Yeah, you just so be gaming with a smartphone using physical triggers. That's right, this is the Black Shark 4. This is a gaming phone from Black Shark that has physical triggers that are retractable, which is amazing.  It's got a 6.67 inch display. That's 144 Hertz. That is absolutely amazing. You can switch between 144, 120, 90, 60, all that fun stuff there. But it also has this intelligent mode to actually see what games will support the refresh rate that it does have. So that's actually cool. But again, those trigger buttons, right? Now, let's talk about them for a second. They're on the right side of the device and they're easily activated by these two mechanical shutters. Boom, they open it up and you have access to the trigger buttons, which is great because it adds so much more to gaming. As gamers, we want physical triggers and we've seen touch sensitive buttons on other devices, but this takes it to the very next level. It's got robust software allow you to remap those buttons and also the buttons have a secondary function where you can long press for, of course, a second action if you want to. So again, there's more functionality to it and it adds so much to your gameplay experience. Playing Call of Duty mobile on this, I mean, I just mow down people because the physical buttons are there and I don't have to cramp on screen. Now, as I mentioned, the screen is really fast and smooth, but also comes with a really fast processor. You're thinking Snapdragon 888? Nope, it's the Snapdragon 875G. And this is a process I really like because it gives you almost the same performance as the Snapdragon 888, with that, of course, the cost benefits that you find there or the cost disadvantages, if you will. Now, moving to a game like PUBG Mobile, where we expect to see a lot of performance from something like the Snapdragon 870, we're gaming PUBG Mobile, usually play at ultra HD ultra or sometimes smooth extreme. With the Black Shark 4, we can play at smooth 90 frames per second and it is amazing to play PUBG at that frame rate. It is fast, it is smooth, combined with those trigger buttons, I was moaning people left and right. Daniel was not happy because he was like, man, you're getting good. Actually, it was literally just a device, but that being said, it was a great experience to use that there. Now, you're thinking, what about peak performance? So we played some Genshin impact. Now, in Genshin, we maxed out the settings to, of course, 60 FPS. And this is where we saw flocked waiting frame rates. So, lowest drop down to about 47 frames per second, went up to highest, about 57 frames per second. This is roughly just within 10 to 50 minutes of gameplay. And this is consistent even with my 30 minute gameplay sessions on this device. Now, the 870 is capable of running, it was not gonna run closer to 60, I would say the average there is probably around 53 frames per second for a game like Genshin Impact, but it also runs really hot. It reached about a max temperature of about 43 degrees Celsius, which is around 120 or so, which is pretty high. But, of course, Black Shark has an offering for a cooling fan, which is sold separately. Now, this is the cooling fan from Black Shark, looks like a standard fan, and it clips onto your device, but it doesn't have a proprietary port. So how do you charge it? Or how does it actually power on? It's got a USB type-C port, which you can connect to an external port, or you can actually connect it to your smartphone, which undoubtedly will drain your device. But this has a cooling pad behind it, which will cool your device quite effectively. I've noticed that it's dropped temperatures by around five to seven degrees, or even a little bit more, depending on the game. With Genshin, it's really pushing it about five or so. But it is useful. As I said, will drain your battery a lot if you do that. Now, battery drain needs to be expected because you're running games at 144 Hertz, you've got, of course, the cooler with there, and you've got a 4,500 milliamp battery, which is good, but how do you top it off? Well, the Black Shark 4 comes with a 120 watt charger. Yes, 120 watts. And I did a charging test with this bad boy, and I did zero to 100 in roughly 23, 24 minutes, which is amazing. I mean, even right here in the studio, while I was actually recording and recording gameplay, I had about 10% in, and in five minutes, I went up to 35%. Which is nuts. So having that fast charger is absolutely great. Another cool feature with the trigger buttons is that you can remap other functions to those buttons that have nothing to do with gaming. So you can map out, say, a flashlight to your left trigger, so you can use that as a flashlight if you want to, or I can map over screen recording to the right trigger and use that to screen record. But there are a bunch of other options to use that, so it makes it more versatile than just being gaming trigger buttons, which is great. Now, the software with this device is really robust, allowing you to customize and do all the things you want to do gameplay-wise, that I think a lot of people will like, whether it's customizing the fan, or even customizing some of the features you will find on the device, I absolutely love it. Now, the camera system is also pretty good. You've got a triple camera system on here that actually does a good job, but you know what, just take a look at the video here. So video is 4K60, again, a sound sample, in the city, just kind of walking around. And you just get a quick idea, walking closer towards the Shake Shack. New York is alive. Honestly, that's amazing. I mean, I was shocked to see a gaming phone give me that kind of quality video, and also some of these solid photos. The portrait mode was okay, but again, really solid offering, and you're wondering how much does this whole package cost? Yes, with trigger buttons and all that fun stuff, this is only 500 bucks. Yes. Can you believe it? $500 for a device that gives you a solid camera, a great gaming smartphone, physical trigger buttons and 144 hertz.  Plus, combined with 121 charging, absolutely amazing. This is probably gonna take my top billing for best gaming smartphone for this year because it covers everything. So there you have it, guys. If you have any questions or any comments about the Black Shack 4, let me know. Otherwise, you wanna see some more gaming phones. I do have more on the channel. I definitely check out my next video, which will be coming out on the Red Magic 6. So, head over to that video. Otherwise, don't forget to like, share, subscribe, and always enjoy your entertainment.


So to begin the proceedings, may I call on Mr. Vinish Jain, Managing Director of the Times of India Group, to deliver the welcome address. Prime Minister Sheena Reena Modi, Ministers, Ladies and Gentlemen. On behalf of Economic Times and the Times Group, I welcome you to the fifth edition of the Global Business Summit. We launched this summit in January 2015, not long after the Modi government took office. Our vision was to make it an India-focused global melting pot of ideas and innovations. We are honoured that the Prime Minister has chosen this platform on multiple occasions to outline his vision for India and its economy. It is deeply satisfying to see this summit keep growing bigger and better. It is today a fixture on the calendars of global and Indian decision makers. Honourable Prime Minister, we thank you for being with us through this journey. You have never shied away from dreaming big and from setting yourself bold targets, even when they have seemed almost unachievable. Many of your initiatives have been game-changing and life-altering, from Swachh Bharat, Ujwala and Swabhagya, to Jandhan and Ayushman Bharat. Direct benefit transfers for payment of subsidies have not only plugged leaks in the system, but touched millions of lives. Inflation, which is like a tax on the poor, is down to 2% from 6% in 2014. And that is what has made the five years of your government so full of purpose and vitality. What is particularly heart-warming is that you have been able to do so much for the underprivileged, while at the same time promoting the cause of trade and industry. Later this year, India will become the fifth largest economy in the world. Ease of doing business has improved dramatically from a very lowly rank of 142 in 2014 to 77 now. Landmark reforms such as the Indian Bankruptcy Code and GST have promoted tax compliance and ensured that companies pay lenders and suppliers on time. These are deep reforms, the benefits of which will become more and more apparent over time. Similarly, RERA has greatly improved transparency in the murky real estate market. All this would not have been possible without a strong and stable government, one that is able to innovate on policies and provide the governance to see this through. Even as structural reforms change the Indian business landscape, the challenges on the regulatory front have become even more complex. There is increasing recognition all over the world of the need for a level playing field between traditional and new media. In order to ensure plurality of choice and net neutrality, the issue of convergence between telcos, digital content providers and distribution networks needs to be addressed. If innovation is to flourish, political leaders and global influencers, many of whom are assembled here today, must frame fair and robust rules for business. Technological breakthroughs can have a real impact only if they benefit everyone. We are already seeing the consequences of an uneven playing field where the benefits of global deals don't touch the common man. These effects are being felt in some of the world's richest economies. Brexit could hit world trade, upsetting established trade relations and putting many a small business at risk. The US-Shina trade standoff is already taking a toll and it could get worse. India, with its steady growth, has been a standout amid global economic volatility. It now needs to step up and help make the world a better place for our children and grandchildren. In Mr Modi, we have a visionary leader who has established closed rapport with his counterparts around the world and can play a lead role in coming up with solutions to the pressing problems of today and tomorrow. All of this has heightened anticipation in the Prime Minister's speech. Knowing him, he must be planning to cross many more rivers and climb many more mountains. Honourable Prime Minister, we are eager to hear your thoughts on the road ahead. We are glad to have all of you here to discuss and debate ideas and solutions. We believe the Global Business Summit is a great platform for helping shape a more inclusive world. Thank you. Thank you, Vinit, for your wise words and thoughts. My favourite story of Prime Minister Modi is when he got elected and somebody said to him, what is your vision, sir? I said, vision? Bhai, mai toh yahan chai beshte beshte aayam. Beyond that light-hearted banter and good human response that he gave, the fact of the matter is it is his vision and its bold economic initiatives that have transformed India into a nation that is progressing faster than most people imagined at every possible level. Even the ease of doing business. India has shut up in the world rankings, which should be of great cheer to investors across the globe. All over India, or rather all over the world, people have been fascinated with India. Mark Train, the iconic American author called India, cradle of the human race, mother of history, grandmother of legend, and the great grandmother of tradition. But beyond its great traditions, India is looking forward to an even greater future. And I call on our Prime Minister to share his thoughts on India at this historic Global Business Summit. Please welcome the Prime Minister of India, Narendra Modi. Srimanik Jain, distinguished guests from India and abroad. A very good morning to all of you. I'm happy to be here once again with you at the Global Business Summit. Let me first compliment you for choosing the word social. At the first word of your theme for a business summit. I'm also happy to note that the people present here are discussing the challenge of how to make development sustainable, which happens to be the second word of your summit. And when you talk about scalability, which is the third word of the theme for this summit, it gives me hope and confidence that you are indeed discussing solutions for India. Friends, who know better than all of you present here about the challenges the country was facing during the second half of 2013 and early 2014? Runaway inflation was breaking the back of every household. Increasing current account deficit and higher fiscal deficit were threatening the macroeconomic stability of the country. All these parameters were indicating a gloomy future. The country was facing total policy paralysis. This was preventing the economy from reaching the level which it was worthy of. The global fatality was worried about the health of this member of Frazile Five Club. There was a perception of surrender to existing circumstances. Friends, it was in this background that our government came to serve the people and today change is clearly visible. After 2014, hesitations have been replaced by hope. Obstacles have been replaced by optimism. And issues have been replaced by initiatives. Since 2014, India has made significant improvements in almost all international rankings and indices. This is not only show how India is changing, but also represents how the world's perception about India is changing. I am aware that there are some who cannot appreciate this rapid improvement. They suggest that ranking only improves things on paper, but nothing changes on the ground. I think this is far from the truth. Rankings are mostly lagging indicators. Things change on the ground first, but reflect in ranking after a time lag. Take the example of ease of being business rankings. Our rankings have improved from 142 to a historic high of 77 in four years. But the change in ranking had been preceded by improvement in situation on the ground. Now construction permits for starting a new business come faster and so do electricity connections and other approvals. Even for the small traders, compliance is getting easier. Now a business with a turnover of up to Rs. 40 lakh does not have to register for GST. Now a business with a turnover of up to Rs. 60 lakh does not have to pay any income tax. Now a business with a turnover of up to Rs. 1.5 crore is eligible for the composition scheme with very nominal tax rates. In the same way, India's ranking in the world travel and tourism competitive index has gone up from 65 in 2013 to 40 in 2017. Number of foreign tourist arrivals to India increased by around 45%. Number of appraved hotels went up by 50% and foreign exchange earnings in tourism also went up by 50% between 2013 and 2017. Similarly, India's rank in global innovation index had gone up from 76 in 2014 to 57 in 2018. The search in innovation is clearly visible. This improvement in culture is also visible. The number of patents and trademarks find also show a great increase. Friends, the change is due to a new style of governance and is often visible in interesting ways. I would like to give you such an interesting example of how things have changed since 2014. We are now witnessing various forms of competition. A competition between ministries, a competition between states, a competition on development, a competition on achieving targets. Today, there is a competition as to whether India will get 100% sanitation first or 100% electrification first. There is a competition as to whether all habitations will be connected by road first or all homes will get gas connection first. There is a competition as to which state will attract more investment. There is a competition as to which states will build houses for the poor fastest. There is a competition as to which aspirational district will progress fastest. Before 2014 also we heard of about a competition although of a different kind. A competition between ministries, a competition between individuals, a competition on corruption, a competition on delays. There was competition on who can do maximum corruption. There was competition on can do fastest corruption. There was competition on who can do most innovation in corruption. There was competition as to whether coal will get more money or spectrum. There was competition as to whether CWG would get more money or dependent. We all saw that and we also know who were the main players involved in this competition. I will leave it to you to decide which form of competition you would prefer. Friends, for decades a narrative was made that certain things are just impossible in India. The progress our nation has achieved since 2014 gives me confidence that nothing is impossible for 130 crore Indians. It was said that making a clean India was impossible but people of India are making it possible. Corruption-free government in India was impossible but people of India have made it possible. It was said that it is impossible to remove corruption from the process of giving people the due but people of India are making it possible. It was said that it is impossible for the poor to leverage the power of technology but the people of India are making it possible. It was said that removing discrimination and arbitration in policy making was impossible but people of India are making it possible. It was said that economic reforms in India were impossible but people of India are making it possible. It was said that governments cannot be pro-growth and pro-privileged at the same time but the people of India are making it possible. I have also been told that there is a perception or theory that a developing economy cannot grow at higher rate for a longer period without facing the problem of inflation. Post-liberalization, that is after 1991, almost all governments from in our country had to face this problem what many experts call overheating of economy after a short period of growth. As a result of this we never had sustainable higher rate of growth. You may recall that we had a government between 1991 and 1996 where the average growth was about 5% but the average inflation was more than 10%. The government just before us between 2009 and 2014 had an average growth of about 6.5% with an average inflation again in double digits. Friends, well I am not a economist, I am talking about the previous government. Friends, during 2014 to 2019 the country would register average growth of 7.4% and the average inflation would be less than 4.5%. Post-liberalization of Indian economy, this will be the highest rate of average growth and lowest rate of average inflation witness during the period of any government with these changes and reforms. Transformation is happening in the way our economy has moved. The Indian economy has expanded the bouquet of its financing resources. It is no more dependent on bank credit for investment needs. Take the example of fundraising from the capital market. During 2011-12 to 2013-14 that is three years prior to this government. The average amount of fundraising through equity was about rupees 14,000 crore per annum. In the last four years, this average is about rupees 43,000 crore per annum. This is almost three times. The total amount raised by alternative investment funds during 2011 and 2014 was less than rupees 4,000 crore. Our government took various measures to level up the source of financing in the economy and you can see the results. From 2014 to 2018 in four years, the total amount raised by alternative investment funds is more than rupees 81,000 crore. This is a jump of the order of 20 times. Similarly, let us see the example of private placement of corporate bonds. The average amount of fund raised through this during 2011 to 2014 was about rupees 3,000,000 crore or about 40 billion dollars. Now the average over the last four years has gone up to rupees 5.25 lakh crore or about 75 billion dollars. This is a jump of almost 75 percent. All these are examples of confidence shown in the Indian economy. Today, this confidence is shown not only by domestic investors but also by investors from all across the world and the confidence shown in India continues breaking the earlier trend of pre-election years. In the last four years, the amount of foreign direct investment received in the country was almost equal to what was received in seven years before 2014. To achieve all this, India needed reforms to transform. And by having the Bankruptcy Code, GST, Real Estate Act to name a few, a solid foundation for decades of higher growth had been laid. Four years ago, who would have believed that rupees 3 lakh crore or about 40 billion dollars would be returned by defaulting borrowers to financial and operational credits. This is the impact of Bankruptcy and Insolvency Code. This will help the country in allocating financial resources more efficiently. While we attended the plumbing work on economy, which was not attended for so many years, we also decided not to put a caution board of slow work in progress. All these reforms were implemented without halting work for the well-being of the larger section of the society. Friends, India is a country of 130 crore aspirations and there can never be a singular vision for development and progress. Our vision for New India caters to all sections of the society irrespective of their economic profile, their cause, creed, language and religion. We are working hard to create a New India which fulfills the aspirations and dreams of 130 crore Indians. Our vision of New India includes addressing the challenges of the future while also solving problems of the past. So today, while India has made its fastest train, it has also eliminated all unmanned railway crossings. Today, while India is building IITs and AIMs, at a rapid pace, it has also built toilets in all schools across the country. Today, while India is building 100 smart cities across the country, it is also ensuring rapid progress in over 100 aspirational districts. Today, while India has become a net exporter of electricity, it has also ensured that crores of households which were in darkness since independence have got electricity. Today, while India prepared to send a man to Mars, it is also ensuring that every Indian has a roof over his head. Today, while India in the fastest growing world economy, it is also removing poverty at the fastest speed. Friends, we have moved away from the ABC, from the ABC mentality. That is, A for avoiding, B for burying, and C for confusing. Instead of avoiding and issues, we deal with the issue. Instead of burying it, we duck it out and communicate to the people. And instead of confusing the system, we demonstrated that a solution is possible. This has given us the confidence to further upscale our positive interventions in the social sector. We are reaching out to 12 crore small marginal farmers by providing them a comfort of Rs 6000 every year. This will transfer 7.5 lakh crore rupees or about 100 billion dollars to our farmers over the next 10 years. We are rolling out a pension scheme for crores of our informal sector workers. The engine of growth for this government is running on two parallel tracks. One providing social infrastructure to all, particularly for those who were left out. And other providing physical infrastructure for all, and particularly for generation next to shape their future as per their dreams. What happened in the past is not in our hands, but what will happen in the future is firmly in our hands. We often lament and missing the industrial devolution in the past, but today it is a matter of pride that India is an active contributor to the fourth industrial devolution. The extent and magnitude our contribution will surprise the world. I am also confident that India may have missed the bus during the first three industrial devolutions, but this time it is a bus. India has not only boarded, but will also drive. Innovation and technology will form the bedrock of this resurgence. The outcomes of our focus on digital India, start-up India, making India and innovate India are converging and reaping rich dividends. Do you know that while around 4,000 patents were granted in 2013 and 2014, more than 13,000 patents were granted in 2017 and 2018, this is a three-fold increase. Similarly, do you think, do you know that the number of trademarks registered has also gone up from around 68,000 in 2013-14 to around 2.5 lakh in 2016-17. This is almost a four-fold increase. You will be happy to know that today, 44% of the start-ups registered in India are from tier 2 and tier 3 cities. A network of hundreds of utter tinkering labs is coming up across the country and helping foster an atmosphere of innovation. This will give a solid foundation for our students to help them become innovators of tomorrow. I was impressed to see how a young girl from the snake charmer community was literally charming the mouse and making the most of digital India. It is equally heartening to see how youth in villages are leveraging Wi-Fi and digital tools to help in clearing competitive exams. It is technology which is bringing the gap between the haves and have-nots in our country. Stories like this are writing a new chapter in the history of India. Friends, with the support and partnership of the people, India has made rapid strides since 2014. This could not have been possible without Jan Bhagidari, people's participation. It is this experience that gives us confidence that our country can provide adequate opportunities to all its citizens to grow, prosper and excel. We look forward to making India a $10 trillion dollar economy. We look forward to making India the third largest economy. We want to make an India of countless startups. We want to lead the global drive towards renewable source of energy. We want to give our people energy security. We want to cut down on import dependence. We want to make India a world leader in electric vehicles and energy storage devices. With these goals in mind, let us rededicate ourselves to create a new India of our dreams. Thank you very much. Thank you, Prime Minister Modi, for your inspiring, fact-filled and wonderful speech that gives such hope to everybody in the country and internationally. There has been a feeling of enormous optimism and positivity in the country since you came to power and we are most grateful for that. May I call on Mr Vineet Jan to please present a token of appreciation to our Prime Minister, a hand-woven shawl to mark our gratitude of his coming to this wonderful event and speaking to us. Thank you, Prime Minister Modi. Thank you very much. Thank you so much. Thank you. Please be seated. As an actor, I know how hard it is to follow a great act. Thank you.


Hmm, orange red. Yeah. Clean, wide dress. Ooh, pantsuit. Virgin Peruvian, curly. Little keyhole neck. That sleeve. Body looks good. It's not too much cleavish. Number one by YSL. Little twist on the left side. Hands just bump hands a little bit. Straight, Virgin Peruvian. Blue is classy, blue is classy. Curly, body wave. Indy flick. Ooh, it's hot. Go ahead, curl the ends. Blue, more blue. Lots of blue. Yes, nice and soft. Poxy, dark. Hexagram. Light my fire. Slippery dress. I'm on the left side. Electronic yellow. It's hot. Loose weight. Hexagram. Bell, Virgin Indian. Starboard.  My lips red, bell. Indy flick. Mm-hmm. I don't know if it works or not, but I'm really ready. Red, red. It's time to tell my story. It's a good one. No doubt you've come here with prejudice about who you think I am. But all I'm asking is that you hear me out. I've asked as the villain since my first day on television. And I nurtured that persona because it worked for my Hollywood career. Exceptional in everything that I do and I aspire to do. The White House has a problem with the truth. But at least they're consistent. And only too predictable with the lines they tell. I believe that we should keep the truth as a priority. I am a reality TV legend. You need it to get it. You know, just get it. Get what you want. See what you see and get it. Opportunity. I see opportunity. And opportunity shines. Fuck, does it shine? It's my right to shine. Shine means free. Shine means freedom. Spell it. No, actually spell it. I want you to spell it with me. Out loud. E-D-E-E-D-E-E-D-O. That's it. The shiny thing. I reach. I grab. I go. Good. Not bad. Not black. Not white. Not monster. Not evil. Not saint. Not holy. Just simple. Just American. Just free. Whatever you need. Whatever you need. You see. You take. You grab. You reach. You pull. You take. You crawl. You need. You go. You see. You take. You grab. You reach. You pull. You take. You crawl. Well sir, but I am somebody that must be because I am God's heart. Respect it and protect it. That really on my body. Is that my body? I mean is that me? It doesn't care about me. It doesn't care about you. It sees. And you are there. Stuck. Looking that way forever. Good to see you how they want to see you. We've been in a fight. Can you raise your hands? Monster B. Monster grab. Monster eat. Monster run. Monster walk. Women sweat. Women bend. Women beat. If you see me fight with a bear. Diva. And dinners. And who? Black honey. Spice. Pirate. Lady danger. Russian red. Blue dress because it made me feel. And the yellow because it was stunning. You can trust it. The sky is blue and you can trust it. Ice and cherries. Number one by YSL. Number 400 by Armani. Always red. Rouge. DR Rouge. Dragon Rouge. A little cleavage. Not too much cleavage. Blue red. Orange red. Yellow red. Black red. Plum. Brandy. Made me feel pure. I liked that. Diva. Indie flick. Leave the arms out. I like 14 inches or it's not worth my time. I do the Condoleezza Bog. Ice wave. And a swoop. Love a swoop.  A little mystery but not too much. Just perfect. Just perfect. Just colors. Not good. Not bad. Not black. Not white. Just colors and shape and image.


So this is the second part of the first lecture in which we will discuss some cubic curves. The first cubic curve we will discuss is the curve y squared equals x cubed plus x squared. If we draw a picture of it, it looks something like this. And what we'd like to do is to find rational or integral points on the curve. Well that's not very difficult. Suppose we've got a point x, y. What we do is we draw the line through this point and the origin. And the slope of this line will of course just be y over x, which we will call t. And obviously if x and y are rational then t is also rational. On the other hand if we choose a line through the origin with rational slope, it's going to meet this cubic in three points which will be given by the roots of some equation with rational coordinates. And two of the roots are already rational because they're just both zero. So the third intersection point must also be rational. So in other words x and y rational correspond to t being rational. So this means we almost get a one-to-one correspondence between points on this cubic and rational numbers. Well we don't quite get a one-to-one correspondence because you notice that something funny is going on at the origin. In fact t equals one, t equals minus one, both correspond to the point x, y equals zero, zero. We can of course work out x and y in terms of t. So we have y equals tx. So if we substitute that in there we find t squared x squared equals x cubed plus x squared. And if we divide through by x squared because we're not interested in the point zero, we find t squared equals one plus x. So if we find x equals t squared minus one, y equals t cubed minus t. So we see we have another birational equivalence between this curve and the line of rational points t because the map's taking x, y to t, or t to x, y are both polynomials or rational functions. You can think of this cubic curve as really just a copy of the rational line except that two of the points on the rational line are identified and mapped to the same point here. What we have is an example of a resolution of a singularity. So a singularity is roughly a bad point of the curve. So you see something is going wrong here. And a resolution means you want a nice map from some curve without singularities onto this curve here. This is the simplest example of resolving the singularity. In fact, this resolution is done by a process called blowing up. Blowing up is a very powerful method of resolving singularities. We will see a little bit later. Hiramaka showed that blowing up resolves singularities in non-zero characteristic. Sorry, in zero characteristic. The problem of resolving singularities in non-zero characteristic is a very difficult unsolved problem. Probably about the most basic unsolved problem in algebraic geometry. Finding points on curves or rational points on curves can be very difficult. For example, suppose you try to find all rational points on the curve x to the n plus y to the n equals 1. Well, if x is equal to x over z and y is equal to y over z, for some integers y is z, we just have to solve x to the n plus y to the n equals z to the n and ask whether this has any solutions other than the obvious solutions where x or y is 0. Well, this is of course Fermat's last theorem, now proved by Andrew Wiles, and it took several centuries of effort to prove it. So even a simple looking equation like this can be really hard to find the rational points on. Anyway, that's much too difficult. So let's look at a slightly simpler example. This example comes from a book called, let's see if I can show it without that light shining, The Canterbury Puzzles by this guy called Duttony who lived about a century ago and he had a newspaper column or some sort of column where he would give mathematical puzzles. And the one we want to discuss today is the one called The Problem of the Doctor of Physics, where he has a nice picture of it and the problem says there are two glass spheres, one of radius one and the other of radius two. So one has eight times the volume of the other. And the problem is to find two other glass spheres which sum up to the same volume. And you have to find spheres of rational radius. So the problem is to solve the following equation. We want to find rational numbers with x cubed plus y cubed is equal to one cubed plus two cubed, which is of course just nine. So this is a bit like Fermat's last thing for n equals three except we've got a nine here instead of a one. And there's one obvious solution which is x, y equals one, two, or for that matter two, one. And the problem is can we find some other rational points? Well, the easiest way to find rational points is to look up the answer in the back of the book. And if we do this, we find, not quite sure if it's in focus, but if you look just here, if I can do this. So just here it gives the two solutions, which are these amazingly impressively large 12 digit numbers divided by 12 digit numbers. Okay, when you look at these, you should remember that Dudney did not actually have a computer or a pocket calculator. He did this calculation by hand. So, well, it would be difficult enough to check these were a solution. So the problem is how on earth did Dudney find these numbers by hand? And the answer is he used some algebraic geometry. So what we first do is we draw a picture of this curve. Let's see if I can read this red mark. So we first draw a picture of this curve. And it looks something like this sketch it roughly sort of comes in like this. It's off like that, something like that. And here we've got these points one, two, and two, one. So we have two known points and the problem is to find others. There's a very clever idea for finding these points, which goes back to Fermat. And what you do is one way of finding points is you can take the tangent line to one of these points and see where it intersects the cubic curve. And the key point is that this intersection point is rational coordinates. And let's try and think why that is. Well, if you solve for the x coordinate of this, it's some sort of cubic equation because there's three roots because you want the intersection of a line with a cubic. And it's coefficients are rational. And two of its roots are also rational because they're both just one. So the third root must also be rational. So we get the third rational point, which is you can sit down and calculate it. Well, calculating isn't all that difficult. So the tangent curve is, if this is the point a b, the tangent to this curve is going to be y equals a squared over b squared minus a squared over b squared times x minus a plus b. And you can substitute this in and find the equation for x, which says x cubed plus minus a squared over b squared x minus a plus b all cubed is equal to nine. So as I said, this is a cubic in x and two roots are x equals a. So we can work out the third root, which must be essentially minus the constant term divided by the leading term divided by the other two roots. And you find the third root is given by x equals a cubed plus b cubed or cubed minus nine b to the six or divided by b to the six minus a to the six times a squared. And see these coefficients can rapidly get rather big because you're taking sixth powers of something. So, and this point here turns out to be minus 17 over seven 20 over seven. So that is one solution minus 17 cube plus 20 cubed is nine times seven cubed. Well, that needs original problem. Asked for diameters of gloss spheres. So obviously these numbers have to be positive. Well, here we found negative number. How do we find a positive number? Well, we can use another idea or actually really the same idea. What we can do is we would take this point and join it to this point and look at the intersection point of this line with a cubic curve. Now, just as before this line will be given. You can write down the equation of this line and its intersection points with a cubic will be roots of a cubic equation of rational coefficients. Two of the coefficients of rational the third must be so we can work at this point here. And turns out to be I can find it something like minus 271 over 438 919 over 438. So already it's getting a bit tedious to work out. And again, one of the coefficients is still negative. Well, we can keep on repeating this process. We can take another two points and take the intersection with the cubic curve and keep going until sooner or later. If we're lucky with one whose two coordinates are both positive. And this is roughly how Dudley came up with this spectacularly large example. The first two examples we had a circle or a cubic with a node were both birational to the line which makes them particularly simple to deal with because finding points on the first two curves is more or less the same as finding points on a line. This curve is not birational to a line. It's easiest to see if you look at it in over complex numbers. So if a curve is birational to a line, it must be essentially just a complex fear. If you ignore a few points, so curves that are birational to a line, meaning they're rational curves, sort of look like a Riemann sphere, except you might have to remove a few points or add a few points. If you draw a picture of x cube plus y cube equals nine of the complex numbers, it doesn't look like that at all. It looks like a torus. Or more precisely a torus with one point removed because we haven't yet done projective geometry, so we've actually missed out one point at infinity. And taking birational transformations of curves only modifies a finite number of points, and there's no way you can modify this by a finite number of points, removing them or sticking them together or whatever to make it look like a sphere. So this example is fundamentally harder than the first two examples. In fact, we've got a sort of algebraic operation. So on our curve, I draw our curve again, we've got an algebraic operation where if you've given any two points at that point, you can form a third point by drawing the line through them. So if this is A and B, we can form a third point. Let's call it A quiddle B. So we've got a binary operation on points. There are two minor problems. For instance, what happens if A is equal to B? Well, then you have to take the tangent line. The other problem is what happens is if you choose two points, say there and there, and you might find that line through them doesn't actually intersect this qubit curve in any other points. These two only intersect in two points. Well, you can see it does sort of intersect the qubit curve at infinity. So in order for this operation to be well defined, we have to add a sort of pointed infinity, which is what you get if you go off in this direction and infinitely long distance. To make sense of that, we need to use projective coordinates, which we will discuss later. Anyway, we've got a sort of operation and is it a group operation? Well, first of all, it's not a group operation because we haven't chosen an identity yet. So you might choose an identity and the simplest identity is the point at infinity. It's the most canonical point. And it's not actually a group operation because however, what happens is it turns out we do get a group operation if we say that A, B and C lie on a line is equivalent to being A plus B plus C equals naught in the group. So we're going to define a group law by saying that if three points on a line, then their sum is zero. So we see this operation here is not actually a group operation. It's really minus a group operation. So it counts as minus A plus B. And this operation is obviously commutative and it obviously has inverses and the problem is, is it associative? So we can ask, is A plus B plus C equal to A plus B plus C? And this is really rather a pain to check if you do it in coordinates. So if you actually write out the formula for A star B, it's a bit of a mess. And when you start having two group operations, it's really rather painful to check that law is associative. Fortunately, it turns out there's a much easier way to check it's associative. The point is that A1 plus B1 plus A2 plus A3 and so on turns out to be equal to B1 plus B2 plus B3 and so on. It's equivalent to saying there is a function, a rational function with poles at all the Ai and zeros at numbers Bi. And using this fact, it's quite easy to check that the group operation is associative. So we get a group operation on this elliptic and this cubic curve. This turns out to be something you can do with any reasonable cubic curve. You can usually make it into a group. There are a few minor exceptions. If the cubic curve has singularities, as in the previous example, then you sort of, if it's only got one singularity, you can sort of sometimes get a group law if you throw out the singular point. But if it's got too many singularities, you don't get a group law on it at all. So these groups are for rather strange historical reason called elliptic curves, which is a bit unfortunate because these cubic curves have almost nothing whatsoever to do with ellipses, but the name has stuck and there's nothing we can do about it. So elliptic curves are the one-dimensional case of things called abelian varieties. So abelian varieties are algebraic groups that are projective, which means roughly they don't have any missing points. There's one thing I should give a slight warning about. Abelian linear groups are not abelian. The reason for this is that abelian linear group is an old name for a symplectic group. And it was rather embarrassing that abelian linear groups are non-abelians, so Hermann Weier changed the name of abelian linear group to the symplectic group. So if you ever come across the name abelian linear group in an old book, be rather careful, they're not abelian. In the next part of the lecture, we will discuss Bezut's theorem, Pappas's theorem and Pascal's theorem.


Hey guys, it's Nate, AKA The Foot Account, and welcome back to the channel. FIFA Freeze is here today. We're gonna talk about the new promo that's coming today. We're gonna talk about icon swaps, a new team in packs, the SBCs that we're gonna be getting, as well as a Bruno Player the Month SBC, road to the final upgrades that should be happening soon, and some foot watch code that came out tonight, some tweets from Foot Watch. There are some big packs coming as a part of this icon swaps set, and a lot of the market is moving because of it. So we're gonna talk a lot about that today on the video. First things first though, I wanna cover the promo that is coming today, and that is FIFA Ultimate Team Freeze. Let's take a look at the loading screen that was dropped earlier today. Now this loading screen has been removed, basically, and we have another one behind it now, telling us information about icon swaps. But this is the official car design, which I'm a huge fan of, that cracked ice look. Looks really, really dope to me with the ice around the edges. I love it. And we learned a lot from this loading screen as well. For today, we will be getting a new team in packs.  It looks like, honestly, just another reason for EA to put special cards into packs and to sell some packs is what this is right here with a new FIFA Freeze team that will be out. Looks like we're gonna have one player SBC per day as well, so a lot of people are unhappy with this because this kind of replaces foot miss, honestly, what it seems, right? And foot miss was always a promo where we were getting two or three SBCs per day, player SBCs. All I say is this, I'm okay, I guess, with this because hopefully that means that the player SBC that we get every day should be hopefully decent value. Now during foot miss of years past, three SBCs every day was cool for card collecting, but usually, only one of those SBCs was somewhat worth it or it was good value, right? And the other ones were always just very expensive and overpriced, so hopefully that the SBCs we will be getting will be decent value, probably getting, it might not be a foot freeze item every day, might be some flashbacks, might be some Champions League flashbacks possibly, who knows, so we will see what then happens, but we will get one player SBC every day and one puzzle SBC every day possibly for some packs of some kind and then icon swaps is gonna be a part of this FIFA Freeze promo as well. One of the things I'm the most interested in is, how long does this promo go? We're gonna find out today of course, but I'm curious to see how long that it goes. I'm not gonna talk about icon swaps just yet, I wanna talk about more of this FIFA Freeze stuff. How could just the FIFA Freeze promo team and the player SBCs impact the market today at all? Now of course, you guys know that we have just had a team in packs called Team the Groupsage Cards, very high pack weight. Last year, right after Team the Groupsage, we had Team of the Year nominees, which also had a very high pack weight. I don't expect these to be Team of the Year related at all, but it's gonna be interesting to see as it always is with a new promo team, right? When we got all these players last week, you had other players that have other cards in the market that were impacted, right? This Kimmich, right? Kimmich got a 90 rated team in the Groupsage. His Inform card was 135,000 coins before this came out. Of course, now the Inform is down under 100K because of that new card coming out, right? So we always have market movements like that every single Friday. When a new team of promo cards comes into packs, that's gonna impact other stuff on the market because it's basically, it is substitute and complimentary goods or cards, if that makes sense to you guys, those terms, if you know what those mean. Some cards that come out will replace a card that people already use, or it will link to a card that people already use a lot and it will cause some link investments to go up. So of course we have a new team coming in packs today, so that's gonna be something to monitor. I do think you are gonna see panic selling this morning on a lot of very popular players that are in this game, a lot of Informs. Some of the current team week and other cards are already down a little bit. Some of these team of Groupsages are getting sold off a little bit too. Some of the golds are dropping a bit. So I would expect to see panic selling in the morning on icons as well. We'll talk about that in a second. But I think you can keep an eye on your out of packs Informs and your rule breakers, your record breakers, the road to the finals we'll talk about in a minute too. But I think you can keep an eye on those for a rebound because a lot of what we're gonna talk about today, as long as E8 is not released like a repeatable mid base or whatever icon SBC, I don't expect the market to really like crash a ton. Yes, it's a lot of content, but icon swaps is all intradable content that is grind through objectives and stuff that you can't attain like this, like you can't through an SBC. So I think that part of the market today, you will see a rebound on some of the meta stuff that does get panicked sold just because people need to buy things back to play weak in league. So that's gonna be on our minds today as well. Now, obviously team of the group stage is ending at six p.m. today.  Other things that are gonna happen today right off the bat. We are gonna see a Bruno Fernandez. I think it's gonna be Bruno Fernandez, player of the month SBC coming out today. All right, the Sun SBC I think expires very soon. It's player of the month Friday, first Friday of the month. Well, after the voting it started, first Friday of the month, after the voting ended actually. So Bruno player of the month should be coming out today. Now how expensive should that be? Now I know the Bruno card right now on the market is like 820,000 coins. It's close to 800K on both consoles. And a lot of people are hoping that this SBC will come in right around that range. Now with SBC fodder being in the place that it is, it was low but now it's starting to rise up because of some pack code. I'm really curious to see where EA values this SBC at. Player of the month this year so far have really not been that great of value if you kinda look across the board. Joao Felix is like one of the best value player of the month that we've had all year. So I'm not sure if I really expect Bruno to be that much under 800K today, maybe like 750. I think it's gonna be a 90 rated card and that will be released before the content drops. So we might see more SBC fodder movements. I also think that this card right here is maybe a bit lower, not panic sold, but people are waiting for the player of the month to come out to see if it's 90 or 91 rated before buying this card. If the SBC price is like more than this, then I would expect to see this card rise up because a lot of people want to use this card. So we'll keep that in mind for today as well. You might see a bounce on this in the scenario that EA releases Bruno Player of the month and it's really cheap. Then you might see this drop because people would just go do the player of the month. I don't think that's very likely though because SBC fodder is one thing that we need to talk about and it is on the rise after some tweets that were released just a little bit ago by Footwatch. And I wanna take a look at these tweets because these are big, right? So with foot, with icon swaps coming, right? We'll take, we'll talk icon swaps as well. This is the loading screen that is out right now. We're getting six icons and pack rewards available in icon swaps at one. So right off the bat we think, wow, six icons. That's like nothing. It's not a lot. What's up with that? Well, I wonder if they're gonna make the time period for icon swaps a lot shorter than what they have had in the past. We might not have just three icon swaps this year. We might have more than that since there's even more icons that are out in the game this year. They gave us a teaser for these icons, right? We have a 90 rated, 87 physical, 90 shot, 90 defense, center attacking mid, and a Dutch flag. So there's a lot of possibilities here with these cards. So of course we can get speculative, we can kind of figure out who these might be. It's the first icon swaps. One thing I do wanna say though is I think there will be prime icons involved today and this is why I think so. If we take a look at this tweet here by Footwatch, right here. Earlier today, EA updated this code in the game it was for Davor, Souker, right? Now of course, Souker already has and where this language and where this verbiage is gonna go is on every single icon in FIFA, as I'll show you right now, every icon has a story, right? If you right click on the card, you can go to the icon profile and there's a story that is listed there for that icon. Honestly, what this looks like to me is this is the icon description for the story of prime Souker because obviously primes have been searchable on the market, right? Inside the transfer market but they're not actually out yet of course, right? So 90s Souker, I think the reason why they had to update this in the code is they're gonna put this guy out in the game and they have to have his story show up under his name and I think he's gonna be an icon swap today. That's why I think they put that out and if you technically look at the code or look at the loading screen, there is a 90 rated card option that is in here. Now other people are looking at this first card and seeing 90 shooting and thinking that it's gonna be mid Souker. That's why you see Souker and Essian, a lot of other icons kind of getting very high up and popular in this list. I think baby Essian is the top pick for the 87 physical card. So if we're getting prime Souker and baby Essian, those aren't too bad of choices right there off the bat for some of our first icon swaps. That could be kind of a W. So we'll definitely watch out for that but let's talk about these pack rewards because there was some big time tweets again by Foot Watch tonight. Base or mid icon pack, mid or prime icon pack, one prime icon and a mid icon, 89 plus or higher. Now what in the world are these packs? I think honestly boys that these packs are not gonna be released as SBCs yet, all right? I think these are purely icon swap packs because they're getting released tonight. Now the market right now in terms of SBC fodder is going crazy. People are buying SBC cards right, left and center. Check this out, the 86 market has just boomed since this came out. We're from 223 points up to 229 and I think it keeps going if I'm being completely honest. If we look at some of the cheapest players by rating, you've got 88s that are at 35,000 coins that were just at 31,000 coins, 89s are up. 87s were 22K, Bernardo Silva was 22,000 coins. He's now over 25K. So a lot of people are investing in fodder right now because I think they're expecting these to be SBCs and for these to come out in packs, I don't think that's gonna be the case with these items. Today, I think this is gonna be all icon swap related and that's maybe since we're only getting six icons, there's maybe gonna be five or six pack rewards. So that could get very, very interesting today with the amount of pack rewards available from icon swaps depending on the amount of tokens we have and stuff like that. That's gonna be very interesting to keep an eye on. And a big pack that they released today that a lot of people were very interested in, 85 plus rare players, five packs. So five rare players, 85 plus or above and then an 83 plus pack with 25. 25 rare gold players, 83 or above. Now this is a typo, Foot Watch corrected it, they said. The code was fixed. It was not actually 25 players rare golds above 85. It's only for the 83 plus that we have a 25, 83 plus pack. That's so ridiculous. Can you think about the 83 plus packs in the game and you have like an 25 to choose from? Like opening that kind of pack during team of the season or team of the year, if that pack is gonna be available during that timeframe, would be kind of cracked out. Would be kind of cracked out in my opinion. So that's kind of a crazy pack, especially during team of the season, man. All the special cards that are in packs, that'd be crazy. But I feel like this might be a, this pack right here, like an 83 plus 25 players pack. It's crazy to think about, but that is literally a club stock in a pack, all right? You're probably gonna get 86, maybe 84, 85s, some 83s, but that's like a club stock in a pack, which is pretty nuts. So I think that's gonna be a part of icon swaps as well, unless it's gonna be like a daily SPC and that'd be crazy if it was. But honestly, right now with SPC fodder on the horizon, on the horizon, on the rise, we were talking about this live on stream just a little bit ago, Bernardo Silva went from 22,000 coins and is all the way up to 25,500 coins. He's even more than that. He's up to 26K at the moment, it looks like. Yeah, 26K for Bernardo Silva. If I'm you guys, of course, we have Bruno Fernandez coming this morning. The SPC should be out pre-6PM. If you bought fodder tonight on the release, I honestly think that you're selling pre-6PM because I think what's gonna happen is everybody's buying up this SPC fodder, but these packs aren't actually going to be released through SPCs. I honestly think these packs are just gonna be released through icon swaps and all the people that bought fodder today. Yes, I was recommending to buy fodder because it was low, but now with it getting invested in and getting bumped up, if you bought fodder yesterday, you're chilling, right? You're feeling good because you're already making coins and especially with all these SPCs coming, like Bruno, an SPC every single day for the Freeze promo, you're feeling pretty good about it, but this whole code and things being put into this game and people investing right now is making that a bit sketchy. So if you bought fodder tonight, if you wanna do a quick flip, like if you bought it when the code was released, especially on the high rated fodder, the only thing that would make this stuff really go up a lot is if they did release a repeatable or some sort of SPC for a base icon and mid icon or for any of those packs they put in the code tonight. I don't expect to see anything as an SPC. I think they'll all be in swaps, but I guess that is a possibility. So kind of keep that in mind. And maybe the safe route is, you know what you bought, let's say like Cruz, literally Cruz tonight was 21,000 coins, sorry, 31,000 coins and now he's up over 35. So if you bought these at 31 and you can sell them at 35 today in the hype, go for it, right? Especially after Bruno comes out, he might require some higher rated squads. People might start working on that, little bit of extra demand there and you sell those into the content drop if you wanna be safe. Now if you wanna hold onto it and risk it for the biscuit, be my guest, but you really need a big repeatable or an icon SPC to come out today to make that stuff continue going. So if you bought earlier though, you're feeling good, you're looking good because the stuff is starting to rise because of that content that has been released. So that is that. Just general market thoughts for tomorrow. I think we are gonna see a nice market rise after the content drop because again, icon swaps and we're gonna talk about road to the finals right now. Icon swaps, they don't impact the market in a sense that, you know, a lot of stuff is going to get supplied, right? All the icon swap stuff is untradable, right? The icons that you get from completing the objectives and the swaps, you get them untradable. There's no like tradable packs even from the rewards. So a lot of what you might see today, not tomorrow, on Friday today, is panic selling on icons. You might see some icons like the Tsukera of course, because people are thinking this 87 gets in. He's dropped from like 640K today. He's down at 575. Wow, this guy is dropping at the moment like a rock. Now if it's the prime that gets in, I think this card probably rebounds because this is the best available Tsukera that is available on the market. And if you're gonna do icon swaps for the prime, you're not gonna be able to get him right away. So watch the panic selling on icons specifically this morning because nobody's gonna be getting those icon swap cards from icons right away, right? If they wanna play Weekend League with one of those cards still, the people that are panic selling Tsukera, we're probably gonna use them in Weekend League this weekend.  So I do think you're gonna see bounce back on icons today. The ones that do get panic sold, definitely keep an eye out on the icon market for sure. For that panic selling and be able to, if you want one for your team, I think you will see a buy opportunity and then a rebound after the panic selling ends because again, a lot of these icons are very rare. A lot of these are very rare. Baby Eskin was around a mill, I think. Is he still there or is he dropping underneath? 980, so we'll watch these, right? I think there was an open bid listing there too, maybe not, but just watch the panic selling cards and I do think they will rebound because they're icons, people want to use them in Weekend League and you can't get these icons from swaps right away. It takes a bit of time. So those are kind of my thoughts on the panic selling with icons today.  I feel good about buying those in the panic today as well. I do think there will be a nice market rise because again, people have to play the Weekend League. Now, some point either tonight late or tomorrow on Friday, we should be getting road to the final upgrades and a lot of these cards, they might bounce when they get to upgrade for a hot second, you know, if the card was possibly undervalued before or if there's a lot of hype for that card, you know, some of these guys might bounce but overall, I'm feeling like all of these cards, 90% of them are going to drop once the upgrades come out because right now I still feel like a lot of these are overpriced for the state of the game right now with the game being kind of dead as it is and the amount these guys have risen, I know they're rare, I get it, but I feel like these guys, most of them dropped today just from that panic. Now, of course, there were some crazy fluctuations today with the Europa League. You had guys like Kulabali who were 480, he went down to 430, now he's back to 460, you had Port 2 who was 160, then Napoli scored on Sociedad, he went to 120, now he's back to 190. So a lot of these cards, I think, are going to drop after they get the upgrade. Again, because Champions League is not until February, so if you still have any of these, you might want to cash out on them. It's going to be fun to watch these cards fluctuate, it honestly is, and to see the upgrades and to see how EA juices them. So be on the lookout for that. That could happen anytime in the next 24 to 48 hours, but it should happen pretty soon because all the games are done and EA knows which cards they need to, they need to upgrade. So all those spots have been secured, I do believe. But that's kind of the day, boys. Foot freeze is here, icon swaps again, is what a lot of people are looking at and watching out for. So it's another promo Friday, man. Good luck if you're opening packs, as always. And again, just a quick side note, this is going to be my last video sitting here at the usual setup for a little while. I am going on a little vacation with the family and I'm going to be gone for about a week or so. I'm not going to stop uploading. I'm going to be uploading from my phone. Might not be every day. It might be every other day. We'll see. I need to figure some things out related to that, but you'll still see uploads from me. It'll just be different, right? I'll be on the companion app. I'll be talking over it using Footbin and Twitter and stuff like that to make those videos. So just a heads up there. You won't be seeing me here at the setup for about a week or so. So just in case you were wondering, where the heck did this guy go? That's where I went. So I'll be here, boys, don't worry. Check me out on Twitter below in the description as well. And we have a pretty cool announcement coming up. I already shared it with the Twitch stream tonight. We're going to have a little creator code sort of thing going on with a really cool website. I'll be sharing that with you guys pretty soon as well in the YouTube videos and in the comments down below in the description when that gets finalized a little bit later. So if you enjoyed this one today, smash the thumbs up on it. Comment down below if you have any questions or who you think these icon swap cards are and of course, subscribe to the channel if you're new. It's been Nate the Boat Accountant. Catch you guys later. Peace out.


Another detail in the chanpiyo form is we're doing the pivoting. You want to initiate the pivot with your hips. So just do this. Shake your hips. So practice by shaking hips. And then now you can use that to turn. So initiate with your hips until you get really nice and smooth transitions. So here's some more details on the next portion here. So we are going to talk about the lancel. So when we do the faxel, go straight out to the eyes. And when you drop, just drop the elbows. So here, straight out to the eyes, fingers are straight, your thumbs are tucked in. And then when you drop, sink the elbows and flip your hands up. So you can feel the weight dropping on your elbows. When you do the jeep stop or the folding hands, you want to fold like this. Now when you're folding, now both hands are here. When you're folding, both hands move into the center. So I'm not just going one, two, three, no, that's incorrect. Here's the proper way. This hand goes in the center and this one folds in the center. Now when you do the other flip, this hand goes both hands in the center. Notice that my back hand is doing a little bit of a up motion. That's what the back hand is doing. So while the other hand is folding and coming back down, the other one is turning and coming up. So from here, we do a little folding and coming back down and the other one comes back up. So in the side, this one folds and comes towards you. This one folds and comes out in a rotation. So if you come here, you have actually a thumb movement. So you see, there's a little circle action that's happening here. Imagine there's a little ball and you're moving the ball, rotating the ball. So once again, when you're doing the right hand, right one, this one comes in the middle and it also drives up with the elbow. Right here, again, this one drives up with the elbow and also twists. So twist. This also twists and contracts out. And then we're going to drive with the elbow again. So from this side, you can see I am turning and driving with the elbow upwards. This one is turning and folding down with the bottom part of your palm. So combine together and get this action. Now actually, you want to have about one hand distance in between. So you don't want to be going in this. You want to keep it nice and tight. The next part of the palms, we're just going to do vertebral palms like this. I'll try to replace each palm with the other palm. This one comes down a little bit and this one, replace it. This one comes down a bit and this one, replace it. Make sure that the palm comes back to this position once the other palm is out. So this one, when it's coming back, it's coming back to here. When this one comes back, it drops down to here. So it does a little circle. So from the side, you can see this one does a little circle, comes back down. When this one's out, this one replaces it. So now, what that does is it prevents your palm from having to go over your own hand. Because now you can go straight out. You just need to roll this one and this one can go straight out. You get more power than if you have to go over your own hand. So this one drops out. This one drops out. This one drops out. Do it quickly. Like this. So that's some details on the palms.