Okay, so welcome to GSS, and this week we have Antoine, who is going to talk about knots. So, my first time, for example. And I have to start with, I guess, an apology or disclaimer, perhaps. I was introduced to knots working with physicists, so we were looking at this as a magical tool box, which allows us to say a lot of really great things. But I have to admit, the goal, when I started looking at this stuff, wasn't to try and prove anything, obviously. So, I'll have a few baby proofs in there, but mostly I will state a bunch of really, in my opinion, interesting facts about knots and what they allow you to do and bring all these tools that they allow you to do.  And really, the key idea here is that we're going to define them in such a way that we can only worry about simple diagrams we're going to draw, right? Because they're going to be curves in arc three, which can get messy, so we're going to restrict it so that all we have to care about is knots we can draw. So, to maybe not just motivate the definition, let's look at a couple of things that can go wrong, if we're not careful, I guess. So, basically, because you want to have the right notion of knot equivalence. You want to have a sensible idea of when knots are the same, because, for example, if I look at something like this, so on something like this guy, and knot to which I, I mean, I just take a loop and I start knotting it at the top. But then I could say, okay, clearly this knot has to be the same, the same thing but with a smaller loop up there. I mean, just as this is sensible so far. I mean, the loop doesn't say the same, but the knotted part gets smaller. But surely these two things should be the same. The problem is, if our notion of equivalence is too weak, then by taking the size of this little knot there to zero, we would get that all these things are equal. So we have to make sure we rule this out, because obviously they're not the same. And the other thing we have to be careful about, because they can get nasty, are those what are called wild knots, because they get pretty wild, pretty messy. And it's essentially the same problem again. We have this pattern here, but let's, and then I add some sort of big loop and then I'm knotting things. But let's say that I keep adding tiny little knots like this. I keep going on, what do I get? I promise you they will do lots of pictures, so. And I keep adding little things, I keep adding them smaller and smaller.  So that seems like you've got no reason for me. Anyway, so this is basically two things we have to be careful about. So now we can define knots in such a way and knot equivalents in such a way to rule out these things. So we will say that a knot, a continuous injection of S1, and you can play the same game if you go up in dimension with both of these guys, but obviously it gets harder to draw, so I'm not going to do that. And then we want to know when two knots are equivalent. So two knots are equivalent. And the idea is that it's not enough to say the equivalent when they're curved, when you can deform their curves into one another. It's a wing more than a wing to be able to deform the whole space into one another. And this is called an ambience isopic. You have to modify the whole space with it. And that's a equivalent when there is an ambience isopic between them. Your one doesn't seem to rule out this knots. Yeah, there's going to be a creep for that. We're going to say this is a wild knot, and then we're only going to care about the other guys, which are whole tables. So this is still a knot, but it's wild. And we're very tame, because we're mathematicians at the very least. No, it's still a knot. And for the rest of the talk, when I say knot, I really mean tame knot. We're in an isopropy, a manual isopropy, so I e some, let's say, k1, it takes the knot k1 to k1 at n0, and to k2 at n1. Well, essentially it was the problem here. We have infinitely many knotted things. So it's going to be tame when it's equivalent to a polygonal curve.  It's tame when it is equivalent to a simple closed polygonal curve, so not self-intersecting. And I link them with three lines. It's not self-intersecting, and that's closed. Okay, so I know what a knot is, but that's not... Do you require any continuity in the bubble T? Yes, we do. I should have said that. The whole F is continuous. Yeah, but that's only when I fix T as a map from R3. Yeah, otherwise it just has a bunch of math that don't need to enter there. This is like really a composite problem. So k1 and k2 are the knots, right? k1 and k2 are the sub-function. The sub-function is R3. You can say F of k1, 0. Are you ready for composing? Yeah, okay. This guy is going to be the image of k1. Oh, you just required the image. Yeah, just the image. Oh, okay. I guess the right method is something. Yeah, sorry. So, again, in the definition, the knot is... I mean, it's the same thing when you deal with curves in general. You just end up talking about the subset, that is the curve, not the T. But that's a good point. So I guess when I say knot, I mean tame knot, and I'm just looking at the subset, unless I read the embedding itself. Okay, but basically this is... Okay, we know what we're working with, but we don't know how to work with it. And how to work with it is basically because I've drawn these things now, like these already examples. I mean, each of those sectors is an example of a knot diagram. So I just want to know what we're allowed to do when we're drawing these things. And basically then say that we only have to care about this. You know, it's going to be... Since we're only considering very simple knots, it's going to be... It's pretty clear that... The problem is going to be what? The problem is going to be... I want to... So this thing is not this in R3, and I want to make sure that there is a projection that is good enough where... If I'm looking at this guy, this circle and projecting along, looking down this, then I'm just seeing a line. Obviously I don't want that. But you can always move your projection a little bit and have something that's good. And by good, that's an definition that's seen what projections are allowed to use. And the idea here is going to be the same spirit as requiring knots to be tamed, which is essentially having finitely many things here we want. We only want to worry about finitely many points where the projection is degenerate where it crosses. So this is a quick sign of why it's not interesting to talk about knots in R4, because basically you can always unknot it, right? So this is not going to feel knot. This is going to be a link, right? I have two circles, so they're sitting somewhere in R3, but now if I put them in R4, I can cheat and say that I can... Because I can just say they're in R3 cross zero, say, and then I can move this part like R3 cross one, and just move it up somewhere, I move the other part down, and now they're in completely different spaces, so I cross it and it's nothing interesting. So in the definition of knot, we're going from S1 to R3, and if you go up in dimension, like the same amount in both, you get more interesting knots, but if the difference is not two, things are not interesting. Okay, a projection from R3 to R2 is regular. Potentially only finitely many bad things can happen. So finitely many... So like every time a point is not two, there's only finitely many points that are not two more than one, more than once. So regular is like pertaining to some things to knot? No, it's a projection. Yes. Otherwise... Yeah. Oh, and actually, okay, this is just vocabulary, but I'm going to keep talking about knots. Most of the same things can be said about links, which are just taking copies of S1. This, for example, is a link, because I have two copies of this to just use the word knot throughout. So finitely many multiple points, and each multiple point is only a double point, so why am I ruining out, like, every time? I don't want... I don't want two strands to look something like this. This is bad, but of course I can just change the orientation of it and I'll leave it. And the second one, what I don't want to go wrong is, I don't want to have something like this, like this, this is bad, change the orientation of it, I always get only a double point, so every multiple point is only a double point. What else do I have to worry about? Yeah, I have to worry about this, that I don't have this strand going like this and then another one doing this, like, every time they intersect, I want the intersection to be transverse. All intersections I'm doing is building up to saying, all I have to worry about are knot diagrams. So, let me tell you what a knot diagram is. It's actually a knot diagram where we can make sure I'm not, yeah. So, it's going to be a regular projection, but I have to tell you more, because that's a perfectly acceptable projection of a knot, but I don't know how to reconstruct a knot. So I have to make sure that I know how to label the crossings and for some purposes, the orientation will be important as well. So, a knot diagram will be a regular projection of a knot where I label the over and under crossings and the orientation. A regular projection with enough information to reconstruct a knot, such that under and over crossings and the orientation is over. And now, here's why all of this works. Essentially, two knots are going to be equivalent if the knot diagrams are equivalent in a very nice way, because essentially, there's only, I mean, right, so a knot, well, it's still there. Knots are equivalent when there's some taking one to another. But actually, it's going to be, but I'm going to have a lot of things to check, I have to check all of those. So instead, we're just going to look at, it's enough to look at any knot diagram of each knot, and then we have a sort of finite number of all these three of them, three moves that we can do on the diagram to just get from one to the other. So there's not much that we have to check, but that's fine. The proofs are not terribly, there's nothing necessarily deep. It's just going to take, it would take like half an hour or 45 minutes, and we wouldn't get to this fun stuff, so they just think about that. To knots are equivalent, of course I should tell you what you can do with knot diagram. So those are called Ryder, Meister, and the surprising thing about those is not that they're allowed, like that's pretty obvious. The really important thing is that there's only three of them and they're enough. That's all you have to do. So the first two are pretty obvious, just telling me that if I have this or that, it's the same. It's pretty straightforward. The second one is the same thing. If I have this, it's the same as just two powerless times. That's pretty obvious as well. The third one is much trickier, but what happens when we have something like this. Essentially, all I want to say is that this guy is underneath the white one and above the blue one, so I can shift it to still be underneath the white one and above the blue one, so I can shift it there. That's all I'm saying. So I have... And two knots are equivalent when you can go from one to the other by finitely many of those moves. It's not surprising that these things are true, not equivalent when they're related by this. What is surprising is that this is all you need. You don't need anything else. It's the same after finitely many or I even match the moves. Okay, so now we can get to work and we can actually draw some knots and say things about them. So this is really nice.  The problem is it would be really nice to say that starting with any diagram or the knot, I have a nice way of just simplifying the diagram at every step to go towards. Like if I have something that is just a really complicated way of the unknot, I want to know that I can just simplify my diagram. The problem is that there are some examples of knots where you start with a certain number of crossings in your diagram and you have to go up before we start going down. And I'll give you such an example now. So this is nice, but then there's something that's likely better than this. So given the number of crossings that your diagram originally adds, you know how many moves you'll need to go to the simplest form. But that bound is really just a big upper bound. So you know it's far into many, but it's not very useful. Statement that they don't know how many moves you would need. They don't have a good upper bound for how many moves you need to simplify knots. It's a pretty elementary question, but it's not going to be very hard. Because you have very simple examples, so let me see if I can draw this one. So that's enough, right? And the problem here, I mean the reason why this is an interesting knot is that it's quite clear that this is a really easy way to simplify the whole thing. I have this one here that's underneath the whole thing. I just want to push it away, like push it all the way up there. Like that's easy to see. But it's an easy example of why you have to make the knot more complicated, the knot diagram more complicated before you make it simple because I can't simply push this across. What I have to do if I do one of those at a time is I start by saying okay I want to take this trend here and put it there and then I want to take this trend and push it across here and so on and so forth. I do that step by step which makes it trickier. I mean it means that I don't have a simple monotonic sequence in terms of number of crossings and the number of crossings has to go before. Right, so I know I have knots. I know what I can do with them.  It could be that they're all equivalent to the other knot. And there's a really... It's not hard to show that there's a non-trivial knot but there's a really cute way of discussing that that is due to William Thurston that was a huge geometer and he's got to really easily explore it. So I'm not going to look at it. Okay, so first of all I want to use this discussion to show you that there's a knot that's not the other knot. So let's talk about the... Let's talk about the other knot first. Find interesting properties of this and show that the other knot has different ones. And we're just going to consider this loop to be some sort of portal. Okay, let's say it takes us to Narnia. Okay, so if I go through the portal I'm now in Narnia. I'm walking around in Narnia seeing lots of weird things. And then when I walk through the portal again, it doesn't matter which direction I'm going.  So the knot doesn't do a lot of interesting things.  And that's it, right? So now let's see if we can do some more interesting stuff with a more interesting one. All right, so now let's see what happens here.  Then let's say I go through this one. And then I meet lots of adventures.   And now I want to see where these other two portals lead. Do they lead anywhere interesting and do you relate nicely to the others? And, okay, so let's look at this. Let's say that I go through let's say that I go through the portal A first. So I'm going through A and then this. But if I just move this trend through here this is the same thing as if I go through the middle one immediately from this color, right? I'm just taking this guy and moving it here. I'm doing this because this trend is above this one and below this one. So if I move it here I'm still going to be above this one. So this portal here is the same thing as doing A, B, right? And now let's see if I can play a similar game here and it's not a surprise. I can. Let's go through one here I get that I can get this. So if I go through I'm going to come back through B and underneath here. And this is the same thing as just going through this guy, right? Same thing as... So this guy is also equal to what? It's also equal to doing B minus one first and then A, B, right? So now I found out what did I find out that so this now turns out to be different than the other one, right? It's creating a lot more portals but they're related a nice way. I guess Matt I start here. If I go back if I go through it again I could just get back here. There's nothing interesting. Or I can do this and then up in A, B I can do this and then up in B, A and then the whole point is there's only one... Then what can you do? You can see this guy as a shortcut basically. It's taking me straight from this to there but it's kind of a boring shortcut because I can just go back and forth. And this guy is actually much more interesting because if I go along the middle I now have to go through the portal three times if I want to go back home. It's a different not a different situation. This generalizes to nice way of describing that because essentially all we're computing here is the fundamental group of R3 minus the other. If you're in Narnia and you want to go back home does it matter which side of the portal you go through? No it doesn't. It's just the portal like Narnia at home doesn't matter which way it is. Seems reasonable. If you accept that Narnia exists it's not a group at all. Can you briefly mention this is the fundamental group of R3 minus the other. So does that mean that the fundamental group is generated by A and B subjects of the A and B? Yes, that's exactly it. There's nothing else to it. Alright, so now this is just like some basic generic not stuff. I want to talk a bit more about essentially more of what drew which is that really nice knot you can actually say that you can knot the whole space using the knot. The idea is that you can decompose the whole space in a way that is consistent with the knot. I'll make that precise in a second. First, as an intermediate step between this idea and what we've done so far let's talk about another way to distinguish knots which is to talk about the whole structure you can do which is given any knot you can find a surface whose boundary is that knot. That surface is going to be orientable as well. You're not going to know what the commode is for. The construction is simple. This is interesting because basically what we want to do now is what we want to do. What we're wondering is if it's possible to have a knot sitting in R3 and then to have a whole bunch of surfaces whose boundary is the knot that fill up the space without self-intersecting which doesn't seem obvious that you can do that. I mean the knot might just twist in a weird way and so on. But first of all we can check the case where we just want one surface and that is something turns out you can do for every knot these are called C for surfaces. Essentially I just want to find a surface such that the boundary of the surface is the knot or link. And the construction is very simple so let's talk about the same knot again. This is my knot. And I have to get an orientation so let's take this. Now I want to construct a surface whose boundary is that knot and essentially the only thing I have to worry about is what I do around these crossings. And there's a simple rule which you follow which is that you're going to glue the strands following the orientation so I'm going to I'm basically going to delete the crossings following the orientation of the knot so I want now this thing instead. So I end up with what? I end up with two disks and think of this thing that this is an R3 so think of this as I have one disk here and then the other one is kind of like sitting somewhere on top of it. And so and now I have to essentially glue the two disks in the right way such that the surface I get its boundary is the knot I started with. And again the algorithm like the recipe is always the same whatever knot you have so I'm going to have essentially little little strips going from one surface to the other but twisting because I want to make the the overall surface orientable at the end of the day so let's see so I I mean again I just hold the orientation right? If I'm along here I'm here along the original knot so I just want to go to this guy and I do the same thing everywhere I had to cross it so now I follow this one which gives me this okay and you get there and now you can see that at the edge I always have the same rotation so I can just orient this and essentially here I'm always looking at the same side of the surface for the other side I don't see this picture and of course I mean it seems like I didn't really do anything but I'm going from here to there because these crossings they're the same that's the whole point I want the surface whose boundary is the same knot so of course when I just look at the curve there it's going to be the same thing otherwise I'm going to stop this one I want to do this in different ways so you can see the twisting a bit more because here you always see the same surface but the twisting becomes a bit clearer with a second another example and the twisting is just to ensure that the final thing you get is orientable is that twisting in the top right to the right around let's see yeah because I start from the outside and go inside so you're right it was the wrong way the others yeah because it was going the other way the other way the thing probably wasn't even something interesting well it wasn't so much I know it no no no you're right I was going from in to out which is not what so no you're right and now so I'm right here then I start twisting and I'm still right here the color the color scheme didn't make sense before but no it's consistent okay and okay so I want to look at I exercise to the reader show that they seem not no there's actually there's a very easy way to see it in the same if I if I just okay I'm going to look at these two points here essentially what I'm doing by saying this is like I can imagine this is sitting inside a cylinder and then gluing the ends right I get the same thing and I can see that's actually exactly what I get here I can think about like my tourist going around here and have so let's say that my two blue points are right here and there what are these turns doing they're just coming over each other every time this and it's exactly what these guys do like this one comes over and then the other one comes over and then the other one comes over so they're they're the same they're the same not but we'll get a different representation of the surface which makes the twisting so again I get the same recipe like this and now two surfaces and now like this but now I have to add the twisted ends and again it's going to be the same guy just remember this guy with it somewhere and so my twisted ends look something like and now this one shows you a bit more going on with the colors because now so here I have some orientations called this positive orientation just rather rotation and now so see the this orientation just flips behind here as I go along the band I twist behind and so this is the opposite orientation and then it's just that it doesn't seem to be much going on here because it's coincidence we only see one of the surfaces and then that allows you to again distinguish not because you can define the genus of a knot to be the minimum genus of all the surfaces you can build on top of that knot so like these surfaces are going to have a certain number of holes like on those holes I take the minimum that I can do that have another boundary and then that's the genus number of holes that the knot has wait so just to be sure these two surfaces are the same up to uhhhh or quote unquote by is it the kind of how they're going to do a standard one well these two might no I think those two might I think yeah so let's see because I want to like take the bottom like the blue one flip it over and move these things around I think they're probably the same just flipping and twisting no right because like these three things remember these three twists exactly these three twists here so like these three I'm sort of confused by that picture actually because what's the middle section doing there like I could imagine a surface where you just see the surface part in the three connected components are on the outside but it seems like in the picture you drew at every crossing three of the four bids have a surface next to them I don't deny you three of the four bids over the four bids so when you have to one screen crossing over another that sort of divides the blackboard into four regions and you're drawing a piece of the surface of three of those regions and I'm not sure I see how that's physically possible so I have I have like this pancake here and then I have like three other things that can take I have pictures coming up at the end of this thing in 3D okay I don't remember if it's this one or that one I think it's no it's this one so we can have a look it's probably going to be easier otherwise we can stare at this for a while okay three pictures they're not of the same latitude right you need to have that as boundary that what is that at the middle of this yeah this is like okay yeah this is not all flat like this middle middle like sticking out this is like this would be like a good idea for a water park you have this middle thing and then you have like slides going down like these are slides it's like here it's like there and it's like here all right this thing that is sticking out and then if I it's like not you have a strip and twist it twice and then glue the end together to form the same like oh you want I know it's here but you won't get the same knot on the boundary well I guess you cannot twist this thing you cannot no no no you have a strip like with wrist and then you twist with the dough and then twist again and then twist again you have three of those and then you glue the ends together oh and you want to say you get the same thing can you form the same thing with just the strip yeah I think that's what you get like just here right yeah I feel like without the middle part you can visualize the like this oh the middle part makes it harder to do you can just take off the middle part then I can sometimes visualize the strip and now it's coming now you don't think this is the surface I want to know if it's the surface oh so you're saying you just take oh so that's for your boundary you don't have this going down is that the same thing that's also good so my question is first of all is this thing even though yeah you can have a problem because you have two different circles right I think it's a you start with a strip that has two boundaries ah yeah I guess if you do three of those I'm free to do so what I'm trying to do is some of us so you have one boundary it's a moment it's a moment it's a moment it's a moment it's a moment it's a moment it's a moment it's a moment it's a moment it's a moment so this either either its boundary is not the same as the component but two components or else it's not a random moment yeah that's a good point no no this is a this is a yeah exactly I think there's another one happening over there as well okay so yeah I guess it's a few problems I guess but let's move to the more the picture that's even like this one I'm not even going to try and draw which is when instead of having one of the surfaces I have now a whole family of those that fill up all of our free in a nice way because the boundary is going to be the knot and you know and they're not going to intersect each other that's the thing that's the knots that are going to decompose our free in a nice way I'll have to do that in a second we can always think of I mean actually that's how they usually define them you always usually think of think of now as I would say for surface because this is not oriented or not oriented sorry I'm here to make get people in focus so that's good yeah so the problem with the construction surface the one you get is the one yeah so we need it for the tax technical reason but you can always everything we talked about is fine because our treatment channel just out of the point you get everything we talked about is just more general planning and that's how they define us in general like okay so this is what we want we want you to be able to construct knots that we'll say that next to our S1 because we're sure in a second it will be here family of seaford surface so seaford surface is just the way of saying their boundary is enough okay I'm going to draw the big example I mean S3 now so this is a legal knot because it closes up at infinity so essentially like a simple vibration in this case it's just going to look something like a book like these pages coming out actually these things are called open book decompositions so this is what you have so okay for this thing which closes up at infinity is is the there's nothing interesting there as soon as I close it up and as soon as I knot it up like this it's not clear at all that I can find a whole family of these things that are going to cover my space okay I wouldn't be talking about this if you couldn't but so it turns out you can and it turns out it's really the representation is really simple and this is a a theorem due to the sky the sky which is the sky sorry we're curious about what's happening there but don't I don't know because this building has a ninth floor so this isn't just coming through the roof I don't think the ninth floor exists above here I think it's central there's gravity inside so even if there was a ninth floor it would just go through I know full well because this happened in my apartment alright so what this theorem tells you is it's essentially it's not going to be true for every knot that I can do such a thing but given essentially you can represent those oh I didn't write it but a knot such that there is a knot for which there is a vibration is going to be called fiber and it turns out that you can get a whole bunch of fiber knots by just looking at complex polynomials in two complex verbs because if you have a complex polynomial in two complex verbs it lives in like S3 isn't going to be inside of this so then if I look at where that polynomial is 0 I get some surface living in let's say like R4 pretty much I have S3 inside I intersect my complex surface with S3 and that's what's going to give me my knot essentially and provided my polynomial is nice enough in the right way then because what is the polynomial going to give me where it's 0 it's going to give me the knot and then around 0 I'm going to have all my I've got the angle of my polynomial so that the angle of the polynomial is going to give me how I index this family of fibers so Miller vibration theorem tells you that then if I took oh and isolated 0 singular point then if I look close enough I want to 0 as a map from this small S3 minus where the polynomial is 0 to S1 that gives me a vibration because so this this S3 I can just identify I can I can project down from S3 to R3 using say stereographic projection and then I have saying F takes complex like signs of complex language everywhere in R3 or it's 0 it's going to be my knot and then everywhere else I'm going to get the the complex like any on which of those pages I have basically an example which we've actually already seen that this guy is that this the truffle or not that's it that's that's all the information I need to give you for you to be able to tell me to write down at every point in R3 on which of those pages I'm going to be so the reason why physicists think about this as the knot knotting all of space is that now you can talk about this document interested in which is knotted singularities of vector fields basically because what do I like if I have a vector field in the plane like my singularities are going to look like what you're going to look like something where orientation isn't defined so in the plane it's kind of boring but now a thing if I take this in R3 that my singularity could be along the line now if it's along the line I could knot that line and I could knot it in non-trivial ways and so now that I have like a vector field knotted around this can I still assign a direction everywhere else and still get something the only singularity I get is my knot well this tells me that yes I can for some knots some nice knots for fiber knots I can actually not necessarily every it's a vibration so I mean if I take the preimage of here this is a really cool theorem for them because now I can have a vector field in R3 there's going to be I'm going to have a knotted singularity and I can write down the expression is easy to write down because I know like look here for the truffle knot if my singularity is a truffle this is all my polynomial is and then I just have to project that from S2 to R3 but ok I just use thermographic projection that's not too bad so it's a really simple way to write down some vector field which has a bus promised this is not the worst case yes because one of us starting out at the level of the city and one is starting out higher beam and dropping like that as you can imagine there's so we have to use umbrellas in this case so it's well in fact you can like see the mystery love how there's also like plates missing so as a result you can have this thing where a drop starts falling another drop beats it to the ground no this is I need my block software mathematics mathematics you can have I'm assuming on everything at the bottom where it's at where you can do that alright so that's the truffle knot with ok so there you can see is the truffle knot it does look like a water park sorry it does look like a water park yeah see it does have the slides this is the this is the surface we were looking at before I have this is my inside disk and this is the now very not this like outside disk and these are my water slides right so that's exactly what we had before sorry we're convincing yes yeah I don't know is it like a fan yes does this inspect itself no no no no no it doesn't well you can look inside let's look inside that's what happens see so it's it's all bent and I guess it's really neat and this thing how do you get this thing well you take this guy and then you know you do like you look well no I go back I start from 3 I look where the point on S3 is like you pretty much under that direction and then that point I know what my the value of my polynomial is so this is the surface which where the polynomial its angle is like 0 and then I can cycle through all of those and I cycle through the pages of my book so now you can see what's it's behind the it's not very clear it's so you have to think about this as so my not as like kind of almost planar and then because I had was here and then this surface is going to start like bubbling up in a way and then it's going to go up to infinity and then it will start closing up the upload so that's that's when it starts bubbling up on one side I'll show you more details for another not in a second that's where it's that's where it's at infinity now so the water part before was sitting exactly here and now I have basically what's on the outside of that so is this like the complement of the surface we've done before in a sense I mean it's not complement because it's not great so ok what you could say is that here they're going to be like continuous well even more than that like smoothly like if you take two of them together you still get a smooth surface like they'll continue nicely across the knot that is proved so in that sense and also I mean technically you require see-through surface to be like compact this is compact because I mean it has to be so like the other guy which now you know it was bubbling up and now it's going the other way so I mean this is this is basically so this is when the fiber is looking at say pi over two and it's going to be like the mirror image of the ones I have when I have three pi over two ok but so now I want to show you so now the one this one is the hopsling which is just the very simple thing which is just this guy right and you can do I mean this drawing the surfaces I did it for a knot you can do the same thing for a link so essentially this is a fiber link so in this one I have a few more so we have a better idea of what it the idea of like it's cycling through the whole link right so it's closing up then it's going to come through down the middle and then back the other way are these two is this a link of two things like together or knot the it's not a knot it's a link it's this guy two circles but they're linked together I couldn't put them apart they're not just these own circles and so ok this is as you cycle through the pages and I mean you also have to when you look at this remember I'm using stereographic projection so like it kind of everything that's inside the knot it's kind of squashed down inside like if you look at like S2 like the whole S2 or to the stereographic project all the upper hemisphere is going to get squashed and it's going to blow up so it seems like it's spent forever sheer but that's just that's the deformation from that I mean now that you have this in hand physicists can go and enter this in this simulation and see what happens when they put knots in the quick crystals in the water this is basically the surface I get if I were to play the same game with just doing it by hand the last one I mean it's the same thing but these this is another ok so these these links are so this is just so essentially I have three links that are pairwise disjoint but when I add the third one now they're going to be links so what do I want to do I want to add one that's going to be so now together they're linked but pairwise they're disjoint and ok you can see in the game I guess ok and I mean again a lot of a lot of how it's wrapped is also due to stereographic projection but it's not ok and you have and it gets really really intricate but that's it that's the fault


the mall and just walking by just a a booth here that had a slideshow going and we realized it was a touchscreen and me and my daughter both touched the screen at the same time and somehow we killed the application that was running I guess it was chrome and uh they're running ubuntu desktop here and I just thought I'd film that and share it with everybody so very cool I finally got the keyboard up and running on this screen and I got a game that I created oh and my daughter just closed it let's see there we go so let's see let's play and click this guy oh look at this here we go click me oh look the guy's falling and uh click oh make him bounce the touchscreen is not very uh sensitive I've noticed trying to type stuff in on the keyboard and stuff there we go I got that guy bouncing up and somehow I opened up chrome console there we go anyway I'm gonna leave my game running Marcus maybe I should also let's see how do I get out of full screen mode on this thing there we go maybe Amber how'd you do that earlier oh well this is my daughter playing a game that I created on a really big touchscreen at the mall that we shouldn't be playing this game on but my daughter figured out how to get to the desktop and so we were able to redirect the web browser go ahead boop the member good job you having fun it's a tv


Welcome! Let's decorate my New York City apartment! Thoroughly sweating. Ahhhh! Go away! Go! Welcome to episode 2 of my Decorating My New York City Apartment series with me. That's a mouthful. I should probably rename it, but who cares? If you've seen episode 1, I just finished kind of like reorganizing my whole apartment setup so everything is like backwards and different and I love it. And in today's episode, episode 2, we will be hanging up some wall art. Preferably on this wall here. So let's just get right into it and start, you know, kind of unboxing these picture frames that's been sitting in my apartment for like, now. Okay, if you watch Vlogmas, then you might remember this package.  It was a surprise, but at this point, I think you should know it's picture frames in here. Hopefully, none of them have broken or... that would really mess up this video. Is it hot in here? Because ah, it's very hot! Sorry, my dishwasher's going. I hope it's not too distracting. Alright, moment of truth. Let's see if these frames are still intact. We're in good shape, guys. Good shape. Everything is in mint condition. Do you drink water? And then there's one last frame. It's the biggest of all, but, you know, so it's not that the ones are broken. I think we're gonna be fine. And we're good. Y'all, I am so proud of us. We are really doing the thing, decorating my apartment. Like, ah, I just feel so, so blessed. I mean, maybe wondering what art I'm putting in these frames. I was at the Whitney. I'm quite sure I bought this. In fact, I know I bought this. It was actually probably one of my first vlogs, and I saw this art that I loved, so I bought it. Why is my cat meowing? The whole Whitney experience, it was actually really fun. And when I saw the art, I was like, actually embarrassing, because you get really weird when you're by yourself and just talking to a camera. I actually know how to hang things onto the wall, but, you know, I'm not gonna let that stop me. I am still going to find my joy, and we'll figure that out at a later point in time. Let's get back in. This is a mess. This is Gav, and this says 24 by 36. Okay. And this says 24 by 32. You know what? It's fine. It's fine. We're just going to have, like, an inch or so of furniture around it. I think that might look nice. This had a brilliant idea. I'm just going to put this behind it. It's white, so you probably won't even be able to notice, and it's only like two inches. It'll be good. We got this! The poster has been rolled up for so long. I literally have to, like, sit on top of it, so it doesn't roll. You know what I mean? I'm really, really struggling here, guys. I am hot. I am thoroughly sweating, and I'm really struggling with this poster. I think because it is trying to curl, like, the frame won't stay closed, so I'm just going to use some books and some paperweeds. I'm actually going to leave this like this overnight. Jock! Stop. Go. Go. Go away. My cat, dude. He's, like, trying to eat my books. He's always in my business. Okay. So hopefully we'll tune in with that tomorrow. I kind of want to call it a day because I'm so sweaty and I'm so hot, and I'm nervous that maybe I ordered the wrong size for the other frames as well, and I just want to, you know, I'll see you guys tomorrow. For you, it'll be like three seconds, but I will see you guys tomorrow. I went to Michael's, and I actually got a frame that was properly sized, and so now the poster's in it. It looks great. I clearly was getting really frustrated in the last video, so I just had to do that. I couldn't do it on camera because I thought I was going to have, like, a meltdown. I'm not even kidding. But in today's little section of Decorate My Apartment with Me that's now turning into a month-long progress project, I realized I have to go to IKEA, which I think I'm going to film in a separate vlog, which you can probably see here because I think that vlog's going to go live before this video does. Let me move y'all. So I did order new frames and some, like, creamy gallery wall art that should be around here somewhere. I still have my posters that sadly were too small to fit in these frames that I got, so now I have, like, eight of these frames and not a lot to go in them. I think I maybe have, like, two pictures that should fit in them, but I figured in today's portion we could just put the pictures in the frame and then, I don't know because I still don't have anything to hang them on the pulse with, but at least I will feel like I'm making some progress, which I really just need to win today, okay? I really need a win. So these are my Chantel Martin picture frames. I got these from the Whitney and a vlog that if you're an OG here, you remember the vlog. Then these came from House of Hughes. They're like Monets and stuff, but I don't remember what I ordered, so they'll be fun to open. And then these are the new picture frames that hopefully will fit in here or will fit those. Let's see. More frames. Like, just a little art. I thought it was cute. It's, like, one that I got, like, whatever was green. I love this. This is the Van Gogh. Another motise. I just wanted to bring, like, some color into this face. That would be cute. Another motise. Shock. Now it's not your time. Now it's not your time to shine. Go away. Go. I'm actually me. I'm happy you guys love me anyway. 20. It's now 2022. Okay, maybe I'm being dramatic. Maybe 2021. It's been a long time and we are finally here. We're finally, finally here. My goal is, like, everything that can be framed will be framed right now because I'm tired. And I need to feel like I'm making progress because it has been way too long with absolutely little to no progress made. So this at least feels like a step. Leave the plants alone. I'm giving him mixed messages by yelling at him but then also putting him. What are you doing? Oh, I just framed literally every single photo I have. Well, not every single photo I have. I put a picture in every single frame I have except for this one because I didn't have anything that could fit in it so I need another photo that's allowed by 14. But look at all these photos. I think they all look really, really cute. We're gonna have some gallery walls going. I have so many Matisse's. I'm not even like a huge Matisse fan. Like I would much rather have like a Degas or a Dolly. But you know, it is what it is. I am obsessed with these. I think they came out so, so good. And honestly, I think that is it for today. I need to, oh I told you guys, I have a good idea. So once I do that, we should be able to start putting things on this wall. And then I also kind of want to put some stuff over here like next to the TV. I also want to move the mirror that's in my bedroom over to the TV. But I'm really excited. I'll see you guys in like 30 seconds. It'll probably be like five weeks later and I'll finally, finally be ready to hang some show on my wall. But you know, it's all in divine timing. So I'll talk to you guys. Why am I signing off? This video is not over. Okay, to cue the Spongebob clip, the whatever transition, whatever I'm doing, whatever. Bye.  I have to watch out for this one because he will eat my photos that are not framed. The moment has finally arrived. We are ready to make the gallery wall. So I'm so happy. This has been a long time coming. I've realized that I actually put in the frame upside down. So like the hook is up here, but then the picture is upside down. So I have to fix that. And then I'm also going to head over to my neighbors and borrow some tools so I can actually complete the project. But like we're in the home stretch. Let's go. I want this one to go kind of like up here ish. I don't have any tape. I've also never done this before, but I saw on YouTube, the most reliable source for information, obviously. That you just put like a little toothpaste here, then that's like, you know where to hang the wall for nail. And hopefully this works. Luckily, we're at the end of the tube. So like, I really don't care if I put my fingers on this. All right, let's see. So I'm going to put a little toothpaste on it. Literally just a little bit pasty. Being Bob the Builder is work. It's in the process. Honestly, I got these photos, some of them over a year ago. So I am very happy you guys were able to come with me on this journey. I'm going to end this video here. There will be more videos in the series, especially because now I'm feeling like inspired. And I think I should just honestly hang all of the photos that I have while I'm in the hanging mood. So look out for episode four, five, six, seven, eight, nine, 10 of me hanging stuff in my apartment. Thank you guys so much for watching. Make sure you subscribe for more decorating my luxury New York City apartment.


Η ασφαλήτητα στην Βανγκή λάστηκε μόνο για μήνες. Στην χρησιμοποιήτητα, αυτή είναι among the worst I've seen in the 11 years I worked for ICRC. We have to remember that the people here did not have much to begin with. We are talking of one of the poorest countries in the world. If you add conflict, looting and displacement to the long existing poverty and underdevelopment, you end up with a population in despair. Some of these people are now in their fifth month of displacement, which means that for the past five months they have been drinking water of very questionable quality, they have been eating whatever they can find. They've probably not seen a doctor or a nurse and their children have not been to school. In Bangi hospitals are now almost back to their capacity before the 24th of March, so we can say that the most urgent medical needs in Bangi are taken care of. I'm afraid though that we cannot say the same about the rural areas. Many people who have fled in the bush have practically no access to healthcare and this for several months now. As many health centers have been looted and their personnel has fled to Bangi or to other places. I would say that the most urgent need is to improve security throughout the country. Humanitarian organizations have been playing a very important role because the state is often unable to provide services to a large part of the population. These very same humanitarian organizations which have helped the local population for many years cannot work because of the insecurity. Unfortunately, the international community does not seem to have the Central African Republic very high on its agenda. But I feel that more should be done for this country in terms of making more funds available for humanitarian organizations. Humanitarian programs in the area of health, water supply, food security for example are of a life-saving nature and no effort should be spared to secure funding at least for this kind of operations.


Good evening. This is Guillermo Sabatier, your host and of Perspectives on Energy. I'm Director of International Services at HSI. And joining us today is Brad Schmidt, Chief Commercial Officer at Trident Industries. And they are manufacturers of composite utility poles. So Brad, welcome to the show. Thank you, Guillermo. Happy to be here. Glad you could be here. So I had the pleasure of meeting Brad at the EITD MMA. That long acronym stands for the Edison Electrical Institute Transmission Distribution Measuring Mutual Assistance Conference. Or we're both booth neighbors, right? So would you please share with us more about that and your backgrounds? Yeah, absolutely. So again, Brad Schmidt, Chief Commercial Officer at Trident Industries. I'm from and live in the Cleveland, Ohio area. My background is in chemistry and polymer science. So I spent the last nearly 11 years with the material science company and various sales roles. The last six of which I was the sales director for their composites business. And then this opportunity to join Trident presented itself last fall. I really believe in the product and what they're doing. And it seemed like, you know, the right next step for me. So, you know, made the decision to join Trident and haven't looked back and it's been a good short but good first, you know, six months or so. All right. Well, definitely it's this product definitely brings a lot of value to the industry, right? And it is, it is quite a, I mean, quite an accomplishment really to actually come up with this new innovative technology and then have the industry begin to accept it, you know, in more and more areas. So tell me more, so tell me more about this value that added value that this brings. Yeah, absolutely. I mean, right now a lot of utilities that we hear are facing issues with availability of one polls that they used to be able to source either extended lead times or just inability to get polls that that used to be readily available. So, I think it fills that gap first and foremost but beyond that then there's a lot of advantages to composite so just if we wanted to start with a little history on Trident. We were founded in 2007 installed our first polls in 2008 so we've had polls in the field now for 15 years or so. Our process, which we'll talk about in a minute is one where we have a consistent cross section so opposed to a tapered poll. So we made our uniform diameter from base to tip so we made four diameters up to 110 feet tall and you know can meet any of the antsy wood equivalent instructions. So as far as availability because that again is one of the biggest pinch points right now. I think for Trident alone I think most composite poll manufacturers are in the same boat where most actually all of our raw materials are domestically sourced. We carry a fair amount of inventory for emergency response as well as just general lead time so we operated a six week lead time which right now seems pretty attractive compared to some other material options. So our process is concerned so I mentioned earlier so we use a process called poultrusion which makes the continuous cross section polls. There it is. So, yep. Perfect. So as the name implies the whole thing is driven by a pulling system. So pulling the fibers and and multi directional fabric through resin liquid resin that that wets out the fiber. Ultimately it goes through a heated dye that cross links the resin and it comes out the other side solid and then we cut to length at the end of the line. So there's a couple ways to manufacture composites this is just one, but the other thing you mentioned the value or innovation I suppose. The other thing that I've heard has come up regarding fiberglass poles is UV stability and that's always something that you know gets questioned and I assure you we've gone through all the testing I did hear about a this is going back 10 years or so where there were some fiberglass lighting poles that had some UV issues and blooming after seven or eight years in the field, which threatened to give the industry you know somewhat of a bad name so we've been not just us but the entire composites community working really hard to overcome that and I think we've done a great job we've gone through all the UV testing past you know with no issues like I said we've got polls in the field now for 15 plus years and have had no problems there so the other thing that we bring that's a little unique or innovative I'll say to the to the market is a multi layer design. So, so here's here's just an example of our construction which which notes the UV resistant veil, just below the surface so that really helps to promote the resin rich surface which contains the UV inhibitors and ultimately protects the you know for its lifetime. As far as the multi layer design, yeah, go ahead. So, so, so tell me more about that multi directional versus unidirectional like fabric right so. So, in our process, the majority I'll say the fibers are running in the length of the pole, we still need reinforcement in the 90 degree or plus minus 45 so we introduce fabric on either side of the roving that gives you that called transverse reinforcement. Okay, the other method of manufacturing composites is a filament winding process where you're winding around a mandrel so in that case most of your fibers are in that circumferential direction as opposed to the longitudinal if you. Oh, so that that definitely adds a lot of a lot of like stress resistance right compared to for example a spawn concrete pole, or even a steel pole in that regard right where this can actually site like. I imagine it's probably a little more resilient some of these steel poles once a steel pole burns that's it. 100% I mean that that is really value. The value of composites is the ability to flex and then return to their natural. But I'm not I'm no stranger to to storm hardening and storm issues and areas of tropical climate set that you know we live in Florida so I spent 30 years working for the one of the bigger utilities here in south Florida. And I can tell you that every year was an interesting exercise and replacing wooden poles and. I mean up to a point they replace all other wooden transmission poles with concrete poles and then they had the square the square poles that eventually broke quite a bit. They have success with the with the spawn concrete but but even then those are what I was there for the last few years. Those are getting pretty hard to source at some point I mean that that's a long lead time on those concrete poles. Absolutely we're here in the same thing with steel and obviously would so. You know compare if we're going to talk that about concrete or steel I mean there are some other inherent advantages to composites first being weight. Right so much lighter weight easier to transport easier and safer to install. And then non conductive right fiberglass conduct electricity so whether it's you know the linemen safety or even avian protection. Not being conductive is a big advantage for composites. I imagine the poor body can be run inside the poor than outside because then you also run into that risk of copper theft which I'm very familiar with as well as leading with that nonsense so can you imagine you you mitigate inside right. Absolutely so so when we ship a pole it's basically ready to install we will we run the ground wire internally top cat base plate drill all the holes. That's the utilities specification so yeah. We were trying to take as much of the pain points and labor out of the utilities hands as possible right. Yeah, so so in an environment like Hawaii, I'm sure like he go for example Hawaiian Electric. I mean what's there what's the benefits to them and that particular environment right in that particular application. What you could look at for example as as to select this over any other the competing competing designs right. Sure, I obviously being an island or even at a coastal region like the southeastern US deposits have that advantage of being a nurse so they won't rust. They won't rock like would right so in that salt water air. Impervious we we've actually are wrapping up about a five year project in the US Virgin Islands where we've installed thousands of polls for their storm hardening effort and one of the reasons they went with composite is just you know for that exact reason. There you go there's some nice pictures of our polls in service. Yeah, yeah. Yeah, thank you. Aside from that, though, again, you know the lightweight so transportation to Hawaii fairly remote can be costly. The fact that these can be transported more, you know, more easily because of the weight reduction is has a big deal. And then we we do something unique and try to where we have a multi layer poll design so we will nest one of our profiles inside another. When you do that you get a really a much more robust poll right. So we do a lot of work in self supporting or on guide applications. So I know, you know, we never want to drill more holes than are necessary so eliminating those guide wires eliminating that that extra easement or drilling and labor is a big advantage and value that I see we could bring to the island. Well, tell me more as well because it really in an island environment same as the tropical environment where I'm at, these wooden poles have that the issue would rot whenever water just begins to you know settle on top and find us way in or somehow at the base you know you have to do those annual inspections where very few years when you're looking and then down there begins to rot away. How's that compared to those particular assets. I mean, there is no rock right like these things are intended to last you know hundreds of years in in service or even when they're after service life you know they're they're not going to decompose which brings up a point right at the end of life. There we find we often find outlets for them to be repurposed thinking that if not you know there's a lot of work being done right now and wind blade recycling. The material is very similar to what a wind turbine blade would be made of and so there are some current technologies to do so and and there's a lot of research being done and in recycling these sort of materials. I'm sure that that could be a purpose for like constructing building some structures. What was one thing you cannot do with a wood pole would pull has all sorts of or you know, like really interesting chemical. No, exactly that was the other. No good stuff for me. Yeah, no leaching and no maintenance. So that's the other thing is the inspection other than visual inspection. Once these polls are installed really shouldn't have to touch them. So tell me more about a line worker right having or like, but on spurs and go up on these polls what's the approach there regarding because I'm sure that's the question most line workers are going to ask, how do I claim this poll. Right, so of course, yeah, I mean bucket truck right now, but we do have. We do have steps working and permanent steps. So again, we would drill the holes or they can be drilled in the field as well. But but we wouldn't install, you know, steps at whatever height up the pole utility would would request the biggest thing. So the polls can be installed very much like you would direct barrier would pull. The biggest difference I guess the really the primary is the type of hardware so avoiding the cleated hardware, because you want to maintain that UV resistant surface those, you know what I mean. So other than that non cleated hardware and then the, yeah, you're not going to climb a pole like you would a wood pole but if you have the steps. Yeah, it's a simple solution. Not much of a learning curve I imagine way with with with with the lineman school or line worker school. And so so that's really an obstacle or shouldn't prevent anybody from actually thinking of acquiring when they regard. I mean, I'm a, I'm a, I'm a pretty strong advocate right of composite polls, given my experience in the past when it comes to like storm hardening. And, and how resilient the composite polls are compared to these other assets. The only thing I think people will probably question would be the wildfire susceptibility whereas you know concrete pole but if you got a concrete pole that's that's that's that's got a fire around the chances are the conductors are going to have issues anyway, or or. So that's fiberglass process is going to it's going to have a problem. Well, no, not not necessarily so there are technologies out there and there are composite polls that will withstand the wildfire temperatures and so no this has been highly engineered over the years to be able to withstand those brush fires that 20. 2100 degrees for for a few minutes at least. That's actually another advantage of composite. Definitely good advantage and for me, one of the things I've also seen right with salt water intrusion from the from the base up is that you end up seeing some of those like rebar just begin to like corrode and then burst. You know, slowly correct the actual pole along its length and then crack it and then collapses at some point I've seen that happen. So that's something that you're not going to deal with here either so. No, exactly there's no water. We've done all that there's actually some moisture some standard moisture test moisture or water absorption and it's. I mean fractions of a percent that that's not a concern. So, so, so definitely we have some really really significant advantages right over over these materials. I mean also from an environmental standpoint right you're not cutting down trees you're not having to grow entire forest so then cut them down and really that growing those trees takes six years, sometimes decades. So, so in this case, you know, using all this land to grow these trees when in reality, you can use that number or something else. So this manufacturing you can probably turn out more or more of these composite poles. In the time it takes to grow one of these like this lumber, you know, yeah. No, we joke we grow trees at a foot a minute right so much faster than mother nature and to your point then you're not having to cut down trees and replant. So, no, it's certainly another advantage and especially given the availability issues right now that we're talking about. Yeah, the supply chain issues I think some some of them were saying they're almost up to a year to get like a certain inventory of poles we start in some cases. So it's definitely a challenge right for some of these utilities. One of the things we're also so one of the concerns that I was asked I was at a I was at a delivering training at a co-op up in Tennessee somewhere, and they asked the whole situation well what's it like with a vehicle impact what's it like with ice loading right and that sort of things. That's usually their concerns the ice loading and the vehicle impact. We'll start with the ice loading because that's an easy one. I mean, we size our poles based on certain ice loads and wind criteria right and so long as we're accounting for that up front. I mean we've yet to in all honesty with our multi layer design we've yet to be be given an application and call it sub transmission or distribution that we haven't been able to meet the loading requirements we've even done some steel lattice tower placement projects with with some of our multi layer poles. The other thing on the vehicle impact so while we haven't done actual crash testing. We've seen plenty of polls be impacted and actually the Society of Civil Engineers has a whole FRP poll standard or guideline, and they did comment on the vehicle impact specifically so essentially it's it's safer I'll just you know start there so for a few reasons number one they're hollow so they can they're able to absorb energy more than a solid would pull for example and fiberglass or composites just by nature can absorb a fair amount of energy. Secondly, if if they are impacted and sheer they typically do so fairly clean, if you will, and we've even seen instances where because they're relatively lightweight. The conductor is actually holding the pole, still in place rather than coming down on a car. And then the last thing I think is the fact again that they're non conductive. If you did have a live wire situation. The poles not going to at least you know be that and that's definitely a once again and added plus right because there's some regions where you have a lot of some of these poles are though. They're within the foot of the ending of that of that pavement except I've seen that right now far away from the road so I mean it's not always a case is not usually the standard. It's usually quite you know, at least 56 a feet away from the, from the outside edge of that of that road but still, you know, there are times where they get awfully close was definitely good to know. And so, so, so advantages again salt they're right those difficult environments closer to the ocean, of course as a lot of advantages over overwood and definitely over steam right or even like rebar reinforced concrete. And again the severe weather right so the storm hardening this definitely has so many more advantages over those other three types of assets. So, so, so here's where we'll get to the question whether we're always going to wonder right it's it's how does this compare cost wise and to the other assets. It took you 15 minutes to get there so it's that's better than most meetings I go to know. So, obviously that is the, you know, our biggest challenge is the upfront costs so as a general rule of thumb obvious depending on on height and class, we are called it two to three x the upfront cost of wood. Now, when you so you really got to look at composites over the service life. If you if you anticipate a typical wood pole to last 40 to 50 years, you know, we, we anticipate our composite poles to last 80 to 100, and we weren't everything for, for at least 40. So, when you consider having to purchase well, remove an old pole install a new and purchase a new wood pole in the same time that you would have, you know, one composite pole that alone makes up for the difference typically but then. I mentioned that you know I mentioned earlier the lighter weight, we find often you can use lighter duty equipment to install the polls than you would otherwise the transportation cost especially you know putting it on a boat to Hawaii, you can fit more poles in a container. So, one of these things when when you consider the the overall life cycle cost of a pole are actually more attractive than most, you know, the other material option. We also got to remember right now there's even an additional group of savings that we didn't talk about it's the personnel hours. Now you're going to have to replace that pole as personnel hours right that gets involved in that so now you got to go in there to get a clearance you're either going to have to like work it hot which is usually what they do. So now you're running that risk of having having a flash, you know, hopefully you won't but then also the risk of creating an outage for the customers. Then so so so add all these personal hours for that project right that's an additional cost that that we're not even talking about yet because you know when it comes to replacing that. And the and the the pole inspections of course are not going to happen as frequently I imagine because of the fact that there there's a lot longer interval here. And then the other thing I can imagine as well is that the type of equipment like you were saying that you're using is not as expensive. So so you can probably offset a lot of this cost because now you're not you're not investing in this this more heavier class of equipment to operate with you know whether it's a Derek or these other cranes or something that's why she like install these poles. And the environment. Yeah. I mean, the only other not only other but just thinking about the storm hardening right I mean, on a normal scenario if you expect your wood to last 40 or 50 years, but here comes a hurricane or whatever right now that pole that you installed five years to replace so just and I think that the utility industry is really coming around and thinking about things differently. We can't do it the same way we've always done it and go back and replacing the same assets every 1020 years even so everything that you mentioned but then there's that that hidden cost of what happens when the power goes out because we lost you know a number of distribution. Right. And that's, and that's the other big cost or their safety or may fear safety minutes they were talking about, which is the amount of time for example that a customer is out that ultimately is translated into into. There's dollars behind that right where it's not really party not selling but rather there's there's a whole other index right a customer satisfaction that is involved in that. And then of course there's some environments to where I imagine these polls are probably easier to transport with with with aircraft, whether it's a road, you can airlift them a little bit easier right then a concrete pole or steel pole. No, I mean we've had instances where rather than having to build a service road out to a remote remote location. You know, rent a helicopter for a day or whatever and just just drop the polls and so especially in mountainous regions and I have been to Hawaii. Yeah, yeah, so I was there. It's probably been 10 years now but beautiful obviously beautiful place to visit and to live. So, make the infrastructure is beautiful right I mean these polls are, I'm biased but I think they're, they're pretty good looking and we've actually have customers who will only put composite polls and like their, you know, main street because of the aesthetics so. But well there, there's believe it or not there's cases where I heard of a few lawsuits where a customer got splinters on their hand, because they because they they grabbed or held on to one of the wooden poles on the sidewalk, which I guess had been have plenty of like splinters taken out because splinters going up and down. And they I'm not sure who you know which end of the web but they they they got splinters in their hand they were able to get a pretty good loss about it because some some infection and injury they had but so just that that that that's another possibility that that comes to mind I'm reminded of that incident right where this and one of the reasons they change those polls out and they put a concrete poles on there was that was one of the contributing factors you know to justify the concrete pole besides storm hardening. It was the the the litigious nature of that customer base in that area. Well, and that's a challenge though that we face to go back to the UV comments earlier right wouldn't be splinters but you know people have this conception that when fiberglass ages, it will bloom the glass blooms to the surface and that's what we are working and have prevented with our UV. You know the surface veil I mentioned and then the inhibitors in the resin systems, but there's still this this notion that that will be the case. Yeah, so that that's our challenge to overcome but again we've done all the testing and have had no issues regarding you know dry fiber, as it's referred to. Right fine. So, so, so the cost you know is is is might be a little more than I mean a bit more than would a little more than steel right it's it's and it is a lesson concrete or or. Concrete it really from my experience limited I've been here six months but it kind of depends more on where you're located if you're close to a concrete boundary and the transportation costs is minimal. Then we're certainly more expensive but if you have to transport concrete a long distance you know that it's heavy right so right so so it varies, but but even steal yeah the upfront cost is going to be a little more but the lack of maintenance you know and then inspection over the years again. We find we typically come out ahead. Well, that's definitely some great applications and and and so so so let's circle back to the idea of of. Going back to like how this could be an advantage for like Hawaii for example right now or country like he called when what would like really motivated to want to look at this in this in this environment. Yeah, I mean I certainly storm hardening and with ours at least in particular the the unguided or self supporting applications to eliminate the need for easements and drilling extra holes and we do a lot of work and in eliminating. Guiding issues or concerns.  No woodpecker issues no insects shoes so all of that and then lastly I think you know, comparing to steal or reinforce concrete with with steel rebar. So just the long term aesthetics to that I mentioned and you know, complimenting the beauty of Hawaii I think.  Yeah, that's something also it's the the animals unable to close way up their eating as well so it's ready. City little details that that they're really but you get them all together and they point in a certain direction right so. So, as far as HSI we can do I imagine we could help for example with just helping with the initial training or or even getting these line workers qualified electrical workers. So we have a program that really has a lot of embedded training regarding line workers, qualifying electrical worker or even anything distribution so so I'm sure this is something that will be easily incorporated into like a training program like ours and just minimize that learning curve right so for these like. Yeah, we'd love to partner with HSI and developing some sort of whether it's online training or even in person we do a lot of in person training, prior to a pilot installation with a utility. We find that you know there's a little apprehension at first but really the similarities to installing a, you know, traditional wood pole or really, you know, people get over that learning curve pretty quickly. Okay. Alright, so I think we're at the end of our show. Wow, we've really used up to 30 minutes pretty fast. So is there anything else you think you want to add or go ahead and wrap it up in this case. Yeah, I really appreciate you having me on I think it was a great discussion hopefully some folks took took something away from it and great composites continue to gain market acceptance they sure do they sure do and once again Brad thank you so much for appearing the show. I'm really great to have you here and have you introduce you to our things like Hawaii community and viewers and hopefully you know expose you to the rest of the industry in this part of the world. Mainly he go and then all the other like tropical island type of utilities and munis and call so you know will definitely benefit from from from your products and services. Well, thank you very much for appearing I look forward to seeing you again in the show pretty soon and. And so, for all the viewers, I mean, Brad's contact info is has been pasted on the out throughout the show and also you see it in the show description as well so thank you all for joining. Thank you for that. And have a wonderful afternoon and evening everybody. Thank you, Brad. Okay, thank you. Take care. Check out our website think tech Hawaii.com. Mahalo.


up with Brian Hoek filling in for us doing some work for Yes, up north in Canada. Marwan 11 consecutive wins for this team. What is the feeling in the clubhouse when things are going this well? I mean, it's a good feeling. When you're winning, it's always fun. Everybody knows that. And, I mean, we're having fun in the clubhouse. We're not giving up. Give up, I mean. It was a tough game today. It was a really good game. I don't keep us in the game. Really good game, one run.   How were you able to score there? Well, to be honest, I don't know. I was just trying to let the guys to get there in second. And I was able to do something in there and score the run, which it was nice to keep the line going. These 11 wins have come in a lot of different ways, a lot of different contributors. What's your favorite part about how this team has come together?  It's like a different guy every day. It's the pitching. We're playing good defense, too. And the offensive side is every day someone different. That's what we're in team, too. Marwin, thank you for your time.


Hey folks it's Hari Swaminathan from Option Tiger, it's Wednesday July 28th and just wanted to give an update on the swing signals been going really well last month we closed almost $15,000 in profit. Now this month this week we're going to be closing some of these trades you can see Apple is up we'll let it develop some more. Adobe also we're going to let it develop some more we've got a bear call that expires this week. Chipotle is doing fantastic and there is still premium in the bear call that expires this week. So is Facebook, FedEx is the only losing trade here but we've already booked about 900 in profit so it's only down about 400 and PayPal is up a 70 Starbucks 2000 and Visa 1500. So the swing signals is going really well and with this email you should receive an email with a special for August and September. So this is going to be about 75% off so it's a two month deal and if you get it for you can get it for one price at $99 so usually the list price is $199 per month and so now for August and September you can pick this up for $99. So it's a one-time charge it's not a subscription so if you wanted to try the swing signals this is a great opportunity and to do it in a very cost effective manner. If you have any questions please email us at info at optiontiger.com. Thanks.


Hey guys, I wanted to talk to you a bit about what sort of content you can expect from me in the near future so recently I've really dug deep into spirituality and not kind of you know levitating or Weird voodoo shit Just like inner peace you could say because my life has always been an up-and-down cycle where Everything is amazing and then everything is shit regardless of external things like I could have an amazing life situation and feel really bad or I could have a really good life situation really bad life situation feel really good So it's not really related to what's going on in my life and it's always been because of my mind like I would always Just I don't know like either chase things Seeking completion completion, which is what led me to take such extreme actions during my past couple of years you could say just kind of willing to risk everything and putting it all on the line again and again and again and And also times of like desperation were just things didn't work out so Something happened a couple of months ago Where my mind sort of broke down? like in terms of ego I Felt so bad everything was so horrible. I just couldn't bear it anymore. And again, I'll get it into later and I stopped like identifying with my thoughts and Like my natural state become became like not thinking in 90% of the time Which is amazing So I've experienced the deepest most rewarding piece that I've ever experienced In the last couple of months which completely changed everything about my the way I go about life That's one of the reasons. I was you know missing for such a quite such a long time because I needed to really dig deep See what happens, you know when I really get in touch with my peace That's on the spiritual side of things now whether I'll give you quick kind of Demonstration of where I'm at Kind of a nice view so The second side is the business side which also changed a lot so I realized that I want to focus less on coaching people like on the high ticket, you know two thousand three thousand dollar coaching clients and focus a lot more on passive income Just so that I can create income By while not doing anything you could say by selling products stuff like that so I'm going to also Kind of focus a lot more on teaching that side of the business and as I go about it you'll learn more how to go about it and My my teaching style will shift a bit. I'm gonna talk a lot less about extreme things You know extreme and a lot more about How to do it like in the peaceful way where you don't have to put a lot of effort like it's very natural But you get like incredible leverage results so basically on the business side, it's how to create situation where you could very in a couple of weeks Create like a business where you make at least like four or five thousand dollars a month you know within the first month or two and from then on how to actually Make it like a passive income business as well where you have a ladder by the way I usually sign with my hands, but I'm holding this shit. So I can't do the whole hand movement thing so It's gonna talk a lot more about how to Structure your business where people go up kind of like a ladder of value where people for example Sign up to your email list and I'll show you how to set up that really easily and for free and then they buy like 10% of these people buy like a $40 product from you.  Sorry. You basically make one times 30 You make like 1200 a month like 12 $1,200 $1,200 every month passively just from the Traffic you generate and I'll show you how to get like a sale a day with just 20 visits to your website From there there on like how to build information products like courses stuff like that I basically had a few courses, but I deleted them because I was like no only coaching I just love to coach people, but now I kind of came full circle about that. So a lot of really cool content And again, it's gonna kind of split between kind of finding inner peace and Finding outer success. So on the inside. I want you to feel peace and and and just Nothing can shake you anymore and and life is good. I'll put this down for a moment so, yeah, like create a situation where your life is just good and And you just enjoy it and there's no drama. There's no ups and downs It's not like it's good and then it's bad and I'm happy and I'm unhappy You just feel fulfilled.  It's it's like the Ultimate peace basically all the true happiness in my opinion because regular happiness is based on things being good in your life This is deeper than that. This is feeling peaceful Whether things are good or bad and I don't mean that like you know peaceful in the sense that you are Don't care. I mean you take action if needed. You deal with things that are needed, but you don't let things like dictate how you feel Basically and even if they do change how you feel or at least it seems like that it doesn't affect you Because you have a deep roots within so you don't like get swayed into an emotion So I'm gonna talk a lot about the psychology of inner peace How to feel peace how to really find yourself and and have a good like no matter what happens in your life if even if you just stay poor your whole life or never find a girlfriend whatever which obviously never will never happen but But just in case it does You're always gonna be at peace with what happens. You're never you're never gonna feel the need to escape and from there Amazing things happen because when you stop creating drama and you stop feeling like you have to do something and feeling bad all the time Like you have to fix something you create a lot less problems And then you can actually focus on the right things like for example imagine you're working on your business But you constantly feel that need like something is not fulfilling Something's not good in inside of you like there's something missing. So you're always like, okay, maybe it's this maybe it's that maybe it's this So you always like fix stuff But you never actually are able to focus on what needs to be done because you suit too busy finding Problems, maybe there are no problems and actually if you don't touch it, it will be better so so that and again that feeds into the business side and How to really create a situation where you can travel the world Make thousands of dollars from the get-go build it up into a huge business and I'm also backed up by many awesome friends. I've met people Making millions of dollars a month a year. Sorry in online revenue just through passive product selling So I have a ton of new information a ton of content a real brand-new perspective and I know you'll enjoy it You know if you enjoyed my content this far you will enjoy this one even more because it's also again, it's also about Peace now not just about success. It's about inner peace outer success Which and they don't contradict and each other by the way and and you know just an awesome Continuation of things and I'm really happy to be back Thanks for all the new subscribers again. Everybody's new. This is what you have to look forward to now so if you don't like it stick around, you know, it might get better and And I'll be traveling a lot more to so expect to see a lot more beautiful vistas Around me instead of just kind of the same old stuff so thanks for watching this far thanks for being with me all the way and We have a really really cool time ahead of us so No, I'm excited


All right, let's say that you are dealing with a spreadsheet where there is a lot of information in each cell, so I'm just going to go ahead give you an example. I'm going to paste a paragraph from one of my recent blog posts. So there's just it's just really hard to look at when it's like that. So what what I'd like to do is I'd like to select a cell. First of all, and I like to go to the toolbar sometimes you have to click more to find this exact tool sometimes it's already there. I like text wrapping so I click on the text wrapping, and I select wrap. Okay. And this now makes it of course really hard to work with because it's so long. So what do I do then I can widen the column by moving my mouse over the top of the column, clicking and dragging the right side edge click and drag. I can go to maybe here. And see, now, there's still a lot of, you know, words in this one cell but it's at least readable. And I can work with this with multiple cells that are like that so I hope this helps and give it a try. Let me know if you have any questions below the video.