All right. All right, Andy, what I'll do is I can do some more research, see if there's anything coming out here in the next couple of days. I do have your number. If I'm finding anything, I'll reach out to you. Come on, man.  Do you want to sell me this car? Let's make it happen, man. She's like a vengeance. You gonna see me in this. Okay, guys, so here's what we're gonna do. I'm gonna take this one. I'm calling on a Tesla 2022 Tesla with 56,000 miles. I'm gonna tell them, oh, man, I just saw the miles. All right. Hey, Chris, I was calling to get some information on a vehicle I saw on the website. It's gonna be used. Will he get my name? Yes, hold on one second. I'm gonna pull this up for you. It looks like it's M034465. M034465. Will he get my name? Will he get my name? Come on, dawg.  Can't get their name. You can't build a relationship. Member order takers. Is he an order taker? Can he make connections that others can't? Come on here locally in Bakersfield. Sure am. I ain't got my name yet. Hold on. Oh, Andy, don't put me on hold. I already saw the pictures on the website. I just wanted to see if you still had it. Never tell them you wanted to talk to your manager. Yeah, yeah, but I can hold on my lunch break. Okay, I'm gonna tell you what he did wrong. Number one, super important. I'm gonna bust this guy's up here in a minute, okay? But number one, couple things that he did wrong. Number one, he got my name too late. Hope you have the best day of your life. This is Andy. How can I serve you today? Oh, you're calling on that vehicle? Awesome. I've got a bunch of these in stock right now. You know, let me pull up my computer that way I can make sure I get the exact vehicle. By the way, where are you calling from? Oh, okay, cool. Awesome, you're local and I area. That's awesome. We love serving our community. Our community is most important to us. Okay. And by the way, if you have the chance to drive one of these yet, you know, you can go into, you know, what got you interested in this vehicle? Well, I'm pulling this up. Number one, never say I need to check on my manager. Everybody listen to me. Never say I need to check on my manager. By the way, now I find no authority in him. I find no reason to deal with him because he needs his daddy. Hey guys, what's going on? It's Andy. A lot of you leave comments, telling me that you need help. Do me a favor and tell you the best way to get a hold of me. Shoot me a text message right now,<PHONE_NUMBER>.<PHONE_NUMBER>. I'll help you with whatever you need.  Let's get back to the video. He can't help me. He needs his daddy to help me. Is it his job to walk the inventory when he comes into work? Is it his job to walk the lot and see what cars are for sale? Or is it his manager's job? So if it's his job, then he's valuable to me. But if it's a manager's job, why am I on the phone with him? Is he an order taker? Like what is he doing? And by the way, did he come to work today prepared? I went to the website just now and I see 50 cars in stock. Okay, awesome. Real quick, Chris, how many miles are on that? Okay, all right. Yeah, I know the miles are too high. I didn't see the miles. Okay, I'm gonna look for one with a little less miles. I love that car. I just wish it had less miles. Chris, let me ask you a question real quick. Do you wanna sell me this car? Chris, let me ask you a question. If I looked for a lower-mile car, would it cost me more money? Chris, listen to me. If I looked for a lower-mile car, would it cost me more money? Okay, so I saw this vehicle because I was interested in the price. I saw the price. I call you on it. I like the car. I hit you with an objection. I say the miles are too high.   Am I right? Correct. Okay, do you think I'm gonna wanna do that? Or do you think I like the price of this car? This one. Okay, so can you overcome the miles are too high? I want you to write this down. Go ahead. Andy, I totally understand. However, with this vehicle having a few more miles, all the depreciation has already been taken into consideration. You know what that means? This is the Tesla. These vehicles are ready to run a half a million miles. This has got 56,000 miles on it. That's nothing. I don't know how long your plan on driving it or how many miles you drive a year, but you could buy this car, save money, literally have a lower monthly payment, pay less money, and then when you go to trade it in down the road, not be upside down and owe more money like if you spent more money on a lower mile vehicle. If you know anything about Teslas, they're rated to run a half a million miles. So if money's your biggest concern and getting a lower monthly payment is important to you and the vehicle's gonna drive the exact same and if you cover the odometer on one that had 56,000 miles or 30,000 miles, they drive the same. Most of our clients actually reach out and try to find these Teslas with more miles so they can make a better deal. Does that make sense? Got you. Good, so you must have a magic rabbit foot in your pocket cause you just won the lottery and it's your lucky day. When are you gonna make it down so you can touch it, feel it, smell it, make sure you love it, and then in the end we'll sit down and talk about it if you don't like it and I'll look for something else a little miles if that's what you really want. Is that cool? That's awesome. All right, come on, man.  All right, listen to me. Next time somebody says an objection, I want you to run through it and I want you to close them, okay? Remember, write this down. The biggest part of the depreciation has already been taken into consideration. You always start out like that. If you had to buy a vehicle that had lower miles, you would spend more money. More money would be a bigger payment. Okay, if you cover the odometer on a car with 56,000 miles or 30,000, it is 2024. These cars are rated to run a half a million miles. There is no difference. This isn't 1999 anymore, sir. Okay? You feel me? Yes, sir. All right, all right. Don't let anybody leave again. See you, buddy. Okay, so that was a good chance to coach somebody, right? So notice, what did I say? The biggest part of the depreciation has already been taken into consideration. Listen, Chris, if that car, if there was a car and it had less miles, it would have cost you more money. I'm sure at the end of the day, you saw the price tag on this vehicle and you're like, dude, that's a good deal. Then you reached out, the miles are too high. Had it been 1999, the difference between a car with 50,000 miles and 20,000 miles was a lot because cars only ran 100,000 miles and then they blew up, but it's 2024. 2024, these cars are ready to run a half a million miles. That's nothing. This car's not even broke in. Literally, the oil change used to be every two to 3000 miles on cars. Now on most cars, it's every 10,000 miles. Yes, see, it's all perspective. Selling perspective could be the greatest thing that you ever do, which means getting people to see things the way that you see them. Okay, Chris was seeing that the miles are high, so that's a bad thing. I see that the miles are high because it's a good thing. Does that make sense? I understand this. Most of our clients, Chris, they actually reach out. Guys like the miles are too high. I'm like, oh wow, that's crazy. You've never heard that before. Most people are upset because they actually don't want one with really low miles because they have to spend way more money and they have a way higher payment.  Most of our clients actually call in and want something with a little more miles because all the depreciation has already been taken in consideration so they can make a good deal. They beat the depreciation cycle so that really today when they buy the car they have a lower monthly payment in three years and they trade it back in, they're not upside down and actually a lot of them have equity in cases like this. You guys see it? Flip it. What eyes do they need to be seeing out of? Your eyes, not theirs. Your job's a self-respect. Hey guys, I just want to tell you you're the true one percenters. You made it till the end of the video. Do me a favor, share it with the friend that wants to go to another level. Make sure you like the video, comment below so I know who you are. Set your notifications and then subscribe to the channel. We got daily sales training videos dropping. I'll see you soon.


I have a new spider. Bear with me, there's a point to this. This is an atypus affinis purse web spider, also known as an atypical tarantula. She's about 25 millimeters long, jet black and lives underground. I found her the other day walking across the pavement outside my apartment, which is very much the wrong place for a burrowing spider so I took her home with me and put her in this enclosure.  Her burrow is under here and you can see here the end of her trap which she uses to catch prey. This blob, by the way, is a spider turd. Now the problem is these purse web spiders, they live underground and they're only active during the night. So if I want to get video of her building her trap and various excavations over here, I will need a camera that works at night. That is why I'm making this video. So she has gone back to the study allowing me to bring out my second exhibit. This is a Fuji Finepix F5700 digital camera, as you can tell from the label. It is the camera I had before I had the camera before the one that I'm recording this video on. It's old, it's not particularly brilliant and honestly I thought this was broken until I turned it on before this video. Turns out that this camera is actually pretty good at picking up infrared. So if I can build myself an infrared lamp out of an LED ripped out of an old remote control, I'm sure I have one somewhere. And if I can remove the infrared filter from this camera, I should be able to rig up some kind of infrared filming system which will allow me to record what the spider does during the night. Now a little bit of background. The CCDs that these cameras operate on, which you cannot see through the lens there, are actually sensitive to infrared. But this causes the pictures to come out weird.  And with this camera, it's allegedly pretty straightforward to open it up and remove this filter. Just thus allowing the camera to pick up infrared and there's all kinds of interesting visual effects you can do during the daytime. But what I'm interested in is doing nighttime recordings. This is a little bit risky in two ways. Firstly, digital cameras are pretty delicate. And there's a reason why I want to do this with this old camera because this is worth nothing. I actually thought it was broken until I tried it earlier. The second risky part is that the camera flash is driven off a pretty meaty capacitor. And it's important not to let the capacitor discharge through me because this can be potentially life-threatening. So I am going to have to be extremely careful and possibly make sure it's discharged using my patent discharge resistor, which is not patented. So the first thing I need to do is go and find a copy of the instructions because I am not doing this blind. Okay, well, I've got the instructions set up here and I've got my tool. So let's give this a go. The first thing it says to do is to undo these two screws here. I do also have a Canon 1000D. And now it wants these two. A Rebel XS in American. And that is also convertible. But the process looks incredibly fraught and I don't want to do it. That will produce much better results. It doesn't record video, but it is possible to budget using a PC so that you can get video out of it. There we go. All right. We're already on to step three, which is undoing more screws. This will record video, but it's only 640x480. So we'll see. It'll do for a first try. That's better. Okay, we do not undo these two, but we do undo these three. That's this one, which is a little bit fluffy. I think a battery has not had a good time there. Three. All right. Step four is this side. This is where the card lives. And you want to undo this screw. All right. Now it says gently lift up back cover. I think that's this. It does seem to be quite a lot of stuff coming with it. Oh, that's interesting. This is broken. I hope I just didn't break that. Just needed coaxing. The screen has not separated. I think the stress was supposed to have been left behind. What fastens this in glue? You can see in there the screen is still connected. There's a solid metal back. Right. It's glued. So gentle pressure and it's coming loose. There we go. Yeah, it's ancient adhesive. This thing is years and years old. Is there a manufacturer date? I don't see one. There we go. Right. Wow. That's disgustingly dirty. Okay. Disconnect the marked ribbon cables. This one is should be flipped up like so. And it just pops out.  Giving access to this connector. And that comes off. Yes. That probably wants to clean before I put it back in again. We need to remove the screws for the cage. Okay. So that exposes the PCB. Another warning about terminals up there. And instruction to flip this open. Now we're here. Just going to have a quick look at the PCB. Here are the buttons for the controls. Little cast and net things. The main chip is a Sanyo evincer. And some code numbers. Piece of transparent plastic there for some reason. This, the shape looks like a flash or a RAM chip. I suppose it could be either. This thing has a small amount of internal storage. Well it'll have internal flash for the program. But it's also got some internal flash for storing photos. Not very many. I think there's enough space for about four seconds of video. Okay. Gently unscrew this one. And disconnect that ribbon cable. Gently lift up the circuit board. This exposes. This is the monster flash capacitor. Which is definitely to be avoided. There's a sensor of some description here. It might be to detect whether the case is open. Apparently it does have something that does that. Thing is, can I get this folded out of the way? Because you need access to this little board inside. Are there any tight looking wires? I think all we need to do now, we need to take out four screws. This one. This one. This one. This one. Can I actually reach that? Yes. That screw has fallen into the case. Disturbingly close to the high voltage lines. Let's try and remove the rest of this. Question. Do I want to try and discharge that capacitor? It's my resistor. It's a one mega ohm resistor. Which provides enough resistance to avoid sparks. But it'll still discharge reasonably quickly. Let's get this one out and then see what's changed. All these little silver screws are the same, thankfully. Okay. So does this now allow us to lift this PCB up? Yes. Not very well. Yes. Let's discharge this. That should be all that's needed. Assuming it made contact, that is. But that should at least make it a little bit less fraught working on the thing. This board is tucked under this metal thing there. The instructions do not actually show that metal piece. So let's just pull that out. There we go. And this reveals here. This is the sensor and that shiny pink piece of glass. I don't know if it's showing up pink on camera. It says it's called the hot mirror. This is the filter. And it says it's not glued. So I should just be able to lift it off like that. Beautiful, clear piece of glass. That's going to get horribly dirty as soon as I put it down. Then we tuck this back in and it's time to reassemble. Before we do that, just remove that screw. All right. That's a different size to the others. So let's just deal with that now. So this goes there. Let me do up the other screws. There we go. This, I don't know what it is, but it pushes against that piece of plastic there, which is interesting. Anyway, this now folds down. That's ribbon cable out of the way. It should push into place. This I think goes over. No, this goes under like so. So screw here. This was the only one we took out from the PCB. Okay. So let's do this ribbon cable up. So the clamp folds up. The ribbon cable drops in and the clamp goes down. Very simple. I like these connectors. And now we simply go in reverse. We've done this bit. Now we want to put the cage back on, which goes here. This is the most dubious screw hole because it's got this ground thing there. So let's actually start with something easier. Let's do this one. Now look at the state of the viewfinder. I took this to a lot of places. I took some quite nice pictures with it. As a starter camera, it worked quite well, but the sensor left a lot to be desired. Well, not so much the sensor, the lens. It suffered badly from chromatic aberration in bright environments. So trying to take pictures of trees against the white overcast sky. There'd be rainbow banding all over them. Okay. Now we want the... Let's actually take a moment to clean this. Yeah, I don't think that did anything. Okay, so the screen sits on like this. So make sure the flap is up. Push the Mylar connector into place. Push the flap down. Come on. No, that's not working. I think the cable wasn't in right. That's better. Okay, and then there's this ribbon cable. This is the one that operates, that is used to get access to these buttons and the wheel. In fact, not the front panel buttons. The front panel buttons, of course, push these castanets switches through the cage. So this is another of these. This one's probably trickier. Mylar goes in like that. Push down. Come on. There you go. That's in squint. Let's do that one again. The folds in the Mylar are all permanent. So in fact, it's very springy and doesn't want to go into the right place. Come on. There we go. Like so. Good. And now this should just push down into place. Except we need to put these back on. That goes on there. And this goes in here like so. So push the back on. Good. That has actually gone into place reasonably well. Now it's this screw. All right. So with luck, we should now have an infrared capable camera. So I'm just going to have to hook it up. What's my PA on that? So we're just going to, I'm going to have to now hook it up and see what comes out. And more importantly, see if it still works. Better. Still not brilliant. All right. I will be right back. All right. I have the camera all hooked up and ready to go. I have the AV output from the camera fed into a video capture thing, which is why you're seeing this box up here, which contains what I will be seeing on the screen. Sadly, the AV output resolution is dreadful, which is why everything is so fuzzy. I don't think it's 64480. I think it's more like 320 by 240. It's really bad. But it does at least show how the thing works. So the first thing I will do is get out this remote control and demonstrate that it is showing up. It gets on camera UV. And yes, most cameras will do this, but if I hold the filter glass in front, come on, you can see that it is blocking out nearly all the light. So you can just see a bit flicker with the filter, but without it's good and bright. And in fact, you can use it as a infrared flashlight, which is nice. And of course, my real camera is showing nothing at all because it does have an infrared filter. Okay. Now, the bad news is that the autofocus on the camera doesn't seem to be working properly anymore. It works all right at close range. So I have it pointed at this screwdriver so that I can focus on that. And it is succeeding. The picture on the screen looks all fuzzy, but if I take a picture, I can then use video editing to slap that picture I took up and you see it is actually mostly in focus. However, if I pull it back and pan up to this focus target I set up and try and focus, you see that it is complaining that autofocus has failed. And I'm not sure why it's doing that. Now, I forgot to actually test this before I did anything, so it may be that it was in fact broken before then. However, I can switch to manual focus, which is kind of terrible on this thing. To do manual focus, I have to hold down the button here and then use this rocker switch to adjust the focus. And it does it really slowly. So that is the wrong direction. And that is as far as it will focus. So I am not really sure what's going on. This is a flat piece of glass. It shouldn't be affecting the focus properties of the camera at all. So that's interesting. I wonder if the focal plane of the sensor has moved somehow. Maybe this thing is supposed to act as a spacer. But I wouldn't have thought it was be that loose. It certainly wasn't when I undid it. However, you can work around it by using the zoom. That thinks it's focused, but it hasn't. So let's just manually adjust. Come on. Oh, yeah, it won't go in that direction. There we go. And you can see from the yellow circle in the middle of the viewfinder that it thinks it's in focus. So I will take a picture there. It thinks the camera is shaking probably because my hands on it. Let's just use the timer like so. So you can see that this photo and the other one has actually worked reasonably well. I mean, it's not a brilliant camera. It's years old and wasn't particularly expensive, even when new. But I think this will do fine. What I'm going to do is not try to use the camera's own controls to actually film the spider. I'm going to try and drive it from a PC using the USB connection, which is a non-standard thing that the AV is coming out of. It can either be analog, composite video, or USB. At least so I hope. Anyway, I believe that I now have a working infrared camera, which is nice. The next step is to light the spider's enclosures somehow, and for that I will need an infrared floodlight. So I am going to tackle that one next time. I hope you enjoyed this video. Please let me know what you think in the comments.


The word firmament is mentioned 17 times in the King James Version of the Bible. The Day 2 creation account in the first chapter of Genesis describes God making a firmament to divide waters above from waters below. What was this firmament? Understanding what God made on Day 2 can lead to some stunning astronomical conclusions. Coming up on today's edition of Origins, the firmament of Genesis 1 with Dr. Danny Faulkner. Hello my friends and welcome to Origins. My name is Don Chapman and it's my privilege to be your host. During this program we showcase interesting guests who present evidence from science along with other important facts validating the truth of creation and the accuracy of God's Word. Today's guest Dr. Danny Faulkner earned graduate degrees in physics and astronomy and taught at the University of South Carolina Lancaster for 26 years. He has been extensively involved in creation science, writing many articles and serving on the board of directors of the Creation Research Society. Several years ago Dr. Faulkner retired as professor and now has joined Answers in Genesis in Kentucky as a full-time scientist and speaker. Dr. Faulkner it's such a privilege to have you with us. Thank you. Now today we're going to talk about firmament. I've got to tell you that title doesn't do anything for me. And I know this is something that is kind of new things that have happened in you that you want to share with us. Well you're bringing the listeners on board. Don I want to tell you over the past year or two my whole understanding of this has changed, I've changed my mind about stuff and it's rocked my cosmology to the core. So I'm excited about it. You still believe that God made the heavens in the earth. Oh yes, in six days a few thousand years ago but I've got a different appreciation I think sort of where things are and how we put it together. And I think this is important because I've been stymied for decades trying to put together what I consider a good creation model of astronomy. If we can't get something this fundamental right then what hope do we have? So I think we're making progress now. So I'm excited about this. We're excited to share your insights. All right. Well anyway, the firmament or I'll call it expanse is probably a better term for all this. Let's go back to Genesis we should go back to Genesis and read about this. The very first verse of Genesis is in the beginning God created the heavens and the earth. That's pretty straightforward. You'd think it's talked about separate things maybe but you're looking at those kind of jump out at me. The heavens and the earth. What does this mean? By the way, you may notice that it's heavens here but in some translations it's heaven. So which is correct? Yes. We'll talk about that more in a minute but it's tricky to do this and you'll see why in just a minute but that's the very beginning thing here and many of us including me for many, many years thought that this was the heavens here was the creation of space as we know what we call outer space today. Now of course you know in ancient times the Hebrews, well nobody really understood what we mean by outer space today. It's a different way of looking at things. That's a modern concept. First of all I want to show this photograph to you. That's a photograph of the center of the Milky Way. I took that recently. I was in South Africa and I took this with my camera put on a tripod and had some help with it and fellow helped me do some Photoshop on it but that is a really nice photo of the Milky Way I do believe. You know the Milky Way is our galaxy. It contains a few hundred billion stars and we're just one of those huge, huge array of stars but you know we read on day two. At the beginning of the day one account just as one one but we learned that on day two God made this thing called the Affirmament and I put in there expanse because a lot of modern translations render it expanse rather than it as as firmament and I think that's a better better rendering altogether. And you know going back 45 years ago when I was in high school I read this in the Genesis account and I wondered what is this firmament thing? And I just puzzled over that for years and I'm glad to share with you today some of my conclusions I've reached. Well we know we made it on day two whatever it is and I want to read out here if I could the day two account only found in Genesis verses six through eight here and it says in God said let there be an expanse in the midst of the waters. I'm not going to pass waters there too. And let it separate the waters from the waters and God made the expanse and separated the waters that were under the expanse from the waters that were above the expanse and it was so. And God called the expanse heaven and it says there the evening and the morning or the second day. Notice the expanse is mentioned several times there and the waters are mentioned several times it turns out waters are mentioned a number of times. Lots of water. And the numerous times in the Genesis account of creation. You know 2 Peter 3 talks about the waters going back to the creation being very abundant. So let's note a few things here. By the way this is a photograph of the Pleiades. I didn't take that but a friend of mine did. The Pleiades is a star cluster. It's prominent in the winter sky and it's mentioned three times in the Old Testament twice in Job and once in the book of Amos. Well what can we note about what we've read so far. First of all what we've talked about so far is day one and day two. And day one and day two appear to be different things being talked about. So we need to be careful we don't read into day one some things that maybe were on day two and vice versa. That's tricky and it's caused some rethinking on my part in recent year or so. Also there's waters above this thing. Whatever it is it says it's to separate the waters from below from the waters above. Again water playing a very key role in the creation account. And I've been puzzled a lot really these waters above what are they? Where are they? And what are they doing today? That's a big question and it's changed my way of looking at this entirely once again. And also as an astronomer I'm very interested on stars because well I study stars and people specialize. People do different things in astronomy like stellar astronomy. That makes me a stellar astronomer. You see. I think so. But the stars were not made until day four. So whatever is going on here on day one and day two it didn't include stars. That's right. We need to keep that in mind. Again we don't want to try to bring things from day four into day one and day two. We want to keep day one and day two straight. I think many times we've kind of blurred those distinctions. We need to be very careful because God went to the trouble of making a distinction. He did. And so we need to honor that distinction and maybe there's some subtle clues that we can pick up in all of that. Now remember it talked about the heavens. God made the heavens on day one. Heaven's on earth he says. But then he makes this expanse on day two and at the end of the day two account he equates the expanse with the heavens. God called the expanse the heavens. So it kind of puts us in a curious position. Did God create the heavens two times? Once on day one and once on day two? A quick reading would have you think it's on day one and it's also on day two. And that's tricky. It is. And I don't think he created the same thing twice. He created it once, whatever it was. Now he could be talking about two different things. A lot of different possibilities here. But for a very long time I want to point out that I thought that God made space on day one. And so when he starts talking about this expanse on day two, what is that? What is that sort of thing? And the way we interpret that will have profound effects upon our cosmology and ultimately upon our astronomy. And hey, as an astronomer, as a creation astronomer, I'm keenly interested to find out what kind of model I can build based upon the Biblical data there. I just build models or theories all the time. We creation scientists do the same thing. It's just our worldview is different. We start with Scripture rather than starting with man's ideas about billions of years and evolution of everything and existence. Well, firmament, heaven. These two terms sometimes used interchangeably, it seemed. Well, take a look at the word heaven. The Hebrew word used there is shemaim. When you see that I am ending it means it's a plural. What's interesting is there's no singular form for it. It's a plural form that works for both heavens. So it's never heaven as always heavens. Yes, right. Well, wait a minute. Expanse or expanses. It can work either way. Think of the word deer. You can have one deer or two deer or three deer. It's the same word, moose, elk, same way. You don't have mooses or deers. And you usually tell from the context how many you're talking about. Particularly if it's a subject of a sentence, the verb will help you. It can be plural or whatever. Unfortunately, in the vast majority of times, and by the way, it occurs 420 times in the Old Testament. So there's a lot of usages. That's a lot. But in the vast majority of situations, it's used in the objective case, not the subjective case. By the way, the word is translated heaven most times. I think 398 times either heaven or heavens. 398 times the other 22 times it's talking about things up above us can be the sky above us, for instance. So there's no doubt what this means, really. It's pretty clear. It's talking about things above us. Now, the thing translated firmament, and again, a lot of us today would say expanse because that's most modern translations say that. It comes from the word rakia. Rakia. No, I got to get that sound inside if you want to do it right. Unlike Shemaya, it only occurs 17 times with such fewer instances. It's more difficult to translate. And it occurs over half of those times, 9 of the 17 in Genesis 1 alone. There are the verses right there. So it's only used eight other times outside of that. And even then, it's not talking about the same thing many times. So when it comes down to rakia, firmament, expanse, whatever you want to say, it could have some wiggle room on what you think that it means. And this has always been a problem in trying to decipher this. Well, the day four account comes along right after that. And I'm going to quote here directly from Genesis 14, 1, 14, 15, and 17. And it says, first of all, let there be lights in the expanse of the heavens. Quite literally, you would say, I guess, mixing English and Hebrew, you would say the rakia of the Shemayim. I like saying that, rakia of Shemayim, but expanse of the heavens. Those two words together in one's modifying the other and one's in a prepositional phrase with it. Well, what do you think those lights are done? Day four would be, that's the creation of the stars. Yeah, the stars and the sun and the moon. We're talking astronomical bodies. And by the way, I think that would include all the things you can't see with a naked eye, like asteroids and satellites and planets. But I think it's talking about astronomical bodies here. And the next verse it says, and let them be lights in that again, expanse of the heavens, that rakia of Shemayim. And then finally it says, and God set them, talking about the lights, the luminaries in the sky, set them in that expanse of the heavens. The same phrase three times in just a few verses, just three out of four or five verses there. And keep in mind that God had just created this expanse in the day two account, whatever it is, the rakia, and he equated it with heavens at the same time. There's an exact equation made there. God said, called the rakia, the Shemayim, called the expanse, heavens. So I think the fact that God went to the trouble of identifying this Shemayim or the expanse on day two, equated it with the heavens, and then almost, you know, with day three in between comes back to this. And he uses the phrase, expanse of the heavens, expanse of the heavens, expanse of the heavens, three times to tell us where he put the stars. I think it's pretty clear what he's talking about. Wherever he put these lights in the heavens, he put them in the expanse. And that's a pretty strong case I think we can make here. Well, conclusion we reached then is that the expanse is where the stars are. Maybe you could just expand that just mean not just the stars, but also the sun and the moon and other things as well in the heavens there. And astronomical bodies in general going in this expanse that was made on that day. I don't want to get ahead of you, but does that word now become a synonym for space? Well, again, we've got to be careful because space is a modern concept. But yeah, I'm thinking in terms of space, if we want to take the ancient concept... It's the place where the stars are. That's what we would call space. We used to say outer space more in the 60s. We kind of dropped the outer now. But yeah, I'm thinking astronomical space. I'll put it that way. Yeah, that's a good tune. And what I'm trying to do here is I'm trying to put it in how the modern people can understand it in a way that the ancients could have understood it because they were the principal audience. And also you have the Bible itself telling you I think propositional truth. And it has to make sense to the original readers. It has to make sense to us. Well, you know some of the ancient people got this. We have here the ancient cosmology. This is a photograph of the celestial spheres or models I used to use in my teaching of astronomy. The ancient Greeks thought the earth here in the center was surrounded by this celestial sphere. It was hard. It was crystalline, meaning it's transparent. We had a glass or something. And you see those little yellow dots on here. These yellow dots are all stars. And those stars are kind of located on this celestial sphere. And the things spun around us as we rotate it each day. I used to use these in my labs to show my astronomy students illustrate some of the principles we see of aspects in the sky. And unfortunately people, they call this the stereomaw. That's the Greek word for this thing. It means something hard and rigid. And unfortunately many people began to read that as the expanse of the firmate, the rakia. They identified their biblical concept with this physical thing. And that led to problems. Again, I could give a whole presentation on that, not enough time today. But I'll tell you this. It causes us then to have pause. We need to be very careful that we don't interpret Genesis in the Bible in general in terms of our current cosmology because it can lead to all sorts of troubles. For instance, this. There's this thing called the Flammarian engraving. It's supposed to be medieval. Here's flat. Over here, flat earth, right? That's not true. People didn't believe in flat earth in the Middle Ages, but that's a common misconception. Here's the sun and the moon and the stars. There's the firmament right there. And here's the edge of that firmament. Maybe there's some water along the edge here. And this intrepid explorer managed to find his way to the edge. He stuck his head out. Exactly. And he's seeing the workings of what's really going on behind. Is that pretty much what you think the people in the Middle Ages believe? That's pretty cool. I think so. That's what people tend to think, you know? That would be my assumption. You could believe this engraving came right out of the Middle Ages. Sure. It didn't. It came from 1888. Flammarian was a French man who wrote a book on meteorology and he used this to illustrate in his book. And it was supposed to represent the medieval sort of thing going on. The 20th century brought a new approach. People then rejected it. We ran into trouble with all of that. So what we did is this became common to believe in the 20th century that the heavens of day one, the creation of very verse one, was the creation of the space of the universe. And I said that was my thinking for a very long time. But then the idea became around the expanse of day two wasn't space but was merely the Earth's atmosphere. And that was a whole new replacement we had. And I think we need to spend a little bit of time talking about how that led us astray at some point. So this led to what we call the canopy model. And the belief there of the canopy model was that the, remember the water is above the expanse. There was water out here above the Earth. And that supposedly protected us from harmful UV radiation. Radio waves could pass out and visible light could come through but harmful UV radiation didn't come. And that would protect us from bad things, why people lived for 900 years before the flood. And the idea was that it collapsed at the time of the flood to produce the waters from above. However, this is largely rejected now. Most creation scientists have backed away from it. Doesn't seem... But not a lot of creationists who are average folks still kind of hold to this, don't they? A lot of them do. I was surprised to learn that. But it just doesn't work physically. And there's some questions exegetically, as we shall see, more towards the conclusion. So if we reject the canopy model, should we not re-evaluate the cosmology here? We need something to replace it with. Yeah. We need to re-evaluate this look at it entirely differently now. And we're going to do that when we come back. We've got to take a break right now. But you're going to, if you've always believed in the canopy model, you want to see what is maybe a better alternative. And we're going to share that with you when we come back. Don't go away. We hope you're enjoying Origins TV. It all started at Cornerstone Television in Pittsburgh, Pennsylvania. We've been producing new episodes for over 37 years now. We praise God for the success of the program and are excited to introduce you to Origins and to us. If you're interested in watching more episodes of Origins, you can find them on our YouTube page. Simply go to YouTube and search Cornerstone Television Network. Click the like and subscribe buttons. Then you'll find the best episodes of Origins in our playlist. You can also visit our website at ctvn.org slash Origins. One more way you can stay connected with us is to subscribe to our free monthly Hope Today newsletter, which you can do from our website. And if you have any questions, call us here at Cornerstone Television at<PHONE_NUMBER>. We'd love to connect with you. Thank you for watching. We are back. Welcome to Origins. We have Dr. Danny Faulkner with us. And we were talking about firmament in Genesis 1. But right before the break, you were sharing with us that your studies have led you to some discomfort with the canopy theory. But if you're going to take that away from us, you have to give us a viable alternative. Can you do that for us, sir? Indeed, I think I can. Okay. I've gotten really excited about these alternatives. First of all, come to the conclusion from some of the reasons I've already shared. Sure. That the expanse is what we would call outer space today. Okay. The atmosphere, too. It's not real clear necessarily, but I definitely think it is what we call outer space. Yeah. And that then leads to some very interesting conclusions. Three startling conclusions, actually, as an astronomer, these are huge. Okay. Number one, if the expanse, this rakia, this firmament is space, then remember, it's separating waters below, on the earth, waters above. So there must be waters just beyond where that is. If the waters are just beyond, then there must be an edge to the thing. There must be an end to the universe. Wow. And that's something that cosmologists, astronomers, physicists can't even fathom today. And it took me, that's all that, whoa, it's like having a head-on collision. It was jarring, but I'm very comfortable with it now because it seems to come out of the Genesis creation account. Number two, since it expands, the rakias, these things expanded or stretched outward, it's coming from the center and where's it, what's at the center of the earth is. So consequently, the universe has a center and by the way, we're pretty close to it. Again, that's even worse than the universe having an edge perhaps because... We're not the center but we're close to the center. We might be the center but I don't have to be, it's like horseshoes and hand grenades. Close is good enough. But there's some evidence, by the way, dealing with redshifts of galaxies that suggest this is the case, astronomers ignored half for 40 years, but there is evidence to suggest that this actually is the situation. Now think about that. If this vast universe has a center, we happen to be near it. What does that suggest? Suggest there's a creator. We've got some sort of special location. We have a special relationship with the creator. And so consequently, most scientists don't like this conclusion at all. These scientists don't want to go there. Quite a few. And then finally, the water is at the edge of this thing. There's water out there. And you know, they say, well, in space, it's got to be, well, maybe ice or baby vapor. In fact, in the universe, we see evidence of water all over the place. Water is the second most abundant molecule in the universe. But everywhere we happen to see it, it seems to be in the solid or in the gas form. But you know what, Don, there were Hebrew words for ice and vapor. And neither one is used there. It's the word Maya, meaning water. So you're not going to go for gas or ice here. You're going to get water at the edge of the room. And how it stays that way, I haven't a clue, but I'm simply taking God's word at what it seems to suggest here. And on top of that, I know from physics that if water, any state of matter, has any temperature at all, it's going to have to radiate. That is, it gives off radiation. Now it's very far away. It's very cool. Also, I believe the universe is expanding. That's good, well-documented from a cosmology and astronomy. So does that mean the edge is expandable? Probably. I'm thinking that. But as this radiation comes towards us, it gets stretched out and it's sent to longer and longer wavelengths. So here's what I would suggest, based on what I read in Scripture, the universe should be, we should be bathed near the center of the universe by all this radiation coming towards us, long wavelengths. Well, Don, that's exactly what we see. That's what you got. Back in 1965, two astronomers named Penzius and Wilson discovered this uniform radiation coming from all directions. It's called the cosmic microwave background, or CMB for short. And 50 years ago when they found this, this was heralded as being a prediction of the Big Bang and the universe started with a rapid appearance of space and everything. But as it turns out, if someone would have taken the Bible very seriously, they might have been able to predict this before this discovery, had they taken this seriously. So today, we've got an image here of what the background radiation looks like. This is like a map of the entire world. There are so many places on it. I think this may be. I'm not saying it definitely is, but I'm simply saying if this, what I've developed is halfway right, this could be radiation coming from the, from the rakia, the waters above that God created on day two. Wow. And I find that fascinating. This is new, very new. In fact, your audience here is hearing this, some of the first people to hear this. And I think that this represents some nice challenges in this sort of thing. I like to show the Hubble Deep Field. This was taken 20 years ago. Each little smudge you see on there, about 1,700 of them are all galaxies containing hundreds of billions of stars. If you held a large grain of sand at arm's length, it would just barely cover this up. That's how small that is, giving an idea of how big the galaxies are. We believe that this is near the edge of what we call the observable universe. The assumption is that the universe is a lot bigger than the universe. I'm beginning to think that maybe the observable universe is the universe and God's allowing us in this late date to finally encompass all of creation. See all of it. See all of it for the first time as a possibility. Well, you know, one of the fascinating things about science is when you discover things, it doesn't leave less. It always makes for more study. There's more to be studied. And you've certainly given us some insight. Let's go back real quick in just a minute to the first verse because one of the things that you said first was that a quick reading of Genesis 1 and 2 almost looks like we make the heavens twice. So how do you reconcile that? I'll come to conclusion. We find the term phrase heavens and earth that God made there. I think it's like an introductory statement of the entire creation account. It's a phrase that says God made everything. And by the way, here are the details of how he did it. So it's an almost like in a written page where there's something in dark print that kind of states what's going to be in the paragraph below. Exactly. And that's what God is doing for us there. Well, that's fascinating and I think it's, I think it makes a lot of sense. Thank you, sir, for your work and thank you for sharing it with us. And folks, I hope it has been meaningful for you. You know, one of the things I love is that in creation, scientists are never afraid to stop looking and developing and finding new truth. And you know, it's God's view that he created you. And that should always be your worldview too. I hope you found this fascinating. I hope you found it enriching. I hope you'll join us again soon for Origins. And until then, God bless you, my friend. Thank you for watching this edition of Origins. If you'd like a copy of the PowerPoint information presented today, you can download an episode guide at OriginsTV.org. Origins is made possible by the faithful prayers and financial support of you, our Cornerstone family.


So first example is we want to prove that these two triangles are congruent First off, let's figure out which triangles we're talking about. So let's name them Now as you remember from other videos naming triangles in order to prove that they're congruent is an important thing It's important to keep the order correct. So let's take a look at this triangle on the left Maybe we could start at angle t here if we follow t and kind of head in the direction of I end of that C We could say triangle t I see well, what is angle t this angle up top here? What does that correspond with? Well in this other two this other triangle off to the right that angle is made up of the shared side and also the segment with one Congruence mark so the angle that shares one congruence mark and fits the shared side is this angle So we'll begin naming our second triangle with C in Triangle T. I see we follow T towards I And up at C in other words we go down the segment with one tick mark and follow the segment with two tick marks In the green triangle the one off to the right. We're gonna follow one tick mark Head towards these second congruence tick marks. So triangle C Is where we'll start head toward a end up at T So we want to prove that triangle C a T and T. I see our congruent How are we going to do that? Well, let's take a look at those congruence marks again. I see I've got one pair of segments Let's call this I see and AT Must be congruent because they both have these two pairs of congruence marks on them and likewise this segment Ti Is going to be congruent to segment a C And then finally just from the way that these these two triangles are drawn. We've got a shared side of the middle And so what that means is I've got the green pair of sides blue shared side up the middle and I've got the red pair of shared sides So we're going to prove that these two triangles are congruent using side side side. So let's get to it So first off remember we were trying to prove that triangle TIC was congruent with triangle C a T We were given the two green sides are congruent So that's Ti and C a and then also we have the two red sides are congruent So we've got what we have given we have what we're trying to prove now. Let's start filling in our three boxes In the previous slide we established that we are going to use the side side side congruence theorem for this proof so we can fill that in as the reason right now And so in order to prove that these two triangles are congruent. Well first off we should Name them. We wanted to prove that triangle TIC Was congruent to triangle C a T in order to do that we need to first prove that we've got a pair of sides another pair of sides and A final pair of sides that are congruent The reason we need to do that is in this Triangle congruence theorem we have the if part of the sentence the hypothesis and that must be satisfied in order for the then The conclusion to be true So which pair of sides do we have I? Know AT is congruent to IC and the reason that I know that to be true is that's given information By is the green segments segment TI and CA are congruent for the same reasons that given Given information And then lastly we need to talk about the shared side. So that shared side is kind of strange in triangle TIC in Triangle TIC I see that this segment is If we follow the order of the letters then the segment would be called TC however, the corresponding segments in Triangle C a T Would be instead of TC it would actually be CT and That follows from the order of the letters in the names of the triangles So we have that shared side and we need to talk about the fact that that shared side gives us congruent segments So TC is shared by both triangles and as a result It must be congruent in both triangles and the statement that we use is called the reflexive property of equality And now we're done each of our different puzzle pieces has fallen into place We've proven what it is. We're trying to prove and now we're good to go proof number one done


e a new version of the string and reassign it to that same variable name. So the methods you've seen here are dot upper and dot lower to make the string all uppercase or all lowercase letters, dot count to find how many occurrences of some substring occur in the larger string, dot index to find the first position in the string where the substring can be found. That strip gets rid of all the white space at the beginning and the end of the string and that replaces all occurrences of some substring with a different substring. We'll see you next time. Welcome back. There's one more method for strings that's a little more complicated and important enough to warrant its own video segment. We can concatenate a string together, including some hard-coded parts and some variable parts like this one. We've got a hard-coded part, hello, period, your score is. Then we've got some variable parts like the name and the score. If I run it, we concatenate, we get hello, we get Rodney Dangerfield, that's coming from name, your score is minus one that's coming from there. So one thing to notice about this is it's just sort of a little hard to read. It's a little hard to read this and figure out exactly what it's gonna look like over here. And you gotta be careful about things like getting the period, which really belongs with the end of the name, but you gotta stick it on there, you gotta remember to put spaces there. You have to remember that score is a number, so we gotta pass it through the str function in order to turn it into a string. A lot of stuff that's not so convenient here and not so readable. So we're gonna have a new command, the .format method, that's gonna make this a little cleaner. Before we get to that, though, let's just do a slightly more complicated version of this where instead of saying just Rodney Dangerfield score, that we're gonna get a whole list of tuples. So we've got Rodney Dangerfield with a score of minus one, Marlon Brando getting one, and of course, you would get 100. And we're gonna loop through all these people. For each of them, we're gonna print out something like that, like what we did for Rodney Dangerfield.  What I'm gonna do next is show you something that's gonna replace that concatenation with something that's a little cleaner. So I've just replaced line five with something that is little cleaner. We have a first part of it, which is called the format string, and it's got some things in it which replaces where we're gonna do substitutions. So we have a complete format string and you can kinda look at that and get a sense of what the shape is of the thing that's gonna come out at the end, but we're gonna have some substitutions. And this first set of curly braces says do a substitution here, and we have positional replacement.  So looking at this, we have a format string and then we are calling a method on it, the dot format method. So it's a method on that string and we're passing in a couple of parameter values. The first parameter value is gonna get substituted in for the first curly braces, the second parameter value for the second curly braces. So when I run this, the first time we get to line five, name will be Rodney Dangerfield and score will be minus one. That's what's gonna get substituted into the hello string and the next time it'll be Marlon Brando and so on. So we get the same result as before, but our code is a little more readable. We'll be doing this more and more as the specialization goes on using these format strings rather than concatenating together strings out of individual parts. So a little vocabulary that we have here, we have the format string, we have parameters and these are the parameter values that are getting passed in and then we have references close to substitute in those parameters. Here's another example that's a little more complicated where we can give some hints to the format method telling it how many decimal places to use for numbers. In this program, we're first asking the user to type in an original price for an item and then a percentage that it's going to be discounted. We compute a new price from the original price and the discount and then we're gonna just create a string and finally print it out. The string that we're gonna create is we're gonna have a whole sentence that includes some information about the original price, how much the discount was and what the new price is and those things are gonna get substituted in. The original price will go here, the discount will go here and the new price will go here. The new thing that we're seeing here is this colon 0.2f and what that says is the thing that's gonna get substituted in here is a floating point number. That's what the f is saying and the period two is saying after the decimal point have two more digits. If I run this, let's see what it looks like. I'm gonna have an original price of $89.99. We're gonna get a 20% discount and that comes out saying that $89.99 discounted by 20% is $71.99. Now it isn't the case that 20% off of $89.99 is exactly $71.99. It's actually a tiny bit less than that but the closest number that's in dollars and cents is $71.99. If I told the Python interpreter that I wanted four decimal points instead of two, then I would print it out with more precision. Let's take our $89.99 item, get a 20% discount and now it turns out it's $71.99.20. So we can control how many numbers we get after the decimal place by specifying it in that inside the curly braces. If we remove the hint entirely about how many decimal places to use, then it just goes and uses its default. In this case, it's giving us three decimal places. If we had some different value, it might choose to give us more decimal places or less because we weren't giving it any instructions on how many to do. It was using its built-in algorithm to decide it. If we want to control exactly how it comes out, that's when we use this little hint. And for dollars and cents, it really makes sense to have two decimal places because that's the precision for dollars and cents. All right, so that's the format statement. Just a reminder, a format statement begins with a format string and then we call the .format method on it and we pass in any values that are supposed to get substituted. The substitutions happen where the curly braces are. We'll see you next time. You've now seen the most important methods that you'll be using on lists and strings and a few more obscure ones that you'll only rarely use. You should now be able to read and write code using those methods. You should be able to extend a list using either a pen or concatenate to add more items onto the end of it. And you should be able to identify whether a method mutates an object or creates a modified copy of it. Methods on tuples and strings, stream reminder, they can never mutate them. They can only make modified copies because tuples and strings are immutable. Some operations on lists mutate them. Assignment, deletion, append, insert, reverse, sort, remove and pop, those all mutate lists, index and count, leave them alone and just tell you some property of those lists. So today's joke. How can you get two cats in the same room? You concatenate them. See you on the flip side. Hi, welcome back. We're going to use the accumulator pattern a lot in this course. Previously, you've seen how to accumulate a number, a count or a sum. In this lesson, you're going to accumulate lists and strings. With lists, you'll start with an empty list and then you'll mutate it repeatedly by appending another item each time. With strings similarly, you'll start with an empty string and extend it repeatedly with concatenation and reassignment so that you get a longer and longer string accumulated. At the end of this lesson, you should be able to read and write code that accumulates lists and strings. See you later. Welcome back. You've seen the accumulator pattern before. Now we're going to accumulate a list instead of a number. So in this code example, as with all accumulator patterns, we have to have some sequence that we're going to iterate over. In this case, we have a variable nums and we are binding to a list containing three, five and eight. And we're now going to accumulate a list. We'd like that list to contain the squares of all the numbers from the original list. So nine, 25 and 64. As with all accumulator patterns, you have some accumulator variable.  We could call it something else, maybe squares would probably be a reasonable choice. And anyway, it's called the CUME here. And we initialize it to be just an empty list. And this is typical when we're accumulating a list. We start with an empty list and we're going to keep appending to it. This is the analog of starting with zero when you're going to take an accumulation that gives you a sum. We start with the empty list and then on line three, we start our iteration. So we're going to iterate each time W is going to be bound to one of the items from nums. In the first iteration, W will be bound to three. We'll set X to be the square of three or nine. And then we're going to append the current value of X, nine, into the accumulator. On the second iteration, W gets bound to the second value, five. And so X gets bound to 25 and we append 25. The third time, W is eight, X is 64 and 64 gets appended to the list. So this is following the same logic of your accumulator pattern before. Each time through this iteration, an additional item is going to be appended into a cube and so really a cube is the squares so far that we've managed to accumulate. When we're done with this iteration, we finished with all three of these. We can print out a cube and the cube will have all of the squares. So let's run it. Sure enough, we get nine, 25 and 64 at the end. So it's a little check on your understanding. Let me try changing one thing in this. Suppose that I indent that print. Can you predict what the output will be? It's a good chance to pause and see if you can predict it. At each stage, we're now going to not just change the contents of the accumulator but we're going to print what we've accumulated so far. So we're now going to have three lines of output. First just the list nine and then the list with nine and 25 and then the list with nine, 25 and 64. So as before, this is a useful debugging strategy with the accumulator pattern is to print out what you've accumulated so far and see how it grows over time. So in summary, to accumulate a list, you will initialize the accumulator to be an empty list. You'll iterate and at each iteration, you'll append a new item. At the end, voila, you've accumulated a new list. Catch you later. Welcome back. We can also use the accumulator pattern to accumulate strings. In this case, you'll start with an empty string and keep appending to it. But when you append, you'll have to reassign to the accumulator variable because you can't actually change the original string. So here's an example, sort of a Michigan example, Michigan winter example where we've got someone who's got chattery teeth because it's so cold outside, all of their letters are coming out double. So they're going to say a word like hello and because their teeth are chattering, it comes out as hello. So here's how we do that. We're going to start by asking the user to type in a value. That's on line one. They enter some text. And that gets assigned to the variable s. Let's suppose that, well, let's make it easier for us. They say cat. The accumulator variable is going to have our result so far, our teeth chattering version of that string that we've accumulated so far. Initially, there's nothing, but it's going to accumulate things. And then we start iterating one letter at a time. The variable c is going to be bound to the letter c. And then we are ready to execute the accumulation part, line four, for the first time. So it's going to take our current value of ac, which is an empty string. It's going to add the current value of c, which is the letter c. And then it's going to give us a dash and the letter c again and another dash, which yields a string c dash c dash. And that becomes the new value for ac. The old string is still there, but we don't worry about it anymore because ac has been reassigned to this new string c. We're now ready to go on to the second iteration. When we get to line four for the second time, c is now bound to the letter variable c. C for character is now bound to the letter a, the second letter in our string. And we're now going to make a, let me write it over here, we're going to make a string that has the old value of ac.  And that becomes our new value, caca. And similarly for t, we're going to extend this each time that we do all this concatenation, we have to reassign to a. Because we're not actually changing the old, we have to reassign to the variable ac, I should have said. And we have to do that because ac has not been changed. So we've made a new string and we reassigned it to ac. So in summary, to accumulate a string, you start with an empty string. On each iteration, you reassign the accumulator variable with a concatenation of its old value and some new stuff.  So let's run it, I enter cat, I get caca at. Michigan frozen winter, speaking cat, or if I run it and ask for a dog, I'll get dd o, o, g, g. See you next time. Congratulations, you've now learned how to accumulate lists and strings in addition to numbers. For a number, you usually initialize the accumulator to 0. For a list, you initialize it to an empty list. For a string, you initialize the accumulator to an empty string. You can accumulate all kinds of things now. I hope you're accumulating friends and not enemies. So instead of an accumulation joke today, let me close with a little information about Ann Arbor, Michigan, for our learners who are joining us from around the world. Michigan is in the northern part of the United States in the Great Lakes region. In the winter, it gets very cold here. And in the western part of the state, they get lots of snow, the lake effect. You might say it accumulates there. See where I'm going with that. In Ann Arbor, however, we don't get so much accumulation. We don't get much snow here, just the cold. And that's snow joke. See you next time. Welcome back. In this week's Way of the Programmer lesson, we'll be encouraging a habit of drawing reference diagrams and offer some tips on how to recognize when to use the accumulation pattern and how to do it well. The learning objectives, at the end of this lesson, you should have developed the habit of drawing a reference diagram to resolve any potential confusions. And you should be able to recognize when you should use the accumulation pattern based on the words that are in the problem statement. See you at the end. When in doubt, make a reference diagram. Even if you only might be in doubt, make a reference diagram. It's gonna seem slow, painful, even to watch me do it. When you're doing it for the first few times, it's gonna be even slower and more painful, but it's worth it because it gives you a way of understanding things that can be pretty confusing otherwise. So here's a little code example, four lines, and then we're printing out what's the result, but it's not so easy to figure out exactly what's gonna print out. And so let's make a diagram to follow it. So we're gonna basically simulate like what code lens would do, but we're gonna do it ourselves. So X on line one gets bound to a list of three items. One, two, three. On line two, Y becomes an alias for X. On line three, we have this X plus equals. Now I gave you the suggestion that when you're dealing with lists, just don't use plus equals, but sometimes you have to read other people's code and they don't follow that good advice. So suppose you had this, X plus equals, that's the version where we're gonna take the new list four and five and append them on to the old list so that we now have a list of five items and line three changes the object that X is pointing to. Since Y is pointing to that same object, Y now has five items as well. Next, on line four, we're gonna use the better version that is a little easier to understand where we do the normal thing of figuring out the right-hand side which takes the list one, two, three, four, five and appends another list to it making a new list. So then we have one, two, three, four, five. That's a list. We concatenate on this other list which contains six and then we reassign it. That's what this equal is doing so that Y no longer points to what it used to point to, it now points to this new value. X, however, still points to the old value. So when we print out X on line five, we're gonna get five items. When we print out Y on line six, we're gonna get all six items. Let's check and see if that analysis is correct. Sure enough, line five prints out five items, line six prints out all six. Trying to do this in your head, especially if you ever end up with more than four lines of code that are doing things like this, very difficult to do. So remember, if there's anything even remotely confusing, make a reference diagram. Practice now, even when it might not be so confusing, you'll thank me later. Onto the next, we're back with a little more way of the programmer advice. You've seen the accumulator pattern in various guises now. And this is some advice on how you can know when to use it and some little tricks for getting it right. You may remember back in elementary school, maybe you have kids like I do who've been in elementary school recently and they start dealing with word problems and you look at the problems and you say, wow, you're just gonna, that's three plus five. But somehow converting that word problem into three plus five is challenging. So they learn little tricks, like when it says how many do they have altogether, they should know that it's an addition problem or how many are left is gonna be a subtraction problem. So here's something a little similar for how to recognize when you're gonna be dealing with one of our accumulation patterns. We've got these phrases on the left in this table and we've got which accumulation pattern that might suggest to you that you're gonna use. So if the problem says how many things are in a list or how frequently does something happen, that's gonna be account accumulation. If the problem asks for the sum or the total, that's gonna be a sum accumulation. If the problem asks to generate a list of things, that's gonna be a list accumulation. And if it says to concatenate or join things together, that's probably gonna be a string accumulation. Next on this page, we've got a little bit of advice of how to think about what you're gonna do before you write any code. And one thing to ask is, which sequence are you gonna iterate through? And the second question is, what kind of value are you going to accumulate? Are you going to accumulate a number, a list or a string? And then our third set of advice is about choosing good names for your accumulator variable and your iterator variable. Names that'll help you keep track of things. As we've said for any iteration, it's a good idea to use a singular noun for the iterator variable name. And if you are iterating through a list of words, then it might be a good idea to use an iterator variable name like W-R-D to just remind you that each time, on each iteration, W-R-D, your iterator variable is going to be bound to a word. For the accumulator variable, I sometimes just use a generic accum, but it also can be helpful to sort of remind yourself of what you're accumulating. So, got suggestions for names like countsofar or totalsofar or cubessofar? Could be good names for your accumulator variable. Having that appendix sofar sort of reminds you that on each iteration, the accumulator is getting more stuff. And so what you have at a certain point in the execution of the program is the totalsofar, not the grand total. But after you've finished all of the iterations, you're going to have the grand total. There's a bunch of questions to help you check your understanding on this, but I'm just going to go through a few of them with you. So, and we've got several of these in the book. I'll just go through a couple, and you're supposed to sort of pick out what, if anything, in this problem should make you think that you're going to do an accumulation. And I'll tell you now that some of them, there is something, and for some of them, it actually isn't an accumulator pattern at all. So let's start with this one for each string in words, add ed to the end of the word in order to make the word be in the past tense, and save those past tense words to a list called past words. Does this suggest to you an accumulation pattern? And if so, why? We've got two possibilities for why here, either because it says save some things to a list, or because it says add ed to the end of the word. The correct answer is saving a bunch of things to a list should suggest to you accumulating a list. What goes into each item, that's not what suggests that we need an accumulation pattern. Let's try the next one. Write code to sum up all the numbers in the list seat counts, store that number in the variable total seat counts, and here our correct answer is to sum up, because to sum up suggests that we got a bunch of things and we want to get the grand total, so that is going to be a sum accumulation. So there's some more, and I encourage you to try those. Here's a couple questions about what type of object you should expect to have stored in your accumulator variable. So the question here is, write code that will count the number of vowels in the sentence S and assign the result to the variable num vowels. Now we haven't quite got all the mechanisms in Python to be able to count only the vowels and to leave out the consonants. You're going to get that pretty soon in this course. But even so, the structure of this is enough that you know it's going to be an accumulation pattern, and you're going to count the number of vowels. A count is a number. So our correct answer here is that it is an integer because we want to keep track of a number. So different question about that same problem. What sequence will you iterate through as you accumulate a result? And we have two possibilities here because we have a sentence S and we have variable num vowels. Which of those are you going to iterate through? And the answer is you're going to iterate through S. You're going to accumulate your results in num vowels, but the sequence that you're going to iterate through is the characters in the sentence S. So there's a couple more of that flavor. And then we've got some questions about what should you name your accumulator variable and what should you name your iterator variable? So let's try this one. For each string in words, add ED to the end of the word to make the word past tense. Save these past tense words to a list called past words. So a couple possibilities here. We're either going to name our accumulator variable word so far or we're going to name it changed words. And our iterator variable name can either be W-R-D, short for word, or X, or it could be ED. And my suggestion is this is just a matter of style, but these style things help you to avoid confusion and can help readers of your programs also not get confused. Is that words so far is kind of an ideal name for your accumulator variable. It tells you so far says it's an accumulator and word says what kind of thing you're accumulating there. And for your iterator variable, you're going to be iterating through this string W-R-D-S. Plural, that's a list of strings. Each of those strings is one word. So having an iterator variable of W-R-D seems like a really good choice to me. There are a few more questions like this and I encourage you to go through all of them just to reinforce the way of the programmer around recognizing when you need to use an accumulator pattern on choosing the right variable names and on recognizing what kind of thing you're gonna accumulate a string or a count or a number and what sequence you're going to iterate through. So go through those and you will become an expert on the accumulator pattern. See you next time. Welcome back. I hope that you are traveling the way of the programmer, making a habit of writing reference diagrams, choosing good variable names and training yourself to recognize the telltale markings of an accumulation problem. Above all, practice programming. To borrow and horribly mangle a quote from Mahatma Gandhi, there is no way to programming. Programming is the way. I didn't find a great joke for you, so I'm gonna give you just a random pun verse that I've always enjoyed. One, one was one race horse. Two, two was one, two. One, one, one race. Two, two, one, one, two. I'm here to tell you about your end of course project. So this course project that you're about to do will cover a lot of the concepts that you've already covered in the course. You'll have to do a series of problems that are of varying types and covering varying concepts. But all of these problems that you'll be doing are the kind of programs that lots of people use in their real lives. Accumulation, gathering data together, changing what it looks like in this little program. So these kinds of programs that you're about to write in your project are possibly very applicable to your everyday life in school or work or whatever really. I wanna remind you of some tips that may be useful as you start to work on this project. So first of all, as you know, you should always change one thing in a program. Predict what will happen when you eventually run that program after changing this and then try it. That way, if you've only changed one thing, made a prediction and then tried it, you will know whether or not that worked or whether or not your prediction was right. And so you'll know if you have a good understanding of what you're working on in that moment. If you do a bunch of different things and then try it, you might have to dig through all those different things to figure out what was good and what was not good and what you need to do to finish that program and get it to happen the way you want. So always change one thing, predict and then try it. I also wanna remind you to use variable names that are clear to you. For instance, if you're using an accumulator pattern or any for loop, you never want the iterator variable to be plural because it's always gonna be bound to one singular thing. And you wouldn't wanna plural variable name for a singular thing because that can be really confusing when you talk and think about your code. Similarly, I would advise you not, for example, to use the word L-I-S-T inside a variable name that couldn't be a list because that's gonna get confusing too when you read your code later and you'll think, oh, it's a list and then it will not be a list. All of these problems that you're about to do in this end of course project are different but they're all similar patterns to problems that you've seen or done before. And as you work on them, I'd advise you to think about those and think about how they're similar to other stuff you've done and that will make it easier to progress on these. For each one, you should go through, make a step-by-step plan in words, no code at all for how you're gonna solve the problem and then make sure that you can translate each of those pieces into code. For example, in an accumulation problem, you should talk through step-by-step as if you're talking to a robot or write down what each of those steps are that needs to happen in that program, that little task. And then you can think step-by-step about how to translate each of those things into code, how can you translate your words into a program that will run and continue with changing one thing and then trying it to make sure that the code runs. Finally, if you see a problem, for example, maybe the last problem in this end of course project where there's a complex task to do for each one of a set of things, do something with each string, for example. You should think about your plan for each individual task, say for doing that complex task for one string and make sure that that works, that everything is fine for just one string. If your code for doing the task one time with one string is successful, then you can move to building all of your code and putting it into a for loop and implementing the full solution so that all of your code is successful for that program. All of these problems are really useful for applications in almost everybody's everyday life in one way or another. I think they're fun. I hope you will enjoy yourself and I wish you good luck.