, as we have seen in the MATLAB demonstration, if we invoke this with sine of 3 which is now present in the underlying signal, then definitely dot product will generate a peak at the frequency of 3. The same holds true for cos of 8, because cos of 8 is present in the original signal. And as a result of that you can clearly sense that correlation parameter is very high, correlation index is very high and if you take the dot product, then that is going to give you a peak at a frequency of 8. So, this idea of correlation we have been using with Fourier transform for quite some time. Now, this is a good time to invoke the same property of correlation in the context of wavelets. So, let us do that. We know the formula for convolution very well. So, we will start with the convolution formula, move towards correlation formula and then see what is the significance of movements when it comes to deciding the basis wavelet function for analyzing a particular type of underlying signal. So, let us write down the formula for convolution first, because we are quite familiar with convolution. And if we want to find out the convolution between f 1 of x convolved with f 2 of x, then that is going to be equal to integration from minus infinity to plus infinity f 1 of x minus t into f 2 of x into d x. Now, if we get rid of this flipping operation, then the convolution will become correlation. And so, I can very well write down the correlation formula like this. I would say correlation between two functions say f 1 and f 2 will be f 1 of x. Well, this stands for correlation. This is not a very familiar mathematical notation. So, please pardon me for abuse of mathematical notation, but just to understand. So, this is correlation between f 1 of x and f 2 of x. And that is equal to integration from minus infinity to plus infinity. I would say f 1 of t minus x now into f 2 of x into we used d x in the last formula. This should be d t just a correction. So, this is the correlation formula. Now, see since we are often interested in detecting sensitive activities in the signal such as spike or jump discontinuity in its higher order derivatives, we would like to know about what kind of wavelets will be able to see such activities. And indeed it turns out that we can find wavelets that can detect or see linear or quadratic or higher polynomial structures. And that brings us to the subject on maximum order of vanishing moments. So, let us define what do we mean by moments first. And then we will understand the significance of moments when it comes to selecting a particular type of mother wavelet. So, moments the moment of order m say m of m of function f of x on interval a comma b can be given as m m to be equal to integration from a to b x to the power m f of x into d x. So, this is how I can go about defining the moments. And this is of order m. So, I can find out zeroth moment by plugging in m small m is equal to 0. Correspondingly I can go about finding out first moment and second moment and third moment and so on. Now, when these moments of higher order they vanish, they in a way tell us something very very special about the underlying wavelet. So, what special information these moments convey we are going to understand in few minutes. But before that to understand whether the moments actually vanish or not let us very quickly solve a simple problem with the Haar wavelet once again to really convince ourselves that the moments indeed vanish out. So, let us take a case of Haar which is also the first member in the Dobash's family. So, Haar which is equal to Dob 1 psi of x.  And we know the formula and I can plug in the values from 0 to 1 that is because this psi of x exists only between 0 and 1. We typically know how this psi of x looks. So, this is my psi of x which exists only between 0 and 1 and that is where integration limits are from 0 to 1 and then x to the power 0 psi of x into d x. And now we will have to split this integration into two parts from 0 to half we have x to the power 0 is going to go to 1. So, 1 into from 0 to half this value this function takes a value of plus 1. So, I can plug in 1 of d x minus because it is going to take a value of minus 1 between half and 1 and then 1 into d x. So, that will result into x 0 to half minus x from half to 1. And so, we are talking about a situation where we have half minus half and this goes to 0. And so, I can very well say that the zeroth moment of her mother wavelet vanishes whether this holds true for the first moment as far as her mother wavelet is concerned. Let us try and find out. Let us do the same exercise for her psi of x, but let us try and find out the first moment. So, m of 1 is going to be equal to between 0 and 1 and then now I have x to the power 1 psi of x into d x. And that leads us to from 0 to half x into d x minus half to 1 x into d x. And typically we know that this is x square by 2 in 0 and half minus x square by 2 between 0 and half. And if you solve this, this is going to go to minus 1 by 4 which is not equal to 0. And so, we can very well conclude that the first moment of her mother wavelet does not vanish or in other words as far as the her mother wavelet is concerned, it has only one moment which vanishes which is the zeroth moment interesting. Now, that will take us to one very interesting question. And that is vanishing higher moments by higher we mean higher order moments of wavelet how this is a measure of quality. So, this is one interesting question that we are going to in a way pose. And there are two ways in which we can answer this question. And these two ways are I can probably say that as far as my vanishing moments are concerned, these vanishing moments they definitely number 1 gives me savings in computations. And number 2 they are definitely useful in detecting higher derivatives. And this second property is of great importance, it is of great significance. Now, why this is important well we are going to revisit the problem that we solved last time. So, we will refer to the slides once again, we solve this particular problem last time if you remember. And this is a very typical application which is required in many real life situations where we are trying to in a way find out the hidden discontinuity, the hidden jump in the underlying signal. And we took this particular function as an example where g of t is equal to t between 0 and half and t minus 1 between half and 1. And there was this clear jump at t is equal to 0.5. We did the integration of the original signal g of t by virtue of doing this integration we are able to generate signal h of t. And still in h of t we realize that there is this cusp jump at time t is equal to 0.5. So, we integrated this h of t again in order to finally, generate f of t. And now if we plot this f of t then this function would definitely appear very very smooth to our eye. And if you remember last time we did this small exercise in MATLAB. So, we are able to generate these different functions and these different functions they look like this. So, in the original function the discontinuity is obvious. In the integrated version there is a cusp discontinuity. And then by virtue of integrating twice we get a very smooth good looking function. And we also saved this function in a test underscore sig underscore f dot mat. And if you remember we did this small exercise last time that we invoked the windows menu of wavelet toolbox given by math works. And we tried to interpret this particular function. So, I am loading this particular signal that we have generated which is test underscore sig. And we know that in this particular signal exactly midway through there is a discontinuity which is hidden. Because we have done double integration of the original signal. So, it is not apparent to the eye it looks like it is a smooth signal, but we know that there is a hidden discontinuity over here. And now if we try and do the analysis let us say using har. And I am selecting the maximum possible scale I am going all the way till level number 9. And if I do the analysis and if I see the detail after scale 1 then oh har wavelet analysis misses out this discontinuity. So, I cannot really detect this discontinuity using har. By the way har is also known as dobash 1. So, har is the first member in the dobash family. So, dobash 1 if I do the analysis then it is the same thing. And we clearly miss out this discontinuity. As against that if we invoke dobash 2 and now if we try and analyze then you can clearly see that I can now very clearly find out the discontinuity over here. I can zoom on to this part to really understand it better. And you can clearly see at 256 because we are doing a 2 512 level analysis. So, exactly midway is 256. And at 256 this pattern goes abrupt and it tells us that there is a discontinuity at 256. So, har was not able to detect this, but dobash 2 was definitely able to detect this. And if you allow me to select dobash 3 the discontinuity will be more apparent. So, it tells us that oh there is indeed this discontinuity present at this point in the original signal. Correspondingly we can go on selecting dobash 4 and the discontinuity will become more and more apparent. So, what we are trying to say is which mother function should be selected is one very interesting question. And it depends on what kind of data we are trying to analyze. Continuity or the hidden jump was detected only using those wavelet functions which are above dobash 2. And there is a strong connection between number of vanishing moments associated with these different mother wavelets and their capability in doing the underlying task. We will stop here as far as this lecture is concerned and in the next lecture we will continue hopping on the same lines. We will realize that vanishing moments are of great importance and only certain type and certain kind of wavelet mother wavelets they are capable of doing certain type of jobs certain type of tasks. Through the correlation through the vanishing moments we will try and make sense of what we covered in this particular lecture that we will conclude in the next lecture. Thank you.


Hey everyone, we have resin tint and we're going to show you some really cool ways to color your art resin You can mix the resin tint right into art resin and then pour it into molds and you can mix different colors in different little cups and pour it and just let it flow and even floats on water and Wait till you see what you can do with that And it comes in a 10 pack of original colors including black and white And then we have our metallics and pearls is three metallics and five pearls and then our six pack of Neon brights Which is Dave's favorite Resin tint is oil based and for really good reason. We want it to be non-toxic Alcohol looks awesome, but it's a solvent and we really really wanted it to be so and even when you torch it It's still not toxic because all you're doing is heating up the oil a little bit as long as you move fast You don't want to burn the oil. You're gonna want to shake well loosen the cap a bit to let in some air Give it a really good shake and you hear there's a nut in there to mix the color with the oil really nice Also, these are squeezy bottles and it's just great as opposed to glass. You'll see why we picked squeezy squeezy Color enthusiast Josie Lewis flew all the way here to play with us and resident. Yeah, and here's some of the fun that we had with it It's really mesmerizing And you just really can drop into this great heavenly endless rainbow time party unicorns and chocolate Really excited to see what you make show us what you do on hashtag resident


As the United States Marines, we're always ready for whenever the nation needs us most. The desired end state of the training was to validate our amphibious capabilities of pulling us anywhere at any time, as well as test us in mountain block environments one through three. At any given notice, we have to be ready to place in a difficult and austere environment, help those less fortunate, and bring stability back to those areas that need it most. By working with third-world nationals or individuals from other, you know, NATO alliance countries, it's imperative that we know how to bring back stability. Proficiency is gauged, obviously, on the battlefield. You know, at the end of the day, the bullets and bad guys have a lot to say with it. How we can best prepare that is through reps, which I'd argue we got quite a bit during this retreat.


I have a confession to make. I really feel like my coverage on Spider-Man 2 last time was a little too negative. So today, I'm actually going to make a video about Spider-Man 2 that's mostly positive. Well, mostly positive. It'll get better the higher we get up the tier list. That's right, baby! We're doing a whole Spider-Man 2 suit tier list video today. All 70- 78? I think it's all 78 suits. I've blurred the list out so you can't see the results just yet, but as you can see this list is pretty stacked towards the top, which means I liked a lot more suits than I disliked. We'll start from the bottom and go all the way to the tippity top. The last hunt suit. In dead last, we have the last hunt suit. This one is at the very back of the list because this thing barely even looks like a Spider-Man suit. Now I understand it's clearly a Spider-Man Craven mashup suit, but this costume has the same problem I usually have with every superhero mashup costume, and it's that one of the superhero designs gets super lost within it. Spider-Man here just looks like Lion Man. This spider logo barely even has eight legs! Fuckin' both Peter and Miles get this same suit for some reason, so this suit actually takes up both of the spots in Dead Last. The Aggie Mount suit. Alright, I'll admit I was a little too easy on this suit pre-launch. I'll tell you what the problem with this suit is. It's not the color palette, it's the fact that this suit is so complicated and the design is not at all easy to follow.  Oh my god, does this suit have toes?   No. No. No. I won't- I won't have it.  The Spider-Man Souls thing was a joke.  Please never again.  I'm done. I'm done. I'm done. Next suit. The only reason this suit is above the last one is because you could at least like feasibly tell this is Spider-Man. The Absolute Carnage Suit. Now this suit is a bit of a stinker to me, which is why it's at the bottom of course. I don't like the formatting of the web pattern. It highlights Miles' midsection in a way that makes his body look kind of odd. I also think that the red is so dark that it doesn't pop against the black enough. To elaborate on the web pattern, why does it stop at the neckline? And why are the top legs on the back logo so small? And again with the toes! The Kumo Suit. Okay, they're fragments of things here that I like. This is how you can tell that we're just about to break out a D-tier. I really like the eyes within the spider lenses, which already have a pretty great shape. I like the idea of tattoos serving as the detailing for the red sections, especially with how the back logo forms.  Is this fabric? Why is the texture of it so weird? I honestly kind of wish this was skin instead, even if it was red skin. The spider logo on the chest is barely trackable. It just feels like there's a head and a body on his chest, and it's never really clear where the rest of the spider is. And after all that, he's just wearing this really dull outfit. This suit has such boring colors combined with all this weird execution. The tactical suit. So I'll tell you what's not wrong with this suit. I think the color palette is just fine. I really like the bright pinkish red with the otherwise monotone color scheme. It's just this suits undying need to be so overly complicated that kills it. These weird goggle visor things on Peter's forehead actually looked like they could be used. And maybe if the armor paneling didn't look so aimless and unnecessary. Like I get that this is a tactical suit, but what kind of tactical is this? It sticks out like a sore thumb. And it looks like Peter's wearing an NES power glove. Like this suit has some small stuff going for it. That's why it's at the top of D-tier, but I could see someone liking it? The way the spider runs through the suit is cool, and I like the red marks leading into the lenses. It's kind of like a worse armored advanced suit. All right, so that covers all of D-tier. I promise it's the least filled tier in this whole list. Meaning there are but a few of the in-game suits that I would deem irredeemable. C-tier is about twice its size. So after this, we'll probably start to be a little more positive. The stone monkey suit. I swear, I feel like I'm looking at something that should be in D-tier. And maybe it should be. But I have to say, this suit has a nice color palette. The leathery red, the slightly washed out blue, and the gold elements mixed together with the lightly colored fur aren't painful to look at. I like the spider fabric texture used on some of the fabric here. But this design is like super wacky.  It's a weird design, and I don't see myself liking it or ever wearing it, but you enjoy it. Go ahead and do so. Everybody's got their guilty pleasures.  The smoke and mirror suit. I feel like this suit is one of those cases where as long as the lenses and the spider emblem look cool, any design can manage to look all right. Except this mask barely even has lenses.  Along with that, the logos are really nice. I just think this design is just a little too covered in random seams and the usual sort of over design that happens with a lot of insomniac spidey suits. I kind of wish this suit implemented the Mysterio quilt pattern from the original Mysterio costume into this design. It could have worked as both a web pattern and a homage to Quinton Beck's old costume. It's an okay suit. It's fine to enjoy it. The apocalyptic suit.  Like otherwise, the design of this suit is actually all right. Once again, I understand how this suit could have some fans, but this mask really, really ruins this suit for me. If the web pattern didn't look so weird and if the lenses fit the suit, I'd enjoy this costume. And personally, I could do without the Mohawk, but it's fine. To elaborate on the lenses though, I just really wish they fit his face more.  Give him some jagged menacing looking ones. You'll see me repeat this same complaint later. Insomniac doesn't know what punk looks like. The biomechanical suit. Now, this suit has three really cool things going for it. I like the pedipalps on the mask, making them look like a real spider. I like the logos, but I definitely think the one on the back should glow just like the one on the front, because without it, it gets really lost in these other plated sections. And honestly, I like the idea for this suit too. It's like they wanted to make a spider exoskeleton suit. And I mean, it's cool and all. But if you're going to wear a Miles suit, do you really want to wear the ball sack texture looking one? The Wakanda Forever suit. So even I'll admit that the Wakanda Forever suit does the thing that I'm always saying most mashup costumes don't do. It looks like a perfect mix between Black Panther and Miles Morales' Spider-Man costume. I think the reason this costume mixes these two together so well is because both of these costumes are primarily black with some added accents.  I really don't like the web pattern that forms around Miles' upper chest, especially since the webs are going the wrong way. The eyes are really squinty, and yet they take up a huge chunk of Miles' face. Not only that, the lenses are a whole football field apart from each other. Honestly, now that I look at it a little more, maybe Black Panther's design does kind of get washed out in this suit. The red shoulders really just make him look like Miles Morales from a distance.  The 25th century suit. Now this suit isn't horrible. It's just completely beaten out by another similar design you'll see way farther up the list. The pinkish red and the light blue accents do work well together. I just think that the Spider logo isn't really recognizable on the front, and you can really only see the Spider clearly on the back, which is already really tiny. I don't know, it's just Spider-Man in a big funky space suit. I don't know what to say. They tried to mix in some seams on the web sections here too, which looked kind of dumb. I don't know. I have kinder words for the better version of this suit. The inside-out suit.  The lowest ranked theatrical Spider-Man costume on this list.  First of all, design-wise, this thing is basically just a completely blacked-out Spider-Man costume with only two-thirds of the web pattern still remaining in gold. Now normally, that wouldn't be bad. It even has some motherboard-esque detailing on the fabric, which is subtle and honestly looks kinda cool.   It could have at least looked okay. You expect me to believe that this is the inside-out version of the MCU Spider-Man suit mask when the lenses still look exactly the same on the inside as they do on the outside? We've seen what the insides of these lenses look like. It makes no sense that they just look exactly as they do right side out. And what about the web shooters? Aren't they on the outside of the suit?  Now aside from this being a pretty shitty design, what makes it even worse is that instead of looking at this inside-out garbage, we could have been looking at the far from home suit.  And now he's gotta wear it inside out or some bullshit, whatever sells more toys.    And even after all that, it's a poorly executed idea that manages to contradict itself when you actually question its design traits.  Damn, we're really just getting all these shitty MCU costumes out of the way immediately, huh? Anyway, this is one of the most rightfully hated Spider-Man designs of all time and I'll tell you why. It's a redesign of a pre-existing and much better looking costume. But I will give credit where it's due. The design on paper doesn't sound too bad. A Metal Spider-Man suit with a red, blue and gold color scheme honestly sounds kinda cool.  Pretty much the only thing I can forgive about this costume is the logo work, which could be worse. But everything else about this Godforsaken outfit is super nasty. If it had brighter colors, then I'd probably bump this thing up a couple spots. But honestly, this thing is pretty unsalvageable. The Evolved Suit. You know why this is here. The only reason it's above the Iron Spider is because it has brighter colors that pop out more than that shitty shiny red and pissy gold. But that doesn't change the fact that this costume has a huge focus on the chest and arms, leaving the rest of the suit to be pretty much lacking in terms of style. The mask is a boring one color with nearly the same lenses as the default Miles mask. It has his hair coming out of the top, which doesn't add to the design at all. It honestly feels like a half-assed attempt to make this suit different. Honestly, this suit could have been boosted up a few spots if the hair wasn't out. The least they could have done was flick the hood up so that it could poke out the front a bit like the Red Spectre suit does. But not only that, it would have made the face of this suit look a lot more interesting. Miles mask looks blank and naked, but with the hood up, you could have had a nice cool blue background behind it that would have looked way more eye-catching.  It's like they didn't even try to find a reason for why the blue lines just randomly start back up on the thighs and down to the Adidas. You know, people are actually starting to suspect that this suit was an ad for Adidas on Twitter.   I don't understand. How did you fumble this bad? I don't know who designed this suit, be it Adidas or Insomniac, but whoever did clearly needs to go back to the drawing board and try again, or never again, whichever results in a bad Spidey suit not being made. The integrated suit, one of the biggest downgrades of all time right in front of us.    And why not keep the eyes white too? That certainly wouldn't blend into the design better if they were gold, right? They honestly could have kept the golden web shooters from the MCU Iron Spider suit. It certainly would have helped balance out the gold on this garbage. The only reason this thing is as high as it is is because the colors are really vibrant, except for the gold, which looks like shit, the red Spectre suit. And now the design that fell pretty far from grace with me upon finally getting to play with it myself. But this costume is still no slouch. There's a reason why it's just at the top of C tier because at a passing glance, this suit actually looks really cool. The hooded mask with Miles' hair peeking out from the front is cool, especially with the red dyed tips. And yet again, black, white, and red prove itself to look really good on the younger Spider-Man.  And there's a lot of over designing going on. It's certainly not the worst Miles has ever looked. And you can definitely catch me wearing this suit every now and again. It's got sauce, okay? But not too much. And with that, we have wrapped up C tier. Oh man, this video is gonna be super long. I wonder if I'm even gonna be able to get this video out to you guys in a timely manner.  Anyway, now that C tier is all covered, we can finally get to the suits that are smack dab in the middle of quality lane. Not bad, but certainly not the greatest. Life Story Suit, Miles Edition. Okay, maybe this one should swap places with the red specter. This one's just kinda meh. At least the red specter tries to be something, you know? This suit has a four-legged spider on the front and it's pretty bland otherwise. Or maybe it should stay here. Because while the red specter does try to be unique, it definitely falls short in some places by simply doing too much. This suit just does too little and lacks four extra spider legs too. I like the red webcrest on the back. I don't know. Which suit do you think is better? I genuinely wanna know what you think down below. The Life Story Suit or the red specter? I have a feeling that the red specter will win more favor and honestly I might agree. So just imagine that the red specter was always at the bottom of B tier and the Life Story Suit is at the top of C. And while you're at it, you can pretend that I'm a competent YouTuber. Hey Fred, give me a p***o with extra d***s. Extra d***s. And hold the d***s. Hold the d***s. And hold the d***s. Hold the d***s. Hey Jimmy, give me a d***s with not... Not now, you can have the... MCU stealth suit. What do you want me to say? It's a completely black tactical Spider-Man suit.  I mean, it's just a completely black suit. If anything, you should be bored by it. But I don't know, I personally don't mind it. The Brooklyn 2099 suit. Alright, this is one of those suits that only looks good in the nighttime, otherwise it just looks really reflective and all the pink starts to get washed out. This design has some really interesting Spider-Logo work, especially the one on the back. But I don't know, it just feels like you can lose a lot of the flair with this suit in the daytime. He looks like he's being pumped with Coca-Cola when the light's on. Why the f*** would I wanna wear a suit that only looks good if the sun's f***ing gone? What if it's 2 p.m.? The programmable matter suit. The only reason that this suit is above the last one is because the red pops at any time of the day. If you ask me, the last suit has a better design but with worse coloring and material choices. This suit is only above it because the colors look so much better and I guess that should really tell you about what I value in a Spider-Man suit. Good colors are everything. The strike suit. You know, I've talked about these suits in older shittier videos, specifically my video where I said that Miles had better new designs from Insomniac than Peter did in his first game. And this is one suit that I think holds up pretty decently. The color palette does carry it a bit. The glowing yellow was a really, really nice choice. Like, I can't believe there aren't more Miles suits that try to implement his electric powers into their designs. The glowing gauntlets, the venom coursing through the suit, the bright yellow soles. This looks awesome when you're ignoring the weird-looking helmet. Man, these lenses are tiny. The advanced tech suit. What do we got? Huh? Oh, sorry, I got distracted. Anyway, yeah, yeah, yeah. The suit has some weird lenses.  It may be wrong, but I'm tired of acting like this suit doesn't have really cool logos. Even if they don't match, it's an okay suit. Maybe even cool. The crimson cowl suit. Oh, this suit kind of just looks like Michael Jackson Miles Morales. Even if I had problems with the overly geometric design of the Spider logo and other stuff on the suit, I can't complain about having the classic Miles mask still being pretty present in the design. What do you want from me? I like the color red. What can I say? All of the best things in life are red. Like Spider-Man. Or Spider-Man. Or Spider-Man. And Spider-Ham! The saving live suit. Stupid name aside, this suit is pretty decent. Honestly, I kind of wish they called it the Spider Wraith. It's got some really nice logo work and lenses too. It's a suit where Spider-Man is put in a completely different color palette with a completely different suit format. And it looks like some sort of leather motorcycle suit. It looks pretty awesome. Give or take a bit of over design. The purple rain suit. What can I say about the purple rain suit that I haven't already said in my previous video discussing it? Nothing. It's a good suit. It works surprisingly well as a Spider-Man suit with a Prowler themed color palette. Although the suit is a bit overly complicated, but even so, the darkness of the costume is able to blend it out pretty well. Not bad. It's pretty cool. The... Hold on. The... The board... I don't even wanna hear. Let me look this up. How do I say this? Hold on, chat. I'm fucking, there's an ad playing on this pronunciation video.   Oh my god, please just tell me how to pronounce this word. Boracwa.  The Boracwa suit. So basically imagine the Miles design and work the Puerto Rican flag into it. Except scratch the part where I tell you to imagine it and look at your screen. I like the stars on the boots. That's a nice touch. But these gloves really feel like an afterthought. I much rather would have seen the flag somehow worked into the glove or honestly just go lazy with it and give Miles his old gloves back. It's a pretty decent look for Miles but I'm not jumping up and down about it or anything. It's got a satisfying web pattern and it reminds me of the Tasm 2 suit in some ways. The best there is suit. You're asking a Spider-Man fan about his opinion on a Wolverine suit?  What do you expect him to say? I don't know, it's a cool suit I guess. It definitely doesn't look like Spider-Man though. Should that be a reason to place it like around where it is on the list? I don't know. Anyway, my answer is 50 stories long. The new blue suit.  The Spider logos sure are though.      Not six or four or two, eight! Eight!   The formatting being pretty safe saves this suit a whole bunch. Plus it has a pretty interesting glove design. It's a basic suit, but sometimes basic isn't really a bad thing. The sportswear suit. This one took me a long time to figure out where I wanted to put it because it's not really a traditional suit, you know. It's a Spider-Man suit with a jacket and shorts over it. At least they're red and blue respectively. It definitely helps Miles look more like a Spider-Man in this costume since a lot of the suit is covered. Thing is though, I kinda wish the puffer was black instead of blue. It'd be like a call forward to Miles' iconic red and black Spidey color palette. It's a casual look but it's also a pretty solid choice. Miles' homemade suit. This is honestly a pretty solid homemade suit. I can't lie to you. It's got a nice design on the jacket that lightly homages to the Spider logo. I really enjoy the subtle approach to the Spider logo design and I'm not exactly sure which comic artist designed this new first suit for Miles, but whoever did clearly had the sauce. The big blocky goggles are nice and I honestly love when Miles lets his web shooters sit on the cuff of his hoodie sleeves. This is a nice suit. You gotta respect the Timbs. The Scarlet Spider III suit. Okay, this one was one I didn't really understand the hate for when it first came out. It's definitely not better than the original. I'll admit that, but it ain't horrible. The mouth is horrible, yes, but we all make bad choices sometimes. And Insomniac made sure not to repeat that again. I definitely don't like the lenses on this suit though, but the hood being up definitely helps cover them up. The logos are pretty decent and the utility belt isn't too intrusive on the design. It's a solid outfit. I don't think it's worth hating on. The Antioch suit. This design is basically a pissed on, less impressive black suit. I mean, it's Spider-Man. I can certainly tell it's Spider-Man, but I will say it's got a nice set of logos and some really rainy-esque eyes. I have no clue why this weird cube thing is on his abs. I think Spider-Cube might be making a comeback Insomniac, you might wanna get on that. The Family Business suit. Now, the only reason this suit is above the Antioch suit is pretty much because it's just a better design, albeit with less saturated colors. The gold elements are better distributed throughout the costume and there are lights that fly through the suit. All I want from this suit is for the gold to pop more. That's pretty much all I gotta say, it's a nice suit. The Dark Ages suit. Ah yes, the venomous look for miles I asked for in my suit wish list video. I'm pretty sure I asked for that thing in this video. Anyway, this one looks nice, although I wish there was a classic black and white variant like the one in the comics. I still enjoy the subtle red lining on the lenses, the spiked hoodie, and the really nice Spider logos.  The Ramy suit. Oh boy, we're at the tail end of B-tier and here this suit sits before me. It's certainly a version of the Ramy Spider-Man. I think the colors of it look a bit off. The blue is really, really bright and the bread, and the bread. The red feels too toned down to work with the blue. And the webbing on the suit is ungodly thick, so much so that it washes out the red in some shots. But it's not horrible. At the end of the day, it's still a classic Spidey suit, which definitely boosted up a whole bunch. But I do wish some things about this adaptation of the Ramy suit were way different. I take back my rant in my really old Ramy video about people complaining about this thing, all right? I get it. It looks way more crappier than all of Insomniac's other movie suits, the Black Ramy suit. All right, now this choice may throw some of you for a loop. I complain about this black suit all the time, I know. But at least this game actually makes it look decent compared to the red and blue version of it. Like, the previous suit looked unfinished, but this one looks how it's supposed to. If the classic Ramy suit looked good, it would definitely be above this one. But that one's got some funkiness going on and I have no clue if it'll ever be fixed. But for those new to the channel, what's my problem with this suit? It looks really cool. Yes, it does.  I wanted a classic black suit, Spidey, and instead I got a classic Spidey suit dumped in black paint.  This pretty much wraps up all the suits I think are okay to pretty solid. And now we move on to A tier, which is the most populated tier on this list. These suits are all amazing in their own right, and just barely make it in the S tier due to a couple issues with their designs.  Okay, now I know I'm gonna get shit for this, but let it be known that I am aware of the problems with this suit. I know it's got a little too much weird red lines all over it. It's kind of over-designed in some areas, but doesn't this sound a little familiar? Ah, yes, the integrated suit.  They pretty much do the same exact things, except one of these actually wants to be its own thing, as opposed to slapping itself over a preexisting design like the integrated suit does. It's got some cool-looking lenses, some really nice spider logos, and a much more interesting color palette.  The Agent of Shield suit. This suit is a pretty awesome reference. It's a throwback to issue nine of the second Miles Morales Spider-Man run, if I remember correctly, where Miles dons a shield outfit for the cover. It's not a very spidery look, sure, but it's a cool outfit all by itself. I really like the white paired with this light blue. It looks really good. Although, I could do without the over-designing though. It seriously litters this thing. You expect me to believe that this is a uniform? You know, uniforms are made hundreds of times, right? These poor shield uniform makers have to put in all these extra seams and panels into their jumpsuits, just cause some jackass thought it looked cooler. Well, that's why you aren't S-tier, little buddy.  The Anti-Venom suit. Oh boy, we got another hot one on our hands.  Well, let me just complain about it for a bit to make the angry half feel a bit better. I'll tell you what, it's definitely not better than Spidey's other white and black looks. The Future Foundation pulls off this look so much better because it had more of a purpose and a clear vision when laying out the black sections, while also making sure the black sections balanced out the suit's white to black ratio. But this suit just slapped some fuck-ass paneling on the waist and calls it a day.  At least the black on the arms is tied into the Spider logo. And honestly, from the chest up, this suit looks really cool. But it's like the lower you go, the less sure of what they were doing. But it's got really nice lenses, really nice logo work, so hey, it can't be that bad. The King and Black Miles suit. You'll start to notice a pattern here.   Not to mention the flowing symbiote texture over the black parts of the suit. Absolutely gorgeous. The Tokusatsu suit. Power Ranger Man here has a real nice set of lenses and logos. Can you tell that this script is already 5,509 words long? Me neither.  Anyway, I have very little issues with this suit. It's got some nice simplistic web shooters and while it's a teeny bit over designed, I'll give it a pass since that might be a homage to the source material this suit is referencing. The encoded suit. So I've made it pretty much no secret that this is my favorite Miles design from the Deluxe Edition skin pack. It was designed by the goat, Chris Anka, the man responsible for so many of the beautiful designs from across the Spiderverse. Who am I to tell this man that he made a bad design? It may look over designed, but I would argue that this costume needs those features to make this suit look more robotic. It's like a Mecha Miles suit thing. It makes it work. The only place I'd say it maybe doesn't look great is the helmet. I think the exposed bolts and circuitry distract from the lenses and honestly, I do really like the red and orange color combo. I saw a couple people saying it should be one or the other but come on, at least this costume is consistent with it. Orange stays near the top of the design and only slightly comes down to the bottom but the limb ends are always consistently red.  They sit right next to each other on the rainbow for God's sake. Chris Anka, please follow me back on Twitter. The Iraq Knight suit. I'll tell you what. It's cape boosts this thing up really high. It's got nice logos too and you can barely even tell they reused the advanced suit 2.0 lenses here but this arm paneling is really ugly and the shade of red is so dark that it almost looks brown and I don't know whether that's a positive or a negative because on one hand, the dark red definitely helps emphasize the spider logo and helps the white pop more. Maybe it is a positive. Sorry, sorry. My hatred for unsaturated superhero costumes is muddying my opinions again. Okay, my bad. The advanced suit 1.0. I am one of the most inconsistent YouTubers on the planet. Last time I had a pretty mixed opinion on this outfit but confession, I've grown to really like it. All the design issues I've talked about in my previous videos are still valid, all except one. It being orange.  I changed my mind.  I felt like I was smoking crack using this suit again because there was no way it looked like this last time. There was no way it was this dark, at least not in the remastered version. Maybe that was it. I did replay the remaster a bunch while wearing the advanced suit right before Spider-Man 2's release. But anyway, this suit being the slightest bit darker puts it back on the tier list a few paces for me. I wish it was vibrantly orange at least because I think the bright colors worked with the new white logo really well. If it was like this, it would definitely outrank its replacement. The Miles Morales 2099 suit.  My only issue with this suit is the under implementation of the web pattern. Even the over designing is hard to see with the dark blue as the base color of the suit.  It's a great suit. The Secret War Civil War suit.  Now I can't complain about a good spin on the classic suit. This Spidey suit has got some super tactical green army pants on. Personally, I think the green works really well with the red and blue, especially since the Spidey suit is a bit lacking in detail this time. These are some really nice color choices too. Nice and bright and nothing too dull. Not to mention the custom wing set for this suit. I completely forgot to mention this one in my last video when I was complaining about the web wings. My bad, I'm sorry. Not to mention these really cool goggles. Insomniac pretty much had to improvise a whole new mask for this suit, and I'm so happy they didn't just give Peter the classic one. The great responsibility suit. I really can't help but find all of Miles' first Spider-Man suits really charming. Like I know they're supposed to look really lacking and some might think that that makes them so, but they aren't. This suit is everything. It does everything it needs to do to tell you what it's supposed to be. The gloves are a little baggy and so is the neck of the mask. The suit looks just high quality enough that you could think this is supposed to be some sort of Spidey trainee suit. The logos are really simple and nice, and the lenses are really big and appealing. I can't help but feel like a lot of the Spider-Man iconography is simplified to tone up this trainee Spidey vibe, and I gotta say, that's pretty genius. The 2099 black suit. I did the finger quotes. This is a really good Spider-Man 2099 design here. A real nice blue being used, which I actually prefer over the black variant. The iconography is real nice and sharp, perfect for that menacing 2099 look, but this design is missing a huge part of the original 2099 suit. The web cape. Now normally I'd feel bad for judging a suit for what it doesn't have, but this is a pretty huge feature of the original outfit. Like, imagine if the Arachnite suit had no cape. I mean, maybe that's a little different, but the back of this suit is just so boring to look at with nothing on it.  There's nothing else here. Some of these suits ahead of this one on this tier list actually make it above 2099, simply because they have an interesting design on the back. Here, there's nothing. Put a cape on this suit and it's S tier, the upgraded suit. Now I don't think this mild suit is as good as this old one, but it's certainly a cool one.  I really like the black they used, and I like the shape of the chest arc just a little bit more, but I certainly don't like the inconsistent lining on the gray parts of the outfit, and I honestly wish the gray parts were as dark as the black on the mask.  I really do like the glove design though, but I still prefer the original red finger design. The life story suit. I love the idea of the Spider-Man pattern being rearranged to make a whole new design on a costume. This suit explores the idea while also working it in with the space suit theme, which I doubly enjoy, even if the belt is really weird. There's a really nice spider logo, and the lenses look really awesome. The end suit. Now this is a great Miles suit.  But everything else looks awesome. Great hoodie. I love the spray paint. I love the base suit under it too. The digital camo pants are really fun, and I dig the boots. Fix the lenses and it'll move up. The spider punk suit. This is a good suit. There are things to like about it, but I do not. But if you don't like it, why is it so far up the tier list, you may say?  Anyway, it's this high up because while I may not like it myself, it still has bright colors, a nice web pattern, and a generally pretty clean spider punk design. Therein lies the problem.  You could have given me something more fitting for this version of the character. Maybe some bagley lenses like he has pinned on his jacket or some McFarlane's. Spider-Punk is a punk.  This version of this suit just makes him look super tame. I'm not into it. The city sound suit. I don't even know what to tell you right now, just look at this man's fit. Look at the shoes, the dress shirt, the vest with the spider logos on the front and back. So good, the end of the Spider-Verse suit. Some might have said it was a stretch to call Spider-Man 2 the best Spider-Man game of all time. To that I say, what other Spider-Man game can you play as Nicholas Cage Spider-Man in? It's kind of funny that Insomniac booted their own noir design in favor of using the most popular version of noir from recent years. It's a pretty good thing they did though. Their old noir design is pretty alright. The big trench coat is awesome and I really like the hat. Seriously looks like he jumped right out of Spider-Verse and he fits perfectly with the rest of the Spider-Verse skins in game. R.I.P. Peter B Parker though, I'll miss you forever. The shadow spider suit. Now this is a real certified banger.  Wait what?  Are you kidding me?  Moving on shadow spider has to be one of the top comic suit adaptations Insomniac has done. There's no immediately apparent spider on this suit but the giant web cape makes up for this in my opinion. The half mask thing Miles has going on here is also really cool too. It's a great suit with a lot of details that I really enjoy. The advanced suit 2.0. I have been shitting on this thing for a while now and in all honesty, I definitely have been way too hard on it. It's got super bright colors which is a huge plus and the spider logos look great as always.  Well okay, it doesn't have to be a pair of boots but can there at least be some red on the legs? Like I swear Insomniac only listens to fans sometimes because it explained why they went for such a bright red and blue this time. But then why would they make one of the most complained about features of this suit even worse by removing the red on the legs? It's a good suit. I'm just tough on all the important ones. Also why did they pattern it so it looks like he peed his pants? The Across the Spiderverse suit. This is another case of me being really hard on an important suit. This suit is not a perfect one and the one that came before it is definitely better but the red lines aren't bad. They're just really really basic. Like they look cool here especially during swinging but I cannot understate the simplicity of this design. It's cool but just in a low key sort of way. Just too low key for Miles Morales. And thank God the light armor plating is almost as dark as the suit itself because if they were any more visible this suit would probably be in B tier. This suit is carried by its awesome logos.  The Insomniac black suit. This suit is definitely something. It has amazing logo work, big buggy eyes, and redesigned gloves. I cannot lie to you. This has to be one of the coolest black suit designs that have ever been done. I understand that the dookie texture may be unappealing to some people and I won't blame you if it holds you back from liking it. It does kind of look odd at times and I'm a little iffy about how the armor plating makes his body look but it definitely still looks awesome.  The symbiote suit. This one is just the last suit but without the poo poo pattern, a bigger logo, and with top legs that hang over the shoulders and pointy your eyes. I had to put it just above the last suit because I really enjoy the presentation of this black suit a lot more. I dig the veins more than the poopy plated armor. I do miss the white patch on the hand though. The suit looks really empty without it. The eyes here have a lot more character which the last suit didn't lack but here it's a lot more appealing to me. I also really enjoy how the logo wraps around the body too.  The 2020 suit. What can I say about this suit that would accurately describe its greatness? I know the lightboard on the chest is kind of dumb but everything else about this suit makes sense and looks awesome while doing it. The back logo on the jacket is just, ugh, chef's kiss. The Scarlet Spider suit. I really, really, really wanna put this design in S tier but I can't do it because of these ugly bright red panels on the base suit. It's a really, really good Scarlet Spider. I love the new web shooter design. I love the hoodie. I love the utility belt but this suit is really unfaithful.  Peter with a steady job made this suit. Look at how clean it looks. I'm not saying it's a bad thing. I'm just simply pointing it out. The homemade MCU suit. Now get ready to burn me at the stake. If the Scarlet Spider was a bit better, it would beat this suit out but I really like this MCU suit. It's one of the greatest but I still do wish it looked a little better in this game. I wish the proportions of it were more like the hot toy and I think something about this in-game suit looks off but I love the added sock boots, Peter's new web shooter gloves and I really love these new goggles. This is some of the MCU's best work right here. The classic suit. The best superhero costume of all time in my opinion is the classic Spider-Man suit and here before us all is Insomniac's rendition of it. My issue with this suit is that I do not think it is done right in this game. There is one thing holding this suit back from being asked here and it's something holding a lot of suits back from being asked here.  I would have put this in S tier. You see this video?  When the colors on this suit are hot, the suit is hot. I'm sorry for saying it wasn't, I was wrong. The Stark suit.  This suit has really nice colors.  I really like the logos and the lenses.   I'm sorry.  Stan's costume shop suit.  Anyway, I can't stress to you enough how much I love this thing. I would have put it in S tier if it weren't such a gimmicky outfit.  What? It just looks so... It's like a really funky look for Miles. A skinny boy in a cape running around in a Party City Spidey suit, but he's actually Spider-Man? Like come on, this suit is so cool. I was never upset to see Miles wearing this thing throughout the Spider-Verse films. I'd put it in S if it had the open eye holes. The track suit. Oh, this is another suit I would put in S tier again if I could. It's just so close to being perfection, but I can't put it all the way up there in a good conscience. It's a really good Miles design. No doubt Miles already has a great color scheme, but adding white was such a genius move, but I really do wish that Insomniac didn't have to overcomplicate this design with the paneling on the white and weird spots and I really don't like this plastic texture on the mask. The classic suit, Miles Morales. There's really only two problems with this suit that keep it out of S tier. I think the suit is way too gray and I don't like how visible it makes the armor plating, but this suit is still phenomenal and it's one of the greats. I really love the logo work. The lenses are great and resemble Miles' art from his original run. I think the water shoes were a really nice addition and I really dig the candy red they used. Awesome costume and I would let this one pass into S tier if no one was looking. We have finally made it to the Golden Gates. These are the kings of the list. I will probably have the least to say about these, but these are the suits I consider to be the cream of the crop, the best of them all. They usually only have the smallest of flaws, but the suit at the very top of this list is one I consider to be absolutely perfect. The Superior Spider-Man suit. This suit has a really nice blood red and a black, dark enough to make the over-designing way less noticeable. Great logos, great lenses, great webbing and it looks great in game. The Bodega Cat suit, the Cat Man. This has got to be one of the coolest right here. It does have some over-designing, I'll give you that. But Spider-Man in the bag?  You're just looking at him for a second. You'll forget all about that over-designing. I really love the copper webbing and I seriously like the shade of red on the suit paired with the hoodie. It's got great lenses and the logo Smaxio Granny, the far from home suit. This suit has got to be one of the coolest redesigns of classic Spidey there is. The black lining looks really great when some light hits it. The bright candy-ass red looks awesome and the white accents pop in just the right ways. I could do without the black belt pieces though. The Iron Spider Armor suit. I've talked about this suit before. It's great. The ruby red looks awesome with the gold.  The classic black suit. This suit is like if you took the Web of Shadows suit, made it black and gave it bigger eyes. So basically fixed it. But the purple still looks awesome though. That's not the problem.  I know we're supposed to be talking about only the default editions of these suits, but man, this is just like a really good classic black suit here. The 10th anniversary suit. Miles Morales' new look is practically lifted right off the page for you to use. No room for Insomniac to add any weird shit to it and honestly that's made it way better. The pink is awesome, but if you're worried about the use of the pink version demeaning your manhood, you can pick a red version that looks just as good.  The new MCU red and blue suit. We are in the top four. I honestly couldn't have put this guy any lower. It's pretty much just classic spidey minus the back logo, which still looks great. Some people might think the blue looks ugly, but I don't. The web pattern looks great, the logos are awesome, and this suit deserves its spot and maybe more. The Tasm 2 suit. This suit deserves an apology video from me, a big one. While the spider logo does hang low on the chest, I can't say no to the big buggy eyes, immaculate web pattern, and the light seam work on the blue.  The colors on this suit look great, and this suit looks great. The Tasm 1 suit. You know why I love this thing. It's such a unique take on the classic suit that somehow sits in this purgatory of being so unique that it can be considered its own thing, but it's also still a classic suit. The sportswear influence is not lost on this suit, but it also doesn't overdo it either. The yellow eyes are really cool, and the soccer cleat soles are so, so nice.  Ladies and gentlemen, the final suit. The one I consider to be the perfect Spider-Man suit, and that is the Into the Spiderverse suit. The spray painted elements that drape over Miles' shoulders like spider fangs highlighting his musculature. The fingers and boots being left untouched by the black spray paint to balance out the red from the top of the suit, all the way down to the bottom. The spider logos are so fresh, being some of the most unique spiders that we have ever seen on a suit before. The red elements are fuzzy at times due to the spray paint, sometimes fading or dripping. The massive white lenses that emphasize Miles' youth with the light reflection of New York being cast upon them. Not only is this suit great, but it's also built off the back of one of the greatest Spidey classic designs that have ever been made, which already gives it a great framework to work within. It's also what this suit means on a greater level. This suit is about Miles Morales literally taking the Spider-Man costume and making it his own thing by using his art to make it into something of his own, which in itself is a metaphor for what Miles must do as a character. He must take Spider-Man and do it in his own way to succeed. And this costume does succeed more than any other suit below it on the tier list. Argue with me in the comments.  This video is 9,393 words long.  Oh man. Oh man.   I wanna know if you guys think I'm a fraud.  I want you guys to tell me if you think I should up myself because of my placements.  This is the longest video I've ever made. And man.   And if you at me on Twitter, on my Twitter at, which is on screen, you can show me your tier list ranking, which would be cool. But anyway, thank you to all my channel members. Thank you to all my subscribers. I'm clocking out on this video. I've recorded it all. I'm good. I'm good. I'll see you guys in the next one. I'll probably be making a non-Spider-Man 2 video next time just to get some variety going, but don't worry, the Spider-Man 2 gravy train still come and chat. I'll see you guys next time. Love y'all.


The question is how to teach spelling and how well it can be incorporated into the language teaching classroom. One of the ways of teaching spelling is to expose students as much reading as you can in the classroom. And of course outside the classroom as well. So one of the ways is like called extensive reading which is to make them read simplified texts. And in this regard, as you might remember, we have already discussed the concept of graded readers which come in simplified versions which are interesting, encouraging and motivating for the students. So we can expose them to extensive reading, reading which interests the students which appeals them, right? So continuous encouragement and motivation on the part of the teacher is important element to make students notice how spellings work. And of course, there should be some dedicated classes like for instance, if you are teaching sixth class students or ninth class students, you can dedicate some of your lessons to especially spelling teaching. So another key way of teaching spelling is to identify issues of sound and spelling irregularity and how it works, what are the rules, what are the exceptions. So you can bring in those rules and exceptions in the classroom and make the students notice. And then you can of course give some exercises of word formation. For example, you can dictate class in the classroom, ask your students to follow you. So word formation can be an interesting area to teach spelling. Then we can bring in some spelling patterns and exercises. And then we can make the use of digraphs, which means a pair of letters which associated with one sound, as you can see on this slide. You can try graphs, usually some of the three letters pronounced together or in the same way as you can notice it on this slide. So another way of procedures or strategies you can use in the classroom is to read aloud. You can read aloud shorter texts and we can make students listen carefully to the word spoken or read aloud in the classroom. And we can make them repeat and write. And it shouldn't be like a mechanical activity, rather we can encourage students to feel what they are doing when they are reading. They should have the flavor, the taste of reading and how to notice the spelling sound correspondence or the irregularity. And then we can make them read and listen to a series of words. And then we can bring in rules of convergence and divergences of sounds and how they work and how they don't work. Why they work? Why don't they work? Another activity by which we can develop spelling or teach spelling in the classroom is we can bring in some group of words like which are pairs or group of words like clap, clapping, how, limp, limping. And then we can make the students make the constant use of dictionary. When they are using dictionary, they are not using for the sake of using rather they are noticing, pay attention and making them conscious about the rules that work the spellings. Another way is to dictate, dictation or reading aloud can be a handy tool in terms of developing spelling. And then we can incorporate listening in the classroom like playing videos on the YouTube or if we have multimedia in the classroom or if we don't have multimedia, we can do it on our own. We can bring in tapes or other ways of, you know, developing listening skills in the students. By listening, they will identify what they are listening, repeat, feel, write. And this is how there are various although these strategies may vary from teacher to teacher. But these are some of the strategies established in the area of English language teaching which can be helpful in teaching spellings to the students.


Let's look now at an example of a related rate problem that's going to involve some trigonometry. We have an airplane flying east at 500 feet per second at a constant altitude of 4,000 feet. A search light on the ground lies directly under the path of the plane. If the light is to be kept on the plane, how fast is the search light revolving when the horizontal distance of the plane from the search light is 2,000 feet? So let's try to draw a picture, but I'm not going to attempt to draw an airplane for you. So here's the ground, and here's the airplane. I'm just representing as a dot because I cannot draw. Now we know that plane is flying at a constant altitude of 4,000 feet. So that's a quantity that's not going to change in our problem. So we can go ahead and put it into our diagram right away. Now the plane is flying east, which let's assume is to the right. So the plane is flying this way. Now remember, there's a search light on the ground. Let's put it over here. Put it in red so we can see it. And we know that as the plane is flying east, we want to know how fast is the search light revolving when the horizontal distance of the plane from the search light is 2,000 feet. So it sounds like we're going to need a variable to represent this horizontal distance of the plane from the search light. So let's go ahead and call that x. So think about this for a second, and I gave you a hint that it's going to involve some trigonometry. If we're talking about how fast is a search light revolving, if you imagine the search light revolving, it's creating an angle. So let's think of this as like a right triangle, and we have here an angle theta being described as that search light revolves. So let's think about the items that were given. We knew this 4,000 was a constant. We know that we're trying to find how fast is the search light revolving when the plane happens to be 2,000 feet from the search light, and we know the plane is flying east at 500 feet per second. Well, that horizontal distance x is really the distance from the plane as it flies east from the search light. So we can assume that dx dt is going to be 500 feet per second, and what we're trying to find is d theta dt. How fast is the search light revolving that angle? At the point in time when x is 2,000 feet. So if you take a look at your right triangle and the parts that you're given, try to think of what trig ratio we could set up. We could easily do a tangent ratio and set it up as tangent of theta. Remember tangent is opposite over adjacent. So that's going to be 400 or 4,000 rather over x. And that's what we're going to go ahead and do our implicit differentiation on. Now we will get to the point that we're going to, we know what x should be at the particular point in time in which we're finding d theta dt. We are going to have to figure out what theta is at that point in time. So we'll get to that in a second. So if we go ahead and do our implicit differentiation, remember derivative of tangent is secant squared, but remember we need to multiply that by d theta dt. Over on the right side, our derivative of 4,000 over x is going to be negative 4,000 over x squared dx dt. So now that we've done our implicit differentiation, we can go ahead and substitute in the values we know. We're going to have to find theta. So we'll do that in just a second. d theta dt is what we're trying to find. So that will stay as d theta dt. The x remember is 2,000. So we'll be substituting that in there. And then dx dt is 500. So really we need to go ahead and do a little side mass to figure out what theta is at this point in time. And we're trying to find d theta dt in the end. So let's go ahead and try to find theta first. So you have a little side work to do. So remember we knew tangent of theta was 4,000. And we're talking right now at the point in time when x is 2,000. So that's something you can simply solve on your calculator by using inverse tangent. Remember to be in radiant mode. So if you go ahead and try that, make sure you get the correct answer. It should come out as approximately 1.107 and that would be radians. And we're going to want to store that. And I'm going to store it as a in my calculator for angle. But that is a value you will need the full decimal value as you work through the remainder of the problem. So you are storing it in your calculator to use, but it's perfectly fine to round it off to thousands as you're documenting your work. So as we substitute everything in, we'd be doing secant squared of 1.107. D theta dt remember is what we're trying to solve for. We'd have negative 4,000 over 2,000 squared. And dx dt is 500. So let's go ahead and do the secant squared of 1.107. Definitely you'll be using that on your calculator. Secant is reciprocal of cosine. So get out your calculator and make sure you can do it correctly. You'll need to do cosine of 1.107. And actually you'll want to pull up whatever you stored it as. So I called it a. So do cosine of that. Get your answer for that. Do 1 divided by it. Get that answer. And then square it. What do you get? You should notice this quantity right come comes out as a nice perfect five. Now, if you had not stored that value, chances are you will not get it as nice as just five. That's actually how on the AP exam we can figure out if students stored their values to use or not. Because these problems are often rigged to come out really, really nicely if you store your decimals. All right, that's why you want to get in the habit of doing that. So simply five d theta dt. How nice that worked out. On the other side, if you simplify all this, well that just comes out as negative a half easy. So what we end up with is d theta dt is a negative one-tenth. So for our final answer and conclusion, we would have that when the horizontal distance of the plane from the search light is 2000 feet, the light is revolving at a rate of one-tenth radians per second.


Our planet has the Arctic Ocean and the Southern Ocean and we know that these amazing regions are critical to the climate of our planet. They're also full of amazing wildlife and in the Arctic indigenous peoples as well. Now for the last 50 years we've explored their basic geography and we can now understand the future impacts of our carbon emissions on the great Polar ice sheets. Ultimately we're learning about how the polar regions will affect us for example through sea level rise and through changing our weather. Now mine and many other scientists' research has fed into major television series about the polar regions that are co-produced by the BBC and the Open University and have been seen by tens of millions of people worldwide. In the Open University we combine components of our broadcast with real-time data so that our distance learning students can get a really good understanding of basic science and what's going on in the polar regions right now. Join me to hear my thoughts on what will likely happen to the polar oceans over the next 50 years and to take part in this critical debate.