I'm here today to participate in civil disobedience to protest the intolerable heinous U.S. drone program. I came down here because this is where we're preparing people to fly drones. Drones are part of a mechanized system for and for. Killing people is notoriously unfair, unjust innocent people. And we as American citizens have a responsibility for what our government does, and we need to stop this. Drones are causing terror around the world, especially disrupting the lives of children in many countries. You know, imagine drones in the air and you don't know if you're next to the target, so it terrorizes everyone besides the people that they kill. We're killing civilians. I'm here in support of this action and also to make awareness of the military effect on the climate. And we are all standing for peace. That's what we need, peace through the entire world. No country should have the right to fly over another country and decide what human beings should live and or die.


Welcome back to my channel and welcome if you're new here today. I have a very fun video for you I'm going to be sharing with you my top 15 most popular WW items that I no longer eat and what I've replaced those with now I want to preface this with I follow a clean approach to WW Which means that I try to eat as clean whole food as humanly possible now I don't say that I'm a hundred percent clean eating I just try to do my absolute best. I like to follow the 90-10 rule where 90% of what I eat is extra clean And then that 10% gives me a little bit of leeway to bring in some of my favorite foods But there are some really popular foods in the WW community things that I see on YouTube Instagram Facebook Just all over even at my WW studio that I have found cleaner healthier whole food replacements for So I wanted to share those 15 items with you today now I am not a doctor or a nutritionist and I do not work for WW And this is my personal opinion and the swaps that I have made personally now You feel free to eat whatever you'd like on WW. That's the beauty of the program But for me, these are just some healthier alternatives that I've chosen So I wanted to share them with you to give you some ideas and maybe some brand new food finds that you never thought were WW friendly, so let's jump in to today's video Number one is popcorn I see all over the WW community about skinny pop boom chicka pop all of those low fat low calorie popcorn options Now I know the best alternative for popcorn is popping it at home yourself where you can control the ingredients But sometimes we just need an on-the-go snack So I have substituted the boom chicka pops and the skinny pops of the world with this olive oil popcorn from Trader Joe's Now this popcorn is Delicious all that is in here is popcorn olive oil and salt it tastes really good It's crunchy like popcorn should be just the right amount of salt and popped in olive oil Which is best in class oil great price about two dollars a bag at Trader Joe's So whenever I'm in the mood for popcorn, I now reach for the Trader Joe's olive oil popcorn Next is diet pop diet soda That's another thing that I have eliminated from my diet for several reasons one because drinking any type of diet Soda or pop can make your body crave sugar Also, even more important than that of why I've moved away from diet soda is because it contains caramel coloring Which I try not to have any caramel coloring in my diet at all If you're not sure what some of these ingredients are and why I've chosen not to eat them I will link my ingredients to avoid and why video down in the description box for you How do you recommend you watch that I go in-depth to all of the ingredients to avoid and the reasons why? Also in diet soda and diet pop is Aspartame and aspartame is a sweetener that I do not want to consume for several several reasons It is not good for your body your body doesn't know how to digest aspartame And we've heard all about this over the years in the media about how it's just not a good sweetener alternative So between the caramel coloring that in the fact that it wants me to eat more sugar I just have eliminated diet soda and I've replaced it with Zevia Zevia. Zevia I'm not sure exactly how you pronounce it But basically this is a soda alternative It is sweetened with stevia and it is made to be colorless So when you pour this cola or root beer into a glass it is clear because they remove the caramel coloring Which is huge for me now this does have natural flavors, which I don't love But this is a great alternative if you're looking to cut out diet soda diet pop out of your diet for all of the reasons Mentioned before the next one is a very popular WW staple for so many of us and that is the premiere protein Now I have never been a big fan of premiere if you follow my channel You know that you don't see it very often here on my channel because I've never been a fan one of the taste and two of the Ingredients so I wanted to find a protein shake in the event that I needed one and again This is not something that I eat drink very often I generally try to eat a more whole food But sometimes if I'm traveling and I want something for my coffee You know the famous protein coffee or I just want to add a little bit too Maybe a protein shake or a smoothie or maybe I just want a protein shake after a good workout I no longer drink the premiere and again the laundry list of ingredients is the primary reason I could go on and on as to what ingredients in premiere I don't want to consume but I just went ahead and found an alternative for protein shakes and that is iconic now Iconic makes a grass-fed plant-based protein shake with excellent excellent ingredients They even use high low eggs high low egg sunflower oil as the oil just full of a really really good ingredient So I have just transitioned over to iconic. They have several flavors. You can order these on Amazon You can order these online. I will put a link down in the description box for you This is the cafe latte. It actually has caffeine in it So this is great as just a protein shake if you want that little boost of caffeine and it tastes really good in coffee as well They have vanilla, matcha, chocolate, caramel, all the things and just far for better ingredients than the premiere protein So sorry in advance for those of you that love your premiere. You can continue to drink that of course I just have found a little bit healthier alternative.   This is a fabulous brand of yogurt this maple Hill. It's a hundred percent grass fed So I'm getting all the nutritional benefits and to be honest with you guys if you lower the serving size It's not a lot of smart points. You can have a quarter cup of full fat yogurt for about two smart points So I would gladly take the points for it to get all of the nutritional benefits And we haven't even talked about the taste the taste of this is incredible So I now just go with a full fat regular or Greek yogurt another extremely popular item in the WW community is I can't believe it's not butter light the spray the tub all the things I no longer eat light butter because of the oils that are used in light. In fact as a general rule I don't consume anything that's low fat fat free or sugar free So you're gonna see that kind of theme throughout these items But I've eliminated a lot of the tubbed butter the spray butter all of those out of my diet Now I didn't want to transition entirely over to real butter because of the smart points I was hoping to find an alternative for light butter that tastes really good And isn't really high in smart points and I found just that and that is melt plant-based butter This is so good. It's in a tub just like the I can't believe it's not butter the country crock Whatever tubbed butters you're using but the ingredients in this are so incredibly good They use an expeller pressed oil, which is best in class. No artificial flavors No natural flavors no artificial colors and it tastes really really delicious now I know that I can't believe it's not butter or a light butter spread You can generally have a tablespoon for about one smart point a tablespoon of the melt butter is three smart points But I find this better to be very rich and flavorful that I can get away with a half of a tablespoon For one smart point and get as much if not more flavor than I did with a light butter And I'm eating really good ingredients I find this just in my regular butter section at my local grocery store And I've also seen it at pretty much every natural food store as well while we're talking dairy. Let's talk cheese I do not eat any fat-free cheese any longer. In fact, I don't really eat any light cheese either I try to go with just a traditional cheese I try to go with one that's organic when it ever possible and grass-fed is even better It's just really really hard to find so I've subbed out my fat-free craft or great-value cheese both in cheddar and mozzarella For full fat cheese like this. So this is from my local health food store natural grocers This is a full fat Italian blend cheese. It's organic and it is only three smart points for a quarter of a cup So it's really not that much more in smart points from a light cheese But you don't have any of the filler that you have in light cheese. It's literally the cheese I also love the traitor Joe's organic mozzarella You can have an entire quarter cup of that for two smart points and it's mozzarella cheese and it's organic So I've just chosen to take the fat free out of my diet number one I don't like the ingredients but number two and most importantly the cheese is very Plasticy it doesn't melt it's flavorless and to be honest I'd rather take points and enjoy the food that I'm eating That's what my points are for is to really like and enjoy and feel satiated with the foods that I'm eating So I just go with my traditional cheeses another popular item is diet or low-calorie bread the serri-lea breads The nature's own butter breads. I don't eat those any longer either primarily you guys know I've talked about before I do not like the serri-lea bread. I find it very cardboardy and airy. There's holes in it I don't really feel like it's bread. It doesn't taste like bread. It doesn't satisfy me It doesn't cure my craving for bread now the butter bread is better in that respect But the issue is the ingredients in those breads. It's enriched flour Generally using a canola or a soybean oil and just things that I try to avoid So I just looked around and I found a bread that was way way better ingredient wise Nutritional wise and really not much more when it comes to smart points and that's going to be a sprouted bread So this is the Trader Joe's sprouted bread There is also Ezekiel, which makes a fantastic sprouted bread. I've talked about this a hundred times in my videos I also use the Ezekiel English muffins in replacement of any other type of English muffin whether it be sourdough Thomas like again ingredients and just not feeling satiated and like I'm having real nutritious bread Sprouted bread is always your best option Generally, it is found in the freezer section because it does not contain preservatives So they have to freeze it in order for it to last this Trader Joe's bread you guys is two smart points of slice The slices are pretty similar to your Sara Lee's or your butter breads of the world But they're heartier and more flavorful and so good and full of fabulous ingredients Not a single ingredient that's questionable in sprouted bread and it's affordable if you buy the Trader Joe's bread I think it's about three dollars a loaf I know that the Ezekiel can be a little bit more But again, I will gladly take an extra smart point to have a better quality bread next is sugar-free syrup I no longer have any type of sugar-free syrup. This includes syrup in my coffee I do not use Jordan's skinny syrup those contain sucralose, which is something that I avoid as well Spikes your blood sugar makes your body crave sugar and it's just an artificial chemically processed sweetener Same with sugar-free syrup that you put on pancakes. So all those delicious sugar-free syrups out there Flip them over and check out the ingredient label. It's not even syrup. Generally. It's rice syrup over from China That isn't even actual maple syrup. So I too have switched over to an organic maple syrup I'm gonna insert a picture because I'm out unfortunately. I really like this Vermont maple syrup from Trader Joe's You can really just get any organic pure maple syrup now Of course the smart points are going to be higher But I will generally just put a tablespoon or two on my pancakes my waffles Keen wobbles and take the smart points for it because I know what I'm giving my body is a real whole food that my body knows How to process so I've just chosen to take out really any chemically processed syrups and put in a real syrup So I'm gonna talk a little bit about what I put in my coffee mix So I mentioned that I no longer drink sugar-free syrups Jordan's skinny syrups Turani da Vinci whatever you can find I also Sad to say and I was very sad you guys in the beginning that I no longer drink sugar-free creamer I was honestly Disgusted when I flipped over the sugar-free creamer and read the ingredients now This is just me you may be like me and love your sugar-free creamer And I say if you like it you continue to drink it But for me it was just ingredient-wise not what I wanted to put into my body. Does it taste good? Yes Is it low point? Yes, but just for me the ingredients were just not something I wanted to eat any longer So let me just tell you I was on the hunt for a flavored Creamer that had good ingredients and that task was very challenging I was just for a while having just half-and-half or heavy whipping cream or Milk in my coffee and putting in like a whole earth or a monk fruit sweetener packet until I discovered this This is a coffee creamer. It's a superfood creamer from Layard lard. I don't know how to pronounce it.  It comes in several flavors including Unflavored luckily the flavored ones are not natural flavors That's what you're going to find in a lot of flavored really anything But in this creamer he uses extracts like vanilla extract or mint extract My favorite flavors are the vanilla the chocolate mint the cacao and the pumpkin spice I have never tried the original or the turmeric, but they make those as well You can have one big tablespoon of this creamer for two smart points and it is so good I literally do this my collagen and some half-and-half and it's absolutely delicious The flavor is there the sweetness is there. It's made from coconut sugar, which is best in class for sweeteners Love this creamer so much. They do sell the big bag of unsweetened at Costco or at least at my Costco But I buy these flavored ones online. They're not very expensive. I think they're 1495 and they last forever I mean there's a ton in this little bag. They reseal and I just throw them in my coffee cup I'll link these down below for you guys, but if you're like me and you loved your sugar-free Coffee-make creamer. This is a great alternative. It's equally as delicious and the ingredients are on point Another thing I was very sad about was my fat-free ready whip.  I loved my fat-free ready whip now Not only am I not a fan of the oil in there But what I'm most not a fan of when it comes to any whipped topping and I'm not just saying fat-free or light I'm talking whipped topping in a can in general is carrageenan and that is an inflammatory And I have eliminated that a hundred percent from my diet So I even looked at these expensive organic whipped creams that are five or six dollars a can and they still Contained carrageenan. So I thought my days of whipped creamer over Over until I found this and this is the so delicious cocoa whip Now I found this at my local health food store in the freezer section So basically the same place you're going to find cool with this No, carrageenan and the only questionable ingredient in this is natural flavors Not something I like to see but I would rather have natural flavors any day of the week over carrageenan So I love this. It's delicious. I've gotten a lot of questions on whether or not it tastes like coconut Nope, it does not and you can have Depending on how much you have it's one to two smart points So instead of zero points of fat-free ready whip You're going to have to take a one to two smart point hit But you know that you're eating good ingredients and I'm telling you guys, it's rich and creamy. Ha. I love it I no longer miss that free ready whip Next item is another extremely popular w w food and that is your Dan and light and fit yogurts your oikos yogurts all of those light yogurts on the market Now I mentioned earlier when we talked about full fat plain yogurt That I don't eat any light or low fat yogurt because it The process strips the nutrients out of the yogurt But that's not the only reason that I stay away from flavored yogurts like Dan and light and fit Number one, they all have natural flavors. So anytime you buy a flavored yogurt It generally has natural flavors There are a few like the one I'm going to show you on the market that does not and is still flavored But most of them are going to have natural flavors a lot of them have sweeteners I don't eat and some of them even have oils that I don't prefer to eat So I found this and this you guys is delicious. This is the siggy. So this is actually the 2% This is the strawberry and lingonberry Now I actually prefer the full fat siggy so the 4% But it's very very hard to find in my area. So I picked up some of these 2% ones These are really good and literally the ingredients in here. There's four Let's talk about it because I want to show you that there are yogurts on the market That are flavored that do not have natural flavors. So this has pasteurized skim milk pasteurized cream berries Cane sugar. Oh, I'm sorry. There's more than four. There's six live active cultures and fruit pectin So it's flavored with actual fruit not with natural flavoring. So love this yogurt. It's really good This container is going to cost you about five smart points. Now. I know that that's a lot of points for some of you So I want to talk a little bit about siggies and bringing siggies into your life Even if you don't want to spend five points. So siggies does make a zero percent yogurt now again You're missing a lot of the nutritional benefits of a full fat yogurt But the ingredients are just as great as the full fat yogurt and they are only three smart points So well worth the extra point compared to light and fit for the better ingredients Your body knows how to process everything in siggies. It's thick. It's creamy. It's delicious So if you don't want to take a five smart point hit pick up the zero percent siggies And it's only going to cost you three smart points. Next is ice cream. Now. Let me just tell you What a feat this has been I've yet to find an ice cream like an actual ice cream bar Other than if I have a full fruit bar. I'm talking ice cream Like creamy ice cream with chocolate and all those delicious flavors That is something that I will eat. They all contain some sort of ingredient that I don't want all of the light Yogurts like your halo tops those Enlightened those are all have a lot of sugar alcohols and I try not to eat sugar alcohol at all And if I do it's in a very very small amount So those ice creams are out the full fat ice creams contain a lot of oils that I don't want So I'm still my friends on the hunt for a good clean ice cream And when I find it I promise to share it with you But if I am craving ice cream something that resembles like a chocolate coated ice cream bar I choose clio bars and I'm going to insert a picture because I am completely out My walmart has not had them the last couple of times But clio bars are excellent now. They are kind of high in smart points They're about six smart points per bar and they're small. I would say that they're about I don't know two and a half inches, but they have really really good ingredients their whole food You still get that feel of ice cream You can even pop them in the freezer and you get a little more ice cream feel and they're coated in the most delicious chocolate So if you want to have an ice cream dupe that's cleaner and you're okay spending the points Clio bars are definitely the way to go and again, you can find these at walmart and on the clio bar website I'll link that down below for you guys and generally they're about a dollar a piece at walmart So really really affordable and I'm telling you they are delicious. It tastes like chocolate covered cheesecake. Next up are w w snacks Sorry, w w But all those snacks that you buy at your local workshop their chips their cookies their two point bars All the w w snacks. I know that they reformulated their ingredients about a year ago but I flipped over quite a few boxes at my local workshop of Pretty much all of the different snack options that they have and there is not a single one that has ingredients in it that I wanted to eat unfortunately The mini bars have a lot of artificial sweeteners They even have like malatol and some of the really not good for you artificial sweeteners The chips and things are just made with processed ingredients So I wanted to have lots of snack options So you may have already seen my favorite w w snacks where I bring you all the delicious clean eating snacks Or it may get posted later. So stay tuned regardless for that video But I just found a few of my favorite snack alternatives I found sweet and I found savory. So first let's talk savory Let's talk about alternatives in dupes for the w w chip snacks like the little nacho chips The I don't even know what all they have the barbecued chips and that's these these are the siete grain free tortilla chips These are incredible the ingredients in these are absolutely 100 percent perfect. They taste really good These are the lime. I love these the nacho is really good. They even have just your traditional tortilla chip This is a great alternative to a chip and these are about five smart points per serving But you just cut down the amount of chips that you have make sure you weigh them out You get more and you can lower the smart points, but if you want a good chip, this is a fantastic option Also, what if you really really really like the little two-point bars and you just want something sweet from w w So I found a few options. So first there are these these are the chalk zero milk chocolate squares Now these have pretty darn good ingredients.  I'll show you the size of the square So this is what it looks like So that's the size of the square and it's only two smart points and it's much better ingredients It's the same smart points as the mini bars But really good and much better ingredients like I mentioned You can pick these up off of the netrition website. I'll link that down below And also for the sweet tooth. These are amazing. These are the lily bees brownie fins in chocolate mint You guys these are like little crusty corners of the brownie pan I'm obsessed. They have chocolate mint chocolate and salted caramel. I buy these off of the thrive market I'll link the thrive down below as well. There is 20 dollars worth of free product from the thrive market right now So if you're looking at joining, this is a great time It's a fantastic place But I buy these off of there and I am going to literally buy like 10 packages the next time I place an order It's five smart points per serving But if you have half of a serving which is about six to eight brownie bites It's two points.  So there are some good replacements for those ww snacks And also another thing I want to point out is those snacks are pricey at the ww workshop These are much more affordable options as well. So it's kind of a win-win And last but certainly not least is probably the one a lot of you are going to come at me for And that's okay. You guys continue to eat what you want to eat I'm just simply sharing some alternatives that I've come up with and that is an alternative for the Olay wrap or any of those low smart point wraps I know the tomorrows the mission carb counter If you look at the back of those wraps, they generally contain a lot of unhealthy oils For one, that's the main thing and a lot of them are made from process flowers Like enriched wheat flour wheat flour just flowers that generally contain a lot of pesticides like glycosate The active ingredient in roundup. So I went on the hunt and I found a couple of options First I'm going to insert a picture of the first one. These are the siete tortillas now Let me preface this with these are very expensive. I've yet to purchase them because of the price point They are about $9 per package now if you get The tortillas with the almond flour, I believe that there are three smart points But I'll put that here on the screen if I'm wrong But this is a great alternative In fact, these actually have the cleanest ingredients of all the tortillas I've ever been able to find But again, they're pricey, but I did find a fantastic option Law tortilla factory low carb tortillas you guys these are just as big if not bigger than the olay wraps These have excellent excellent ingredients two smart points.  I'm obsessed with these. All right, so that is it on my top 15 Favorite w w food items and some healthy alternatives I hope that I gave you some great ideas of maybe some things that you can look for The next time that you're doing your grocery shopping and you're adding some of these w w favorites to your grocery list Again, if you choose to eat the items that I mentioned more power to you That's the beauty again of w w is we can eat whatever we want I'm just here to share with you some of my new favorites that follow a little bit better with my clean approach to the W w program. So thank you guys so much for watching I'm going to link everything down below that I can find for you guys And I'll even list out these 15 items and what I substituted them with So it makes a little bit easier for you to add to your grocery list. So thank you for watching if you're new Welcome, I'd love for you to stick around and join my channel I am on w w the blue plan and I do follow a clean approach to my weight loss journey So hit that little subscribe button And the bell so you're notified whenever a new video is uploaded. You don't want to miss out I upload almost daily give this video a big thumbs up if you found some great new items And if you made it all the way to the end of this probably really long video again Leave me the thumbs up emoji down in the comments If you're on a computer or a laptop and you don't have emojis just write thumbs up And I'll take that as a win. Thank you guys so so much for watching and I'll see you all in my next video. Bye


Hello, I'm Zor. Welcome to Unisor Education. Today's topic will be induction, a problem in the category of induction problem number five. And in this particular case, it's a real problem. It's much more difficult than those little exercises we did before. So let me go straight to the point. This is actually a theorem which was attributed to a French mathematician Cauchy. Here it goes. First of all, there are two definitions. The arithmetic average and geometric average. Now, arithmetic average of n numbers is, as you know, their sound divided by their number. The geometric average of the same numbers is an nth root of their product. Well, intuitively, it is kind of obvious that both averages are really average. They are somewhere in between these numbers. However, they are quite different and there is a famous inequality between these two averages. Arithmetic average is always greater or equal than geometric average of n positive numbers. We'll talk about positive numbers just because we don't want to have something like a square root of negative numbers or whatever. So all numbers are positive and arithmetic is greater or equal than geometric average. The problem number one is let's prove it. Well, first of all, let's start from a simple case. Only two variables and we will try to prove it for this case when n is equal to 2. So we have to prove that x1 plus x2 divided by 2, that's average of two numbers, is greater than square root of their product. So this is arithmetic average. This is the geometric average. Well, this is actually quite simple because if you will take this obvious inequality, since this is the square root of x1 minus square root of x2, now this is obvious because this is the square. So every number positive or negative being squared will give a non-negative result. But if you will open this, you will see that this is square of the first, which is x1 minus 2 product plus square of the second, which is x2 and that's greater than equal to 0, which basically gives us this inequality. This goes to the right, so we'll have x1 plus x2 greater than 2. Now, the multiplication is product of two square root. The root is obviously a square root of their multiplication. That's the property of the power and this is the same as this, that just divide by 2. So in case n is equal to 2, it's really very simple thing, straightforward check and there is no problem. Now, obviously since I started the whole problem in the category of induction, we will try to prove the whole thing using the method of mathematical induction. So we have proved for one particular beginning value of n and a typical way of proving something using the method of mathematical induction is, well, first you check it for some beginning number like for instance n equals to 2 and then you prove a theory assuming that the formula or the quality or whatever is true for n is equal to k, assuming that that is true, prove that it will be true for n is equal to k plus 1. Then, using the standard logic from n equals to 2, using this theory, we go to n equal to 3 from 3 to 4, etc. And that's how we prove it for any finite number. In this particular case, it's not that easy because if you will go to 3 for instance and you have to prove this, the third root of n x1 x2 x3. Now, it's not really obvious how from this we can go to this. However, let's make another observation. If I will use n is equal to 4 instead. So I have four numbers and I have to prove that this is the fourth root of their product. This actually is quite easily deducible from the previous one. How? Well, very simply. Just divided by two pairs. So it will be x1 plus x2 divided by 2, x3 plus x4 divided by 2 divided by 2. Now, obviously, this left part is the same as this one, right? The common denominator 2. So it's the sum of these 4 divided by 2 and divided by 2 more, so it's divided by 4. Now, but this, let's consider this as a one number and this another number. And we know that their arithmetic average, just two numbers, we will use this thing, is greater or equal than square root of their product, right? So these are individual numbers and I'm using my theorem which I have actually proved for n equals 2. In this case, it's one number, two number. Two numbers, their average greater than their arithmetic average is greater than their geometric average. Now, in turn, I can say that this is greater or equal than. Now, let's consider just these two arithmetic averages and use this same theorem. So it was the square root of x1, x2 times square root of x3 times x4. Now, obviously, square root of square root is the fourth root, right? So this will be fourth root of x1, x2, x3, x4. And that's exactly what we had to prove from the very beginning. So we have switched from 2 to 4 elements from n equal to 2 to n equal to 4 very easily, which is divided by pairs. Now, if I will have instead of 4, if I will have 8 numbers, how that would be? Well, it's kind of obvious that I will use exactly the same technique for 8. I will divide, so for n is equal to 8, what I will have is, I will have x1 plus, etc. plus x8 divided by 8. That's my beginning on the left, right? All 8 numbers. I don't want to write each one of them. But then I can pair them and I will have x1 plus x2 divided by 2 plus x3 plus x4 divided by 2, etc. x7 plus x8 divided by 2. And then, divide by 4. Well, probably if let me just write down all 4 components would be nicer. So next one will be x5 plus x6 divided by 2. And next will be x7 plus x8 divided by 2. So obviously, the arithmetic average of 8 numbers can be represented as average of 4 numbers where each one is a pair average of the previous 2. Okay, now, but this is the same as this because I can just consider these as separate numbers. And if I will use this previous theorem for n is equal to 4, I can say that this is greater or equal than fourth root of their product, right? x1 plus x2 divided by 2. x3 plus x4 divided by 2. x5 plus x6 divided by 2. And x7 plus x8 divided by 2. So here we're using this one. Now, again, let's use the same theorem for a pair. So instead of x1 plus x2, I can reduce it even further. So it will be square root of x1 x2. Same here, here, and here. So basically, it will be greater or equal than fourth root of 2 roots, which means it's the 8 roots of their product. And that's exactly what we had to prove. So as you see, we are relatively easily going from 2 to 4, from 4 to 8. So my first step in the proof of the original theorem for any number n would be not a transformation from n equals k to n equals k plus 1. I really don't know how to do it easily. Instead, I will transform it from n is equal to 2 to the k's power to 2 to the k plus 1's power. So from 2 to 4, from 4 to 8, 2 to the third power, from 8 to 16, 2 to the fourth power, etc. Now, I will prove this as a separate step in the whole theorem, in the whole proof of the whole theorem. Now, so I'll have, instead of having every number, I have 2, 4, 8, 16, etc. Now, how about 3? How about 5, 6, and 7? How about 9, 10, etc.? Well, this will be the second step of the theorem, of the proof. Instead of going forward now, since I have any big number, basically, at my disposal, where the theorem is already proved in the first step, I will go backwards. Apparently, to go backwards is easy. So my second proof will be, second step in the proof will be, if the first step is equal for n is equal to k, then it's equal for n is equal to k minus 1. So, again, it's a very important difference. From the traditional one step proof, from k to k plus 1, I will do it in 2 steps. First, for n is equal to 2 in the k's degree to k plus 1, that's how I will get my big numbers. And in the second step, I will prove that from any number, I can go backwards. And that's how I will cover all the steps, how, for instance, I can get to number 9. Well, very simply, the theorem was proven for 2. Using this, I can therefore say that it's true for 4 and for 8 and for 16. Then, if it's true for 16, using the second step, I will go backwards to 15, 14, 13, etc. to 9. So that's why the combination of these two steps basically completes the proof for any number. Alright, so we have the plan. We know more or less how to prove this one. I'll just repeat the same thing I did, like 2, 4 and 8. And then this will be a separate step. So step number 1. Right, before whatever I was talking, before was just a preliminary kind of explanation of why I have chosen to do it this way. And you're obviously welcome to try to do it in a classical mode, like from k to k plus 1. Personally, I found it extremely difficult. I just wasn't able to prove it that way. So maybe there is no good proof. So anyway, you're welcome to try if you want to. But in any case, if you would like to follow this particular plan, which I definitely recommend this one, this is a good point in time to place the pause button, try to do it yourself. And obviously, this one you have already basically seen in a couple of examples how to do that. And as far as the next step, I can give you a hint. To transform from k to k minus 1 is relatively easy. If you know that for k it's true, but you have to prove that it's true for k minus 1, you just have to add extra number to these k minus 1. And so you will get the k numbers. And I will not tell you which number to add. That's kind of up to you. But this is just a little hint. In any case, I will do both steps right now without any interruptions.  Okay. Now, let's consider the theorem is true for n is equal to 2 to the k's degree. And we have to prove that it is true for 2 to the k plus 1. Well, very easy.  And we divide by their numbers. And obviously, to prove that this is greater than their geometric average, I will separate pairs of these numbers. Now, if total number of my numbers is 2 to the power of k plus 1, and if I pair them, how many pairs do I have? Well, obviously, I have to divide the total number of numbers by 2, since every two elements will give me a pair. Now, if I divide 2 to the k plus 1 by 2, I guess I will have 2 to the k's degree, 2 to the power of k. So, if I will do it like this, divide it by 2 plus x3 plus x4, 2 to the 2 plus et cetera plus. My two last elements will be x with an index 2 to the power of k plus 1 minus 1 plus x with an index of 2 to the power of k plus 1. That's my last pair. It's a little bit difficult on indexing here, so it's x with an index of 2 to the power of k plus 1, and then minus 1, because this is the previous member. And the last member is x with an index of 2 to the power of k plus 1. So, how many pairs, as I said, to the power of k? So, if I divide it 2 to the power of k, that's what we will have. Now, in this particular case, so far, this is not greater or equal, this is just reticle. So, all I did, I separated into pairs, divided each pair by 2. So, now I have to divide by 2 to the case, and all together will be, this 2 will go down, so 2 times 2 to the case, it will be 2 to the k plus 1, exactly what we have in the beginning. So, that's how we reduce the number of elements from 2 to the power of k plus 1 to the number of elements 2 to the power of k. Now, since we have assumed that our theorem is true for number of elements equal to 2 to the power of k, I will use it here right now, and I can say that this is greater or equal than their geometric average. Now, the geometric average is, the number of elements is 2 to the power of k root, same number as here. So, this is 2 to the power of k. And under this root, I have their product, which is x1 plus x2 divided by 2 times x3 plus x4 divided by 2, etc. And the last number is, again this kind of a difficulty to write, x with an index 2 to the power of k plus 1 minus 1 plus x with an index of 2 to the power of k plus 1 and divided by 2, the whole thing. Okay. So, that's what we have. And obviously, now we put even greater than, greater than even more. Now, since our theorem is proven for n is equal to 2, each arithmetic average of a pair, I will replace with their geometric average, so I will have the same 2 to the power of k root. And here I have a square root of x1 times x2 times again, square root of x3 times x4, etc. And the last root, square root will be product of x with an index of 2 to the power of k plus 1 minus 1 times k with an index of 2 to the power of k plus 1. Okay, that's my last square root, and this is my 2 to the power of k root. Well, and now it's basically obvious. If you multiply all these square roots, you can have only one square root from everything, and if you will have a square root and then root of a degree with a degree of 2 to the power of k, obviously the result will be 2 to the power of k plus 1, root of their product. And the last one is x with an index of 2 to the power of k plus 1, which is exactly what we needed to prove. So, from k, 2 to the power of k, we can always step forward to the next element, the element 2 to the power of k plus 1. So, that's basically the first step of the proof. Since it's true for n is equal to 2, it's true for 4, for 8, for 16, for 32, for 64, etc., etc., we double and double the number of elements, and that's how we can move forward in bigger and bigger steps to get the points where we have already proven our theory. Now, let's talk about the second step, how to move backwards, and from let's say 16, we can go backwards to 15, or from 32, we can move backwards to 31 and then 30 and 29, let's say. And that would complete the whole proof for any number. So, let's assume that the theorem is true for n is equal to k and we have to prove it from k to switch to k minus 1. Okay, so for n is equal to k, we assume it's true and we have to prove it for n is equal to k minus 1. Alright, so let's have k minus 1 elements divided by k minus 1. Alright, here is an interesting thing. It's kind of obvious that if you have an average of certain number of elements, arithmetic average, and then you have one extra number which is exactly equal to their average, the whole combination shouldn't really be different as far as the average is concerned from the one before. So, what I'm saying is that if I have an average of k minus 1, let's call it y. And now let's have an average of k elements which are original k minus 1 plus their average y. And I have an average of k elements now, original k minus 1 plus their arithmetic average, divided by k. I would like to say that it's very obvious that we should really think about this combination as really not being different as far as its average is concerned from the original one. And how to prove it? Well, let's just open up this thing and check if we will go and we will be reduced to the same formula as before. So, what this is is x1 plus x2 plus x3 plus et cetera plus xk minus 1 plus.  That's what it is. Okay. Now, we will use k minus 1 divided by each of those guys to bring them with the common denominator k minus 1. So, what is this? Well, it's x1 will be k minus 1. Okay. We will put k minus 1 down and this k.  So, x1 was k minus 1 here and 1x1 is here from here. So, all together will be k times x1. Same thing for x2. We have k minus 1 times x2 and plus another x2. So, it's k again, kx2. As you understand, it will be exactly the same thing for everyone up to k minus 1. And we divide by k minus 1, k. And obviously, you reduce it by k and you have a arithmetic average of k minus 1. So, this is a proof that adding arithmetic average of k minus 1 numbers does not change an average of a set. If it was y, it will be exactly the same y at the end. So, adding average to a set of numbers does not change the average of the combined set. This is a very important project and we will definitely use this in this particular case.  I have to prove that this, a arithmetic average of k minus 1 is greater than their geometric average. But since I know that this thing is the same as x1 plus x2 plus xk minus 1 plus their average, average by k, since I have just proved that, now I will work with this. But now this is an average of k elements, right? And I can use an assumption which I have. Because we started from let's assume that it's true for n equals k and then let's just move to k minus 1. I can actually represent as an average of k numbers original k minus 1 plus their average. And this we can use our assumption for n is equal to k and say that this is greater than k root, case root of x1, x2, xk minus 1 and what is this? This is k minus 1 root. Well, let me do it in two steps. x1 plus x2, et cetera, xk minus 1 divided by k. Okay. This is the product of from 1 to k minus 1 and the kth component is, sorry, k minus 1 is their arithmetic average. It would be a little easier for me. If I will use, instead of roots, I will use the powers. You know that ath root of b is basically b to the power of 1 over 8. It's just easier to work with.  Now, you see, here is a very important thing. This component is exactly equal to this component. So what I will do, I will just transfer this piece into this link, basically, the regular transformation. Because this is equal to, since this is the power and this is the product, I can separate the components. So it will be x1, x2, et cetera, xk minus 1 to the power 1 over k times x1 plus x2 plus, et cetera, plus xk minus 1, to the power 1 over k. So, this is inequality which I have. This piece is greater or equal than this piece. Let me just write it again so it would be a little easier to understand what I have done here. Greater or equal than this.  So that's what I can prove immediately. So, again, what I'm saying is that this member you see, looks like this member. So, what can we do about this? Well, first of all, we will raise those left and right to the power of k. What will be is x1 plus x2 plus, et cetera, plus xk minus 1 that's plus to k minus 1 to the power of k. Greater or equal. Now, if I will raise to the power of k these guys, the powers are multiplying. So that will be x1, x2, xk minus 1, 1 over k to the power of k will be 1. So it will be just this. And same thing here. 1 over k to the power of k will be the same thing. And now I can obviously reduce by this number. I will put this and k minus 1 here, right? That's the reduction. And this is basically the end of the proof because now we will just have the k minus 1's root from both sides of the equation of the equation and we will get what we want. Greater or equal k minus 1's root of their product. And that's what we have to prove. So, again, what we have done here, how to switch from assumption that it's true for n equals k to the proof that that would be true for n is equal to k minus 1. To k minus 1, original elements, I added the k's element, which is their arithmetic average. And since it doesn't change the whole arithmetic average, now we have k elements, original k minus 1 plus their arithmetic average. And I have applied the formula of the inequality for n equals k, which we have assumed is true. And then it's just pure arithmetic reduction power here, power there. That's just very simple. So that completes the proof of the whole theorem. Again, it's attributed to French mathematician Cauchy and it was actually very interesting theorem about this comparison between arithmetic and geometric averages of two sets of numbers. Now, there are many averages and by the way, in finance, if you're interested, all these averages are used quite substantially. Let me just talk a little bit about something which is called moving average. Now, moving average average is a concept very often used in the finance when you are analyzing stock market quotes or something like that. Here it is. If you have, let's say the value of Donald Johnson industrial for at the end of every day for a few years history. So you have date number one industrial average had the value of x1. Day number two it has the value of x2, etc. Day, I don't know, 3,000, that's it. And industrial had x3,000. What is moving average? Moving average is the following. If this is today, date number 3,000. What we can say is okay, what's the average of Donald Johnson industrial during the last 100 days? Well, you should really add together x3,000 plus 2,999, 2,998, etc. So you go backwards by whatever number of days I decided to have my average, let's say it's by 100 days. So this would be 2,9001. So x2,901. So we are averaging these numbers.  This is an average of the last 100 days as of today. Okay, great. What was it yesterday? Well yesterday I had to add from x2,900 to x2,999. Yesterday it was 2,999 and 100 days before it was this. So this constitute y2,999 of 100 days. So for every day for today, which is 3,000, or yesterday, which is 2,999, or the day before, which was 2,999, 8, we can have the average of the previous 100 days. Now these numbers constitute another sequence. It's the sequence of averages. So if x were sequence of values, y is sequence of their moving averages, where average is calculated always for the last 100 days. So that's basically something which again financial specialists are using every day to analyze how certain indices or certain stocks or certain markets, whatever, currencies for instance, exchange rates, how they behave. What do they accomplish? Well obviously every individual day can represent certain hectic movement, up, down, etc. But if you're averaging throughout let's say 100 days or something like that, you are smoothing the curve. So if originally a daily graph would be something like this, your moving average graph would be much more smoother something like this. And it represents bigger ways, so to speak. If these are daily ways then averaging by the last whatever, 5, 10, or 100 days you are smoothing out all these daily fluctuations and only the bigger waves are actually staying in this particular graph. So just one of the examples of how averages are used in finance obviously they're used everywhere for statistical purposes, etc. But again what's interesting is that even in finance if you are saying which average, arithmetic average, or geometric average, and there are other averages like quadratic average for instance which we might actually have another problem about. So all these are important and as you see if you use arithmetic average it's always greater or equal than geometric average. Okay that completes for this problem for today. There is one interesting detail that I would like to mention for those who are interested in these arithmetic averages or geometric averages. This inequality which we have, that arithmetic average is always greater or equal than geometric average, I said it's always greater or equal. Now the question is when is it greater or when is it equal? Well, interesting point is that if you take only two now obviously the equal sign will be if they are equal to itself. If both are the same x plus x divided by 2 will be x, x times x will be x square and the root will be again x. So if x1 is equal to x2 this is equality and the interesting thing is that for any number of elements, equality will only be in case when they are all equal to each other. And I'm not going to prove that try to prove it yourself that's an interesting problem. Thank you very much, enjoy it.


Pardon me while I get everything situated real quick. I hope you're all having an awesome today. It's a Tuesday. Yeah Live and it's early Two o'clock Tuesdays. I am late, but So vamp is moderating today She's all the way over there. I don't think that you guys will be able to hear her From here, so she'll just let me know if you guys have a question for me versus something she can easily answer for you guys also, Bowie is Very invested in the inside of her elbow He's so funny. He likes the fan blowing right in his face, but Someone blows in his face So you guys I'm still Pretty obsessed with this piece from yesterday, so I'm gonna do a large geode With these colors and I'm very pumped about it. There's people looking at the colors so We're gonna do more that and I hope you liked yesterday's video I'm gonna talk you through my entire Process and show you everything that I'm gonna use to make this piece And my plan is for it to take less than an hour cuz I haven't sent out one order today We'll see if that actually happens though That's not even I could do it. I can I can do an 18 by 36 geode in less than an hour In theory We'll see. No, no My head is possible You know like for IRL Pardon me. I just had to step over and grab almond What's up friends? Just trying to see if there's any other colors. I want to grab and I don't think so. All right I do have to grab cuz I'm prepared Tg. Did they confused emoji? Yeah, I don't know So if you guys are new welcome. Hi, I'm Erica Jeff is off cutting clear shapes of things for our shop And Vamps here moderating. I am planning on doing a messy style Hey, Claire, how you doing? I think I'm gonna see Claire later this week So we go live every day usually at 6 p.m. Central except for on Tuesdays. It's 2 p.m. Central and It's always art. It's usually resin but sometimes it's alcohol ink sometimes acrylic sometimes spray paint sometimes glitter It's usually resin today. It's resin So I'm just mixing up some stone coat art coat If you're using a shorter working time resin I wouldn't advise mixing up your resin first because it'll start to set up on you as soon as you mix your two parts together But since this is a two-hour working time. I can mix it up. So decide Do what I got to do Okay, so my first step is to Kind of map out the flow of my geode And to do this, I'm just gonna add my fire glass All the stuff I'm using today. You can get on my website artistledest.com. It even says so right here on my gloves Okay, so I think I think I'm gonna do I think I'm gonna do a corner of glass and then other glass so The reason I start with a glass is because if I don't like it I can just Scrape everything off and just start over without having resin on the glass That's possibly wasting the glass Once resin gets on something. It's hard to Get resin off of that something At least in my experience. Oh, no, maybe Some people out there figured it out. I Haven't so I'm gonna start this party by I think I want it to come upwards a little bit You know, you're welcome in Texas any time So I think I like that and then I'll add more You're here And then we'll do something else over here Hey, Judy So I'm using fourth inch. Nope. Yep Half inch Glass over here and then I'm using fourth inch glass in my other Little areas I'm not cold today So I'm just doing a thin line of thinner glass right here. Oh, I know I have my headphone in so It's gonna be kind of hard to hear vamp. I don't want I'm Just a straight line Wanted to have some character some movement And I'm gonna try to vary the thickness Sizzes of this Don't want everything to be uniform at all because nothing in nature. It's perfect I think that looks fun and now You have to do something on this other side for balance. So I think In terms of balance, I'm gonna put Tiffany up Thank you So I'm pouring on a an 18 by 36 cradle board Which means it's it's a canvas board but since it's not Exactly canvas. Well, it's not even almost anything like canvas Zero percent like canvas and except for the fact that you can paint on it Yeah, it's zero like canvas except for you can paint on it. It's an 18 by 36 and they're available in the shop Right. I think I like think I like what we got going on right here. So we're good with the glass At least for now Sorry about all that ruckus I have windows open for ventilation You remember how much I mix this up before starting the live feed. So I'm just gonna do this for in Momento Thank you, Clara Hi, this is an 18 by 36 cradle board So now what I'm gonna do is start mixing up my colored resin I'm just gonna mix them in these smaller cups because it never fails that I have Too much of one color and not enough of another color So I'm just gonna start out in these smaller cups And then we'll just make more of whatever color we need Because I know that I'm gonna need at least this much of most colors first color probably gonna be one of the main colors is gonna be Just resins Turquoise luster And I'm hoping I have enough in here. Yeah, I'll be fine This is a very shimmery Turquoise I was trying to find another word for turquoise But turquoise just suits it because that's its name So what I really love about the paste as opposed to Micas or acrylic paints is that they melt into their resins so easily They're so pigmented. So you don't even need that much and I don't really have to worry about Putting too much pigment And setting off my resin too soon Because it's made for resin That is just a delicious color Okay Next color is going to be seafoam by resin art This Looks like a powder kind of but it looks more like coffee grounds to me This is a dry paste And I always overload my powders Just because I don't want it to be translucent. I want to have very Pigmented color and it looked like those particles wouldn't melt in like they do but It takes almost no effort for those dry pastes to melt into resin Again, you can get all of these colors on my website artisttillthat.com This color has An awesome sparkle to it. Okay Now I'm going to mix up a copper and this copper I use yesterday. It is called intense copper The name suits it. I hope you feel better soon and all the procedures do well Megan Talking about what?  Let me tell you I'm not a big fan of orange But this as a color that's akin to orange. I have more so called this like an electric Sienna or It is very intense copper All right Um a color that I did not use yesterday that I'm gonna go ahead and mix up is almond Because I just want a dark chocolatey I don't see myself using More than what's in this cup if I even use The amount that I am mixing up right now Thank you, Angela Evelyn's leaving Bye Evelyn freedom Hope your freedom goes well And the last color I'm mixing up is Snow white from color obsession If I can get this lid off I agree tg almond is an awesome color I'm trying not to get the almond that's still on my fingers Into this snow white because that would be not fun This is a very pure super ultra pigmented flat white It's thinner than the just resin white But it still does awesome and amazing things When I do faux finishes, I like to have a translucent white and an opaque white, but Right now today right now I'm going for absolutely opaque Thank you 755 I'm also going to mix in a little bit of the base tint from Color passion This is got some kind of magic in it Don't ask me what it is That's in it because I have no idea If I knew y'all know I would tell you But whatever it is that's in it Creates a different effect In resin Than any other pigment that I've put in resin that was Color obsession white I know I usually use titanium Snow white is not out pretty sure We updated that inventory yesterday, but I could be wrong In this moment. I'm not sure However, I know that speaking of products That are just in-house. I don't know what it says in the system now. I'm second guessing myself. So we have it Okay, so we got our white now First thing I'm going to do is put some clear resin Over my fire glass. This is going to do two things. It's going to help On my fire glass to my surface And it's going to help with my glitter glass sticking to the fire glass Glitter glass are going to put on glass I feel like I'm icing a toaster strudel You don't want to put too much here because it will push all your Other colors of resin outward So you just want a little bit The rest of your resin will start to fill in some right See this potty started I think first one I'm going to add is going to be the seafoam Yeah, I felt like I was icing a toaster strudel a second ago Hello Tim So now that I have that color down I'm just going to push it inward just a bit You'll use less resin this way And you won't risk your resin Blowing off your substrate quite so easily Really in the whisperer is vamp Also, it's not so much whispering. She's just a little bit away from Where I am and the earpiece that I'm using I'm just trying to shape my color This will be what I follow for the subsequent colors I always kind of do little peaks But it's a geode it can be whatever you want it to be Go home and what? Oh art So the next color I'm going to add is the Turquoise luster from just resin The center glass is fourth inch and the This ring of glass is I'm sorry the center glass is Half inch and the outside is fourth inch So I'm just pushing up the resin the first color of resin that I have down Trying to thin out the lines of resin because If I just poured directly on it would be too thick Y'all aren't missing anything vamp saying I'm repeating everything so you guys can know what she's saying Since resin self levels I can kind of push The resin around and it'll just fill in Thank you deal stewart. I appreciate that right What do you guys think a copper line an almond line? Or a white well, that's Too many colors. Yeah, I'm going to put a line of white. I think separating the two greens I'm going to use the copper because this is a darker teal. All right just as before I'm just going to move Resin around a little bit doesn't have to be perfect. It will self level What's up nj? These areas is just going to be quicker if I just use enough finger sorry Sorry if my fingers being vulgar It's just my longest apparently most dexterous appendage At the moment. I am very excited that you're feeling better mj Beautiful beautiful. All right meow Think I'm gonna do I'm gonna mix up some Thornton shimmer There that was not the intent Just happened.  It's Definitely very unique Which is important in such a Big market. This is a super dark turquoise. It's very similar to Blue diamonds from just resin I think appetite blue from lores So I'm actually not gonna put this right here. I'm gonna use a different color Let's do chocolate Nope almond. We probably end up putting more clear through This fire glass So filling it in with the chocolate isn't nope almond isn't that important Hey, george. How is your day going? Mj. We're just glad you're feeling better Super love that resin self levels It would be a whole pain if it didn't Kelly let us know How it goes and if you have any questions Okay See foam I don't have to mix more resin I started with 20 ounces which should be Enough I'm pretty sure it'll be enough. I'm just saying Just trying to match these lines up without Full ridder huffing I haven't but vamp has I think claire So joella Um, did you have a question about it because I'm sure someone here can answer it Remember scarlet did Scarlet's channel is called display of color I'm sure if she's done it she did a video She has on a checkout vamp's instagram. She has A lot of her skulls up there that have Ink dye glass I think the thing that trips up so many people when they do geodes is They're looking for perfection And it's just not that serious There's so much beauty and imperfection in my opinion You could drop ink like that, but you're going to get a regular color If you want a consistent color across the board, that's not going to be the way to do it Because still look really awesome though Joe said what? I'm glad you got it joe I'm going to see what you do with it All right, I'm trying to find a clean finger to move colors Just taking a little bit too long with that cute little stick that I would do them And I don't mind sticky fingers I would be instructing you guys through all this, but it's pretty repetitive Have you all ever done a geode? Also, what's the prettiest color geode you've ever seen?  I was like, what is the jewel tone pink? I would say and with this sapphire ruby If you guys ever Get some other color in To another color don't stress out about it We're about to do a whole bunch of manipulation And it's not going to be obvious for a long you can see this the resin kind of invading the glass It's turning a different color What? Oh, yeah, looks good. I know you guys are giving me so many good ideas That now joe you've been super busy. I thought I was busy Tammy always makes pretty things. She rocks. I only poured just right over that star stick All right, you got a lot of coloring in to do right here That's okay Well, thank you I do pieces this size. I almost feel like I should time lapse them instead Because it's just such a repetitive situation. I'm like, I don't know if you guys want to hear me say I just push the resin around with my finger until it's where I want it over and over However I love going live with you guys So I appreciate everyone that sticks around See how things turn out also Do you guys do mostly black fridays shopping or pre black friday? Maybe if you do pre black friday shopping I'm trying to decide if I should do a pre black friday sale on the shop or Just a black friday sale That is what I was thinking, but I just didn't know if Everyone else shop pre black friday like I prefer So I wanted to get you all opinions Aw, thank you watch out Judy only has eight cases left Is it ornament? So if you guys are trying to get those glass ornaments that I did the other day Well online black friday I can't remember the last time I went into a store for black friday. I think I was in college Two more cases down judy Those things are so fun to make Yeah, I don't do in-store black friday I'm gonna do my groceries in store. So what would I do? Christmas stuff Well, that was like 20 minutes ago Now you're talking about doing resin ornaments Pretty sure I did that Last year the year before And it's all right if you can keep them rotating like on a tumbler turner That's still a fad or people still doing the tumblers So close I'm willing to bet this little corner Fully flows off once this piece starts to settle, but There we go. Yeah a minute All right, I'm gonna take My concentrate on nozzles. Yeah, I got it trying to follow The line that I already have on If I were to let this resin set up So maybe an hour I would be able to stretch this line The whole length do it you can do it So I want to add You're gonna do a darker. Nope A thicker white right here Then blow that this part out Hello, John Thanks you guys Once your surface is full Like mine is Every time you add resin it's gonna push And redistribute your resin so keep that in mind Knowing that I'm about to manipulate it with heat and air and a bunch of stuff I'm not concerned But if I like the way everything looks What I've thought twice about adding those colors that I just did I'm just popping bubbles right now Make sure I'm having a little floater See guys Now I thought I was gonna blow The turquoise over the copper, but I think I'm gonna blow the copper over the turquoise I'm using a concentrator nozzle You get on my website artistislet.com I'm using a concentrator nozzle. It's gonna give me those little ripples I use this when I do ocean quite often Like that I'm trying to match it just lightly on both sides. I'm gonna push this side in That's starting shimmer, but I did put a thin line of the luster down, but I don't think you can see it That looks fun Thank you, sherry All this awesome movement kind of the magic of using Some transparency colors or colors that may end up transparent All right Now I need to do other magical things I usually only do one area or one color with this otherwise you're going to get real busy I might Do that out here actually Just for a balance sake You want to do a piece for your husband's firehouse in black white and gray And black red and gray black red and gray A little white. Oh, what was the actual question? Marvel is always classic for a male's space more geode So now that I know I'm gonna have this much extra of the clear. I'm gonna go ahead and apply it Into any areas that didn't get present on it But I'm not just going to dump everything on here because As you add resin it's going to push outward. I'll I'll show you a little Demo of what that looks like in just a moment Sapphire pollution or is an awesome color You know, there's so much I haven't gotten to quite yet on this one No, you don't always have to add glitter to geodes. In fact, I Can't really remember the last time I added actual glitter to a geode. I know I just got you guys situated, but Follow me down here see this lighter area and this trail right here. That's where I accidentally dripped clear and this These bulbs coming out That's where the clear is pushing outwards Which is fine just know that that's What's causing that and if you don't like it You can avoid it by being mindful of how much resin you're putting down but Sorry about some of the motion in Not quite the ocean, but kind of the ocean Right. I'm gonna add a thin brown line to separate these two teals I should add a what? Add oak lawn So I'm not going to add oak lawn because It wouldn't lay flat so it's not going to give the look that we like about oak lawn However, that's a good suggestion Okay, I'm gonna put a white Just on the inside of this I don't know why I like that look but I do Bye tg. Love you. I'm gonna put some of this See foam through the white Susan oak lawn is our newest glitter. It's A rainbow glitter that is Magical and it lays in A perfect rainbow. I don't know how I don't know what kind of Weird magic it is. It's actually a powder glitter You could probably use it as makeup I haven't read the sds on it. So Don't go wearing it until you wear the nope till you read sds right Let's start adding some of our liquid copper This stuff is by Montana. It's like this You should try geode. I have all the faiths in you So you could add oak lawn I mean you could add oak lawn now, but once the geode cures I could go in and add Some sticky pin and oak lawn and I don't know if oak lawn would work under a flood But I also don't see why not So I'm trying to get some of the propellant to soak into this cup. You can I don't know if you guys can see Out here Can you see how the cup's turning yellow? That's the propellant soaking into the cup I don't have it on the inside of the cup because most cups are like wax line So it's not going to absorb but see that dark Wait and try to get it to come back out that dark when it breaks Just know that it's in there damn says it would probably work and I'm willing to believe that she's probably right because she uses Yeah, something similar on nails So this I just did a roadside test which for me is just testing it on some of this overflow resin And it's not really blooming anymore. So I'm going to go ahead and Start applying it where I want it I'm going to run a line right here. I almost always use some kind of floating metallic It just adds another dimension Today's a tumbler is like a yeti cup Yeah, I vamp has one with her and She's on her way to show you with tumblers right that one's not decorated but um, you can get tumblers spinners And you can put resin on them It's a thing Kelly floating metallics are everything I have silver and gold available for like 10 mils for five dollars on my website If you want to just try them out before you invest in the big bottles I'm trying to wipe off my applicator or stir stick before I go back in for more of the floating pigment because you'll end up mixing Resin into your pigment and that will change the color of it. It'll dull it just a little bit They try to wipe it off every time Yeah, boy cat just walked through I'm sure he is He likes to walk on the wild side He went that way All right, I think I'm going to drop some on the center because it's a little bit light and then probably a little bit down our sides Because I'm thinking I want to put some through here However, if we're going to drop it on that may take away my Like what I'm seeing for that area. Hi, buddy. Don't come over here. I sticky hands Always like is it my turn to be on this show yet or no? I have to grab a pipette real quick Stay bowie a pipette Adam before you use The Montana series anything Shake it up really well because the stuff settles super quick. I did that yesterday I put a drop everywhere Now that's there It's gonna have to be happy accident because I can't get upset about it resin's gonna resin As long as it doesn't bloom too bad, it'll be fine Over here where I'm being like I'm already over it The area It's like no, I'm not gonna do that over here I will I just have to Read the room in a minute and see where we want to add it Oh, yeah, there's no accident to my artwork if it's on there meant to right right Should I leave that hollow or May just leave it as is and then balance it, but we'll see in a minute I know some of this is gonna bloom out and we're gonna have to address that but We will Waiting for his perfect moment to jump in the resin All right Just fix this little bloom that right here Oh, I guess it is It's a lot more subdued well That's a dude Oh, I can see it from here. Yeah It's very Miami Dolphin. So if you guys can see these Little gear looking floral Situations, that's what I'm talking about blooming. If you like that Then that is awesome Not a fan personally. So I'm just going to Before it dries Just gonna run a stick through them. I will accept gorgeous or I was looking about All right Now Let me see what we're gonna do to fix That I don't know that glitter glass will fix this Break it up some Put some more almond over it You want to know if what can be port and mold? I wouldn't just Fill a mold with art coat because it's not gonna off gas for you. You'll have a lot of bubbles So what I recommend doing is It's gonna have to be layers or casting epoxy unless you have a pressure pot and none of that matters And you'll be just fine. All right, I'm gonna hit it with heat again. See if there's anything I need to pull out of it not trying to move anything at this point because that Copper that we added It's not gonna want to move And if it does it'll kind of break apart and it won't look that pretty They're all under and I know it's kind of top bubble So the G-Lade has a pretty complexion I'm gonna get a pressure pot one day just because I want to be able to Answer people's questions. So pressure pot is basically a little chamber that by Clara that Squeezes all that air And air bubbles out of a piece. That's the short very simple version I'm not sure why I thought it that needed to happen but It felt like it was getting a little bit I do need to I do not but you can get the casting epoxy from stonecoat countertops.com Use code y'all I'm adding some little extra dollops Do you just say you ordered the small for me and you want to know where to get it? I had a call So for fireglass I have two sizes I have that Yeah So you when you're looking for something smaller than what you got from me If you got the small from me, then you got this size And that's a quarter inch then I also have the half inch And then glare glass which is Super small So casting epoxy actually takes forever to cure I want to say that You have a pretty long working time It also is brand Sensitive so some brands have a longer or shorter working time Now it's time to add one of my favorite things and that's glitter glass There's always time for glitter glass. There's always a need for glitter glass It's very fine Can be pretty sharp shards A tea tiny baby glass and it Reflects and looks so pretty Clear glass is always an option because it's not actually glitter and you can't really see it till it sparkles It's just an awesome little accent to make things That are already sparkly even more softly The clear glitter glass you cannot put under Resin keep that in mind if you're going to do multiple layer Geodes or artwork or whatever The glitter glass needs to be in your final layer because it's clear.  I wouldn't tell me sweet perfect All right, so, uh, let me get you guys down Hello, shilly Let's show up as a first layer on a clear substrate the glitter glass So if it's the color glitter glass Yes If it's a clear Then it's just gonna disappear I made a rhyme Yeah, it is the same color as yesterday's video Because I just wanted to investigate it a little bit more Thank you for talking Glitter glass is bomb. Look at that. I'm just gonna go fast so it sparkles better So you can see those shards floating so extra splatters of the gold or the copper to balance out this This takes happen. So you just got to make them work, you know Ask Petra. She does geos all the time also these are actually like Die-high socks that have just a lounged on me That's fine Anyways, I will do a true color video of this piece and post it in ATD's port people So you guys can see What's up And I hope you like it. Just let me know what you guys think Leave me a comment. Thank you red epoxy art I hope you give it a shot. It took me 84 minutes. I did not meet my one hour situation Goal, but Our 24 minutes isn't bad either So give it a shot. Let me know how it turns out And There's been bobo Bobo, what do you do boy? I'm camera. Oh boi. They're on camera over here over here. Oh, but Boi Hi, baby I'm the babe. I have I have a glove on boi. Hold on. Thank you I agree Does make it look more organic. Come on.  Oh, I would love to see those Arlene. Thank you very much So, yeah, you guys rock for sticking with me and watching all of this And yeah, let me know if you give it a shot I'd love to see So yesterday's turned out Pretty nice You can find all of the products that I used on our website artistilldat.com And we'll see you guys tomorrow 6 p.m. Central And y'all are amazing forever and ever you kind of want another you never know what someone's going through and atv does the test Y'all are amazing. We love you. Bye Oh, you say bye.  Yeah, you said bye


Hello, you're watching Dispatches from India by People's Dispatch, where we bring you some of the major developments in the country, what Indians are talking about, and the impact it will have in the coming weeks and months. We begin with our News This Week section. In our first tour, Indian Prime Minister Narendra Modi inaugurated a Jaivar Airport project on November 25th. Jaivar is the district in the state of Uttar Pradesh, which is going into assembly elections in February 2022. In the first phase of land acquisition for the airport construction, the government acquired nearly 1,327 hectares of land, of which 1,240 hectares were acquired from eight villages in the district. It was reported that nearly 4,000 families were affected in the first phase, having been rendered homeless with no aid or assistance by the government. Recently, in the second phase of land acquisition for the project, 1,344 hectares was acquired from six villages. The land belonged to local farmers who were extremely unhappy with the development, as they say they have not been provided adequate accommodation or compensation. The per square meter rate for rural land is nearly twice that of what it is for urban land. Though Jaivar is classified as a rural area, farmers alleged that the government has termed it urban area on technical grounds and compensated them accordingly. Farmers have been protesting for many days, demanding fair compensation. Here is a ground report. Ajay and his brother Pramod had to leave his land. They are still fighting for it in the court. The government and the officials are aware that the way they have treated us, they have been threatened and insulted by us. In 18, 17, and 9, it is written that each person is insulted by the videographer. So, when the insult has not happened in the first phase, it has automatically ended. All the cases have ended. In fact, these people have lost their jobs. The people who have lost their jobs in the first phase have lost their jobs in the second phase. When our jobs are done here, we will not be able to move forward. We need all the facilities. First of all, we need the documents from these people. The government is deceiving everyone. There is no one to speak ill of anyone. Their work is done. Then they do not talk to anyone. This is the biggest problem that our government is facing. We are being told that something is going on and something is happening with us. And the biggest thing is that the land that is being taken from us, we will not be able to move forward. The entire village will not be able to move forward. We did not start the airport earlier. We are not doing it today. We want to become an airport. But the government has said in the beginning that it will be very difficult to become an airport. But now it seems that it can be difficult for the government to become an airport. But we are going to be disappointed. In the next story, security forces in the union territory of Jammu and Kashmir shot and killed three youth on the night of December 30th last year. The families of 17-year-old Atar, 24-year-old Ajaz and 22-year-old Zubair claimed that the boys had no connection whatsoever with militant groups and were falsely charged and killed. Massive protests began in the valley the next day with the demands that the security forces be held accountable, the boys be exonerated and the bodies be returned to their families. It has been one year since the incident but the families still wait for their children's bodies. Our reporter spoke with the father of one of the victims. Here's a ground report. What was your son like? How did he get interrogated and first killed in two hours? Then his dead body was thrown down from above. Ask us about this. I go there today on the cover that I have dug up with my own hands. I am waiting for my son. I will keep it open until I am alive.  We now move to our in-focus section where we take a detailed look at some issues. Last week we had reported on a major controversy that broke out after a Hindu right-wing religious conclave was held from December 17th to 19th. The event took place in the city of Haridwar in the state of Uttarakhand. At this event, speaker after speaker spewed venom against minorities, especially Muslims. There were even calls for genocide. The police filed a first information report after the incident but so far no one has been arrested. Meanwhile, some of the participants went to the police to file a complaint against Muslim clerics and they alleged that they have been conspiring against Hindus and so should be punished. After the conclave, the Communist Party of India Marxist has said that the speeches were akin to supporting terrorist acts. It called for the immediate arrest of those responsible for the promotion of not just hate speech but also incitement to violence. We spoke with Communist Party of India Marxist Politburo member Subhashni Ali on the issue. This is what she has to say. It is extremely disturbing and horrifying videos that have become very viral after that so-called dharma censor. Actually it was an adharma censor. But at some other time or some other point in our history, they could have been just dismissed as ravings of lunatics and madmen not worth paying attention to. But because they are happening in a particular context where the government follows a certain ideology, the government is directed by the RSS which follows a certain ideology, which has been talking about the establishment of a Hindu Raj which preaches against hatred of minorities. And it has also happened at a time when there have been increasing numbers of attacks on minorities, both Muslims and Christians. It is at this particular time that this becomes so dangerous and something that needs intervention, that needs action. All the laws do not permit this kind of hate speech. The constitution doesn't permit this kind of call to genocide. I would also like to say that inciting children to violence. This is not about teaching children self-defense or asking them to learn to protect themselves. This is inciting children to violence and violence against people whom they don't know who have not harmed them, who are to be attacked only because they belong to a particular religious group. This is just atrocious. All over the world we are seeing what this kind of training in violent acts does. You have people who have easy access to guns, committing crimes that are just spiralling all over the world. Similarly in our country where we do have very strict gun laws, where people are not supposed to be using and brandishing weapons, this kind of incitement to violence in children, telling them that attacking people who belong to another religion is something good, something heroic and something that should do, is just absolutely atrocious. It cannot be acceptable. It has to be stopped. And those perpetrating this kind of violence must be punished with the full might of the law. And finally India has seen a tumultuous 2021. On the one hand the farmers agitation had a dramatic impact on the country. The victory of the farmers in their struggle against three controversial laws will have a massive impact in the years to come. On the other hand many observers have pointed out that there is a major decline in the democratic space in the country, with critics of the government being hounded or even jailed. The country also saw a horrific wave of the pandemic in April. Pranjil from Newsclick analyzes the year that was for India. Year 2021 has been a year of ups and downs vis-a-vis Indian subcontinent. The country saw massive farmers agitation, but we also witnessed thousands of people dying because of COVID. The economy is in crisis and the democratic spaces are shrinking day by day. There have been a lot of attacks which have taken place on media houses. They have been raided continuously, one being Danik Bhaskar which is one of the biggest Hindi media organizations of the country. Then we also saw massive crackdown on students' protests and continuously bills being bulldozed by the parliament without any discussion. The situation has come to such that even 11 member of the parliaments were suspended for raising people's issues in the parliament. And the government has remained silent on all of these and in most of these cases they have given tacit support to such moves. Economy has seen a lot of crisis. There has been joblessnessness. The unemployment has increased many fold and the no creation of jobs is taking place. One must remember when the Modi government came to power, they had promised 20 million new jobs, but they have completely failed to deliver any of these. And especially because of the COVID lockdowns, unplanned COVID lockdowns. The government comes, prime minister comes on the TV screens, announces lockdown all of sudden and people have to migrate from cities to their rural areas. The industries have remained shut and people have not got any work to do. Even when we see one of the major schemes which provides rural employment, the funding in those schemes have also been cut down. And as a result, there are also no jobs in the government schemes. The youth is unemployed, the workers are unemployed and the economy, the prices of commodities are going up day by day. Even petrol and diesel are being sold at 100 rupees per litre. And the government has not done anything to curb either the inflation or unemployment or has continuously taken space to make sure that the voices of dissent are crushed on day to day basis. Apart from that, the country also witnessed massive COVID surge in form of second wave and also parallely the massive COVID mismanagement. People could be found posting SOS messages on Twitter, SOS messages on telegram groups, asking for oxygen cylinders and hospital beds. One can't forget the visuals of dead bodies being buried on river banks uncovered and which were witnessed found later. So the government has basically failed on all these fronts, especially when it comes to controlling COVID. But all has not been low in this year. The country has also witnessed massive resistance in form of farmer's irritation. The farmer's irritation which began in year 2020 had gained pace by 2021. Thousands of farmers had gathered on Delhi borders asking for repeal of three farm laws, repeal of electricity amendment bill and a minimum support price should be guaranteed. In the end, the government had to give up on these demands and they had to take back these three laws. This farmer's irritation also witnessed massive, massive support from all sections of the society. The trade unions, the women organizations, the student organizations and seven society groups came together and stood in solidarity with the farmers' irritation. Not just that, the workers' organizations trade unions have been continuously on the streets opposing the four labor codes which are anti-worker. Then the students have been fighting against new education policy and a lot of such things have been happening. We have seen massive resistance of defence employees who are talking against the privatization. The bank employees who are talking against the privatization and hopefully in year 2022 these struggles are going to be intensified day by day and these battles will be won. That's all we have time for today. We will be back next year with more news from India. Until then, keep watching People's Dispatch.