We have a final session which I'm looking forward to is an absolutely delightful conversation and I want to simply introduce the person who will organize the conversation, a person who needs no introduction and therefore I will spend no time introducing him, William Perry, Bill Perry. Thank you, Jim. Every president since President Eisenhower has proclaimed that the United States energy dependence was a national security problem and we should do everything we can to eliminate that dependence and every president since President Eisenhower had presided over a decrease in that dependence. That's a historical fact, but what may be that may be about the change with the fracking revolution in particular in the last few number of years seems to be turning around so if you modify the proposal to be energy independence for North America not just the United States and if you define independence not to mean we don't buy any oil but we buy less energy than we sell then that's I think that's an attainable goal five to ten years so I have a few questions to ask my two colleagues here. The first is is that a reasonable statement of the problem namely North American energy independence as I defined it in five to ten years. If so then what is the economic value of that position how does that change our economy economics and secondly what is the security value does it really improve our security and let me start off with the security first and turn to Jeff on that one. You think we do have a security problem because of energy dependence and you think removing that dependence or decreasing that independence improves our security. Well I think we have a security problem because of our dependence on petroleum because I do think that our markets are subject to disruption and and our economy is subject to substantial disruption because of what happens in the in the oil markets of the world and I think it's it's great I think there's some substantial benefits to reducing our imports of oil and getting to a point where we are perhaps a net exporter of energy or petroleum but as long as we are dependent on petroleum and as we are today that's that security problem continues to a very substantial extent so so we haven't solved the problem the total problem we we've we partially solved our our current balance of payments with the rest of the world if we dramatically reduce our imports but we have not solved our security problems that'd be my take on it. Steve would you comment on the first of all the five to ten years being a reasonable goal secondly economic impact and third the security impact any of those. Sure first let me do a reverse order the security there are two parts of the security one is the security having to do with an interruption of supply if there's unrest in the Middle East and and something some key straight is mind this is an interruption of supply that scares a lot of countries and then there's the and that's an issue we actually get less and less oil from the Middle East but it's still an issue because oil ships very easily around the world and because of that if there's an interruption supply of other countries you you see an impact and we see impacts there and it's more on the financial side the volatility and the nervousness of of that is is another issue having North American your point about North American energy independence I think is a very real possibly not so much United States but North America Canada US Mexico it won't relieve the price volatility of oil because it is an international issue because oil ships so easily it could certainly relieve some of the supply issues of interruption of supply and so I think now the question is we are blessed with a lot of fossil fuels in North America we are blessed with a lot of land and sun and wind in North America as well and if you consider that plus all the other things for example the trading of energy across borders we're beginning to do this with Canada and hydro and actually can actually start to trade and think of trading energy using hydro storage and so these there's tremendous opportunities there where if you look at North America as a whole and not each country separately there are a great deal of opportunities that we're just beginning to scratch the surface of the bill we should think about now a major factor in this progress in the last decade has been the fracking revolution first with natural gas and now with oil as well and here my question is what could this be upset by an event like it could we have a TMI female lion type event some ecological disaster which causes a stop at least a dramatic slowdown with that thought in mind what could be done to minimize that probability is that we talked about more regulation than the regulation is it a state regulation or federal regulation how do we go about that approach Jeff will give you a crack at that first what about the regulatory issue well Secretary Chu had a commission which did a very good report I thought back to him and to the Congress and everyone talking about the whole issue of fracking and horizontal drilling and and the economic and the environmental impacts and we had a hearing and brought those folks to tell us what they concluded my recollection and Steve can can correct me on this but my recollection was that they said the problem of of spills polluting groundwater was was a problem with all boiling gas drilling but it was not a some fracking did not add to it that substantially except that fracking of course is causing us to do a lot more drilling that the real economic or the real environmental issue was the release of methane and that this was something which did require additional regulation and which I understand the EPA is looking at now as something that they are going to try to regulate more effectively than they have in the past do you have a view of the relative importance of state versus federal regulation in this area well to the extent that the federal government will step up and do it it will be more effective in my view deep well in the eastern part of the United States first a lot of the drilling the horizontal drilling fracking in the eastern part of the United States term private lands then so it it's out of the formal purview of the federal government it's it's the state regulatory agencies however I will agree with Jeff that on federal lands especially in the western part of the United States the U.S. government should step in and develop a set of standards and every increasing better standards as the technology gets better so that this resource can be extracted in the safest way possible I would say that the through my through my own Fukushima or whatever you want to use as an example if a major water table does become contaminated in a major sort of way that would have a profound impact on on how you know that a lot of states and a lot of communities will say no more and so in in the study we were doing and we were doing this and as you well know because he was the chair of the secretary of energy advisory board and there was a subcommittee that was doing this so he was asking a question he knew the answer to yes don't don't let him fool you but in any case I think what the commission the study also recommended is please adopt best practices yes you need regulatory authority but industries should also step forward and say hey don't don't don't kill the scoots and and and there are a lot of best practices that one could adopt to to mitigate a lot of the risks the fugitive emission is an issue not you know the monitoring of this all these things the the base lining before you start of water tables all very important things long before it becomes mandatory I would hope that industry would step forward and say we're going to do this because what they should not want is a ecological mishap that's significant that could really stop this okay okay so so I think one tries to get the industry to step up the plate to do this partly on their own but they still need a regulatory push without a doubt and I think the federal government is in a good position to set those standards it's the self-regulation within the nuclear industry a good analogy for that do you think uh well it's partly self-regulated and partly we have the nuclear regulatory commission and so they keep the industry honest but I think the US nuclear industry especially after three mile island recognize that this you know anything and with one mile island there were no deaths there were no there was a very insignificant amount of radiation that leaked out it turned to that it's less than one per in the 10 mile radius around it's less than 10th of a percent of background Fukushima a entirely different story okay and and you saw what a profound impact Fukushima had on many countries attitudes towards nuclear energy and so so you so the nuclear industry in the US is pretty good but they also have the nrc you Steve this morning you gave I thought a very eloquent statement about the importance of solar energy the question I want to get to is how long is it going to take to get solar energy to a significant scale you can define significant however you like a significant skill in terms of a supply of electricity in the United States and when that happens or American industry have a significant part basically play a significant role in the supply that those solar energy as you see the things trending today I'll define significant is at least 10 percent okay we're in the US we're about 10 percent all renewables of which six percent hydro and most of the others currently wind but but solar is getting into the one percent range now I would hope in the next decade it gets into the by itself gets into the 10 percent or higher range especially as the cost come down dramatically and you get rid of these figure out solution to solve costs also the energy storage will be a major part of that you know I I would love to see renewables be 50 percent of our electricity generation or by you know 20 or 30 years from today that I would love to see nuclear continuing this century I think by the middle end of this century I hope we don't need it anymore but unless we move in this direction you know we have a serious risk of some adverse climate change so now I think it needs new business models as I was discussing if you can get the utility companies and the regulators to embrace hey there's a profitable way of doing this which instead of being scared of solar it becomes their growth industry because and I've known enough about these things and talked to them where they would love to have especially on the energy storage side in building energy storage in a distributed way they would love that and so if they make that part of this business plan then I could see it taking off because instead of getting scared and beginning to fight it they they embrace it as a growth industry where it becomes at least as profitable as as you know building a new gas plant so I think when you get things like that and you get over those humps then you can really see it take off because then interests are aligned and and and so you know in the last year I was Secretary of Energy I started to try to talk to the utility companies the regulators and say this is a real opportunity of a completely different business model in the time scale when solar becomes 10 to 20 percent of electricity in that time scale what other renewable energies do you think hold the most promise well wind and solar hold the most promise with wind in certain countries around the world now I don't what I mean by wind let's say if you look at Ireland which is about 10 percent wind by generation the Iberian Peninsula is about 20 percent wind and solar I'm picking those examples because they have very small ties to the rest of the world if you're Denmark it doesn't really matter because you have you know convention access to conventional electricity for the but if you're an island or you're more isolated then it becomes can you get self-sufficiency and the the experiments are they're not experiments they really you know Ireland's 10 percent going one and going 20 25 percent Great Britain wants to go to 20 percent Iberian Peninsula wants to go even higher and so we have existence proofs that at least at that level you can manage this and where you're you're not tied into a bigger system that absorbs all the fluctuations let's go back to North America it's incredibly large area with the right transmission systems with the right trading things with all these other things even in the United States alone there's an incredible opportunity we you know we have fossil fuel energy resources we have renewable energy resources also come out of our years that we should take advantage of and if you include all of North America then it becomes very good the case of the solar 10 20 years from now who's going to be making the solar panels well I hope the United States goes back to making in big time I think a lot of it depends on a lot of things what has happened over the last several years is there have been as I said exuberance of expectation and availability of very cheap capital particularly in China where there was an overexpansion and then you coupled that with the recession and all of a sudden there's an oversupply that's going to work itself out the price is still going to go down as I said if I look I see at least 15 years of technological headroom where it's just going to march down in the electronics in the distribution transmission systems and in the panels themselves and so now the question is okay where is it going to be made the United States should be a major manufacturer if you consider where as I mentioned briefly most of the photovoltaic silicon that goes into the Chinese factories actually comes from the United States because the companies that make silicon photograde silicon in the United States have access to very inexpensive power and it's very energy intensive so we ship silicon to China in a highly automated factories in China they dope it they put on the electrodes they do all this stuff okay and then they ship it around the world consider another thing that also you know remember in the good old days and steel you would you would make the steel where there's coal because the shipping of the coal the transport of rail of coal is more expensive okay yeah I grew up in Pittsburgh I know all about that right the iron ore is easier shipped than the coal so you should okay now who are the where we buy a lot of our steel from Asia which to have neither the coal nor the steel so China is buying coal from the United States Korea you know they don't have coal and Japan they don't have coal they ship the coal they don't have the iron ore and they're able to make better cheaper steel than us what is wrong with this and what is wrong with it is the US for decades did not retool and did not reinvest okay so so for me to hear people say oh no no we can't we can't capture back you know steel manufacturing it's kind of crazy so can we and so because we have a very inexpensive energy and great natural resources surely we you know in highly automated plants you know it's not it's not the labor but it's more important because even in highly automated plants there's a whole supply chain for that plant that's usually domestically supplied so in terms of jobs it's not in the plant itself it's the supply chain and all the secondary and tertiary jobs and so we should be really looking hard at ourselves and saying why can't we we capture steel manufacturing as well as solar we should Jeff we'd like to weigh in on this this whole issue well I may be somewhat cynical after hanging around Washington so long but my view is that I agree we have the capability to regain a portion of the world market for manufacture of solar cells but unless we adopt policies to support that or to lead to that result if the Chinese have policies to do that and the Germans have policies to do that in various other countries then then they're going to wind up manufacturing the solar cells it's like they're going to wind up manufacturing the LEDs and and perhaps the batteries now we we put some as while Steve was secretary we we did a lot to try to stimulate manufacture of batteries in this country and I hope very much that that will continue but again I think we've got to follow through with those policies in order that we not wind up buying all of our batteries from overseas as well just like we may wind up buying all of our photovoltaic cells. I agree with everything you said Jeff you know there's a myth going around that China was developing solar cells to sell to Germany or the rest of Europe and the United States now they started that way but because of the continuing recession especially in Europe China is now in 2012 for 2013 for sure will be the biggest market for renewable energy in the world domestic China now why are they doing this well there's a couple of reasons they want to keep their solar matter fact all this huge investments those hundreds of billions of dollars they want to keep that alive to get out of the solar supply ride that and and they also actually are very concerned about climate change in their country and so but they they see this as a and if you have a home market which is to what Jeff was saying of a robust home market that's the best thing you can do for manufacturing but you you want to make in the United States to be used in the United States as well as the world market and so China China's willing to say okay we're going to start helping deployment of solar to write help them ride through this overproduction problem and that's you know if you have to think about that that makes a lot of sense in a lot of ways but in the long term they just see this as an opportunity not only for their domestic market for world market and they make no bones about it let me have pivot over now to from supply to demand and I commend all of you the remarkable speech that Steve gave this morning on the things that could be done in demand it could really make a great difference I want to just pick up a few of those and talk about them a little bit and because of the fracking evolution we have natural gas and bountiful supply and getting cheaper and cheaper one of the potentials for that is to use it as a fuel for vehicles in particular for trucks all of the calculations I've seen say it makes a lot of sense for trucks to be using natural gas for fuel there's sort of a chicken and egg problem though they're not going to use it until they get gas stations along the freeways and the and the uh companies are reluctant to build those gas stations and sort of say there's enough trucks so it's a standard chicken and egg problem is there a role for government in breaking that you know getting that long jam broken to get a moving the outcome will be a free market bonanza but how do you get to that outcome you know first Steve and then to Jeff what can government do to get that moving fast well let me first have what the federal government is doing there wants to do if you take a and we're talking about long-haul trucks these are the 18 wheelers the average distance the long-haul trucks drive is about 100,000 miles a year and they get about five or six miles to a gallon of diesel okay so that's a lot of money all right 100,000 miles five by five let's say uh and so there's 20,000 gallons but you multiply by five the other way so it's 100,000 dollars a year just for fuel and um if you take those the same internal combustion engine it can be retrofitted and not even and the newer ones are will be optimized better and it already makes good sense as you well know from your CF these these are all loaded questions he knows the answers to these are all leading questions you understand but but it already makes good sense and so what now with trucks to retrofit a truck they sometimes would charge or even to build you know a new truck out of the assembly like a mack truck or kennel worth the truck itself is 100,000 dollars and they're charging up to another 100,000 dollars to put in the the gas handling system and the liquefied containers now what should it cost about 30,000 all right but if you build new it it's not going to be that much more and so as you begin to do this the first thing you want to do is get enough competition out there at least in several manufacturers so the price should never be it shouldn't today it shouldn't be 100,000 and most it should be 50 and just get it down to 50 30 20,000 dollars and also you know at that price point you know you're paying for yourself in one year I mean the cost of liquefied natural gas including shipping and a few central stations in the United States still looks to be two or three times cheaper okay now Shell I don't know where their program is now they were going to invest about 300 million dollars in stations in stations around the United States and there's another consortium of companies that were going to do it more in localized areas but if you look at the map of the United States there's some major interstates and you need a station about every the range is five or six hundred miles you fueling station every hundred hundred fifty miles to get from the edge of one city to the other than another city and and so it's not like a personal vehicle where you have to have lots of so and so the uh the trucking industry heavy-duty trucking industry is 20 percent of our energy of transportation it's big and if you do this interstates in the maps that I've seen you can get half of that so that's a significant savings but it's it's the economics already look very very good and so the administration is proposing let's help you know if someone wants to spend the extra 50 or 80 thousand dollars we'll pay for a certain amount up to that and then just to nudge it forward and to keep companies like you know Shell and others to invest because that would do a lot again for energy independence you know offloading oil which is I see it mostly prices mostly going upwards gas I see as being stable for the next couple of decades well the market system is going to make this happen sooner or later the question is how do we make it sooner rather than later Jeff what's your view on that well I I think Steve's given a lot of good information there about what is happening and I think to the extent that the government can step in and partner with with the private sector to accelerate this we certainly should I I'm encouraged that you can buy a ram pickup now that is is equipped with both natural gas fueling capability as well as gasoline and that's to me a substantial step forward and I hope that there gets to be competition between various manufacturers in this country even at that level because there there are a lot of fleets of pickups that are in operation around the country that could be using natural gas that are that are stuck with gasoline right now by the way that technology has an huge advantage when you're at the delivery truck or personal vehicle level because you could have it's sort of like a plug-in hybrid you can run a natural gas if you're there but you don't have the anxiety that if you ever got stranded with a taze mire an engine you could a direct injection engine you could you know flip the computer and the computer says okay my feet is now natural gas will natural gas tank go the first 40 miles flip it my feet is now gasoline and so this this is technology that existed isn't deployed quite it's beginning to be and that becomes very exciting because natural gas this is going to be a lot less expensive in the u.s than oil and diesel and gasoline let me give you one concrete example I I was having lunch with the mayor of a small town in new mexico secoro new mexico some of you probably know secoro where new mexico tech is located and the mayor was complaining that the city is the natural gas utility and the city was trying to figure out how it could use its own natural gas to operate its own fleet of repair vehicles and and city vehicles around there and he said the cost was prohibitive of trying to get these things retrofitted and so when uh when dodge came out with their their uh truck that allowed for natural gas usage I called him up and said you know this is this is a reasonably priced vehicle that will allow you to do what you need to do and and as far as I know they're they're following through on it but but there's a lot of opportunity for for the use of natural gas in the transportation sector that we haven't exploited yet those of you who are new to this area if you've been driving around campus around Palo Alto you discover a profusion of hybrid cars priuses and others in fact you'll see a lot of priuses you'll see a few teslas the tesla uh showroom is just about about a mile or two from here and you'll see a few kind of cars i drive which is a plug-in hybrid and the question that i'm going to ask these two is what is the future and more economical automobiles is it hybrid plug-in hybrid all electric or is there fourth technology out there not yet on the market um you know really agnostic uh you know and it it but it's also it's deeper than that because it really depends on your usage if you're in a farm in the midwest or west you range is a big deal for you and and so uh an all electric is probably not going to do well okay you know you really want to go three or four hundred miles now ten years from the day you maybe go 300 miles uh in a 25 000 car you know teslas you know 75 000 or 82 000 dollars for the teslas but but we'll but uh so it really depends on what you're going to use in suburbian and cities uh you know there's a lot of things that do work uh you know once you get above 150 or certainly 200 miles uh for city suburban driving there's there's you know there is some anxiety i know some leaf owners have some anxiety at at 100 miles but uh and so they have to think a little more deeply about their trips but is there anything in the diesel fuel which is going to be a competitor uh in the diesel fuel well natural gas uh for heavier duty things um in the medium duty things one issue has to do with natural gas storage in the cost of the carbon tank uh which you know that's where r&d can do a lot of things i um again chemical fuel is is really very high energy density and despite the fact that the engines are only 35 percent or diesel maybe 40 percent efficient uh it's such high energy density that the range is issue but but i don't know because maybe 15 years from now we get the battery that you know and and everything changes uh so you just don't really know i think you just invest in all these things to see what happens invest in the research and all these things and let the private sector make investments jeff well i agree with what steve is saying i i think that at the current the current state of technology development the plug-in hybrid has a lot of attractions for people and in my part of the country where where you may wind up having to drive over 100 miles on a on a trip or during the day uh i think that all electric vehicles are getting better and better and uh and the cost is the cost of of getting that extended range is coming down and so i think uh there's there's potentially great opportunity there but at the current time i think there's more of a market for plug-in hybrids like the one-year driving i want to pivot to build although i must say i i do salivate over at teslas that has enough range for me pivoting now to buildings uh there's a huge potential to be realized and making buildings more efficient and steve touched on that this morning in his talks and the question in my mind is how do we get more energy as a misambiguous word or how to get more action by the people who build buildings particularly industrial buildings to build in these features that are say energy saving all of the mathematics i've seen that suggests that the math is in favor of doing this that the payback period is very attractive but yet it doesn't seem to be happening what can we do to get some moving here and does government in particular have an important role to play here so again steve i'll throw that question first to you and then to see well first i think the biggest one of the biggest barriers believe it or not is uh inertia and information many many architects and structural engineers actually don't know what's available at no extra cost uh and how you can save and one of the things i started when i was director of berkeley lab but pushed even harder is how do you how do you get people aware of the existing technologies and even design tools that they can plug into this this is the concept of what you want how can you put in something really simple like air ducts right angles and air ducts very very bad uh it costs a lot of energy to move around air with it has to go like that but but people when they draw the air ducts they use you know right angles well you know it when you're building a new building it doesn't cost them it doesn't cost more the very very simple things having the ventilation system not fight convection is something that is not fully understood you know hot air rises uh and and so you have profound examples even in modern buildings built in the last five years where they just say we're going to use energy and power to overcome natural convection whereas you should be using natural convection to actually assist in the circulation now we have a we just bought a home here in mellow park it's a two-story home um uh it has no air conditioning we don't need air conditioning you open up the windows and the ground floor at night and let it cool on the top floor and then you close the windows at eight or nine o'clock in the daytime and your house stays at 70 or 68 or you name it that's what's happening and so that just the sensible use of what you have is something that most building designers have forgotten about over 200 years ago and and in europe today where they don't have much air conditioning they know this stuff so just even getting that stuff into the design of the buildings is is a profound and it saves money you know just not forcing against you know hot air rises color sinks just things like this passive shading uh when the south and west facing sun in a hot day use some white shades okay and so again this is stuff that you can build in to the automated things i will go around and do this managing myself uh my wife won't do it but you know i will open the windows at nine closing during the day and do all these other things so so it has to be automated okay but but you can do those things and and so those are things that don't cost much money and then it saves on the size of your chiller it saves on the size of your hbac system it saves on everything and and but i think the ignorance and inertia is is is a lot of it what can the government do they can be the information barrier they can be the convener they can be helping invent software tools that help the architects and social engineers automatically say well this is kind of what i want conceptually and so you tell me where i should put the air ducts and how big should they be and you can tell me how to use passive shading and make suggestions jeff anything on buildings well just that this is a difficult issue for the federal government to fix uh i mean the tradition is that the state and local government determines building codes and that's always been the case and it's not i think i've i've determined in the time i was back there that it's not realistic to think we're going to have federally uh mandated building codes that have any real teeth in them so i do think the federal government's role is is as steve describes it and that is to try to show the way try to try to encourage try to provide incentives for states and and local communities to do the right thing and for builders and architects to do the right thing and when we build federal buildings hey you let that be an example we build things in military bases let that be an example we're going to turn over now to the audience to ask questions to this panel and there's people with microphones if you raise your hand somebody will bring a microphone to you and you can speak here we go john massey could you give us your name first john massey quick question i grew up just north of pittsburgh as well and used to work for the us bureau of mines pittsburgh mine research center which sort of watched over the coal guys an interesting experience so i have a question about fracking and the potential role of insurance and the reason was there were a lot of coal mines in western pennsylvania that were out of use for 20 30 years the companies were gone they would collapse they would burn all kinds of stuff to what extent is it possible to either have regulations or involve the insurance industry in making sure that people in an area don't get hurt 20 years later and therefore give shorter-term incentives to the companies to do it right engineer the the wells right and do the geology right that's an excellent question i'm not sure we have an answer in this bound to that question i'm going to turn over to c for us to see if it's yeah that's a great question because there are plenty of examples of mining companies that do this and then 20 30 years later they're belly up they no longer exist okay and you get you know acid conditions terrible runoffs all these things and and then you know ultimately either you you've got this really polluted site or else the taxpayer has to clean it up and i it we shouldn't be thinking about that just as you know after the macondo oil spill the Gulf of Mexico you know TransOcean was the company hired by BP to do this but a much smaller company could have done that which has no assets and they could have done equal damage because it was TransOcean and and there has to be protection against that now it was suggested by the oil the presidential oil spill commission that everybody who extracts oil out of the Gulf of Mexico pay into a pool an insurance pool that you know and then depending on how much you're extracting how much profit you're making you pay more you know so the big guys who are getting a lot of oil should pay more into that but it allows the smaller people to have this pool of protection i thought it was a great idea the company strongly resisted that okay so a similar thing you know in all mining operations you know in fracking the the biggest fear is actually the smaller companies who can do equal environmental damage pollute a major water table or have fugitive runaway fugitive emissions and they don't have deep pockets and they just they don't even go through chapter 11 they just go straight to chapter 7 and then who's left holding back the people and the taxpayers so insurance pools things like that to give it more longevity i don't know but but these are some ideas but amazingly industries the you know i was thinking this is a great idea for the oil industry to help help itself and yet huge resistance jeff do you want to add anything to that just that i i could also support the kind of establishment of a fund to deal with oil spills but i i really think probably the government's most effective efforts are done at the front end in trying to have effective regulation and monitoring of what's going on i mean i think instead of coming along behind and trying to trying to provide some kind of recompense for for folks that are injured by inadequate regulation i think we're better off focusing on on better regulation and better monitoring of what's happening at the beginning next question yes my name is very very china and kubitino city council the united states infrastructure ranking is number 25 in the world when the government is going to spend more money in improve the infrastructure especially the massive public transit to help reduce the co2 jeff do you want to add that well i i think it's not likely to happen soon we we of course had a substantial infusion funds into infrastructure as part of the so-called stimulus bill that that the congress passed to try to help us pull out of the recession i don't think there's much appetite in washington uh to try to do that again right now particularly given the size of our deficit and given the sentiment of many people that we we need to be shrinking government not increasing the size of government and and certainly there's very little enthusiasm for raising taxes so so what you're proposing has some good logic to it but i don't think you're likely to see uh a groundswell of support in washington for uh substantial additional public spending on infrastructure in the near future okay there's a question over here hi my name is elliott hoffman and i run a company called true market solutions and i have a quick comment and then a quick question as of a couple of hours i was walking through the the hallway here and i noticed on this beautiful bright sunny day in this beautiful building filled with glass every single light bulb was on and there are roughly i just counted about 60 bulbs in here plus the side panels and it's just our behavior is a big part of what we're doing the question is is related to a a meeting that i was out a few weeks ago in napo with people who are focused on climate energy and ab 32 all focused on california and there was a professor from stanford one of your colleagues dr chew uh mark jacobson and be curious to your thoughts on his his findings along with somebody from uc berkeley and that was that they've they're now saying that in california and new york and i'm not sure about the whole country that by 2030 we could convert all of our energy to electricity and produce 100 of our electricity with wind water and sun power and convert this by 2030 add another 10 or 20 years who cares but what what are your thoughts on that well i don't believe that let's see what steve and jim you may want to comment on that one also steve let's start with you i think that's a way over optimistic i think that for uh airplanes um i don't see liquid fuel being replaced uh in the near future so then the question is can you make uh liquid fuel renewable liquid fuel rather than um you know from fossil fuel that's something that certainly is good got a lot of department of energy attention a lot of other people's attention um so while i'm very bullish on on technology i think 20 years was was the 20 years your number uh yeah that's um i don't see that happening in 20 years um i i we are going to need some point sources of energy just for peaking and other things like that so so and for the next 2030 40 50 years at least just just for things like that so jim do you have a different view on that than steve i think in fact technically you might be able to do it if you don't care about the cost if you don't care about the economy if you don't care about the reliability of the you don't care about the reliability of the system and if for airplanes you have a very long extension card next question yes my name is richard hilt and um i'd like to i'd like to thank both dr chu and senator vigaman for for um bringing up some very interesting technical energy issues and the policy issues and not withstanding dr chu's belief that physicists are smarter than economists jim you had a lot of restraint there but these are these are very complex issues both in terms of the technology and in terms of the policy how do you how do you communicate the complexity to the average moke in the street effectively first of all i did not say that physicists were smart all i was saying is that um you might have inferred that what i what i was saying was uh that uh i would love to dearly have more data-driven stuff and and spend a lot of time getting valid data that other people can say where'd you get that data how'd you get that data this is what astrophysicists do with each other and astronomers they can't do experiments we don't go start a star and say okay now we understand how stars work but you get better and better information and then and it eliminates models it refines models it gets rid of some of the stuff the underbrush thinking and so i think jim i will both agree that that data-driven stuff and get better at getting data more reliable data and the discussion is is the data reliable how did you analyze it all this other stuff and then start from there and and that's really what i was pushing so yeah and let me comment we have data-driven physicists and you have theoretical physicists you have data-driven economists and theoretical economists and hopefully each group talks to one another at least the physicists were the physicists and the economists were the economists yeah the the the string theory guys um since they can't make predictions uh they kind of fly off in some deep space and so i'm an experimentalist as you can probably tell next question my name is chris varma i have been in the silicon valley for 35 years in microelectronics industry uh manufacturing part of the microelectronics has gone to asia so is the solar panel the question to secretary especially is it really practical to bring those back here now economically let me begin i i said can we do it not should we spend taxpayer money to do it huge difference and i would agree with jeff there's a role and they're not you know the proper role of the federal government is one thing and there is not an appetite going for at least for the next five six years of huge federal dollars going to things so so um so it it's and there was another question that had something to do with this most of this stuff has to be private sector driven it just simply has to be that way that's the way the u.s. society and markets and everything else would work and so what you should be spent what we should be spending our time doing is thinking how to tweak things to to drive private sector investments that make it a good business decision right and and to say we can do this and not and ignore the economics is saying no we really can't you know many time people have commented say we can do x and it it's only a matter of money and said well excuse me energy is about money right you know a 10 difference in energy costs mean huge things to a lot of people and and and so it's a not start to say it costs five times as much so going back to whether we should be bringing solar companies backing out states it's gotta you know first the whole market but but unfortunately solar modules ship everywhere in the world now it's like automobiles so so it's you know what are the incentives that are don't use a lot of taxpayer money to actually get american companies to reinvest in themselves i go back to steel what what should one be doing that doesn't require a lot of taxpayer dollars to get the industry to reinvest in itself and that's the cruise that's the sixty four dollar question in my life do we have another question this will be the last question by the way and i'm going to turn over to jim find a word thank you very much my name is bobby populace i have a question about um federal policy we talk about um ways that you guys can change it one of it is the divestiture of oil companies through the sunsetting of their subsidies there seems to be a lot of money that goes into idc's or or subsidies that are no longer relevant or not nearly as impactful as they could be if applied to renewables or other things in the in the non-carbon or low-carbon energy can you talk about that um and those policies and you know obama talked about repealing those didn't really get anywhere but i know he's talking about bringing that back love to hear about that jeff do you want to add that one uh well i think uh everyone's talking about doing a major reform of the tax code clearly that should be one of the things that uh should be looked at as part of that and the president of course is advocating i think in the budget the president has sent the congress for the last several years maybe since he's been president each each year he has advocated the repeal of those various tax provisions that uh that favor the uh fossil fuel industry basically so i think uh i think it's only going to happen as part of a major tax reform it's not going to happen on happen on a one-off basis and uh and of course there'll be a lot of fight about whether it happens even in that context well please join me in thanking these two amazing people


We're not in a black void this time. No. This is a white void.  Hey, welcome back to our Stupid Directs of Corbin. I'm Rick. You can follow us on Instagram, Twitter, and more juicy content. Thank you to everybody who supports on Patreon, follow us on Twitter, and subscribe and hit the like button. We're voiding. This is actually, like even when we filmed them, that maybe it's because we're normally in like a parking garage. Yeah. And so there's like- Parking garage, and the last time we were here, it was something that's already gone down. Yeah. Anyway. Hi. Ah! Pick up your lung. Sorry. So today we are in the car because we are doing a movie review. Because we just saw the new 2023 film. Jagarathanda, double X. Yes. Directed by, is that Karthik Subaraj? Yes. And written by him as well, starring Raghava Lawrence and S.J. Surya. Yep. And Shine Tomo Chaco. As we're in a whole- Tomo Chaco? Is that what it is? Yeah, I like that. Oh yeah, it's Tom Chaco. No, I like Tomo Chaco. Tomo Chaco. It just came out. Yeah, like Friday. Friday. So this will be, we'll start with non-spoilers. And then if we're gonna get into some spoils, we will let you know before we do that because it's a new film. So like obviously if you guys aren't new here, you know how we do it. So if you haven't watched it, please go watch it. Come back, but this will be our non-spoiler review of Jagarathanda, double X. Rick, your initial thoughts of Jagarathanda, double X. Initial thoughts are really, what's the word I'm looking for? A herculean attempt at a story as far as I was concerned.  It is, the score for me was the primary standout. I think the score is extraordinarily good. I thought there were pretty solid performances across the board. The one drawback for me was that I didn't get connected in the plot line to the characters in a way I had really hoped I would when we reached, because all stories, this is a spoiler, all stories have a conflict climax and a resolution. And once you get to that point where you're reaching the climax before the resolution, particularly a story like this, I had hoped I would have been more connected to my caring about our characters and the caring of the story. So the fact that that didn't happen to me made it a little bit less than what I had expected. But there's more good to say, couple of CGI things that didn't work, but there's more good to say, but it just, it wasn't as great as I was hoping it would be. No, I really enjoyed this one. And I love that it's a, and in a different way than like other films that we've seen, it's a love letter to cinema as a whole, really. Tamil cinema specifically. Yeah, and I bet there's a ton.  I heard originally that, something maybe you guys could tell me if this was a lie or not. He wanted superstar Raj Chakant in the lead and Kamal in the supporting. Wow. That was, I believe somebody told me that was his original hope. Yeah. Nutsprout, I think those characters probably based off of those people. And so that's probably like, this is who I'm thinking of when I'm doing these characters. The certain characters are just, you could tell they're inspired by these legends of Tamil cinema. Yeah. So that I really enjoy. I actually got quite connected to these people. So that's interesting that you didn't feel that. I understand it, I think, because obviously I think this was more, a lot more metaphorical than a full on, I don't know the correct word, but. Literal? Yeah, I guess literal. There are, I don't think it's totally not literal either. So it's kind of complicated in that way, but I get why you say that, but I actually kind of got connected with these. I can't give anything away, obviously. Yep. But I got that, but the main, the score for me is what you mentioned, the score was absolutely brilliant. The score is incredible. Very owed to Tamil cinema, South Indian cinema, Indian cinema as a whole, and some Western as well. Yeah. So that was great. As were some cinematography things. Absolutely. For the most part. The cinematography pretty much throughout, you just are really enjoying top notch quality cinema. Yeah, the statements overall, one about cinema, nature is another big one in this one, but also how cinema can affect the world around us. Yeah. I think that it's. Politics is incorporated. I think that was a big mess in it. And I think that's one of the main reasons he wanted to not only to celebrate, but to also Tamil cinema, but to celebrate cinema as a whole and the power that it holds. Yeah, yeah. And so I think that was another thing I really enjoyed. My biggest drawback would probably be the runtime. I think they probably could have cut, not that anything, and it was bad, that I was like, oh, you should have cut that. It was just. Right. Snappier films are always, I think, better. That also helps with the caring aspect. Absolutely. The points of that where you lose connection because of the runtime. Yeah, yeah, absolutely. And this one, even though it was, there was lots of moments in it that were evident of like, this is Tamil cinema that you're just playing on screen. They also did a lot of buildup to that. So this is not like, I wouldn't even classify this as an action film. No, I wouldn't either. It's more of a drama which has quite a bit of action, but I still wouldn't qualify it as an action. To a certain extent, and maybe they did this because they wanted to, in their mind, they thought it would be a pleasant surprise. To a certain extent, the trailer and what we saw leading up to it, the teaser and things of that nature, are a bit misleading because I think one of the things that might help somebody, I don't consider what I'm about to say a spoiler, but let me just say that in the same that the trailer itself only gives you one aspect of the film. There is a large amount of this film that doesn't feel anything like the trailer. And that for me, I felt myself at those points wondering, are we gonna get back to that? You're talking like you almost felt it, in parts it did, the trailer gave you almost a Nelson vibe. It gave you a Nelson vibe and guns and Gulab, right? And this actually becomes, for those of you who might know, had I had this expectation, it might have helped me a little bit more in the following of the story, because that's something that threw me. I felt like we went off and didn't get back to that feeling of there's a great film that has Robert De Niro in it and Jeremy Irons, an old film called The Mission, that's very similar, really, really similar in its story. I can get to that in spoilers. Not so similar that I think it was stolen, but it's very comparable. And that film has the emotional impact where you care for the people and you have certain things happen emotionally on the spectrum of the storytelling. So yeah, I agree with you. I think the runtime could have done with it. That would be my biggest drive with it because I actually really enjoyed the performances and the, because I kind of saw what they, I saw what they were doing with it in terms of like who they were trying to emulate, who they were trying to celebrate, what they were trying to do with the cinema and a lot of comedy throughout. Not as much as like a Nelson film, which the trailer did give you that vibe of the entire thing's gonna be like this. And there's quite a bit of it, but I wouldn't say the entire thing is like that. Like how Nelson's film, the entire thing, there's always comedy throughout. Don't expect that. There is comedy though. And I think they do well with it. The songs in it, I thought were very, very nice. The singers, the score, as you said, was absolutely fantastic. There's a lot of references that I picked up on and I'm sure there's a billion others, especially Tamil references that I did not pick up on. You guys will. Like I said, cause this is just an ode Tamil cinema. And I think it gave you, there's parts of the end that I really, really enjoyed and there's parts that I would have just done differently. Me too. To make it hit harder. Me too. But also, that's also Tamil cinema or Indian cinema, not even just Tamil. Of how you end films. It's a different way than I would end films. Right. And we've seen that many, many times. Yeah, yeah, yeah. And so obviously he's a Tamil director. You guys know Tamil cinema better than I do. So that was probably on purpose because of just how it's done. But there's certain moments that would have been a great moment to end on right there. And actually I think they had a really good end moment but I also like, there's a difference in how somebody would have made a film as opposed to somebody else. What else, for non-spoilers before we get into some. This is actually the first time I think we've seen actually a lot of these actors. Raghava Lawrence, who we know more as a dancer. One of the best dancers in all of India, I think went to the same school as Prabhu, I believe. But I thought his character, I don't think it's, I think it's definitely inspired by Superstar Rajnikanth. Surely. To the fact that if that was his first choice, it's evident. Because. There's also tips of the cap to. But American Western. American Western. But like, this is basically, if it's a celebration of Tamil cinema, you can't tell it without Rajnikanth, right? Yeah, that's who that's supposed to be. And so there was lots of that, which was very fun to see. I liked his performance in it, because it was, and the way they did it, I think it's in the trailer. They're filming a film and real life. And so they kind of switch back sometimes, which leads to some comedy and stuff like that. And it kind of goes all over the place in the runtime of, and it goes through similar beats that a lot of Tamil cinema goes through. Yeah, and leaves certain plot points and just decides we're not going to talk about those things anymore as it goes off in a different direction. So there's a lots of that, which I did really appreciate. How much of it is, I didn't even pick up on, but I got connected to them in the end. I was feeling it in the, not that I cried, I don't do that. Sorry guys. Unless there's like a dad and a kid now. That will, more than ever, that gets me now. But overall, I really enjoyed the film. My biggest gripe would be, you could have cut 25 minutes off of this thing and made it snappier. And still had the same impact of everything. I don't think that would have taken anything away from the story. That would be my biggest gripe with the film. You said yours more though.  It didn't gravitate. And I don't know that it necessarily has to do with the fact it could, that I'm neither Indian or Demillion. I think it's just the human element of it. Cause there's universal truth in the storytelling, which is very, very good. It just didn't magnetize my heart to the characters and the story the way I wanted it to based on the payoff. That's very evident when you get to the end of the film. Yeah. And I think, like I said, in the beginning, I think some of that was, which I totally understand because I think they were going more for a lot of the metaphorical, dommel celebration part of it, which in turn takes away the direct, cause they're doing a lot of different things that can take you out of your caring for certain characters or just because they're trying to do something different other than make you fully care. Right. Even though I did have a different experience with that, but I absolutely see why you would say that. Other than that, in terms of the non-spoiler stuff, no, that would be a spoiler. I don't want to talk about that later. But yeah, the composition, the composer is Santosh Narayan. Yeah, that's a big standout for me because you can tell there was a lot of celebration in it, one, but also blends of everything from West Gorge's to dommel, to just Indian cinema as a whole. He did a, and it was unique. Yeah. Everything he did with it was unique. I mean, had every, I mean, the amount of genres that the music covered and when it needed to be cinematic, it was. This is one of the best scores of the year. Absolutely. And it was, I felt like there was a lot of, even Superstar Rajakann's theme and a lot of it as well. Like that. That's I just associate with him now. But there was just a lot of that. There was a lot of just different genres blended together, Western stuff blended together, that I really, really appreciate. And also kind of even if the film was stretching at times, the score helps bring you in. The score is what held me through. Yeah. Anyways, so that will be at the end of our non-spoilers. So if you haven't seen the film, please go watch the film. It's out now. In some part, it doesn't have a wide distribution. This is just, it's a crowded field right now. Dommel obviously does. The theater is so crowded right now. But I have seen like in other states. Yeah. It's not getting as wide of a release. Obviously, Tigers came out this weekend and other things, but so if you haven't watched, please go watch it come back because we're gonna get into some spoils. You said there was something you wanted to talk about in the beginning, but there was a spoiler? Or do you remember it or what? I don't remember what it was at the very beginning. Okay. But anyways, so the end, I'm guessing you said you didn't, spoilers. Yeah. Spoilers now. It was kind of, I felt like a full-on ode to Dommel Center because how many times in Indian cinema as a whole do we see the hero be the savior of the village? And so it hit those same exact beats. Recently, it's just, it happens all the time. And so I felt a lot of that was kind of like just not only celebration, but also metaphoric. I thought they were gonna end after he fell and that I thought they were just gonna have the politicians win. Yeah. And I was like, this is, but then obviously you'd have to bring in the element of cinema that can kind of... And the movie they made. The movie they made to change and hopefully bring about that. And so I get that. It was just such a strong statement. It would have been a really nice, beautiful statement of the, I can't think of another word, but the damnable negativity of hierarchies in politics and bureaucracy crushing goodness. But also I see the flaw in that is the film is not trying to do that specifically. It's more trying to celebrate cinema. Right. As a whole. And the power of cinema. I get that you have to bring that in. Exactly. I actually thought that the ending they did was cool in terms of like, it was another ode to Western cinema and Tamil heroes and all that kind of stuff. And so that was cool. And it's just, if you could have blended both even better. And the power to change. Like I think that line is really great when they're coming out of the theater and you hear the person on the news saying 30 years of her career has been ended in three hours of a film. And then that film has the power to change people's minds that way. So I do get that at the end. Because if your entire films about celebrating cinema, you have to end it with celebrating cinema, but then he also ended it with, oh, leaders, why? Right. So that's a very strong statement in which I really appreciate it. And that was where the, you know, the why, the why everybody is dying and why everybody is willing to sacrifice all of this. And it becoming that the prime minister hopeful, the woman that she's just ultimately very, very evil and is just trying to obliterate every elephant and every living thing and every human being in the jungle because she's got some people who want to buy the land. The simplicity of that and the non-believeability of that for me to just paint the picture of the bad guy distanced me from what I think had the capability. And do you remember the movie? Did you see the movie, The Mission? No, I didn't. The movie, The Mission is a story, I believe it is a true story about a crusader that's Robert De Niro and a priest who are in the same tribe. And the priest's goal is to convert them to Catholicism and the crusader's goal is to obliterate them. But he gets captured by the people and it becomes one of those dances with wolves things where he sees the beauty of the people and simultaneously the good priest, Jeremy Irons, discovers that what he's going about to try and bring these people all the progress of the 20th century and also what he believes is the salvation of their souls, he discovers that the Catholic churches it's just as corrupt as the crusaders who are coming in and they both decide that they're gonna stand with the villagers because the villagers are the more humane and decent people not the people they came from. And it's a really beautiful revelatory thing that sees these two standing against all odds with these people and you watch them in the same way you do in say dances with wolves or there was another movie with Dustin Hoffman way back in the day where he too was a white guy who's raised by Native Americans where you get and I know what you said and I agree this is more metaphorical than it is literal so that's for me why it didn't really hit. And I saw the director, I'm thankful it wasn't as heavy handed as it could have been but the director was trying to grab our heartstrings. There were a lot of things that were done that were trying to get us emotionally connected and that just doesn't ever work for me. Gotcha. No, that in part did work for me. I actually liked what they did with the score, the non-score at times. So the score was amazing. At the end of it when they were all being massacred basically, I thought it was a really cool scene. I really liked that a lot. The whole saving from the evil bad guy I just thought was like another just an ode. Like a trope. Yeah, a trope thing but also the same trope that we've seen even in RRR of the hero going back to doing everything he can to save his village. We even saw it in RRR obviously. That was one of the elements of that. And I think it probably also, there's also Hindu elements that we got because they showed a God many, many times. And the names. And so that stuff I'm still not gonna ever pick up on as much as people that have lived it their entire lives. And there will always be something about the utilization of emotion in Indian cinema, irrespective of region. It's something that's done that is just not part of anything within the Western spectrum of storytelling. Yeah, it's very, very unique to them. It's very, very unique. And for them, they don't view it in a way that comes across as trying to use particular disciplines that have a manipulative aspect to it. Because that's what cinema has been for them for such a long time. Yeah, yeah, yeah. Sorry, I have a question with Mike. Did you catch the Sholay reference? With the sidecar? Or was there another one? The sidecar, it was definitely one. That was the one I only, that was the only one I got. What did I miss? I'm pretty sure, correct me if I'm wrong, when he, when was it? Sorry, long film. He was questioning his men. And he said, he didn't say Kittin' the Obnite, but I believe he said how many were there. And then he said, and he shot them. And then it was when he was questioning his men. Good call, you're right. And they, the opening shot was a, I know it because I've looked, I've seen that scene many, many times. But the opening shot was like the direct on his foot, which is how that scene opens, which is on Gabar's foot. Yeah, good call. And it's a very similar scene. And I'm sure there was a billion other similar ones. I don't know if this occurred to you at all at any point, but it's so germane to what we've been going through here in Hollywood for the past several months. But when they did, and I liked it, but when they did the moment where it was clearly Clint Eastwood giving him the camera, my thought was, does Clint know they're using us like me? Probably not. I'd imagine no. Yeah. But yeah, the end sequence, I really appreciated it. A lot of the dances were really great. What did you think about the baby surviving in the triple X at the end? Hinting very, very firmly at a sequel and the baby having survived that car crash. Yeah, I, that was, that was...  I've gotten to the point now when I see stuff like that in the back of my mind I go, just remember John Wick for it, Rick. Yeah, yeah. Just remember John Wick. It's just done for the excitement of the audience. Yes, and these are more for entertainment purposes. But one, this is not a continuation, right? I was told over and over, obviously the jigger's Honda, which I was told is not a, it's not the section not related. Maybe he's just telling three different cinema stories. Well, and to make it more... No one made it look like it was a direct. To make it all the more confusing, when we looked up the film, at least when I looked it up, I found two different places that said this was a prequel and one that said it was a sequel. Yeah. So, if it is a direct sequel, because they and made it seem like it's gonna be almost a direct continuation. Yeah, and the couple of spots particularly, for the most part, there were a good job, there were a couple of CGI spots with the elephants and the fire that you just have to just kind of, it's that don't look at the guy behind them. I liked a lot of the cinematography and I liked that kind of the villain guy.  Yeah, covered in mud. Yeah, a lot of their sequences were really cool. This had a lot of like saving nature elements as well. Obviously big elephants, which obviously very pro. Not killing elephants, don't ever do that.  Please don't.  Yeah, I'm gonna America. Yep. We famously did that. And we still do. Yes, yeah. I'm just trying to think of anything else before we end here. Any other scenes that we wanted to talk about? Yeah, I enjoyed a lot of the humor in it. You can tell certain elements were Quentin-esque in how they did it. A lot of really creative shots. There was one that was really cool.  Twisted it around. Yeah, it looked like he had fallen and was being held upside down and it was just him walking down the steps with a towel over his neck. A lot of great violence, you know, I appreciate that. Yep. And so overall, I really enjoyed the film. Looks like Rick enjoyed it as well, just not as much. Yeah, I'm ultimately glad I saw it. Yeah. Just I didn't love it. Yeah, yeah, absolutely. Let us know what you thought about the film. If you liked it, if you didn't like it, if you loved it, if you didn't love it, let us know what you thought, what should be our next for this director and what should be our next Tamil cinema excursion. What is the next Tamil cinema that can... Well, they're all being delayed now. Right. Merry Christmas might be delayed. Did you hear about that? Again? Yeah, after Christmas. Oh no. But apparently there's Eastern Christmas. I didn't know that actually. How do you... Like, it's apparently like January 12th or something. I didn't know that. Maybe. Anyways. So let us know what should be our next film down below.


This is part of a series of lectures on elliptic functions. I will start by giving a very quick review of what was in the previous lecture. We were talking about the Weierstrich elliptic function p of z. So this is elliptic, which means it's periodic for lambda in some lattice L, which is a subset of the complex numbers. There's a double pole at z equals zero, and all elliptic functions can be written as polynomials in the elliptic modular function and its derivative. What I'm going to talk about this lecture is variations on the group law associated to it. So we've got this group C modulo of the lattice, and we can think of Weierstrich's function as being a function on this lattice taking values in C union infinity. This is a group. Since L is isomorphic to sum of two copies of z and C is the sum of two copies of r, this is just isomorphic to product of two copies of the circle group. So its structure is very easy to see. And what we want to do is to describe this group structure in terms of the values of p. In other words, we would like to know what is p of z1 plus z2 if we're given p of z1 and p of z2. So this is the sort of analog of the addition formula for sine or cosine. You know sine of z1 plus z2 is sine of z1 times cosine of z2 plus something else and so on. Well, we'd also like to know what it does to the derivative. So we recall that if we've got a map from C modulo L to the projected plane, which takes a point z to p of z, p prime of z, at least of z is not in L. If C is in L, it takes a point of L to the point at infinity. So this is just a point of C squared which is contained in the projected plane. Now I'm just writing the affine coordinates because these are a bit easier to think about. And if we call these points x and y, then we recall the differential equation satisfied by p says that y squared is equal to 4x cubed minus g2x minus g3 for suitable constants g2 and g3. And this is an example of an elliptic curve. So it'll be a curve looking maybe something like this. This is a cubic curve in P2 and cubic curves in P2 are a very famous group law on them where three numbers lie on a line if and only if their sum is zero. So these are the points a, b and c and a plus b plus c is not in the group if a, b and c are collinear. This doesn't mean their sum as vectors. It means their sum in the group law on this curve. And the point at infinity is the zero of the group. So we've got a map between two groups. We've got a map from the group C modulo L to this cubic curve. And obviously we would like this map to be a homomorphism or an isomorphism of groups. So we would like to check that it is indeed. So let's first of all recall what it means for three points to be collinear. So if we've got three points x1, y1, x2, y2, x3, y3, these are collinear if the following determinant vanishes. So we take x1, y1, 1, x2, y2, 1, x3, y3, 1. And if this is, this being zero corresponds to the three points being collinear. And we want xi to be p of xi and yi to be p of, p prime of xi. So what we should do is we should look at the following determinant. We take p of xi1, p prime of xi1, 1, p of xi2, p prime of xi2, 1, p of xi3, p prime of xi3, 1. And we want to know what is this determinant or at least we want to know what are its zeros. Well, this determinant probably vaguely reminds you of the Vandermonde determinant. You remember the Vandermonde determinant is like 1xx squared, 1yy squared, 1zz squared. Of course, you could put in more variables and higher powers if you wanted. You remember this is easy to evaluate because it's divisible by x minus y because it vanishes if x is y because the first two rows are equal. And it's divisible by x minus c and it's divisible by y minus c and both sides are degree three. So this determinant is plus or minus this expression here. And we can do the same trick for this. So we notice that this is zero if z1 equals z2 or z1 equals z3 or z2 equals z3. And we would like to know, does it have any other zeros? It turns out that it does. So if we look at this determinant, we think of this as a function of just z1. And you see we've found two zeros of z1. So as a function of z1, it has a pole of order three at zero. And if you expand it out. And so how many zeros does it have? Well, if you've got an elliptic function, the number of zeros is equal to the number of poles. That's in a fundamental domain. And the reason for this is that if you take a fundamental domain, so here's zero and omega one, omega two, and here's omega one plus omega two. Then you can find the number of zeros of a function f just by integrating the function f prime of z over f of z dz. So this is equal to the number of zeros minus the number of poles for any holomorphic, meromorphic function that you're looking at inside some contour. And if f is elliptic, this is zero. And that's because the integral along the bottom and the integral on the top cancel out with each other by periodicity. And similarly, the integral along the left and the right cancel out by periodicity. So a function f of z one has three poles or rather a pole of order three zero zero zero and it's got two zeros at z one and z two. And if you look at this, you see there's a missing zero. There should be three zeros and we've only found two of them. So where's the other one? Well, there's an easy way to find out. We said the number of zeros is equal to the number of poles. There's another nice result which says that the sum of the zeros is equal to the sum of the poles modulo the lattice L. So if the zeros are z one, z two and so on, then z one plus z two plus z n is equal to p one plus p two plus p n plus something in L where the zeros are at these points and the poles are at these points. And to see this, all we do is we take one over two pi i times the integral of z f prime of z over f of z. And again, we integrate over a fundamental domain. And this thing here has a as a pole of order one at zeros with so pole of residue one at the zeros and more generally a pole of residue n is zero order n. So so the sum of the zeros minus the sum of the poles is just this expression here. So this is the sum of the zeros minus the sum of the poles. Well, in this case, the integrals over the top and the bottom don't quite cancel out. This expression here is d by d z of log of f of z. And so log of f of z can change by two pi i n under elements of the lattice L. And if you work this out, it means the top and the bottom integral don't quite cancel out. What happens is you get omega one times some integer n and similarly the left and the right don't quite cancel out. You get omega two times some integer. So this integral turns out to be omega one plus times an integer plus omega two times an integer, which is some element of L. So so that proves this identity here. Now let's apply this to our function f. So so you remember the poles are zero, zero and zero. The zeros were z two, z three and a mystery zero. Well, we've seen that zero plus zero plus zero is equal to z two plus z three plus this mystery zero. So this identifies the mystery zero. It's equal to minus c two minus c three modulo the lattice L. So we've identified the missing zero. So our determinant. Let me just go back since I don't want to write out this determinant again has a third zero. It's also zero if C one plus C two plus C three is equal to zero. And these should all be mod L, of course. So we found the three, three zeros of this as a function of Z. So now if we compare this with the cubic curve, we see that the PZ one, PZ one prime, PZ two, PZ two prime and PZ three, PZ three prime, a collinear if if z i equals z j mod L or z one plus C two plus C three is zero mod modulo the lattice L. So these being collinear is the group law on the elliptic curve and these summing to zero gives you the group law on C modulo modulo L. So the group law on C modulo L corresponds to the group law on the elliptic curve but by this map taking taking Z to P of Z, P prime of Z. I have a sort of exercise you can generalize this so so so here's an exercise. Let's find zeros of the following determinant. Let's take P of Z one, E prime of Z one, E prime of E double prime of Z one, one. And then I'm going to take P of Z two and I'm not going to write all these out. P of Z three, P of Z four and previously we had a map from C modulo L to a cubic curve in the plane. Well if we take Z to P of Z one, P prime of Z one, P double prime of Z one, one. This gives a map from C modulo L to a curve in three dimensional projective space and for the elliptic curve. We saw that three points added up to zero if and only if they lie in a line for this curve. Four points have some zero if and only if they lie on a plane in P three. So you can prove all these by sort of imitating the proof I gave for the curve in the plane. These are actually two special cases of a whole sequence of projective embeddings of our elliptic curve. So we can take a number N to be one or N equals two or N equals three or N equals four and so on. And for N equals one I'm going to map the point Z to the point one in P zero. So this is not terribly exciting, it's just mapping C modulo L to a single point. N equals two I can map Z to the point one P of Z in one dimensional projective space. Of course this is sometimes infinite so you have to sort of renormalize it a bit. So this maps C modulo L to P one and it's almost a double cover. It's a two to one map except at four points. There are four points where P has derivative zero and you get the inverse image of a point and P one is only one point here. So here we get C modulo L maps to a point. P was three, we map Z to one P of Z, P prime of Z. And here we're mapping C over L to a cubic in P two. And the next one we map Z to one P of Z and so on up to P double prime of Z. And this maps C over L to a degree four in P three and it continues like this. So you can map it to a degree five curve in P four and so on. And this gives you a whole sequence of embeddings of C modulo L into various projective spaces. And for all of them you can describe the group law by saying all the points lie on some hyperplane. If you've done algebraic geometry you may recognize these as being projective embeddings associated with various powers of a certain line bundle. There's something called a line bundle on an elliptic curve and its first, second, third and fourth powers give you these four embeddings. The reason why we usually use the case N equals three is N equals one and two are too small because the curve isn't isomorphic to its image. And N equals four is just more complicated than the case N equals three because, you know, dealing with a curve in P two is obviously a lot easier than dealing with a more complicated curve in P three. So that's why everybody uses this embedding of C over L as a cubic in P three. It's the simplest case that gives you an embedding. Well, we've got a bit of a problem. We found an addition formula for which relates P of Z one plus C two to P of Z one and P of Z two. But it doesn't quite because if you look at the determinant we had, it's also got the derivative of Z one and Z two. And we can eliminate this because you remember there's a differential equation relating this. So what we really want to do is to write, have an explicit expression for just P of Z one and Z two in terms of P of Z one, P of Z two and their derivatives. And I'll show you how to extract that from the previous result. The problem is really the following. It's really a geometric problem that purely algebraic problem.  Y squared equals four X cubed minus G two X minus G three. And the problem is find X three in terms of X one and X two. In other words, we want to describe the group law on the cubic explicitly. Are we going to do this as follows? We notice that X one, X two and X three are roots of a certain cubic equation. I'm going to write down a bit of this equation.  So where does this factor come from here? Well, what you do is use the fact that they lie on a line which is given by one X one, Y one, one X two, Y two, one X three, Y three equals zero.   Now the cubic equation says that four X cubed minus Y squared minus something or other in X and a constant term is equal to zero. So if you notice Y is given by this expression here. So Y squared is really that this expression here. And I don't care about the linear in the constant term. All I need to know is that if you've got a cubic equation, then the sum of the roots of the equation is that is the term coefficient of X squared divided by the coefficient of X cubed. So we find X one plus X two plus X three is equal to Y two minus Y one over X two minus X one squared divided by four. And this gives us the answer. So this tells us what X three is in terms of Y two Y one X one and X X two and X one. And if we recall that X I is equal to P of Z I and Y I is equal to P dash of Z I and expand this out. We just find that P of Z one plus Z two is equal to quarter of P prime of Z two minus P prime of Z one over P and Z two minus P and Z one. All squared minus P of Z one minus P of Z two. So this gives us the addition formula or the bias stress P function. As you see, it's really just the group law for a cubic curve in a slightly disguised form. We can also put Z one equals Z two and get the duplication formula for the bias stress P function. So P of Z times two is equal to a quarter of P double prime Z squared over P prime of Z squared minus two P of Z. You see, if C one is equal to Z two, then this vanishes and this vanishes. So you have to use Droppertal's rule to figure out what this quotient is, which means you take another derivative of P. So this is the duplication formula for the bias stress P function, which is the sort of analog of the duplication formula for sine and cosine. Now I'm going to give an example of how to use this. So an elliptic curve is isomorphic as a group to S one times S one. So it is n squared points Z with n Z equals zero. So these are the points of order n and they form a little group. And number theorists are very interested in these points because they give Galois representations. So the idea is if you've got a cubic curve with coefficients in the rationals, say Y squared equals four X cubed minus G two X minus G three. If G two and G three are rational, then if you look at points of order n, these are algebraic coefficients. And these coefficients generate extensions of the rationals and you can using using the elliptic curve gives you very good control over these extensions. They give you nice Galois extension with nice Galois groups. So number theorists wish to know what are the points of order n. So we now have a problem. Let's find the points of order n on this curve. Another way of doing this is to find an elliptic function vanishing on the non zero points of order n. We can't have it vanishing on all the points of order n and nowhere else because the number of poles has to be equal to the number of zeros. So what we're going to do is to put a big pole at zero and zeros at all the other points of order n. So let's do this for n equals two and n equals three. Well, n equals two is easy. All we do is we look at the derivative of P and we notice this vanishes at the points of order two. We notice there are three points of order two. If I draw a fundamental domain has zero omega one, omega two there and the points of order two are just these three points here. So these three points of order two and so these points will be omega one over two, omega two over two and omega one plus omega two over two. By the way, these points of order two turn up so often that a common convention is to call the periods two omega one and two omega two. So these points of order two are sometimes written as omega one, omega two and omega one plus omega two. But what we notice is that P of z plus omega one over two is still even. So it's derivative vanishes at zero. So what we're doing is using the fact that if you've got an even periodic function with period omega, so I suppose I've got some sort of periodic function. I don't know what it might be. It might look something like this. You notice the derivative is always going to be zero at these half periods. And that's just what's going on here. The P is an even periodic function. So it's derivative automatically vanishes at all the half periods. Well, P prime of z has order three because it's got a pole of order three. So it has a pole of order three at zero and zeros at the points of order two. I'm using the word order in two different ways. It's got zeros of order one at the points of the elliptic curve of order two. So n equals two is easy. Now let's try n equals three. And this time we've got eight non-zero points of order three. So if you draw a picture, here's the fundamental domain zero, omega one, omega two. And there will be nine points of order one or three sort of living on a little lattice like that. And we're trying to find elliptic function that is zeros of order one here. But here it has a pole order eight because there are eight zeros. Now you notice that if three z is in the lattice L, then P of z is equal to P of two z. And because two z is congruent to minus c and P is even so P of z is equal to P of minus c. So now we can recall that we had a duplication formula. So this is just a quarter of P double prime of z squared over P prime of z squared minus two times P of z. So this gives us the points of order three. We just want three P of z minus a quarter of P prime of z squared. So P double prime of z squared over P prime of z squared. So this should be zero. Well, this isn't quite the right answer because P prime of z also vanishes points of order two. So this is giving us a few extra poles that we don't really want. What we can do is we can now just multiply it by the square of this. And we may as well get rid of the four as well. So we get 12 P of z times P prime of z squared minus P double prime of z squared vanishes at the points of order three. And if you look at this, you see this as a pole of order eight at the zero. So we found all the zeros because we found eight zeros and it only has eight zeros. So this is the function we want that vanishes at the points of order three. Obviously, you can continue this for other values of n. So for n greater than three, we can do something similar. And we can find a formula for P of nz and find functions vanishing at the n squared points of order n. However, it's pretty obvious that for n bigger than three, the algebra is going to get more and more complicated. And you're probably going to want a computer algebra system to go much further than this. So this sort of illustrates that there are enormous numbers of algebraic identities involving the viastrice function. In fact, books will sometimes contain pages and pages of them. I've got a few examples here from Whitaker and Watson. You see, here are some complicated looking identities between the viastrice function. These go on for several pages and some of them are pretty scary. I mean, I was looking at this one here. Let me just magnify it so you can see it. Okay, so this one here, I honestly have no idea how to prove it or what it's good for. The really scary thing about this identity is this apparently was an undergraduate mathematics exam question back in 1897. So back in 1897, undergraduates were expected to do things that I have no idea how to do. Actually, I suspect most of the undergraduates at that time couldn't do it either, but anyway. Okay, so next lecture will probably be on the Jacobi elliptic functions.


You are an individual and you are meant to be a separate person from other people. You are meant to have a distinguished character and personality. You are meant to have your own qualities and beliefs. But narcissists have a weak sense of self. They have no inner sense of value so they get their value from other people.    They want to be you and they want you to not be yourself. Which is why they will push you to live life outside the boundaries of who you are, outside of what you would normally tolerate or accept, until you no longer act in harmony with your authentic self.  You're not allowed to be happy because if you're happy they get mad, so they have to level the score by getting one over on you and taking your happiness away and even if you're angry, you're not allowed to feel that emotion as well, so they will invalidate how you feel, as though it's not normal for you to feel that way.  Your brain has to take specific neural pathways so that you can feel certain emotions, neural pathways that your brain would not normally take, in order for you to feel emotions that you would not normally feel, and the narcissist trains you to see different pathways as dangerous, as a result of the pain you're feeling from the abuse, so your brain rewires and no longer travels those pathways anymore, those pathways become weak, so you no longer feel those feelings, you feel erased, you feel like you've become a shell of who you used to be, you feel like you're not being you, you feel like you're living in a way that is not in accordance or agreement with who you are, because you've lost touch with your authentic self, who you are right now is very different to who you used to be, it's like two separate people, because you haven't been allowed to be you for a long time, and it's not because you didn't want to be you, it's because any time you tried to be yourself you were met with punishment, because they were molding you into who they wanted you to be, which means that you had to give up authentic pieces of yourself, so that you could revolve around the narcissist and do think or feel whatever the narcissist needed in that moment, whatever served them, so when you're having to endure that sort of treatment for a long period of time, those personality traits and character traits that you had declined in effectiveness due to underuse and neglect, but that doesn't mean they're gone forever, they've just weakened like a muscle, but that muscle is still there, when you're a rounding narcissist you will feel like you've lost control of your life, your body is still there, but you feel like you've lost control of it, as though it's being operated by another person, because now your nervous system is running your life, your body's command center is controlling your movements, thoughts and automatic responses, so your objectives or desired results feel like a magical story, like something you can see, but you don't feel like you could ever attain them, you feel detached from anything that reminds you of the person that you used to be, because the narcissist has to make you question yourself and doubt yourself so that they can control you, so that they can tell you who you are and justify the abuse, every abuser needs to have an excuse in order to dodge the accountability and shame, but you can never even have a normal conversation with them because there's actually nothing wrong with you, everything you are and that you've become is simply a result of what they've been doing to you, you've just been involved with the wrong people, people who are destructive and no good for you, because they're playing on your weaknesses to break you and preventing you from strengthening or empowering yourself, so that you're at the whim of whatever they want you to think or believe, because they will push your buttons to turn you into the type of person they want you to be, so that they can feel comfortable and sane around you, which is why you need to think about the things that you are once passionate about, the things that brought you joy and meant something to you, because if you look at your life right now, it looks like there's no place for any of that right now, it's like you left everything that you once enjoyed, and even though it may seem logical and sensible for you to engage in those things again, there's a lot of resistance in your body, as though you're in opposition to it or you don't want to be affected by it, this is refusal to accept all this version to it, a lack of desire, enthusiasm and motivation to where you feel like you don't even want to do those things, because the narcissist has rewired your brain, they've caused you to let go of things that you were once passionate about, until you gave up things that you once loved, and you no longer have the desire to re-engage in them, because you feel stuck, you're so used to just doing what you have to do to survive, you haven't been able to recreate yourself and your life in the way that you want, which is a typical result and effect of narcissistic abuse, because narcissistic abuse is all about molding you and rewiring you from the inside out, so it seems like you made those changes on your own, and you chose to become that type of person, it's because narcissistic abuse creates negative neuroplasticity to where it weakens certain neural pathways in your brain, and you get stuck in negative emotional states and an extreme and intense negative thinking, you develop limiting beliefs, beliefs about yourself that restrict you in some way, thought patterns that keep the past alive, and intense negative emotions that are attached to your past, which will not change until you recondition and rewire your brain with positive neuroplasticity, which involves training your brain to have more positive beneficial experiences, which improves your well-being, because the brain can change, it changed negatively because of the abuse, so it can change positively if you do the inner work to your brain, because when you're around the narcissist you can't be yourself, it's so damaging and painful to be around them that your brain creates a character to protect yourself, a character which has many coping skills which were meant to protect you, but it also prevents you from being your authentic self, because who you are is who you choose to be, it's not who you need to be to protect yourself, so when you're out of the narcissist grip it can still be difficult for you to form healthy relationships, when you're operating from a state of self-defense, when you're healing and recovering, you will be able to break through this protective self, and then you will be able to become your authentic self, and by that point you will decide to not be around anyone who is toxic, but before that you must process and release these traumas and emotions that are stuck inside of your body, which can be challenging and it will require a lot of self-love, so that you can repair your brain and get your authentic self back, because the only other alternative is that narcissistic abuse broke you, and then you have to stay broken, which of course is not something that you would want, and it's why you must do the internal work, you must avoid the narcissist and distance yourself from them, by recognizing that they are damaging and destructive people, and you will become aware of that, by seeing the change in yourself since you've been around them, because you have changed, and it has had a negative effect on you, but many of them already know that they are toxic and dysfunctional, and they actually enjoy laying in their own filth, it brings them pleasure to turn a strong confident person into a shelf who they used to be, it makes them feel powerful, it makes them feel like their false character exists and is real, it's why they have to disempower you, and try to prevent you from engaging in any activities that promote and encourage your authentic self, because they need to be an extension of them, rather than your own separate person, they want someone who they can mold into being who they need them to be, so that they can feel comfortable and secure around you, they don't want you to become the best version of yourself, which is why if they see that they will come back just to destroy it, and anything that is associated with it, because they want a desperate fool, someone who will do anything for them, someone who is at their beck and call, they don't want you to stand in your own power, because they're very weak and fragile people, which is why they would rather if you would just follow their lead, and if you believed in anything they say, instead of you trusting yourself, because they want your devotion so that they can control you, even if they know that it's destroying you, because all they care about is themselves and what benefits them, they have an inability to connect to you and understand your feelings or situation, all they see is themselves and you become an extension of them, when they see that you have something that could benefit them, which is why they will stick around and try to leech off you, to use that power and energy to benefit them, because they have a weak sense of self, which is why they're at the whim of everyone else, so they don't want you to be your own separate person, they want an enmeshment, they want themselves to be you and you to be them, thank you for watching, if you found this video helpful please give it a thumbs up, share your thoughts in the comment section, hit the subscribe button to receive the notifications, if you would like to support the channel, you can donate at paypal.me slash narcsurvivor, you can book a one-on-one with me on my website, it's narcsurvivor.co.uk, thank you for watching and I'll talk to you soon.