وسيد المرسلين حبيبي إله العالمين المصطفى بالقاسم محمد الموضوع اليوم هو فمانيزم قبل أن أرى الموضوع أنه مهمة أن هذا الموضوع هو مدينة وموضوع يمكن أن يتحدث عنه في كل أسبابه في one night في حال đây it is a course that can be taught at university over a whole semester one can look at it from the perspective of the rise of Western feminism one can look at it from the influence of Western feminism on Islamic feminism يمكن أن يجرحها من المؤكد الإسلامي مع المؤكد من العالم المسكولي يمكن أن يجرحها من المؤكد من العالم المسكولي أو المقابلات الذين يقولون أن يجب علينا أن نذهب إلى أجهزة التعامل التعامل الأسلحة ومن ثم يجب عليكم الذين يسمعونهم أسلاميك الذين يقومون بين أسلاميك والأسلاميك الذين يريدون أن يقومون بين أسلاميك والأسلاميك والأسلاميك ولكن يجب عليكم أن تبحث عن طريقات التعامل الأسلحة ومن ثم يجب عليكم أن يقومون بين أسلاميك والأسلاميك ومن ثم يجب عليكم أن تحديث عن طريقات التعامل الأسلاميك الذين يقولون أن يجب عليكم أن تبحث عن طريقات التعامل الأسلاميك في مقصد التعامل الأسلاميك الذين يأتيون من أشيعي المدرسة لذا فرح أن تحديث عن طريقات التعامل الأسلاميك والأسلاميك والأسلاميك في مقصد التعامل الأسلاميك توجد تقديم ذلك أو تأخذ طريق الانشعي ربما سنذهب إلى أمينة ودود توجد هيفا جواد هذا الموضوع يمكن أن يكون. هذا أتمنى أن يجب أن تقوم with you to appreciate that it is impossible to discuss this topic in one lecture unless you want to stay here until Salatul Layl which is good مستحب إن شاء الله but i don't think many of you will remain and then it will be you and I إن شاء الله therefore our discussion tonight has to be very specific hence we are going to take a look at four points إن شاء الله the first point is what are the standards that the Quran sets for the rankings of humanity are these rankings based on gender are these based on race are these based on some other factors so we're going to take a look at that and that will be the first point second we will need to define feminism because feminism in itself has many definitions third based on the definition of feminism we need to take a look at are there any possible gender differences and fourth we come then to the islamic context with regards to the definition of feminism that we will be using and seeing if islam supports such a definition or not and we'll take a look at only very specific examples some of you might leave tonight and say well the sheikh did not touch upon this idea he did not touch upon this حديث as I mentioned it is impossible to discuss everything within an hour long lecture but we'll just touch the tip of the iceberg إن شاء الله so the first point on what basis does islam rank humanity is it on the basis of race and the answer is no الله says explicitly in the Quran لا فرق there is no difference between an arab and a non arab أعجمي except with one thing what is it تقوى god wariness and god piety تقوى can be translated as piety god consciousness or god wariness that is the first mode and way الله سبحانه وتعالى ranks humanity بسم الله رحمن رحيم الله says in surah الحجورات يا أيها الناس oh people إن خلقناكم من ذكر وانثا وجعلناكم شعوبا وقبائلة لتعارفوا إن أكرمكم عند الله أتقاكم oh people we created you from a male and a female and we've made you into societies شعوبا and tribes this may be a reference to the rural world the rural life where الله talks about قبائل and the urban life شعوب societies so we've divided you or we made you into these different societies different cultures different traditions on what basis so that you can get to meet one another recognize one another and الحمد لله in this part of the world you get a taste of different cultures in one city but then الله says إن أكرمكم عند الله أتقاكم the most honored of you before god is the one with the greater god wariness or god consciousness or piety that's one second way الله سبحانه وتعالى evaluates people and ranks them is on the basis of knowledge علم الله says قل هل يستوي الذين يعلمون والذين لا يعلمون do those who know equal those who don't know there is a difference those who have knowledge versus who don't those who do not have knowledge but what kind of knowledge any knowledge some of the مفسرين they suggest that those who definitely have knowledge have علم they cannot be treated equally to those who don't have علم regardless of what that علم is what that knowledge is educated people definitely make more contributions to the society than those who may not be educated that's what some people suggest however others say not necessarily as we mentioned last night you have many educated people yet they use their education in the destruction of humanity like i mentioned last night those who create all these weapons of mass destruction who makes them educated people and therefore what they refer to as علم as knowledge is the علم of الله سبحانه وتعالى the knowledge of الله recognizing الله سبحانه وتعالى for you may have someone who is uneducated yet he is a humble submissive servant to الله سبحانه وتعالى and you have someone you might have someone who is highly educated yet he or she may not even recognize Allah سبحانه وتعالى and that's where Allah سبحانه وتعالى says raises the ranks درجات means the ranks in jannah raises those who have believed amongst you so belief is important but those who believe and have knowledge in other words they fear الله they have god consciousness والذين اوتوا العلم درجات those who are believers are god conscience and they have knowledge yes الله will raise them into higher ranks in jannah indeed it is the scholars who fear الله سبحانه وتعالى the most greatest so that is the second basis of الله سبحانه وتعالى differentiating upon humanities the first one is تقوى god consciousness the second one is علم the third one is عمل actions actions he is the one who created you والذي خلق الموتى the one who created death and life to test you to examine you which one of you has the best deeds the best actions of course these actions are virtuous actions blessed actions and then we come to the ayah that we recited at the beginning of the majlis from surat الناحل الله سبحانه وتعالى says بسم الله الرحمن الرحيم من عميل صالحا anyone who performs virtuous deeds من ذكر او انثى بيت ميل او في ميل وهو مؤمنون and he is a believer or she is a believer فلنح ينه حياتا طيبة we will make them live a blessed life a good life a life with good quality ولا نجزي انهم اجرهم باحسني ما كانوا يعملون and we will reward them with the best of what they used to do their believers their good doers they perform actions الله says we'll reward them with the best this is out of Allah's رحمة this ayah shows us how merciful is الله سبحانه وتعالى how much Allah wants us to go to jannah he says he will reward us with the best of our deeds how many times have we prayed a person reaches the age of 50 60 years how many times has prayed or she has prayed how many times have we fasted the month of ramadan some people go several times to hajj in their lifetime الله out of his رحمة out of his mercy will choose the best salah that you performed in the 50 years of your life or 60 years of your life that one day when you had some خشوع in your صلاة he will choose that صلاة and he will make all the other صلاة equal to this one out of his رحمة احسني ما كانوا يعملون with the best of what they used to perform you fasted for 50 years which day did you fast with sincerity to Allah you did not backbite anyone you did not disobey Allah you spend the day reading the Quran helping the people الله will choose that day and will make everything equal to this day out of his رحمة you see how merciful Allah is that's why i don't want to get away from the topic but i'll mention this very briefly إمام السجاد عليه السلام was told there was a scholar at his time by the name of الحسن البصري they told him he says i am not surprised at those who do not make it to heaven they end up in the hellfire i'm not surprised how they end up in the hellfire i am rather surprised at those who manage to make it to jannah because of all the desires all the temptations of this world et cetera et cetera إمام السجاد says says that's what he says however what i say and we know whatever إمام السجاد says is the saying of رسول الله صلى الله عليه و آله is the saying of الله سبحانه و تعالى he says however what i say he says i am not surprised at the one who makes it to jannah how he made it to jannah i am rather surprised at the one who ends up in the hellfire how did he end up in the hellfire why what does الله say my mercy has encompassed everything الله عارب his رحمة really wants people to go to jannah he created us to go to jannah not to punish us but a person he or she himself chooses to go to jannah he chooses or she chooses going back to the point we see that there are three things تقوى god consciousness علم knowledge about الله سبحانه و تعالى believing in الله the greatness of الله سبحانه و تعالى greater submission to Allah that's what the greater knowledge would lead to and the third is what forgot already masha'Allah العمل good masha'Allah the ladies are really paying attention tonight i have to really watch myself tonight عمل your deeds your actions your virtuous deeds and all those three things الله سبحانه و تعالى did not say men only it's general اكرامكم عند الله اتقاكم انما يخش الله من عباده العلم هل يستوي الذين يعلمون والذين لا يعلمون perform the deed الله will see your deed et cetera et cetera none of these three الله سبحانه و تعالى puts any preference to male or female and in the ayah in surat al-Nahl that i recited الله سبحانه و تعالى يقول هل يحدث من يقومون بفرحة فرحة فرحة be it male or a female الله سبحانه و تعالى يقول and he or she is a believer then these people will have a blessed life all right so now this tells us that these are the three criteria on the rankings and they are neutral men and women okay so that's first thing second with this in mind then we see that islam is not against the rights of women but before we get there what is the definition of feminism here there are many definitions of feminism the one we are going to take is the one by the encyclopedia britannica which is written by doctor elinor burkett who is a professor of journalism at the university of alaska and she has written on the field of women the definition is simple she says or she writes in the encyclopedia britannica feminism the belief in social economic and political equality of the sexes so feminism is the belief in social economic and political equality of the sexes and hence this is the definition that we shall take tonight based on this definition are there any differences than between men and women in here some say yes some say no when we come to the moral psychology and the developmental psychology of people there is a very prominent name that comes up a man by the name of lorence colberg he was a professor of psychology at harvard he developed he was a student of another psychologist by the name of piaget a swiss psychologist and piaget is considered to be one of the first people to look at the moral development of children that children develop in stages they go through phases and of course this is in the academic world so piaget is one of the first who wrote about this whole thing he was a contemporary to another psychologist by the name of vygotsky who also wrote about children development colberg was a student of piaget colberg became a professor at harvard he developed what he called the six stages of moral development that the child or the people people go through six stages of development the last two stages of the moral development he says the second to last stage is the stage where people do what's right because it's the law يعني if the law says it's legal to do this people do it if the law says it's illegal to do this they will not do it he says most people will achieve that level most people get to that level however he says there is another a higher stage a higher rank and not every person achieves that level what is it he says doing what's right because it is right even if it challenges the laws doing what's right because it's right the examples people can give for example they give martin luther king jr martin luther king jr led the civil rights movement in the united states even though it was against the law but he challenged the laws he said we have to do what's right because it's right we need to ask for our rights another example people site is gandy in india although it was against the laws for him to protest to ask for peaceful demonstrations yet he challenged the laws he said we need to do what's right because it's right it's our right to ask for our rights and therefore challenge the laws you have to change these laws according to colberg not every person achieves that sixth stage interestingly however according to colberg he suggests that women do not make it to that sixth stage quite interesting one of colberg's students who graduated with him by the name of carol gilligan carol gilligan she became a professor later on in new york she went back to her professor's findings she noticed something all the test subjects of colberg were males or females males colberg only studied males so she said you know there's a flaw in the conclusion according to carol gilligan colberg has studied males and he says or he suggests that the pinnacle of moral development for the male is to do what's right because it's right even if it challenges the laws that's what he suggests how do we know this is the same pinnacle of moral development for women what if they have a different pinnacle of moral development so that's what she went out to study that's what she did her research on and she published a book in 1982 called in a different voice and that's where she made a very interesting discovery according to carol gilligan who claims to be a feminist however she says this is what she points in her words feminism is one of the great liberation movements in human history it is the movement to free democracy from patriarchy in that sense it's a movement to free everyone from the gender binary and the hierarchy of patriarchy in the interest of women and men and in the interest of love it is a way of dealing with human conflicts other than though the use of force and the imposition of hierarchy it seemed to me then to say if you think and listen what she says if you think you can explain the perpetuation of systemic patterns of injustice that is the repetition of a history of violence without a psychological or dynamic understanding then she comes to the conclusion psychology is integral to a feminism that is defined in those terms so she says psychology is very important when you talk about feminism you cannot isolate psychology from it what does she find what does carol gilligan find she finds that the pinnacle moral development for women is something she calls the ethic of care that women care about others for a woman she says their morality was based around care for others rather than appeals to seemingly universal codes of behavior so this is what carol gilligan suggests i repeat what she says the morality of women was based around care for others rather than appeals to seemingly universal codes of behavior يعني the conclusion of colberg that women cannot achieve that pinnacle of moral development is incorrect because the pinnacle of moral development is ethical care to look for others to care for others interestingly in 2014 there is a university by the name of vendor bolt in the united states they did a study this is a very interesting study they went to back in the 70s back in the 70s they went to gifted students these students were like the 1 top of their class gifted they had over a thousand boys and about 600 give or take girls they studied those individuals and then they went back to them for decades later so 40 years later when they studied them they were 13 year olds so four decades later how old are they don't scare me guys you don't know math come on i'm serious here four decades later they were 13 you know الله صلى الله عليه وسلم محمد thank you ladies for you they were in their 50s now so here is what they want this is what they wanted to study what did these people do these were gifted people very intellectual very intelligent they were the top يوخ الأفاضل ارفعوا أصواتكم بالصلاة على محمد وآل محمد الله صلى الله عليه وسلم محمد وآل محمد لقضائي حوائجكم ولتنالوا شفاعة السيد أم والبنين ارفعوا أصواتكم ثالثة بالصلاة على محمد وآل محمد شرفت سيدنا مولايا العفورج المعدة رحلة جسارة من عدنا الله سلمكم شيخنا الكنبي حياكم الله سلمكم شيخنا ما they found after four decades these were the top here is what they found they found the following the men are more likely to work in technology and engineering and to be ceos the women however were more likely to work in general business education and healthcare when it comes to finance medicine and law they were about equal the men are far more intensely engaged in high-powered careers they're engaged in high-powered careers they work long hours and make lots of money and listen to this only two-thirds of women work full-time these gifted women gifted men two-thirds of them only work full-time however listen to this and sisters you'll only like this one the women who are married have high earning husbands who make more than they do and the married men have wives who make much less both agree that family is the most important thing in their lives then they go on to say these differences do not stem from workplace discrimination it's not because the discrimination in the workplace both of them have that choice but this is the choices they made they're rooted in different preferences values and temperaments the biggest gender differences concern the role of work and achievement versus family and community the men want to make money excel at work and make an impact the women care more about free time and flexibility than money at the end they say what do these findings mean maybe that the women have been brainwashed but the authors suggest it's that there are multiple ways to construct a meaningful productive and satisfying life the authors suggest there are more ways multiple ways to construct a meaningful productive and satisfying life they do not quote carol gilligan in here in this study what's interesting is carol gilligan says that the highest pinnacle of moral development for women is to give up for others to look after others to care for others what this study showed that 40 years later these gifted boys and girls the boys became very successful ceos technology but the girls were more inclined to work in education and health care etc and two thirds of them only had full-time jobs so that tells us there may be a difference here between the demoral development of men and women according to carol gilligan the psychology of women differs from the psychology of men they have different psychologies different physiologies that's given that's taken but different psychologies that was something that was in you that she introduced so based on that we then come to the third point so what does islam say does islam give women social empowerment political empowerment financial empowerment let's take a look at the history of رسول الله صلى الله عليه واله and امير المؤمنين سلام الله عليه a lady came to رسول الله صلى الله عليه واله she said يا رسول الله we bear the children of the men of our husbands we take care of raising them we look after them when our husbands go for the fight the battlefield we take care of the children yet it is our husbands who fight in the way of الله do جهاد في سبيل الله they get killed they get martyred and they get these higher ranks how is that fair so the women of مدينة have requested me to come and speak to you رسول الله صلى الله عليه واله looked at them and he said at his companions he said have you seen a woman so outspoken like her they said no يا رسول الله she's very outspoken the prophet صلى الله عليه واله looked at her and said go back to the women and tell them رسول الله صلى الله عليه واله says that the work you are doing is not any less than what the men are doing in the battlefields and your reward is not any less than what the men are gaining in the battlefields islam recognizes there are some differences physiological differences maybe psychological differences and therefore islam gives different legislation for example with regards to جهاد fighting in the battlefield that is not imposed and mandatory upon women but it is imposed upon men just because men are the ones who go and fight in the battlefield that does not make them any better than the woman that's the reality and here is the حديث of رسول الله صلى الله عليه واله looking at this affirming this with regards to the political matter الله سبحانه وتعالى افرص to مؤمنات في سورة الممتحنا يا ايها النبي إذا جاءك المؤمنات to you بايعنك على أن لا يشكنا بالله شيئا when the female believers come to pledge their allegiance to you that's a political matter they're pledging the allegiance to رسول الله صلى الله عليه واله and there are some conditions that the quran lists tell them that they should look after الله فير الله and so on so forth there are some conditions six conditions listed in the آية the last آية of سورة الممتحنا on the day of غدير when when رسول الله صلى الله عليه واله introduced امير المؤمنين or announced that امام عليه صلى الله عليه is his official successor من كنت مولاه فهذا علي مولاه the muslims came and pledged their allegiance to امير المؤمنين سلام الله عليه then the women had to come how did they pledge their allegiance just like they pledge their allegiance to رسول الله صلى الله عليه واله how did the women pledge their allegiance to the prophet صلى الله عليه واله the prophet brought the big bucket of water filled it with water he put his hand on one end the woman came and put their hand on the other end of the bucket and that was their pledge of allegiance to رسول الله صلى الله عليه واله and that's how they pledged their allegiance to امير المؤمنين سلام الله عليه so they are practicing they are participating in the political process here is a question just as a side note very side note does رسول الله صلى الله عليه واله need the bay'a from the muslims الله made him رسول الله صلى الله عليه واله he Allah made him the prophet of Allah so why would why would رسول الله get the bay'a bay'a رذوان بيعة العقبة those bay'as those allegiance why would a رسول الله take them it is so that the people don't have a choice don't have a way of refusing or refuting so the prophet is dealing with the situation from the humanly perspective similarly with the bay'a of امير المؤمنين سلام الله عليه وان امام عليه became the caliph of the muslims is خليفة الله في ارضه does امام عليه need the muslims to pledge allegiance to him no he doesn't but to demonstrate that people chose him and therefore امام عليه use this logic this kind of logic to معاوية ابن ابي صفياد because that's the logic معاوية understands when he wrote a letter to him and he said when the ansar and the مهاجرين pledge their allegiance to someone then you have to be binding by that allegiance whether you were present or none present that was the logic معاوية understands otherwise to tell him i am خليفة الله i am حجة الله في ارضه معاوية doesn't understand that logic he doesn't accept that logic so to use that logic so that people can understand and hence when az-zubeir and t'alha wanted to negate the pledge of allegiance he reminded them you pledge your allegiance to me and therefore they became anakitheen those who revoked their allegiance to ali ابن ابي طالب صلاب الله عليه on that context the women participated in the political process even today in some muslim's countries in some muslim countries there are more female representatives in the parliament than in the united states senate so until this day and age islam does not stop women from participating in the political process islam from the women from voting their economic values their social values a woman comes to رسول الله صلى الله عليه و آله and she says يا رسول الله my husband has rejected me المجادلة صورة المجادلة he did he basically said you are haram to me like my mother is haram to me the prophet صلى الله عليه و آله ordered the man to come and he immediately dealt with the situation so the prophet صلى الله عليه و آله dealt with the matter the ayat of the quran المسلمين والمسلمات والمؤمنين والمؤمنات to the end of the ayah الله addresses male and female believers therefore from the quranic context from the history of رسول الله صلى الله عليه و آله and امير المؤمنين عليهم السلام they guaranteed the rights of women and they accepted their testimony a lady by the name of suda bint عمارة الهمدانية she was from the city of همدان in yemen when معاوية became the خليفة the people of همدان were very close allies to Imam علي عليه السلام very close supporters they supported him especially in صفين they were next to him when معاوية came he poured his wrath against them he seized all their land معاوية poured his wrath against anyone who supported Imam علي عليه السلام in مدينة for example he tripled the taxes so you can buy rice in مدينة the cost of rice well though there wasn't rice but قامح wheat and barley القامح in مدينة was tripled the price than the قامح in شام triple the price he tried to impoverish them so he fought against anyone because the people of مدينة الانصار most of them with where with Imam علي عليه السلام most of them so he poured his wrath against all those who supported كوفة he poured his wrath on them he put زياد ابن أبيه as their governor مدينة he poured his wrath on them he increased their taxes impoverished them همدان يمن he seized their lands so he poured his wrath his anger against them why did they support علي ابن أبي طالب he seized the lands from the people of همدان so suda this lady a lady gets up travels all the way from yemen to شام comes to see معاوية she enters معاوية looks at her says suda what brings you here weren't you the one standing next to علي ابن أبي طالب on the day of صفين reciting verses of poetry to encourage his army to fight against me and my army she says yes and if time were to go back i would do exactly the same thing i did but unfortunately علي سلام الله علي is gone times have changed and put you in power يا معاوية she says what brings you here he said what brings you here she says you have seized my land and the land of the people of همدان i am here to reclaim that land give us back the land he says what you have come to ask me to give you the land back get back get out and if you don't leave right now i am going to force that they put you on a camel with no respect and no dignity and be taken all the way back to همدان in a disgraceful manner suda at that point cried and she recited couple verses of poetry she recited two verses of poetry where she said that with the death of this great man justice was also buried when he was buried justice was buried with him she was among the first to say that justice was buried with علي ابن ابي طالب سلام الله علي she was among the first معاوية when he heard her he said suda who are you referring to is it علي ابن ابي طالب she said who else who other than علي ابن ابي طالب she said i came to علي ابن ابي طالب one day from yemen i came to كوفة i arrived at مسجد الكوفة علي was about to start صلاة الجماعة when i called him i said يا امير المؤمنين he left he stopped he didn't start the صلاة he came he attended to me he said what would you like what do you want what's the problem she said يا امير المؤمنين the governor you have imposed on us you put us on us in yemen he is not treating us fairly she said when i told him this امام علي cried and he turned to Allah and said يا رب do not hold me responsible for what he's doing i ordered them to treat people with respect with fairness with justice this is not what i told them to do he's asking Allah for forgiveness then he took a piece of what we call today paper he had a piece of leather in his pocket he took it out and he wrote a letter on it like a piece of paper and a pen he wrote a letter on it where he said the minute that you received this message of mine you are dismissed from your post and someone else is going to come and take over from you he closed the letter he gave it to me and he said suda go back and take this letter to him he says that's how علي ابن عبي طالب dealt with the situation and look at the difference between you and him i come to you and i tell you your governor in yemen is stealing our lands and you're telling me this is how i'm going to treat you and send you back disgracefully look at the difference between you and علي ابن عبي طالب علي ابن عبي طالب سلام الله عليه listen to me he gave me dignity respect and then imam علي went back to the salat you see imam علي علي سلام did not tell her you're a woman what brings you here go back not at all with utmost dignity with utmost respect listens to her complain answers deals with the situation and then sends her back when معاوية hear this he says okay suda okay i'm going to give you your land back i'll give you your land he says to his writer he says right please make a note that suda bint عمار الهمدانية gets her land back she looks at him and she says معاوية i didn't come here just to claim my land i am here to claim everyone's land tell your writer to write all the lands are back he looked at her with anger he says علي ابن عبي طالب made you guys in such manner that you can talk because he was so fair he was so just he would not punish you he would not harm you so you guys became outspoken she said معاوية right he turns to his writer he says okay خلص give her all the land she takes that land she takes that paper and she gets out that's suda bint عمار الهمدان that's one example this is how أهل البيت عليه مسلام this is how the prophet امير المؤمنين dealt with women in the political process in the financial process looking after the welfare of the women they came to imam علي عليه السلام they said there is a lady who is working she takes takes care of preparing the brides when they get married the brides she's the one who it's like today what we call the salon the hair salon back in those days she was the one he says لابس he says no problem what's wrong with that that's fine she can do that so when we talk about equal opportunities when we talk about and social matters and political matters and economic matters Islam is full of such examples so here then we come to two important points if that were the case then how about the issue of حجاب because some feminists especially the secular feminists the secular feminists are you against this point they say حجاب limits the woman حجاب does not allow women to be liberated to be free in here there is an issue that i touched upon couple years ago in محررام so i will not invest a lot of time on it i will touch upon it very briefly but the question is about حجاب and sisters do we have unlimited freedom is there such thing as absolute freedom are you free to drive on the road any way you want or are there laws to limit how you drive especially here in london masha'Allah with all the cameras masha'Allah the other day someone tells me even in the parking they have cameras they're waiting for you not to pay so masha'Allah the minutes you don't pay you'll receive a gift card in the mail when people know this they will adhere to the law سبحان الله again a side note i don't want to go into this field or talk about this people are worried about the cameras of the police but they're not worried about the radar of الله سبحانه وتعالى and the cameras of الله سبحانه وتعالى الله سبحانه وتعالى is watching us الله is looking after us yet we don't care we do whatever we want that's why Imam السجاب عليه السلام says i am the one who disobeyed the great one of the skies nonetheless can you drive any way you want no you can't can you get up on the plane as it is on the middle of the air and you stand by the emergency exit door and you say الله أكبر الله أكبر huh what will happen someone comes to you what are you doing freedom of speech i'm practicing my freedom of speech they say okay when we descend insha'Allah there you will find out your freedom of speech in the prison go therefore there is no such thing as absolute freedom and that's why i quoted back then a paper which i will remind you again of it a paper that was published back in 1998 by a professor of political science at the university of oklahoma his name is dr herzk h e r t z k e dr herzk has a paper called the theory of moral ecology in that paper he says that notion of freedom has led to the problems some of the problems we see in the society today because it's a false notion to be free to do whatever you want there is no such thing as absolute freedom but it's something that used in different ways when it comes to disassociating yourself from religion not implementing religious values people say freedom we are free to do whatever we want and people are promoting this but when it comes to driving when it comes to speaking in certain areas starting in certain things there no no no here we have to limit what you say and what you do well that's double standards in a book that was published back in 2004 by a professor by the name of petrice oplinger from boston university this is what she says i will not read the title of the book but you can look at her name petrice oplinger o p p l i g e r she says in the book instead of advancing women's power popular culture tends trends in the united states appear to be backsliding backsliding into sexual exploitation of women advancing for women power this is not advancing women's power what she's saying what she's saying is popular culture trends in the united states it's backsliding it's backsliding there is exploitation is the word she uses when it comes to hijab of course there is a physical form of the hijab and then there is a social form of the hijab and this applies to men and women how do you deal with each other how do you interact with one another with modesty with respect and the same rules apply online people these days when they go online they feel that no the guard is down i can say whatever i want i can write whatever i want i can do whatever i want and that is not true these guidelines exist and parents really need to pay attention to the technologies to what's going on today it's really a difficult world today to keep up with all the apps and the technologies and what's coming up we give our children these tools but we don't look after what's going inside them there is an app which i will not mention its name but that app looks like a calculator on the outside it's very innocent it's a calculator so if you come to your daughter or to your son say can i see you gadget there you go you look at it oh mashaAllah everything looks halal here no problem it's a calculator but once you enter a specific code on that calculator the app changes and opens a whole world of pictures there is where some of the teenagers and the youth are hiding stuff why would they keep their pictures there well i'll leave the answer to you why aren't their pictures in the photos well we'll leave that up to you but that's what we need to look up and look after what are our children doing online nonetheless and this is causing a lot of problems men are talking to women none محرام they don't really care about the guards the same guards rules apply whether you are talking physically or you're talking online with respect with dignity with modesty therefore these things are extremely important that's the modest part that's the social part then we have the physical form of the hijab which for women is to cover the whole body head to toe with the exception of the face and the hands up to the wrist and to make sure that a woman does not wear anything tight to reveal her figure in addition the majority of the فقها they also add that no makeup visible makeup can be shown the men too one day i was صلاة and my صلاة was so after i prayed i moved back to the line when i moved back there were some youth praying in front of me in the line every time we go to ruku i have to close my eyes if you know what i mean and i'm thinking to myself why are you wearing this to the حسيني or to the mesjid fashion so that's the social form of the hijab and there is also the physical form of the حجاب now what does the quran say in صورة الأحزاب الله says ذلك أدنى أن يعرفنا فلا يؤذين when they wear these losing clothes clothings it's best that such that they are recognized as مؤمنات and they are not harmed here is something interesting listen to these brothers and sisters because the feminists argue they say why should i dress the way so that i will not be harmed by the men the men have their own problems they need to turn their faces away خلص i should not that's the whole essence of feminism to do what i want to do wear what i want to wear not to be dictated by other person i have news for you this harm may not necessarily be coming from men it may be coming from women how so شيخ in a study that was published in 2008 by a professor by the name of shelly grave g r a b as in boy e shelly grave she wrote that 50% of girls and undergraduate women in the united states suffer from physical and psychological disorders because of the perceived or portrayed image of perfection by the media in the media when they look at women how they're portrayed female models continuous exposure to this message that this is the perfect look the perfect ideal than when girls 50% of girls and undergraduate women in the united states are suffering because they look at that image and they look at themselves and say i am not pretty enough in the united states there are 100 330 million people so when we talk about 50% of female how many of girls are undergrad how many are we talking about here let's say 330 let's say 300 to make the math easy divide them by half you know 50 50 male female okay out of the 150 million how many of them are girls and undergraduate women what 50% 10% 20% here we're talking about 30 million 40 million do you know something that's the population of canada so almost the whole population of canada is suffering from mental and physical disorders because of that portrayal of the perfect image not by man but by woman زمانسكي another professor he wrote another paper called the objectification of women he says continuous or she says continuous exposure to these beautiful looks make women want to objectify themselves treat themselves as objects and here we have problem with the boys as well because the boys are also looking at these beautiful women when it comes time for marriage if they look at a محجبة they say no i don't want her i don't this is she's not pretty i would like someone who puts makeup on someone who wears the tights that's what i would like and unfortunately what happens is sometimes a lady would say i would like to get married but nobody wants to come and marry me i am محجبة مؤمنة i wear my abaya that's the fault of the boys the men we need to really address this issue as well therefore when it comes to hijab it introduces this modesty the save guard for women the protection of women not necessarily from from men as the feminists might argue we say women from women so that's something important the second point and we'll finish with this inshallah that will be the last issue we discuss and that's marriage marriage is extremely important in islam some feminists would argue they say no i want to be liberal i want to do whatever i want we read the a lady comes to imamo صادق عليه السلام and she says i do not want to get married he asks her why not she says i am a person who is a devout worshipper i don't want the husband to tell me you can't fast today you cannot fast the other day you know i want this i want that i want to be free to worship Allah the way i like he looked at her and he said who is better you or my mother فاطمة عليه السلام she looked at him and she said obviously she's صحراء صلى الله عليه وسلم much better than i am he said then she got married to ali ابنى بيطالب سلام الله عليه you think her marriage to amir al mu'mineen decreased her عبادة stopped her from worshipping Allah decreased her status before Allah but what's important my brothers and sisters is that the men and the women need to discuss if they are going to get married if there are important things for the man or for the woman you need to discuss them before the marriage don't say i'll wait until the marriage happens and then we'll talk no for example if the husband to him if it is very important that the woman for example if they have children he wants the wife to stay at home and raise them for example he needs to address that issue if the woman decides no i want to work i got a degree and therefore i want to work after marriage then discuss that issue discuss it and come to the agreement come to the consensus how do you want to move on in your future and move on in your lives it's important you can have conditions in the marriage contract even when it comes to the according to some interestingly amina wadoud says is the right of the divorce it's in the hand of men what's interesting about amina wadoud when she writes she writes from a non-shi'a perspective when i read about her writings and what she's doing a lot of her interpretation comes from the or similar to the shea she quotes non-shi'a and she says there is a problem with these we say well look at what the مفسرين say because the تفسير is not up to a person it's up to what Allah says فسألوا أهلا ذكر بيس on the حديث of أهل البيت عليهم السلام even the مفسرين of أهل البيت they read they look the شيعة مفسرين the scholars they see what did رسول الله say what did أهل البيت عليهم السلام say and that's how they discuss and interpret the quran not based on whatever they think not about this قوامية it's divorce correct the divorce is in the hand of the man however in many countries in the muslim world iran included you can have a condition in the marriage contract you can have a condition that if the husband for example if he abuses me emotionally physically if god forbid he becomes you know alcoholic if he starts gambling والعياذ بالله if he starts taking drugs والعياذ بالله then i have the right he gives me the power of attorney and the authority to divorce myself if he accepts this condition then it materialized in the marriage contract so the marriage life is really important but it's a partnership brothers and sisters marriage is not about you have to do this and i have to do this my way or the highway it doesn't work that way الله says about marriage مودة ورحمة love and mercy mercy this is mercy if i see the wife tired خلص i go help her with the chores in the house that's what imam علي used to do سلام الله علي help a say the zahra in the chores of the house not the concept the concept where i am the man of the house خلص any man who helps his wife in the chores of the house achieves the ranks of the صديقين at the same time the wife helps the husband if she sees him tired he's working hard if there is love amongst them if there is agreement mercy between them she helps them husband the husband helps her that's really the example we see in the life of امير المؤمنين سلام الله علي and the say the الزهراء and أهل البيت عليهم السلام لذلك هل اسلام يدخل فمانيزم if we define فمانيزم as ترغب المساعدة ترغب المساعدة ترغب المساعدة but keeping in mind that she and the man are different فيزيولوجيا maybe different فيزيولوجيا and therefore the rules are different then islam is talking about جندر اكوتي not the gender equality and that's what we have to understand اكوالتي is an equation 2 plus 2 equals 4 two sides are equal men are not equal to women فيزيولوجيا they're different, psychologically possibly they may be different and so on so forth but there is gender equity the prophet one day goes comes to the house of a say the الزهراء عليه السلام he finds امام علي is working with her on the hand mill so he asks which one of you two is more tired امام علي answers he says يا رسول الله i am stronger than افاطم عليها سلام she's more tired than me she's she's tired so the prophet says يا فاطما step aside he sits down and he starts doing the hand mill working in the house of a say the الزهراء عليه السلام this is the اخلاق of رسول الله ان اهل البيت and in the sheeah school of thought brothers and sisters we have great examples and role models like a say the خديجة a say the الزهراء السيدة زيناب الكبراء عليه السلام السيدة نفيسة who was a teacher of الشافعي الامام الشافعي he used to study with a say the نفيسة he would go visit her he would go visit her السيدة فاطم المعصومة in fact i was teaching i'm teaching at one of the local universities in canada i taught a class i told them them to the best of my knowledge the only dynasty in the history that is named after a woman is the فاطم الدينس تي that is named after فاطم الزهراء عليه السلام the sheeah give high reverence to the status of women and this is being practiced until this day and age what we need to understand كالتر is different from religion yes in some cultures women's rights are abused correct we don't deny that but don't mix this with religion and that's what haifa jawad who is a feminist she's written an article about feminism that's what she asserts don't mix culture and religion culture yes you may have oppression of women but the religion does not oppress women إسلام تريد women with utmost dignity utmost respect and when the quran gives examples to the males and the females Allah gives examples of two women not men and later on و مريم ابنة عمران الله uses the wife of فرعان أسيا and مريم as an example as role models for men and women these are real we have فقها today who study the فقه of السيد الزهراء عليه السلام we derive knowledge from her so if a woman is more payas than a man she has a higher rank than than him in the eyes of Allah سبحانه وتعالى if she has greater knowledge she has higher rank if she works more diligently in the way of Allah she has a higher rank this is the reality brothers and sisters that's reality and this extends to this day and age until this day and age and hence when the islam religion comes to the lady a noble lady what a virtuous lady what a great lady this lady who served أهل البيت عليهم السلام to the point where she became among أولياء الله الصالحين بابن of أبواب الحوائج one of the gates of حاجات the followers of أهل البيت give utmost reverence to a سيد أم البنين فاطمة الزهراء عليه السلام and back to the rights of women this lady when the family and the caravan of إمام الحسين عليه السلام left it went over to now she's waiting for them to return back she's waiting she lived with أمير المؤمنين such a loving life such a great life and أهل البيت gave her utmost respect she became one of them as we read in the مصاعب when زيناب عليه السلام came back to her house and she said no one to enter and they heard the knock on the door they said أم البنين is at the door can we allow her she says of course she is of us she became of أهل البيت عليهم السلام that's the reverence that's respect but she continued to wait hearing back maybe one day her sons will return إمام الحسين عليه السلام will return she used to wait until she heard one day the cry coming يا يا يا قاتل الحسين يا فأدم عين مدرا الجسم منه بكربا لا ورأس منه على القناع هيه دا بشر ابن حد لمدس بوته إبام السجاد مات at the outskirts of Medina. He said, Bisher, do you know some poetry like your father did? He said, يسي ابن رسول الله. He said, then go into Medina and mourn. The loss of my father, the martyrdom of my father, as we want to enter Medina when it is in the state of Azad. Grief, mourning. So Bisher says, I went to the city of Medina. I went by every house and I started calling them all people of Yathrib, which is the old name of Medina before the prophet arrived. Leave your city, leave, which is an ayah from the Quran. He started with that. People came out saying, Bisher, what is the matter? He says, the news will be delivered at the grave of Rasool Allah, صلى الله عليه و آله. When they arrived to the grave of Rasool Allah, he says, not a single person remained in their house in the city. Everyone came. That's what I delivered the news. Oh people of Medina, leave the city of Medina. As my tears are flowing from my eyes. Hussein has been killed in Karbala. His body is under the horses of Bani Humayah. And the head is on the spears of Bani Humayah. To ring from one city to another city. He says, when the people of Medina hear this, everyone started crying. Oh Imam, oh Hussein. He says, at that point I saw an elderly lady carrying a child. Approaching me, I asked, who is she? They told me, Bisher, be careful. This is أم والبنين الارباع. This is the mother of Abbaia. And his siblings. She approached me. I asked, who is the child? She's carrying. They told me, this is Al-Fadil, the son of Abu Al-Fadil Al-Abbaia. She came to me and she said, ya Bisher. I heard you have news about my son, He's my son. Tell me about him. She never asked me about her own children. He's my master. He's my beloved Abu Abdullah. He's back. He says, I didn't know where to begin with this lady. How can I tell her the news? I thought a little bit. So I told her, ya أم والبنين. Your youngest son was killed in the battle. She said, I didn't ask you about my youngest son. May he be sacrificed for Abu Abdullah. Tell me, did Abu Abdullah come back? I told her, ya أم والبنين. Your second son was also killed in Karbala. I didn't ask you about my second son. Tell me about Abu Abdullah Al-Khusein. Ya أم والبنين. Your third son was also killed in Karbala. She said, ya بشر. Tell me about Abu Abdullah Al-Khusein. Is he back? At that point I told her, ya أم والبنين. عظم الله لكل أجر. يا أشيعة الحسين. بمصاب أبل فضل العبار. Karbala. And you taught me. The news. The news is a lot. At that point بشر says, I saw her dropping the child onto the ground. And she cried and said, ya بشر. لقد مزقتني أطقلبي. You cut my heart into pieces. May all my four children be sacrificed for my master. أبي عبد الله Al-Khusein. Tell me, is Imam Al-Khusein back? At that point I told her. يا شيعة الحسين. قتل شهيدا فيي كاربالا. جسدو has been killed in Karbala. That's when she dropped the child and cried. ايو مدفو. She went to the grave of Rasul Allah. صلى الله عليه وآله. السلام عليك يا جدا. جئت كناعية ولدك الحسين. ها يزين ابديت. Then she went back to the house. What an empty house it is. As she enters into the house. She looks on one side. This is where أبي عبد الله used to pray his Salat. That's where علي الأكبر used to sit down and talk to me. This is where أبو فاضل العباص used to take care of me. This is the room of القاسم ابن الحسين. And that is the cradle of عبد الله الشهيد. In the morning they are in grief. She tells the women that close the doors. Don't allow anyone to enter. As we are in the state of عزاء. Morning of عبد الله الحسين. At that point they hear a knock on the door. One of the maids goes quickly. And then she runs back. She says Sayudati. أمو البنين is at the door. Shall I allow her to enter? She says of course. She is of us. So she enters. سلام الله عليها. The minute she sees Zainab. She cries. Zainab answers back. What happened in Karbala? I told Abbas to take care of you. How is it? I heard that you became a prisoner. She replied. أمو البنين do not blame أبو الفضل العباص. هده را هده صحيح.  عن ساعدة. صوت قسر أضلعي. سيدنا الجليل مولايت فضل. دعائلكم غجاءا. من خادمكم صغير. فضل مولايت. شيخنا الجليل مولايت فضل. فعو اديكم بالدعاء. اخذوا الهدس في الدعاء. This is the time when Hajat are accepted. باب الحوائج أم البنين. You are the guests of أمو البنين. سلام الله عليها. And insha'Allah she would not leave you leaving the house that is of her guests without fulfilling your Hajat. إن شاء الله the Hajat will be accepted in these eyes that are full of our tears for this noble lady and for her children and for أبي عبدالله الخسين. We raise our hands and our biggest دعاء is may Allah make us and our children till the day of judgment among the sincere shee'a of أسيد الزهراء عليها السلام. And the sincere servants of إمام الحسين. سلام الله عليه. Everyone together we have many مؤمنين who have requested us to remember them in our dua. Some are ill. Some are in difficulty. Some are imprisoned unfairly and unjustly. They are all in need of our dua and we all have Hajat. Everyone together. I don't want anyone to remain silent. أعود بالله من الشيطان الرجيم بسم الله الرحمن الرحيم أما يجيب المضطرة إذا دعا. ويكشف السوء. ويكشف السوء. ويكشف السوء. سنك وندعوك باسمك العظيم الأعظم الأعزل أجل الأكرم. Ten times together. يا الله. أودع فيها. اكشف عن السوء. يا الله. أغفر ذنوبنا. كفر عننا سياتنا. مع محمد وآم بباب الحوائج. أم والبنين. اقضي حوائج المؤمنين والمؤمنات. يا الله. شاف وعاف جميع مرضى المؤمنين والمؤمنات. يا الله. على الخصوص من أوسونا بالدعاء منهم. الله. اقضي حوائجهم. شاف مرضاهم. احفظهم في أنفسهم وفي أهلهم وفي أوطانهم بحفظك ورحمتك. يا أرحم الرحمن. اللهم اكشف هذه الخم عنها إلى يوم الدين. من شيعة الإمام الحسين المتقين. يا الله. ومن خدمتي المخلصين. يا الله. ورزقنا شفاعتهم في الدنيا وفي القبر وفي الآخرة. يا الله. ربغفر لي ولوالي دير وللمؤمنين يوم يقوم الحساب. ربغر حمهما كما رباني صغيرا. اجزهما بالأحسان يحسانا وبالسيات غفرانا. ربجعلني مقيم الصلاة ومن ذنبيتي ربنا وتقبل دعاء لوليك الفرج وجعلنا من شيعته وأنصاره وأعوانه والمستشهدين بين يديه اللهم كن لوليك حجت بن الحساب. ساعتك عليه وعلا في هذه وفي كل ساعة تسكنه كاتم اتعه برحمتك يا أرحمر رحمي لقضاء الحوائج شفاء المرض كشف هذي الغم عن هذي لما ولتعجيل فرجم ولانا صاحب والمشاركين وإلى رواح الشهداء والعلماء والمزيد من موافقية سماحت آية الله السيد هادي المدرس وأهله وعائلته وأولاده وسماحت الشيخ الكرام الأفاضل والمزيد من وطولته عمرهم إن شاء الله رحم الله من يقرأ السورة المباركة الفاتح


On July 1st, 1914, during the era of prohibition, General Order 99 was put into effect, banning alcohol consumption by sailors. Much of the order still holds up today, although sailors can now choose to drink responsibly ashore and on liberty. The Keep What You Learn campaign encourages responsible drinking by celebrating sailors' achievements in their careers. Through recognition of their hard work and dedication, sailors are reminded of their accomplishments and how much they have to lose if they make poor choices. The campaign aims to inform sailors on what it means to drink responsibly, promote alternatives to drinking, and educate sailors about the consequences of poor decisions regarding alcohol. To find out more about the Keep What You Learn campaign, visit the Navy Alcohol and Drug Abuse Prevention website. For more information about General Order 99, visit the Navy History and Heritage Command website.


Okay, so it says, name the period 3 element with the following ionization energies in right it's electron configuration, so the ionization energies are 1, 12, 1903, 2910, 49, 56, 62, 78, 22, 23, 0. So it says it's a period 3 element, that would be sodium, right, so where's the big one? And right here, right, okay, so sodium, right, magnesium, alumina, silicon, phosphorus, salt, right, and then it says write the electron configuration, let's just do it since the question says that. Let's write the electron configuration for phosphorus, what is it? 1s2, 2s2, 236, 3s2, 3p, so, and then another way, 1, 2. Questions on that before we move on to lab? Okay, good job guys.


In the previous lecture, we have seen that the interpolating polynomials may give poor approximation if we have too many node points. Especially if the node points are equally spaced, we may observe a visible oscillation in the graph of the interpolating polynomial near the boundaries of the interval of interest. One way to improve the approximation is to go for piecewise polynomial interpolations. We have learnt piecewise polynomial interpolations in our previous lecture and we have seen that there is still a drawback in this approach. What is the drawback? Well, the disadvantage is that piecewise polynomial interpolations using Lagrange's or Newton's formula can be non-differentiable at the node points. We can overcome this difficulty of loss of smoothness by imposing more smoothness conditions on the interpolant at the node points. There are at least two ways exist to construct piecewise polynomial interpolations with more smoothness at the node points. One approach is to use piecewise hermit interpolation and another one is splain interpolation. In this lecture, we will learn the hermit interpolation and postpone the discussion on splain interpolation to the following lecture. Let us first define the problem of our interest. We are given n distinct nodes x naught, x 1 up to x n and we also assume that the given function is sufficiently smooth. Well, before defining our problem, let us recall what we did so far in polynomial interpolations. We seek a polynomial of degree less than or equal to n such that the polynomial value at the node points coincides with the value of the functions at the corresponding node points. This is the interpolation condition that we have demanded on our interpolating polynomial and we got a unique polynomial of degree less than or equal to n when we are given n plus 1 distinct nodes. Now, in order to get more smoothness at the node points, we will have to demand more smoothness at the node points. For this reason, we will assume that f is sufficiently smooth and we will look for a polynomial h of x such that the polynomial value at each node point x j coincides with the function value at x j that is in this expression. I am talking about when you take k equal to 0 that will look something like this and in addition to this interpolation condition, we now also demand that our polynomials derivative of certain order that is let us denote it by m j for each j and we will demand the value of the derivative of the polynomial should coincide with the value of the corresponding derivative of the given function at the node point x j. So, this is what we will demand and at every node point, we may have different order of smoothness included in this condition. This is a general problem that we pose and we will ask the question whether we can find such a polynomial for a given set of n plus 1 nodes. Of course, the polynomial has to be of certain degree we will come to that point little later and such a polynomial is generally called the osculatory interpolation or it is also referred to as the general hermit interpolation. Let us see an example which is familiar to us the Taylor's polynomial. Let f be a c 1 function on the interval a b then we know that the Taylor's polynomial of degree 1 about some point x naught in a b is given by t 1 of x is equal to f of x naught plus f dash of x naught into x minus x naught. Now, let us take x is equal to x naught and see what happens. You can see that if we take x equal to x naught then t 1 of x naught is equal to f of x naught and in fact, we can also see that t 1 dash of x naught is equal to f dash of x naught. Now, let us compare this property with the definition of osculatory interpolation that we have defined in the previous slide. In the case of Taylor's polynomial of degree 1, we have only one node that is x naught and in this polynomial that is in the Taylor's polynomial of degree 1, we have taken m naught is equal to 1 and therefore, our condition now has to be h of x naught is equal to f of x naught that corresponds to k equal to 0 and h dash of x naught is equal to f dash of x naught. So, this is what we have obtained from the Taylor's polynomial of degree 1. Therefore, Taylor's polynomial of degree 1 is an example for the osculatory interpolation at one single node x naught with order 1 at that node right. We can in fact, increase the smoothness condition and the node x naught by one more for this we need to assume that the function f is a c 2 function on the interval a b then we can see that the Taylor's polynomial of degree 2 about the point x naught in the interval a b is given like this. Now, the question is this an osculatory interpolation at the point x naught if so, what is the order? Let us see it is not very difficult for us to see that if we take x equal to x naught in this expression then t 2 of x naught is equal to f of x naught then you differentiate t 2 once with respect to x and then put x equal to x naught you can see that t 2 dash of x naught is equal to f dash of x naught. Similarly, you differentiate t 2 twice with respect to x and then substitute x equal to x naught you can see that t 2 double dash of x naught is equal to f double dash of x naught. Therefore, you can again go back to the definition of osculatory interpolations and see that t 2 is an osculatory interpolation for the function f with single node x naught with order 2 at x naught that is m naught is equal to 2 as per the notations introduced in our definition of osculatory interpolations. Well, in our course we will restrict ourselves to a particular case of the osculatory interpolation and we refer this particular case as the hermit interpolation what is this particular case? Well, given a c 1 function defined on an interval a b let us consider n plus 1 node points in an interval a b. Now, the problem is to find a polynomial h of x well I will not always say this suffix 2 n plus 1 I will just say h of x this polynomial h of x is of degree less than or equal to 2 n plus 1 such that h of x j is equal to f of x j that is the interpolation condition of order 0 and then we will also impose the interpolation condition of order 1 that is h dash of x j is equal to f dash of x j and this should happen at all the given node points. Can you see why we demand the degree of the polynomial h to be less than or equal to 2 n plus 1 s? You can see that there are n plus 1 conditions from the function value and another n plus 1 conditions from the derivative of f. Therefore, totally we have 2 n plus 2 conditions right. Therefore, you have to have the degree of the polynomial h as 2 n plus 1 because in order to achieve this 2 n plus 2 conditions we have to have the degree of the polynomial as something like a naught plus a 1 x plus a 2 x square plus up to that many terms that results in 2 n plus 2 unknowns right. For that you need the degree of the polynomial to be 2 n plus 1 so that you have 2 n plus 2 unknowns a naught a 1 a 2 up to a 2 n plus 1 that is why we need the degree of the polynomial to be something less than or equal to 2 n plus 1. Recall that this kind of condition is not something new to us the same idea was also adopted when we were constructing the polynomial interpolation in our previous lectures right. The same idea now, but we have some extra conditions that forced us to increase the degree of the polynomial right. There is nothing new in this idea note that we are only demanding order 1 here right at each node. Therefore, if you compare the definition of escalating interpolation in our previous slide what we are doing here is we are taking m j is equal to 1 for all j equal to 0 1 2 up to n right at every node we are only demanding the smoothness of order 1. In that way this problem is a particular problem of finding escalatory interpolation in general, but in our course we will call this particular problem as hermit interpolation. Now, the question is whether hermit interpolating polynomial exists for a given set of data right. Well first let us see how the data set should look like. Recall that when we were constructing polynomial interpolation using Lagrange and Newton's form we had only 2 coordinates x and y right, but we need one more extra coordinate now to construct the hermit interpolation that corresponds to the value of the derivative of the given function. Well here I have only given the value of the function as y naught y 1 up to y n and the values of the derivative of the function as z naught z 1 z 2 up to z n because these values may not come from some function in general they may come from any other source something like they may come from some experiments or so on. For that reason I have just posed the data set in a general notation. Well once we provide this data set then our theorem says that we can construct a unique hermit interpolating polynomial h of degree less than or equal to 2 n plus 1 with the required interpolation conditions as given here which we have shown in our previous slide itself. Now I am just using a different notation here instead of f of x j I am just using y j and instead of f dash of x j I am using the notation z j. In fact the theorem also gives us the explicit form of the interpolating polynomial and this explicit form is given like this the first term is the linear combination of h i's where h i's are given like this and you can see that h i's involve square of the Lagrange polynomials recall that l i of x is equal is the ith Lagrange polynomial you should go back to our previous lectures and recall how these Lagrange polynomials are defined. Now h i's are defined in terms of the square of Lagrange polynomials and also it involves the first order derivative of the Lagrange polynomial and you can see that the first term is written as the linear combination of x i's involving the function value y i's. The second term is written as the linear combination of h i tilde and also it involves the value of f dash at the nodes denoted by z i's here h i tilde of x is given by this formula again you can observe that h i tilde of x the square of Lagrange polynomial is involved in the definition of h i tilde also well in this way the Hermit interpolation is written in terms of Lagrange polynomials we can also write Hermit interpolation using Newton's divided difference we will not cover this in our course but interested students can learn how to write Hermit interpolation in terms of Newton's divided differences from many books for instance you can see burden and phase for more details well let us prove this theorem it is not very difficult to observe that h is a polynomial of degree less than or equal to 2 n plus 1 why is it so well you can see that each h i's and also h i tilde's or polynomials of degree 2 n plus 1 why because l i's or polynomials of degree n right and now you are squaring them therefore l i square is a polynomial of degree 2 n and you have one more degree coming from here therefore h i is a polynomial of degree something 2 n plus 1 ok similarly here also you can see that l i's or polynomials of degree n and since you are squaring this will be a polynomial of degree 2 n and then you have one more degree coming from here that will clearly tells us that h is a polynomial of degree less than or equal to 2 n plus 1 now our aim is to further show that the expression given like this is indeed the Hermit polynomial for that we have to show that the polynomial defined in our slide satisfies these two conditions at each node point let us see how to prove this let us take the first interpolation condition of 0th order that is h of x j is equal to y j for j equal to 0 1 up to n let see how to prove this recall in one of our previous lectures we have to this important property of the Lagrange polynomial right let us use this property to prove this interpolation condition how to do that well you can use this property of the Lagrange polynomial directly into the definition of h i and h i tilde and you can see that h i of x j also satisfies the same property as the Lagrange polynomial and also you can see that h i tilde of x j is equal to 0 for each j now going back to the expression of h that we have proposed in our statement you can see that h of x j is equal to summation i equal to 0 to n y i h i of x j and you can see that h i of x j is equal to 1 only when i is equal to j all other terms will vanish in this sum leaving only y j and what happens to the second term well the second term will vanish fully right therefore our first interpolation condition is satisfied by the h that we have defined in the statement of our theorem therefore the interpolation conditions of order 0 and 0 is proved now let us move on to prove the interpolation condition of order 1 for this let us first differentiate the given expression of h with respect to x to get this expression there is first understand how h i dash and h i tilde dash are obtained well just differentiate h i with respect to x we get this expression you can see that keeping this and differentiating this gives us the first term and similarly keeping this term and differentiating the second one gives us this term right well let us not disturb this part because this is not required in our proof therefore we will not try to compute this we will keep it as it is and see what happens to this expression when we put x is equal to x j you can see that when you put x equal to x j then this term vanishes for all i not equal to j right for i is equal to j you will have minus 2 l i dash of x i right because this term will become 1 in that case and let us see what happens to the second term again the second term will vanish for all i not equal to j here also it vanishes for all i not equal to j and what happens when we put i is equal to j then again this part of the term will vanish and because you have j here and i here when j equal to i this term vanishes and you will have only the contribution coming from the first term which will be plus 2 into l i of x i which will be 1 into l i dash of x i right.  Therefore, you can see that the first term of h dash now becomes 0 and we are left out only with the second term. Now, let us see what happens to h i tilde dash of x j for that first we have to differentiate h i tilde with respect to x whose expression is given like this when you differentiate it you get this expression again in this we have to put x equal to x j and let us see what happens when we put x equal to x j we get this expression you can see that this is equal to 1 if i is equal to j and it vanishes for all i not equal to j and then what happens to the second term well for i not equal to j this part will vanish when i is equal to j this will not vanish, but this will make this second term to vanish right. Therefore, as a whole the second term will vanish for all j equal to 0 1 up to n whereas, from the first term you will have h i dash tilde of x j equal to 1 if i is equal to j and 0 if i not equal to j from here you can see that h dash of x j is equal to z j and that proves the second level of interpolation conditions also right thus we have proved the existence of the hermit interpolating polynomial for a given data set and the formula is also given to us explicitly. Now, let us prove the uniqueness of the hermit interpolating polynomial for a given data set if possible we will assume that there exists another polynomial of degree less than or equal to 2 n plus 1 with the same condition and let us see what happens remember we already constructed a polynomial in this form and now what we are doing is we are assuming that there is another polynomial with the same property. Now, what we have to show we have to show that the polynomial that we constructed should be the same as the polynomial that comes from somewhere right. So, that is what we want to show if you show that then it means that this is the only form that you can have for the hermit interpolation. Let us define r of x as the difference between these two polynomials therefore, in order to prove that these polynomials are equal for all x we have to prove that r of x equal to 0 for all x right to do this let us first observe the following properties of r of x first is that since both h and script h are polynomials of degree less than or equal to 2 n plus 1 you can see that r of x is also a polynomial of degree less than or equal to 2 n plus 1 right. Second thing is since r is a polynomial of degree less than equal to 2 n plus 1 r dash of x will be a polynomial of degree less than or equal to 2 n also from the first set of interpolation conditions we can see that r of x has n plus 1 distinct roots which are precisely the distinct node points from our given data set right this is because at any node point x j r of x j is equal to h of x j minus script h of x j right. But we know that h of x j is equal to y j and script h of x j is also equal to y j therefore, they get cancelled and you will have r of x j is equal to 0 and this happens for each j equal to 0 1 2 up to n therefore, r has n plus 1 distinct roots also you can see that r dash has n plus 1 distinct roots y again you differentiate r with respect to x that will be h dash of x minus script h dash of x again when you put x equal to x j you have the second set of interpolation conditions that will make r dash of x j also equal to 0 therefore, the polynomial r dash of x will also have n plus 1 distinct roots. Now, let us take this condition that is r of x has n plus 1 distinct roots and we will use the roles theorem that implies that r dash of x will have at least n distinct roots. That is in between two node points say x j and x j plus 1 say r is something like this then you can always find a point in between x j and x j plus 1 let us call this as xi j at which r dash of xi j will be equal to 0. It means all this n roots which you found from the roles theorem are different from the n plus 1 distinct roots which we have already from our data set. These xi j's may not coincide with the node points that we have in that way r dash of x already has n plus 1 distinct roots plus now you have n distinct roots therefore, r dash of x will have 2 n plus 1 distinct roots that is what I am saying here r of x has n plus 1 distinct roots implies r dash has at least n distinct roots difference on the node points how well using the roles theorem and once you have this you can see that r dash of x has 2 n plus 1 distinct roots what is the problem with that well r dash of x is a polynomial of degree less than or equal to 2 n, but now it has 2 n plus 1 distinct roots that implies that r dash of x is a 0 polynomial that implies that r of x is a constant polynomial, but we know that r of x has n plus 1 distinct roots. In fact, if you know that r of x has 1 root that is enough to say that this constant polynomial is equal to 0 thus we have proved that the polynomial r of x defined as h of x minus script h of x is indeed a 0 polynomial that implies that h of x is equal to script h of x for all x in r and this proves the uniqueness of the Hermite interpolation. Let us take an example and construct the Hermite polynomial for this given data set remember we have 2 distinct nodes x naught and x 1 right which implies that we have n is equal to 1 and therefore the degree of the Hermite polynomial is 2 n plus 1 which is equal to 3 right that is we have to construct the cubic Hermite interpolating polynomial from the given data set. Let us recall the formula for h 3 from our theorem h 3 is given like this where now we have n is equal to 1 and h i's and h i tilde are given as they are in the theorem right to compute the cubic Hermite interpolating polynomial. We first have to find h i and h i tilde and then we can write them in this form right remember in order to find h j and h j tilde first we have to find the Lagrange polynomials therefore we will start with computing the Lagrange polynomials as a first step we will compute l naught of x remember this is your x naught and this is your x 1. Therefore, l naught of x which is equal to x minus x 1 divided by x naught minus x 1 is given like this similarly l 1 of x which is equal to x minus x naught divided by x 1 minus x naught is given like this. Now we have to construct the cubic Hermite polynomial from this data set let us recall the formula for h i of x which is given like this where i is equal to 0 and 1 for i equal to 0 h naught of x is written in terms of l naught which is given like this and for i equal to 1 h 1 of x is written in terms of l 1 of x which is given like this remember we have to also differentiate the Lagrange polynomials in order to substitute here right. Let us see how to get h naught of x h naught of x is equal to 1 minus 2 into x minus x naught therefore you have x plus 2 and then you have l naught dash of minus 2 you can obtain that from here and you can write it here and finally this term will become like this into l naught square of x. Similarly, you can get the expression for h 1 of x also and that is given by this right once we have this let us now go to find h i tilde how h i tilde is given recall the formula for h i tilde is this and again for h naught tilde we have to use l naught of x and similarly for h 1 tilde you have to use l 1 of x and for h naught tilde of x we obtain the formula like this and h 1 tilde of x is obtained like this. Now, we have h naught h 1 h naught tilde and h 1 tilde therefore we can now go to write the cubic hermit interpolation polynomial remember the formula is given like this right you have y naught h naught plus y 1 h 1 plus z naught h naught tilde plus z 1 h 1 tilde what is y naught this is y naught this is y 1 this is z naught and this is z 1. So, you have to substitute this values and you can leave it in this form or if you wish you can also simplify it to see that it is indeed a polynomial of degree less than or equal to 3. Let us visualize h 3 and in fact this data are taken from the sine function with the x values are taken in radians here the black solid line represents the graph of the sine function this one and the red solid line this one is the graph of the hermit polynomial h 3 that we have constructed just now. Note that from the given nodes x naught and x 1 with only the function values we will get the interpolating polynomial of degree less than or equal to 1 from the Lagrange form or Newton's form right, but here with two node points we got a cubic interpolating polynomial of course we have to also provide the information of the value of the derivative of the function that is the cost we are paying here, but we are getting a higher degree polynomial with just two nodes this is what we observe here you can see that at the node points the function value and the polynomial value are coinciding this is the first set of interpolation conditions and also you can see that at the node points the slope of the polynomial and also the slope of the function are coinciding this is the second level of the interpolation condition which is clearly visible in this graph right well as a next example let us consider three nodes and the corresponding function values and the values of the derivative again I have taken these values from the sine function with two digit rounding note that with this data set we can obtain the fifth degree hermit interpolating polynomial, but my interest is to obtain the piece wise cubic hermit interpolation for this let us first give the data set in two pieces the first piece has two nodes x naught and x 1 and the corresponding function values and the derivative values right this will give us the corresponding cubic hermit polynomial interpolation remember we have constructed this polynomial in our previous example, but now we will denote it by h 3 comma 1 of x because this is the polynomial that is coming from the first piece of the given data right now let us take the second part of the data set that is the nodes 2 and 4 and their corresponding values of the function and the derivatives again we can construct the cubic hermit interpolation in a similar way as we did in the last example and let us denote this hermit interpolating polynomial by h 3 2 of x because this polynomial is coming from the second piece of our data set now we will join these two to get the piece wise cubic hermit interpolation remember with the same node points with only the function values we can also obtain quadratic interpolating polynomial in the Lagrangian or Newton form or we can also find piece wise linear polynomial interpolation right you can see that the piece wise linear interpolating polynomials with the same data set can be given like this here p 1 1 of x is the linear interpolating polynomial written in the Lagrangian form coming from the first piece of the data set and p 1 2 of x is the linear interpolating polynomial again written in the Lagrangian form coming from the second piece of the given data set remember here we are only using the function values, but not the derivative values to construct the Lagrangian polynomials right the derivative values are used only for the hermit polynomials again combining these two piece of linear polynomials we can obtain the piece wise linear polynomial for the given data set and we also can obtain piece wise cubic hermit interpolating polynomial for the given data set let us try to show you see graphically how they look like the blue solid line represents the piece wise linear polynomial interpolation as expected we can see that there is a sharp edge at the interior node of the linear piece wise polynomial interpolation as remarked at the beginning of this lecture and also in our previous lecture the piece wise linear polynomial interpolation is not differentiable at the interior node point right whereas you can see that the cubic hermit interpolation is coinciding with the slope of the function at the node points that is at minus 2 here as well as at the node point 2 here and similarly the second piece that is h 3 comma 2 is again coinciding with the slope of the sine function at the point x equal to 2 and that makes the piece wise cubic hermit interpolation to be at least c 1 at the point x equal to 2 that is the interior node point whereas as I told the piece wise linear interpolation has a sharp edge here right so that is the main advantage of the hermit interpolation when we go to construct piece wise hermit interpolation we will gain one order of smoothness at the interior nodes whereas this is not the case with the piece wise interpolation coming from the Lagrangian or Newton form of interpolation as we remarked at the beginning of this lecture there is another way to construct piece wise polynomial interpolation with more smoothness condition at the node point called this plane interpolation we will discuss plane interpolation in our next lecture thank you for your attention.


Today's price is not the same as that one. This is the price you raise over. And then I got in trouble with cop killing. Okay, okay.  So it would have been a part two maybe.   Yeah, they had a script for it. Yeah, we on Boss Talk 101, 101. Yeah, we gon' talk. Y'all going to New Jack City. Yo, this is Queen Latifah. Bring the song to you. At this point. That New Jack City thing, I gotta get this out, man, so.  You know what I'm saying? That's how you livin', baby, even large, brother. When you think about the New Jack City, have you seen Wesley Snipes and those guys since all that happened? Yeah. Have the co- I mean, I always wanted to, you know I wanted a part two of this New Jack City. You know, in my mind, it was gonna happen.  I'll buy it now. You know, I'm like, we gon' get that thing. It got derailed because Wesley, when it did, he went and did Demolition Man. He got $7 million worth of New Jack City. That was the full budget. So he went up in his, today's price, not the same as that one, raising the price over. And then I got in trouble with cop killin'. OK, OK.  So it would have been a part two, maybe.   Yeah, they had a script for it. You ain't asking all these questions, man.  You put a lot of ads for it. No, I'm asking because that's my history. I'm just looking at what I love. And the script basically started with pretty much Wesley on a gurney in the hospital. That's what I thought. So he made it through. Damn. Yeah, that would have been lovely. And they wanted me and him to go after the actual people that were bringing the drugs in. He was going to go over to the other side. I was going to get gangster from that perspective. Wow. But with such an iconic film, I'm like, it should have came out. Well, it's all business. It's all money. You know, people that make movies don't watch movies. They just invest money, so the money doesn't add up. That's all that matters. Wow. My husband and I, we always have a debate on something. Well, let's finish this debate. Shut that down. Yes. Who started hip-hop or rock? Oh, yeah. Oh, that's an impossible answer. Yeah, yeah, yeah. You've got people like Coca-Cola Rock and, you know, I mean, the legend goes that had a lot to do with Ku-Herk. That's why she's Jamaican, man. This is not a good conversation. The legend goes that Ku-Herk was the first person that had the stereo that threw the parties. And he created the ability. See, hip-hop started with the breaks, the breaks of the record. That was the genius of hip-hop. Ku-Herk decided every record has a breakdown. It's a drum break. And it's where the music gets down. So he figured out why play any other parts of the record, only play the breakdowns. And they, now you've got only instrumentals. You've got the get-down. That's the best part. And he did parties where he would not have played anything but the breaks. Now there's a legend that says that the dancers were called breakdancers because they danced over the breaks. But then I just heard Crazy Legs, one of the OGs, Rock Steady Crew, say that breakdancing made up by his manager, Lady Blue, who just out of nowhere called it breakdancing.  I get a call the other day and say, Rudy Ray Moore Ryman was one of the first entries to Ryman and flipping. And you know what I'm saying? That's what I heard. It's possible. I don't know Ryman. Tina Marie Wrapped, a fatback band, King Tim the Third. But hip hop is in rapping. Hip hop is the culture. The culture. So rapping is a vocal delivery. A lot of people have tried, like Iceberg Slim, rapping. There you go. But the reason the rapper, like Melly Mel was the first person to use the term MC. The Last Poets. Last Poets, right, but it wasn't over a beat. So this rapping, the stuff I was doing wasn't over a beat. So it was a mixture of a bunch of things and stuff. Cowboy from the Furious Five was the first person to say hip hop. So all these things turn into a culture. And the hip hop culture is four elements. It's DJing. You could be a DJ. That's part of the culture. A graffiti artist or a graffiti writer. They call them writers of dancer or MC. The MC's early job was because the DJ was playing and these breaks was to talk about the DJ. But then like from Jamaican, you have the toasters. You have the people that chant over the DJ. But it's really all about the DJ. The DJ, how great the DJ is. That's why early rap groups are Grandmaster Flash and the Furious Five. Jam Master J and Run DMC. Fresh Prince. I mean, Jazzy J and French Prince. The DJ starts first because without the DJ ain't no party. I can't show up rapping. Ain't nobody playing no records. I mean, he got to come with all the equipment so I can do my thing. That's why you wanted to be a DJ in the beginning when you came out. And I started to get more love from getting on the mic.  New crates. Yeah, so I hooked up with the New York City spin masters, Hengy and Evil E. They were from Brooklyn. And they were already spending at parties in LA. So I hooked up with them. They knew how to scratch. I said, look, let me show up at your parties with you. And next thing you know, I got my name on the flyers and stuff and that's how I started getting around LA. I told Faze on last night.  Said that he won a contest and you was the one that he won it.  Hey, but I actually asked him how he got to deal with the good names. You really want to hear this? Oh yeah? Yeah. Yeah, that's another story. Wait a minute, Faze on top of it. He said he was a DJ. He said he used to make some scratch. Said he won a contest. He won one of your contests. He might have. And I'm like, I don't remember. I won a contest. I won a contest at Carolina West where Curtis Blow was the judge. Whoa. See y'all don't forget that. And you can't forget that when you win some at that early, early over stage. And really that was the moment I thought I really could do it. Because Curtis Blow was a real rapper. Yeah. And he was a star. And for him to say, I had enough to win that contest, I left that night like, I might have some action at this. And then I didn't really take it serious. Then I saw Run DMC at the Sports Arena.    So I was like, now I'm hustling. So my nigga's like, you better get this money, man.  Yeah, nobody bought no cars rapping. Like, cause no one had made no bag yet. You know, it was just something to do for fun. So when I saw them, it was like, this is about to be big. And that night I think I went home wrote an album. Like, I went home and started working on my craft. Motivation. Yeah, that was the motivation. Yo. Boss talk one on one. Now get it. Yeah, we on Boss Talk TV. Shout out to Ihi, the reason you see me. We doing numbers. Y'all looking PV, y'all looking hungry. We looking greedy. Remember back then, we were Pope. Next to you.