One of the most common questions I get asked is, you know, how do I start day trading? So what me and my mentor about it for our viewers on YouTube is create a free mentorship course that reveals our 12 secrets that every single brand new day trader should know before they get started. But please take note that there is limited seating every single week. So please reserve your spot at myinvestingclub.co. The link is in the description. That's the first time I've ever heard that. Well, that's nice. Did you guys hear that? It just Did you guys hear that? You guys did? That's the first time I've ever heard that. They probably got too many.  I didn't record and they need to that's more that's now a reminder for everyone. Oh, I didn't hear recording in progress. So anyway, but now that we're recording, I'll resay what I just said. My internet went out today. So if this screen kind of ends or there's two parts, I'm sorry guys. Zoom update, zoom to the moon. All right. So yeah, let's get started. And I mean, this was a this was definitely a different week out of out of all the other weeks. So that was pretty just more more balanced this week and we'll go over it. Anyway, so let's pull it up. So today I'm going to do this webinar on adapting and changing because it's a it's a very it's an eternal thing.    It's and everyone always says, like, adapt to Paris, adapt to Paris, adapt to Paris. And it's frustrating when you want to be consistent, but you're constantly having to change. And so I kind of want to unpack a whole lot of that because it's it's one of those statements where you just say, adapt to Paris, you know, like, kind of a it's very open blanket. And so I want to, you know, uncover some of the blankets, I guess, give my thoughts on that. So today, we're going to talk about like, how to adapt, how to change, like, what what's too much of a change and all that kind of stuff. And then my screen's a little dirty. All right. So let's get going. So this is your first, if this is your first webinar, welcome. This is kind of a standalone webinar. Like, I kind of touched on this a little bit on probably almost every webinar of them, but now I'm doing one so I can point to it. So this is going to be one of those there is no prerequisite webinar. So you can just watch this one cleanly. I thought there'd be some people that that got a kick out of that. So anyway, we're going to be going over the market segment as I do every single week. Then we'll go into all of the movers of the week and kind of identify good spots for entries or exits or, you know, depending on your thesis, what kind of risk levels were good and stuff like that. So I'll ask you guys to think of some pickers to go over this week. Then we'll get into adapting and changing and Q&A is open throughout the whole webinar. So if you have a question, just go ahead and ask them out. You know, if I miss it, post it again later. And I'll probably catch it. All right. So let's get going. No time to waste. All right. So let's pull up the spy here on the cues. That's what I mean. So last week, right, we saw this big, strong, positive bounce on the cues, right? We saw, we started to see this, this, this strong pop up right here. This, I think this was the day, right? When was my last webinar day? 13th? Yeah. So it was like right here, right? It was, yeah, this strong bounce day, right? We were, it was right here on this strong bounce day. And so, you know, we were kind of, like, I was kind of talking about how this is like a strong positive bounce off of, and it happened at the same time as the Bitcoin flash crash that we had. And last week, I kind of brought up the idea of like major market, like events and triggers.  And so I thought that that could be a positive possibility there with the Bitcoin flash press, but it ended up being a flash press, right? It bounced. I don't even know what Bitcoin price is at right now, but I know it didn't just fall to its demise. So it wasn't like a crash. But, you know, and, but on that day we were seeing bounces like left and right all over the place. And I said that, like, we needed to maintain this 320 level on the Qs, the 405 level on the spy, and that I thought it would take a little bit of consolidation, a little bit of proof to prove that we can hold on to these levels. And if we could hold on to these levels, that we could have a nice move up. And if we didn't retest or didn't have any consolidation, I think that we would have a, you know, kind of a choppy move up with pseudo confidence, kind of like we had a couple of weeks ago, right? When we were talking, and we kind of had, when we kind of had like this, this, this move up, it was just, you know, it was just too fast. And then like, it was just choppy, right? We couldn't, nobody, nobody had any confidence there. And so basically I thought 320 was the level that needed to hold for the Qs. And the, the cool thing is that we dipped, like this was the day where we dipped, you know, we gapped way under 320. And on that day, that's the level that reclaimed. And that really showed me that, hey, I was right on that level, that was the level that we needed to, you know, like, this is where this is where it all happened, right? It all happened right here at 320. That was the, you know, this is where the, that huge reclaim kind of came in on this, like 320. This is the support, the major support that held. Yeah, thanks for giving them that. And this, I mean, this kind of showed it right there.  We were going to dip back under and the market said, no, we want to be above 320. And so this was the level here. And I think something similar happened on this slide. Hey guys, my name is Toss Bradley. I'm one of the head mentors and moderators at my investing club. If you have any questions about getting started in the trading, getting started in the MIC, MIC in general, text me at<PHONE_NUMBER>. This is not a robot. It is me directly on the other end of my business line. And we'll get you in the club. We also have special promotions going on that I can get to you depending on your trading needs. Hit me up. Thanks for the video. Kind of, kind of right there. Despite didn't get this hard, but so it's, you can't reclaim a level that you didn't dip under, but 405 was the level that held. So it's kind of saying that like these were the levels that needed to hold. And they did on a big double bottom. And double bottoms are always, like longs always love to see double bottoms. When longs see double bottoms, they, they get super excited. Like it's a confidence booster. It's, it's, it's like a consolidation hole. Right. And so that's the click on. And so we saw that, right? So we got that, we got that, that kind of, that confirmation and the sense of like, I, the more confirmation for me, the better, you know, as we're here at all time highs with inflation and taxpayer looming, the more confirmation technically we can have, the more comfortable I'll feel. But what do I think is next is, well, starting off, we're seeing a lot of bounces on a lot of the names, right? Like just, just look at, I mean, we can look at a little index here. Arc looks like this, right. That's not what I wanted to, but yeah, we're holding Baba too, but you know, kind of Tesla kind of looks like that. What was some of the other names that I did? But the Netflix, Netflix is kind of trying to hold on here. Like it's showing that we're trying to hold on to these bounces. What are some other data names that I had on that webinar? Same ones. You know, I can't forget, but we're seeing a lot. Yeah. Like, we're starting to, like we kind of held the support here we dipped under and reclaimed back over. So we're seeing a lot of that kind of positive, positive energy where it's, hey, maybe if this is double bottom, then like, you know, a lot of buyers might be saying, hey, this is a great price to buy a lot of these stocks, right? Like this is the bottom. I love the risk for reward here. So as soon as long as can start to think and confidence can kind of change to where it's not like, oh no, this is going to be a breakdown. And instead it's a, well, maybe this is just a long-term double bottom and that sentiment and that idea, that idea kind of switches over to maybe this is a good buy area. That's how confidence and sentiment starts to build and starts to stack. And, you know, I still think that the, that there's some disconnect between, you know, the spy and the cues and all of the Momo stocks, but all of the, all of the, you know, the leading stocks, because I keep clicking on it. All of those like leading, all those leading stocks and Momo stocks, they, the, the connect needs to come back, but it's, you know, we're looking in the right direction in the large pipeline as far as I'm concerned. And I probably will do some swing study over the weekend. I don't know if I will be buying on Monday, but I mean, I, I'll probably do some study and like, see, see what's out there, do some stands or something like that, just to see, and you know, I haven't even been interested in doing that at all for weeks for, for months since February, like 19th or something like that. I haven't even been interested in like looking at all. But oh yeah, the markets closed on Monday. I really don't know, Wes. I'm, I'm still looking for it. Yeah, but so, you know, we'll see how that plays out, but I am starting to look, I will be looking at some swing opportunities. Now just looking for some, just teasing my way in kind of what I'll be talking about this season. But, you know, we're starting to see these recoveries off the bottom. That's always bullish. But what we do need to see is the after effects of this balance, right? What we, this is, I mean, the ultimate proof is like, what happens after this balance? Like this reclaim off the bottom, this potential double bottom, does it just kind of stuff right away? And when I need my right of ways in the next one, four weeks, right? Like that's the thing is like the large, these Chocters, these stocks are so beaten, it's going to, it's not like a minute chart where you can just be impatient and get, you know, it's going to take a couple of weeks. But we're going to know in a couple of weeks, if people are, you know, kind of ready to, you know, they want to continue the downtrend, like the confidence isn't there, or people start to see this as a good buying opportunity. And as far as I'm concerned, as far as like swing trading and large cap trading is going, as far as longs are concerned, you just need the market to be on your side to have a good time. You know, like you don't need the market to go up necessarily, or like up, up, up, up, you don't need that hyper bullish market to make money. But what you need is just, you just need the market not to be in the toilet. And right now, like we're recovering off of toilet land. So like that's, that's, that's basically my view on it. And I think that we're getting close. I think this is the closest we've been to kind of coming off of what I, what I call the bearish market for the last few weeks. So I'm interested to see how, how we open up in the next week. But anyway, it's basically, we need to see how this balance kind of continues to know if the downtrend continues or not. Remember, all of these, this is supposed to take charts, these charts have a hard path up, right? None of these charts look pretty. So like I said, it could take a few weeks. But here's the thing I want to talk about. Basically, the tech, tech stocks basically just crashed when on our last market crash, right? Now, the thing about, I think that the market is changing its dynamic a little bit in the sense to where just because we have so much more participants, we're starting to see, we're starting to see that like momentum stocks for the larger cap market can change, right? Like, it doesn't, like the whole, the old Momo stocks might not necessarily be the Momo stocks that we see in 2021. Like they have been like, you know, the Tesla, the Neo, the Tiger, Tiger, JMIA, how are those charts right now? I want to look at those charts. Tiger, JMIA, right? What is the other one I just said? That's going to follow Tesla. But yeah, like these were and, you know, were the Momo stocks, but maybe they're not, you know, maybe they aren't, right? It doesn't have to be, but the Momo stocks that, you know, of the past don't necessarily have to be the Momo stocks of the future. That can change.  It could be other things that drive the overall market, right? So what I'm talking about when I say this disconnect between, you know, like the, that the, that the Momo stocks start to need to have better charts that match the spy, because I do think that the bullish market works the best when the spy is charging and the Momo stocks are charging. What I'm trying to get through is it doesn't have to be the same Momo stock. So I'm currently on look for, you know, any kind of other Momo stocks, any kind of other Momo sectors that could potentially replace the old ones, right? Because that could definitely, you don't want to be just waiting for Tesla to go back to all time ties because maybe it doesn't, right? Maybe other Momo stocks take the lead. And so we want to keep an eye on potential new Momo stocks and sectors that could, you know, whatever's matching with the spy, whatever energy kind of flows off of that, that's the, that's what we want to keep track of as far as sensing.


At the Federal High Court, Inaboja has stopped President Mohamed Buhari, Attorney General of the Federation and the Senate President from Temporan, with a newly amended Electoral Act 2022. Justice Inyang Iqor, in a ruling on an expert aid application filed by the People's Democratic Party, agreed that the Electoral Act had become a valid law and could not be tampered with without following any process. The PDP threw its council, James Inaboja, assay in, so the President, alongside others, challenged what he described as a beta-teencare with a newly amended Electoral Act. The party also applied for an order of the court stopping the National Assembly from giving effect to the President's request to remove Section 84, Subsection 12, from the Electoral Act hearing of the matter has been fixed for March 21st. Hello, hope you enjoyed the news. Please do subscribe to our YouTube channel and don't forget to hit the notification button so you get notified about fresh news updates.


We are discussing the notion of minimal polynomial right and see the objective as I stated before is to characterize diagonalizability. We already have one characterization you compute the Eigen values compute the dimensions of the Eigen spaces if the dimensions add up to the dimension of the vector space then it is diagonalizable okay dimensions of the Eigen spaces add up to the dimension of the vector space then it is diagonalizable we will look at another characterization in terms of the minimal polynomial okay this is another cornerstone one of the cornerstones in linear algebra that we have seen is a rank quantity dimension theorem okay. Now to prove this theorem you need certain notions today we will discuss two of them one is the invariant subspace invariant subspace of a linear transformation and then the notion of a T conductor okay so let me make these notions precise so I will first discuss the notion of an invariant subspace. T is a linear operator on V a subspace W is called an invariant subspace of the transformation T of the operator T if this condition holds T W is contained in W that is an invariant subspace okay. That is a meaning that is for all x element of W it must follow the T x belongs to W okay let us dispose of the trivial examples of subspaces W equal to singleton 0 and W equal to the whole space they are obviously invariant so we will be interested if there are proper subspaces that are invariant under T okay and you will see how this plays a role in characterizing diagonalizability. Let us look at some examples may be before examples before numerical examples let me also tell you that the range space and the null space are invariant under T these are easy to verify so I will leave the proof for you the range space and the null space are invariant under T okay we also have another set of subspaces that are invariant under T let S be a linear operator on V such that S T equals T S S is an operator that commutes with T suppose S is an operator that commutes with T then the range and the null space of S are also invariant under T okay remember for us T is fixed for us T is fixed S is an operator that commutes with T then range and null space are invariant under T all these are little exercises for you okay to verify. In particular what is relevant to the present context is the eigen space corresponding to any eigen value these are invariant subspaces for any operator T because of this result look at look at T minus lambda I for any eigen value lambda and this commutes with T T minus lambda I commutes with T so in place of S I have T minus lambda I where lambda is an eigen value so by the previous theorem a previous result which we did not prove null space of T minus lambda I is invariant under T but null space of T minus lambda I is precisely the eigen space of the operator T corresponding to the eigen value lambda so eigen spaces are invariant under T eigen spaces of an operator T are invariant under T okay this is the most important consequence for us okay let us now look at one example where the operator does not have an invariant subspace if you want operators for which there are invariant subspaces just look at any operator which has an eigen value this theorem says the eigen spaces are invariant okay so I want to give an example of an operator which does not have an invariant subspace this goes back to the example that we have seen before okay I want you to look at T from R 2 to R 2 whose matrix is okay I am really looking at the rotation operator so the matrix of this okay I will straight away define T, T is defined by the rotation operator T of X is minus X 2 X 1 this is the rotation by 90 degrees rotating the vector X by 90 degrees this is the linear operator I want to show that this operator does not have any non-trivial invariant subspace okay 0 and R 2 R trivial is invariant subspaces so if I take a subspace which is non-trivial which is invariant under T the subspace must be of dimension 1. Let W be a one dimensional subspace invariant under T I look for a one dimensional subspace and see if it is invariant under T so I am assuming there is one such it is one dimensional so the basis consists of one element so let me take W to be span of a particular vector X star X star is not 0 okay X star is not 0 suppose T W is contained in W if T W is contained in W, T W is in particular for X star I will have T X star also as an element in W T X star should also belong to W but W is span X star so it is a multiple of X star this must be alpha X star for some scalar alpha W is span by X star so anything is a multiple of X star but this means a alpha is an eigen X star is not 0 this means alpha is an eigen value for T but we know that T does not have eigenvalues this is a contradiction so this T does not have an invariant subspace this is a contradiction to what we had seen earlier and so this T has no proper invariant subspace okay so much so for invariant subspaces let us keep this aside and then look at the notion of the T conductor of a vector into a subspace is this example clear this operator does not have a proper invariant subspace we had looked at this example before and we have shown that this operator does not have an eigenvalue if lambda is an eigenvalue we had seen that 1 plus lambda square is 0 but this is an operator on R R 2 to R 2 so the eigenvalue must be real so there is no root for 1 plus lambda square equal 0 so it does not have an eigenvalue if it had an invariant subspace it would have had okay next is a notion which is rather similar to the minimal polynomial okay but little more general than the minimal polynomial that is another notion we need for characterizing diagonalizability of operators the notion is the following I am having a subspace let W be an invariant subspace of the operator T let W be an invariant subspace of an operator T see for us the framework is T is an L of V V is finite dimensional we are trying to characterize diagonalizability okay W is an invariant subspace of T let Y belong to V but not in W the T conductor the T conductor of Y into W that is the name the T conductor of Y into W I will define this to be the following subset of F of T is defined by the notation is S T Y W the T conductor of Y into W W is an invariant subspace Y is an element that does not belong to W T is the operator that we started with S T Y W this is the set of all polynomials G in F T set of all polynomials with coefficients coming from the underlying field for us either real or complex over the single real variable T we know it is a principal ideal domain so collect all those polynomials that satisfy the property that G T Y belongs to W Y does not belong to W but G T Y must belong to W G is a polynomial G of capital T is a linear operator on B so G T Y make sense I collect all those polynomials that satisfy this property for a fixed Y fixed subspace W and T is of course fixed collect all the polynomials that satisfy this property for a fixed Y for a fixed invariant subspace W that will be called the T conductor of Y into W okay this is the collect set of all polynomials I am going to leave it to you to prove that this is an ideal this is a subspace and has a property that if G belongs to this and F belongs to capital F then the product belongs to this is an ideal so it has a generator that is each element each polynomial in this is generated by a unique polynomial that polynomial will also be called the T conductor of Y into W but before that is this non-empty first question we have defined something similar the minimal polynomial is there any relationship between the minimal polynomial and the T conductor of Y into W what is the property of the minimal polynomial one important property it is an annihilating polynomial M T of any X is 0 so this Y also M T of Y is 0 what is the problem the minimal polynomial is an annihilating polynomial so M of capital T of any vector must be 0 W is a subspace so that must belong to W so to begin with the minimal polynomial belongs to this okay but there are more general elements that is the important point here there are more general polynomials but they cannot be annihilating polynomials remember that because if they were annihilating polynomials of T different from M of T their degrees will have to be greater they cannot be smaller there are annihilating polynomials agreed but the degrees of those annihilating polynomials will be greater than the degree of the minimal polynomial minimal polynomial definitely belongs to this so this is not M T okay this is non-empty ideal of the principal domain F T so this is generated by a single unique element that will also be called the T conductor of Y into W okay so I will simply say that the unique we will be interested in the monic generator the unique monic generator of S T Y W will also be called the T conductor of Y into W it is also called the T conductor of Y into W so depending on the context we will know whether we are talking about the subspace or the unique monic polynomial okay see we have seen that the minimal polynomial belongs to this so can you immediately conclude that this T conductor divides the minimal polynomial what is the meaning how does it happen let us denote G let us denote let us denote the T conductor by G that is we have S T of Y W this is generated by the single polynomial G that is what I mean G is the unique monic polynomial which generates this ideal then what we know is that since M belongs to S T Y W it follows that G must divide M G must divide M G must divide M but this G cannot be an annihilator because of G divides M then the degree of G is less than or equal to the degree of M in general this cannot be the this cannot be an annihilating polynomial of the operator T I will give you an example of this G okay but before that let us prove the following result so remember G divides M so this is more general than the minimal polynomial the T conductor of a vector into a subspace is more general than the minimal polynomial of the operator T okay then we have the following result see our problem is to characterize diagonalizability but what we would right now do is to settle with something less is to settle with the triangulizability so let me give the definition an operator T is said to be triangulable is said to be triangulable if there exist a basis script B of V such that the matrix such that the matrix of T relative to B diagonalizable it is a diagonal matrix triangulable if it is a triangular matrix such that this is triangular, triangular means either the lower off diagonal entries are 0 or the upper off diagonal entries are 0 we will stick to the lower being 0 so we will say that T B is it does not make a difference we will say that the lower triangular part is 0 so it is upper triangular an operator T is said to be triangulable if the matrix of T relative to some basis of V is upper triangular let us first characterize upper triangular matrices we will need the following result it tells you something about the structure of G I want to state this lemma before characterizing triangulability this lemma will be useful there T is a linear operator on V and W be a proper invariant subspace of T let lambda 1, lambda 2, etc lambda k be the distinct eigenvalues of T and let us suppose that the minimal polynomial M stands for the minimal polynomial let us suppose the minimal polynomial can be written as a product of powers of linear polynomials that is T minus lambda 1 to the R 1, T minus lambda 2 to the R 2, etc T minus lambda k to the R k the minimal polynomial is a product of powers of linear polynomials then we have the following first there exists x which does not belong to W condition 2 is T minus let us say lambda i x there exists an x that does not belong to the subspace W T minus lambda i x belongs to W for some eigenvalue this is what we will show there exists an x which does not belong to the subspace W but which has the property that T minus lambda i of x belongs to W for some eigenvalue lambda okay we will prove this lemma and then use this to characterize triangulability and then characterize diagonalizability see remember already the minimal polynomial appears here okay so the minimal polynomial will play a crucial role in the diagonalizability which is what we will at least state today the proof is as follows see before that I told you I told you that we will have some information about the polynomial G the information that is provided in this theorem is as follows under the very mild condition that the eigenvalues of the operator T exist under the very mild assumption that the eigenvalues exist if the eigenvalues exist then you can write the minimal polynomial in this form okay so except for operators like the rotation operator this condition is satisfied under this condition what this says is that this T conductor of the vector x into W is a linear polynomial can you see that the T conductor see we are interested in the T conductor of x into W from this can you see that x does not belong to W but T minus lambda i x belongs to W so all you have to do is look at the polynomial little T minus lambda this polynomial has a property that x does not belong to W means the G is not the constant okay G is not the constant polynomial from constant you go to linear polynomials this says that G must be a linear polynomial there exists an x which has a property that the T conductor of x into W is a linear polynomial that is second condition really okay that it is not constant is a first condition okay as I told you I will give a numerical example but let us first look at the proof of this result see W is not equal to V W is proper subspace W is a proper invariant subspace so this is not the whole of V so there exists x in V such that x does not belong to W I will look at let me call it y there exists y such that y does not belong to W I want to now look at let G be the T conductor of y into W W is not the whole space V it is a proper invariant subspace I pick one element y which does not belong to W and then construct in principle the T conductor of y into W I am calling that T conductor as G can you see that G cannot be constant G cannot be a constant why because if G were a constant then what is the property that G satisfies G T y belongs to W okay this property satisfied by G in fact among all those polynomials that satisfy this condition G is the one with the least degree coefficient of the highest degree is 1 etc coefficient of highest degree is 1 this is a unique monic polynomial that satisfies this condition so if G were a constant then this would be a constant constant times y belongs to W means y belongs to W but y is something that we started with does not belong to W so G is not a constant G is not a constant polynomial so it must be T minus lambda J into H of T where the degree of H is strictly less than degree of G so H T y does not belong to W also if you look at T minus lambda J I x it is T minus lambda J I H T y that is G T y which belongs to W coming from this okay G is not a constant so it must be at least a linear polynomial so G is T minus lambda J into some H H could be a constant but H definitely cannot be a constant because otherwise you will get a contradiction here so the degree of H is less than the degree of G and so H T y cannot be in W I am calling H T y as x now this x satisfies the second part x does not belong to W alright but look at T minus lambda J x that is T minus lambda J I into H of T into y which is this operating on y that is G T y G T y belongs to W so we are through okay so this is the x that satisfies these two conditions so what follows is that G is a linear polynomial that is the consequence so to summarize there exists x which does not belong to W such that such that the T conductor of x into W is a linear polynomial okay okay I want to give a quick example you please verify the details yeah yes H T cannot be a constant actually oh we are proving H T is a constant yes we are proving H T is a constant we are proving H T is a constant H T is a constant is also consistent with this statement H T is a constant this is a multiple of y y does not belong to W so this does not belong to W H T is a constant is what we are proving yes okay the T conductor is a linear polynomial. Let us use this in characterizing triangulability okay I told you I will give an example you please verify the details I just have the information this example is that of the second example of an operator which is not diagonalizable I want to look at the operator over R 3 whose matrix is this 3 1 minus 1 2 2 minus 1 2 2 0 the characteristic polynomial of this matrix is we are using P for that P of T is T minus 1 into T minus 2 the whole square that is what I remember T minus 1 into T minus 2 whole square I will call lambda 1 as Eigen value 1 lambda 2 equals lambda 3 equals 2 this is an example of an operator which is not diagonalizable let me take let me take W as W 1 the Eigen space corresponding to the first Eigen value set of all x in V such that R 3 such that A x equals x A x equals lambda x lambda 1 x that is A x equals x so this is the Eigen space corresponding to the Eigen value 1 the first Eigen value remember that in this example we do not have enough Eigen vectors for a second Eigen value the second Eigen value has only one Eigen vector span by 1 0 2 okay the second Eigen value has only one independent Eigen vector the Eigen space corresponding to second Eigen values of dimension 1 I will take W 1 this is an invariant subspace any Eigen space is an invariant subspace of the operator T so this W 1 is invariant I want to give an example of the Y that is constructed in the theorem so let me give this Y as 1 1 2 take this Y what is the T conductor of this Y into W 1 verify it is T minus 2 for this Y please verify it is T minus 2 okay now remember that for in this example we have verified that the minimal polynomial is the same as a characteristic polynomial okay but the T conductor is a linear polynomial so this is something more general than the minimal polynomial okay but it pertains to only a particular vector Y so please verify the details here this should sort of consolidate what we are doing there okay I want to characterize the triangulability it is just one factor no see minimal polynomial is T minus lambda 1 to the yeah here T minus lambda 1 to the R 1 etc G is just one of those factors what is the problem M is a multiple of G G divides M G divides M so M is a multiple of T multiple of G so one factor T minus lambda J for some eigenvalue rest of them are here one more factor no we are proving it is a constant if it is a constant then how it is divided that is my question that constant is 1 yeah the constant is 1 that constant is 1 it is T is 1 pardon we do not know presently we do not know in this proof we do not know what H T is the only thing that I know at this stage see it is not a constant so it could be a linear polynomial quadratic polynomial whatever okay but at this stage I can this right this much there must be a linear factor forget about H but H now has a property that its degree is 1 less than G so H T Y cannot be in W that is the property we are exploiting okay remember G divides M the degree is less than or equal to the degree of M but G in general is not an annihilating polynomial okay so I need to yeah use this lemma to yeah use this lemma to characterize triangulability let us see how far we can proceed so I want to characterize triangulability this is the general theorem an operator tree is triangulable if and only if the minimal polynomial is a product of linear factors an operator tree is triangulable if and only if the minimal polynomial of the operator is a product of linear factors there are possible powers okay but it is a product of linear factors okay so I do not think I have enough time to prove it but I will at least make this observation that if an operate if the eigenvalues of an operator lie in the underlying field then the operator is triangulable if an operator has all eigenvalues in the underlying field then it is triangulable okay but not all operators are diagonalizable okay we have already seen operators examples of operator at least one which is not diagonalizable but all operators are triangulable provided you only meet this minimum condition mild condition that the eigenvalues must belong to the underlying field okay.


Imagine being at sea hundreds of miles from land the last thing that you want is a fire to break out All hands magazine visit a firefighter training course to show how sailors can work together to be able to correct their shipmates and ultimately the ship It's more about a team building throughout the week Cohesiveness working together A lot of times when the ships come down They're coming out of an extensive overhaul period or they're about to deploy and they've got a newer crew So it's all about kind of coming together Working together knowing each person's job and that's what we tell them each one teach one That's what we kind of tell them throughout the week to learn more about how to attend the course and what it offers Visit the natc website Stay tuned to all hands magazine for an extensive look at the shipboard aircraft firefighting course


Hello! Let me go back in time. Five years. I'm at a thrift shop with my wife, looking for stuff for my daughter, who was one at the time. I see this horse, made by Fisher Bryce. It bounces, but it's also digital. It comes with a little unit that you hook to your TV and your kid can ride this and play simple little games up on the TV. I'm looking at it. It is priced, it was $6 or $7, which I thought was a good deal. I didn't know if it worked or not. I thought, you know what, if it doesn't work, she can still ride it. And maybe I can put electronics in it to make it to work, to get it to work. Well, while I was there, I looked it up online on Amazon. These things were like 120 to 150 bucks new. I was like, of course I'm gonna buy it for $7. So I get home, and it did work. And the games came with, were decent for, you know, one year old. It had different levels, so you can make it more difficult. But basically, it was just, you know, they bounce around it. Again, it moves like this and it's got two buttons on the back here, and it's got the spin thing. Different things would happen.  And all that was controlled through infrared LED lights right here, which sent out a digital signal, which I did once quickly look at with an Arduino and an infrared receiver, and it sent out a barrage of information. It would take me a while to fit through all that. But theoretically, I could program this, or I could program an Arduino to receive those signals, send them to a computer, and control the game. But I went one step simpler. So this was five years ago, and it has been sitting on my porch most of the time since then, collecting dust. My wife has asked me to get rid of it, and I said, well, you know, I've been pulling on to it to make a video, because, you know, I'm so quick at doing those things. So again, the video done now, so that we can get rid of this now.  I just started doing Linux videos on YouTube. And some of my earliest videos were on this device. These are amazing pieces of hardware. We control. This is a real weak controller. I also have some third party ones. You know, they're 10 to 20 bucks when you buy them, at least last I checked when I bought mine. I don't own a Wii, but I own a couple of these. These things are amazing for their price. They have microphones, they have speakers, they have LEDs, they have multiple buttons, they have accelerometers, they connect through Bluetooth, and the front here is an infrared camera that can detect the movement of infrared light. This horse sends out infrared signals. And yes, like I said, sending out signals, digital signals based on where the buttons are pressed, where the horse is moving. But I didn't care about that. I wanted something very, very simple. So what I did was I designed a very simple platform gamer, if you can even call it that. We're just a character, runs across the screen and collects stars. And how do you make the character run across the screen? Well, you move the mouse. You fast you wiggle the mouse, but faster the character would move. So all I had to do was install the packages using my package manager to connect to the Wii controller through Bluetooth and tell it to look for infrared light and use that to move the mouse. It doesn't matter where the mouse is moving. They would just detect mouse movement, hook the computer to the TV, set this on the counter in front of my daughter, and as she rolled the horse, the character moved across the screen and collected stars. It was good. She had fun for about five minutes. But the thing is that the games it came with, she was amused for about five minutes as well. Kids just don't have attention spans. But the point of this video is telling you that if you're interested in getting into hardware, definitely there's a lot you can do. But the simpler you keep your projects at first, the less discourage you'll get. This was so simple to do. And you may already have one of these lying around. And you know what? If this didn't work and it didn't have the infrared lights up here working, this also can control the mouse through movement with the accelerometers. So theoretically, I could just take this here and the movement of the horse making the control move could have moved the character across the screen. So if you have any type of rocking horse or riding horse, you can hook one of these to that and have it control the mouse cursor moving the character across screen. Again, very, very simple. But it's a starting point. And move on from there again. I could detect the signals from here infrared signals and read the raw data on whether the buttons are being pressed. This is being spun this way or that or whether it's moving up and down. And I can correlate those to keys in a game. And like I said, theoretically, I mean, I got two buttons here and I think it does different signals ready to go this way or that way that that's at least four buttons and then movement. I don't know if I can do that if that's enough to play do maybe a little bit. I guess I can go left and right and shoot. I don't know. And then this can move forward. I have to look into that. Anyway, this video was put up my films by Chris. I'm Chris. That's Chris Decay. There's a link in the description films like Chris.com. And I just thank you for watching again. This is wasn't a very technical video, but I just wanted to just throw ideas out there. If you're looking into getting stuff, don't over complicated at first. Don't discourage yourself. You can do very simple things. If you don't have a Wii controller, it is a fun thing to play with. Even if you don't have a week because you can program it to be any keys on the keyboard or game controllers. You can program for any game on your computer. You can install a couple packages on Linux and you're ready to go. Anyway, I do thank you for watching. As always, visit filmsbycris.com. That's Chris Decay. There's a link in the description. And I hope that you have a great day.


So our next speaker is Dave Asprey. He's a new speaker to the 21 convention. He's a Silicon Valley investor, entrepreneur, blogger, computer security expert, and notorious biohacker. Cool stuff. He's got, on average, 150,000 unique visitors coming to his site every month. He's also featured on CNN Nightline, so he's got some amazing stuff to share, I'm sure. And you can find out more about him at his site, which is bulletproofexec.com. Help me welcome Dave to the stage. Thanks. Thanks for having me here, everyone. I'm going to tell you a quick story. This is me. When I was about 22, I was featured in Entrepreneur Magazine because, well, I was the first guy to sell anything over the internet, literally, the first guy. I don't look that old, do I? I paid for my computer science undergrad education, selling t-shirts that said caffeine, my drug of choice, you can see one back there, to 12 countries, over Usenet, because we hadn't invented the web browser yet. I ate 1,500 low-fat calories a day, not all the time when I was in college, but when I got serious about trying to lose some of the fat you see here, I got to the point I'd work out an hour and a half a day, six days a week. I couldn't lose the weight. I had 297 pounds when I was in my fourth year at University of California, Santa Barbara. And because this is a conference where we talk about things like dating and whatnot, I'll tell you about my first internet date. Working in the computer lab. Yes, I did hacker terminal. I was trying to find a picture of what that looked like, and I think I got it down, because when I'm hacking, I hold my laptop like this, I type like this, and I wear a mask. I still do that. You and me both. About 13 years ago, I ran the program for the University of California. These are all public photos you can prove. This one was published in a bunch of course catalogs. It's hard to see with this light, but I was puffy, and I was pretty fat. My career's on fire, though. I made actually $6 million when I was 26. Not bad. A little bit less exercise, though. See, fewer carbs. I've only lost about 50 pounds. Not a bad deal, really. The problem is my stress levels are going up, and stress goes up as you start working more, and you start dating more. Oh, wait. It actually happens, and for me, my brain started misfiring. I literally was at work, and I would think about this and say, I can't remember what happened to me today. Something's really not working very well here. I took a computer game called FreeCell, and we have way better tools today, but FreeCell's a solitaire game. Some days I could perform well, some days I couldn't, and I got a verifiable quantitative metric that said my brain is doing this every day. Otherwise, our ability to know how well we're doing it any one time is pretty fuzzy using data help.  All the seventh graders were right. Decided I was gonna make money fast and live forever. What the heck? There we go. I was featured in Monster Careers, one of the first books about how to do online networking to have an amazing job. Accompaniment bankrupt. My brain got really broken. If you think that you've had stress in your life, try being set for life with six million bucks when you're 26, when you're 28, realizing you're gonna have to work for 20 more years.  I put my anti-aging research online for the first time and I was actually about Jolly's age when I was 28. So I've been doing this for a long time. When I was 29, I took some measurements. It's hard to read any doctor's handwriting. Sorry there, Dr. McGuff. This says increased risk for stroke myocardial infarction.  That was bad. This is a picture of my brain. Colors are a bit hard to make out with these lights. The red parts are the parts where there's no metabolic activity when there should be. This is not a good thing when you're trying to have a successful career, things like that. And worst of all, interesting referral.  So the good curious doctors like that, but the patients don't. A decade later, I spent a quarter million dollars on my own money biohacking myself, working on upgrading every system I could find. My career is pretty darn good. I got my MBA from Wharton while working full time. I have an angel investor. I have two young kids, a happy, healthy family. My book comes out in January published by Wiley and Sons. Gary Tobs introduced me to my agent. So this is all top tier stuff. At the same time, I'm a vice president at a large internet security company. I'm about 210 pounds, give or take muscle mass. 45 minutes a month is the amount I exercise now. I can do five hours of sleep for two years in a row and maintain my cognitive function and my autonomic nervous system stress. I have highly optimized biohacker nutrition, which you're gonna hear about in a little bit. I've raised my IQ by more than 20 points, between 20 and 40 actually, depending on what day it is.  My vision, my hearing and the way my brain works are all very different than they were when I was younger. I'm quoting a world-class anti-aging doctor who does metrics on my blood with me. He says, my risk is as low as it gets for diabetes, for heart disease, for stroke, and for cancer. All the markers that we monitor, they're very low, yet I eat a stick of butter every day. Hmm, so how'd I do this? Systems thinking, which is basically the way hackers think. What that means is it's not just my body. My body is a system and the system interacts with the systems around it, all of the things that are here. When you look at things that way, rather than this is a knee or this is a joint, you can actually do things with your body and with your life that you wouldn't expect. You correlate things over time. You can't just notice something once. You need to look for patterns all the time. In real time, feedback has been transformative for me. You can reprogram the way your nervous system works by getting feedback on what it's doing.  The people who are really good at that spend all day everyday meditating. They're called Buddhist monks and they can basically dry a sheet in an ice storm with body temperature that they raise consciously. I don't really have a lot of time to sit into bed and meditate. So how do I get that ability to have really good wiring to really understand what my body's doing? Well, I use technology. I've also learned a ton from a ton of really smart people because I run an anti-aging nonprofit group and I've been involved with them for more than 10 years. So more than 100 experts I've had personal time with as well as all the ones I've paid to be with me. I threw money at the problem. I'm here today to show you all the stuff that works best so you don't have to throw money and spend a decade doing things to yourself. I've hacked my sleep. I mentioned five hours and I just just fine. That's a conscious change that I made to improve my sleep efficiency. If you only remember one thing from this presentation this is what you need to do with everything in your life including dating, including weight loss, including putting on muscle, including getting a raise at work. It's you try what's supposed to work. When it doesn't work you ignore it instead of trying it over and over and over and over. And then you try what shouldn't work. So if you try the normal things it's all right to go out on the deep end and see what's going to be there.  No one. I did an experiment. I said, hmm, I know that butter and other healthy fats are the cleanest burning things in the body that cause the least inflammation. What if I try just increasing the amount of this and then I looked at what happened? So you're just creating a feedback loop for yourself. You can discover amazing things about what works in an online company, what works in dating, what works anywhere just by following this iterative process. It's the same one they teach you in business school and it's the same thing hackers do when they're breaking into your computer. So what did I do? This is me in Ecuador. I saw a shaman did ayahuasca in the jungle. Yeah, that's not exactly a Western thing but it worked pretty well to help get some more awareness of what's going on in my body. This is a picture of me when I was still somewhat heavy with Barbara von Dyson. She's the head of the American pre and perinatal psychology association. She's spent her entire life teaching people how their emotions work. I did basically 20 years of therapy in a week. It was a really hard, painful week but I learned more about why I am the way I am than I ever would have known before which gave me the power to change. You wanna effectively be able to date people, understand what's going on in your emotions all the time at any time and then get conscious control of that. When you can do that and you can turn down your stress response like that because it's a learned skill, you can walk into any situation. It doesn't matter. I can walk on stage in front of thousands of people and I do it regularly in my job. I don't have stage fright. Not a bit of it. My heart isn't even racing. I'm not sweating. I'm not feeling any of those things. I'm just feeling turned on and engaged and you can learn to be in that state. This is me in Nepal actually.  These guys. That's Mount Kailash. I climbed around the headwaters of the Ganges in remote Western Tibet. Spent some time learning. Became really good at yoga. Although I don't practice it every day. It's not necessary. In fact, I haven't practiced it much since I had kids. Normally I'd be able to right now put my ankle behind my head but I did that cool machine we had last night and I can barely stand. My legs are so tired from it. So. This is a cave outside Sedona in the middle of nowhere. I spent four days fasting under the guidance of a shaman. All by myself. Didn't eat anything. Had nothing but water. Just to see what's it like to be alone. Really alone with no one for 25 miles in any direction.  It was a really good experience and this is the kind of thing that you do.  You understand what happens outside my norm. There's no slide for it but I did an urban escape and evasion course in LA. The final exam after two days of training they handcuffed me, hooded me in the back of a van with other people and I had to pick the lock, escape and spend all day with 12 bounty hunters chasing me. You know what? I learned more about how I behave under pressure doing that than I ever have in the rest of my career. I'm not kidding. This is me with a 64 channel EEG. You wanna know what's going on in your head? Look. This is a $15,000 seven day super intensive course of EEG training I did. This is another slide from that where you learn to consciously control your brains. This course teaches you to have the same brain state as someone who spent 40 years of daily Zen meditation practice and advances in master seven days. Side effects, 12 IQ points, 50% increase in creativity and the ability to turn off the voice in her head that says she doesn't like me. I learned from a lot of experts. I'm the chairman of this anti-aging nonprofit group that's been around for a long time. We've had an incredible roster of speakers over the years like Steve Fox. He wrote the book on smart drugs and nutrients called smart drugs and nutrients too. He's a personal friend and a source of guidance for me. Aubrey de Grey, bio gerontologist from Cambridge University. I can email him anytime, he's a great guy. Bruce Lipton, one of the leaders in epigenetics and understanding how the environment and how your thoughts affect your genes. Gary Tobs, good calories, bad calories and all sorts of other weird stuff like neurofeedback, ozone. All this stuff I've boiled into the recommendations I'm making here because I'm gonna give you guys six top bio hacks from a quarter million dollars in 10 years of actually 15 years of work that I've done. And then I've got a special one that I added on that has never been presented before. Wow, this is kind of a tough image. It's a little bit washed out, but there's something you need to know about you. You control which of your DNA actually gets used. Your DNA, which is the picture here, stores your genes. It's like a hard drive. Over here, your RNA. It, and I'm simplifying things quite a bit here, it copies your DNA. Around your DNA, you have something, again simplifying some steps, we call a regulatory protein sleeve. This acts like a firewall. And these gaps in it are controlled by a few things. They're controlled by your exposome. We all know we have a genome, 23 and me. You can measure your genes. The exposome is the source, is the list of all the things around us that we're exposed to. The light we're exposed to, what we eat, the toxins we're exposed to, all the stressors in our life.  And this one sucks, but it's your emotions. What you think about and what you feel, change which genes get expressed. What's going on in here and in here and in here actually changes your genes. Cool thing is hacking your genes is really difficult because you need to write a retrovirus to rewrite your genes. Good luck with that. But you can actually hack your exposome pretty easily. You can change the room temperature. You can eat a healthier diet. You can calm your emotions. You can control your biological processes with your exposome. And if you tie immediate feedback in, you get, wow, I did this. And look, I feel better today. I can feel it. My brain works better. I can measure that using a five minute online tool from Quantified Mind. You can see it throughout what you do. Even the strength of your grip changes based on your environment around you. And it passes down to your kids. My book that comes out is what do you do before and during pregnancy in order to have healthier kids? Not just healthier but smarter and ones who have better genes that pass on to their kids. And I have a bit of dating advice for you. Women can smell men who are fertile and healthy. It's in your BO. You eat the right diet. You walk into a room. You have pheromones like other men don't. And I will tell you I'm happily married and all. At a recent conference, a woman sat down next to me at dinner. It was a paleo conference. And she looked at me and she said, what is it about you? I said, what do you mean? And she basically said, I don't know how to really say this to you but basically I want to eff you more than anyone I've ever wanted to in my entire life. Okay. I wasn't picking up on her. Like I have a three year old and a five year old. But what was going on there was that's a pheromonal thing and it's common. Tim Ferriss writes about it in his books too. How when you eat the right diet for him, he was maybe he went off beans for a little while, which I would not put in the right diet. But he raised his eggs and red meat. And he says, you walk through and people turn and look. So what you do, your emotions they pick up on that. They pick up on your body language and what you say and what you do. They also pick up on how you smell. And that comes because women are optimized for knowing when is a good time to have kids. When is fertility going to happen? And who's a good mate? And you can make yourself a better mate by simply controlling the toxins you eat and by having healthier diet. And you tell the woman after you've been dating for a little while, hey, my swimmers, don't make deformed children, which is true. If you control your toxins, do you eat the right things? You become way attractive as a mate. A little early for most of you, it happens.  It's the next part of this. So you can rewrite your genetic code, your physical body. What about your brain? We've learned about neuroplasticity.  We've blown that out of the water. But neuroplasticity is important because it shows there are many things you can do that change the way your brain works. There's something called myelinogenesis. When you put insulation around specific nerves, which is called myelin, they conduct electricity 3,000 times faster than unmyelinated nerves.  Practice makes perfect, practice also makes myelin. So does eating a lot of fat, which is what myelin is made out of. If you don't eat the fat, it's hard to make myelin and your practice doesn't stick as fast. Synaptogenesis is the other thing that you do. When you think about something, including being happy or being successful, the parts of your brain that do that get exercised just like your muscles get exercised. And when you do that, you build new synapses. And when you build new synapses, then you can put myelin around your nerves and you can continue to improve this. We have MRI studies showing that you change the physical structure of your brain as you do things with what you think about and even what you feel. From there, top six biohacking upgrades. It's hard to see on this, but this is like a cool biohacker laboratory setup at the bottom here. Number six, this is quick and simple. Strengthen your immune system with the sunshine vitamin, vitamin D3. How many of you in here take vitamin D3? Look at this, we've got a good portion, maybe a third.  Sorry, it's like $3 a month for the amount that you're likely to need. And if you do this, by the way, the amount you need, 1,000 I use per 25 pounds of body weight according to the vitamin D research council, I recommend a $40 blood test to see what your levels are so you can actually tie a trait to get them there. Some people respond well, some people don't respond as well. This will bump your numbers up pretty substantially. The reason you do this is that having vitamin D levels that are adequate will actually be more effective in stopping the flu than a vaccine against the flu. It also stops things like cancer, heart disease. It doesn't stop heart disease, but it diminishes your chances of it and it reduces inflammation. Vitamin D is involved in more than 1,000 processes throughout your body. It'll take months after you start taking it to fill up all of the different metabolic pathways that need to be filled up with the stuff. It's cheap and it's simple and if you're not doing it, you're just short changing yourself. It also affects mental function. If you're brown, you need more. The reason is that we form this when we're in sunlight without clothes and without any sunscreen on. If you have dark skin, or if you especially have dark skin and live in a northern environment like Canada where I am, it is vitally important that you get your vitamin D because you're optimized to make vitamin D after all day in the sun near the equator. And if you're not near the equator or you're in an office building under fluorescent lights all day, you've got no vitamin D. Sunlight is other things besides vitamin D and you still should be in the sun without sunscreen whenever you can, but at a minimum, make sure you do this. We actually have cases in the US now of really caring parents who restrict the sunlight that their kids are exposed to so much that kids get rickets. Yes, and there's even cases, especially among black people who have the highest need for vitamin D because they respond less to sunlight where parents are accused of beating their kids because their kids have broken bones. The bones are broken because there's not enough vitamin D to put calcium in the bones. There's no abuse going on. And it's one of those tragedies happening. It costs $3 a month to fix.  It's just easy. Maintain your hardware. This is a picture of the bulletproof diet. It's an infographic, one page you put on your fridge. It'll summarize all of the knowledge you need to know. It's related to paleo. It's not derived on paleo. It's derived from biochemistry and biohacking. It's paleo with less toxins. And I'll explain why. There's no cost. There was six weeks to make the infographic. There's more than 1,000 references that went into the research that makes it. If you eat that diet and you exercise at high intensity for short duration, in fact, I'm pretty sure you'll hear about that with the Body by Science guidelines. I have links to Body by Science, which is Dr. McGuff's work, linked to from the blog. And it's totally worth understanding this. If you wanna have more time, let's see, you just took your vitamin D, so now you don't get sick as much and your body works better than it did. Now you have more time for work or for dating.  Or do I wanna work out every other day? Or do I wanna work out for 45 minutes a month? I'm not the most ripped guy in this room, but I think I work out the least amount of anyone in this room. I also don't sleep nearly enough, compared to what most people have to do in order to generate muscle. And that's because I've optimized these things over time. Here's the basic, basic tenants of the diet. Divide your calories like this. Tons of fat, 50 to 70%. Your animal protein, about 20% of calories. I'm gonna plug a product here because I brought some for you guys. This is upgraded whey. This is a whey protein that I formulated myself to be the most effective whey, because 20% of it is a pharmaceutical grade, bovine serum albumin extract, which is the active ingredient in whey that gives you the most immune function. A couple tablespoons of that a day raises immune function, things like that. This is an animal source protein. So is the one I recommend most of all, beef, lamb, eggs, things like that. That's what you wanna do. The idea that you're gonna eat soy or wheat, or just that protein as protein is total BS. Vegetables, up to 20% of calories. It's hard to eat 20% of your calories from vegetables. Actually really hard, don't force it. If it's only 10%, you'll be fine. And fruit or starch, up to 5% of calories, but not a lot every day. I recommend you do some starch of a specific form that's all in the bulge of diet. Every, basically once a week, maybe every three to seven days if you're exercising a ton.  Here's the variables. And no one teaches how to think about food like this that I've come across. The first thing you look at is macronutrients. Does it have the right kinds of protein? Does it have the right kinds of fat? Does it have the right kinds of, or lack the right kinds of starch? If that's right, then you go on to the next step. Does it contain anti-nutrients in it?  They make me less healthy. That's the part that lots of nutritionists skip entirely in favor of number three, micronutrients. Oh, it has potassium in it. I have a diabetic friend who weighs about 380 pounds.  I'm like, what are you doing eating bananas? You have diabetes. He says, well, I have potassium, I have high blood pressure. He clearly didn't understand this, okay? This one was wrong and he went right here. And if the banana was black with spots in it, he was getting a lot of anti-nutrients from the fungus that makes the spots, which is called fusarium. So you just need to pay attention. That's the order of operations for food. If you get this, when you look at a soybean, you'll recognize that you really shouldn't eat it or even feed it to the things you're gonna eat. I don't know how to put it any more bluntly. Calories are mostly a scam. If you wanna measure your food, you can weigh it in grams or calories. But to sort of make a point here, it's the quality of what you eat. It's possible to eat too much and get slightly heavier from that. But I did an experiment, 4,000 calories a day with tons of butter and fat using the Bulletproof Diet, a low carb, even lower carb than that for two years. I grew a six pack during that time. I slept less than five hours a night, 4,000 calories a day and I didn't exercise at all for two years. My markers of inflammation were low. My autonomic nervous system stress levels were low. I did a whole bunch of lab work to try and prove what I was, what harm I was doing to myself. I couldn't find it. I'm not saying you need to eat 4,000 calories a day, but I will tell you, 20 to 30% of your calories are going up here.  Eat high energy foods. That's fat. Be in fat burning mode often. And eat happy things that are healthy. So that's grass fed meat.  Before we get into using your body, I'm gonna give you a few hints. Butter will satisfy you and keep you going all day long. Problem is a lot of people fly. This is a soap dish. It costs 99 cents. When you put butter in a soap dish, it looks like soap. In fact, you could even argue legally with anyone who wanted to say otherwise that you use it to cleanse your skin. Therefore it is soap because soap is made of fat mixed with lye. You can carry this in your carry on luggage. Even if you don't check your bags, you can bring it onto an airplane and it's legal. And then you've got basically a half a pound of butter. That'll keep you going if you ration it for at least a week. I do that. I went to Asia. I found a butter with me. It wasn't the only fat that ate by a long shot, but it meant I could have butter in my coffee every morning. I could skip breakfast. The other quick and dirty thing, eggs. You don't have to cook them. You crack them into a glass and you take them rocky style. If you need protein, it takes no time at all. It tastes basically like milk.  And if that doesn't work, the coffee maker in your room will make boiling water. So brew just water with no coffee and it put two eggs in there. Let them sit in hot water for a while. You get soft boiled eggs in your hotel room. I never waste time on going out to breakfast unless it's a meeting.  I get to put that towards the steak and lobster dinner on my expense report. It's not a bad deal. If I'm not in business meetings or if I'm in flight, these are the primary foods. Sakai salmon, it's smoked. People on the airplane don't like when you eat it. I don't really care. I don't like what they eat either. Most of them smell bad. Sakai salmon is the lowest mercury salmon. It's also got the best fatty acids because they feed primarily on small krill. Stuff keeps without refrigeration for quite a while. Not several days. You can get sick from eating bad fish. But if you slide it into your laptop bag next to your laptop or just in the other part of it, you can eat that for a day or two. Two is pushing it. But if you do that, you've got all the protein and fat you need to keep running for essentially 24 hours straight. If you're looking for a few carbs, Hail Mary is available across the US. This is raw chocolate. It has a very cool ratio.  You still want fat, in my opinion.  Although one of these is three of those. So I would not feel terrible about myself at all if I ate one of these for lunch in a hurry. It's a dessert, it tastes awesome and chocolate is a health food with all kinds of anti-inflammation benefits. The final thing you need to know about is butter. Unsalted Kerrygold, this is the silver label, is the preferable one in the US. In the rest of the world, especially Asia, you want anchor brand. The reason you choose these ones is that these cows ate grass. It's more important that they ate grass than that they're organic.  This stuff tastes good, it's actually yellow naturally and I go through a ton of this. In fact, you can use it in ice cream. All right, where'd I put my remote control? There we go. Learning to use your body. You have muscles, you don't know how to control. A ton of them along your spine, the back of your arm. When you do multiple compound movements, you'll oftentimes find some. But we also store emotional tension in muscles. And if you have a muscle that's tense all the time, it might be tense because of something that happened to you when you were 12 months old. And you have no conscious recollection of this. The way our brain works, you have a brainstem and it's a pattern matching machine. And it will match patterns in microseconds when your conscious brain takes about a third of a second to look at someone. What that means is that if a guy in rose colored glasses beat you up in second grade, your reptilian brain says, pattern match, rose glasses, threat. And you get the physiological threat response. You bear the stress burden of that. Whether or not you have any conscious knowledge of it. So your conscious brain says, oh, that's the speaker, I got nothing to worry about. But your heartbeat already changed. Your respiration already changed. You actually got a thin sheen of sweat on your skin that changed the resistance on your skin because you prepared to either fight me or run away from me. You need to get on top of that. We're gonna talk about how to do that. Figuring out how to control your muscles is one of the ways you do it. First, you can go in how to relax these muscles and then you can get them stronger. Strengthening this muscle when you don't have control of some other muscle over here is not going to lead to an optimal result. In fact, you might even get an injury that way. You can use basically something called EMG or GSR to a certain extent to control your, to measure certain muscles. You can't even reach all of your muscles with sensors though, which is why things like yoga or functional movement will be helpful. For me, I use yoga. A lot of people use functional movement where you bend forward, for instance, and you figure out which arm is stretching more than the other and then you do specific corrective exercises. I'm actually still doing some work in that space. If you do this, you'll be able to dance better. You'll be able to stand more appropriately, have a straighter posture. A straighter posture makes you more attractive and it essentially makes you more functional on many levels, including cognitively.  You need to learn how to breathe. Most people breathe shallowly from up here. You want to send a signal that you're relaxed? You breathe from your stomach down here. And most people just haven't learned to make it a habit. So specific breathing exercises can transform your nervous system function as well as make you feel good. I recommend something called Art of Living. Art of Living is practiced by 25 million people around the globe. It's a set of exercises you do for about 10 or 15 minutes in the morning. They, when they teach it, oftentimes the teacher wears white robes. The first time I took it, I was in my mid-20s and I thought it was kind of the dumbest thing ever because frankly incense, white robes, flowers, like not my thing. My grandmother has a PhD in nuclear engineering. She met my grandfather on the Manhattan Project. I'm as Western scientific as it gets. So I didn't connect with it. The second time I took it, it was a different class for executives. It's one of the early executives from Intel. I just sprawling mansion. He said, oh yeah, I'm having this training in the back. It was taught by a venture capitalist named John Roberts from Santa Barbara. And I sat in there and I finally connected. All right, if I just do this and I just suspend my disbelief and say I'm gonna experiment six weeks, I'll do the exercise.  Life is better, I've actually lost weight but everything got easier, everything that I do. For several years after that, every Saturday morning, I would meet with a group of hyper successful entrepreneurs in one of their, basically their basements in their mansion and Saturday at 7 a.m. we'd get together and we do breathing exercises for about 45 minutes together. I think if I look back on it, there was somewhere between 100 million and 500 million of net worth in that room among those dozen to maybe 10 or 20 people that were there. That's pretty amazing.  Cause it works. That's why we did it. You can go to a yoga teacher and learn pranayama. That'll help too. The trick is daily practice for six weeks. Even just breathing in and then breathing out for five seconds in, five seconds out will change the alpha in the front of your brain. Feeling nervous before you approach someone? Five seconds in, five seconds out. That's gonna help. In through the nose, out through the mouth. 40 days is what they'll tell you in India or China or the Bible. In the West we say 42 days cause six times seven is 42 in six weeks. So either you've got the religious side or you've got the hitchhiker's guide. I don't really care. It's the same number, 40-ish. What's going on there is that's the amount of time it takes us to build a new habit. You do it every day for that amount of time. It'll settle in and then you'll decide to keep doing it or not doing it but you'll feel the benefits. Your immunity gets better when you do this.  You'll find you're more clear. In fact, one of the guys who did this, one of the entrepreneurs said I feel like I'm taking a mental shower when I do it. That's why I come here every Saturday just because I'm better all week long. And I found in my own life that it made me better to the people who work for me. Like I was just a better manager and better at interacting with people because I was calmer. Now we get to the good stuff, training your heart. In case it hasn't been made clear by our speakers so far. Cardio makes you weak. Here's what we haven't talked about though. There's something called an ejection fractions. The amount of blood your heart can pump in a heartbeat. People who are really strong can go from little bit to one pump that moves a ton of blood. People who do cardio all day in the little spinning class they have a heartbeat goes do do do do do do do. It's even which because they're over-trained and stressed and each beat pumps a small amount of blood. That's not optimal functioning whatsoever it's actually inefficient. You want to be able to go from small to big. I'm talking about heart rate variability though is the main focus of this slide. How many of you have heard of heart rate variability? I got like three people in here, medical professional friend, another friend. This is a device. I'm an advisor, an unpaid advisor to the company that makes these. It's called the HeartMath Institute. Been around for 20 years. You don't know it but a very large military organization just placed in order for these because they found out that troops who are trained to control their heart rate variability don't get post-traumatic stress disorder. That's basically destroying militaries all over the place because you see your friends get blown up and you don't come back from that. When you have your autonomic nervous system under control you can and do come back from it. This little thing, let's hope it's charged it is. It has blue lights, breathe in, breathe out. And on the top here is a light that goes from green to blue to red. When you're doing your heart rate variability right the light turns green. When you do it wrong, it's wrong. You could practice meditation or something but you'll do it wrong. How the heck do you know your meditation is right? You have no signal whatsoever. So the typical person meditating sits here and then close their eyes, they do the meditation and they're meander here, they meander here, and here, and here. It takes a lifetime. When you have devices like this, they turn red and bing when you fall off the path.  And you end up going up. So you can learn to do things that would take you years to do in literally six weeks. This is a huge, huge benefit for you. In fact, I will tell you, this is my most impactful in terms of amount of time and amount of money per unit of improvement, most impactful of everything. It's a $200 device, it's not even very expensive. And when you use it, it clips on your ear, it just gets a signal from your heart. But what you're doing is you're teaching yourself to have spacing between your heartbeats that changes regularly because animals with less spacing when their heartbeats are very even are stressed, in fact, oftentimes they're about to die. Animals with lots of variability, especially rhythmic variability, are metabolically more efficient, they're also more relaxed. This balances your autonomic nervous system. We all have these parts of us. We have our sympathetic and our parasympathetic nervous system. If you have stress in your life, which almost all of us do, you tend to be sympathetic dominant, which means you're actually, you get more inflamed, but it also means that you're ready to fight or flight.  It doesn't understand that God, I might fail when I go to approach this woman at a bar. It's a sense of failure. And your body says, God, there might be a tiger and your heart beats fast. You've felt that nervousness feeling. This is your body doing its damnedest to keep you alive because there might be a threat. When you're in control of that and you can say, no, no, no, this is not a threat, stop.  You have an unfair advantage.  Your heart is a seed of emotion and it is part of your nervous system. In fact, it's part of your brain.  And if you think this is just where you are, you're sadly, sadly mistaken. It turns out heart rate variability when you're trained will modulate your endocrine function, your hormones and your immune function. You live longer when you have high heart rate variability. We're talking 10 minutes a day for six weeks to learn the skills. This device is just training wheels. This is the HeartMath Institute M-Wave 2. I have them on upgradedself.com. You can click and order one. I don't make a ton of money from selling them. I just think that they're an important technology so I try and get the word out.  That's what the science is showing us. The most bang for the buck. Here's a picture of what it looks like if you use the software. The device works by itself. You can plug it into your computer and get a real-time graph of your heart rate variability. When it looks like this, this is sort of the cumulative amount of time I've spent in a state of high variability. This is a graph of it and this is a relatively good session. When you first start out, let's see how chaotic your heart rate variability is or even worse, the line won't be anywhere near this big. It'll be kind of narrow and kind of chaotic which means you have stress. That's all right, you're over-trained. You've been eating the wrong foods. You're not happy, whatever it is. The cool thing is this is a switch like training wheels that lets you turn on happiness. You learn to ride a bike, you toss the training wheels. You do this for six weeks for 10 minutes a day and you will have a new skill. Right now, we all know how to snap our fingers but if you've never snapped your fingers when I say snap your fingers, you'll be like, once you learn it, you know it. This is the same way, it's just a skill and the skill is turn off stress, turn on happy. So you can sit in a room when someone's yelling at you. You can accept, reject and being rejected over and over and over because it simply doesn't feel it. You don't feel it here the way you did before. You're in control. Number one, most like very impactful but also expensive and a little bit time consuming bio hack is you upgrade your head. Smart drugs is the first thing I recommend. Anoracetam is one of my favorites. Paracetam is another. And I'm kind of famous now for my 15 minutes because I've been on national news talking about another one called Provigil. Provigil has very strong upsides especially for productivity and performance and jet lag and things like that and for mental focus. I do recommend if you can try it and your doctor agrees because it's prescription that you give it a try. Not necessarily to use every day but because if you wanna feel like what your brain is capable of when you have full on focus and you're just dialed in, you try this and you understand what kind of a day you're capable of having with or without Provigil. We all need guidance to show us how good we can be. And one of the points of the bulletproof diet and all of these recommendations is to give you one day, one perfect day where you have limitless energy, you feel awesome and you literally feel bulletproof. That's what it's about. When you have that day now you have a yardstick to measure against and you can say okay, why was my next day not as good? How do I make it better? And you can start the process of improvement but until you've had that perfect day it's very hard to know what you're capable of. Provigil, well meditating, meditation's about focus and awareness. If you take a drug that helps you focus better and you meditate, you'll see what your brain can do and then whether or not you're on that drug you'll learn something from that experience. Eating healthy fat, your brain runs on fat. It is made out of fat. If you do not eat egg yolks that are soft cooked, hard boiled egg yolks are inflammatory. Scrambled eggs are inflammatory, poached eggs, soft poached are not inflammatory. This matters enough that I'm making a difference from it. Eat coconut oil, especially MCT oil and extractive coconut oil that's six times more effective and reverses Alzheimer's disease. In fact, there's a podcast on my blog from a physician who cured her husband's early onset Alzheimer's using coconut oil. So coconut oil, butter, animal fat from healthy animals, you do that. Your brain and your hormones will work better. Meditate, for sure, to upgrade your head. Or you could do it the way I just talked about earlier. Seven days, a lifetime of Zen practice. I don't need to meditate nearly as often as I did to remain calm and focused but I still get benefits from meditating. I just know how to do it right because I felt what it was like because I had electrodes stuck all over my head. Yeah, it looked sort of weird but if you want to make rapid progress and not waste time, this is the way you free up countless hours. EEG-based neurofeedback is the name for that kind of training. You can do it for less, $2,500. We'll get you about 10 sessions over the course of a week of something called Brain State Technologies. Brain State Technologies isn't as advanced as the other one but it'll give you a lot of autonomic nervous system control as well as it can resolve some pretty amazing health problems. Unless you've done extensive therapy or unless you lived an amazing unusual life since you were born, you have inbuilt weaknesses psychologically that are under your conscious level. They're part of your body self-defense mechanism. We all have them. Until you do something to blunt what they can do to you including neurofeedback or high rate variability training, they'll be in the driver's seat some of the time and you won't be and they will sabotage you. It's not that you're sabotaging yourself.  So I say this is the most impactful biohack of all, 12 IQ points, seven days. It doesn't get much better than that in my experience. And finally, you can fix your sleep. I have data on my website that shows that people who sleep six and a half hours a night live longer than people who live eight hours a night or certainly people who live people who sleep eight hours a night. If you sleep more than eight hours a night, your chances of dying from lots of causes go up more than someone who sleeps seven hours a night. Your need for sleep is going to be individual. It varies, it varies depending on what you eat.  I'm not saying just go out willy-nilly and sleep less. What I'm saying is that there is evidence that people who live a long time sleep less than eight hours a night and there is not a ton of evidence based on this research you can see on my website that says you need eight hours a night. Sleep is critical, efficient sleep is more critical. So I use a ZEO on occasion, I don't do it every night. It monitors my sleep. How many times did I wake up? How much time did I spend in deep sleep? How much time did I spend dreaming? And how much time did I waste in some other kind of sleep that was a light sleep with very few physiological benefits? When I see that I had a night where I wasted my sleep, what do I do to change it? Now I've got a yardstick. And now we've got about nine minutes left so the timing's good. This has not been in the presentation before.  Kale, the new superfood. What, bacon is a superfood? That said, I have a prize for the person who can tell me what this is. This superfood will improve your glucose tolerance, lower your type two diabetes by 50%, not cause osteoporosis. People who take it live longer than those who don't. The number one source of antioxidants in your diet in the West. Doesn't decrease insulin sensitivity, 20% lower chance of prostate cancer for women, oh by the way, for women 100% lower prostate cancer. For women less likely to be depressed or get stroke. And there's more.  All right, let's see. You're cheating if you answer this one. Sorry, Jolly. All right. Based on the subway commercials, I'm gonna say avocados. Avocados, that is a good guess, and it is not true. Let's see. That is also a good guess, and it's actually true for some of these, but not all of them. That is also a killer guess, and it is not true for everyone I've heard. Those are all superfoods in my book though. Coconut oil. Coconut oil, which is the source of MCT, same sort of answer as the last two. Almost. It's not caffeine. Who said coffee? It's coffee. This is coffee, for God's sake, drink coffee.  Here's your bag of coffee. Now, oh, I forgot. There's this thing called mTOR stacking. If you do the bulletproof intermittent fasting protocols that are on the website, there's the way you build muscle, and this is simplifying some things. You suppress your mTOR, and when you do that, there's three big things that will suppress it. There's fasting, like intermittent fasting, or full-on fasting, and there's exercise, and there's coffee or chocolate, or to a lesser extent, green tea. So what you do is you suppress your MCT, and then when you stop suppressing it, it springs back and you build muscle. The way I actually got more ripped when I wasn't exercising was I was doing mTOR stacking. I was doing intermittent fasting in the morning, and I was having coffee with butter in it. So I had lots of calories to maintain muscle mass, but I didn't have any protein, so my body was doing its cellular regeneration thing called autophagy. But I was getting the caffeine benefits, sorry, the coffee benefits, because coffee does it, but caffeine doesn't do it the same way. And I was getting this other benefit. So coffee works, but there's your answer. Here's the thing about coffee. About 91.7% of green coffee has mold in it. These are referenced on my website. This is all stuff, I didn't make this up. That's a picture of moldy coffee. Something called biogenic amines. These are neurotransmitters like histamine forming coffee. You ever drink a cup of coffee, you feel good, and then you feel blah, an hour or two later, so you drink another cup, and you go up, down, up, down, up, down. That's not what coffee does, that's what coffee plus mold does.  Decaf is bad for you, skip it. If you feel like you want the taste of coffee, drink coffee with caffeine or don't drink it at all. Caffeine is an potent anti-fungal that helps to protect your coffee. Here's what happens when you drink bad coffee. You get jitter and anxiety from coffee, you don't get that from good coffee. Your adrenal glands get stressed. Good coffee doesn't stress your adrenal glands nearly the same way as basically drinking poison. You get headaches from coffee, it's not the coffee most likely. There are other cases of that. Inflammation throughout your body. You wake up with sore joints after you have a cup of coffee. I give up coffee for five years because of that problem, and I ended up creating upgraded coffee here by looking at every step of the coffee production process to remove all the sources of toxin formation so I could have a consistently clean cup of coffee. When I travel, I bring my own beans because when I drink Starbucks coffee or hotel coffee, I get these kinds of symptoms.   It's available at a discount for you guys because I figure you might want some. The other thing is, if you drink coffee and it makes you pee a lot, actually it's not that caffeine itself is just a diuretic, it is, but if you drink the coffee and a half hour later you have to go, it's because your body is saying, for God's sake, get rid of that toxin. It's called ochre toxin and coffee is responsible for about 25% of your daily consumption of the maximum allowable government level of that toxin. Let me tell you the maximum allowable level of that toxin for me, zero, because it's potent at any amount. You don't want any of it. So minimize that, you feel better, you perform better. How to prepare a bowl of coffee and then we've got four minutes for questions. Number one, beans. You want mechanically processed beans with a clean process like mine. Those are the best, mine cost two bucks more than Peets or Starbucks whole beans. Wet process is your second best choice. If you're in a town, there's a coffee shop, find the guy with the most tattoos where they roast their own beans and ask him, he'll know. Single origin, high altitude, Central American. Central American beans have less insect infestation problem and less environmental stress. So Central American beans make less toxins than beans from Southeast Asia or Africa. You want caffeinated or you don't want it. When you brew it, you can use a paper filter, but you get these two important substances sucked out of there. If you use a metal filter, you get very potent brain anti-inflammatories. Not antioxidant anti-inflammatory like aspirin or Tylenol for your brain.  You feel different when you drink French press coffee than paper filtered coffee if the coffee is clean. In fact, you feel very different.  MCT oil is clear odorless liquid. I travel with two of these. Actually, I took three of them because I've been on the road for 19 days. I landed 36 hours ago from Singapore. So I take this, I usually pour it on a little bit of sushi or I put it in my coffee in the morning and I have that for breakfast. That said, there's a quote here. I hope you can read it with this lighting. It's from Henry Miller. It says, the goal of life is not to possess power, but to radiate it. And I try to live by those words to say, I'm not out for doing all this stuff for me. I'm doing it because I would like to be a more powerful person, but more powerful over myself. And when I do that right, people around me can tell it and then I have something to offer. It's the reason that the content on my blog is free. The reason I make the stuff that I do, I sell it at very low margins because it's the best I have. And it's also the stuff that I want to be available for myself. So by sharing it, I make it more available. That said, check me out bulletproofexec.com. My Twitter handle is at bulletproofexec. I actually answer it on occasion when I'm not in the air. And we have time for a few questions. A couple questions about the coffee. Because I usually get pretty anxious and my heart rate starts increasing when I drink coffee. Did your coffee, do you already have like the butter kind of in there with the beans? Or do you add that after? You add butter yourself. It's possible to roast coffee with butter, but it kind of destroys the butter. They do that in Indonesia. It's not something I'd recommend. So you just add the butter afterwards, just brew black coffee, add the butter, blend it. What do you think about the supplement that the four hour body recommends? Hooperzine? Hooperzine is a double edged sword. I've used it. About a third of you are sympathetic dominant. Sorry, are choline dominant? Not sympathetic dominant. When you're choline dominant, that means you have extra choline in your brain. Hooperzine is a colon esterase inhibitor, which means so 66% of you, you take it, you'll probably feel good. The other ones, you can actually get symptoms of chronic fatigue if you have way too much choline. And I've made that mistake in the past of just having too much choline. So I don't think Hooperzine is a really good idea unless you know that you benefit from choline supplementation on a regular basis. You could test yourself by just taking lots of choline and seeing how you respond. If you get tired or headachey or jaw tension, Hooperzine is not for you. Not really a question, Dave, but I wanted to reiterate about your vitamin D. I think I started it taking it about 2007, 2008.   Twice this year, I felt like I was starting to get one. You know that weird feeling in the back of your throat? Bam, you know, 20K IU, two days gone. Yep. It's pretty amazing. But get your sun, too. Yeah, sun does something called sulfating. When you get sun, you get vitamin D sulfate. The only source of this is either a tanning lamp or sunlight. And cholesterol sulfate, which is formed when sunlight strikes your skin, is terribly important. And it's almost unknown what this does. But it's one of the ways that your body uses cholesterol better. So sunlight's an important vital nutrient, but, man, vitamin D by itself is kind of magic. Yep. Those are good numbers. Maybe about two more, maybe? It's going to touch a point. You said the question you asked, you said chocolate or coffee, right? Are they about the same when it comes to the properties or are they? They're similar for mTOR inhibiting. As I understand it, chocolate is not quite as strong as coffee. Chocolate has a set of health benefits aside from coffee, but it shares the problem of mold during processing and storage. So I've, in fact, this week, I launched a bulletproof upgraded chocolate powder and cocoa butter that are designed to not have the toxins in them. So the quality of the source matters enormously. If you use them properly, they're like herbal supplements with definite benefits. If you get low quality stuff, you're not taking just chocolate or just coffee.  You were so close.  If the chocolate had hit the warehouse in time to ship it here, I'd have given you a thing of chocolate for your answer, but I don't have it with me, so. All right, we have another one? Oh, where? I don't know where the mic went. No, there it is. I noticed you have protein powder. I guess my question's like two parts. Where do you mix with that? I guess where do you feel, what's your feeling on milk in this bowl proof diet? Milk of any types, you know, standard milk, almond milk, coconut milk, or none of the above? If you're going to drink cow milk, it needs to be raw. And even then, a lot of people have problems with raw cow milk. What I recommend is get milk without protein. Butter has very little protein in it. If you're really sensitive to milk, you might need to use ghee, which is clarified butter. If you're doing cheese or liquid milk, the pasteurized stuff, it's just bad for you. It contributes to inflammation throughout the body. A lot of people break gluten, which is also off the diet, wheat protein, and milk protein down to something called caseomorphin or gluteomorphin. These are morphine analogs. They're opiates.  They make you want more bread. And they're the reason you feel really crappy if you stop eating those things for two or three days.   Even on the once a day cheat week, my cheat day per week is not even cheating. It's a starch refeed day. And I have sweet potatoes or white rice because they're the lowest toxin sources of starch. And when I do that, I feel awesome the next day.  So why would you throw away four out of seven days of the week just to have one day of eating pizza and chocolate croissants? It just doesn't work. Is this, wrap it up? All right, thank you everyone.