Around 150km west of Port Maputo, South Africa, the remains of a huge metropolis can be found. An ancient site, measuring an astonishing 1500 square kilometres in size, suspected by some to in fact once have been part of an even larger civilisation, estimated by some to have been around 10,000 square kilometres in size, and constructed 160,000 to 200,000 years ago. The region is somewhat remote, and the stone circle remnants were only ever encountered by local farmers, who assumed they were made by some indigenous people within the past. Amazingly, or rather conveniently, modern archaeology has seemingly forgotten to investigate this amazing place. Fortunately, this all changed when researcher and author Michael Tellinger, in association with Johann Heiner, a local fireman and pilot, who had actually been looking at these ancient ruins for years, decided to investigate. Heiner had the unique opportunity to see these incredible structures from the air, and knew that their significance was undoubtedly not appreciated. Quote, When Johann first introduced me to the ancient stone ruins of Southern Africa, he had no idea of the incredible discoveries we would make in the following years. The photographs, artefacts and evidence we accumulated all point towards a lost civilisation that precede all others, not for a few hundred years or a few thousand, but many thousands of years. End quote. According to Tellinger, these discoveries are so incredible that they will require a complete paradigm shift in how we view our human history. Quote, I see myself as someone quite open-minded, but I admit that it took me over a year to figure it out, and I realised that we are actually dealing with the oldest structures ever built by man on earth. We have been taught that no ancient civilisation of significance ever existed within South Africa. Powerful civilisations all emerged in Sumeria and Egypt and other places, Michael Tellinger stated. Regardless of what certain individuals claim regarding the age and indeed size of this site, it is certainly of historical significance, going against all currently upheld understandings of the timelines regarding ancient civilisations within South Africa. As Dan Eden from Viewzone put it, quote, I would suggest that the Sumerian story was given as a base metaphor for actual ancient cataclysms that caused the diminished planetary resonance and a spiritual injury to the psychoacoustic field of human consciousness. He continued, the tablets of Sumer describe the Anunnakai as a race of extraterrestrial beings, who enslaved humanity for the purpose of exploiting our goal for protective use in the atmosphere of their home planet. I understand the Sumerian mythology as a metaphor for the cataclysmic changes that occurred in the deep human past, which offset the psychoacoustic balance of human consciousness. End quote. Mesopotamian art indicating a strong importance to their cultural beliefs. It is now understood that the Lama Su were perceived as household protective spirits within ancient Babylonian belief systems, becoming associated later as royal protectors, which were placed as sentinels at entrances. The reason for our video, however, does not surround the religious importance or indeed cultural history of the Lama Su. Instead, we wish to explore the enormous inexplicable size and thus weight of these incredible ancient statues. How did an ancient people that, according to academia, existed within our own well-studied cycle of development, accomplish the movement and placement of such gigantic stone carvings? If we look at the efforts of Henry Lainard, for example, made within 1847, you soon realize that the mammoth scale and as yet unexplained undertaking, the placement of these masterfully decorated stones must have been. After discovering more than half a dozen pairs of these colossal statues, some depicting lions, some depicting bulls, often weighing up to 27 metric tons, Henry Lainard decided that he would attempt to bring two of these smaller artworks, weighing in at a mere 10 tons each, to England. However, he found that after an 18-month painstaking, torturous journey, which included several near disasters, just how incredible the placement of these monuments once were, he eventually succeeded in bringing them to a British museum. Although this involved loading them onto a wheeled cart, lowered with a complex system of pulleys and levers, operated by dozens of men, he initially tried to hook the cart up to a team of buffalo and have their brute natural strength haul the stones, although they refused to move. He then selected a reinforced cart for their transport, which required over 300 men to move it. This was soon realized to be far too hazardous, so he then wrestled with and opted for the decision to load them onto a barge. This required well over 600 goat skins and sheep skins just to keep it afloat. After eventually arriving in London, a custom-built ramp was constructed at great expense just to allow the crew of many hundreds of men to haul them up the steps and into the museum itself. An astonishing and clearly exhaustive exercise which clearly demonstrates the civilization capable for constructing and placing these statues in their original positions were clearly far more capable than our recent ancestors placed a mere century ago. This dramatic sequence of events is clear indication that the national museums involved in the funding and transport of such exhibits, even back in 1847, were more than aware of the astonishing feats these monuments were, yet are seemingly committed to a conspiracy, which we believed is severely limited in accurate chronological events. Although claimed as a Syrian, dating back as far as the 25th century BC, these monuments, we feel, were clearly reused by this culture, possibly due to their astonishing size. Who carved the Lamassu? How did they move statues weighing nearly 30 tauts? We feel that these monoliths were left by a lost, once highly capable, advanced civilization, and as such, we find them highly compelling. Bosda Cave, within modern-day Turkey, is unquestionably an astonishing place, an enormous cave system that many people simply assume is a natural formation, with select areas quarried out, subsequently used to build numerous ruins throughout the area. However, what many people have seemingly overlooked, and we presume funded academics have deliberately ignored, are the signatures left all over the stonework throughout the network of caverns, strongly indicating that this huge complex was once somehow hewn by ancient man. Also, and perhaps most intriguingly, is that this task was completed using a number of different advanced tools, whose marking, thanks to ours and others astute research, has also been found scarred upon many other ancient sites, some located far away from this enigmatic cave system. The stone, once quarried out to create this enormous cavern, subsequently located as having been used to create a number of remarkable precision-cut monuments, including a once existing wall, which surrounded an ancient site known as Hyron. Additionally, due to the realization of this quarried stone having been used in Hyron, in addition to our own previous research, we have successfully linked Basda to yet more ancient ruins, all dated to vastly different areas within history. Thanks to our channel's creator possessing a photographic memory, we have correlated undeniable characteristic similarities, connecting many of these ancient sites throughout the world. Firstly, the signatures left by advanced stone-cutting technologies, tool marks left upon the cave system's walls, scars upon the stonework, which are present at many other sites, Balback in Lebanon, Petra in Jordan, Yangshan quarry within China, and at least two rock-cut monuments within India, the roof of a precision-cut cave, and an unfinished temple known as Veduvankoyl. This crescent-shaped scarring, often of an overlapping fashion, we feel, is reminiscent of scars left by modern-day tunnel-boring equipment. Yet due to the lack of in-depth research surrounding such anomalies, with these tool marks, as far as we are aware, only receiving limited attention at Balback, and merely photographed at Yangshan, have begun to name such markings ourselves in an effort to categorize and identify such curiosities being discovered worldwide, with these now known to us as crescent cup and ring marks. The second form of scarring, found upon much of the cave's roof, now known to us as groove and ridge markings, are distinctly different in form and appearance to the crescent cup and ring marks. These rows of grooved scars, however, are identical to those found in plain sight upon the unfinished obelisk located within Aswan quarry, Egypt. A stone monument well over a thousand tons in weight, which has long been academically argued, has having been abandoned where it lay, due to a fault line discovered during the quarrying process. However, interestingly, others have presented strong evidence that this crack appeared later within history. A fellow alternative researcher, Chris Dunn, argues within his book, Advanced Technology in Ancient Egypt, that the crack happened later on in the obelisk's life, and that the monolith was abandoned before the fault appeared. Backing up his claim, he shows that details upon the monument were being engraved over the top of the location of the fault line, an undertaking that would have clearly been illogical. Although he does not put forward a postulation as to why this crack occurred, we believe it may have been due to a shift in the surrounding geography, more than likely a ground shifting earthquake, not only cracking the obelisk, but possibly due to, and accompanied by, a cataclysmic event which quite possibly caused the demise of the civilization, who were liberating the obelisk, thus leaving it unfinished. But I digress. Our focus is upon the scars left by enigmatic clearly advanced stone cutting tools, preserved with clarity upon the erosion-resistant granite of the obelisk. These exact markings also undeniably litter the ceiling of the Bosda Cave. Additionally, these groove and ridge marks are also found upon the megalithic, often polygonal stonework within Peru, at Cusco, the fortress of Sacsayhuaman, and Machu Picchu, to name but a few. The third set of signature scarring upon the cave stone walls links Bosda Cave to another, similarly gigantic, artificially created cave system. Known as Longyu Caves, located within China, once an undoubtedly immense excavation, yet the quarried stone from this undertaking has never been located.  However, thankfully, the quarried stone from the Bosda Cave systems, as mentioned, was utilized and located. However, the civilization responsible for shaping these quarried stones at Haran were unquestionably responsible for several other sites found around the world. YouTube channel New Earth first linking these curiously shaped stones to Nimad's fortress on Mount Hermann with Jarash in Jordan, with us continuing this trail of connecting ancient dots, thankfully due to the uniqueness of stonework. Let's compare the Nimrod fortress with this historic city in Jordan, which according to mainstream sources was conquered by the Romans and they built their typical Roman architecture, consisting of columns and so on on the top of the older ruins.  Now, those very same blocks, when they are in Balbek, they are telling us it's Roman.  In Bosnia, they are telling us they are whatever, 3 or more thousand years old and of course they are built by some obscure unknown tribe of which even the name they had to fabricate, enabling us to link the Royal Kurgan and Crimea to New Earth's discoveries and now to the ancient ruins of Haran in Turkey. Not only can we argue that this cave system was indeed man-made, but is the only site we know of that possesses such an array of these enigmatic stone-cutting technology scars, allowing us to successfully link it to at least 15 ancient sites around the world. The cave itself, Bosran, Haran, Balbek, Petra, Jarash, Yangshan, Longyu, Vetivankoyl, Malmala Param, Kusko, Saksehuaman and Machu Picchu, Nimrod's Fortress and the Royal Kurgan, possibly many others we are yet to recognize. In conclusion, the vast array of different as yet unidentified advanced stone-cutting equipment scars present within the cave, each leaving its own unique signature upon the stone. The shaping of these stones, unique to an unknown civilization's signature handiwork, found worldwide, used within an array of as yet unexplained ruins, academically claimed to be of vastly different ages and the work of vastly different cultures. We find it not only clear evidence of academic fallacy, but incredibly compelling.


Greetings and welcome to Math Help for Science Courses. In this lecture we are going to go through and talk about some of the different types of scientific calculators that are around and how to go about using those. So let's look at an example of one scientific calculator. And here is one that many of you may have seen before, a standard Texas Instruments calculator. And it works, a scientific calculator has more functions than a general calculator. An ordinary calculator has basic functions like addition, subtraction, multiplication, and division, which are also present on a scientific calculator. Sometimes a traditional calculator will have a square root key or some other basic functions. But what you note here is that there's a lot of other functions here, we have the trigonometric functions that we may use, we have different ways to do exponents here, here, and here. So we have a number of different ways and we also have logarithms here. So there's some other things that we may use in various science courses. Now there are traditional calculators which would be the example that we see here. However, there are also other calculators that you can use. If you don't have a scientific calculator, unless your instructor requires you to have one, you can often use an online calculator. And here is one example of that. And that is the website given here is web2.oCalc.com. So you can go there to see a free online calculator that you can use. And as we see with a traditional calculator, it does have the basic functions, addition, subtraction, multiplication, and division. And it also has a number of the other functions here, primarily those related to the trigonometric functions over here. Different values, different ways of doing exponents here, and again the logarithm is down here. So there are more and more functions as you get to more complicated calculators. But again, all of the same functions that you might use are here. And we can also look at the other things that people use. We had the traditional calculators we looked at, we had online calculators. You can also, most people now with a smartphone will also have calculators that are built in there. And here is an example of the scientific calculator built in to the iPhones. So you can use this. There are also a number of free apps that you can download for both Apple and Android devices that you can download that will also have similar functions. But this is one. And on the iPhone, for example, if you use your phone in the portrait mode holding it straight up and down, it will just give you the basic functions. It will only have essentially mostly the stuff over here. You can add, subtract, multiply, and divide. However, if you turn it sideways into landscape mode, then it actually turns into a scientific calculator. And you can then access, as we've looked at before, various trigonometric functions, various different ways to do exponents here, and different parts of logarithms over here. So those are all present. Now, for most science courses, you will need these. You will need to be able to enter numbers in these, be able to raise numbers to various powers or take various roots, and to use some of the trigonometric functions. And occasionally in courses, you may even use logarithms. Another one that you'll often use is the double E button here, which is the button for scientific notation. So when able to put the number into scientific notation, you would then press the number you want, and then the double E key, and then the power of 10. So for 5 times 10 to the second power, you would write that as, put that in as the 5. You'd press the double E key, and then press 2, and that would enter the same number. And what you will find is that equals 500, and your calculator will automatically convert that. If it's a small enough number, it will automatically do that conversion. Now, we've looked at a couple of different types of calculators here, and what you want to remember is that each of these is different. So there are some differences in how things are set up on these calculators, how they go about looking at various things. So we have, they're in different positions. So if we look at how things are set up on the iPhone calculator here, the trig functions are down at the bottom, and the exponentiation functions are up above them. However, on a Web 2.0 calc that I mentioned, it's done differently where the trigonometric functions are to the left, and then the exponentiations are in between. So how they're set up may be different, how they're used can be different as well. So in each of them, you can have a little bit different settings, and in the TI calculator, again, things are all a little bit different in terms of how things are set up. So let's look at some of the uses, and for this I'm going to use the Web 2.0 calculator that you want to look at, and one of the ways to use, one of the things we can do with that is that, of course, it's accessible to everybody. It's one that anyone can access because it doesn't require that you have a specific type of calculator or a specific type of phone, you can simply go to the Web site and use this scientific calculator. So what do we have on these? We have the basic math functions which are over here, addition, subtraction, multiplication, and division. So you can do those exactly the same. Powers and roots. So if we want to square a number, we can just put the number in and then press the X squared button, and that will give us the square. So if you put 5 in and press the X squared button, then you would get 25. If you want to do a square root, you can do the same thing, put in 25, press the square root button, and get the number 5 out. So those are some of the things that you can do. You can also do third powers and third roots, but in some cases you may need to do different powers. What if you wanted to find, for example, 5 to the 2.5 power? Well, there is no 2.5 button in there. What you'd use is this X to the Y. So you would put in the 5, then you would press the X to the Y button, and then you would press 2.5, and that would then take 5 and raise it to the 2.5 power. So you can do that. You can also do roots the same way. If you want to raise things to take the 2.5 root of something, you would push that key instead. So there are various ways to be able to do that, and sometimes in a calculation you'd need that. We use sometimes the trigonometric functions in various classes. Primarily sine, cosine, and tangent would be the most often used here. Others would be very rarely used in most basic science classes, but you may see situations to use these, or they're inverses. Now inverses can be accessed by pressing usually a second key. On some calculators it might be the inverse key. So there are various different things that you might have to push there, but that will then access and turn these into their inverse, turn the trigonometric functions into their inverse functions. So what you would see is if we were to push that second button, you would see this, and if you note how things have changed, a lot of it stayed exactly the same. We didn't have anything that changed here. The powers are still exactly the same. The logarithms are still exactly the same. But these have changed from sine to asine. So, and cosine, cos to a cosine. So they now are doing the inverses. And there are some cases where you need that function. You just have to push that second button, or sometimes the inverse button first. Now in some cases it will lock. In other cases it will not. And again you're going to have to experiment with it and discuss with your instructor the exact details of the specific calculator that you are using. There are also various constants that are embedded into these. You have the constant button here. And you will find when you start out, if we go back, that originally that shows the pi, which would be the most often used constant. However, if you have the second function enabled and you push that and then you would see this as the constant button. And if you actually push that on Web 2.0 calc, it will come up with a menu that will have dozens and dozens of different constants that may be used in various scientific situations. You can use that of course. You can also enter the numbers manually as well. Now one of the more important things that we do use here is to have numbers in scientific notation. So we want to be able to enter numbers in scientific notation and this again does vary depending on the type of the calculator that you use. I showed you an example previously of how to do this on the iPhone calculator using the double E button to enter it. You can also use the EXP button on some calculators which will do the same thing. So again, 5 times 10 to the second, you would do 5 double E2 on the iPhone calculator. You might do 5 EXP2. Again, these are the buttons that you would push on other calculators that have an EXP button. How about for the Web 2.0 calc button? Well, let's look at how we would do that. Well, in this case you would use the E button. If you look at this little E up here, it is used then for the scientific notation button. And you have to be very careful with what you use when you're trying to enter numbers in scientific notation. It's often wanted to use the 10 to the X key here and just to multiply. So what you often people want to do is write 2.5 times, hit multiplication, and then 10 to the third power, for example. That does not work out well because it will cause problems with the correct order of operations. It sees that, and if we have a number as 2.5 times 10 to the third, it sees that as 2 numbers, so you're multiplying. Then if we try to divide that by another scientific notation, or take, you know, 15 divided by this, it will divide it by the first number and then multiply it by the second, which is not correct. In this case you would have to put this in parentheses. So let me show you the easier way to do that here, and that is using the E key. And you use that just like you use the double E key on the iPhone or the EXP key on other calculators. And all you have to do is if you want to write a number, you would write 2.5, press the E key, and then you're exponent. And that would automatically do the calculation in the scientific notation, and it will look at that as a single number. So you don't have to worry about keeping track of all the extra parentheses you would need if you wanted to use the multiplication key. So I strongly discourage using the multiplication key when entering scientific notation. It's not the way it's supposed to be done. So let's finish up here with a little bit of what we've covered. First of all, we talked about there are a wide variety of scientific calculators. They're all different. And you're going to need some of those extra functions. The scientific calculators have many functions in addition to the basic math, adding, subtracting, multiplying, and dividing that you are used to. You would use these in science classes, but you'll also use many of these other functions to make things a lot easier. And as I mentioned, each calculator can be very, very different. You're going to have to look at the instructions and perhaps talk to your instructor to find out the exact details of how to do a specific calculation on your calculator. So that concludes our discussion on using a scientific calculator. We'll be back again next time for another topic, another math topic in science courses. So until then, have a great day, everyone, and I will see you in class.


In this video, we'll talk about Ease's interface and we'll work through our first example problem, which will consist of a couple of simple equations. When you open Ease for the first time, you'll be presented with a big primary window and then a single secondary window. I'm going to refer to these as secondary windows. Seems like good consistent nomenclature. Unlike, say, Photoshop, your individual files do not appear as secondary windows. If you want to have multiple files open in Ease at the same time and you don't want them to interact with each other, they need to actually be entirely separate instances of Ease. These secondary windows are all belonging to this single file and all of your data input and output will come through these secondary windows. So you have different secondary windows for different purposes. The equations window is where you'll be entering your equations, which, oddly enough, you do a lot in the engineering equation solver software. But you can access the other windows by clicking on this Windows button up in the title bar. The equations window is here. If you close it at any point, you can access the window again by clicking on that button. The other one that you'll use a lot when you're first starting with Ease is the solutions window. So the solution window is where your solutions are presented. The other windows become more useful when you get into some of the more complex features of Ease. For example, the plot window is where you will plot data. The tables window is where you input and output tabular data. The report window is where you might format a report given the information that you calculated. The Windows button is just one of many buttons up here on the title bar, and most of them are pretty straightforward. The file button contains commands for opening and saving your files and libraries. That's where you would generate a report if you wanted to or if you wanted to print your solved solution or your report. The edit button contains copy and paste functions and, most importantly, the undo and redo options. The search button contains commands for finding and replacing. The options button is a little bit more complex. That's where you have commands to set your guest values and bounds for your variables. That's where you would select the unit system. That's where you get information in and out of the user-supplied library functions. You can set the program preferences, etc. The calculate button contains the commands to check, format, and solve your equation set. The commands are also there to check the unit consistency of your equations and update your guest values if you want. The tables button is where you would access tabular data. So there are two big tables that you might use in Ease. There are parametric tables and there are lookup tables. The parametric table is pretty similar to a spreadsheet. You can set your equations to calculate variables based on changing of some selected variables. So if you were working on a power cycle, for example, and you wanted to calculate a thermal efficiency for several different input temperatures, you would use a parametric table for that. So you would select the thermal efficiency as one of your outputs in the parametric table, and then you would select the ambient temperature as your input in the parametric table, and then you could have the parametric table actually run all of the equations and calculate a new thermal efficiency for each one of the values that you input in the parametric table. If you wanted to plot, say, how one variable affected other variables, so if you wanted to generate a plot of that thermal efficiency versus input temperature, you would do that by creating a parametric table and then generating a plot from the parametric table. The lookup table is useful for storing user-supplied data that you want to interpolate between. So if you were using a custom material and you had a lot of material properties and you wanted to generate information from those tables, you would enter that data as a lookup table. The Plots button provides commands to prepare a new plot of data from the tables, and you can also access some of the plots that you've already created. Most importantly, in my opinion here, there's also a property plot, which unlike a regular plot, can show your data relative to information about the property or information about the material. So if you wanted to plot thermodynamic state points relative to saturation lines, you would do that within a property plot here. The Windows button we've already talked about, that's how you access the different sub or secondary windows, whatever I decided to call that. The Plots button contains a lot of actually extremely useful information. You can access the help index, which is very, very useful. If at any point you're trying to figure out how to do something in ease and you can't find one of my videos to explain it to you, you might search for it in the help index. So for example, if you were trying to remember how to solve a differential equation, you could open up the help index and then just type in differential equation. Now ease has a nice explanation of how to go about doing that and what the different variables mean in the different functions. Help index is very useful. There are also commands here to open up YouTube tutorials that the manufacturer of the software created and posted on YouTube. You can also get to their website directly from a button here. If you've purchased the Mastering Ease book, you can access your book directly from this interface, etc. The Examples button is also extremely useful, especially when you're first starting out, because this contains just a whole bunch of example problems for different situations. Each one of these buttons will actually open up another window where you can select an example problem. So if you were trying to figure out how to run differential equations, if you click on differential equations, you open up a window with all of these example problems. Each one of these is a full-fledged ease problem. So if you clicked on it, it would open up that window. So the example problems are also very useful.  Also note that sometimes the options available in these drop-down menus can change based on which version of the software you're running. So if you're following along with one of my videos and you don't see a button that I clicked on, it's probably because you're running a different version of ease. Again, I'm running the academic professional version. So back to the equations window. You type in equations in the equations window just like you would in a text editor. For example, if I was trying to solve two equations with two unknowns, let's say the first equation was x squared plus y is equal to 16, and x minus y was 7, let's say. I type those in like this. Then when I want to solve the equations, I click on the solve button. So you can access the solve button by going up to calculate and then solve. A lot of these functions within these drop-down menus are also presented in the toolbar up here, but you always have more options available to you by going up to the actual drop-down menu. So from the toolbar, we could select the solve button or the check equations button or the min-max functions here, but if we actually went up to calculate, we have those options plus a lot more. So when you're learning how to use ease, I think it's better to get used to these drop-down menus, and then you can think of the toolbar up here as shortcuts rather than your options, if that makes any sort of sense. But anyway, we have our two equations, two unknowns. The best procedure here would be to click on this check mark first. The check mark will check your equations and it will tell you if you have any typos, etc. before it commits to actually solving the program. Again, when ease solves, which I can do by clicking on the solve button, it actually guesses values for the unknown variables and then it proceeds to guess and check until it decides that what it guessed was the correct answer. And the way that it decides whether or not its answer is correct is based on residuals, which is the difference between the different guess values. So once it gets to a point where it's not changing its guess values very much, a threshold that you can control, then that is how it decides that that answer is correct. So that can take a long time if you're running a lot of equations on a slower machine. But here I have two equations with two unknowns and that took 0.0 seconds. So the answer to my two equations problem was that x is equal to 4.322 and y is equal to negative 2.678. You'll notice that I typed in x squared by typing x and then a carat and then the number 2. The carat represents the exponent operator in ease and it's just one of many operators or many formatting rules that ease has for entering equations. So I'm going to dump a whole bunch of formatting rules on you right now, at least the ones that I'm familiar with, so prepare yourself. First up, upper and lower case letters are not distinguished. Ease will optionally change the case of all variables to match the manner in which they first appear. So for example, if you were running a problem and you had both volume and specific volume or say volume and velocity, you might be tempted to type those in with a capital V and a lower case V. So you could say my volume is 10 cubic meters and my velocity is 3 meters per second. If you type them in like this, ease thinks that those are the same variable. It does not distinguish between lower case and capital letters. If I were to try to solve this right now, ease would throw up an error. That error would be because I overdefined V. I told that V was 10 and I also told that V was 3. I'd have to come up with a way to distinguish the variable names from each other. But variable names don't have to just be a single letter. They can actually be up to 30 letters. So I could type in the word volume and have that be my variable for volume or I could type in the word velocity for my velocity variable. Two, blank lines and spaces are ignored by ease. So you'll notice that I typed in my two equations with this blank line between them. That was just a way that I kept my two equations separate. It's kind of a personal organization thing. The blank line is ignored, so I could have as many blank lines as I want and ease would see this as exactly the same as earlier. It still sees it as two equations. I could also use spaces to keep my equations organized. I could say increase the indent here if I wanted to. I personally use that for hierarchical equations. For example, if I had the same equations for different state points, I might say state one and then have my equations for state one and then I might have state two and then have equations for state two like this. I think that it's an easy way to keep things organized. And speaking of keeping things organized, you can use comments and ease. And comments work the exact same way as they do in any programming language. And in ease, they are denoted by either quotation marks or curly brackets. And comments are ignored by ease. They are intended to present information to humans. So I could put a comment in above my first equation and say, this is the first equation. And I could put in a comment above my second equation that says, this is the second equation. And ease will ignore those two lines because they are in quotation marks. So if I were to run this now, you'll notice that ease changes the color of those two lines. It color codes information in your equations window. If at any point you want to trigger the color coding, you can actually do that by just checking the equations. You don't actually have to click the solve button. But if you wanted your comment to span multiple lines, you just place the start and end comment operators, denoters. You place the symbols on separate lines. So in this case, this is the second equation comment actually spans these five lines. So that can be useful for entering just a whole bunch of information, like say a problem statement. But it's also useful for adding in extra information to your comments. For example, I use equations, excuse me, equation marks like this, equation signs as a means of keeping my file organized. So if I wanted to clearly partition off sections of my equations window, if I wrap them with equation symbols like this, that's an easy way to do that. It just sort of stands out. And again, because they're within quotation marks, ease ignores them. I personally will be using the curly brackets in my examples a lot more than I will the quotation marks. And my logic on that is a little odd. I think it probably only makes sense in my brain. But the quotation marks are the same symbol. The same symbol opens and closes the comment. So think of a situation where I had a lot of comments. So I had these two comments and then maybe a third comment at the end that said, this is the end of the equations. So this is the end of the equations. Well, let's say that I had forgotten this quotation mark. Now ease still sees this as three comments, but it starts the comment with the first quotation mark it sees, and then it ends the comment with the next quotation mark it sees. So if I had forgotten this quotation mark, ease now sees this as the first comment and this as the second comment. That can be a little bit difficult to debug because now ease sees this as a second equation and it thinks there's a variable this and a variable is and a variable the and a variable second and it doesn't see any operators between them, so it doesn't know what to do. If I were to hit solve now, it would probably panic. Yes. Then it sees this last quotation mark as starting a third comment, which is never closed. So by using curly brackets instead of quotation marks, you have a different symbol to start the comment and a different symbol to end the comment. So in the event that you forget one of your symbols, it's a really convenient way of keeping track of them, at least in my opinion. Another shortcut for using comments is if you highlight whatever region you want to declare a comment or to uncomment, you can right click and activate or deactivate the comment symbols here. That's a very convenient way of temporarily disabling an equation when you're working through a file or if you want to switch back and forth between two equations. So let's go back to quotation marks and remove this line. Then we'll proceed on to number four. Variable names must start with a letter and can consist of any keyboard characters except for those symbols which have some other meaning within ease. So that shortlist is these characters. You cannot use any of those characters in your variable name because that goes back to how ease ignores spaces. For example, I could have typed in my second equation by typing in x minus y equals seven with no spaces. So you might think of this as a variable if you were trying to use the minus and equal signs in part of your variable name, but ease would parse that out as an equation. So you can't use any symbols that have some other meaning to ease. Number five, equations can be as long as you want. If you want the equation to actually span multiple lines, you would separate the lines with a semicolon. Number six, the caret symbol is how you denote an exponent. So like I said, caret two here, ease will treat that as x squared. If I typed e to the fifth, that would be, or x to the fifth, that would be parsed out as x raised to the fifth power. If I were to put parentheses here, I can group other operations within that exponent so I could say, for example, five plus y. And now that'll be parsed as x raised to the five plus y power. If I wanted to have say, x to the k minus one over k, I would have to use multiple parentheses to do that. If you want, you can actually use two asterisks, x to y, asterisks. You can use two asterisks instead of the caret symbol if you prefer. Ease will still use that as an exponent operator. Number seven, the underscore symbol is used to indicate a subscript. So if I were to type, say, m underscore one is equal to five. Ease will parse that as m with a subscript one. You can make that be multiple symbols if you want. Say, m the first. And if you wanted to have a common, or rather a comma up here in your subscript, you would use another underscore for that. So I could say the specific net work out like this. Ease would see that as a w with a subscript and that subscript is net comma out. The underscore is also used to modify variables. There are special variable modifications that are listed in their entirety in the ease manual. I use dot and bar a lot. So x underscore dot will appear as an x with a dot above it. X underscore bar will appear as x with a horizontal line above it. Like this. So if I wanted to write the net power output, I could do that by saying capital W dot net out. So it sees w underscore dot and it'll use a w with a dot above it for that. And the next underscore triggers the subscript and then the third underscore is a comma within the subscript. Like this. So net power output. You can also include other symbols within the subscript if you like. So if you wanted to have a variable for the heat transfer in occurring between two and three, you could type that like that. So it would appear as q in comma to arrow three. Next up, Greek letters. Greek letters are denoted in ease by actually typing the name of the Greek letter. The downside here is you need to know how to spell your Greek letters or rather spell the word that we use to represent the Greek letter. So for example, if you were working through a problem and you had a density appear, you would probably denote that with a Greek letter row. So you would make that appear in ease by actually typing the word row. So if I typed row equals five, that would appear as the Greek letter row. And ease differentiates lowercase Greek letters and capital Greek letters with lowercase and uppercase words. So if I typed a lowercase rho, that would appear as the lowercase Greek letter row. If I typed capital rho, ease would see that as the uppercase Greek letter, which apparently looks very similar. Okay, that's boring. Let's go with a fancier one. Delta. Let's say delta. A lowercase delta will appear as that thing that looks kind of like a two. Yeah, that looks kind of like a two, right guys? And if I were to type the word delta in uppercase, that would appear as a triangle. If you want to have more than one symbol, rather a Greek letter and then some other symbols appear in your variable name, you don't put spaces between them because that would separate the variables. You just continue the name of the variable. So for example, let's say that I had m underscore one is equal to two and m underscore two is equal to five. And I wanted to show the difference in my mass. I would type delta and then m immediately after it. And I could denote that as m two minus m one. So ease will show delta and then an m immediately after it. And again, because that delta is written in uppercase letters, ease will use the uppercase delta for that symbol. But just like with the other characters, if I were to type delta equals five and uppercase delta equals two, ease will see this as over defining the same variable because the lowercase and uppercase variable are not distinguished from one another. I could combine these formatting rules in my equations if I wanted to. For example, if I were to type eta underscore th, that would appear as the eta symbol with a subscript th. Or if I wanted to have say eta underscore alpha, that would appear as the Greek letter eta with a subscript of the Greek letter alpha. The last thing I want to talk about in the formatting rules is that the order of the equations and the order of the variables does not matter to ease. So I could put this equation first and this equation second if I wanted to. It makes no difference to ease. It solves them all simultaneously. Also the order of the variables does not matter. So I could write ease minus y, or ease minus y. X minus y is equal to seven. I could just as well write x equals seven plus y. And that will end up being the exact same thing to ease. The one exception to that is when you're typing equations, if you had something appear maybe like this. Let's say I could write this equation as being x is equal to seven over y, or x times y is equal to seven. Well, remember that the way ease solves for variables is to guess values and then guess and check until it decides that what it guessed was correct. Here, if I happen to begin a situation where ease guessed a value of zero for y, it would quit and have an error here. So when you have variables appear in a denominator, that can sometimes be dangerous, or other situations where you run into a mathematical uncertainty or impossibility. So if I had x times y, that is the same way of writing the equation, but this is a little safer, because if ease guessed a value of zero for y, then it would be able to continue its operation. That's not something you probably need to worry about often, but that'll show up when you least expect it. The best practice is to type denominators as a numerator on the other side of the equation, if that makes any sort of sense whatsoever. Another tool that's very useful when you're learning the formatting rules is the formatted equations window. So if I had gone back to my example of x squared plus y's, no, this would be x minus y. So if I had x minus y is equal to seven, if I open up the formatted equations window, that will show the equations with the formatting rules applied, like this. So it shows x to asterisks is two x with a superscript of two. That's a very convenient way to get, I guess, a better view of your equations. It makes it easier to see your relationships between your equations. When you're running a program that has a lot of equations in it, it can just end up turning into a giant wall of text. So the formatted equations window is presented in a more aesthetically pleasing way that's also more useful. So let me give it something complicated here. Say I had a third equation that was z is equal to the x minus one over y minus one. Then the formatted equations window will show that as separate lines. So I could also wrap these in more parentheses and say raise to the k minus one over k. Now you see how these symbols start to blur together. If I go up to formatted equations, it's shown in a slightly more readable way. So that concludes this video. Next time on Ease Tutorials, we'll talk about a more complex example problem. We'll get into an actual realistic problem, say something involving the ideal gas law, and we will incorporate units into our equations. Stay tuned.


addition of Islamabad today on Think Tech Hawaii, I'm your host, Council Representative, and today we're going to be discussing the significance of technology in impacting social change when we talk about education in general. Now we all know that the technological revolution is taking place all across the world. You do have artificial intelligence, you have chat PPPs, you also have hybrid warfare. But what kind of impact does technology actually have on social change? When we talk about social change, education is one of the fundamental pillars to try and make sure that next generation can actually create it. I have with me CEO of Lamprow Mellon, Ms. Sababrafi. Sababrafi, thank you so much for joining me on the show. Thank you so much for having me. All right, so let's start off with the basic question here. You've worked all across the world, you've worked with education, you try to make sure that a meaningful impact can actually be realized as far as primary education is concerned. What in your view is the role that technology can play in building a generation and building up educational infrastructure all across the world? I think the best thing that the technology is doing right now is that we're creating with all the artificial intelligence platforms, we're creating a huge democratization of access to information. So that is a fundamentally huge opportunity. Second thing that it does is that over years as new and new information was being generated, it was becoming harder and harder for students to keep up with all the knowledge that was being created or facts that were being being created. And as we were amassing all this information around us, it was education essentially became regurgitation of facts or knowing facts. It moved away from its fundamental purpose, which was to look at the facts, be able to reflect on them, expound on an idea, experiment with it and create new knowledge. So with all the technology, the facts or knowledge is now equally accessible to everybody. And that gives us a whole new opportunity in the field of education to take it to the next level and take it back to the basics of creating new knowledge and creating things that will take knowledge and education and the information economy to the next level. So for me, technology is a great equalizer. Technology is also a platform to create new knowledge, but we have to be aware of the pitfalls and make sure that our education system, especially in countries like Pakistan, is keeping abreast of the changes and we prepare our students across the globe to come to terms with the new challenge. So there is a huge opportunity, but there's also a huge challenge. And only those students or those nations will come out ahead who are willing to take the challenge head on and capitalize on it rather than become a victim of the digital divide as we speak. Okay, so when we talk about you mentioned the developing world and obviously the developing world does encounter fundamental challenges, whether it's structural challenges, you talk about poverty, you talk about alienation, you talk about lack of employment, you also talk about soaring inflation rates. And that really has a great impact on the resource space that governments can actually use and utilize to try and make public policy. When you take a look at these factors in mind, how do you think you can navigate through the landscape of the developing world given that there are challenges and you also need to make meaningful change as far as technology is concerned in the educational context? First of all, I would like to highlight that finding a job is not a fundamental requirement for education because historically education is something that creates the whole landscape of how we live our lives. And philosophy, which is the mother of all sciences of the mother of all knowledge is not necessarily a means to gain employment. That being said, let me come back to something that I said earlier and expand on that idea a little. When we say that we have all these chat deputies and AI platforms that are creating this opportunity for democratization of education, one thing that the third world in particular needs to watch out for is that as these platforms are being developed, they claim to be net sum of all knowledge on a certain date. But that net sum of knowledge is being derived of a basis which are on Western. The knowledge set from where all these information is being derived does not include my narrative, does not include my history, does not take into account all the libraries that may exist in Sanskrit, Urdu, Farsi, Latin. So that is one thing that we need to make sure that as all these platforms are being developed, our narrative, our knowledge is either a part of it or we should have our own platforms so that the cumulative knowledge when somebody starts gaining, you know, gaining access to knowledge, our story is not so. To give you an example, if you were to go to chat, for example, today, when you put a question about crusades, or you put a question about 1857, you will get a certain narrative. They may be a small note at the end that says the other narrative as well. But by and large, for us to make sure that our narrative is also reflected in the new information made, we need to work in the third world actively on it proactively on it. Certainly in nations like Africa, there are a lot of knowledge is just knowledge. Likewise, music in Pakistan, that's also just knowledge. So again, we need to make sure that our narrative, our set of knowledge is somehow built into all, into the ways people access knowledge. Right now, libraries are the fund, you know, for the last few decades, that has become less important, but library, by and large, remained that access point. Now, there will be other access points. Technology is putting that information on my fingertips on a cell phone. And people may not spend time to go to the libraries and further research on those ideas. So the way we archive our history, the way we archive our news, the way we make sure that our set of knowledge becomes part of the information economy, that is an important part, a point to ponder for, in particular, for the third world. And especially those economies in particular African nations, where documentation is not our strong point. Right, so let's just center this on maybe Pakistan for that matter. I mean, when you talk about Pakistan, what kind of challenges did you actually encounter when you actually reached policymakers? Because obviously, if you take a look at your career, a significant portion of it is to try and make sure that you can leverage technology to try and make meaningful impact on primary education in Pakistan for that matter. So was there any resistance that you encountered? And if there was resistance, what kind of resistance was it? I think the fundamental resistance comes from the fact that our policymakers are, pardon my saying so, are maybe not knowledgeable enough. They're not knowledgeable enough, they lack the vision. And they may be mired so much into day to day affairs. See, education is something that is part of nation building. And I would like to highlight that whatever problems we have today are because of lack of it. And what is the solution we may devise will be when we make it accessible to our population. Pakistan remains from the bottom, number two, in terms of our school children. And those who are educated are either underemployed or unemployed. Okay, so we have to first recognize our policymakers, unfortunately, when they come out in public forums or even in private forums, because they are worried about election cycles and because there's a fundamental instability in the political cycle. So even your election term is not fully served ever. So people would like to pretend and would like to say that we've done a lot of things. In reality, we haven't. We're still throwing away a lot of our money on teacher training, in which we try to teach them a pedagogy of which they have no knowledge or no capability to go back to apply. So we in Pakistan are still grappling with the fundamentals of education. We are still living with the left overs of a colonized system of education, which was wrote memory-based, which was based off of selective study. Even whatever our curriculum is outdated in primary school, pre-K to 12th grade, measurably on all indices, Pakistan's education system is 80 years behind the first one. Private schools may be 35 to 50 years, but by and large, we are really, really behind the curve in terms of how and what children are taught across the globe, in particular the first one. So if that is the delta, without even articulating what the issue is and failing to form a clear policy, we are not going to go anywhere. Now the way the education field is changing so fast, the world has moved to inverted education models, and we still haven't perfected the basic one. So to me, the basic difficulty is to even explain to the policymakers how far behind we are, because they see that as a statement on performance. And it is not politically exigent to recognize the failure or to articulate the failure, because I'd like to stand up on a podium as a politician and say, I did this, I did this, I did this. In reality, we have done next to nothing, in particular Punjab, which used to be a little bit ahead previously, with the introduction of the single national curriculum, we are going to fall behind. And nobody is willing to talk about it. Nobody is willing to talk about it. Under the ambit of whatever is called single national curriculum, we have pushed back Punjab's education system by at least two decades. And so rather than catching up, we're falling behind. Take an example, how many hours do kids spend in a school in a first world environment? 8 o'clock in the morning to 3 o'clock. Yeah, 8 o'clock in the morning, yeah. We keep our kids in school till 1. So already we're not even covering the basic curriculum. Now you add to it the, the owners of Nazra. Literally what we have done is that we've made the yellow schools, as we call them, the Pila school, is the public system. We've literally turned our Pila school into Madrasas. And rather, and it took us decades to go over the hump and try to mainstream the Madrasas. But the single national curriculum, we've pushed it back. People have to lie. Even, you know, good private schools are struggling. They have to lie and say, we're following it. In reality, we can't. We simply cannot. It is but the criminal to charge people money for what is being taught under the essence. So to be very honest, that was one thing. Another thing that they did is that they made the medium of instruction Urdu, which again was a step back. Either we should have had the political will and the courage because what is the nag? I understand that there are a lot of studies which talk about that teaching kids in their mother tongue enhances the learning outcomes. Guaranteed and agreed and agreed. But then as when we say my mother tongue, does my mother tongue have enough information in the libraries? Do we have enough research material published in our language? I may become an engineer and I will not be able to offer anything for IEEE simply because I would not be able to access all the research material that is out there. Nations that have taken it upon themselves to make their national language. The language of instruction have also had the political will and their financial bear with all of converting all information in libraries into the mother tongue and making it accessible to their students. So their students are not left behind in in an information age where new information is being generated. We still haven't translated all the data there or the knowledge that we have in the libraries right now. Forget about translating it live when new information comes out every every year. So our kids would be left behind in all of it if we do not have the political will or courage to implement the national language in a way that it fulfills all the requirements of language as we and you know we talked about early about employability. Yeah well if you're so to be very honest if our kid is not relevant to the 21st century he may be educated in language A, B, C or D that language has to be the lingua franca of most people in the world for it to be for them to be relevant. So limiting people's access to language may make it easier for us politically to sell narratives but it will not make them productive citizens of the world. Alright so let's come to Africa now we can talk about because you've dealt a lot with the developing world. Africa has the toxic history of colonial history and history over there I mean of many African students and many African institutions would argue that history over there is written by the conqueror not the conqueror. So when you talk about the colonial history that many developing societies have actually gone through how difficult is the challenge to try and make sure that technology can be leveraged to try and indigenize the system or trying to make sure that the system responds to indigenization given the colonial history that actually exists in many African states. That is a problem that that we talked about for all of us. You know if you think about it when we formed the Aligarh College the literature that was translated was mostly the one that was palatable to the colonizer's narrative. So the bulk of your history or my history still remains in Persian and Arabic language even that has not been translated and Bindi made Urdu as the language of you know as a medium of instruction we did not create enough new material in that language. Now Africa's problem is a step further away because the traditional African way of teaching was just knowledge that has never been documented. So we face one set of problems which is a huge set of problems because our language of instruction or our language Urdu that we speak does does not have enough research material, enough political thought, enough philosophical thought in it. But African problem is far more complex because their history, their narrative, their knowledge has not even been documented in their own language. So their problem is far more and when we talk about you know to be very honest if education is about regurgitation of facts then you will have a problem with colonization and education is enlightenment of mind, your capability to reflect a set of facts, your capability to reflect on a set of facts presented to you. That itself will clear out the problem of colonization. So give me an example when I was young one of the nuns at my school she taught me because she was Irish and we were being taught let's say church history. Now when we read church history and we read British history you will see the same set of facts being presented in two different ways. When you study park studies and you do British history again you see facts same set of facts being explained in two different ways. So at an early age we were taught that truth is somewhere in between and you know you could read French history and English history. So what you can develop is a good reading habit which is a good research etiquette don't take one set of facts and take that as if it's a word of God it's not. If you all understand so maybe it is how we and in the new information age where chat gpt's are available where information is available reading multiple set of facts and driving your own conclusion and having a good research etiquette having a good reflection etiquette having a good way to come to your own conclusion is something that so it's the way we teach the colonizer may have left a legacy but how we teach will undo that legacy and that is an important part that all third world Africa, South Asia, China everybody included we need to deal with it. US was able to undo it I mean US itself was a colonized nation but as they went on their education system they made their education which is reflection based. Sometimes a lot of people in Pakistan have this wrong impression that maybe the US education system is not rigorous and maybe it's not rigorous from the point of view that they don't load you up with a lot of homework but they load you up with a lot they load you up with a lot of way to come to independent decision. So to me education is only education if it gives me the etiquette of obtaining facts obtaining multiple threads of facts being able to experiment with them being able to to think about them to reflect on them and then come up with an idea I always like to give an example that suppose if education was just regurgitation of facts if the apple fell from the from the tree Newton would have said well that's how it all this is. It is his capability to reflect which gave birth to the concept of gravity likewise Archimedes going into a bathtub if you were to just not have the habit of reflection you would always just say yeah that's how it is you go in a bathtub and water is displaced it was only his capability to reflect on it that he could he was able to solve. So education is about critical thinking education is fundamentally has to be about critical thinking about giving kids and adults whoever is getting that education the etiquette for authentication and verification of facts the capability to reflect on them and create new set of knowledge minus that education is not education it is basically the same as going to a library and just getting or going to a chat gpt platform and getting a set of facts getting a set of facts and knowing what to do with them are two different things and until an endless education goes back what is the socratic way of teaching the father of education as we know today only taught kids how to ask good questions and in our way of teaching today we teach kids how to answer questions not to have new answers and so that's an important part. Absolutely we talk about critical thinking and reflections obviously important to critically analyze societies as well when we talk about societies in general in developing worlds female literacy rates tend to be you know they're pretty abysmal as compared to you know their bell count. What what roles can technology play in trying to make sure that they can bridge the gap as far as female education is concerned you mentioned high school dropout rates in Pakistan and elsewhere as well and you know we ranked the second worst as far as that is concerned what about female illiteracy and women's inability to actually get access to quality education how can technology aid in that regard? You know surprisingly in Pakistan you see a lot more women in universities and colleges now and there there is a renewed focus on making sure women are educated but there may also be a policy by the way Hamza because a lot of times you know in my work in Africa I realized that as outside donors we focus so much on women education that we forget about local law so for example in Africa and and I'm not trivializing the thing will come back to the real issue of female literacy and why it is important for empowerment but you know sometimes a little isolated pockets of problems exist in the following way. In African nations and some African nations there is a bright man so men and young kids able-bodied young kids write about when they hit puberty they are pulled out to work on the fields lot more than women because women with a some degree or you know maybe even high school will fetch better bride money so her brothers can get better brides right so the systems work in reverse and likewise in Pakistan I see the problem that girls go to colleges or schools simply to get better brishdas honestly that is sometimes and you will see a lot of girls do medical college you will see a lot of girls go through engineering colleges you will see them go through so many different fields but you don't see them reflected in the same way as they are in colleges in the workplace primarily because the moment they get married they essentially lose interest in using that knowledge and because in Pakistan college education is subsidized by the government I see that as a huge disservice to the nation that we take public money and invest it on individuals who do not wish to be part of the economy so there has to be a way in policy making to enforce participation in workforce in the same numbers as we see in colleges and universities at least for publicly funded programs rest you and I cannot make the social change that being said the main problem still remains for women empowerment in neighboring nations and in villages where women are almost forbidden to to go to college in Afghanistan as we speak women are not allowed to work women yes the latest regime I mean when you talk about the Taliban they have a very very you know ambivalent attitude towards women going to school so that's again a challenge even that is coming at the official level yes and the sad part is that as Pakistan's economy continues not to do that well people have started even quoting Afghanistan as a nation that is seem to be doing better than Pakistan we emulate success so a lot of people do say regressive things about women education and quote Taliban as an example so you know some of the negative impact of woke movement in Pakistan have been that they've worked for disadvantage of women empowerment as opposed to true empowerment which we felt a few years ago maybe we were headed that way so and you cannot take 50% of the population and not keep them educated but what type of education that is important if it is education to get a job for boys and to get hand in marriage for women then we're focusing on the wrong end of the problem so that to me also remains a problem for at least Pakistan and some other South Asian countries nations that have overcome that problem now that those are the ones that we should emulate when you see countries like China that have actually moved the poverty needle measurably measurably in just two decades 200 million people in two decades that's a lot of people you do see that those are nations that do not discriminate that do not and I cannot say that China was any less misogynistic in the 40s and they have overcome all there and it was a very patriarchial society and yet they have overcome poverty only after overcoming these attitudes towards women and towards patriarchial systems so if we have to emulate we should look at these examples and make sure that women when they do get educated they're also as much a part of the economic milieu as they are of the education system absolutely that's a lot of faith thank you so much for joining on the show thank you so that's all that we have from Islamabad today on things like Hawaii a very enlightening discussion that we have at this point in time for further updates you can follow us on our social media pages until next time take care


I mean, it's like, that's like only like an inch difference. And this was like, two inches different, right? But that's because the scale is different. You have to know what the scale means, you know, on the left hand side. So that's another kind of thing that could happen. If I was to another one, if I insert another one and make another histogram and we'll like, we'll pull this one down. And pulling it down, okay. And so now, oh, I didn't mean to undo, undo. So now let's get rid of the title on this one and let's click on this side again and let's go over here and say, if we make the minimum, let's say we start the minimum at like 10, you know, so now, right? So now it started at 10. So now these, you know, these, these ones down here are kind of been wiped out. That would be somewhat of an unusual, that looks manipulative, right? To do, that looks a little bit funny unless they were really tall type of ones, right? So then, but again, you could see how that of course would give a different feel than this one, right? You're like, you know, there. So now let's try something where they, we remove the outliers. So let's add another one. Let's select the data again, select the data. And then I'm gonna scroll down before I insert. So hopefully it'll insert kind of down here. And then I'm gonna go to insert. Well, I still got the data selected, but I'm scroll down, histogram, insert and boom. All right, so now let's say, let's say that I go to this bucket size, but I wanna get rid of these outliers, right? That's another thing that might be useful to do, but it also might distort the data a bit, right? Because the outliers, you know, could skew the data. We'll talk more about it kind of later, but it could, but it also is somewhat misrepresenting the data to some degree as well, because they're outliers, that's not the norm. So let's go into the information on the right for this brackets, and I'm gonna leave. Well, we could go from automatic to like, let's say we wanted it at like 2000 as the separation. So that's a pretty decent separation. So you're like, all right, that looks good, but maybe these are kind of messing it up on the outside and kind of making my graph look a little messy. So we could say, well, what if I, well not here, what if I go to my overflow bin, and I say that every, so it's currently on auto. If I make everything that's over like, I'm gonna bring it in here like 77,000, 77,000, then it kind of packs it together, right? So now you've got this, all the stuff that was way on the side is kind of packed in. It's kind of nice to on one side, because now I've got a, now I don't have this data with all these empty buckets in it. But at the same time, it's a little bit misrepresentative because you're like, well, how outside were those outliers, right? And then if I click on this one, the other side, this one's an outlier on this end, let's bring it into like, I don't know, like 63,000, right? So we'll say this one, 63,000. So now you've got everything over 63,000. So you notice that kind of cleans up the data because you're like, yeah, those are outliers. And I just packed them in so that you can actually read the bucket size, which makes sense. But it also distorts a little bit the look and feel of the outliers. So you can see how even when you're trying to be as honest as possible, when you're choosing the bucket size, it can be difficult. And when you're dealing with people who you know have an agenda, meaning they're trying to argue for a particular case, you know that going into it, then you're gonna have to be a little bit skeptical as to how they're gonna present the data, right? So then you gotta be like, well, you know, why did they choose to present the data in this way? Are they really presenting the data accurately? Are they giving you multiple pictures of the data?  So these are, and this is why again, what you really would like to do is say, I would like to get a look at the actual data and do some of this testing on my own so I can make my own representations of the data and get an accurate idea of what is being said here by it.