In this second part we're going to discover how to work out whether a number is in a sequence or not. In part 1 we looked at how to find the nth term rule, how to generate a sequence from the nth term rule and how to find any term in a sequence. How do we answer this question? 7.30 isn't the term so we can't put it in place of the n. We have to make the nth term rule equal to 730. Is 730 in this sequence? Then we just solve the equation. Because n has come out as a decimal it means 730 is not in the sequence. Whereas for this question, because 65 is a whole number it means 265 is in the sequence. 265 is a 65th term in this sequence. So here are a couple of questions for you to do. Pause the video, answer them and click play when you're ready. How did you get on? And that's everything you need to know about arithmetic sequences. You can find the nth term rule you can generate a sequence from the nth term rule and you can find any term in a sequence. You can also work out if a number is in the sequence or not. If it's a whole number then it is. If it's a decimal it isn't. If you have any questions please comment below. I'm here to help. Please like and share our videos with your friends.


Today I have the pleasure of speaking with Jack Lifton. How are you today Jack? I'm pretty good Tracy. Thank you. Jack, there's a lot of buzz on lithium-ion batteries on investor Intel. Can you tell us what the catalyst for this is? Yeah, what's happening is that the American car makers are finally stepping up to the mass production of lithium-ion battery-powered electric cars. GM, the Detroit intergalactic auto show starts I guess the next couple of days and we still call it international even though nobody else does and GM is introducing the Chevrolet Bolt. It's 200 mile range electric car which which goes on sale this year at the end of the year as a 2017 for $30,000 including your government kickback on tax breaks. So it's really cheap and it's good timing for them in the in the market because Tesla's having a problem bringing their low-cost car into production. So Ford's got a huge program which at the Consumer Electronics Show the other day in Las Vegas, their current president Mark Fields announced a huge electrification program and self-driving cars and all that stuff and on top of that the Chinese five-year plan coming out in March for the next five years. Mandates a switch to to electric propulsion for cars to reduce pollution in the large cities and the Chinese are actually targeting five million units a year by 2020. Now these are the drivers for for the interest in lithium-ion batteries. That's what's going on here. These very large scale applications and at the very least you're looking at millions of cars being made by by the end of this decade with using lithium-ion batteries and I know that the companies here in Detroit there are we have several lithium-ion battery companies are very active right now. Now to contrast this or on the other side of the coin the national newspapers like the Washington pollster saying well the the electric car is another flop it didn't work and all that and what I found in in my life is that whenever the national newspapers and I say say something isn't happening it's for sure happening and if they say tomorrow's weather is great I'm getting my overcoat. They're always wrong and they're consistent in that. I think that this is we finally hit this is going to be a very good period for for lithium batteries. Okay, so what I hear you saying is that the real demand is from China for lithium-ion batteries and I think you told me that the driver is going to be once again you know China for this market and that this industry is going to in essence mirror what happened with the rare earth industry. Can you kind of comment on this a little further? Well, I I don't think we're going to have the silly season here with lithium. Lithium is basically one item and its costs are very well known it's it today it's it's very low price however in my opinion we're going to run into a deficit of this material in the very near term because in fact as I as I mentioned it's not just China it's United States also which is the world's third largest car market after Europe and then and first is China is now Going full steam ahead into electric car production. I want to point out something people Investors in particular do not seem to understand inertia. It takes a long time to design a car and Once the design is fixed You're three you've got three years to source the parts and you source everything People who think that because there's some discovery in a laboratory this afternoon It's going to change the world of manufacturing are completely inexperienced Things are set. They're going to make a lot of lithium-ion battery Powered cars in the next for the rest of this decade Whether they whether they want to or not the parts have been sourced the the factories have been scheduled They're done years in advance the Chinese are doing the same thing. It's momentum here now getting back to price All right, lithium to I don't know what the current price of lithium is last time I looked it was six or seven dollars a kilo It's got to go higher because we're already at the limit of how many of these batteries we can make and Another thing there is no public company I'm aware of that's recycling lithium-ion batteries to recover the lithium the electrolytes the cobalt, etc This is going to be look for those companies because we're woefully short of that And one of the things you lithium-ion batteries are not difficult Chemically to to recycle. They're a little dangerous Be much more dangerous than than then then let's say recycling lead acid batteries Because of the fire hazard. So you've got to know what you're doing. This is going to be another market I expect to see companies popping up now that are that are recycling lithium-ion batteries So we're looking at I'm looking at the whole supply chain. What's missing? Well, we have a little bit of lithium production in the United States note that not anywhere near enough for our own industries projected production So something's got to give because the Chinese like as they are chasing rare earth companies are chasing lithium companies They're all over the place and when when a Chinese company buys a lithium producer or a junior that they think will be a Producer that material is for the whole market. They are short also So it's going it's going to be a race. There's don't anybody bid lithium up to the price of gold It isn't gold or maybe maybe today who knows with gold, but Lithium is a is going to be a very active market, right? Starting now and for the next five years, we'll see if the public likes these cars You're they're going to be offered Dozens of models and millions of units Okay, well fantastic. Jack. You've just answered my next two questions So I have one more for you, but I want to read this because it's it's very specific and we're notes from a conversation that we had earlier Since the Chinese will be putting a major push for lithium-ion batteries and that their interest is really to benefit China Okay, we hear you What should the US be doing because I've heard on the grapevine for instance said the Department of Defense wants the US to be Self-sufficient in titanium. Okay, for instance, can you comment on this and of course? Yeah As John Peterson my my new colleague and investor Intel pointed out the lithium titanate the electrode Which is called lithium titanate for for lithium-ion batteries. It gives you maybe the best performance at least Laboratory-wise it's it's not the cheapest one and it's it's not the one with the the highest power But it's it's very good because it gives you a long live battery I Happened to know a company right here in Detroit lithium-ion battery company that is now switching over to the titanate electrode Well again, we don't produce titanium metal in the United States We import all of it from you know our Sort of sometimes friends the Russians and even the Chinese are importing from them There is a push on to source titanium in the United States domestically or at least from a friendlier place than Russia so One of the drivers is the need for it in batteries But the other driver is the use of titanium structural alloys and aircraft missiles And and strong lightweight construction if we had titanium freely available You you would see a lot of civilian uses bridge Reinforcement buildings things like that, but titanium today is strictly an imported material and this I think will change I know I know personally of several nano technology companies that are looking at titanium To make as a pot to produce titanium powder for 3d printing and this is another push It's called the additive issue in the Defense Department is is Absolutely nuts for additives of high-strength titanium Even some steel alloys aluminum to be printed so parts to be print, you know It was a fantasy a generation of science fiction now. It's real. I Understand that they're designing a system to be taken to the moon and print all the parts for Needed by a lunar colony now.  I your age, but today I'm thinking it's real Okay, I've seen some things that surprise me. So it titanium lithium These are these are hot Topics right now in in in the world and in particular in the United States where we don't produce enough enough lithium Or as far as I know any titanium we have titanium all over the place or but we don't produce the metal this it's it's a chemical issue which I Advise look on Wikipedia. You'll see the problem. Okay, but It's a future it's definitely the future it's it's here Speaking of the future in about a hundred and twenty days We're you're gonna be in Toronto for the clean tech and technology metals summit And we're gonna be talking about this in in upcoming interviews But with regards to the lithium ion batteries and any of the technology metals required to make these I'm trying to Determine and of course you will be assisting like you did last time on the topics and the panels Whether or not this is the clean tech or the technology metals day Which which which day are we gonna have this discussion or both? Well, I think the public understands clean tech and and they don't seem to understand technology technology metals explanations require a bit of physics and chemistry and and you know that that usually borers people Clean techs easy to understand the technology. That's that pollutes less than the one being used now That's clean tech. I would go with clean tech crazy Well, thank you so much Jack, and I hope you have a great day. Thank you


Good morning everybody. We're starting off another week here. We're headed off to Kanora again. Nice little rounder. I don't know if it's gonna be a rounder yet. I don't know where I'm going after I deliver, but taking the usual load from Kanora down to Brainer to get the week started We'll see where the ball rolls from there. So let's get all blue loaded up I need to go grab a step deck trailer or a flat preferably a step, but either one will work Let me go grab a trailer and zip on over there Trailer 125d for drop deck So when we're married to right now Well, I'm married to Britt. My truck is married to 125d right now Hopefully they stay married all week. I just greased my fifth wheel underneath there and That's what trailers all my grease goes to someone else. That's half my grease. It stays on the trailer, right? Half it stays on the fifth wheel some of it stays on the trailer I just like to keep the same trailer as much as possible. I would like to have it that I always have the same trailer Always man, I'd polish that thing up. I keep it clean. It would always always be married to my truck then, right? But we do a lot of dropping hooks. I'll drop an empty trailer. It'll get loaded. I'll grab a different loaded trailer That's why I don't own my own trailer do a lot of dropping hooks And if I had my own trailer would limit the amount of loads I could pick up Because then I couldn't pick up a preloaded trailer I'd always have to go there and get my trailer loaded myself because I'm not gonna send someone else with my trailer So they could wreck it I have trust issues You're not gonna pull my equipment if it's my trailer. I can wreck it myself. Thank you very much So It is what it is I pulled their trailers No or Trailers that I don't own but it's my truck, right? So I'm contracted to move freight around on these trailers so Speaking of freight speaking of trailers speaking of trucks. Let's take this truck pulling this trailer Let's take it over to where our freight is in Kenora. It's sitting on the ground over there We want to take it off the ground put it on our trailer tie it down tarp it bring it down to Brainerd, Minnesota Where it's supposed to be Just in case you don't believe me Because you don't trust me.  This is that blasting zone again still blasts on away the rock Probably takes a lot of time I mean I'm guessing all right. There's a little sign person up ahead there. I gotta wait for them to Say it's time to go No one coming up behind me yet. So I have my four ways on just so that when they come around the corner They'll know we're stopped I can get down to Brainerd no problem, and we'll fuel up totally there Where the prices are a little bit better? I don't want to make sure I can get there no use waiting to fuel there if I'm gonna run out of fuel before I get there Line up will be on this side here already Dax You gotta be like 15 feet high petrol pass and do so along my route today Unless if I were to be able to wait all the way to Brainerd, but I don't think I've got enough fuel I've got just over between a third and half tank. So what is that like? Five eighths of a tank no three eighths or eight three eighths of a tank enough to get there in my opinion I'm not gonna risk it. It was a good drive down. We had some delays at the border though I always some issues with the paperwork getting cleared. So that cost me Over two and a half hours. So I didn't get here as early as I wanted to so I'm not gonna be able to get going as Early as I want to tomorrow. I was supposed to run back and grab another load before end of day tomorrow and now that's Might not happen. We'll see. I'll get out of here as fast as I can in the morning Like I said, I just have to unload around the corner around over there and We'll see what happens Hopefully I can still get there by end of day tomorrow. If not, maybe I'll have to pick it up the next day or Or I might go to someone else Hope not. So today's been a bit of a shorter day Another rush day. There's been a lot of these kind of days lately I'm tired now to that two and a half hour delay really Really upset me and really just threw me off today. I was just I'm always in such a rush, you know And then when I'm finally starting to catch up, there's a big delay But there's this there's a name we have for that It's called trucking It is what it is. I'm just tired and frustrated. Maybe I'm a little grumpy. I need to go to sleep and just get some Get some good shut-eye and tomorrow is a new day and it'll all get sorted out tomorrow We'll figure it out. So today wasn't the greatest day, you know, I Trucker Josh always seems to have great days, right? Wrong. I have bad days. I Have more than I'd like but Tomorrow is another day. I'm still excited to get up tomorrow and excited to see where life brings me and What's in store for me in the future And I'm always a bit of an optimist, I believe the future is bright At least I want to believe the future is bright So thanks for hanging out with me tagging along with me keeping me company. I don't know if I could do it without you guys I appreciate all your comments that you leave for me and Everything else to do for me you guys have came and helped us out more than once before and I really appreciate all of you. So remember just stay safe out there everybody.


Hi, this is Ashley walks more Toyota. I wanted to send you over a quick video greeting that way you can see who you'll be working with I noticed that you were interested in the new 2016 Corolla I want to hit and send you over our new and pre-owned inventory for you to look over at your Convenience if anything interests you, please let me know that way. I can get more information You can give me a call. My number is<PHONE_NUMBER> or just email me back. Thanks. Bye


Mindig a srácival báræ formalitára volna egy, kísérkező srácuknak. A srácISEgát egy pabúlások és ember srácja egy ilyen, hogy művissza, hogy a srác abstraction látsnak, és hogy ésből a kisérkiscs az időséges srác kapcsolatokkal aggózitekkel beszélhetem. Aztán az első életben lehet, hogy az időségesi főjét, mert ha nem nagyon fődül, akkor valamit nem elég a főjét, amikor hogy az egyetlen felenkény, ezt meg az elérvezősége.  Az benne az egyik eszletet is is tudottam egyébként, hogy a két Csúb jövök kiegéled a másik két Csúb kiegéled a másik két Csúb kiegéled a másik két Csúb kiegéled a másik két Csúb kiegéled a másik két Csúb jövök kiegéled a másik képel. then what I can tell you in this lecture, then you can head over there and read more. So the Fourier transform is a widely use theoretical and practical tool, and originally it was developed to isolate different periodic parts of function, signal or something similar. And it has a lot of applications in theory, és úgyhogy és készen a szükségek választulom, az az újságú fálolgásrázó, és a két-két criticizing konflikáció működik a helyzetetésmet vagy a rövben. Most érdemes csak, haatta, nem tudom, hogy meglátszok az obj Principle Linket, ezt a másikféleслő szátásoknak tanulni, minden, kéményével jártam, amelyeket, a másikére se jövénkben. De eszelать a flékezt, amelyeket rá lesz egyébkéntek, psychologically processing, processing music or sound, image processing for example, JPEG compression, fast multiplication of polynomias and of course quantum computing. We have lots of interesting applications that we will cover during this week. I will tell you more about the connection to the continuous Fourier transform and how the two relate that will be a topic for tomorrow. De first, let's cover the discrete Fourier transform. The discrete Fourier transform is a unitary map over complex vectors of dimension N, and it's a particular matrix whose matrix elements are evenly сыged out in the sense that they have the same absolute value in a computational basis. So, in particular, this N dimensional quantumathyahh a Grant-Furrián curated transform is a followed而已mit X. All the matrix elements,And all the necessary elements are some powers of a root of unity, Which is this exponential to the minus 2 Pi divided by n. So this omega n is this part of the root of unity And the most surveyed problem and the jthrow and theن and beat column of this matrix quickly, this route of unity to the power j times k, so this is just element in the jave column k, k column, and so here these indices are running from 0 to n-1 for the rows and the columns. Most gyorsanak nem sergedetek a Hadamart-transform, ahol az után egy furiaj-transform máskutul nyomjuk egy kis element.  A különkére a különkére a különkére a különkét ugye elmennem a fúriátag. Köszönöm ez a színűtésben. Aztán ez a különkére a különkére életben, és megyek ezt a különkére. A legküledegyszerűen és az egészségek, aki színes, ahogy nem kezdünk egy másik legtöltes fokhagyás, és ez nem a képe.  Oké, hogy az együttel, hogy a fokhagyás és a fokhagyás, hogy a fokhagyás, hogy a fokhagyás, a fokhagyás, It's a unitary matrix. And you can see this just computing what's the inner product between the k-th column and the k-pride column. I just wrote this out exactly here for you. And so if you do this calculation, you realize that taking this complex conjugate here just means that we are putting a minus sign in the exponent of this root of unity. So this is omega n to the minus jk, and omega n to the jk-prime. Then I just put together the exponents, and I get this expression. And this will be 1 if and only if k equals k-prime, and otherwise it will be 0. Yes. So one way to view is just algebraically doing this summation of a geometric sequence that gives you this exactly. Or you can also view this in geometric picture. So here you have your nth root of unity, and as you are taking powers, it's just going to rotate your root of unity. Excuse me for my drawing skills, the angles should be equal everywhere, but imagine that they are equal. And so because you are summing up over n rotations, and this was nth root of unity, or maybe not exactly this one, but some higher one, they all point in a different direction in a way that they exactly cancel out. So this is a geometric picture of the same thing that you can also do algebraically by just summing up this geometric sequence. Yes. Some other properties are that if you look at this matrix, it's a symmetric matrix, and therefore it's a unitary matrix, which is symmetric, so if you take the adjoint, which is the conjugate transpose, transpose is the same. So the inverse of the Fourier transform will be just its complex conjugate. So we just replace all these omega n's by their complex conjugate, which has the opposite sign in the exponent. And for notation, it's common to denote the Fourier transform of a vector by putting a hat on top. So if we had the vector v and we applied the discrete Fourier transform, then the Fourier transform vector is often denoted by v hat. And there is an important classical algorithm, the fast Fourier transform, which can compute this Fourier transform vector in only n log n steps, which is much improved compared to the naive algorithm that would just compute the matrix vector multiplication. And since this is an n by n matrix, that would require you going through all the n square elements, so it would require n square steps. Now, using this clever algorithm, you can just get away by n log n steps instead. And this fast Fourier transform algorithm is really important, not only in quantum computing, but also in classical computer science. Really, it's very widely used in signal processing. Whenever you do some MRI imaging or something, signal processing is heavily using this fast Fourier transform algorithm. OK, so now let's switch to the quantum side of the story and take a look at efficient implementations of this discrete Fourier transform, but inside the quantum computer. And for this, let's assume that for simplicity, this n is just the power of 2. And then, well, by definition, we know that the k-t basis state by the discrete Fourier transform is mapped to the uniform superposition over these j's, but with these phases described by this root affinity to j k power. And one of the key observations will be that this is easy to prepare state. And in fact, I will show you that only lowercase n square 1 and 2 qubit gate suffices to implement this Fourier transform. And so in a way, this gives an exponential speed up because capital N was the dimension of the vector of which we compute the Fourier transform. And we can get away by doing lowercase n, which is its logarithm, or polynomial many in logarithm, quantum gates. But one important thing to note here is that access to the output is limited. So in classical case, we get all the coordinates of this vector fully written out. So we have much stronger access to it in the quantum computer when we only have a quantum state whose amplitudes are Fourier transformed. So the quantum Fourier transform does something different in this sense that it prepares a quantum state, but does so much more efficiently. And the key property that helps for this efficient implementation of this Fourier transform is that if you just take a computational basis state, this k, then its discrete Fourier transform is really a product state. And to explain why is it the case, it's useful to write out these j and k numbers in binary. So that's one of the reasons why we stick to capital N, which is a power of two. So in particular j and k can be described by n bits, j1 being the most significant bit and jn being the least significant bit, each of them having value 0 and 1. This is really just a binary string corresponding to this number j and k. Ok, now this is a bit longer equation, but I will walk you through it step by step. So the first is just the definition of the discrete Fourier transform of the basis state k. And we can just write this out by first writing out j in binary. So j, which was a number between 0 and n minus 1, we just write it down with n bits. And correspondingly, we compute the corresponding exponents. And so it used to be a division by n, but that is counteracted by the place value of these bits. And so when we just write out j in binary, then we get this formula. And we use that these phases just can be taken as a product. So basically we separate the contribution of each bit to this phase. That's what happens in the first step. We're just writing out everything in binary. So the second step, we further collect together these bits. Well, one of the observations is that the absolute value, the amplitude absolute value of everything is 1 over 2 to the n. So if we decompose it to n qubits, then the amplitude of each of them should be 1 over square root 2 in this tensor product. So that's clear. And if you expand this second term, then you see that in the alt position you pick up this phase in the exponent exactly when the corresponding bit is 1 in the left-hand side. So the phase is picked up by the alt qubit, if and only if the alt qubit is in state 1. And that's exactly what is on the left-hand side. So this is how you can collect these terms together. This is this second equation. And the last one is really just rewriting this. So interpreting this number k over 2 to the l in binary. And so here one observation is that when you divide k by 2 to the l, then it will have some integer part and some fractional part. But integer times 2 pi i that just wraps around. So the integer part we can forget about. And this effectively means that only the last n minus l bits of k matter in this expression we can drop the previous ones. Because that's just wrapping around some integer multiple times 2 pi i. So yeah, this is now compact rewriting of the Fourier transform of the basis state k. And this is going to the basis of the efficient quantum circuit implementation. So I will rather describe the circuit for the case of 3 qubits. And then you will see how it generalizes further. But for simplicity, let's discuss this case. So if I have basis state k1, k2, k3, these are the bits. Then it's a dimensional Fourier transform has this product form. This was the expression that we devised in the previous slide. So in particular in the first qubit, this phase only depends on the third bit of k. For the second qubit, its phase component depends on the second and the third qubit, but not the first one. And for the last qubit, actually its phase depends on all of the bits of k. So what we will do is that we will first do everything that depends on the first qubit. And while that is only present in this last term, so we first construct this qubit. Once we construct this qubit, we can forget the value of k1. Then we proceed and here it only depends on k2, k3. So now we process this second qubit from the end. And after this, k2 can be jettisoned and finally we do the last qubit. And for the actual implementation, we will need some rotation gates. These rotation gates will be the ones that add these phase factors to the qubits that we wish to apply this. So this rotation by S will be not affecting the zero qubit state, but for the one qubit state it applies this e to the minus 2 pi i divided by 2 to the S phase. And here we should note that this is really once again a generalization of the Hadamard. Sorry, this is for the Z gate. Or what? Sorry, I'm doing something here. Sorry, this is the typo. So I'm sorry, this is not the Hadamard gate, but the Hadamard gate is the Fourier transform over a single bit. This is the typo, I'm sorry for that. So what this h does is that it prepares, if k1 was zero and it prepares a uniform superposition of zero and one, so when the k1 bit was zero, then there was no phase contribution from k1 here. And if the k1 bit was one, then it adds a phase because Hadamard matrix has a minus one here that adds a phase factor here as necessary. And sorry, ignore this line, that was a mistake. So once we did the Hadamard transform, we collected all the information necessary from this k1 bit and put it into this final bit here. Then we still need to apply a phase depending on the second bit of k. And that is exactly done by this rotation. And the angle is correct because we divide by the necessary power in this exponent. And then, well, this last qubit's phase of the one is also dependent on the third bit and once again a controlled rotation does the job for us. So this first three gates here prepare the product state for the last qubit of the output exactly as we desired. And similarly as before, now we apply a Hadamard to correctly put the phase information from the k2 bit here and then also add the phase information from the last bit.  This phase means that it is a plus or minus one depending on just the value of the third bit. But as this story shows, we first prepared the last qubit of the desired state and then a second and a first, so ultimately we need to swap the order of the output bits to get the correct representation of the Fourier transform state. And the case for n larger than 3 is exactly analogous. We just have one more rotation gate with one smaller angle and so on you can do it for every n. So this is the efficient implementation of the quantum Fourier transform for powers of two and while you can see that basically preparing the n qubit of this product state we are using n quantum gates for that qubit and we have n of these qubits and therefore you get roughly n square divided by two gates in total. Ok, so I assume that most of you probably have seen this but this is really a fundamental circuit for all the applications in the week so I thought we should definitely cover it. One thing that is less known probably is that you can also implement an efficient quantum Fourier transform circuit when n is not a power of two. It's a bit more complicated but you can do an exact circuit and that has similar complexity to this. So ultimately we don't have to assume that n is a power of two there is efficient implementation otherwise but in a way we can implement that an arbitrary Fourier transform over arbitrary integers and using this power of two quantum Fourier transform circuit and there will be exercise about this. So the exercise sheet which you should receive after lunch contains some standard exercises which are helping you to understand this concept if you are not so familiar with and contains two much more advanced exercises which is for those of you who are already fluent with these basics but you want to learn more about this topic and in particular this exercise about doing this quantum Fourier transform for arbitrary n, which is I think a very interesting exercise. Ok, so now this was the first part about quantum Fourier transform so I think it's a good point to stop and ask if you have any questions because the second part will be slightly different topic. Ok, well if you don't have any questions now then just ask me questions as we go on. Ok, so now it's a review of the hidden subgroup problem for Abelian groups and this is once again I am following the lecture notes of Ronald DeWolf there is no need to invent the wheel so if you want to get more background material once again you can head to the archive and look at Ronald's lecture notes. So in order to define and correctly describe Fourier transform on finite groups we need a bit of background on representation theory of groups. So representation theory in general uses linear algebra to study groups. That's the idea. And so if you are given a well these concepts can be generalized to infinite groups as well but from now I will specialize to finite groups because we want to implement these on a quantum computer and our quantum computer is mostly finite so that's the relevant case but these concepts have infinite dimensional and infinite size analogs which we don't cover but those are nevertheless very interesting theoretical extensions. Ok, so what's a representation? It's a homomorphism from your group into the multiplicative group of d by d complex matrices and such a homomorphism is called the d-dimensional representation. So what it means that if you have two group elements then you can either first multiply them in the group, get a new element and map that using the homomorphism and you should get the same result as if you first take the two group elements map them to the corresponding matrices and multiply the matrices then you should get the same result. And such a representation is called irreducible if and only if no non-trivial subspace is invariant under all linear maps or matrices in the image of phi. So what it means, phi maps your group elements to matrices these matrices have some eigenvectors, eigenvalues and accordingly they have invariant subspaces. The trivial invariant subspaces is the empty subspace that's always mapped to itself under linear map and also the entire space is always under such a map. And so representation is irreducible if there is no subspace that which is lying between zero and the entire space which is invariant under all linear maps that are in the image of this map. And so we will now mostly focus on the Abelian case and there we will focus on one-dimensional representations which are also called a character. And so in particular a character is a map from your group to the multiplicative group of the complex numbers and while if you just apply this homomorphism property you can see that the character mapping the unit element while it maps since unit element is equals its square its homomorphic image is the same and now we are using this property or homomorphic property that this complex number equals its square and this means that the unit element must be mapped to the one of the complex numbers and using this and Lagrange's theorem for groups we get that one equals the image of the unit element of the group and the unit element of group by the Lagrange theorem is the same as any group element to the power of the number of elements in the group and by the homomorphic property that's the same as the image of the group element to the g-t power and so this little computation shows that such a character must map every group element to a g-epsute value so the size of the group root of unity for every group element so this just gives you a bit more handle that every character is mapping group elements to some root of unities which are matching the size of the group and once again for a billion groups we have the nice property that all the irregisziu representations are in fact one-dimensional and they are exactly as many characters one-dimensional representations than the size of the group itself and the character group is also called sometimes the dual group of this group g and that contains the one-dimensional representations of the group g and we denote this character group by g hat and that also inside the Fourier and Ithik relevance of this concept and this is a group under point-wise multiplication so if we have two characters two one-dimensional representations phi and key from g to c then the point-wise multiplication or in this character group is which is denoted by phi times key g that just multiply the image of g times the image of key as you would multiply two functions point-wise and under this action they form a group and so now let's discuss the Fourier transform on finite a billion groups cikli groups are the easiest we already defined basically that so we can consider the k-th column of the discrete Fourier transform as a character such that we define the image of j as simply the j-th row of the k-th column of the Fourier transform and there is a normalization we need to multiply this matrix 7 by square root m and this way we get this root of unity omega n to the j times k and clearly because key kj equals omega to the j times k we have that this is indeed a homomorphism so let's look at the image of j plus j prime under this map and that by definition is just this root of unity j plus j prime power times k and while that is just the product of the corresponding characters point-wise so indeed we have this homomorphic property that key kj plus j prime just key kj times key kj prime and so here I use the additive notation for these elements of the cyclic group because it's an abeljan group and we can consider therefore this discrete Fourier transform as a map from the group g to g hat because Fourier transform maps the k-th basis elements to the k-th column and that's just a normalized version of the vector corresponding to this k-th character and this is not just any map but it's also important that this map is actually a homomorphism so if you take here two different elements k and k prime then k plus k prime is mapped to the product key k times key k prime so Fourier transform is a nice homomorphism acting between g and g hat and so this is for the cyclic groups the cyclic groups and their Fourier transform is just this homomorphic map between the group and its character group and in general we know that any abeljan group has just as many characters as the group itself moreover they are orthogonal to each other and this is a very good property because we want to study unitary transformations in quantum computing and the characters of abeljan group are already orthogonal to each other so we have a chance of defining a unitary matrix that is useful for quantum computing and moreover there is this so-called basis theorem from group theory which states that every finite abeljan group is in fact isomorphic to a product or if you are using additive notation to the direct sum of cyclic groups so you have a finite abeljan group g that's always isomorphic to product of these different cyclic groups n1, n2, nc, nt with those orders and this hints at the generalization of this Fourier transform the characters of g according to this decomposition will be simply tensor products of their cyclic components so in particular the character group will be isomorphic to the product of the character group of the n1-length cyclic group n2-length and so on which are of course themselves so we have seen that the character group of n1 is basically itself but we can think about this in a different way so the discrete Fourier transform is this homomorphic map which maps the cyclic group zn1 to its character group z hat n1 and that is exactly the Fourier transform fn1 discrete Fourier transform now we have a product structure both over the group and its character group and accordingly the Fourier transform over the group is just isomorphic to the tensor product of the Fourier transforms over each cyclic component so if if my group is really not isomorphic but is actually the product of these cyclic groups then the corresponding Fourier transform is actually the tensor product of the Fourier transform but now we have this isomorphism so we need to use this isomorphism which translates group elements in g to group elements in this product and exactly we need to take that isomorphism which is just basically a permutation or like a bijection between the elements and under this bijection we get the Fourier transform for the general group fg so this is how you define Fourier transform over an arbitrary Abellian group and this homomorphic structure of this Fourier transform will then follow naturally from the homomorphic structure of each of the individual Fourier transforms so we keep this property that that this is a homomorphic map between g and g hat for every Abellian group and so now it's time to now after this representation theory recap we can finally state this hidden subgroup problem which is where quantum computers excel and this is a generalization of Shor's algorithm and lots of other interesting algebraic things including the discrete logarithms and so on so here is the abstract definition as input we assume a function which maps the group elements to some set x really this x does not have to this doesn't have to have any structure this is just a set the only requirement is that this f should hide g1h in the sense that 2 group elements should be mapped to the same x value if and only if these 2 group elements are in the same coset of the hidden subgroup h meaning that g1h as a set equals g2h so in other words we have a function which we can think about this as an injective function on cosets because the value of the function only depends on the coset of a given group element and otherwise for different cosets it gives different values so this is the requirement we need to have such a hiding function which hides in this sense the subgroup h and of course the goal is to find the subgroup h itself with a few queries to f well one thing is asking a few queries and one thing is being efficient so well we will not only want to have a few queries to f but actually also an efficient quantum circuit which uses only a few gates to solve this problem and so this is the this is what is solved by this main algorithm and so here is the quantum circuit for the algorithm that solves the hidden subgroup problem on a quantum computer so here we need to start with the uniform superposition over the group elements so we need to assume that we can somehow prepare this uniform superposition that's assuming we can do that we just need to apply this this function which is either we don't need to buy an oracle so this is some quantum circuit that computes the function values and then we measure the output register and apply quantum Fourier transform over the group G finally measure it so this is the circuit quite a bit of explanation what it does and why it makes sense so let's just see how this acts so we have a uniform superposition over the group elements in the first register and we have a zero state and this zero state is just here to accommodate the function evaluation so this oracle f which I didn't specify in details what it does that it maps somehow it was misbehaving all the time ok alright so this oracle what it does if you provide it with a group element G and the fresh register containing a zero anszilla then it just computes the function value in the second register and it only needs to compute it and this anszilla register is zero in the initial state so we have the uniform superposition over the group elements and then a fresh anszilla here we just applied the oracle and then for every G we get the corresponding function value here nothing special happens but then the measurement we perform a measurement on the output register where the function values are stored and we get some x like a lowercase x value which we don't know what we get but it doesn't really matter we get some element and we know that so which are the group elements that are consistent with the equation that f of G equals x well take any preimage of x so that f inverse x is just any any group element which i don't need my s here which is map to x and we know that this function is constant on cosets so we can get all the elements of which map to x by just looping through this subgroup H and shifting this this initial element by by every element of this subgroup so this is exactly the part of the quantum state which is consistent with the measurement outcome x and so we had the uniform superposition previously the uniformity is retained but now this particular measurement outcome restricts the elements over this set and so here comes the last step so here comes the last step the key ingredient is when we apply finally the quantum Fourier transform and so what it does it maps this s plus h group element to this character key s plus h and while this last register i wrote it out it remains but we can really forget about it it doesn't really matter what x is and we will explicitly to drop it in the next slide and so remember this normalization the one over square root h comes from this uniformity over the group elements h and this one over square root g that was just how we defined the Fourier transform so this character every element so every point of this function if you would describe this character function is the root of unity so to get a unit length vector we need to divide by the square root of the size of the group and so this is why we have this in the denominator and so now the question remains why does it give anything useful if we measure the first register which is not the x value that we got and so this is what we need to understand what is the outcome of the measurement of the final state so I dropped now here the value x and just wrote this superposition over these characters after the Fourier transform and well basically I just write down the definition of this character state that is just the value of this s plus h character evaluated at g and then we have the group element as well so really it is just writing out what was the definition of this character state and in the next step we use that this character is a homomorphism so when I have the s plus h character then it is just the product of the s and h character so I just write this a product and notice that this key as g that doesn't depend on anything in h so I can just pull it through this summation so this is how I get this second line equation and so the final step which is a bit more challenging is that we will get some some state like this but let me explain what is written here and why is that the outcome so for the last equality we need to understand a few things about the structure of these characters so if you take any any character on the group g then you can restrict it to h so a character is a map from the group to the complex numbers now you have a subgroup a homomorphism and also it will be homomorphism on a subgroup itself still a map on it so you can restrict it and it will be a character of h itself and now we also introduced the notation h perp which will be a subgroup of the character group and exactly those characters are contained which will be the constant one function on elements of h clearly if you have two characters they are constant one on the subgroup h if you multiply them that is just multiplication point wise they will still be constant one on every element of the subgroup h so this is a subgroup and it's a well defined set it for example certainly contains this unit element so we can define it ok, so now I introduced this h perp group and so now I'm studying this part of this equation this sum over all the elements in the subgroup and the character evaluated at this element g times this group element itself in this notation so here one important thing is that you can swap the argument and the subscript of this of these characters so remember it's not in the board sign that for zm we had that he, k I don't know can you see it from the background can you see it from the last rows ok so key k j that was just omega m j times k ok and for this clearly you can see that this is now the same thing as pi j evaluated at k ok, so it has a product in this root of unity so you have clearly this equation now if you have something like zn1 cross zn2 then the characters are just products of the individual characters so key k1 k2 the element j1 j2 this will be just the product of k1 j1 times k2 j2 and here you can swap thing individually as we shown so this will be equal now k1 j1 k1 k2 k2 ok, so now we swapped the subset and the argument and once again you can just put everything together that will be k1 j1 j2 k1 k2 ok, so this swapping works for cyclic groups by definition very clearly and also by this product structure it works for product of two cyclic groups or more cyclic groups therefore for every finite abelian groups by the basis theorem ok, so in this first equation we can just swap the argument and subscript and so now the next thing that we should understand is that this summation well clearly if you are in this h-perp that means that this chi g is constant one on every element of the subgroup and so you get just the size of the subgroup h and otherwise it will be not the constant one and similar to how in the cyclic groups this rotation and times cancelled exactly that same thing happens here and this will be exactly 0 for the other elements yes well one other way to see it is that there is no room for here everything has to be because the normalization makes it sure that it has already maximum norm so already these elements in this summation give rise to norm one quantum state so there can nothing as be here, that's just another way of seeing this identity ok, so this summation over this idensa group is to a factor which is the size of the group so this divided by square root h becomes by a multiply by square root h but only those g's remains which were for which the corresponding character was in h-perp and otherwise oh yeah and we have this multiplicative factor the s character evaluated g but this is just a root of unity so when we measure this state this factor really doesn't matter what really matters is that we have uniform superposition over g's that are labels of this h-perp group so ultimately what we get is a uniformly random element of the group such that the corresponding character is in h-perp and this uniformity is the only thing that matters and so how you finally decode idensa group is that you repeat this argument several times and each time you will get a new uniformly random g and this is a linear constraint on the subgroup h because we determined that chi g on h will be one for every element of the subgroup so basically as you obtain more and more labels g that gives you more and more constraint on the element h and while essentially collecting a logarithmic number of constraints when you have this uniform something property that we ensured actually little argument shows that it suffices to uniquely determine the subgroup h now of course you can have some tiny error probability but if you repeat this process a few times then this will exponentially go to 0 so with very very high probability you determine the correct subgroup h and yes so this finishes the abelian idensa problem and in the exercise sheet you will see examples that show how period finding discrete logarithm and generalized discrete logarithm problems are all instances of this abstract looking concept and therefore we have efficient quantum algorithms for them we know the implications breaking shore and even discrete logarithm based cryptography the exercise sheet has some hints so if you get stuck or don't know just start a beginning of the exercise just look at the final page i'm not sure if the printed exercise sheets will have the hints ok now my time is over if you have any questions then maybe ask it or you can also ask me after the lecture


The nationwide pandemic has changed the way we do business. The 2021 Regulatory Information Conference will be completely virtual on March 8th through the 11th, 2021. You can watch us from wherever you are and you can participate from any device. You'll hear featured remarks from our Chairman, Commissioners, and Executive Director for Operations. Registration begins in January. Check the website often for updates. Whether from your office or the comfort of home, we invite you to attend and participate. See you at RIC 2021.


We had over 119 medics deploy up to Detroit, Michigan, and they were in support of FEMA operations in providing vaccines to the men and women of Detroit in the surrounding area. And they've been out there for approximately two months, getting ready to come back today, excited to see their families. There's nothing like getting to hug them. It feels really good. I've always wanted to feel a part of the mission and like we're doing something and what better way to do it than actually doing something in our own country to help end this pandemic. We went when there was a third surge going on in Michigan and for us to be able to get as many shots in people as we could is a great feeling. We're going to give some of our airmen some R&R time on the back end, some rest and recuperation time as they get back from this deployment because they have been working very long days and a lot of days out of the week to make all these vaccinations possible for the state of Michigan up in Detroit. But let's be honest, when we take over 110, we actually had up to 119 people at one point up in Detroit away from our medical center. It makes it harder to do our mission. But our team here still rallied to the cause and still made sure that we were providing trusted care for our beneficiaries here in the area while supporting to our members going up to Detroit and doing such a great job in giving vaccinations up there. We're certainly happy to have them back though. This pandemic allowed our medics to showcase their talents just like the medics across the communities and so we've had nurses appreciation week just last week. We've got all kinds of appreciation and love going out to our medical community. I cannot say thank you enough to all of our medical community for what they're doing rising in this pandemic and serving.


In the previous modules, we talked about how the client communicates with the database, how it invokes an action, how it invokes or it initiates something to access the database which is placed somewhere on the internet. Now in this module and in the next module, we will go into some details about how actually things are happening, what CGI is doing, what is happening at the server, what technologies, what tools, what is involved in it, other than just invoking, so that is spread across two modules. So let me first tell you briefly about what I will cover in this module. So I will briefly talk about the APIs, application programming interface, libraries, native database APIs which are related to certain specific databases. And of course, database independent APIs also, which can work across the databases using something called as ODBC, okay, I will explain this, and what are the benefits and shortcomings of APIs. So let's go into more detail, database APIs are a core and foundation, and they are used way, why and how to connect and work with databases, to do what, to send queries and get results, and they have been around, and they have been around in the client server architecture for a while, okay, of course that's not a 3D architecture we have been discussing, and it has a wider usage, why, because it is beneficial, with this people can access the databases and make the results available to the clients. And how it is done using the CGI using the fast CGI libraries, and these libraries are used in application packages, these libraries are used in building tools, these are used in packages, etc. And all of this is transparent to the end user, or the developer, basically, the developer because we are talking about things which are happening at the server side, which are the programmers. So what are the native database APIs native database are API dependent oracle has independent APIs also, which work with non oracle products also, that's the power of the approach. What is the benefit of native APIs, they are fast because of the architecture, right, and others are slow, why they are slow because of the ease of use, because of the customization, it adds a level of programming on top of the actual native database APIs, so I can use a tool, okay, which is kind of neutral to the to the underlying database, but because of the programming layer, okay, the response is not good. They are not inherently dependent because with using the CGI, okay, and native API can work with other server types also. What is the benefit CGI is language independent is a protocol. So using this combination, I can work around things, I can make things happen also database independent APIs, okay, database they are supported by developed by Microsoft, ODBC, and it is supported by many popular databases oracle also, SQL server also, of course others there also, but what it requires it requires ODBC client, you need to install the ODBC client or your client, okay, and then the client doesn't have to know that the underlying database is access or SQL server or its oracle, but the disadvantage is obvious on how many clients you can install this, right or not. So you need one option is using a JDBC and ODBC bridge, the benefit of this bridge that you have the bridge on one client for two way translation, but again the issue is that you have to do it on the client side to the three tiered approach for client or server else need on every client, you understand what I'm trying to say over there. If you have the three tiered approach, then you don't have to install these independent APIs on the client side, you install them at the server end, because client and installation is not feasible. What are the shortcomings and what are the benefits of these APIs, they are flexible and they're efficient, obviously, they provide fast data access, why because they are native to it, right or not, and they have been around even before the web was there. Why because this the traditional client server architecture was there, and these APIs were used to access the databases, okay, for that architecture. But for rapid application development, you need high level tools, okay, and it doesn't support access to native SQL database calls. So there's a trade off over here. And as a web based database designer and developer, you should be aware of these shortcomings and the strengths to make the right choice.


On February 27, 1923, the Homestead Enterprise newspaper published a notice that E. Leedscalen of California has purchased an acre of the R. L. Moser Homestead and is planning to erect a home soon. Working alone and mostly at night, Leedscalen eventually quarried and sculpted over 1,100 short tons of Olight limestone into architectural and engineering landmark that would later be known as the Coral Castle. Leedscalen devised a means to single-handedly lift and maneuver blocks of coral weighing up to 30 tons each. What's that all about? The evidence for Coral Castle is on show for all of us to see. It is a stunning feat, even if it is amateurish compared to the pyramids or the Colossi. It is simply spectacular, especially at night. How did he do it? No one knows exactly how he did it, but he claimed to know the secrets of transporting and elevating more weights than is humanly possible for one man. He was able to quarry and construct an entire complex of monolithic blocks of coral in an arrangement that reflected his own unique character. He labored for 28 years to complete the work, which consisted of a total of 1,100 tons of rock. What was Leedscalen's secret? Is it possible for a 5-foot-tall 110-pound man to accomplish such a feat without knowing techniques that are uncommon to our contemporary understanding of physics and mechanics? Leedscalen was a student of the universe.  He crowned with a gable-shaped rock. These personal accomplishments have astounded and surprised many engineers and technologists who compare them with those achieved by workers handling similar weights in industry today. For his miracles of construction engineering, Leedscalen received attention not only from engineers and technologists, but from the US government, who paid him a visit hoping to be enlightened. Leedscalen received them gracefully, and they left none the wiser. When questioned about how he moved the blocks of coral, Ed would only reply that he understood the laws of weight and leverage well. On the ground level of the building where Leedscalen resided, sometimes called the tower, he constructed a room to house his tools. Within this room, there is a mysterious flywheel, which is constructed of concrete and magnets, with a cloverleaf shape at the center. When holding a compass next to the wheel as it rotates, the compass also spins, indicating each U-shaped magnet was set opposite in polarity. Next to the wheel, there is a metal pole which enters the ground. There are many clues in the layout of Coral Castle itself, which indicate there must have been a celestial importance. The position of the earth within the solar system almost seemed essential to Leedscalen. The Polaris telescope, which is said to be 25 feet in height and weighing 20 tons, can be used to determine the location of the earth in its orbit according to the position of the Polaris star within crosshairs. In order to observe Polaris, you would have to peer through a hole which is drilled through a block at about eye level. When looking through the hole, it aligns with a large hole at the top of a 25 foot block of limestone. The amount of the effort put into this elaborate device should indicate its importance. There are a couple of credible accounts of adults witnessing strange occurrences as Ed worked. The man whom Ed hired to move the stones with his truck stated that he had forgotten his lunchbox one morning and went back to the castle to get it. He had only been gone for half an hour and when he arrived, Ed already had several of the monolithic stones stacked on the rails of the trailer like cordwood. He never saw how Ed loaded them, just that Ed had no heavy machinery that should have been necessary to manipulate such heavy stones. Researchers have speculated that Ed learned the secret of levitation and one theory in particular caught the imagination of many. The planetary grid hypothesis postulates that the earth is covered by an invisible web of energy which is concentrated at points of toleric power, the convergences of which create unusual phenomena. These toleric grid dynamics played a vital role in the construction of the castle. There exists an all-encompassing global grid with direct harmonic relationship to the speed of light, gravity, magnetics, and earth mass. All major changes of the physical state are brought about by harmonic interactions of these manifestations. The controlled manipulation of these forces would make it possible to instantaneously move mass from one point to another in space-time. He understood the critical nature of identifying the most energetic location to erect his massive castle and seemed to have known the secrets of anti-gravity and its relation to cosmic events. Ed proceeded to develop a means of leverage power generated from the geomagnetic grid and produced a system to generate anti-gravity waves. Ed Leedscalen knew exactly what he was doing when he created his fantastic castle. In 1951 Ed took his secrets to the grave. The mystery of Coral Castle was never revealed. Rumor persists that a plaque was found in Ed's bedroom that read, the secret to the universe is 7129-6105-195, a sequence of prime meridian numbers.  What do you guys think of the secrets in the construction of Coral Castle? Comments below. Thanks for watching. This is the only known photo of Ed apparently working. Although he seems to be breaking the block free with wedges, a close look reveals that the block is already cut free with a cable underneath. Engineers have been puzzled by this photo. He's moved stones up to or Coral blocks up to 25 tons and he'd put them up overnight just on his own. After he died they checked some of the instruments he was using and they're very primitive, chisels and hammers and rapes and pulleys and things. Nobody can understand even today now how he'd done this. I found when I applied the harmonic mathematical basis to his position on the Earth's surface geometrically that the same harmonic values popped up on the area where he was. He always said that he had the secrets of anti-gravity and magnetic fields and he also said that he knew how they built the pyramids. It's out of place if he was telling the truth that looks like he did have these secrets. They also found $3,800 in crisp $100 bills and what resembled a treasure map. All attempts to follow the directions on the map were futile. Nothing seemed to correspond to our normal three-dimensional geometry.


I'm gonna be doing now, right? I don't know, have you ever whacked your weakness on a door? I'm not gonna talk about whacking my weakness with you. Well... Most guys do it.  I'm Rek and he holds an Instagram... Come on! It's so juicy! It's a great page on Pong. Twitter, Comrade N'Balbo and make an action squad. OW! Description. Bengali! We're doing it. It's a song. It's a Bengali song. Sweet. It is from Shreya Gosho. Yay! I think it's... Okay, so these are the two names. I think this is the song name. Tomake. Tomake. And then... I think this is the film name. Peranita. And it's with... Ritwik Chakraborty. The song is from the Bengali movie Peranita. And it's sung by Shreya Gosho. The lyrics and music are composed by Arco. The word Peranita means married woman. It stars Ritwik Chakraborty, one of the lead actors of Nagakirtan and lead actor in Shabdo. And Subashri Ganguly. It is directed by Subashri's husband Raj Chakraborty, who is a popular director in Bengali industry, mainly known for his commercial movies. So it's Tomake. What are you thinking of right now? Balabashi. It's just you. Because Anitomake Balabashi is. I love you. Isn't there a Hindi film Peranita? Yeah, we've reacted to this song before. Payu Bol. With Sai Balakhan and Vidya. We've reacted to that song. 100%. What? In the Hindi version? Yeah, see. Okay, so we've reacted to the trailer and we've reacted to a song with Sai Balakhan and Vidya. So there's a Hindi version of this Bengali film and we're now reacting to the Bengali... But this song is from 2019 in Bengali. So I think this film was way before. So it was a Hindi film that was then made in... No, it was a Hindi film first? Yeah, it was a Hindi film first. Unless Hindi stole it and then... Hindi stole it from somewhere and then Bengali stole it from them. Or it's a completely different thing and it's a common name like Guru. I don't know. You guys can let us know. Vidya Si. Just voices. I feel like it was getting it. That one killed me. I just wasn't really focusing at all on the visuals. I was looking at the words and listening to the song and hearing it in her mother tongue and I just... I freaking missed her so much. Congrats, guys. You made him cry. What a feat. What a feat. What a feat. What a feat. What a feat. You made him cry. What a feat. All those words. That's true. Shreya... She's Bengali, right? She's Bengali. Why haven't we interviewed her yet? What's up? Doesn't Nandrani know her? Wait, do you think all Bengalis know each other? Do they not? Well, I don't know because she knows Tillatamo. They talk to each other. Did you meet Tillatamo? Yeah, you did. You just don't know it in Delhi. You also thought we met. I know this one for sure. There were a couple of Bengalis that were in New Delhi besides Rohan. Because Rohan lives there even though he speaks. I remember it. There were a couple of girls that were from... It was her? That's Tillatamo. Hi, Tillatamo. She is regularly communicating with Nandrani and they met.  Thank you for doing that, but that killed me. Yeah? Well, part of it. Can you relate to any of it? 100%. I don't go to bed with a picture. I'm able to go to bed thanks to technology. I get to see her when I go to bed through the phone. For two people our primary love languages for both of us are exactly the same. It's words of affirmation and physical touch. To not be physically present I literally, as I just said that I got an ache right here, so it sucks. But hey, one day closer. One day closer to being together. So thanks for destroying me. You're welcome. I'm trying to figure out what my love languages are. Well, there's five. What are they? Words of affirmation. I can pretty much guess what yours are. Words of affirmation. Physical touch. Quality time. Acts of service where you do things together. But is that for me or what I like? Both. How you like to express it and how you like to receive it. They're often similar. And then gifts. I don't know. You like to give gifts or receive gifts and that communicates genuine love. No, I don't like getting gifts. Acts of service. Like somebody does something for you. I like to do it for other people. I don't like it being done for me. Right. Quality time. Yes. I bet your primary love languages spending time together. And physical touch with my woman. Yeah, well that's... Toucher. But yeah, I'd assume those would be mine. But the ones I like... Yeah, that you like to receive. Because it doesn't have to be the same. They often are, for me, it's exactly the same. Well, I like... Those are the ones I think I like for me. But the ones I like to give... I like to actually give service, I think. And I also... I enjoy giving gifts to my wife. And is that a love language for her? Does she like to receive gifts? She knows if she... No, I mean, she appreciates them. But it doesn't flow down. Her physical touch and words of affirmation. Yeah. 100%. That is not mine. No, I guarantee. I knew for sure those were not yours. I know she knows them. But she probably knows the ones I am very well. But here's a beautiful thing about that. Though yours are not physical touch and words of affirmation. No, I like physical touch. Yeah. Nobody else. No, of course not. This is your love relationship. Your intimate love relationship. That's what we're talking about. Don't touch me. There's people I love. I don't want touching me that way. No, you like more people touching than I like touching. It's true. I like to be touched. No. I think, because she knows the love languages. I don't. So she'd probably be able to tell you which ones I am. I'm sure it's quality time. But I know I don't. There's a lot of affirmation. It's not gift. In terms of receiving. It's not gift. It's not service. I bet it's quality time. They're combined. If you were to do something with Stephanie that you're helping others together. That that would be a bonding time for you and your wife. Or the two of you get to spend time together helping other people.  It's definitely not words of affirmation. You could care less about that. I don't need anybody else's words. What about hers? Do you need that? If you went a month and she didn't say I love you would that bother you? Then you are words of affirmation. People who don't need words of affirmation could go 10 years without the loved one saying I love you and it would be like I don't care. I would just weird do it. I probably wouldn't notice. I like it when she says I love only people if I'm doing something that if I'm doing a performance I would like her affirmation. Affirmation that she enjoyed it. Nobody else.  I don't care. When we're talking about your love language it's with your significant other. I wouldn't say that's my because I feel like words of affirmation is people that need to be told all the time. There's an unhealthy level of that as well. But yeah, it's definitely not that one. Anyways, that's all we're going to do now. Let us know your love language down below. And... You killed me.


dystopian time you know the conservative movement has been fixated on mr potato head cat in the hat and lately they've taken a liking to uh the muppets now i hope that this doesn't get me like copyright claims because he's gonna play a clip of the muppets but we're gonna watch the muppets folks i'm sure that some of us grew up with it and and see what all of the uh the noise is about with regard to conservatives and why they're outraged here get away from the transgender issue right it's everywhere even though transgender issues well really affects a very small number of people but it seems like they wanted to affect a lot more especially our children meet gonzo uh gonzo is a muppet i just gotta pause it real real quick because like he's he's trying to create this ominous image and then he cuts to this beautiful bright picture of the muppets and i just i love everything that's happening right here or one of these characters disney characters uh i didn't know gonzo was a kid but gonzo's big and uh well gonzo had a secret for uh gonzo's friends there you are you missed our royal ball we made the most amazing princess but they ran a winged was this everyone there's something i need to tell you the prince waiting for your ball tonight was me gonzarella based why didn't you tell us because you all expected me to look a certain way i don't want you to be upset with me but i don't want to do things just because that's the way they've always been done either i want to be me oh gonzo we're sorry it wasn't very nice of us to tell you what to wear to our ball you're a friend and we love you any way you are yeah of course we need let me pause it right there before he goes on his rant we can you know already anticipate what he's going to say but is that not the most wholesome wonderful thing you've ever seen like how could you not love that it's incredibly chill i i just want to add this before any discourse takes place that um gonzo has been like basically canonically non-binary since the 1970s you can actually find episode segments of it really wearing a a dress with like the hand muffins i mean way back before it was born so this is yet no seriously multiple times multiple episodes this is completely uh yeah this is this is you know what this is canon very base gonzo species of alien that doesn't have gender okay so you can already anticipate what is going to be said here we'll also cut to one of my favorite political commentators on the right who's going to also weigh in here but um let's let him um tell you why he's deeply offended apologies gonzo i sorry uh why is this being pushed i don't know if gonzo is a cross dresser or transgender but if gonzo is transgender that is a disorder gender dysphoria jesus a disorder it's an alien so all right so before we discuss this true that is all so kandace owens actually reacted to this i can't believe i'm tweeting this but they are pushing the trans agenda on children via muppet babies this is sick and perverted in all caps everyone should be disturbed by predatory cartoons meant to usher children into gender dysphoria bring back manly muppets anyone folks what is happening on the right what is happening on the right i'll just leave this open to the panel because i this makes me want to kill myself we're we're all thinking of the sweetest chef right like it's she's she's got to be talking about the sweetest chef that's funny cross dress 80 years ago what i think so i'm just i'm just saying that like they're they're act first of all they act like this is this trans issue when no it's not there are stories of people dressing up for comedic effector because they enjoy doing so for literal centuries does anyone remember avatar the last airbender if you haven't seen it you should see it soca dresses up as a kiyoshi warrior an episode like five makeup and everything but back then there wasn't this obsession with using every instance of a of a guy or whatever wearing a dress as part of the culture war battle against trans people so it went largely uncommented on but if it came out today you know people would be screeching about nicolodian pushing transgenderism on the youth or something go broke go go go grab her yeah well and and to really speak to how much things have changed like i'm wearing a zelda shirt in breath of the wild there's this like part of the game where link has to dress up in women's clothing to like get into some area am i like i've seen drawings of those uh of those segments right and it like i don't remember we can we can dive into the legend of zelda lore but i mean like i don't remember it being controversial even back then i mean maybe i saw an article about it like praising it or something but now every like conservatives are hypersensitive to where they're fixated on these weird like cultural war issues that don't even make sense like you know the cancellations of mr potato head and cat in the hat when this these weren't actually cancellations please do why they don't care about um about legend of zelda or anything that we that is done today there's so many examples of things they could get mad about that are way woker or way more trans agenda as the representative of the demonic trans is who are undermining the world here but uh the the it's it's that old people recognize muppets and old people recognize mrs butterworth and old people recognize uncle ben and old people recognize um dr seuss but they don't know their toys they're like a like a link in a chain fence like that's a great one i don't get it that's very true it's that and like i don't know it does seem to be that they get most mad about things that old people would real would recognize which to me plays into that whole idea of like the news max and fox news being boomer daycare right like yeah yeah i i'm looking through these images of ganzo in a in a in a in a dress they're from like a million years ago back when everything was drawn on animation cells um yeah it's it's completely toothless i i don't even know if they believe any of this stuff when they say it like i haven't heard when are we gonna get the cancellation of bugs bunny that guy crossed dressed not all the time he kissed men all the time he no it's oh yeah it's true the voice and the aspect and the makeup yeah wow i didn't know this about bugs bunny on my tv man maybe that's what maybe that turned me gay is that possible like i don't remember seeing bugs bunny kiss men in you yeah yeah also i i just i want to know how the logic on this works because i think you can make people trans by showing them by showing kids trans people but kids are shown cis people pretty much all the time every human who has ever lived is constantly being shown cis people so i don't does it only go one way is it and six like sorry cis sexuality in everything everywhere like every single cartoon that you grow up with there's like oh yes two muscles he man you know and hell here we go it's gonna be amazing like the things are very subtly changing i have never seen an instance of a masculine character being feminized in what i thought was a cynical attempt to promote like an affinity for trans people i don't think i've ever actually seen that once with all the cynical woke shit that comes out to appeal to millennials i don't think i've ever seen that can anyone does anyone have any like can anyone think of that happening no i mean that's the thing like if you want to look of examples of like trans representation and and and like stuff like that in film and pop culture it's like overwhelmingly negative like you just get to like the the ace ventura like the most extreme examples of just just truly like i don't know like going back and watching like ace ventura silence of the lambs so bad yes silence of the lambs yeah oh ace ventura is really bad yeah it's really bad i rewatched that one a couple of years ago and i was like whoa whoa it just keeps going it's actually just keeps going never stops and so yeah like it doesn't make sense no no go ahead i was just i know we got a glow up though if anyone's been following one piece for the past hundred years um where we actually have i think two trans characters who are treated well and beloved in the current arc um all right yeah wow you have um uh fuck you have yamato and you have um what's the name of the nine foot tall lady is it three oh anyway i don't know but okay i don't know if you guys read one piece i don't know i i so i follow a couple of conservative commentators who i think are particularly fun to watch on this particular topic um kandace owens is always a classic um of course but my personal favorite is matt walsh and that's because matt walsh will lose his absolute mind over the smallest thing and i i mean truly uh like he read a book uh once on stream on his little stream that he does and it was like and he just read through this book and it was literally a book that was just like this is karla she was assigned male at birth by her parents but but later on realized that she was a girl and he was like this is perversion this is child abuse this is like i'm not kidding you he's losing his mind like being truly angry and i'm like what are you even mad about and and and he does this to to anything and so it's uh the the like like the the hysteria around this like trans i mean i'm not gonna lie look i'm demon mama so like i don't mind being feared a little bit okay like let's be real i like that a little but it's kind of to an unbelievable degree and you can't escape it it's everywhere last night i got on twitter i'm like oh god why is why is the word trans trending on twitter and i'm just like and and and i'm like oh god every single time it gives me a small heart attack because i'm like well what's what is it now is it gonna be like some other just unbelievable like just you would think that trans people were orcs if you listen to just conservatives like it's like it's it's it's beyond it's beyond even it's almost beyond parody the the amount of misstep between um like reality and their idea of reality and and i mean it really does parallel like calling joe biden a a a chinese communist but see on that one only alex jones will say that whereas with trans people like any conservative online will have a meltdown about just seeing that a trans person exists and they're like that's child abuse and i'm like wait for because somebody else that you don't like exists like i don't know it is a level of it's a level of of fear and derangement that is genuinely concerning


Hey, welcome to my channel guys. Today we're going to talk about the top seven craziest things that are quite common here in New Zealand and you may be surprised how many of these I have actually done. So you're not going to want to miss this video. Here we go. If you don't know who I am, I have my family of six from the U.S. New Zealand and have been here for seven years and just sharing my experience. So if you like the content, please subscribe, click the like button because it really matters and it communicates to me whether you like this topic or you like these sort of videos. Also, if you are thinking about visiting or moving to New Zealand, definitely reach out to me because I have some amazing resources that will help you. But here we go. Let's get into the seven crazy things that I think are awesome here in New Zealand. Now, just as a little bit of a disclaimer, there are these things in the U.S. and other parts of the world as well. But I'm just talking about some of the things that are quite common here and can be a little bit more dangerous because of the landscape and that sort of thing. But let's just dive into it. So number seven, the craziest thing is zorbing. If you haven't heard of zorbing, it's basically you put a person in a giant inflatable ball and push them down a hill.  Have I done it? No. Do I want to do it? Yes. And here are some tips that other people have said to me. They're like, don't do the zorbing with another person because sometimes you can do it with another person and then you're like all over each other and you're getting knees in your eyes and stuff. So there's a tip for that. I haven't done it, but I will be doing it alone when I do do it. So check out zorbing. It's kind of a crazy thing here. Okay. Number six, let's talk about cliff jumping. Now, I don't mean just like this is an organized place where you're just, you know, it's already been figured out how deep the water is, it's safe, whatever. No, no, no, no. They jump off of cliffs everywhere. New Zealand's so beautiful. You know, just Google it. Image is unbelievable. There are lakes, rivers, little bodies of water all over the place that are so amazing that you just want to swim in. Now, as a side note, New Zealanders love to just swim all the time. They'll just be like on a hike. Oh, that looks nice. Let's take a dip. Driving a car, see a nice lake, want to take a dip. They're getting hot. Let's do it. And then it's just, it's just like they get in and then they get right back out. Like that is just not something that I grew up with and just our family just doesn't really do that. But it's so interesting that when people, when they're doing the cliff jumping, it's, it's not, it's in remote places. It's like, oh, this is a cool place. I think I'm going to climb up there. Oh, I'm going to go higher. I'm going to go higher and higher. And I'm just going to jump out. I don't know the fascination with going higher. And I'm just looking at like, and they just kind of evaluating it deep enough. I'm like, oh my gosh. And this is like across the board, like all different friends, all different situations. People are always jumping off of cliffs, jumping off of wharfs. They love to jump off of things. And so that's really good.   And number five, if at number five is hella skiing. Now that's not like a hella skiing. It's heli skiing, like helicopter skiing. Now skiing, snowboarding, winter sports, huge here in New Zealand. If you love that sort of thing, this is the place for you.  No, no, no. You can like a higher helicopter coming to take you and drop you into like fresh snow on the top of a mountain and ski down it. Now I have not done this. I have skied here in New Zealand, just on regular trails. I'm not a huge skier. It's not my favorite thing to do. I do enjoy it. The views are amazing and you should definitely do it if you're here in New Zealand. But like, I'm not getting on a helicopter and I have friends I have and it's a thing here. It's not uncommon if you really like skiing to be dropped in the middle of whole place and hopefully you can get down and it's like straight down. It's like, oh my gosh. Okay, number four, bungee jumping. Have I done bungee jumping? No. Has my kids done bungee jumping? Yes, as teenagers like pretty, like under 18. I think it was like 16 and 18 maybe they were. But I was like, I mean, it was really hard for me to watch them to be honest and that my son's whip. No problem. My daughter screamed a little bit more, but I mean, I probably would have had a panic. I just, you know, if you think that it's exciting to jump off a cliff with a rubber band, do it. I believe bungee jumping was created here in New Zealand and so you can do it a lot of places. Even the tallest building in Auckland, the Sky Tower, you can do the Sky Tower jump and just jump out to the middle of a city on a rubber band. And so yeah, so I haven't done it. My kids have done it. Not sure I'll do it. We'll see. Number three, jet boating. Now, if you've seen my other videos, you know I have jet boated. I have jet boated in Queenstown and multiple times actually and it's great. And I did scream the entire time. I'm not gonna lie because what they're doing is they're taking a very fast boat and they're going like what it feels like as fast as a boat can possibly go.  Have you closed your eyes? But it just like and it's just it's so fast. It's, I'm just wondering, it had to be a New Zealander that's just sitting one day. What if we just took a boat and we just went really fast through these canyons and and sell that? Like I just, like who comes up with this idea? If you, if that sounds great, it's definitely something everything should try. It's not too scary. Your kids can do it. But it's just like, wow, we are going really fast and it really looks like we're gonna hit that mountain, but we don't. So check out jet boating. Number two, let's talk about mountain biking. Now I know mountain biking is a very popular thing all over the world, but it is, I just had to put it on this list because it's so significant. I have mountain bike.  It's not for me. It's not for me. I've done it. I've done it a couple times.  So if you love mountain biking, you're going to have to try here. It's just what the reason why I added it because I think it feels quite dangerous. I know people that do it all different crazy ways as well. And they just, there's no fear here. I'm telling you, no fear. Number one, crazy thing in New Zealand. These are all crazy, but like, canyoning is a big thing. I have been canyoning. I've also been canyoning in the US. It's very cool. It's like where you rappel down into a canyon and sometimes multiple waterfalls and then go for a hike. Also rafting, I'm going to kind of add that is a big thing here. And I've obviously been rafting in the US here, but man, it is, I haven't been rafting here, but I've heard it's quite exciting for all of you thrill seekers. And so, yeah. So those are really cool, beautiful way to see different parts of New Zealand as well. So check out canyoning and whitewater rafting. Okay, I hope you enjoyed the video this week. Definitely comment below with any crazy things you've done in New Zealand experiences, hopefully not, you know, hospital visits, but comment below or like, what are some things I mean, there's other, I've looked at a lot of lists, I've thought about it. It's just it's summertime here and everybody's out and doing things and it just kind of prompted my thoughts to think about some of the crazy things. So comment below what you've done. Definitely subscribe if you haven't and hit the like button if you liked this video and I'll see you next week.