I have handicapped feet, therefore, if I don't rise, a social rise, I can't really do it properly without throwing over everything here. Now talking about Ludwig von Mises of a man, and we speak about his cultural background, and my lecture is really restrained to that subject, you must realize that he is difficult to order in socially, and as you will see, to order in nationally, ethnically, he's a man between all camps and all situations. He's born in Lwów, that is the Polish name, Lwów would be the Ukrainian name, Lemberg would be the German name of Galicia, the kingdom of Galicia was southern Poland, really southern Poland, incorporated into Austria in 1700 and 72, the first partition of Poland, and of course his origins were Jewish, his grandfather was the head of the Jewish cultural community, which was a state institution to teach and to practice religion, like the Catholic church or the Lutheran church, and as you will see there by then the grandfather, grandfather became nobiliated, he belonged also to the minor nobility, and his upbringing was in a society which was largely Polish, naturally Jewish, Polish, he spoke German from childhood on, but he also spoke Polish, in all likelihood he did not speak Ukrainian because there were really three nationalities in Lemberg, the vast majority of the inhabitants of that city were Polish, make him a very large Hebrew sector and finally also Ukrainian sector, so he was conversant in all likelihood with the German script, with the Latin script, with the Hebrew script and with the Cyrillic script, I mean from the upbringing you can see in the school, in other words he was faced initially by enormous variety of cultures, civilizations. Now the Hebrew element had come into Poland from Germany, in Germany the Hebrews lived in large quantity, especially on the Rhine, but constantly disturbed by popular rising which mobbed the ghettos, I never forget here one thing, a ghettos was a privilege, it was self-government, it was certainly not an action of the government to enclose them, but through their demeanor and their closing and their accent and their rituals and their religion and unfortunately since they were the moneylenders, because according to their own face they could only lend money to Gentiles and in the Middle Ages the Gentile was prohibited of lending money to another Gentile, in other words a Catholic to another Catholic, so they were in a difficult position and King Kazimierz the Great of Poland who had ruled of an agrarian country, an almost purely agrarian country without any bigger cities called into the country German settlers and with them also the Jewish settlers, both of them could converse with each other obviously because Yiddish after all is a form of medieval German and then they built the cities and that is the background, in Poland on the other hand they had no ghettos, they had no such privilege if you like and they lived together together in freedom, they had a kaha'i, it was a sort of community and since they couldn't walk on the Sabbaths more than 2,000 steps so they congregated, naturally congregated. Now that is you see his also his religious background, however he lived and that is now very important, he lived in Galicia that is southern Poland and this southern Poland under Austrian administration in other words of a country which had a variety of nationalities I mean German, Czech, Polish, Ukrainian, Italian, Slovenian, this country became that part of partition Poland, partition between Austria and Prussia and Russia which had the greatest liberties, there were two universities, there was a university in Lwów in Lemberg where he was born, a university in Krakow and many Poles said that the restoration of Poland was only possible having greater rights, greater privileges and becoming the foundations of a once later reunited Poland so they were very loyal to the Habsburg family, the Polish delegates in the parliament in Vienna were always perhaps for Austrian at the same time of course thinking we are going to be the basis of a reunited Poland and maybe under certainly under the same house under the same dynasty always bear in mind very very important to bear in mind that monarchy in Europe was an international institution, not a national institution if you take the year 1910 you only find two dynasties which are truly native, the dynasties of Montenegro and the dynasty of Serbia, the house of Saxe-Coburg also for instance ruled in England and in Belgium and in Saxe-Coburg and in Portugal and in Bulgaria and the house of Sonderburg, Luxburg, Augustenburg ruled in Norway and in Denmark and in Greece and the whole Solons are not Prussians they are Alemanics they come from a different part of Germany they also ruled in Romania so you see the idea was here of countries ruled by foreigners who had a real distance from the local population very curious to Swedish laws for the Swedish dynasty they can marry aristocrats and they can even marry commoners provided they are foreigners but nobody within the country because then of course you get a sort of either with industry or agriculture you get a connection you should have an equal a sort of feeling of equal distance now you see then of course in Poland and that Polish atmosphere Poland had an enormous nobility in other words in Poland according to one Polish scholar about one quarter of the Polish population claims nobility now in Austria for instance in little Austria it's about a third of one percent but they are 24 percent and 11 percent can prove it with documents another maybe five six percent who are noble but don't have the necessary documentation and this nobility prior to the partition of Poland had its own sense of equality there's a Polish saying which means the little noble man in his primitive abode is just equal to the great magnate who might have 120 servants and then of course the pride is very very important I mean this nobletarian aspect which we then see in the development of the Austrian economy that all all has a relation to it that of course led to the to the transformation of the kingdom of Poland into an elective monarchy of course elected by the nobility huge masses were electing the king and after 1572 the Polish kingdom was revaptized into szeczpospolita and that means republic so you had the Polish republic with a very powerful parliament the same but in the same since any nobleman were really equal and the idea that one nobleman could rule over another one was distasteful every decision had to be unanimous in other words the vote of one man the liberal way to say I don't accept that law of course made the law unacceptable and that of course led finally to this to this big realm never forget the Polish-Lithuanian szeczpospolita was a country bigger than France it was a huge country led to its weaknesses and its partition but you see here that spirit of freedom the spirit of freedom another Polish saying was fight against other kings but oppose your own one you see so you see here that spirit very very important for the development of young looting for mises living in this atmosphere now he belonged to the nobility never forget in the old times any Hebrew became a Christian it happened of course again and again immediately automatically was becoming a member of the schlachter of the nobility because obviously I mean being a Hebrew you were a relative of our lord so therefore you have it you see here a world so radically different from yours but with an enormous love for freedom and an enormous tolerance religiously speaking Poland was the most tolerant country in Europe as far as religions go when you compare let us say Poland with England there's just no comparison a Poland actually when the big wave came the big wave of the reformation you know one third of the Poles became Calvinists became Presbyterian another third became Unitarian but when I say Unitarian please forget now totally Boston and Unitarianism quite quite quite different from the Bostonian kind but then the Catholic Church regained it but with all pressures culturally the Jesuits of course played a tremendous role at that time the Jesuits still were devout Catholics which today they are only sporadically so these Jesuits then finally had the right schools they took anybody into their schools then they're propagandized their faiths would they see it they never forget the Jesuits are the founder of the technology of the modern stage theatrical performances to school the building of wonderful baroque churches and paintings and culturally so finally the Unitarians disappeared completely without without duress and the Presbyterians also disappeared almost I would say without leaving a trace so there he grows up you can imagine a young Ludwig von Mises belonging to the nobility but still officially remain remaining Hebrew remaining Jewish then later on comes to Vienna but starts his schools in Rwuf and then he comes to Vienna and now you take the schools in which he has been I mean what were the schools first the four years elementary and he went to public schools as as most of the children go private schools in Europe are very very rare my own children those of my wife my father we all went to public schools they were highly disciplined I can assure you and then after four years of elementary you had to make an entrance examination into a school which is a combination of quasi combination of high school and college but without without real choice of subjects eight years and these eight years are the worst years in your life I can assure you the concentration camp or the cancer ward comes as a relief and you ended up at the age of about 18 becoming a bachelor and then you go to a university which is purely a graduate school and you study either theology or medicine or law or what is called philosophy so you see that is the that is the career he studied law that is the career the education which he received in other words obviously he could read Latin and Greek and he spoke he spoke he spoke Polish and he spoke fluent German and I'm absolutely certain absolutely certain that if you take the social position of his family he must have spoken also French and certainly had even long before he came to America he must have learned English because needless to say that he knew all the great English economic writers in the original so that is the that is his growth now you take liberalism liberalism was in Europe at the nine in the 19th century leading a very powerful party powerful parties in all the country but at a still restricted election system and that helped them in other words there were qualifications to vote now in Australia these qualifications disappeared in 1908 after 1908 you have one man one vote and then the liberal parties receded now the great party of Bismarck Bismarck originally was a conservative but he ceased to be one and it was the national liberal party which helped Bismarck and of course in the principle of liberalism is freedom now we must go into the analysis of the word liberal as the word is used worldwide and that means when I speak I call myself an arch liberal uh when we speak about American liberalism what you call in your country liberalism it is just the opposite and there are so many misunderstandings between I think about Santa Claus who has nothing to do whatsoever with Christmas or the word Holocaust which really is nothing to do with genocide and so forth and so forth or the Middle East you put Palestine into the Middle East and where's the nearest of course you don't find it so in other words here what is liberalism whereas democracy answers the question it's also very important for our lecture answers the question who should rule the answer it gives is the majority of politically equal citizens either in person or through the representatives whereas liberalism rightly understood doesn't answer the question who should rule but how should government be exercised and liberalism says regardless of who rules whether it's an absolute monarch or a dictator or a political majority in the parliament government must be exercised in such a way that each individual has the greatest of course reasonable amount of freedom you can't say I'm a great liberal I'm going to drive 100 miles an hour through a village but you see here freedom is the essence and there were really four phases there are the pre liberals a man like Adam Smith who never caught himself a liberal and the word of course politically is comes from the country which had always the greatest enthusiasm for freedom and that is Spain now the supporters of the constitution of cadiz called themselves los liberales and called their enemies los serviles the servile ones south in england used the word in 1816 the first time and he spoke about our british liberal less l e s spanish form and so what the scott spoke about libero a u x he took the french form the origins of liberalism of course is continental it's not british it's not english and then after the pre liberals who get the early liberals very very important the early liberals and of course these periods overlap in time the early liberals would be the toqueville would be monta norm bear would be lord acton these are the early liberals then you have the old liberals the cumulator cobden for instance now our friends mesas really was an old liberal hayek was an old liberal and then finally after 1961 after the breakup of the morpela society you get the new liberals i call myself of course a new liberal following grotke rather than hayek or rather than hayek and and mesas but of course i knew them all i knew hayek well i knew mesas quite well i knew repke very well he was also a very personal friend with hayek i spent the summers a week in the alps he was an inexhaustible source of information both hayek and mesas as you know really died as a non-agenarians no but of course the liberalism got into a crisis in europe especially when you had one man one vote because the vast majority of people we have to face that fact if they make a choice what they believe not what is but what believe is security and freedom well of course they choose always security the bread daily bread and security and freedom and the people who have a real vested interest in freedom i mean i say a vested interest a realized interest in freedom uh other people of a minority usually people who are creative one way or the other now what's of course mesas experienced in world war before world war one then especially after world war one never forget mesas was in the army because the system was if you had your bachelor's degree which he had then you had to serve in the army but only one year all the others had to serve in also three years in the army but he served only one year and at the end of one year you got a commission as a reserve officer so he served as a reserve officer in world war one in the imperial and royal army i say imperial and royal imperial for austral and royal for hungry there were two different citizenship don't forget that there's many things in common but two different citizenship uh he then was wounded not very seriously but wounded sufficiently to be no longer capable of participating in the war and after the war he was seeking as you do know for an academic career in the university where he had of course difficulties difficulties not on account of his racial background if you like but difficulties around of his liberal outlook because the university was increasingly professors were increasingly either catholic oriented with a conservatives land but as a minority the majority really was nationalistic liberal the german expression is via schlinder in other words in which we fell accidentally that it became a war between nations of course that it was a war between nations already is due to the french revolution prior to the french revolution we had mere cabinet wars the cabinet war was king against king and he had to look into the till did he have enough money and then he called in for ruffians and cutthroats who like to fight the war and they had his officers members of the nobility who had to bribe a government he had to buy a commission bribe a government to die not waiting for the cancer war but to die and noblery on the battlefield he had to pay for that and didn't burn your draft cart as many americans did during the vietnam war so that was the old system and of course tiny armies and now your gigantic armies and you had democracy you had parties in the parliament and you had to marshal now entire nations against each other you also an ultimatum against syria would have merely resulted as a matter of fact in a local war against austria against a small country and count with the former russian prime minister said oh these serbs he said they're only badly baptized turks anyhow but that it became really a world war was really due and you see how history how cruel history is a conspiracy between the chief of the russian general staff and the minister of war who mobilized not only on the austrian border to which they had to brief right because austria was mobilized but also against germany and then came this frightful exchange of wires between the two the war minister and the chief of the staff lie to nicolas the second william the second is now convinced that he's lied at by nicolas the second and then finally declares the war on russia and then the austrians have come as as allies of germany the austrians have to declare the war against russia not the russian secretary i mean i couldn't tell you 99.9 percent of all europeans sink it the other way around history is so many many facets are entirely different but you see the war between nations and nations we are taught now to hate each other you know his war between nations is then converted in 1917 in something different something we didn't quite have before and that is into an ideological crusade and it is now since the russian monarchy falls russia becomes a democracy under kierinski and now woodrow wilson has a chance to pervert his war between nations bad enough a war between nations into an ideological crusade to make the world safe for democracy that means now safe for the absolute victory of one party and if hitler had had any sense of humor he would have erected a colossal statue to woodrow wilson because only in the conversion you see into democracies as play though has clearly foreseen if you replay the book eight and nine of the republic you see the absolute xerox picture of the change of the weimar republic into the nazi tyranny but of course even before that you have the onslaught of socialism and socialism ludwig for me is his face that in austria this rise massive of socialism also at the university you see that socialism is of what the talk will would have called and he used the expression in another connection enforce idé claire a clear but false idea socialism you can explain to any high school student at the age of 15 and 15 to 20 minutes but the working of a free economy you need a seminar for that so naturally in that democratic framework one man one vote where the masses vote the attraction of socialism has become enormous and he saw that with great great fear and of course he realized naturally that the monarchy was a sort of bulwark against this development and of course also nationalism now with the artificial humiliation of certain countries the nationalism also rose and therefore you get now already the stage in the sense you see prepared for a national socialism and that could very well even be combined with anti-semitism because in our central european mind this is not generally true the idea really was judaism on the jews and the hebrus and that is capitalist now the stock exchange in vienna was entirely dominated by by hebrus so you see here then gobels also once declared we are anti-semitic because we are anti-capitalist there is this combination the destruction you see important of the old vertical order now into something horizontal you know the old vertical order got father in heaven and the holy father in Rome and the king is the father of the fatherland and the the father as a king in the family it went up and down you looked up and down now you're doing timidly right and left because there the parties and the parties are based upon masses and and these masses of course obviously uneducated facing without real any political education or knowledge the issues they can become prey now of demagoguery of popular leaders it means of demagogues and Bezos saw that this development very very clearly and of course his mind is how to save freedom and he knew very well that the material aspect of the problem of freedom was very very crucial especially in view of the socialisms i speak now in the plural of because don't forget there are there is national socialism and international socialism there are the socialisms and in the year 1934 the dorfus regime which was a dictatorship which was carried by a minority of decent people who were supported by mesis mesis worked as an advisor for dorfus for a catholic dictatorship i have nothing against the dictatorship i'm interested in freedom if a dictatorship protects my personal liberty and freedom i'm all for a dictatorship because i mean my vote alone means really nothing i'm a microbe in the voting process and certainly mesis realized that he became a financial advisor of the dorfus regime and in that year 1934 there are two civil wars in austria there's the one in february against the socialists and the one in july against the national socialists international and national socialism and austria was really uh in the middle of these two enemies now you must realize that at that period as you know very well mesis has been accused of having favored fascism in italy and he has he he really favored his rise because his interest was not democracy his interest was really always freedom and since in italy freedom was really seriously menaced by socialism hyphen and communism he thought that fascism really was certainly by all means the minor evil and i can assure you have lived also in in fascist italy in fascist italy if you were not a complete fool you could live very freely because that fascism had really two uh that how should i say two breaks on the one was the monarchy and the other one was the catholic church and you could live quite quite freely you could speak freely out that we know what they hear your speech was never censored newspapers were books were but otherwise you lived a very you lived a very free life and italy was then the only power which really protected the independence of austria when then the nazis in july 1934 who revolution tried to get the upper hand the italian army mobilized i was in that time in the tyrol i saw the mobilized italian army and he was made to know that if he moved into austria the italians would come to the defense of austrian independence because muslimi naturally realized that if austria is lost then czechoslovakia would be entirely surrounded and if czechoslovakia felt and poland would be entirely surrounded there was a domino theory which certainly like the other one was perfectly in right so that is his idea rather having italian fascism and you had sometimes you had liberals and socialists fleeing austria went even to fascist italy and then italy was driven into the arms so far into the arms of hitler by answering the eden and the british foreign policy in the abyssinian war and then muslimi said to a highly placed austrians i i can't do anything else i'm completely isolated from the west i must somehow collaborate with hitler and he very very reluctantly as you all even know he went into world war two only in the summer of 1940 with great great reservation thinking now that hitler is going to dominate everything and he should get a little bite here a little bite there to an order at least to save his own freedom of power of a country pushed practically that by hitler into the Mediterranean so that is you see the the reason why uh and there exists an article about the relationship of visas to italian fascism and to call national socialism fascism fascism of course is a leftish not a rightist fascism is a leftish phenomenon the the fastest which you also find on your dime at the back is a republican symbol and it started out to be a republican movement muslimi only being the son of an italian anarchist changed his mind now you get in you get also mesas then now i'm going back we come to world war two the calamity of world war two the calamity of world war one was enormous george f kennon whom i also personally know is the man who says rightly all the sources all the roots of our evils really go back to world war one that is the great catastrophe really in our life world war one which brought in an order which favored the rise of national socialism and which was won by germany fairly in mind on october 15 1926 uh his magnificence dr. erz kornemann magnificence is the is the title of a president of a german university or awesome university delivered a lecture and we said of course we have suffered the loss of valuable provinces we have suffered the loss of islas laurel and of eastern uh in eastern germany to poland and our middle class was nearly destroyed and brought to starvation and ruin but we have won the war we bordered on three major powers france austria honey in russia now we only bother on uh on france in between us and russia there's a whole cluster of new mostly except poland unhistorical countries small and defenseless and when the time comes we take our picking and of course hitler follows that it is a result of not knowing geography so that was this frightful heritage now then comes world war two the result of world war two the quasi dominance of sovietism of the of communism and then the rallying for the few surviving i must say on the whole few surviving liberals who are drawing together in 1927 they are forming then in near veve in switzerland the more peller society of which mesis was one of the founders mesis and hayek and röpke i mean these three men really had banded together organized and had quite a cluster of men who came together but then again something very very typically happened and that is that uh they made these three men the proposition to call the society first of all not a more peller society but the detox will act in society and their professor night of the university of chicago rose up bang the table and say if you call that society after two roman catholic aristocrats i'll quit then in the despair what should we do and so say we're living here in the more peller and park hotel let's go more more peller society which is now but you see here the the aristocratic aspect very very important and the nobillitarian aspect of the liberal idea i was tested and said all all aristocrats are born anarchists and never forget here you see never forget if i used to what anarchists bear in mind that anarchist is a liberal in the real sense of the world not in the american sense a liberal run wild is an anarchist and you find anarchism obviously therefore you find it only really in the catholic and in the russian in the russian orbit you don't find them anywhere else you remember the sacco and vanzetti case probably and all the one of yours sacco was probably guilty vanzetti in all likelihood innocent what happened to the ashes of vanzetti here we go back to italian fascism the vanzetti ashes were brought back to italy were buried and became a center of pilgrimages under the observance of the fascist authorities and even the pope even musolini had really protested against the execution of sacco and vanzetti and the man called luigi rustigucci wrote a book tragedy i supplicio the sacco and vanzetti tragedy and martyrdom of sacco and vanzetti and the preface was written to that book by arnaldo musolini and musolini of course has declared of course i despise socialists but anarchists we all really are anarchists you see rum romanism and rebellion leveled against the irish there are no danish or norwegian anarchists i can assure you or prussian anarchists and that's the gross of the catholic world because you see the the catholic theology is profoundly is profoundly personalistic the first idea of course is the idea of free will which are reformers denied of course of free will and the denial of predestination you are really responsible for yourself you're not you're not a puppet in the hands of a creator i mean the personalistic aspect and of course that always has been also the strength of the nobility in general and of course of the catholic nobility in particular the man who tries to slay the beast couched off and beg is of course a catholic a catholic aristocrat so you go back to that and then you see the interesting phenomenon of the whole austrian school now if you take the austrian school that would be manna and visa and bermbabak and hayek and mesis and harbour and then finally the only man who is not a nobleman is machlup of the original the whole austrian school consists of nobleman and all of them hereditary that means they were not a no built they inherited that already the noble father house runny mead 15 12 uh 1215 the barons who were trying to get rights and resist resist the monarch the font in france is against the nobility the nobility always against an almighty an over mighty king so see that is that is the thing which americans do not realize apart from the fact that you see no militation was an instrument for social mobility because you get always new now no longer possible of course now the only inheritance you can have is hard cash so no no more no bilitations are taking place you know the son of the even sometimes a great actor the son of a great artist the son of a great professor the son of a of a great general is only the son of the manufacturer who can act or the banker who can inherit the father's strength or the father's achievement if you like but all that was always realized by uh all that was really realized by uh they get to know him i get to know him through the arch to god of austria because he was obviously uh i mean a man entirely open to the uh monarchically idea he knew very well how francis joseph when anti-semitism rose in austria and he did rise in austria as it was elsewhere too i mean that is not only in austria that francis joseph in a letter to his empress which has been preserved went out in violent terms against anti-semitism the jews they are my subject like everybody else i mean he felt to be the part of patrie in other words a non-political entity you see when teddy rosewell visited francis joseph around 1908 or nine or 10 anyhow in the beginning of the century he asked francis joseph said your majesty do tell me what after all is the role of a monarch in this progressive 20th century and of course in 1910 you still could think that this could be a progressive century which it indeed wasn't and francis joseph said well it's my task to protect my peoples from the governments governments austrian and hungarian so in other words he was the man who thanks to his birth and to the accident and he could say no i'm not going to sign that law and i'm going to appoint that man and so on he could really do things for the protection you see of the nations apart from political convictions so you see here the the role of mesas of course he was very sad about the break between the old liberals and the new liberals that happened in 1961 i was present i was member of the morpela society for only two years 1960 i lectured there in 1961 for there were many personal reasons but many impersonal reasons the new liberals really harked back and looked back at the early liberals and the new liberals were adverse to what they call mammothism in other words to monopolies and cartels and so on because he said we must have freedom and freedom means there must be several enterprises not one big enterprise and we end up of course we're having no freedom we must have the right of choice by this good or that good or supporting this or supporting that and poor rapke had the first heart attack in 1961 in 1963 i participated still in the neoliberal catholic discussion which took place in augsburg but you see here the the confusion you get for instance i know encyclopedias you find them morpela society being neoliberal which it it was mixed until 61 then it became old liberal really the old liberals on the other hand started slightly to lean towards the neoliberal side but mises whether that through what sort of man was he well not not very tall sharp features as you know by his bust and by his pictures very decisionary in his in his words this is right this is wrong this is nonsense this is good uh he was not conciliatory neither my of course i like that i admire that i admire that uh not adverse to extremes in the other support table could be shows extreme and there's only the extreme things are bearable as an ator farce used to say he was a man of the sort steadfast he was a steadfast man and he gave you the impression to be a steadfast man of course profoundly interested in cultural values you see as i told you when i met him how he deplored the fact that the death of robot musil was not generally and and the theater music everything was near to him also of course to hyac in in many ways the man were of very similar opinion the neoliberals were somehow let us say more culturally conscious a man like hopke uh was very near let us see the catholic outlook specifically the catholic outlook hopke was a member of the papal academy of sciences hyac i know headed a short little discussion with pope paul the second in latin and the pope said a long last civilized language you see in other words that they're all had sense of humor our great our great liberals and of course i mean as a final judgment i must say that both ruppke the neoliberal as well as hyac both told me expresses verbis we all are the samples of ludic for muses i mean they were very emphatic about it but they got their basic ideas from ludic for muses in my case it was somehow different i believed so many young people on the right that was anti-capitalist and anti-socialist at the same time there must be a third way but there ain't no siege animal you know there's no third way in other words we have to look towards free enterprise i usually don't use the word capitalism i say free enterprises or free market economy because actually bolshevism is also capitalism only state capitalism not private capitalism it's the whole difference so we have to look at these differences but certainly therefore if you take the the teaching role which ludic for muses had i think the teaching role he said in this world is something permanent is something permanent he was not a man of my faith hyac was more or less an agnostic both respected the catholic faith probably röpke more than anybody else which i can take from his letters which he also wrote to me and part of these letters really have been published hyac wanted the catholic funeral and the funeral speech was held by a jesuit whom i know shushing but uh uh who was not an ordinary jesuit he was a specialist in economics so he had the funeral oration at his burial in frybook in brice carl because let us finally honor the memory of uh mesis who was a fine man and a real character a real character and as a real character he remains in my memory thank you so much 64 000 questions i'm expecting i won't pay them to you but but i would like to yes please yeah that is very difficult because they were uh there were personal reasons the loyalty of röpke to the then secretary not the president the secretary called honald but actually it was also the fact i would say that uh you know one two three four stages of liberalism that the old liberals really harked back purely to adam smith whereas the neoliberals harked back in other words three to one and four to two that means the neoliberals really harked back to the early liberals they held them and then and they then forget that the early liberals at the very distinct religious coloration and uh man life röpke now even rüsto who is a real giant now i'm afraid that you probably know hardly hardly anybody of you know much about rüsto who was a neoliberal he has a son in america i think he teaches is john hopkins who published that more new mental work of rüsto or's bestimmung the gig in wart difficult to translate effort to establish the momentary moment in our history in three large volumes with an enormous material and uh rüsto a immensely close friend of röpke also with an anagnostic but with an enormous admiration for the catholic church you know very interesting person son of a prussian general who became an anarchist and then was saved from starvation by a famous catholic priest who also was a literary person who provided him with a band and a typewriter and a chair and a table and paper and so on who then emigrated to constantinople so did so did röpke röpke and rüsto were both in constantinople but then rüsto stayed in constantinople and röpke went to geneva röpke spent the war years in geneva röpke also wrote a memorandum for the allied powers to restore the monarchy in germany after the war and uh they did not go to america in other words they wanted to stay as close as they could to the frightful center of infection which was the heart of europe now you see in other words it is the entire mammothism i think i already used the expression of the neoliberals which uh bothered uh mesis said mammothism is not is perfectly avoidable we need no state intervention in other words antitrust laws or anything of that order of course at the same time i can assure you a man like röpke would certainly not have approved of the specifically american antitrust laws who to him seemed often very very silly you know and as you probably also realize but he wanted to keep the idea his idea was keep competition open and of course if nobody else can do it well we must rely on the state to keep competition open there is nobody else who can assure that which was denied by hayek and denied and denied by mesis that is the main i think that was really the main ideological difference between the two other questions please no body yes please it is the book of 1919 yeah jesus was very much the venerable and the he sort of read it on the hereditary monarchy he regretted that the mammothism couldn't be the game hope in prussia and in Austria but he planned that when he mixed up with different nationalities all living together in certain territories but he thought that in countries where you couldn't have democracy well of course the people would vote for the policies that's so very he was a real democrat but he must have changed of course of the change came about through history you see history took all these nations of central europe over their knees and spanked them and i felt this i felt this so vividly about four years ago the pan europe union you must know the pan europe union is a private organization founded by count kudunhof kalleri in the 1920s and that is really the source and the father of the present tendency no tendency i mean is the flow now to unite europe and in 1900 and i must pinpoint that no 93 yes yes four years ago in prog we had the great meeting the pan europe union i spoke i read speeches in a variety of languages i don't master at all but i'm a very good parent and then spoke otto the last the oldest son of the last emperor and there the cheques gave him a standing ovation they had experience first a corrupt republic and then then the nazi rule and then the communist rule and they had bitterly learned the lesson at least the people who were there now the standing ovation would have been unthinkable 100 years ago or 50 years ago see in other words history also taught taught mesas and i've changed my mind also because i actually in my novel called gates of hell i have three pages in a novel against capitalism but i got the uh i got a good education by röppke röppke took me by the ear and converted me to free enterprise now that was very obviously in the case of mesas yeah anybody else anybody else yes continue as the financial advisor in the meeting or not what resulted in the shushlik regime yes also he continued with mesas but only until 1936 because by 1936 he realized in all likelihood that austria was lost that also had lost his protect in italy because italy had been driven into the arms and of course to save his skin unlike freud freud for instance who was also i mean if you like a supporter very much an anti-democrat freud never forget and politically was a man of the right freud was was a man who as a matter admired christianity i mean he was against promiscuity and freud was terrified about the idea that his theories might fall into the hand of psychiatrists because he said i mean i mean a treatment of people for years and high expenses perfectly you should only be used for the education of children and for cultural analysis that was freud but the people are very often misunderstood what they are after but then of course he went over to geneva and kept up his connection with the hand of scama that is the chamber of commerce and in the chamber of commerce he he collected young people young and old people no no people and men and women and held seminars in the chamber of commerce it was a very important thing but he never got really the full professorship of vienna but he got the title of professor and there's a very highly prized professor in europe is a is a man who can only be compared in prestige with a diplomacy or with the general staff he got it from the emperor for Francis Joseph met him professor for it i'm speaking about for it and the role of mises was only that of a well you could say by american standards of an assistant professor he didn't get the full he didn't get the full professorship i mean he was treated badly by the university of vienna as uh finally by the by the universities in this country here he had to swim always against the current but he swam courageously that's the wonderful thing about him he never gave in he fought his noble fight other questions nobody nobody yeah well i think i have to thank you then for your attention


Righty, I have a construction update for you guys today I feel like I have to stop saying that because I just have a construction update for you guys almost daily now But to truthfully I am so tired. I am working way too much right now. I'm working 10 and a half hour days Every day. In fact, I went from five shifts to six shifts this week, but oh well, I'm still gonna do these Alright, so today we have welding on Leviathan. So The cherry picker up on Leviathan yesterday was installing new weld points to basically have mesh netting To go over any part that goes over the guest area. So it is confirmed that Leviathan will have netting Over here, by the way, this is a really exciting construction update You can't tell because of how tired I am, but we have the excavator heading in so there is already one tiny little footing dug out Inside the tunnel and right there on the flatbed if you were looking close enough you have what Is called an encasing essentially, so that's a big encasing that'll basically get placed down And they dig out a big square footing essentially. So what you're gonna see Is either A footing that is getting dug out or they're going to extend the tunnel Okay, so I feel like this is something we haven't talked about And it's interesting food for thought because I just thought about this They may be extending this tunnel Which is really interesting, but if you look there there's a footing ish dug out and They're gonna place this so this was filmed at 10 a.m. Because I work in the evening and then Craig a wanton flew in the evening for me and that's when you're gonna see them almost like extending the tunnel or digging a big footing It's one of the two So we'll have to see how that plays out because things are getting really weird Okay, and I feel like again back to that subject. We haven't thought about the tunnel needing to be extended for the entire launch Why would you want half of it outside and then it to head inside the whole story that they presented was you were launching through a Subterrain type conditions, but yeah, anyways this giant excavator is heading in towards the mountain tunnel And in the next shot you're gonna see exactly why so they were digging out a giant square Section like they do for Yukon so they have those giant casings If you remember Yukon construction you would have seen it a lot when they were digging a footing They'd put these metal crates the square ones You see them right there at the entrance to the tunnel and the excavator will go in and dig out that and then they put in the rebar and The the formations and they will pour the concrete which will then turn into a footing That's really the dumb way of explaining what's going on But yeah, we'll have to see things things are getting really weird Okay, this whole construction process because first of all there's a whole section of it that we have not seen them Do that is done inside the mountain That is now heading out from the mountain so we will start to see things now as you can see in today's footage Rutherford or Rutherford was arriving with their vehicles and all that So we're gonna start to see some heavy construction going on it'll be really interesting to see which building they choose I mean it's already chosen, but I guess what building they choose based off of the footage We're watching because we're all discovering this project live together Which building gets chosen for the the station is it gonna be extreme sky flyers gonna be international showplace or is it gonna be the ugly arcade building in world Expo comment down below I want to hear from you guys, which of the three places? Do you think the station is gonna be located? Anyways, that's all I have for you guys today again subscribe to patreon for Up-to-date information and exclusive access to earlier construction updates Thanks for supporting the channel and thanks for watching drop a like for me because I feel like I deserve it I'm sorry. I'm begging, but I'm really tired, but I had to get this out. It's like two in the morning I'm editing this right now For tomorrow or today when you're watching this anyways. Bye. You don't care. You're just here for construction. Bye


Mi'n nhw Tim Register. I'm a Drupal developer. I'm Freelance, and I'm from Suffolk. Being a volunteer is really a good way to meet lots of people at Drupal camp. You meet the speakers and you get to know them fairly well, especially when you manage a session. And on the CXO day, you get to meet a wide range of people, especially. But at Drupal camp, you generally meet lots of people, but you also get to help people, which is what I do anyway. I've gained business through being a volunteer, and I've also got to know various Drupal people better by being a volunteer, and got to know them and communicating with them online and in person. It's bigger. I haven't been to one of the Drupal cons, or Drupal Europe, but it's bigger than other Drupal camps I've been to. Because it's now in the same place, it's familiar to people. It's becoming familiar to people, so they know where everything is now. Drupal Tastic.


Hello, so today will be the last lecture or the denouement of this course on Fourier analysis and applications, last time we discussed the continuity or the differentiation operator with respect to the weak star topology on this piece of Schwarz distribution here continuity refers to sequential continuity. Today we begin by proving the corresponding result for the Fourier transform, the Fourier transform maps s prime r to s prime r, this Fourier transform as an operator will be sequentially continuous with respect to the weak convergence of distribution or the weak star topology as it were. So, theorem 123 that you see displayed in the slide, suppose u n is a sequence of tempered distributions converging weakly to u, then the corresponding sequence u n hat converges weakly to u hat. So, take an element g which is rapidly decreasing that is the Schwarz class and let us compute u n hat paired with g, for the definition of Fourier transform of a tempered distribution simply put the hat on the other factor, so the u n paired with g hat, but u n converges to u weakly, so u n paired with g hat converges to u paired with g hat that is what you see a red arrow and then put the hat back to where it belongs namely u hat paired with g and that completes the proof of the theorem. The proof is exactly similar to the earlier proof of continuity of the differentiation operator, a simple exercise find the weak limit of root pi by root epsilon e to the power minus x squared by 4 epsilon, either you can use a definition of weak limit or you can recognize this as a Fourier transform of e to the power minus epsilon x squared e to the power minus epsilon x squared converges weakly to 1, so by the continuity of the Fourier transform by theorem 123 the corresponding Fourier transforms will converge to the Fourier transform of 1 that is 2 pi times the Dirac delta, so I have given you the exercise and I have given you 2 different ways to proceed. Some more exercises consider the distribution u equal to exponential of i a x squared where a is a real number, now because a is a real number u is actually a L infinity function, so it is a tempered distribution. Now what I do is that I change it, I change a to a plus i epsilon, I change a to a plus i epsilon prove that u epsilon converges to u in the weak sense of distribution. Now take epsilon bigger than 0 and you just proceed in the usual way, so if you replace a by a plus i epsilon what happens to the exponential, the exponential becomes e to the power i a x squared and there is a minus epsilon x squared because the presence of the minus epsilon x squared suddenly the function has become from L infinity it has suddenly landed up in the Schwarz space S of r it is rapidly decreasing so we can compute the Fourier transform by using the integral formula. Proceed along the usual lines how you compute the Fourier transform in chapter 4 and put the definition complete the square and you land up in the integral that is displayed in the slide integral over r there is a factor in front of the integral exponential of minus lambda times x plus i chi by 2 lambda the whole square where lambda simply denotes epsilon plus i a just for simplicity I use an notation lambda. Now we want to reduce this integral to integral of e to the power minus t squared dt how will you transform this to an integral e to the power minus t squared dt, you must go back to chapter 1 see how we computed the Fourier transform of the Gaussian by using Cauchy's theorem right we shifted the contour of integration using Cauchy's theorem you imitate that idea and you complete this problem for a slightly different approach you can look at the book of stretch arts page 47 and that completes this exercise. There are many other exercise and here I am going to take a couple from stretch arts book and this is a very nice exercise that you see on page 50 before we take it up we must know what are radial functions and radial distributions in chapter 4 towards the very end we talked about functions which are radial and we proved that the Fourier transform is also radial but this was the context of the schwarz space now we want to do the same thing for a distribution when will a distribution be radial okay before that what are the radial function a function phi is said to be a radial function if phi composed with r is phi where r is a rotation matrix for example e to the power minus mod x squared is a radial function so anything which depends only on mod x is a radial function there is a way to describe which tempered distributions are radial there is a way to compose a distribution with a diffeomorphism we do not need this general result and that is discussed in chapter 6 of hormone does book the chapter says composition with smooth maps but the rule that we will apply it will be to distributions which are actually functions so we are going to be looking at functions which are locally integrable etc and those are going to depend only on the mod x in r3 our examples are going to be in r3 and the in fact that examples are going to be specific we are going to be looking at the distributions mod x to the power minus 1 and mod x to the power minus 2 they are locally integrable functions and they decay as x goes to infinity so they both define tempered distributions in r3 and what radial means is very clear here and so we will not elaborate on this concept anymore just that these are radial functions and the Fourier transform of one of them is going to be the other one with a constant factor thrown in so let us get to the example itself so that is theorem 124 the locally integrable functions 1 upon mod x and 4 pi by mod x squared both define tempered distributions on r3 how do you make them as tempered distributions you are going to tell me what does it do to a function g in the schwarz class this g comes from the schwarz class g maps to integral gx dx upon mod x to the power k remember I will write dx in polar coordinates and so k is either 1 or 2 and I will get r squared sin phi dr d theta d phi remember that r squared will cancel with the mod x to the power k where k is 1 or 2 and then you will be left with simply integral of gx times either r or nothing and gx is a rapidly decreasing function so there is no problem as far as the convergence of this integral is concerned and you can see that 10.21 does make 1 upon mod x and 4 pi by mod x squared into tempered distributions if you want you can directly prove that they are continuous if gn converges to g in the schwarz class the corresponding integrals converge first part is very clear now we turn to the second part of the theorem how to find the Fourier transform of 1 upon mod x the Fourier transform computation is a very different matter call this distribution 1 upon mod x is u and we proceed as usual so what are the definition of Fourier transform you see the last display u hat paired with g is simply u paired with g hat the hat goes on the other side and so now we use the definition of Fourier transform of a rapidly decreasing function as an integral so right hand side basically becomes integral g hat dx upon mod x we use the definition 10.21 and the definitions of Fourier transform both and the left hand side u hat paired with g is simply this okay now what we are going to do is that we are going to put the definition of g hat and that is one more integration e to the power minus ix dot y gy dy of course the next step is pretty obvious we are going to switch the order of integrations we are going to switch we are going to integrate with respect to x first let us try to do that and let us see what happens the inner integral is e to the power minus ix dot y dx upon mod x I am going to put x equal to az and a will be thrown to the other factor it will become a transpose y and I am going to select the rotation matrix a in such a way that a transpose y is simply aligned in the e3 direction again you must go back to chapter 4 when we proved that a Fourier transform of a radial function is another radial function and you see the same technique was used there and so I will leave that for you to verify and I can choose this a in such a way that we will get mod y times e3 and this becomes z and z can be written in terms of polar coordinates and you get an integral e to the power minus rho mod y cos phi remember there is a rho squared sine phi one rho cancelled because the denominator we had a rho remember mod x will be the same as mod z because a is a orthogonal matrix and mod z is rho and so one rho get cancels and you left with the rho d rho and the radial coordinate goes from 0 to infinity and there are two angular coordinates theta and phi theta goes from 0 to 2 pi and that is why picked up a 2 pi here and the phi variable goes from 0 to pi e to the power minus i rho mod y cos phi sine phi d phi how convenient put cos phi equal to t so sine phi d phi will be minus dt and the limits of integration will become minus 1 and 1 and you can actually perform this integral e to the power minus rho mod y t perform that integration and so one more integral has been dealt with only the integral with respect to rho remains and what you see you see trouble in front of you you see integral 0 to infinity sine mod y rho d rho that is an oscillatory integral and you need to deal with oscillatory integral by now you got sufficient experience in dealing with oscillatory integrals whenever you deal with an oscillatory integrals what comes to your mind is x of minus epsilon mod x squared trick of course you will try to throw in e to the power minus epsilon mod x squared and take the limit as epsilon goes to 0 we have seen this several times in the past so no need to dwell on this but if you put in this e to the power minus epsilon mod x squared you will run into a messy integral you may be able to come out of it but it will give you some little bit of trouble but there is no need to choose e to the power minus epsilon mod x squared some other modification of this trick will also be sufficient for our purpose so instead of using a e to the power minus epsilon mod x squared trick you use e to the power minus epsilon mod x instead and the same logic will go through but this time you will get an integral that you can quickly evaluate namely the inner integral becomes e to the power minus epsilon rho sine mod y rho d rho now we must go back and consult tables of Laplace transforms that you taught your undergraduate students the Laplace transform of sine and the Laplace transform of cosine so what you see the inner integral is the Laplace transform of sine or go ahead and integrate it using integration by parts twice whichever method suits you but I am going to make my life easy simply by recalling the formula for Laplace transform of sine you are going to get a mod y by mod y squared plus epsilon squared and one mod y cancelled off you simply left with integral over r3 g y dy upon mod y squared plus epsilon squared well now we need to take the limit inside the integral the dominated convergence theorem will immediately come to your rescue remember that we are in r3 when you write polar coordinates in r3 it is r squared dr d theta d phi sine phi and there is a r squared below and r squared above so the fact that there is a mod y squared below is going to give you no difficulty whatsoever you can use a DCT and we will get the result it is basically this epsilon will go away and you get integral g y dy by mod y squared which is exactly 1 upon mod y squared paired with g there is an 4 pi factor of course which always remains and we are established the theorem and so I explained to you how to prove the last equality it is an application of the dominated convergence theorem now let us discuss Fourier series again from the point of view of distribution theory so in the very first chapter we talked about point wise convergence in the second chapter we talked about L2 convergence and third chapter we talked about Cesaro convergence in the final chapter we talk about distributional convergence of Fourier series so four different modes of convergence we are discussing and the weakest one and the most useful one is here so let us go back to one of those examples from chapter one the Fourier expansion of mod x and that is displayed here in the slide now because the presence of 2k minus 1 the whole square to the denominator the series converges uniformly to mod x the 2 pi periodic extension of mod x and uniform convergence of a periodic function will imply weak convergence in the sense of distributions and in other words the partial sums s and fx converges uniformly to mod x and so it will also converge in the sense of distributions so why are we weakening it why are we doing this why are we getting rid of uniform convergence and harping on weak star convergence because differentiation is continuous if I know that if a sequence of distributions converges weakly the derivatives will also converge weakly so I can differentiate sn once twice etc so let me differentiate sn once the sequence of derivatives will converge weakly when I differentiate what happens the cosine becomes a sine and the minus sine goes away 1 2k minus 1 goes away and you get the next one so from the right hand side I get 4 times summation k from 1 to infinity sine 2k minus 1x upon 2k minus so the left hand side when you differentiate mod x you get the signum function remember that we are looking not at the mod x on the entire real line if you do the mod x on the entire real line the derivative is a signum function but you are looking at the mod x which has been periodically extended beyond minus pi pi so you are going to get a periodized version of the signum function what is it this signum function of x is 1 on the interval 0 to pi it is minus 1 on the interval minus pi to 0 extend this as a 2 pi periodic function and you get this result this falls under the purview of Dirichlet's theorem that we discussed in the last chapter namely this converges pointwise except at the discontinuities and at points of discontinuity it converges to 0 we have seen this in the last lecture but now I want to differentiate it once again when I differentiate the signum function I get the Dirac delta in fact I get the twice the Dirac delta and I will get a twice the Dirac delta placed at 0 pi minus pi etc so I am going to differentiate this term by term now once I differentiate it term by term I go outside the realm of classical analysis and I must resort to distributions the series of derivatives will no longer converge pointwise it will converge in the sense of distributions so what happens a sequence of derivatives the one of the 2k minus 1 which was the denominator that goes away you simply got summation k from 1 to infinity cosine 2k minus 1x and when I differentiate the signum function I get the Dirac delta but here I get a minus 1 to the power n and I want you to tell me why is this minus 1 to the power n appearing you should draw the graph of the signum function and you should understand what happens when I go from pi to 2 pi and from 2 pi to 3 pi in which way the graph ascends and descends accordingly the derivative will pick up a plus sign or a minus sign and at that because of discontinuity you are going to pick up a Dirac delta so I leave the amusing details for you and we get 10.22 10.22 has to be understood in the sense of distributions summation n from minus infinity to infinity minus 1 to the power n time the Dirac mass placed at pi n the sum of Dirac deltas left hand side is obviously a distribution and the right hand side is an infinite series that does not converge in the classical sense but it converges weakly in the sense of distributions. Now I take the Fourier transform of both sides of 10.22 both sides are distributions and both sides converge weakly in the sense of distribution that is the partial sums of the two series on either side converge in the sense of distributions the Fourier transform is a continuous operator in the sense of distributions and so I can take term by term Fourier transform of both sides. So calculate the Fourier transform of delta pi n remember this is not the Dirac delta at the origin the Dirac delta at pi n so go back and put the definition of the Dirac delta and put the definition of the Fourier transform and evaluate the Fourier transform of both sides term by term and look at the equation that you get the resulting equation will be the Jacobi theta function identity in disguise. Let us now do another exercise instead of taking the Fourier transform of both sides let us directly pair both sides with a Schwarz function gx which Schwarz function gx am I going to choose no prizes for guessing I am going to choose my gx to be e to the power minus tx squared t real positive and so what happens to the left hand side it is gx paired with delta pi n what am I going to get I am going to get g of pi n what about the right hand side cos 2k minus 1x paired with gx is simply integral gx cos 2k minus 1x dx. So what do I get that is exactly what I got on the right hand side integral from minus infinity to infinity e to the power minus tx squared cos 2k minus 1x dx left hand side is summation minus infinity to infinity minus 1 to the power n e to the power minus t pi squared n squared the g evaluated at pi n. Now let us combine this let us simply for the left hand side is pi times 1 plus 2 times summation n from 1 to infinity minus 1 to the power n e to the power minus pi squared n squared t and the 2 factor was taken the right hand side so 2 cosine a is e to the power i a plus e to the power minus i a each of these 2 pieces is a Fourier transform of a Gaussian you know how to calculate the Fourier transform of a Gaussian it is another Gaussian and the result is displayed over here the last line let us go a step further. So I am going to take the last equation and I am going to replace t by 1 upon 4 pi squared tau in the previous equation and just do a simple algebra here 10.23 what you are going to get is when you replace t by 1 upon 4 pi squared t that is a routine algebra you are going to get equation 10.23 1 upon 2 root pi tau times 1 plus twice summation n from 1 to infinity minus 1 to the power n e to the power minus n squared upon 4 tau equals summation k from minus infinity to infinity e to the power minus pi squared 2k minus 1 the whole squared tau equation 10.23. Now go back to chapter 1 go back to chapter 1 and recall the formula for the Jacobi theta function identity that transformation formula that was equation 1.25 and I repeated it here for your convenience and I want to compare 10.23 and 1.25 before comparing I am going to put t equal to pi when I put t equal to pi cos nt is minus 1 to the power n and you see we get the left hand side of 10.23 on the right hand side I put when I put t equal to pi I get exactly the right hand side of 10.23 so you see that the equation that we got 10.22 is exactly the Jacobi theta function identity in disguise. So now we want to look at this in a slightly different modern perspective the equation 10.22 that we got the left hand side was a bunch of Dirac deltas right here I can split this sum into two sums those with odd n's and those with even n's. So let us do that let us separate out the two and we get each of those two pieces is a sum of the form 10.24 it is an infinite series of Dirac deltas placed at mc where m varies over the integer that is a it is an integer lattice the set of all mc's forms a cyclic subgroup of r and the series 10.24 converges weakly and the sum is a tempered distribution now we want to study this tempered distribution closely I am going to omit some of the routine computational details. So I am going to take a Fourier transform of both sides as before so u hat will be take the term by term Fourier transform that Fourier transform of Dirac delta is basically e to the power minus i y mc and I am going to combine the exponentials with opposite signs as 2 cosine mcy. Now what I want to do is that this summation here converges in the sense of distributions and this is the second derivative of something it is the second derivative of what look at 10.26 so look at the series on 10.2 so the series on the right hand side of 10.26 is a uniformly convergent series and the sum is a nice function f of y when you differentiate the series 10.26 twice in the sense of distributions mind you I get 10.25 so 10.25 has been written as 1 plus f double prime y it will be very nice if I can find a better formula for f of y if I can sum this series on the right hand side then it will be nice that is what we will do now what you do is you start with a sawtooth function the sawtooth function is s of x equal to x on 0 to 2 pi extend this function as a 2 pi periodic function and you get a sawtooth function and you can write its Fourier series take that Fourier series and do a term by term integration take the Fourier series and do a term by term integration and what you will get will be pi squared by 3 minus twice summation m from 1 to infinity cos mx upon m squared so in some sense the summation cos mx upon m squared I have an expression for that namely I just have to take the sawtooth function and integrate it and I need to replace x by cx so that I get cos mcx upon m squared and so I can calculate explicitly what this f of y is going to be and that f of y has been displayed over here minus pi squared upon 3c squared plus pi times mod y by c minus y squared upon 2 in this interval now the first term is a constant and and the last term is an even function and the and the middle term is also an even function so you go to extend it as an even function as a 2 pi periodic even function with period 2 pi by c the period is now 2 pi by c because I scaled the variables I won't take the second derivative remember but I am going to take the second derivative in the sense of distributions the constant term will disappear when I take the distributional derivative of minus y squared by 2 I am going to take a minus 1 what are the distributional derivative of mod y it is the Dirac delta and it will be weighted by 2 twice the Dirac delta so you get 2 pi by c into the Dirac delta at the origin if I get the Dirac delta at the origin I am going to get a Dirac delta at 2 pi by c 4 pi by c etc because it's a periodic function f of y is a periodic function with period 2 pi by c so I get the whole bunch of Dirac deltas equation 10.27 the f double prime has been computed put this value f double prime in the previous equation 10.2 further one goes away I cancel to this minus 1 and you are left with this beautiful result theorem 125 this theorem 125 is called the Poisson summation formula for c not equal to 0 you take a lattice of Dirac deltas concentrated at the points mc the Fourier transform is another lattice of Dirac deltas concentrated at 2 pi m by c with a factor of 2 pi by c thrown in front of it now let us evaluate both sides at a function of the Schwarz class so if I take a phi in the Schwarz class and apply both sides of 10.28 to phi left hand side becomes summation phi of mc right hand side becomes summation phi hat of 2 pi m by c with a factor of 2 pi by c in front of it in chapter one the relevant phi was the Gaussian and we got the Poisson summation formula for a special case in chapter one this is the general theorem the most general Poisson summation formula now what happens that this is in one variable what about several variables what happens if I take Rn and take a lattice of Dirac deltas in Rn the formula becomes even more interesting in several variables the Poisson summation formula assumes a much more interesting aspect in several variables the book of Strichards page 120 contains a beautiful discussion on lattices and dual lattices you think of a lattice of Dirac deltas as a crystal structure and the Fourier transform corresponds to the x-ray diffraction pattern that emerges out and experiments have shown that bright spots appear at points of the dual lattice so this physical experiment with crystals and x-ray diffraction patterns arising from crystals has a beautiful mathematical description namely the Poisson summation formula the student can scarcely do better than undertake a systematic study of Strichards book after the scores the best thing to do would be to take up Strichards book and look at those topics that we could not touch upon in the scores here is a list of topics the Pochner's theorem on positive definite functions Heisenberg's uncertainty principle in quantum mechanics the Paley Wiener theorems and a glimpse into a beautiful area of analysis called micro local analysis wavelets and the Haar systems and how that gives rise to Vietta's formulas beautiful formulas in classical analysis and a glimpse into pseudo differential operators and I wish you good luck with your studies of Strichards and beyond and this is the end of this course. Thank you very much


Hi, I am welcome to the session. I am Deepika here. Let's discuss a question which says simplify and express the following in exponential form 4 is to power 5 into a raise to power 8 b raise to power 3 over 4 is to power 5 into a raise to power 5 b square So let's start the solution Now we have to simplify 4 is to power 5 into a raise to power 8 bq over 4 is to power 5 into a raise to power 5 v square Now this can be written as 4 is to power 5 into a raise to power 8 into bq over 4 is to power 5 into a raise to power 5 into b square Now we know that a raise to power m divided by a raise to power m is equal to a raise to power m minus in So by using this law of exponent, we have this is equal to 4 is to power 5 minus 5 into a raise to power 8 minus 5 into b raise to power 3 minus 2 And this is again equal to 4 is to power 0 into aq into b raise to power 1 or simply we can say b Now we know that For any integer That is for any non-zero integer a we have a raise to power 0 is equal to 1 So by using this law of exponents, we have this is equal to 1 into aq into b And this is equal to a q b Hence the answer for the above question is a q b I hope the solution is clear to you. Bye and have a nice day


Hello, everybody Andrea here with dental L. Let's talk about how the quality assurance study guide prep course helps you prep for the quality assurance exam. So if you are a dental hygienist who has been audited, depending on your location, not all of us are lucky enough to get audited. I'm not so lucky, but you know, I'm here when we get audited we have the choice of either submitting a portfolio, or taking do I have on my coat there, or taking the quality assurance exam. If you pass the exam you're good to go you don't have to submit a portfolio. So what I have offered sorry guys here's driving me crazy it always doesn't I do these videos. What I have offered is a quality assurance prep course so a full prep course that gives you exactly what to study to pass your exam, because you can be a dental hygienist for two years five years 10 years 20 years. So if you want to take an exam for your dental hygiene, you know, skills, ethics, pharmacology special needs dental emergencies, you're not going to know what to study the last thing you want to do is buy a textbook and read 1000 pages, you know, that's a waste of your time it's not happening so I'm going to share my screen here I do have the quality assurance prep course link in the description for you down below definitely check it out and I do have a sneak peek. On the website to so if you want to see what is involved in the course, you can see it exactly there. So basically how does it work. When you register, you would register with your email, and it will it will ask you to create a password so check your email because it will send you an email so check your junk folder spam folder, and then you click the link to create your exam and then you can log in you have full access for one full year so don't worry if you, you know, if you're thinking I won't have time to study like the next two months do I have full access, you have full access for a whole year so no rush. It's now September so you will need to take the exam by January 31 in order to pass your audit if you don't take the exam, you fail the audit and you could lose your license right so you don't want to do that you want to take the exam, but don't take it tomorrow, study first. So I have all of the modules for you so I have module topics so you study per topic. There are PowerPoints. There are videos, there are quizzes and then a video also of me going through the answers and rationales of each quiz. What I like about the quizzes is they are very interactive so you can read the read the question click the answer their multiple choice and then it tells you right away. If you get the answer wrong or not so you don't have to guess what's the answer did I get it right. It tells you right away so I make things as easy and stress free as I possibly can for you so with this course you do not have to buy a textbook you don't have to buy anything else to pass your quality assurance exam. So people have passed with just using my course there is still a 97 just checking 97.8 success rate in passing so that's pretty good. If you study, you will pass if you don't study you're not going to pass that's not my fault but why not right study. The WHO suggests that you study for 75 hours for the quality assurance exam. So if you take in two hours to study it's not your time to take the exam you're not going to be successful. Some dental hygienists tell me they have gone through the whole course in two weeks, no problem. They passed the exam they were so happy others tell me that took me three months to go through everything I did pass but I felt like I needed the extra time. You have as much time because you have a full year, you have full access to the course, and I do update the course twice a year normally. It was just updated in August depending on when you're watching the video because new updates did come out for the exam so I wanted to make sure you had what you needed to pass. So definitely sign up this is the easiest thing you can do I tell you exactly what to study to pass. There's not too much information to study there's there's not too little. You get literally everything you need I keep it simple just go through the modules, one by one I go through everything this is what I do you guys this is my passion. I've been doing now for 16 years so this is my passion. And if you have questions, reach out to me I will also leave the link down below to the quality assurance prep. Facebook group so you can network with other dental hygienists who have also purchased the course. If you want to kind of talk about things if you want moral support because you're nervous stressed out. My job is to make things as less stressful as possible for you because I know it's overwhelming so thank you guys so much for listening I'll talk to everybody soon. Look at the links down in the description below I have them all there for you. If you liked the video please click like that does help me and my channel, and make sure to be a subscriber because I do upload videos often, lots of free content. Thank you so much for listening. I'll talk to everybody very very soon.


One of the ways that FDR changed the government was expanding the role the government had in managing the economy. And he did this in several ways. He did this with the Banking Act or the Emergency Banking Act, which set up standards, regulatory standards, practices for banks, that banks had to meet in order to be federally insured. Let's look at the National Labor Relations Act or the Wagner Act. This said, for the first time in our history, the first time that it was legal for a worker to join a trade union. Then let's look at Social Security. The government began to set up a retirement system for the American public. FDR hoped what happened would be a three-pronged stool of Social Security payments, corporate retirements, you know, company pensions, and individual savings. The other thing that FDR did was with the income tax, with the graduated income tax, have it taken out of your paycheck rather than having you have to write the check at the end of the year. So they really helped set a way to manage the cash flow of the federal government. He also put the federal government, in some cases, in direct competition with private industry to spur private investment. So we have the federal government involved in almost every aspect of the American economy, from regulating the stock market and setting rules for how much you had to have in the bank to buy stocks on margin, what standards banks had to meet to be healthy, how you insured deposits in the bank, how you addressed issues of overproduction and underconsumption in the farm economy, how do you deal with the volatility of a skilled and unskilled labor force, how do you deal with labor conflict, organized labor conflict between labor and management, how do you deal with reforming the income tax system, and how do you deal with the federal government controlling the way that monies are spent in the states. So in many ways, what the New Deal did was establish the tax policy, the wage policy, the farm policy, the banking policy, the utility policy that governed modern America. I mean, you'd never have the great society. You'd never have public housing. You'd never have the national endowment for the humanities. You'd never have federal aid to education. You'd never have Medicaid and Medicare and Social Security index to the cost of living if you didn't have the New Deal. Because the New Deal is the bedrock. It's the platform upon which all modern government policies are based. Because the bottom line for this is that the New Deal said that the government had a role to play in propping up capitalism in a way that benefited the broadest number of Americans.