So, now let me begin with the topic at hand today and the topic at hand today is properties of fluid. In the properties of fluids, we have looked just now at so far at gases, which we say are simple compressible systems or a system containing a gas is a simple compressible system. And in particular, we looked at a special kind of gas, an ideal gas. We looked at it for two reasons. One reason is it has a very simple set of isotherms, the equation of state is very simple. An ideal gas is obeys two laws, Boyle's law, which says that p v is a function only of temperature and we define the Kelvin scale. So, that we can write it as in a simple form p v equals r t and it also obeys Joule's law, which says that u is a function only of temperature. Then there are gases, which do not behave like an ideal gas. We have real gases for which none of this is valid. We will have a very complicated equation of state and then we have liquids like water, engine oil, mercury and all that. Gases and liquids can flow. So, we call these as fluids and then there are substances similar to liquids, but which cannot flow. These are solids like stone, rubber, metal, what have you. But all these materials are such that a thermodynamic system when you include them is likely to be a simple compressible. Of course, certain assumptions will be involved. For example, we will assume that the gas is not charged or the molecules of the gas are not dissociated because if they are charged or they are dissociated then we can do electrical work on them and then it would not remain a simple system. Similarly, a liquid it is expected that it is not a magnetic liquid or electrically conducting liquid like mercury or it is not a dielectric liquid because if it is so, then we can do electrical work or magnetic work on them and again it will not be a simple system. And the same thing is true of solid. We expect the solid to be not a charged solid or not a magnetized solid because in which case it will not remain a simple compressible system. So, whenever we have a gas a liquid and a solid under certain simple situations, we can consider them as forming a simple compressible system. But it is necessary for us to look at the basic difference between them although they are compressible system. Let me draw a huge p v diagram so that I can make things clear. And let us say that we consider two pressure levels say one at one bar and one at two bar. Let me write specific volume let me say I am taking 1 kg of that substance. If I take a gas typically the density is low the specific volume will be large. And if I compress it I will find that my volume for a gas from an initial state of one bar if I compress it isothermally I will end up with a final state at two bar where the reduction in volume will be of the order of 50 percent. This is what happens for a typical gas. A liquid typically has a much higher density than a gas. So, you take a liquid at one bar and try to compress it it does get compressed. But the reduction in volume is pretty small you can say this will be of the order of may be a few p p m say approximately 5 parts per million or 50 parts per million of that order very small not 50 percent 50 parts per million. So, this is typical of liquids for solids typically solids liquids have the same density. But let me show it slightly different for solids also when you compress it from one bar to two bar there will be a difference in volume difference in volume will be so small that is this is of the order of 1 to 5 p p m for a typical solid. So, this is the main difference between a solid a liquid and a gas. And we have equations of state for gas rather simple if you assume it to be an ideal gas we will have a very simple equation of state p v equals r t later on we will see more and more complex equations of state. For liquids the equations of state are still complex for solids they may turn out to be still complex. But whenever we have a system containing a liquid and a solid and we have it as a simple compressible system then we can say that solids and liquids are almost incompressible. And just the way we can say that many gases are almost ideal and continue using the ideal gas law for them. Quite often we can say that solids and liquids which are almost incompressible can be considered to be really incompressible. And in that case we will have a very simple method of managing their properties thermodynamically. When we come to the properties of water and steam in their state space there is a zone where we using some approximation like this we will come to that when we come to exploration of that part of the state space of steam. Now when we work as mechanical engineers there are two most important fluids for us one is air and another is water. But unlike air which quite often is always in the gaseous form we know air can be liquefied and we work with liquid oxygen, liquid nitrogen and other components of air. But usually we can get away by assuming air to be made up of a single component and remains always in the gaseous form not only that unless we go to very high temperature or very high pressures we can assume that air behaves almost like an ideal gas. And most of our engineering calculations and design of aircraft compressors is done routinely assuming air to be an ideal gas that is not true of water. Water we know is easily available in three forms or three phases solid which is known as ice, liquid for which we do not have any name water and gaseous or vapor form which we know as steam. The technical name for all these things together and to remove the confusion between water as a chemical compound and water as a liquid a proper thermodynamic name for this is water substance. Water substance means the chemical compound known as water either in its solid liquid or vapor form gaseous form. So, a water substance in the liquid form will be known as water, water substance in the solid form will be known as ice and in the vapor form will be known as steam. Now, if you talk to a high school student for a chemist you will say that look we generally write water as the chemical compound represented by the formula H 2 O. But we also have heavy water known as D 2 O. And if you take naturally occurring water it is a mixture of H 2 O and D 2 O the abundance of D 2 O is of the order of 70 p p m in naturally occurring water. Most of it is H 2 O, but D 2 O forms a small part and D 2 O is an important industrial fluid particularly useful for nuclear power generation using certain routes. We use it in India in a large number of our nuclear power plants and that has to be extracted by separating it out from this naturally occurring water. And when we talk about properties of water we must be very clear which water we are talking about. Are we talking about pure H 2 O? Are we talking about pure D 2 O? Or are we talking about the naturally occurring mixture of H 2 O and D 2 O? It turns out that the abundance or the fraction of D 2 O in naturally occurring water is so small that no effort is ever made to obtain pure H 2 O. So, all the water which flows through our pipes, falls as rains, fills our lakes and rivers which we drink this water contained in this bottle which I will drink sooth. All this is this naturally occurring mixture and this is what we call as ordinary water substance, ordinary water and in any of its phases it will be ordinary water substance. And when we now use the word water or steam or ice it is actually not H 2 O, but the ordinary water substance which is the naturally occurring mixture of H 2 O and D 2 O. And this is an important fluid unfortunately it is so complex occurs in all three forms that there is no simple equation of state. Of course, using a large amount of experimental data and very powerful computers people can use it. People have fitted a very complex equation of state, it requires something like over 200 parameters compared to that remember our ideal gas law P v equals R T uses just one parameter and that is R. And because there is no simple equation of state the properties are tabulated or they are graphically expressed. The advantage of a graphical expression is that you can see a large amount of information in a small space, but the resolution is poor not good for calculations. And hence for understanding we may look at it graphically, but for calculation we will be using the tabulated data. And that brings us to our steam properties as tabulated in the steam tables. Now, I will assume that all of you will have a copy of the steam tables available with us and we will soon start exploring that, but before we come to steam table let us appreciate the state space of water. Now, initially there may be some confusion because when I say water I may mean water in the form of this liquid water which we drink or I may mean the ordinary water substance which may mean water ice or steam as appropriate. But soon we will get over this confusion when I wrote here state space of water I actually mean state space of ordinary water substance. Since there are three phases the first projection we see is what is known as the phase diagram. The phase diagram is nothing but the projection of the state space on the pressure temperature plane. And if you look at the phase diagram for water that is for ordinary water substance you will find that the phase diagram looks like this. It is split into approximately three parts by approximately we will soon see. There is some sort of a crooked y there. There is one point from which three lines go out one goes south west one goes almost north slightly towards west one sort of ramps up slowly in a crooked fashion, but ends at a point. And the roughly three zones because this ends you can say this is one zone, but we will consider them to be two to begin with. Tell us that if the temperature is low enough you end up with the solid phase this is where ice exists. This is where the liquid water exists and this is the vapor phase where steam exists. So, this is plotted by doing an experiment you put say 1 kg or some amount of water in a cylinder piston arrangement. Pressurize it to a pressure p bring it to a temperature t and see what is inside. If you see ice note that you are here if you see water liquid note you are here if you see vapor you are here. So, you will go on point plotting solid points liquid points and vapor points. And you will see that there is a boundary between solid and liquid which you will plot that is the way this is plotted. There is one point at which all these three lines converge and that is known as the triple point. Now, why is this a unique point a question was asked what is the importance of this. Remember that whenever you have more than one phases or more than one components physical chemistry tells us that the phase rule is in operation. The phase rule defines a relation between the number of phases the number of degrees of freedom will come define this number of components. We will not go into the detail if you really want the detail we study books on physical chemistry or recommended book for those who want to get into the absolute detail of the phase rule is a book by Findlay F-I-N-D-L-A-Y title is the phase rule it is a very old classic somewhat readable somewhat not so easy to read. The number of phase a phase is a distinct part denoted by a density. If at the same pressure and temperature you find if you slightly change the state you end up with liquid if you slightly change the state you end up with vapor you have two distinct phases. So, the phase is a generic name for the solid liquid and vapor these are three phases they behave slightly differently liquid and vapors flow, but solid and liquid have their own volume vapors will generally tend to occupy any volume that you make available to it. Solids will have a surface liquids will have a meniscus vapor will not have a surface of their own their surfaces will be defined by either solids liquids or other boundaries in which they are confined. Component are distinct chemical species now although we say that ordinary water is a mixture of light water H2O and heavy water D2O. There are two issues here that the amount of heavy water is pretty small just 70 ppm and whenever we work in our domain of thermodynamics in power plants we never change that composition. So, our number of components when it comes to water is 1. So, the right hand side 1 plus 2 becomes 3 on the left hand side we have this degree of freedom this degree of freedom is the is the measure of the variables like pressure and temperature which we can change and still remain in the same phase. So, for example, out here we have single phase vapor. So, number of phases is 1 right hand side is 3. So, number of degrees of freedom is 2 that means if you are here then I can change my temperature slightly and I will still remain in the vapor domain I can change my pressure slightly and I will still remain in the vapor domain. So, I have freedom to move temperature to a higher or a lower value I have a freedom to move pressure to a higher and a lower value. So, I say that number of phases is 1 the degrees of freedom is 2 and that is what happens in this zone in this zone as well as in this zone. Now, let us look at the triple point this is a point where you may have a solid from one side liquid from one side and vapor for one side this is a point triple point is all three phases are in equilibrium together. That means at the triple point the number of phases is 3 since the right hand side is also 3 the number of degrees of freedom is 0. And what does number of freedom of degrees 0 means I have no choice of varying the pressure I have no choice of varying the temperature. So, for a given component the triple point will be defined by a unique value of pressure and a unique value of temperature. And experiments with water show that this is 0.01 degrees C temperature the pressure is 0.006 1 1 2 bar that is about the triple point. Now, let us come to these three lines these are known as the phase separation line interface lines or simply phase lines. Let me draw this clearly again on another page this has become slightly too much theta it is almost straight slightly in line solid liquid vapor. Now, let us look at a point here I have here liquid plus vapor in equilibrium. Now, there are two phases in equilibrium the right hand side is 3. So, the number of degrees of freedom is 1 that means out of pressure and temperature I can select only one it is like this if I select pressure. And if I want to change the pressure and still have this liquid and vapor in equilibrium I cannot independently choose temperature if I change pressure I must change the temperature also. That means given a pressure the temperature for this liquid vapor equilibrium will be fixed as well as given temperature the pressure will be fixed for this liquid vapor equilibrium. And that is why we have this as a line indicating that for a given pressure if you want liquid and vapor in equilibrium this should be the temperature. And for a given temperature if you want liquid and vapor in equilibrium this will be the pressure. So, that is the meaning of this degree of freedom 1. Now, some nomenclature these lines which are interface lines in our thermodynamic nomenclature these are known as saturation line. So, this line going from triple point it ends at a point known as the critical point we will come to that later is known as the liquid vapor saturation line. Similarly, this line from the triple point going upwards there is no real end to it inside separating the solid phase from the liquid phase is the solid liquid saturation line. And similarly this line going from the triple point towards the south west if I may say. So, separating the solid phase from the liquid phase is known as the solid vapor saturation. We will come to the critical point when we study the liquid vapor saturation line in some detail. Now, let us look at some processes we may have an initial state in any one of these three zones. The final state may remain in the same zone does not matter, but interesting things happen when the initial state is in one zone and the final state is in some other zone. For example, if I take a liquid and increase its temperature at a given pressure. So, that it makes a transition from the liquid zone to the vapor zone that means the system initially contains liquid then during the process it converts itself into vapor. This is the process of vaporization or evaporation or boiling. On the other hand so, from liquid to vapor is the process of evaporation. If you go back from vapor to liquid like this that will be a process of condensation from here to here it is a process of condensation. Similarly, if you start with a solid and increase its temperature and end up with a liquid you have a process of melting. If you start with a liquid and go over to the solid domain you have a process of solidification or sometimes we call it freezing. So, this is the process of melting the reverse of that is the process of freezing or solidification. Similarly, if you come in the in this zone where there is a solid vapor equilibrium line solid vapor saturation line. You can start with a solid and increase its temperature and you notice that the solid converts itself into a vapor form that is the process of sublimation and you can take a vapor at low enough pressure reduce its temperature make it become a solid make it into a solid. You have the process of either solidification sometimes it is also known as condensation or sometimes it is known as desublimation of a vapor. So, this is sublimation and this is solidification or condensation of a vapor into a solid. In our study of mechanical engineering and mostly in power plants and refrigeration plants and typical heating and cooling utilities. We generally do not deal with the solid part although we create ice.  So, our interest essentially lies in the liquid and vapor zone and hence most of the steam tables tabulate this part of the state space pressure from triple point to higher values and temperature from triple point temperature to higher values. Again one should notice and remember that the temperature of the triple point for ordinary water substance is 0.01 degree C. The pressure at the triple point is 0.6112 bar 0.6112 bar 0.6112 bar 0.00 I forgot those two. Now, let us look at the liquid vapor saturation line in more detail. Now, I am sketching I will start only from the triple point I will not show the other two lines and I will go up to the critical point. I have called it critical point, but we have not discussed it yet. First let us see let us open our steam tables. Can you give me the steam table from there? We have this steam table with you you should have it and you should open it up. What I am going to do is I have a scanned version of this and which I am going to look at. So, that both of us are at the same page first we have to find out this relationship between pressure and temperature. This line is the liquid vapor saturation line and the terminology is this relation between pressure and temperature is known as the saturation relation or the saturation line relation. If this is the temperature T, then the pressure corresponding to the saturation line is known as the saturation pressure at that temperature and if you take any pressure P the temperature at which this line exists will be known as the saturation temperature of that pressure. This information saturation temperature as a function of pressure and saturation pressure as a function of temperature is provided in the steam table in tables 1 and 2. So, first I request you to open your steam tables on page 3, page 3 table 1 look at the first two columns only just now first column is temperature the second column is pressure. The pressure is the saturation temperature saturation pressure corresponding to that temperature. Now, this is not my copy. So, there is do not blame me for this mistake here this is triple point with a single P not double P should be t r i p l e and now notice that in this copy the first line has been struck off and I would like you to strike off or erase or use white fluid or mark off the first line and why is that that is because the liquid vapor saturation line starts from the triple point which is 0.01 degree C. You cannot have liquid vapor saturation line existing at 0 degree C.  So, just first row. So, just erase and neglect the first line the saturation data starts with 0.01 bar 0 1 degree C saturation temperature. Notice that the corresponding saturation pressure is 0.006 1 1 2 bar and you will notice that as the temperature goes up the pressure also goes up at the end of the first page at 35 degree C it is 0.05628 bar go to the second page 1 point here you notice when the temperature is 100 degree C the pressure is 1.01325 bar which is 1 atmosphere and that should be so because 100 degree C is the standard boiling point of water at 100 degree C water will boil if the pressure is 1 atmosphere 1 atmosphere is 1.01325 bar. And after that the tabulation is a bit crude only about 50 degree C till you come to the last point which is 374.15 degree C a pressure of 221.2 bar this is the point at which the table ends why does it end there that we will see soon. Now, this is the table where you have temperature sorry pressure given temperature. So, given temperature the saturation pressure is found from table 1 this is the information about this line the liquid vapour saturation line. Now, we go to table 2 where the same information is provided with pressure as the independent variable in table 1 you would notice that temperatures have round values there are only two temperatures here which are not round values 1 is 0.01 degree C triple point. And the second one is the last point 374.15, but now you come to the next page which is table 2 the title of table 2 and table 1 are similar saturated water and steam table 1 says temperatures from triple point to critical point. And table 2 says pressures from triple point to critical point look at the first two columns they are slightly different instead of temperature and pressure now you have pressure and temperature. So, table 2 provides the same information, but the other way round given a pressure obtain the temperature this is table 2. And you will notice that table 2 is printed at a finer detail starts with the critical point sorry triple point 0.006 1 1 2 bar goes at reasonably round values of pressures. And you will notice that the triple point temperature is 0.01 degree C goes on over a number of pages notice here pressure of 1 bar slightly less than atmospheric the saturation temperature is 99.6 degree C go to 1 atmosphere 1.01325 bar a non round figure, but important because it is 1 atmosphere it is 100 degree C as it is expected to be. And you will find that this is in much more detail this is its third page fourth page up to 20 bar fifth page up to 70 bar sixth page ends at 221.2 bar where again the temperature is 374.15 degree C. So, the information in the first two columns of page 1 and page 2 is the same information tabulated in two different ways one is tabulated with temperature as the base round values of temperature the second one is tabulated with pressure as the base round values of pressure.  So, this is the liquid zone this is the vapor zone. So, suppose I take a state here I will see only liquid suppose I take a state here I will see only vapor, but suppose I take a state here exactly on this what do I see what happens is if you approach this state from the liquid zone you will end up with a liquid which with a slight rise in temperature will move into vapor. And if you start from this end you will end up with vapor which at a slight decrease in temperature will move into liquid I will I am not showing the origin indicating that I have taken a part in between, but this is pressure I am enlarging small part this is liquid vapor. And I am taking a point here and looking at the state here if I come from this side I get the limiting liquid state if I come from this side I will give a limiting vapor phase. And it is possible that because the two states will have the same pressure and same temperature if I enlarge this I will see a system containing liquid and vapor together. And you know we will always be under the influence of gravity however low. So, if you look at it the thing will look something like this you will have liquid and you will have vapor in equilibrium with each other. So, both of these will have the same pressure and same temperature the liquid will settle because of gravity, but let us neglect the small pressure difference because of the gravitational pressure gradient. If you neglect gravity then you will have a mixture of liquid bubbles in vapor liquid droplets in vapor mixed with vapor bubbles in liquid a very foamy type of a thing is what is going to happen if you really take it to a place where there is absolutely zero gravity. But what you have is liquid and vapor in equilibrium and that is what we mean by two phases together the pressure is the same temperature is the same, but the density here is different this is density of vapor and this is density of liquid and the denser part will settle under the influence of gravity. So, this is what is the scheme and now because there are two distinct densities there are two distinct phases. So, we have the limiting liquid phase and the limiting vapor phase the limiting liquid phase is known as saturated liquid and the vapor phase is known as dry saturated vapor. The technical meaning of these terms is the saturated liquid phase is the liquid phase which remains in equilibrium at the same pressure and temperature with its vapor phase saturated liquid is a liquid that remains in equilibrium with its vapor phase and dry saturated vapor is the corresponding vapor phase which remains in equilibrium with its liquid phase. The word dry is used to indicate that the vapor does not have even a speck of liquid inside it. This word dry or the adjective dry has come up from the fact that when you create the vapor from a liquid the vapor rises over the liquid and quite often droplets of the liquid are carried with the vapor. So, by dry saturated vapor we mean remove all those droplets have a vapor which is free of liquid that is why the adjective dry and the term dry saturated vapor. Since the densities are different properties other than pressure and temperature are all likely to be different. There is no guarantee that they are different the densities will definitely be different other properties are likely to be different and our steam table tabulates those properties. The nomenclature is let me use another page so that things are not cluttered. The saturated liquid state is denoted usually by the symbol f the dry saturated vapor state is denoted by the symbol. For example, the internal energy will be u f enthalpy h f specific volume v f specific entropy s f we have not yet defined it, but it is tabulated. So, we will look at the values similarly for the dry saturated vapor corresponding properties will be noted as u g h g v g and s g. Let us look at our table again and see those values and again you have a choice of either table 1 or table 2. Let us look at any one of them let us begin with table 1. Let us come to page 4 and let us say at 100 degree c let us look at the figures at 100 degree c the saturation pressure is 1.01325 bar that means when I go to the this thing if I select my temperature to be 100 degree c my pressure is 1.01325 bar and now let us look at the properties of the saturated liquid state and dry saturated vapor state at 100 degree c which means at 1.01325 bar and out here you will notice that the specific volume of the liquid I am rather away from the title I cannot bring it. It is here just about there 001044 meter cube per kilogram is the specific volume of the liquid 1.673 is the specific volume of the vapor meter cube per kilogram. Notice that the vapor occupies a much larger volume compared to the liquid. So, the liquid is very dense the vapor is very light. Now, you have the internal energy of the saturated liquid state uf 418.9 kilo joule per kilogram and internal energy of the dry saturated vapor state at 100 degree c. Similar you have enthalpy of the liquid state neglect this column for the time being enthalpy of the dry saturated vapor state and entropy of the saturated liquid state and entropy of the dry saturated vapor state. Again you will notice that for enthalpy between h f and h g there is a column which is h f g and for entropy between s f and h g there is a column which is s f g.    But even if you drop these two columns the value of the steam table does not get reduced because that information can very easily be computed from the neighboring columns. And just the way you go down to say the pressure base table come to page 10 let us look at what happens at higher and higher pressures. Let us go to a pressure of 100 bar saturation temperature 311.1 degree c. Notice that the difference between the specific volumes of liquid and vapor has now reduced 001452 meter cube per kg and 0.180 meter cube per kg. You go to still higher pressures you go to 200 degree c 200 bar temperature 365.8 degree c pretty high. You will notice that the volume difference is still low 0.002036 and 0.00583 and you go to higher and higher pressures in corresponding higher and higher temperatures you will reach a point 221.2 degree c sorry 221.2 bar as the temperature is 374.15 degree c where you will find that the liquid specific volume and the vapor specific volume is the same 0.003155 degree c meter cube per kg. That means when you come to the critical point there is no distinction between the liquid phase and the vapor phase. And because of that you will notice that the saturation line ends at the critical point. As you approach the critical point the distinction between the liquid and the vapor reduces and at the critical point difference between liquid and vapor vanishes. So, they do not remain to distinct phases anymore and that is why this line ends at the critical point. Going back to our table notice that critical point is at 374.15 degree c, 221.2 bar pressure. The liquid specific volume and vapor specific volume are the same not only that you will notice that the specific internal energy of the liquid and vapor is also the same enthalpy of the liquid and vapor is also the same giving you hfg to be 0. And entropy also of the liquid and vapor is the same giving you hfg to be 0. I think it is just past 11. So, we break for t we will continue our discussion at 11.30.


I'm Victoria Adebayo, I am a senior studying physics at Howard University and I am a member of the IBM HBCU Quantum Center. The IBM HBCU Quantum Center is a consortium of institutions, primarily historically black colleges and universities, that is working with our industry partner, IBM, to bring quantum research and education to the black community. This is a new field. So one of the goals of the center is that we can diversify the population and the people that are thinking about how we build the technology, but also how it's used. Being a part of the center is about having access to this entire network of black people who are interested in quantum research. The focus since the beginning has been on making this technology available to as many people as possible. If the people who are using this technology don't look like the full representation of the human population, then we're not attracting the best talent. We founded the IBM HBCU Quantum Center in 2020 with Howard University. It was at the height of the pandemic and right after the murder of George Floyd. It was also the start of all of these black and x movements, black in computer science, black in physics. We got to see all of these communities coming together celebrating black scientists and researchers. Often we are getting funding for the postdoc and the graduate student, very limited or no funding for the undergrad student. IBM Center is giving us that opportunity. HBCUs have created so many of the black professionals that we have in the US today. Supporting and nurturing talent at these institutions will prepare the nation for what's coming. That's the Quantum Revolution 2.0.


بداية بسلاعة عمار noise كانتا مرضنا ومن المريضه رفعه كانتا مرضنا الأمراض الخبيت لكن تصنع بالاستاذ بالجهد تصنع بالاستاذ بالجهد وكانا تعاون تعاون كل شيء ممتاز من الاستاذ بالجهد بشأن يج сдنديه دكتور راع و الحمد لله توصن لديكتور أكثر من راع هو الدكتور صنجيف الدكتور صنجيف دكتور أكثر من راع وديكتور الإنساني أكثر من ما هو ماتي أكثر يعني دكتور ببعنى الكلمة والحمد لله وشكرت أجران العملية وكانت العملية كل الش صعبة وناجحة ونجحت وطولة العملية تغريبا أكثر من 11 شاعة أكثر من 11 أو 12 شاعة والحمد لله وشكرت كله من نجاح والآن الحمد لله كانت نسبة الدم نسبة الدم هي المريضة صفع المياه والحمد لله هالآن هتعاش ملبية وكانت عراد شديد للألم والحمد لله الآن سوف نرجع غدن إن شاء الله إلى العراد أخبر صنجيو كما أنا كنسا سبيتاليس فأنا نظر after gastrointestinal cancer so my patient, Mrs. Bada she traveled all the way from Iraq she was suffering from recurrent rectal cancer a cancer which has record and this time it was very bad it was involving the uterus it was involving the urinary bladder and also the rectum she had received chemotherapy and radiation but of no use she came in a very bad state in India when I saw her in the OPD her hemoglobin was 7 her body weight was only 27 she was wheelchair bound she was not able to move and she was not smiling the surgery was very challenging because the urine passage and the rectum passage had communicated and stool and urine was coming out through the vagina and she was an infection so she was optimized for surgery and she underwent a very challenging surgery which is known as supra levator total pelvic exteration in which her urine passage her stool passage and also the uterus was removed by God's grace they recovered surgery well and she was discharged from the hospital on post of day 7 and she is doing fine she is gaining weight now she is 35 kg she is walking around and also her hemoglobin has improved to 11 she has received her first cycles of chemotherapy after the surgery and she is flying back today home happily


Now, let us now take this specific special case, the special case is this. So, now my dynamics are given in this sort of form, I have x k plus 1 is given as a function x a k x k plus b k u k plus w w k and this is we define this for k equals 0 till n minus 1. The cost function, if you want to minimize, you want to minimize this cost function over all such policies, cost function in this takes this form. So, the terminal cost is actually is quadratic in the terminal state in this form. So, it is x n transpose q n x n and the cost at each stage, the stage wise cost are also quadratic and in this sort of form, it is x k transpose q k x k plus u k transpose r k u k. Now, the matrices here are of appropriate dimensions. So, we assume that these matrices q n, q k, r k these are all square matrices a k, b k are matrices of appropriate dimensions so that they have so that this state equation can actually the dynamic state dynamics can actually be written out properly. Now, we assume that these q k's are so assume that these q k are symmetric, they are symmetric and positive semi definite matrices and for all k and also assume that r k are symmetric and positive definite matrices. So, q k's are positive semi definite, r k's are positive definite. Now, there are no constraints on the control actions, the u k's are unconstrained constraints. So, we do not impose any constraints on the control action, the constraints actually would make the problems somewhat complicated. We are not mentioning any putting in any such constraints that the disturbances or noise w k are independent. We are also not assuming that they have any particular distribution such as Gaussian or anything like that, they are just independent. But we will assume that their means are 0. So, we will assume that they have been centered means the mean is 0 and we will also assume that their variance is finite. So, the second moment is finite. So, now, so this is a very popular formulation of the problem. These problems arise all the time in control theory, in inventory management and so on. So, quadratic cost is often is a very reasonable cost because it many costs can be modeled in this sort of way where one is trying to say orient, minimize the distance from a particular target or minimize the deviation from a certain nominal value, etcetera. A lot of these errors end up taking the form of the errors that we want to minimize often end up taking the square quadratic type of form. So, that is one of the motivations for this particular problem. So, there are many generalizations of this particular problem also, but I am not looking at any of those generalizations. Let us look at this simplest one, much more general problems can be considered. For example, you can also have terms that are that involve a mixture of these q, q, xk and uk in your cost. So, we are ignoring such terms here and for simplicity it makes it does not add too much more to the problem. So, now let us apply the dynamic programming and let us now apply the dynamic programming algorithm. So, what is the what is the approach we would have to start from start from the last time instant and over there we define simply the value function to be simply the terminal cost. So, we define jn of xn to be identically equal to xn transpose qn xn alright. This is our this is the initialization for the dynamic programming for the dynamic programming algorithm. Now, what we need to do is do this what would be the dynamic programming equation at each time step k. So, let us write jk of xk that is going to be equal to the minimum of uk of the expectation of xk transpose qk xk plus uk transpose rk uk plus now jk plus 1 ak xk. So, let me write this a little neatly plus jk plus 1 of now remember I am I need to I am going to substitute in jk plus 1 xk plus 1 xk plus 1 is given through this equation. So, I am going to substitute this as ak xk plus bk uk plus wk alright ok. So, now let us let us do this this does not help us much because we do not know what the form of jk plus 1 is. So, but let us put do this more more concretely. So, let us so what what I want you to observe is that through these calculations they may seem a little you know kind of routine or mundane first, but the thing I want you to observe is the following that it will turn out that when I since that jk plus 1 would be quadratic and that would ensure the if jk plus 1 was quadratic was a quadratic function then this entire function that we have here the entire function that we have here would end up becoming a quadratic function of u and once it is a quadratic function of u minimizing it in and moreover it would be a positive it would be a convex quadratic function because because of the choice of because our R k's are symmetric and so on and so forth all of that will ensure that this is actually a symmetric convex quadratic function of u alright and when I when you minimize it it will turn out that you would get uk to be a function you would get uk by setting simply the derivative of that quadratic to be equal to 0 and on solving that equation where you the derivative is set equal to 0 the uk the optimal uk uk star would be a linear function a linear function of xk. So, when this jk is quadratic you can imagine that they the only terms the only cross term between xk and uk would be would be coming from this and those also would basically involve uk lean a term where the degree of uk is 1 and the degree of xk is 1 putting that together you would get uk star as a function of as a function of xk and it would be a linear function therefore alright.   So, for k equal to n minus 1 I have got what I wanted which is simply that I which was you know I wanted jk plus 1 to be a quadratic function. So, for j for k equal to n minus 1 jn which is j is already a quadratic function. So, all I need to do is just put this in. So, now I am going to put in xn I am going to substitute for xn from here using this ok.  So, the expectation is now of this entire term. So, remember the expectation the bracket opens here and it closes here. So, there are it is a sum of all of these terms out of all of these remember xn minus 1 is just the term xn minus 1 is simply a nominal initial state. So, it is not a random variable it is not the true state realized during the problem it is just a nominal state that any candidate state that we are starting off with ok. So, and so now and we are now finding un minus 1 as a function of that xn minus 1.  So, the last the last term here that we have this last term this term can be expanded this can be expanded. So, if you expand this term out. So, let me write out this the last term the last term when we expand this out let us see what kind of form it takes see it would take the following form you I would get term which has wn minus 1 transpose qn times this whole thing an minus 1 xn minus 1 plus bn minus 1 un minus 1 right and now the last term has this plus several other terms. Now, what can we say about this particular term. So, notice that because I as I said xn minus 1 is simply some constant or some deterministic nominal value that we have taken and un minus 1 is also deterministic it is a function it is simply a function of xn minus 1 right. So, as a result of this the only randomness here is in wn minus 1. Now, when I take the expectation of this particular term. So, let me write out the expectation of this what would be the expectation of this expectation would necessarily be 0 right. So, this term would have expectation 0 and that is because wn minus 1 is remember we assume that all the W's are of all the W's are of mean 0. So, this term here would have expectation 0. So, this term would be 0. So, what you would be left with. So, essentially the only kind of terms you would be left with are the following you would have a term that in that is this term multiplying this term via Q you would also have a term in which wn minus 1 multiplies wn minus 1 via Q right. So, there will be terms that are quadratic in a quadratic in these 2 in this and quadratic in this. So, this is the sort of term we would get right. So, now let me let us actually write that out.  So, let me run you through what these terms are these terms are simply. So, the last term here is the product of wn minus 1 transpose Qn wn minus 1.  So, remember this cross term this is with un linear in un linear in xn that is the sort of term you get. So, what is the lesson here the lesson here is that now what whatever is there in the bracket let us look at what is all in the bracket and the stuff which is deterministic and the stuff which is which is which is random here. The only thing that is random here is actually just this wn minus 1 this is the only quantity that is random right that is because xn minus 1 is fixed un minus 1 is obtained is deterministic as a function of xn minus 1. So, the only randomness is here. So, I can actually move my what I can do is I can move this expectation from here all the way till just here. So, this is great because now I have this is the only expectation and moreover this term that I have underlined this is also has nothing to do with un minus 1 it is a constant it is a it is a it is an additive constant that you have picked up right. Now, what else is a constant here let us look at this. So, you can see this term here has is constant as far as minimization is concerned. So, this was the only random term so the it was all the other terms were constant for as far as the expectation was concerned this is a constant as far as the minimization is concerned. So, it has been moved out this term is also a constant as far as minimization is concerned because it depends only on xn minus 1 this term is also a constant it depends only on xn minus 1 this does not affect the minimization right. So, I have therefore left I am therefore left with only these 3 these 2 or you can see these 3 other terms there is this one which is a quadratic in I am left with just these 3 other terms which are which are going to be which are my which which actually affect my minimization the terms are this one this one and finally this one. Now, let us observe these green green these green boxes you can see these are these are there is something to be noted here these are actually quadratic terms. So, the u this term up here u appears in a quadratic form here also u appears in a quadratic form this is a bilinear form in which this is linear in u as well as in xn but point is as far as the minimization is concerned it is just linear in u. So, this is therefore a quadratic function of u and what kind of quadratic function well you look at this the Hessian here the Hessian here is Rn minus 1 these are supposed to be symmetric positive definite matrices. So, this is a positive definite matrix the other Hessian here is Bn minus 1 transpose Qn Bn minus 1 you can verify easily that this is all this is now a positive this is a positive semi definite matrix. So, this is a positive semi definite matrix this is a positive definite matrix. So, consequently what we are minimizing is actually a strictly convex function strictly convex quadratic function of u n minus 1. So, its solution can simply be obtained by setting the derivative equal to 0. So, setting derivative or gradient with respect to u n minus 1 as 0 what we get is actually this equation.  You can see what we have got here we have got that u n minus 1 star is a linear function. So, this is a linear function of Xn minus 1. So, what this means is that your the optimal policy at time step n minus 1 should take the form some matrix multiplied by the state at that time alright. Now, and you substitute this back in you actually can evaluate also you can also evaluate Jn minus 1 which is the value function as a function of Xn minus 1 that turns out to be taking that turns out to take this form.  Now, what is this Kn minus 1 this Kn minus 1 is actually something that we I will explain what is Kn minus 1, but where did I get that last trailing term that last trailing term is actually nothing but this term.  So, since u n is u n star is a linear function of Xn minus 1 all these green terms will combine together to give you another quadratic in Xn minus 1.  But what is the lesson here the lesson now is that your the value function now at time step n has also turned out to be quadratic. So, the value function at time step n has also turned out to be a quadratic function and so this so what is also a quadratic. So, what we got in the previous time step what did we conclude when if the if the value function at time n was quadratic then the value then the value function at time n minus 1 also ended up becoming when the value function at time then in computing the value function at time n minus 1 all you had to do was set derivative equal to 0 and you got a linear policy. Moreover what is happening now is that the value function at time n minus 1 is also turning out to be a quadratic this is also turning out to be a quadratic. So, as a result now the value function if I now put this back in into step n minus 2 then I would be able to repeat similar calculations. If I put this back into step n minus 2 then also my value function at time n minus 2 would become quadratic and the policy at time n minus 2 would be linear in the state at time n minus 2 which is xn minus 2. So, u n minus 2 star would also become a linear is would be linearly dependent on xn minus 2 and this would go on and I would therefore be able to recursively work back all the way till time step 0 where again I would be solving some sort of a some quadratic optimization. It is of course true that you are the Hessians of these quadratics and the coefficients involved all of them continue to get complicated but that is much better than having a non quadratic optimization. So, the beauty of this particular problem structure is that there is this inherent invariance that you start off when you have a quadratic cost and linear dynamics the there are lot of nice coincidences that come into play in such a way that the complexity that of the problem does not change as you go backwards through the dynamic programming algorithm. You continue to keep getting quadratic function quadratic optimizations and you continue to get linear policies. So, this helps you very elegantly find the optimal cost function, optimal value and optimal policy. So, this can solve to for completeness let me state this here.  Like this ln minus 2 times xn minus 2 for some matrix ln minus 2. So, for I will give you the formula also for ln minus 2. So, this there would be therefore, this kind of a relation. And moreover hence this will also be quadratic hence for each k jk will be quadratic and uk equal to lk times xk will be the optimal policy. So, what is this lk the lk is this term the lk actually can be given this way lk is negative of bk transpose kk plus 1 bk plus rk this is a capital K this is a small k please note inverse bk transpose kk plus 1 ak what are these kks they are k at time n is just simply qn and the k is at every time can be computed recursively in this way.  And what would be the optimal cost the optimal cost is j 0 of x 0 which is equal to x 0 transpose k 0 x 0 plus. So, this is your the initial the cost due to your initial state and plus these terms that you were picking up at each step you recall we were picking up one quadratic variance like term for the W's. So, that is exactly the term that you would accumulate at each step this would be the optimal cost as a function of x 0. So, it turns out that the optimal cost is also quadratic as a function of the initial state. So, very several nice things happen as in this problem the optimal policy turns out to be linear. So, this is so uk is equal to so maybe I will write it here. So, the optimal policy is the optimal policy is to simply apply lk on xk just this application of the linear of a matrix on the state. And the state the matrix itself can be computed through this matrix kk the this particular equation is what is called the Riccati equation this equation is what is called the Riccati equation the through that equation you can recursively compute the kks and substitute them back in to get your optimal policy. Now, here there are a few other things to note here which are not related much to optimization but but something more again about this this structure see notice that lk has no dependence on the W's you notice the way the noise appears in the problem is that it somehow drops out of a lot of the calculations and only keeps adding up as a term as you know an additional term here. So, if the noise was deterministic means the variance was 0 this term would vanish this last term would vanish and you would be left with just you know you what you would be left with is just simply this this particular term x0 transpose k0 x0 where k0 would have to be calculated recursively through this Riccati equation. But look at the look at the amazing result here that uk is uk star the optimal policy to take that a optimal policy or the optimal action to be applied is simply lk times xk so that means whatever be the state you just apply this particular matrix and this matrix itself has no dependence on the noise on the variance of the noise. So, the noise makes no appearance in the calculation of this matrix. So, if you see the KK recursion the only things that appear here are the R's the Q's the A's and the B's and the W's have make no appearance here whatsoever. So, which means that the Riccati equation is the same regardless of whether you have noise in the system or you do not have noise in the system which which also means therefore that your feedback or the optimal policy that you have to choose is also the same regardless of whether you had noise in the system or not. This is again an amazing miracle actually that comes about due to this particular problem structure. It is effectively telling you that you can pretend as if there was no noise whatsoever and continue to apply the same control that you would have or the continue to apply the same policy that you would have in the absence of noise. In the absence the policy that you would have applied in the absence of noise you just continue to apply the same policy in the presence of noise but on the state that would get realized in the new system of course. You do not take the same actions necessarily because the state itself would be different but the plan or the strategy or the policy that does not change due to the presence of the noise. So, the only way the noise affects is that it keeps adding this little offset term to your cost function to your optimal cost which depends on the variance of variance of the noise. So, it keeps adding this little bit of you know an error due to noise in some sense or an offset due to noise but it does not affect how you are going to steer your system. So, this because of all of these reasons this particular problem structure is a pet problem and favorite problem across many disciplines operation research control and so on many people have applied this. In fact, much more deeper coincidences are coming to play in more general problems again with quadratic cost and so on and that is a subject for later. So, with this I am also I also end the content of this course there is this forms essentially gives you a way by which you can relate deterministic optimization and dynamic optimization. There are other ways also of relating deterministic and dynamic optimization those are for instance there is something called as the a minimum principle of dynamic optimize dynamic control problems or dynamic optimization problems and that can be obtained through KKD conditions in KKD conditions that is something that is beyond the the purview of this course but this is something that you can look up. As my all my credentials are there on the NPTEL website if you would like to get in touch with me about any problem you are working on or if you would like to talk about anything feel free to get in touch with me you can look me up also on the internet. So, this brings us to the end of our course on optimization we have covered a vast and vast domain we have started from unconstrained optimization and gone on to constrained optimization KKD conditions and finally we have ended up with dynamic optimization but the subject itself is much larger than all this it is an extremely evolved and well developed subject. If there is anything you would like to talk to me more about feel free to get in touch with me you can look me up on Google you can simply search for my name Ankur Kulkarni on Google and my webpage should show up there you will find all ways of contacting me you can also you can email me at on on kulkarni.kuru at iitb.ac.in. So, if there is anything you would like to talk I will be happy to respond do get in touch. Thank you for this course.


Hello, my name is Roger Jelonek, I'm your host for Think Tech Book World, and my guest today is James Rumford, a fabulous children's book writer, and so let's get to it. Jim, how did you start? Before you, before you, you started very late, so where did you come from? Before I answer that, just thank you for having me on this show, and where did I come from and how did I get started? I grew up in California, but I've lived here for about 40 years, and I got started in writing and illustrating children's books about a little over 20 years ago. That's pretty late, I mean you were not in your coming out of art school to doing it. No, in fact I never went to art school. I think it, the realization came many years after I had published my first book that I had always wanted to be a children's book writer and illustrator. And as it was materializing, I guess what I had dreamed all along, I came to understand, gee, this is what you've always wanted to do, and now you get to do it, so it just took an awful long time to get to that point in my life. So what, how did the first one come about? I, where I worked there was a retired librarian, and one day she said, aren't you going to write a children's book? I said, no, she said, why not? I have no ideas. And she said, you must have ideas, and I do not know why even to this day, I told her a story. She encouraged me to write it down. Then she said, I bet you can draw pictures. Why don't you draw the pictures for it? And pretty soon, it was finished, and then she said, what are you going to do with it? And I said, I don't know. And it was my wife who said, you got money for stamps, send it to a publisher. So I looked in the library for the books I liked, and they were all published by Houghton Mifflin in Boston, and I said, okay, I'm going to send it to them. So I did. And two months later, they sent me a contract. Fantastic. I didn't realize it at the time, but yes, it doesn't happen all the time. Fantastic start. So you've written 25 children's books? Yes, about 25. They're on every conceivable subject. Not every conceivable, but a lot of them. And so that's the cardinal sin you've committed, which is to never do the same book twice, which publishers hate, because how do you sell a different author every time? But which just tell us about some of your adventures, because they really are adventures. What I have to say, too, when you said publishers really hate it, that might be so, but I know that the salesman really liked it. Because when I go back for a sales meeting in Boston, or you talk to the salesman, they say, oh, we are so glad that you write for us because we never know what you're going to give us. And it makes it a lot more fun to go out to these bookstores and schools with your book. I thought that was a very nice thing for them to say. I don't know if it materialized in a lot of money, but, yeah, it... But you, early on, were in the Peace Corps? Yes. And where were you in the Peace Corps? I was in, we were in two places. One was in Chad in the middle of Africa. And so some of my books are based on that. This one is based on being in Chad. And so is this one, the Kalabash Cat. And there are some others I've written to that are based on my experience there. And after Chad, we went for one year to Afghanistan. This was before all of the troubles and things, mainly because I knew how to speak Persian. And I had a friend in high school who was from Iran, which was an unheard of thing then, in Los Angeles. Now, Los Angeles is little Tehran, so it's totally different. I like languages, so I started learning something from him and also he would invite me home to his house where his mother cooked delicious Persian food. So that helps a lot. And then after that, I decided to get a graduate degree in Persian at Berkeley. And I got a year into it and said, you know what, what's the point of this? And so then, I'm seven or eight years later, I, we went to Afghanistan for one year and then came back. And I then went to Rwanda in Africa through the Fulbright. So I don't have any books here about Afghanistan. There's a few in my head, but they haven't come out yet. And I don't know. But you've done books of numerous different cultures, quite different from each other. And you've generally learned at least the basic language in each case. Sometimes, yes, sometimes, yes. I really like different cultures. I like different languages. And I try and put this in these books because, you know, somebody said to me, well, who are you writing for? And I decided that I'm writing for little Jimmy Rumpford. Yeah. These are the books I would have wanted to see on the shelf when I was a kid. And I'm assuming there must be a few more like me, you know. And I'm hoping to encourage others who are interested in different cultures, who are interested in different languages, who are interested in times and places that are so different from the times and places that the child or the reader lives in. But we're running into a period now where there's anti-immigrant passion and there's also multicultural passion and a direct conflict with each other. Has that affected your... I think a lot. And for two, for two instance, when I would often, I still go around to schools, but I went to a lot more schools and once I was in California. And I was at this school and I had just written, well, I had made the... For this book, I had made just the rough draft and a few pictures. Now, this book is about Ibn Battuta, who was a Moroccan, who traveled all over the world many centuries ago. And I love maps. I love Arabic calligraphy. And so I put all of that in this book. And so some of these pictures were finished and I was showing this to this class in fourth grade class in Southern California. And afterwards, these two girls came up to me and they said, Mr. Umfrey, can you read that writing? And I said, yes. I said, can you? And they said, yes. I said, where are you from? And they said, Afghanistan. And I started to speak to them in Afghan Persian. One of the girls burst into tears. And the other one, and the kids were all wondering, what had I had said?  Afterwards, the girls told me that this was the first time that anybody had ever acknowledged them as coming from another place. And several months later, when this book was finished, and it was going to be published, and the publishing date was September 12th, 2001. So now it's September 8th or something, 2001. And I'm at a school here. And I'm showing them this book. And this girl raises her hand and I said, yes. And she says, can you read that writing? I said, yeah. And I said, can you? And she says, yes. I said, where are you from? Yemen. And I said, what's your name? She said, Mona. And I wrote it on the board or tried to. Mona's very hard to write in Arabic script. You'd think it's easy, but it's not. So I had her come up and I said, well, you'll have to show me. Afterwards, I heard from the teacher that all of the children, she wrote the names of all the children in her class in Arabic and they all were thrilled to have that. I only hope that something like this book, I only hope that when September 11th happened a couple of days later, that those kids thought about that moment, that they thought about what it meant to share something with somebody from another culture. And I have to say the same thing, too, about this book, this silent music, which came out in 2003. I know, 2006 or 2007, I don't remember. But I wrote it because of the Iraq war. And I wanted to write about calligraphy and I wanted to write about a little boy in Iraq. And I knew the book would never get published, but somehow it did by McMillan. It was the same thing. It was to validate a culture that was going to be vilified and I knew it was going to be vilified. The political institutions of that culture are all the other things. You can have them as enemies and you can vilify them, but the culture itself, that's off limits as far as I'm concerned. It's something else. But you've had other adventures in foreign languages, you did Beowulf. Beowulf, yes, yes, Beowulf. And I would like to show you it, that it's green and it won't show on this board. But yeah, I had never read Beowulf. And a friend of mine said, I think you ought to do Beowulf as your next children's books. And of course, my excuse was I'd never read it. So she gave me Seamus Haney's translation. Well, his translation is really very nice. And afterwards I said, well, yeah, I'd like to do this. I'd like to write something about my culture, since a lot of my ancestors came from Northern Europe. And I then another friend said, well, why don't you write it using only Anglo-Saxon words? We have about 80% of our vocabulary is Latin or French. Only 20% is Germanic or Anglo-Saxon. But that 20% we use 80% of the time. So I rewrote the whole poem in English, using only words that could be traced back to Anglo-Saxon. And it was it took years. Because I had to look up a lot of words in the book, I thought, Oh, a word like big, surely that's Anglo-Saxon. No, it's not. It happens to be Norse or something. And it was a lot of fun to do. I've only had experience of that kind of book once before. There was a famous architectural historian Yale, who wrote a book about Greek architecture and using only Greek, rooted words. Now that would be hard. That would be almost imperitable for most people.  Whereas I can only imagine the other would be difficult. A lot of these books, too, I I once I get into it, I decide that I'm going to write little notes in the book. So that maybe some kid some day might figure that out. So I write it in a different language or I'm hoping like, for example, this one was my first book. This is the story I told that librarian about a Chinese grandfather and his grandson and how they make clouds. And they don't really make clouds. They make paper. But oh, there are pages in here that I like Chinese, too. And I like Chinese calligraphy. And there's Arabic, too. So I wrote different things on different things about me or about whatever it is. I wanted some kind of, it's kind of notes in the bottle that maybe somebody might pick up. And this one, no one ever figured out that this is about the man who deciphered Egyptian hieroglyphs. Champagne. I was always fascinated by him. Let's let's return to this. We have to take a break. Right. Thank you. This is Think Tech Hawaii, raising public awareness. Aloha, I'm Kay Lee Akina, and I volunteer at Think Tech Hawaii as a host of the program Hawaii Together. Why? Because Think Tech Hawaii is doing a very important job in making sure that there is a conversation ongoing between people of all backgrounds and all views. That's what civil discourse is all about. And Think Tech is an important part of finding solutions for a better Hawaii. For the first time, Think Tech Hawaii is participating in an online web based fundraising campaign to raise $40,000. It's called Give Thanks to Think Tech, and it will run only during the month of November. And you can help. Please donate what you can so that Think Tech Hawaii can continue to raise public awareness and promote civic engagement through free programming like mine. Please send your tax deductible contribution by going to this website on the screen, www.thanksforthinktech.cozvox.com. On behalf of the community enriched by Think Tech Hawaii's 30 plus weekly shows, thank you. Mahalo for your generosity. Back again. You were telling us about the secret of knowledge. I just wanted to mention that along with a lot of these books, I've written little messages to kids. I have no idea when they will be able to read these messages. Maybe they will have to be adults. Maybe the book will be on a shelf and they'll pick it up and they will be an Egyptologist. And they'll open this book. And maybe they were on an Egyptologist because maybe I influenced them somehow. Wouldn't that be great? But I'm not claiming that, you know, any of that's going to happen. But I wrote the whole story in Egyptian on these pages. No, is that real? Yes. So that's amazing. No, I decided I decided that why not. And a couple of other places in here. Do you learn this? I bear that with a dictionary. There's a dictionary. There's a grammar books. There are others that have cut, you know, books speak Egyptian. Nobody knows how to pronounce it. No, the Egyptians, as clever as they were, were so clever that they figured out that if you don't write the vowels, you can write a lot more words faster. That's true. A lot of Middle Eastern languages. That's right. Arabic, Hebrew work like that. So does this. So nobody knows how to pronounce it. And there is Coptic, which is still alive. You can go live only in the church, you can go to the Coptic Church and hear them. There's a Coptic Church here. And say the gospel in Coptic. But saying you left messages for people. Did you mean that? Yes, like, for example, in a couple of these pages, since this book was made by James Rumpford in the year 2000, and I finished this picture. This one, in particular about Gutenberg, there are messages all over, but when the pictures got reduced, I can't read them anymore. And I don't, I think the kid would have to have a real magnifying. I think this says in Latin, I have finished writing this on this day, 13th day of October, you know, 2000, something or other and there are several in here like that. So were you the kind of kid who wrote messages and textbooks? No, I wasn't. But I have been writing messages and books and a few odd books. You know, why not?  Right. So I want to get into Gutenberg in a bit, but just tell us about your publishing adventures here in Manoa Publishing. Well, I am Manoa Press. I began that in 1986. And I made handmade books. I set the type of made the paper, I bound the books. And then paper as well. Yes, I made the paper as well. And I enjoyed doing that. And then when my first children's books came out, I abandoned all that because I had no more time. And then later, so many things have changed. And the computer has made everything so different that you can create books on the computer. And now in Google and other companies, you can have these books published in some cases free. And it's print on demand. And so I've done a lot of that. And it's a I'm not a very good promoter. So some of these books like those, the yellow one and this one. I like this book, it's about an African King. But I can't find a publisher for it. So I published it myself. And I did the pictures and all of that. And Manoa Press and this is what you get when it comes back from this print on demand. So I've done quite a few books like that. And I make maybe $10-12 a month. So it's just super. But I don't care. I like making books. I like drawing pictures. And I like putting a lot of that together. And so this is a way for me to do that when I am not doing more serious things with a contract where you have the specifics of a particular job, and you have to get it done. These are more for fun. Here isn't this one. And this one, I decided that for this Gutenberg book, I would publish myself a companion guide. This Gutenberg book is very simple. It's all about how to make a book in the 15th century. What got you into that? I like making books myself.  In the city of Mainz in Germany around the year 1450, there appeared a mysterious thing. It was made of rags and bones, soot and seeds. It wore a dark brown coat and was filled with gold. It took lead and tin, tin, strong oak, and a mountain to make it. What was it? I have the least idea. Well, when you read a book, I tell you what it is. So rags make paper. The bones make the glue in the paper. The dark brown coat is a leather. And the gold inside that they would paint with gold, lead and tin is the type that they used to use. And strong oak is the press. And the mountain that made it, it's Gutenberg. Because in German, it means good mountain. So you really started with the riddle? I wrote the riddle and that's it.  And darned if one of my editors didn't like it, because I had not one idea how I was going to illustrate it. And so it took me years to illustrate this book. And when I finished, I realized I had put so many things in these pictures. They are so complicated because they are like late middle a pictures of late manuscripts of late middle ages, with thousands of little things going on in each picture. I realized that all that needed to be explained. So I published this my own book about the explanation. What does it mean to have a big letter in the beginning? And how is that done? How do you set type? And what is it? How do you correct it? And all of that. The biggest thing I found in here, the Gutenberg Bible, which you can look at online. And there are several different copies from different places. I didn't realize it was riddled with typographical errors. I was so shocked. So the first Bible has so many errors in it that he had to do it again. And he had to smush the lines because he didn't want to wreck the next page. And then he made mistakes on the corrections. I was absolutely shocked. I can remember years ago when you were going in the production process, if you had a widow or an orphan, a short line at the bottom of the top of the page, you had to edit the page in such a way that you did not alter the page before and after. I still do that. I'm in the process of writing this more of an adult book thing with my brother. And I'm looking through the whole thing for the widows and the orphans. And my brother is like, why are you doing that? Who cares? You and I would care. All right. Well, you do care in a printed book because it just looks like a mistake. Right. It does. But a lot of people aren't on the ebook, you know, it wouldn't know. Oh, yeah. Well, that's the trouble. The ebook just totally throws typography and the whole thing out the window. But you're not totally retrograde. You fell in love with a website. You have a very beautiful, very elaborate website. Thank you. Tell us about it. Well, I figured that. Right. James from James from isn't it James Rumpfer.com? Yes, James from James Rumpfer.com is really worth a look. I didn't know really what I should put on a website. So I looked at a few and then I started adding stuff to mine. I learned how to do a website. And pretty soon I had more in it than anybody would ever care to look at. But it's all there. And I also have one from Manoa Press. And so you can there I don't keep it up as well as the one for the children's books. But as long as the technology is there, for me to be able to add and change things, it's it's a lot of fun. And the space is infinite. Yes. Yes. And I have enjoyed doing that. I can't do fancy things like move things around and and have little animations. But hey, it's okay. Well, you have you have strong thoughts about publishing. What's what's going on there with you? Oh, well, I think that publishing is in a state of flux. And I think that ever since ebooks came on the market, and the collapse of brick and mortar stores that publishing has had to change, I look at the whole thing as it must have been like in 1450, here comes along Gutenberg with the printing press, he's going to put all these scribes and copy us out of business. And the first thing that happens, then when Gutenbergs type to look exactly like what the scribes do. So with all the curly cues and all the funny things. So he does that. And they don't know how to treat this idea of publishing, because publishing was really different. Today, I look at it as the same. Instead of something like Gutenberg, its ebooks came along, and the whole internet, and that has changed things, I think so dramatically that I don't think publishers know what they're doing. I don't know if they know how they're going to make enough money to to control things and make a business out of it. And I think we all have to stay tuned because it's going, there's going to be changes, these things are going to work themselves out. In another 10, 15 years, we're going to look at something totally different, I think. In fact, in this book, at the end of this book on Gutenberg, I said to the kid, I said to the reader, you know, this is how books were made in the 15th century. But when you get to be 50, 60 years old, they're going to be different. So maybe you'll write a new book about how things used to be made in the early 21st century. Because I think that's how fast things are going to start changing. One interesting consequence of this publishing revolution, I run the Hawaii Book and Music Festival. And I'm astonished that book festivals are flourishing around the world. Ours is expanded considerably. But they're everywhere now. Every major city around the world has a book festival because people are really hungry to hear those voices. And to me, the voice is the key. And when I look at this array of 25 books, if they were all in a shop window, I would say that every one of those is a rumford book. I don't know how you know it, but there's just something about it that speaks to one. You know, I think that's the nice thing about the era we're living in, that people do have a channel, a means to get their voice heard. And some of it's print on demand. Some of it is going to be blogs and other things like that. But people who are educated and have something to say, there are people who want to listen. And I think you found that in the Book and Music Festival here. And just as you say, they're occurring all throughout the world, which is a wonderful thing. The only problem with such a the volume of books that are being self published and published is how do you find the one that's right for you? If there is such a thing, you can't browse in a bookstore and you don't have that impulse anymore. I don't know how that's done. In fact, I think that is putting a lot of pressure on authors and illustrators, because now they want you to not only write the book or illustrate it, they want you to have an immense web presence before they even want to look at you because they realize that that's what's going to count. And that's, that's, that's a big burden. If you self publish on create space on Amazon, the result looks like every other book. I mean, in other words, you have all the bells and whistles. But how does anyone go to that page is some mystery. I don't know. And in fact, I do not know. And that's why, you know, there are some of those books I've put on create space that are being sold on Amazon. I only sold one copy for one because I don't, I don't have enough time in my life to go around and advertise. For some odd reason, some Korean publisher saw this, wrote me and asked for the rights to publish this in Korean, and they translated the whole thing. And I was absolutely amazed. How did they hear about me? How did that all come about? Well, there's something magical about that, Senator and deputy. Yes. And that's what a book is. My first editor said, you know, well, now the book's done. So we'll just let it sell.  You want to mean you're not going to, you don't have a destination for it. You know, it's not going to go here and it's not going to go there. You're going to just let it go. Well, the wisdom of that is taken. It's taken me 20 years to understand the wisdom of that. Well, look at this table. I mean, it's just the most astonishing array you've achieved in relatively short time. Thank you very much. Thank you. It was a great pleasure. Thank you.


I think it's impossible to know the exact amount of memes that are being produced each and every day. Seriously, we tried to look it up, but new memes are being made each and every day. You kids are working hard. Nevertheless, each year certain memes make their way around the internet and are more popular than others. And we're here to count them down in today's video. Now we've all seen them, we've all laughed at them. Hell, a lot of you have probably made one or two yourselves. Maybe even a few on me. But what is a meme? Now most people, they probably associate the word with just a funny picture, but let's take a look at the definition before we start this list. According to the Oxford Dictionary, a meme is defined as, An image, video, piece of text, typically humorous in nature that is copied and spread rapidly by internet users, often with slight variations.  Yeah, go figure. What's going on guys? What's your favorite meme of 2018? Whether it's your favorite celebrity or simply an internet trend, we all get a good laugh and join some memes, and we thought a meme video would be an appropriate way to end the year. A lot of them have gone viral on this channel, some of our biggest videos of the year. If you feel like we've missed out on one, make sure you let us know in the comments down below. Also, what was your favorite meme of 2018? For me, 100% it was Thanos Carl. I even interviewed the guy. Yeah, be sure to check out that video. Alright, let's get into today's list. Kicking the list off of the number 5 spot we got Mason Ramsey, aka Yodeling Kid, aka Walmart Kid, or Walmart Yodeling Kid. I dunno, he's got a whole bunch of nicknames. After performing Love Stick Blues by Hank Williams at a Walmart in Illinois, the 11-year-old boy went viral and stole the hearts of millions around the world. As a result, Mason's singing had spawned dozens of popular memes, and several people even built the courage to go to Walmart themselves and film, well, singing in the aisles. Everyone was doing it. This is one of the few examples of memes that were made to compliment the subject's talent rather than putting them down. Mason's popularity online had opened several doors, including an appearance on the Ellen DeGeneres show. Mason Ramsey was also given the chance to perform at 2018's Coachella Music Festival, where he was incredibly well-received by a crowd who was not necessarily there for country-style music. I mean, the crowd, they went absolutely crazy. I think he even took a photo with Justin Bieber. He was a star. Okay, the kid's still famous to just get worried what happens when puberty hits, sometimes he can go either way. Coming in at number 4 we're going to go with Uganda Knuckles. Uganda Knuckles is a funny-looking character that arose after Greg Zilla, a YouTuber who included the character Knuckles, in his review of a Sonic video game. The character reportedly originates from the Uganda film, Who Killed Captain Alex? It took a while for the character to catch on with the public. By the end of 2017, an artist known as Devin Art created a 3D version of Knuckles that found itself in VRJet. It began being used by gamers to troll other players online. The question, do you know the way? Do you know the way? I know the way. You have to have a bullet to know the way. Well, it became a popular catchphrase. Do you know the way? By early 2018, Uganda Knuckles had gone viral. However, the meme had sparked controversy with many considering it to be a racist caricature that mocked African people. Despite the issues some people took with the meme, Uganda Knuckles continued to be used as a troll in online games. VRJet was eventually forced to take action against anyone who used the meme to harass other players and ruin their gaming experience. While that clucking, eventually it had to end. Do you know the way? Do you know the way? Do you know the way? Do you have to have a bullet? Coming in at number three, we have Tidepods. Not because of the popularity this product had in the laundry aisle, but more because people just wouldn't stop making it a meme, calling it one delicious snack. In January of 2018, Tidepods became a world-class meme. It ranged from pictures of the product replacing actual food to real videos of people eating the product. What came to be known as the Tidepods Challenge began circulating all over the web. Most users who showed themselves eating the product assured people that it was all in good fun. We actually made it before they were famous on Tidepods and that video got demonetized. Really goes to show you how out of control this meme was. They're so dangerous. Let's move on. In second place we're going with the angry Lebron meme. This meme came after a mistake made by JR Smith that lost the Cleveland Cavaliers game one of the NBA Finals against the Golden State Warriors. Caught on camera, Lebron instantly expressed his frustration to his teammate. Of course, like anything in life, while the internet, it could not go without it's say. The photo went viral and from there, well, the rest is history. The internet spiraled out of control with hundreds of memes making fun of Lebron's facial expression and body language. He stands with his arms reaching out, being a particular point of focus. One particularly hilarious meme was of Lebron handing Drake a baby. Yeah, that's because of the other popular news story about Drake finding out that he was in fact the father, you know, with his love child, with the chick out in Paris. Her name's Sophie Brasov. We did it before they were famous on her as well. And finally, taking our number one spot is Lil Tay. Now nine year old Lil Tay, she became one of 2018's most viral internet sensations In just a short amount of time, she dominated social media in every way possible. She was on websites, she was on Good Morning America, she was on everyone's Instagram feed. It was an absolute nightmare. I'm just getting sick talking about her. Now, it wasn't so much because of her young age, but it was because of the amount of profanity and racial comments that she spewed from her mouth. Each and every video she put out just got worse and worse. Seriously, the girl needed some anger management. Lil Tay ended up garnering for herself 2 million followers on Instagram and 200,000 subscribers on YouTube. Don't be fooled though, she also garnered a lot of hate. And you can thank her haters for the dozens of memes they began spreading around the internet. From a picture where she appears with a bundle of $100 bills, to photo montages that portray her as a demon. Some were actually rather mean and uh, well, it didn't stop these from circulating. Now I feel bad for the kid. Alright, so that wraps up the best of the best from 2018. I gotta give a shout out to my man Thanos car. He didn't make our list, but it was a really great meme, especially like when I talked to the guy and how much he changed his life. He never felt so appreciated in his life. It was just a purple car he loved, and it just, well, turned out to look like Thanos. My name is Michael McCrudden, let us know if we missed the meme that should have went on this list down below. My name is Michael McCrudden, maybe you guys can make some memes about me. My name is Michael McCrudden, love to see your memes, hit me up on Instagram with all the memes you've got, and I'll see you guys in another video. My name is Michael McCrudden, subscribe, I'm a meme.


Hello Earth citizens. In this video, I'll show you a 10 minute routine to boost your internal strength. Did you know that the powerhouse of your body is in your second chakra, which is located two inches below your navel and two inches inside? Imagine a space kind of like this existing literally in the center of your body. That is your powerhouse. So when we do mindful movements to focus and compress energy into that powerhouse inside of your body, in brain education, we call that banchan, the center of your energy. If you can focus energy into that core, it's like recharging your battery inside of your body.  So let me show you some movements and some postures where you will hold a certain angle of your body and do mindful breathing to focus energy into that core so that you can build your internal strength and also recharge your internal battery. So to start, hug the back of your thighs like this. We're going to do some rolling back exercises to loosen up our spine. Let's do 10 rolling back exercises. All right, ready? Start. One, two, back down to the floor and move your lower back side to side. Massaging your kidneys side to side. Exhale out through your mouth. In your feet down to the floor. And now we're going to do hip bounces. So lift your tailbone and tap your sacrum and tailbone to the floor like this, as if you are breaking up the blockage in your sacrum area. So right behind your second chakra. Let's do 30 times. One, two, three, four, five, six, seven, eight, nine, ten. One, two, three, four, five, six, seven, eight, nine, 20. One, two, three, four, five, six, seven, eight, nine, 30. Great job. Now drop your knees to the left side and twist your head to the right side. And now switch knees to the right side. Head turn to the left. Feel the stretch in your lower back. It's good to open your lower back first before we try to accumulate energy into your tension. Okay, now return. All right, now place your low, your hands on your lower belly. And now I want you to lift your legs 90 degrees, have about a fist width of space between your knees, a fist width of space. So they're not together and they're not far apart. Fist width of space between your knees, make your knees 90 degrees. And then lastly, pull your toes inward. So you can feel a nice opening on the bottom of your feet, especially your Yongchun point. This point is linked to your kidneys.  If you feel that slight bit of pressure, you're doing a good job.  And if you go too out like this, it'll be way too difficult. So a nice 90 degrees. Pull your toes in. Fist width of space between your knees. And stay here. And as much as you can breathe into your lower abdomen. If this posture feels very uncomfortable, you're doing a great job. It's not supposed to be easy. You're essentially compressing energy, all the energy that you have down to your core. If you're very sensitive to energy, you will immediately start to feel hot. So we'll just breathe here. You can close your eyes now because we will not move. Hold this posture. If you feel shaking, that's a good sign. Shaking means blockages are opening. No matter what, hold this posture without moving. Try to breathe deep into your lower dungeon, energy center. Your body will feel hot very quickly. Blockages will open. Your mind will become very calm. Hold this posture and tap into the internal strength that you don't usually tap into. Breathe. And even though this posture is hard with each breath, try to relax your body into the ground a little bit more each time. Relax your body to the floor a little bit more each time. You can do it. Let's hold this posture for one more minute. You can do it. And now for the last minute, please lift your palms into the air, pull your wrist back and bend your elbows slightly. Not too much. Not lock them. Just slide bend about 5-10 degrees and you will feel that air pressure in your lower abdomen becoming much stronger. Feel your lower abdomen and hold it for one minute. Keep saying to your body, I am strong. I am strong. I am strong. And no matter what, don't give up. I am strong. I am strong. I am strong. I am strong. I am strong. I can do it. I can do it. I can do it. I can do it. I can do it. I am strong. I am strong. Keep telling your body that positive information so that whatever pain, blockage, heat you feel, you burst through all of it and you hold this posture to accumulate powerful energy in your core. Last 30 seconds. I am strong. I can do it. I can do it. I am strong. I can do it. I can do it. I can do it. I can do it. I can do it. I can do it. I can do it. Okay, now for an added boost, we're going to lift our head for 10 seconds.  Lift 10, 9, 8, 7, 6, 5, 4, 3, 2. Bring the bottoms of your feet together. Lower your knees, hands down to your lower abdomen. Drop your knees to the floor. Relax your shoulders, relax your chest, relax your whole body. Even relax your lower back, sacrum, tailbone. Arms to the side, stretch your legs. Turn your body to the left side and sit up, please. How do you feel? Did you feel heat as you were holding that posture? The thing about charging your second chakra, one of the first things you feel when you bring energy powerfully down to your core is you feel hot. So if you feel heat, that's a good sign. Some people actually feel colder when they do this. That's also a good sign too. That means all the toxic stagnant energy is being pushed out. So know that if you have chronic fatigue, if you, no matter what you do, sleep for a long time, eat a lot of stuff, you still feel tired and drained. Know that energetically you are low in your second chakra. So holding this posture, although it may be hard to do it for one or two minutes right now, with more practice, you'll be able to breathe deeper into your core and then hold the posture for longer too. The longer you can hold this posture, actually, the better it is. Just like when you charge your phone, the longer you charge, the more charged you get until you get 100%, right? So you want to work up to, I would recommend maybe like 10 minutes is a good timing or even maybe 20 minutes. If you can get up to 20 minutes, that's a really, really, really good sign. Building this as a tool to recharge your energy center. You did a great job. To experience a full one-hour brain education based class, please visit a local body and brain yoga studio near you.