No. So, do, do I have your attention, yes? So for the some, I mean, because you ask. So for the exam tomorrow, so the, let's say the, the weight is structure you have, I mean you will have a, I mean a list of questions, I ta je zelo najbolj, da jaz sem učujem, skupajte do vso nekaj dobro. Tako. Tako, je zelo, da je... Masih, da jaz sem učujem, da je... Zelo, da je, da jaz sem učujem, da jaz sem učujem, zelo, da jaz sem učujem, zelo. Čekaj, jaz sem učujem, da jaz sem učujem, zelo. in v komputeru, ker je veliko spes, in je bilo vsega, tako da je ne v druži. Zelo konceptu. Super. Užitejte svojo svet. Znamo, da je bilo na zelo v zelo v materijali, zelo, da se prišli, da je bilo vsega. Zelo ne bilo komplikatni. Poj Edgarine? Ne znam. Tega v picočku na taj poten. If you can bring materia, I would say yes. I think it's one hour and half in total time, so it's not very long. I don't know, you have other? Who asks? Sorry. I don't know you have other materia. Nismo ne zidim, da je etan natruh, ve. Pomin imam prebst. Zanimamo sprem. Odavimo je na to. Danes vstupijo nekaj, da je zemljen na wizijo relčen. Zanimamo, da mi ve quasi ne potrabilo vzaj. tudi tudi, ki je še vidjamo. Zelo, da teb Nem Boom tudi je ocu ljubek vse se tem, da se isto priče tudi, bodo sem neče dobljela tudi vse neče dobljela, pa izred sem čudovati volumen. Tudi teb po nekakov, zelo sem razljuval. zelo zelo, da je zelo, da je tudi zelo. Zelo je početno izgleda, da je tudi početno izgleda. Izgleda početno izgleda. To je sreda energija. To je, da je... moja energija je k. Zelo da imam tudi treba, in zelo antropi. Če bi se naredil. Zelo je zelo, da je tudi sreda energija. Kb je boljceman, ko je zelo zelo. Zelo, da sem bomo nedeteta, da se včešte. Tako, to, da bomo počutili, tako, to je izgleda, če je počutila, tako, je vsega monomer densitva vsega volima vsega volima vsega volima vsega volima vsega volima. Przesta, sem izgleda, vzgleda, kako sem ga počutila. Nekoj, dar je zelo, je to, vsega volima, vsega volima, vsega volima.  Prefaktor in negrativam prefaktor. Znamenje, prefaktor numerikala, ker sem bil Raz, zelo sem bil všim da. Masne, tko ne jaz tudi izgleda v istimitvi kvaliti. Tudi tudi izgleda, če je raz, zelo je zelo, n-r, je densit, nr monomer tudi z volumem vzela všim trvene. Tukaj tukaj je kruč, ker so kako imelem vama trih.  Pon reviewsa le pwesi. A kar tukaj povrano, tukaj, Seveda je... Zelo je izgleda prejam, da je naredena kB vs. logaritm kaj je tukaj ložite svih srbi hrti. Ok... So situacije sem, pa naredena tukaj ložite kaj... In pak, kako delilo izgleda, ase da, Flori bilo vsego od vsega vsega, je bo nekaj, da je bilo šega gaušanished Baj začeli. Ko se je vse, je to načal, ampak zelo. To z analizim, začeli je to doživ Kožane. Na seglucki se z別nimi. Spodg nekaj. Na 10 monomer. Jse, zrej, ovo je dobro. So vsega tega. In taj je zelo prefakto. Znam, da je, da se... da je tudi konečno propečne, ker smo v vsočenju se, da je tudi nr. poslupovana konformacija v polimeru n po 10 monomersi, je tudi pravda eksponentialna. Tudi je tudi ne prefakto, ne jaz je prefakto. Zato je to ne 한국u v finačnji komputč. Zato smo zelo vzpečnje, tudi na logicalne različnosti. Fay statistical reasons. And then too add here to the fact of function of factor which gives the total which is proportional to the number of conformation with this sis r. And this is exponential of minus r square over nB square, times a factor something like that where is this typical monomer sis, Ta bovanje je vrstivaj. If I do all this math and I took the logarithm, in the end, I have the following expression, which is the one written there, which is this quantity here, so it is V2 n square r to the d.  Ok, and this is the quantity that is written there. And I have to do this minimization, and basically I have to take the derivative of this quantity with respect to r, and just making it zero. Ok, so then I do the f over r, no, and then I impose it equal to zero, and from this I get that r has to be like bn to the nu, ok, where this nu turns out to be 3 divided by d plus 2. Ok, ok, so one thing that I have not told you yesterday is that from here you can see that for d equal 4, ok, because now this quantity depends on the dimension, so it's already, as I said, it's already non-trivial result, because actually it has to be so, no, because excluded volume interactions, of course, are more important in lower dimension, simply the polymer has less space if you want, right, so it feels more the effect of excluded volume. And they decrease, ok, as d becomes larger and larger. However, this formula stops in the validity of some dimension, and the dimension is d equal 4, because if you insert here d equal 4, you get one-half, and one-half is the exponent of, let's say, for an ideal polymer, ok. This means that this, let's say, for, basically the correct result is the form that nu is equal to 3d plus 2 for d smaller or equal 4, and nu is equal one-half for d larger than 4. So, and this 4, ok, is called the critical dimension of associated to the excluded volume interactions. So, that means that for d larger than 4 you still have excluded volume interaction, but they are not important, ok. The polymer remains, is described by this exponent, by the, let's say, the Gaussian exponent, ok. So, this is something quite important, ok. Ok, so why, so now let's go to, so I tell you that, because let's go now to, so this is not important, so let's go now to, yes, yes, yes. So, this is estimating this, well, the argument can be made slightly more, actually more rigorous, but this is just, let's say, the more hand-waving way of deriving it, ok. Yeah, because of that, I mean, the more rigorous thing would be required to much time, and I don't have such time. Ok, so now, yes. Sorry? Hawaii. Ok, so good question. So, you can, well, there is a, again, and also an hand-waving explanation. Look at this formula here, ok. So, you have that, this quantity here is always large, I mean, you can check it easily. It's always larger than one alpha, provided d is smaller than, is smaller, let's say, or equal. I mean, for d equal 4 is exactly one alpha. No, it's 3 over 6, so one alpha. For d equal smaller than 4, it's always larger than one alpha. This means that correctly, that's what the volume interaction makes the polymer more swollen with respect to ideal conditions, ok. For d larger than 4, this becomes smaller than one alpha, which would make, let's say, exclusive volume interaction, making the polymer less swollen than the ideal condition, which is a bit absurdity, ok. So, this means that for d larger than 4, this is the right exponent. Just basically exclusive volume interaction just stops to be important, ok, in this respect. If you want to see it more, slightly more rigorous, lean, you can look at this quantity here, ok. Because if you look at, let's say, to the estimation of this exclusive volume interaction, because if I look at at this quantity here, ok, maybe green is not the best choice. Red. So, if you look at this quantity here, the way to compute these, I mean, to estimate this critical dimension, so basically replace r, ok, replace r by let's say by its ideal size, ok. So, make the substitution here, ok. So, you would get something like v2 n squared times, ok, b to the d, which is a prefactor, n d over 2, ok. So, then this thing becomes v2 d to the d, ok, fine. And then n 2 minus d over 2, ok. So, then you see that this can be also I mean, this is, of course, the same as n. So, minus d minus 4 divided by 2, ok. So, now, for d large smaller than 4 this term here and for n large, which is, let's say, the limit of very large volume, this quantity here goes to infinity, ok. Which means that this term cannot be neglected when I mean, compared to ideal conditions, let's say, when you have a nice volume. Viseversa, for d larger than 4, this term goes to 0. So, which means that it's not important, ok. And it's, ok, so this is another way of seeing the same thing, if you want. Actually, it's typically the more solid argument how you see such a thing, ok. And in fact, d equal 4 is called the critical dimension. I mean, critical dimension with respect to let's say, to the two-body of the volume interaction, ok.  So, now, just I mean, I repeated this argument a bit here, because it's a bit necessary for the following. So, can I move further? You have had the question? Ok. So, now, what I'm going to say now is a bit of an application of let's say, polymer theory, let's say, but now for branched polymer applied to RNA secondary structure, ok. This is a bit of a work we did actually with Tangier. I mean, it's more broad in the sense that this theory of, let's say, of branched polymer was already applied to these to RNA molecules, especially to RNA secondary structure. I mean, not basically, you have seen with Tangier that, let's say, RNA molecules of course, they live in 3D, so it's important not only the secondary structure, but it's especially important in tertiary structure when basically these molecules really fold in 3D space. I'm not talking about that, I'm talking about this part here. And now one can sort of model or understand this secondary structure by using the physics of branched polymer. Ok. So, now, I mean, there are some other applications here, but they are not important in this level. So, what are branched polymer? Ok, so far we have talked about, so these are maybe needed here, so just branched polymer are, let's say, a more complicated class of polymers, because they are not linear, but they can be branched. And this happens so, let's say, the typical view of polymers is that you have monomer units followed by other monomer units and they keep growing, and they form linear chains. Ok. However, it can happen that you may have monomers not with, let's say, doubly functional monomers, but each monomer can be 3 functional. Ok, that means that two monomers can be attached here. Ok. Something like that. And so on and so forth. So, you can have here and it keeps growing, but now this monomer can be 2 functional and they increase. Ok. And you form, let's say, a branched structure. Ok. So now, why this is relevant for RNA, because you see, no, if you have this doubly, let's say, the RNA falls into, I mean, like this, then let's say on large scale you can, I mean, imagine that you forget these, let's say, these double folding here, if you want. And you adjust focusing on, let's say, the backbone of this structure. So the backbone can be thought as a branched structure. Ok. So this is the idea. And the idea will be like, ok, let's for the time being, forget about these, let's say, the base pairing and just focus on the backbone and try to see if we can understand if we can predict or say something about the structure of the backbone in terms of what we know about the physics of branch polymer. That's a bit of the idea. I mean, if there is anything interesting that we can do. So now the physics of branch polymer is, of course, I mean, you may imagine that it is quite more complicated, actually, than linear polymers. And in fact you can introduce, I mean, a larger set of, let's say, scaling exponents. So now, for linear polymer, we introduce this exponent nu that describes how, let's say, the total polymer size increases with the total number of monomers. So this exponent is still, let's say, this definition, is still perfectly valid also for branch polymer, because we have a number of monomers and we can always ask what is the typical generation radius as a function of the number of monomers. Now you see why it's important to define the generation radius because the end-to-end distance now is defined because we have many ends, actually. Then you have another quantity. OK, another quantity is, and this is actually something that is interesting for what I'm going to say, is suppose that let's say, suppose that you have, let's say, you take two monomers along the chain, and you ask what is the average path, I mean, on the backbone between these two monomers. OK, so now this quantity and you average over all possible realization of your polymer chain. So now this quantity is also scales, let's say, with total number of monomers with some specific exponent, which is called rho, OK, it's defined in this way. And you have two more exponents. So another exponent, so this is clear, so what I'm doing, let's say, I'm picking to, let's say, for instance a monomer here and another monomer here and I'm computing, let's say, this path here in terms of the number of bonds between these two monomers. I let you notice one thing, this path is unique, OK, because I'm not considering, so I don't have cycles in my molecules. OK, so then if I pick two monomers, the path that connects them is unique. The minimum path, I'm going from here to here to here to here, OK, I have no other choices. So I'm doing this for any pair of monomers inside the molecules, OK. And then I'm averaging over all possible conformation, because the bonds can be rearranged everywhere. And so this is the quantity I'm looking at, and I mean I can define this exponent here, because it has to scale with total number of monomers of the chain. Then I have another exponent here, which is defined as the following. So now suppose that I have my molecules and I cut at random one bond, for instance this one. Then I'm considering how many monomers are on the left part and how many monomers are on the right part, OK, and I, I mean just measure them. And I average over all possible cuts in the chain, OK. And so this is a sort of this is called the average size as a function of, so the average the mean branch size, sorry. And this is also as a scaling property. This is also scaled as the total number of monomers or bonds inside the chain as an exponent, which is called which is defined epsilon, OK. So now these two guys Fandres, Munch and Madras proved that whatever it is, let's say the molecule you have and what is the ensemble is epsilon is equal to rho, OK. If you are in this, I mean this is a very, very nice work. It's a bit mathematical work. So if you are, if you like mathematical details, they prove this by using statistical physics reasoning. So it's not a simple argument, OK. For the time, I mean just accept it. I mean it's a very impressive work that you did here. And then you have another exponent, OK. This is less interesting for what I was saying for your personal culture. So suppose that again you take any two monomers on the chain, you compute the path between them and you measure the spatial distance, OK. So this quantity scales with the path length as L to the two new paths. So you see why basically I introduce an exponent to new, but it's related to the path on the chain. It's like this is an independent polymer and you are measuring, let's say, another exponent. And let's say now, by scaling argument it's easy to see that new path is not independent by rho, but it's just the ratio between the two. It has to be so, OK, just by scaling argument. But this is not important from God's angle to say, so I mean just keep it, but I mean yes, this one. No, actually you take two points on the chain, two monomers, for instance these two and you do it for any possible path and you measure how many steps I have to walk on the molecule to go from here to here. OK, that's easy, that's it. The next you mean this one? Second and the third. Ah, the third is done. Suppose that I cut this one bond. You count how many monomers are left here and how many are left here. OK, that separates in two independent molecules. OK, and you have so, and then you have some size and some size, and you do all this do the same operation for all bonds and you average the possible conformation of the polymer. OK, you get this quantity. Subbranches, the typical size of the subbranches. OK. To be honest, in the calculation I always took the smallest of the two to avoid finite size effect. I mean, you can take just one because I repeated the procedure for all possible polymer conformation because you have to imagine that the ensemble I'm talking about is where let's say this branch it's a randomly branching point arranged everywhere. So you have a high number or possible it's even higher than the ones of a linear chain. I don't have only, let's say, the exponentially high contribution from the fact that the chain can assume all possible spatial conformation but they have only another entropy if you want associated to the fact that the branches can be arranged everywhere. So in this creates let's say the other like yeah, this creates a higher ensemble if you want. Is it OK? So this is the physical meaning of this spawn. So now, OK, for this, so now this can be also understood in terms of the flow theory. I have to do some let's say some additional ingredients. I mean, the contributors of this work were let's say Isankson and Lubenski and yeah, this work here especially I mean, if you look at this it's a bit simpler work. It's based on the use of the flow theory. OK. And so let's look again at this quantity here. So now, the flow theory again for now for branch polymer randomly branch polymer OK, so I mean it contains again the same terms. OK, so always an enthalpy contribution and entropy. OK, so now this contribution here OK, I'll explain this terms that are on the blackboard, on the slide. So this terms here is the same. OK, so doesn't doesn't change. Approximation, of course. But doesn't change with respect to one that I have defined and I have introduced for linear change. So this is still let's say v2 n squared r to the d. Really the same. I mean, why doesn't change? I mean, I can make the same approximation if you want, I mean conceptually. Because to compute this term I have, let's say I have not really used any information connected in a chain. I mean, OK. So it's just like it's just like, let's say, collection of particles with a screw volume interaction. And that's it. So the fact that is, I mean, linear chain or branch polymer doesn't really matter for estimating this term. So this is why it remains the same. OK. Well, the trickest part is this one which is the entropic part. OK. Because as I said now the entropy is more complicated. And this is the main basically contribution of this work here. Which is, by the way, it's not a long paper. I think it's four, five pages. But I mean, it's pretty clear. So in my opinion. So if you want to understand a bit, you can look at this paper here. So and now it is estimated. So let's, OK, sorry, I can't set the molecule, but let's draw it again. Basically, the scheme that I have there. OK. So now this term, if you want, it actually contains two contribution according to these guys there. OK. So I write let's say S over so I write D like S1 divided by KB plus S2 divided by KB. OK. So these two contribution are highlighted here. This one and this one. OK. So the reason why I call it this way is for the following reasons. So this first part here let's say S1 is sort of reminds of the same entropy contribution that is let's say that comes from a linear chain. OK. For a linear chain, you remember, I had that this is R squared divided by N saluda by NB square. OK. Here in this case, because I have a branch polymer let's say so in this term here comes from the fact that I have, let's say, a linear strand of N monomers. OK. Here my effective linear strand is not made by a monomer but it's made by on average, let's say, by L over B monomers, because let's say my linear strand is the one that is effectively playing a role is the typical length of a single path on the chain. OK. So then I divide by L over B because this is the number of monomer belonging to an effective path. OK. And this is why I have this term here. Which is basically this one. This is the first one. OK. So in these are more or less the same physical, of course I mean I have many possible paths but let's say the idea of, let's say, the hypothesis of these people is that that tends eventually only in some prefactor because again here I'm completely neglecting the prefactor. And the second term here, this one, which is the less obvious, let's say, is related to the entropy of branching. OK. Because as I said, I mean the branches can be, I mean all these branches can be arranged everywhere again. So if you want this is a bit of a term which is similar to this, I mean in let's say in the power law form but is of this kind. OK. And so what is the physical meaning of this? So suppose that so now I have to work a sort of in the space of branch of, let's say, of the branches nest. So where now the typical size is not played by R but is played by the length of the path. OK. And then I have to divide by NB squared to the usual term which is R squared over NB squared but where R now it's L, it's not R because this is an entropy associated to how I can rewire my branches on all possible molecules. OK. I don't know if I've been clear. I mean it's the same, it's a sort of Gaussian term if you want, but where now the typical size is L so it's the average path R. OK. So then I have two contribution here which is this one which one is the elastic contribution and the other is the entropy of let's say the entropy associated to the all possible size in real space plus the entropy associated to all possible sizes but in because of the rewiring of the branches in the space of all possible connections. And now I can in fact if I for the time being I completely neglect these well, OK let's do it story. So now I have these so in the overall I have the following let's say I basically now these these free energy which is now it can be written like this. OK. Cancel this so now I have V2 N squared over R to the D plus this one which is R squared LB this term here plus this one so now this term here is more complicated in sense that because now I have two variable so it's a sort of function of two variables the free energy I don't have only to minimize with respect to R I have also to minimize with respect to L because it's also let's say there are two variables one is the spatial sides of the polymer and the other one is the typical path on the branched on the branched molecules. OK. So as you can see it's I mean this is simple, I mean it's not complicated but let's say these it's more sophisticated like of course I mean because the molecule itself is more sophisticated. OK. So the interesting one thing that you can OK. I mean we can see another feature of these OK. OK, first of all we can see quite of a simplification in this formula that the two terms here oh well sorry the terms here the square volume interaction as I said does not depend on L. OK. So you can let's say here you have to perform the two following minimization you have to do first the derivative of F with respect to L and imposing that equal to 0 and then the derivative of F with respect to R and then imposing it equal to 0 in these two conditions. OK. But now the first one is the one that you can do first because this basically at this term does not enter. OK. Because does not depend on L. So you minimize this first and then you minimize the second one. Yes. Yes. No this is OK maybe drawing is not ideal but this means that this defines what is this R of L. Actually you don't have to worry because I'm not going to take I mean this quantity is not applicable I mean it cannot be measured in RNA. OK. So it is rated in RNA but if you want to know about this so this quantity here it measures how to say this so take to let's say a pair of monomers along the branched polymer you compute the typical special distance is a function of the linear path on these molecules OK. And this is this quantity. OK. Is a function of path length is not as a function of the total number of monomers. OK. So that's the thing. While here R is the the typical monomers, the typical molecule size is a function of total number of monomers to separate quantity. OK. I mean I'm not saying that they are not related actually are related by this scaling relation. That's why this new path exponent which is defined for the paths is the ratio between where row. OK. I mean I understand maybe it's not obvious but this let's say but this is a bit critical I mean if we want to apply this to RNA molecules. OK. For let's say if I'm assuming that the typical secondary structure of RNA molecules I mean we look like this then in the secondary structure let's say analysis what I can measure I can effectively measure the length of the paths OK. And this quantity here which is the ones that I'm going to talk about so this one and this one. OK. But I don't have access to neither to this one because that will involve a measurement of the molecule in space and if I'm measuring the secondary structure I don't have access to that. OK. I need I need some spatial information but which I don't have. OK. So when I'm talking about yes. So now basically you have to do this exercise. And so I think I have it in the next slide. Yes. So let me see. Yes. So the if you do if you minimize this one the result is so it gives you this one. So basically you can try yourself. OK. If you do this. OK. It gives that R like L over B cube times N. OK. So this is anisimatomy. It gives you just this. OK. So now of course I mean R because now I'm minimizing with respect to L. OK. And of course R from this one will contain the terms which still depend on L and the terms which depends on N. OK. This one. So in order then to minimize to this you put relationship back here. Now you have that F will depend only on L and N. You minimize it and you get a relationship between L and N. OK. And this will give you from this will give L as a function of N which defines my exponent which I call it rho. OK. And and then once you have that you basically reinsert this one here and you have a relationship between actually rho and N. OK. Which is the relationship which appears here. OK. So now to well this is a bit of a so I mean so now you have sort of some prediction. OK. For for the exponent N for the exponent sorry we have a relationship between the exponent rho and the exponent N. OK. So you can compare to to the available let's say numerical results in the literature and this is a bit of a comparison but I mean this is a bit technical so I think we can we can skip this. So what is more what is more important also that you can also move further of this of this flow theory in compute it's the corresponding distribution function for this quantities. OK. And this all obey some let's say some scaling relationship. OK. And let's see maybe this is a bit so let's let's look at this. OK. Let's maybe let's go to RNA and hopefully that will become a bit clearer. OK. So this is the maybe some kind of secondary structure that I guess you have already discussed a bit with OK. So RNA we know that RNA because of the base of the base pairing. OK. It takes this peculiar form. OK. So you have that because of this base pair formation you have what is called the secondary structure. OK. And this is basically I mean it's so this is so this is a pairing. OK. But it's not I mean it's a pairing along the sequence and though and you have so this is for a very short RNA fragment but you have a longer one you can form many of this base pairing and you can have a larger molecule that will resemble like a branch structure. OK. Then this structure will fold presumably in 3D space and you have the so called the tertiary structure but here I mean what I'm going to talk about here it's a bit this secondary structure not the tertiary one. OK. Because this is a bit the goal of this of this lecture. OK. So now this is something that is related to a larger molecules where you have you have talked with Ange about multi loop so this is a structure where you have basically you have this multi loop of degree 5 means that you have this structure which is not completely base pair but you have many arms that protrude from it and this is called the multi loop of degree 5 because you have 1, 2, 3, 4, 5 let's say arms protruding from this quantity it's one of these bigger monster let's say from bigger RNA molecules that produce such kind of branched branching structures so this is a specific example from a long non-coding RNA which is just a specific RNA molecules which is 600 nucleotide long that form this kind of structure OK. I don't know actually why it's called Braveheart but that's that's the name for this molecule. So now this kind of I mean I guess Ange has told you that so this kind of structures are the ones that are predicted based on some let's say the empirical force field so basically we have some programs that try so you have your many RNA sequence and what you would like to know is how many possible faults these long RNA may produce so there are let's say there are empirical programs produced in the literature that can be fed by your favorite they can be fed by your favorite RNA molecules and they will produce a certain number of these typical faults OK. Secondary structure so they will give you a hint I mean an idea of what is the secondary structure associated with that that molecule I mean we know that these secondary structures are not unique in the sense that you have many typical I mean a lot, I mean a very huge number just because the pairing between the different nucleotides is not unique OK. I think that was a stress many times already so because it's not unique you can actually produce a large number of these molecules OK. And the idea is that OK because you can produce a large number of these molecules this can be mapped into a corresponding high number of branch molecules and it I mean and maybe by comparing to this kind of theory we learn something from let's say from the typical statistics of these of these molecules. So now this is not completely new and it's quite known in the literature in the sense that there were a I don't know if I have no sorry so this is a collection of let's say of precisely of these kind of results so people in the literature have measured the following. So suppose so you have many many molecules of RNA molecules and what you do you are using precisely this program, these tools to predict secondary structure and you do so once you have let's say your produced molecules from from these programs what you do you can analyze the output of course in this program we have introduced a quantity which is called which was called the maximum ledder distance. Basically this quantity measures the typical let's say the largest path on these let's say on the resulting branched molecule as a function of the total size of the molecules. If you want people have measured this not the typical L but let's say the average largest L but in the end it's the same thing because by scaling argument this I mean the the maximum ledder distance should always obey to the same scale in relationship. As a function of the total number of base pair of total number of bases in RNA molecules namely as a function of total of n if you want where n here now is not n but it's n then nucleotides so now you have to just imagine that instead of a but it means from the it's the same thing. So people have measured this quantity so for for RNA molecules and they found here you have I guess you have a picture from you have an indication for these quantities I mean why this is so interesting I mean I've been so excited about that because you can do two experiments here one experiment is I measured this quantity for specific RNA in particular they measure that for RNA viruses so many RNA viruses here one is the tobacco but you can do it for many of them and you can compare the same quantity for random RNA molecules and random I mean that you construct artificially they don't exist in nature artificial RNA molecules made for instance which homogeneous composition of bases like 25% of A, T, C and U and then you but they are not like you say that the total number of nucleotides is some number so 25% is A, 25% is T, 25% is T, 25% is U and you just make a random sequence out of it and you use these the same programs to measure the faults and interesting results they got is that the not random RNA namely the RNA of viruses have a more compact path distance then do one let's say for random RNA so this is so the results for viruses are this one so this is let's say the maximum letter distance is this one so the results for random RNA is here this one so it's systematically higher the results for random RNA which means that problem of course not surprisingly that viruses I mean living organs have an RNA which is cannot be considered as random but has to be I mean it's different ok and this also means that presumably evolution as far as of course I mean this should be expected but this is the first let's say one of the first quantitative experiments that have shown that there is I mean there is an amount of non randomness that can be quantified for real for real bios and the quantity that people have measured is precisely this one ok is it clear so you can I don't know why I didn't put the references ah yes ah yes these people here so a lot of work was done was done in the group of Bill Gelbart in the United States plus the collaborators of course and I think to my knowledge the first work that has put forward these that have used this sort of relationship is this one predicting the sizes of a large RNA molecules published on PNAS as you can see in 2008 now so now it's 16 years ago ok so this is another plot basically showing the same thing probably this is with less points this is more clear so here you have maximum ladder distance if you want this quantity here as a function of the sequence length ok so what these people have found have found the following relationship have found that if you measure the maximum ladder distance for random RNA the curve you found is the one that is shown here these are the points for random RNA and they found the dependence as a function of the total number of nucleotides of about two-thirds 0,67 that was let's say it's a fit so this relationship seems very robust basically and these are the points that you have here as you can see it's for different families so these kind of things so the tobacco is here the tobacco virus is well it's one of the largest one ok so basically how do they just a few details on how do they get these points they so let's say how do they get the random RNA and then they compare to real RNA they had the same so they did two things actually I said here so they consider a homogeneous composition of nucleotides namely 25%, 25%, 25%, 25% it fixed n sorry it fixed the number of nucleotides or they've also taken let's say the non-homogeneous composition of each RNA virus and they have reshafled it so basically they said ok the composition not the one, let's say not the one that you have been linear in real sequences the amount of nucleotide is the same but it's let's say you randomize the position along the sequence so this is another way of doing randomness if you want and if you do this so if you compare this to operation you basically get the same exponent here however for the real and non-random one let's say taken from nature and which let's say with the distribution that you have you get this data as you can see this maximum letter distance is comparably lower with respect to the number one and and this has to be I mean according to the interpretation of course but I think it's really I mean something that you can believe in that is sort of is a sort of let's say in information saying that evolution has pushed strongly for having real non-random sequence not only non-random in let's say in terms of the choice of the right amount of of base pair composition of base sorry of basis composition but also in terms of how let's say the molecules are exactly allocated along your sequence because then you have to form this base pair and this base pair has to be functional of course because this virus is I mean sort of so this is for instance this is something that you can also see a bit qualitatively so this is a phage so a phage is a virus that infects bacteria ok is a single strand RNA virus it contains about 4,000 nucleotides so this is the sort of conformation you get for its corresponding secondary structure and this is the same let's say secondary structure you have for a similarly composed RNA but random I mean randomize the one of the way that I mentioned here the same size more or less is 4,000 nucleotides is 4,200 otherwise it's pretty much close you see that the non random one has a much larger than this one you can also appreciate that by just by by inspection and this is a bit the message contained here so what these gentlemen also did and this is an hypothesis they said ok now I mean again this is a a ladder distance is a sort of measure of the size of your molecules but it's not a measure of the size in space because let's say this kind of cause, I mean of this kind of structure you get for let's say from these programs they only tells you how much frequently two bases interact, they form base pairing but they don't tell you I mean the extension of molecules in space because they don't know anything about that ok so this is the important thing however what these people have done so in this is an hypothesis is the following ok now I have my maximum ladder distance so then assuming that the maximum ladder distance is let's say is a measure of the average path on the molecules then I can assume that ok then the average path falls randomly in my in space and then so the associated generation radius, so now this is the generation radius of the molecules in space has to be just has to just grow like the square root of let's say the this ladder distance because I mean if this is randomly folding in space then this has to be like if you want just a random polymer to be like the square root of this quantity and this seems very interesting conclusion for the following reason because if you take the square root of this number which is very close to 2 third you get that how the typical RNA molecule has to fold in space has to be like 1 over basically n to the 1 cube, 1 over 3 and if you have such a kind of folding means that my polymer the RNA molecules has to be basically space filling has to be compact you see this you see this because if you compute let's say the typical monomer density within the space occupied by the volume so this has to be like n again like this divided by the typical size this one sorry the typical size r cube and because r I'm predicting that has to be like 1 over 3 this one then so you have r to the 3 and 1 third is n, so n over n just cancels and this means that this is order of 1 so basically the typical density of let's say of my RNA molecules inside its volume is constant and the polymer is space filling so it's just occupying all sort of possible monomer inside the space and this is so this is an hypothesis of course it's a prediction more than a hypothesis because of this work but it's an interesting one because it tells you that it's an interesting one for two reasons the first reason is that because the molecule is compact then can fit inside can be efficiently if you want inside its own volume and the second in my opinion more interesting conclusion is that by measuring let's say something which doesn't know anything about let's say the special folding of the molecule you actually are giving a prediction about how the molecule would fold so now the interesting conclusion of this work is that why this is important why the density has to be constant is important also in other respect because you have to think how the virus is and in RNA viruses I don't know if I mentioned to you but they are the RNA is containing some in a structure which is on the capsid of the virus so now the capsule of the virus is a very tight environment so if RNA attains the maximum compaction then it means that basically it has done efficiently this work let's say the RNA can really stay inside its own volume and this is again this is a conclusion that you can only deduce from the properties of these which again doesn't know anything about the special size so it's somehow itself consistent with the physical expectation and otherwise it's the only, yes because you are only applying let's say the physics of these paths, okay you don't know anything about the special size I don't know if well in the end we have a bit repeated this analysis but maybe sorry, so it was confession ah, okay sorry I don't know what sorry, let me just check with the time no, because I mean maybe we are entering too much details later so it's probably because this it's the thing that I wanted to tell you so now maybe it's good if you have some question this point, yes ah, this is simple because so it's not so suppose so now, okay, what I can measure I hope this is clear it's only by this the outcome of my numerical experiments I can measure this maximum ladder distance which is basically the longest path on this branch 3 this is something that I mean it's not complicated to measure I mean you just count so this is what you get these are just an example but you can have many so this is for a again this is for a real virus it's a virus that attacks bacteria and this is for the similar size RNA I think also we do more or less the same composition but just randomize I mean that I just shuffle the position on the sequence of the different nucleotides, okay and I get this thing here that you can see that it has a larger distance okay sorry, it has a larger maximum ladder distance okay now, suppose that as you can see, I mean from here if this makes more intuitive you can consider this one and you measure this quantity here or this quantity here as a function of certain number of nucleotides and you get this scaling relationship that basically the maximum ladder distance as a function of the number of nucleotides scales like n to about two-third in sequence is random because I mean there is a complication when you cannot do really I mean this is the work we did with Ange but it is a bit too detailed so I don't think it is really work, we don't have time in if I had more time I could explain you but let's say if you have only this kind of measure it is difficult to get any scaling maybe you can have an idea but it is difficult to get any scaling for specific molecules because basically you have only so to get a scaling you need many n for a single molecule n is fixed so you cannot do any scale scaling out of it although it can be done but it is a bit more complicated so I don't have the time to talk about that but the interesting conclusion is that but you can do that for certainly for random molecules in the sense that you have the same it is a random molecule you can create it artificially you can do that if you want you can play such a kind of game or you can do what these people have also done here and also I think Andrzej has done this kind of work you can have your specific RNA sequence because RNA sequence in viruses they span in enormous range so you can have small RNA small in terms of nucleotide or very large RNA in terms of very large number of nucleotide so you have such a kind of data on top of that you can have the same sequence composition and you just randomize it you can move nucleotide around and you can create your own ensemble of folds and you can this is also a sort of randomness then and then you can repeat the game and you can compute this maximally as a function of number of nucleotides you observe this power law after that so now we have this power law now and this is a bit some kind of discussion that did in this work I think it was already in this first two work you can say that ok, now I have my maximum the distance as a function of n now assuming that this ladder is a sort of let's say now this ladder has to fold in space but how can fold in space in kaj fold just randomly it's like a random walk then I have no other possibilities that the generation rates of the polymer in space of the average RNA molecules in space has to be just because it's just like a random polymer has to be the square root of the maximum ladder distance no, exactly like if you have a random polymer you have the square root of the number of monomes if you have a linear chain and then if I took the square root of the maximum ladder distance it has to be like n to the one third you see, it's just the square root of this is it clear? well, because all the random points follow on this curve also if you take these points here jamil, which are non-random and you randomize that in the way I said that you just reshuffle the sequences they all fall more or less here if you want to think no, I don't think there is this data here but yeah, they are all fall on this actually there is it's not completely true there is a small difference but okay, yeah, okay I will not complete this up, they don't fall this curve refers to an homogeneous composition of nucleotide if you don't have a non-homogeneous one but it's still random in the sense that you randomize along the sequence this curve I think can become a bit lower but the scaling is the same so this exponent is still one third so this is the important thing actually it's more than so this is a log-log plot maybe it's not evident but it's a log-log plot spacing is not the same so it's a log-log plot so if you are doing the same curves but for different folds and the composition not homogeneous what you can see that you have another set of points but the curves I think it should become a bit lower but the slope is the same which is the important thing the fact that so basically this means that the pre-factor is different and that can maybe be related to the composition here but the scaling remains the same which is of course the important information of course the pre-factor is also interesting but it's probably related to but if you want the pre-factor is sort of renormalization of the effective bond let's say the effective bond here but if you don't touch the scaling behavior then it's fine so this is the important thing that enters by the way in all polymer theories it's the scaling, it's not the pre-factor yeah, they are error bars this of course depends on the statistic of your sample here I'm not sure because it's the report from this paper I'm not sure if they are error bars or standard deviation but they should be error bars I think at least I just don't remember I'm sure it's written in the paper because why do they think they are too large ok, no ok, but consider that well, producing these folds the statistic is not really enormous anyway I think when you produce these folds I don't remember exactly the right statistic but typically it's not like you have an ensemble an exponentially large ensemble when even for random RNA I think the amount of folds you have is on the order of if you are lucky with this kind of program calculation is about maybe 1000 so 1000 means that you have an error you know about what, 30 or one third of the value so it's possible that the error bars are quite I mean they are not negligible they are computed by some calculation they are quite because what this code does ok, the Ange has mentioned to you the presence of pseudonauts these folds what they do they put all possible they spare they have an energy score and they minimize this energy score but of course they produce sequences so you can give I think I have ah yes so this is how it's very empirical there's nothing really holy in that so this is called Vienna RNA it's called Vienna I think because it was developed in Vienna and you have a different version of it it's one of the it's very used in the work with Ange we use this but if I remember correctly there are others anyway so you have an energy score that you need to minimize inserting that your favorite RNA sequence and so basically the minimization of this energy score so you have a term which is just an offset which has to be there for some technical reasons then you have a term which favors or penalizes I mean depend on the amount of these term branches I mean like this or a term that favors or penalizes the number of unper nucleotides and that produces these more or less I mean a more or less large number of these of these holes and that's it but out of it you don't get only one structure one possible structure you get many so then you make a ranking and well this is a bit rule of thumb you may decide how many of those you want to retain because the energy you get they are all very close to each other but in the end I think in the best case scenario you get 1,000 so I have to say as you can see now let's say the first version of this Vienna René was published so now this is the newest version but the first version of this Vienna René was published in 1981 so not really let's say wow and there you go and there are now new versions but all the time they have I mean in these new releases they have changed a bit these weights here so the way these terms were established were based on let's say on the best agreement with experiment I think it was from calorimetric measurements but otherwise it's very empirical the important thing of let's say a very important assumption of these kind of models is they completely neglect the present they don't take them into account the presence of pseudo nodes because as I guess they make the things much more complicated and much more if you introduce pseudo nodes in the calculation basically the problem starts to be you can do that only for very short RNA molecules if you are going to large RNA molecules like the ones analyzed here the problem becomes impossible to solve the number of conformations you have to estimate becomes exponentially large so let's do that I can give the slides but this is a bit too much detail no, what was fun what we found is that basically so these terms I didn't put the precise values here but basically from it changed in the course of the years so in the first version this branching term was higher compared to this amperonuclotide no, sorry, it was higher no, sorry, it was in the sense that branches were penalized more so now in the newer version branches are less penalized compared to amperonuclotide but it becomes a bit it's a bit of an empirical work but still, if you want to get understanding about how your RNA molecules should work you use this kind of tools there are others but they also produce different results but it's kind of it's basically the first thing you are using and there is a server for it in case you want to play you can just use it, it's called V Vienna again it's called Vienna RNA and well, there is a lot of stuff we have done but this is just the acknowledgement of the different people which I think deserve some acknowledgement and otherwise I don't know I think we can stop here because I think it's a bad time I don't know if you have questions or questions about this okay so I guess I'll see you tomorrow for this so as I said it's just a basic question so don't be too worried what time is it, 11? 11, right? okay I'll come a bit earlier that's it


The Uyghur State Government has called on corporate, spirited bodies and well-meaning Nigerians to support the government in social responsibility by delivering dividends of democracy to their immediate communities for the betterment of the people. This call was made by the State Commissioner for Agriculture and Rural Development, Barista Olasukomi Olaleye, while commissioning a modern borehole donated to Ulukaya community in a better local government area of the state. Uyghur State Commissioner for Agriculture and Rural Development, Barista Olasukomi Olaleye, who was represented by Dr. Adény-Ran, Mobolaji said that a gesture was part of social responsibility expected from responsive businesses that have continued to benefit from the good governance in the state under the leadership of Governor Shayy Markinde. The donor, Mr. Olamileco Salao, said that a move to donate the borehole to the community was necessitated due to the unavailability of potable water in the area which had imposed hardship on the residents for many years. We are imploring other communities to do the same by accommodating the government officials, the government representatives that are collecting revenue or representing government in one way or the other, so that they will benefit fully with what the government is actually expressing. To compliment the efforts of the government, everything can be said on the government, government, government. They are confident, they are in charge of revenue, but they have been doing fine. I think this is the thought of the fifth war that I will witness. I am very happy, I know methods, in terms of an infrastructure that they know, when they get to a community, identify their needs, whatever you can do, you can do it. You know from the people, you have to pay back, after paying back to the government, you have to pay back to the community that they can just, I mean they can also derive from the revenue. And I think this is not the first time we have one in Al-Qaeda that they have the same body, even the police station, they have to innovate the police station, they are just part of the pay back to the community.


I'm going to talk about taxes and history, also sort of the prehistory of taxes. What is the likely way that taxes came about? There's a philosopher and writer named Franz Oppenheimer who distinguished between the economic and the political means of gaining wealth. There's the economic means which involves production. You can farm and produce your own crops and produce wealth that way. Or it can mean trade. And then there's the political means where you just kind of take what you want. Now obviously taxation would fall under the political means. And taxation and the political means are very old. In fact, they might be considered older than mankind itself. You might consider the animal kingdom as operating according to the political means, sort of taxing each other all the time. You might consider a lion who takes down a zebra that he's taking what he needs, what he wants from the zebra. And the zebra is not giving it in return for anything else, it's just the law of the jungle. Or after words, when the lion's eating the zebra and a jackal comes over and snatches some of the food away from the lion, that's not economic means. That's sort of political means too. That's sort of taxing the lion in a way. Just taking what you need, what you want from the lion. Now that sort of law of the jungle is also what Montaigne, a French philosopher, he had what Marie Rothbard called the Montaigne fallacy, which is that no man gains except what another man loses. And that's sort of the way it is in wildlife, that the lion doesn't gain unless the zebra loses. The jackal doesn't gain unless the lion loses. Another philosopher named Thomas Hobbes, he characterized the state of nature as a war of all against all, and that also describes the political means. And so, but taxes usually aren't thought of in that nature red in tooth and claw kind of way. It's considered more gentlemanly. And so it'd be interesting to trace how you can go from messy violence like that to gentlemanly violence like the nice little process that we have when we fill out our tax returns and we mail our check to the government and it all seems very genteel and civilized. Another way of looking at the law of the jungle is what Mises called biological competition. Now humans also engage in biological competition, sometimes in ways that are very little different from the animal way. For example, cannibals, when cannibals go to war with each other and one side wins, they just eat the other side, just like the lion and the zebra. But then there's also biological competition with non-cannibals too because if some barbarians sack a city and they take no prisoners and they just kill everybody and just take all the food and eat all the food, that's pure biological competition. There's no society there at all. The inkling kernel of some sort of social thinking can start, society is whenever someone takes someone else's purposes in mind with regard to their purposes. So with an animal, with a barbarian who just sacks a city, they don't care about the other person's purposes at all. But then maybe a barbarian might realize, wait a minute, if we just kill everybody in the city and then if we come back next year, there won't be any food grown because everyone was dead. So maybe it would make sense if we'd left people alive so that they could just take their food, leave them alive and then they can grow their crops for a year and then we'll come back and just take the crops again. And so then at least you're starting to, it's not even really society but it's sort of the inkling of a society because you're at least taking other people's actions into consideration a little bit. And then another step might be that the barbarians come and the people in the city say, look, if you invade us, we're going to fight back and we're going to kill some of you and it's going to be really hard and eventually you'll probably win and you'll take our food but if you don't invade us, we'll just give you this much of our food outright in exchange for you just leaving us alone. And so the barbarians might take them up on that offer, they might say, okay, it's easier this way.  You could consider the booty as a sort of a tax but it's sort of a short-sighted tax. It's like a one-time short-sighted tax where you don't realize that, oh, if I just take all the booty I want then they won't be able to produce much anymore and then, you know, I won't be able to get very much booty in the long run. Whereas with the tribute, you know, it already seems a little bit more civilized and it already seems more like what we would normally think of as a tax. But sometimes the barbarian invaders, instead of, sometimes they'll take the tribute and then they'll just leave, sort of like the golden horde, these Mongols who would just sweep into Russia once in a while and they just take everything and they just leave. Or sometimes they would come in and they would settle in among their victims and take their tribute throughout the course of the year as they live there. One group that did that were the Spartans. So the Spartans were these Greeks who came down from the north and they invaded these people and the native people became what were called helots and they lived separately and they did all the work and the Spartans became a sort of a nobility, a noble class that they didn't do the work, they just fed as parasites off of the helots. And so that's another step where booty can become tribute and tribute can become a sort of a tax. Another way of thinking about tax is as a ransom. What's a ransom? Who can tell me what a ransom is? Anyone? Oak? Oak? Yeah, that's... Well, we have ransom even nowadays. For example, if someone kidnapped someone and they would demand a ransom that the only way they'll let them live and let them free is if they get some money for it. So it's like money for your freedom. And you might think of tribute as money for your freedom or taxation as money for your freedom. And when you think about it, if you don't pay your taxes, like today's April 15th, if you don't pay your taxes and if you keep not paying your taxes after today, what will eventually happen to you? Essentially, it's slaved. Right. Essentially, it's slaved. Exactly.  So it's money that you pay for your liberty. Like Lou Rockwell's article that's up on the Mises Sorgh site today, it's your money or your life, or you could say your money or your liberty. So in a way, a tax is also a ransom. There's an economist who made a distinction between stationary bandits and roving bandits. So roving bandits would be just like the pirates and the brigands and the barbarians who just sweep in and then sweep out. And the stationary bandits are just bandits who just settle in with you and eventually you get to be familiar with them and they don't, you forget that they were bandits in the first place. This is what's called the conquest theory of the state. It was a theory that among other people, Thomas Paine believed in this theory, that that's how the state governments start out and that's how taxation starts out. Of course, what will happen when the bandits are stationary and they're living among you is that they want you to forget as quickly as possible that you're a bandit. And so they will, especially, they'll have intellectuals who sort of create what's called apologia, sort of intellectual defenses of the bandits. And one apologia that they might say is that they might say, oh, well, you know, the gods will favor us if we are obedient to these rulers.  And people will start, especially if this view is supported by the intellectuals, people will start thinking, wow, that's so generous of them, that's so nice of them, that they're giving me some stuff. It's giving me some food and they're taking care of me, forgetting where they got that stuff in the first place.  It's like that's how it works. And so that helps to legitimize the state, the bandits. Another thing that happens is the state will institute democracy. And what can happen with democracy is that one set of people can use the state to mug another set of people. And so the state kind of serves as a mugging medium, like a middleman for mugging, whereas because if one group directly mugged the other group, it would seem uncivilized, un-gentlemenly, but if they do it through the process of elections and voting for people who will take from other people and give to them and then they do it back, then it all seems very then you get the myth that like Obama recently said, the government is us. So you can't really worry about what we do because we're democracy. The government is us. And that kind of legitimation really goes a long way in empowering the state to basically do whatever it wants. Now another way of looking at the state is thinking about the difference between hunting and gathering and farming. So you could think of as the roving barbarians and pirates and brigands. By the way, Murray Rothbard said that the state is a band of brigands, writ large. You can think of them as hunters, whereas you can think of the stationary bandit who settles in. You could think of them as farmers that they don't just outright kill the people and just take things once. They live with the beasts of just like a farmer lives with his pigs and chickens and takes the substance from them as they go along. And so when you look at a political map of the earth, instead of just seeing countries, you could kind of see a bunch of farms. And then that kind of puts wars in a different perspective that wars can be considered as one farm invading another farm. Sometimes in order to directly tax the people, sometimes it's about farming farmers because instead of taking over and directly taxing the people, you tax the taxers. So for example in England, when the Danes would come in and then the English kings would have to gather what's called the Donageld, which was the money to pay as the tribute to the Danes, to the Vikings. And so that's sort of like farming farmers, that the farmers take from the people and then they give to people who in turn farm them. Now states often have a motivation to limit taxation. It doesn't make sense to tax completely. You don't want to kill the golden goose, the goose that lays the golden egg because then there won't be any more eggs. And then you get, you start to getting back to where you were before where you're just, where it's just pure biological competition and you're just destroying them and it's just like a one time tax and then over the long term you don't have as much. Another way of thinking about this is that free range farming is often, if you're gentler with the chickens and the pigs, that they'll be more productive. And so if you let them trade with each other and feel free, then they'll be more productive and then you can tax more from them in the long run. So this gives us some perspective on the history of taxation, once we understand sort of the nature of taxation.  That was more like the war of all against all. And now that we have the state, you know, everything's, we're all richer. We're all more civilized and more productive. And that gets things backwards, that puts the cart before the horse. What happened is that property and the division of labor came first. People on the earth didn't always have private property and trading and the division of labor. In primitive societies, there was a lot of, it was just very communal. Even though there wasn't a state, there also wasn't very much in terms of private property. Everything was just communal. And then what happened is that when private property, but in that time, there's nothing to tax, you know. If everything's primitive and there's no private property, there's no division of labor and there's no wealth being built up, there's nothing to tax. The parasite has to have a host to survive. So the parasite couldn't have come into the scene until the host got big enough. And so civilization developed first, and then the state came. And that produces the myth that the state caused civilization. So all the early civilizations that we see, so the first civilization was in what is now Iraq. It was called Sumer. And they had private property first before they had a state. There's a book called Ancient Iraq by George Rue where he demonstrates this. And it became a flourishing civilization in spite of the parasitic state that was on top of it. And then you had the civilization in Egypt. But back then taxes, it was pretty clear what they were. It wasn't as genteel as it is now. There's a scribe, an ancient Egyptian scribe wrote this about a tax collection. He said, does thou not recall the picture of the farmer when the 10th of his grain is levied? 10th is where the word tithe comes from. That was kind of the classic rate of taxation in the ancient world was the 10th. Mountains have destroyed half the wheat, and the hippopotami have eaten the rest. There are swarms of rats in the fields. The grasshoppers alight there, the cattle devour, the little birds pilfer. And if the farmer loses sight for an instant of what remains on the ground, it is carried off by robbers. Moreover the thongs which bind the iron and the hoe are worn out and the team has died at the plow. It is then that the scribe steps out of the boat at the landing place to levy the tithe. So a scribe is someone who writes. And so back in ancient Egypt, not very many people knew how to read and write. And it was usually the people who read and write, those were the administrators who served the pharaoh and who staffed the state. And they were the ones who were able to keep tax records. And so they were generally the bureaucrats. And so education at the time was often about becoming a scribe, becoming in order to become a bureaucrat and often to become a tax collector, to levy the tithe. So levy means to raise, to pull out. And there come the keepers of the doors of the king's granary. So at the time they collected taxes in kind. So it wasn't so much of a money economy. So they would collect grain. Grain was the tax. And so it would be a certain percentage of your grain. And they're crying out, come, now come. There is none. There's no grain.  His wife is bound with him. His children are put into chains. The neighbors in the meantime leave him and fly to save the grain. So IRS audits are one thing, but that was when taxation was really recognized for what it was. So what can happen is that, like I said before, states have an interest in limiting the taxation. Now if you don't limit the taxation, then you're going to be pretty poor. And if you do limit the taxation, you as a state are going to be richer. Now a richer state is going to be able to conquer a poorer state a lot more easily. So that produces what's called the paradox of imperialism. Now imperialism means an empire. Now normally we think of freedom in the domestic area going along with freedom in terms of foreign policy. That if you're liberal in one area, you're going to be liberal in the other area. But actually that is often not the case because it's the states that are liberal in the domestic area that don't tax their people as much. They end up having more resources, and so they're able to conquer the other states. And so you have, like for example, the Athenians were pretty free, the Greeks called Athenians. And so they were able to create their own empire. But it was a pretty vicious empire. They had what was called the Delian League. And League kind of seems to mean like a voluntary association, like the Justice League. But it wasn't voluntary. And they realized that. There was a famous speech by the leader of the Athenian democracy named Pericles. And he told the people, he's like, we have an empire. Let's just admit it. We have an empire, and we've got to be, we've got to act like an imperial nation. We have to be cruel in order to maintain our empire. And so there were a lot of city states in Greece that wanted to get out of the Delian League. They wanted to get out from under the thumb of Athens. And one of them was called Milos. And they didn't want to pay tribute to Athens anymore. And so they were completely depopulated.  They executed every single adult male in Milos for the temerity of not wanting to pay tribute to be part of the League. And so eventually then the next big empire that came along was the Macedonian Empire launched by Alexander the Great. And the Macedonians were, their base were the Greek city states. And so again, they were able to use the civilization of the Greek city states as a base to fund their empire. Roman Empire was similar. But the Roman Empire was also brutal in terms of how much it exacted as tribute from the people. There's a great quote from the historian Tacitus who recalls a speech by a Scottish leader called Calgacus. And the Scots were being invaded by the Romans. And Calgacus said of the Romans that they are the robbers of the world, having by their universal plunder exhausted the land, they rifle the deep. If the enemy be rich, they are rapacious. If he be poor, they lust for dominion. Neither the east nor the west has been able to satisfy them. Alone among man they covet with equal eagerness, poverty and riches. So you can kind of think of the American Empire in that way too, that not only have we tried to, especially in the past, take over rich areas, like we had imperial designs on China for a long time. But we're out there bombing caves in the middle of nowhere to take over these poor people too. So rich or poor, it doesn't matter, the empire just spreads. To robbery, slaughter, plunder, they give the lying name of empire. They make a wasteland and call it peace. Tacitus talked about another leader in Britain named Boudica, a female, and she said this in one of her speeches. She said, how much better it would have been to have been sold to masters once and for all than possessing empty titles of freedom to have to ransom ourselves every year. So again, there's that notion of the ransom as a tax. Just like with us, it's like an annual ransom, an annual money payment for your freedom. So that was the Roman Empire. The Roman Empire fell largely because of taxes. Eventually it got bad at limiting its taxation so it could continue to feed on the population. Jesus talks about how first the Romans, they debased the currency, which itself is a tax because when you create money out of nowhere, that's what's called an inflation tax. And instead of collecting taxes in the debased currency, they started to requisition just goods and services from the people in order to support the army. And then Diocletian, this Roman emperor, he turned that requisition into a huge tax. Eventually people started getting poorer and poorer and some people wanted to move into the countryside. Some people wanted to escape to go be with the barbarians. They thought, oh, if I got to escape this Roman Empire, I got to go be with the barbarians where I can be free. And so Diocletian tried to freeze everything. He put a price ceiling on everything. And he tried to pass a law where every person had to stay at the job that they were in and that their children had to stay at the job that their parents were in. And Mises talks about the upshot of all this. He said, to avoid starving, people deserted the cities, settled on the countryside and tried to grow grain, oil, wine, and other necessities for themselves. On the other hand, the owners of the big estates restricted their excess production of cereals and began to produce in their farmhouses the products of handicraft which they needed. For their big scale farming, which was already seriously jeopardized because the inefficiency of slave labor lost its rationality completely when the opportunity to sell at remunerated prices disappeared. As the owner of the estate could no longer sell in the cities, he could no longer patronize the urban artisans either. He was forced to look for a substitute to meet his needs by employing handicraftsmen on his own account in his own villa. He discontinued big scale farming and became a landlord receiving rents from tenants or sharecroppers. And so that is basically how the medieval economy started was from this process that Mises talks about, which came about because of the excess taxation. However, the middle ages weren't so bad. The middle ages after the initial dark ages that happened because of this Roman folly, the middle ages had actually very limited taxation. Rothbard talks about that there were no regular taxes in the medieval era while the king was supposed to be all powerful in his own sphere. That sphere was restricted by the sanctity of private property. So the king had to often come hat in hand to ask for taxes. And that was the origin of the parliament and the estates general in France that they were holding the purse strings. They were having to decide whether to let the king have those taxes or not. And so the middle ages were actually a time of great economic prosperity. People think of the Roman era as great and that the middle ages were poor, but it was in the middle ages where iron was first used on a widespread basis. It was when they had windmills and watermills that could produce things that used energy in a continuous manner. And so cities were springing up all over medieval Europe in these places in northern Europe where the Romans didn't even really cultivate. Like it was just wasteland during the Roman era. Basically the Romans was just a parasite city living off of the east. It was still the east, Egypt and Greece and Asia Minor where all the wealth was, that mercantile civilization. And Rome was just living off of that as a parasite. People living in Italy were exempt from taxation. More than that, they started getting breaddoll. People were coming in to Rome just to basically live off of welfare. And so it was really a parasite civilization. And it was in the medieval era when there were limited, more limited taxes. That's when economic growth started really getting underway. Rothbard talks about the 14th century depression and that's when kings started to become powerful again and some of the prosperity that had built up through the middle ages was destroyed, especially Philip the Fair was not fair to the people, the Fair meant handsome, that he was kind of handsome. Rothbard says that in the early 14th century Philip the Fourth, the Fair, King of France, moved to tax, plunder and effectively destroy the vitally important fares of Champagne to finance his perpetual dynastic war. Philip levied a stiff sales tax on the Champagne fares. He also destroyed domestic capital and finance by repeatedly confiscatory levies on groups and organizations with money, including the Jews, who he just completely confiscated their wealth and kicked them out. The Lombard bankers, the Italians, did the same thing to them.  And so it was with kings like Philip the Fair, later on strong kings like Henry the Eighth and Louis the Fourteenth, they became really strong and they started taxing people a lot more. And that ultimately ended up with the revolutions that happened starting in 1688 and then through the 18th century. What happened with the kings would want to go on all these wars. They'd have all these dynastic wars and they'd have to tax the people. And so especially the dynastic wars of Louis the 14th and 15th, that it was because of the taxes to support those wars that people were so upset and ultimately the French Revolution came out of that. And the American Revolution, I mean, it's very politically incorrect, but the American Revolution was a tax revolt and it was a war of secession, two things that people don't really like in certain circles these days. But that's exactly what they were. And it largely came out because of the Seven Years War of the British that it was really expensive war and then that's how the British Empire started really was the result of the Seven Years War. And they needed to fund the war and to fund the empire too. And so whereas before with the colonies, they had what's called benign neglect, where they pretty much left the colonies alone. The only kind of taxes weren't for revenue. They were for regulating trade and they're mostly tariffs, not internal taxes. But they wanted to start to tax the colonies. And so they started with a sugar act and the colonies said, wait a minute, with the 1688 Bill of Rights, we should have taxation only with representation. We're not represented in parliament. And then the Stamp Act came about. And that's the dumbest thing to do is you don't want to tax people who publish newspapers because they'll rabble rouse. And so the Stamp Act was hugely unpopular. And Benjamin Franklin went over and said, we don't want internal taxes. And so the British said, OK, fine. We'll do external taxes.  And so the American colonies said, wait a minute, we don't want any taxes actually unless we are represented. And so they did boycotts, tax revolt in terms of boycotts. And so most of the Townsend Acts were removed except for the T Act because they wanted to keep just one little tax, even if it was inconsequential in terms of revenue. It was the principle that mattered. The people in the government, they wanted to keep the principle because they wanted to be able to expand on that principle later. They wanted to be able to get serious revenue later. So they wanted that symbolic last thread of taxation. And then, of course, the T Act resulted in the Boston Tea Party, which precipitated the American Revolution. And there you have it.


Egas Fiontek vs. Arena Sabalenka is the women's final for the Madrid Open for 2023. And both ladies cruised for their semi-finals to get to this stage. Sabalenka started the tournament off as the number two seed and get a buy in the first round. In the second round she take on Castella who had actually beaten her earlier in the year in Miami. But Sabalenka got her revenge, getting through in straight set 6-4, 6-3. In the third round she take on the wild Cardo Sorio who had had some solid wins to get to this stage. This was no problem for Sabalenka, getting through in straight sets 6-4, 7-5. In the fourth round she take on another wild Cardo, the teen sensation on Drava, who had taken out Adajmaia and Lynette to get to this stage. And after a close first set, experience showed and prevailed. Sabalenka winning 6-3, 6-1 to get to another Madrid quarter-final. In the quarter-finals Sabalenka would take on the unseeded Sharif, who had been very impressive to get to the quarter-finals. And after dropping the first set Sabalenka would have to fight back to win 2-6, 6-2, 6-1 to advance to the semi-finals. In the semi-finals Sabalenka would take on the number nine seed Zachary, who she had never played on a clay court. And after a close first set Sabalenka would run away with it 6-4, 6-1 to advance to another Madrid final. Shriyantek started the tournament off as the number one seed and will get a buy in the first round. In the second round she take on the lucky loser Graba, this was no problem for Shriyantek getting through in straight sets 6-3, 6-2. In the third round she take on the number 28 seed Perra, but again this was no problem for Shriyantek getting through in straights 6-3, 6-2. In the fourth round she take on the 16th seed Alexandrova, who had taken out Zheng in the previous round. And this is where the battle started. Shriyantek being up a set and a break, with Alexandrova coming back the fourth or third. Shriyantek eventually winning in two and a half hours, 6-4, 6-7, 6-3 to advance to the quarter-finals. In the quarter-finals Shriyantek would take on the number 27 seed Martich, who had just beaten Krajikova along the way. But this was by far the best win for Shriyantek so far, getting through in just over an hour, 6-1, 6-3 to advance to the semi-finals. In the semi-finals Shriyantek would take on the number 12 seed Kunmatova, who had just beaten Pagula in the previous round. But just like their last three meetings this was no different, Shriyantek winning easily 6-1, 6-1 to advance to her first Madrid final. This would lead to seven times the four with the head-to-head lead to Shriyantek 5-2, including their last match was actually two weeks ago in the Stuttgart final, with Shriyantek getting the win. If Sabaleng is going to win this one, she's going to have to use the conditions to her advantage. We know this court is a little bit quicker than the average clay court. There's a little bit quicker than the Stuttgart court as well, so she's going to have to serve big, hit big and try and be aggressive. If Shriyantek's going to win this one, she needs to limit the errors. There were times in that Kunmatova match where she was under a little bit of pressure from Kunmatova, and we do know that it gets Alexanderova. Shriyantek did have a struggle there with that power. This would be the most powerful opponent she plays for the entire week, so she's got to be prepared. This is such a fun matchup. It's been such a long time since we've got the number one and two in the world, playing each other in consecutive finals. So I'm excited to see this again. I reckon Sabaleng might get a revenge here. I think she might win in three sets. I'm going with the upset. I reckon Sabaleng is going to get in three sets, get revenge. We might go to the French Open. Hopefully we get round three on the clay over there, but let me know down in the comments below. Who do you think is going to win the final?