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Hello, welcome to Modern Day Debate. I'm very excited to have you here for this special edition, you might say. Basically, we're debating whether or not there's evidence for God today, or the Christian God in particular. And the reason is that it's a special edition in several ways. One is, I am thrilled to have our speakers here. We have two brand new speakers that we've never gotten to have before. It's going to be a blast to have them here. It's a topic we haven't done in a while. It's been so busy that with other topics like does God exist, or we're starting to go into politics now that we haven't gotten to do one on Christian evidence in particular. So thrilled to have today's debate. And if you're new here, consider hitting that subscribe button as we love trying to host. Ideally, you know, hold us accountable. We hope that these debates are fairly moderated. And also we do a monthly charity stream in which 100% of the super chats will go to a charity such as Save the Children, like Starving Children Around the World, or Breast Cancer Research. So we are excited to have that one coming up on July 20th. And let me know, we are, because we're traveling, and you could say that's another reason this stream is out of the ordinary is a couple of us are on the road. I'm not sure how well it will come through. My picture looks okay over here, but as I look at it through YouTube, I'm like, ooh, that looks pretty gritty. Can you, in the live chat, if you're able to let us know if it looks pretty bad or not, that's really helpful. And hopefully it's maybe just me that looks kind of gritty. But hopefully you can hear me. I'm just gonna quick check really quick to see how the audio's coming through. It looks pretty bad. I think we should be good. So with that, wanna introduce our speakers who will have their links in the description that you can check out. And we will go from left to right as I introduce our speakers. So for me, I've already introduced myself, I will introduce Misha next and give him a chance just to share about what he's been up to as of late as he is also on the road. And then if you wanna share anything that you've been doing at your channel or blog or just even anything that you've been researching, we're glad to have you here. Thanks for coming on, Misha. Hey, great to be here. And yeah, I've kind of backed out of all social media. I guess you call it a bit of a personal protest to the juggernaut of Facebook and everything. But I'm always happy to appear on any channel, any time. What I'm working on right now is I'm mainly focusing on Dr. E. Michael Jones's Culture Wars Magazine. I'm just writing articles for him. I used to write articles for a lot of daily newspapers and I worked in talk radio. That's all behind me now as I'm turning gray and becoming healthier and wiser in my old age. But yeah, mainly just Dr. E. Michael Jones's Culture Wars Magazine. And the latest thing I'm working on is an article about creation for Culture Wars. And then also one on a totally unrelated topic that might interest some people on why bear crop science paid $66 billion for Monsanto right in the middle of a class action lawsuit involving over 13,000 claimants. So that's totally unrelated, but that might interest some people. You got it. Well, thank you very much. We're glad to have you here, Misha. And he is in Cancun, by the way, and which is very exciting. We're happy for you. We hope you're enjoying it. We, it looks like your service is stronger there in Cancun than mine is here in, I'm in Malaysia right now. I'm really excited to be visiting Samuel Nassan, who is a friend of the channel. And he's come on to debate before he debated. Does anybody remember the debate between Samuel and Apologia? That was back in, I think it was September of last year. And then he debated JR just recently, a couple of months ago. So Samuel is doing well.  It looks pretty rough, but hopefully the audio's coming through well. And Daniel Stoke to have you here. If you want to share about what you've been up to, thanks so much for coming on. We appreciate you spending your time with us. I appreciate it as well. So my name's Dan Ausche, and this is sort of out of my domain. I usually focus on evolutionary biology. That's my specialty, but I'm excited to debate it. I grew up as a Christian, slowly lost my faith because of textual inaccuracies and stuff like that. So I'm excited to have a debate sort of based off of the Christian God rather than just evolution versus whatever creation myth you would like to add in there. So very excited. You got it. Very excited to be here. And so with that, we will hand the discussion over to the speakers. So we appreciate your patience guys. We've been trying to schedule this one for a while. So I'm glad to be here and the floor is yours. Usually the affirmative would start speaking, but given that it's just a discussion, like it's really up to you guys. Oh, we're doing that 10 minutes, 10 minutes, and then discussion. Okay. So sorry about that. I have it mixed up with another. Oh, it's okay, it's okay. I was thinking about another one we have. I am starting the clock, we're setting the clock for 10 minutes, and I will start it on your first word. And is that me or Dan? You. Yes, I'm the affirmative. Yeah, thought so. Great. So proof that there is God, and specifically the Christian God or Jesus Christ. It begins, of course, before we meet Jesus, but we'll get to that here in my intro. And where it begins is that it was around early in the 20th century, the scientific community realized the universe had a beginning. And prior to that, of course, we had sort of the Aristotelian position, which even people like Sir Isaac Newton and Albert Einstein adhered to, which is that the universe just always existed. So, but the problem with that, they realized before they came up with some nuts and bolts evidence to the contrary, but the problem was a philosophical problem. If the universe always existed, that means it goes back infinitely in time. And if something's infinite, it has no end. So if the universe was infinite since its beginning or it had no beginning, in other words, then you'd never get to the present. So that's the philosophical problem that you run into with an always existing universe. And I know Daniel already agrees with that, that the universe had a beginning. So what happened was we think that was sort of a schism between science and religion, and it was nothing of the sort. The Pope at the time, I believe this is around in the 1930s, it's prior to the Second World War. The Pope said, great! You guys finally figured it out. Cause as far as the Pope is concerned, of course, God created the universe. But no, no, the scientists involved said, well, no, no, no, there was no God. It was a spontaneous event. And that's where we begin here. That's where I begin proving that, well, there has to be a God because it couldn't have been a spontaneous event. You could not have had nothing and from nothing everything came forth. That would be an infinite leap. And there are actually three infinite leaps that I wanna quickly cover here. That's just the first one. To go from nothing to something. So even before we get to the Big Bang, that this infinitely small dimensionless dot in space, which can't exist, before we get to that exploding into everything, and remember, it's not just creating all the matter in the universe, it's also all the energy. So all the heat of all the stars that exist today and have always existed, all that heat and matter has to be packed into this. It's not even a microscopic dot, as I'm sure you'll agree, it's a dimensionless dot. So that's impossible. But again, sticking to the philosophy, to go from nothing to something, just to one molecule, nevermind the entire universe with all the tables and chairs and houses and people and stars and planets, just to go from nothing to something, that is an infinite leap. As infinite, in fact, as a perpetual universe, which scientists agreed could not exist, they came to that realization. So that's the first infinite leap you have to make if there's no God, to go from nothing to something, just as I say, just one molecule. The next infinite leap is to go from inanimate matter to living, living organism. And funny enough, there's actually a scientist, I'm sorry, I don't have the reference, but I'm sort of throwing you one here, so maybe you'll accept it. There's actually a team of scientists working on trying to create a synthetic cell, a synthetic living cell. And I say it's ironic because I would have thought they'd start first by creating a synthetic molecule, or a synthetic atom. I mean, you have to go in order, right? I mean, God went in order, first he created the inanimate material universe, and then from that, he created life from within the existing material universe. So I would have thought scientists would first tackle the material problem of going from nothing to something, but they're gonna jump right ahead that this team of scientists, I don't know who's backing them, but it's insane, they're never gonna succeed. I guess I could be proven wrong before the end of this interview or tomorrow morning, but I kind of doubt it. And they're gonna try to create the first living synthetic cell. Well, that, as I predict, they will discover, is another infinite leap to go from inanimate matter to a living organism. And a lot of biologists have sort of discovered God, maybe not the Christian God, maybe not Jesus Christ, but they discovered after a decades-long career studying biology and the complexity of the living cell, they decided, you know, this is too complex. I mean, mathematically, the odds are just astronomical beyond what mathematicians consider possible that a living cell could just spontaneously be created from inanimate matter without a helping hand. Now, I promised three infinite leaps. The third one is admittedly theological, or perhaps you'll admit philosophical. And that's the leap to our salvation. So a loving God who is nice enough to create the material universe and then create life within it, he decided to provide us salvation. And that's the third infinite leap.  And also with rape, kidnapping, I mean, God knows what, all 10 commandments have been broken routinely by human beings. Whether you think we evolved or not, I'm sure we can all agree on that. And through the success of Jesus Christ's ministry on earth, we now have grace.  So once something is infinite, there's no measuring it. So the first infinite leap was infinite to go from nothing to something. The next one to go from matter to living organisms, that was infinite. And the third one, which of course, if you're not religious, especially if you're an atheist, you're not gonna care about it as much. But again, I assure you, I underline it. It's again, infinite. So if it's infinite, it's infinite. There's no use saying, well, yeah, the third one is less important than the first two. If it, as I say, if it's infinite, it's infinite. And that's all there is to it. Now, am I okay for time to add one more point here? You got it, three minutes. Ah, three minutes, perfect. So now we get into the nitty gritty. Those are philosophical arguments, all three of them. Because indeed it could turn out that we're all wrong and the universe did always exist, even though that's impossible. There could be some explanation for that. But just going off work, current science stands, it really looks like you need the person of a God, an almighty God, to get all these three things in motion. The third one though is the nitty gritty evidence.  Of course, he saved many Jews, like all of his disciples, except for Luke. He himself was Jewish, born of Jewish parents. And he saved as many of them as he could before turning to save the Gentiles. And all the Jews who didn't wanna be saved, well, that they really turned on Jesus, which apparently was part of the plan from the start. But yes, Flavius Josephus writing soon after he died, he lived, Josephus is like the man just before Jesus was crucified. And from firsthand accounts, he writes, and I just wanna read this, that at the time there was a wise man called Jesus. Now remember, this is a Jew writing this and Flavius Josephus never converted to Christianity. His conduct was good and he was known to be virtuous. And many people from among the Jews and other nations became his disciples. They reported that he had appeared to them three days after his crucifixion and that he was indeed alive. Accordingly, he was perhaps the Messiah, concerning whom the prophets, the Jewish prophets I'll add, had recounted since from the Old Testament. Now, some people, we can get into it. Some people say, well, you can't trust Flavius Josephus because he was trying to save his skin after the Romans sacked Jerusalem. But he would have made no friendships with the Romans who could have killed him, they could have executed him. He would have made no friendship with them, no alliances by propping up this Jesus guide that the Romans just 40 years earlier had crucified. So it really seems to be like a reliable third party, disinterested support for the life and times of Jesus and most important fraction. You've got it. Thank you very much, Misha. We appreciate that opening statement. I just realized there might have been, forgive me, I appreciate your guys patience. I think you had said, Daniel, if you can help film me and I don't know if I had the other moderator send me the format for this debate. Is it 10 minutes, five minutes, and then? I think it was originally 10 minutes, five minutes discussion. I'm not sure if Misha wants to do the 10 minutes, five minutes discussion. I think that's what we originally agreed upon. Deal. Works for me, thanks for your patience on that. I can promise you that Hunter, the co-moderator, will be punished severely. He's a really nice guy, man. Yeah, he's awesome. So thanks so much for your patience. And with that, Daniel, thanks for being here as well. And the floor is yours. I am going to start the timer on your first word. All right, thank you very much. So he proposed three infinite leaps. I would like to propose one more between the evidence and his conclusion. So, everything he said in the beginning was arguing for the evidence of a God, right? But we need the evidence of Christ Jesus who died and was resurrected, right? So that's why he brought up Josephus in the end. His third giant leap, which was the leap of salvation, I don't agree upon. So that's not a leap that I take. So if you look at a majority of cultures around the world, they don't view a need for salvation. Like you would have to have evidence for the need of salvation before you can say there's a leap to salvation. So I'm going to go along with my opening statement. Paul says in 1 Corinthians 15, and if Christ has not been raised, our preaching is useless and so is your faith. So basically what Paul is saying right here is the Christian faith rests on the resurrection and rests on the truth of resurrection. And I know Misha agrees with me upon that. So the resurrection of Jesus is the only truly necessary condition in Christianity. The Old Testament can be completely true. There could be a God. Jesus could have lived, he could have preached and he could have died. But if he wasn't resurrected, Christianity is false. So the truth of the resurrection, the truth of Christianity are wholly interchangeable. So he gave the evidence of Flavius Josephus, right? I'll get to that in the end why that doesn't actually count as evidence. Most believe that it was a scribal interpolation. They found a nucleus and they went with it. So, you know, I'm just gonna go straight to Josephus. So Flavius Josephus was born after Jesus' death. Flavius Josephus was born at 37 AD, right? He wrote the Testimonium Flavinium, which is what he referenced. And the Antiquities of the Jews. The Antiquities of the Jews was a history book that he wrote in 93 to 94 AD. So it is unanimously agreed upon by scholars that it is completely fabricated. So Flavius Josephus was a Jew. He did not believe in the resurrection of Christ. The Testimonium Flavinium claims that Christ was resurrected. I'm not sure what he was quoting, but that wasn't exactly what the Testimonium Flavinium says. The Testimonium Flavinium directly says that Jesus was resurrected. So you can't have that and a Judaic belief. You'll never have a Jew that believes in the resurrection of Christ. Because as we spoke about earlier, that's the necessary condition of Christianity. So the only other evidence is the Gospels. So let's look at the Gospels. When were they written? The first Gospel, Mark, was written in 70 AD. Matthew and Luke between 80 and 85 AD. And lastly, John was written between 90 and 110 AD. So the Gospels were written 40 or more years after Jesus' death. Who wrote them? It wasn't Matthew, Mark, Luke, and John. They were written anonymously. They were attributed to Matthew, Mark, Luke, and John centuries later. And a vast majority of New Testament scholars agree that they were not written by who they were ascribed to. Are they consistent? No, they contradict many times. They have contradictions in Jesus' timeline, his birth, his death, and his resurrection. Nearly every significant event recorded in the Gospels have a significant canonical contradiction. Are they historically accurate? No. There are many historical inaccuracies in the New Testament. From the false, ahistorical details of Jesus' birth to the false, ahistorical details of Jesus' death, the Gospel accounts are full of significant inaccuracies. So one of which being, according to Matthew, Jesus was born during the reign of Herod the Great. But according to Luke, Jesus was born during the first census of Israel when Quinarius was the governor of Syria. This is impossible because Herod died in 4 BC and Quinarius was the governor of Syria in 6 AD. So that's a 10-year gap in Jesus' birth laid out in Matthew and Luke. Also, the Gospel of Matthew claims that Herod slaughtered all the children under the age of two. We know this not to be true because the historian that he cited, Flavius Josephus, was, he was particularly antagonistic towards Herod.  You know, that would have been an event that definitely would have landed the historical record. So, all right, let's go back to the Josephus thing. I can't wait to talk in the discussion about the Josephus thing because I feel like there's no way that you actually researched it deeper than just its surface because it's unanimous that it's a forgery. So, yeah, I guess I'll concede my time at that. I'm just ready to get to the discussion. Thank you so much. And next up, we'll go into the five-minute rebuttals. So, we can put that four minutes into the discussion, which I'm looking forward to as well, for the rebuttals, so it'll be five minutes and I will start the timer on your first word, Misha. Sure. Yeah, so we have to deal with the claim of forgeries and also the claim of that, well, the Gospels were written by people who maybe had a vested interest in perpetuating this story. But first to the issue of forgeries, yeah, anything from ancient text is potentially a forgery, but we have more information about the life and times of Jesus than we do say about Alexander the Great or about any Greek philosopher, Aristotle, Plato, Pythagoras, often what we're hearing about when we read about ancient Greek philosophers, we're reading about someone else writing about them or in the case of the most, the more famous of the Greek philosophers like Aristotle and Plato, we have fragments of their work and even within their work, they're referring to other work, which we don't have anymore, but we have them referring to their own work. But yeah, then when you get to secondary Greek philosophers, like I said, like Pythagoras or Heraklites, the Greek historian, often you're dealing with other people writing about them. So yeah, if you want, you could throw the whole of ancient history into question. I mean, it also mentioned that the disciples didn't write about Jesus until later. Well, that would make sense, you know, they're kind of scared for their lives, which helps prove the case here that they really had nothing to gain, but certainly they were scared for their lives. They thought they were next, but then they saw Jesus risen and it fortified their spirits, so they carried on. But far from writing, as you suggest, 70 or AD or later, a lot of scholars disagree because why? Because Jesus predicted in, I think in two of the four Gospels, he predicts the temple will be destroyed. So you'd think if they were writing after 70 AD, which is when we all agree that the Romans destroyed the temple of Vespasius, finally came in after two or three emperors failed and some generals were dragged back to Rome and scolded or executed. Finally, Vespasius sacks Jerusalem in 70 AD and everyone agrees on that.  And now it's a missing argument, but I would suggest that as long as we're in the realm of suggesting that these guys were just editorializing, why wouldn't they have put that in? So a lot of scholars agree, no, no, they were all written, you're right, Dan, except for John, except for John who was away and probably didn't even know Jerusalem had been sacked. He's the only one who survives into old age. They tried Jews, tried killing him, boiling him in oil, but he survived and he ends up writing not only the book of John, as you know, but also Revelation, the book of Revelation in his old age on the Isle of Patmos. But I don't wanna occupy all the time, I know it's five minutes for discussion, but I think you said we'll do discussion, sorry, instead of just a rebuttal. But I do wanna point out that really, it looks to a lot of people, not just myself, that all the Gospels, except for John were written, and that Acts and Paul's letters, they were all written before 70 AD. A lot of people think that. Now back to Josephus, I know there are people who theorize that it was all made up, but again, I'll just go back to my first, what I said in the first point of my rebuttal here. Then you could say that about all ancient writings. And the difference, by the way, in who is emperor at the time of Jesus' birth, that's actually still being debated. I don't think it's really settled. You said a couple of times, scholars unanimously agree. Not really. And by the way, there was one thing, I think it's in the book of John, where he had a local governor. People thought he had it wrong, but it turns out the governor had a brother, and after that first governor left, his brother, there was a six-year gap, and then his brother took over from him, and people didn't realize that for like 1700 years, that wasn't discovered until the 1800s, that there was this other governor with the same name as his brother. In any case though, I just want to say it again, Dan. A lot of the argument that we can't trust the sources, that goes for then all ancient texts. Okay, thank you very much, Misha. Next up, we will go to Daniel for his five-minute rebuttal section, and Daniel, I will start the timer on your first word. Thanks so much. All right, you okay, Jeremy? Yes. All right, so he's saying we'd have to throw away the whole of ancient history. I'm not throwing away the whole of the gospels. I'm throwing away the miraculous claims, because with miraculous claims, it requires a little bit higher standard of evidence than normal claims. So if I told you my girlfriend was a school teacher, you'd probably take me on my word, but if I told you I was dating the queen of England, it would take nothing short of like a sex tape for you to believe me that I was actually dating her, and that's because we know intrinsically that extraordinary claims require extraordinary evidence. And the gospels just do not rise to this standard of evidence. I'll get to that in a little bit, but I really wanna talk about the Josephus thing. So he's saying anything could have been forged, right? We know to a degree which ones were forged and which ones weren't. We can't be fully certain, but we have good reasons to believe, right? So we have plenty of documents that don't seem forged, and historians take them at their face value basically. But when it comes to the Testimonium Flavinium, there's all kinds of problems with it. So first off, the paragraph preceding the Testimonium Flavinium, and if you didn't catch that, the Testimonium Flavinium is the passage that referenced Jesus that he is citing. So the previous passage talks about how Pilate demolished an insurrection of Jews by ordering them all beat to death, right? So they had a little uprising of Jews, so Pilate got them beat to death, put them in check. So then the passage underneath the Testimonium Flavinium starts out with the sentence, and then another thing happened to put the Jews in check. I'm paraphrasing, I have it somewhere in my notes, but it basically says, all right, another sad thing that happened that put the Jews in check, like that Pilate did. So it's obviously referencing the passage that is above the Testimonium Flavinium. And the Testimonium Flavinium just does not flow with the reading of Josephus. Also, Josephus uses a lot of language that he has never used before in any of his writings. And he also uses the word Christ for the first time, Christos, and he does not back reference it or give a definition. So Josephus was a historian, a very respected historian. And whenever he introduced a concept that he thought was foreign to the Romans, he would introduce it and explain it. The concept of a messiah would have been completely foreign to his readership, you know? So those are a couple of reasons why we think that the Testimonium Flavinium was forged. Another reason is the earliest Christian historians, like one of which being origin of Alexandria, he scoured Josephus. He read all of Josephus trying to find Christian, like proof of the gospel accounts, right? So he tried to find things that cooperate with the gospel accounts. And he did not mention the Testimonium Flavinium. So we had a early historian that could not find it. And he was obsessed with Josephus. So that sort of shows that it was a, well, it doesn't show, but it leads to the conclusion that the Testimonium Flavinium was inserted into the text after origin, which was about 200, 230 AD. So the Testimonium Flavinium is widely thought to be bunk. You were saying that not all scholars agree. So from all the scholars that I've read, I read critical scholars, right? So critical scholars often, they insult the evangelical scholars. So you could have evangelical scholars who their entire mission is to vindicate the Bible rather than be historically accurate. And of course they're gonna agree with everything the Bible says. But when it comes to critical scholars, almost none of them believe that Mark was written before 60 AD. Like you cannot find any critical scholars that do that because it's a laughable assertion. And this isn't me saying this. This is pretty much every single book I've ever read on it. I don't really touch the evangelical books. So probably in evangelical books, they have that. But unless you're going into history with an already made conclusion, you do not come to the conclusion that the Gospels were written 10 years after Jesus' death or 15 years after Jesus' death. They were written long after. And it's funny, the example that you gave of the temple being destroyed is exactly one of the reasons why we date Mark after. Because not only do they reference that, but they reference multiple other things that happened in that time that did not happen during Jesus' time. 30 seconds. All right, we can talk about this in the discussion. You got it. Thank you so much, Daniel. And if you have any questions, feel free everybody to shoot them into the live chat. If you put an at modern day debate at the start of your question that you put in the live chat, that'll make it easier for me to see it and then ask those questions at the end during the Q&A. Thanks for your patience. I know it's, I appreciate it. I love that you guys are so, you guys just love the idea of this. Because I know that, let me know if it's buffering. For me, it's buffering, but I don't know if it's because of my internet. So I'm joy for me to get to be here. You're lagging a little bit. Or is it like on the YouTube output or within the Google Hangouts? Within the Google Hangout. So. Yeah, yeah, me too. Oh, okay. You got it. Good to know. Thank you guys. I will work on that. And we will now move into the open discussion. So for this, it's going to be, now we added on about 24 minutes. So we'll have about 34 minutes of open dialogue where our guests can just kind of speak on these issues in a more open format. So thanks for being here, gentlemen. And the floor is yours. Thank you. You might have asked you a question, Misha. Sure. And first Dan, I want to say you were right. I said, Josephus was born before Jesus was crucified but you're right, he was born just after. All right. But yeah, go ahead. That's a critical point, but yeah. Yeah, yeah, definitely. Do you believe that extraordinary claims require extraordinary evidence? So do you believe that there is a differential in the type of evidence required to claim a miracle happen rather than a run-of-the-mill historic event? Yeah, yeah. And so the evidence here is that these guys carried on.  Of course, Peter denies Christ three times. We all know that story. But beyond that, in the book of Acts, even after Jesus is resurrected and returns to heaven in glory, they're still scared.  So the extraordinary evidence here is the fact that we know what Christianity is today, that we live with Christianity. And because there have been other examples where people tried to create the false Messiah and those examples, they fell flat. So these people, fearing for their lives with no backing from anyone, they start the world's greatest religion. I'd suggest to you that's worthy evidence, might not convince you, but you must admit that if you view that as extraordinary evidence, so you're taking the belief of them to vindicate their truth claims. So there's plenty of people that have had much stronger belief. So for instance, if you look at the Heaven's Gates cult, right, they literally killed themselves. Yeah. That takes absolute full belief. They had absolute full belief that their bodies would ascend onto a comet. That doesn't, that does not give evidence for their claim that they ascended into a comet, whatsoever. And I think you would agree upon that. And then if you look at a Saitisai Baba, he's an Indian guru, right? He has hundreds of thousands of followers around the world, right? They attest to his public miracles. He's a miracle worker. He died, I think in 2012. But he would go perform miracles in the street and thousands and thousands of people dropped everything that they had to follow this man in his aesthetic lifestyle, basic homelessness. So belief does not vindicate the truth of said belief. Because if you believe that, we have to believe pretty much every religion because the early adherents believed it. Yeah. The difference being that those followers of the crazy, the comet people, yeah, you're right. They were so deluded. They're willing to sacrifice their lives. And then the followers of that Indian guy, I believe you, I don't know who he is, but yeah, they're willing to sacrifice over earthly belonging, basically become homeless. But what we're missing is that they weren't fearful for their lives. To follow Jesus was a death sentence. And indeed, that was carried out with all of the disciples and the apostles, except for John. So yeah, that's what's missing in those two examples. I think you're giving a false distinction. So you're saying because they feared for their life rather than took their own life. Like, I don't think fearing for your life vindicates your belief more than taking your own life. Like the beliefs are definitely equally strong. If they were willing to take their own lives, then we're definitely willing to put themselves in circumstances where others would take their lives. Like, I don't think that's a prerequisite, Dan. So yeah, those Comet people were obviously fully committed. And by the way, they didn't, nothing sprang forth from that, except that we know the story. I do know that story. But yeah, there's no future followers of them that followed in their footsteps because they were inspired by their sacrifice such as it was basically suicide. But no, what I'm talking about is a prerequisite here. So yeah, those Comet people, they were just walking around, life was fine, and they started following this Guru or false messiah, whatever he was, just like the Indian people. And there was no punishment for doing so. They were free to do that. The disciples and the apostles feared for their lives. And everyone agrees on that. I mean, that was revolutionary at the time. I like to say to people, who's the... They're the followers of Charles Manson, right? So they believe that Charles Manson could perform supernatural miracles. They thought he was the reincarnation of Christ. Like they literally thought he was a messiah. And they followed him to murder people, lose their freedom, get jailed for the rest of their lives in pursuit of this man that they knew. So their belief was sufficient to face persecution and basically the ending of their freedom. So that is a more bold thing that many of the early Christians did. Many of the early Christians, they lived in hiding and they really didn't have many repercussions. Like in the very early days of Jesus, there was no repercussions. Maybe later on, there was heavily persecution. But there's no evidence that there was early, early persecution of the church. If you do have evidence. What do you mean? When his ministry began? When his ministry began and soon after. So within the 60 to 70 years, within the living range of Jesus' disciples, there is no evidence for heavy persecution. Oh yeah, there was for, it's in the Bible. If you Google the quote, for fear of the Jews. Even before Jesus is crucified, he cures a blind man. And then the Pharisees asked for parents. Was he really blind, insured? Is this some scam? And they're scared because the Pharisees have said, if anyone proclaims the same, Jesus is the Messiah. I'm sorry, you're lagging really hard a mile. Oh yeah, I'm sorry. Can you restate what you just said? Yeah, even before Jesus is crucified, there are examples in the Gospels. It's called the fear of the Jews. And to be fair, it's not the fear of all Jews. That would be anti-Semitic. It's fear of the Jewish leadership. But in order to be leaders, they have followers, they have a lot of, and yes, for fear of the Jews, the parents of the blind man that Jesus cured, he spits on the mud and puts it on his eyes, and then he can see. They don't want to answer when the Pharisees asked them, well, was your son always blind? You know, is this true? What just happened? They don't want to answer. You think whenever they said, for the fear of the Jews. For fear of the Jews. So when you say they said for the fear of the Jews, you think it was fear of death? So you think that the people whose child got healed, they thought the religious leaders in the area were going to murder them? Like that's definitely not a reasonable. Well, yeah, they would stone them. And we know they tried stoning Jesus a couple of times. So long before he's crucified. Wait, how do we know this? That you're saying we know this as if we have like historical documentation outside the Gospels. Like you're basing this partly on the Gospels like accounts. Yeah, it's all in the Gospels. But I would admit to you, you can't discount them using the Gospels then.  Oh, yeah, yeah. I would never have discounted the Gospels. So such as the- Like the account that you just gave with the Gospels. But I would discount the Gospels as a whole, as a source of historical evidence. Why though? Why? It's, I know now we might say, well, they have a vested interest. So sorry to interrupt. I'll give you guys the time. Misha. What? Oh, I'm sorry. I'm sorry, I was- Yeah. Misha. Yeah. Sorry to interrupt. Just wanted to see, I think there's a lot of lag. I think I might actually try it too. If you and I go to just audio, I think it might make the stream run smoother because I think that basically hangouts trying to pull in our video with our weak internet connections is making the stream choppy. Are you willing to try that with me where you and I turn our cameras off? I just turned the camera off. Eric, can you hear me? You got it. I will try it too. And then sorry to interrupt there. I can definitely hear you. I think your connection is a little bit stronger than Misha's in mind, just because we're on the road. Sorry about that. So, go ahead. Sorry, I didn't mean to interrupt you, Misha. Yeah, yeah. I know the argument against using the Gospels is that, well, they're biased. They have a dog in the race, as the expression goes. But this goes back to your examples of Charles Manson, the crazy Comet people.  None of them were prevented.  They were perfectly free to do so. But here, the restriction on the disciples and the apostles is potential and indeed became a real death, except for John. So, what vested interest do they possibly have other than to tell the truth? Because they truly believe it. So, we know that people can believe things as if they were true when they are not true. So, I'm sure you believe that Islam is false, right? Well, that's a loaded question because yeah, I don't believe Muhammad was, I believe he may have been a prophet, but he was pretty bloodthirsty. And I believe there's truth. I don't mean to dice the answer here, Dan, but yeah, I don't believe he rose to heaven on a horse. Okay, well, let's change. Do you believe that the emperor of Japan around World War II was a descendant of the sun god? A good example. Yeah, I do not believe that. Not at all, yeah. But you might want people to believe that. His people believed it to the point of killing themselves for him. You can say that they didn't have societal pressure to not. They didn't have fear of jailing. Nobody was stopping them from doing it. But continuing to do something, even though somebody is preventing you from doing it, is a sign of dedication, right? That's what it is, a sign of dedication. And there is no greater sign of dedication than intentionally taking your own life in the pursuit of the thing. Like, no matter their level of dedication, their early apostles, no matter their level of dedication, that doesn't vindicate the truth claim that Jesus was resurrected from the dead. It just vindicates that they believed it. Yeah, yeah, let's start with that. And that belief was a death sentence. So, believing the emperor is the descendant of the Son of God, risk involved, just as joining Charlie Manson in the desert or the Comet people. Well, that was a death sentence. So ever, except as you say, yes, if you end up being a Kamikaze pilot, that could be considered risk. Well, the Comets was a death sentence as well as the Kamikaze. So those were both death sentences.  Joining the Comet people is like joining the Rotary Club. I mean, once you get used to it, it's crazy, but nothing's... That's definitely a distinction without the difference, because what you're trying to prove whenever you say that they were willing to be persecuted is their level of dedication. And you're saying they wouldn't be that dedicated to a lie. Am I right? Is that the point you're trying to... So I am not saying that they were dedicated to a lie. I'm saying that they were dedicated to a mistruth. So sometimes people don't have to lie. They can believe false things, like the Comet. So the people that killed themselves because the Comet was about to pass by, they had an equivalent, if not greater amount of dedication to their cause, even though it was completely false, which proves you could have unending dedication to a false belief, right? And they were there, right? Like they knew personally the cult leader. They knew everything he said. They knew the claims that he made, they were false. They continued and persisted anyway. Yeah. So if your point is, is the amount of dedication they had proved that it actually happened because they wouldn't have based their entire life on a lie. That's the equivalent of me saying the people that killed themselves to fly up into the Comet were lying.  They weren't based in their life on a lie. It was just a misunderstanding of reality. Like their mental map did not map on a reality. I'd say, Dan, you have to reverse it. If joining the Comet cult or joining Charlie Manson, if there was something preventing them from doing so up to an including death, then that would be remarkable that they would go ahead and do it anyway. The fact that the Charlie Manson people ended up. What about Hinduism? What about Hinduism in the middle of any, in the middle of past Islamic rule, right? So if you were a pagan under Islamic rule, that was a death sentence. You were going to be killed as commanded, right? So they persisted and they still won converts. So you have people converting to paganism under Islamic rule and guaranteed persecution and death. Does that guarantee the validity of paganism? Point, all sorts of challenges throughout history. You're absolutely right. But none of them caught on like Christianity. So now you're saying because it caught on, like saying that like because of how popular it is. Well, if you look at Islam, Islam is growing at a faster rate than Christianity. Does that guarantee its validity? The spreading of a religion has nothing to do with the truth of it. Because then you'd have to say each religion is a little bit true, but Christianity is the most true for now, you know? Yeah, but again, we've got the threat factor, call it death, the threat of death. We've got that backwards.  With Christianity, it's the opposite.  What about paganism though? What about my example of paganism and Islamic Ryan nations? Yeah, yeah, you're right. Because in that case, they're so upset with Islam, the invading force that they're willing to adhere to something that Muhammad or whoever it was at the time, I'm afraid I don't know the history of that, but whoever it was, warning them, hey, if you're pagan, we're gonna kill you. That is remarkable. But then paganism doesn't catch on. And yes, there is a popularity argument here to be made. And if I couldn't just briefly, it was after the sacking of Jerusalem, immediately the Jews decided, well, let's do exactly what proposing the Christians did. Let's go ahead and just create our own Messiah. And that was the Simon Bar-Kobka. There was another rebellion after the fall of Jerusalem. Or sorry, the Simon Bar-Kobka, that led to the fall of Jerusalem. Sorry. And then after him, there was another one, I forget his name. And yes, the Jews, so after they crucified Jesus, they try to do exactly what you're proposing. They say, well, let's just go ahead and say this Simon guy is the Messiah. And just like with Christianity, which was illegal, the Sanctis was death. And sure enough though, it was crushed and led to the crushing of it. Okay, so your argument for the spreading rate of Christianity, is that because of the truth of Christianity, that's why I was allowed to spread. Am I expressing your- Yeah, don't forget, I wouldn't hesitate to reject Islam because of that. Because I think Islam is totally misguided, but they do recognize Jesus as a prophet. So I think there's- All right, let me go into that example though real quick. So because of the spreading rate, right, it has to be truth. So do you know that whenever, like right after Jesus' death, the spreading rate of Christianity was about equivalent to that of Mormonism. Christianity didn't really pick up speed until the second and third centuries. You know, it's not like right after Jesus' death that was when the bloom of converts happened. If you imagine that there was a truth of a resurrection that occurred to hundreds and hundreds of people. And it was a well-known thing in Jerusalem that Jesus rose from the dead. You would expect it to be a real explosion. You'd expect it to be an explosion, but that's actually not what happened. So in the first century of Christianity, it grew at about the speed of Mormonism and obviously a ridiculous cult. So how would you, like, so you're saying that this spreading speed of it dictates its truth, but the spreading speed of Christianity was that of Mormonism. It just reached a critical mass in which it just increased exponentially long after Jesus' death. So that gives no validity to the truth claim of it. Well, yeah, except that Mormonism is being spread and what was it that, sorry, the 18th or 19th century, I'm sorry, I don't know which, but it's relatively modern times with modern communications. Whereas we're talking about... So what is that happening? Well, it's easier to spread something when the more modern, the era, the more, and of course, these guys are still being hunted down and killed, Paul and Barnabas, well, they're thrown out of some cities by the Jewish Pharisees and the Sadducees in those cities. And they're stoned and Paul is thrown off a wall. And again, according to the gospel, such as you may or may not believe it, it looks like he's dead and is actually raised from the dead. He's left for dead outside the city, whether he was dead or not. This shows the opposition. Now, you're right, Josiah Smith faced opposition, but nowhere near. I mean, he was run out of town, but wasn't stoned to death nor were his followers. And all they had to do to spread Mormonism was keep moving west. And they finally got, of course, to Salt Lake City, which became their Mecca. But so there's a huge difference. You're making a lot of distinctions without difference. So if your point is their level of dedication, their level of dedication vindicates the truth. And I give you an example of another person who had equivalent level of dedication to an erroneous truth claim. That's what matters if you're talking about the dedication. You're not talking about the means of dedication. You're talking about the dedication. So now if we're talking about the spread speed. The means, as you just said, the means were terrible in the first century. The mean by which Christianity was being spread. Not the first century. All the means were working against them, whereas the Mormons, yeah, they faced opposition. They were chased out of New York state, but nothing like what the Christians, I'm talking about the other example I gave you though. Which one's that? The paganism. The paganism? That totally doesn't matter. The paganism, it's because the spreading speed was slow. Sorry, what? So the paganism, the reason why you believe that it's not a good example is because secondarily, the spreading speed wasn't as fast as Christianity's. Oh yeah, I mean it doesn't exist, I would say. There's no paganism. There's no pagan temples in existence today, whereas there are Christian, and yes, Mormon. Yeah, I know, but so I just, so your premise is that because Christianity took over the world, it is true. Because Christianity spread in the face of fierce opposition, which I think is unprecedented. So again, the Muslim example, the fierceness is on the Muslim side. That's how it's spread by the sword, which is its downfall, I would say spiritually. But Christianity is facing that opposition, and no other, I mean Josiah Smith never faced that ferocity of life and limb to be crucified or boiled in oil as the disciples did. So basically the root of your argument, like if we really get down to it, is the amount that people believe it, and the quickness people are to believe it, and the dedication with which they believe it. That proves the truth of Christianity. The precedent, which is the opposition to the sword. Just the fact that it's superior. Wait, so your perception is that it's superior in dedication, and it's superior in belief. Like the people that believe it, believe it more seriously, and can spread that belief more effectively. So that makes it true. I would explain it like this, if you were living anywhere in the, around the Mediterranean, after the crucifixion of Jesus, you probably heard that it was a death sentence to become a Christian before you heard from one of the apostles or disciples. You would have heard from the authority in your community, whether it was the Jews or the Romans, two global empires. The Jews are still very powerful at that time. And you would have heard of the punishment you would face before you heard the good news. And so for anyone to hear the good news after that, and yeah, follow it. I'd say yes, that's a good thing. That makes it more sexy, honestly. So, oh no, no, no, death isn't sexy. Yes, it's not sexy unless you're looking for the ultimate truth.  So if you're looking for the ultimate truth of Christianity, it makes it more sexy in hindsight. You're absolutely right. I just want to give, hold on, Misha, I just want to, Misha, I just want to give Daniel a chance. I think we'll come back to you. I just want to let Daniel clutch that one. I get what you're saying.  You spend all your time in glory, right? That is a good exchange. That is a good exchange. So if I truly, like if I had somebody reputable, and I was a first century Palestinian, right? I was very gullible.  And I would do it. That's a very reasonable thing to do. And the fact that they're being persecuted like it makes it more sexy. Like we know that cult leaders, the cult sticks to them closer, whenever you have outside persecution, whenever you have us versus them dynamic, it makes everybody else look like sinners and you look good. It makes you believe stronger. So the persecution might actually help a religion spread. It might help the strongest believers believe. Well, how many people are following David Koresh after Bill Clinton wiped them out? I mean, I'd say the opposite is the case. But again, Dan, Dan, you've got the cart before the horse. Before they hear about that you'll be rewarded with a life in heaven. Before they hear that, they're hearing that, hey, a disciple might come to town preaching something called the good news. If you follow him, you're dead. That's what they're hearing. Yeah, that's what they're hearing. And that's supposing that that happened. Like, I did not take that. I would like a historical example outside the gospel of that. Sure, how about Nero? How about Nero? When was that? Right after the crucifixion of Christ. He's before Vespasian, so he's before the fall of Jerusalem. And yeah, Nero is feeding Christians to the lions.  Or to be... If you go in the heaven, yes. The other one they would do is they tie you to a bull and let the bull loose in the arena. And the bull would, you know, you see guys, men can't stay on a bull for nine seconds in the rodeo.  And the bull would just buck you to death. So it's not just that you'll die, Dan. It's how you'll die. Crucifixion, emulation or to be fed to lions. And listen, and they're hearing that before they hear the good news. How do you know that? You're asserting that without proof. And even if that was true, that does not vindicate belief. Do you agree that, like, okay, so individually, can people believe stuff that will have them killed when it's not true? Do you believe that to be true? I obviously believe that to be true. I need an example because the examples you gave. All the examples I gave. So if we're talking about in the Middle East, right?  As commanded. Yeah, but the three examples. Why would one person convert to paganism? Well, I dealt with that. They were wrong because you can have false belief and false belief does not vindicate itself. No matter how many people believe something and no matter how strongly they believe it, that does not prove the truth of that claim. Oh, no, I totally agree. Yeah, I totally agree, but- So where is your truth coming from? So you're talking about the amount of people that could believe it strongly vindicates the truth of the claim? Yeah, well, I was gonna go for your examples one by one.  But I totally believe you. And yet they were pagan, but there is no pagan temple anywhere. There's no pagan worship. So I mean, that one, I guess we'd say, I guess the Muslims were successful, I guess. But the power of the Jewish power at the time and the Roman Empire was not able to snuff out Christianity. And yeah, because it's a truth. I believe it's a truth claim. And yes, it's a simple matter of headcount.  One of Paul's travels, he goes up to Antioch. That's the 200 mile journey from Jerusalem. Now he may have ridden on a donkey road. I believe he was dedicated. I never said he wasn't dedicated. But before he's getting there, no, there's no internet. Don't you think the Sadducees and Pharisees can get word to the synagogues in Antioch before Paul and Barnabas get there? Of course they can. And they have their own little empire of all this interconnected temple, Jewish temples and synagogues in the Holy Land. And still it's... I agree with all that. I think where we're grinding our gears is you think that a certain level of belief and dedication by a certain amount of people vindicates a truth claim. I do not. If threat of believing it is death. So threat of believing it is death goes along with dedication. So it's the dedication and the belief, the dedication to the belief that vindicates the belief. No, no, you go to backwards again. The... No, no, I don't really want to say... Call it people. There's nothing stopping the Comet people from following that. That is not what I'm talking about. I'm just talking about the premise of your belief in the truth of the resurrection. So it's based off of the strength and the dedication of the belief by the people around Jesus. Yeah, put it this way. They must have seen something astonishing. Like you say, a miracle requires extraordinary efforts. They must have seen something astonishing to believe it with all their heart. Is that the claim you're making? Yes, yes. Especially when... Something astonishing to believe it with all their heart. Death, yes. We know that. We know that.


This is a 440 Hz tone. The A above middle C for any musicians amongst us. This is a minus 440 Hz tone. They sound the same, don't they? That's because they are. At least when you think of frequency as how many times an event, like a vibration in the air, occurs every second. However, if you look at frequency like this, then the concept of negative frequency becomes a little easier to understand. In this video, we're going to find out what negative frequency is, why negative frequency imaginary numbers and the complex conjugate are so important to the magnitude spectra of signals, and what effect negative frequency has in the real world, just in case you thought it was only a quirk of the maths. Ooh, we'll be taking a quick look at the inverse Fourier transform too. Hi, I'm Mark Newman, and this channel is all about helping you understand the fascinating world of signals and systems. Ask any mathematician why the Fourier transform of a signal produces a magnitude spectrum that is symmetrical about 0 Hz, and they'll probably answer, because your signal is real. Well, of course it's real, you might be thinking. I didn't imagine it. The thing is, what you mean by real, and what a mathematician means by real, may not be the same thing. I'm willing to bet that all the signals you've ever met in your life are real signals. That is to say their amplitude at any given moment in time can be described by a single number. That number might be in decibels, volts, meters, or any number of measuring systems, but it will be a single number that perfectly describes the amplitude of the signal at that moment. But the Fourier transform describes how much each frequency contributes to an overall signal in terms of the cosine and sine components at that frequency. Take this simple 5 Hz sinusoid as an example. If I break it down into its component cosine and sine waves, they look like this. They both have a frequency of 5 Hz, but their amplitudes are such that when added together, they produce the 5 Hz sinusoid we started with. If I perform a Fourier transform on the signal to transfer it into the frequency domain, the cosine component looks like this. Here's the peak at 5 Hz. But where is the amplitude of the cosine wave in the time domain is 0.8? The amplitude in the frequency domain is only 0.4. And there's another similar peak at minus 5 Hz. Looking at the frequency domain representation of the sine component, something similar happens. At the 5 Hz frequency, the amplitude is half of that shown in the time domain graph. But at minus 5 Hz, the amplitude is minus a half of the time domain amplitude. What's going on here? And what's this negative frequency? In order to answer this question, we need to look at frequency in a slightly different way. Instead of calling it frequency, you may have heard the term angular velocity. It's often represented by the symbol omega. This is especially useful when we consider the complex plane. The complex plane combines the cosine and sine components of a signal into one image. The x-axis represents the amplitude of the cosine component at any moment in time, and the y-axis represents the amplitude of the sine component at any moment in time. The frequency of the sine and cosine waves can be thought of as the speed of rotation of a line in the middle of the circle. This is the angular velocity for this line. If we use the z-axis to plot the angle of the line, then our circle becomes a spiral. The speed the line moves up the z-axis is its angular velocity. However, just as the line can move up the z-axis, it can also move in the opposite direction down the z-axis. If we look at this in two dimensions, this is equivalent to rotating the other way. When the line moves up the z-axis, its angular velocity or its frequency is positive. When the line moves down the z-axis, its angular velocity or frequency is negative. This is one way of understanding negative frequency. Let's go back to looking at this idea in two dimensions. I'm going to make the rotating line into a triangle and plot how the height of the triangle changes with the angle. Look, it makes a sine wave. Now I'm going to do the same with the width of the triangle. See how it makes a cosine wave. But what if the triangle was to start rotating in the opposite direction? A rotation in the opposite direction is the way we just conceptualized negative frequency. The cosine graph looks the same, but the sine graph is a mirror image of itself. Any positive value on the sine graph during a positive rotation is now negative during a negative rotation and vice versa. Understanding negative frequency in this way explains why the amplitude of the cosine component at negative 5 hertz is positive and why the amplitude of the cosine component at positive 5 hertz and why the amplitude of the sine component at negative 5 hertz is negative and the amplitude of the sine component at positive 5 hertz is positive. In the frequency domain, the cosine and sine components at each frequency are represented by a complex number. The cosine component is represented by the real part of the complex number and the sine component is represented by the imaginary part of the complex number. There are two non-zero frequencies in this signal. 5 hertz and minus 5 hertz. So this signal could actually be represented by just two complex numbers. 0.4 plus 0.3i for the 5 hertz frequency and 0.4 minus 0.3i for the minus 5 hertz frequency. In order to recover this signal and move from the frequency domain back into the time domain, we need to perform an inverse Fourier transform. What is the inverse Fourier transform and how does it work? We can answer this question using a special diagram which I'm going to call a Fourier cube. Here's my signal. The Fourier transform breaks the signal down into its constituent sinusoids giving us a representation of the signal in the frequency domain. The inverse Fourier transform as its name suggests does exactly the opposite, putting all the sinusoids back together again to recover the original time domain signal. But as we saw before, the Fourier transform does more than just break the signal down into sinusoids. It breaks each sinusoid apart further into the constituent cosine and sine waves making it up. Therefore, before the inverse Fourier transform can add all the sinusoids at the different frequencies together to recover the signal, it needs to first recover the sinusoids themselves from the cosine and sine components. This is what is happening inside the integral of the inverse Fourier transform. X of f is the list of complex numbers representing the amplitude of the cosine and sine components at each frequency. Each complex number is multiplied by a cosine and sine wave at the frequency we are currently interested in. But multiplying two complex numbers in this way at a single frequency doesn't recover the two-dimensional sinusoid we saw in the Fourier cube. This is because the result of the multiplication still contains an imaginary component. It's complex. It looks like a three-dimensional spiral. Now you may have noticed that the frequency dimension has disappeared from my graph. This is due to the fact that in order to draw the complex sinusoids for each frequency I've had to borrow a dimension. We live in a world with only three spatial dimensions in it, but in the abstract world of mathematics there are an infinite number of dimensions. However, if we want to represent these dimensions visually it can become a little difficult to draw more than three dimensions at once. On the Fourier cube I've already assigned all the dimensions I can draw. The x-axis represents time, the y-axis represents the amplitude in the real dimension, and the z-axis represents frequency. Unless I borrow a dimension I cannot represent the amplitude of the complex sinusoid in the imaginary dimension. Therefore, I've borrowed the z-axis, the one I used for frequency, to represent the imaginary dimension. Our signal is real. This means it only has an amplitude in the real dimension. The amplitude in the imaginary dimension must be zero. All the sinusoids making up the signal must similarly be real. But the sinusoids which the Fourier transform calculates for us are complex sinusoids. They're all spirals. How can we turn these spirals back into the real sinusoids that make up our signal? This is where the negative frequency component comes in. This graph is only showing us half of the story where the Fourier transform is concerned. For every positive frequency component there exists a negative frequency component containing a complex sinusoid that is equal and opposite to the sinusoid at the positive frequency component. The final stage of the inverse Fourier transform requires us to add all these complex sinusoid together. When we do this, look at what happens. The sine component of the negative frequency in each frequency pair is the exact opposite of the sine component at the positive frequency in the pair. These two spirals are complex conjugates. When we add them together, the sine component in the imaginary dimension cancels out, leaving us with a real sinusoid. So now we know what negative frequency is and why it is present in our signal. It's there to ensure that the imaginary component which the Fourier transform left us with cancels out when we reconstruct the signal. In other words, it's just a trick of the maths. Isn't it? Well, no it's not. I'm going to show you a real-life example of the effects of negative frequency and what it means for the bandwidth of a signal. Whenever you tune your radio to pick up your favourite radio station, what you're actually doing is tuning a filter to a certain frequency called the carrier frequency. The carrier frequency is a sine wave onto which the audio signal of the station you want to listen to is modulated. The most well-known modulation techniques are AM and FM. In AM, the audio signal is multiplied by the carrier frequency to produce a modulated wave whose amplitude changes in proportion to the amplitude of the audio signal, hence amplitude modulation. You can see how the amplitude of the carrier frequency changes with my voice. However, if we look at it in the frequency domain, it's like this. This is a frequency representation of the modulated audio signal I just recorded. What has the modulation process done? You can see the modulating frequency represented by this line here. Either side of it are these sidebands. This is the frequency representation of my voice. What the modulation process has done is to shift the frequency spectrum of my voice from its baseband range the range of frequencies you hear when I speak all the way up to this new frequency range around the carrier. But just look at this. The baseband frequency spectrum of my voice contains negative frequency. If it didn't, then the frequency spectrum of the modulated signal would look like this with the only frequencies present in the signal being above the carrier frequency. However, this is clearly not the case. The sidebands are symmetrical, meaning that this negative frequency is far more than just a quirk of the maths. It's a totally real physical phenomenon. A phenomenon we have to be careful about when assigning frequencies to different radio stations. As the use of radio communications is increased over the years, the airwaves have become more and more crowded, meaning that the distance between different radio stations and the frequency dial has become smaller. However, if one radio station is assigned a carrier frequency that falls within the range of another's sidebands they will interfere with each other. Therefore care must be taken when assigning these carrier frequencies so that enough bandwidth is left between stations to avoid interference. This has led to the development of techniques such as single sideband modulation which manages to modulate the audio signal using only one of the sidebands, meaning there is more bandwidth available for additional stations. So negative frequency is far more than just a quirk of the maths. It's a real phenomenon which impacts on our world. We've covered quite a few concepts in this video. Negative frequency, imaginary numbers, the complex conjugate, the Fourier transform and the inverse Fourier transform. All of these concepts are covered in more detail in other videos on my channel. See the links at the end of this video. If you would like to learn more about Fourier and his theories and how they led to what we now know as the Fourier transform then take a look at my book on how the Fourier series works. In the book I take all the basic concepts contained within the Fourier series, look at each idea visually and then put them together just like Fourier did in 1822. The book is available to buy in paperback and Kindle e-book formats however you can download the first few chapters for free by signing up to the mailing list. Links to the full book and the mailing list are in the description below.


The use of nanotechnology in medicine has the potential to revolutionize the way we treat disease. Nanoparticle-based medications, nanomedicines, offer a promising alternative to traditional pharmaceuticals by providing more efficient and targeted delivery of drugs. However, there are many challenges associated with bringing these products to market, such as biological challenges, large-scale manufacturing, biocompatibility and safety, intellectual property, IP, government regulation and cost-effectiveness. Despite these obstacles, nanomedicines hold great promise for improving patient outcomes and reducing the cost of care. This article was authored by Susan Hua, Susan Hua, Maria B.C. DeMotto's and others.


Oh, sorry. Um Hello, everybody. It is just after lunch on Sunday, January 17th. I spent the morning sleeping in having coffee and I filmed a quick journal video and so here I am Fun fact I Hate editing the vlog. I Hate hearing myself talk and it's like Somewhere between one and four hours of video clips of hearing myself talk And I've got to edit it down to 30 minutes or less preferably 20 minutes or less although I don't often manage that and I dragged Bob away from the football and on TV and We're gonna go get some steps in It's a little nippy out, but it's not too bad. I don't think So we're gonna go get some walking in Because we've both been kind of sitting on our butts all day, so You know exercise is a good thing. Try it. Why don't you? All right, I'll be back. Okay, so Here's a little known fact about me to all of you, but a very well known fact to my friends and family I'm a very much a creature of habit I have the same exact two cups of coffee and cottage cheese or yogurt for breakfast every day. I Have yeah, it's Bob is saying the same exact thing for lunch. I've almost every day unless we're not home. I Like to walk the same routes Bob's taking me opposite. He's making me do opposite. I like routines. I like the same thing It's okay. I can handle it Maybe We'll see I'll be back Hey guys, it is Monday afternoon January 18th. I think holy cow. I don't know. I think it's the 18th. Let's see. Hold on Let's check the computer. Shall we? Yes, the 18th and it's after two o'clock that I know to 221 not confidently, but yeah, I have to look at the clocks and stuff Anyway, it's just been a slow go this morning. It's Martin Luther King Day here in the United States And so it's a holiday generally plus, you know, hello the inaugurations coming. So Everybody's kind of staying home Not doing it much us included. I Have since we moved in Struggled to do laundry in that we get these Costco size or Jumbo size bottle of liquid laundry soap and they're really heavy to lift up and then pour into the little cup to get into the washing machine and It dawned on me recently because hello and slow to the program sometimes I bet you somebody makes a stand to like sit the bottle sideways so that you know, you can have it just like that with a cup underneath it and fill it up as you go and Sure, they do they make laundry soap stands They're expensive. Holy cow. I looked at them went don't I have a plastic basket or something? I can stick under there Yep, I do hold on So I fixed it for free It may not be the prettiest thing on the planet, but it works for me. So we're out for a walk Before it gets too dark We thought we'd come down to the river here. That's not far from our house And see how high the river was because we kept hearing about the water being really high Yeah, believe it or not somewhere down there is a dock But it's completely underwater and you can't even see it It's really high Holy cow That's crazy Before y'all get too concerned Bob and I aren't in a low-lying area. So don't be worried our house is high so But I'm glad I don't live over here closer to the river Well, I know there's a dock down there somewhere. Yep I can't even see it. I don't see it. It's down there somewhere. Yeah Good afternoon everybody is Tuesday afternoon 305 p.m. January 19th Yeah, cuz tomorrow's inauguration day. Anyway, we are not going anywhere until like Saturday like yeah, nowhere My allergies have been getting the best of me the last couple of days. So that's a thing I need some more cough drops. I Spent the morning And it's just allergies. It's not the big C. Anyway, so that's the sunset view out of our back window How pretty are all those colors Hey guys, it is 405 in the afternoon on Wednesday, January 20th Inauguration day here in the US for our new president Congratulations to president Biden and vice president Harris Anyway, our cleaning lady has been here all day working safely of chorus We stay well not only well out of each other's way. She wears a mask the whole time She's here and if I need to get close to her to talk to her I put one on Anyway, she's still working poor thing she's been here all day Um, okay, you know, it's a crazy time when I'm forgetting to vlog Holy cow My hair looks like Einstein sister I had to trim my eyebrows again because they were starting to resemble Einstein and that you know I have my dad's eyebrows that grow straight out this way. I have to give him a little trim anyway I am headed out to get the mail Okay, I wanted to show you so I got one of the watercolor journals out From my closet that I had and it's a pentallic Um watercolor journal. It's I think it's eight and a half by 11 or something close to that I'll try to find it in the at amazon and link it down below um and inspired by Donna Downey and her Posts on social media about her new class. She's teaching I did this today And I'm really inspired to do some color mixing of some paints that I have and sort of Do sort of a reference practice book Um, she has a class for this so I'm never going to film tutorials for this I can't afford to take a class. It's too expensive. So I'm going to do my own version off camera Um, and you'll see it here. I might do the occasional still shot But again, I'm no tutorials for me if you want to learn how to do it. You should go take her class Um, I will link her website down below if I forget somebody tell me Um, not that her class isn't worth it. I just don't have that in my budget right now So anyway, that's I spent a good portion of the morning working on That painting and playing with that and having fun. I'm gonna do one In my moleskin journal probably before I wrap up today so we'll see about that and I need to Finish the editing first All right, I'll be back Hey guys, I have a feeling this is gonna be the week where I forget to vlog So rather than last week where I had almost five hours of footage to edit to 30 minutes or less This week, I don't know what I'm gonna end up with anyway Good afternoon. It is Friday, January 22nd 207 p.m I was live this morning with patrons and supporters Oh, that reminds me of something I have to do before I forget Um, I'll do it right after I'm done with this And and before that I was talking with someone I haven't talked to in a while a friend Um, she's going through a tough time. So I sang some good thoughts out there for her um Had some lunch so it'll fattled around I did a journal page and some painting papers for the live this morning And I'll share still images of on social media later I have of course other projects I could be doing But I don't know if I want to get started on any of them It's just gonna be one of those days. I think I just took yet another I sent an old picture of myself because you know, god forbid. I'm a professional youtuber or anything Anyway, here's a project that I might be able to do and in the mindset to do Um, that might not take too long. I have these sort of bins like this of crayons and markers I haven't been using them like this and I'm kind of wondering if I changed the way they're displayed up here and or went through the stuff that's up here just decide if there's I really do need everything that's up here I do I have an alternative to this I think I'm gonna play I'll be back things that were there before and replaced them with these drawers already had I used what I had I had a pair of bookmarks in the other room used what I had I sort of yes collect storage containers But I'm really whittling down my collection that when I get these impulses I can just switch out say these drawers back for the other bins that were here I probably won't get rid of them And or I'll repurpose them for somewhere else, but I'm liking this much better And uh, yeah, all of these little things up here. These are my props when I'm I'm taking photos for still lifes. I use these to fruit and different things and so Yeah, much better. I replaced a few labels that label was completely the wrong thing for that bin And I got rid of a few pens and um, yeah I like it. We'll work with it for a little bit. We'll see how we like it And meanwhile, there's a few more things in the purge box for the end of the month All right So yeah, I like the way that looks plus all of these little things And the books were over there on the top of the drawers, which was okay, but it wasn't my favorite thing. So now they're gone from there. So I like that much better Yeah, very much All right, that's it for the minute. I'll be back Good morning people. It is just after 10 a.m on saturday january 23rd, I think it's like 10 15 a.m. Ish um Bob and I are getting a later start than I I would have liked Um, but we slept in this morning or at least I did anyway Um, we have a number of different places to go. So it's going to be a little bit of a people-y day But we've literally been home for a week um Not seeing anybody The downside of that it means that all of my Things I need to do have kind of added up. So we don't have to hit a couple of hardware stores the p.o. Box and the grocery store So of course, we're going to do it safely. We're going to mask up and all that stuff and um Yeah, let's get to it. Shall we okay? So we're back from running our errands and we've had some lunch Did a little bit of filming for an upcoming class. I'll be teaching later in the spring But we're getting ready now anyway, we are puppy sitting for a little bit they're there and While the kids run some errands and so we're going to go out for a walk novel idea doing it during the daytime when it's not dark outside It is cold though and it's supposed to get fairly cold tonight and tomorrow we may actually get some snow for the first time this season so We'll see if that happens Anyway, we're going to go see what we can see and get some steps in and I'll be back So it is 6 15 and Bob and I are obviously in the garden we are Heading to go do some Curbside pickup on dinner. So once or twice a week. We try our trying hard now as safely as possible to support the local community and And get take out dinner from a mom-and-pop restaurant or something somewhere tonight. We are trying Jb O'Brien's Irish pub, which is actually walking distance from the house But we've already done more than 10,000 steps today And I don't think either one of us are up to walking down to Jb O'Brien's to get dinner and Then back again and plus it's a really cold tonight. So Yeah, so we're gonna go drive and pick it up I see lights up ahead. It looks like an ambulance. Yeah, you should be able to and then left into that Thing so anyway, we're gonna go do that We hope you all have all had a great week. Don't forget if you can and you're able Safely support your community by doing, you know curbside pickup on a takeout meal or You know if you need I don't know this morning I was looking for pieces for a class that I'm teaching so we went to the local hardware store first rather than the big box store so Do something that you can safely. Let's be kind to one another. Please Support your the free content here on youtube and over in the facebook art groups. I know all of your artists and your small Art supply companies. They're all suffering right now Just like the rest of the world is and they would appreciate the support So please do so check my video link for relevant links for how you can do that or just follow me on social media Um, I know check theirs out too. I know they'd appreciate it. Don't forget to stay safe. Stay healthy. Stay creative Please wear a mask go out and do something nice for yourself because you deserve it and we'll see you next week. Bye guys


So there, Keemik Bros. in Skexil is an exclusive to a sub-bus, Skrake, within the Ascension Bluff area and Prometheus. How's it going guys? My name's Nipi Gen. I'd like to thank you for stopping by and checking out my videos. If you do enjoy it, leaving a like truly helps out and subscribe if you want more while I launch three videos. So this elemental pistol is actually pretty damn epic and I found this a while back but I've held on to the video because I thought people would have come across this already but it seems after having a look online, not many people have. So the weapon not only looks crazy bizarre, it's actually a decent weapon for your setup.  But I can confirm there are different versions to this weapon that drop from this sub-bus. Now I realise going back here to get this if you haven't already completed the game, it will drop a low. So maybe save it until you enter that true Vault Hunter version. So it's obtained from Skrake within the Ascension Bluff area and Prometheus. Using the route I take, go here and farm this dude until you get this thing to drop. You won't be disappointed with this weapon as it is indeed great. If as per usual it doesn't drop first time, quit outload it back up and repeat. Do this until you land yourself this legendary and good luck people trying to farm this. On that note guys, we have come to the end of the video. If you enjoyed it leaving a like truly helps me out. If you are new around here and want more boardlands 3 videos, I've posted plenty of a legendary weapon locations and the bosses to get them and I've got many more to come so stay tuned for that and subscribe if you are new around here. But guys, thanks as always for stopping by, hopefully you enjoyed the video and hopefully I will see you on that next one.


Attention Baker residents. This is a community notification of a new sexually violent predator in your area. Please stay tuned to the following short program for more information. Hi I'm technician Ron Hackett with the Denver Police Department. The sex offender registration and compliance unit at DPD is responsible for the registration monitoring and tracking of all registered sex offenders and sexually violent predators who live in the city and county of Denver. Here's a brief history of sex offender legislation in Colorado. Our state laws trickle down from federal government mandates. In 1994 we had the Jacob Wetterling Act which mandated that states would establish a sex offender list. Maganslaw of 1996 said that the public would have access to those sex offender registration lists. The Pam Litchner Act of 1996 stated that some offenders might have to have lifetime registrations and the Adam Walsh Act of 2006 unified sex offender laws across the country. In Colorado the legislature has determined that sexually violent predators by definition pose a higher risk to the community at large and therefore mandated that upon their release from the Department of Corrections the community must be notified. Sex offender notification in Colorado happens in two ways. The first is passive and ongoing through the sex offender registration process which is a list maintained by local police departments. The second way is active via community notification for those offenders determined to be sexually violent predators by the courts or by the parole board. Most sex offenders in Colorado are supervised by the criminal justice system in our communities. Most sex offenders engage in crossover behavior which means they may have been arrested for one type of crime but be apt to commit another.  There is no typical sex offender but all tend to be deceptive, manipulative and secretive. 80 to 93 percent of sex offenses are committed by someone known to the victim. Sexual deviancy begins in mid to late adolescence. Sex offenses are not impulsive.  The community has a vested interest in helping offenders to be successfully managed in the community. Sex offenders have the same need for housing and employment as any other citizen.  There are approximately 16,500 registered sex offenders in the state of Colorado. About 65 percent of convicted sex offenders are placed in the community on probation. The remainder are in the Department of Corrections or Community Corrections. Offenders may be caught for one type of offense but be at a high risk to commit another type. Crime of conviction is only one indicator of risk.  The offender's residence must be verified quarterly by the Denver Police Department. The full sex offender registration list is available by calling the Denver Police Department Identification Bureau at<PHONE_NUMBER>. Convicted felons and those with multiple convictions are posted online at denvergov.org slash police.   Now, here's a look at the newest sexually violent predator living in Denver. Here's an overview of the registered sex offenders currently living in Denver. There are 2,597 total living within city limits. In Denver Police District 3, there are 376. Precinct 311 has 47 registered sex offenders. Of those, 31 have felony convictions and 16 have misdemeanor convictions. Joseph James Madrid is a sexually violent predator currently living in Denver. He's 51 years old and was born on August 16, 1970.  He's currently living at 830 West 3rd Avenue in the Baker neighborhood of Denver. Schools located within one mile of this offender include Denver West High School, West Early College and West Career Academy, all at 951 Eladde Street, Gall's Schools at 750 Gallopago Street, Denver Center for International Studies at 574 West 6th Avenue, Compassion Road Academy High School at 1000 Cherokee Street. Parks located within one mile of this offender include Sunken Gardens Park. Bus routes located within one mile of this offender include Route 9, 8th Avenue and Mariposa Street, Route 10, 10th Avenue and Santa Fe Drive.  He's currently on parole and registered with the Denver Police Department on July 14, 2021 to 830 West 3rd Avenue in the Baker neighborhood of Denver.  Joseph James Madrid has been determined as sexually violent predator after meeting the following criteria. Criteria one, age 18 or older on the date of the offense or under 18 and tried as an adult. The offender was age 38 at the time of the first offense. Criteria two, the crime must have been committed honor after July 1, 1997 and convicted honor after July 1, 1999.  The offender was convicted on October 24, 2011 for attempted sexual assault on a child. Criteria three, the relationship to the victim was one of the following. Victim was a stranger to the offender or the offender established or promoted a relationship with the victim primarily for the purpose of sexual victimization. The victims were a five and a seven-year-old female. The offender was known to the victims. Criteria four, positive results or the passing of a risk assessment instrument administered by probation parole staff and a qualified treatment evaluator. Positive results include an assessment for the presence of a mental abnormality, a level of denial regarding the offense, treatment appropriateness and motivation, presence of sexual deviant interests. The offender was evaluated by the Denver district courts with positive results determining him to be a sexually violent predator.