Yn ddweud hynny, hens Hopihe has kindly invited me to speak to you on the subject of the global bell curve. So we will come to this in a minute or two. But first of all I must explain what is this thing, the global bell curve? Well let's get rid of this term global. I explained the bell curve. The bell curve describes the distribution of intelligence in a population.  Intelligence is the ability to learn rapidly, sometimes difficult material, and retain this and also the ability to solve problems when they are presented to you. So some people are better at this,probably intelligent people and other people are not so good at this. Ymgyrch yn ymgyrch yn ymgyrch, a ymgyrch yn ymgyrch yn ymgyrch yn 100, ond mae'r rhai yn ymgyrch yn 70, a 130. Y 2% o'r cyd-diw yn ymgyrch yn 70, a dydyn nhw'n mynd i'r cyd-diw, a ddannu'n 2% o'r cyd-diw yn 130. Mae'r rhai cyfryl, a'r sydd yn bwysig i'ch gael y bydd ychydig ar gyfer hynny. Gydigolio i chi'n ffordd hynny. Felly ydych chi'n ddefnyddio'r gweithio'r myfr? Felly ydych chi'n ddefnyddio'r gweithio'r gweithio'r gweithio? Mae yma yma eich ceir ydych chi wedi'u hwnnw, ei geithreithu am y lleolau ei gyfrifiadu'r cyfrifiadu dechegetaeth. Mae'r problemau cy kerfwyr wrth cymryd anhygoelol, i'r rhannu cynnig wedi gyda gael gan awr iawn, dyna'r problem honiad, debyg pa David Lang. Beth rheson rhai oed yn ei placef? Mae mae rhaid oed yn ymddangos. Felly yn gweithio ar y tŷ sydd hyn. Mae'n gweithio ar y ychydig ymddangos, rhaid oed yn gweithio ar yr tŷ. Mae mae'r gweithio ar y tŷ, rhaid oed yn gweithio ar y tŷ. Mae'r gweithio ar yr ysgolr ar y tŷ. problem which economists have been concerned with and as I say also historians here. Now our leftist friends have a standard answer to this problem. They say the reason is that we whites are not very nice people and we discriminate against the browns and the blacks. We don't really like them. So we don't give them jobs so they remain poor. Well if there's legislation to ensure that we do have to give them jobs we only give them low level jobs where they're poorly paid and once we've got the employment we don't promote them so they remain poorly paid. So that is a standard leftist social science answer to this question wherever it's raised in any countries and of course there are a lot more of these people that is the general consensus view I suppose in social science. Nevertheless there are people who have descended from this. They say oh no no we don't dislike these people we're not prejudicing against them it's not that. The problem is the problem lies in them. They have some deficit. Something inside them that stops them earning as much money as we do and we even had the President Barack Obama take this very view a few months ago when he addressed the black youth in the United States and he said look I know what the attitude is very prevalent among you lads you don't like working in school you think that's a whitey thing working in school so you dissociate yourself from it but that's all wrong. You should be working like I did and Michelle we worked hard at school you should adopt us as your role model you work hard and then you'll do like us and maybe get to Harvard or some lesser place perhaps but nevertheless you'll do well.  Well there is this minority of social scientists generally right-wing social scientists who say that the answers problem is not that we discriminate against these people but they have some deficit. The nature of this deficit is not very widely explored so my agenda is to promote the idea that this is an intelligence deficit and the reason that we are rich and they are poor is that we are more intelligent than they are. Now this view was you can you could adopt you can tackle this problem within countries take one country in the United States or wherever or you can look at it between countries and say well why are the European peoples rich and these other nations, brown skin and black skin nations poor and this by the global bell curve which I have here the publisher is with us today Richard Spencer if anyone would want to look at this in detail this is really a sequel a global bell curve to the book just called The Bell Curve by Richard Harnstein and Charles Murray published in 1994 in that book they presented a racial hierarchy in the United States of IQs of the different racial and ethnic groups and then they presented the earnings and similar rate of phenomena, social economic status educational attainment of the races now the results of that, it was set out in that book was the fact that the Jews are the people with the highest IQ they have an IQ of 110 and the highest earnings the highest social economic status other indices of intellectual attainment winning Nobel prizes and everything below then come the northeast Asians the Chinese, the Koreans and the Japanese the IQ of 105, they are the next best they become the whites, IQ of 100 then quite a long drop here to the Hispanics with their IQs of 87 and below them the blacks complete linear relationship between these variables as I said well this is the answer to this problem the reason some people do better they are more intelligent than others so this my subject of presentation the global bell curve examines this question all over the world hence the global and the question is does this same hierarchy appear elsewhere in the world and the answer is it does look at some 14 nations or aggregations of nations like Latin America, Caribbean we find the same hierarchy everywhere wherever you look it's always the mongoloid peoples that we call them in classical anthropology Japanese, Chinese and Chinese together with the European peoples who come to top of these hierarchies wherever they are and then the brown peoples white often mixed race peoples such as Latin America or Caribbean and we move letters whites, black mixes, mestizos whites, native American Indians mixes and then we have the pure blacks and whites come at the bottom of these hierarchies we see that everywhere as I say in Latin and Caribbean variants of these hierarchies appear in different places for example in Southeast Asia Singapore, Malaysia, Indonesia and Thailand we have apart from in Singapore we have smallish minorities Chinese but they have much more they are much more intelligent than the indigenous populations so they do much better in terms of earnings and possession of wealth control of the banks and the big companies they do much better even though they are quite small minorities of the population in Indonesia they are much 2% of the population but there in Thailand about 10% of the population but they are immensely powerful so this is rather discomforting to the discrimination problem discrimination answers this problem it is not possible for 2% of the population in Indonesia to discriminate against the native peoples they are not powerful enough nor even in Thailand but it is just through their own abilities that they have acquired this powerful position so 10 years ago I decided with Tattree Van Halen a collaborator in Finland to political columnist to collaborate with him to examine this question of whether the same differences would appear when we look at nations not within nations but we look at nations so the division of labour here was that Tattree Van Halen would do all the economic detail of it and I would gather the IQs of nations to see then we would look at the two and see whether the IQs of nations would predict the per capita incomes of the populations of these nations just as it is the case within nations so I can move on here well have you ever heard about this thing hang on, hang on, hang on okay so I could result of my collected IQs all over the world and I summarise these in this IQ world map and this IQs of nations are set on 100 for Britain and these are slightly although all European nations have an IQ of around 100 it is the same metric as we use within nations if you see that China is a bit darker red and the same is true of these other mongoloid peoples in Japan, Taiwan and South Korea and Singapore they have an IQ of 105 exactly the same difference as was found within nations in the United States so they are these mongoloid peoples I know they are the one I am too present but I speak for our European audience here they are a bit more intelligent than we are and then we have a band running across North Africa into the Middle East, India through to South East Asia and the IQ is about 85 and it drops to sub-Saharan Africa of around 70 then these IQs are 100 are present among the European peoples wherever they are in North America in Australia and in the southern parts of South America Argentina, Uruguay and Chile they are all about the same as you go north from Brazil Ecuador, Paraguay and these places dropped because these are mixed race peoples generally with white minorities so it is an average depending on how much what the mix is in these places so having got the IQs contributed by me and the Pair Caper Incomes contributed by my collaborator Teddy VanHannon we've run correlation fees too we've run correlation of about 0.68 the IQs have explained quite a lot but they mean so totality of these differences between nations in Pair Caper Income I've just been reminding you of of course as I was saying the problem goes back centuries and Adam Smith of course is concerned with this problem in his famous book The Wealth of Nations in which he said one of the things that it turns into why some countries are rich and some are poor is that some countries have a well functioning market economy with the rule of law and property rights and attendant constituents of a well functioning market economy those countries do well and are rich these countries that have various kinds of poorly functioning market economies are poor so we can all live with that there's no problem with that and this is another major contributor of course to the answer to this question why are some countries rich and others poor so we see really two major factors that determine whether a country is rich or poor or somewhere in between one is they have a well functioning market economy the other is that they have high or low IQs so this is our general conclusion here we also add in natural resources as some rather more minor component but in some cases an important contributor to the wealth and poverty of nations or some countries like the ways of this example the IQ is quite modest they have that well functioning market economy so they are rich so they have a per capita income just much the same as we have in Western Europe the correlation across nations between IQ and GNI is between gross national income at PPP purchasing power parity is the correlation of 0.6H meaning IQ contributes about half the variability in per capita income so we think we have achieved here an integration of the social sciences of economics and psychology as Hans Hoppe said in his introductory remarks this morning economics is the queen of the social sciences so I'm happy I'm happy with that and I say psychology is the king of the social sciences but this is I'm not implying that the king is anyway superior to the queen this is a marriage between equals and we hope that we have brought them together this will be a successful marriage and they will have many progeny will be produced as a result of this integration of these two sister social sciences now there have been some particularly our friends on the political left have not been very happy with this analysis it's all, you know, more IQs these are you say these are genetically based really these IQs so this means there are genetic differences between these peoples well that's not very good news for us we aspire to a world in which everyone is equal or generate these inequalities between people can be reduced so we're not so happy about this so we had a certain amount of criticism as you might imagine from these this analysis so these are the objections this is racist I suppose it is so racist yes well there are we are talking about facts here not ideology there are these race differences in intelligence well understood they have a genetic basis race differences in brain size for example which are exactly the same as these race differences in IQs the Mongoloid peoples have the largest brains and the Europeans and brain size decreased and brain size is one of the contributors contributing to IQ we've got a big brain and we've got a higher IQ so that's one objection and then the others the data are questionable this is what you might call nitpicking objections someone would say well this IQ you've got for Indonesia 84 that's all derived from one city in Indonesia that's a big country of 120 million how can you be sure that this city is representative of the total population of Indonesia so all I can say as far as why shouldn't it be well you can't say much more than that so the critics nitpick these various things you can go through them all and question this one and that one and the other and say they rise as all rubbish and stuff maybe we're lucky here we were extremely lucky because after we published this book in 2002 the OECD Organization of Economic something in development a well respected body perhaps not among us here but so much but nevertheless a reputable body took it upon themselves study the educational achievement as they called it in a number of countries 180 in all we studied came out in 2003 and 2005 after we published our book and they studied the 15 year olds very well drawn samples in all these countries in reading comprehension in mathematics comprehension and in science comprehension and these are really IQ tests all they're very close to IQ tests all they're very very close to IQ tests there's no real distinction between an IQ test which contains in it items of this kind and these educational tests these educational tests are curriculum free they measure general understanding of the principles not of where they happened to have studied calculus in one country or another the object of this was to see which countries do better and others and then try and figure out why this would be does it depend on the size of the classes or the qualifications of the teachers we could go with all these things and then we could find out why some schools do better some countries do better and others do worse and if the ones that don't do so well can copy these ones they can reduce their class size so they produced all this for 108 nations so what I had to do was to look at these and look at them in relation to the IQ data and it was also exactly the same as correlation of one across these countries so this validates our IQ data and confounds our predicts so we think we've really established now as we have these two totally different lines of evidence on these IQ differences between peoples this must now be accepted as a fact that our leftist friends will have to come to terms with of course they will find it painful to do so with their aspirations for an equal world so this eventually I think the evidence is so strong both between nations here and within nations that they will come to accept this that it will take some time but eventually they will come to accept this because the truth triumphs in the end or as our ancestors in medieval Europe used to say magna est veritas et privalabit Thank you gentlemen and ladies


Today's lecture we will continue our discussions on Boolean algebra and later move on to Boolean functions which are functions on Boolean algebras. So let us recall the definition of a Boolean algebra a Boolean algebra is a complemented distributive lattice having at least two elements and also having a greatest element and a least element we will define functions on Boolean algebras which are induced from the idea of greatest lower bound and least upper bound of lattices. So two binary operations are denoted by plus and dot so we have two binary operations plus and dot where plus is the greatest sorry is the least upper bound of two elements so a plus b is equal to the least upper bound of the two elements a b and a dot b is equal to the greatest lower bound of the two elements a b these greatest lower bound and least upper bounds are defined as we define in lattices because after all Boolean algebra is a lattice next we have the complementation operation which gives us another operation on a Boolean algebra but in contrast with the previous two operations this operation needs only one element and so it is called unary operation. So we have a unary operation complementation a unary operation called complementation denoted by prime is also defined on a Boolean algebra now this complementation when it acts on an element a suppose a is an element of a Boolean algebra then an element of a Boolean algebra then the complement of a a complement plus a gives me 1 and a complement dot a gives me 0 now the fact that complements exist is due to the definition of Boolean algebra where we say that it is a complemented lattice a complemented lattice means that any element has a complement and complement means that when you take the conjunction or plus of that element with its complement you will get the greatest element and when you take the product sorry it is not conjunction when you take the disjunction or plus with the complement of an element then you get the greatest element and when you take the conjunction or what some sometimes people say and or the product of or dot with the complement you will get 0 so thus these things are defined on a Boolean algebra thus an algebraic system Boolean algebraic system is is a is a is a system which consists of some elements so a Boolean algebraic system script B can be represented as script B well which content consists of a set B which is a set of elements then the operation plus and dot which are two binary operations then we have the unary operation complement and then we specify the least element and the greatest element so it is a six tuple consisting of a set B then plus dot the complement which we denote by a prime 0 and 1 now we have already seen in the next in the previous lecture some examples of a Boolean of Boolean algebras like we have seen the simplest possible Boolean algebra consisting of 0 and 1 and then we have taken some tuples some three tuples of elements and of 0 and 1 and have seen the Boolean algebra that we can construct by by using them so we have basically seen that by taking Cartesian product of the set 01 we can construct Boolean algebra with larger number of elements however we should also check the basic axioms underlying the Boolean algebra and we should also check some basic results which can be derived from the basics basic axioms of Boolean algebra so now we will be doing some kind of axiomata so we have the algebraic system which we call a Boolean algebra we have defined operations and we say that these we explicitly write down a set of axioms that we say that this Boolean algebra must follow so the axioms of Boolean algebra the first one is that there exists at least two elements in B the second axiom is that for all a, b belonging to belonging to the set B well here we will be often calling the script B as Boolean algebra but the other capital B also we will be calling Boolean algebra now so for a, b belonging to B a plus b belongs to B and a dot B belongs to B so this is a version of closure property so we can write it down as closure third property is that for all a, b belonging to B a plus b equal to b plus a and a dot b equal to b dot a this is called the commutative law now at this point one may stop and say that wait a moment we proved all these for lattices indeed we proved all these for lattices but in this case we are trying to write down Boolean algebra with a explicitly defined axioms involving the set the operations and the greatest element least element so later on we will not be looking back to lattices but we will be looking at Boolean algebras and trying to derive more results by using these axioms although if we like we can of course see that all these things are satisfied in the environment of lattices now we have got the commutative law this is now an axiom here and then the fourth one is the existence of so-called additive identity so there exists an element 0 belonging to B such that a plus 0 equal to a for all a belonging to B and there exists one belonging to B such that a dot one equal to a for all a belonging to B so the first one is existence of zero and the second one is existence of unit so we write existence of zero and existence of unit so we will call this element 0 in a Boolean algebra and this as unit in a Boolean algebra now we have seen some axioms and we will see some more axioms the fifth axiom is the distributive law axiom number 5 so we have two kinds of distributive laws for example if you have a plus b dot c then we can write this as a plus b dot a plus c and if we have a dot b plus c we can write this as a dot b plus a dot c and this must hold for all a b c belonging to B this is called the distributive law now the last one is the complement it relates to the complement so for all a belonging to B there exists complement of a again belonging to B such that a plus a complement equal to 1 and a dot a complement equal to 0 now if we look back to all these properties we will see that they appear in pairs for example if you look at these two these two laws we will see that they they are in pairs in some way then these two are in pair we see that we can in fact transfer from one one expression within this pair to the another expression by interchanging plus and dot and 0 and 1 let me give an example suppose we start from the first equality in 5 so we write it down again a plus b dot c equal to a plus b dot a plus c now let us somewhat mechanically change the pluses to dots and dots to pluses so what will happen so I start from a instead of the plus I write a dot then of course here this means that I have a bracket over here so I will put a bracket and then see this is B instead of dot I will put a plus I put a plus here and then I write C this should equal now I have a bracket so I write a dot b put a bracket around it and this dot here is replaced by a plus and then we write a dot c and since we usually traditionally take the precedence of dot over plus therefore we will write a dot b plus a dot c thus we see that we arrive at the second law now let us consider the laws or equalities that we have derived in the sixth axiom so we have got a plus a complement equal to 1 what I said sometime back is that we have to change plus to dot and dot to plus and 0 to 1 and 1 to 0 if I do that then I have got a instead of plus I will put a dot and then I have got a complement and instead of 1 I will get 0 and in fact this is this second one now this principle is called the principle of duality so the principle of duality in Boolean algebras which indeed makes our life easy in several occasions now basically when we prove some equation or some relationship in in in a Boolean algebra like we have one expression and we say that okay this expression is equal to this expression then this will carry with itself a dual law or dual equality so what we can do is that we can change the dots to plus and plus to dots and exchange 0 and 1 and we will get another expression which is also valid so we will write that every theorem that can be proved for Boolean algebra every theorem so I made a mistake here every theorem that can be proved for Boolean algebras has a dual which is also true and is obtained by interchanging plus and dot as well as 0 and 1 so very soon we will see the principle of duality in action now now we move on to some results that we prove on Boolean algebras so I will start writing a sequence of theorems well it is somewhat somewhat tedious to do that or to listen to that but we have to do that if we want to study Boolean algebras because these are the basic results that we need to work on Boolean algebras and work on Boolean functions which are defined on Boolean algebras so first theorem over here theorem one states that for all a a plus a gives me a all right now if you are looking at numbers if somebody gave you usual plus with numbers then suppose you take 2 and of course 2 plus 2 gives you 4 but it does not happen like that in a Boolean algebra here we have a plus or something some binary operation which we are denoting by plus which is such that when I add that is a with a itself I do not get anywhere else but only a now the question is that how do we prove it now let us go to the proof now I start from the left hand side which is a plus a and I recall one axiom which says that in a Boolean algebra anything dot 1 is that thing therefore I will write a plus a dot 1 and I then recall what is one one is nothing but a plus a complement that is also an axiom of Boolean algebra so I get a plus a dot a plus a complement and now I will do something that is I will use the distributive law we will ask that how I am using the distributive law so please see here that a is repeating in these two terms I take a out and write plus over here and I will put a dot a complement inside a bracket let us recall here distributive law distributive law recall that if you have a plus b dot c then you get a plus b dot a plus c this is something that does not happen in numbers if you are considering plus as the usual plus in numbers and dot as usual product it does not happen but it happens in case of Boolean algebras so C a plus b dot c gives you a plus b dot a plus c now in this case we are putting b equal to a and c equal to a complement and that is why we are getting what we have we are getting so now we know that a dot a complement gives me 0 therefore I have got a plus 0 and this lets me prove that a plus a is equal to a so this is the end of theorem 1 we move on to theorem 2 here we state that for all a a dot a is equal to a question is how to prove that the answer is principle of duality so I write in the place of proof principle of duality we already know that a plus a equal to a for all a belonging to b and the duality principle says that if I interchange plus and dot 0 and 1 then the relationship will hold so I write a dot a equal to a for all a belonging to b and that is the proof so we will now go to theorem 3 okay now the theorem 3 says that the elements 0 and 1 that we have defined in a Boolean algebra are unique that is there cannot be more than 1 0 and there cannot be more than 1 1 that means there cannot be more than 1 least element and there cannot be more than 1 greatest element now let us see how to prove that now our way of proving is that we will start by the assumption that there are two elements which work as 0 so suppose 0 1 and 0 2 are two elements having the property well 0 now I know what is a 0 because we have already seen in the axiom all right so suppose I take a 1 and a 2 in b then a 1 plus 0 1 is of course a 1 because of the property of 0 because we know that 0 1 is a 0 so it must follow the property of a 0 but this is for all a 1 belonging to b similarly I have 0 2 and a 2 which will give me a 2 now this should also work for all elements a 2 belonging to b now the question is that what happens if I take a 2 to be 0 2 so see suppose a 2 is equal to 0 2 and a 1 equal to 0 1 so see we will start from this one so it will come over here so I am putting let us let me change it a little so a 2 I will I will take 0 1 all right so let me let me correct it so instead of a 2 I will take 0 1 and instead of a 1 I will take 0 2 all right now we are starting here so we have got 0 2 plus a 2 is 0 1 and this is equal to 0 1 and if we consider this equation we have 0 2 plus 0 1 equal to a 1 but in this case a 1 is 0 2 but please note that this and this are one and same therefore 0 1 is equal to 0 2 thus we have proved that we cannot have two zeros in a Boolean algebra and more or less in the same way or using the principle of duality one can prove that the unit element 1 in a Boolean algebra is also unique so I leave it as an exercise over here and move on to the next theorem which is theorem 4 in the order in which we are discussing theorem 4 so theorem 4 states that for all a belonging to be a plus 1 is equal to 1 and a dot 0 is equal to 0 that is all now the question is that how do we prove it in order to prove it we have to start from a plus 1 and understand that a plus 1 can be written as a plus 1 dot 1 only 1 well because we know that 1 dot anything is that thing so that the that is property of a unit now replace 1 by a plus a complement and then use the distributive law so take this a out so I have got a plus and then we have 1 plus a complement no I do not have that I have 1 dot a complement so let me change it so here this is inside bracket 1 dot a complement please see because if you have 1 plus 1 dot a complement we can use distributive law this plus is distributing over this dot so I have got 1 a plus 1 dot a plus a complement right that is what we started with so we will have a plus a complement because of course 1 dot anything is that thing and a plus a complement by your axiom is 1 so we see that ultimately for all a belonging to be a plus 1 is equal to 1 we have proved that and now to prove the other part as I said just sometime back principle of duality makes our life easy so to the other part we have just use principle of duality so write a instead of dot plus write dot instead of 1 write 0 and instead of 1 write 0 so this is the other part of the theorem so we have done theorem 4 at this point well I know that this becomes tiring somewhere in the middle people start thinking that why we are doing these things but we have to remember that we are laying down the rules in an in an algebra so after that we would not have to think about lattices partial order set GLB LUB and all that so we will just think that we have a set of elements we have a set of binary operations one unary operation some special elements and we know what we can do with that so next one is the theorem 5 this is theorem 5 and this state that the element 0 and 1 are distinct and 1 complement is 0 and 0 complement is 1 the elements 0 and 1 are distinct and 1 complement is 0 0 complement is 1 we need a proof for that and the proof goes like this that suppose these elements are equal suppose 1 equal to 0 then what will happen take take any a belonging to b all right and then we can start from a which is equal to a dot 1 and we know that by our assumption 1 is 0 so it is a dot 0 therefore it is 0 and that is the point if 1 is equal to 0 then you cannot have any other element then any any element other than 0 in B so we start with an element a in B and we end up showing that that a is also equal to 0 which is equal to 1 so that means the whole Boolean algebra will collapse to a single element and by definition we say that a Boolean algebra must have two distinct elements so therefore 0 and 1 are distinct and now if we take one complement one complement plus 1 should give me 1 and one complement dot 1 should give me 0 now 0 plus 1 gives me 1 I know that because because of the theorem 4 and 0 dot 1 gives me 0 thus we see that 0 works exactly as a complement and we have seen in one of our previous theorems that complements are unique now well we will prove it later but what we can prove here is that we will need something else over here so I can I can prove like this that 0 complement equal to 0 complement plus 0 which is equal to 1 so that makes 0 complement equal to 1 and 1 complement equal to 1 complement into 1 which is equal to 0 thus we see that 0 complement is 1 and 1 complement is 0 now I could have done something else that is here I could have shown that since this happens and if we can prove that complements are unique then also this theorem holds but the problem is that we have not yet proved that the complements are unique so we will now prove exactly that which is the sixth theorem which says that theorem 6 for all a belonging to b the complement of a is unique proof now now we will suppose that there are two distinct complements suppose suppose a subscript 1 and a subscript 2 are two distinct complements a therefore we have a 1 equal to 1 dot a 1 equal to a plus a 2 a 1 which is equal to a dot a 1 plus a 2 dot a 1 which is equal to 0 plus a 2 dot a 1 and then I will replace 0 by I will replace 0 by a dot a 2 and here a 2 dot a 1 and therefore I will have again by using distributive law a 2 dot a a plus a 1 and we know that a plus a 1 is 1 so a 2 dot 1 and this is a 2 thus we see that we get a 1 equal to a 2 thus complements are unique and therefore as I said we could have written a different proof for the previous theorem by showing that 1 plus 0 is 1 and 1 into 0 is 0 so 0 works as a complement and therefore complement is unique therefore 1 complement is 0 and 0 complement is 1 so that is all so we will now come to another theorem which is called theorem 7 in the series in which we are discussing this is called absorption law is states that let a, b belonging to B then a plus a dot b equal to a and a dot a plus b is also equal to a we need a proof for that so if we start with a a plus a dot b now we will replace a by a dot 1 plus a dot b which is equal to a dot 1 plus b now we know that 1 plus b is 1 this result we have already proved so a dot 1 so it is equal to a thus we say that a plus a dot b is equal to a now we use the principle of duality to write a dot a plus b is also equal to a that proves now the next theorem that is theorem 8 states that for all a belonging to B a complement of complement is equal to a now this is called the involution law alright how to prove that now we shall prove that in this way that suppose I take a complement and then a complement of complement this should give me 1 and a complement dot complement of a complement should give me 0 but we already know that since a is a complement is the complement of a we have a complement plus a equal to 1 and a complement dot a equal to 0 but we have already proved that complements are unique therefore I will have a equal to a complement of complement theorem 9 now theorem 9 is the associative law says that for all a b c belonging to b a plus b plus c is equal to a plus b plus c and a dot b dot c is equal to a dot b dot c now I will leave this proof for self study this is a result that we all expect to happen but as a word of caution this does not happen in all the algebraic systems there are of course algebraic systems which are non associative but Boolean algebra is not an algebraic system like that it needs a proof though from the basic axioms but as I have said I leave it as self study and move on to probably the most important result of today's lecture that is the last one that is the last theorem in this series of theorems and this is called de Morgan's law de Morgan's law states that a plus b complement gives me a complement dot b complement and a dot b complement gives me a complement plus b complement now please see that again the principle of duality holds here I can arrive from this to this relation by interchanging plus and dot and well 1 and 0 does not occur so we do not have to do anything now how to prove this one for this we will just prove that a plus b is the complement of a complement dot b complement therefore we have this proof that we take a plus b and consider a complement dot b complement and this is equal to by our distributive law a plus b plus a complement dot a plus b plus b complement now I can use the


Cody Ko, who is best known as the superstar YouTuber and actor, comedian, soundcloud rapper and internet bad boy, has managed to snag some pretty luxurious real estate, including a snazzy Venice compound in September of 2020. Cody Ko and his partner, preschool teacher Kelsey Krepple, opted to live a quiet life in the trendy LA neighborhood of Venice Beach, and the couple recently spiced things up with the purchase of their very first home, a $3.8 million dollar architectural compound built in 2005. Ladies and gentlemen, this is a house tour that you do not want to miss. In these videos we don't reveal any real addresses and even though we've done house tours of our own, please do not show up at any private residences because it's not safe for anybody. Cody Ko has quite the lucrative career on the internet garnering a net worth of $2 million. His content on YouTube is basically comedy, where he posts commentary on various funny things that he finds on Instagram. Before YouTube, Cody was a Vine sensation who created the viral hashtag 6 Second Audition and was able to accumulate over 2.7 million followers on the platform. Interesting enough, Cody took a programming job in LA where he met his future collaborator Noelle Miller. Cody said, Both making YouTube videos and we followed each other on Vine. So we had spoken a little bit online, but my new boss on the first day of work took me to my desk and Noelle was sitting at the desk across from me. Both of us looked at each other and were like, are you stalking me? Cody grinded out his YouTube and podcast, then decided to quit his full-time job and started the Tiny Meat Game podcast, which currently cracks the top 25 Patreons. The two made bank, touring the country with their podcast and since dabbled in music, by launching a mixtape that has been streamed 10 million times. We even trash-talked Jake Paul from time to time. Cody has garnered over 5 million subscribers on his YouTube channel. With nearly a million views per day, that should generate an estimated revenue around $4,750 per day or $1.7 million a year. In addition, Cody makes bank from his merch, not too shabby at all. So it should come as no surprise that Cody Co and his partner snag the glamorous Venice compound in September of 2020. What's going on guys? It's your boy Clyde Smith and today we're bringing you another house tour right here on Famous Entertainment. Now I did notice that about 95% of you watching aren't subscribed, so be sure to hit that subscribe button because we post a new video daily. If you like these videos, ring that bell for notifications, follow me on the gram to chat, and as per usual, let me know who's house tour is next in those comments down below. Well let's get into this video. Cody Co made his first big real estate splash in September 2020 with his partner snagging their first home. Built in 2005, the 3.8 million architectural compound features 3,911 square feet and boasts 3 bedrooms and 3 and a half bathrooms and offers a number of glamorous features including 3 full levels of living space and a guest studio area plus a rooftop balcony with views of the surrounding neighborhood. A pretty decently sized dig with nearly 4,000 square feet of living space, the 2005 built house is certainly large if not quite labeled mansion sized. Geez, that's a distinction for being a mansion 4,000 square feet? Hmm, guess we're all far off from owning a mansion. The home is contemporary in style and the cement colored structure lies on a nearly quarter acre corner lot that is fully walled, gated, and sheltered behind a towering green wall perfect for privacy. On the main floor, guests lucky enough to visit are greeted to a front door that swings into an open concept living area, decked out with concrete floors, dozens of recessed lights, and floor to ceiling sliding glass doors that flood the house with natural sunlight. Seriously, with the amount of sliding glass doors that Cody has, there is no shortage of in and out flow virtually throughout the entire home. In addition, the home features a profusion of oversized windows that give the home a nice bright life, perfect for soaking in the California sun rays. The open concept living area leads to a cozy family area, decked out with lavish furnishings, custom fixtures, trendy paintings, and a fireplace in one corner. On the other side, there's a dining area that features a profusion of space, more custom fixtures, bundle of windows overlooking the grounds and steps away from the newly installed chef's kitchen. This top-notch kitchen features top-of-the-line stainless steel appliances, marble countertops, custom cabinetry, and a breakfast island perfectly centered in the room. In addition, the kitchen features a butler's pantry with more room than you know what to do with. The home's second level includes the two guest bedrooms, where one of them is much larger than the other, and share a single large bathroom. Combined, the rooms offer plenty of space, sleek hardwood flooring, and an abundance of windows. The bathroom features dual sinks, marble countertops, and a large standing shower, and striking views. However, after going up another set of stairs, it's the room on the uppermost third level that's truly the star of this house tour. This huge space is devoted entirely to the lavish master suite, which opens directly to the elegant cupboard balcony. But we'll get to that in just a minute. The master suite features an abundance of custom built-ins and packed ample amounts of space and a large flat screen, perfect for binging.  The master bathroom features dual sinks with marble countertops and a large cozy soaking tub that boasts spectacular views and all-glass shower. Perfect for relaxation. Probably the most low-key relaxing spot in the house is this discreet balcony that features a wealth of outdoor lavish furnishings, fireplace, and outdoor entertainment system. Whether you fancy a quiet relaxing night, or a little dance party, this spot has it all. At the far rear of the property, there's a convenient two-car garage, accessed via a narrow alleyway that runs behind the house. Directly above the garage lies a loft-style studio that is decked out with custom hardwood floors, big comfy sofa, and custom built bookcases and shelves. In addition, the discreet room features a kitchenette with sleek cabinets and countertops, modest-sized dining table, and a wealth of oversized windows. I'm telling you that the setup Cody has going is perfect for conversion into a YouTube room or podcast studio. We're willing to bet that Cody probably gets a lot of bangers recorded in that room. While Cody's backyard isn't particularly big, it does boast a number of lux features. The backyard features lush landscaping throughout, a sleek grassy patch of lawn, a few alfresco dining decks, and a couple of spectacular tranquil fountains. In addition, the backyard features an outdoor barbecue area and firepave. Perfect for entertaining. Can I get an invite to the barbecue, Cody? Probably an unfortunate omission for a $3.8 million home LA is the fact that there's no swimming pool or spa, but you'll be happy to know that the Pacific Ocean is just a few minutes away. Yo, what's up? We're Delta Epsilon and we are a frat at Miami of Ohio. Yo, what's good? We're the what's good house. Yo, what's up? We're the WAP house and I'm Addison Ray's mom, and I'm the only member. All right, so I think I'll bring this hoster to an end right here. We got to take a quick look at Cody Co's house in Venice Beach that features his very own dazzling master suite with secret balcony. After seeing that fancy little abode he snagged, what did you think? Was it everything that you'd expect at a Cody Co? Personally, I'm a huge fan of the guy's backyard. I mean, sure, it doesn't have a pool or spa, but that outdoor barbecue area decked out with his own fountains. Like, are you not entertained? Out of Cody Co's features, which were your faves? You guys can even go ahead and let me know in the comment section down below. My name is Clyde Smith, and I'll see you guys in the next video.


you guys ready for this? Everyone ready? That's what I like to hear. So this is uh uh a little talk of him putting together and uh been working on this for a little while. So let's start off with a little bit about me. Um my name is Mike. Uh I'm also known as Dark Matter. Um I consider myself a mad scientist hacker uh who's particularly obsessed with wireless if you couldn't figure that out. Um I also love reverse engineering. I love uh doing wire uh website pen testing. Um just everything in this field I absolutely love. Uh I've created this project. I've also created another project called the hashtag wifi kraken. I'll be doing a demo lab. Plugged my demo lab tomorrow at ten a.m. Uh in uh Planet Hollywood at the demo lab. So come check that out. Um also I'm a Kizmet cultist. Uh Kizmet is the most amazing wireless software for scanning. Uh also recently I've become a runner. So I love running and doing all the running things. Alright, let's talk a little bit about the history and background. Um in the early 2000's uh we wanted to get out and uh figure out what's uh what wireless networks we could connect to because we didn't have internet service at our home that was better than like maybe jank DSL, right? So we wanted to find better service. So we're driving around trying to get it so we could get all of our sweet wears off of our CF serves and and kizaz and stuff, right? Uh things have changed a little bit now. Uh uh uh almost all of us probably have unlimited data plans now on our 4G et cetera, right? So internet is not that hard to find. So why would you want to start doing wireless stuff? Well it started for me in 2015. I had this idea that I wanted to monitor uh all of the wifi's at Defcon. So a few days before the conference I took a single board computer and threw some wireless antennas on it, put it in my backpack and started hoofing my way around Defcon thinking yeah this is going to be amazing. Well I learned a lot from that. I didn't catch very much data, I learned a lot. And from that, that led me to the project the the following year. And that project was Project Lana and what I was able to do is deploy 12 boxes around the conference, sensor nodes, that we're able to gather a bit more data um and they were covering 2.4 and 5 gigahertz wireless. Uh that project was uh sponsored to shout out to Warhawk who helped me uh secure the equipment to be able to pull that off. And then that led to, I learned a lot from that project and that led to the creation of the wifi cra- the wifi cactus. Uh the wifi cactus basically solved a problem that I noticed with the previous year's project. Uh I only had 4 radios per box and I was missing a lot of data and I want to catch it all, right? Because you got to get all the data. Um and so I was talking to Darren Kitchen from Hack 5 and I'm like hey you know I had some problems and he's like I think I can help you with that. So he hooked me up with uh 25 pineapple tetras and I was able to pull off the cactus. Okay but why though? Why why would you want to do this? Well the number one thing that I always would typically hear is DEF CON's wireless network is the most dangerous, well network in general is the most dangerous and crazy network in the world. Um and I wanted to know why. Like why is it that way and how right? So what did I do? I decided to build a thing. Once I built a thing then I could start to understand this and try to figure it out. So another interesting thing is uh we live in a world where literally everything is interconnected now right? So you've got like smart fridges right? And you probably have a smart toilet too right? So it comes to a situation like maybe you haven't pooped in a few days.  And of course those devices are wireless right? Because it wouldn't make sense to connect your toilet to your to your fridge with a wire. So anyways I mean we've got I we've got um devices tons of devices around us all the time uh that are broadcasting. You probably have multiple radios on you right now. So I kind of think of them as Pokemon. We gotta catch them all right? Uh and then the other thing is hackers. It's important for us to verify trust right? There's a lot of uh claims and you know everything's secure this VPN will keep you you know super you know I go through seven proxies type stuff and it's like but do you really know that you know you're going to uh that your data is not out in the clear. So as hackers it's important for us to do that. Alright let's talk a little bit about the data. Um this is a graph of the data over the years of the the evolution of this project. And as you can see it kind of grew a little bit. Kind of got bigger and bigger. Um the interesting thing is like the DEF CON one on 2018-2019 kind of got a little small and the only reason for that is because I ran into a new problem is I kept running out of storage space and so that would limit the amount of time I could capture. Uh which was entirely new problem that I hadn't had ever experienced before. Um but basically like you can just see that year over year I've been iterating and creating uh an environment where I'm getting more and more data creating hardware making changes for thank you. Uh so that's how this is going to work. Okay good to know. Um I love you guys. Basically you're I'm creating a situation where I'm just collecting more and more data and figuring out the bottlenecks and figuring out how to do it. So when you have that much data um how do you do an analysis on it? Um it gets kind of rough right? Uh I don't know how many have opened up uh a 2 gig p- uh 2 gig file size PCAP in Wireshark before. Anybody? A couple of you? What does that feel like? It's painful right? It hurts. Like you're just like I want it to query faster and it just doesn't and I mean it's it's PCAPs are complicated. They cover a lot of data. So um yeah and then uh I used another tool called Network Miner. Network Miner uh the the creator that offered uh supported me with a license because he thought my research was kind of cool. Um and that's great for data spot checking right? But if you're going to thoroughly look across your entire data set that's maybe not the best solution. Uh another tool that I use is I use Kizmet as I talked about. Uh Kizmet has a wonderful web UI that allows you to search in real time. So that's great for like if I'm trying to figure out what the threats are in the environment, what's going on right now in real time I can pull that up. Also you can now load your previous capture files into uh a running session and then from there you'll be able to then replay all that fun you just had. Um and then the other cool thing about Kizmet is it's stored in SQLite database. So you can just immediately open it up in your favorite SQLite data browser or even you write some Python scripts and start scraping out some really interesting data without getting into you know processing PCAPs. So and then I came to a point where I'm like all I want to do is I want to run a thousand instances of T-Shark at the same time. And I couldn't find anything that exists so I built a tool. Uh shout out to Ellicontaro for making this sick logo for me. Thank you sir. Um so PCAPinator basically it's a tool that runs a ton of T-Sharks at the same time. So here's the uh the help file for it um and it gives you some of the base information. Uh right now what it supports is it will pull like DNS out, it'll carve it out, it'll carve out uh wireless information like all of the MAC addresses involved in commute wireless communication, the frame types, SSIDs, fun stuff like that. It'll also grab handshakes and it will push, it will convert them all the way to HCX files so you can dump them right into a hash cat if you're down with crack and passwords for some reason. I don't know why that would be useful. Um and then also the GitHub link is right there on there and I'll also have it at the end of my slide. Uh that is live right now so I just opened it up a little while ago. So you can go get on that. Uh don't judge me harshly, it's still really rough around the edges. It's uh first like major release of code into the wild so uh yeah we'll see how this goes, yellow. So this is just a quick example of PCAP destroying my uh 96 core uh 48 core uh 48 logical or uh 96 logical core server. Um yeah so it's it's pretty effective I'd say. Alright let's do a quick demo video. Okay so in this demo video oopsies. Let's see I would have had a demo fail. Uh so in this demo video basically what we've got is we've got a 2.5 gig PCAP file and on the top we have just a single T shark instance running and on the bottom I'm running PCAPinator and so uh they're running the exact same query basically I'm just pulling out uh Mac address and a bunch of wireless information and what this is doing is it's actually taking the PCAP and it's uh splitting it into a bunch of uh individual PCAP files and then it processes each of those smaller PCAP files uh on um uh on uh uh at the same time. And so uh that that file took 5 minutes and 49 seconds to process whereas traditional T shark took 19 minutes. So that's significant and also there's still room for improvement. I always leave like you know things in my code so that I can always make it better and faster later because you don't want to you don't want to do your best work on the first shot right? Okie dokie. Alright so what did y'all do last summer huh? Let's get into this shall we? First off let's let's get to know you a little bit shall we? So uh people bring their devices to DEF CON you know as you do and those devices are happy enough to probe out you know things and look for networks that they want to connect to and there's this wonderful website called wiggle dot net that you can then cross reference those SSIDs to and from there you can create a map of where you're from! And so the other interesting thing is on here, oh cool 10 minutes, um uh the other cool thing about this is uh you've got uh uh uh a lot of WPA2 so I'm really happy you guys are using it your home networks and at your work it looks like most of you are using WPA2. However Russia there's a lot of unknown up there and I don't know what you're doing but I want in on that action I want to get some more unknowns on wiggle. So if you know that secret let me know. Alright let's dive in a little bit now too take this from a little bit different angle uh this is uh showing population throughout the world where you're coming from and so the larger it's a heat map so you know the larger the dot the higher the place that you're coming from. So this was pretty interesting to me too. I don't know what's going on over there I believe that uh uh oh I just forgot Baton Rouge I believe is what that is. So I don't know what they're doing over there but there's either a lot of people there or a lot of devices or something's happening there. Pretty interesting. Alright let's look at South America. The one thing on this one that was really interesting to me is over in Chile. Like you see that just nice heat map all the side up that uh on the side of Chile over there. That was pretty interesting. Alright let's look at uh let's look at Europe now. And for me the most interesting thing on here was the one in Iran. Whoever's wiggling in Iran in Tobriz dude shout out to you let's keep it up let's wiggle all the things. We need every place wiggled on earth alright. I need that I need that to happen for you guys. And now we're looking at Asia you can kind of see what's going on here. This is it's it's crazy you know we can kind of see these heat maps and look at where people are from. Okay another thing that we can do too is because I don't just know the SSIDs you've been beaconing I can know the MAC address of the devices you're beaconing or probing or connecting to so your MAC address. And what can you do with that? When you've captured data at multiple conferences uh thanks to this tool called graphistry uh I was able to create this wonderful graph and each tiny little dot that you see on the screen there is a MAC address of a device that's been at a conference and so this is the only filtering that's here is uh if it has been at two or more conferences. So as you can see there's quite a big flow over from black hat 17 to DEF CON 25 which makes sense you know there's some pretty good overflow from there people come over um and then there's other some other small conferences uh St. Con, Shmucon, Cactus Con and DEF CON uh DEF CAMP uh to say a few um and I mean it's just interesting to see these these groups uh and then the ones that are most interesting are the ones year to year. So we can definitely see that DEF CON has some retention um for people coming back. I don't know why. Why why do we keep coming back? It's amazing that's why. It's amazing. Alright let's talk about wireless attacks. They happen. We have wireless attacks. Strange right? So a number one thing that I I see and it's really noisy and it's really loud is de-authentication attacks. And one thing that's kind of helpful is you randomize your MAC and then when you randomize your MAC address you did it so it's an unknown OUI, an unknown vendor. So basically what that's telling me is this is somebody doing shady stuff so I'm gonna keep track and try to then figure out where you are and triangulate and try to track you to try to track you down. Uh so maybe pro tip for all of my red team fellows in the audience or not fellows excuse me all you red teamers in the audience um uh uh uh go ahead and use like a Cisco OUI or something and they'll and someone will look at it and be like oh my gosh you've got an AP that's malfunctioning. It's not really de-authenticating it's an AP. Let's go track down this AP that's miss that isn't working correctly. Uh so the other types of attacks that I saw was there was a couple of um what looked like cracks attacks. And cracks attack the key reinstallation attack is is one it's really difficult to identify by just passive monitoring. So I am just passively listening. I do not connect. I do not make an active connection with anyone. I'm just sitting in the environment doesn't even know that I'm here. So um you need more information than that. But however based on the fact that these are unknown vendors uh we know that it's something really weird is happening um and so that we could go do more uh more investigation into what's going on. Um and of course it's DEF CON so we're going to see you know Pineapples Karma attack uh Pine AP uh we're going to see man in the middle stuff that's going to happen there um and what's even more awesome is when you leave the MAC address is zero one or zero zero one three three seven uh you know because who knows what that is. Um and there were at least 50 of those. Now on the other side let's say you want to go freak out somebody that's got a wireless IDS uh you might as well just start using that OUI for everything. Uh another thing too is people really like to mess with SSIDs for some reason. Wait what what number was that? Okay uh they they like to mess with SSIDs for some reason. They throw in more data and just it's it's crazy. So yeah there's a lot of things you can look for in this data. Uh also there's a little bit of wall of sheep action. Um most of this I think is just super trolley people trying to trying to uh do some clear text stuff to be funny. I don't think any of this is like legitimately like wall of sheep. Um but uh yeah some pretty funny stuff up there. Uh also there were some data leaks uh you know cause sharing is caring uh this is from uh website called met dot no. It looks to be some sort of weather related uh could be an app. I'm not sure I couldn't find a lot of information on it. Uh but it does leak uh your latitude and longitude. So if this was something that was given privileged information for that from your phone um yeah yeah you you just gave me your your latitude and longitude thanks in a get request uh completely in the clear. Also the API is is been upgraded. It's been upgraded to 2.0 as you see at the bottom there. Uh still is in the clear though. So uh and there's another one too. This one is uh Accu-weather and this is a ZTE desktop widget or yeah desktop widget from an Android phone. So uh yeah what's up with these leaks on these APIs? Another one I found was this is uh an Alienware bloatware um and it contacts back to the server with uh serial number, Windows build, etc. So uh thanks to you know Dell support website I was able to find out that your warranties expired. So I'm sure they can help you with that. Uh we also can see DNS right?  Um so we know that people at least wanted to go to these websites. I don't know if they did, I don't know what's going on but they definitely tried. Um at least looked it up. You know there's a couple on here you know Fine Aid you know who's going to come fill out their financial aid. I mean this is a great place to figure out your career and what you want to do but doing your financial aid at DEF CON maybe wait till you get home for that one. Uh huh also uh Pornhub uh I know I know I just go there for the stats too. Oh another wonderful thing is um yeah like uh Slack uses uh uh sub uh sub domains which is beautiful right? So now I know all your super secret slacks. And why haven't I been invited? Alright so let's talk about some of the summary real quick here and wrap this up. DEF CON is truly a global community. We're going to have DE-Auths uh it's a protocol level issue we've got I mean we we need stuff to happen to get that better. Pineapples are a thing and they are going to happen. APIs are going to leak. Uh DNS is DNS. For some reason I don't know why you guys use Slack. Uh and also I just want to say you know don't believe the hype because that was one of the things that I looked into this the reason we brought this out is like this is the most dangerous everything's your own as soon as you connect. It's like don't believe the hype like use common sense like don't just connect to the open wifi and then log into your bank right? Um use the secure there's a secure for a reason there's you know use cell phone service uh uh uh uh instead not 3G not CDMA none of that make sure it's 4G or 5G uh which leads me to my next asterisk um I don't know I heard there was research being presented on the LTE stuff uh so uh asterisk I'll get back to you on that uh some other points I want to just point out on how to counter measure and protect yourself. Don't auto enable auto connect um I know phones now have the ability to do geofencing so do that so the that way you're you can broadcast uh only connect to the the geofenced area where you're there. Also use VPN but verify your VPN actually works uh the way you think it is so scan your traffic cause you don't want to be leaking out of your VPN. Um I just want to say thank you to DEF CON and hack 5 and Kismet, Sankon, DC801, Network Minor, Graphistry, the uh and so many more there's so many people even in this audience that have that have helped me and built me up and made me like able to do this to be here on this stage I'm so thankful for that and I especially want to say thank thank you to every single one of you because you know the the likes on Twitter the you know the fact that you're here like it blows my mind thank you so much I'm super honored uh to have been able to do this project and to present it to you and and to see your guys's reaction your reactions I'm very thankful of that and with that I thank you.


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