Hi everybody!  In this war, we propose a new codebase signature scheme built from zero-knowledge proof. To design this signature, we chose to focus on the syndrome decoding problem for which cryptanalysis is stable for many years. Then, we used the MPC in the head paradigm to build a zero-knowledge proof of knowledge for this problem. This paradigm provides a generic method to build zero-knowledge protocols using techniques from secure multi-parted computation. To apply the MPC in the head paradigm, we need to have an efficient MPC protocol that checks that a vector is a solution of the syndrome decoding instance by checking those two relations. The linear relation is easy to check with MPC, but it is much harder for the constraint on the having weight. For this reason, we replaced the second constraint with an equivalent one involving polynomials. This new constraint consists to prove the existence of a polynomial Q such that f divides the product sq, where s is a polynomial for which the evaluations and some product points give the coordinates of the test vector, and f is the smallest polynomial for which have for roots all those evaluation points. In practice, such polynomial Q can be easily built from the tested vector. We simply need to take a unique polynomial of degree w so that the non-zero position of the tested vector in coding has roots. Now that we have the exact statement we want to check, we can use the usual techniques to build the wanted MPC protocol. Then we convert this protocol into an interactive zero-knowledge proof of knowledge using the MPC in the head paradigm. Finally, we apply the Fiat-Scharmier transformation to obtain the signature scheme. We selected three parameter sets targeting a security of 128 bits. The two first sets rely on the syndrome decoding instance on the binary field, while the third one relies on the syndrome decoding instance on a larger field. For each parameter set, we proposed two trailers. The first one lowers the communication cost, and the second one lowers the computational cost. Let us compare our scheme with the other code-based signature built from zero-knowledge proofs. We can observe that the obtained signature sizes are less than for all the former schemes. We have the first such scheme, which can produce signature size along the symbolic cap of 10 kilobytes. Now, let us compare our scheme with all the other code-based signatures. We are far to have the shortest signature. However, our scheme outperforms all the signatures when considering the sum of the size of the signature and the public. To conclude, we proposed in this work a new code-based signature relying on the syndrome decoding problem for random linear codes. And this signature has competitive performance regarding the current state of the art. Thank you for your attention and see you on the 16th of August for the complete talk.


Welcome back to JSA TV live here from PTC 23 the biggest PTC to date I'm Buffy Harakitas and joining me today is Raj to Wardena EVP of business development and transformation for five percent Raj welcome to JSA TV. Thanks very much for the opportunity Buffy really excited to speak about five cents today Yeah, I'm really excited to have you. I really love your title. We were just talking about it So transformation so critical in our industry today That businesses are continuing to transform especially in today's landscape So super excited to have you. So how are you feeling about the conference so far? It's been a great conference Every year we come to this conference. We're more recognized. We've got more product out in the marketplace People understand the value that we're delivering to the different verticals that we're servicing so it's yeah It's been a really good conference. Yeah, it's definitely a really great conference here in sunny Honolulu So fiber sensors technology has some extraordinary Monitoring capabilities. Why don't you tell us a little bit more about the monitoring capabilities of your product? Sure There's fiber itself has a unique property that it's very sensitive to vibration So if you've got you know objects in motion in proximity to the fiber It strains their fiber and we use that property to develop some monitoring and detection solutions And so the the underlying product that we've developed and released into the market places that is a product called digital asset Okay, and that's really intended to secure critical infrastructure so power water gas telecoms submarine cables and so forth and We basically deliver a solution as a service that You know detects threats such as excavation in cities such as anchoring in in an ocean environment we localize that threat and we Notify our clients of those dangers Definitely critical in today's world You were recently featured in subtel forums offshore energy edition featuring evolving subsea technologies Why subsea monitoring so imperative? There's a couple of critical reasons why we need to protect Subsea infrastructure. There's the there's the power side of subsea. There's more and more High voltage interconnection between countries. So we have these cables that are on the ocean floor There's more generation that's happening in in the form of wind offshore wind and when you couple that with the Fundamental fact that 99% of our internet travels across submarine cables With tens of trillions of dollars of commerce on a daily basis Any interruption to those that that infrastructure is going to have a significant impact on their daily lives for sure And it seems like you have some big plans post PTC to attend some other big conferences Coming up in March. Why don't you give us a little bit more details there? Sure. So we're going to be attending Suboptic, okay, we're going to be attending OFC And not only attending to join the conference, but we're actually speaking about what we're delivering what products and services that we've created And educating the market about what the benefits of this type of proactive monitoring is Be to their particular industry and how they can utilize that the services that we're providing to improve Well, that's great, I mean that's coming up in March So be sure to mark your counters viewers to check them out at the suboptic event in my Bangkok this March So we'd like to congratulate you. It seems like fiber sans had a stellar year of award wins Each of them in involving innovation Is there anything else you want to add or tell viewers what makes you so innovative? Innovation is a fundamental part of our DNA We're all of that our business is all about how we can do things better how we can be more efficient How we can deliver solutions that are more impactful for our clients We've got a world-class R&D team that's that's ably supported by the rest of the business and You know, it's it's a real Drive for us to continue to innovate and new products and services out in the marketplace that are actually effective I'm gonna add something to your title should be EVP business development of innovation and transformation Thank you very go five percent folks. So yes, definitely Innovation is so critical in today's today's world and you're doing some great things You know protecting the subsea cables with your monitoring products. So great to have you here today. Is there anything you want to add? Yeah, I'd like to add that, you know, what we've done is created a service model as opposed to You know providing selling hardware and that type of thing and what that fundamentally means is our clients don't need specialized expertise or equipment to Protect their infrastructure That can outsource that to us to you. So as a service model, correct, right? So there's so many as a service as a service, but this one is definitely as a truly as a service Provided by five percent. So be sure to check them out and and where can viewers go if they want to learn more About your as a service model where you're gonna be speaking about this critical product Well, they can go to five percent stop calm Okay, follow us on LinkedIn Those probably are the two main places that they can learn about concepts We're happy to talk to anyone about what we're doing and how we can help them All right, so five percent calm follow them on LinkedIn and thank you viewers for tuning in Thank you so much for joining us today For another episode of JSA TV live here at PTC 23. Happy networking


This is a special Listener Terrorist episode. The stories sent in by you are likely terror listeners. Send in your own story at Microterrors.com. Welcome to Microterrors. Scary stories for kids. Where it's always the spooky season. Full of chills. Thrills. And spine-tingling spooks. Microterrors are family-friendly frights for those ages 8 and up. And while our stories are for younger ears, we are still talking about things that go bump in the night. And some children may not be able to handle what others can. Parental consent is recommended. Now, for tonight's Microterror. Story number one. UFO Fest by Autumn Road, age 8. Ned and Zed loved festivals. They loved festivals of all kinds. Halloween, winter, fall, summer, you name it. But their favorite one of all was just around the corner. The UFO Fest. They couldn't wait to see everyone dressed up as their favorite space creatures. Another thing they were looking forward to was the green cotton candy and the lime-flavored Space Ooze drink. The day of the UFO Fest had finally arrived. It's here, yelled Zed. I can't wait, screamed Ned. The brothers were all decked out as their favorite space creatures. Ned was dressed up as his favorite space alien, Blorf. While Zed was decked out as his favorite creature, the alien space commander. As the boys got ready to leave, they said goodbye to their pet turtle, Sarah. When they got to the parking lot, there was a UFO Fest sign on the left and a replica of an alien spaceship on the right. Ned and Zed were super excited to get a picture in front of the spaceship. They heard that you could even go inside and sit in the commander's chair and work all the controls. When Ned and Zed walked into the festival, they were excited to see all sorts of food stands, people in costumes, and a huge row of games where you could win tickets for prizes. Ned and Zed played a lot of games. They played Alien Bingo, pin the staff on the aliens, ring toss, alien cornhole, and lots more. When Ned and Zed counted their tickets between the two of them, they had won a thousand.  The boys only had three tickets left, and the only thing they could get was a tiny glowing alien balloon. Zed said, hey, we can tie this around Sarah tonight while she's walking around the front yard. That's a good idea, said Ned. Once the boys arrived home, they got Sarah out of her tank and tied the balloon around her. Then they took her outside to the front yard to walk around. She was having a lot of fun.  After about ten minutes, the balloon started to flash. The boys looked at each other in confusion. All of a sudden, the boys heard a whooshing sound coming from the sky. When Ned and Zed looked up, they saw an alien spaceship. The door on the spaceship opened and a light shined down right on top of Sarah. Zed and Ned looked on in horror as Sarah began to lift up off the ground towards the light and into the spaceship. Sarah's little legs were frantically kicking the air. At the same time, Ned and Zed screamed, what's happening? The brothers lunged towards Sarah, but it was too late. Sarah was in the spaceship and the door had closed. The brothers' eyes filled with tears as the spaceship flew away. Story number two, Terror on the Slide by Mad Alexander, age seven. Once upon a time, there was a seven-year-old named Zach. Zach was at a playground with his friends. He watched one of his friends, Abby, go down an enclosed tunnel-like slide. He was at the bottom, waiting for her to come out to the other end. But she never came out. He climbed up the ladder to check at the top and see if she was just pranking him. When he got to the top, he realized she was not there either. He called his other friend, Mark, up to the top to help look. But Mark decided to slide down the slide too. Zach said, No! He rushed down the ladder to see if Mark came out the bottom. Zach was surprised to see his friend was there. What? Zach said. You didn't disappear? I guess not, Mark said. Then where is Abby? Zach asked. I didn't see her anywhere, Mark said. Right then, another little girl climbed the ladder to slide down. I'm sure she'll be okay since Mark came out of the slide, Zach said to himself. The little girl then slid down. Mark was also watching to see if the little girl came out. But she never did. Zach climbed up the ladder to see if he could figure everything out. He went down the slide. But when he came out, he found himself in another world. He saw a man with a squared off head who just stood there and groaned. A portal appeared out of thin air behind the man. I don't need you, he said in a scary voice. The portal then sucked Zach into it and he reappeared at the bottom of the slide in his own world. He didn't see Mark right away but quickly realized he was at the top ready to slide again. Wait! Zach yelled and then climbed the ladder. Together they decided to go down again. Zach was hoping for a better answer about what was going on this time around. This time they both ended up in the other world. The man with a squared off head stood there still groaning. Hmm, maybe I'll keep you after all. He said with an evil smile. Earth's episode, the stories sent in by you are Microtarrer listeners. Thank you for listening to Microtarrers. Join us each Saturday for another scary story. For more fun visit our website at Microtarrers.com where we will also have spooky games you can print out and play like wicked word searches, mysterious mazes and more. Microtarrers.com is also where you can find us on your favorite social media and even send in your own scary story for us to tell. Plus, you'll learn more about our author Scott Donnelly who has other horrors for both young and old. I hope you'll join me again soon. From Microtarrers, scary stories for kids.


I want to talk about a story that is truly at the intersection of so many issues, environmentalism, indigenous peoples' rights, police militarization, and the over-policing of majority black cities, the American police state, so on and so forth. That story is Cops City. Now, fortunately, people are finally starting to pay attention to Cops City, but the heightened awareness of Cops City comes at the expense of one activist's life, Manuel Teran, who was a 26-year-old queer Afro-Venezuelan forest defender who was killed by police on January 18th following a deadly raid on Cops City. Now, in order to understand why Manuel was caught on the crossfire in the first place, we need to understand what Cops City is and why these activists were opposing it so vehemently. Kendall Glenn of Decaturus Explains, Cops City is an 85-acre police slash fire training facility located in Decobb County's South River Forest. The location has historically been the old Atlanta prison farm site and a police shooting range. Former Atlanta Mayor Keisha Lance Bottoms announced the plan to turn the location into a state-of-the-art training facility in April of 2021. The project will cost approximately $90 million and the area will feature a burn tower, space for high-speed chases, a helicopter pad, a shooting range, and a mock village. Yeah. Now if that doesn't already sound positively dystopian to you, well, destroying this forest is going to have catastrophic impacts on the community because this forest is essentially a shield that protects them from anthropogenic climate change. In an article for The Atlanta Voice, Scott Roberts explains, clear-cutting the forest will have devastating effects on the environment, including worsened air quality and flooding in the predominantly black neighborhoods of southeast Atlanta. Furthermore, the Atlanta Police Department's current and future use of chemical weapons will poison the soil and the waters, endangering Atlanta's health. So needless to say, clearing out this forest in order to create a massive military-like training facility for cops isn't just going to lead to more brutalization disproportionately of black and brown people, it's also taking away a shield that will defend them against climate change. And to add insult to injury, Cop City is being constructed on land that was stolen from indigenous people and then subsequently turned into a slave plantation. The land belonged to the Muscogee people, who referred to it as the Wallaunee Forest for generations. Beginning in the early 1820s, the Muscogee were forcibly displaced from the area through a series of treaties. The removal continued into the 30s. The land then became a plantation for the remainder of the 19th century and into the early 20th century. In 1911, the city of Atlanta purchased the land. 18 years later, it became the Atlanta City Prison and Dairy Farm. From 1922 to the late 80s, the area ran as a prison farm. In 1990, the city began auctioning off farm animals and equipment. And soon after, public notice was issued to discuss future plans for the site. Now make no mistake about it, the city knows that a majority of the residents are against the creation of Cop City. They just don't care. And they also know how important this forest is for its population. Back in 2017, the Planning Department of Atlanta designated the South River Forest as the city's lungs. And this was because of the environmental significance of that forest. Now because it was so important they initially planned to turn the forest into an urban park. However, that idea was scrapped in favor of Cop City. And here we are now. So activists have been pushing back against the construction of Cop City in an effort to protect the South River Forest and prevent even more brutalization of black and brown people by police. And to resist, they've established encampments in the forest and have occupied it for prolonged periods of time. But cops, however, had been trying to forcibly remove the protesters for quite some time to no avail. And as a result, their tactics have become increasingly violent as time progresses. And during a raid on January 18th, one activist was shot dead. And that activist is Manuel Teran. Now, a Georgia state trooper was also shot and hospitalized with police claiming that Teran shot him. And Unicorn Riot reports that witnesses heard 10 to 12 gunshots all at once. So it was a fairly chaotic situation and police are claiming that Manuel fired first. But the evidence that they released thus far does not substantiate that claim. And there's no body camera footage of the incident as well, since no other officer was close enough to capture the incident. Now Georgia's Bureau of Investigation has released this photograph of a Smith and Wesson nine millimeter handgun that they claimed was in Teran's possession at the time that he was killed. And bullet sticks experts confirm that the bullets from this gun do in fact match the wound of the cop that was shot. But activists are disputing the cop's narrative and calling for an independent investigation by an impartial third party to figure out what really happened. And activists are rightfully skeptical of the cop's narrative because they've been caught lying to justify the use of deadly force against protesters in the past. For example, as Unicorn Riot reports, in June of 2022, Atlanta police officers were caught on radio traffic justifying the use of lethal force against protesters who used Molotov cocktails to defend themselves and the forest in the midst of a police raid. No force defenders have been charged for use of molotovs or incendiary devices. Quote, I told you deadly force encounters said one officer. That's why I brought it up. As long as we're all on the same page, Molotov cocktails, a deadly force encounter, a deadly force encounter is a situation in which cops are legally allowed to shoot and kill. Yeah. So that right there is why activists are rightfully skeptical of the cop's narrative about Terran. If they lied before to justify the use of lethal force against these protesters, what's to stop them from lying again to justify the use of lethal force against Manuel? Right. Now, me personally, I fundamentally distrust cops. So I automatically just assume that they're lying every single time that they open their mouths and I work backwards from that conclusion if and only if they provide the public with an overwhelming amount of evidence to substantiate the claims that they're making. But with respect to this story, they have not done that. And I simply have not been swayed. So I remain at my default position of distrust cops and assume that they're lying and short of an independent investigation, local activists don't seem to be buying it as well. And they're not letting police demonize Manuel Terran. And it seems like the community also isn't buying the official narrative from police. There was a vigil that was held for Manuel and that turned into an impromptu march and that impromptu march ended up turning into protests across Atlanta. And those are still going on till this day with activists calling for justice for Manuel and an end to the construction of Cop City. And some protests have turned into riots, which has predictably been the overall focus of media in an effort to obscure the overall message of these activists. But it's important to re-center this conversation around the activists message and not the message of the media or the cops. Cop City is an absolute abomination and the force defenders who are protecting the environment and the city are unquestionably heroes in my opinion. But some of the force defenders are being charged with domestic terrorism and criminal trespassing. Because if you refuse to allow cops to bulldoze this forest to create Cop City to brutalize that very community that they claim to be serving and protecting, then you're apparently a domestic terrorist. But the real act of terrorism, in my opinion, is the destruction of this forest in the first place. Now, one last thing that I want to leave you with is this. There's a GoFundMe for Manuel's family. And at the time that I record this video, they are halfway towards their goal of $100,000. So I'd encourage you to consider donating if you're able to. But either way, if you didn't know about Cop City, now you know. And unfortunately, one activist, their death led to people knowing about Cop City. So don't let that sacrifice be in vain. People need to spread the word and acknowledge that Cop City is a disgrace. But it's not necessarily a shocking thing to see in the dystopian country that we live in. It's just it's sickening. But here we are.


part 2 of my Doom modification tutorials. Even if you're not interested in Doom, this is hopefully giving you an overview of how you can modify source code and later on we're going to get into using hex editors to modify binaries of files. But it's also just fun. Doom is a great game and I'm going to show you today how to create cheat codes. Again, this is part 2. Be sure to watch the previous video. Hopefully there's a link in this video to the full playlist. So go ahead and check that out because we've already installed the stuff we need to compile the game. We've actually already downloaded the source code, compiled it and have made some changes. But today, again, we're going to be looking at cheat codes. Again, I'm using Vim as my text editor. Use whatever text editor you prefer for editing. Just make sure it's text editor and not a word editor. So inside our source folder, there is a file called m underscore cheat dot c, which is where your cheat codes and their functions are stored. So let's go ahead and just have a quick look at this. So back up to the top here, including some header files, not going to really worry about those. But here we're defining all of our cheat functions. So we're we're creating them, but we're not we're not actually writing up the code for the functions yet because we want to have that because next down here. So for example, you know, there's a function called cheat God, cheat choppers, cheat must for changing the music kfa no clipping for walking through walls. So those are we're defining the functions without creating them yet here. We're going to create a little array of of the cheat. So we're saying we're calling a function called cheat. This is what you type to create to get that cheat function to happen. It's the name of that function. And I'm not really sure what always never are, but we're not going to modify that anyway. The next thing is the actual function, which we defined up here, we'll create below that. And that's why we had to define them up here, because if we create them after this, you would get to this point in the code and go, I don't know what function this is, it doesn't exist. You haven't created it yet. So the main things we want to look at is what you type, what it's called, and what the function is called. So for example, ID kfa is the happy animals and keys, it gives you all the keys, all the weapons, all the animals, think a bunch of armor up to the full and I think it might even give you full life too. So that function is called cheat kfa. If we come up here, cheat kfa is right here. And if we just search downward, we'll find a function called cheat kfa. So here, this function actually is calling two other functions. And it's also displaying a message. So in this particular file, when you see PLYR pointing to message, and then this, this is a variable. And if you remember last tutorial, we looked at the folder where or the file where a lot of strings are contained. This is a string that's defined. You can actually type the string right there or use a variable. So for example, before we get into the other functions, what I'm going to do is I'm going to just go into the game. And I'm going to type in ID kfa. And you can see up the top left of the corner, it says very happy ammo added. That's the message that displayed there. You can also see I've got all the keys and ammo and armor and all that stuff. You see my health is at 555 because we changed that in the last tutorial. So let me go back in here. So again, we can find where this string is defined. Like so I can say grep for that string in our source folder. Look at all the files. So right here, you can see that it's defined in that file that we were talking about last episode, last video. So I can come in here and search for that. Oops. Let me go back out. It's called that. So I'm coming here, search for that. I haven't already passed it. There it is. And it says very happy ammo added. So I can say very nice or whatever I want. So going back into our cheat code, so it's calling that variable and that variable just is defined in another file. So I can say make now. And once it's done compiling, I can come in here, start the game. If I type in ID kfa and look at the top left of the screen, it says very nice. So that's one way you can do that by changing the value of the variable. But I'm going to go back into the cheat here. I can also put the string directly in here. It's always good to use variables because if you want to change it, especially if that's used that strings used in more than one place. Variables are good. Plus, it's nice to have all your messages defined in that one file. But you can change the messages just like up here. They used a string. We can use a string too. I'll say ammo ammo happy. And I can make that. And then I can go into here. And if I type in ID kfa, it says ammo ammo happy. So you can do either you can you can change the variable or the string itself. Next, let's go back into our cheat codes here. And again, this is calling two other functions. So let's go ahead and look for this function. So I'm just going to go and search for that. It's defined there. It's called there, right there. TNT k a I'm not familiar with that sheet. I don't know if that's an original cheat or something added as added in 98. According to the comments there. So that that isn't from the original game. But here it looks like only prints message if last key added, however, overview. Oh, so that's that's a key, it looks like it's giving you all the keys. So again, our kfa function is calling a function called k. And that gives you all keys. So you have a cheat code that will give you all the keys. You also have a cheat code that will give you all the weapons and ammo. So instead of redefining all that in this function here, they're just calling the functions they already created. Since this function does what two other functions do, but you still might want to do those functions separately. I hope that makes sense. So that is that let's create our own cheat code now. So first thing we need to do is define a function for our cheat code. So let's come up here, let's go to the bottom of this list. And I'm going to say static void. Again, it doesn't have to be called cheat something just nice to define everything similarly. And I'll just call this my awesome cheat. So cheat awesome. So we're defining the function, but we haven't actually created it yet. Next, we're going to want to come in here. And I'll just I'm just going to copy and paste the lines that type in all this out. And I'm going to have it just so when you type the word awesome in the game, awesome in the game, we're going to call this the awesome cheat. And we're going to come over here and tell it to run the function. Awesome, which we've defined but not created. So now let's go down here, where all the cheat code functions start or wherever you want to put it. And I'm going to say, I'm going to say static void. And we called it cheat. Cheat. Awesome. And oh, actually, let me think about this. Awesome. Yep. And next, we're going to go here here. So our functions going to go between these brackets here. So now I'm going to say, plr, pl, why are saying player, we're going to point it to the players health. And we're going to say the players health is equal to so whatever the players health is currently at, it's going to change to 2%. And then we're going to say, let's change the players or to the player. We're going to display a message. We're going to say, you're so awesome. Again, it doesn't matter what the case sensitive because it's all going to be capitalized in the game. New line. And I say, I think you can beat the I don't want to be too long. That's why I put this on the line. I'll say this game or this just this with, I'm trying to keep it short. 2% health. So we're saying, you know, we're setting their their health to 2%. And then we're going to display message saying, you're so awesome. I think you can beat this game with 2% health. That's the awesome cheat. It's actually kind of the reverse of a cheat. So I'm going to say make, and I'm going to run doom. I'm going here and now at any time if I type in awesome, if I type it properly, okay, I must have typed something wrong in the code. Oh, no, there we go. I was just typing awesome wrong. You're so awesome. I think the game with 2% health and put our health to 2%.  Let's go ahead and add something else to that just to make it so it does that. But anytime you get hurt, we should play a sound that you're getting hurt. So I'm gonna say s, I'm gonna say start sound. Now this is case sensitive. We're gonna say zero comma, and the sound of someone getting hurt, or the player getting hurt, which if you look at the list, if you look from the previous video I did, they're all inside that the header file, the sounds h file, and they all start with SFX. And I have it written down that the player pain sound is PL pain, although you can play whatever, play whatever sound you want from that list, or create your own, but you have to add it to a wad file. Don't forget your semi call in there at the end. So now we save that compile it and run the game. And we turn my volume up. And now if I type awesome, it's displays the message sets their health to percent, and plays that sound of the getting hurt. So that is the crash because I've tried changing the volume while I was in the game like that. Okay, so yeah, that's creating a cheat. So again, it's the m cheat.c file, you want to define it, and then set up what you want the cheat code to be, since such as awesome, call it whatever you want. And then here, you know, say what function you want to run. So I could even, you know, if I come in here and I say change this to God, like the line below it, which normally is ID, DQD. And that would run the God mode function. If I put that up here. Now if I type awesome, it'll run that same function. So you can also flip these all around. You know, if you want to mess with someone, they try to type in one cheat code, it runs a different cheat code, or sets their life to 2%. So now that I've done that, if I make the game, and I run the game. And now if I type in awesome, I'm in God mode instead. So that is creating a cheat code. Next week, we're going to look at creating or modifying the current weapons. So if you want to make take a weapon that's already there, and make it a bit cooler. That's what we're going to do next week. So I hope you're enjoying this again. It's just to give you a look at, you know, maybe you've been afraid to look at the code of a large project, because you think it's going to just be too much, because there is a lot of source code in a game like this, from the original game, and then all the modifications people have added to it. But hopefully you're getting an idea of how things work, how things are possibly defined, maybe how to search through and find what you're looking for. Grep is a very great tool for this. And just also just having fun with Doom, which is a game that I love, I still play fairly regularly, and it's always fun to modify. So that's it. Thanks for watching films by chris.com. That's Chris the case should be a link in the description. Also in the description notes to everything we did last week and this week and some notes for next week as well. So if you want to get ahead of the game, you can start looking at that. And I just thank you for watching and hope that you have a great day. Okay, this is an introduction to films by chris.com. I'm Chris. That's Chris the K. That's me right there. My daughter and my wife, Jennifer. We pretty much live in the swamps of Florida. I'm a firefighter by day, as well as by night. We work long hours, but that's not why you're here. You're here about the videos I put up on YouTube. These videos are mainly about computers and programming, which means most of my videos look something like this. And if that's what you're interested in, great. If not, that's all right. I do videos on other topics too, such as video editing, special effects, photo editing, 3D design, and music creation.  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Welcome to module 2 of NPTEL NOC on introductory course on point set topology part 2. So, today we will take the topic of differentiation on Banach spaces. So, many things run parallel to what we will do in calculus of variable, one variable calculus or two variable calculus and so on. Actually, you will see that it is copied one variable calculus, but the things have to be put in a proper perspective. So, start with two Banach spaces. One can possibly do many things with just normal spaces also, but we will concentrate only on Banach spaces. Because our idea of this presentation of these things is not to do the entire thing in a very general setup, but to cover the implicit function theorem and inverse function theorem for Banach spaces as a sample, as a sample of application of topological methods. So, that is why we will concentrate only on Banach spaces.  So, there is open subset system makes sense because we are using the norm to induce a metric to induce a topology. Start with an open subset U around a point. A function defined on this open set into another Banach space is said to be differentiable at a point X naught. If there is a continuous linear map from T, T from V to W such that this X is, this limit X is equal to 0. What is this? It is f of X naught plus Z minus f of X naught divided by the norm H. I cannot divide by H. So, H is a vector inside this normed in space V. Therefore, I cannot do just this limit, but I have to do it by subtracting T H where T is a linear map which is going to be the derivative. Then I can divide by norm H. This limit as X tends to 0 which is same thing as saying norm H tends to 0. This limit must exist. So, where is the limit existing? What is this one? f and you know f is taking values into W. T of T is also from V to W. So, T of H is also inside W. So, all this numerator is taking value inside W. It is a vector inside W. So, divided by norm H of course, that is just a scalar. So, it is a vector inside W. This limit must exist. So, the important point here is that we must have a continuously linear map T. This is the part of the definition. I want to caution you that there are slightly varying definitions. You know weaker or stronger and so on. There are different definitions possible and then they will make under this condition this will be equal to that one, that will be equal to this one and so on. We are not going to study all that in this course. So, let us take this definition. Namely, there must be a linear map which is bounded. That is continuously linear map from T to V which satisfies this equation. Limit of f of x0 minus fx minus T H whole thing divided by norm H. This limit must be 0. As soon as such a T exists, it has to be unique. You cannot have two different linear maps T1 and T2 having satisfying the same property. This is an easy consequence of just similar to what we do in a real analysis or any other different you know multivariate calculus and so on. Uniqueness is not a difficult thing. So, that unity is called the derivative of f at the point x0 and I am using the same notation df of x0 standard notation. The only thing is you might not have called the thing as a Frechier derivative, we are going to call it as Frechier derivative. This Frechier was started with Banach space calculus. Frechier derivative of f at the point x0. If f is differentiable at each point x inside an open set, then we say f is differentiable on the open set tube. Further, if the function which assigns to each point you its derivative, remember derivative is a bounded linear map, T is bounded from v to w. So, it is taking values inside b, v, w. If this function for each x here inside you, you take dfx that will be denoted by df. If this itself is continuous, then we say that f is continuously differentiable on you or we can say it is a class C1. There are ways of making class C2 definition C3 and so on. So, we will stop here only class C1 here. So, if you go back, the very first thing you do is the so called increment theorem for differentiable functions or function which has a derivative at a single point. Rewriting this equation, you know as what we said clearing the denominator, reinterpret it. That is called increment theorem. Same thing is true here also namely f of x0 plus h minus fx0 minus T of h0 is equal to this norm h as one on the other side. I am writing that as the remainder R of x0 depending upon h, it depends upon x0 as well as h. So, you can write it as f of x0 plus h is fx0 plus dfx0 h plus some error term. This is called the increment theorem on the first approximation, linear approximation path. If you increase the value of x0 by h, the increment is roughly dfx0 of h. You can ignore this one, you can ignore the last term, that is the whole idea. Why should you ignore this one or why?  It is not always possible but because of this definition what we have is if you divide this by h then take the limit it is 0. So, remainder after the first term here has the property divide by norm h and take the limit it is 0. So, this is called increment theorem. Exactly as in the case of one variable calculus here. The following statements are all easy to check exactly as in the case of one variable calculus. Every constant function is differentiable everywhere. Everywhere means what on the whole of v, on the whole wherever they are different. And its derivatives are always 0. The derivative at all the points is 0 for a constant function. For every vector v belonging to v, the translation function see on a vector space you have this u going to u plus v where v is fixed. It is a translation function. I have written t upper v by u. Maybe I will forget to write this notation every time. So, translation function is very easy to determine. This is differentiable everywhere and its derivative is the identity function. Remember translation is from v to v. So, the derivative will be also from v to v it will be linear map it is a continuously linear map. In this case your identity of v all that you have to check is you know go back this definition f of x naught plus h minus f x naught will be what now?  So, what should I take take a identity map then this numerator itself will be identically 0. There is no need to divide by nor match and so on. So, it will be always true that is all. So, the translation maps adding a constant you know this is a rule you can differentiate this function u going to use identity right. So, identity map derivative is identity that v is constant. So, it goes away. So, that is another way of looking at it. Every bounded linear map is also differentiable here one lucky thing is that we do not have to make a further assumption. Start the linear map you do not know that it is continuous. So, you have to make the assumption you know you have to put that extra condition continuity. Once it is continuous it is differentiable and its derivative is again the same function t at all the points x inside. This is against standard result inside R n, R into R n if you have linear map you know that its derivative it is a linear map itself. You can directly verify it by taking t itself as in the in the slot in the third slot here. It is a t of x naught plus x minus t of x naught minus t h is 0. So, that will give you that t itself is the derivative of t ok. And then this standard addition rule and scalar multiplication rule if f and g are differentiable at x naught alpha beta scalars alpha f plus beta g is differentiable at x naught ok. Indeed if alpha beta from u to k are scalar functions which are differentiable at x naught then this alpha times f this is not a composition this is just multiplication right the scalar multiplication. So, derivative of alpha f makes sense it will be differentiable similarly beta g makes sense the sub makes sense. So, this will be also differentiable at x naught ok. Of course, you have to use Leibniz rule here ok. So, f is differentiable at x naught then it is continuous at x naught same same proof as in the case of one variable this is a one variable calculus ok. The logic the definition the you can just look at the increment theorem here ok. You show that if f is differentiable this rule is true now you can show that f is continuous ok. So, far except in the definition I have started the continuous linear map this is just like one variable calculus in the in the one variable calculus you are just a real number. But if you think carefully if you know that you have you must have done it already a real number is actually represents a linear map from R to R ok they namely multiplication by that number. So, there is so far there is no difference at all. So, it may be noted that if f is differentiable at x naught then all is directional there is sorry. So, let me let me call this one ok and jump here. All the directional derivatives are also axial will also exist is what I wanted to say. So, let me what is the meaning of directional derivative again this is same thing as in the multivariate calculus starting with two Banach spaces V and W again opens up set U of the domain x naught belonging to U. So, now you take any vector preferably a non-zero vector even vector 0 is also valid ok take any non-zero vector let f from U to W be any function. So, the directional derivative d V d V of f at x naught. So, this is derivative of f in the direction of V at the point x naught ok E is defined as follows ok namely it is a vector W inside W such that in this third slot whatever your T of H you are writing instead of this one out T of W multiplication by T here or you know the vector W is just the direction that. So, f of x naught plus T x naught plus T times V now we are not arbitrary H minus f of x naught minus T of W this entire thing is now function of a one variable T real variable. So, you are dividing by T itself ok no norm. So, see f x naught is fixed V is fixed W is fixed. So, it is function of real variable one variable this function must be this limit must be 0. In other word if you just look at f of x naught plus T times V this function must be differentiable as a function of T and this derivative is W that is called directional derivative exactly same definition as in the case of usual multivariable calculus ok. And you can immediately verify that all the directional derivatives will exist as soon as the derivative at x naught exist. So, often one calls the other derivative which you have defined as total derivative ok these are direction derivatives total derivative. You can talk about partial derivatives, but then you have to fix up coordinates in Banach space is coordinate fixing is something very fishy you do not want to do that. So, let V and W be any two normed spaces a continuous linear map T from V to W is said to be an isomorphism if it is invertible as a function and the inverse is also continuous ok. So, here I have taken this definition for all normed in spaces also ok. The remark here is that the inverse of a linear function is automatically linear this is elementary algebra on any vector space ok. If you have a continuous in a bijection which is sorry which you have just a bijection which is linear then the inverse is automatically linear that is not a problem. But inverse may not be continuous this is what we have been telling even if it is a bijection even if it is bijection it is continuous the inverse may not be continuous. So, we have to mention it separately ok. In the above situation some author simply called T an invertible operator this is another name they did not isomorphism inverse is inverse is continuous etcetera they will just say invertible operator. So, I will also use that term ok. If V and W are Banach spaces then for any invertible continuous linear transformation T from V to W automatically T inverse will be continuous ok. See remember invertible just for me it does not mean that it is continuous. So, I want to be very careful invertible operator when you say by convention a inverse is also continuous a linear map may be invertible ok it has an inverse, but it may not be continuous that is why I am making discussion. But if V and W are Banach spaces no problem automatically the inverse will be continuous ok. But this one needs a deeper theorem there namely what is called as open mapping theorem ok. We are not going into that deep into function analysis not a course on function analysis, but I am just mentioning this I will never use this property though ok. I will never use it because I we are not going to prove inverse I am just mentioning it as a information that is all ok. If T is an isomorphism from definition that we have taken applied to both T and T inverse we get two constants this right hand side constant says T is continuous right norm of T is less than lambda x. Similarly, I must have other way around also for T inverse which will give you a lambda prime on this side lambda prime of norm x is less than equal to norm of T x which you can write it as you know norm of T inverse of f x is less than equal to lambda at time lambda prime times norm of x also you can write similar way. So, both sides you get a constants here remember this was the definition of that two functions are similar two linear transformations are similar ok. So, this is what we are so T itself is a similarity here because it is similar to the identity map it is not identity map but it is similar to the identity map. So, T from W W is called a similarity of two normed spaces such as the app ok. We have studied similarities in the in the part one. Now, here is a theorem that I need to use. So, go through this carefully start with two Banach spaces put A equal to A V W. A is a short form here when V and W are understood what is this A V W is all set of all similarities from V to W ok. Not all transformation it is only similarities consider the function eta from A to B W V the other way around from W to V defined by eta of T equal to T inverse. So, each element here is invertible. So, I can take the inverse again I am getting inside A V W. So, this eta is actually lands you from A to A W V ok, does not matter. So, it is inside B V W B W V which is a Banach space ok. So, let A be then sorry then A is an open subset of this B V W and eta is differentiable on the entire of A ok. So, I am stating a non trivial thing here. First of all I say that this subset is an open subset of B V W. Remember B V W itself is a Banach space ok and eta is differentiable on A. Further the derivative d eta which is a map from A into B W V ok because eta itself is the map into B W V. So, its derivative is of taking values there ok. For each point A you have a linear map given by d eta of d eta operating at a T will be a linear map operating on S ok. This is nothing but you know pre composing with inverse and then post composing with T inverse and taking the minus. So, it is a complicated derivative here ok for every S belong to B V W start with for every S. S is not invertible, S is arbitrary element ok arbitrary element of linear C. A is a subset of this right and I am claiming A is an open subset. On an open subset you have a function you can talk about whether differentiable the statement is that that is differentiable and this derivative is this one ok. So, that is the statement. So, let us see the proof is not all that difficult at all. First of all what may happen is this A is empty. What is the meaning of that? There may not be any similarities between V and W ok. So, if you want to say anything there is no statement about this being an unempty here, but on empty space whatever I have made they are vacuously true.  Otherwise you do not have to prove anything all right. So, assume A is non-empty then we can follow. What is the meaning of A is non-empty there is some similarity which means V and W are similar already that is a non-trivial assumption ok. The above theorem implies in particular that A is continuous because we have already remarked that any function which is differentiable at a point is continuous at that point. So, we are going to prove that D this eta is differentiable on the whole of A. Therefore, it is continuous on the whole of A which is not stated here, but it is an easy consequence of that. So, we will use that also ok. Towards the proof of that A is an open subset. In the last lecture we have already made the preparation for this. So, let us see how take a point T inside A what is it? It is a similarity from V to W ok. So, it has some norm ok. I am taking K equal to norm of T inverse ok.  So, that will show that A is open. For each point you have a ball open buffer contained inside that set A. So, A is open. So, how to show this? So, this is what we want to claim right. So, let S belong into B V W ok. This ball is taking place where inside B V W right, A is a set of B V W. It is such that norm of S is less than 1 by K. Then we know that T inverse composite S is less than or equal to norm of T inverse into norm of S is less than 1 right. That is the whole idea why I took norm of this K equal to T inverse norm of T inverse ok. T inverse norm of T inverse T inverse will cancel out. So, it is less than 1. Therefore, by lemma that we have proved you know that we have stated and indicated the proof also lemma 1.63 follows that identity plus T inverse of S is invertible. There it was identity minus you can take minus S here and you can put this will become plus identity but T inverse of S is invertible ok, because norm of this one is less than 1. But then you can write T plus S as T composite identity that is T plus T and T inverse cancel away S ok. So, this is T is invertible, T is a similarity this is invertible. So, the composite is invertible. So, T plus S is an element of A ok. So, these are the points inside the inside this ball every element here looks like T plus S where norm of S is less than 1 by K that is the ball. So, the ball ball is contained inside A that is all we have proved that A is open all right. Now, we want to show the derivative ok. Fix a T I want to show that D is that eta is differentiable at T ok. The map S going to T inverse composite S composite T inverse again is a bounded linear operator why S is the variable here I am taking the right composition in the left composition by some other bounded linear operators exactly T inverse on both sides now ok. So, we have seen that composing left or right is again a bounded linear transformation you have twice what are they they are actually L T inverse and R T inverse. So, this map S going to T inverse S T inverse is nothing but I have a short notation S V T which is minus of R T inverse plus L T inverse that is its minus sign coming here you see in the statement with minus sign. So, I have put take this as put minus V T V T equal to minus R T inverse S T inverse this is a linear map from B V W to B W V ok. We want to show that this minus V T is the derivative of eta at T ok. This is the same thing we are showing that now remember what is eta T plus S inverse see eta take in the inverse minus T inverse it is like f of T plus S minus f T right. It is like that f is T plus S T inverse minus T inverse plus this map V T operating upon S which is T inverse S T inverse. So, V T operating on this one that way. So, there is a minus sign. So, here I will get a plus sign divide by the norm S tends to 0 must be equal to 0 this limit must be 0. So, this is what we have to show ok. Then the proof is over right. So, first of all T plus S can be written as identity plus S T inverse T. T if you push it inside here now I have stopped writing composition S T directly I am writing ok. So, this is just for convenience everywhere composite composite I have already stopped writing compositions here. Here I wrote here when I am doing computation I am now no no long it is just like multiplication now ok. You must understand that these are compositions that is all. So, identity composite T plus S T inverse T inverse is S. So, that is T plus S ok. So, since we can choose norm S to be less than 1 by k ok. So, that norm of S T inverse is less than 1 then we have this identity plus S T inverse can be inverted. Identity plus S T inverse inverse will be nothing but 0 to infinity minus minus 1 raise to n because there is a minus sign ok. If this is plus sign everything will be plus here if this is minus sign here then everything will be plus here. This is plus this is alternative minus 1 minus 1 raise to n S T inverse raise to n this is geometric series 0 to infinity. Therefore, T plus S inverse minus T inverse plus T inverse S T inverse I am computing this one ok. So, T plus S inverse can be written as now the T plus S was this one. This inverse will be T inverse into identity plus S T inverse identity plus S T inverse is this summation. So, I am writing that T inverse into that summation minus T inverse plus T inverse S T inverse as it is their terms ok. So, from here to here what I have come I have just used this T plus S inverse is this way I have written inverse of that will be first T inverse then inverse of this, but this is like this this is a geometric series. So, I have substituted here now look at the first term here n equal to 0. So, it is just T inverse that cancels as this one what is the first term here n equal to 1 what is this S T inverse into T inverse on the left. So, that is this term that also cancels out that is a minus sign here with the first term for 0 term this plus sign this minus sign here. So, those to cancel out what you are left out is this summation from n equal to 2 onwards ok. So, S T inverse raise to 2 comes out. So, T inverse into S T inverse raise to 2 and 0 to infinity S T inverse S T inverse powers S T inverse raise to n. So, up till here you have computed now what we have to do we have to divide it by norm s and then take the limit when you take the norm of this part the norm s comes here with a power twice right. So, one power cancels out when you divide by norm s other power norm s remains rest of the terms are anyway bounded function there they are just some bounded functions when you take the norm of the whole thing right. Therefore, as norm s tends to 0 this will be 0 ok the claim follows only one norm s comes in as in the square term cancels out other one remains the rest of them is bounded s tends to 0 norm s tends to 0. So, this is ok. So, we have shown that eta is differentiable from an earlier remark it is continuous I have already told you I am repeating it ok eta is continuous how to show that d eta is continuous now we have formula for d eta look at the formula formula says d eta is caught by T inverse phi T inverse sorry minus T inverse on the left T inverse on the right ok. So, there is a minus sign does not matter. So, is discontinuous that is phi T over right T going to T inverse is continuous multiplication is continuous light hand side is continuous and so on this is what we have seen. Therefore, continuity of eta d eta also follows ok continuity of d eta follows because of first of all eta is continuous and phi is continuous ok. The phi is what taking the left multiplication and right multiplication may be taking minus sign also whatever. So, all that I am heavily using 1.53 here right this part I am using that L and R are continuous L corresponds to left multiplication R corresponds to right multiplication before that you have to take inverse T going to T inverse is continuous also you have to that is that is the eta itself combining this what we get is the derivative d eta is continuous at all the points and the whole of A. So, here is an exercise I am not going to use it in the in the course, but this is something which is very very useful for people who do Lie groups and so on. So, that is precisely what it is. Take any Banach space that B will denote the space of all bounded linear operators from T to E ok. Then this becomes a group of the order obviously right you can compose you can take the inverse and this is a group what is more important is that this is a differentiable group or what requires topological group is more than topological group. Namely the multiplication mu from Bv cross Bv to Bv mu of st put st this itself is done differentiable taking inverse is differentiable we have seen but that makes it to a what is called as a differentiable group or what is called as Lie group except that the word Lie group is used only for manifolds this is what is called as a Banach manifold ok modeled on a Banach space. So, if you want to study Banach Lie groups this is the starting point. So, I am giving you this is an exercise show that mu is differentiable compute its derivative let GLV denote this opens of space Bv consisting of all isomorphisms they form a group not this Bv ok along with our theorem above exercise implies that GLV is a Lie group modeled on Banach space. So, that is just an exercise the only thing is you will see how to differentiate this one where is the derivative and where the derivative taking value if you figure it out then you will know what is the derivative ok. So, thank you very much this is all for today.


If we take a strip of paper, like this one, with the blue side and the red side, and we twist it like this, then we make a cylinder. Now if we take a pencil and we trace it starting from this point, and then go around the cylinder, we see that we only drew on the red side of the cylinder. But let's say we take another strip of paper, again with a red and a blue side, and we twist it like this. Now this shape is called a mobius strip. It kind of looks like a cylinder, except it has a twist in the middle. If we start drawing from the blue side, we take our pencil and go all around the mobius strip. We see that it crosses into the red side. Now this is very strange, because for the cylinder, we only traced on the outside, which is the red side of the cylinder, and never touched the inside. But for the mobius strip, we touched both the red side and the blue side. So what exactly is the outside and the inside of the mobius strip? Well the truth is, there is no outside and there is no inside. It's one-sided. The cylinder is an orientable surface, while the mobius strip is a non-orientable surface.  I would then sew all up the seam, producing a proper mobius loop. But I could do something even cooler. I could knit a mobius scarf, starting from its center and introducing the twist when I first cast on. Then, by knitting all along the mobius strip's one edge, I can gradually widen the scarf to produce a loop without any seam. Behold a wearable mobius strip. We can also represent other non-orientable surfaces as models, but they're a little bit harder to represent. As hard as it was for you to take off that scarf? So if we think back to the mobius strip, we were taking a two-dimensional surface and essentially lifting it into the third dimension and introducing a twist, thus allowing us to create a non-orientable surface. We could theoretically create a three-dimensional non-orientable surface by taking the cylinder which has length, width and height and lifting it into the fourth dimension in order to twist it in on itself. I have a hard time picturing it and it looks like you have a hard time making it, too. Well, we do live in a three-dimensional world, so it's kind of hard to go into the fourth dimension to do things like this. We can get pretty good approximations, though. Let's take a look at a computer model to see what we're talking about. This bottle is a non-orientable surface and it's known as a climb bottle. The words inside and outside have no meaning for this shape. So we can't make a true climb bottle, but we can get pretty close. So Chris over here is an MIT senior and one of the founders of MBOTS, and he's going to help me 3D print one. This printer takes the spool of plastic, runs it through this device called extruder, which operates like a hot glue gun that melts the plastic so that it can print the bottle layer by layer. So this is actually a pretty good representation of the climb bottle. If you look at the bottom half of this bottle, you can see that the outer surface looks back into the inner surface so that there really is no outer or inner surface. There's only one side to this bottle, just like the one side that's in the Mobius strip. But if you look at the top half of this bottle, the neck comes out and goes back into the bottle through a physical hole. In a true climb bottle, this hole doesn't exist because the neck comes out into the fourth dimension and then looks back in and the bottle is connected the whole way through. Thank you.


Felly, mae'n fwyaf o'ch gweithio'n gweithio, bydd eich stori recruit yn cael ei gweithio yn y cyd-dwyngh. Yna, mae'n gweithio'r gweithio, mae'n ei gweithio'r ffeilio. Felly, fyddwn i'r llwyswch y club, llwyswch y syniadau, y'r olwch chi'n gweithio, mae'r ffifindio gweithio. Nid gweithio chi'n gwybod, oherwydd, mae'n gweithio'n gweithio, y gall, ac yn y cyd-dyliau'r cyhoedd yn ei fod yn gweithio. O'r 24 o'r 24 o'r ochr o'r cyhoedd, y Llyfrgell Hickory yn gweithio'r llyfrgellol i Llyfrgell Llyfrgell, o'r cyhoedd Cymru Gullwn Golf Cubs. A gydw i'n gyflwyno Jack Whites, o'r dda i ddweud cyflwyno Hickory. I'n gweithio Jack White o'r cyhoedd i Llyfrgell Gullwn Ice Street. Ac yn ymddangos, mae'r cyflawn i'r gyflwyno Boris. First of all Boris, thank you for taking some time to give us first of all a brief story on Hickory Clubs and our first question I ask for you is when did all star or when did Hickory Clubs first originate? Yeah, brief history is good, yeah. Yeah, we've got a bit of cover. Yeah, well it's certainly developed on the links. Some say developed in the Netherlands and on the ice when ships were waiting. It's certainly sure that we received leather balls from the Netherlands and it was played on the ice while they couldn't sail and they were playing it towards a stick in the ice and that was 14th, 15th century. 16th century it's documented that golf was played in Scotland. And there was just just moving on a bit so then the last sort of time that Hickory Clubs were used in a sort of world world organisation event. Well the last time they were they were winning was with Bobby Jones in 1930. He won the Grand Slam with wooden shafted clubs and his philosophy is that golf is played with wooden shafted clubs 1931 Tommy Armour who was a Hickory player before he had steel shafts in Canustin one with those all right in the next year because I think I read it in 1929 that's when the steel shafts were approved by the the governing bodies there were steel shafts in 1904 already but they weren't any good all right and then they were with a certain shortness of Hickory or the inconsistency of the quality of the shafts they moved to the steel shafts maybe the price point as well so in 1930 they became I think even 1928 they became legal right but it was Bobby Jones who didn't use them right and won he stuck to the Hickory good on it good on it now a few things in terms of I've also read but you can confirm for me no numbers they the clubs had names yes they had names that developed basically the earliest names really one of them is the clique yes and that was a metal shaft a metal head on a wooden shaft and I believe the origin of the name clique comes from the fact that lobstas are being scored out under the under the rocks with the clique and that's how the earliest clique looked like and a clique is more like a one iron isn't it is that right yeah it's a long it's a one iron it's from the clique willy park developed the the metal headed potter yes and patented that so that was it said that he played with a clique and then came to the use of that shape for a potter yeah so that's how we got the metal potter and then we've got it is a mid iron a mashy then you have well you have you have a clique yes you have a driving mashy yes a driving iron you have a mashy iron a mashy a mashy niblig yeah in a niblig okay and then niblig is that pitching match or so niblig would be like a pitching wedge there was no sandwich so the niblig you need to get out of a bunker out of a hazard that was the most lofted club and the heaviest club there is different versions like a jigger like a spade mashy a sammi there's loads of different clubs but we want to focus on the few main ones okay and again early the earlier clubs no grooves in the face they were purely so 1895 there was smooth face and then they introduced sort of dots was it I've seen in yeah it was you know in the wet a smooth face comes quite slippery yeah and all of these theories about you know how the ball carries better when it has cuts yeah how we get better grip when the faces holes all these things were developed around 1900 the socket headed a wood not the splice nick anymore all the the woods were spliced until 1904 about six seven then they switched to socket heads and then the last thing just on the equipment the ball the gutty ball as I think it's commonly known isn't it the gutty ball was the one that that brought the change from the feathery yes and then there came the rubber ball yeah and then the the haskell the wound ball around 19 1905 to 10 that broke through so I want to talk about the the world hickory championships in a minute too but when they compete the players that compete in those events would they use a a gutty ball or no they would use a modern ball would they today everybody plays soft field balls those are good for hickory play all right okay so it's not necessary that you play the the good no the gutty balls there is gutty balls they are smaller they're 162 yeah you've seen yeah and they actually have the right proportions for the earlier clubs because the people played with smaller balls okay uh but it would be a pricey yeah I believe that there's a five pound of ball at the moment is it something like that well there is only a thousand two hundred gutty balls left that are unused and that were a recreation from pennfold right in the early 90s but there isn't any you have to play with the old one so we've got three minutes to find the ball at the moment I think I'd be spending half an hour if I had one of them in the back you spent seven yeah before I give that one up um so that they were up to coincide with the five hickory world championships being played over kill spindy and gullun um and you run an event to yourselves as well I don't do but what time you use that um we also have an april event yes which is called jacks opens the tournament of the shop yes and both of these events will draw crowds from all over the planet chinese australian uh canadian most canadian swedish players yeah it's a good gathering well that's what what what do you think of the idea sort of well obviously preserving that the history of the game the history of hickory shafts and what's your sort of general overview of that how long will that sort of that will all this continue for uh I just see it being continued already I mean there's there's a load of clubs they're all made in scotland that's the good thing about it yeah and uh in the in the next step there would be replicas needed there is replicas as well they're also very good golf clubs but you kind of enjoy the the history of it and uh is there a rise in popularity over recent years back to the sort of tradition of the hickory club well I think the main point is the fact that the modern equipment you hit the ball farther but the course designs didn't change you can put a t back you can change that a bit but let's say you play a james braid course and you play that with hickory clubs the whole course makes sense and is more fun to play than just trying to outright the bunkers unsuccessfully yeah yeah a and then and then finally um jack whites so first of all who is jack whites jack white he was born in dealton nearby gullun and he was the only eastlothian champion muslim burrow wasn't eastlothian in the 19th century he won the open in 1904 in sandwich yes and he had a I believe a shot just down there over he had the shop down where the pharmacy is yeah and that was a rather popular shop until the end of the demise of the hickory clubs okay he gave evening lessons how to maintain them so people keep on playing them and then the war broke out and then wood shafted clubs were completely forgotten so you've opened this shop up to us you say three years you've been here yeah so it's all about the sort of the selling of the clubs you you restore clubs and well it's about continuing to play with them it's a way of recycling that's what I like about it too but it's also it could be a way to improve your game yeah because you you will instinctively find the rhythm for the shaft you okay confronted with so if a shaft is a bit whipier you'll you'll smoothen your swing you slow down and as we know slowing down isn't a bad thing for you no no it's right we all get a little bit carried away at times so then the next part of the process is uh we're going to get fit if you like for our set of golf clubs which we're going to take out on a course and play and I say we lose this behind a camera and we're both going to go through this next part of the process where we'll get a few clubs together and we'll see you out there on the golf course do you have the tailor-made mini driver um yeah I do I do I give you the tailor-made mini driver is this one here right it's uh yeah I'm feeling that all day perfect yeah so that takes you 120 that's a very long shaft okay and with some feel you can start from 120 to 150 with this one okay I can't promise any important okay serious you pick out the niblet yeah butter knife with bounce ha ha ha ha we're pinky a good player I'll see how you hit that it has a bit of a little bit in the grip but it's a it's a two iron let's see how good you are with that and uh that's a challenge that's a butter knife without bones and loft that's your that's your risk I was going to laugh for so long I'd say you want to tear it up yeah I think you want to tear it up yeah don't don't break it no it's not about that it's about you know you think you're gonna take it off leave me safe you're really hitting the grant here driving 325 yards to the green great start hello Luke they leave that in there good good good two family right there so Luke first have you hit hickory clubs before never no so literally the t-shots you've seen is it on that little part three to start that's the first time I've ever hit a hickory club yeah so it's a great track this is uh proper getting through links the right place to be trying these clubs out first opinions right so uh what are we about three shots in I think I had six on the first I was impressed I've made up that I hit it first of all I think was the main thing but I got good fit from Boris yeah yeah to be honest here pot of smile on your face that means absolutely this is very enjoyable anyway let's go and see if we can uh really drove the green on this old 17 fantastic Luke first experience of hickory what do you think loved it loved it it's great isn't it I got my my kind of golf do you know what it's so enjoyable and like I said four four or five clubs in a bag whiskies to start whiskies to finish amazing yeah that's over all this birdie putt but there's one challenge to go yet right so I did say that we have one more challenge left we'll get to that very very short before I do that the pleasure of staying in in Duxin on many occasions when I visit Slavia alongside Malcolm duck did you see any yeah and you too um first of all I just want to talk about Duxin great location perfect for all the Slavia coastline it's um yeah Aberdeity's right in the heart of Scotland's golf course and you can set that up as a little bit of a competition to St Andrews and over golf because golf really all started at leaf links and the new stanch has been built there for the first captain in Muirfield that's that's where life started the muscle rule course inside the racetrack that from the first hole was cut yeah and now we all play into that size of all all across the world yeah so really you know it's all going on and really over golf sorry st Andrews yeah or the cradle we go but you know Scotland's a lot of golf really so um competition's good but you know we've got a fantastic stretch here and if you have done lots of videos in here but what I want to talk about I will get like is that there's a challenge that I want to have a look at but we've we've just been I've just shot a video which is all about um the history of higory clubs the fact that the world championships the higory world championships has come into this area in a few weeks time what are your thoughts on some of the the history and the preserving the history of higory clubs well again we've talked a minute ago about the home of golf and where it all started all these courses in scotland have done for higory clubs yeah yeah we talked about setting what yeah this is a cool start and cool we're in earlier on we're just at the donnell championship and higory saying it's it's too easy yeah it's not about life it's it's it's and the more we've new balls new clubs new new equipment likes they would actually it's about getting the ball of that size of hole yeah and you play with a career is you did it today for the first time oh yeah first time and um the club end here yeah you could move the ball a lot more you have fewer clubs it's quicker yeah and uh it's just great fun so i think it's really important before we do that and actually the future of golf i think if more people played with fewer clubs like you did with higory i went back to higory and played with them i didn't really enjoy it higory golf is great for your swings great for your golf well that's what i was just going to say if you think it teach people to play the game on the move absolutely dad you hit higory you've got a commitment shot yeah your rhythm's got to be good and your tempo's got to be good yeah you go to slow okay we've now got a look at the final challenge in this video and i believe it takes place on that bar over there not easy no no not guarantee you'll succeed and get it on film right but it can be done it's just a loaded fun and on the names on the wall yeah all that left hand side they've all done it better be able to do it correct will the average golfer be able to do that we'll find out very soon for now thank you to mountain pleasure having you great have you yeah thanks for all the video to enjoy and uh we'll get up on that bar to see finish off one final challenge in this video that's where we're going oh i didn't have mine on the front yeah so that takes you 120 at the very long shaft okay and with some feet you can start from 120 to 150 of this one okay i can't promise anything important okay there is a special club now comes a special club this is a jigger right this is a bit rusty but it plays well it's a shallow faced machine or less yeah it's it's picked the boy it's the center of gravity is below the ball yes the ball will go up but it's used for from chipping around the green okay up to a long high shot you want to do right you want to approach the green from farther than your niblit can do okay try to get under the ball with this or you chip it from 120 yeah let it fly 50 meters and roll the rest yeah that's a tool universal tool for that can i ask you a question i didn't get on the uh i forgot see is that is there any is there a change from the way i would play golf um into the technique or swing or what how does it only one rule as slow as you can okay you'll have the most fun so it's more it's more it should become your inner schweinerhunde german would say right uh to swing as low as you can you suddenly feel like you're playing golf because you're in sync with the club okay you feel that way more fine better thank you do you have the tailor made mini driver um yeah i do i do i give you the tailor made mini driver is this one here it's a a small little head the shaft was broken it was so soft somebody broke it okay and i put a very sturdy long man's shaft in it and that's the tailor made mini driver there you go beautiful and if you play it like a slightly longer then it's a bit longer and uh the head is rather light but gives you a fast head speed yes it's more hydrodynamical than any modern club it's beautiful that's nice yeah and when you hit that straight it's much much smoother and you will be able to repeat it yeah when you once you have to find this the spot in your stance and the speed of the swing for every shaft when you find that and you can and you adjust to it yeah it's for the skilled golfer i was just gonna ask the question again now that it's just come up from it is that do you think golfers were more skilled at playing these clubs or is that too much of a when it comes to shot making it was more of a game yeah some not some another yeah and it was match play yeah you know they didn't they played the course but they played the appell yeah yeah it was uh interesting isn't it pick out the lible yeah butter knife with bounce we pick out yeah we're talking about special clubs the big ball model yeah that's for the 168 that doesn't have to do with any other balls than golf balls and this would be the the spade mashy top so to hit it far and low this would be like a clique and i know you're a good player i'll see how you hit that it has a bit of a little span in the grip but it's it's a two iron let's see how good you are with that and uh that's a challenge that's a butter knife without bounce and loft that's your that's your wrist gone that's gone a lot more so a lot better you have a wood don't you uh yes yeah you have the you have the tailor made yeah and you give your head cover for that


Hi you guys, Lindsay here. Welcome back to my channel, Inside the Hymn. This is a really fun one that I found on the internet. Thank you, Pinterest. So this is an adorable little Christmas tree utilizing your fabric scraps. So all this is is a cinnamon stick. You can get cinnamon sticks, like food grade cinnamon sticks, you can get at the grocery store, but just for crafts, you can actually find bags of cinnamon sticks at places like Michaels and Joanne. They will have cinnamon sticks for crafting.  I used a navy and white gingham as well as like a solid navy. The gingham is like a cotton material and the navy is like a lining. So you can really mix up your materials there. Oh, there's also a third one, a quilting cotton with little arrows on it. You tie them around the cinnamon stick and then take your scissors and cut in a diagonal shape from the bottom to the top to give it that Christmas tree shape.  And that's it. You've got a fun little Christmas tree to hang made out of fabric scraps, which I know we're always trying to find ways to utilize our scraps.