Item number SCP-686 Object Class Safe Special Containment Procedures Samples of SCP-686 are to be stored under standard protocols for Class-II Biohazardous Liquids and G-II Facilities. SCP-686 is infectious, but not virulent. It can only afflict the new host when taken orally, and is not multi- or otherwise active. The infectious agent's mechanism operation is not known. SCP-686 does not contain appreciable amounts of nucleic acids and prion activity is not apparent. Due to the large quantities of SCP-686 that are being produced by various test subjects, the principal requirement for this substance is not so much containment as it is disposal. While pasteurization has proven completely effective at sterilizing the infectious agent, whatever its nature, it is recommended that all unneeded stocks of SCP-686 should be incinerated. Human consumption is not recommended by anyone other than designated test subjects. Description SCP-686 is an opaque white liquid consisting of a suspension of lipids and proteins that is indistinguishable from ordinary high-grade dairy milk without detailed analysis. At a biochemical level, there are certain subtle differences. The protein content is much more complex, with most of the peptides so far proving difficult to sequence, and it contains a richer blend of vitamins and minerals than is typical of cow's milk. SCP-686 was first isolated from cattle at a small-scale commercial dairy farm near ████████. Records indicate that the farms heard begin increasing its milk output and quality to unusually high levels approximately two years before the infection managed to make the jump through the farms' human workers and the foundation became involved. It is not known with certainty whether this farm is where SCP-686 originated or if it came in from some other source and was simply first recognized there. The infection increases the host lactation rate, or if the host is not lactating causes it to begin doing so. It appears that any mammal is susceptible to infection regardless of gender. The initial symptoms of the disease have a rapid onset but are relatively minor, swirling a mammary gland tissue, causing breast development of males, and increased sensitivity of the nipples in both males and females. On average, a human of either gender in this stage of the disease will produce between 0.5 and 1 liters of milk per day. If this milk is extracted on a regular basis, with milking intervals of no less than once every 8 hours, the disease appears to remain stable indefinitely in the state. Everything can be performed with a standard breast pump. If a host is not milked adequately, mammary glands continue to develop. Left unchecked, this development will diverge from normal human growth patterns. Rather than remaining confined to a single pair of breasts, it will begin spreading down the front of the chest and abdomen. Additional pairs of nipples will develop along the way and the nipples will lengthen and thicken dramatically. The eventual result resembles an enormous fleshy udder stretching along the entire front of the torso, with between 6 and 8 pairs of teats. A human at this stage can produce upwards to 40 liters of milk per day. This is the maximum extent to which the disease will progress in humans. The metabolic demands of such a large and productive glandular system are considerable and a human victim in this state will find him or herself preoccupied with eating most of the time. With hair to her energy fully devoted to milk production, the victim will often suffer from a general state of mental illness and facility. Mental removal of mammary tissue is a temporary measure, as the disease is able to cause regrowth, even if all of it is excised.


But let's start with a quote from Mises. Why gold? Why do we support the gold standard? And you could substitute for gold commodity money, okay? People who are in favor of the gold standard tend to be in favor of anything that the market chooses and the market did choose gold with some help from government in pushing out silver in the 19th century. But this was one of the two metals that were chosen as money. Through centuries of evolution. So Mises basically says the reason why gold is because it makes the purchasing power of money immune to the attempts of politicians to manipulate its value for their own benefit and for the benefit of their cronies and constituencies. So here's the gold standard makes the determination of money's purchasing power independent of the changing ambitions and doctrines of political parties and pressure groups, which we would call today special interests. And there's a number of, Mises continually goes back to this theme throughout his works, that takes the power of determining the purchasing power of money out of the hands of politicians. Now here's a spectrum of international monetary systems going from what I consider to be the best, a 100% gold standard, all the way through to the worst. We're gonna focus on two today, the classical gold standard because that existed in history. Of course, all monies came into existence in some sense as pure commodity monies, as a 100% commodity backed or commodity monies. So the world has had experience with commodity monies for centuries, for millennia. Now, usually if you've taken an international economics class, you'll note that what they do is they mix the best, sort of the classical gold standard and 100% gold standard with fixed exchange rates. So instead of having commodity money, a division here between a sharp division between market supply commodity money and government monopolized fiat money, they go from fixed exchange rates to fluctuating exchange rates. So they'll mix these gold standards, so whether they're fixed exchange rates and they'll include in here the Keynesian ideal of fiat reserves created by a world central bank. In some sense, that's the ultimate fixed exchange rate system. Austrians don't focus on fixed versus fluctuating. We don't like that spectrum, okay? We like the spectrum that puts on one side commodity money and on the other side fiat money. Okay, and there is a sharp division between the two. Now, without going into too much detail because I don't have that much time, if we were to, if we have a fiat money, we would choose for the most part, at least for large countries, fluctuating exchange rates with the government completely refrains from interfering with the value of money established on foreign exchange markets. We don't like pegged exchange rates. There are things that are wrong about them. In other words, they fact, though, if you have fiat monies issued by different national central banks, then you have different commodities and they should fluctuate in value. So this is not on the other end, for example, of desirable monetary systems from the point of view of Austrian economics, okay? Once you get into a fiat money system, well then we would want exchange rates to tell the truth about the values of different monies. Okay, so what I am gonna focus on today is a classical gold standard, which operated in history and we have records of, and a fixed exchange rate system, which were false gold standards, the Bretton Woods system, and then today there's a, as we'll see, a bill in Congress for the, what's called the dollar bill system, which would mandate the Federal Reserve system to target the price of gold, and this is called the gold standard, and there's been a number of books written on this by people like Steve Forbes, Nathan Lewis, and others whose names are connected with the gold standard. Well, in fact, they're proponents of fiat money. What's the main characteristics? Now we're talking about the classical gold standard in which there were elements of government intervention. If you sat in on Guido Hulsman's class yesterday, he talked about all the elements of intervention, even in the 19th century, at the height of the classical gold standard. So, these things are true of the gold standard. The monetary unit is defined as a weight of gold. Gold and nothing else is money. And I'll get to that in a moment. Banknotes and deposits are instantaneously redeemable at par for gold, and gold coin is in circulation. Mises stressed this, that for a genuine gold standard, you have to have gold coins in circulation among the population. Therefore, the banks and the notes, the bank deposits and notes are merely money substitutes, what Mises calls money substitutes. They're claims to gold, whether they're fully backed or not, that are acceptable in exchange in lieu of the gold coin, okay? They're just more convenient. They're a more convenient way of transferring the ownership of gold from one person to another. Just as the pink slipped from a normal bill in New Jersey, there's a lot of drag racing, and you bet your cars and so on, at least when I was growing up, and people would, they would run for the pink slip, the pink slip being the title to the car, and they would put up the pink slips, and then the guy lost, he would get the other guy's pink slip, that is the title of ownership. Wherever the car was, he now owned it, didn't matter. And the central bank may or may not exist. The first central bank, or quasi central bank came into existence in the 1690s. Central banks were initially, the Bank of England, they were basically set up to fund governments, okay? To print money for governments to spend on palaces and wars and so on. So they were the financiers of the king. Monetary unit under the gold standard, there are some examples from 1834 to 1933, the US dollar was legally defined as 23.22 grains of gold, which works out to be about 1.20 of an ounce of gold. So for about 100 years, that was its legal definition. And in Great Britain, it was from 1821, after the Napoleonic Wars, until 1931, the pound was defined as equivalent to about one quarter of an ounce of gold, and the French franc to about 100th ounce of a gold. So that was the monetary unit. In other words, the dollar was just simply a name for a different weight of gold than the pound was and the franc was than the Deutschmark was. Exchange rates and the gold standard, this harks back to the first slide I showed you, or second slide. The gold standard is not a fixed exchange rate system, okay? The only reason why $4.86 plus or minus 1% exchanged for one pound was because of the arithmetic relationship between 113 grains of gold and 23.22 grains of gold. In other words, the British pound contained about five times the amount of gold as a gold dollar, therefore it took $5 to purchase, approximately $5 to purchase an ounce of gold. And so it's a law of arithmetic, okay? So today the US nickel is defined as one 20th of a dollar, US quarter is defined as one fourth of a dollar. There's no fixed exchange rate, okay? It takes five nickels to get one quarter because of arithmetic, okay? They represent different denominations of the same monetary unit. Here are some example of gold coins, 1921 and in 1906, US gold coins. These were actually in circulation. People walked around with them and purchased things with them. They were only a very small percentage of the transactions that were carried out of the money that people held. Here's British sovereigns, 1894, 1931. So this was the money proper, as Bezos would say. So gold was money proper. Banknotes and government issued notes under the gold standard were not money proper, okay? As I said, they were just simply money substitutes. They were not money themselves. They were simply titles that were evidence of the ownership of a certain quantity of gold. Or in another way to put it, there were claims to gold. So for example, in 1903, now there were a number of national banks that were set up in the 1860s. There's a national banking system in which Wall Street banks were dominant. And banks, certain banks were allowed to issue their own notes as well as their own deposits. That, they were eventually taxed out of existence and they were completely abolished in the 1920s. Private banks could no longer issue notes. But in any case, here is a title to money. This is not money itself. The title to money issued by the farmer, the farmers and merchants national bank of Los Angeles. Notice what it says here, will pay to the bear on demand $20. That isn't $20, okay? It's the weight of gold that represents $20. That is the $20, okay? That's a claim to $20, it's a title. And just one other. Here's the first national bank of Fort Myers who's a claim to $5. Will pay to the bearer on demand $5. Doesn't say that this is $5. It doesn't just have $5 on there. Simply a claim to the gold, okay? So under the gold standard, there was no paper money in the strict sense of the word. There were money substitutes, okay? And they functioned under fractional reserve bankings. They did function as part of the money supply, okay? To the extent that people had confidence that the banks would indeed redeem those claims to money on demand, they were part of the money supply. And increases in these paper titles would affect the value of money, okay? As Mises points out, and he had a different approach to this than Rothbard does, Mises doesn't think this is fraudulent, but he think it all depends on goodwill because to get technical for a moment, the liquidation value of the assets of the bank, okay? Are always less than the liabilities. So in other words, if the bank has $1,000 in demand deposits that it owes to people and maybe has $100 worth of gold in the bank and then has lent out the other $900 or invested it. If everyone came in, if they lost confidence and everyone attempted to redeem their titles to gold at one time, the banks couldn't pay off. And Mises says at that point, the goodwill evaporates. So let's say those loans and investments were only worth $500 at their liquidation value, right then. Then the bank can only pay $600 worth of gold. It will sell those things. So the goodwill is worth $400 in that case, okay? I haven't seen anything honest. There's a few pages in Mises, a few paragraphs in Mises that suggests this and I've written it up. So there's the accounting. We're not talking about fraud or anything here. The accounting for fractional reserve banks is wrong, okay? The assets should always be accounted for at their, what would I call their liquidation value. So whether the classical gold standard had principles of operation that the central banks followed. Now they followed them not because they were following the rules of the game. That's often the phrase that's used that central banks have to follow the rules of the game or play by the rules of the game. They were following them because they understood and the people understood that this was their property. At a point in history, more and more gold began to be centralized in the central banks. And by 1917 in the US, all gold had to be held if it were to be counted as reserves in the central bank. So when one skull was centralized in the central bank, it was often said, well, the central bank has these assets and they have to take these reserves and be careful not to lose them by inflating too much. Mises says, no, no, no, that's all wrong. The point is that's the money that people own. So the central bank doesn't have to play by any special rules, it just has to obey the rule of contract. That is it has to, when it issues its own notes which all central banks do, then it has to pay them off in gold because they themselves are only claims to gold. So let me just put these up here. So they didn't involve any fixed exchange rate or price fixing of gold, as I mentioned. In redeeming $20 for one gold ounce, the central bank or government is not selling gold. It's not selling gold to keep the price stable or something. It's fulfilling its contract to redeem a property title to money.  Banknotes and deposits can only increase as new gold flows into banks. So if you don't have gold mines in your nation then the other way that gold could flow into your banks is through a surplus in the balance of payments where you sell more abroad than you buy from abroad. And so then the balance is paid in gold. This was known as the golden handcuffs on government. They could not expand the money supply, at least in the long run, to a greater extent than the inflows of gold. So the result was that prices tended to fall over time and saving and investment improved and more goods flowed onto the market from this cornucopia of capitalism. And there was improvement in technology. And we've seen this with high-deficient television sets that in the old days were $3,000, $4,000, $6,000 when they first came out, and today you can get for $500. Or computers that were $3 million, the mainframes that filled the whole room in 1979, they were $3 million. And now you can get a laptop with more computing power that is faster for a couple of hundred dollars. Okay. So as the increase in goods under the gold standard tended to outstrip the increase in the money supply and therefore prices tended to fall, okay? Supplies of goods increased more than the monetary demands for goods. And I call this in an article I wrote growth deflation. And there was a very gentle price deflation during the 19th century. In the U.S. you can see prices falling from an inflation that had occurred in the after the war of 1812, banks were permitted to suspend payment and they increased the money supply. And in other words, they were permitted to suspend payment of gold for their notes. But as that abated, you see that prices tended to fall and they fell 53% between the Civil War and their height in 1819 or so, 1818. And then again, we had the Civil War in which the government inflated through the issue of greenbacks that they promised to eventually pay in gold, okay? And then again, when we went back to the gold standard, prices began to fall. Part of that fall in prices has to do with the fact that the greenbacks were retired, there was an actual deflation of the money supply. But a lot of it was also due by 1870 or so then, by 1879, you began to get a fall in prices because the U.S. was rapidly industrializing and there was a tremendous flow of additional goods and services onto the market, okay? So when the gold standard is allowed to operate unfettered, without a lot of government intervention, you will tend to see a fall in prices. An ink or to put it another way, some people say it's a deflation. Mises likes to use the term appreciation of the value of money. That is the value of money increases over time because each unit of gold can purchase more and more. Let me talk a little bit about the price species flow mechanism, which was a mechanism that operated as the golden handcuffs on government. A species is another term for precious metals, gold and silver. And this mechanism as we'll see was really the balance of payments mechanism. BOP always stands in economics for balance of payments. So this mechanism as we'll see maintained, at least in the longer run, maintained equilibrium in the balance of payments that ensured that what was imported was paid for by real exports, okay? In other words, a country couldn't continually run deficits when you run to the gold standard. Otherwise, all its reserves would leave the system and long before it lost all its reserves, it would be internal runs on the bank and people would attempt to get their gold and the banks would collapse. This mechanism also distributed gold throughout the gold standard area according to the relative demands for money. So if gold was mined in the US and in Australia and other parts of the world, prices would rise in those parts of the world, goods would become more expensive, people wouldn't want to buy exports from California and other parts of the world where new gold was flowing in and pushing up prices because of the gold mining. And eventually what would happen is that imports would increase into that nation in exchange for the gold. So deficits in the balance of payments did serve a purpose. They served the purpose of distributing new supplies of gold from the gold mining areas to other countries throughout the world. They also served the purpose of giving additional money, having an increase in the money supply in those parts of the world that were prosperous. So for example, in the US, there's balance of payments between the various states. We don't know them, which is good because there are no statistics. We don't calculate balance of payment statistics. Otherwise that would be something else you would hear politicians and journalists, media people complaining about. But some place like California in which you have great growth in Silicon Valley and California wines are sold all over the country, so let's say Napa Valley. As those areas grow, they require additional amounts of money. People's income increase, they want to buy more goods, they need more money to buy goods. So as their goods increase, prices fall in those areas and money dollars flow in. Whereas in areas that are declining like the Rust Belt, like let's say Detroit and Michigan, they lose money, but this is a natural loss in money. We wouldn't call this a deflation. This is a redistribution from areas where there are not many goods and people have very low incomes to areas where people have higher incomes and there are additional goods being brought to market. So it's very important distributing goods and as I said, it operates inter-regionally between the states. Between any currency area, any area using the same currency, you're going to have these balance of payments flows that are very, they're healthy for the system, keep the system in balance. Okay, overall though, it limits the increase of the money supply in a given country and it limits, therefore limits inflation by the central bank and the banking system and let's see how that actually happens. Okay, so there's a lot of symbols here but they're very simple. If the US increases its money supply, MS, that will drive up prices in the US, okay? Above world prices, so sub-W's world prices. When US prices exceed world prices, you'll see exports from the US which are now more expensive falling. You have fewer tourists coming to the US, you have the US selling less aerospace equipment, fewer engineering services abroad and on the other hand, you'll see Americans turning away from higher priced domestic goods and increasing their imports of foreign goods, okay?  As a result, you have a balance of payments deficit. Balance of payments becomes less than zero, comes negative, okay? So more money is leaving the country than is coming in but foreigners under the classical gold standard didn't want the US pieces of paper that are titles to gold, they want gold itself, okay? So that they can turn it in and use their own money substitutes. So the US gold stock falls as we pay the balance in the form of gold that drives US money supply down, lowers US prices, either back to world prices or below world prices and you get a reversal of this movement and the exports go up in the US, imports go down and then we have a surplus, okay? So that there's a balance and the US gold stock goes up. Okay, if you don't follow that, that's okay. Basically, we're gonna come back to that. The important point to realize is that when the government's inflate, it drives prices up in the domestic economy above world prices, makes the domestic economy a worse place to buy and a better place to sell in. So people buy more goods from abroad than they sell to foreigners and that results in a balance of payments deficit. So banks could temporarily increase the money supply and they could cause an inflationary boom and a recession. They could cause the Austrian business cycle to occur but these were minor fluctuations compared to what we had after the classical gold standard was killed off by government. It didn't collapse on its own as we'll see, okay? We'll come back to that. Now if you look at this figure and ignore all the red and blue font, just look at the black font. This is what a typical structure of money would look like under the classical gold standard and this is what Hayek called the inverted money triangle. So what happens is that the very base support on the very basis is the gold stock through which all the deposits and notes are claimed. So let's say this country has $2 billion in gold or the central bank does. The central bank then will issue its own notes and let's say it issues $5 million on top of that so it's fractional reserve. So it'll keep a ratio of 40%, let's say. Then those $5 billion of central bank notes are used because the gold is centralized in central banks. Those are used as reserves for the commercial bank notes and deposits. We saw that the commercial banks were permitted to issue notes under the classical gold standard. So let's assume they keep a 55% ratio. So now you have $25 billion in bank notes and deposits circulating and they are claimed to $2 billion. As Hayek pointed out, this national reserve system where the reserves of all banks are held by the central bank is extremely unstable. Now what would happen if the central bank wanted to issue a billion dollars of additional notes? So it would reduce its reserve ratio to 33 and a third percent, one third. So now it would increase its notes to six billion. This would cause inflation because when the extra $1 billion got into circulation it would wind up as reserves in the commercial bank vaults and the banks would then expand that $1 billion by five because they're holding 20% of all the deposits. So they could create or pyramid on top of the additional $1 billion, $5 billion of new checking accounts and notes. So notice that this starts to become unbalanced. And so that becomes wider. Now what happens though becomes even more unbalanced because US prices rise as a result of this. And as US prices rise, residents begin to buy more foreign goods and you have more imports and foreigners buy fewer exports from the US. You have balance of payments deficits which have to be paid in gold. So suddenly the central bank starts to lose gold reserves. As people come in, the importers who want to pay their foreign suppliers, they come in and they turn in their local currency, is how I pointed out, their less acceptable currency for more acceptable bank notes and eventually for gold that is sent abroad. That's where the price-species flow mechanism comes into being. According to some economists or most economists, oh well, the bank has to raise interest rates or defend their gold reserves. They have to cause a deflation in the economy. That's not true at all. All they have to do is to pay out the gold that they owe people who have claims on that gold by contract. They shouldn't have inflated in the first place. Now they're simply fulfilling their contracts and that's what binds their hands. They can't keep increasing their own notes to central bank under the gold standard without making this dangerously unbalanced as I'll show you it became in the 1960s. Becoming very, very narrow at the bottom as gold leaves the country and very wide at the top which implies higher and higher prices. So the US classical gold standard existed from the 1834 to 1933 sort of.  The government intervened more and more by inflating, a central bank did, by inflating and other measures. During World War I, as I mentioned, the US was the last to really centralize gold reserves. They were centralizing the Fed. A heavy tax was placed on the private issue of bank notes. This is when private bank notes began to disappear and we began to use Fed notes. In the 1920s it completely prohibited the issue of bank notes by private banks. And then the Fed cut reserve requirements in half meaning it basically doubled the money supply during World War I. Now let's talk about the destruction of the gold standard. The Fed expanded reserves during the 1920s to help Great Britain to return to the gold standard, Great Britain and all the other belligerents. Within two weeks of the beginning of World War I, every single belligerent had gone off the gold standard because they knew it would tie their hands in paying for the war. None of the belligerents wanted to raise prices. They wanted to raise taxes. That's very unpopular. The war would have stopped very quickly. Instead they wanted to pay through just creating printing money and that's exactly what they did. Most of World War I was paid for by printed currency. So that was the first blow against the gold standard. The US inflated or the Fed inflated during the 1920s. And as I said, part of the reason was to push US prices up so that Great Britain did not lose exports, did not lose their export markets and lose their gold. There was a Great Depression struck. There was a run on the banks between 1931 and 1933. There was a bank holiday that was ordered by President Roosevelt. I think it was March, no, it was May 1st, 1933. The banks were all closed.  Or if you had any other kinds of loans from banks, you still had to pay those. Ownership of gold was prohibited when the banks reopened a few days later and the dollar was devalued from $20 per ounce to $35 per ounce. In other words, it was now equal to 1.35 of an ounce of gold, but that didn't matter because you couldn't get gold for your dollars any longer. It was illegal for anyone to own gold. Here's the executive order. It says, from the president, honor before May 1st, 1933, all gold, coin, gold, bullion, and gold certificates now owned by them must be returned. All persons are required to deliver honor before May 1st, 1933, all gold, coin, gold, bullion, et cetera, owned by them to a Federal Reserve Bank, branch, or agency, or to any member bank of the Federal Reserve system. And then criminal penalties for violation of executive order, whatever that number is, is $10,000 fine or 10 years imprisonment or both as provided in section nine of the order. The only people that could retain their gold were licensed dentists and licensed jewelers. It was even illegal for US citizens to hold gold outside the country. You couldn't hold gold in Canada. And there's the destroy of US gold standard. In politics, nothing happens by accident. If it happens, you can bet it was planned that way. That refers to the destruction of the gold standard as well as World War I, World War II, okay? These things were all planned. It doesn't mean there's conspiracy necessarily, but it means it's in the interest of the politicians and their cronies that certain things happen and they'll work to bring those things about. Okay, let's talk a little bit about the gold standard, the false gold standard. Bretton Woods was established in 1946, okay? There was a meeting of the Allies in 1944 at the very plush resort in New Hampshire known as Bretton Woods. And the Allies wanted to reconstruct them World Monetary System without tying their hands. But they knew 1930s, by the way, were terrible. Every country tried to make its currency cheaper so it could sell more exports to foreign countries, but of course there was retaliation. And so what you had was world trade almost coming to a halt and world investment almost coming to a halt. They wanted to avoid that. They wanted free trade to some extent after World War II. So the Allies got together and concocted a monetary system in which gold was a sort of a cover, okay? It was a phony, false, counterfeit gold standard. So it was an attempt to bring water to the chaotic fiat monies. Everybody had their own fiat monies and they were all inflating at different rates and devaluing and so on and trying to get the advantage to make their goods cheaper during the 30s, okay? The main architects of this were the US and the British governments and their leading financial experts. Harry Dexter White was the US Treasury expert that was the main representative of the US and John Maynard Keynes was the Treasury expert from Great Britain. And there it is, there's Bretton Woods. I visited there two years ago. It's still very beautiful, set in a very nice area. These are the two architects, so to speak, of Bretton Woods. Keynes is on the right, White's on the left. White, as it turns out, was a Soviet spy. No, it's, I mean, there's more than enough evidence now there's a book that by Ben Stiles just came out a year ago called Bretton Woods, okay? And this is from his book. In August, 1948, White testified and defended his record to the House on American Activities Committee. Historians agree, almost every historian now, left to right, agrees he passed secret and state information to the Soviet Union during World War II. He did do that. It's a very interesting book, you should read it. It's not just about White, but it's about Bretton Woods. It's written for the popular audience. Now, Ben Stiles says, White acted out of idealism, not as a member of the Communist Party. He didn't, he had not joined the Communist Party. Well, he worked for the US government, so he couldn't. Not simply because he believed, this is according to Stiles, not simply because he believed that the Soviet Union was a vital US ally, but because he also believed passionately in the success of the bold Soviet experiment with socialism. So, I guess Hitler wasn't bold, so that's why he didn't like him, but the Soviet experiment under Stalin was bold. White was not a Communist Party member because according to Stiles, he would not take orders from Moscow. Well, if you read what Stiles says in the book, he gives a lot of things to Moscow. He gives a lot of secret papers and so on. He worked on his own terms, okay? It really comes across as a real pathetic man if you read it. In any case, what were the key characteristics? The US was the key currency. It was the only currency that was convertible into gold, but not for our grandparents or great-grandparents, in your case. Regular Americans could not convert dollars into gold. The fact they were still prohibited from owning gold and that continued until 1976, I believe, the prohibition on Americans owning gold. So, it was gonna be convertible into gold for foreign official institutions including central banks and foreign governments. So, all other currencies, the British pound, the French franc, the German mark, were convertible into dollars, but at fixed exchange rates, okay? But they could adjust them. In other words, they inflated too much. You sort of rewarded them and allowed them to devalue their currency and increase their exports. It was a crazy system from the start. The dollar was only convertible into gold for foreign official institutions, as I mentioned. All other currencies were backed by dollars. So, this is the key. All other central banks held dollars, not gold, to back their currencies. And this gave the US a monetary spigot. In other words, the US could print money, as we'll see, and did so without any negative effects, without any effects on the balance of payments. Basically, this provision neutralized the balance of payments adjustment mechanism or what we call the price-species flow mechanism. So, foreign currencies were expanded and pyramided on top of the dollar. So, now you had this international inverted, as I'll show you, monetary pyramid. The balance of payments adjusted mechanism, mechanism that limits inflation under the classical gold standard was neutralized. I won't go into that. Basically, because everybody accepted gold, okay? So, it was world inflation. So, in words, what happened was that the US could inflate the money supply, as we did in the 1960s, to pay both for the Vietnam War and for the various welfare programs, social welfare programs, implemented by the Johnson administration. So, Johnson and his economists said, you know what, we're gonna give the American people both guns and butter. We don't want them turning against the Vietnam War because we have to raise taxes. So, taxes weren't raised that much during the Vietnam War. It was a very expensive war. What they did was they printed dollars. That pushed the prices of US goods above world prices. People didn't want to buy as many US goods. We bought a lot of goods from Europe and other parts of the world. And guess what? We didn't lose one ounce of gold. Well, over time we did, but mainly, especially in the beginning, up until the mid-60s, foreign governments were willing to take our dollars. And when they took our dollars, they pyramided their own currencies. So, if an exporter from a foreign country had dollars that he earned from an American importer, he just went to the Bank of England and or its branches or his own bank and in exchange, got currency. That currency was printed up by the Bank of England and then it accepted the dollars as backing for that currency. So, that's what it looked like. So, now you had almost all the gold hoarded by the Fed, though France had quite a bit of gold, also, on top of that were the Federal Reserve notes and deposits, the Central Bank notes and deposits. On top of that were US commercial bank deposits and then they were held as backing for foreign currency and commercial bank deposits. They would take those commercial bank deposits and they would buy US short-term securities with them. So, they basically, securities that could be easily turned into dollars. So, they basically backed their, the foreign currencies, foreign countries backed their currency and commercial bank deposits with US dollars. So, it got wider and compared to the base, the base was very narrow. Therefore, we had what a French economist, Jacques Rouef, pulled deficits without tears. We continued to inflate the money supply to pay for the welfare programs and so on and the Vietnam War and we flooded the world with dollars. We had continual deficits year after year from 1958 or 59 onward. But as long as the governments, foreign governments and central banks were willing to accept and hold the excess dollars and did not demand gold for them, they didn't have to worry about the balance of payments. We didn't have to worry about balance of payments deficits. Eventually, the French advisor to French economist Jacques Rouef, who was advisor to President Charles de Gaulle, French president, convinced him to demand French gold from the US in exchange for dollars. The US was very resistant. Germany also made demands. However, Germany was an occupied country. We threatened to withdraw our nuclear umbrella, protecting Europe from the Soviet threats so called. We threatened to withdraw that if they persisted in demanding their gold. Germany back down, France didn't back down, France dropped out of NATO instead of knuckling under to the blackmail and they set up their own nuclear force. They also sent a warship to get their gold. Okay, they didn't want to send a merchant ship and risk any accidents on the way back or on the way there. They sent the warship, which took the gold and brought it back to France. But in the meantime, the US was losing gold because there were free gold markets. In London and in Zurich, people could buy gold with dollars. So what they did was they realized that the dollar was overvalued. That if you bought, if you took $35 and bought gold and then bought another currency, you could actually get more goods and services by just getting dollars, buying gold, and then buying dollars at the official exchange rate, it's overvalued the dollar, made it more expensive, made it seem to be more expensive than it really was. So you get hold of dollars, buy the gold and then buy foreign currencies and you would be able to buy more goods and services. So what happened was eventually the demand for gold in terms of dollars went up and the gold price began to break above $35. It was $38. So the US had to sell gold into these markets to push the price back to $35. So we began to lose gold, not directly to the foreign governments, but to the public that was able to buy and hold gold in these foreign countries. So it paid to use gold to buy foreign currencies and then use them to buy goods, export to the US for even more than $35. And that's gold arbitrage, okay? So you have $35, you buy an ounce of gold, you get 70, a Deutschmark was two to one, but the Deutschmark could buy more goods than $35 could, so you could export them to the US for $40 and you would make a $5 profit. So there's pressure to get the gold. So the US had to sell gold and here's what happened. Oh well, I'll get to the statistics in a moment, but very quickly, so I mentioned this before. Okay, we don't need to look at that. Okay, I went through all of that. There, so we had $25 billion of gold and we only had $12 billion outstanding. Foreign countries only owned about $12 billion of deposits in the US that they could exchange for gold. So knowing that the US citizens weren't able to turn their dollars in for gold, there was more than 100% coverage of these foreign liabilities, which I believe also included short-term securities. By 1967, gold had leaked out of the US. Our gold stock had shrunk to $12 billion, but yet now foreigners had $50 billion of dollars that were claims on the gold stock. And this is when France and Germany, even before this began to get nervous and began to demand gold. And this is when foreigners began to demand gold in the free gold markets and so on. By 1968, we had a further loss in gold. There was a run on gold and so we lost more gold and we have more liabilities piling up. Finally in 1971, there was a run on gold again. There were two or three weeks left of gold reserves in other words that the rate at which gold was leaking out of the US into these markets and into the foreign governments. Actually governments agreed not to sell gold in foreign markets anymore in 1968, but the foreigners were demanding gold and so we lost more gold and now we had $80 billion that we had flooded the world with and paying for the Vietnam War and so on. So as I said, the two-tier system was implemented that is central bank could only sell gold to one another and never to the free market again. And then Nixon closed the gold window. He said, I have directed Senator Connolly to suspend temporarily the convertibility of the dollar into gold or other reserve assets except in amounts and conditions determined to be in the interest of monetary stability and the best interest of the United States. Basically the US reneged on a solemn pledge made in 1944 that it would always stand ready to convert dollars into gold at the rate of $35 per ounce. And then by the end of the 1970s, we had great inflation. Gold had risen to something like $800 an ounce. Now, just to finish this up, a few economists made the claim that in the late 60s, early 70s, Milton Friedman was among them, Fritz Makla, big names. They claim that the dollar was supporting the price of gold and that if the dollars cut loose from gold, if it could no longer turn dollars in for gold, the price of gold would drop to around $10, which was about its industrial, their estimated industrial value of gold and the exact reverse happened. This is one example, I'm gonna end here, in which the Austrian school showed that their theory could predict, we call it a pattern prediction, the pattern of events that would unfold from certain economic policies. It's something that should be written up. It would make a great dissertation because all during the 60s, mainstream economists were claiming that the dollar supported the value of gold. And so here you see that that certainly wasn't the case. And well, we didn't get the dollar bill standard, but that you can ask during the panels. We have, as I said, a bill in Congress to more or less reestablish the Bretton Woods hype system. Thank you very much.


What is the riskiest thing you've ever posted on a brand social account? I was the social media lead for Anteans and Jamba and we were launching mini dogs and a peach frosty and I just tweeted the hotdog emoji and the peach emoji and when I tell you the internet went after Anteans telling us that we were horn dogs I instantly deleted it but people took screenshots of it and haunted me about that tweet for like a month. I was like oh my god we're not horny on man we just are selling pretzels


was the metric of flat space, the unit 3 square, the unit utility A is A square, ok.  Now, these two A's are the same thing because the coefficient of what multiplies is equal to minus d s 3 square, ok. So, it is the same A, it is just that you are using that there is a coordinate change going between them. And let us write out this coordinate change to the middle of this picture, I mean d e j by e d A, right now.  And sometimes we use this coordinate system and sometimes the other one, some things are easier and some things are easier, ok. So, I am going to do the following, lambda which is the only ever used, well, if the guy here should only ever use this one, ok. And so, I am going to follow the notation that prime is equal to d by d, ok. In a bigger lambda which is well dot will be d by d, ok. So, from this fact we find that A prime of A dot is equal to 1 by A and alpha prime, alpha prime, right. So, this dot is d by d t which is d eta by d t times d by d a, d eta, so by the j, ok. This will be true for every one. And it will be useful when we move between the three points, I cannot make it on the right side, on the top, ok. So, we started last class trying to find the equations of motion for A and epsilon, the energy density in the fluid stress tensor that we talked about a lot in this class, ok. So, let us continue with this, if we sum this up. If you remember, we had an expression for r 0 0 which was equal to 3 by 8 to 4 into A prime square minus A eta. And this expression is correct, whether the space is x 3, flat x or infinity, ok. But, and then we also had an expression for r i j which was equal to delta i j times something. Now, the something was, so ok, this is equal to delta i j times minus 1 by 8 to the 4 r i j is equal to minus 1 by 8 to the 4 delta i j and then times for the sphere we had 2 A square plus A prime square plus A eta prime. If you remember, these terms came from the intrusive curvature of the sphere, this would have been the three dimensional r i j of the spatial metric of the sphere, we derived that. But, because these terms came about again because of the 0, because gamma is equal to 0, ok. Now, clearly if we were dealing with a flat space guy, this would be 0, this would be replaced by 0 and if we were dealing with a negatively curved guy, this would be replaced by minus 1, like minus 2, ok. And it turns out that these terms are affected, by the way because it turns out, ok. So, if we are doing this in more generality, we keep it track of or we try to do all cases at once, you just put a 2 k A square again, where k is plus 1 to the sphere, 0 for the flat space and minus 1 for the Euclidean atmosphere, ok. Once we have done that, these equations are everything we do from now on, we will be correct for all the three cases, ok. This is the only, this place is the only place in which the original tensor knows about the difference between the sphere and the flat space. This is Euclidean atmosphere. Now that we have got this, next thing we are going to do is to compute the Ritchie scale. The Ritchie scale R, which is R 0 0 plus R i i. So, let us compute that. So, that is equal to 3 by 8 to the 4 into A prime square minus A A prime, that should be R 0 0. Now from here, we get a factor of 3, we are tracing all these patients. So, that is that everywhere. Everything is minus this A to the 4 and then there is minus 2 k A square minus A prime square minus A, this cancels this. So, we get 3 by 8 to the 4 into actually 6 by 8 to the 4 and then the minus sign A A double prime plus k A square for the Ritchie scale. Now that we have got these things in hand, what we need to do, whether we are forced to check, we need to derive the Einstein equations. There are effectively two equivalent Einstein equations. One of the Einstein equations is all the 0 0 Einstein equations and the other one is either the 1 1 over 2 2 over 3 3, they are all the same because everything is provoking at that time. So, we can conveniently look at these two different Einstein equations. I first looking at the equation that you get from 0 0 and second looking at just the trace, the trace of Einstein's equations. That will be some linear combination of 0 0 0. So, let me write down the trace equation first. So, Einstein's equation is R minus R by 2 R to the nu minus R by 2 g mu nu is equal to 8 by 15 nu. Take the trace of this, we find minus R is equal to 8 by k. You get minus R because you can argue and then you get minus 4 R by 2 because the trace of g is 4. So, let us also remember the stress tensor form t mu nu is equal to epsilon plus p mu mu mu mu mu minus p g mu nu. So, in particular we find that t is the trace of this guy. You get plus 1 from here, minus 4 from here. So, it is equal to epsilon minus 3. Let us immediately write down Einstein's equation that we have from here. This equation is minus R is equal to 8 by k times t. So, we get minus 6 by 8 to the 4 a a double prime plus a a square. But there is a minus, there is a minus here. So, that equals plus is equal to 8 by k times times t and t was epsilon minus 3. Now, we go to the second equation. The second equation is a plane from the other zero to the zero component. So, let us keep this stuff on the board. Look, I have to give you a minute to look at and copy down whatever you want. We are going to clear this and all of this because unfortunately we can't stuff on the board. Oh, I am sorry. We also need an other zero. I lost something to me. The second equation we want is this zero-zero component of Einstein's equation. So, let us write the static weight without the zero-zero minus half delta zero-zero so that is 1 times R is equal to the time the t zero-zero components 8 by 8 k times epsilon. You see that this just becomes epsilon because we are looking at fluid flows in which U mu is 1 zero zero. We are looking at a fluid that is stationary in this coordinate system to maintain the isometric, the symmetries. So, the zero-zero component of this resonance and whether it is or not it makes no difference. Oh, I am sorry. Now, I am working in, I should probably be kept, I was thinking of working in this coordinate system. Then, I am easy to know what it makes So, half zero-zero is equal to 8 by k times t zero-zero. Now, let us compute this. So, we have t zero-zero. First, let us remind ourselves what U zero is.  And U is equal to the fact that g zero-zero is x squared. Is this clear? So, our metadunium is equal to U zero-zero zero-zero where U zero-squared A squared is equal to 1. So, U zero is equal to, U zero with an upper is equal to or is equal to 1 by k. What about U zero with a lower? Somebody correct? U zero with a lower is equal to 8. In many ways. You see, this one, the simplest is, you take U zero with an upper which is 1 by 8 and lower it. In fact, you select it, which is the A squared. So, A squared is 1 by 8.  So, just waste what it is. But U zero is equal to what? p cancels the guarantee. So, yeah, just relax. So, it was correct what I did. It was correct because it is much lower. It could not be correct because it is a lower set. Excellent. So, now let somebody please read up our zero-zero. 4 a number, 3 by 8 to the form, right square. Minus 8 theta by 4. Okay, correct. Minus r, 4 what? I don't know, r is equal to, I'm sorry. Somebody please read up our zero-zero. Yes sir. It was minus of less? Yes sir. R is equal to minus since we are making it less. Then, we have, we want r by 2. So, we make the 6 by 8 to the form. Into? Into. So, take it. Into equal to? Into. Into 2 times plus this. This, just k. So, we get 3 this is equal to a to the power of a prime square plus a plus k a square is equal to a to the power of a prime square plus a plus k a square is equal to a to the power of a prime square plus k a square we proceed actually let me for the two three things I want to do first of these is to take the equations well actually this is not the basis in which the equations are normally obtained the basis in which they are normally obtained is this equation as it is but then subtracting twice of this equation from this equation ok. So, that is what I am going to do I am going to obtain a new equation by taking this minus 2 times this to make the combination here epsilon plus that of epsilon plus 2. So, let me do that here. So, I want this minus 2 times this. So, what will I get because the two everything becomes 6. So, we get 6 by e to the power 4 and now I have a e double prime plus k a square minus k a square minus a prime 2 prime square is equal to minus a to the power of k a to the power of regarding this and this is the fundamental equation in that regard this and this as you will see actually this equation this is simple equation ok. So, I am going to clear this and write this. Now, we are not doing all proceeding pre obtain the equations in terms of derivatives respective rather derivatives respective. Now, what I need to do is to employ the simple chain every time this you can say in alpha prime I will replace it by 8 times alpha prime ok. So, let me do that. So, how about this equation this equation is very simple it becomes 3 by e to the power 4 into and a square I can take an a square of this a square into a dot square plus k a square plus k is equal to a by k epsilon. Equation a little more involved because it was the same ok. So, what do we do? So, this a prime square is the same thing.  Now, this dot this one term where you get dot acting here this one term where you get the dot acting here where you get the dot acts here that cancels this term. So, it is only the double dot term to survive. So, that is 6 by a to the power 4 into 6 by a square a double dot by double dot a is equal to a to the power k epsilon plus and yes this is a this is 8 and ok. So, now maybe a need all these equations write these equations once again. So, the fundamental equations are prime square plus a square which is equal to 3 by a square a dot square plus a a by a epsilon x by a a double dot which is equal to 6 by a to the power 4 a a double prime square is equal to minus a a by k epsilon. Now, we got the basic equation of cosmology and we are about to start studying that ok except for one more little thing. I have wondered here there is something odd. But first thing what are the variables? Variables can be thought of as epsilon you know epsilon you know the pressure and ease. But two variables we have got two equations so from this we might have thought that look it is a bit odd that we did not have to use the matter equations. We just use Einstein's equations and we are going to ask equations to solve everything including the matter why is that? Good so why is it true that we did not have to use why did not we have to use the flu equations that is the equation of state that is just some statement of what kind of matter there is also an equation of motion which is the conservation of the stress. Why do we have to use that? Because that is automatic. The stress tensor on the right hand side of Einstein's equations must be conserved it is consequence of Einstein's equations. So, I would like to see that I would like to see that more explicitly. So, I mean what if I had a motion of equation of motion. Why? In addition to the conservation of stress. And some other equation of motion. Then you will have to impose this. Then there will be new variables in the fluid. The whole fluid would not be captured by just 5 percent. That would let's say be a charge density. So, you have to be charged. And then you would have to impose the equation then you would be able to see that as a second equation. That would not be enforced by Einstein's equations. Now, Einstein's equations just impose the four energy conservation. In this case, the conservation equation is imposed by the form of Gminu. No, Gminu was the form of Gminu does not mean that it is conserved. It is imposed by the fact that you put on the right hand side of Einstein's equations. So, in some sense you are getting some part of the animation of sharing Einstein's equations. Yes, yes. By putting on the right hand side of Einstein's equations. Because Einstein's equations are inconsistent unless the stress tensor is in the equation. Okay? Now, I am going to see this a little more directly. So, I am going to just write out the equation of conservation of the stress tensor. Okay? And try to see if I can show that this, that that follow. I will show you. Okay? So, what is the equation of the conservation of the stress tensor? Where is the, in your first problem, hey, I have a really problem set. Give me your second problem set. This has been second problem in the last week. Maybe one more. Maybe we will have one last problem set as an example. We need to have some sort of evaluation that we vary. We want to have a real thing set. Maybe just a problem set, which you have two or three years. Okay? Fine. Yeah, the conservation of the stress tensor. So, now, let's remember what the equation of the conservation of the stress tensor was. We started our discussion of the energy moment of pseudo tensor. And the equation was, when you look it up, you know, what is gradient of a symmetric state? So, it's 1 by square root of minus g, l, u, square root of minus g, d, u. And then that's because of x addition. The term that may cause the energy moment to be difficult to define. G alpha beta, l by l, x, u, x, d, u. Work this out for the particular case in hand. I mean, I'm going to work it out. Let's say in this coordinate system. Okay? So, now, in this coordinate system, T00 is equal to x. So, now, as you see, Tij is equal to p. Let's work this out. We've got epsilon and p, both of which depend only on t. So, the whole stress tensor is a function only on t. So, the only derivative, also, the matrix is a function only on t. So, the only derivative that's not 0 is the unit. Okay? So, this term, mu has to be t. Therefore, mu has to be t. Therefore, mu has to be t. So, this term is 1 by a cube, that's square root g, and dp, d by dk, of a cube epsilon. The temperature must be constant for, because it's a matrix. Yes, it must be in space. Okay? Minus half, once again, the only not 0 derivative is the g derivative. But, g00 is independent of time. So, it's a certain gij that this matters. So, that's d by dp of gij times d by dp. Gij is a d times d by d. So, the ij of 1 of 1,000 is d. You raise it with one more, and you get the last sign. So, gij had a negative, and negative is square. Gij had a negative is square. The ij, also has a negative. The ij of 1 of 1,000 is dp. So, this is the sign. We have three such signs. Very good. We have three such signs, we get extra. Thank you. Now, this we can make d by d, a d by d. Canceling the two. Let's look at this. Suppose, we let the d by dp act on a cube. We get exactly the same term as this, except that we have p instead of epsilon. And epsilon is nothing. So, this is equal to d a by dp. Actually, the sign epsilon is very important. Let me see what we have got. Epsilon minus p. Okay, let's epsilon plus p. Okay. One by a, three by a plus a. d epsilon by d. Let's check what I have written out. I have written as epsilon plus p. The ij of both lower was minus p. It was plus p. Let's look at it. Remember, T mu mu is equal to epsilon plus p minus p j mu. What dictated this minus sign? It was dictated by the fact that it is a 0, 0 component p s. Now, there's no freedom in changing the sign. So, that's the case. So, this speaker is minus gij. And so, it's plus with both of them. Because gij is equal. Raising once makes it minus. Raising twice makes it minus. Okay. So, this is correct. But this here has a plus. Because the minus here cancels the minus. So, this is correct. So, this is the equation that follows from the conservation of the, this is the equation that follows directly from the conservation of the stress. So, now we've got this equation. So, now we've got three different equations. This equation. This equation. And that equation. The three equations are two variables. So, either we've got a consistent set of equations. Or they're dependent. Okay. They're not dependent equations. Of course, the actual situation is that they are independent equations. And how do we see that? Well, in order to see that, what I'm going to do is to show that I can deal with this equation. And this equation. I can derive this equation. So, I'm going to do two equations. This guy. And 3 by a squared. a dot squared plus k. Is equal to 8 by a epsilon. And use this to derive the 32. Just to check that. Okay. Okay. So, how do I do that? Well, straight forward. I take this equation. So, I take this equation to the a squared of the right hand side. And that's it. So, I get 3 into 8. So, 6 a dot a double dot. Is equal to 8 by k. d by d of epsilon squared. So, that does. That gives me an equation for a double dot. So, I have this equation with, what I have to do is to use this equation now. Yeah. So, now, let me substitute this again. Okay. So, this is equal to 8 by a d epsilon by d into a squared. So, this is equal to 8 by k epsilon into d a squared by d j. Okay. So, that becomes 16 by k into a d into a a dot. And here, I use this to relate this to. So, this is equal to, well, let me keep the 8 by k. So, this is equal to 8 by a into, this was 2 a 2 epsilon a a dot. And here, I have this guy is equal to minus 3 by a. So, that's, this takes this a a dot in epsilon plus 2. Yeah. So, the a a dot comes out. 8 by a a dot in a 2 epsilon minus 3 epsilon. So, it's minus epsilon plus minus epsilon minus 3. Put a minus of epsilon. So, exactly. That is you. But, that, we can forget about this place given the second Einstein equation. Just use the equation that came from the conservation of energy momentum. Plus this equation, which was the 0 0 Einstein equation. Okay. And that gives you all the information that you want. Because the space part of the Einstein equations obtained can be derived from these two. Okay. Now, we can adopt these two as our fundamental equations. Okay. Now, with these equations in hand, how do you go around, go about solving the problem? Okay. So, it's very straightforward. This equation looks like it has time derivatives. But, that's actually a phase. You can't study these. It's a differential equation that allows you to determine a in terms of epsilon. So, we write this equation as 3 by a integral dA by A. So, that's d log A. So, log A. So, that's 3 by, that's 3 log A is equal to minus integral dF. So, that's an equation of state. You need to know the equation of state. Once you have that equation of state, you can do the integral on the right-hand side. And that gives you A as a function of epsilon and epsilon as function of A. Once we have this in hand, then we take the second equation. That's this. And solve it for, solve it for, solve it as follows. We find what dA by, this is now like an equation in classically mechanics. And I think that, in terms of the potentials, you use the equal tricks. So, when you use the tricks, you write this as, you first solve it. So, you got it is equal to 8 by kA square epsilon by 3. Now, we're using k for 2. This is, this is 0, 1, minus 1. Let's make this a g. Let's make this one. 8 by g by 3 epsilon square. And then, minus k square. In the absence of minor, the equation of state and the iris simply goes up there. Very good. This is for the common logic, right? Yeah. Yes. So, what does that tell you? Then we should just look at the equation here. Take the dA down here. This tells us that because epsilon just plays 0, dA by dA, d epsilon by dA is 0. Which means epsilon doesn't change. Which we know. Epsilon is the basic property of the vacuum. It doesn't change because of the vacuum. Right? So, in that particular case, you don't have to go through all of this. You just replace epsilon by the constant value in every lambda. And p by n is the same constant. Minus 1. Okay? Excellent. And so, this can now be integrated by dA by square root of 8 by g e squared epsilon by 3 minus k integral as equal to d. That's good. The answer is like in the system. Okay. So, let me first do the realistic results. Let me write the equation of conservation of stress tensor. Yeah? So, that's 3 dA. Well, let me write this as 3 by a epsilon plus p is equal to minus p epsilon. This is not the energy moment. Energy momentum conservation equation. Okay? So, the solution was log A is equal to minus d epsilon by epsilon plus p A by root by g by 3 e squared epsilon minus k is equal to d plus n. This is what the solution was in terms of the dynamic equation that referred to the dynamic data. So, it must be the same. It's the same. It's the same. And it's not the same. And so, this is close to, this is an absolute relation. There's your A is in terms of this thing. Resonance to what coordinates we're using. Everybody's using the table. But this of course changes depending on whether we're using the A or E term because this will change. And let's see how that goes. Here we would have used this equation. A dot squared plus k a squared by e to the 4. Okay? So, we would have had an extra a to the 4 here and an extra a squared. So, effectively the a squared, this answer of course, but effectively there is an extra a squared in the denominator of the expression for a prime. Right? So, a prime would have had an extra a squared. And so, an extra a to the a prime squared would have had an extra a. So, we would have a pi a squared root of 8 pi g a squared. So, 9 5 3 k is equal to x. And this completes our formal listing of the equations of course. In the next few minutes we're going to try to understand physics. What this means? Any questions or comments? Then learn an awful lot about the behavior of these equations without actually solving them just by looking at them. Let's first look at this equation. Let me work in the dot. Okay? So, let's look at the equation. 6 8 I mean dot pi a pi k epsilon plus. We'll get what's the reason? For all different, in the case we can. Yeah. For three k's are different discrete choice. For all discrete choice, we can get all these. All district is not dependent on k. What's the reason? When you have k? It's your independent choice from what's the equation of state. For given k, we will be given k. For given k? Yes. It's your independent choice from what's the equation of state you're on with. It's a discrete choice chosen once and for all. And then, all right, but we'll be seeing that these three different values of k have different kinds of physics. So, in order to try to get a feel for this, we're going to start let's look at this equation. The first thing that we see from here is that as long as epsilon plus 3P, in epsilon there's an energy density. So, it's reasonable that it's possible. If the matter in question has positive pressure, it's true many kinds of equations of state are not. The cosmological constant with one sign does not have positive pressure. It does not have positive pressure. But if the matter in a question has positive pressure, then the right hand side is possible. Okay? Does there appear another matter? What? Does there appear another matter? No. No. No. Okay. How it passively collapses and collapses? It collapses. You're part of the evolution of the universe. Okay? You know, the universe is not staying still. Partly because things are crashing. But once there you seem to be my impression of that question. But the universe is never ending. Okay? Right. Yes, you're right. Yeah. Negative pressures are to do with the analysis. Negative pressures are to do with the fact that it wants to. Pressures like positive pressures. But just like positive pressures, you can keep something with negative pressure in negative pressure by holding its ends. It's like a positive pressure is a balance between war and strength. It wants to expand, but it can't because it wants to. Similarly, negative pressure can be held by me. But what about it? What? Neuron is actually a pillar of the universe. Negative pressure, right? Can we sort of map that? Yeah. And you know, the matter that we're going to consider, we'll have, we'll have more. You know, we've got one sign which has negative pressure. Yeah. Supporters for a moment, when dealing with the right-hand side, where epsilon plus degree is positive. So then this acceleration is negative. It's the in-cuter figure expected from the table. What? It gave it the impossible. K, we can, this K is... Which is really positive. Do you really mean what you expect from that? You know, it's like the universe is panning, but it's a decelerating point. It's panning, but it's decelerating. Now, suppose this is the case. What was the curve for A versus D? A versus K, because it's decelerating, must look something like this. Because it's finite today in this equation. Because the curve looks like this, then at some finite time in the past, A must be equal to Z. We'll take that time for everything to be the origin. We'll set the origin to be at that time, where A is. So we get rid of these constants and the equations by making this choice, where A is equal to zero, when G is equal to zero. Okay, let's look at the next thing. Let's look at this energy conservation equation. It was more interesting. It was D... What was it? D, A, Q, epsilon, 90, C. The original form of the equation somebody had given. The first equation we wrote down, the energy conservation equation that we first wrote down, this was the energy part, and what was it? The other part. Minus P8R, something like this. This is the number, right? Did I get the same weight? It's minus 3G. My very Q. Something like this. Adjust this. I want to make this in the sign. I want to make this in the sign. Suppose the left and right hand side will see it. And suppose the right hand side will see it. Okay? Then this will tell us that epsilon might take 1 over H. So epsilon is decaying as A increases, like 1 over H. Now, if the pressure is positive, we know it not as positive. If the pressure is positive, that's our second assumption. Just to get a feeling, we're doing various assumptions. Just to get a feeling for all these equations. And if the pressure is positive, then the right hand side is negative. Which means that epsilon has to decrease faster than one day. So epsilon, as A increases, epsilon decreases into your positive equation. At least as fast as one day. Now, why do I want to know this? I want to know this because of this equation. Because of the equation here. 3 by H squared into A dot squared plus K is equal to 8 by K epsilon. As A increases, let's put D squared. Epsilon A squared decreases. Because epsilon decreases at least as fast as one day. Okay? So the right hand side here decreases. Now, what does that mean for A dot? Let's look at the three possible cases. The first case is that K is equal to 0. Okay? At some point, the right hand side hits 3K, at which point A dot is 0. So the equation of the universe stops and then the universe turns back. A dot. Okay? And then the universe turns back and comes back and turns. Take into a lot of details. If K is positive, if K is positive that the pressure is also positive. So then epsilon plus 3K is also positive. It is a generically true thing that the universe will expand, go to maximum size, stop and come back to absolute. So K positive, along with the assumption that the pressure is positive, always gives rise to any universe that is. Okay? Along with the same assumption for pressure is positive. This, as this decreases, as it decreases A dot, so this thing goes to 0, A dot square goes to a fixed constant value. The value of the cancels is K.  So then it cancels minus 1. In this case, the expansion of the history of the universe is this. Expansion, but the pressure is nothing. When K is equal to 0, in this case, as this goes to 0, A dot goes to 0, but never reaches. So it's shhhhhh to the three kinds of orbits in 1 by 1 potential. K positive is like the elliptic orbit. You know, you throw chalk up and if this was the center of the earth, it would just lost it. K equal to 0 is then not like a hyperbolic orbit. Just with the escape velocity. It just makes it in. K negative is like a hyperbolic orbit. It's not a hyperbolic orbit. Now K negative is like a hyperbolic orbit. It makes infinity in some velocity. This is a little like that. I mean, it's just an energy. It's not particle or whatever. It's a little like that. All of these analysis however, has been made under the assumption that the pressure is positive. How is the pressure when negative is positive? You could well have acceleration rather than deceleration here, because the epsilon rest will be equal. And all of these analysis could completely change. This right hand side here, looking at positive, A neither. All so fast, and analysis I made here, that this goes to 0. As a unit of large, it will not be true. And this can completely change. Pressure is negative and in addition, there is a gravity. So, what would explain that acceleration? What explains the acceleration? That's a good question. You could have made more sense in the sign that appeared in the first one. This has bothered me a little bit. I didn't like reading. Let me just check where it points to the other side of the line. There's probably something. It's something about the gravity that responds to negative pressures and strains. Somehow it anti-gravitates in the presence of negative pressure. Something like that. I don't have a good answer here for this question. Let me think about it. It's a very important question. One should have a way of thinking of this. I have to say that when I was working on these equations last time, I expected all these results to come up with the opposite sign. Sign of pressure, precisely. This is the sign I got. This is the sign I got, yes. From the line, from the way of pressure.  Let me get back to you. By Thursday. I would like that. There's some way of saying it, I think. I think it's right. I think there's some way of saying it that rationalizes it, but it's failed. It's just, you know what I mean? Yeah, okay. I'll get back to you. Okay. Now, in order to get even better sense of what's going on, let's take a few particular equations of states. Equations of state and solve. Exalicy. So we're looking to at least some of the equations of states. Okay. So, let's take the A sub p is equal to 0. Equation of state of dust. Galaxies. Okay. In this case, I really think it's very simple. This equation here tells us that 3 epsilon by a is equal to minus p epsilon by a. Okay. So that tells you that 3 log a plus log epsilon is 0, which means that epsilon is equal to some constant alpha by a.  You remember we said that epsilon must decrease at least as fast as 1 by a cube if the pressure is not negative. In this case, pressure is 0. So it's such and such. So energy density goes as 1 by a cube. Does that mean that energy continuity is constant? Yes. Yes.  But you see, what's going on here is that what you've got is dust. Okay. So you just, let's say we've got n units of dust. And each of which has one unit rest mass. What's going on is that the number of galaxies has been concerted. And so the total rest mass has been concerted. What the energy of the space has got is not one of these asymptotically flat spaces for which we had this nice discussion over that direction. I don't know of a good way of defining the energy of the space or even if there is this closed universe.  Well, I think the only equation p is equal to sq. Then the slightly thin units of what I know, you know, you could think of it like maybe it's best to think of it as the limit of p is equal to epsilon to the alpha 5 and the limit alpha to sq. In that case, let's let's write it. So p is equal to sq. In that case, how would I know if you just associate a particular temperature with a particular energy density? Just like the usual formula. And you could ask what temperature is associated with this? It's something you're... I won't try to work it out here. We could easily... Here it's a well defined question. And then we could take the alpha goes to zero limit. What is the plausible answer? Either the temperature is not defined or the actual dust system we're looking at. In its local restaurant, there has no random motion. So I would suspect that if there's a well defined temperature, it's effectively in this situation. Either the equation of state is so similar or the temperature is in this particular case. Yes? Sir, in the limit of alpha going to zero and p going to zero... What? We wrote epsilon raised to alpha, right? Yeah. Oh. Thank you. I'm going to venture as p is equal to j. Yeah. So... In this situation, I think it's quite easy to actually work this out. But I won't try it. Okay. Great. So now let's... So we call epsilon equal to alpha by a cube. Okay, this is now the alpha. By the way, we can give alpha an interpretation along the lines that the hungation was suggesting. Because the rest mass of the system, total number of galaxies, okay, is as we suggested, is a cube in a 2 pi square root of x. So this is the total number of galaxies times the n-axis mass. So let's call that quantity wherever it is in. Total n-axis mass of our universe. So then, in this situation, what do we have? We have epsilon is equal to... So this constant, alpha, is m by 2 pi square root... So this is just the... So this is a three-dimensional sphere. We can work this out, but I think it's too fast. I think it's too fast. Okay. So epsilon is equal to... Yeah. So giving an interpretation to what that constant is, is this... Okay. Now let's put this relationship into this one. Okay. So we have integral dA over a square root of 8 pi g by 3 epsilon, which is m by 2 pi square times a cube. That's a square, so that's 1 by 8. Okay. Minus k. What is the mass corresponding to the total energy of the galaxy? Total rest energy. Total energy of the galaxies. They have the rotation. Yeah, it's the total rest energy associated with each galaxy. It's true. All the energy associated with the galaxy, that gives rise to some rest energy. But the energy of that collection, that I don't know how to define. Yes. Now let's look at this in cases. Suppose k is equal to 1. Okay. So suppose k is equal to 1. What do we get? We get...  Let's call the whole thing in on-screen. Okay. So let's get 8 pi, so 4 by 3 pi g. So k is equal to... So, okay, in general, this is dA by A, A naught squared, not that A naught squared c, we've got to call it A naught squared. A naught squared by A minus k, is equal to d. Is equal to d. This is... You know, I think that means you see a square root of 1 minus positive minus something. You make a trick to make substitution. Okay. So let's make the substitution Let's make the substitution. Okay. Now let's suppose k is equal to 1. Then we make the substitution. A is equal to A naught squared in a sine squared. And it turns out we can make theta by 2 by... Okay. So now let's see how this integral goes. So we have dA is equal to A naught squared. The 2 goes because sine theta by 2 cos theta by 2. A itself is A naught sine theta by 2 squared with this. Sorry. A was... I'm sorry, I'm sorry. A was this thing squared. So we got that right. dA was equal to A naught squared sine theta by 2 cos theta by 2. Yeah. Now this is A and then this becomes square root A. Square root A is A naught sine theta by 2 and then this quantity here is A naught cos theta by 2. So this here is parametric guys vanish. This is why we made the substitution. A naught is vanish. Okay. So we have d eta is simply equal to eta is theta up to some kind of constant. Theta in terms of A. Theta was A was equal to A naught squared into 2 minus cos theta. So it tells us that A is equal to A naught squared. This is what we know. Whatever it was. So 4 by 3 by gm by an addition of 2, 2 by 3 by m into 1 minus cos theta. This is the function of A. At eta equal to zero, we've chosen zero correctness. At eta equal to zero and eta equals 2 pi A is zero again. So as eta runs from zero to pi, the universe expands to its maximum. And then from pi to 2 pi, it shrinks back again. So this is our straights, this general analysis that we have. That I previously discussed. One more quick thing. Let's also determine the relationship between eta and t in this analysis. So we have v eta by v t which is equal to 1 by A. 1 by A is equal to 2 gm by 3 which implies that t is equal to integral of this to eta and then the integral of cos eta is the minus sign eta equal to 1 minus cos t. t pi by u or what? This type of problem. We know in our pattern, we know how A depends on eta. So let's start with A and t. So as eta goes from 0 to pi, that is just constantly increasing. But about the same things. How the t clock runs? How the t clock runs? Changes. Let's plot these things. What was A? A looked like this. On the other hand, t looks like it's constantly increasing. It starts off with 0 slope. Probably accelerates a lot of things.  Or it would be messy if you tried to actually determine things out of it. This is one advantage of eta. It's often easier to solve the equation in eta. And then raise rest terms of that. Okay. Now, I wanted to have a quick comment. Maybe I do a K-negative case first. And then we'll have one of the quick comments. The K-negative case can be not exactly the same, okay? I'll just write it. Something I should do is check I got 2 gm by 3 pi tonight. So 2 gm by 3 pi. This is quite amazing. Let's just comment on the K-negative case. In that case it turns out that this relation goes to 2 gm by 3 pi into cos h to the power minus 2. Okay. And this goes to sin h to the power minus 2. Sine h to the power minus 2. Okay, so there's nothing about this in science. Okay. Of course. But qualitatively this is, of course, very different. As eta goes from eta equals 0, once again it starts at 0. But as eta goes to increases with our power. And you can also like I understand about the big idea of time this. You see, if this A increases exponentially fast at large eta in eta. But t also increases exponentially fast. And in fact with the same coefficient 2 gm by 3. Right? So that dA by dt asymptotically is 1. Exactly as we predicted. You remember, general grounds we predicted that dA by dt asymptotically is 1. Okay. So this is an explicit solution showing what's happening. If you have dust in an open universe. By the way, the universe k equals once for the closed universe. For obvious reasons. A spatial manifold is a spherical object. The universe with k equals minus once for the open universe. Also got all these reasons. You can knock out that spatial section. Okay. So the total amount of rest mass in the open universe is equal to the amount of mass in the galaxy. In the open universe is equal to just because the volume is reduced. Okay. And we can also work this out for the special case of k equals zero. Okay. That gives rise to power of type behavior. I'll leave that for you to work out as a basis. I'll leave you to work out as a basis. It's simpler than the integrals we've got here. Because in that case, this term is not there. So the integrals aren't even symmetric, they're just integrals of power. And so you see immediately that we get dA by E squared. So you get 1 by A as the integral. So it can go like 1 by A and A goes like 1 by A. Yeah. That's the case of dust. Now, very briefly do you have anything going on now? I just realized the next, we're missing two classes next week. Because Monday and Thursday are always. We have to do something about that. I may request you to come on. But anyway, I'll take a little extra. Thank you. Okay. So we discuss the case of dust. Very briefly let's talk about what you see. In the actual universe as far as we understand it today it looks like stress energy is a combination of three kinds of matter. Okay. Of dust which is a cold matter including dark matter which isn't a matter. Radiation. Which is an negligible fraction of what's going on today but it was a very important part of the universe in the early part of the universe like photon radiation. And it looks like cosmological constant. Okay. So that's why I wanted to take you through the analysis separately of dust radiation and cosmological constant before trying to put all these three together. Okay. So now we want to discuss the case of radiation. So when we put these things together the exchange between them also has to do with them. The exchange between them has to be taken into account. Yes. However cosmological constant doesn't exchange with any it's just constant. So it's the exchange between matter and radiation. Now matter and radiation couple once matter at the early part of the early age early epoch in the age of the universe up to a few hundred thousand years the universe was ionized. So the matter was ions of, you know, ionized hydrogen electrons and protons from here on and then the matter and the radiation were interacting very very immediately the important way. But after matter we ionized, sorry, we unionized, you know, we combined. Then the matter was essentially neutral and essentially the matter and the radiation have formed two non-interactive fluids then after. So it's true that during the era where things were ionized you have to work harder. But after recombination these were essentially two non-interactive fluids. Of course the cosmological constant always is non-interactive. So does this Well, if it's really a constant if it's just a lambda term it does not interact with it. If it's a what? But can't be sure that it really is a constant. Yes, but can't be sure. Well, you know, the question is whether you know what lambda, you need to give it dynamics. I'm asking, does that does any sort of dynamics come from here on? No, no, you see in the in the Lagrangian I have a general relativity. If lambda were anything but a constant it wouldn't have a break if you're more physical. The only way for lambda not to be a constant would be for


October is here and falling temperatures are bringing big savings. Get the phone you want with free activation all month long on post-paid service. That's up to a $30 savings per life. Better service, bigger savings. That's today's Appalachian Wireless. Students throughout eastern Kentucky are learning about fire safety thanks to Pike County Emergency Management and a state-of-the-art fire safety trailer. This is the only trailer of its kind in the state. And it's only one of about three in the nation. This teaches them in a non-threatening atmosphere but with realism. You get smoke, you get to see the digital fire, and they can put that out. During October, which is National Fire Prevention Month, Pike County Emergency Management officials work with fire departments across the region to take the trailer to schools where students learn how to handle situations they may encounter at home. They've got several scenarios they go through and learn how to deal with and one of those is an oven fire. A lot of people think if your oven catches on fire, you want to open the oven door and try to put it out. Well, the best thing to do they learn is to keep the oven closed and turn it off and it will smother itself out. Students are even taught how to handle a fire that may happen at night. They learn what to do when the smoke detector goes off in the bedroom. They know to fill the door. They learn how to do that to see if it's hot. If there's smoke coming from under the door, which we create that scenario, we show them how to put something under the door to stop the smoke. This week, the trailer was at Pikeville Elementary School, but Pike County Emergency Management officials say the state-of-the-art trailer is available across eastern Kentucky. It's also a regional asset, not just a Pike County asset, because that's the way we wrote the grant for fire safety throughout our region. So the trailer has been as far away as Moorhead and Corbin, and the more fire departments that see it and see the potential for teaching fire safety in their communities, that circle grows even bigger. For more information about the trailer or to ask how to get it scheduled at a particular location, you can contact CJ Childers at the number on your screen. In Pikeville, I'm Shannon Deskins, EKB News.


Hey guys, welcome to another fresh week of the rundown. This week we have 10 things you need to know on the Uniform Change. Military OneSource is hosting a webinar on the new blended retirement system, and the Navy wants your feedback on preventing alcohol and prescription drug abuse. Last week we told you the Navy's transitioning from the NW type 1 to the type 3 beginning October 1st. This week, All Hands has a blog that covers the 10 things you need to know about the Uniform Change. In addition, there is greater detail on the patches for the type 3 and the new logo design for the Navy Fitness Uniform. If you check it out, you might see a familiar face. Military OneSource is holding a webinar on the new blended retirement system, Tuesday, August 16th. The webinar will provide an overview of the new retirement system and offer a Q&A session with program and policy directors. To register, visit the website below. Also, there is a new webpage with info on the new blended retirement system, including an infographic for active duty, answers to questions, and videos. Check out the webpage by visiting militarypay.defense.gov and click on the blended retirement system. Finally, the Navy is surveying sailors to get their feedback on alcohol and prescription drug prevention efforts. The survey will measure sailors' attitudes and perceptions to develop more ways to combat abuse and build more effective prevention programs. Senators can take the survey by visiting the website below. Well, that's all for this week. For any questions, send us a message at usnpeople at gmail.com. For the Chief Naval Personnel, I'm MC2 L.J. Burleson. Thanks for watching.