Yeah I was talking about standardization and normalization, if you have a variable which is taking values x1 to xn then a way of standardizing it is you just write new values as yi this is the write the new values as yi yi you write it as xi- the mean x bar the mean x bar of this n observations divided by the standard deviation sx is standard deviation of standard deviation of these observations x1 to xn I hope all of you know the meaning of standard deviation the square of this is actually going to give you the variance the square of this is going to give you the variance this is a way of doing standardization of the variables now what is the specialty of this once you do this one then the mean of yi that is y bar 1 over n summation i is equal to 1 to n yi this is actually equal to 0 you are making the mean to be 0 and you are making the variance variance of y is to be equal to 1 you are making the mean to be 0 and you are making the variances to be 1 so the example that I was telling you 0 to 100 since the variation is more you are going to get more distance values once you do this one you are making the variance to be equal to 1 okay so if you have an have a worry have a variable where its variance is something like say 0.5 then after you do this thing it is going to become 1 and if you have another variable whose variance is say 100 after you do this one that also going to become 1 so both these variables where for which the variance is for one of the variables the variance is less than 1 for another one the variance is say greater than 1 for both of them the variances are going to be 1 and the means are going to be 0 so this is one of the methods this is one of the this is generally accepted way of standardizing a variable but whether you will do standardization or not that depends on the problems that you have I am not saying that every time you should do it neither I am saying that every time you should not do it it depends on your problem whether you will do it or not if you do standardization then your variance covariance matrix it is going to become correlation matrix that is all the diagonal elements will be 1 and all the off diagonal elements will be the correlations between those two variables the correlation between those two variables that will be the there will be the off diagonal elements and the diagonal elements will be all 1 I hope all of you know the meaning of the word correlation okay I hope all of you know the meaning of the word correlation so if you do standardization then the variance covariance matrix is going to become correlation matrix and we generally we do PC on variance covariance matrix then you may try to do it over the correlation matrix normalization this is standardization normalization is again if you have x1 to xn then you write find max maximum of xi values find minimum of xi values then you write yi as xi-minimum by max-minimum this is a way of doing it this max is maximum of the xi values min is minimum of the xi values so find the minimum of the xi values find the maximum of the xi values then you write new variable yi as xi-minimum divided by max-minimum so when this xi is actually the minimum you will get the value 0 when the xi becomes maximum you will get the value 1 so then all the values are in the interval 0 to 1 all the values are in the interval 0 to 1 this is slightly different from this here the mean is 0 variance is 1 here all the values are lying in the interval 0 to 1 this is a way which many persons follow for normalization again one can think of a few more ways of doing these transformations this is not the only such thing you can think of a few more ways of doing it whether you need to do it for your data set or not that again depends on you and if you do it then which particular transformation you will do and why that again depends on the data set that again depends on the data set with this basically I would like to go to actually another with this one I will end this the lectures on I should say classification class if with this same thing I will end the lectures on classification now I will actually go to clustering that is unsupervised classification please this one modification that range can be changed to you can do that I mean you can actually instead of making it from 0 to 1 you can actually make it from minus 1 to 1 so I mean probably a way of doing it is this is from 0 to 1 so multiplied by 2 then this will become 0 to 2 then you just subtract 1 and this will become minus 1 to 1 this will become minus 1 to 1 so you need not have to make it always between 0 to 1 you can think of one particular interval and you can keep everything with confined to that interval please. Sir can you just give an example where doing the standardization and normalization will not be useful or may not be useful yeah basically there are some places where you need the information on variances to be preserved when you are doing the standardization then you are reducing or increasing the values of variances generally it is reduction but so those places where you want the information on variances to be preserved then that is the place where you should not use and there are many examples where variance provides lot of information about the phenomenon under consideration about the phenomenon under consideration many times variance provides lot of information so they are the places where you should not you should not do the standardization you should not do the standardization and you the places where you are forced to do the standardization is at those places where you have some variables with smaller variances but they have the capability of distinguishing between the classes and you do not want those variables to be submerged by the variable with larger variance but it does not have any capability of distinguishing between the classes then they are the places where you want the one with larger variance to have smaller one and the one that has smaller variance you want its voice to be heard so that is the place where people try to do and if they feel that they are the problem under consideration is like that then they do the standardization one of the places where you want the variances to be preserved is the example about Punjabis and South Indians doing the classification we are taking the height you see there the height information for I am assuming that Punjabis are generally have larger heights but there are also many Punjabis who have smaller heights so probably their variances that variance has more I mean variance is more for Punjabi class then probably for the South Indian class but there that variance should be preserved the variance information you should not change there and the other example about length of the I gave that there you need to change it there you need to change it because the variance for these things this is very very small and you need this variable to be heard so and many of these things I will try to discuss in future selection when I give lectures on future selection I will try to describe these things I will try to I will connect up this thing with that ultimately these are connected to future selection when you are given a data you will do standardization or normalization that depends on the problem at hand and for the problem at hand which features are giving you the information about the problem at hand that you need to somehow do the make the decision and that actually becomes the problem of future selection so problem of future selection problem of standardization normalization they are very much connected they are very much connected our questions please please Sir when we are doing standardization is the topology of the data preserved what is the your meaning of the word topology how it is distributed the structure I am not getting please explain scatter of the data the distribution of the classes is that preserved I am not understanding but what I can tell you is this for two different variables the reduction and increase it is not in the same proportion if that is what you want me to say I think that is what is your doubt for two different variables the increase or decrease is not in the same proportion it is not in the same proportion different proportions so if you have different proportions of the distribution information will be lost when you do standardization how the line in the space feature space so that is not preserved suppose if you are scaling it down so equally if you are scaling down so saying I think you see there are many words the word for example use the word topology and there are some such words these words in my opinion they should be used very sparingly because they have they contain lot of lot of things probably in my tomorrow's lecture I will I will be actually talking about topology there I will tell you I mean the meaning of open set close sets closures compactness connectivity all these things are there in topology. So the word when you are using the word topology I do not know which one you are trying to mean I do not know which one you are trying to mean basically the word topology is used by computer scientists in one way somehow if they preserve the distances then we say that it is topology preserving am I right between the point she could mean the IC control lines around the mean same distance around they are not going to preserve the distances that is what I said different proportions they are going to change yes for both the variables here you have two variables for both the variables the mean is going to become zero and the variance is going to become one if you have two variables and I was giving you an example yesterday where one variable has variance two another variable has variance one if you take a if you look at the scatter plot how it looks like it looks like an ellipsoid if you have the covariance is to be zero now here that two and one they are going to become one and one and the covariance is zero means there will be a circle that means what is happening it has changed the distances have changed I am not saying that in every situation you need to do the standardization neither am I saying that in every situation you should not do the standardization you need to make a decision whether you will do standardization or not and that decision is imperative in many many problems in many problems the decision is imperative other questions noise okay yeah I had been talking about classification methods now I will be discussing the clustering in clustering the basic problem is you are given a data set and you really do not know how many groups are there in the data set the word group I am using it loosely okay it is not the group that you would see in group theory rings and feels the word group is the way an ordinary man uses a word group uses the word group in the same way I am also using it for example look at the two data sets that I have given here in this data set you would say that there are two clusters this is one cluster that is one cluster or there are two groups of point this is one group that is another group and in this data set again you would say that there are two clusters this is one cluster that is another cluster right now this is something when we are looking at the data set we are saying it and you want the same thing to be said or to be concluded by your algorithm your algorithm should automatically state that in these two examples the number of clusters is two number one and number two once it says that number of clusters is two in the second one it must be able to state that the first cluster is this this is a cluster of points this is one cluster and that is another cluster of points similarly in this one this is one cluster of points and this is another cluster of points this is what your algorithm automatically should state as the name of the subject is recognizing patterns pattern recognition so you are given a data set we are able to recognize the patterns and you want your algorithm to recognize them automatically. Now let us see what are the difficulties here so if you want to state the problem the problem would look like this you have you are given a data set S maybe in m dimensional space here the number of clusters K may not be known and then there is something called a choice of similarity dissimilarity measure and algorithm what is this choice of similarity and dissimilarity measure you somehow feel that this whole thing since it is you are saying this is one cluster somehow they are I mean similar to each other similarly these points are in some way they are similar or they are connected to each other and here also this point and the same is the case with this you have some sort of a similarity relationship that relationship somehow you need to mathematically state it the clustering problem which in many books it is stated as you would like to find groupings in the data set so that in each grouping the points are similar to each other and from one group to another group you will find dissimilarity let me repeat it in many books the problem of clustering is stated as you need to find groupings of the data so that in one group the points are similar to each other in every group the points are similar to each other and between one group to another group you will find lot of dissimilarity so this word is similar and dissimilar they need to be properly defined and that is this point choice of similarity and dissimilarity measure and the number of clusters has is it the case that someone gives you number of clusters and once you are given the number of clusters you will find them are in some problems you need to find the number of clusters on your own in some problem you need to find the number of clusters on your own it is not necessarily true that someone gives you the number of clusters always let me tell you an example where you may not know the number of clusters where you may not know the number of clusters the example that I state it is again related to satellite images it is related to land cover types it is related to satellite images it is also related to land cover types my examples they are based on the Calcutta data because that is the place where I reside I use I always ask my students that how many land cover types are present in Calcutta and then they would say water is surely one land cover type and then you have concrete structures sure that is building areas and you have vegetation where you have some paddy fields and there is open space that means barren land not in Calcutta but in the suburbs and there is one place called Maidan in Calcutta that is also just barren land so these are basically main four types of land cover type mainly four types then I would start asking them questions like well you have pond water and you have river water do you think there is any change in this then initially they would say no all the water should be same then actually what happens is that when the satellite is taking photographs it is giving actually it gives two different signatures for pond water and river water and it is true of Calcutta and I assume it to be true of even this place you have river Cauvery right and I do not know because I have not seen the data set but I presume that the Cauvery river the pixel values would be different from the pixel values of the ponds I presume that I do not have any way of judging it I have not seen the data but I presume it usually this is a mistake that people make all the water should be same the answer is not correct it is not true surely seawater is different from river water and in most of the cases river water is different from pond water seawater here in Madras you have see also there is water in the sea the seawater is different from river water we all know that seawater tastes salty right whereas pond water or river water at least the taste is not salty this is something that we all know and you would see that they have different signatures so you cannot put the word the water as just one cluster you need to have that thing to be broken into two three components okay you need to have that thing to be broken into two three components they may not possess the same signature from the source which is giving you the values for these things it may not give the same value for all these types of waters okay so this is one thing that you need to keep on your mind you may think that you know the number of clusters but that may not be the case you may not you might have made some assumptions in saying that you know the number of cluster that may not be true you need to verify those things okay so this is an example where you may not know the number of cluster even though you know the place and you know the whole area yeah so number of clusters K may not be known in fact I can tell you very many examples where the number of clusters is not it is just one example I can tell you one example relating to Telugu language my own mother tongue I can tell you one example to Telugu language Telugu vowels we say a a e u a o these are the vowels right but there is also one vowel that we always use but that is not mentioned in the textbooks there is a one word all these things I am telling to him one word called Tataku to him Tataku there the vowel is not neither a not a this something in between so this has come when ISI has done project on Telugu vowel recognition this particular thing has come as a separate vowel Tataku that sound a that separate that has come as a separate vowel so there again the number of groupings is not known even though the mother tongue of most of the persons who are conducting this experiment this Telugu so I mean you assume that you know these things but you may not I mean ultimately you may need to change so once you somehow get K and once you somehow get this similarity or dissimilarity mention then the next step is you need to have an algorithm to do the clustering before I proceed to all these things let me ask you a question given the data set do you think clustering is unique I will repeat given a data set do you think clustering is unique that means given a data set is it possible to get two three equally meaningful clustering the answer is unfortunately yes given a data set you can get many meaningful clustering I will give you an example probably all of you know what playing cards are posh in Hindi that is the same thing in Bangla you have 52 cards okay if you ask a child to do the clustering of this 52 cards probably the child will divide the cards into two clusters all black cards all red cards and if you make a slightly grown-up child to do a clustering probably he will put into four clusters clubs diamonds hearts and spades some other child may put all the face cards on one side and the other cards on the other side some other person may put all aces as one cluster kings queens jacks like that one may have 13 clusters now so I have told you four different clusterings I am asking you which one is better and why can you give me an answer so given a data set you can have equally meaningful clustering given a data set you have equally meaningful clustering then when someone gives you a data set and ask you to do the clustering usually the person has some particular or some specific property on the mind on his or her mind so you need to do clustering of the data based on whatever he or she tells you I hope you are getting the point that I am trying to state so it is not necessarily true that you have the same I mean unique clustering of the data so then when I say that the number of clusters is somehow you will find you will find some choice of similarity or dissimilarity measure dissimilarity or dissimilarity the example that I gave you I think the choice of similarity or dissimilarity is very clear if someone says all black cards and one cluster right card there the similarity measure is very clear to you if someone says clubbed diamonds hot spades four different clusters there also the similarity or dissimilarity is very clear to you right similarly aces kings queens jacks like that 13 clusters there also similarity or dissimilarity is very clear to you note that if that similarity or dissimilarity measure changes then your whole clustering will change am I right if the similarity or dissimilarity measure if it changes then the whole clustering changes. So depending on what you want to achieve you need to define the similarity or dissimilarity measure properly otherwise what you want to achieve you may not achieve okay so then the last part is algorithms we all know we all know what Euclidean distance is before I talk about this dissimilarity measures let me tell you little bit of what a metric space is there is something called metric space you have a set x this is not a null set okay you have a function defined from cross product of x to 0 to infinity now D is said to be a metric on x if D of xy is same as D of yx let me explain to you these three properties the word D is used D is for distance the word D is used the symbol D I am using it for distance we use the word distance very loosely so in mathematics they have given a separate word for it and they gave a definition to that the word that they gave is metric METR I see metric and this is the definition of metric D is said to be a metric on x if these properties are satisfied now what are these properties if you go from x to y whatever may be the distance that is the same as distance from y to x which is totally true distance between x and y and y and x they are the same for all x and y and distance between x and itself is 0 okay and if distance between x and y is 0 then x is equal to y if distance between x and y is 0 then x is equal to y then what about this this is distance between x and y plus distance between y and z it should be greater than or equal distance between x and z for all x y z belonging to x this property is known as triangular inequality take a triangle sum of two sides is greater than or equal to the third side am I right in fact it is strictly greater than the third side then only you can have triangle okay so this is basically sum of two sides okay if all the three points are on a straight line then you will get equality if all the three points x and y x y z are on straight line you will get equality otherwise you will get inequality so this property should hold good for all x y z belonging to x so a function D satisfying these properties is said to be a metric on x is said to be a metric on x and such a space is called metric space and there are the spaces that we are seeing R R square R cube all to the power of 4 matrix are defined on that and we are using those matrix probably without knowing that they are matrix on real line it is basically if you have two values x and y the distance is measured as modulus modulus x-y and you can show that that is a metric it satisfies all these properties okay and if you are in the m dimensional space these are two vectors then for every p you take some value for p let us say p is equal to 2 and you find this that you are going to get basically Euclidean distance if you take p is equal to 1 what are you going to get if you take p is equal to 1 what you will get is say this is a point a 1 a 2 say this is a point b 1 b 2 say in two dimensions and if you take p is equal to 1 what you are going to get is this plus this right there is a standard name for it what is it city block distance and these are all matrix if you take p is equal to 1 you will get a metric if you take p is equal to 2 you will get a metric if you take p to be a fractional value any fractional value greater than 1 then also you will get a metric any fractional value and any integer value greater than 1 you will still get a metric p is equal to 3 4 5 6 p is root 2 you will get a metric root 5 p is equal to E metric p is equal to pi that is an irrational number even then you will get a metric so these are uncountably many metrics uncountably many metrics even then you may define you are in a position to define some more such metrics it is not the case that I have exhausted all metrics here. So metric is a or this is a measure of dissimilarity between two points these are all measures of dissimilarity here this D this is a measure of dissimilarity distance is a measure of dissimilarity okay so there are very many metrics now the question is given a data set you need to choose which particular metric you would like to use given a data set you need to somehow find or you need to somehow calculate or in some way or other you need to get which particular metric you need to choose now I will give you some examples where probably for the same data set you may want to use two different metrics this example let us just say there are two students there are five subjects there are five subjects there are two students I will give you the marks of the students the first student you got 90 90 90 90 90 in five subjects okay the next student you got 100 100 100 150 and you would like to say who is better that is what is actually your problem 90 90 90 90 95 subjects in the same five subjects other student has got 100 100 100 150 and you would like to say your problem is somehow you need to judge who is better and what you will do is that you would like to calculate the distance of this thing from the ideal one ideal is 100 100 100 100 whichever distance is minimum you would call that student to be better okay now my question to you is what distance measure you would like to use city block okay I mean let me just make it 60 because city block means then you are going to get to be same okay so let me just make it 60 then if you use city block probably he will be better okay because here it is 100-90 10 10-10-10-50 you will get here you would get 40 so he is better but if you take p is equal to 2 that is Euclidean distance then here it is 10 square 100 100 100 100 500 and here it is 40 square 1600 okay if you use Euclidean distance he is better now which distance you would like to use it depends on whom you want to call better okay we would like to call this one to be better because it is 460 his 450 450 is less than 450 but supposing this is 50 okay okay let me just take 40 then we can you think of some way of calling this one to be better suppose this is what he just passed this subject is there any chance to call him better the second one probably in our usual subjects mathematics physics chemistry algorithms data structures networking that one this one probably we do not we do not want to call the second student to be better we would like to call probably the first student to be better but supposing your five subjects are learning five different karnatic raga karnatic music raga you know that mastering a raga is extremely difficult and this person has mastered four raga then probably you would call him to be a better candidate because he has the potential of mastering this one whereas this person he could not master any one of them maybe if it is a subject of about learning karnatic music or Hindustani music learning those raga probably you would want to put him to be a better student than this your choice of distance measure it depends on the problem at hand and how you would say someone is close to some or someone is far away from the other one it is very much problem dependent is it understandable to you can we take a small break let us take a yeah so the choice of distance measure it depends on the problem at hand and it depends on what the problem tells us I mean the problem actually forces us to calculate the distance between the quantities in that way and since you are trying to model the problem at hand you need to define your dissimilarity and similarity measures according to the situation or according to the constraints that you are facing so in the previous slide I was mentioning about dissimilarity measure and in this slide I am mentioning about similarity measure similarity between two vectors yeah is summation i is equal to 1 to m these two are m dimensional vectors a i b i divided by square root summation a square summation b i square can you tell me what this similarity measure is this is basically the angle between the two vectors a 1 a 2 a m is one vector b 1 b 2 b m is another vector how do you calculate cosine ? this is the formula for it in fact your expression for correlation it came from this cosine ? has been existing in mathematics for a long long time statisticians used it to get the expression for correlation coefficient that is it and with that they said that it lies between – 1 and 1 that is why this is cosine ? it lies between – 1 and 1 okay does it lie between – 1 and 1 cosine values they lie between – 1 and 1 so this is similarity measure if the value ? is 0 cos 0 is 1 you have maximum similarity maximum similarity and when you are going to have ? to be ? by 2 then you will have get cos ? by 2 to be 0 then they are perpendicular and one is on one side of one vector is like this another vector is completely the opposite that is 180 degree then you are going to get – 1 then you will get – 1 so there you have the maximum dissimilarity that is the basic feeling when you are using this similarity measure this is also just an example there are many other examples of similarity measures in the literature and there are many other examples of the similarity measures also note that here in this slide I gave these are all known as LP norms for P is equal to 1 that is called L1 norm P is equal to 2 that is L2 norm and by the way can you tell me the value of this as P goes to infinity what is the value of this as P goes to infinity this one as P goes to infinity what is the value of this this is called L infinity norm and this is also a metric this is called L infinity max modulus a-bi is equal to 1 to m now if you look at one of my previous lectures where I multiplied the differences by some meant by matrices I called one of them to be positive definite matrix you attended those lectures positive definite matrix you may try to do I mean that is one way of looking at different I mean distances where you keep x1-y1 whole square plus x2-y2 whole square square root you keep it like this there you start adding first some weights to each of these terms then ultimately you will write a matrix there also you are generating many matrix here also you are generating matrix Mahalanobis distance which Mahalanobis defined way back in 1930s he wrote that paper to Kolkata mathematical society Kolkata mathematical society there that paper was published Mahalanobis distance paper that is I am not going to talk much because he will be discussing all these things Mahalanobis distance okay there also you are going to get one xi-yi I mean x-y prime there is sigma inverse x-y or mu1-mu2 prime sigma inverse mu1-mu2 which is again a quadratic form which is again a quadratic form and that sigma inverse that is a positive definite matrix so that is why he called it as ?square that is why he called it as ?square so that we can talk about square root of that if the sigma inverse is identity matrix you will get the usual distance the square of the usual distance that is why he denoted it by ?square there is a square added to it so you can go on generating matrix in different ways depending on the problem at hand.


It took me a while to realize, as a kind of student, that the way I saw things being done in Sainte-Hermé Tibetan was not really quite how they were done in Indo-European. And then as a kind of companion piece to my 2019 book, then I put an article together that kind of discussed this contrast in methodology between what I was seeing happening in Sainte-Hermé Tibetan and what I think is more normal in, how can say, traditional historical linguistics. And then I teamed up with an Indo-Europeanist to make sure I didn't make any serious mistakes. Honest Fellner, who's at the University of Vienna. And the article was published and maybe one or two of you know about it, but it's fairly detailed and I think gets kind of to the core of the way I think about methodology. So, you know, with your permission, I based that lecture around that article. So, hopefully it will, even if you've maybe seen the article, it will still, this variant format will still prove sufficiently interesting to you. In any case, it's what I have to say, so here it goes. So, I'll discuss, you know, you may come to realize this kind of preoccupation of mine. First, a little bit about the history of scholarship and then I'll be discussing this idea that in Chinese linguistics specifically is called the word family. But then in Tibet or Burman, associated with the kind of theoretical writings of James Matasov, has been come, has come to be called an alepham, based on where fam is family and aloe is like in alomorfer or alephon. But you can see alepham and word family is basically meaning the same thing. And then I'll look through if you like different types of relationships that I think have been covered by this term and then have a conclusion. So, as a starting observation, word families or alephams are discussed a lot in sign of Tibetan linguistics, but not really in Indo-European, for example, or other traditions of historical linguistics. So, let's look at where the term was coined. This is an article by Bernard Kahlgren about word families. So, I'll just read it. He says, it is not allowable to identify Chinese Mu with Tibetan mik, so long as we have not first established the word family to which Mu belongs. The kin to Mu is undoubtedly the word, I don't know the reading of this one, probably also something like Mu, which means pupil of the eye. And it is just as likely that this word is the one that corresponds directly to Tibetan mik. And I think there's a reasonable point here, which is that it's not always words with exactly the same meaning that correspond across related languages. But I do find his formulation, it is not allowable a little bit strange, because it's kind of a moral position rather than a scientific methodological position. So, that's all Kahlgren said, although he's definitely the person who invented word families. But Stuart Wolfenden, who followed quickly after him, gives a more elaborate discussion of what he sees as the kind of methodological program. So, here we go. He says, in pursuing comparative studies of the vocabulary of signative and languages, we are today possessed of two methods of approach. The first of these and the older is that of setting up simple word equations from language to language. The second, that of comparison by word families only. Taking the family as the smallest operating unit. The first method passes from language to language, lifting single words from each without delving down in any way into what we might call the soil beneath them. So that we might in fact term such surface operations the horizontal method. We have as it were plucked a flower without looking to see which bush we were looking at. We took it. The second method, on the other hand, seeks in the first place, not to set up equations between single words and two or more languages, but first of all to gather the word families of each separate language. And only then after we have gained a clearer view of the general background of the words composing them to begin comparative work. This method from the fact that we dig down into the soil as it were, from which the individual words have sprung, we might, if we wished, call the vertical method. We have then not only the flower, but the actual bush on which it is growing. So a nice sort of gardening metaphor from Wolfenden. And I should mention that the context is he's criticizing Walter Simon, who had an early paper on Tibetan and Chinese comparisons. So as it happens, the proposals that Wolfenden goes on to trying to exhibit his methodology ways in terms of saying like, see if you did it this way, you'd make a mistake. And if you did it this way, you'd do it right. All of his proposals are no longer believed to be right. So let's say I think Primafeisha that maybe suggests that his methodological views are maybe not 100%, right? But of course, any method can also lead to mistakes. So we shouldn't be too hard on him and he was writing a long time ago. But in case that's the sort of, I think how that's how Sino-Tibetan came to see itself as needing a different method than was being used in other fields. And then Matasoff comes along on the Tibetan side and says, when he's coining this term a la fam, he says, we need a word to refer to the relationship among the various members of the same word family. I think that the observation I would make at this point is, we haven't seen anyone define what a word family is or how you can tell whether two words are members of the same word family. It seems to be a kind of art and not a science, yeah? And then about the criticism that operating with word families is messy. This is what Matasoff says, he says, we must assume that the proto language itself was a wash with alophamic variation, both systematic and unsystematic. Why should a proto language be any more monolithically invariant than any living language that we can observe with our own eyes? No language is ever perfectly regular at any stage of its history. And this is a, let's say, a criticism that is often made towards sort of traditional historical linguistics. I think in the first instance by people like Suchart in the tradition of romance linguistics, that historical linguistics in the Indo-European tradition is overly hair splitting and sees, kind of insists on cleaning up any mess that it identifies. Whereas, in fact, we know languages in reality can be a little messy. But as an extreme case in this same article or book actually from 1979, Matasoff himself reconstructs 21 different variant forms of the word for lung. And I personally find that a little bit, you know, strange credulity. Like no language I know has 21 similar words for lung. But our case is like this precedented methodologically. What I will now look at is the closest thing to word families in Indo-European linguistics, which are called doublets. And they're something that Matasoff himself draws comparison to. In terms of he says, you know, my Alephans are like the Indo-European as doublets. So let's look at doublets. So this is what I just said that Matasoff says doublets in Indo-European are what we mean by word families in Asia. And a real viewer of our paper can make a similar point that Matasoff has also made from time to time, that in the Indo-European we have things like oblate grades and root affixations. And if Indo-European nests can get away with that kind of, you know, association of different forms of a word, despite having different oblate grades or different root affixations, then we can do similar things inside of Tibet, no problem. So that reviewer drew attention to the following entry in the American Heritage Dictionary, which is an English dictionary, has a appendix of Indo-European roots. So here we have the Indo-European root wek, which means to speak. And we have the ograde form wok, which gives us Latin vox and words like vocal, voice, and vowel in English, and gives us Greek ops, which comes into Greek with the word calliope. We have a suffixed ograde, so wokwa, which gives us all of these words, all from vocare in Latin. And then we have a suffixed form in the e-grade that gives us these other words. So isn't this a word family? You see these different competing variant reconstructions. So let's look at this example in more detail. So we have the root wek, that in the hei wrist, which is a past tense of Greek and Sanskrit and Indo-European, it would have been wekweu, which gives us avocat in Sanskrit and apon said in Greek. So from this root, we can make a root noun that gives us vox in Latin and ops in Greek. And then as far as this second form that we discussed above, this suffixed ograde, if you just project backwards from Latin into Indo-European, which is something we call a transponent, is a kind of mechanical backward reconstruction from one language, you would get wokwech with this ech suffix, and that's what would lead to vocare in Latin. And from a perspective of Indo-European morphology, it's perfectly legitimate thing to do, but it's only supported by the italic family. So in this word, it's probably not of Indo-European provenance. It's an italic innovation by applying this denominator suffix to the verb for voice. So rather than forming a verb directly from the root, they've taken the root noun and applied the denominator suffix to it. And that is how you get this verb in Latin. Okay, so that's the second option. And then in the third, we have another sort of known way of forming nouns in Indo-European, which has to do with an accent class. I won't get into it too much, but the accent class is called protokinetic, and it's an estem. So this gives us apos in Greek and vachas in Sanskrit. So those are the three, let's say earlier we were looking at how they're presented in the American Heritage Dictionary, here they are, and now I'm saying it's not really the case that they're just kind of three variant forms. We have ways to explain them as morphological derivatives from a single root. So in a sense, there are only two variants. One is the root noun, because the second variant is formed from the root noun through a suffix that changes it into a verb. And the second one is an estem. So now if we look at the English words, all these different words in English are borrowed from either Latin or French, one way or another. The details are there, no point going through it. So we have this long list of Latin words. And they are either nominal or verbal derivatives of the same Latin word, vocare, and all of the morphology that relates them was productive and transparent in Latin synchronic grammar. And the developments from Latin in the Romance languages is also well known and well understood. And when they were tested in English and how they came to be used today is also all documented. So all of this apparent word family variation disappears once we look carefully at the linguistic system, use the comparative method, and apply philology rigorously. And that's the kind of, let's say, the key methodological point that we are trying to make is that if you see someone talking about word families, it means that they are not quite done with their work. And instead, if you continue studying the problem and really come to solve it, then you don't need to invoke this idea of a word family. So that was the case that was mentioned by this reviewer, all of these words coming from Wequa in Indo-European, which was kind of easy for us to deal with in a way. But we want to be fair, so point to a kind of really more tricky example. And this actually comes from Trask's introduction to historical linguistics. And he has a dictionary of terms in historical linguistics where he looks at different kinds of cognates. And this is his example of an oblique cognate, which are words that go back to different forms of the same root. So then it seemed like Trask, who was someone who worked on Basque, is also happy with this idea of there being different forms of the same root in a proto-language. And we're not happy with it. So we want to look at his example and say, OK, well, if we can deal with this harder example, then that proves our point as well. So we're looking at feather in English and pteron, which means feather in, sorry, it means wing more than feather. But it means feather and wing in Greek. And I assume most people probably know the word. But it comes up in English words like helicopter is a wheel-like wing. And pterodactyl is a dinosaur with wing fingers. So the Greek word comes up in English as well. So here are the, let's say, if you like to transpose it again. If we just take the English word and throw it back according to regular phonology into Indo-European, we would get this pet rech. And if we did the same with Greek and said, OK, we just throw the Greek pteron back into Indo-European, we would get ptero. So the point then, let's say, from the opponent's side is these are not the same. So if Indo-European had both pet rech and ptero, then it must be the case that there are such things as word families. So now comes kind of the heavy lifting. And if Indo-European is in your thing or you want to just sort of have your eyes glaze over, then that's fine. The point is just that we can explain it. So also, this will maybe give you a kind of glimpse of what an explanation of a phenomenon like this in Indo-European linguistics looks like. But don't get too worried about the details. So originally, Indo-European had a proto-kinetic heteroclite where proto-kinetic is the accent class. And heteroclite refers to nouns that have an R ending in the nominative, but an N ending in other forms. And you actually will know cases like this, like water ends in an R in English because it comes from the nominative. But oh, I don't know, like the Sanskrit word for water has an R in the nominative and the N in the accusative, as does the Greek one. So anyhow, so Indo-European had this kind of accent class and this kind of conjugation pattern for this word. So that means the nominative looked like ptero. And the oblique stem from which all the other case forms were formed was something like pretend. And you can see this directly attested in Hittite, which has the nominative petar and the oblique stem petan. So that's the original thing you should reconstruct in Indo-European. Now, how do we get from that to these forms that we see? So English derives from pet-rech, which should mean something like a collection of feathers where this ech suffix is put on the inherited nominative petar. And this is just a parallel to show this sort of thing happening, but not in exactly the same way, also in Irish and Latin, whereas Greek instead started from an adjective, a possessive adjective, that meant feathery thing that came from petar, which itself was an analogically renewed oblique stem. And we give an analogy of the type we saw yesterday. So let me just talk us through it. So pet-per-tu is to pur-teu, which are two words that meant something like crossing in Indo-European that give us fjord in Norwegian and portus, like door in Latin. So that morphology was there. And then if you forgot that the accusative of the word for feather in Indo-European should have been peten and you sat around wondering, you might have formed this analogy and then you would have come up with an answer like petar. So that's our explanation to use four-part analogy to explain the invention of this alternative oblique stem. And then once you have petar-peter, then you can add the o to it to make an adjective. And then that gets you the form we need in Greek. So thank you for sticking with me through that. While it is correct, from a certain perspective, to reconstruct both petar and pter in Indo-European, the point is at no moment did any community of speakers have both of those words for feather or wing. You have to have forgotten what the inherited accusative is to get to the second one. So no proto-language had both variants, which is to say there was never a moment where we can say there was a word family. And both of these were variants that were part of that word family. That's the point we want to make. And just say, in fairness to Matasoff's 21 words for lung, cases like feather in Indo-European can approach that level in complexity. So in particular, Nussbaum in a 1986 monograph sets up 12 related words for head, horn, and skull in Indo-European. It's a very hard problem that had been sitting around for a long time, and he tried to solve it. And I think his solution is seen as pretty good. And in this 300-page monograph, he explains each of these forms one by one, as ultimately deriving from a single noun, kech, which meant head bone, the bone of the skull, and uses different combinations of derivational morphology, analogy, semantic change, as the case may be, to get to these various attested forms. So our conclusion is that these 21 forms for lung is not totally unprecedented or unreasonable, but until each form is rigorously accounted for in an elaborated theory of sign of Tibetan historical phonology and morphology, it's not helpful to describe these as members of a word family, but instead just as problems to be solved. So that was the first section. And now I will go through a different phenomena that we think have come to be described under this rubric alepham or word family. And we'll start again with where Matasov defines things, because I think that when he initially came up with the idea, he was not very far from traditional perspectives. But over time, as the discipline has gotten used to talking about word families, it's become a way of avoiding progress rather than making progress. So this is what he says. He said, word families are groups of forms which bear a non-fortuitous phonological and semantic relationship to each other. The sound-meaning relationship among the alephams of word family may follow a more or less productive pattern so that in favorable cases, variations may be traced back to systematic or at least plausible alternations in the proto-language itself, often involving proto-affectations. In many cases, however, the synchronically observable intra- and inter-alo-fammy follows no particular pattern that repeats itself elsewhere, which is to say, we would agree entirely with that, put that way, which is basically when it's easy to figure out, it's easy to figure out. When it's hard to figure out, it's hard to figure out. So he goes on to say, the situation may result from conflicting or overlapping morphological processes that obscure each other's outputs, unsystematic or sporadic increments to roots inference or contamination from genetically unrelated forms, a dialect mixture, or of course, it is always possible that the forms in question were never co-alphams at all and their resemblance is entirely specious. So again, in formulating his proposal for alpham, he recognizes that they have multiple possible origins and that in principle, we should figure out what those origins are. So looked at carefully, we think each alpham tells a story that combines in some measure regular phonology, borrowing, and analogy. So we're back to basics. In the history of language, there is phonology, borrowing, and analogy. So let's just try to stick with those and not bother with word families. So now we'll go through examples of different phenomena, both looking at an Indo-European case and looking at a Sinotubetan case that has been analyzed as a word family that we propose should be analyzed along the lines of the Indo-European example. So first, dialect variation, misanalyzed as proto-variation. So hopefully some of the Indo-European cases are familiar just to make it a little bit easier, which is that we've tried to choose simple ones. So all English words that begin with V are loan words, like Vary is from Verre and Vicar is from Vicar. But what about vein, vat, and vixen? Because if you look at German, they have quite good, dramatic etymologies. Pfanne, which means flag, fass, which is barrel, and Füchsen, which is the same as vixen. So why don't they have an F in English? Well, a very strict application of the comparative method would require that you reconstruct some kind of variation back into proto-Germanic, where you had the V for vein, vat, and vixen that, let's say, changed to an F in German, because there's a different correspondence than you see, for example, in fass to Fuchse, where both languages have F. But that's not right, that would be wrong. And we can tell that in the history of English alone, where vein was Pfanne, that was Vat, and vixen was something like Füchan, yeah. So the answer is actually that these are inter-dialectal borrowings, and the canonical explanation is that in Somerset dialect, they changed all of their Fs to Vs, and so they said things like vis instead of fish, and var instead of far, and that there was a kind of concentrated immigration from the Somerset region to London at one point, and for some reason, and this part is maybe a little bit where the card comes out of the sleeve, why was it that mainstream English borrowed these three words specifically from the Somerset dialect? Well, that's one of the ways, I think, that historical linguistics is history. They could have borrowed different ones. So another example of inter-dialectal borrowing from Sanskrit, so Sanskrit R and L both correspond to both R and L in other Indo-European languages. So I'll just look at some examples. So R corresponding to R, we have Raji direction in Sanskrit corresponding to Orego, reach in Latin in Greek and Orego, guide or steer in Latin and English write. So we have R in all the languages. Beautiful, we reconstruct R, right? We also have responding to L, where we have Rocha T in Sanskrit, it shines which then corresponds to things, I'll skip the Hittite and Cocharion, things like Leukos, bright in Greek, looks light in Latin and English light. So here we have R in Sanskrit, corresponding to L in other languages. Then we also have L and L, so loka world in Sanskrit, corresponding to Leukos, sacred grove, for example, in Latin. And then we also have L and R, so something like loha copper in Sanskrit, corresponding to Rudus lump of bronze in Latin. So again, according to the sort of textbook version of the comparative method, we would have to set up a different proto segment for each of these in Indo-European. So the R, R one would clearly be an R and the L, L one would clearly be an L, but then what about the R, L and the L, R? So four liquids in Indo-European? Well, no. For one thing, often Sanskrit itself has internal variation like hair. You have both Roman and Loman in Sanskrit, where external comparisons suggest R. And another example is rojita versus lojita, meaning red. But also if you do your philology, in those cases where both R and L are options, in Sanskrit, R is more prevalent in older texts and more Western texts. And L is more prevalent in the East and in younger documents. So this suggests that there were sort of two early dialects of Sanskrit, one further in the West, which is also where the older documents are from and one further in the East. And the one had an R, changed everything to R and the one changed everything to L. So what you get is a collapse of R and L into a single segment and then a split, a kind of unconditioned split of R and L again. And that's the explanation of why you have those four correspondences. So now I look at an example from Chinese of dialect, inter-dialectal borrowing. So some phonetic components in middle Chinese have both ya final and n final readings. So here's none and nay, and you can see that the whole character none is sitting on top of the radical meet in the second character. So if phonetics are used to represent sound, you would expect the second one to be none, but it's not, it's nay. So that's the kind of phenomenon we're interested in. And we can't propose either final n or final ya because there are series, phonetic series that have clearly one or the other. So I give this first example where every member of the series has a final n and then the second example where every member of the series has a final ya, although if you look at the middle Chinese readings, they don't have that. That's because of a kind of late sound change which is why I've added the reconstructions of the rhyme. So, yeah, which is to say, we have solid reason to have the pure n series and good reason to have the pure j series. So how are we gonna handle these mixing n and j series? Well, Sergei Starostin proposed that in all Chinese, there was a separate final r and these series that mix n and ya are evidence of this original final r that in the west changed into n and in the east changed into ya and then its subsequent dialect mixture that leads to these mixed series. So generally the reading tradition continues the Western readings, but for some characters, for whatever reason, they were borrowed from the Eastern dialect into mainstream Chinese and that's why you have the ya series. So this proposes actually a little controversial in Chinese linguistics, but I'm convinced of it and I think it's making the evidences is pointing more and more in that direction over time. So in any case, now you've seen an example from English, an example from Sanskrit, an example from Chinese of inter dialectal variation and I think that some of Matasoff's proto variation can be explained along these lines. So he reconstructs a root that means good where he gives three forms, liak, liang and medyak and points to Tibetan jak as evidence for this, but actually in the dictionary he's using, Yeshka, the dictionary author points out that this is what he calls a vulgar pronunciation of the normal Tibetan word jak. So it's a borrowing from a Tibetan dialect that has regularly changed ya into ja back into Tibetan, not recognizing that that was a Tibetan internal inter dialectal borrowing, Matasoff projects the variation back to the proto language. So that's our first example of some word families are not real because they're inter dialectal borrowing that have been misanalyzed as proto variation. So now the next case is non-edimological resemblance misanalyzed as proto variation and I start with the classic example of deus and theos. So deus is the Greek, sorry, Latin word for God and theos is the Greek word for God and early inter Europeanists assumed that they were related because they look sort of the same and they have the same meaning, but they're not. And it was only when we figured out all of the sound changes in both languages that you could really prove that they weren't related. And let's just look, I think, a fun example of habeo in Latin and English have, which look too similar to not be related and mean the same thing. But in fact, you have two different inter European roots here. One is kep, which gives us kapio, which is to take in Latin and have in English. And then the other one, which is geb, that gives you habeo in Latin and give in English. So those are the correct comparisons.  And I don't think there's anything, oops, I don't think there's anything wrong with that in theory, because you know, what are the chances that inter European had two unrelated words for to have or to take that both started with a vealer and both ended in elabial, something like that. But no known process in inter European historical phonology or morphology can relate these two roots. So they're treated as unrelated roots. And I think that's the prudent thing to do. Now looking at an example from Sino-Tibetan, Matasov reconstructs a word, l'chak, meaning iron, that he sees as having cognates in Tibetan and Burmese. So chak in Tibetan and jack in Burmese. But native Burmese words never begin with voice stops. So it can't be, right? Also, the semantics I think are weak, comparing iron to bridal bit, it's not impossible, but they're not strong. And most maybe, or helpful in this regard, is clearly the pro-Sino-Tibetans didn't know iron because iron came after bronze and bronze and iron were, let's say, discovered by the Chinese in historical times. More or less, bronze, a little bit pre-historic. So iron is too recent to be reconstructable. And then I think this case shows kind of some of the principles I was talking about yesterday where like, well, if the semantics were perfect and the phonology were perfect, we might have a problem in terms of, well, okay, I guess we need to reconstruct iron and then figure out, maybe they were talking about unprocessed iron ore or some other kind of a shiny rock or something like that, yeah. But in this case, the semantics, the phonology, the morphology, and the archeology are all pointing to this being wrong. So let's just say it's wrong. And then, so now that's another type of phenomena that can be misanalyzed as a word family. So now I move on to another one, aerial words. So let's look at wine in Indo-European. This is a fun one because there's lots of similar looking words for wine, but they reconstruct slightly differently into Indo-European. So if you take Oinos in Greek and project it back into Indo-European, you get this ochno, whereas if you take vinum in Latin and project it back into Indo-European, you get ochno, which is a little bit different. And there's no obvious way to reconcile this evidence, which means the Indo-Europeans did not have wine. And the perspective that maybe the Indo-Europeans didn't have wine is helped by noticing that Semitic also has a similar word for wine as does the Cartivale in the family. So what I think most people, this is controversial still, but what most people think happened was that the caucus speakers figured out how to make wine and gave it a name from their language. And then that name spread with the commodity quite quickly after the Indo-European language family had already broken up, but not very long after, which is why these different Indo-European words point to quite similar protoforms, but that are irreconcilable. So this, I think, makes sense, right? The same thing happens more recently, like I was saying with coffee tea, with iPods. And another similar example actually in Indo-European is hemp or cannabis. Isn't quite reconstructable. So we can know that the proto-Indo-Europeans didn't have wine or cannabis, but quite early on in the dispersal of the Indo-Europeans, they got wine and cannabis. And I personally am sort of amused by the idea of someone showing up at a campfire and saying, look at this thing I got from Georgia, you'll love it. It's called wine, which is what now happens with things too. So some things never change. So now looking at an aerial word in sign of Tibetan, and I touched on this yesterday, horse. So Matasov actually reconstructs horse, this monstrous thing, Samarang. Yeah, I'm not quite sure what all the slashes and hyphens mean, but these are the forms he cites. So Marang in Burmese, Ramang in Old Tibetan, and Mra in Chinese. So they look quite similar. But the proposed reconstruction violates something that I call Simon's law. It's a discovery of Walter Simons, which is that an MR in Chinese should correspond to a BR in Tibetan. So you get the word for a fly, you know, like fly, is Zbrang in Tibetan and Mran in Chinese. And the word for snake is Zbrul in Tibetan and Mrui in Old Chinese. And also Matasov's reconstruction for horse doesn't work in terms of the finals because you see where Chinese has a with a lot of stop, Tibetan should have a. So let's just look at the horse forms, right? So if Chinese has brang, then Tibetan should have brang, basically, but it doesn't. So we conclude that horse is a Vandervort. That's what the technical term for these sort of cultural technological words that spread quickly across language families. And this is supported by archeology, as I mentioned yesterday. So moving on to another kind of source for proto-variation. One is overlooked to sound laws. So Sagar in his review of Matasov's handbook says that he has missed sound correspondence pointing to this, which is a G in Tibetan corresponding to a W in Burmese. And this is a fun sort of tit-for-tat between Sagar and Matasov, if you are bored, some rainy afternoon. So Matasov dismisses around because he prefers to compare one in Burmese is to Val in Miso. And I don't even quite know what his logic is, but anyhow, that's what he says. It's not related to, I guess it's that he thinks it should be an L final and not an R final in Tibetan. But it's not totally clear. And then he accepts the comparison of groma, which is some kind of root vegetable to Wa in Burmese. But this is what he says. He says the only way to make sense of it is to assume a form like grwa, which was treated by Burmese as having a double prefix gr. So Sagar paraphrases that opinion as saying Burmese has treated, he says Burmese has treated G and R as prefixes, understand has lost G and R as a result of untold random processes so that only W remains. And I think that's a good paraphrase, which is what my co-author Hannes and I are objecting to. So, and then just by way of reminder, so he says, Madison says, the only way to make sense of this. So I just wanna point out that there are other ways to make sense of them. So for example, Armenian changes wa into ga, which is why we have the word work in English, but the Armenian word is gork. So if Armenian can change wa to ga, why can't, why can't it bend? I'm not necessarily that I am proposing that. That's actually not the solution I propose in my book, but it's just to say, I think whenever someone says there's only, the only conceivable answer is blah, it should raise a red flag in your mind. I think maybe this is more about someone's lack of imagination than anything else. Okay, and then next, I come to contamination. And contamination is a type of analogy, but a very specific type that, that I, and I mentioned this before, where words that are part of a sort of semantic subsystem influence each other's form. So the textbook example is female, which should be femelle has been influenced by male. Looking at an Indo-European example, the Indo-European word for four is quetvore, which turned sort of randomly in protogermanic into having a P initial. So it became petvore and then fedvore, which gives us four, for example, in English. And this is under the influence of the P in five, where Greek and Sanskrit show you that P had had a, sorry, the word for five had a P. So basically, the protogermanic speakers copied the P of five back onto four. And I think something like this happened in Sino-Tibetan, where Mattof reconstructs le-ba, sorry, le-bonga for five with either an L or a B prefix. But actually, this is a sort of problem with using slashes in your notation. I'm not quite sure. Does it mean either an L or a B, or does it mean either an L or a B or nothing, or does it mean either an L or a B or nothing, or both an L and a B? But in any case, it means something along those lines. So we think the L is etymological, which is to say, the Sino-Tibetan word for five was le-ga, like we get in Tibetan and in dakpa. And we think that words like mi-zu-ponga with a P, the P has been copied from four. So sort of like almost the mirror image of what happened in Germanic, where Germanic copied a P from five to four. And we think the P inside of Tibetan was copied from four to five. And you see that in the word for four, both mi-zu has a pa and Tibetan has a pa, and kurtop, which is a language spoken in Bhutan as is dakpa. So that's our explanation, is the B is new caused by contamination, the L is old. And moving then on to our next type of cause of seeming word families is misanalyzed language internal developments. And this basically is a point about philology, where we're studying texts in the original, especially early texts has been the sort of staple of Indo-European, whereas it seems not to be very popular in sign of Tibetan. And I'll let's look at the root right. So Matasov reconstructs a root for sign of Tibetan bre, which means to draw or to write. And he says that this is on the basis of Tibetan alophams like a deriva, sorry, I should pronounce it in Old Tibetan, a briwa, draw or write, bris, a picture, and a ris, figure, form, and rimo on the other hand. So basically, let me just make clear. The first two support the B, the second two don't support the B, which is why he has the B hyphen.  But actually the old Tibetan conjugation of this verb is different. So it has a D in the present and a B in the past and the future, which is totally regular, according to Tibetan historical morphology. So we think that what happened was the D, B alternation, although regular was a little bit untransparent to speakers, so they generalized the past slash future form into the present, which is to say the B in the nominal forms, or yeah, the two examples that Matosov gives of the B in Tibetan are not, don't prove the claim he's making, because in the verb, it's an innovation, and in the word picture, it's derived from the past. A picture is something that has been drawn, yeah. So the root is Rhi, and no Tibetan evidence supports the reconstruction of the B in Bre. The present is late and analogical, and the word for picture is derived from the past. And I also just want to point out that it would be really surprising if the sign of Tibetans had a word for to write, yeah. But maybe that's a little bit unfair as a criticism, because it can also mean to draw, and the protestant of it probably could draw or scratch, oftentimes verbs for drawing or scratching come to mean write. Okay, and then just another example. Matosov reconstructs the Tibetan word sal to a protestant of Tibetan root sal, so gsal, which means to clear away, like a stain. But written Tibetan S actually merges two things in Proto-Sino-Tibetan. One is STS, and one is S. So if we look at old texts, we can see that in this case, it's the STS form that's original. So we have dikpatamche bsalg, clear away all sins. So this is the past tense of the verb to clear, B-S-T-S-A-L-D. And here's another example from Tibet. Completely clear away all hindrances. So barche is hindrance, tamche all, yomsu completely, bsalgte, with B-S-T-S. So the root is sal, not sal. So the reconstruction to Proto-Sino-Tibetan must also be wrong. Okay, so that's my little kind of a survey of different, or let me put it two different ways. One is survey of the kinds of phenomena that can lead to the appearance of Proto-Variation. But we're saying then that proposing Proto-Variation is never a legitimate move. So word families are a bad idea. But we want to make the point now, kind of at the end of this methodological comparison between how historical linguistics is done in San Tibetan and how historical linguistics is done in Indo-European that this isn't some great new discovery of ours, right? It's essentially conservative position. So August Conradt, back in 1896, said about Sino-Tibetan that sound laws are what we should be looking for. Now, unfortunately, that call wasn't really answered. And then in book reviews of Benedict's 1972 volume, Miller was very critical in particular, saying that there is a considerable chasm between Benedict's method and the comparative method with its sound correspondences. And similarly, Chang-Kun said that systematic phonological reconstruction is the first requisite for historical work in linguistics and it is generally absent here. And then for sort of specific reasons, the quotes weren't convenient to give, but Tatsuya Nishida and very recently George Tarostin have also criticized word families and alophams. But for whatever reason, somehow the mainstream traditional historical linguistics methodology perspective in Sino-Tibetan has always been kind of the outsiders looking in. So like Chang-Kun, George Tarostin, Miller, were all sort of active in Sino-Tibetan linguistics, but not as active as Matasoff or Benedict and their students. So that's the end of my presentation on comparing methodology between Sino-Tibetan and Indo-Europeans.