What is up you guys, welcome back to another one. If you're new to the channel, hi, I'm Gold Pony, I do new car truck SUV reviews on YouTube. And today we are in the new 2022 Volvo XC40, courtesy of younger Volvo in Hagerstown, Maryland. For more information on their inventory, please feel free to check out the link in the description box below. And so, I'm in this one today because this is quite a good looking small SUV, mainly built in Sweden with a little bit in Belgium as well, the final assembly is actually done in Belgium, but first introduced back in 2019 with some minor changes for this particular 2022 model year. And so in this video, I will be testing out and going over everything about this one from acceleration to braking, steering feel, ride quality, sounds like some exhaust clip, all that fun stuff. So having said all of that, what do you guys say? Let's just go ahead and jump right into it. And as always, let's start with pricing it. So as you can imagine, there are a few different trim levels that do come with the 2022 XC40. First one being the momentum, starting at $35,195, inscription for $40,945. And lastly, the R design, starting at $40,445. But that was all pricing for the front wheel drive configuration. If you wanted to add all wheel drive, simply add $2,000 then to any of those prices. But so then when it comes to the power plant of the XC40, I do want to mention, depending upon if you go with the front wheel drive or the all wheel drive, it's going to be two different configurations, two different power numbers. So for the front wheel drive configuration, you get a two liter turbocharged inline four cylinder, 187 horsepower, 221 pound feet of torque, of course, sent to the front wheels, through an eight speed automatic, zero to 60 time for that front wheel drive configuration, 8.1 seconds with MPG numbers coming in at 23 in the city, 32 on the highway. But so then on the other side of things, if you were to opt for the all wheel drive version, like we have today, you still get the two liter turbocharged inline four cylinder, but this time cranking out 248 horsepower, 258 pound feet of torque, sent to all four wheels, of course, yet again, through an eight speed automatic transmission, zero to 60 time coming in at 6.1 seconds with MPG numbers coming in at 22 in the city, 30 on the highway. And so before we do any kind of fun acceleration test here in our XC40, I did want to mention to you guys, the drive modes, which are all located within the infotainment screen front and center, they will include comfort, eco, off-road dynamic and individual adjusting quite a bit of different aspects to the XC40, including shift points, throttle response, steering sensitivity, climate control settings, all wheel drive system engagement and braking characteristics as well. That's quite a bit and substantially more than other manufacturers that typically just do those first three. So having got all of that out of the way now, what do you guys say? Let's go ahead and find a straightaway. Let's put this acceleration here to the test and let's see how quickly we can get this new 2022 XC40 here up to speed. All right you guys, so we are in dynamic driving mode, the more fun one of course. Here we go. Yeah buddy. Oh my gosh. Quite surprising. Honestly, I didn't expect that. This is a small SUV. It's not supposed to have that kind of power, but dang you guys, that was fun man. I like it. Definitely go with the all wheel drive version for that alone. My goodness. Anyways, to go along with that acceleration as always, braking is equally important.  In the back, 11.9 inch solid rear discs. As far as that 60 zero stopping distance goes, it's going to commit at a very respectable 120 feet. As far as the braking feel goes, it's okay. I feel like Volvo in general has this distinct braking feel that's unlike any other manufacturer that I typically test out. It's not a bad thing. It's not a good thing. It's just kind of in the middle. It's just so-so. And honestly, that braking number though, that's completely fine. So you're definitely not going to have any issues there. Then touching on suspension and handling.  In the back, independent multi-link rear suspension. As far as ride quality goes, it's been perfectly fine actually. But we are riding on some extremely smooth roads in Hager style right now. But I will say, I make said that the ride quality is still completely fine. So no issues there. Then touching on steering feel, it's okay. I still have it in dynamic and I really like it in dynamic. You can tell it has a heavier weight to it. It's literally points you in the direction that you want to go. My favorite part though, about the steering feel about being in control here is the thick grips. This has substantially thicker grips than the Volvo S60 that I just got done driving. And I like it. I like the thicker grips in the XC40. Like I said to you guys, it gives you that better feeling of being in control. That's all. As far as cabin noise goes, it's been perfectly fine. I'm going 50 miles per hour right now. There isn't a whole lot of wind noise at all coming into the cabin. Even with this panoramic, this dual pane panoramic moonroof that we have. Still, that is laminated. So there isn't a whole lot of exterior wind noise whatsoever coming into the cabin. So I love that. As far as visibility goes, it's excellent, especially with the shape of the XC40. You're not going to have any issues, but it really is quite excellent. So no issues with that whatsoever. And brain sensing windshield wipers also come standard on every single trim level across the board. So you got to love that as well. But that about rounds out the performance segment of this review. Guys, let's now go ahead and take a look at the exterior of our brand new 2022 Volvo XC40. All right, so here she is, you guys. The new 2022 Volvo XC40 finished in Onyx Black Metallic. And actually, if you get close enough, let me go ahead and get close enough real quick.  It looks so dang cool. Hope this is coming out on camera. But anyway, so let's go ahead and start up front on this one. LED headlights with LED Thor's Hammer daytime running lights coming standard for all trim levels across the board. Kind of Volvo's signature look with the Thor's Hammer LED daytime running lights. I love that. Automatic feature of course, coming standard across the board as well. And automatic high beams coming standard across the board. You don't always get that coming standard. So you got to love that. Essentially what that is, it's when you got your high beams on at night and it sends the vehicle coming in the opposite direction. It's going to automatically dim your high beams back to low beams until the vehicle is gone and then it's going to put it automatically back up to high beams for you. So it's pretty darn convenient. Aluminum accents on the lower portion of the front bumper unless you go with this awesome R design trim level that we have today and then you're going to get gloss black accents as expected. When it comes to the front grill, it's really the easiest way to determine which trim level that you're looking at when you're actually on a Volvo lot. For example, the black front grill with chrome surrounds is going to be the momentum. Black front grill with vertical slats and chrome surrounds is going to be the inscription. And the completely blacked out with gloss blacks around front grill is going to be the R design, of course, that we have today. But LED front fog lights with the cornering function also coming on the inscription and R design. So cornering function, meaning when you go around the bend at night they are going to swivel slightly dependent upon the direction of your steering angle. Better help illuminating what is around that bend. So very nice looking front end all in all very signature Volvo but pretty much rounds out the front. Let's go ahead and make our way to the side of this one. So now since we are around to the side of the XC40 silver roof rails coming with the momentum and inscription black roof rails with the R design trim that we have today. Of course, rear privacy glass coming standard for all trim levels, black windows surrounds for the momentum and R design. Otherwise you're going to actually get chrome belt line molding if you were to go with that inscription trim level. When it comes to the side mirrors they are body colored power adjustable side mirrors for momentum and inscription. Gloss black side mirrors then for the R design and then heated with LED integrated turn signals for every single trim level across the board. So you got to love that.  That sounds fancy of course coming with the inscription and then 19 inch double five spoke alloys with the silver slash matte black finish. So that is of course what we have today coming with the R design trim level but pretty much rounds out the side profile of this one. Let's now go ahead and make our way to the back. All right so now since we are around back body colored shark fin antenna all the way to the top just below that we're spoiler with an integrated brake light. Just below that rear window wiper of course you got the Volvo lettering spelled out horizontally and if I were to go up underneath of the XC40 here you will find dual exhaust outlets both tucked away of course but having said that I do believe you guys know what we have to do next as always here is that exhaust clip. All right you guys it's so nil since we are around back here of the XC40 when it comes to opening that rear tailgate there is a button on the key fob. There is of course a button on the tailgate itself any button by the driver's left knee as well and by the way there is a power tailgate available that costs an additional $200. Which of my personal opinion would be well worth it for this thing but once opened up cargo capacity comes in at 20.7 cubic feet behind that second row but with that row folded down it will come in at 57.5 cubic feet which isn't that bad by the way it is a 60-40 split. In case you were curious when it comes to in that cargo area itself there are two cargo lights which you don't always get usually just get one. There is a 12 volt power outlet back there there is a cargo cover back there as well and there are two grocery bag hooks located on both sides of the cargo area but it gets better because if you kind of fold up that rear cargo floor there's actually two more grocery bag hooks illustrated by the picture that it's giving me that's telling me that they are grocery bag hooks so that was pretty cool I've never seen it done this way before and it basically just locks in place and it gives you a little bit extra cargo capacity for perhaps some groceries so I thought that was pretty darn cool and of course there is a spare tire under that cargo floor in the end but anyways making our way up to the rear legroom that comes in at 36.1 inches so for reference I mean even six feet tall this is how much space I had in that second row there rear center armrest with cup holders does come standard 12 volt power outlet back there as well there are two phone charging ports not USB but phone charging ports back there as well and just above all of those charging ports there is rear ventilation that comes standard on this thing as well which you don't always get in this size of a small SUV so I do like the Volvo included it on the XC40 now let's go ahead and make our way up to the front seats power driver's seat with power lumbar of course coming standard we'll get memory settings for up to two different drivers coming standard as well that is going to be found just underneath that nice shiny Harman Kardon metal speaker there which we'll get to in a little bit here but leather seating coming with the momentum and inscription however my favorite seating in the world is always going to be a suede leather combination like I have in my own car and that's what you get here in the XC40 and that's what you get with the R design it's actually a napple leather suede combination which is even better so absolutely wonderful seats as far as the material goes so big fan of that heated front seats also coming standard on all trim levels across the board and perhaps my favorite part is the little flag of Sweden found on the passenger side seat here it's just a little attention to detail that you got to do that Volvo definitely has accomplished there with that little flag I think that's so stinking cold anyways seats were pretty comfortable not my very most favorite out there but they'll definitely do the job they'll get it done then take a look at the steering wheel it is tilt and telescoping it is leather wrapped for all trim levels across the board and like I said previously these 10 and two grips are definitely leaning towards the thicker side of things which I personally prefer then make your way to the startup let me first start by showing you guys the key here we do have an orange key because this is key number two apparently when you buy a Volvo key number one is going to be black and key number two is going to be orange I like the orange you never get that you guys know I like vibrant colors but anyways it is all keyless entry with a push button start so all I'm going to do here is simply put my foot on the brake and press that engine start button and so upon startup speedometer is all the way to your left with a small digital speedometer within that tachometer is found all the way to your right and it doesn't just slightly the gauges do it just slightly dependent upon which drive mode that you put it in eco changes it up substantially but then the others pretty much look the same so wouldn't have minded if Volvo added a little more customization between the driving modes or kind of like Mercedes Benz does I guess you could say it of course will also give you your outside temperature how many miles you have left until you hit empty also speed limit of any given road found just underneath of that digital speedometer which is pretty nice so definitely a very high end very nice looking digital gauge cluster for the XC40 without a doubt then making our way to overall interior quality there is a panoramic moonroof coming with the inscription and R design charcoal headliner coming with the R design and I didn't know what to expect I thought it was just going to be a basic black and I guess I kind of is black of course but there's a nice texturized finish to this headliner I really like it it's not a suede headliner but it's almost just as good because of the texturized finish so I'm a huge fan of that headliner universal garage door opener for up to three different garage doors coming standard of course with a frameless rear view mirror you gotta love that wireless phone charger coming with the inscription and R design found just in front of the shifter there is a crystal gear selector found on the inscription trim level only developed by Swedish glass design company so of course everything's from Sweden in the XC40 so I absolutely love that feature wouldn't have minded if they added that to the R design that we had today actually but gloss black center console trim coming with the inscription and R design I'm a big fan of that because the alternative is the black plastic so this gloss black finish I am a huge fan of so thank you Volvo you really should put that on all trim levels though aluminum foot pedals coming with the R design which I am definitely a big fan of and I like this little I don't know the little square design found just above the passenger side glove box and also on the doors I think that's a nice added touch I mean they could have put anything there but this works I definitely like that just in front of the shifter by the way you do have a little bit of storage to the left and the right of that wireless phone charger you have a 12 volt power outlet dual USB charging ports behind the shifter there's an electromechanical parking brake you have dual cupholders there is a smidge bit of storage just behind these cupholders and of course you got plenty of space within the center armrest then as well so definitely no issues there a lot of soft touch material as well like I said to you guys earlier also have metal speaker covers that is extremely high end and we'll test out the sound system in a second here and overall there's like maybe seven buttons found underneath the infotainment screen so it's a very simplistic look which I personally prefer but anyways let's go ahead and get to that infotainment screen nine inch color touch screen display coming standard for every single trim level believe it or not gotta love that bluetooth audio streaming coming standard of course android auto apple carplay meaning if you have a smartphone you can simply hug it up via USB connection and you have free navigation displayed up on that nine inch screen as well radio information can of course check out up there you have your climate control settings in the bottom left and right hand corner there as well as your heated seat buttons on the bottom as well but let's get back to those radio settings cause when it comes to the speakers they of course will differ eight speakers with 250 watts coming standard but there is an optional 13 speaker harming card and sound system that goes for eight hundred dollars well worth in my opinion because you get 13 speakers plus 600 watts so having said that let's see if it is worth I don't know how I can say that without testing it out first but let's go ahead and turn to the radio see what we got playing today and let's test out the clarity of this one the bass the bass the bass the bass was crazy in that harming card and sound system clarity was good as well but the bass that was perfect and really there's speakers everywhere there's a speaker just above the infotainment screen right now and all of the speakers are metal they're high quality you got 11 not all the speakers but most of them anyways last thing I wanted to mention to you guys on the infotainment screen is of course when you do put the XC40 in reverse you will find a very high quality rear view camera that does come standard across the board and there is a 360 degree camera with the advanced package which goes for $1450 that's going to give you that bird's eye view of everything all around you which is pretty darn cold but as always that is going to lead us into safety and so first let me start by saying this is a Volvo so therefore it is an IIHS top safety pick plus which is the very highest designation given by IHS that pretty much says it all right there front side, side current airbags do come standard driver's knee airbag as well in the back you're going to have latch aka lower anchors to have those for children for the rear car seats rear child door locks tire pressure monitoring system I'm getting tired of saying that in every video but fun stuff the advanced safety that you got to love is blind spot monitoring system with rear cross traffic alert coming standard rear parking sensors standard power retractable door mirrors lane keep assist lane departure warning roadside recognition all that standard then if you were to go with the inscription or R design that is going to add front and rear parking sensors as well so overall when it comes to my final thoughts here of the XC40 Volvo has always been known for safety and that has not changed throughout the years as evidenced by that top safety pick plus rating flag of Sweden on the seats one of my favorite features in this thing you got to love that and the seats themselves I love the suede napple leather combinations that's just about as high end as you can get when it comes to seating great styling both on the exterior and interior the digital gauges are 100% on point I love digital gauges and cars the only thing I would add just like I said with the S60 Volvo I think it's time you had some really cool really fun multicolor ambient lighting to this thing and that it would be perfect but anyways let me know what you guys think of the XC40 in the comment section below that is about it for this one you guys thank you so much for watching if you're free to follow me on social media at the bottom of the screen there if you wanted to see what's coming next on the channel before it actually gets to YouTube be sure to hit the subscribe and the bell notification button if you're into new car reviews that is what we do here on this channel after all do appreciate you guys watching more than you know and I will see you guys all in the next video stay gold


Good. So, today I want to explain you what does a dynamicist mean when he or she says a deterministic system that behaves in a probabilistic manner. And of course, and to also explain how this concept is related to ergodicity. Let me write a note here. So, we remember what I am talking about. So, deterministic system, let me write larger, behaving probabilistically, and it's relation to ergodicity. If you respect the roots of these concepts, you will probably end up studying works by Poincare or maybe Boltzmann where they try to study complex physical systems. It's possible to sort of explain these concepts in a modern way by using two theorems which I will try to explain first. So, these two theorems that I want to explain will be strong law of large numbers. This is from probability theory and Birkoff's ergodic theorem. This is from dynamical systems. And I will do it one at a time. So, I'll start with strong law of large numbers. I'll try to explain it using examples. I myself, I'm not a probabilist. I do more geometry. So, if you find anything that's not comprehensible or seems suspicious, do feel free to stop me and we can discuss. So, I'll start by stating this theorem or law and try to explain you hopefully in less than half an hour what it means. So, first I'll write theorem just as it is and then I'll explain it. So, don't worry if there's something that you don't understand. Let me write it here. Let this be a probability space. So, this is not a very good choice of letters. They all look like each other. But anyway, it will be clear what they are once I explain them. Be a probability space. Let xk be a sequence of random observables which are in particular some functions which have some properties which I will explain later. But there are some functions from your space. This will be the some set or some space that we are working with. Will be some random let xk be a sequence of random observables which are independent and identically distributed. Then for mu almost every point in your space you have that this limit exists and is equal to this. Can everybody see this? Okay. So, here the particular choice of zero does not really matter. As we'll see identically distributed means that you can replace this with any i but I just don't want to write an extra sentence so I put there zero. So, this gives somehow some statistical or average information about behavior of some objects that are defined on our space. Let's try to understand this theorem shortly or I mean as quick as possible by some simple example. If you are throwing dice, so let's first try to explain what are these. We are here if for those who already know it this will be our space. This is the measure and these are the measurable subsets of our space. But for those who don't know it, let's say that you are doing a probability experiment where you throw a dice. Then your outcomes will be inside this set. Well, of course when you are doing a probability experiment generally you are not just interested in one throw but you are interested in and throws, one million throws, two million throws. So, you would ideally want to work with a space that is of this form. An infinite product which is of course can be written as a sequence inside s where x i are from s. So, this means that this is the result of your first throw, this is the second throw, this is the third throw so on and so forth and this represents an ideal probabilistic experiment. Now and then in this particular setting you can take this guy to be just the all subsets of your set M and then the measure will be the following. I will explain what it means after I write it. So, the measure, so note that if you take any, so the measure will be first of all a function from here to real numbers in fact 0 1. So, it takes a subset of M and then gives it some value which will be the probability of observing an event inside that set basically. And you can define it like this. So, if you take a element from here which are all subsets here, all possible subset here it will be of the form a 1, a 2, so on and so forth where a i are from s and then the measure is defined as number of elements inside your set. Note that this set is finite and the number of elements can be at most 6 or 6 product from 1 to infinity. Let's see what does this thing do. It's just an extension of basic probability calculations that you see in probably undergraduate but not in this form. For instance, let's take a set of this form to be this. The first subset of s will be just the element 1 and then you take this, let's call it a. Then measure of a by this rule will be 1 over 6 because there is just one element here and then there are 6 elements here. So, these are just 1. So, as you see this just calculates the probability of getting 1 in the first row and then you can generalize this experiment to other kind of observables that you want to study but this is the basic setting that you should keep in mind when for instance you are looking at this theorem. Now, using this let me explain what it means to be independent and identically distributed. So, again by the way for those who are not familiar with integration with respect to arbitrary measures just imagine this to be volume for now for the purposes of this lecture is much more general of course but anyway this is some notion of integral that we have here. So, here you are just integrating a function over your space and so it should be integrable in particular these observables. Now, I am going to explain what it means to be independent and identically distributed. So, let us start with the easier one. A sequence of random observables are identically distributed if in some sense your chance of seeing a certain value is the same for all of them and this can be formulated in the following way. So, it should be by now clear that notions such as chance of seeing or probability of something happening is precisely related to this measure. So, you should expect a statement about measure now when I say identically distributed. xk are identically distributed if measure of the set of points p where xkp are in j is equal to measure of x i okay let me put i and j for all i j and let me call this maybe l so we do not have double j's. So, again this in some way sense could be seen as the probability of observing values inside l for the jth observable and the same for i and this is saying that this is the same for all i j and possible range of values. So, you see the same behavior probabilistically for two random variables then they will be identically distributed. Now, independent means I have to go like this sorry if it seems okay for everybody I guess. So, now I want to explain independent. Independent drastically means that if you know that one of the random observables achieves a certain value you don't gain any information about what the other random observable will be that they will be basically independent from each other like if you toss a dice and you wait and you toss another dice the result of this will not affect the result of this role. So, the results are like independent observables I'll also formalize this but first let me write what it means to be independent. So, xk maybe I should put this to make sure this you understand this is a collection of random observables xk are identically this are independent if measure of the points or probability you can call it if you like such that this probability should be the same as this probability times this is p sorry this should be same for all k and l subsets of r and for all i j. So, if you look at the second product this is just the probability for this guy to to get the values inside k. So, here also sorry l is a subset of r in our particular setting could be also integers but anyway. So, this is just the chance of obtaining xi obtaining values inside k times the chance of xj obtaining values inside l and this is saying that if you are given that xi p is already inside k and you want to look at the probability that xj p is inside l then it is the same as this. So, they are not sort of affected by each other. So, an example in the case of dice is just the following and in fact this just formalizes the feeling that the dice is I mean is a formula to write that dice throwing is independent and identically distributed you define the following random variables. So, I will write the sequence with y is now it just selects the kth element of the sequence. So, it means that this random observable will tell you what the kth outcome is and then if you look at these random observables I will leave it as an exercise to show that xk are iid which is independent and identically distributed and now if you want to apply this for instance strong law of large numbers in this particular case of random observables what you get is the following you can compute that integral on the right hand side is an exercise again, but the crucial point is almost mu almost every p. So, I will just make a side remark here for instance if you take the sequence 11111111 obviously it does not satisfy this, but if you take all the collection of sequences inside here which represent possible outcomes of your dice throws and if you collect them together they will still be a very small set in sense of measure. So, here mu almost every point p means the following for those who are not familiar with the notation that there exists a set inside m which has full measure by the way note that since we are working with a probability measure okay not very good choice of letters since we are working in a probability space the measure of our whole space is one, but this is saying that on some subset of full measure this equality is true and this is what we obtain here this says that this also says in this ideal case a typical dice throw will have this statistical behavior. So, by now let me check okay by now it should be also clear that when you take a physical phenomenon and when you want to model it using probability the aim is not to do the following the probability does not do this okay I have this dice here I know at which angle I am going to throw I know it is weight I know the direction so on and so forth what is the next result that I get this is not probability aims to get so probability aims to get some statistical or averaged behavior about the system that you are studying so this brings up the question which is also related to the the concepts that we are trying to understand let me make sure I'm on track okay so this pops up the question if you are given a physical system like dice throwing or other systems like economy propagation of a disease how do you know is there a mathematical formulation or a mathematical way of showing that such a system can be reasonably modeled by probability how do we know that when we write a model like this for dice throwing we we get that the results we obtain by calculations here reflect the patterns that you get by throwing real dice this is very much related to the concepts that we are trying to explain in fact you will see after the talk ends that ergo this it is a partial answer to this and is a mathematical partial answer to this and in fact it was some of the main motivation of let's say Poincaré or Boltzmann to basically to say that complex physical system complex physical systems instead of finding an exact model for them you can study them probabilistically this was the idea and direction which led to things like ergodic theorem and which in fact led to the notion of a deterministic system behaving probabilistically so to pass to that part now I am going to explain Birkoff ergodic theorem okay I'll keep this here so that you see the similarity between the two theorems so this theorem is supposed to give us some information about statistical behavior of deterministic systems whatever it means you will understand now tells the following let this be a probability let m mu and m fancy m be a probability space let f be a measurable map so here measurable map just is some sort of regularity condition which is lower than continuity but which is as reasonable as you can go if you want to decrease the regularity of a function beyond that is not very reasonable so this is just a weaker form of regularity let f be measurable transformation from m to m assume that the measure is f invariant and ergodic now take any random observable on your space not a sequence this time take some random observable and define the following then we have basically I don't need to define anything then for mu almost every point p we have that limit n goes to infinity one over n i from zero to n minus one converges to this integral so of course I will also explain this theorem but the similarity is more or less obvious that I mean the similar part is always it's not always how they are related at the moment but obviously the similar part of the two theorems is these results and in both cases you have a set of critical conditions which gives you the result you want so before I explain the relation between these conditions I will make a small remark for people wondering what does this even have to do with a deterministic system what is the system that you are studying so this is just the simplest abstract model of a physical system that you can imagine let me motivate it as a side remark in the following way for instance the original systems that Poincare or Boltzmann were studying were Hamiltonian flows of three bodies three planetary bodies or Hamiltonian sorry Hamiltonian flows of uh interacting particles gas particles inside a box so that would in general in the face space defines u a flow where n is the number of particles six and and r will be the time defines you a flow in your face space let me call this variable t the variable time variable of course one way to simplify this is just to take a discrete time fix a small scale time and look at this this is just one way of discretizing a map there are many other ways some of them are known as Poincare maps so on and so forth but here basically f is supposed to represent the time the discrete time evaluation of a certain physical system whatever it is and then if you want to if you look at the further iterates let me continue there of this map if you look at the further iterates of this map starting with a point you are just more or less following the discrete time evolution of a system for instance in this kind of setting or there may be more complicated ways but i'll not talk about them also for dice throwing you can see that each dice throw you can see as a so i mean you can try to although it will be almost impossible i guess try to model a dice throw as a set of maps with some parameters like the speed of the throw the angle of the throw such that at the end step when you apply that map given the speed so on and so forth you get the next result that could also be modeled as a family of maps not just one map but this is another example where such a setting comes into play so this is to make this question the relation between deterministic systems and probability mathematically rigorous this is the simplest setting of a dynamical system that you can imagine now that we at least hopefully understand that this represents some behavior of a dynamical system let's try to understand the relationship between these conditions so of course i'll first give the definitions as always mu is f invariant if you take any measurable subset here so some set who you can calculate its measure is tautologically if this equality holds true of course one might be wondering why you are inverse iterating a map rather than forward iterating i mean the most satisfactory answer that i have for this is it's a technical issue because if the map is for instance not invertible then if you take a measurable set you don't know if its forward images are measurable or not but you know that its inverse image is measurable so this is one technical reason why you would want to formulate it like this and geometrically this means the following since f is not invertible this f inverse is a set valued map meaning that when you look at all the inverse images you will get some b1 b2 b3 all of which map in a i mean if this is not invertible all of this map to this in a none one to one manner like they might end up in the same point this is saying that if you compute the volumes or measures of this it's the same as the measure of this so this is somehow a notion that something is left invariant so we'll later see that this will be related to let me just make a side remark remark to a identical distribution now the second condition is mu is f ergodic if f inverse a is equal to a implies that either the measure of this set is one or measure of this set is zero so the dynamical intuition about this condition would be the following if you have this condition again this is to be viewed as a set map in case it's not invertible if you have this condition then for instance you can decompose your space into two spaces such that the map such that the two sets do not interact with each other in terms of dynamics all the points here are sent to here all the points are sent to here so in some sense you can divide your space into two parts which you can break down and study separately but this is saying that to a nonsignificant level this is not possible if there is some invariant set inside your dynamics then it's almost the whole space so you don't have this picture it's almost the whole space that you are working with or sorry uniqueness of what yes yes so this condition this it happens basically I mean it happens basically as what I have said in any case if you have such a set you can break your whole set into this case and into these two parts all of which just sort of evolve inside themselves so this condition is enough to get that but now you look at the measures of these sets whether if that's a significant part of this whole space or not and this is saying that this basically says that if you have such a case then either this mu a is one or mu a is zero so you cannot decompose your space into two significant parts which are not interacting it always sort of mixes within itself it looks something like this intuitively that it always mixes by itself it doesn't if you start at a point it's not restricted to just here but of course these are all defined up to full measure so there will be probably some small sets here which do not satisfy this if you have this thing yes it violates ergodicity like if you are there is a flow I mean there is a significant amount of initial conditions for which if you start and you stay in some trapped region then it violates ergodicity and then our aim is to see that this is related to this will somehow be related to independence having said these I have to go here sorry of course when you see this theorem the first time these two theorems together you might wonder can I not prove this simply by demonstrating that x i written by like this are i id i id is ah yes sorry i then independent and identically distributed so this is where determinism kicks in these are as I will explain now a deterministic iterate of a certain map so there is no way they can be independent and I want to although they're invariant so I want to demonstrate that first with some maybe five minutes let me see okay I want to demonstrate that first so x i are identically distributed let's look at what it means so we let's look at the how the values of x i are distributed in this case measure of the points p such that x f i of p are inside some j where j is a subset of real interval so this means basically that f i p are inside x inverse j where this is also again just the set map which means that p are inside f minus i this i just denote the inverse of the this map so if you take the set of values q such that x q are inside j which is this set then you see that this guy is equal to this set inside here is equal to right q here so if you keep iterating this map you can also prove the following that for any k for any number of inverse iterates you have the same basically which is induced by the first condition and then you obtain that this is equal to measure of q so all of these guys which are the iterates of your map their values are distributed according to just the original random observable so they are identically distributed and this is how a invariance is related to identical distribution now to show how our godicity is related to independence i first need to show that these guys are dependent actually so x i as random observables are not independent well heuristically this is this could be explained maybe in a dynamical manner in the following way let's say that you know that for a fixed j your values is inside some range of some range of values this particularly means the following you know that this holds true then you know again by the same calculations that we have done is that your initial starting point is inside some region in your face space or configuration space or what you like now you can look at all the possible orbits so basically you look at the all the possible iterates of this set where your point falls and then this will give you somehow the distribution of the other random observables because x k of p is just x k x of f k of p so in particular this information tells us that our initial point is here and then this tells us that all the forward iterates are possibly trapped inside some region and this will prevent possibly again from x k achieving some values that it could have so this is an heuristic argument that tells you why they are not independent because they are related to each other by a deterministic manner this can be formalized a bit more with a more convincing argument although one would of course need a specific example to show this in the following way take some subset of u such that for some k this is not equal to u so you have u and you have some inverse iterate of u possibly also something like this all these are the inverse iterates such that it does not coincide with the original set and such that measure of f minus k u difference u is positive this generic situation you can imagine happening in many systems so this would be a way to construct an example now take any set here sort of take any set here so that its inverse images mapped to here and you will have that measure of f minus k of a f minus k of a a is zero while measure of a square is one now to to see so because this is empty set while this is obviously some positive measure set so not one is bigger than zero why does this imply independence as your random observer will you just take this function i'll leave it as an exercise which is equal to one if p is inside a and is equal to zero if p is not inside a and if you write the condition of independence using this function and using this particular form you see that you need to get this whereby invariance this will be again just measure of a so as i have demonstrated with a thought let's say thought experiment that this this is not reasonable to expect in a generic situation so these things are related to each other in an obvious way by a deterministic algorithm and if you know the value of one then you know the value of the others more or less so they are definitely not independent so in this case what happens is that instead of independence the independence condition of random observables are basically replaced by the ergodicity assumption and once you have once you have proven that a particular physical system that you have at hand satisfies invariance and ergodicity then it becomes reasonable to study observables on this space in a probabilistic manner by a probabilistic manner i mean that you look at for instance x could be here the energy of your configuration at that point and then this would just say that instead of evolving your system instead of finding an exact solution for your system and computing the energy everywhere if you are just interested in somehow asymptotic behaviors of course that's also very hard to estimate but anyway asymptotic behave by which i mean that when do you sort of get close to your limit but anyway i'll leave that aside then instead of calculating the exact thing you just do an averaging process so this is what is called of course by physicists the case where the time average is equal to space average so you see that this thing here that looks like just the summation is actually a time average you just follow the orbit of your point sum your observable here and then just divide by total time in a discrete manner there is also an analog for this for flows but this is the discretized version and this is obviously the space average or what people call our ensemble average where you just compute the average energy considering all configurations rather than a simulation or an exact solution and of course this also tells that this also tells that if you take this particular system which is invariant and ergodic and now as in the dice example you construct this space of infinite products and define the measure in the same way so measure of a set would be again let's call it bar measure of a1 measure of a2 now if you pick some points here with a probe pick some points with some probability using this measure this is a vague thing i know but this is just a way of thinking of this is again the dice example that you certain sets have certain probabilities so if you pick a generic point inside this or up the full measure if you pick a point inside this space a random point which means a sequence of points then asymptotically it is behavior will be same as if you are calculating this average along the orbit so this is also another way to see how now this turns into into a probabilistic setting this gives a partial answer to understand when can you study a physical system statistically at least studied statistically using probability now of course comes some other questions which i have little time for but i'd like to give a few remarks on which goes back to original questions of poincare and of course other people is how do you for instance can is it possible to study ergodicity of physical systems so for those who are interested basically well the answer is not always positive that because they were expecting probably that almost all or generic hamiltonian systems should be ergodic by hamiltonian system i mean some physical system that obeys newton's laws basically but there is a theorem called colmogorov arnold mozer theorem that says that there are actually quite large classes of hamiltonian systems which are not ergodic i mean yes basically which are not ergodic and anybody interested in going further i would suggest to look in that direction okay let me see if i have anything left okay i still have 10 minutes so i will just also add one more final remark what we have done here is that we have taken a physical system and show that it behaves probabilistically but you can also show that if you take a truly probabilistic setting like this you can view it as the most basic ergodic dynamical system in the following way so this is somehow establishing a relation in the reverse direction so always the example to keep in mind is the dystro and now assume that we are here that we have all these things here if you take your as in the dice example take your infinite product space which will be a space of sequences and assume that each probability experiment is independent and identically distributed which means that you can define a measure on this space in the following way where mu is the first given measure and if you define the following shift map on this space so it takes a sequence and gives you the next basically shifts the sequence to the left you can show that sigma is invariant and ergodic with respect to mu and this will somehow imply you i'll just show briefly that then you will obtain this theorem for a special class of functions so if you take again this characteristic function which is as i said is p is equal to one if p is inside a and is equal to zero if p is not inside a so i will just leave this as a small exercise to check these things then you can see that basically x i sigma k so i will let also p represent this sequence now p is one if x k is inside a so this function checks whether your kth result falls in this collection of results or not you do some experiment and you wonder if it falls where a is a subset of m you do a collection of experiments and you wonder if one of some of them falls inside a now if you apply Birkoff's ergodic theorem to this sequence of observables what you get is that this is equal to this so what is this quantity this quantity is precisely the average number of times your experiment results in an outcome inside this set and this quantity is precisely saying that this is measure of a yes yes sorry k i of a where this is equal to over m okay so this is equal to integral over a of d mu which is equal to mu of a so if you know for instance if you assume Birkoff's ergodic theorem now you can turn your probability space of independent and identically distributed trials which basically means this this means that you have identically distributed and independent trials given by mu then you can turn this question to a dynamical system and prove this famous theorem about observing a certain class of events in a sequence of experiments is equal to its measure or equal to its probability you obtain this theorem in a dynamical manner and finally i didn't have enough time of course i i realize after i prepare to talk that i had too much to talk about but i'll put some notes in the web in my web page so as you see this is just an average information about certain random observables or an average the information about let's say the energy of your system so this is a very crude probabilistic behavior let's say you just have some information about the the averages you can actually also relate what is called central limit theorem in probability and decay of correlations well this is both a probabilistic term and a dynamical term i guess of and decay of correlations that that is present in a dynamical system to show that actually there is even in some cases you can even get much more finer information about these guys individually rather than that's average but i will leave that to people who are interested to look at the notes that i will put in my website finished i don't know but it is inside so if you write sisa and my name to google there will be a directory inside there will be a directory inside sisa web page which links to the my web page here i don't remember right now sorry and yes you can find it like that or you can email me okay you can email me that's also another option which is less painful okay


Filling out a judging card the correct way begins with knowing the county you're from, your contestant number, your name, and the title of the class you're about to judge. The most important item listed above is your contestant number, knowing this and putting that number on every card you turn in. This will ensure you receive points for every class and the points are going to you, not another contestant. Depending on how many classes you have, each contestant will need to fill out multiple cards. There is one card for each class judged. One tip that may assist in decreasing stress while judging is having each card filled out before classes enter the ring, so the judge will be ready and focused on the class at hand. Once the personal and class information is filled out, focus on the class in front of you and place the class. The next step is finding the correct placing order on the card. Let's say I place the class 3412. I will go over to the list of numbers, go down the list until I find 3412, then I will mark on the blank space next to the placing. I will put a check mark or an X, some sort of marker. Not only will I put a marker, I will also draw a box around the selected placing order. This provides extra clarification and confirmation that 3412 is the placing order that I have judged, allowing the person who is inputting scores into the computer to have full confidence in my placing and provide accurate results that I earned. Thank you for watching. Be sure to check out our other livestock judging videos as well as the Alabama Cooperative Extension YouTube channel.


And so there was that. So unless you have a required tax year, you adopt a tax year by filing your first income tax return using that tax year. So you want to make sure that you get this right from the start. Again, a lot of small businesses that are sole proprietors will be a calendar year, but if you're going to make a change, you want to research it and try to get off the first step on the right track, because it might be a little bit difficult to change it after you've already started adopting one particular calendar year. A required tax year is a tax year required under the Internal Revenue Code or the Income Tax Regulations. Calendar year, calendar tax year. A calendar tax year is 12 consecutive months beginning January 1st and ending December 31st. Straightforward, right? Just like it is on a calendar. So you must adopt the calendar tax year if any of the following apply. So what are my restrictions? Do I have to have a calendar tax year? Well, possibly it depends on the situation. If these apply, you do not keep books. So you have no annual accounting period. So your present tax year does not qualify as a fiscal year. So your use of the calendar tax year is required under the Internal Revenue Code or the Income Tax Regulations. If you filed your first income tax return using the calendar tax year and you later begin business as a sole proprietor, you must continue to use the calendar tax year unless you get IRS approval to change it or are otherwise allowed to change it without IRS approval for more information see change in tax year. So again, you want to get off to the first start. The way you want to go forward, you want to plan that out because it's more difficult to change it. Not impossible, but you have to have rationale to change it and you've got to go through a process to change it because the IRS wants consistency. So people aren't cheating by adjusting cutoff dates by changing years and methods. So if you adopt the calendar year, you must maintain your books and records and report your income and expenses for the period from January 1st through December 31st of the year. Fiscal tax year. What is it? A fiscal tax year is 12 consecutive months ending on the last day of any month except December. So clearly we still have to have 12 months. You can't say, well, my fiscal year is only three months. No, that's a quarter. It has to be 12 months, but it has a date an end period that's other than December. So a 52 or 53 week tax year is a fiscal tax year that varies from 52 or to 53 weeks, but does not have to end on the last day of a month. So now we're drilling down to the weeks. We can define a year by basically 12 months. 12 months are not exactly even because they have different days within them. We could try to break it down into smaller increments of weeks. When you think about weeks in a year, there's either 52 to 53 weeks in the year generally. So if you adopt a fiscal tax year, you must maintain your books and records and report your income and expenses using the same tax year. For more information on a fiscal year, including a 52 or 53 week tax year, you can see publication 538. If you want to dive into that in more detail on the IRS website, change in tax year. Generally, you must file form 1128 application to adopt change or retain a tax year to request IRS approval to change your tax year. So you could possibly change it, but it's difficult. That's why you want to get off right on the right foot when you start. Otherwise, you could walk forward. You could still move forward, but you're going to fall on your face as you're moving forward, which isn't the best mode of transportation. So see the instructions for form 1128 for exceptions. So if you qualify for an automatic approval request, a user fee is not required. If you do not qualify for automatic approval, a ruling must be requested. See the instructions for form 1128 for information about user fees if you are requesting a ruling.


Hi everyone, Joe for Jaspy's casebrakes.com coming at you with 2022 Panini National Treasures baseball four box picker team number 35. We did find another case So we just loaded it up So if you missed out on your teams the first time do not miss out this time. Guess what gang? We were able to fill this up straight up. No filler. Love it Don't have to break any hearts in a filler. Let's get it done straight. I would just break hearts in this break Daniel Lewis last spot mojo Marlins You win some you lose some but I appreciate everybody given this a shot. Thank you Thanks for taking the risk. All right, so let's pop this guy open See what we got here boys and girls Okay, sorry about that.  There's a little bit of a ding right there, but at 17 out of 99 That'll go to Riley in the Royals Right on my apologies on that. We'll figure out some a little compensation for you on that all right next up is 23 out of 99 one yep as Field gear I grab a second card here field gear for the Cardinals. That's gonna be for It's gonna be for Alexander Got Andrew Jones 32 out of 99 Field gear for the Braves. That's gonna be for Brian C. And we got Trey Turner 18 out of 25 That will be for the Dodgers. That's gonna go to David M 33 out of 49 die-cut material signatures That's gonna be for Joe Ryan. That's Joe Ryan for Ed P and the twins 29 out of 99 Connor Siebold bean town Jersey and autograph that will be for Jason K in Boston out of 25 We got Chas McCormick the Chas manian devil. They really calm that seven out of 25 Houston That's gonna be for Jeremy Resnare 23 out of 49 Padres Jeremy Razor with the Friars nice rookie auto O'Neill cruise seven. I'll check that two out of 25 It's Ed errands and the Pirates nice and Hall of Fame material is 44 out of 49 Orlando sepata That is for the Giants that's gonna go to Jared who has my rivals. All right next All right, see you Chris have a good night man. All right, we got Ryan McKenna for the Orioles 90 out of 99 Slide that blank card out there to Slow play some of the hits a little bit That'll be for Kevin and the Orioles 75 out of 99 Alec Bohm That'll be for Chris Butler and the Phillies and a one of one Randy Johnson, I feel like we got a rainy Johnson earlier today in a different break But a nice rainy Johnson one-of-one in this break Was it flawless? nice and That is Diamondbacks edition Ryan Gamgee Ryan all aboard the Big Head Express That's three right the flawless, that's right. That's three our One-of-one total we set earlier today beginning of the day at three and a half The hook the hook will get you 54 out of 99 Jorge Alfaro Padres Jeremy Razer They got Taylor Tremel 40 out of Looks like 99. Yes 40 out of 99 for the Ems. That'll be for Colin Kay Plate an autograph. That's Kevin Vigio. It's got a unique autograph on plate autograph another one-of-one The hook won't get you that's gonna be for Toronto. That's for Ivan All aboard the Big Head Express There you go the over hits over three and a half for one-of-one today 44 out of 99 Chas McCormick. That's gonna go to the Astros. That's gonna be for Jeremy Razer Yeah, if you've been following along all day on the one-of-one total What an exciting moment and there's another train whistle one out of five Rhino Ryan Samberg You got a piece of the Cubs logo there his autograph Hall of Fame material signatures Jason Kay with the Cubs All aboard the Big Head Express The book four out of 99 dual signature materials Wow Wander Franco on the left side O'Neill Cruz on the right side Is this one happy one sad? Yeah, it is Daniel Lewis has the raise Ed Aarons has the pirates it's a randomizer's we one happy person one sad person at the end Yeah, I think we've hit a lot of those cards and there's Trish speaker highlighting his doubles That's for the Red Sox. That's for Jason Kay Fingers crossed Daniel fingers crossed Ed Good luck to the both of you we could go should we go like If you know your old testament should we go King Solomon style and offered it to cut the card in half And the first person say no, don't do it will be the one who honorably deserves the card. All right, Thomas Sapuke field gear 53 out of 99 that'll be for That's a giant that's gonna be for San Francisco that'll be for Jared. We got boba shut 24 out 25. That's for Toronto Ivan That's true. Yeah, you might have used up your you're begging to the gods for tonight Daniel at least for I Don't know how long at least for how long how long do you think you can't do that anymore? three out of four Lou Gehrig For the Bronx bombers David M with the Yankees old-school Jersey Game warden That's awesome David all aboard the Big Head Express Patrick Mazzica 45 out of 99 for the Mets. That's gonna go to Chris Butler. He's with the Dodgers now We got Dean Kramer 26 out of 99 That's for Baltimore. That's gonna be for Kevin M We got Hassan Kim 13 out of 49 for the Padres Jeremy Razor 8 out of 99 Josiah Gray RPA nice patch Ed P Nationals and there's Roberto Almar 3 out of 10 Hall of Fame signatures Toronto it's gonna be for Ivan and the book is Luke Williams rookie signature jumbo material a Little bit of that Philly's pinstripe right there as well going to Chris Butler and the fight and fills 99 out of 99 The last one ever made Alright last box. Good luck. All right last one here.  Luke Williams is with the Dodgers There's Reed Detmer 44 out of 99 Piece of the Jersey for the Halos. That's gonna go to Chad Went to the big had a couple of big games of the Phillies and went to the Giants then Marlins now with the Dodgers There's Yachty 8 out of 49 century materials We're not seeing him Suit up with the gear this season Alexander with the Cardinals We got big Mike 7 out of 99 Big Mike Bowman for Baltimore Kevin with the Orioles There's Heston Kirk stop 23 out of 25 Three color relic and on-card autograph for Kevin and the Orioles one of their one of their high first round picks We got a dollar's Garcia 2 out of 5 Texas Rangers Ed P out of 5 Rangers and the All aboard the Big Hit Express Spencer Torkelson nice 4 out of 10 RPA three color patch and autograph Looking for a nice season from him this year Anthony For the former number one overall pick Oh Daniel saying Heston curious or what's for Arizona folly again VP there you go Kevin We got Michael Harris 32 out of 99 century materials nice season for him in the Braves That's Brian and the Bravos legendary material signatures out of 25 It's a legend Clayton Kershaw nice David M with my Dodgers there you go David and last one is Cole Franklin 31 out of 99 Jason K and the Cubbies there you go ladies and gentlemen that was the break Pick your team 35 in the books now We got to make one person happy and one person sad raise pirates randomizer and let's flip over to Ran about org You got the raise wander on the left side pirates O'Neill cruise on the right side That was four out of 99 dual relic on dual on-book autograph as well Fingers crossed good luck one and a five six times team on top gets it after six one two three four five and Sixth and final time Goes to the Pirate so apologies to apologies to Daniel Louis D. Lo and the no check that apologies to Ed Aaron's in the Pirates No, I'm losing my mind here apologies to D. Lo and the raise congrats to Ed and the Pirates Your teams on top after six and you're gonna get that dual auto dual relic four out of 99 Let's hope both of these guys have amazing seasons and there you go everybody. I'm Joe for jasky's case breaks calm Thanks for watching. Thanks for breaking with us, and I'll see you next time for the next one. Bye. Bye


I learned something huge. At 16 years old, I ate a bunch of food. I think I ate a steak, a bunch of potatoes. I went outside running around, and I ended up, I literally ended up throwing up in the driveway, in the front yard, and I had to be to work literally in about 15, 20 minutes, right up the road, a local grocery store, I worked there as a kid, and I'm like, gosh, I'm throwing up. I feel miserable, I feel horrible, I hate it, I'm puking everywhere, it's nasty. I don't wanna go to work. I told that to my father, and you know what he said?  You'll quit in the future, when stuff gets hard, the stuff gets hard, you'll quit, you won't show up, you won't go the extra mile, and if you skip work today, you'll skip work other days in the future, and to be transparent, I've never missed a day at work in my life, and I own a few companies, and by me showing up, I set the precedence and the example that it's not okay to miss, that when you're sick, do it anyway. When you don't feel like it, show up.  Do not quit and show up, and that was a huge life lesson in my life at 16 years old.  Do it anyway, because if you quit now, you'll quit forever.