Well, ladies and gentlemen, Mr Chairman, it's a great pleasure for me to be here and thank you for the invitation to play this role. Let me tell you at the outset that I am not going to read to you a prepared text, so this is not something that was taken from the deep freeze to be put in the microwave today. It's freshly baked, but it may not be especially perfect. Had the timing of this been a week or two ago, we would have been on the eve of Bloomsday, and I think perhaps if I was describing what you're about to listen to, it's a bit of a stream of consciousness, but not with the elegance of Joyceian phraseology. The first thing I'd like to do is to thank the Institute of International European Affairs and the European Commission for undertaking this initiative, and both to those present and those who have left a great word of gratitude to the participants who contributed as speakers and to all those, including all of those of you still here, who have been participants at this conference. The timing of course was deliberate, although picked long in advance, lucky that it actually happened to coincide precisely with the European summit, and especially lucky that it happened to coincide with two significant Italian victories in the last 24 hours. One of them the sports one has been remarked by one or two speakers, but I think the other, it's by no means an exclusive victory for Italian diplomacy, but I've little doubt that the European experience of Mario Monte was a critical part of the chemistry of consent by of course putting some sand in the cogs of the wheels late enough yesterday evening to cause people to sit up and take some notice of some of the issues that in other terms risk to be deferred for another occasion. It has been said here today by Patrick Honohan that we now have a sense from yesterday of direction with political backing, and I think the new initiatives especially in the so-called banking union area are particularly important because I agree very much with the very summary, high summary phrase of President Herman van Rompuy to the media in the small hours of the morning, that it's designed to try to attempt to break the vicious circle between sovereigns and banking, and I think that is good. I think the union itself has shown a considerable capacity to learn by doing, certainly and it started today already with the remarks of Barbara Nolan. Then several speakers talked about the pace of democratic decision making in a complex union with multi-level governance and the multiplicity of interests and not always interests which run in the same direction, and the instantaneous quality of market reaction, and these are two very different time cycles. My own sense for what it's worth, and I've said this before, I think we need to bring the decision making system of what Brendan Halligan today referred to as the toolkit. I think he said Mr. Van Rompuy admitted when he arrived in his job he looked in the kit and there were no tools. It's a pretty good description for a deal of what has been learned, but I think in this regard that the development of a toolkit which has three characteristics is important. I would call it a political triple A rating. The first day is about assessment in depth with conditionality as a consequence, and clearly we have moved in that direction and we may deepen that. The second day is about the availability of a sufficient volume of funds, whether through the ESM and or funding capacity of the European Central Bank or the residual funds of the financial stability facility. So the second day about availability, and the third day is to find in Europe the toolkit that permits a degree of automaticity, that if you're in this space there is an agent, there is an agency, there is a capacity to respond. Because every time that we have a response that lacks that quasi or actual automaticity we will have exactly the time cycle clash between the quality of markets and the quality of European decision-making. I think the sooner we can get our decision-making process into this political triple A zone of assessment with conditionality and in-depth availability of sufficient funds and of a degree of automaticity of response we risk to have the triple A to do with states and their credit rating or banks and their credit rating stay in a period of extended stress. I'm reminded of a speech today that A. J. Trappler gave to Trinity College students during one of his visits here to Dublin where he chose to introduce his speech by quoting the Roman dramatist and philosopher of in and around the time of Christ and after Seneca. And I give you the quote, when a man does not know to which port he steers, no wind will be favourable. And I think there's a lot of wisdom in that quote. And a large part of Europe's search to a response to this crisis has been indeed to try to distill down what is the question, what are the questions. And I take my cue from that Seneca question, what is the port, to say that I think today has been very good on this. I think a lot of our speakers from many different angles and perspectives and places coalesce around this question of trying to understand the question and what is the question. I was struck today by the nature of John Bruton's opening analysis. The origins of a crisis, he said, being deeper than finance. And I think it's at its own for the day. The finance part is important, but it's not the whole part. And I think there's much weight in what he said. The emphasis he said on adjustment that is respectful of underlying social solidarity is to do with striking a balance, an important dimension, a question that's indispensable to the evolution of the policymaking. He challenged the narrowness of the wise men analysis, the references by Herman Van Rompuy to a greater role, modestly quoted in terms of the number of sentences of European Parliament and national parliaments. And he said we need more. We need the energy of direct democracy that someone of these presidents has to go and search for a mandate and search through that mandate for the shaping of the big issues of governance and in a way that respects, because you need a plurality of votes across the union, that respects the diversity of the circumstances and the needs of different states. I dare say for what it's worth, but this is not the time in a closing speech to develop it at length, I actually think this question needs another dimension as well. I have a deep conviction that in its own terms the process of European integration has been a powerful gift to several generations of Europeans and I believe that Ireland's engagement in it has been a powerful gift to the nation and to the people of Ireland. But I have been disturbed in the course of this crisis for some reasons which I can appreciate, but for other reasons about which I remain anxious, that larger states have of course a large say, but that they've exercised this in a way that has appeared to exclude others and to be fully open to the voice of smaller states. And I do think if there's a new politics emerging to do with the sharing of sovereignty in more spaces, that as well as direct democracy, part of this equation has got to look at the recalibration of the balances that validate the rights of all without confusing the scale of all as being equal in scale. For my own part I've often used the formula about our own small state that we are not in the construction of Europe a tale and the European dog. We are through our own democracy, constitutional rights and shared sovereignty, a perfectly formed if small dog in our own right. And it's nice that we should be friendly and wag our tail a lot, but we should also reserve the right occasionally to bark and to bite on our own account. And it seems to me that this capacity has been somewhat absent, not just to do with ourselves, but to do with the willingness of others to listen. And I think if we're having a discussion that touches on politics, this should be a part of it. I'm reminded too very much of a phrase that comes from Italy from the Conti Cavour. After Garibaldi's unification 150, well this year, 151 years ago, he said, We have made Italy, and now we must make or find our Italians. Well I think in a way one of these issues now comes up again. We have made Europe, we are now remaking it, crisis is reshaping it, globalization is reshaping it, but we cannot do it without our Europeans. I think Europe as a project of the elites or a new compact to do with political, fiscal banking union and so on, that is wholly exclusively and only driven by the structuralism of circumstance, is a deficient Europe if it doesn't have somewhere the heartbeat of engagement and active citizenship. And I would agree with those commentators today who spoke about that. John Bruton and Alan Lamassour, in their own way, both touched on the need to avoid being imprisoned by what is just good for oneself. That there is that wider sense of mission. Alan Lamassour reminded me of the three musketeers when he asked us to operate all for one and one for all. But he was again touching on that essential European-ness of finding the way the via media to work through this. His sense, and I think John Bruton sense earlier today, once once the omelette is made to quote Alan, you cannot retrieve the eggs, as he said. And indeed we've had a very interesting economic debate there, whether or not to do with interests, capacity, and the evolution of this crisis over time, whether the omelette could be unmade or not or whether it should be unmade and where the different interests might lie. If I parked those political questions, I think a very interesting second set of questions came in the economic and financial domain. What should we expect from a banking union for Europe and for Ireland? Carl Whelan today gave, I think, a very erudite exposition of the diversity of Irish bank debt, of the difference between the debt for dead banks and for others that hope to have a future. He raised the question if we get European funding as a result of what happened yesterday and with its evolution in policy substance over the coming months, what would be fair value if the European stability mechanism was giving money, investing money in the Irish case? How would you deal with all of this in getting the money and deal with the implicit sense that it's a second bailout? And how do we in Ireland prepare the way to get back on markets but to get our share of what's available? And we need to develop this discourse, not to be frightened of it. We may not want to call it a bailout. Let's find what the language is and let's work our way through that. I taught his analysis about the complexity of retrofitting Irish debt to do with any new European model was particularly interesting. Governor Patrick Honahan then, in quoting the IEA study of 20 years ago, and indeed his own part, but which in all modesty he didn't himself recite, but Brendan Halligan reminders of that, reminded me a little bit of a sign that I saw many years ago on a visit to Bray. For those visiting Ireland, Bray is a seaside town in County Wicklow, south of Dublin, and it had in a lovely sunny day a little sign in a window for a fortune teller, and it said, Madam Lisa, your past, your present, and your future foretold. And it seems to me, think about it, foretelling your past was one of the things in a kind of a way this issue reminded me of today. And I think Jens is here in the audience with us. I think drew up a very interesting second channel about the sovereign banking crisis, which wasn't the one that we know in Ireland of a stressed sovereign loaded with the socialized debt of bank recapitalization, but a different thing. The kind of Italian example I suppose is the biggest one on his bar chart, if I could see it at the distance I was of a very large debt to GDP ratio that traditionally and without problem has been financed and refinanced by Italian banks. But when the sovereign starts to hit a crisis, it feeds back naturally into the banks. So almost the reverse of the Irish case, the more the sovereign is stressed, if so fact or the more the banks are stressed. So whether you're coming at it through the Irish route in or the Italian route sovereign out, the banking union thing clearly is very central. I thought Patrick Hohn had made a number of important, drew a number of important distinctions that an Irish audience, particularly in political debate, needs to keep a clear focus on. The clear distinction between that part of our indebtedness, which is banking related, and that part of the public indebtedness, which is the underlying budgetary case. And as we see, the budgetary part is the most significant part, even though the banking part is by no means negligible. I think the second thing which is interesting and frequently absent from appreciation in Ireland is the extent to which public official funding has managed to slow down the Irish adjustment process and curiously difficult as it is to render it less brutal than it might be in the absence of such funding. I suppose that's hard enough to appreciate, but it is, I think, conceptually and empirically, a very strong observation not to be set to one side. The question was this summit a seismic event. The Taoiseach said yes this morning, I heard him on the radio. Carl Whelan expressed his doubts. Patrick Hohn had called it an important turning point. My own summary is I think it was a seismic event because it was groundbreaking and ground changing. And for that reason I think it's seismic. But I would still hold my judgment on how powerful will it be on the economic Richter scale because we need to see how far and how fast will its implications go. Donald Donovan raised a very interesting question. I go back to my tale or dog analogy about Ireland. Can we Irish contribute more? I think the answer is yes. And I think this institution is a leading example of it. We have things to say. We have capacity, political, intellectual, experiential which is powerfully real. And we should not trade it off only and always to wonder what is the implication of someone else's thought process for its impact on our small state. That is the great part of pooling sovereignty. You lose bits but you gain bits. Please do not squander our say in the bigger space by simply the reductionism of wondering always its impact on us without bringing to it our own legitimate and valid view, not overstated, but not to be underestimated if it is coherent and broadly disinterested in terms of the broader project. I think in terms of locating the future and where all this brings us today shows that we need to deepen these kinds of reflections. I was fascinated by an exchange between Peter Matthews and John Bruton this morning about the respective guesstimates of what the size of the Spanish banking bailout could be and it reminded me of what is my favorite quote in this regard which I share with you from Nils Bohr, the Danish physicist who won the Nobel Prize for Physics in 1923. Bohr said, spelled B-O-H-O or not B-O-O-R-E. He said, prediction, he said, is very difficult, especially when it's about the future. Joseph Janning of the EPC and I'm bringing my remarks to the chairman to a close, underlined the way in which for many years there were some key questions we chose to avoid and this crisis has crystallized those questions in a way that makes them unavoidable and striking the new balances. For example, the consequences of adjusting Europe to the new global realities of the 21st century, touched on by many speakers but not wholly developed at length today, striking the balances and interests between creditors and debtors, understanding true federalism because true federalism is some part which needs strengthening of the center but counterparts which need logically strengthening of the periphery and in other words, not some large Euro homogenization as federalism but something with subtleties and shades of gray. The backdoor logic I rather liked. I think we've had Europe by small steps of integration. If something bigger is coming, if a moment of distillation, of crystallization that gives a big choice between more integration or disintegration, if that is the moment whose moment has come to slightly recycle the phrase of Patrick Honahan today, then I think it's a moment that we should confront through the backdoor, welcome it in through the front door, excuse me, and close that backdoor, recognize it as a generational moment, a big question not a small one, worthy of intellectual rigor and honesty in our political discourse, precisely because so much is at stake. And if we go after it honestly, there's no necessary reason with the collective experience we have that if what is available is good, it cannot be argued for. So today, even as we've explored their margins, tomorrow's Europe, how wide, how deep, how democratic, how fundamental the change, I think it all calls for honesty and debate of which today has been a good example. I think we are approaching a rather bigger rather than a smaller moment, one that can have a generational sense about the choice and a multi-generational consequence in terms of the answers. And we should have the self-confidence, no arrogance, but based on our experience, based on our needs, and based on our capacity to step into this debate, willing to lead and not only to follow and to understand that where you bring that capacity with an honesty and a vigor, it's not your size that counts, it's your imagination.


We finally begin the discussion that we have been promising from the beginning of this course. We talk about the first atom the atom hydrogen atom where Schrodinger equation can be solved. Well it can be solved let us just say that let us not say easily. So, I hope all of us are as happy as this pretty little nucleus here. We have got the cartoon from this website and the reason why I put it here is to remind ourselves that in all this discussion of quantum mechanics that we have done we said at the very beginning that Rutherford model had shortcomings. But the experiment was right. The experiment performed by Rutherford students Marsden you might remember we had talked about it in the very first module that experimental result was not wrong. It said that almost all the mass and all the positive charge of the atom is centralized on this big fat and in this cartoon happy nucleus and the electron goes around it. Now the only thing that we have shed from there is that the electron goes around in circles or the electron goes around in ellipses or we have shed the we have shed any pretense of being able to say what kind of trajectory the electron has in the atom that we cannot say. But the essential model is that you have a heavy nucleus at the center and in the rest of the atom which is mostly void you have our electron and this electron wave function is obtained by the Schrodinger equation. That is what we are going to discuss over quite a few modules after this and in all this discussion techniques that we have learnt earlier in free particle, particle in a box, tunneling, simple harmonic oscillator, rigid rotor everything is going to come handy. That is why we discussed all these systems before getting into the first real chemical system that is hydrogen atom. So perhaps this is not even required anymore because we have done so much. But just to recapitulate Schrodinger equation, let us we forget is really a classical wave equation for Deepak leaves. Essentially it is an eigenvalue equation where you have an operator operating on a wave function to give you back the same wave function multiplied by a constant. This wave function is called an eigenfunction of the operator. The operator we use in Schrodinger equation is Hamiltonian operator, total energy operator. So the eigenvalue that you get is the value of energy. Expectation value as we have discussed is integral psi star a psi d tau divided by integral psi star psi d tau. Well if psi psi star is normalized as a well behaved wave function would be then denominator would be 1 anyway. And most important thing is we have learnt that quantization does not fall from the sky unlike Bohr model. Quantization arises naturally when we use boundary conditions and we have to use boundary conditions because we are working within the ambit of bond interpretation that these waves are probability waves psi psi star is probability density. This is what we need to remember and use as we go from here. So the first thing to do is to build the model of hydrogen atom. And the model as you said earlier comes from your Marsden experiment. There is a nucleus let us say the coordinates of the nucleus are x and y and z n and there is an electron x c y e z e. This dotted circle is you can just neglect it for now. So it is a two particle central force problem. Well dotted circle is not completely relevant why am I calling it a central force problem? Because the electron no matter where the electron is on the circle the potential energy will be the same potential energy is directed towards the center of the circle the nucleus. So it is a central force problem and we will see in a couple of minutes how that greatly influences our choice of coordinate system. So we will take baby steps. Let us try to write the Hamiltonian in the simplest possible form. The Hamiltonian of course would have three terms. First is the kinetic energy operator for the nucleus. Second kinetic energy operator for the electron and finally the potential energy between the nucleus and the electron. That is what your Hamiltonian would look like. So since we know what the kinetic energy operators are we can expand a little bit. Instead of T n we can write minus h cross square by 2 m n del n square. So del n square is the laplacian for the nucleus. Instead of T e we can write minus h cross square by 2 m e del e square e for electron minus well we do not always do this because it is just a constant but to keep it in SI unit and we are following Atkins convention here minus 1 by 4 pi epsilon 0 Z n Z e square by R e n. What is Z n? Z n is this capital Z remember this is not this small z here. Z n is well Z n e is the nuclear charge e is the fundamental unit of charge Z e into e is the electronic charge of course Z e is going to be 1 well minus 1 and R e n is the separation instantaneous separation between the nucleus and the electron. So that is the Hamiltonian and let us forget the laplacians are essentially del 2 del x 2 plus del 2 del y 2 plus del 2 del z 2 with the appropriate subscript nucleus n for nucleus and e for electron great. So this is what it is now to simplify the notation a little bit we will write Z instead of Z n and for Z e we are going to write 1 okay. So we will keep this minus charge explicitly we will not write Z n if you wrote Z equal to minus 1 this minus charge would have become plus charge this minus sign would have become plus sign. So we will write Z equal to 1 and instead of this 1 by 4 pi epsilon 0 we could have written it 1 but let us just write q for now. So with this the Hamiltonian becomes minus h cross square by 2 m n del n square minus h cross square by 2 m e del square minus q Z square by R e n okay. Now if this is Hamiltonian what is Schrodinger equation h psi equal to e psi. So let this h operate on psi well when I write psi total I mean psi of the entire atom I do not mean the so this is still time independent okay not the time dependent part we got rid of the time dependent part in one of the early modules we only work with time independent part of the wave function but psi total means it is a wave function of the entire atom nucleus as well as electron okay. So the Hamiltonian operating on psi total gives us e total once again e total means the total energy of nucleus and electron multiplied by psi total okay. So the psi total I hope is not very difficult to understand is a function of 6 coordinates x n y n z n x e y e z e it is not enough to specify just the coordinates of electron or just the coordinates of nucleus you need to know both because you need to understand the interaction between the electron and the nucleus when talking about potential energy okay. So psi total is really a function of 6 coordinates 2 pairs of x y z coordinates one for the nucleus one for the electron okay. So next part I will sort of skim through a little bit will not really go through all the math. So first thing we need to do is we need to separate Hamiltonian into the motion of the center of mass and motion of electron with respect to the nucleus let us discuss the physics or the philosophy of it maths is a little laborious there is no need to get into that at the moment. So what you are saying is this your atom consists of nucleus and an electron okay the electron and nucleus move with respect to each other to body problem and we know how to reduce it to a one body problem by considering reduced mass. Okay a question here I have a heavier body and a lighter body does the reduced mass resemble or is closer to that of the heavier body or the lighter body okay please work out let us say m 1 equal to 1000 and m 2 equal to 1 what is reduced mass going to be is it going to be 1001 is it going to be 999 or is it going to be something close to 1 okay I leave you I leave it to you to figure that out okay when you do it you will see that it is actually closer to 1 okay. So we reduce this two body problem see it is like the sun and the earth when we say the earth goes about the sun the sun also goes about the earth it is just that since earth is much lighter than the sun the effective mass in the system is like that of the earth. So approximately we can say that sun is stationary and the earth is going around the sun similarly here the electron is much much lighter compared to the nucleus so the reduced mass will be close to the mass of electron and the problem essentially boils down to something with mass that is close to that of the electron going around a stationary nucleus that is what we are going to arrive at eventually. And the other thing is the entire atom is moving if you think of let us say the earth and sun combine are they only moving about each other the entire solar system is moving the entire galaxy is moving yeah so that motion has to be separated unless we separate we will have too many terms and we will not be able to solve it. So we have to separate the Hamiltonian into center of mass and internal coordinate remember it is not enough to do it in terms of nucleus and electron because internal coordinates has both you are talking about potential energy so you need the coordinates of nucleus as well in addition to that of the electron. But if you can figure out how the center of mass moves and how electron moves with respect to each other electron moves with respect to the nucleus these are two separate kinds of motion we should be able to separate them. So let me just show you the definitions and not go through the math let us say this is the position of the electron which is mass Me this is for nucleus this is the center of mass let us say this diagram is definitely not to scale. So this is the position vector of the nucleus Rn position vector of the electron Re and you know how they are defined position vector of cm. So what we do is we define this kind of a system where x is equal to xc minus xn y equal to ye minus yn z equal to zd minus zn what is that just think of the x coordinates. So if this is the x coordinate of the nucleus this is the x coordinate of the electron xc minus xn essentially is the separation of the electron and the nucleus in x direction. Y y minus yn is the separation between electron and nucleus in the y direction same for z and this is this separation is the important parameter when you talk about potential energy this separation is important when you talk about the motion of electron with respect to the nucleus relative motion and this R is Re n so that is the Re minus Rn do not forget that the vectors you get when you do the vector addition vector sum you get root over x square plus y square plus z square. So these are the internal coordinates and these are the center of mass coordinates this is once again very standard techniques of rotational dynamics from classical physics when you invariably have to separate translation from rotation lots of motions can take place lots of kinds of motion can take place at the same time but you have to separate each kind of motion otherwise you cannot really formulate your problem. So X Y Z denote the position well mass weighted position coordinates of the center of mass and R is also for the center of mass. So what happens is that this Schrodinger equation in terms of electronic and nuclear coordinates can be rewritten in terms of your relative coordinates and center of mass coordinates. So what we see is how you do it I will just browse through the appendix one if you are interested in the detail you can go through it it is not required for this course but what is important to see the reason why we have two colors of highlights is that the first term is minus h cross square by 2 m capital M remember capital M is the total mass of the atom minus h cross square by 2 m del capital R square. So this would be the kinetic energy term of the center of mass the second term is minus h cross square by 2 mu what is mu the reduced mass multiplied by delta small r square. So the second term is the kinetic energy term of the electron with respect to the nucleus I am repeating this so many times because it is important to understand with respect to the nucleus I am not talking about motion of electron in the free space coordinate we are talking about movement of electron with respect to the nucleus does the separation with nucleus increase or decrease does x c minus x n increase or decrease y e minus y n z e minus z n what happens to those that is what we are dealing with. Please remember relative coordinate means how the electron is moving or what is the situation of the electron with respect to the nucleus. So second term gives us the kinetic energy term in Hamiltonian for the motion of electron with respect to the nucleus. Third term minus q z square by r r remember is the separation between electron and nucleus so minus q z square by r obviously is well it always has been throughout the discussion the potential energy for interaction of electron with the nucleus. So second and third terms together are in relative coordinates and they talk about the motion of movement of electron with respect to the nucleus the first term in a different color highlight is for the movement of the center of mass. So Hamiltonian is nicely separated into two parts one for the center of mass one for the electron with respect to the nucleus how this is how. So Hamiltonian is sorry Hamiltonian can be written as h n plus h e and for nucleus e for electron with respect to nucleus now we have to worry about the wave function what are we trying to do we are trying to do separation of variables we are trying to separate the center of mass motion out and forget about it and worry only about the relative motion to do that we can conveniently well we have already said this we can conveniently write the psi total as a product of two wave functions one function in the nuclear coordinates one function in the electronic coordinates relative coordinates this is what we have been doing from the beginning whenever we have a complicated situation and whenever we want to break down a more complex equation into smaller simpler ones. So now see minus h cross square by 2 m del r square will operate on chi n and psi is going to be constant as far as it is because it is a different coordinate system the second one h e will operate only on psi e as far as it is concerned chi n is going to be constant we have once again encountered it as recently as when we wanted to separate theta and phi for a rigid rotor remember. So e total also can be written obviously as e n plus e e. So what we can do is I am not going through the steps of separation of variable because we have done it several times I hope all of you can do it if not please post your difficulty on the forum and we will try to address it. So the first equation we get if you look at this highlight here is h n chi n that is minus h cross square by 2 m del r square operating on chi n no potential energy remember we are talking about one hydrogen atom we are not talking about a hydrogen atom that interacts with anything else that equal to e n chi n only kinetic energy term is there. So a system which has only kinetic energy term no potential energy potential energy 0 have you encountered something like that yeah yes we did that is a free particle a free particle is something that does not care about anything else in the universe does not have any potential energy any interaction with anything else. So this is what gives us an idea about how fast the atom as a whole is moving kinetic energy of the atom if you go back once again to the sun earth combination it gives us an idea about how the combine of earth and sun is moving in space translation and motion and we know the energy do not we what will be the energy e n n means for the center of mass energy will be h cross k square divided by 2 m this is what we learned when we talked about the free particle and as we know k can take up any value including including 0 yeah and this is it can take up any value so this is essentially for translation motion of the atom as well atom behaves as free particle that being said at the moment we do not care right we have talked about free particle that is done and dusted we are only interested at the moment in the electronic part of the Hamiltonian for the rest of the discussion this is what we are going to talk about electronic Hamiltonian operates on the electronic wave function to give you electronic energy and this is energy of the electron in the field of hydrogen atom so h psi operates on e psi on sorry h e operates on psi e to give you e e multiplied by psi this is our hydrogen atom right now Cartesian coordinates is what we are most comfortable with so we know very well that the Laplacian is written as del 2 del x 2 plus del 2 del y 2 plus del 2 del z 2 and even if we do that we can perhaps try to write psi e as product of psi e x psi e y psi z and try to separate the variables we would have been successful in doing it if the second term was not there the second term is q z is minus q z square by r and r is square root of x square plus y square plus z square and that is a problem because this electronic wave function which is a function of x and y and z if you try to separate it out in terms of something like psi e of x multiplied by psi e of y and multiplied by psi e of z this term in the Schrodinger equation is going to create a problem because you cannot break it down into something in x multiplied by something into y into something into z how do you do that with square root of x square plus y square plus z square so because of this problematic term it is not possible to separate out the Hamiltonian into 3 different coordinates we cannot proceed further even with hydrogen atom if you want to stick to Cartesian coordinates so we need to use a new coordinate system what will this coordinate system be well it is not really new we are already familiar with it the coordinate system that we are going to use is spherical polar coordinates and as we know spherical polar coordinates and Cartesian coordinates are interrelated so once we know theta phi and r we can actually work out x y and z without much hassle z can be worked out by r cos theta x can be worked out from r sin theta cos phi and so on and so forth so if required we can go back to Cartesian coordinates also but it is easier to formulate the problem in spherical polar coordinates why because remember what was the problematic part in our formulation the problematic part was that r in denominator r is square root of x square plus y square plus z square so we said we cannot separate it into something in x something in y something in z but here r itself is a coordinate in spherical polar coordinates that is the beauty of it so since r itself is a coordinate at least during formulation we do not have to worry about it that is point number 1 point number 2 is it makes perfect sense to formulate this problem in terms of spherical polar coordinates because as we said a little while ago it is a central field problem the electron is attracted to the nucleus right so no matter where it is if you draw an arrow so that is the direction in which the attraction is central field problem and central field problems are best handled in terms of spherical polar coordinates so this is what we are going to use and the next step of course then would be to convert the Laplacian into spherical polar coordinates right remember we have already done that when we talked about rigid rotor at least we pretended to do it what we said at that time is this here is the kinetic energy operator in spherical coordinates and we showed you some appendix 2 remember appendix 2 it was called appendix 2 because originally it was here in this representation I lifted it and took it there okay so anyway axiomatically we take the kinetic energy operator in spherical coordinates multiply it by well this is Laplacian so multiply it by minus h cross square by 2 mu and to get the Hamiltonian we add minus qz square by r okay to get Schrodinger equation for the electronic part in spherical polar coordinates we make this Hamiltonian in spherical polar coordinates operate on psi e to give us e e into psi e okay now all this is in r all this is in theta all this is in phi what is the next thing to do the next thing to do is to separate this into 3 equations 1 in r 1 in theta 1 in phi okay to do that again I will go through this a little quickly because we have done it many times but please do it yourself and make sure that everybody is on the same page okay to do start the separation we multiply with minus 2 mu r square divided by h cross why because I have this minus h cross square by 2 mu on this side and here we have r square multiplied by sin theta d phi so if you do this then at least a little bit of cleaning up is there the first term becomes del del r this one del del r multiplied del del r operating on r square del psi e del r the second term becomes well now this r square is gone 1 by sin theta del del theta operating on sin theta del psi e del theta what about the third term we get 1 by sin square theta del 2 del psi e del phi 2 so in the third term only there is a little bit of mixture of theta and phi the first term is only in terms of r second term is only in terms of theta last term is only in terms of r okay and then what we do is we bring the term in energy to the left hand side as well so all this is in r what does that mean before going further what it means perhaps is that the energy will depend only on r and nothing else it will not depend on theta and phi of course it is a little premature to say this because we are still not separated the wave function into r theta phi components but I hope it is not very difficult for you to understand that that is where we will inevitably be headed anyway yeah so that is interesting and that takes us back to Rutherford's model remember Rutherford's model energy would depend only on the separation right what we call the radius of the orbit or in Bohr's model in Bohr actually worked out something where expression of energy was there and there was something in 1 by r square right so now it appears that we will reach somewhere similar after all this sophisticated treatment this is in theta and phi so what we have is we have one part in r one part in theta and phi so we can take them to different sides if we write the wave function as capital R which is a function of r capital theta which is a function of theta capital phi which is a function of phi and for the rest of the module we just write it as capital R into capital theta into capital phi so you know how to do the separation I will not say all that we just do the separation do the differentiation I just do one maybe when you differentiate with respect to r capital theta capital phi are not functions of r so they come out and you are left with del capital R del r only similarly these functions come out and now this is what you get how do you get the terms together just multiply with 1 by capital R capital theta capital phi like what you have done for rigid rotor and then you get on the left hand side 1 by capital R del del r operating on r square del r del r plus 1 by capital theta 1 by sin theta del del theta operating on sin theta del capital theta del theta plus 1 by capital phi 1 by sin square theta del 2 capital phi del phi 2 plus 2 mu r q z square by h cross square plus 2 mu r square by h cross square E E equal to 0 E E means electronic energy okay just rearrange it a little bit take everything in r together on one side take everything in theta and phi in one side you get one upon rearrangement you get this so left hand side is entirely in terms of the radius r so you call it the radial part right hand side is only in terms of theta and phi angles we call it angular part so as usual we equate it to a constant beta because otherwise something that is function of r but not theta phi cannot be equal to something that is function of theta and phi but not r they have to be constant so this beta is a constant that links radial and angular parts okay so we have been able to separate Schrodinger equation into a radial equation and an angular and the angular equation is familiar to us we have encountered it when we talked about rigid rotor remember so we know how to separate the angular equation into its component as well so that is what we are going to do in the next module and we are going to recapitulate what we have done in rigid rotor and we will see how the quantum numbers emerge nicely from using boundary conditions in the subsequent discussion.


So welcome to the the second lecture So if you weren't in the first lecture, it doesn't matter Completely independent except What you could have learned from the first lecture is that it may be a good idea to try to solve TASAP Okay So I'm Unfortunately for us or maybe fortunately for the world TASAP was solved a long time ago 1997 20 years ago by Gunter shoots So let me tell you shoots is formula for TASAP Well first if you remember what TASAP is let me just remind you what it is So TASAP you have these height function which look like this And then there's kind of a code one wants to use which you've seen in a couple of talks, which is that the The the up guys are called particles So we're on we're over Zed here, and here we just put a particle here. We put a particle No particles and here there's a particle so maybe put axis for no particles and then What's that? That's an axe and then there's a particle and then there's two axes and then there's Three particles. Anyway, you get the idea, right? So you can just encode it in particles and the dynamics of TASAP was just that the the up guys go down They jump down to down guys at rate one, but of course, that's exactly the same thing as this particle jumps here With the rule that there's only one particle per site. So if there's a particle in the way, it just doesn't jump Okay, so the entire rule of TASAP you can just think of as particles on Zed and The particles are trying to jump to the right at rate one, but they don't jump if there's no particle in the way Okay, so that's our new view of TASAP here Okay, and then there's an old convention So so here if I just decided to use this notation X's or holes and O's are particles which may seem a little odd. Okay, sorry There's a convention that we number the particles X 0 X 1 X 2 X 3 Okay, backwards. Okay, so you can also think of the positions of the particles Fair enough. Okay That's the next line. So right now. I'm gonna assume. There's a rightmost particle. Actually, I'm gonna assume. There's finitely many particles Okay, so there's seven particles Okay, seven particles So shoot solve the system for seven particles well seven could be N. So there's particles. So there's there's X Which is X N There's a Y Y N So we have n particles and we want to make the exact transition probability So the probability That X T X T is now the whole configuration of n particles as they evolve X T is equal to X given that X 0 was equal to Y Okay, so and this is going to be a formula for each n Okay, this thing is given by a determinant of A particular function so it looks like this F Of I minus J F is a function. I'll describe in a second of X N plus 1 minus I minus Y and Plus 1 minus J. It's also a function of T and This is an N by N determinant in I and J Okay, so there's an N by N determinant and Once again, I just remind you the X's and Y's are ordered backwards And the F of course is important So F and X T is given by a certain contour integral. So it's a contour integral Gamma zero one just means a contour which contains the points zero and one DW over W One minus W To the minus N To the X minus N e to the T W minus 1 That's a T Okay, so That's the formula It's not that hard to Derive this formula and I'll actually explain to you why it's true So it's not that hard to derive and it's particularly easy to prove that that this formula is correct Okay, so to prove it's correct We want to write the dynamics in the following way so this has become It's a really useful way to write the dynamics So we've got the P and we'd like to write the forward equation for P So P is these transitions, right? This is call this thing Let's call this thing P of X. So let's just fix fix Y and call it P of X And I'll just show that it satisfies the forward equation the forward equation in this language is just a minus K equals 1 to N Grad K minus Okay, so wait, this is the free evolution so grad K minus is Grad K minus just says I take the kth particle and take the minus gradient So grad minus of f of X is just f of X Minus f of X minus 1 so that's the minus gradient then there's a plus gradient I'll use sometimes to call grad plus which is obviously f of X plus 1 minus f of X This grad the K just means that it's applied to the kth particle Okay, so this is what's called the free evolution this free evolution Of course, it doesn't include the fact that the particles are not allowed to jump on top of each other Okay, so there's a free evolution, but then there's a boundary condition which stops them jumping on each other which is Grad K minus P is equal to 0 X K is equal to X K plus 1 okay So this free evolution is going to be satisfied inside this vial chamber the vial chamber just means the set of X's where X0 is bigger than X1 is bigger than X2 such a and then Couple with this boundary condition. This is actually the evolution operator Okay, okay, so why does this?  So if you differentiate Fn Well, what happens when you differentiate fn and t? There's not much that happens except the w minus 1 comes down Right The w minus 1 can be included in the other variables and so you just get this simple equation. It's minus grad minus Fn Fn is just a function of one X variable Okay, so you can see this so I've been satisfying this Now when you differentiate the determinant You just get the sum of all the time derivatives in each one of the columns right So you get a sum of the determinant with one of the columns differentiated in t Right, that's how differentiation of determinants works When you differentiate that column You get dt fn is minus grad minus of fn But in that column Is only one type of X? Right, the X is determined by the column. So all you get is grad I And that just pops out of the determinant by linearity So that's why that happened that's works. Should I say it again? Maybe I'll just say he's really that simple You differentiate the determinant if you differentiate the determinant you get the sum of the time derivatives of each of The determinant with one of the columns having a time derivative Now if you take the time derivative in the column, there's only one of all the X's Being differentiated. So you just get in the if column you just get from that formula Grad minus of f in that column, but only in that column But that grad minus can just come out now by linearity So that proves that the P satisfies that You know, why does it satisfy that? now So again if you If you take grad k minus Then you get a grad k then you get a grad minus but grad just in the in the in the kth column right, so just the kth column that is Acting on by this grad minus because this is grad k minus, which just means it's only acting on the kth variable Okay So you get a you get the matrix But with just the kth column with a grad k minus on it Now so you get grad minus K of fn of x k say Okay, with with the y's too. I'm just being the word with minus y of course Okay, but that we could rewrite it as grad k plus of Fn of x k minus one So let's erase that just so it's clear No, it's just the same thing Like talking you get minus. I'm sorry minus grad came up grad k plus of k minus one But now if x k is x k plus one plus one This is just grad k plus Fn of x k plus one, but now what happens when you take grad k plus of fn Well grad well, okay Grad plus of fn Grad plus of fn just acts on the x So all it changes is the end The grad k plus fn, which you could just think of as grad plus of fn Is actually just fn plus one Of x. I don't think that I think I really made a typo there. I think it's that is that correct? Constantly, I think it's a typo in here. Okay. Anyway But what that means is two columns are exactly the same That's where you get zero from the then the determinant is equal to zero. So these two properties this Property of the function and and this property Show that this determinant actually satisfies the equation that it's boundary condition. Okay, it's really that easy and This crazy contour integral is just some weird construction to get something to satisfy those two things Okay, it's just a representation of solution of this equation Sorry, I got to talk a little louder and I can't even see. Oh, yeah Yeah, so of course This is the evolution of the P and then you would really need to show initial condition Which is completely correct, right? If you have the initial condition and then this this is actually just a representation of the forward equation Okay, so I showed it satisfy the quarter equation. You can also check it satisfies the initial condition I just don't feel like doing it right now. We got to get somewhere today. Yeah. Oh, okay So you take a grad. Oh, I hope it's true. You take grad plus in then you're taking a grad of x, right? So that means I have a w x plus 1 on the bottom, right? So there's one thing so it's 1 over w Minus 1 times that thing but whenever w minus 1 is w minus 1 over w. So you just get an extra n It's nothing more than that. You see how the thing works. It's amazing Okay, of course, this thing is just constructed out of these these objects Are just some general solution of these equations and then this construction is a special thing to get you the initial condition corrected It's in the notes. So I won't do it Well, we all know that if you have a P and it satisfies the initial condition and satisfy the forward equation And then it's your P Right. This is just the forward equation. It's just not the way you're used to writing it Okay, okay Well, there's several steps here. Okay, so so that's it. So that's how you solve TASAP That would be the end of the talk Except Except I don't like this very much because we're trying to go you see what if you remember from last time We're trying to go to a huge time and space scales So if I have seven particles that kind of gets washed out in the limit, right? So of course, we need a formula which goes to n equals infinity nicely and this formula doesn't that's the problem there's another thing which is that It turns out that the thing doesn't really want to ask you what's the probability to go from one point to another if we saw last time The right question to ask is if you start with some function What's the probability you're less than something at some later time? And if I want to look at the KpZ or the say sub height function I want to look at some later time and I just want to say well at this point here Is it less than that or maybe at two or three points? That's the kind of question I want to ask but that means I want to start with 1,000 particles and Then end up with three Points later. I want to know what's what's less than or equal to y at three points later But here you only have 1,000 to 1,000 or what was our 1,000 to 1,000? So that would mean I would have to sum over the other 997 variables and so I'd have to write a sum of this thing, but that's some is intractable Fair enough So the moral of all this is there's formulas and then there's formulas Sometimes you have exact formula, but they're useless. You need a formula which is useful Which can pass the limit, okay? so actually The person who discovered what to do is is sasamoto Yeah, this amazing idea in 2005 Okay so You want to try to create out of this a formula Which is a formula for starting with a lot of particles and then you're just less than or equal to some X's at maybe one or two or three points Fair enough Here's what he realized Okay, you're the following thing This is just from this this guy here It means fn plus one x T Is that correct? The problem is all I have is all I have my notes The following thing is true and and if I have to change that I think I made a typo here Daniel or Constantine is there a plus one or a minus one there? What Daniel? Oh, thanks Of course, we could do it in a second. Maybe someone can just check in this. Well, I'm talking okay But but anyway, if you just sum the thing you get this Sorry, why? Okay, you get a summation like that But now this is wrong This this is this is correct The other one I think there might have you a one plus one. This is a minus minus one here and This is mine and minus one and this is minus one No Okay, I'm very bad at getting these things exact. I'm sorry Okay, let's look at the last column. So the last column of the thing looks like this All right, of course, I wrote it sideways Okay, so the last column looks like that now What it means is that you could rewrite this as the summation Over some variable I'll call z to two and you'll see why in a second greater than x one of fn minus two of Z to two minus yn f minus one Set to two This is just this is just that same formula that written in for the cold column. Okay, or you could do it again So it said to three Greater than said to two X one now I've got fn minus three I've said three three because of that fair enough. You just did it twice. Ah Okay, so this guy you could just think of as the sum of these guys. Okay. Well, okay That's because there's a difference operator, right? But also, of course, you need to know that as y goes to infinity this thing goes to zero But actually that's not too hard because you have any any contour around zero one So if you make the contour size two or something then you let x go to infinity that goes to zero. So that's fine okay, now Now this thing is just a sum of those so this guy just the sum of these guys It's just being written in column notation Okay, it's just the same formula that would be this guy is equal to the sum of these guys Something bigger than I did then then that thing I just write it some all the guys bigger than him. That's it There's nothing deep here Okay Or if I took the second last column So second-last column and you take said 23 again, you'll see why in a second Fn minus three You do the same thing you get that okay, but now You see if you change z two three and Z three Three if you change them then there's a change of sign So you're always looking at fn minus three in these two columns Okay, but now if you change those variables those two very that very those variables only exist in that last two columns So if you change the variables, then you've changed two columns right This is writing the thing as the sum of the determinants okay, and That gives you a minus sign That means that if you look at the whole thing the only part that contributes is the sum So only Z three three greater than equal to z two two Three Contributes well actually z two two Itself has to be greater equal to x one Okay, so this is the only part that contributes There's there's just a cancellation in the other part where the two overlap Okay, what does that mean that means that the probability can be rewritten So of course you do this again and again and again and again You do it over all the columns and the whole probability can be rewritten as The sum over these Gulf and Zetlin patterns So you've pulled the I down to a one By doing this all those times Z one and minus y and plus one minus j and Now the sum is over all okay, so we've got z one three Z two three Three and these things all have to have these inequalities Can you guys see the inequalities like hey? It's just rewriting what's up there, and of course it be this pattern keeps going up all the way to end And down here is your initial data x one x two x three So the sum is over all such patterns. Okay, that must be an eye sorry This is an eye minus j z I this is what it is Sorry, we've seen this before Alright, okay Sorry, what should be here F? Oh, this this is a one. Yeah, sorry. This is an eye This is correct now, right? Yes That's actually the key thing I wanted to show you because because it's a really wonderful idea and Now the thing of course is related to things like random matrices That thing can actually be rewritten You can write this the summation over pattern Z. I am now no longer with the inequalities with z one and is equal to x Z I and That one and is equal to x n. Sorry of W and of Z where W and of Z is equal to the product and equals one Two and that's my number of particles determinant Q or these things have to be defined now So Q Q x y is just the indicator function that x is greater than y and Psi k n of x is almost f It's minus one to the k f minus k X minus y and Minus k t. Okay Now this is the sum over all patterns. They have no order, but You can check that this particular thing. It's an exercise to check that that Because of that Q. This is just the color McGregor formula in a funny form Just tells you this is the indicator function of this thing being a Gelfand's Evelyn pattern. Okay, and Then this is just a different way of writing this. So this is really just the same formula Okay now The reason for all this rewriting is that this kind of thing is Recognizable as some kind of Determinant a point process. It's not exactly These guys are not positive things. They're not probabilities They could actually be signed. So it's come kind of signed Determinant a point process So you can write the whole thing as one Type of determinant on some slightly extended space and Then you know from this language of determinant a point processes That if you want to compute things then you should compute the correlation kernel of this determinant a point process which I won't do and This kernel is basically obtained by inverting Some matrix involving these guys Which I won't say explicitly what it is. Okay? What I'll do is I'll tell you the result of that computation because that would take two or three lectures just to go through it So the result of that computation, which is actually our starting point after we have 20 minutes So I probably won't finish today The result of that computation. I'll leave that up is The following so here's the actual recipe for solving pace up. This is a 2007 Warden was I want to write Corwin. Sorry. We're in Ferrari and Sasamodo Okay So the probability starting with so now now x sub zero is Is the name of the taste up initial condition? Okay It's it's got a last particle and if you want just assume that there's a finite number of particles But it definitely has a last particle to the right So that's the initial condition and now if you want to know Xt and j greater than a j J equals 1 m and here M. M is just one or two or three This is given by the determinant of I minus the Correlation kernel with these kais so I'll remind you these kai bar Has kai bar a at the i-th coordinate is the indicator function that x is greater than a I It's that vector Oh, sorry less


in a program like Under and Is Anonymous. Druggle. So what happened?  And they'll share about like, oh, God, this guy. And they'll go on to describe what it was like sitting next to me at a meeting. You know, if we were alcoholics anonymous, I'd be the guy who smelled like alcohol at the AA meeting, you know? And they'd say, so what changed? What happened? So I want to share a couple of things that happened and maybe even a little bit about my first three steps. Hey, we've got Elliott Blatt here. Elliott, what's going down, bro? Blessings, Luke. Good morning. Good morning. Thank you. Long time caller. San Francisco, I'm listening. All right. So what an eventful week, huh? Yes. So the whole Adderall situation has provoked a lot of controversy. It has. Yeah, no, it felt like, I have to say, you had a very sort of adversarial posture in your last video, the sundown video of Thanksgiving Eve, I believe. Do you feel defensive about this? Well, I'll just repeat my basic point that people in general don't want you to change. And when you're making a change, family, friends will usually try to fight against it.  Okay, back to you. Well, what led you to the conclusion that you feel like you have ADHD? Because you don't seem to, as far from my outsider perspective, you don't sort of exhibit any of the traits I associate with ADHD. I mean, you're pretty productive, you're more than pretty productive, you're highly productive and you seem to work all the time.  So you have a lot of accomplishments and I associate people with ADHD with people who just can't seem to sort of execute on things. Is this a false, you know, I'm making some false assumptions here. Well, I think you're touching on some symptoms of ADHD, but for me, it was humiliation, right? I didn't go and get this ADHD check out, you know, on the wings of victory, right? I came to it on the wings of defeat and humiliation whereby failing to pay attention to mundane details I cost myself thousands upon thousands upon thousands of dollars and I've repeatedly had this problem.   This has happened to me time and time again, a failure on my part to pay attention to non-exciting details, to failure to pay attention to mundane details that normal people in my peer group do pay attention to and failure, humiliation and the loss of thousands upon thousands of dollars is and then talking about that with people close to me and them pleading with me to go get checked out for ADHD.  So here are some of the symptoms being unable to sit still, especially in calm or quiet surroundings. That's basically true for me, constant fidgeting, pretty much true for me. You'll notice I'm usually like squeezing something when I'm doing my streams, being unable to concentrate on tasks, I have difficulty concentrating on tasks that are not exciting to me, excessive physical movement, yeah, excessive talking so I can be frequently I'm overly verbal in context where that's maladaptive, being unable to wait their turn, yeah, I frequently interrupt, unable to wait their turn, acting without thinking, yeah, interrupting conversations, just general maladaptive levels of verbal impetuosity and impulsivity, saying things that are inappropriate and then walking around with this dread that I'm going to repeat this problem over and over again, thus harming other people, but most for myself. So humiliation leading to not, you know, being invited back to meals at the homes of Orthodox Jews because I said something globally impulsive that I thought was funny, but turned out was highly inappropriate and now, you know, longtime friends have stopped inviting me around for meals. So a lot of humiliation led me to this place. Okay, humiliation is one thing, but the connection to ADHD is not entirely clear.  Well, these are symptoms. I mean, people who specialize in this area do regard these as serious symptoms of ADHD. I could retail more embarrassing setbacks that I've had relating to this. And so if I can minimize this problem, why would I not take that chance? You seem to take one little quirk and turn it into a big moral problem. You seem to love to pathologize what seemed to me to be relatively innocuous behavior as being some deep sort of character flaw. So at what loss of money? At what loss of income would it be worth? Because I fail to pay attention to mundane detail. So if I lose $100,000, if I lose a million dollars, at what loss of income do you think it'd be worth checking out this type of problem? At what number of not being invited back to the homes of friends? Like if it happens once, what if it happens a dozen times in a year? At what point is it worth investigating this? I'm not saying, okay, I'm not saying that these aren't behavioral problems. You know, you clearly do, I may say, have a few behavioral problems, but you're making a leap, an inductive leap going from some behavior problems to a physiological medical condition, right? No, I'm not making the leap. I'm going to get a diagnosis from people whose living is based upon making this diagnosis or not making the diagnosis. So do you know people that once had your sort of set of behavioral issues started taking ADHD and suddenly those behavior issues disappeared? Yes, I know a lot of people like that. A lot, okay, fair enough. Now it seems counter-intuitive to me because, you know, one, Adderall's an amphetamine type thing, an upper, a speed-like product, is it not? Yes. And it seems like you would want to go the other direction and maybe you need something more calming. You would think that, but not everything can you just into it as a layman compared to people who spend, you know, decades studying this. So whatever reason, the first line of drugs that are most commonly prescribed and recommended for ADHD are stimulants. So I don't just try to intuit my medication or the world around me. I do try to intuit, but I don't end with intuition. I also want to consult expertise. And I'm not someone who thinks that medication prescribed by a doctor is usually a good thing. I think it's frequently not a good thing, such as with SSRIs for depression. I think medicalizing depression is frequently wrong. I think SSRIs for depression are frequently maladaptive. I think chiropractic is a scam. I think that doctors frequently perform unnecessary operations to make money. I think dentists are constantly scamming their patients. So I'm not someone who automatically sides with the medical profession. Yeah, that's why it was all the more surprising because you do seem to be, in general, COVID exception. You do seem to be a pharma skeptic. Yeah, I have a moderate to above moderate skepticism of all professions, including the medical one. Okay.  No, no, no, I haven't. I haven't said that I said I was disappointed that there hasn't been a burst in productivity. I expected a more immediate change from this medication. So whatever it has done is being exceedingly subtle and just a little bit more cleaning than normal, a little bit more attention to some mundane problems like a buzzing fluorescent light bulb. But there has not been the dramatic burst of euphoria, energy or productivity that many people experience when they take Adderall. Okay. All right, but okay, so all right. So there's some improvement, but minor you're saying. It's very subtle. It's so subtle. I'm not even sure it's there. So I'm going to bounce off people who I trust. I could be completely reading into what I think it changes over the last four days that may not even be there. So I do feel medicated. Like this is a different state. I definitely feel medicated, but it's whatever effect is having on me is really subtle. It's much more hard to put my finger on than what I expected. Now you've tried the nicotine gum and that wasn't effective for you. No, it was effective. I just haven't done it much. I did, I do feel smarter when I take, when I choose some nicotine gum. So like I just, I'm just coming off the period where I sort of had to go to the gum. I've been under a lot of deadline pressure and so I've been having to work past from comfortable. And so I've been chewing some of that gum and it's worked quote unquote, but the side effects I notice I really, they're very noticeable. They're uncomfortable meaning I, my sleep has become really erratic after chewing the keen gum on a pretty consistent basis. So I'm glad that I'm not doing it now, but I had a period of about a week where I was doing it regularly and my sleep became a mess and then it had sort of negative downstream consequences from not sleeping properly. So I was just curious in that regard. Yeah, I also very curious because I have friends who warned me that Adderall just wrecked their sleep and the side effects of Adderall were just absolutely devastating. In fact, you know, we have a mutual friend who abused Adderall for years and getting off it was, you know, just devastating for him. So I haven't experienced any of the reported negative effects. It's had zero effect on my sleep. But again, I take my last Adderall pill usually about 11 a.m. So when were you taking your last bit of nicotine gum? About the same time, around lunchtime after my morning coffee had worn off. Then I would go to... I would do nicotine gum. So that would give me like a three-hour work session because I start to really fall off after noon. My energy level really starts to dip. So I was throwing in the old nicotine gum to try and, you know, arrest that drop-off. And it works. Is the drop-off typically after lunch or mid-afternoon? Basically 1 p.m. Yeah, after lunch. Whether I eat lunch or not. It's not like a digestive coma type of situation. It's not a high carb lunch. It's just any lunch or lack thereof. Well, it's just the time of day. It just seems like that's all I've got, you know? And then my brain just gets really tired. I feel like fluid's draining out of my head. There's like nothing there starting at 1 p.m. I need a nap. Maybe this is just age, Luke. When does your work day typically begin? Pretty early, like 7 p.m. Okay. Sometimes even earlier, sometimes later, but mostly 7 p.m. So, and I find if I have a meeting, like a meeting where I'm talking to people and I'm working through people's broken English, then the energy drop-off is like catastrophic. It's like the plane being shot out of the sky. I just completely spiral into the ground. So, do you have any experience with Ritalin or Adderall? No, none, none. No, I'm a Daphanel. You've never tried a Daphanel. I'm trying to think of last time I took the pharmaceutical of any type, of any type whatsoever. The probably only thing I did was like antibiotics like 20 years ago. What about a condom? Did you use condoms back in the day? Yeah, yeah, but you know what? I lied. I did take, I guess it's probably oxy-cotton after some dental work. Like I took pain pills. I broke my arm. I took the same thing. So, but that's the only pharmaceuticals I've taken or that's worse. Now, how bad would it have to get before you became open to a pharmaceutical intervention? I would have to not be able to function. Okay, so your life would have to be absolutely destroyed before you'd consider a pharmaceutical intervention? Yes, yes, yes. I have a very stoic New England self-aligned attitude with regard to these things. It could be a noise, but... And you've always had this? I have, I have. Yes. I grew up in very austere circumstances. I'm not one of these suburban, you know, powder puffs. So do you feel that because Jesus suffered on a cross that you two have your cross to bear? I do, and I bear it well, my dude. Yeah, perhaps there's a masochistic streak to my personality. I wouldn't deny that.   That's right, man. I have X-ray vision.  Like an un-muddied lake.  I'm glad you understand, Luz. I see where you're going and you're making a leap here, bro. You're making the scene ideological and it's not ideological. No, it's psychological. It's a, we all have to have ways that we feel superior. I mean, I have all my ways where I feel superior to most other people.  No, I don't, it doesn't bolster my self-esteem.  Now, where do you get your self-esteem? Like break it down for me. Get self-esteem from having a productive work session. Okay, so you get self-esteem from work. Yes, yes. I don't go around seeking self-esteem so I never feel it's absence. I, you have transcended the human condition because well, normal average people need to feel, need to have a good reputation with themselves. You have transcended this average form of humanity. No, well, I have a philosophy like I think self-esteem slash contentment slash happiness, these things sort of are a side effect. They're not a goal. They're a side effect of a life well-led, a discipline's life well-led. They're not a goal in and of themselves. They're not like objects that you go after that attain through assiduous effort. They're, you feel these things after doing what needs a doing, bro. Yeah, and so you get self-esteem from a life well lived. Yeah, yeah, I would say so. Well, self-esteem, I mean, that's the term you use. I would just translate that to be like feelings of contentment and satisfaction. I'm talking about the reputation you have with yourself. I assume that you get to walk around having a good reputation with yourself. Is that fair? Okay, we've briefly lost Elliott. I hope people are coming back. So just speak up at any time, Elliott. Encouragement. A few people that talked to me told me a few things that helped me even when I wasn't sober yet. I'm going to try to do this without crying. Elliott, are you there? Speak up, man. All right. Okay, I made the lane change, dude. Okay, beautiful. Yeah, so tell me more about the reputation that you have with yourself having a life that you respect, you know, a life that's well lived. So you are a hard worker.   Tell me more about the way you've developed a good reputation with yourself. Uh, I've made a lot of mistakes and I've reflected upon them and I've resolved to behave differently after my mistakes. I've done the school of hard knocks. Yeah, other people look for help from like psychiatrists or 12-step programs or religion or cults, but Elliott Blatt stands on his own two feet. He is willing to take responsibility for his own mistakes. He takes accountability for his choices.  That's exactly right.  It doesn't work, bro. It's a simulacra. There's no, there's no shortcut loop. That's the first lesson I learned. There are no shortcuts. Once you accept that, that's ironically a shortcut. People burn up a lot of energy seeking shortcuts. When it would just be simpler, it would be more effective to confront the problem head on. So what percentage of the general population would you wish that they had a life more like yours? Every single one. Every single person, bro. Well, I mean, think about it, Luke. I mean, who do you want to have dinner with, right? Who would you rather have a chit chat with?  Would I rather have dinner with, say, someone who earned four times your income and had, say, four times your accomplishments in life than with you? No, I'd rather have dinner with you than someone who was much more successful. It's always about the money with you, bro. They're people, bro. Yeah, yeah, yeah. It's not the money. Oh, dear. So, mom, my way to do some car repair, a little extracurricular activity. I saved myself like 300 or 400 bucks on a car repair by doing it myself. How do you like that? That's a great idea.  That's right, bro. None of this weakness. I'll just get ripped off at the auto shop today. Not me, bro. I take the bull by the horns. That you do. And you do that every night, right? Only one necessary, bro. Only one necessary. Now, why are you pro mushrooms but anti-pharmaceuticals? Excellent question, bro. Because mushrooms encourage introspection. And introspection is a much more long-lasting solution than our sort of an artificial chemical lift. Mushrooms bring you to the point they allow you to examine your decision-making and resolve to make better decisions. Wow. One is system.  Mushrooms teaches a man to fish, bro. And what kind of choices and what kind of revelations have you received from use of mushrooms? Then I have a lot more control over my emotional reactions than I think I do or thought I did. So I don't need to react emotionally when I can just sort of interrupt that process of reacting emotionally and sort of reason my way through it and not do damage to my body. Like when you react emotionally, you sort of poison yourself. Your body releases all kinds of toxic chemicals and things. It takes a while to digest those toxic chemicals after you've reacted emotionally. So if you can interrupt that habit, most people have this habit, if you can learn how to interrupt that habit, you can spare yourself a lot of agony. Well, that's good because nobody ever gets poisoned from mushrooms. Well, you know, that's why you need a good hookup, bro. So let me know if I can help you there. Man, I appreciate that. Come on, man. I can't believe I honestly... So there is theoretically no toxic dose. There is no poisonous dose of... So there's no toxic, lethal dose of medical mushrooms. Silicited mushrooms, by the way. I haven't done them in a long time, but I'm really eager to, I have to say. I'm due for another journey, as it were. They're very safe. That's what you're saying. Yeah. Well, that's what the propaganda says. And when did you last do them? Um... Maybe two springs ago? Terry, that's so great. Why don't you do them since two springs ago? Because...   It's a different thing. It's a moral experience, bro. It's a... It's a... It's like a therapy session with yourself, bro. All right, listen, I'm at my destination. I might have to hang up soon. Blessings. Okay, blessings. I hope this... I hope this was the... Where's your time? Okay. All right. Fantastic. Okay, question in the chat. What low sugar fruit drinks you have this morning? Didn't have any, but I often drink vegetable juice, which is the type of vegetable juice that has no fruit juice, no added sugar that's low in sugar. It's got like two grams of protein, eight grams of carbs, so relatively fresh squeezed vegetable juice. Okay, let's play a little bit more from Shim F. It works if you work it from The Daily Reprieve, which is a podcast from Sexaholics Anonymous. The first thing is, you can't leave before the miracle happens. And I really wanted the miracle to happen. And if I leave, the miracle's not going to happen. The sponsor, not the first guy I told you about. Eventually, a friend in the program took me to a meeting and got me a new sponsor, unbeknownst to me or my sponsor. He kind of just introduced us and told my sponsor, Anthony, you're his sponsor. And then he walked away. And Anthony has been my sponsor ever since recently. I found another one only because of circumstances. Anthony moved down to Maryland. He's retired. We weren't talking as much and I'm working on certain things. I needed someone local, but my sponsor would say to me, you know, suit up and show up. And that's not something I'm powerless over. I can suit up and show up whether I'm sober a day, a week, a month, a year, a decade. It doesn't matter regardless of what's going on in my life and what happened yesterday, tomorrow, right now, right here, I can get my rear end to a meeting no matter what, I can do that. So don't leave before the miracle happened became something important to me and really, really accepting that I'm a sexoholic.  So get on with life. I don't mean that I shouldn't try to get sober, but if I do or don't get sober became, it didn't become the point. The point was that if I wasn't going to get sober, it wasn't going to be because I wasn't going to try. So I was going to do whatever I can do to get and stay sober. Knowing full well, it probably wasn't going to happen. And for me, that's my first step. There's this section in the book that I heard other speakers talk about over the last 24 hours. It's the acceptance paragraph in Dr. Paul's story in the big book. In the fourth edition, it's on page 417. And in there, there's a line. He says, until I could accept my alcoholism, I could not stay sober. That's a funny line. But for me, it meant I wasn't going to start staying sober until I fully conceded to my innermost self. I accepted the fact I'm a sexoholic and doesn't matter why everyone else is getting it and I'm not, but I'm a sexoholic. So the fact that I'm working my rear end off and not having any sobriety was not a good enough reason to give up. Giving up was taken off the table. And if I was going to succeed or not, it was going to be God's business. If I was going to try or not, it was going to be my business. And I can honestly say from that day to this, the only thing I've ever done consistently without any relapses is I've kept on trying without giving up. So when 12 staffers talk about powerless, that doesn't mean that they're arguing that they don't have power over anything. That means that they don't have sufficient power, not reliable enough power. So you drink to excess one out of every 10 times you drink. For many people, that's maladaptive that there's some maladaptive habit in your life and you lack sufficient power over drinking or it went out of 20 times. So when you join any 12-step program, like everybody in it will be struggling with lack of power in some area of their life. But that doesn't mean everyone in it is, just powerless over everything. We have insanity or lack of power in different areas of our life. So we can get help from each other because we have somewhat different struggles. When someone tells you that their sobriety date is June 21st of 2010, I hope you never think that means that whatever that sobriety date is that they never struggled again. They never lost it again. They never raged again. They never had those phone calls with their sponsors. Should I reset my sobriety again or not? Especially early on, there's a few things that happened in the first few months of my sobriety that I laugh at it now because if I would do something like that today, I would not be calling myself sober. But I was so desperate. It was like...


President Mohamed Ubarri has received the first made in Nigeria cell phone known as the ITF Mobile. Minister of Industry, Trade and Investment Adeni Adebayo presented the phone to the president before the commencement of Wednesday's Federal Executive Council meeting in Abuja. According to Mr Adebayo, the phone is one of the 12 cell phones produced using locally sourced components by the Electrical and Electronics Technology Department of the Industrial Training Fund's ITF's Model Schools Training Centre. Model Schools Training Centre, which is part of the Industrial Training Fund, the Industrial Training Fund being an agency under my Ministry of Industry, Trade and Investment, presented and launched a first indigenous mobile phone. So I had the honor and privilege of presenting a sample of the phone to Mr President today at the FEC meeting. So this is a phone, this is a sample of the phone that was presented and I have brought it here just to show it to you so that you see what we have produced as a Made in Nigeria mobile phone. Okay, that was made by the Model Schools Training Centre of the Industrial Training Fund.