Let's get into Epicurean physics. And what I've got here is a bare outline with hardly any references of the main points I want to make. So as usual, interrupt me at any point in time if you want to ask a question about what I'm saying, or even if you just want to direct my attention to a related point or question that you had arising from the readings. Now, like the other Hellenistic schools, Epicurean philosophy divides, essentially, into logic, physics, and ethics. But the Epicureans really downplay the importance of logic. And they consider, essentially, a part of physics. And they even rename it to a Greek word, cannon, or canonic, which means something like the standard or measure. And they think that we don't need to get too much into logic, and we certainly don't need to be focusing on things like rhetoric and that sort of thing. All we need to do is come up with some standard or measure by which we can discern what's true from what's false. And by which we can discern reasoning and arguments that will relieve us of anxiety and give us tranquility. Now, physics, they actually take to be the starting point of the philosophy, and ethics is the end of the philosophy, both in the pedagogical sense and in the sense of the point of doing physics. So in their view, there is no point in doing physics, and certainly no point of doing logic, which is a mere subdivision of physics, unless it has some positive ethical outcome. So look at these radical statements of Epicureans like this one. Empty is the argument of the philosopher by which no human disease is healed. And the word I've translated there, human disease, could, we could say human pathology or even just human suffering there. So empty is the argument of the philosopher by which no human suffering is relieved. Just as there is no benefit in medicine if it does not drive out bodily diseases, so there is no benefit in philosophy if it does not drive out the disease of the soul. So if getting into this logic and physics does not allow us to get rid of mental illnesses, suffering, pathology, human disease, and diseases of the mind, then it's worthless and should not be pursued. It's only if it does have such an ethical effect that it should be pursued. And specifically, with respect to physics, if our suspicions about meteorological and astronomical phenomena, suspicious, meaning things that we can become superstitious about and think that Zeus is causing thunderbolts and Poseidon is sending storms and things like that or that God created the whole universe or something like that, if we didn't have those kind of suspicions about those kind of phenomena and also death did not trouble us at all and was never anything to us. And if we already knew about the limits of pains and desires and we didn't need to figure that out through science, then we would have no need of natural science and there'd be no point in doing it. So we actually have a completely, as it were, instrumental view of why one should do natural science and why one should pursue physics. Essentially, to create human health, both the body, the health of the body, which we need to know about physics and know about the nature of our bodies and so forth in order to relieve diseases and suffering of it and also for the sake of the soul, which after all, according to this philosophy, is just another kind of body within a body and it also has associated sufferings and pathologies. And these are mostly connected to concerns we have about the natural world, what's caused it, whether it's got any message for us and that sort of thing. But if we didn't have concerns about that and we weren't worried and confused about these kind of things, there'd be no point in doing physics. But as it stands, we are plagued with worries about all of these things and confusions about the true nature of pleasure and so forth. And so we need to do some natural science. And at the beginning of the first letter that you read, or rather of the second letter that you read, he says, since this kind of method of investigating natural things is useful to all those who are concerned with the study of nature, I recommend constant activity in the study of nature and with this kind of activity, more than any, I bring calm to my life. So the object of the philosophy is to bring calm and tranquility and relieve yourself of this anxiety that's plaguing you. And according to Epicurus, studying physics is actually the best way to do that. Not just because it provides you a distraction so you don't think about those other things that bug you, but it tells you something about the nature of reality that's actually reassuring and allows you to avoid some confusions and superstitions that plague life and make it less enjoyable, okay? So that's about the overall division of the philosophy and what parts exist for the sake of others. Now, a little bit more about logic and I got one entire slide on logic only, which is about its relative significance in their philosophy. Logic or canonic, canonic the standard or measure which apprehends criteria that apply to basically three things. First, analysis of words in order to determine what if anything in reality they actually refer to. So for example, the word table, does it actually refer to anything? Well, well, suppose we can all agree it refers to this kind of thing, okay? So table isn't that controversial of a concept but what about things like body or empty or void or time or pleasure or glory or virtue or happiness? Some of these terms might not refer to anything that actually exists in the world in which case we should eliminate them not just from our vocabulary but from our minds entirely. In other cases, they do correspond to something but the objects that they correspond to are different than what we think they actually correspond to. And in some cases, they correspond exactly to what we think they do and their relationship is in a way evident or obvious. The second use of logic is to use our sensations and feelings that we all have immediate access to as a basis for distinguishing things that are evident from things that are not evident. So according to Epicurus, for example, it's evident that pleasure is a good thing if you're wondering if it's a good thing just feel some of it and you'll realize this is a good thing or it's even easier to demonstrate pain. You don't think pain's a bad thing? Let me show you how bad of a thing it is. But it's not evident whether something like glory or honor is that a good thing? Maybe that's actually a bad thing. It's not evident whether it is. It's certainly not as obvious as something like pleasure. And finally, we use logic to make an inference of what is not evident from what is evident. So for example, it's not evident that there is a bunch of empty space or void contained within this desk. But I can actually infer from things that are evident that there must actually be empty space in it because it's actually permeable by certain kinds of substances and so forth which could be demonstrated and those things could be observed and we could see those and the only way we could explain those is that there must be hollows or pores or something within the table. Even though it's not immediately obvious to me, I can infer it from things that must be. Okay, so let's start with the basic principles of the physics and you all were quite right to correct me on don't give us an atomistic picture of the universe like Descartes. It doesn't have any void in it because the universe consists of atoms and void according to that and those are the two basic principles of everything and so actually the best representation of the universe that I can find that most resembles this picture is the actual image of the cosmic background radiation of our own universe because after all it consists of a bunch of void space and a bunch of space filled with bodies in greater or lesser amounts of density. Okay, but the actual starting point of the reasoning about this stuff is just the principle that nothing can be generated out of nothing so nothing can just pop into existence out of nothing and nothing can be completely destroyed so that it entirely disappears. You can break things up maybe into smaller units but you can't break it up so much that all of the material basis for it completely disappears and that should be familiar to you is something like the law of conservation of matter in order to bring new things into existence we need pre-existing material rearranged in some way and in order to bring things out of existence we reduce it back to these two smaller parts before it was assembled but we never completely destroy anything and we never create anything new. Furthermore, we assume that the totality of the universe is the same now as it ever was and ever will be there's nothing outside of the universe so there's no place from which it could change or nothing that could cause it to change in any fundamental way. All that can happen is that the things that exist within it become rearranged and juxtaposed into new and different recombinations and this totality consists of bodies in motion through as I said void or empty space and there is an infinite amount of void space and an infinite number of atoms. Okay, so a little more about bodies and void the existence of bodies is evident through sense perception like you've got one yourself and you can perceive a bunch of other bodies in here and not just people's bodies but inorganic bodies so I can see I've got some kind of bodies here and it's resistant to my touch I can not just see it but I can hear it, I can feel it I won't do this but I can taste it if I wanted to and it's pretty obvious that there's a body there, yeah. I was back in the last slide I was wondering how do we know? Let me get to that in a second after I introduce these. Good questions and also how do we know the void is infinite and I'll come back to that in a minute but first of all how do we even know there's bodies or void and the point is that it is obvious or evident that there are bodies, to our very sensation we can tell there are bodies and every mode of sensation reveals there are bodies in fact sensation is just some sort of collision of bodies but the existence of void isn't evident we don't see void as it were it's just empty space but it can be inferred from the fact that there are bodies in motion if there wasn't any void then there wouldn't be any space for bodies to move in and so everything would be immobile but through our immediate sensation we see that things are moving so we know there must be void spaces that they're moving in therefore we have exactly two basic principles, body and void now go back to this slide why do I say there's an infinite amount of void space and an infinite number of atoms? Well, one way to get at this is that we could talk about how we would limit the amount of void or the amount of atoms and then how those two would exist together now suppose there were an infinite number of atoms but a limited amount of void space well then that infinite number of atoms couldn't fit into that limited void space if there was an infinite amount of void space but a limited number of atoms then in the fullness of time all of those atoms would become dispersed in that infinite space and none of them could combine into the kind of bodies that we see and that are visible so if the two options are that void is either limited or unlimited then it must be unlimited in order to accommodate atoms but the atoms themselves must be infinitely many or else eventually they would disperse in this infinite void space now we can also realize that there can't be any limit on the overall universe because the idea of a limit depends on the idea of a kind of boundary but a boundary only exists against some kind of backdrop and so that backdrop itself has to exist in a sense and if it exists then it's part of the universe so for example if I want to say the universe is limited let's just take a simple case where it's a circle or a sphere and then this is the limit of my universe but how do I know that's the limit of my universe? Well I said it was but then it's against this background so I can only see that that's a limit by realizing there's this background that it's set against but then this background must exist in order to apprehend that limit furthermore what happens if I travel to the limit of this universe and then throw a sphere in this direction well it either keeps going in which case there's more void for it to enter and I can apply that argument at any point at any further point and thus it must infinitely extend or it hits up against a wall but a wall is a three-dimensional object that there has to be a certain depth to and then back side to and that's either infinite or limited if it's infinite again the universe is infinite if it's limited then it must have some other extremity or limiting point and the same considerations apply so it's just a matter of there's no sufficient way to limit the cosmos or limit the universe cosmos is a different story worlds are a different story but there's no way to limit the totality of everything yeah so do they think that the soul was just naturally occurring thing that yes they did but we're a long ways from talking about the soul because we haven't even talked about how atoms get combined to form anything or how much less how a living thing could be understood to be a collection or a composite of atoms so we're not we're just not there yet we're we're still just talking about the very basic the most basic principles that must exist anywhere in the in the universe so I haven't talked about how worlds, how heavenly bodies, how stars, how suns, how plants humans animals minerals, I haven't gotten into how any of that exists these are just the basic principles that will be necessary in order to explain any of that stuff yeah the first and the last points sound sort of contradictory to me because you have an infinite number of atoms but you can also say that nothing is created out of nothing they're not they're not created right they're not created but they're not created but there's an infinite number of them yes they well where do they come from they they come you mean like where do these atoms come from right they came from some other part of the cosmos that they that they flowed into and they they've always the presupposition is that there's always been an infinite number they've always been in constant motion in this infinite void that's going to be our basis for explaining everything else and so it's a good question well where did those come from right but the answer is that those didn't come from anywhere everything else comes from them you see not everything can have a cause and that's because some things have to be causes okay and so atoms and void don't have a cause that brought them into existence everything else that comes into existence is a result of their being in existence and there being a recombination of these if we always had to say that everything that came into being always has some prior cause that this will be a vicious infinite regression where we'll never be able to explain anything whereas this is not a vicious infinite regression we're just pausing there's an infinite number of entities and there's no reason to limit them but they give us a handle on causal explanations so I will in theory be able to explain how worlds, how heavenly bodies, how plants, animals and humans come into existence by talking about recombinations of these principles atoms and void okay but they do not come into or go out of existence and so they do not violate this law of conservation of matter there's always exactly the same number of them an infinite number and there's always exactly the same amount of void an infinite number no new void comes into existence which it might be the case that new voids do come into existence like this crazy idea about the expansion of the universe which is actually a standard idea now the epicurians are wrong the whole universe is expanding which means there's more space between everything like there's more space between you and me right now than there was a minute ago that space has itself expanded I mean it's too little for it to make much difference to us now but in 100 billion years even if we just remain stationary space itself would increase and we would end up further apart according to this crazy modern period now that doesn't happen according to epicureanism new void doesn't come doesn't come in new atoms don't come in they might come into a specific isolated world but they don't come into the universe as a whole alright other questions? I'm delighted with these these questions this is what you should be asking now the void doesn't have any properties whatsoever except unless you want to call a property that it always yields to a body passing through it so it offers no resistance whatsoever to bodies and atoms only have a couple of intrinsic properties size, shape, hardness which just means they cannot be divided they can't be cut up any further if they could they could be destroyed and then you could destroy things into nothing but that's impossible so at some point you destroy things into nothing you get down to the atoms or the indivisible entities that it consists of and those atoms themselves only have size, shape and weight basically does void have movement or is it just atoms that have movement? it's just atoms that have movement through the void the void is a condition for their for their moving but it doesn't exert influence or something on them now there is I did notice this morning re-reading this on the bus there's a strange where he says they move because of the void which makes it sound like somehow the void is providing a motive power for them to move but that's not what he means he means the void makes it possible for there to be motion for there to be space in which they they move okay now according to Epicurus and he differs go ahead how do they come up with all these shapes of the atoms do they know that atoms like fire atoms are trying this? well this goes back to democratists as well who speculated about this but for example fire is able to break up other bodies and very much more efficiently than other things so it must be it must have these points be very pointed and then so that it can take even small objects and drive them further apart and create larger voids between them so then it must have the most pointed shape that's essentially a pyramidal shape whereas atoms of other things like of smooth things or rapidly moving things must have a shape that is not immobile like a cube but is more like a sphere because spheres move much more quickly whereas immobile things like earth or stone or something must be made primarily of atoms that are sort of like cubicle or something and that don't have a tendency to move so they make extrapolations about what shapes what various shapes they must have now the most general thing they must say about shapes of atoms is that they they have such different shapes that they can become interlaced with each other and combined and connected with each other if they were all spheres that might not be possible there's no way that they could become entangled and so there wouldn't end up being any compounds but since there are compounds of these they must have to some extent interlocking shapes or an ability to interlock and so the main thing we need is hooked atoms that these hooks can interact with eyelid features on other kinds of atoms so that they become intertwined but we make inferences from sensible qualities things like speed and smoothness and roughness and so forth to the kinds of atoms that the bodies are made out of and democrat has said there's an infinite variation in the shapes but epicurus changed the doctrine slightly and said there's an innumerable or uncountable many variations of shapes but they aren't infinite because he thought if you have an infinite variety of shapes then you would have to have an infinite sizes because you would get there's only so many combinations that can fit into one size and then so you would need bigger and bigger atoms and eventually you would have if you have infinitely many you would have atoms that are the size of whole worlds or you would have at least visible atoms and the atoms themselves aren't visible so a little bit more about compounds so among bodies some are compounds some are simple the simple ones the indivisible entities so compounds consist of combinations of atoms and so they are divisible and we can break up these compounds because we can break them up into their atoms and we can assume degrees of complexity not just atoms but combining atoms into like molecular like structures and molecular like structures into larger and larger structures and more and more complex structures compounds include everything we see in the world all the artifacts like tables and chairs all the plants animals etc are compounds of atoms and void again atoms can't be destroyed because if they could be destroyed then everything could be destroyed and in the fullness of time nothing would exist and we would violate the laws of conservation of matter by the way that diagram there is a bit hard to read the description but was scientists taking an atom taking some iron and differentiating the taking some composite of a metal and then determining actual ratio of atom of iron and platinum atoms within it and making a sort of map of a compound of a chunk of metal consisting of those atomic elements and actually being able to diagram out how they recombined something Epicureans certainly could not do ok now I've already said the universe is unlimited or infinite in extension given the reason for that limitation implies extremity etc I've already said that the universe consists of infinite number of atoms in an infinite void and how there would be problems if you tried to limit either of those so the universe is infinite everything else is limited and there are an infinite plurality of worlds or cosmos of cosmos within the universe all a world is is a temporary of some atoms in a void space and again this can happen on any number of levels we can have micro a micro cosmos or a micro world on a very small level we can have very large and complex things that include entire say solar systems galaxies super clusters of galaxies and possibly even larger structures and they speculate that some of these worlds are very similar to ours some are very different some of them are lifeless some of them have other living things some of them have living things but not intelligent living things others of them have intelligent living things in fact others of them will have things that look like humans in fact others of them will have things that look like humans a lot like us humans sitting in a classroom studying something a lot like Epicureanism and that's because since there's an infinite number of these worlds every possible combination does occur somewhere and then every possible variation on it must occur somewhere so if you think it's really a bad problem that you're sitting here right now you're actually sitting here with an infinite number of other worlds as well but you're also doing an infinite number of other things in other places at other times so if that's consolation for you then good these worlds come into being and then go out of being like every other compound right our world just happens to be this temporary envelopment and juxtaposition of atoms came into being at a certain point of time the star that we're circling around came into being at a certain point of time this planet came into being at a certain point in time the moon came into being at a certain point in time animal life came into being on the planet at a certain point in time and just as surely all of it will be broken up and disappear and dissipate into other regions of the universe and then recombine in other ways now talking about basic causes of motion yeah how did the view of time well they basically neither they have an extremely presentist view of time so only what exists right now in whatever period now is which presents some difficulties should have asked Blythe about this but they things in the past and the future don't as such exist so only present things really exist there's a lot more to be said about their theory of time but in order to explain it I have to explain the theory of motion because time is related to their account of motion so again everybody's trying to jump ahead to explain how the world works and how consciousness works and how plants and animals work but I haven't even explained to you how atoms move in this void yet so let's let's comprehend that so one cause of their motion is the fact that they have weight or gravity and this is an extremely problematic notion actually as it is for us nobody's figured out what gravity is yet but it's some kind of cause that makes bodies fall downwards and fall straight downwards and you can observe this sensibly by doing things like dropping stones or dropping your pen and watching it travel straight in a downward line that's the natural direction that everything tends to travel another cause of motion is that when atoms collide or combine then they rebound and redound in different directions based on based on the speed that they're moving and the shapes of the atoms involved and the angles of their collision then they go off in all sorts of directions and collide but there's a problem if all bodies are naturally moving straight downwards then they're all moving in parallel lines and so how could they ever combine and if they don't ever combine then no compounds are formed and so no worlds no planets no living things no humans but we can see that all these things exist so they must combine somehow but how do they combine the motion of everything is just to move straight downwards when we drop a pen we don't ever see it float upwards or sideways or something so how do we get these we have to posit that there's some other cause of motion and this we call the swerve that there's some kind of random or indeterminate motion that atoms make that we can't account for occasionally one just swerves off this directly trajectory so that it can collide with other atoms so that those atoms can become interlaced and so that compounds can arise so we have to posit that again we can't explain the swerve if you say what's the principle of something swerving I can't I have to posit it in order to explain other phenomena like compound bodies and so on okay so those are the three basic causes of motion they have some sort of natural motion in a certain direction which we conventionally call downwards they have the various kinds of motion they make due to trajectories that happen as a result of them colliding and then in order to get collisions off the ground we have to posit that there's some indeterminacy in this whole system so that we can't always predict the trajectory of an atom and we have to suppose that there is occasionally a swerve of atoms now there must be questions about that point the scandalous swerve this uncaused motion that seems totally unreasonable it doesn't make any sense and we would never believe anything like that there's indeterminacy in atomic motions right we couldn't accept that that was possible you must always be able to determine the space of an atom if you know enough about its direction and its shape and trajectory and so forth right well no it turns out there's this is actually this actually turns out to be a thesis in our own contemporary physics and quantum mechanics that there is indeterminacy in any given physical system now it is not clear for epicureanism how often swerves have to happen one and almost every answer is defended in the scholarly literature so in according to one theory you only need one swerve to have ever happened in the entire history of the universe that was enough to cause a chain reaction of colliding events that got the whole compound of atoms going another possibility is that swerves happen all the time they're constantly happening in fact every time a human decision or something is made there must be a swerve taking a body off of its straight trajectory but that's a complexity we'll get into later yeah what the advent of quantum computing aren't we able to go to simulated environments to answer these theoretical questions like aren't we doing things now that are better able to validate from a more scientific more actionable manner well I hope so I hope that after 25 years 2500 years we can do it a little bit better yeah so the answer is yes I think we do have a better more sophisticated theory of atomism but we still have the a principle of quantum mechanics called indeterminacy and no we're not advanced enough that we've gotten over that so we still essentially have a swerve in our atomic theory we can't explain it it's a phenomenon that must exist but we can't we can't explain it in fact we use it to explain other things but yes these are all real pictures that's a picture of an atomic collision a simulation of an atomic collision happening in a particle accelerator this is actually a map of atoms in an actual piece of metal Epicureans didn't have anything like this they had words written down on paper based on just speculation about these things they didn't have they didn't even have microscopes or telescopes okay so the theory that there's something outside of the visible world that we can see Aristotle looks out at it and says oh it's bounded by that set of fixed stars that always stays in the same relation to each other there's nothing outside of that can't see anything outside of that be totally irrational to think there's anything outside of that well according to Epicureans reasoning a bit differently well could it really be limited what would be on the other side of it what would happen if I went to the edge of it of this sphere and so forth reasoned that it must be infinite okay now by the way the verdict on that still out is it infinite or is it limited did it come into being in a certain point of time or didn't it like none of that has been definitively answered so I mean of course our physics has advanced and I think it's advanced largely along these lines of Epicurean physics but it hasn't what's astounding is how much of this original version of the theory persists within the system like unbelievably much and so that it seems incredible that this could have been speculated about in antiquity and yet it was so we finally get to the burning question that everybody's having how do we get living things out of this and the Greek form of that question is how do you get a psyche out of that psyche meaning a principle that differentiates between a lifeless body like a stone and a living body like a plant or an animal and the answer is that souls are just kinds of bodies certain configuration of extremely small interlaced atoms there is some material recombination of things within a body which will animate that particular body and so there's no you know sort of spirit or ghost or something that's within these bodies because those don't exist there's only atoms and void and so ultimately the brain and everything else in the body if we analyze it enough when we break it up into its simpler components ultimately we're just going to reach these atoms or subatomic particles or whatever but eventually we're going to reach indivisible entities and living things are just really complex recombinations of those so complex that Epicureanism doesn't have that much more of a story to tell about how we get living things out of that but then again neither does our physics still remains a problem we can't exactly answer how do we get life out of inorganic entities so we've been trying to do it for a long time in fact there's lots of great research on this going on here at UCSD can we simulate environments that existed 3 billion years ago on earth when life started evolving here and so we put all these organic and inorganic or we put these inorganic molecules together and we add electricity and so forth we still can't do it we still can't produce living things out of it we can't explain how that happened we have theories about how it happened about how biogenesis happened and they all are theories along Epicurean lines that certain kinds of atoms or complexes of atoms called molecules RNA and so forth combined in these primordial suits and eventually produce something living but we are still unable to confirm that that is how life came into existence and part of the problem is that the only place we've found that it ever existed is on this one particular planet so until we find it on some other one we don't have anything to compare it to and it will be hard to say or it will be hard to say that it didn't say originate in some other part of the of the cosmos and just travel to here 3 billion years ago travel either randomly because some comet or something brought it or deliberately that some other advanced civilizations sent the basic biological material to our world that has enabled it to evolve since then sounds crazy and I wish I could rule one of those theories out and say here's exactly how life comes into being out of lifeless atoms but we don't have that explanation there isn't a satisfactory scientific explanation for that but nevertheless we assume that something like that happened something like the Epicurean story must be on to the right unless you want to think that it's through this panspermia scenario that it originated elsewhere in the cosmos of course the Epicurean line of reasoning about that is suppose it did originate somewhere else in the cosmos well let's go there and then ask how it originated there how did it get started there presumably through some kind of recombination of inorganic atoms in primordial super whatever otherwise it got there because intelligent people put it together but then the question is how did they get there and they must have got there through recombination of things that already existed and so on and so that answer that it originated somewhere else may or may not be true but it doesn't get us to the basic question of where does it come from and why is it there instead of not being there now one thing about living things and about the soul the principle that makes some bodies alive and others not is that soul atoms can affect other bodily atoms and bodily atoms can affect soul atoms and that is why they must all be conceived as some kind of body because only bodies can affect other bodies so I can affect these bodies in my hand by moving my hand and so I'm moving bodies by doing this I can also be affected by other moving bodies like they can collide with me and that's actually what's happening in sensation individual atoms of course aren't complex enough that they can be alive or they can sense these are very complex compounds of them but when these complexes are destroyed or die this is the reason you can't go on to sense anything after you die because you don't have the right configuration or pattern of these atoms that make it possible either to be alive or to sense plants and animals they have got an account that contains some elements of a theory of evolution living things are just recombinations of these more complex parts these atoms combine to form these molecules these inorganic molecules combine to form these organic molecules the organic molecules combine in various ways that give rise to other things in fact things capable themselves of reproducing complex structures and taking other things like food from the environment and converting it into things by means of which they can grow, reproduce, etc and according to their theory basically they again have this combinatorial theory every combination happens that it's possible has happened in our world but only some of these combinations are actually viable and able to survive and among the combinations that are viable and able to survive are the plants and animals that have survived and are around so it's just by virtue of the fact that we are more able to survive in the environment that happens to have been created that just because we have organs that happen to be adapted to allowing us to survive and the ones that weren't able to survive went extinct that makes it look like somebody designed us to be very well adapted for this environment but the fact of the matter is that we just got lucky that our combinations are able to survive in this environment and many other almost infinitely many other combinations that weren't able to survive


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So this is gonna be completely unscripted, so I'm just warning you there's gonna be some rambling. I didn't plan anything I was gonna say right now. I just had some thoughts and I thought I'd just share them with you. So I just worked what's probably gonna be my last shift ever as a medical assistant. I might come back for a few days here and there during the next semester, but more than likely this was it. This was my last one. So like I said on Instagram, oh sharp turn. Anyway so like I said on Instagram today we've got a four week break from PA school for the summer so I just went back to work as a medical assistant. It's a job that I had before PA school how I got a lot of my PCE hours and it was a really good way to do it. And so since this was my last shift as a medical assistant I started having some thoughts. I was getting kind of nostalgic like hey this is hopefully my last time kind of on the staff side of things of the medical office before I start transitioning to the provider side of things.  But that being said in a couple months I'm gonna start going on clinicals. I'm gonna be sitting with other PAs going in the rooms just like a PA and really training to do that side of things. And then of course once I graduate I'm gonna be a PA so I'll be one of the actual providers at the practice or the hospital or urgent care or wherever I end up working. And so this is probably my last time working as a staff member as a support staff you know medical assistant and office folks things like that. So I just kind of wanted to share some of my thoughts and also if this video is still up like a year and a half from now when I start working as a PA it's going to be interesting to go back and see what my perspective is now. So I actually plan to make a video like this just before going on rotations and just kind of sharing my side of things as a staff member as like support staff in the medical office before I really start experiencing the provider side of things in any way. But this being my last day I just thought I'd do it now. Also this is a really beautiful neighborhood. Upstate New York is gorgeous. What else? What other kind of random stuff can I talk about before I even think about what I wanted to say? I think I have ADD. I'm pretty sure I have ADD. Oh yeah hand sanitizer. This video is being made during the COVID-19 pandemic and so in healthcare we're wiping everything down after every single patient. We're constantly sanitizing our hands our surfaces our computers and so we're going through a lot of hand sanitizer and the hand sanitizer we got at work is really gross. It's like this green stuff and it's really sticky. It just like leaves a residue on your hands. It smells fine and I'm sure clean's just fine but it's sticky and it's freaking annoying and it's impossible to put on gloves after you used it. So I've started like shopping around for my own hand sanitizer. I got one of these from Equate. It's the Walmart brand or Target Target or Walmart. Got one of these. That's just the Purell. It's fine. Honestly the best hand sanitizer I've come across is from this company I've never even heard of like Wish or something. I got this from a runnings outdoor shop and this stuff actually smells really nice. It like it goes on fine and it dries and then it actually smells kind of good. So I was really pleasantly surprised when I bought this stuff but anyway no this video is not sponsored by Wish Hand Sanitizer. I have no idea where they sell this stuff besides runnings and I know nothing about the company. I just know that their stuff smells kind of good and I don't know I like it. I definitely have ADD. But anyway okay so my last day as a medical assistant what are my thoughts? First things first and I'll be really interested to see if my perspective changes or if it just evolves when I get on the provider side of things. From my perspective working as a medical assistant, working with the nurses, the support staff are seriously the backbone of any medical office. They do the heavy lifting. They do all the stuff that allows providers to actually be providers and practice patient care. You keep hearing about like about like doctor, PA, provider burnout because they keep having to do all these administrative tasks and all this stuff for insurance and just like all the problems with our modern health care system basically. And so to some extent that's true all the charting, all the insurance worrying about what meds are going to get covered, what's not going to get covered all that stuff is definitely a factor. But guess who lifts 99% of that burden off of the providers? The staff. The insurance, the billing staff, the office manager, the medical assistants, some of the nurses depending on how the practice is run all that stuff is being dealt with by the staff. That's why offices have staff checking patients in, getting their histories, reviewing their meds, making sure all their information is up to date, pulling the latest labs, pulling the latest imaging, seeing if they were at the ER, if they maybe got surgery because if anyone who's ever dealt with patients knows, they don't always tell you everything. Sometimes they don't know, sometimes they forget, sometimes they just think they're going to get away with not telling you something, just going in a room and talking to a patient and basing all of your knowledge off of that is just not good enough anymore. And so we have things like statewide databases, which we have in New York and it's amazing, especially in an emergency situation, you can just log on and with the patient's consent, you can pull all of their latest labs, imaging, ER notes, specialty care notes, all kinds of stuff, and you can basically have a great idea of the patient and their level of care, what meds they're on, all that stuff from that record before the provider even goes in the room. So all of that stuff and putting all that stuff into the patient's chart, keeping it up to date, that's the medical assistant's job, sometimes the nurses help with that kind of stuff. But doing that work basically makes it so the doctor only has to be a doctor, or the PA only has to be a PA. They just look at all of the patient's history, they look at the latest lab results, imaging studies, whatever, and then they go talk to the patient and do their own history and physical and evaluate the patient medically, form a diagnosis, form a treatment plan, all that stuff that PAs and doctors do. So my point with that really long ramble I just gave you is that medical staff are extremely important and they're not to be taken for granted. At work I keep joking around, is that a real person?  That is really creepy. There's like some weird mannequin in some guy's front yard, I couldn't tell if it was a real kid or not. No, he's moving. He's moving. Okay, that was really creepy. Anyway, so that's just a perspective I have as a staff member, as a medical assistant, and that's something I really hope I never lose as a provider, just understanding how important your support staff are, how much easier they make your job, how much more difficult your job would be without those support staff, and how important it is to treat those staff members well, not just being nice to them or saying hi to them or occasionally buying them lunch, but actually understanding that they are professionals, they're very passionate about their jobs, they like what they do, and they think it's important, and you as the provider need to encourage that and encourage them to grow as people, as professionals, understand how much they do for you and how much they make your life easier. So I'm probably going to repeat myself, but one thing I really hope I never lose when I move over to the provider side is appreciating the support staff. And if this video is still up in a year and a half, a few years down the line whenever, and you're one of my support staff, and I'm taking you for granted for it can show it to me and call me out, it's completely not okay to not respect your support staff. What they do is super important and you can't do your job without them. All right, I'm home. So I'm sure there was more I wanted to ramble about, but honestly, I think that was the most important thing, and the shadows on my face are making me look like a skeleton right now. It's kind of weird. Is that better? That's way better. Maybe I should just film with my sunroof closed. I thought it looked kind of cool with you know, the sky going by in the video, but maybe it would be better if this was closed. I don't know, what do you think? Okay, there was a couple more things I wanted to talk about. Why don't we go around the block again, except I need the AC now because the sunroof is closed and it's really hot in here. It's like, okay, it's not 67. There's no way it's 67. It's hot. Anyway, so two other things I wanted to talk about that I was thinking about today, my last day as a medical assistant. My phone just shut down on me. It said it's too hot to run the camera. Have you ever had that? Your phone heats up from the sun so much that it won't even use the camera. Anyway, I just sat there at the stop sign holding my phone up to the air conditioning, just trying to cool it down so it would finally record. So it's finally cool enough to record. Anyway, so two more things I wanted to talk about that I was thinking about on my last day as a medical assistant. So one of those things is if you're pre-PA, you're trying to apply to PA school and you're working a job like a medical assistant or a CNA or an EMT or something to try to get your PCE, your patient contact, or your patient care experience hours, which has a requirement to apply to most PA schools, I think it's really important to find a job that actually gives you good experience. It doesn't just give you the numbers but gives you really good experience. So for instance, my job, I honestly think was perfect. My first patient care experience I started with, I was a CNA, a certified nurse aid, and I ended up working in a nursing home and also in home care. So I was responsible for people's medical care in their own home, doing some range of motion exercises with them, writing down their vitals, communicating with the nurses if I found anything that looked suspicious like a skin lesion. And that was really good. That was a lot of responsibility really fast and it kind of got me right into the medical field. The next thing I did was scribing. I was a scribe at the ER and that's like a baptism by fire. They throw you right in there and you have to learn really, really quick. All this medical lingo, all these lab results, I remember EKGs were my nemesis, figure out what to do when the doctors were dictating EKGs because there's just so much lingo, so much different stuff that you have to know because you're making these charts, you're transcribing what the doctor is saying, which means you have to know the words that they're actually saying. Even if you don't know exactly what they mean, you have to know what they sound like and how to spell them and things like that. So that was just a ton of knowledge really, really quick. It was very stressful, high learning curve, but I'm really glad I did it because it really increased my knowledge base really quickly. But anyway, so there was scribing and then finally I left that job in order to go do this, which is medical assisting. And at this job, I was able to apply a lot of that knowledge of labs, imaging, medical terminology I'd learned about and actually get hands-on with patients, ask them about their history, about their symptoms, how they're feeling, what medications they're on, what they think has been working, about their family and social histories. All kinds of stuff that was really pertinent to their medical care and filling out their chart as completely as I could before the PA or nurse practitioner or doctor would go see them. So at this last job, not only was I in the room with patients, but I was also reviewing charts because I was sorting facts as that came in and so labs would fax the lab results to us, imaging studies, if somebody ends up in the ER, the ER will fax the record over to us. And then as a medical assistant, I had to sort those records into the patient's charts and task the provider with reviewing those records. And so of course as I'm doing that, I'm looking at the chart, I'm reading it, I'm looking at the lab results. I see medication names over and over and over again, and it's just learning by repetition. No, I didn't always have time to look up the mechanism of action or what the medications used for, but then when I saw those same medications in PA school, I kind of had that little bit of an advantage because I had heard about them a lot. And if you've ever studied pharmacology, you understand that it's like a different language. It's not English.  I don't know who made them up, but there's so many syllables, nothing makes sense. And it's just really hard, at least for me personally to study. I don't memorize things well. So having this job where I came across lots and lots of different medication names, yeah, it's stressful in the room when the patient has like 40 different medications and you only have five minutes to check them in and see what's current and what's not. Yeah, that's stressful, but at the same time it's that repetition that I feel like really helped me. So if you're working a job to get patient care hours for PA school, that's something I really think you should focus on, not just getting the hours and trying to be competitive based on the number of hours you have, but really trying to get a job that gives you quality experience that makes you learn something every single day and that'll tremendously help you as a PA student and of course as a future PA. Another thing I think you should focus on is if possible try to get a job that actually allows you to be one on one with patients and practice your bedside manner, practice talking to all kinds of different people, practice talking to people who don't speak English, using a translator. You're going to have to learn how to do all that kind of stuff as a PA and I'm definitely going to have to learn how to do it on a much higher level in clinical year. But I think that the experience as I had at this job where I was one on one in the room with patients getting all kinds of information out of them, I think that's really going to help me because I have that experience and I can much more quickly and efficiently lead a patient interaction in the direction that I needed to go. So I think that's going to be very important for me personally and I highly recommend that you try to find a job that allows you to do something like that because that's probably the hardest thing to learn. It's not the medications or the pathophysiology of the diseases, it's learning to deal with lots and lots of different kind of people that your patient care experience really teaches you and so I think it's important to try to find a job that allows you to do that and really practice and hone those skills. Oh man, what else did I want to talk about? The importance of medical support staff, the importance of quality health care experience, what else? Well, you know what, when I left the parking lot I had two more ideas to talk about but I guess it's only going to be one. I think I've rambled long enough. If anybody's still watching this video, thank you for sticking with me. Like I said at the beginning of the video, thank you. I'm Boris, I'm a first-year position assistant student. I was just working as a medical assistant before PA school and then during this break from PA school we had during the summer and this is my last day as a medical assistant. So I was just reflecting on some things that I learned as a medical assistant and some things that I really want to focus on as I transition into that provider side of health care. Anyway guys, that's really all I had to say. I'm sure there was more I was thinking throughout the day that I just didn't have time to write down. You guys know how it is working in medicine, you just constantly move on to the next patient, on to the next thing, there's always something to do. So anyway, I just wanted to say that if I have more thoughts I'm going to make another video or something. But for now that's really all I had to say. It's kind of bittersweet my last day as a medical assistant. I really did love this job. I'm really grateful to the people that hired me and allowed me to come back every time there's a break from PA school and I can just go and work whenever I have time. So that was just really awesome. If you have anybody working in the medical field you think can get some benefit out of it and I'll see you in the next one.


Hello everyone, this is Amit Dan and on this channel you will find financial travel and more videos. If you like what you see, please do the thumbs up and consider subscribing. Thank you. Hello everyone, this is Amit Dan of amitdan.com. Today I'll have another episode of Chromebook Tips and Tricks video. And I'll be talking about how to find or where's the caps lock button on a Chromebook. So if you are looking at a Chromebook, then you'd not find a caps lock button anywhere. In general, usually it's supposed to be right here, a caps lock button. But if you look carefully, then you'll see that this looks like a search button, not a cap lock button. So if you just press on it, then you'll see that it's pulling up the search screen, but no caps lock button. So in order to use the caps lock button on a Chromebook, you're going to have to use the search button and the alt button, which is right here. So what you need to do, you press alt and then you hit search. Then you're going to see a message right here that caps lock is on. So now if we just type something in here, let's say A, then you can see that it's working as caps lock. So because they're all capitalized, so now the caps lock button is on. And if you'd like to turn off the caps lock button, then you have actually two options. Either you can just do the same thing, alt and search, or you can just hit the shift button. The only difference this time is that you're not going to see any message here, mentioning you that the caps lock button is off. So there is no message, but it will be off. So for example, let's try alt and search button again. Okay, so we did that. We didn't see any message. And if I type in right here, A again, then you can see that the caps lock button is gone. So it's just working as regular now. And if I had hit the shift button, it would have done the same thing. So to wrap up everything, in order to turn on caps lock button, hit alt and search, in order to turn off caps lock button, hit again this alt and search, or you can just hit that shift button. So if you like what you see, please give it a thumbs up and subscribe because there will be more videos coming up. So I'll see you shortly. Thank you.


Let's see on the breakfast and plus CV Africa we look at telecommunication operators and your plan to increase the tariff by 40 percent. We do have an expert who joins the conversation of Kono Abdulahi. Let's go to have you join us this morning. Thank you so much for having me. Okay, so let's get straight to this conversation now. The reason for this action by telecommunication companies, although some persons are saying it is already being implemented, is that they are putting the blame on high cost of diesel and other energy sources and recent introduction of excess duty of 5 percent on telecom services. And this has actually been responsible for the increase by 40 percent. What do you make of all of this? Okay, thank you so much. If you are to go by what we have been experiencing over time in this country, pretending to high the sesance increment in the cost of living, you may want to say that for the operators to come with this idea of an increment in increasing the tariff across both on their services. We will say it is not the one that is surprising. It is not surprising taking a cue from, for example, the electricity tariff that was jacked up enough for the assistance of the part of the organized labor. By now the petroleum comprising also would have been jacked up. So for this also, like they said earlier, it is not surprising that they are coming with this. And I would want to believe that they have started the implementation. Why did I say that? For them to start, they must get an express approval from the NCC, which I don't think that has been given by the information that are disposed of. And the various tabloids that carried it from the, let us know that it be just rules to NCC or approval. And it means that it has not yet been implemented. And if they have started the implementation, that will be very, very appropriate and it is something that is not supposed to be consumed. Having said this, on the increment, I want to say that it is one that is going to be impacted so badly on the consumers. Like I said earlier, everything now is going high. Nothing is coming down in terms of prices in Nigeria. Even it's as bad as, even all the political parties, the politicians, those in government that's supposed to ensure that there is stability in the cost of living for Nigerians. Their own nomination forms, too, are also going high. They are also raising the fees for their nomination forms. So these two tell us that these people do not have the best interest of Nigeria's, of the masques and arts. All right, Abdelai, it is... Abdelai, so fine, let's leave the issue of nomination forms increasing to 40 million and 100 million. But let's talk about the impact of all of this. Now, from what we hear, SMSR, which actually goes for about four Naira, will now have to increase to about five Naira, 61 Kobo. And the per second billing that we have been paying, or price, of course, will now increase from six Naira, 40 Kobo to eight Naira, 95 Kobo. My question now would be, how can this be averted? Don't you think, or do you think that the issue of maybe subsidized energy costs for operators might be a way out? Yes, you are very, very correct. There it can also be a way out, but I don't really see if they'll see the light of the... Why do they see that? You remember, you call that the government has persistently told us that the high cost on subsidy on the petroleum and even electricity for supply as in all that cannot be sustained. So if we are coming with this idea also that they should subsidize for the operators, I don't think it would be a welcome development for them. I think the most important thing is for us, rather for us to be tackling the symptoms, we should rather tackle the ailment itself, the sickness itself, its official tackle. By that I'm referring to getting our, what do you call it, refineries working. You know, if the refineries are working, we will not have any reason for us to be selling, I mean, to be selling at the international price. Then apart from that also, the cost of people bringing all these commodities back into the country will also be eliminated. So the focus, like I said, should be on refining localities. Once you are able to refine localities, you will not have all these, it's a certain, what do you call it, increments in the home price. So I think that would be the way to go. And for the operators, to a very large extent, we want to agree or reason with them, with the reasons they gave because we are also, if we are in the sector and we know what is obtained in Buk Shobin, actually all their base stations are run on generating sites. And the cost of diesel will bear with me, has been going back in the last couple of, what do you call it, weeks going to months now. So then apart from that also, the issues of towels at the various locations, before you, what do you call it, before they offload diesels to all these base stations, you see a lot of paths coming around and then seeking, I mean collecting money before it can offload and you power the generating sites on those sites. So that also, it's also impacting on the cost of doing business. And they talk about that, what do you call it, logistics as well. So there you not be standing that. I think, like I mentioned earlier, the best would be for us to be what you call it, refining locally. Then apart from that also, government should also look at that area of towels everywhere you go to on trying to power the generating sites to see a lot of them. And now it is very funny to let you know that now they have also increased what they collect from the operators before they can power their base stations. So it is a bad situation we have on our hands. It is a terrible situation we have on our hands. And the most, what do you call it now, you wash it will be the masses. People that presently you see majority of the engineers are not fault in their cause. Not to talk of going on internet using the data, you understand. Now we are increasing the cost of what you call it, of these services to them. It will be the pain in the soul as projecting on them. It is one that I want to believe that the intervention of every stakeholder, including the government, the operators should have a retake on this. It is not the way to go for our people. But just looking at it again, looking at the fact that the government has a responsibility in providing an enabling environment categorically, can you state what can be done in the short term, because of course you probably might just have a long term. But what can be done in the interim to avert the situation? Okay, like the point I raised earlier, in terms of tals, I call them tals, all these area boys are here and there. If the government can ensure that there is a delivery of diseases to all these stations, it will reduce costs of doing business for all these operators. If that is done to a very large extent, certain fraction of the cost of doing business will be reduced. So if they look at that, because I tell you, it is running to several hundred millions of Merah. I'm not doing it to billions, I must let you know. So this is the amount of money that people that do not work for the company and they are just making the good money without anybody checking them. So this will come in form of a very large extent, see it from the angle of insecurity, because if you fail to settle these boys, they may want preventing you from offloading your, what do you call it, the diesel. And apart from that, if they allow you to do so, before you can come back, they can also do what demolish or destroy, come back with your base stations. And so if the government can look into this, it will reduce the cost of doing business for the operators, like I said earlier. A very good point was also raised earlier by Austin, though I was pessimistic about the point he raised, which is give a subsidy to these operators. It is doable if the government sees it as one that they are not necessarily doing the favors to the operators, but rather they are doing it for the engineers. It's also a way to go. All right, thank you, Okono. Good day, yes. All right, thank you so much. We have been speaking with Okono Abdelahi. He is the general secretary of the private telecoms and communication senior staff association of Nigeria, Texan. Thanks for sharing your thoughts with us this morning. Thank you so much for having me. All right, that's indeed the size of the show. So if nothing is done in the interim, Nigerians may have to be paying a lot more to your texts at them to make calls. Some service providers have already gone ahead to implement all of that. Probably might just be a difficult time to be a Nigerian. Fingers crossed, let's see how relevant stakeholders step into the situation. But like Justin mentioned earlier on, that's the size of the show. We will return tomorrow. It would be an exciting time. If you missed out on any part of the conversation, you will be all right to follow us on Facebook, Twitter and Instagram. And do subscribe to YouTube channel where plus TV Africa and plus TV Africa lifestyle. I am Messi Popo. Have a fantastic day. And I'm Justin Nakadouni. Many things for being a part of the show. Stand by for the news which comes up top of the aisle.


So, we're interested in corals and what's currently limiting their distributions in terms of how far north and how far south they can grow. And our main interest in this is whether these distributions or these limits will change under climate change. So, what's predicted to happen under climate changes, the areas around the equator are predicted to get warmer and more acidified, and it's going to force corals to have to move out of the tropics. The idea is that as those areas in the equator become less hospitable, areas closer towards the poles might be able to harbour coral growth where they don't presently. What we're able to show is that it's actually light that's limiting where corals can grow and not so much things like temperature or ocean acidification. And unlike temperature and ocean acidification that might allow corals to move closer towards the poles, light's not predicted to change. So, light's going to remain relatively constant and those corals will eventually hit a point or they'll hit a wall beyond which they can't extend their range because they're not meeting the requirements of light much like plants. I think we need to change some practices. I think we need to be a little bit kinder to our climate. And if we really are interested in trying to preserve these species, the first thing we need to do is change our practices to prevent those areas near the equator becoming less and less hospitable for coral growth. There's 120 to 170 species. Some of them will be able to make the transition out, but not all. So we're going to lose quite a large amount of diversity.


But the reality is, you also don't want data chaos. You don't just want data all over the place. I mean, one of the key themes at this event here is security and governance.  It's completely ungoverned and insecure.


So looking at number two what's my base? What's my base? So I would go okay, this is the inverse of three to the x which is zero comma one one three two nine Which means the points that I'm gonna use are the inverse of this it's gonna be one zero three one Nine two oh and this has an asymptote of y equals zero this has an asymptote of x equals zero So far so good. Okay Now I'm gonna do my list. I really didn't leave you enough room here to list things carefully I would admit I didn't type this again. I'd make it bigger with more room anyhow expansions compressions well, I see a Vertical expansion by two Yeah, I See a one-half now. That's a horizontal Expansion by two because it is next to the x and everything's backwards Any reflections that's convenient no negatives one right and One down. Okay Let's walk through the transformations vertical expansion by two means the y's are going to change sure One left Absolutely, it'd be one left. That's what I wrote. I'll make that L a little clearer so you can read it better Note to self fix the recording on the internet so people online.  Don't say those things out loud when you're recording because you can't go Vertical expansion times by two times lost my projector froze really Let's do that All sorts of funny stuff happening today Let's do that should be back again shortly have patience children. Okay, we're back one two three Okay Vertical expansion times by two times by two. Oh, that's an x not vertical Horizontal expansion times by two times by two.  Oh, I should also have horizontally expanded that by two, but what's two times you're still zero One down to become a negative one a one and a three. Okay Here's what I got. I got an asymptote at x equals negative one Yes, I got One comma negative one I think and I got one two three four five comma one What does every exponential graph look like like this or like this? You know what every single log graph looks like it has a vertical asymptote or I got a Vertical can't really do this one really well a vertical asymptote this log graph.   It's harder than it looks on this tablet It's gonna look like that What's the domain Everything to the right of negative one range all reels Asymptote x equals negative one X intercept is a decimal. I wrote this up and then I went I should have not included x intercepts y intercept is Also a decimal I think So the only way to find them would be to cheat and use your graphing calculator or solve it I'm not gonna freak out about that. I'm working you do the graph right now. Is that all right? Am I right anybody get that? Yeah, I'm nodding. No. Yes. I think I'm right. Is that okay? By the way, if you want more practice, of course, you can always do The Examples that I skipped over so where it says example one two three and four if you want a bit more practice You can try those ones and check on your graphing calculator if you have a problem. Yeah Yeah, anyone else? Okay, so I have for you a take home quiz Turn in your workbooks if you would be so kind please to turn to page a hundred and fifty one page a hundred and fifty one and I apparently need to delete the ink in this lesson delete ink page a hundred and fifty one page one five one Incas vanished. Yay Now I want to preface this the first part of this lesson Tyler Ain't gonna be on your test The second half yes And I'm gonna tell you though this concept the title says Identities the concept of an identities is going to be a major part of trig a huge part of trig a phenomenally large part of trig, so I'm showing you the concept of an identity 151 I'm showing you the concept of an identity right now to let it actually kind of percolate so identities Says in mathematics. It's important to understand the difference between an equation And an identity This is an equation and the reason it's an equation is only a few values of x satisfy it You could solve it as our the values are negative two and positive two This is an identity There is an equal sign. There is an equal sign. There is stuff on either side There is stuff on either side, but this is true for an infinite number of x's in fact for any valid Value of x you put it in this side you put it in this side You'll get the same answer and identity is essentially a true statement not an equation a statement That's true for not just multiple values, but all values of a variable x doesn't seem very profound yet but Let me tell you another identity don't write this down. We didn't call it an identity. We called it a rule that was the power rule is That true for any value of x that you're allowed to stick in there any x that's positive and any base that's positive but not equal to yes So that's an identity One of the things we're going to look at in trig is Proving identities. It's probably going to be the single toughest concept of the entire year But we're going to spend like I think six lessons like we're going to do it very patiently very carefully We've already met the following identities the base change law The log base B of C is the log base A of C over the log base A of B The product law multiplying two logs inside the log is the same as adding outside the law The quotient law and the power law We're going to look at today a little bit is trying to prove them Now here's the problem Even though there is an equal sign Because we're trying to prove that they're equal Cara We can't use our equation solving tricks We can't add five to both sides for example because that would be assuming they were equal in order to prove They were equal we can't divide both sides by two because that would be assuming they were equal in order to prove They were equal trying to prove that an identity is equal They are the same thing you have to only work on one side or Only work on the other side, but you can't cross stuff over otherwise they'd be Easy, but that'd be because you were assuming they were equal to prove that they were here's an example example one Says use the following steps to prove That this works we looked at the pattern a few days ago. We say that seems to work It's how we did the log base five of 17 We said that's ln 17 over ln 5 or log 17 over log 5 or log base whatever of 17 over log base same Whatever of 5 Prove it. Okay We would let if we were going to do this one the log base B of C B X There's our first step Spencer, what's the second step? Can you rewrite that as an exponent, please I yelled at you guys last class in love saying it's high time that you were able To glance at a log and see the exponent so Spencer my friend. What to the power of what equals what? No, you can't say log. We're changing it to exponential form. What to the power of what equals what no more logs? Darn right with authority though. No more questions. Absolutely mister do it By the way, this is going to be your first question on your test I'm either going to give you a log and say write it as an exponent I'm going to give you an exponent say write it as a log and I would consider that Less than C minus level question Like this is the one I expect it. Well, this is the one if you get that one wrong you're flunking the test B to the X equals C What does it say for step two spence? Okay, so I'm going to go like this log base a of B to the X equals log base a of C Now what use the power law. Where could I use the power law? Ah What can I do with that X and then it says solve for X? Get the X by itself Brett. How would I get the X by itself? Absolutely, so I wrong Brett that Brett X equals the log base a of C all over the log base a of B and Then for the final step, and I'm kind of running out of room here I had to write a little large replace the X with the original X value, which you said was log base B of C right You see what you have you have the log base B of C that was your original X value But you've also shown that it can be rewritten as the log base a of C Over the log base a of B and what you've just done Alex is you prove the power the change base change Now that's a fairly complicated proof. I'm not going to be asking you to do one like that What I will be asking you to do when we get to trig is what are called t-table proofs Called t-tables because the table looks like a capital letter t turn the page Example three is really what I want to jump down to says this Prove That this is the same as this prove it and What we always do is we draw a great big capital letter t we call this side left side or sometimes even LS abbreviation for left side we call this one right side or sometimes you abbreviate it as what? Qz what are you done? Yeah, RS? Okay, so I'm gonna first thing I always do if they haven't done it for me already I write down the question because it's no longer blank, and I feel better, so I'm going to write down log x cubed plus log of 1 over x equals to log x But not equals I've got a line down the middle that line down the middle is saying you haven't proved they're equal yet Don't you dare cross things over? Don't you dare add five to both like for example? You might think Kara could I minus this to that side? No, because that would be assuming they were equal in order to prove they're equal even if that made the question way way way way easier No, whatever. I'm doing an identity. My rule of thumb is very simple. I start with the uglier side Which side looks yuckier? Left side I'm gonna start with that It's always easier to take something yucky in math and tidy it up But to take something tidy and somehow break it down and make it yuckier, so I'm going to well What could I do with this? left-hand side Make it one log. How did you figure that out? How many logs are there on the right-hand side? One why don't I try right in the left-hand side as one log if I'm trying to show they're equal? So one of the things I'll teach you is whenever you're doing an identity You always flip your eyes from side to side side to side side to side trying to say well There's oh there's hints in what the other side looks like can I combine these are my bases the same? Yes Then let's combine these This is going to be positives on top oh I think it's going to be that actually doesn't it simplify to that log of it's really x cubed times 1 over x because it means multiplied, but wouldn't that be x cubed times 1 divided by x? Yes, oh Does that simplify how many x is on top? How many on the bottom how many left and where what are we trying to show Ellen? Now You will find especially in trig when we're doing like eight line identities that are long and tough Two or three lines from the end often you'll see it You may even get a little nerdy adrenaline rush when you see it seriously So I don't know if you suddenly saw it here, but right when I wrote that down I was oh wait a minute Ellen. What can I do with this too? Does the left-hand side equal the right-hand side? Yes Some teachers will teach you to do this. Don't write this down. What do you think LHS equals RHS stands for? And you can Justin am I somewhat of a nerd just a tad Traditionally for actually for hundreds of years after a proof Back when everybody spoke Latin you would write you can write that down if you want to you don't have to but you can It's Latin it's there for maybe here speak Latin and know what it stands for Had a German student a couple years ago who we did Stands for quo Erthaus demonstrandum Which means which was to be demonstrating which I was trying to prove We used to joke in rock Ryan in university that stood for question easily done And was the biggest lie on earth because most of my university proofs were four and five days Like 40 lines. Oh, there are proofs that are several thousand Fermi's last theorem which was finally proved about 15 years ago by Andrew Wiles I believe this proof is about 600 pages long and probably only about a hundred people on the planet can follow it They checked it and it's correct So three lines nothing. I always like to write QED. That's that's you know when they score a touchdown They spike the ball. That's me spiking the ball You don't have to but it's also nerdy. I like pull out the lap example for example for Prove this Okay, which by the way normally I would write down the question But I've done this one before and I know we're gonna run out of room So just this one if you did that's fine, but there's just this one time. I'm not gonna because it's typed up there Which sides uglier I think definitely left side, okay What else do you notice looking at the left side and looking at the right side because there is something here that's giving me a real hint as To what my strategy is gonna be Do you see something on the left side that doesn't match the right side the bases? I'm positive. I'm gonna use the base change law What am I gonna change the bases to I think 10 because first of all that's one that we kind of like That's the one on the right-hand side and what are the two bases on the left-hand side? 10 See I was able to kind of put those kids five and two come on ten So what's the base change law? Okay? one over plus one over if I wanted to rewrite this as base ten I would write log base ten of X over log base ten of five Mr.. Dook you didn't write the tens when I don't write a base Balmoneek What is the base automatically assumed to be ten? It's a three-level fraction shut up and deal with it and This is gonna be log base ten of X over log base ten of two I have not yet got my nerdy adrenaline rush I have no idea where this is gonna end up. I would probably do this just to tell myself That was one term and that was one term. In fact, I think what I'm doing here Justin is I'm dividing by a fraction Multiplying fractions is the easiest top times top bottom times bottom How do you divide by a fraction? Oh? Someone remembers their math eight if I had to go three divided by five sevenths. I don't what do I do instead Brett? three times Seven over five if I have to go one divided by this I don't I'm gonna go one times this flip This is gonna be the same as one times the log five on top over the log of X plus one times The log two on top over the log of X By the way, Tyler will this one times and this one times make any difference at all In fact, I wouldn't have freaked out if you had just said, hey, I Know that simplifies to that I'm gonna have to do this and I'm gonna have to do this I'm gonna run out of a room otherwise So now what how do I add since how many fractions do I have on the left-hand side here? To how many do I have on the right-hand side? Let's see if I can combine these as one fraction. Now, how do I add fractions? Hmm? How do I add fractions? What do I need before I can add fractions? I need a common denominator. Oh Wait a minute. What's my denominator in the first fraction? Log X. What's my denominator in the second fraction log? I have a common denominator.  You can make a little note Two over five Plus one over five. It's not three over ten. What's two over five plus one over five? Three over five you add the tops and keep the denominator when you're adding fractions so let's add the tops and Keep the denominator Now I have no idea where I'm going But I'm just being meticulous careful and trying to be a bit clever by looking at the right side and saying what does it look like? Now what? Hmm. Oh Did you get your nerdy adrenaline rush? Did you see it already where we're gonna end up? Because you're saying that these bases are the same adding is the same as what and I'll get the log of what ten What is the log base ten of ten? What do I have on the top on the right-hand side? Oh I think we can do this This is the log of five times two Over the log of X and I'm gonna go cross out the five times two. I'm gonna put a ten there and what's the log base ten of ten What's the log base ten of ten? Turns out it works out to a one over and on the bottom I have a log it is base ten what I don't write a base of X coal air-toss demonstration Which was to be demonstrated question easily done. I kicked it Justin. These are weird I'm fully expecting you to have a tough time with these if you do your normal If you don't you're one of the Eric Bing freak types, which is good Helpful, but what I want you to see like if you find this tough.  See if you can prove number four Take a look at number four. Can you tell me what strategy you're probably going to try? There's one that's screaming out to me as the first thing. I'm gonna try base change. You know why three different bases Probably try changing everything to base C. Hey, I don't know try number five Five a is pretty tough eight is good Nine is good Then what I would like you to do No, can you turn me pause for a second in the video here So if you want to turn to the blank page page 150 and Write a little heading. We're gonna practice some if then questions because there's a couple on your quiz So as a heading on page 150 you can write if then questions This is that weird one that I made a bonus question on the last quiz and now I said hey no longer bonus fair game These are almost always multiple choice on your test on the provincial exam They were always multiple choice and since this is the last year. I'm teaching math 12 I'm not gonna change your tests. So here is your first one It says if log bait well copy it out if log base three of y equals c minus log base three of x Where y is positive and x is positive because you can't take the larger than negative Then y is equal to See a few of you squinting you do that It's about as big as I can get it if you're still squinting Two words black says and if you want to also on the left-hand side Quickly copy out the answers because I've tried to teach you Trevor when it's multiple choice for Pete's eggs glance at your answers for help Right, Maria. What's this question asking me to find? Then what? Find the word then then what it wants me to get the y by itself Okay, I'm that you know what I'll eventually do that now I look at this equation this expression that they gave me are there logs in every single thing No, no log there. You know what I would do first I'd get all the logs to the same side because that's how I taught you to solve equations then algebraic Which would probably try the same strategy So the very first thing that I would do is plus the log base three of x over I have no idea where we're going I do notice in my answers. What don't you see in any answer anywhere a log? I Have a feeling will probably write something as an exponent at one point along the way. I do see some exponents So I'm gonna write this as the log base three of y plus the log base three of x equals c Carly I have no idea what to do now, but I'm stubborn. I'm clever. I'm a good academic student. I refuse to quit I've got to try something What might you try what log log can you suddenly now apply? I try combining them because I notice my bases are the same. I don't think that's a coincidence Adding two logs is the same as what okay instead of writing yx all right xy alphabetically How does that help? Or does it? I'm stubborn. I'm clever. I'm an academic student Rhett. There is no way. I'm allowing myself to freeze up by the way I'm trying to show you how I would do these on a test. I would be stubborn However, if I couldn't get it within 60 seconds, I would circle it and come back to it later I'm not gonna spend 20 minutes on one question. That's also bad test writing So I've gone through the rest of the test. I've come back to this one because it bugged me I got to try something. What else could I do if you know one, you know both So you ready Spencer you're going to once again tell us what that is as an exponent What to the power of what equals what Maria? What did you say this question was asking us to do? Oh? Which really means isolate don't get the wide by it. How can I get the wide by itself? Ah? I just got my nerdy adrenaline rush. I see where we're going okay That's one type of if then question The other classic one is it where they give you two log expressions Like example two here says number 17. Yeah, it was number 17 on the provincial exam about 15 years ago Says if log base three of x equals 15 then the log base three of one third x is equal to Haley can you recognize this as an if then question see the if and see the then now sometimes there won't be a then There will just be a comma because when you put a comma in English It sort of implies that but almost always they'll do an if then okay? My strategy is always start with the then This thing try turning it into the if oh and there's apparently Four answers and the answers are all numerical with weird, but we'll see and I Have three things once I look at the then that I check for first thing I always check first is base change are my bases the same in the if and in the then Okay, then I'm not going to use base change If not, I would but Joel they would pick this question very carefully My second base would be a base nine or base 27 or something that works well with a three But base change no Then I look and I ask how many logs do I have in the then if I have one term I break it up if I have more than one log I combine them I think here. I just have one single solitary log So my first strategy is going to be I'm going to break this up. I Have a one third and an x mathematically. What's happening between them? So what will that become outside the log? This is going to be the same as the log base three of one-third plus The log base three of x. Oh Ryan can you read this to me, please? Base three base three big say it again properly log base Can you read this to me? What is the log base three of x the same as according to this statement? Oh kind of nice Hey, hmm What's the log base three of one-third work out to in your head without a calculator? Not one log base three of three would be one. It's a log base three of one-third Negative one elevator. Yes. Yes. Yes. Yes This whole mess works out to that and I'm gonna argue that even mitzvah can get that one in its head mitzvah Add those two together. What's the answer? Kind of see how we're approaching these by the way You need to practice these and there's a bunch on the great big log review that I gave you number three This is actually from an Alberta Provincial exam on the Alberta exams. They had numerical response This was a written if I gave this to you it would probably be a multiple choice question But still we'll handle it if log base B of a equals point eight two Then the value of log base B of B over a correct to the nearest hundredth is Isabel see the then I'm gonna work with This thing flat. What's my base here? What's my base here? Not using the base change law so I always check that first because it's easy to spot Do I have more than one term or just one term? One term break it up more than one term to mine So one term I'm dividing what's dividing inside a log the same as black So you're telling me that this is the same as the log base B of B minus the log base B of a I Agree. Oh Emily, what's the log base B of B with authority, please? One oh and Emily According to this question, what can the log base B of a all by itself with no exposure to anything be replaced with? Apparently, this is one minus point eight two And I think it's fair for me to expect you to be able to subtract two decimals from one in your head with no calculator I would expect you to be able to do that without a calculator to point one eight Yeah, how many sig figs that's physics a couple more. I think three more two more number four What used to be number 32? If the log base two of B equals C then the log base four of B equals Hmm if the log base two of B equals C then the log base four of B equals and And then the options are C over to C squared to see or root C I'm guessing a two is gonna show up somewhere in the answer Down hit there Can you see what I'm gonna try what's screaming out to me as my first plan of attack here? Dominique You're right louder When I say louder, I actually mean louder not the same volume seen one act one and take two and action Dominique base change Can't you see how you can glance at it and tell hey two and four ah, but notice what they picked for the bases They didn't pick two and seven They picked two and four or they might have picked two and eight or two and sixteen or two and thirty two But I'm gonna tell you they're not gonna pick two and 20 They're gonna contrive these So I'm gonna rewrite that second the then as base To if I rewrite this as base two this is going to be the log base two of B Over the log base two of four now It's a base change law and you absolutely want to make sure you know this one now Brett can you read them and can you read me the very very top right here? I Disagree, you know what that really is and oh What is the log base two of four Emily? Hey? Didn't see that coming and tell about one line ago, but hey Starting to get the hang of these a little like there's a there's a science and an art to these and really all I can Do is show you a few and say here's a bunch knock yourselves out last one if log base five of X equals four point two six What's the value of log base five of 25 X squared? Try this one on your own base change No, oh one big log break it up Ryan here was my strategy Multiplying same as adding oh I notice the X doesn't have a squared here. I don't want the X to have a squared And log base five of 25 that's two Plus two log base X of sorry five. Oh log base five X. Oh, oh That's a four point two six with a two in front of it.  What's your homework? I gave you this a Logarithms review quite some time ago. I think did I not the great big unit review? We're approaching the end of the unit For more lessons, I think so I'm gonna start to give you a few questions from here Specifically I'm gonna give you some if then questions that you can start whittling away at now These are not all for homework right now These are due the day of the test, but if you're wanting some more practice on these types of questions Now if you can't find this great big one jot down the question numbers elsewhere and hunt for it later Or I have a few extras still buried away somewhere number five is An if then question Number 15 is a disguised if then question Number 20 is a disguised if then question D5 is a disguised if then question 38 is definitely an if then question 51 52 58 70 sort of It's a simplify log question, but that's okay. I thought there was one more. I knew there was at least one more 85 103 Then you come to some written questions If you're wanting more practice solving the logarithmic and exponential equations Lesson last or two days ago and three days ago, which I kind of yelled at you last day saying was really important You can try something like number seven number nine 11 12 those are logarithmic. Here's an exponential equation number 15 16 is another log equation 18 is another log equation Gives you some to try is all that do first of all try the workbook identity stuff It's good practice then you can start whittling away at this and you have a take home quiz Okay