All right. So, yes, you're going to talk about the APL competition. I will share my screen because you've put lots of cool stuff there. Share. I think that is a really fast way to learn and try to find the problem while learning it. Okay, so there's a whole thread here. I turn lays had some very nice solutions, I thought. Yeah, tell us about your experience of look at you or go cups. I love the way we've gone from like, that's dead up a study session to try and learn all the glyphs and Sirata's like, no, let's get 10 trophies in the problem solving competition. Good on you. Yeah, I think really stretch myself, but I think I learned a lot during the process as well. So, ask a lot of question, try to read a lot of documentation, but I still find the documentation quite technical. I really learned from the example. Again, really helpful point me to some direction but some of them I still can't get past my head. His radio actually really good in the past competition example he read. Yes. Yeah, and now someone starts sharing why is not the fastest one definitely I want to learn from other people, but it's really good to force me to think. Different to to to using APL to solve the problem, even this is very short and small problem but it's really good exercise and yeah I learned a lot. This is a great thread because it kind of this I mean this particular post here actually goes through each of his solutions and he said to have quite especially this one really elegant solution. Yeah, I actually put we put together so people can go into the lookbook and breaking down the solution as well and other person, our AK 157. I'll tell you what, let me make this a wiki. Yeah. So maybe you can put a link to it there. So I, at the moment I put all people solution in one place and then I profile them to see who is the fastest solution so people can learn from the best. Awesome. I love it. Did anybody else try more of the competition questions. I did give it a try but I got stuck on the second or third question, and it was just about comparing arrays. And then I looked at the solutions and people are using the built in glyphs, not equals where I tried to go via each entry. I think that this is super helpful that we'll are sharing so freely their solutions. I looked at the website and it seems that the competition for this year is not available right now, like you cannot go on to the website and submit your results yet but there are competitions for the previous years that are available. And hopefully this year's will be available soon as well. Okay, that feedback loop where you can try to solve a problem yourself first and then, you know, you can look for help on the forums I think that's. And my recommendation for these would be like spend at least a couple of hours on a problem yourself before looking up the solution and also try doing all the solutions, you know like all the questions. You know one kind of like if you're doing a math test at school you're just like, Okay, let's move on to the next one. And then, yeah, you'll learn more by seeing the dumb things it turns out you did or vice versa, then just reading about it. I have a suggestion or question maybe. I'm curious to know how you are planning to use a PL in your workflow. I asked a question on on the forum and somebody suggested pineapple which I find very useful for a PL to be used in Python and vice versa. So just to clarify, you're talking about PYN APL. Right. Yeah. I got stuck installing it on on Mac but that's another separate issue. If you, if this is the way that you envision using it in your workflow, meaning that a little bit of a clever code to clean up data and do pre post processing. I think in the entire workflow inside Python. I thought it might be useful to experience that with you as a part of the walkthrough. Sure.  How do we pronounce your name is it Ramin.  Joining us from today. San Diego. And Diego. Oh, that's a lovely town. I've been watching your videos carefully and pausing them and doing stuff in the background. Well, thanks for joining. So, I think of this in a similar way I don't know if any of you have read Richard Feynman's autobiography. He described how he got it, you know, got he liked following problems that he found interesting and so he got interested in watching spinning plates on their fingers at the university cafeteria. And he decided to take some time to study the motion of those plates. Because that was the thing that seemed most interesting to him at the time. Later on, it turned out that the that the bath and physics he developed and thinking about that problem turned out to be exactly what was needed to solve some critical critical foundational problems in quantum mechanics. You know, I have a similar thing about appeal things interesting and fun. It's my interest is in it mainly as a notation. I have always been kind of interested in mathematics but the notation has always gotten my way. I think I'm like, I must be like particularly anal or something because I just find it's so imprecise and like or like the meaning of it varies from paper to paper or area to area and like I don't know how to like look things up and find that exactly what it means and then it's hard to pin down and so I ended up at university studying metamathematics and formal logic and that like helped me a little bit because I kind of went back to like well what is mathematics and building it up and scratch but I keep getting stuck on notation, you know. And also I'm somebody who's highly intuitive so I really like to experiment with things. I like to know if my experiments are right. I'm really envious of how, I don't know if you've seen Adam on the forum is able to like take an APL expression and treat it like an algebra, you know he'll go through symbol replacement exercises and at each point she'll say here's the symbol replacement rule I'm doing and manipulate an APL expression into a new APL expression that verifies some situation. I want to yeah so he's he's my hero I want to be like that I want to be able to treat it as as an algebra, you know, and use it to deepen my understanding of things. I, I mean I use it a lot right now to teach my daughter math. And so she's six and her friend is eight. And so I tutor them in math and we, we have been doing a series of books called Beast Academy which were kind of great cartoon super fun, very, you know, compelling for kids. And as their math developed we ran out of those and we, you know needed new things to cover you know so like their most of the math stuff they're doing is around like grade 11 grade 12 now and the problem is that materials or boring dry presentation. So they're like the Beast Academy books, it's by a group put out of problem solving. And they have fantastic materials but their highest, their high school level stuff is called out of problem solving and it removes all the comics and all the cool characters and so it's not fun anymore. So, you know, a couple, you know a few days ago, we were trying to cover a topic.  And I was like, Oh, of course we can we can do this exact topic with APL. So we just, we stopped the video, opened up APL and I said okay, solve this math problem with APL. And then they're engaged again and it's fun and they're trying things out. They're both sharing their screens so I can see them trying things and then, you know, then we can go back well why, why did that work and. So yeah, kind of intellectual interest and I feel like there's a. I can see it starting the revolution in education. Yeah, well that's what I was in thought, you know, and he, you know, he wrote this, these books with with high school teachers and somewhere here, you know, here's a okay. So here's a calculus book. Let me turn my virtual background off. Okay, so here's a calculus book. And it's a calculus book in APL. So, you know, it has exercises and derivations and whatnot, but rather than using normal math notation it's all an APL, you know, and so it covers. Let's see. You know, it's got all kinds of interesting math problems and tailored series and why is that students make it more compelling. APL is intimidating can be. Well, not when you're six, because, you know, when you're six, you're everything's new, and everything looks weird. You know, so the biggest problem in our math is when we hit Sigma notation. And I just couldn't get anywhere with it. Yeah, because there's a lot of assumptions going on, like I just sort of thought that was such an easy thing I thought how could anybody ever find it difficult but then when we got there with the kids it's like okay well there's this like implied loop where this index is like looping through the thing and then the thing inside the index is like getting each value of that and then there's this kind of like concerted some. And it's just that that's just a lot of abstractions going on so when we did it in NumPy that helped a lot. You know, but then when we did it in an APL we actually learned plus slash means insert plus between each pair of things in a sequence.  Yeah, it was much less intimidating to people who haven't yet learned normal math notation because this is a math notation that they could execute experiment with has extremely well defined rules if they're not sure what something is they can look it up in the help, you know. Okay that was interesting. Thanks for explaining. Yeah, no worries. Okay, I am on. I just wanted to second like Adam donations are awesome. His rank operator I use that all the time now that he showed it on that one, that one video. Yes. Yes. Listening to the array cast. Yes. Yeah, I have to. It's great. I haven't got to it yet, but there's two somewhat recent episodes called leading access theory and transpose. And they spend about three hours covering what Adam did, you know, in 45 minutes when he was here. It's much better when you've got it visually and I kind of listen to the episode and I was like yeah yeah yeah I know all that. But it was interesting hearing him talk about transpose as well as being as important as the ranks stuff. So it might be a valuable thing to check out. If you haven't seen it. So, I'll share my screen. This time we didn't forget. That's right. Can you believe that. Oh also concept of trains I found them useful and not intuitive. Yeah, we haven't got to that yet. Because we're trying to do all the glyphs first that yes. Does anybody kind of remember, I guess. The last one was in the middle of something last one was mostly Adam so yeah. Okay I guess we're kind of up to here. Actually, I wouldn't mind. Moving these from stuff we haven't done yet to stuff we are doing because it really belongs right at the top. Basic math operators. So what I might do is add this pipe operator. And it's actually pretty straightforward one. Okay, so we're going to do vertical bar. It's working. Never quite sure what's going to work on a new machine. So they call it style or vertical bar monadic. I believe it's called magnitude. Yes it is. All right so unfortunately because I'm using a Mac today I do not have a screen I can draw on. Which is a bummer. So hopefully we can find a picture of what magnitude is. Great. So the magnitude of a complex number is how far away that complex number is from the origin if you represent it as Cartesian coordinates. So, if you've got a number a plus bi. So to remind you I mean square root of minus one. You can represent any. Any of these complex numbers using a single real a and a single real be. Even if you've got squares or square roots or model plies or whatever, because you can send you can always simplify it down to a real number part plus a real number times the square root of minus one. So this is basically any complex number you can represent in the in this form. And then you could draw it, and you can draw it by putting it on a Cartesian coordinate plane by going right by a units and then up by b units to the coordinate a comma b. Does that make sense so far. Anybody who's not. I think radical you're not said you're not so comfortable with complex stuff is this is this makes sense to you so far. Okay, so this is a triangle to right angle triangle. And so how far away is this dot from the origin. Well the answer is it's going to be the square root of a square b square because it's a right angle triangle and Pythagoras told us so. Let's put out it then let's what about this number here. This number here is one plus zero I also known as one. So how far away is that from the origin. One, which is equal to the square root of one squared plus zero squared. What about this number here I. Okay how far away is this will square root of zero squared plus one squared also one. The magnitude of a real number is the number itself the magnitude of a complex number is the size of the complex of the only imaginary part is the size of the imaginary components real number and a complex number more generally is through a square plus b square. So that's what. This means and remind you three J for is how you write three plus four. I also do. Oh, and, you know, in fact, let's do them all together now that we're getting fancy. Have to my. So negatives, the distance that negative three is from the origin is three. And again, negative three squared is nine plus zero squared is nine square root of that is three. Okay. Diatic I think they call residual. Yeah, residue or modules. That one down later. Okay, so much less so we did. Other examples we could steal. So this tells you the residual you're left over with if you do to divided into seven. So in other words, seven divided by two is three remained or one 13 divided by 10 is one. But it's negative. So if you've got a negative right hand side, then what they actually do is they go further they treat that as being they say that's to remain to seven. So if you have a positive right hand side, eight divided by two and a half is how do we get negative two here is two is for remainder minus two. So like it with I haven't really seen this idea before, but normally in in school. Remainders are done always positive. And they have a very clear answer right which is 10 goes into 13 one time with three remainder two goes into eight four times with zero remainder. So the negatives you can kind of like overshoot it on the positive side or the negative side. And so an APL. If you have a negative right hand side. Sorry if you have a negative left hand side, you'll get a negative remainder and if you have a positive left hand side to get a positive remainder. The reason this is also called modulus is because if you're like, if you're, if you're measuring the number of minutes past the hour. For example, then after back a little bit so it doesn't go off the screen. Yeah, it messy huh. Then after one second the minute handle we at one after four seconds minute handle be a four, etc. After 59, so 59, sorry minutes, the minute handle be at 59 after 60 minutes the minute handle be at zero. So clocks count modulo 60. So modular is the same as what's the remainder if you divide by this. And modular modular arithmetic is used in cryptography a lot. And it kind of comes up all over the place. So measuring the angle, you know, that's made as you turn around a circle, if you go more than 360 degrees you come back where you come from so it's kind of that's those measurements will be modular 360. So that makes sense. Okay, so then times. Times tells you the direction. And if you look here, the number one is a real number is to the right. And so you could say its direction is one. The number negative five is to the left you could say its direction is minus one. So five I its direction is straight up you can say its direction is I so the direction of a number is, if you draw a vector from the origin out to that number on this plane. Whereabouts but across the unit circle. And so in most languages that don't deal particularly with complex numbers. We have a function called sign s IGN that returns the sign of a number and it normally returns one if it's positive and minus one of its negative. So for real numbers. Monadic times is exactly that look at this one at eight times 3.1. In other words sign 3.1 is one. Monadic times of negative two. Another word sign of negative two was negative one. And then normally in most languages sign of zero is is called zero. And this is all exactly the same as sign. It's called that in Python isn't it. I guess it doesn't. NumPy has sign. So why doesn't Python have a sign function. Just Python. Yeah, I don't remember using sign without NumPy and Python. Yeah, that says there was a patch but it wasn't accepted because they couldn't agree on what it should return. They couldn't do it at all. That's funny. So in NumPy. I wonder if NumPy sign handles complex numbers. That would be something slightly different. That's interesting. All right. So I kind of like this about APL is I find really consistently it tends to extend basic ideas from other languages and from math like more things in a more general way. Which I think is really cool. Okay, I guess I should mention complex numbers. Okay, so, so here we can see. So what is the magnitude of three plus four I. So the magnitude of three plus four I. Well, we would start with the number three plus four I. And then we would divide it by its length, which we know is magnitude of three plus four I. And that gives us point six plus point eight. So that's going to be the, you know, so point six comma point eight would be its coordinates on the unit circle down, you know, somewhere around here in this case. I'm not going to include it here but I think, you know, as Adam said, I was trying to think of a way to do this as a train. I think this should already work right so when you have two of these next to each other at first of all applies this. Is that right. I can't remember which borders in. Yeah, the first of all plays that right. So you can just, you can just delete the left hand side maybe you can't just delete the left. Well, you could delete the left hand side if you're in J, but APL doesn't work that way. APL would treat this as being the reciprocal of the magnitude. If you put parenthesis on it. Still no, that's the way J works. It's not the way APL works. Okay, you're thinking of a type of train called hook. In APL, you would need to do, you would need to use the self operator. So you would do that with the self operator, which I can't remember how to write it so I don't have to find it. It's the tilde diresis. Yeah, capital P. Capital P capital T. Does anybody know how to make that work working on it. Oh, did I get it wrong. Yeah, I got it right to order diresis y equals y f tilted f y. I could answer you last week. Divide by zero. Alright, so that's an interesting puzzle for somebody to figure out. Is the binding for the complex number less high than. No, that this, this, this is this binds as tightly as upper bar or full stop board as a decimal or. Yeah, or whatever. Yeah, 99.99% sure. Yep. For F three to four. Oh, that's interesting. So, oh, I see the issue the issue is that there's an implied parentheses here, because we go right to left. So actually if I did this, that would break. I'm telling what I actually need to know what I should do really is look it up properly. Yeah, but what we actually need is beside, because beside. Yes, beside is the thing which behaves exactly the way we want. And it's the same as putting two things next to each other, as long as you don't mess with the kind of execution order. So here's beside it applies the monadic G first, and then applies the dyadic to the result, which is what we want here. So, I think that means. All right now. What do we expect this to work so it's going to go. I don't know if it's. Okay that does work that's very interesting isn't it. So I guess the thing is here. It starts looking left. Right, I still want to get better at these parsing rules it starts looking left and it says okay that's an operator. So we're not done yet. Okay. And so then given it's found an operator it then needs to find a function. And it's found a function here but I guess it's not a complete function because it's got an operator to its left and so it keeps looking until it's got a complete function. Something like that. I'd love to see like a really clear documentation of this parsing rule like how is this past. Yeah, I think you're right. And then there's a way to do it with train and without the last symbol for the what's called without the symbol. Right without the tilde. I'm pretty sure you're thinking of Jay. It's got a hook in Jay. I'm pretty sure APL does not have such a thing. See the response from the Adam gave to my computing the mean of a vector. One of them was equivalent to this and one of them the last no that was different he had a fork. A fork is a list of three verbs in a row. So you're thinking of something else, which is the definition of mean, which is very interesting that we are kind of skipping ahead. So the sum divided by the count, which is tally, which I can't remember how to type double quote. Okay, that's the mean. Okay, and this is different because we here we've got one, two, three verbs. The definition of this of three verbs in a row. It's called a fork. And what it does is it applies this to omega, and this to omega, and this to the two results. So, some of omega divided by counter omega. So we're skipping ahead. Jeremy, there's an option you can turn on with the box option to show trains and functions is like parse trees. I posted it in the chat. Okay, great. And presumably that would just be if we remove this. Why wouldn't you always want that it's beautiful isn't it. Yeah. It's still a little bit of a pain kind of deciphering where all of the arguments are supposed to end up but yeah. Well, not too bad right because you've got a. This, this is obviously going to apply to the right hand side. So I guess that's okay. So. And yeah, but I mean you can always and you have, I think that there's pictures they have as nice of like what the side does. Well, let's put that at the top maybe. I've actually got a complex section there so I should move the complex description or just maybe I'll copy it. Maybe it would even be useful to see for J zero. See that's how you just do. Okay, okay. So I think we can now get back to our stuff for 2022 APL competition. So that was our kind of group by thing. Okay, so that. And did we have my attic and dietic. Oops. This is dietic. Oh, right, right, right. We've got the monadic and dietic versions of the function created by the operator call. All right, so the next in our list of these two. Let's do this one then shall we. Oops, something funny happen there. So this is called key. Okay, this is called left shoe. I like it. Oops, I changed the wrong name left shoe. Okay. My attic is enclosed and dietic has a couple of meanings and close. So this enclosed thing happens. It gets used all the time. And it seems to be something like what J calls boxing. Like creating like references or something. Okay, so we're basically, that's a list. And this is row of that list. Row of the list. Okay. And then, so this is a list with three things in it. This is a list with two things in it. And the second of the things in the list. The list to three. So makes sense. And then this is going to be a list with one thing in it. Because it's a, it's a, oh, this is a scalar. That's interesting. Yes. Okay, of course, this is a scalar. So it's empty. It's got an empty rank. An empty shape. Sorry. So this is a, okay. So I think that's interesting. Right. And close. How do I type in close? Right. Right. Right. Okay. So that's what it does. Is it creates a scalar or an atom containing a list. And you've got to do that because a raise kind of like conceptually only contain atoms. So when you strand it like this, it's actually creating, I guess it's enclosing this list, which I think is the same as concatenating. It is. See? Okay. So if I concatenate the scalar one with the atom and close two, three, that's what this is. Does it make sense? It's like a void pointer or, you know, it's turning it into a single object that you can store and move around. Has anybody used this? It seems to come up quite a bit. Sirata, did you use it in any of your solutions or anybody else used it? Yeah. Especially for grouping partition things. Yeah. Tell us more. I think that is your example. Sorry. I think quite expandable already. It's just a simple idea, but once you put the element, it's one chunk and then you can operate individually. I just got somebody at the door just a moment. Sorry about that. I guess we see it in the docs quite a bit. So, all right, let's see if we've got time to do dietic. Sorry. I just want to say, like, using it on a single, what is it, a single scalar. Isn't it, does not enclose anything. So that might be a case to look at. Yeah, great. Okay. Yeah. So that does nothing. Yeah. Okay. Why is a scalar? It's a scalar. Otherwise, it has a depth. The magnitude is one greater than the magnitude of the depth of why and you can add axes. And I guess we're not meant to be worrying too much about axes because Adam says they're a bit old fashioned. And we're definitely not old fashioned. So that's fine. So dietic. Oh God, I don't know what's our quad ML equal to just focus on the default. Shall we one. Okay. Partitioning close. We have better examples for this. The petitioning close. For dietic. Yes. Great. Just click on enclose. I think you're okay. Okay. Where's the good examples. Is the first one. Do you consider that there? Well, it's got a plus before it, which is, oh, or is that what it is? Is it a operator? Oh, there's an optional K. Oh, that's the access. I'm confused about this there. They're doing plus. No, this is, this is, this is a monadic. Because when you have two functions in a row, it applies this monetically and then dietically to the result with the left hand side. And this is a good example for monadic because it's not intuitive. I don't think it's going to do that. Oh, maybe. Okay, so. All right, so that's going to turn the right into a scalar. And so then it's going to be 123 plus four posts. One. Yeah, okay. So if you did 123 plus one, it would add one to each of these things. So if you do 123 plus an enclosed array, it adds this to each of these three things, which is actually very, yes, that's very instructive and helpful. Oh, we could have used this with a tally operator. So for that DNA competition question. 456 would be a CGT and left hand side would have been the DNA sequence. Sounds interesting. Great. Okay. Well, we're kind of out of time. So we'll do the dietic version next time. Thanks everybody. Bye. Bye. Thanks everybody.


get it going camera a little bit and we're good let me make sure everything's good on bookmaps youtube we'll go pretty much today though to be honest we do have a quite quite a bit happening today we have some some big big things coming up today let me make sure I get this link out as well for Twitter if they want the stream a little bit earlier but I don't know why things just canceled out on me so I had to cut the stream short but we're back so we'll go over a few things heavily looking here at book map what's going on here price action not a lot of trade setups in my opinion for the day because I'm watching actually right now it's actually mentioned inside of discord is so Microsoft you have a bit of a head and shoulders kind of happening here setting up at least three hours that back come back to that in a second giving you a visual in the chart what I'm looking at here clear one two three little head and shoulders potentially playing out what you'd be looking for though is a break of the bottom like really the 276 range that's we want to see us get below right this is give a lead to 76 pretty positive we come back over to Microsoft we'll see 276 we had we they show up every time you come down there which is interesting so you there's actively a buyer watching this that means so you can see that it was here this morning when you broke through it you got back down so we started pushing back down to it buyer showed up you broke through it came back up broke back up it was basically non-existent for a while buyer showed back up here to try to hold you there when you came down a few minutes ago bounced again and obviously as you can see kind of head and shoulders forming out here interesting to see that the seller is setting that wall that level on 277 you don't have too much fight going through right now and I just don't see you breaking through that test into FOMC I mean maybe totally possible but I will be watching that pretty closely I also want to bring up IWM I've never actually looked at IWM on a trend spider around book map so this is gonna be interesting to see as well I'm just really curious you guys know I've been watching it all too you know I believe IWM is probably one of the most beat up one of the most beat up of the indexes the Russell yeah see this is why I don't look at the IWM or spy or anything it's just literal walls I mean this will give you a headache just watching this yeah not ideal so yeah I think go to I don't know what the Russell it should be RTYM 3 I think it is that was a good guess okay cool those features up so I'm heavily interested in the Russell obviously because I've been training them as a recently it's more than my few only trades right now so we're at Russell still kind of pushing down here a lot of weakness here so it's what we want to see definitely been just stair stepping down let me pull up discord as well so if I have any questions you have questions I prefer you to ask in YouTube it's easier for me to see but yeah let me go back over here literally looking at like four different chats all at once it's a little bit tough but again today obviously FOMC is the most interesting thing happening right now but yeah Russell breaking down new I think this is a new lows on the day almost yep new lows on day for Russell so IWM making some new lows ideal going back into that chart so you can see as well give you a better visual I like going back and forth so you can really see like kind of what we're watching on the chart and then showing the the connection in between the chart and on book maps you understand so you can see new lows establishing there I would like to see though I'd like to see a wall get established now at this level almost like a resistance at the previous swing lows on the day ES obviously shown weakness as well so let's see if you get back below here the big level here on ES as well was 4029 really big level from yesterday you can actually see about right here 4028.5 was kind of like a little wall that was established there by buyers I'm trying to hold you up there you bounce back down so what I'd be looking for now is a push back up see if sellers set a wall there at 4029 and push you down through if that happens that'd be the most ideal scenario there definitely I'd be watching for for more potential downside into the FMC about 55 minutes until then I had to close my book map so it got rid of all the iceberg order so I didn't get to see where all those were. NQ, NQ still tank though I mean NQ is just sitting at highs I mean in comparison to everything else NQ is a monster literal I mean like 70 points of downside that's it you kidding me like nothing so you got to love that RTY continuing here so it's ideal Microsoft we want to see selling remember we want to get that rejection off of 277 push us below 276 I think you could easily hit 275 from there if you break 276 I think 275 would come really really quick we break 276 but then you kind of be looking towards like 274-ish yeah if you don't ask questions on book map or anything they want me to go over stock wise specifically don't mind doing it but yeah yeah you can see right there as well got too much of a zoom but you can see we pushed up you could even make it back to 4029 you're pushing back down a little bit now I would definitely be looking for to make a cheddar flow as well I would definitely be looking for and this is kind of like the scheme of how I look at things just so you guys know I usually find a setup that I like so let's say I WM I didn't want to swing so I don't need to be an example okay cool yeah is there a way I can just mute I'm actually just gonna mute discord if I even discord message or question just just comment I'm I'm how I can't I can't meet you guys that's unfortunate but basically the the way that I view things so you guys know is I find a chart that I'm liking so in this case Microsoft something that's interesting me so I'll be watching Microsoft heavily obviously I have a good view on futures and where they're at when I'm watching here and then from that point I usually go into book map get this thing or the stock that I'm watching ETF whatever it may be equity right and I'm watching what's happening here and I think ES is the big one that's gonna be impacting Microsoft specifically right now so if you get that rejection off of 4029 and push back down I think Microsoft will flush through to 76 kind of the plan there some awesome big you don't want to spend too much of your time in my opinion on the equity I think the equities like they're important to follow to make sure you have your levels drawn out right but the big thing you want to watch is in my opinion the indexes during to get most your answers to see that confirmation because now we're now we're seeing that buyer set up right here you can actually see I'm setting that position so we start breaking below 4021 you're actually that breakdown occur and you can actually get a better answer when you come back to look at those futures to like get a little bit of a look of okay well where is this 4021 level or this little bit of a range and it's kind of like your previous swing load that we had here this morning at 3 a.m. I route kind of when London opened up their market so a little bit of eye-opening to show you where that level is and why it's there and so it makes a little bit more sense when you go back into this chart also and that's the biggest thing for me too is like understanding why levels are where they are so it just makes things easier to spot out in different trade ideas so that's what we want to see we can see a kind of around 4022 4021 like right below it so that's what we want to see there one sec had a request a blue monster okay so that's what we're looking for there I'll just keep going back to Microsoft I just want to make sure we haven't broken above 277 so you want to see a little bit of downside slow slow slow but not to say downside probably kick in until you break this lower level down here that's what we want to see shark how how do you understand if a level will hold or not so if it's gonna hold or not well obviously so this is a good question great question great great this is this is the ES chart in real time this is this is the US chart it's basically just showing level 2 data right this is also the US chart in real time so shark's question was how do you know if a level will hold or not so it's a phenomenal question and that's kind of the importance of level 2 data and book that so if you're looking at like level 2 data what I'd be looking for is right here that 40 22.5 level right here as you can see that swing low that we had right there okay so that's where I would know that this is like a level that I'd be watching right because it's just like our previous swing low that we just had okay now just like hypothetically your swing high would be right there that's what you'd be watching you can actually see you broke above try to hold and you push back down now the question of is how do you know it's gonna hold how do you know it's gonna fall through you know how do you trust these levels right so that's when you come back into book map in my opinion and that's how you get your answer because you can see actively how many orders are there right how many lots are there and you maybe you don't know the math on how much one think I look a lot is like it's not a lot I don't get the wrong number wrong one lot try to make sure J has this number on on tap I believe it was around 25,000 it could be wrong it could be totally wrong I'm gonna make sure anyways it's a lot it's a lot it's not just one contract or anything like that so you need to understand that as well so what you're basically looking for as you can see that money is just sitting there waiting to buy this up right that's that's what it is it's a buywall it's all this and so when you're looking at it from that viewpoint that's how you know if it's gonna hold or not if it breaks through then obviously you lose confidence and you lose your strength of holding that key level but is there ever a way for me to look at the market and say this has to hold this is gonna hold no there I don't believe there's anything or anyone that can tell you that this level has to hold and it will hold no matter what happens it's all about you know reacting to those levels and that's the big point that's what I'm doing right I'm waiting to see if you're going to get that break through this level and start pushing down which ultimately in my opinion would push Microsoft down as well right so that's what we're looking at here but just like this level right here right we're just using it to line it up so what does this mean so what are we looking at what's the premise of this trade right the premise of this trade or looking at the potential of this trade right is that you got a head and shoulders going on here in the five-minute 15 minute whatever you want to talk about but basically just here on the day so far and it's lining up with that previous you know the shoulder they have on that end right so that's where it's lining up and so you can see that that's exactly where it is buyers or sellers are showing up at that same level as well if there's so many buyers then why wouldn't it hold aggressive market orders if someone's selling it doesn't I mean again I can't I can't tell you why someone sells or buys a position I can't tell you that at all times there's orders as you can see here there was I mean giving you an example right I can't tell you why the market does the things that it does but I can just tell you how you're reacting to it unless we have a fundamental you know breakdown of something that's happening out there right so like if you're looking right here you can see you had a little bit of buyers or sellers on top and buyers on the bottom but obviously you continue to push down right you pushed through those lots right there so that's what's worth mentioning but this is a bigger level down here it's more impactful because you can see the number of lots are there as well you can see on the right hand side also you can zoom in a little bit more if you need to and get a better look you can see there's actually about 344 there's gonna be more it's not gonna push that little one right there there's over a thousand lots of sitting like right about here so you can see around that 422 to 420 level on ES but again the big thing I want to see is I want to see if sellers are gonna put a wall right here 4026 to 4029 a 4029 there's nothing so that's important to realize as well no problem I appreciate the questions appreciate the questions dance the hardest part about doing some of these sometimes is on book map Nala people ask too many questions that's the that's the biggest thing is making sure people get questions so I can answer them RTY finding a little bit of support down here not much though and Q and Q's literally just like I look at the Nass like I'm like Jesus like sees a freight train right now Microsoft trying to push back up to that level nothing really happening here and again there's not gonna be I don't expect too much liquidity or too much longing to flow into the market right now it just wouldn't make sense in my opinion just because we have FOMC literally in 40 what is that 40 minutes 45 minutes so that's the most important thing to understand right now is yeah most time the most time we're gonna see the most volume and get the best one best action I would say mark it open around 830 until like 1030 is like the best time and then probably last two hours of trading but we'll see what we get here this is yeah gonna be less than exciting to say the least but yeah you're not getting any icebergs or anything I actually want to go back and look at the chain as well I want to see what's coming in here on the contracts also so we're gonna really click to premium bring up the biggest orders you're seeing some buyers coming on SPX we saw a lot of those the sell site coming yesterday we didn't know real big sellers on SPX today so we're going heavy into the September's more interested in some of these ETFs though so spy so downside plays are the biggest orders cues downside plays biggest orders but we're not super interested in this one because it's for January not nearly as interested IWM first call we've seen in a while but still a lot of downside orders there also VIX VIX is getting hammered that's where I right now not too exciting go back over want to see what's gonna happen here so you're saying a little bit of a push I wonder I mean again you want to see the at least a wall show up when you have a key level that's like the best way to verify some of your levels in my opinion is to be able to go back and make sure that you're obviously seeing buyers or sellers showing up there that's one of the biggest tools that comes with book map in my opinion is to basically verify levels that you're watching just like we verify 40 22 you want to be able to verify that 40 29 so we'll see in here in a second if you're in discord you have questions you can type them as well in the chat that we have here but basically just waiting on for right now and really the only focus we're gonna do today is gonna be future so that's all I care about nothing else has my interest video back at 269 not bad Amazon cruising at 100 not bad either yes you took that level right there you haven't really been invalidated yet unless you start really breaking like a high over like 277 3 that'd be the big thing you're looking for here but that if you if you just continue to stagnate here at around these levels here on ES then chances are Microsoft just keeps bumping up Microsoft has been inherently strong today I will say that it has been inherently strong today compared to yesterday it was very weak yesterday sorry to see a little bit of a comeback in there I mean but like when you see something like this to where you're moving up and there's not heavy resistance and you just can't get the continuation it's usually a problem as well as looking at overall volume on the day you can see today so you can see you kind of like the volume has come in here you feel a lot of buying volume to be honest I mean I think overall volume has been buying pressure over the past few days and yeah probably the past week or so been primarily buying but when we look at the overall volume here on spy it's in my opinion less than impressive you can see the volume 27 million so far it's noon so we basically have three hours left in the day what I will say those are gonna get a pretty large spike of volume after FOMC you will but I I mean I don't think I mean you might be able to get over 100 mil volume maybe I think your 30 average now is 100 mil I just don't think I'm gonna get it though you're pretty lackluster to be honest right now so the volume has been decreasing to the upside which is also something that's very influential to me what's your Twitter and Discord so we can follow you name do the Twitter I can show the Twitter name they should have it all down below for me but I guess they didn't do they help me check yeah all the links are down oh no those are discord that's for them okay yeah let me post I thought they posted my stuff on there they did not I'll post my Twitter it's all I need to post I posted my Twitter inside of that so you have it I'm I don't know if it's gonna pop up or not but anyways I posted the Twitter link in there so you have it discord link should be an option I don't think there's any available spots you can get in the newsletter though the newsletter is 100% free we're not selling you anything I recommend the newsletter for most people Doug fan thank you so yeah here we are 420 4028 should be interesting so I'm trying to pull this back up so let's me a question yeah I get more lovely thank you this is just surprising very surprising that you're seeing buying pressure and to FOMC after the run that we have already had extremely extremely surprising only sell what we have is up here at 4037 that is also shocking that of all the levels that's what we're looking at go to the chart real quick so we can see why 40 I mean it's near VWOP I guess that makes sense but still it's a big move it's a big bounce I'd be a monster bounce in my opinion for ES I just don't think you make it back up there it's possible I don't like it fan 4035 ish I mean it's around the VWOP though so we'll see the other jacked off at VWOP it'd be pretty interesting but again you only have 40 minutes until this bad meeting if you don't have any stocks when we look at let me know I'll go over them but see you can still even see even with the push up here is having on ES Microsoft is still struggling at this level but again like I said you continue to just grind either sideways or to the upside I think Microsoft will invalidate and start to push back up easy I'm muting I'm muting yeah I don't I don't know why they don't have everyone muted on discord it's kind of all yeah it's bizarre you're trying to push a little bit more can you get Tesla yeah I don't mind Tesla's had a path once you're once Tesla broke over 187 it was pretty ideal to say the least it's got to load up first I can give it a sec so I talked vaguely about Tesla earlier in discord and talked about it on the live stream on my channel for a little bit before I had to hop off if you know why it's not loading back three hours to look back once they let it load but on Tesla the big thing I was watching is like a push above 197 and holding and trying to get back to 200 because you have your 200 SMA on the weekly or no on the daily I'm sorry at 217 I believe I'm like pretty positive it's like 217 ish anyways so I was looking to get back above 198 and then to see some side of pressure to the upside towards towards to 217 and for hopefully a short position but you just never really got that that was the the kind of jarring move is out like Tesla kind of displayed weakness today which is really interesting so for instance like you know pre-market you're up at near 200 you open up or like almost 200 and then you push down and you kind of can't get any support but like in comparison like when we look at NQ you know from market open right market opens here and you just kept pushing up you made new local highs really great movement good momentum so I would say Tesla right now is showing some weakness in comparison to the rest of the market I mean like looking at Microsoft right beginning the market you shoot up like man go on a list like Nvidia market opens shoot up so Tesla definitely weaker than most stocks out there right now and right now I'd even halfway consider this a bear flag you're kind of bear flagging under 197 not the best behavior I could see Tesla getting hammered if the FOMC stuff doesn't go well but I think the press conference is the most important part of FOMC and I don't think it it is sorry 100% it's the most important part of the the meeting to come today but yeah Tesla Tesla's definitely been really interesting and I think when you see some of this behavior like this to where you're not seeing you're seeing a disconnect from the market it's really similar to what we saw two Mondays back right so if I give you a visual here on Tesla just to show you I can't go that far back on book map you can see I think it was right here yeah pull up opens you have it so right here is last Monday or two Mondays back sorry right here okay so you open up and you're just pushing down like all day long okay in comparison like look at what happened to cues on that day March 6 remember the date so March 6 cues you open up and you push up from 301 304 I mean it's a nice push that's a whole percent of upside right on cues and you push back down now it makes sense to like obviously Tesla fell when cues are dropping but the concern was what happened you know while it was going up and so that's what I think you're saying you're seeing some inherent weakness along with them like against the market in my opinion so Tesla's a weak name out there so if you were looking for downside opportunity I think Tesla is a name that probably shows you some decent risk to reward for the downside see a little bit of selling here in icebergs to the downside nothing huge though that's too big nothing on Nasdaq so a little bit of buying here an RTY down here pretty small than big you're above 4029 you're battling out 4029 nothing crazy but again you're not even seeing a wall here so it's like you should be pushing up honestly the fact that you have no wall you're just slowly grinding against nothing I'm just like you're moving with minimal volume which again brings me back to my point of just you're not inherently strong in my opinion yet until like obviously volume is just gradually moving up here at 27 28 mil now pretty decent volume last few minutes but nothing great nothing terrible so yeah that's right yeah so you're trying to push up now but just strange behavior they just really strange going into this that you're seeing these small small small walls come in yeah definitely just like no trades on time is it 30 minutes till then you'll have any questions we'll go over them if not again we're just I'm just watching yes there's nothing really to do here there's no they're not gonna get great trade set up you're not gonna be a great movement it's just not gonna happen to the Fed meeting no possible way 10 video 270 just do nothing spy so spy you're not gonna get too much like again yes spy it's the same thing but spy looking at a book map you're not gonna get too much information you should in my opinion I think you got to use ES to get the information that you want on spy because you'll see here in a second you see how it moves there's no real like just compare and contrast like this is spy this is ES I would stick to ES nine out of ten times it's gonna be better to get your information and honestly you should track futures over the ETFs like yeah you can go into spy you can find your key levels and stuff of you know maybe we'll hit but ultimately you're gonna respect the key levels more an ES than you will on spy and so it's important to watch the futures just because contracts roll over and maybe targets move a little bit here and there so it's the biggest thing I can say about that is there reason why I often get extreme opposite reactions to things like foam see for earnings for the first few minutes and then it moves the other way afterwards again I can't really give an answer on you know why the market does the things it does as far as getting fakeouts along those lines I think a lot of people like try to give answers to things that they don't really have the answer to but in my opinion the it's not really something that you it's not something that you need that I need personally it's not something I need to know I don't need to know why we get fakeouts the upside or the downside all that really matters to me is that I understand what the Fed says understand how to interpret it and how to trade based on the information I think we've done a really good job over the past few Fed meetings on my channel we're interpreting that news and then trading based on it so that's the main thing for me you everyone knows also to I'm not a huge trader going into Fed meetings I don't like the the risk out there for it that's not something that I just crave to do just open myself up to immense risk so yeah it's just I think it's something that's pointless to stress about from for myself because I might usually gonna trade it I have a few IWM puts but that's about it nothing crazy I really exposed yeah so if you start pushing man you start pushing back up you look good you really do yes is coming into its view up so it's going pretty surprising but it's a good push see yes a minute yep view ups right there 4035 give or take pretty weak candle right there on the five yeah it's right right around here where that cell wall is you already because you can only see some of that cell walls right there to not too big but yeah look at Apple yeah I don't mind again this is it's time for you guys you guys have things only to cover you got to ask let Apple load for a sec Apple's been a beast ever since it broke out I'm giving you a visual where it broke out at here real quick so I always recommend zooming out before you even start trying anything so you understand kind of everything that's going on Apple here on the four hour yeah you can see right there so really nice actually pull that 200 back up so you can see so you've lost 200 but you held it held held held see bounce back above but look at that reaction that you had so you can actually see right there kind of top right here right you can also see the big lower here sorry I'm trying to pull it up can be rejected and pushed up mount pushing back up I mean Apple's a beast probably one of the strongest names in the market again everyone knows what I'm looking at things I'm looking at strong names weak names I'm that trade based on that so if I this we're getting strength in the market then obviously I'm trying to to trade a stronger stock as far as Apple Nvidia Amazon so the those are all names that are moving strong if I'm looking to go to the downside here if I was looking to play the downside I'd be looking for an inherently weak stock so I'd be looking at something like Tesla Microsoft's been kind of back and forth maybe banks to the downside but yeah that's where I my focus to be the downside so I want to give myself the best opportunity based on that and you can get the best visual here you can see like just pretty decent size level there on Apple push right through right push right through Apple usually though will follow ES to the tech I mean ES and Apple are almost one in the same so I would never get too disconnected there start to watch one more than the other ES is very influential to Apple and probably a high possibility of why we're running the way we're running on ES is because Apple did have that breakout of that level as well something that we definitely been watching for a while here on the channel you're getting upside you're still gonna just slow and steady the gross no interest I want to see a flow that's a big one that just came in Jesus Christ 519 dear God that is a big boy yes less than ideal a little bit of rejection there we'll see remember we have be well right there at 4035 big level big big big level MD see AMD dear God AMD look at that run since 10 that nice little bottom there and bounce dear God and you went through monster levels big low I mean obviously hundreds gonna be huge AMD over 100 you just have so much room after that that's like the big level I'll be watching yeah I mean honestly things go well today sit my conductors Jesus high chance they can push back up to Nvidia AV Geo is already at I think all-time highs like we're back really close to it and video they have like $80 or something till you get back up there AMD has a lot of room to go it's like $50 to go so interesting things to be looking at right now yes you're bouncing see they're setting up a little bitty walls that you can see them are slowly coming in let me bring that color grade down just a little bit so you can see them more sometimes it makes my camera seem like it's dim or the computer you can see you're trying go back to Apple may be able to see like I mean we look at Apple and just giving you a better look like Apple bouncing you're like 1146 going into EES bounce a little bit earlier here on Apple but yes I mean like we look at this like chart he was looking at Apple shockingly excuse me shockingly similar so yeah pretty similar charts across the board but and Q is just the one I guess why tech is just this is the name to trade right now anything to do with tech easy money we killed on those and be sure it's a couple weeks ago can't believe we're about to be 100 on that I know it's pretty crazy like AMD was fantastic short opportunity but again like that's just like the beauty of some of the stuff that happens with like you know some of the tools we use right like book map and then you know going back into 200 SMA like going back to it like yeah AMD strong but again like so I say zoom out first they get a better view like the whole reason why I went short on AMD like the entire reason was just because like the daily candle that was forming this was the one right here like that was the candle so when we pop back up to like 85 I went short and we obviously wrote it down to the 200 SMA but yeah decent candle on that 200 SMA as well so thank God we got out of that sometimes it can be boring like this is like yeah it's but I think especially with the way that I trade it can get a little bit dry like right now it's really dry I'm not gonna open my soul up to crazy risk and trade stupid trades low quality trades right I should say but yeah it was nice appreciate though I appreciate Nick or HM sorry Nick got about 20 more minutes on the live stream if you have any last questions guys go ahead and start asking I'll be out of here almost right at 1 o'clock though I will not be staying longer today I'll be I'll have a live going over FOMC everything happening on that so I got to get right to that right at 1 o'clock guys have any questions go ahead and ask but again I'm not staying any longer than 1 o'clock today just no yes a little bit of rejection Tesla nothing great I need to get a new boom arm really bad baby I come into a big level 271 how can I get the nice Amazon another big level 100.5 everything's just coming into these big levels right before a little bit of a bull flag happening here on ES as well Microsoft looking a little bit of toppy here we'll see though we didn't have an economic event I still think Microsoft would still be a really good setup and I still would say though honestly like hypothetically you drop on Microsoft and break 276 after the live stream or whatever I would say it had nothing to do with technicals and all to do with fundamentals at that point that's the only thing so we'll see I really was interested to see if we're gonna get any icebergs any big orders coming in but there's really none these are these are tiny they're really small orders I'm sure on on the initial move we get we'll see some icebergs come in I couldn't imagine that we don't but until then this is tough this is a tough day guys I'm sorry this is is a boring one I kind of anticipated it would be like this today kind of limited on what you can talk about today cuz technicals are out of the window with a really high decision like today's again if you have last questions go ahead and ask we have 17 minutes guys so again I know that everyone likes a light way to the last minute as questions we will not be doing it today I just sat on the hands of the CVH my way till tomorrow be able to see how we digest so in my opinion I I don't think you have to wait till pre-market so I really don't I will be I will be a thousand million percent just listening to what pal says I I'm pretty positive I'll have a position established by the end of the day or I'll be holding my position I have right now I have a smaller position on IWM again I think I do I'm just like the risk the risk the last the least risky ETF there is right my my opinion right so if you give up I've been going over this like all day to like spot like look at look at cues here on them like the daily charts going trade up spy straight up IWM will really lackluster in comparison so yeah I think IWM is getting a lot of the the bad end of it here a lot of the downside play is IWM but yeah a lot of Tesla Claus coming in there you're not gonna see as many equity positions being established though the equity positions will be established after today or end of the day sorry Vic I think Vicks is a really interesting because I think Vicks will spike like no matter what like so that's also a cue still there wait wouldn't that keep position good but I must have missed it earlier afternoon not pre-market again I think that the rhetoric will be all you need to hear is like listen to pal what he says about inflation everything and if it's anything bad I think you just you you roll over into the next few days at least until PC at minimum but yeah and then to the good the good note like I mean I'll probably be a little bit more hesitant to go as heavy to the upside 100% from pal yeah I'll definitely be a lot more hesitant to go trade the upside I could we just have to got so much and again I think if you break like in queue if you can get above I think it's like 13-7 I think you are officially out of this downtrend and you probably be starting a new uptrend so that's kind of what I'm watching for there yeah so that's that I think today's really big because it kind of will tell you the tone of what's kind of be happening over the next few days that is where we are literally just everything I think since I've been live we've moved on ES we've been in a 10-point range for an hour it's nice it's always great to see but yeah so nothing really happening here I like to trade BITO on these announcements is that the Bitcoin that's the Bitcoin thing Bitcoin ETF or something tracks Bitcoin definitely looks decent for it looks okay a little top heavy you're at a massive key level on Bitcoin too so you know massive level it says swing lows you had back from 2021 yeah 2021 swing lows huge level I'll be watching that you get above like 28 5 20 29,000 you look really good look really good over that but yeah now I think you have limited upside tools you break that yeah or just not doing anything sorry guys I'm like trying I'm trying to find something that's interesting yeah someone asked in discord Tyler I miss you you said you said after this dream you're going elsewhere stream where is that on my YouTube channel pull it up for you my YouTube channel option drops I go live every single day at 10 30 a.m. central today's live a cut short really unfortunate did but it got cut short Internet went on or something yeah make videos every day it's all in there name is option drops type it in there yeah I'll have the whole pal speech linked on there so everyone can listen I need to find the link real quick too I think it's on the website I'll have it on I will have it live so don't worry I didn't realize it was your was in your page house book map oh yeah this is a book map every Wednesday I do a stream here usually for book map today's is like a really boy it's just like that's hard like when you're I mean you literally have moved 13 points on yes like there's no nothing happening like in cues move like 25 points it's just you can't do nothing about it do you use the vixen trading sometime I mentioned every day's in every video every day I mainly watch levels on vix to be aware of where we usually get action so I do I do use vix yes but I don't like it doesn't dictate my trades that makes sense okay nine minutes left guys get your last few questions in for the hop out of here that'll be it though those last few ones guys are quiet today you guys are locked in either that or you're sitting on your hands which is I'm proud of you guys for not trading this nonsense today yesterday was a really solid trading day fantastic yesterday couldn't have got better not gonna lie it's fantastic what a day today not so much I can't even believe you're seeing a little bit of selling on some of these things I mean Nasek just continues to go up yes continues to go up into the VWAP into this this is wild this nonsense but it is get restream going to and I usually use if you guys aren't familiar with the YouTube channel I usually go over every day like something about like what I'm looking at with book map with futures path of these resistance most resistance where we're at just so you guys know but yeah I need to start screenshotting the days when we have the best movement so I can just go over that as well in these lives it'll help out so much so much more so you guys have better understanding and live examples it's just the hardest thing to remember to do to take those pictures for it I know it's doing the I know we looked at a video but what are you thinking about M.U. I'm not so it means a good company like I'm not like against them by any means like it means fine like not not they're not bad at all but like you're getting a little bit of value because you're obviously buying it damn near the lowest right you're very low but I just don't even have the reach as far as some of the bigger companies that's the only thing I mean you're still buying it at a huge discount comparison like AMD though I really like whatever I have AMD or have M.U. I don't have AMD though AMD I think AMD could easily push back up that's my opinion though so if I was to see I'm pure stock it seemed to trend more with Apple and semis from what I've gathered what M.U. or AMD I don't really talking about what's it what's the first you do when you look at the when you open a chart I zoom out like the four or one day to make sure I understand where rat is there any big levels or anything I'm watching like you can see so you have your fed six minutes till then they're taking everyone's taking orders off the book now they're expecting that volatility to kick in here in a sec Jesus should be interesting M.U. I mean well I'm just not not being mean but like I'm just saying like M.U. like I always like have to say that because people always get mad when I say stuff if M.U. really was falling Apple I'm just saying you'd be a lot higher and I mean that's all I'm saying you will see though about five minutes guys and be hopping out here your camera colors are off or I'm tripping my camera colors I don't know what that means maybe they're off I don't know I don't know what that means I'm looking at my camera looks good at me they went off like five minutes I don't know I'm in black and white that's weird oh he should have told me yeah I don't know why I went like that I don't know that's weird sorry should have told me I don't know why I did that weird really weird but last few questions for hop out of here again you're gonna get you're gonna get bulk of all your movement here in the next few minutes after the Fed Ray decision yeah so that's all I got to say about that there's a there's you can't I can't I can't say I do too much you're predicting the answer to happen here so last questions probably like no it's trying to connect to something else but yeah yes getting a little bit of a push up again you're pushing up because they took orders off the bed on both sides so it's important to understand and Q pushing up again as well I think bangs are gonna be something big to watch today as well go to everyone in three minutes we'll be hopping on here in a few seconds so getting last questions go ahead and ask that is it will be on my YouTube channel going over everything okay all right guys that's it I'll be hopping out of here have a good one


For you to be able to close a $1,000 deal, a $10,000 deal, or a million dollar deal, the biggest skill you could have, number one skill that you can have is can you read a room? Now, a lot of people think the secret to reading a room is something simple like body language. Have you ever heard this conversation on body language like, oh, if somebody leans forward they're more interested in you, or if somebody speaks slower, if somebody has open hands, if somebody, there's people who say, you know, if they're mirroring you, that means they're, those things I will tell you are probably about 20% of reading the room. If you actually want to know how to read a room to close a million dollar deals, more importantly, you have to attempt to close a lot of deals because you'll start noticing patterns in human behavior.


starting our first lecture on Geometrical Optics. So, what is the first thing that comes to your mind when we talk of well Geometrical Optics? I suppose the first thing that comes to your mind is you know the passage of light through lenses, how curved lenses that is a convex lens or a concave lens or maybe reflection from curved mirrors. So, but one has to realize that this is rather pretty old subject, this is rather a pretty old subject in physics. We have been doing things for hundreds of years. In fact, it is the use of these lenses and mirrors which had a huge role in the development of astronomy. For example, Galileo was the one who used just two lenses, he just used two lenses and then put it in a cylindrical tube and he watched the boons of Jupiter and he made the certain astronomical observations. So, in a sense well this subject is it is one of the primary things which was responsible for advancements in astronomy and not only in astronomy, I mean not only in physics for that matter, I mean if you think of the simple magnifying glass to look at small things. I mean I by bet the modern biology owes its origin to the observation of small things. So, the study of geometrical optics had rather far reaching consequences not only in the development of optics, but also in other branches of physics and also in other branches of science. So, now that we know that it is an important thing to study, although it is an old subject, what is the area of applicability? So, rather at what wavelength range range should we apply geometrical optics? Now, why do I say that?  So, what is the area of applicability here? For that, let us draw a simple diagram and define our area of applicability.  Now, we put a screen a little distance away from this hole or from this slit. Now, what do we expect to observe? Well, I mean we have a reasonably big hole here. So, we can draw these two lines, we will come to this point that we are drawing lines here and then we observe the image of this slit or this hole on the screen. Now, which is kept at a certain distance away from this slit. Now, if you observe you have sharp boundaries for this image and you just observe only one image of this hole, then I am sure you are going to say that we are in this regime of geometric optics. Now, why? I mean look at the other look at the other extreme.   You are going to have alternate regions of light and dark regions. Now, that is diffraction. So, you have alternate regions of light and dark regions here. But the field of geometrical optics would not be too concerned with this diffraction, but would be talking of things in which when you have a slit, the image of the slit is very well defined on the screen. Now, when does that happen? That happens if the size of the slit that you have taken, let us say the size of the slit is D. Now, that is much greater than the wavelength of light that you have used. So, this is one important criterion for the application of geometric optics. And well, if it is actually if it is not, if the slit dimension is some way it is very near or comparable to the dimensions of the wavelength, you will as I said you will have to deal with things like diffraction. So, this is one thing about the sizes. The second thing is a bit involved, but then it is another conceptual thing. It is that the light or the energy of the photon in this case should be lesser than the energy sensitivity of the instruments that you are using. So, it should not interact with the instruments. So, basically you are not in the quantum region, quantum regime here. So, we are still in this classical regime and we will be using what we call as these lines or these rays of light. Let me draw it once again. So, these are the rays of light by which you are going to get some sharp images on the screen. Now, what are these rays of light? These rays of lights are nothing but infinitesimally thin. So, these will be using the rays of light. So, they are the infinitesimally thin beams of light. Now, for that reason geometrical optics is also called ray optics. So, that is what we are going to study. We are going to study ray optics or geometrical optics here. Now, let us do one more thing. Now that we know that we are going to deal with rays. So, the next question to ask is what path do these rays take? So, the question that we ask ourselves is what path does the ray of light take? Now, this was something which bothered many people and quite early. And apparently people had lots of ideas where they said that it will follow the least distance between two parts. Well, if it is the same medium, that is fine. I mean the least distance is fine. But that may not be the case in which you have in the media of different refractive indices in between. Now, I will come to that again. Now, apparently there is a principle which tells you what path the ray of light will take. Well, it is called Fermat's principle or in its original form it is also called the principle of least time. So, we will be talking of the Fermat's principle or the principle of least time. Well, it simply states that well the ray of light will follow that path from one point to another in which I have point A and point B. Well, you can take whatever refractive index in between. Well, it will follow from point A to point B the path in which the time taken will be the least, will be the minimum one. So, that was Fermat's principle in its original form. So, that is what Fermat said that light is going to travel from A and B and the path it is going to take and it is going to take is that for which the time is going to be minimum. So, instead of this path or the other path the one from A to B will be the one. The one the light will take and the ray of light will take the other will be the one in which the time taken is the least. Now, apparently the whole of geometrical optics can be derived in principle from this one simple concept. So, that is how important it is. Well, in its this is the statement in its original form it is the principle of least time, but I will come a little later on some modifications, but let me just tell you 2 or 3 consequences of Fermat's principle. So, let us just do one or 2 consequences of Fermat's principle consequences of Fermat's principle. Well, the first is that if from point A to point B let us say light is traveling and it has taken the path of least time. So, point A to point B suppose this is the path and this is the path of least time from point A to point B. Well, if I start from point B to point A the light will actually take the same path back. So, if it was a least time on one way that will be on the other way also it will be the least time compared to other paths. Now, this is called the principle of reciprocity. So, it retraces its path back. So, this is the principle of reciprocity. Second thing is about well I mean what comes to my mind is I mean I started this talk on you but to talk by talking of some lenses. So, let us draw a lens let us draw a simple convex lens and on the axis. So, light let us say I have some point on the axis on the left hand side here. So, this is my convex lens and then let us say light from this point truly comes and then it comes here and then I have well comes on the other side. So, this is the object distance and this is the let us say the image distance which I denote by V. Now, there are well there are infinite paths of light let us just take two or three of them. There is one path which goes entirely through air. So, the one up at this point and then comes and comes back here. There is one which goes partly through air which is actually along the axis and then there is one path which goes through the lens and then comes through and then comes travels in air to reach the image point. Now, if you look at these two points the length of these two points are different the path lengths are different. The actual length from on the axis that is the least compared to the length when it goes to the tip of the lens and then comes to the image point. Now, however, by the principle of least time you can argue that the time taken by these two light rays but this one the one in which I have drawn the one goes to the tip and then comes to the image point and the one in which it passes through the which is along the axis of the lens. They both of them take the same time otherwise you are not going to have an image on the other side. So, of course, I can also derive the simple laws of reflection and refraction using Fermat's principle. But before that I wish to remind you once again about well maybe I have not said this before is about the statement of Fermat's principle. Now, we do not say that the time taken is minimum what we say is that the light will follow that path. So, from A and B so, Fermat's principle the way we say it now Fermat's principle is that light will follow that path will follow that path for which the time taken is the time taken is actually an extremum is actually an extremum compared to the nearby paths. Extremum compared to what? Compared to nearby. Now, when I say an extremum I do not actually specify whether the time is actually minimum or maximum it is an extremum. So, pictorically or diagrammatically how do I write that I mean I have point A and point B let us say point A and point B now there are actually infinite number of paths which connect point A and point B. Now, what it tells what Fermat's principle tells is that light will follow that path for which the time taken is actually an extremum compared to these paths. Compared to for example, it will be it will follow the path in which I have shown by a solid line as opposed to and that will be an extremum path compared to let us say the ones which I show by the dashed lines. So, that is how we know Fermat's principle now. Now, this is actually a far reaching consequence of the principle of least action or again it is the Hamilton's principle in mechanics. Now, let us as I said we can derive the laws of reflection and refraction from Fermat's principle. Let us see how we can do that and so that will give us some more confidence about the applicability of this theory of this principle. So, we want to check what happens during reflection draw a figure first. So, here we have a mirror a plane mirror let us say and say we have a point A and a point B. So, let us say we have a point A and a point B. Now, the thing that we want to do here is that we want a ray of light to come and hit the mirror reflection and go to B. Now, which direction should it go? Well common sense and what we have learnt in school is that well it should go in a such a way that the angle of reflection should be equal to the angle of incidence rather should be equal to the angle of reflection. Now, why is that? Because you see from going from path going from point A to B via the mirror I can actually have an infinite number of paths. Now, why should light choose the one in which the angle of incidence is equal to the angle of reflection? Let us find out using Fermat's principle. So, let us draw a normal at the point of incidence and consider that this point A is at an height h1 from the mirror point B is at an height h2 and the distance on the mirror you know the distance of the mirror is l let us say and let us also think that the distance at which the light strikes the mirror that is x. So, let me see have I drawn all the distances? Yes, I have taken the distance in the mirror the distance where it hits the light hits the mirror is incident on the mirror. So, I have not drawn the angle of incidence let me call this I and the other one here is the angle of reflection let me call this R. So, and this is the normal.  This angle is also R and this angle is I and these are all right angle triangles. So, let me I have not labelled these points height of this is P let me call the point at which the light is incident as O and let me also call this height. So, B this is Q.  Now, the thing now the question that I am trying to address here is I mean light comes and hits the mirror at a distance x here well it could have hit a little bit I mean if it hits at x what happens to the angles this is one thing or to put it in another way round I mean why should it hit only at x it can hit at the other places and come to B. Now, which is the one according to Fermat's principle should be the path of the light here. So, let us do this what is the time it takes for light to go from. So, time to travel let us say to travel the distance A O B this distance A O B let me say let me call that time t and the velocity of light in this medium. So, let me say this medium itself is air. So, velocity of light let us say the speed of light is c. So, what is the distance A O well the distance A O is nothing but h1 square plus x square pi by c that is the time it takes to travel the distance A O and the distance O B. So, that will be square root of h2 square plus l minus x square divided by c. Now, what do I do now? Now, I say that the time will be and compared to different paths compared to its neighbouring or nearby paths. So, this is going to be I am going to have this is going to be a next step. So, that is what I have. So, I have let me let me do this dT dx. So, this is equal to what is dT dx? I am going to taken 1 by c here that is the speed of light that is a constant thing I am going to differentiate the 1 in the square root. So, I will have a 2x at the top and then if I differentiate the entire thing. So, I am going to have a 2 times 2T over h1 square plus x1 square x square in the denominator. What about the 1 on the on the for the for the part O B? So, this is twice l minus x. So, I am going to differentiate this point h2 square plus l minus x whole square and the square root of that. So, that is equal to twice of h2 square plus l minus x whole square. So, I have not taken a minus sign out. So, because l minus x, okay fine I put a minus sign here and then there is a 1 by c. So, when I say it is an extremum I am going to put this equal to 0. So, which immediately tells me that x by root over h1 plus x square is equal to l1 minus x h2 square plus l minus x root of that. So, what does this tell us? So, it tells us that if I want the time to be an extremum, okay, compared to all different parts light can travel. Now, if this is the path light should travel, okay, I better have x by well I should have put an h1 square plus x square root over of that. That should be equal to l minus x h2 square plus l minus x whole square square root of that. Now, what does this mean? Let us look at this figure. Let us look at this triangle APO, okay. Now, what is x? What is x divided by h1 square by x1 square by x square, okay. So, let us look at triangle APO, okay. Let us look at the figure triangle APO. Now, in triangle APO, what is the sign of the angle i? Well, it just happens to be x by x by the distance h1 square by x square, okay. Now, compare that in triangle BOQ, what is the sign of the angle r? Okay. Now, these are what? So, sign of the angle r is l minus x divided by h2 square plus l minus x whole square, take the square root of that in the denominator. So, which tells you immediately here that light will travel that path in which I am going to have just the, you know, in this same medium, the sign of this angle i is equal to the sign of this angle r or in other words, I need this angle i to be equal to the angle r, which is actually the familiar laws of the reflection that you have, okay. So, well, to think of this as a mechanics problem is also quite interesting. Actually, if you, if you, if you give, if you, if you set a problem like this, that I want to run from point A to let us say point B by touching some wall, okay, which is PQ. Now, which path should I take so that the time taken will be released here, okay. Well, actually we will be taking that path for which, you know, the point at which you hit the wall and then you draw a normal to that, then you find an angle, okay. That should be equal and you still call that an angle of incidence, okay, should be equal to the, the angle that you make with the normal when you run away from the wall to reach point B, okay. So, this again will actually follow from the principle of least action in mechanics. But right now we are doing geometrical optics, we are dealing with light, rays of light. So, and we have just now verified again the laws of reflection using Fermat's principle, okay. Now, with this basic verification, how about doing it for the, for refraction, okay. So, you can always say that, okay, fine, I have done this for a medium in which the refractive index is the same, right. So, your reflection is in this, in this region in which, you know, in the region A, O, B, that is in a region where the refractive index is the same, okay. So, let us find out what it is going to be when you have two different media. Let us draw a figure once again. So, okay, so we have two media, okay, which is infinite on both sides, let us say. So, in one side, the refractive index is N1 and on the other side, the refractive index is N2, okay. Now, you have, you are at point A, let us say and you wish to go to point, some other point, okay. Now, what is the point, what is the deduction that you need to follow, okay. In case you want to go to point A to point B, is it, is it the straight line? I should draw the point B here, is it the straight line? Well, that is the distance, that is the least distance. But then remember that the speed of light is different in these two media, okay. So, the time taken is necessarily not the same. If you go, it is definitely not the same when you, if you follow a straight line or let us say you travel this much in one media and then the other here. Or let us say you travel this much in media, in medium one and then the one here.  So, this is region 1, let us say this is land and then N2, this is some water, okay. You want to go from point A to point B, okay. What do you do?  Or do we go, do you want to minimize your swimming because you know swimming, that is, that is a bit tougher than just running on land, okay, because of resistance. So, do you maximize your path on land, okay. Let us say you come here and then you swim a little bit in the sea or in water. Let us not bring in sea or anything else in water. So, which path should you take? Well, the problem is the same. So, let us redraw this figure once again and label it. So, let us say you need this to be the path and this is how you wish to go. Okay, you are in point A and this is the point you are incident on the interface of both the media. So, you want to go to point B here. Let us say again I call this distance, let me call this distance, well, this distance h1, this point as p, this point of contact within these two media where light comes and hits as o and then B and this to be h2 and then I call this pq. So, this point is q, okay. Now, I again take this distance. So, this distance is fixed, this distance pq, this distance pq, this is let us say let us call that as l, distance l. Let me call po. So, that is x, okay. So, that is variable. Where do I want? Where do I want to hit the surface here? Do I want to hit it here, here, here or here so that the time it takes compared to all these paths to go from point A to point B is an continuum. Well, let us do that. So, definitely what is point oq? So, this is l minus x, okay. So, what is the time it takes to travel this distance AO, okay. So, the time again to travel AOB, this distance AOB. So, this is let us say capital T. So, what is this distance by the way? So, this distance is AO in medium 1, okay, where I have the refractive index N1. Now, how is the velocity or the speed of light related with the refractive index? Well, if the speed of light in vacuum, air in vacuum, let us say is C and then I divide that in a medium where the speed of light is V, then the refractive index is N, right. So, what do I get? So, the velocity of light in a certain medium which has a refractive index N, which has a refractive index N is nothing but C by N, where C is the velocity of light or the speed of light in vacuum and then N is the one in N is the refractive index here, okay. So, the time it takes to go to do the distance AO, what is that? Well, let us find the distance. So, the distance is so this is x, okay. So, this is nothing but again H1 square by x square. Now, you need to divide this by the velocity in medium 1 or the speed in medium 1 which is C by N1 because you are in medium 1. Now, we need to add again, so this is the time it takes for light to traverse this distance AO, okay. Now, what about this distance OB? Well, that is H2 square plus L minus x whole square divided by C by N2, remember the speed of light in medium 2, I call that velocity V2 and that is again dependent on the refractive index, the C is the speed of light in free space or the speed of light in vacuum itself, right. Now, we need to take the next term of this. So, which means we simply take dt dx is equal to 0, so which tells us that well C and N and all these things are constants here. So, we need to differentiate this entire expression with respect to x. So, what is that? So, that is N1 by C, I am going to take a 2x upstairs and so and then I differentiate that that will be, so that is H1 square plus x square. So, differentiate 2x square, so I get a 2x here and then again H1 square by x square. So, this half by this entire thing to depend 1 minus half, so that is okay.  So, what is the point? Well, what is the time like we will take once it goes from point A to B and via this, from one medium to another. So, we will be calculating the time and the time it takes to travel from A to A, A OB, we have calculated that. Now, we are estimizing, we are doing dt dx is equal to 0, we are trying to find out what is the extremum of that. We have found a condition okay. Now, what is that condition once again? We have just found the condition that N1 over C, remember N1 is the refractive index in medium 1, so times x by root over H1 square plus x square and that should be equal to N2 over C root over N2 over C and then l minus x root over H2 square plus x square okay. Now, what was the thing that we were doing? We were looking at refraction okay, from medium 1 to medium 2 okay. Now, this angle was i, let us say that is the angle of incidence and then this was height H1, so this was x, so this was A, it is at B and then the angle of refraction was R okay. So, this distance was H2 and so this was P and this was Q, so an OQ, this was l minus x fine, definitely this angle, that is angle OBQ, that is also R okay. Now, you have got a relation regarding some the refractive index times something times x, x by something some distance okay. So, let us find what that angle is, so by the way, so this angle is the angle of incidence, the angle PAO okay, that angle is also i right. So, in triangle APO what do I have sin i to be, I have sin i to be x by the distance AO which is nothing but root over H1 square plus x square and in triangle BOQ what is the sin of angle R, well sin of angle R nothing but l minus x divided by root over of H2 square plus x square. Therefore, when we come back to our old equation which we have got by taking the time to be by making the time to be an extremum okay is if we substituted back into our old equation, when we were this equation here, this one, what we get is n1 sin of i is equal to the is equal to this value n2 sin of R okay, where i is the angle of incidence, that is the angle with which the light makes or the ray of light makes with the normal when it strikes the boundary of these two media and then R is the angle, that is the angle in which light emerges in medium 2 okay. Now, this you know everybody knows this as Snell's law in optics. Now, you see that we have simply obtained the Snell's law in optics using Fermat's principle and remember this mechanics problem I was telling you. So, if you wish to go from point A to point B, let us say and then the region 1 was land and region 2 was water okay. So, what is the route you need to take? I mean you better take the route A or B okay. That is also the thing you can work out using the principle of least action of the in mechanics right. So, to summarize what we have done today. So, we have talked of the beginning of geometrical optics, we have talked of the fundamental guiding principle in geometrical optics which is Fermat's principle which actually tells you how the path of array of light okay. So, we have done that for reflection from a plane mirror and we have also seen the path of light, the ray of light will take when it goes from one medium to another okay and in doing so what we have also found is that we are right because we have reproduced the familiar laws of reflection and the familiar laws of refraction here fine that is Snell's law. So, thank you very much.


Hi everybody, Jeff Hamilton from SfmSports.net here with head coach Graham Miller after the Mustangs lose a close one 2-1 Against Catholic here at Mustang Stadium in Graham. It's the cliche It's a tale of two halves that first half you give up the two first half goals Down to nothing Catholic can only conceded one goal all season coming into this fourth game of the year to nothing down What was the sense of your team talking at halftime? No, we just you know, we obviously Started a little slow, you know, and that's been part of our downfall over the last couple of years So we got to find a way that's what we're just talking about now. It's finding a way to start faster Once we you know at halftime we talked to them about you know, we're still in this game, you know We had two great chances, you know Kelsey and Brianna, you know They could have tied up the game at a half So we've got to be more ruthless in front of goal finish or chances they finished their chances We gave them, you know poorly individual defending So I think we had a good talk at halftime and then the girls were ready and you seen a very good second half performance I mean, you know great goal from Kellen and you know crossbar and maybe a couple of penalty calls and referees coming over so I wouldn't say too much But the so we pushed them hard that second half did a good team regionally ranked and if we just got to play for 90 minutes I want to bring up since you mentioned her the two sports star Kellen She got her first goal of the 2016 campaign. How's that going to help her confidence going forward? Well, I think you know, we we start scoring goals I think the floodgates will open, you know If I think if we got that first one in the first half, they would have given the girls more confidence to freshmen, you know Missing chances Kellen, you know, she's gonna get going as well, you know, she once she starts she did it last year She did the year before so I was happy that she got her first goal and she almost she almost got another one there One in three overall to start the season. I know you had a couple one goal losses including tonight You're in the middle of a six game homestand so home form as we know is very important So how much has that been an emphasis to your girls this early part of the season the home the homestand and trying to pick up Results here in non-conference play before you hit the Commonwealth. Well, that's it I mean regardless home and away, you know, these are tough teams We're playing, you know, Catholic's good for us post good Salisbury is gonna be good next week So both of them are you know, these are all tough games that prepares us for the conference games So we're excited to you know, get ready for Friday again and and be at home And you know, we've got to take advantage of being a home and start faster Since we don't have to ride in a bus, you know, the girls are comfortable They can you know, take the take the day to get ready. So that's what we're we're gonna look to you know Look to get ready for Friday Graham again commiserations on the loss. Thanks again for joining us and we'll see you I hope to bounce back on Friday. Thanks, Jeff. Grant Miller joining me after the Mustangs fall 2-1 here to Catholic and Mustang Stadium