Income tax 2022-2023. Earned income tax credit the EIC with three or more children tax software example. Let's do some wealth preservation with some tax preparation. Here we are in our example. Form 1040 populated with LASERT tax software. You don't need tax software to follow along, but it's a great tool to run scenarios with. You can also get access to the form 1040 related forms and schedules at the IRS website, irs.gov, irs.gov, starting point. Single filer Mr. Anderson livin' 90210 Beverly Hills, 100,000 W2 income which is way over the threshold for the Earned Income tax credit. But that's our traditional starting point, so that's where we'll start. We've got the 12,950 on the standard deduction 87,050 for the taxable income. Page number two, calculated the tax at 14774, 15,000 for the payments. That gets us to our 226. Let's go back to page one. We want to think about an Earned Income tax credit if we had three qualifying children or more because the Earned Income tax credit doesn't give any more benefit past those three children. So we'll think about that remembering that. You typically want to think about the curve in terms of how high your income is and what they support. Accounting instruction by clicking the link below, giving you a free month membership to all of the content on our website broken out by category further broken out by course. Each course then organized in a logical, reasonable fashion, making it much more easy to find what you need than can be done on a YouTube page. We also include added resources such as Excel practice problems, PDF files and more like QuickBooks backup files when applicable. So once again, click the link below for a free month membership to our website and all the content on it. Maximum credit will be per area or per level of one child or zero children, one child, two children, three or more children. And then it's slightly different as well if you're married or not married, although it's not doubled when married. And therefore, especially when we get up to these higher numbers of children. You can imagine if three if someone that had three children that had head of household filing status married another person that had three children of head of household filing status, that there could be a significant decrease and the benefit from the earned income tax credit because the credit doesn't change in terms of the maximum credit. It's at the six thousand nine thirty five and the maximum income threshold doesn't double, but only goes to the fifty nine thousand one eighty seven. And you're not going to get any more benefit from the three kids. Now you'd have six kids right instead of and you're still going to cap out at three kids in order to get a benefit. So we'll take a look at that as well. And we'll try to plot out kind of a graph of what this looks like. So it's kind of interesting and just want to point out that on those major life events on the lower income side of things, if you're dealing with the child tax credit or getting a child tax credit and their income tax credit, it kind of seems like the credits are designed or intentionally or unintentionally to kind of disincentivize marriage in some cases. So you'd want to think about whether or not it would be, you know, you want to take that into consideration. So it's not like a shock. And so we'll take a look at that on the higher income side of things. Marriage is usually beneficial because most things double on the higher income side, like the standard deduction doubles and the tax tables double. Okay, so we'll dive into that as well. All right, so we know that when we add three children, that's going to be basically moving us if we were single to head of household status. So let's do that first. All right, so Mr. Anderson now head of household status on not married three kids. We've got Joe, that should be Jill, Jill, Jill. And then we just started naming them by numbers after their child number three. And then so that means that our standard deduction went up to $19,400. We still don't get the earned income tax credit because of course we are over the income threshold in order to do it. The maximum income threshold to get anything would be close to $60,059.187. So let's do our graphing thing so that we can basically see as our income goes up, what happens to this credit with three or more children. So I'm going to go back on over and say, all right, let's bring my income. Let's do increments of $5,000. Let's start at $5,000 and see what happens. We're going to say that we have $5,000. And so obviously our $19,004 is greater than that. So no taxable income, but may still get a benefit from the earned income tax credit because it's refundable. And it's at the 2261. So let's go ahead and graph this out. So here we have wages $5,000, 2261. Let's bring it up to $10,000. We'll just do increments of $5,000 and bring it on up. Just to graph it on out. Bring it on up to graph it on out. I'm going to get rid of the $15,000 withheld just so we don't have to deal with that. And that's going to give us the $4,511. So let's say, OK, now it went up to $4,511. The maximum is $6,9. So let's $6,935. Let's go up to $15,000. $15,000. $15,000. Can I get a $15,000? Can I get a $15,000? There we have it, $15,000. And that results in to $6,761. Not at the max yet. $6,761. Let's go to $20,000. $20,000. Can I get a $20,000? $20,000. $20,000. Do I see a $20,000? At $20,000, we get the $6,935. That's at the max now. So now we're at $6,935. Let's go to $25,000. $25,000. $25,000. $25,000. $25,000. $25,000. $25,000. And bring that on over. That's at now the $5,904. So we're going to see that right now. It's going back down. $5,904. That's $25,000. $30,000. $30,000. $30,000. Let's do that. Boom. That brings it to the $4851. one so four eight five one thirty five thousand thirty five thirty five thirty five thousand thirty five thousand I should have just there it is that brings it to three seven nine eight so three seven nine eight forty thousand we're getting close to the upper threshold it's going back down now of course as income goes up not four hundred thousand that's too many zeros it's only one too many that's too many two seven four five only one too many crying out loud now you got two little zeros here and you're lucky this is just a practice problem ridiculous all right calm down for forty five thousand forty five thousand let's see what happens then one six nine two one six nine two let's go to fifty thousand almost there fifty thousand boom okay so now we're at six thirty nine so six three nine and fifty five thousand is going to be over the threshold for single it's it's a higher for married but fifty five thousand that should be over the threshold and that should take it to zero boom okay so just to get an idea so when you see this graph it it says you know it caps out here but really you're not going to get that full credit at the AGI cap that's when it goes basically to zero you don't get anything if I was to graph this let's do ahead and insert the graph to get a pictorial representation because pictures I like pictures that's how I understand stuff so we got as the income goes up the amount of the credit goes up it caps off at that six nine three five around the twenty thousand and then it goes back down again so there we have it and so then I can I can compare that to what's on our 1040 instructions similar process except the instructions are you know have a lot more plot points right so if we had three or more three or more over here then as our income goes up then the amount of the credit goes up goes up goes up we're over here three or more incomes going up the credit goes up and then we're still going up over twelve thousand of income and then it's going to cap out at that six nine so it's still going up and then it caps out at six nine three five which is around the fifteen thousand four hundred and then it stays there for some time stays there for some time six nine three five until you get to twenty thousand two hundred about and then it starts going back down so if I look at our graph here there's the twenty thousand it's maxed out twenty five thousand it should be at five nine oh four so twenty five twenty five twenty five thousand twenty five thousand it's at the five nine oh four and then if I go down to the thirty thousand four eight five one thirty thousand thirty thousand is over here thirty thousand four eight five one and so on so I think I got those plot points hopefully mostly right so you can get an idea of the visual chart here all right so so that's the general idea now if I added let's go back to the twenty thousand where it's maxed out let's go back to the twenty thousand so it's maxed out twenty thousand credit maxed out at the six nine three five and let's add another kid why not why not at this point no I don't even know these kids are already driving me crazy one more is not gonna hurt all right so now we got four kids still head of household and four kids over here it's just ridiculous a madhouse only earning twenty thousand so I barely got you know the money to hold on to these kids but I'm still at the six nine three five because you don't get any more benefit from the EIC above that threshold now now if now if they were married like if I if I go to married the threshold will change so you can imagine another curve but it's not exactly doubling everything because you still have the maximum at the six nine three five and you're only having it a maximum agi so you can imagine this whole bell curve basically kind of or whatever whatever you want this curve basically shifting to the right would be kind of kind of the idea so that so that the maximum income level you'd get would be here instead of here but the still you have the max here so you can imagine the situation that if you had two people that got married and let's say they had like like one has two kids and one has one kid or something like that then they could be maximizing the credit of three thousand seven thirty three and six thousand one sixty four between the two of them and if they got married then they would have like three kids which would bring the maximum credit up to to here but it but you'd probably end up in a worse or situation even then even though you're going up to another tier level on the married level because of the because of the income thresholds but but notice if you had like one had two kids six one six four plus three seven three three and you're maxing it out that would be at the nine thousand nine thousand eight ninety seven if you're maximizing these two out and then if you were married and you got three kids then it would be at the six nine three five but it gets even gets worse if for example you had you had two people head of household that were maximizing the six thousand one sixty four times two six one six four times two and then you get married you're losing the benefit from the earned income tax credit of one kid all together right because you don't get any of that credit and then if you had two people that have three or more kids right if they had three kids let's say they had more you know let's say they both had three kids you could just say okay well if they get married do they get a benefit for six kids now no it's still capped at three kids so then you could see that would be a big disincentive you would think on the married side of things so let's just see let's just kind of get an idea of that if I was to say okay there's three four kids three kids doesn't matter for the single filer so let's say we had let's write it down here we've got head of household head of household three or more or more kids and we're gonna say then the income is 20,000 and we said the earned income credit is gonna be six nine three five six nine three five is that what we said it was yeah and then we said that the refund according to this calculation just the total refund for this example because that includes the child tax credit one is nine five six zero so nine five six nine five six zero okay and then if I multiply that times two I imagined two people filing head of household their income total would be 20,000 earned income tax credit between the two of them filing separately 13 870 and their refund between the two of them would be 19 120 so now what if they were married married we know the income would go up doubling it to 40 what happens to the earn income credit and the refund so let's do that let's go back on over and imagine we had two people that are in this scenario with three or more kids and whatnot and then they got married and so now we're gonna have six kids I got four here but it doesn't matter after three anyway so let's add six kids married couple all right so hopefully I got it all correct here so now we got married filing status is married filing joint you got you got Mrs. and Mr. and Mrs. and Mr. Anderson now we have to have a whole nother statement for our dependents over here because there's too many to fit on the lines they provided but we got one two three four five six kids now six kids and we're gonna say okay then 40,000 of income because we had two people that had 20,000 so they were maximizing their their their benefit before from the earned income tax credit at 6935 and the standard deduction doubles like you would normally think you know something would double if married the tax rates are adjusted for married but the credit here is now calculating at the 4036 for the earned income tax credit so 4036 4036 now remember this the maximum tax credit was 6935 that they were both getting before when they had three or more kids but had 20,000 of income because the 40,000 income they did the incomes don't double right so you can imagine this curve kind of shifting to the right but it doesn't like double so they're actually getting less than the maximum credit even though they got six kids now and the 40,000 of income married which as opposed to 20 and 20 before and so that comes out to 9661 so 9661 so you can see again you could come up with some substantial differences between two people filing 40,000 income between the two of them 2020 each and the earned income tax credit you know could have a significant difference between if they got if they got married and it's kind of a sad situation that the the allocation of the kids and whatnot I mean that could be a significant difference on the income could have some influence on you know the whole decision-making process but it is what it is so you want to be so you want to be aware of like if you're in that kind of situation then you got to think that there's gonna be tax you know the tax consequences could be kind of significant and you want to make sure you're kind of mapping them out so that so it's not like a shock if you get married and you're like hey wait a second this came when it is a lot less than we would have got as two separate head of household filers and again on the higher income side of things if you don't have those refundable credits usually getting married is a benefit it's not disincentivized by the tax code because because the standard deduction actually doubles if you got married which usually the incomes don't exactly double because if on the upper income side of things because usually one person possibly has more income than the other because they're splitting up the house and whatnot and then on page number two the tax rates usually are reflected as you would kind of expect if you had twice as much income so that it doesn't disincentivize a marriage situation but for some reason these well it's hard to figure all this stuff out but the refundable tax credits kind of create weird incentives so that is that also remember of course that that the other income such as Schedule C income instead of W2 income would also be earned income and and have a similar function of it increasing and decreasing according to the curve as Schedule C income goes up and down business income and other income that's that's more passive income like investment income does not have an effect on that curve of income and if there's too much investment income you can actually lose the earned income tax credit because if you had a significant amount of interest income and dividend income that would indicate you got a significant amount of money in the checking account or and or in the in investments so you would think you wouldn't need the earned income credit in that case


Usually, when they stand up, one is on this side and the other is on the other side. United States and Mrs. Reagan. Ladies and gentlemen, the national anthems of the People's Republic of China and the United States of America. Today, to welcome you to my visit to China last year, I, Mr. President Lee and I were in charge of the rising standard of living. The American people are working with them as friends and partners and a prize. Trade between this is at a record level and continues to thrive. Scientific record can be expected to improve. Our educational and cultural exchanges, already substantial, are expanding, enhancing our mutual security and bolstering world peace as well. Both our peoples should be proud that in a few short years, a solid foundation of good will has been made. It doesn't mean that there are no areas of disagreement. However, we will continue to put any differences in perspective. Chinese principle that can serve as a tool in building an ever stronger bond between us. Beijing has leaders of great nations which expect nothing more and accept nothing less. President Lee, we Americans highly value the United States. I say, bonding, welcome. Mr. President, a kind invitation of President Reagan. I've come to pay tribute to a great country. On behalf of the Chinese government and the people, I wish to extend our heartfelt thanks and best wishes to the American government and the people. Mr. President, I'm very happy to see that you are recovering so fast and I'm deeply touched by your participation in this welcoming ceremony. The purpose of my current visit is to deepen in the past two centuries or more. The Sino-US relations went through a culture's road with both exciting moments of joy and the painful periods that provoked thought. Thank you for the establishment of a long-term and stable relationship of friendship. The Sino-US relations have made very big progress.  A dozen years has passed. When we look back, we should be able to feel gratified as we do today that as we proceed, difficulties are increasingly reduced and our steps grow more vigorous. Thank you.


Biden. Putin already lost Ukraine. US President Joe Biden said that Russian President Vladimir Putin has already lost Ukraine. Adding that aid to Ukraine during the Russian invasion is open-ended. There's no way that Putin is going to be able to. He's already lost Ukraine, Biden said. He thought that if he invaded Ukraine first of all he'd get a welcome by every Russian speaker. They'd say come on in. Secondly, he thought what would happen is that NATO would collapse. NATO would not do anything. They'd be afraid to act. Go down the line. None of that's happening. He said in a PBS news hour interview the day after he delivered the State of the Union address. Biden said NATO is coordinating in support of Ukraine despite Putin thinking it wouldn't. His comments come after he stressed his support for Ukraine amid Russia's invasion during the State of the Union and recognized Oksana Markarova, Ukraine's ambassador to the US in the audience. Biden also pushed back on criticism from a small group of Republican lawmakers who have suggested that too much US assistance is going to Ukraine. PBS's Judy Woodruff mentioned Republican Jim Jordan, Republican for Ohio, who has suggested money spent in Ukraine should go to Americans and Biden audibly laughed. If these guys don't want to help Ukraine I get it. They don't want to do that but what are they going to do when Russia rolls across Ukraine or into Belarus or anywhere else he added. When asked if aid to Ukraine is open-ended Biden replied yeah it is. The first anniversary of the full-scale Russian invasion will be on February the 24th. Since then US military assistance to Ukraine has exceeded an estimated $28 billion.


Countdown for blast off x minus five minus four minus three minus two x minus one fire From the far horizons of the unknown come transcribed tales of new dimensions in time and space These are stories of the future Adventures in which you'll live in a million could be years on a thousand would be world the national broadcasting company presents One one tonight Universe we are just beginning to discover how boundless our universe really is and Yet as man reaches out to the stars out toward infinity Ironically enough he may be building himself a new kind of prison What would it be like to live all your life in a world? No larger say than a single gigantic rocket ship bound on an endless mercy Yes, just missed me. What was it mutant with a slingshot? I think Dash down that passageway want to go after it. Oh, we'd never catch it Alan Probably 12 decks above us by now. I didn't think they ever came down this far Trolls usually get them before they reach this level. They get more daring each generation This would look like a female male or female. It might have killed us.  We're almost there now. Let me see compartment X 15 level 24 This is the place This area smells if it hadn't been visited by a sanitation crew for generations Part of the ship is almost deserted Yes, is this the compartment of John the witness who are you my name is Hugh Hoylund Cadet from scientist barracks. This is my friend Alan Mahoney. What do you want of John the witness? I'll only to talk Are you a believer in Jordan? Naturally might have heard that there are those among the younger scientists who doubt the word of Jordan to doubt his death We're not heretics Enter I Brought you a gift of tobacco grown on the richest level It smells good, I assure you it's of the best wait here I'll get him What the devil you think he can tell you Alan, I'm not sure I'm not sure Are you John the witness? I am good eating to you. I'm you Hoylund. This is my friend Alan Mahoney What brings a gentleman of the scientist class to my humble compartment? I've heard that you and your parents before you have been keepers of the legend of the ship since Jordan gave the word I'm anxious to hear the word as Jordan spoke it. Why? Because our young scientists Well among them there have been some who talk against the word there are regulations against such heresy Still some of them say the ship has no purpose They say that we are here accidentally that we have no more grace in Jordan's eyes and the most deformed mutant Who dwells in the highest level of the ship? What shall I say to you? I wish to hear the word from the mouth of one who knows In order that I may become more convinced sit You have a gift for the witness be finest tobacco good I will dim the lights Now pay close attention for these are the words as my father's father's father gave them to his son's son's son This is how the ship came into being how our people were created In the beginning there was only Jordan Thinking his lonely thoughts Out of his thoughts came a vision Out of the vision came a planning and out of the planning came decision Jordan's hand was lifted and the ship was born Mile after mile of good compartments Tank after tank for golden corn Ladder and passage door and locker fit for the needs of the yet unborn He looked on his work and found it pleasing meet for a race that was yet to be He thought of man and man came into being Then Jordan checked his thoughts and set for a key Man untamed would shame his maker Man unruled would spoil the plan So Jordan made the regulations and order came to the works of man A crew he created to work at their stations Scientists to guide the plan Over them all he created captain made him judge of the race of man Thus it was in the golden age These are the true words as my father's father taught them But what are the strange beasts like people on the upper levels of the ship? Surely Jordan did not create them Jordan is perfect All below him lack perfection You have heard of the legend of Huff I have heard that he mutinied against Jordan Darkness swallowed the ways of virtue sin prevailed upon the ship And before wisdom prevailed in the bodies of Huff and his followers were fed into the converter Some of the rebels escaped and lived to father the mutants They are tainted with the sins of their fathers witness One more question speak What is the ship the ship is a great sphere 25 kilometers wide and 100 levels deep I know that but the upper levels Regulations forbid us to venture into the upper levels But it is said that beyond the levels of the mutants lies the forbidden place Where Jordan's spirit prevailed so I've heard yet something troubles me Something which prompted my coming here. Yes, my son What lies Beyond the ship What what lies beyond the ship? This is where is the answer me I will not permit such talk The ship is complete the ship is universal the ship is everywhere. The ship is endless Your motherings are those of a frightened old man. They answer nothing. You question the word. I think you lie Hear me, mr. Hoyland for what you have already said I can have your body fed into the converter You're so launched on the endless trip. You threaten me you for Jordan's sake Do you think I fear this dried fig of a man you Sir, my friend is impetuous. He he does not understand I might be persuaded to forget the Substantial gift why you Helen come on the side of this so-called holy man offends me Don't try to frighten me with that gun old man. The main way you are heretic I warn you put down that gun. Oh, no no no closer drop it very well then death to the heretic Allen get him Allen He's not breathing Is he dead? I don't know Come on here. We've got to get out of here right Now where we can't go back. They'd feed us into the converter before we could even What's that an alarm that old woman must have turned it in come on Allen the patrol will be here in no time Where can we go? Where where? The upper levels all the mutants will have to take our chances. Come on, Allen. Let's go Listen, that's the patrol. Come on. We've got to climb There's a hatchway come on the corridor like quickly quickly Allen Pure way Wait How far are we from the outside wall judging?  I've been thinking about it for a long time And he began to give me those stupid tight answers And I just saw red I guess Who are you to question the ways of jordan? When you asked me to go with you to visit the witness I I thought you wanted spiritual help. I never agree. I'm sorry Allen. I'm sorry. I couldn't foresee this Wait a minute. I saw something move. Where near that volcano. I don't see anything Maybe my eyes are going bad Listen You're behind us What are you That knife keep away from me you Who are you I must forgive my friend bobo like so many of my people. He's rather impetuous. We're members of the so-called super racer. Who are you? What place is this? And you can guess from my leg I'm a mutant mutant Where Where is allen? Your friend is dead dead.  Highland Only when necessary You know my name. I read your identification tag Who are your mutants can't read my name is greggory greggory? I'm a leader of my people. You see although we are unfortunate and now I read it to mr.   That monster I've never seen a creature like him bobo is an unfortunate He was born without the power of speech. How can you tolerate such a monstrosity? We've learned to live with difference If we began to destroy our imperfect as you do on the lower levels there would soon be no one left it violates the regulations The word of jordan states the highland your people are really quite primitive and barbaric You dare say that to me and dare say a good deal more. Let us go to my compartment and speak further I'm always interested in information of the lower levels. I'll give you no information bobo Mr. Highland in my cabin, please That requires you to go quiet Bobo has a hatred of superior beings which is unfortunate but quite understandable Proceed And to mr. Highland, this is where you live. Yes But you have books stolen from your libraries mr. Highland Comptons astrophysics philosophy then is still a navigation celestial mechanic You've read these most of them. I had no idea that you why did you bring me here? What do you intend to do? You believe in jordan mr. Highland There is no other belief and the trip I suppose you believe in the trip too. What else is there to believe?  By the centaurus, of course And where or what is centaurus centauruses? Mind you i'm just telling you the orthodox answers centaurus is where you arrive when you've made the trip The place where everybody is happy and where there's always good eating and you believe this Well the Peasants believe it literally but many of the younger scientists like myself know it is figurative and symbolic Why do you ask Did it ever occur to you mr. Highland? But the trip is exactly what your peasants believe it is what and that the ship and all the crew were actually going somewhere moving Ship can't go anywhere. It already is everywhere.   It's forbidden to think such thoughts. Where would it go? I can't think about it bubble We're going to take mr. Highland to the place no Where Where are we going to the top level that's certain death nonsense? I've been there a thousand times No, I won't I want you can't make me. I think we can Please We proceed peacefully or shall I have bobo persuade you? Open the door bobo Inside Places this this mr. Highland is the main control room And mr. Highland you're trembling it isn't true Oh No, there's no such place except in mythology You younger minors so wise mr. Highland except for one thing this happens to be the main control room of the ship main control But it's just a huge room with an instrument panel and what did you expect? How do you know this is the main control room see these instruments? Using them the navigator many hundreds of years ago actually steered the ship on its voyage. I don't understand I didn't suppose you would Sit down very well look up What do you see A huge shield watch it for one moment mr.  Keep your eyes focused on the shield above us ready I It's sliding back What am I seeing the universe mr. Highland The universe and all its beauty The stars the planets the suns and moons and constellation.  Highland. Do you deny it? No No, I can't deny it They've lied they lied to all of us I have showed this to others of your people whom we captured and though they saw it before their very eyes They would not believe it. Please Please tell me all about it Tell me the truth about the ship and about the universe. What are these things? How did this come about? Many thousands of years ago On a planet like those you have just seen and planet called earth A scientist named Jordan Decided to build a ship that would carry men from one planet to another For many years Jordan and thousands of others studied and planned And when they were finished they built the ship The ship so large That it had to be assembled in its own orbit beyond the place called the moon 60 years it took them to construct And when it was finished a whole new science had been conceived Then the trip was begun The trip that was to land a colony of earthmen on a far off planet called centaurus Millions of light years beyond the furthest planet ever reached before How do you know these things? Among my books are the log which Jordan himself kept and the records of the journey for the first 40 years. What happened? There was a mutiny A man named hath led a rebellion of those who wanted to turn back In the struggle the navigators were killed The crew fell into a state of anarchy In the years to follow small groups of men tried to organize the ship for navigation and each time they failed Finally the whole idea was abandoned and so for centuries We have swung in space unmanned undirected living in a lost world of our own making without purpose without direction Why have you told me this? Can't you guess You want to finish the trip? Yes But I can't You can't? Look at me mr. Hoyland You see a mutant A man with a twisted leg My people are outcasts condemned to death if we so much as set foot in the lower levels of the ship The main drive is in the lower levels where my people are forbidden to go Oh, it would mean that both our people would have to work together Our differences encouraged rather than denied All right I'll see the captain himself I have an uncle on the central board. I'll tell him what I've seen here And do you think he'll believe you? Send one of your people with me That's asking a good deal I'm risking a good deal by going back Very well Bobo will go with you Bobo He can't talk There will be no need for talk I will write a message Guaranteeing safe conduct for a group of unarmed scientists to visit the main control room Bobo will take you safely through our territory What happens when you reach your own level Is up to you Yes, what? You quick uncle let us in But this is this mutant He's harmless, please uncle please Now what is this you're wanted for I know all about that uncle listen I must see the captain Captain are you mad? Uncle you're a council member you can get me to see He'll kill you you're wanted for Harrison I don't care I must speak with the captain Now uncle you're close to him you can arrange it I don't understand Listen to me The ship is moving I can prove it do you understand There is a purpose in the ship I don't understand what you're babbling about Never mind Just talk to the captain tell him I have information of tremendous importance Tell him I've arranged a truce with the mutants Truce Here show him this paper signed by their leader Do it uncle for my sake I don't know what Uncle please if I'm to die let this be my last request to you Very well I'll speak to the captain And you say Mr. Hoylan that you saw this with your own eyes I swear it captain I swear it on the word of Jordan Let me see the paper again Commander erst what do you think? I don't know sir it might be a trick I guarantee you safe conduct If these things are as Mr. Hoylan reports them It would pay to risk a few lives A man is a convicted heretic Still we must not discount his word He has a safe conduct And the mutant who risked its life coming with him I think we might investigate Captain You mean you will do it I will have an expedition outfitted Dismissed Mr. Hoylan Thank you sir Captain Commander erst sir You will make the necessary arrangements for an expedition And I trust you understand And Perfectly sir Perfectly Lieutenant Mr. Hoylan Are you a better heart your men here this is the spot Patrol Well I see no welcoming party of mutants There'll be none Their leader will meet you inside the main control room You don't say Just where is this main control room? Beyond that door I see All right man Ready on Lieutenant Why do you ready arms? In case of ambush Ambush Now wait a minute Lieutenant What are those men doing with that ray gun? Just aiming it at the door Are you mad? No Mr. Hoylan But most certainly you are to think that we could be lured up here to be slotted with a fantastic story about some mythical control room Guns ready sir Lieutenant I warn you these people have acted in good faith you can't break that faith Oh mutant Come out For Jordan's safety Lieutenant Mutant Open the door Are these opening ready men?  Yes What's this machinery? These are the controls he would have used to steer the ship Gone out of his mind Lieutenant Steer the ship who?   But I I say to you That you can't keep this from our people They will seek it out The ship will be man And the ship will be steered And there will be freedom, purpose and respect for ourselves This is your heritage Look Look upon the universe Kill him Die! X-1 has just brought you Universe A story written by Robert Heinlein And adapted for radio by George Lefferts Heard in the cast were Donald Buca as Hugh Peter Cappell as Gregory Bill Griffith as Alan Abby Lewis as the woman Edgar Staley as the witness Jason Johnson as the uncle John Seymour as the captain And Ian Martin as the lieutenant Your announcer is Fred Collins X-1 is directed by Fred Way And is a transcribed NBC radio network production And now Next week Next week we have a strange story to tell A sweet blood-curdling little story That is rarely only two sentences long The last man on earth sat alone in a room And then There was a knock on the door What not on that door You'll find out next week on Minus Minus Minus Minus One One When you buy United States savings bonds You help to build your own future security Here is an opportunity to save systematically For long-range personal objective


What is up guys Karma medic here and welcome back to another dose gonna make a quick video today talking about the ucat calculator because I think it's so important for saving time in the qr section and I think it'll help improve your scores a lot if you learn how to use it properly really quick before we start today's video I want to give a shout out to my two good friends Ami and Teddy who got me this karma medic branded sweater for my birthday. I really really like it So thank you very much. Also this video is made in partnership with medify. They're the online ucat resource that I'm sure you've seen me use a hundred times by now They have an online ucat question bank with thousands of questions to help you guys practice for your ucat exam So if you guys are interested in learning more about medify you can check them out in the links down below Okay, so talking about the ucat calculator I'm gonna walk you guys through every single bit of it so that you know how to use it in its entirety And hopefully it's gonna save you a lot of time in the qr section Alright, so I'm gonna pull up the calculator on my laptop and I'm gonna screen record it so you guys can see what it is that I'm doing Okay, so this is the ucat calculator It looks kind of similar to calculators that you might have used before But it doesn't have nearly as many of the functions as we want as many functions as we're used to And so you have to get used to this sort of dumbed-down version of a calculator Anyways, it works in a lot of the same ways as another calculator 9x9 is still 81, etc But it has a couple of functions that I think are very very useful for you to know if you're taking the ucat exam So the first thing that you have to know is how to use these three memory buttons up here So what these buttons stand for is MRC stands for memory recall So recalling what is in memory memory minus subtract from what is in memory and memory plus which is add to what is in memory So let me give you guys an example Let's say you're solving a ucat question and I don't know for some reason you have like 89 orange dogs And you have to multiply them by 536 dog walkers And you end up with this number of 47,704 Now instead of taking your pen going down and writing down this number While looking up and down in order to make sure that you've written down the correct thing You can simply store this number in memory And the way that you do that is that you click memory plus So memory plus means add to memory Since there's nothing in memory right now, we're going to add all of this to memory So memory plus, you'll see this little M appears over here in the corner Which lets you know that there is something stored in memory So now I can clear this, I can do some other calculations like 8 times 6 is 48 whatever I can divide by 3.2 I can still use the calculator to do any other calculations that I would want to do However, at any point I can now recall what is in memory by clicking this memory recall button So if I click it, it will show me what is in memory, which is fantastic Because I might have done a calculation and gone in some really long complicated number And instead of taking the time to write that out, I could just store it in memory So now let's say I want to add or subtract something from this number So let's say I want to subtract 704 from this number What I can do is after doing some other calculation for example I can say 704 and then I can click memory minus So that means take 704 and subtract it from memory So if I click memory minus and then we go do some other stuff whatever And then we go to recall what is in memory, you will see that it's now 47,000 So I removed 704 from memory In a similar way you can add 2 memory So let's say we want to add 53 to memory You click 53, memory plus, add to memory And then if we hit memory recall, you can see that it's 47,053 So this is honestly invaluable when you're doing your UCANN exam You can save so much time by saving numbers to memory And then recalling it and referring to it later Instead of having to write everything down and do calculations one by one And then also very importantly if you want to clear memory If you want to get rid of what is stored in memory You hit memory minus and then memory recall And you'll see that here in the top left corner the M disappears So let's say we had 8 stored in memory You'll see there's an M over here If we recall it, there's an 8 If we want to remove the 8 from memory, you click memory minus And then memory recall, the M is gone and it's gone from memory So please learn how to use these functions in order to solve questions in the QR section It's going to save you so much time and really you'll find it very, very valuable Now these three buttons up here, the plus minus, the square root and the percentage They work a little bit different than the graphic calculators that you might be used to Especially if you're doing the IB On a graphic calculator what I would normally be used to is saying The square root of 64 equals and then I would expect to get 8 However on this calculator what you have to do is hit 64 and then the square root button So it's like you're saying 64, what is the square root of that? And then it will give you 8 So you kind of have to do it backwards if that makes sense Also this button up here plus minus, it just changes the sign of whatever number you have on the screen So right now this number is positive 8 If you hit the minus, this number becomes negative 8 So if we do negative 8 plus 4, you'll get negative 4 as you can see So that's what this button does And then the percentage button, this is useful if you want to do For example, let's say you need to find out what is 75% of 100 Obviously we know that's 75, but just to make a simple example So what you can do is 100 times 75% Instead of writing out 100 times 0.75, which is what I would normally do So that's all the buttons of the calculator The second thing that can really help you save time when you're using this calculator Is learning how to use the shortcuts So the one that I found most useful for the calculator was using CTRL C And that's what makes the calculator appear or disappear Also if you want to close the calculator, you don't have to click the little X that is on it You can click anywhere on the screen and it will just disappear And then the last thing that I want to say about using the calculator on the UCAT exam Is please, please, please learn how to use the number pad on the right-most side of the keyboard In order to input your numbers into the calculator So yes, you can use your mouse to click on the numbers You can use the numbers at the top of the keyboard that are in a straight line But both of these are going to take you significantly longer than if you learn how to use the number pad on the right So yeah, if you can use the number pad, because honestly that's just the fastest possible way to do it If you find that to be a bit confusing or it's too much trouble Then you can use the number pad to input the numbers and you can use the mouse In order to click the different functions So multiplication, division, subtraction and addition Okay, and I think that's everything that I can say about the UCAT calculator Again, I want to emphasize how important it is to learn how to use those memory functions on the calculator They're going to save you a lot of time when it comes to exam day I hope you guys have found this video useful and if you have any questions for me You can leave them in a comment down below Make sure you like this video if you found it useful And subscribe to my channel if you want to see other medical school related content from me Anyways, that is it for me and I will see you guys in the next video Peace


All right, hi everyone. I'm Mike Deemer. I'm a product manager at Dynatrace and an open feature maintainer. And today I'm excited to tell you about client-side feature flagging with open feature. There we go. All right, so, sorry about that, technical issues. All right, before we dive into the technical details of the presentation, I'd just like to do a quick level set on what a feature flag is and why they're basically essential to modern software development practices. So a feature flag is a technique that allows you to control a pivot point in your application at runtime. They do not require the code to be changed or a service to be redeployed or restarted in order for the value to change. Feature Flags allow you to decouple feature releases from deployments and they allow teams to coordinate feature releases on their schedule. Progressively enabling a feature flag allows you to reduce risk by tightly controlling the impact radius. They also allow you to quickly abort a failed deployment by basically instantaneously allowing you to revert the change. Teams are also able to experiment using feature flags by defining a control group and multiple different variations and then testing the impact that the feature has. So really they become very essential to the whole modern software development lifecycle. All right, then I just really wanted to quickly talk about open feature itself. So it's an open, we're a CNCF incubating project that's created an open specification for vendor agnostic feature flagging. We've created many SDKs in popular languages that seamlessly integrate with the commercial solutions or in-house vendors. And then today I'd like to announce that we've released a web 1.0 SDK. This has basically been a long time coming. We started with server side use cases but really we see that obviously the web is extremely important to people and it's been a long time coming to make sure that we can support client side and server side feature flagging use cases with a consistent API that's completely vendor agnostic. The web SDK is foundational SDK that can be used on its own but it also lays the groundwork for framework specific implementations. So having a web or a vendor neutral web SDK means that everyone can benefit from the SDK regardless of where your future flags are managed. And if you're interested definitely take a look at the blog. It's part of the QR code that you can scan right there. Although basically client side feature flags look very similar to server side feature flags there are some subtle differences. It takes advantage of what we call the static context paradigm and that's what I'm going to talk about in a moment. All right the static context paradigm basically in feature flagging you're commonly leveraging relevant contextual data. So in open feature we call it evaluation context. On web or mobile evaluation context typically remains consistent for the duration of the user session. It allows us to perform async operations early and cache the results. In this example we're setting the user session email and browser in the context and then the open SDK or open feature SDK then bulk evaluates all the related feature flags and stores the results in the client until the context or the feature definition is modified. Notice that all the context defined is unlikely to change for the duration of the session. And if any of this is interesting to you we have a lot of practical examples this week so there is a session on compliance and experimentation. It's called feature management improv with Todd Bart. It's tomorrow at five twenty five and then I'll also be presenting on progressive delivery. It's an observable feature rollouts with myself and Dan Dyla from the open telemetry governance committee. That's on Friday at four o'clock and let's see. Also if you're interested we're going to be in the booth we have the afternoon shifts in the project pavilion so please stop by. If you're also interested if you're around on Friday from 11 to 12 30 we're going to be doing a contrib pass so if you want to get your hands dirty on some code and work with some of the maintainers definitely please feel free to stop by. And there's a quick link to our website if you're interested to learn more. So thanks for your time. Appreciate it.


After a lot of indecision, I decided on a method of examination, which is going to be to ask you to give you some questions of which you will be able to opt for four out of more and to ask you to describe in your words in no more than ten lines what you understood of it or what you think of it. You can use your notes. Now, if you're going to prepare super notes so that everything is covered, better still, I've achieved what I wanted, and if you prefer, because this is not a test of English, if you prefer to do it in French or in Spanish or in Italian, you can do it, okay? Not other languages. My resources are limited. So those are the languages I can more or less speak, but that's all. Yeah, okay, and let me tell you, now I see the end of the tunnel. So what we're going to do is the following, and I hope that we will make it. We will see the equilibrium theorems that are important, a linear response in equilibrium today, and then we will do a little bit of large deviations, and my desire is to show you the fluctuation theorem, which is one of the most popular results in the last 30 years in auto-equilibrium, and which will also give you a clear idea of the second principle and entropy production. So it's a very nice exercise, and then the last day or so, we are going to see a bit of active matter, which is the violation of all the things that equilibrium gives you, and I'm going to be very brief, but you will see more or less how it goes, okay? So that should be it, okay? So now, linear response slash equilibrium theorems. So imagine you are in a situation where your system is in equilibrium. Somebody wants to ask? Ah, yeah. Please, before you start, I have some quick questions. Does every equilibrium system satisfy the detailed balance? Oh yes, but let me insist on this point. As I told you a few times, I am using equilibrium, and everybody uses equilibrium in several different senses, so let's be clear. First of all, sense number one, your bath is a good equilibrium bath. This is given to you by all the things we did to construct a good decent bath with response with noise correlated in a way it has to do and so on, let's say of temperature T. Then here is your system, which is in contact with a bath, and we want the system, I remember I used as a notation and I was consistent in doing it in blue. I don't know if you remarked that, where forces that derive from a potential do not derive from a potential as zero, and no time dependence. This you need because if not, your system is breaking equilibrium. That's condition number one, condition number two, and condition number three is that you prepare your system. Now when you prepare your system, sometimes it is not in equilibrium. For example, I pour a glass of water, which is at 30 degrees and mix and whatever, and then I put it in a bath at 20 degrees, which is a perfectly nice bath, and let it stay. Well, the system, for example, it's energy, for example, will go to a value, and by the time I'm here, I can say that my system is in equilibrium. So there are three things. The bath has to be good. You don't have to spoil it with your system, and then you have to give it time to happen. Now, give it time to happen depends on the system. There are systems that equilibrate very quickly, water, and there are systems like glasses that we know that can take, I don't know, a few billion years. So it depends on the system because it has to explore its face-to-face, and it's very bad at doing it. So when we say equilibrium, we mean a bit of everything. So when people say the word equilibrium, it could be a mix of all these senses. But bear in mind this. So for example, yesterday somebody asked me afterwards, I don't know, I think it was you, about entropy production, of which we will talk more. So let's say I have no forcing and no time-dependent nothing, and I prepare my system. There's going to be entropy production because my system is wanting to explore all face-to-face. Once it's in equilibrium, it's very happy. And if there is no forcing, entropy production stops. So it would be something like this, measured in some way. On the contrary, if there is forcing or there is, for example, an alternating field, your entropy production goes on forever and forever. And you are putting work into the system, okay? And what about detail balance? So detail balance is the fact that your bath is a good bath. Detail balance is a property of the bath, not of you. As we shall see, I hope, at the end of the day, there is something very nice that happens that you have a bath that has detail balance connected to a system, and then the system, if it's an okay system, will equilibrate. And then I could ask, okay, can I use this as a bath for a new system? And the answer is, does the dynamics of this in contact with my system now obey detail balance? And you will see that in half an hour, the answer is, this is what the fluctuation dissipation theorem tells you, which is one of the objects of today. But also to get detail balance, you should have no forcing, right? No forcing here, and of course the bath has to be decent. Also two should be true, right? Yes, yes, sorry. Yes, yes, yes, of course. Your system plus the bath have to have detail balance, yes, sorry. Okay, then if you're going to do Langevan or you're going to do Monte Carlo or you're going to do what is called heat bath, these are, they all have detail balance or not, but usually they do, and that's it. Okay, so what we're going to do is the following. What does one want to know? What does Mahesh want to know when he does an experiment? One of the things that you want to know is you prepare your system, and now we will assume it is in equilibrium. So we are in equilibrium. The bath was good, the time was enough, I didn't force it, it was in equilibrium. Remember that equilibrium is tightly related to time reversal. So if I wouldn't be lazy and I wanted to write a book on stat mech, I would divide it in two sections. I would first talk about macroscopic city or not and what can we do with the fact that we have many degrees of freedom as I did with you. And then the book would be divided in two sections. Statistical mechanics with time reversal, statistical mechanics without time reversal. When there is a form of time reversal, your train takes you to equilibrium properties, partition functions, everything where the time has to be taken out. If there is no time reversal, as I told you many times, you do what you can. In the books, the second part, if it occupies five pages, I'm exaggerating. I mean, there's nothing about it. But now with active matter and things like that, we are much more into that. Okay, so now I have my system in equilibrium and I have, this is my system. Let's say it's in contact with a bath that took it to equilibrium at temperature T. And then I have an observable, I don't know the position or the density or the magnetization or whatever. And I have another observable. For example, this could be the magnetization and this the density, anything. And as you know, we have the Langevin, the bath, et cetera, et cetera. So we have an ensemble of trajectories. So let's say we start from a point and then according to the noise, different trajectories and the probability that these do is represented by the Fokker Planck or the Smoluchowski and all the Cramer's equation. So at time T prime, I decide to measure A. Fortunately, it's a classical system, so I can measure it without destroying it. It's okay. And then I continue at a time T prime, I decide to measure B. At time T, sorry, I decide to measure B, okay? Now, of course, this is one experiment, experiment number one. This is experiment number two, which I did exactly the same protocol and I started again. But of course, the noise realization is slightly different. And I do it again and I get another one. So I want to measure the correlation. So it's going to be CAB of TT prime. I always put second the smallest time. I think everybody does, but I'm not sure. Which is the average over all the realizations of the experiments of the noise of A of B of T, let's say, A of T prime. So I measure this, I measure this, I record the value. Redo the experiment, measure this, measure this, record the value, measure again, redo the experiment, and then I take the average. This is what is called the correlation function. It tells you how much B at time T depends on what A was at time T prime. Please have a question about the type of interaction. So when you have your system and you have the buff, so for all the type of interaction, are we going to have equilibrium? Always have equilibrium. Yes. They are type of interaction that doesn't allow my system to. Your system keeps on being in equilibrium. Yes. All type of interaction. Yes. For the interactions that are okay, knows that you're not. For the moment, we are doing things that are, I'm not violating equilibrium. So I start in equilibrium, measure something without disturbing it. Measure again, but the system is like a glass of water at 20 degrees. That stays all day, a glass of water at 20 degrees. I'm not stirring it or doing anything strange to it. Okay, this is a correlation. And then there is another measure that is also interesting, perhaps even more interesting, is I start my system at a time, then go on. And when I arrive here, I am going to perturb it, give it a little kick. So V, or let's make it integrating, starting from minus infinity up to time t, I apply a tiny little field, which means that instead of V, I will have V plus delta H times A. So I am perturbing a little bit my system up to time t prime. And then at time t, I measure B. Yes, the same as it was above. Yes, yes, the same. So this is an important measure. It tells you how much the system responds to a little kick. Okay, this quantity here I'm going to denote. And so it is defined as, I will tell you in a second. Just to be sure, so delta H is non-zero up to time t prime. And then it's set. Then I cut it off. And the calculation we are going to do is in the limit of the perturbation very small. So it is an expansion in powers of delta H, and we keep the first. This gives the name to the topic, and this is how the books call it, linear response. The linear means linear in delta H, okay? And because it's linear, if I do different things, I cannot be effect of different stories of the field. Another way of putting the same is to say, instead of doing this kind of experiment, if I write here, will you be able to see it? Yes, okay. So another way that is often introduced would be I do nothing up to time t prime, and there I give it a kick with A. So this depends on time. It does blip. I turn on the field and turn it off very quickly. And at time here I measure. This one is called RAB, which is how does B change at time t when I gave A a kick at time t prime? And you see, because of linear response, if I consider this thing, I can think of it as blip blip blip blip blip blip blip. A lot of little kicks continuously in time. So this is just the integral between minus infinity and time t prime of R of tt prime d, sorry, tt second dt second RAB. Any other story you can reconstruct from knowing this one? Because it's linear response, meaning that the effect of doing kicks at different times to linear order, they're additive, okay? These two things are super important, super important because this is what an experimentalist can do. An experimentalist can hardly go and look at what every particle in the system does. But these are the things that you can measure, okay? And now we're going to show two results that are for an equilibrium system, only for an equilibrium system, meaning that it's a system that stays, is and stays in equilibrium since time minus infinity, forever and ever. And yes, so, and as you will see, these results are intimately related to detail balance. So first result is called Onsager reciprocity. I believe that Onsager got the Nobel Prize for this, basically. Although you probably, or some of you probably know him more for having solved the easing model, which is a Tour de Force or was a Tour de Force at his time, he was a great chemist. And this is a result. I think that this is why he was given the Nobel Prize. So the thing is, sorry, before that, let's zero is, this one is very easy, so I always forget it. If you think a bit of what you're doing here, remember that the system is in equilibrium since minus infinity. Now you measure at time t prime, then you measure at t. You see that the starting point doesn't really matter. So if I do at t prime plus an hour, and I measure at t plus an hour, because I am in equilibrium, you see this glass of water, if I do an experiment now and one minute later, so I measure, and I do the experiment tomorrow and one minute later, you expect exactly the same thing because it is in equilibrium. So time translational invariance means that CAB is going to be, and the same is true of the responses. If I have a system in equilibrium, give it a little kick at time t prime and measure it one minute later. It's the same as if I do the same thing tomorrow. What matters is the minute, not the starting time. So time translational invariance is not the same as saying equilibrium, but equilibrium implies time translational invariance. Why is it not? Because if I have a system that I'm constantly bothering and it has reached a stationary state, you get time translation, but you're not in equilibrium. Okay. Property number two, which we're going to prove, I'm going to do it a bit quickly, but the most important thing is that you understand the logic. This is an amazing result. If I measure A and then I measure B and calculate the correlation, it's the same as first measuring B and then measuring A. It's not obvious at all. And for example, with active matter, it doesn't happen. Even stationary active matter, for a system that is conducting heat, even if it's stationary, it doesn't happen. For economy, the market fluctuations of the prices, it doesn't happen. You could do correlations of the market, not the price of the kilo of wheat today and tomorrow. It's a fluctuating quantity. Well, and now you correlate two quantities, price of maize and price of wheat. And then you do the other way around. There is no property like this. So of all the dynamics of the universe, equilibrium is very specific. Remember that we have said many, many times that it's time reversal. So okay, I'm going to do it very quickly. You will get the logic. So CAB. Okay. Isn't this because it works only in equilibrium because the quantities A and B have to be canonically conjugate? No, it doesn't matter at all. Any A and B will do. What is important is that systems in equilibrium have detailed balance as you will see and they are in equilibrium. You will see it now. So CAB of t minus t prime, I can write it as. So this process, instead of doing it with Langevin, I'm going to do it with Fokker Planck, yes. The first here, translation. Ah, here, on Sager, that's the name of the gentleman. He was Norwegian. So I'm going to write it and then I'm going to explain it. This is the Fokker Planck thing. So this is the Gibbs measure. We are in equilibrium so we can use it. This is my notation in bracket notation. I measure B, I evolve in t minus t prime. I measure A and this is, remember, the constant. So yesterday somebody asked me, this is what? This is the Qs to which you can go, integrate over everywhere you can go.  I'm going to sum up because once I do the second measure, I ignore the system. So this is how you write a correlation in the bracket notation. You will find it also just by doing integrals. If you prefer that one, you can do it with that one. Now the trick we have to use for all these things is to see that there is time reversal. So now to use time reversal, I want to reverse here B and A. And how do I do it when I have a sandwich of operators? I take the transpose of what is inside and the transpose of this is itself. It's a function of the coordinates of this. This is a function of the coordinates. This is a function of the coordinates. And the transpose of this, remember, is the transpose of this. But the transpose of this, we did it and we can apply detail balance. So let me first write, so Gibbs appears now in the left. Then I have B, remember when I transpose the order changes, then I have E, T minus T prime, and then I have H dagger, poker plank, then I have A and then I have the flat thing. Okay, up to now I have done nothing almost. And now we're going to use the time reversal property, detail balance. So remember that this one, we did it yesterday, is equal to E to the beta B E to the minus T minus T prime H E to the minus beta B. And then I have A and I have B. This, I have just now used the detail balance property, which is, you see, and then here I reverse times and now I put them straight by using detail balance. And now it's very easy because this one multiplied by a constant gives me the Gibbs measure. And the Gibbs measure E to the minus B times unexponential gives me the flat thing. B is a function of the coordinate so I can commute it with these. These are functions of coordinate. So at the end of the day, this gives me, tuck, tuck, I'm sorry, did I, no, I'm okay. I'm using this one. This is a magic of having used detail balance. And so this here, you recognize exactly CBA. If you, okay, ask me questions on this, but the important thing that you have to bear in mind is that I use the time reversal that I have in my problem, which is detail balance. So sorry, just this one. So B and E to the minus beta B commute. Commute because there are some simple functions of the coordinates. And Gibbs times E to the beta B is just flat. You see how important it is that at the beginning I start with Gibbs. If I don't start with Gibbs, I don't get that, which means that this thing works to the extent that you start in equilibrium. It is important that I start in equilibrium. It is important that I have detail balance. Maybe would it help to write explicitly that Gibbs is the same integral times E to the minus beta? Okay, so yes, okay. So this is the flat guy. So if I multiply the flat guy, well, let's do it to the right, by E to the minus beta V exponential times flat, except for a normalization, I get Gibbs. Also, E to the minus beta V should be inside the integral, right? Because it depends on the coordinates. Yes, yes, because you apply it to this one, so you can put it in here. E to the minus plus beta Gibbs, this has a negative exponent, and this is proportional to the flat one. This is the property that we have used for the last step. But the important thing is that I just put the things and look what I've done and everything falls in place. Sorry, I didn't understand why the time integral in that equation is negative infinity. Sorry, here? Yeah, in X, X, V. Why did you write time to be negative infinity to D prime? I decided. You decided? I decided. To define this function, so I can tell the experimentalist, this function tells you what happens if you have a field on until time D prime and you cut it there. If, and then this one is the same thing, it's a derivative because if I put the field up to here and I cut it here, the difference is this. And because I have linear response, it's the difference corresponds to a little kick less. This is why this is the integral of that. So if Mahesh wants to do an experiment where for five minutes he turns the field on and then for two minutes he puts it with a different sign and for five more minutes he puts it twice as strong, he just has to integrate a lot of these blips and within linear response it's additively effect. That's why it's called linear response theory. Thank you. Okay, this is quite amazing, no? I mean, think of it, you have a complicated system of which you don't know anything. You have thermodynamic quantities and now by knowing the microscopy that it's at the bottom of it, you have discovered that if I measure magnetization now and density later or vice versa, I'm going to get at the same times, I'm going to get the same number. It's quite remarkable, no? Okay, now we're going to do the second property which is a bit more difficult but the idea is more or less similar. So we want to calculate this guy, no? So first thing we have to bear in mind is that chi AB of TT prime is going to be chi AB of T minus T prime because if you translate both times the experiment because you're in equilibrium is exactly the same. And now remember what chi is. It's the result of having a little field from time zero to time T prime. So, and then we measure A. So with the same logic as before, I start with Gibbs but with Gibbs with H plus, sorry, V plus delta H times A. This is this part. Then I evolve it, then I measure B and then I don't care, it can go anywhere. And this is chi, okay? Okay, so now we're going to make an auxiliary calculation. Auxiliary but very simple. We want to calculate how is Gibbs of V plus delta HA. So it's Gibbs. Yes, in here I reverse the orders of A and B but okay, I think that I can leave with that. So it's what? It's Gibbs is what? It's E to the minus beta V plus delta HA. And I have to divide it careful with this one by the partition function, the integral which I'm going to explicitly write it. This is what it is. So this is this chi here. And now my job is to expand for small this. Okay, so two places. In one place when I expand, okay, so this is going to be E to the minus beta V divided by DQ, E to the minus beta V, okay? DQ prime, VQ prime and this is V of Q plus things. Okay, this is a bit painful but we shall do it. We first differentiate with respect to delta H plus delta H times. On one hand, when I take this one down, it's minus A times this thing, okay? This is the first term times beta A, sorry, times this thing, okay? It's just that I took this guy down and this is first term, second term. And then I have to differentiate this one. So I take this one down and when you do it carefully and then, okay, we will read it together, I get also the same E to the minus beta V of Q over the integral, this same thing. And here I get the following thing and here it's the same integral. So it's twice and here it's finished. It's just, I'm studying the small modification this does in orders of delta H. So here I took the derivative of what's below so I get a square with a negative sign. So this is what, and then I get the derivative of what's inside, I split it in two so that this and this are the same and this is what I have. And there is a beta that I have, as usual, forgotten. It's just a derivative. Sorry, here I forgot something important. It's the variation when I change H. Okay, and when you look at it carefully, sorry, this is a bit messy. This is the same Gibbs measure and this is simply all this thing here which is minus beta A and this here, you see that this is the expectation of A. So here I put minus A and what I'm multiplying by is precisely the Gibbs without delta H. So all in all what we get is that Gibbs without it. So this is the correction we were looking for. It's long but trivial, just a derivative. So just to recap, I have been applying this field up to time t prime and what I find at time t prime is this. And now I just, because this is a small correction, linear response, I am developing it and I discover that it is the ordinary Gibbs but it has this correction term. And so now I want to plug this into here. The first term is going to be the ordinary thing but we are looking at the variation with respect to delta H. So the result we are seeking for is I need to plug this thing with a sign into here and then I will be okay. Okay, because it's the thing with the delta H, without the delta H, without it's simply this piece and with is this additional term. So this additional term modifies the thing and it will come here. So now I use that formula and I replace this thing here. The first term is going to give me the thing without the delta H. The second term is proportional to delta H and it is the one I'm looking for. And what is it? I have to take a beta, so, and we're done. Just half a step more and we're done. Assign, I think, yes. Really sorry but I'm totally lost since you defined the Gibbs and up to the end. Okay, okay, so when I start my experiment here, I am starting the experiment but I have equilibrium but under a small field. The equilibrium under a small field is this guy here. So it is the Gibbs formula with a delta H A. It's almost like the old one because the field is not very strong but it has a slight modification. And this is going to be important because at time zero, t prime, sorry, I am sort of, I have been disturbing the system up to that time. So the measure of Gibbs was something like this but now it had a field. But the rule of the game is that we're doing everything with very weak small fields. So the correction of the Gibbs measure is going to be small. So small, how small? Well, I just write it down which is what I did and I expand all the exponentials I have. I use E to the minus beta V plus delta H A. I will expand them or take the derivative as E minus beta V and then I have E to the delta H E. So it's one plus minus beta delta H A and then higher orders, I don't care. What I have done here is just systematically use this one. If you use this one everywhere and you keep things properly and you have to do it on the top and in the bottom. So the top is very easy because it's just a term like this but the bottom is a bit more complicated because you are taking the derivative of this. So it's the square of this times the derivative of what's inside and then you get this term and that's it. So when you do all the, turn the crank you get the old Gibbs plus this extra variation that you have to take into account to first order in delta H. Now I want to replace this for the Gibbs without. So I use the Gibbs without but I need to do the correction. So the correction is, well the first term is what it is without the delta H, the second term is this, this is the correction. So I take this thing here and put it here, here. So the Gibbs is this Gibbs here and then I have this extra term which is the one this and this which if you rewrite it is exactly this term here. So if you want this here is the correction to Gibbs. Okay, is it okay? I can, so the difference between the two is going to be by definition this object here. Now this object here I can distribute. So I get BA, term number one and term number two is B times the expectation of A but the expectation of A is a number that I can take it out. So at the end of the day what I get is this, B and B and this is equal to and this is the remarkable result. So what have we done? We wanted to understand how a system responds to a field and after doing some calculation where we have used equilibrium, we get to the point where we discovered that the response to a system of, to this field is given by the correlation, by a correlation. This is very bizarre. Let us write it in the most usual way. You see that chi is the integral of r. So if I take the derivative here I can write it as RAB of TT prime is equal, I'm going to differentiate because I like it with respect to the second one so this will absorb the minus sign. And this is the fluctuation dissipation theorem as you read fluctuation dissipation theorem. And sorry here I could use minus because we are in equilibrium. This is technical but this is the simplest proof there is in the market. You won't, I think, find a simpler proof than this one except for the bracket notation which if you like it is easy and if you don't it's not. Okay, so now let me keep this one on saga we have seen and let me, let us discuss a bit what this means. I'm going to erase, is it okay? Just for remembering you don't need to copy what I'm going to write. Remember when we wrote, when we got read at the very beginning or some days ago of the thermal bath and we arrived at this equation you don't need to copy this one. This was a noise and we said that if I remember correctly this was okay. And we said that this, we said that this, the quality of this guy multiplied by the temperature with this guy was called fluctuation dissipation theorem or relation of the first kind. So the one we have just derived is of the second kind but they are exactly the same thing and this is what I want to transmit to you because it's very, very important. So what is the correlation of noise, noise? Well it refers to the bath which was made of a lot of oscillators, whatever but it is a correlation just like the one we found and what is the friction? This is the hard part. What is the friction? The friction is the response because when I try to move in water, the water opposes me and this is the response that the water is doing to my motion. So the point of this is that the fluctuation dissipation theorem which is completely general for an equilibrium system is what we found before when we integrated all the oscillators was nothing but the fluctuation dissipation theorem as applied to this bath of oscillators. So and this calculation, you can find it in my notes. You take a system that is in equilibrium now. It is in contact with a bath and the system has A and B or whatever. Let's say only A equals B, only one and to this A we connect a thermometer. What is a simple thermometer? For example, an oscillator. It's a thermometer because an oscillator will catch some energy and the energy it catches is a measure of what the temperature was of the system. When you compute how much energy does it get when you're coupling these two as a thermometer, you will discover that you get exactly this equation for the oscillator with the fluctuation dissipation theorem of the system telling you exactly that these two things are the same. It's the relation between the correlation which is the noise correlation. Why the noise? Because for me, if I am looking at the system, my noise is coming from the system and for me, if I look at the system, my friction is coming from the response that the system gives me. You will see this calculation in detail but the important thing to bear in mind is that fluctuation dissipation is telling you that if I am in equilibrium, I can connect, for example, an oscillator but any thermometer will do. This is an old fashioned glass thermometer. And to any observable I like and it will exchange energy exactly with the mechanism that Einstein discovered for the Brownian motion. Exactly, so the fluctuations of this system which are measured by the correlation are going to give me energy and the friction the system applies to me which is given by the response. If you want the detail of how you show that, you will find it in my notes but it is clear that they are the same thing and they satisfy this relation which is nothing but this relation because you see here, yeah, this is the temperature goes there, yeah? So, so. Oh, okay, so, sorry. Yeah, yeah, yeah. So, if I want to interpret this, so it looks like this eta is playing the same role of... Correlation. ...of the H. In the sense that I can think of that equation as being an equation where essentially you perturb the potential by minus eta times q, right? Yes, the eta works like an H for me that I am a q, no? I am q, so it's working for me. But if I couple this thermometer to this bottle, what I will see is that the eta is the noise that the system is doing to me, the noise of A, the magnetization, but the correlations of the noise of the magnetization, so it's a correlation of the magnetization minus the expectation value, is precisely the amplitude of the noise that the system is giving me. But there is a second term that comes from the fact that when my system moves, it acts on the bath, let's say, or when my thermometer changes it. And there is a retro feedback, and this is given by the response function. And when you do it with a bath with oscillators, you do it and we did it and it was okay. But if you want to couple to any system, you can use the fact that it satisfies fluctuation dissipation to show that any system in equilibrium will be a good bath for you. This is very, very important because now you see that what Einstein was doing is that instead of an oscillator, he had a particle of pollen or Brownian particle, and instead of whatever, he had the water where this was dancing. And the correlation and the response of the water, meaning the noise you get from the water, plus the friction, they are precisely given by these two terms. So fluctuation dissipation that sometimes is given to you as, wow, look at this nice property that allows you to measure correlations just by measuring. It's much more than that. It's at the heart of what equilibrium and measuring a temperature means. And what have we used to prove it? This is the important part, the calculation, you can check it tonight, for example. What we have used is that the system starts with a Gibbs measure or if it was under a field, it starts with the appropriate Gibbs measure and that it evolves in equilibrium fashion. So please, you didn't make a comment about the fact that it may happen if in the case where we have a strong field like for the perturbation, because in our case, we just consider the fact that the field is weak. So what's happened if in the case of a strong field? If you apply a strong field, so you could, you see that I did everything to order delta H. And I said that if you computer pulse like this of field and another one like this and you, this one where you do the two are just the sum. This is linear response to order linear. If you go to delta H squared, which a little bit stronger field, you're lost. There's nothing easy, you can say. It all becomes nonlinear, horrible. So beyond linear response, when the fields are a bit larger, life becomes more, you cannot do a calculation like this. So yeah, so it's called nonlinear response. Of course, in life, these things happen, but there are no, it gets really quickly very, very hard. I mean, you can, of course, in the computer compute it, but there are no, the relations are much more complicated and not very useful. You mentioned that this is useful also because it's like more simple for experimentalists to measure it. And is it even like simpler than measuring over the linear, like it's simple to do the linear response? Is it simpler than doing like a higher order response for experimentalists? I think that the experimentalists usually prefer responses because applying a field and seeing how the magnetization grows or applying a pressure and seeing how the volume changes is much better than looking at how the positions of the molecules correlate over time. No? Absolutely, because we don't have access to the microstructure of the system. So we are always trying to infer what are the microscopic responses arising due to some microscopic changes. That is what all condensed matter and statistical physics is about. Yeah, and then these things happen also in quantum mechanics and so on. But it's interesting that my feeling is that sometimes the books don't emphasize how important fluctuation dissipation is and we have to go back to the intuition of Einstein with respect to Brownian motion. He said, put it in a modern way, you would say, I put a particle of pollen inside the water. The particle of pollen measures the correlation of the crashing velocities of the water for sure. But it also measures the response because when it tries to move because of all the crashes it got, it finds that they respond and you can show that the response is precisely the response we defined here. So these two things must be equilibrated because I need that my pollen particle is in equipartition or some form of equilibrium. It cannot heat up because then I would be able to throw in pollen and get energy from water. It has to be at the same temperature and this intuition, which is for us maybe easy but it was quite clever, is the idea behind fluctuation dissipation too. Only that this way we can formalize it. Or the way my advisor taught me the first time he talked about fluctuation dissipation and frequency dependence susceptibility and all those concepts. He said, Mahesh, when you go to buy an old car what do you do?  That was the way he explained it. I have a conceptual question, not on the technique. There is something more constrained, there seems something more constrained about on saga reciprocity compared to FDT and I could be wrong. Which is that there are always the couple transport coefficients. You have the seabag and the peltier. But it's not as if they are response, one is response to the other. But you can do the fluctuation dissipation cross and it will be as, there is a nice way but I didn't do it, I wanted to do it but it's a little bit more complicated but a little bit to derive the same thing we did for the response of fluctuation dissipation with explicitly time reversal. So which was why I asked if A and B have any constraints on what those two observables can do? Or could they, there can't be any two observables? The only thing I didn't say and it's important that I say it now is that I did it about on saga. Let me write on saga. On saga is CAB of T minus, we are in equilibrium. In fact, when you have velocities, you have to reverse them. So if this is Q, something of QP and this is something of QP here, it's going to be of Q minus P, Q minus P. And so here I put a little bar to tell you if you're doing observables that are coordinates like the magnetization, it's okay what I said but if you're going to use velocities, you need to reverse their sign. If you do the same exercise that we did before for reciprocity, you will see that naturally this appears because when you do time reversal, remember that in kramers, there is a flip of sign. I thought it wasn't worthwhile to make it the whole solution more complicated. Okay, so just to tell you there are lots of interesting things. For example, when you think of the financial markets, for example, there you have a system with observables, as I said, the price of wheat and the price of, I don't know, PCs. And then suppose I buy wheat, a lot of wheat, so the price goes up and I want to see, let's say it's a small perturbation and then this may, for example, affect, for some mysterious reason, the price of PCs or something else or the price of wheat, of course. And can I, or I look at simply the fluctuations of the price of wheat and the price of corn and then I measure like this and I measure like that and I ask myself, do I get something like that? Do I get something like that? And I respond in response to buying. And the answer is no, which is amazing because the markets are made of millions of operators and they are fluctuations and everything, but they are not equilibrium. They don't have the specific thing that equilibrium has which all comes from some form of time reversal, detailed balance or something like that. And we will see that you don't need to go to the markets the day after tomorrow. We will see for active matter which, for example, bacteria or motorized particles, the same happens. You don't have all these magical properties. So once again, just to convince you, the moment you put one foot outside equilibrium, you lost the measure, the Gibbs measure, and you lost a formula that gives you the measure. There is no simple formula that will give you the stationary distribution. And you lose the equilibrium theorems and you lose reciprocity. So the restriction now to repeat an old joke that I think was made for linear and nonlinear systems to talk of non-equilibrium, the joke is from Ulembek maybe, to talk of non-equilibrium systems is like talking of non-elephant zoology. It's almost everything. I think that the original phrase is... Markets, okay. To talk about non-linear systems is to talk about non-elephant animals. Of course, most animals are not elephants. And here the same. I mean, thanks God we can... So all the things that are related to equilibrium occupy 99% of your books. And there is very little left for out of equilibrium, but this is a completely unfair and unbalanced situation with respect to how the universe works. With respect to what you know how to solve, then it's perfectly fair because out of equilibrium as you will see, you will see perhaps the most flashy result in three decades, the fluctuation theorem tomorrow, and you will see that it's nice, but it's not great. It's very modest thing. And it's also everything we know out of equilibrium is very modest. This one has to take into account. So I think I will stop here. Yes, just one observation that say the... I mean, this relation... If you consider this relation for the integrated response, the integrated response is minus beta times the connected correlation. When t is equal to t prime, then it's just very easy. Yes, that one you can get without time. Yes, very easy. So the non-trivial thing is that it extends two different times. Yes, yes, yes, yes. Okay, so then the exercise is... Go through the lecture notes now. There is a lot of depth here. So we are going to meet again at 2. To discuss about these things and other things. Yes, and once again, I'm sorry I cannot participate. I have to give a seminar that has been long programmed. And now we are going to take a photo if I'm going to look for the photographer.


Everybody forced here ripping two boxes of 2022 Bowman chrome baseball lights for Todd W Thanks for the order Todd and good luck mini diamond, you also are Garcia James Wood insert your rookie black-and-white mini diamond Edward Cabrera this one's numbered 102 of 199 First bowman Matt McClain black-white mini diamond not numbered Yeah, of course Kyle. Thanks for the order, man Yeah, I didn't see one of the first boxer up tonight Paulino first bowman black-white mini diamond Nelson of Alaska Non-numbered fuchsia Randier Rosarena one of two ninety-nine Jeremy Pena mini diamond Louise Mesa first bowman Jay Allen Ricky refractor Nicoladolo Number 340 499 black-white mini diamond Jackson Job and shimmer first woman Louise Mesa See big color in the second one here that Hansel so hot right now Goal zoo lander blue refractor West calf number 21 of 150 Invicta warming Bernabelle black-white mini diamond Alex De Jesus black-white mini diamond Henry Davis Stas Suzuki refractor Nick York 61 of 499 Black-white mini diamond Yankee Stray Sweeney No one's gonna care that I did that Rookie black-white mini diamond Ryan Valle this one's numbered 162 of 199 and a warming Bernabelle black-white mini diamond Bowman ascensions counts the case hitting hobby. I'm not sure about life, but Louise Rodriguez and Eleover Baguero later brother. Have a good night. Thanks again Todd. We appreciate the order. We'll get those right out to you


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