Category
🏖
TravelTranscript
00:00:00Hello friends. Welcome to Friday Night Live Don Quixote episode 169.4.
00:00:15Let's do some dancing. Happy Saturday evening.
00:00:20Yeah, dancing. Sure.
00:00:24Yeah, I went to Walmart and drove back home and I listened to radio.
00:00:29They were playing Will Smith's Get Together, right?
00:00:32Yeah, sure.
00:00:34I like him quite a bit, Will Smith, okay?
00:01:23Okay, good enough.
00:01:39Good time. Five minutes, please. Thank you.
00:01:44Good exercise, dancing is.
00:01:46Yeah.
00:01:48Oh, yeah.
00:01:50Wow.
00:07:03Welcome, welcome.
00:07:09Yeah, happy Saturday evening.
00:07:13Yeah, I went to Walmart, but before that, I went to Alaska State Fair parking lot only.
00:07:19Why?
00:07:20I mean, they close at 10 p.m. I went there like 9 p.m.
00:07:25Yeah, I wanted to go there.
00:07:28But when I was driving the parking lot, it was I realized that I need to go to bathroom.
00:07:36Yeah, the bowel movement.
00:07:40That's why I have to drive back home.
00:07:43But Alaska State Fair parking lot, yeah, people going home.
00:07:47Yeah, I saw them in the parking lot and good to see people, you know.
00:07:52That was enough for me.
00:07:56Good looking people, yeah.
00:07:59Nice.
00:08:02Yeah, let's have some coconut juice.
00:08:10Cheers.
00:08:17Oh, this is nice.
00:08:21So we found something very interesting in the mathematics, right?
00:08:25Yeah, the inverse function of the ceiling function.
00:08:28Yeah, we can generalize that.
00:08:31Yeah.
00:08:39What an interesting discovery.
00:08:50Sure, let's go for it.
00:08:51Yeah, just a little bit, okay?
00:08:55Yeah, we'll prove this hypothesis, okay, later.
00:09:00For now, you know what?
00:09:04Let's get a whiteboard and let's try to prove it, okay?
00:09:06Sure, sure, we can do that.
00:09:18Oh, right.
00:09:48Okay.
00:10:17Okay.
00:10:21Okay.
00:10:31Let's give it a name.
00:10:33Inverse ceiling theorem.
00:10:42Yeah, this is like Fourier analysis back in the days when we studied it, okay?
00:10:47Is this cool?
00:10:48Yeah, but...
00:10:50Yeah, we're not doing that anymore, okay?
00:10:51So maybe in the future.
00:10:53So, yeah, we can erase this.
00:11:01Because Fourier analysis, yeah, there are textbooks about it.
00:11:05It's all out there in the YouTube.
00:11:07Yeah, I learned from Mr. Black Pan, Red Pan,
00:11:10a Chinese-American mathematics teacher on YouTube.
00:11:16Yeah, he explains it so well.
00:11:22And great sense of humor, too, okay?
00:11:25He's funny.
00:11:26I like him.
00:11:27I'm pretty sure he's younger than me, okay?
00:11:31Maybe even 30, I guess, yeah.
00:11:34Smart man, yeah.
00:11:36I think he went to UC Berkeley, okay?
00:11:39Cool.
00:11:40Okay, so hypothesis.
00:12:06Then...
00:12:36Okay?
00:12:46Inverse ceiling function theorem.
00:12:52Well, now it's hypothesis, but if we prove this,
00:12:56then because of theorem, okay?
00:12:57Yeah, cheers.
00:13:08Okay.
00:13:24Oh, rough ride.
00:13:28Yeah.
00:13:46Let's make some examples.
00:13:54Let's say n is 5, okay?
00:14:04So mathematics is like this, okay?
00:14:10Some mathematical narrative.
00:14:13Now we are doing number theory in the context of
00:14:16greatest common divisor, Euclidean algorithm,
00:14:19and Bezier coefficients, and Chinese real numbers, okay?
00:14:23So yeah, some mathematical narrative,
00:14:25and then we ran into this with some specific examples
00:14:31where n is like 3, right?
00:14:35And then n is 4.
00:14:39And it seems like this is the case.
00:14:42So we generalized that pattern, okay?
00:14:48Now this is our hypothesis.
00:14:50Now let's prove it, okay?
00:14:52Now let's go.
00:14:53We generalized hypothesis, right?
00:14:56Now let's go back to the specific examples
00:14:58and see why this might be the case, okay?
00:15:03And we'll make example when n is 5.
00:15:08We haven't done it quite yet, okay?
00:15:13And also some pattern and why this may be the case,
00:15:16and then, yeah, prove it, you know?
00:15:20Okay?
00:15:22Yeah, sure.
00:15:23Cheers.
00:15:35How interesting, right?
00:15:36Yeah.
00:15:37It's magical, yeah.
00:15:45Mm-hmm.
00:15:50Assume this is true.
00:15:51Then, is this true?
00:15:54Okay?
00:15:55That's what we're trying to prove, okay?
00:15:57Yeah.
00:16:00You want to prove it?
00:16:01Go for it.
00:16:02Okay?
00:16:03Five minutes break.
00:16:06Yeah.
00:16:08Very cool.
00:16:10Okay.
00:16:15Yeah.
00:16:16There we go.
00:16:18Mm-hmm.
00:16:22Very cool.
00:17:04Bye.
00:17:05Bye.
00:17:06Bye.
00:17:07Bye.
00:17:08Bye.
00:17:09Bye.
00:17:10Bye.
00:17:11Bye.
00:17:12Bye.
00:17:13Bye.
00:17:14Bye.
00:17:15Bye.
00:17:16Bye.
00:17:17Bye.
00:17:18Bye.
00:17:19Bye.
00:17:20Bye.
00:17:21Bye.
00:17:22Bye.
00:17:23Bye.
00:17:24Bye.
00:17:25Bye.
00:17:26Bye.
00:17:27Bye.
00:17:28Bye.
00:17:29Bye.
00:17:30Bye.
00:17:31Bye.
00:17:32Bye.
00:17:33Bye.
00:17:34Bye.
00:17:35Bye.
00:17:36Bye.
00:17:37Bye.
00:17:38Bye.
00:17:39Bye.
00:17:40Bye.
00:17:41Bye.
00:17:42Bye.
00:17:43Bye.
00:17:44Bye.
00:17:45Bye.
00:17:46Bye.
00:17:47Bye.
00:17:48Bye.
00:17:49Bye.
00:17:50Bye.
00:17:51Bye.
00:17:52Bye.
00:17:53Bye.
00:17:54Bye.
00:17:55Bye.
00:17:56Bye.
00:17:57Bye.
00:17:58Bye.
00:17:59Bye.
00:18:00Bye.
00:18:01Bye.
00:18:02Bye.
00:18:03Bye.
00:18:04Bye.
00:18:05Bye.
00:18:06Bye.
00:18:07Bye.
00:18:08Bye.
00:18:09Bye.
00:18:10Bye.
00:18:11Bye.
00:18:12Bye.
00:18:13Bye.
00:18:14Bye.
00:18:15Bye.
00:18:16Bye.
00:18:17Bye.
00:18:18Bye.
00:18:19Bye.
00:18:20Bye.
00:18:21Bye.
00:18:22Bye.
00:18:23Bye.
00:18:24Bye.
00:18:25Bye.
00:18:26Bye.
00:18:27Bye.
00:18:28Bye.
00:18:29Bye.
00:18:30Bye.
00:18:31Bye.
00:18:32Bye.
00:18:33Bye.
00:18:34Bye.
00:18:35Bye.
00:18:36Bye.
00:18:37Bye.
00:18:38Bye.
00:18:39Bye.
00:18:40Bye.
00:18:41Bye.
00:18:42Bye.
00:18:43Bye.
00:18:44Bye.
00:18:45Bye.
00:18:46Bye.
00:18:47Bye.
00:18:48Bye.
00:18:49Bye.
00:18:50Bye.
00:18:51Bye.
00:18:52Bye.
00:18:53Bye.
00:18:54Bye.
00:18:55Bye.
00:18:56Bye.
00:18:57Bye.
00:18:58Bye.
00:18:59Bye.
00:19:00Bye.
00:19:01Bye.
00:19:02Bye.
00:19:03Bye.
00:19:04Bye.
00:19:05Bye.
00:19:06Bye.
00:19:07Bye.
00:19:08Bye.
00:19:09Bye.
00:19:10Bye.
00:19:11Bye.
00:19:12Bye.
00:19:13Bye.
00:19:14Bye.
00:19:15Bye.
00:19:16Bye.
00:19:17Bye.
00:19:18Bye.
00:19:19Bye.
00:19:20Bye.
00:19:21Bye.
00:19:22Bye.
00:19:23Bye.
00:19:24Bye.
00:19:25Bye.
00:19:26Bye.
00:19:27Bye.
00:19:28Bye.
00:19:29Bye.
00:19:30Bye.
00:19:31Bye.
00:19:32Bye.
00:19:33Bye.
00:19:34Bye.
00:19:35Bye.
00:19:36Bye.
00:19:37Bye.
00:19:38Bye.
00:19:39Bye.
00:19:40Bye.
00:19:41Bye.
00:19:42Bye.
00:19:43Bye.
00:19:44Bye.
00:19:45Bye.
00:19:46Bye.
00:19:47Bye.
00:19:48Bye.
00:19:49Bye.
00:19:50Bye.
00:19:51Bye.
00:19:52Bye.
00:19:53Bye.
00:19:54Bye.
00:19:55Bye.
00:19:56hour away from here, east of Wasilla. Yeah, well, from this house, yeah. Maybe 45 minutes.
00:20:08But yeah, I mean, it's big event, so like a lot of vendors and families with their children.
00:20:18And yeah, I've been there many times, and it's nice. But like during the peak time,
00:20:25the traffic, like around noon or 2 p.m., just to get to the parking lot, it would take probably
00:20:37one hour or 30 minutes. That's just too many people, okay? So that's why I go there like
00:20:43in the evening. People are leaving, like maybe one hour before it closes, okay? No traffic
00:20:49whatsoever. Also, even parking lot is free, because like one hour left, you know? Okay?
00:20:59Cheers. Because they serve very good food there, yeah. And live music performance, sometimes
00:21:13dance performance, okay? Oh, yeah. Spectacular, yeah. Yeah, I remember like they were doing
00:21:26breakdancing. I think they're maybe like high school students. And I think some of them,
00:21:33so they're on the stage, okay? Fantastic dancers, okay? Mighty proud. And I think some of them
00:21:38recognize me. I was in the audience, just eating food, enjoying their performance,
00:21:43live performance, like breakdancing style. I think some of them recognize me, okay?
00:21:48Because I'm a micro celebrity, like our friends smartly put it, okay? Yeah,
00:21:54very charming term, micro celebrity. I'm a little known. I'm not too famous, but
00:22:04in the world, about 100,000 people know me, about, okay? Yeah, me,
00:22:10performer myself, and like social media stuff, and yeah, so, okay?
00:22:21Okay.
00:22:29Cheers, yeah.
00:22:39Yeah, let's make some examples.
00:22:56But N is five.
00:24:09Okay, so there's a gap here.
00:24:40So, discontinuity, okay? Yeah.
00:24:53Okay.
00:24:59Okay. So, that's A. Now,
00:25:09delimitar.
00:25:18Okay.
00:25:34Eddie Beresix, ceiling.
00:25:49Now,
00:25:57horizontally scribbling line for delimitar, okay?
00:26:04A minus of that.
00:26:18Okay.
00:26:23This one minus this one, okay? Yeah.
00:26:33Which is the same as B, okay? And I don't know why it works. I just noticed.
00:26:53So, that's why we're proving this, okay? It works like magic, and I do not quite understand
00:27:05why this is the case, okay? So, yeah, that's why we're making some examples, okay? It's
00:27:14cool.
00:27:15Okay, yeah. So, let's take five minutes break, and let's try to understand what's going on,
00:27:20because I don't know yet, okay? Yeah.
00:27:25Never seen anything like this before in my life. Possibly, potentially, fourth time in the world.
00:27:33Welcome to Humanology. Yeah, we discover something new in mathematics, like, all the time, right?
00:27:36Okay, five minutes break. Thank you. How cool is that? Yeah, very cool.
00:28:07So,
00:28:26well, let's take five minutes break, okay? Yeah. If you want to prove this, go for it, okay? Yeah.
00:28:31Okay, five minutes. Thank you.
00:28:38Yeah, quite surprising results. Oh, yeah. Okay, five minutes. Thank you.
00:29:00Yes, turn on the heater.
00:29:30Okay.
00:30:00Okay.
00:30:30Okay.
00:31:00Okay.
00:31:30Okay.
00:32:00Okay. Welcome back. We are back. So, what's going on here?
00:32:16Okay, let's do some algebra here, okay? Yeah, it's simple.
00:32:21Kind of informal proof, okay? Yeah, brainstorming.
00:32:32Okay, let's test this one to the other side.
00:32:51So, what we are saying is, if this are both true, then it has to be the case where
00:33:21yeah, all right? If you prove this, then that's top proof, okay? So,
00:33:43so, let's substitute.
00:33:52So,
00:34:08a is this, okay? So, an a over n plus one. So,
00:34:22okay.
00:34:43Now,
00:34:47feeling
00:34:47okay? In general, ceiling function,
00:34:59ceiling function of some x
00:35:05is equal to,
00:35:06well, let's say x over y, okay? Yeah.
00:35:20Yeah.
00:35:35X quotient.
00:35:37Let's say, for example, okay? Before we generalize it, let's make some example, okay?
00:35:45Ceiling of, let's say, 12 over 5
00:35:51is equal to,
00:35:57well, that's three.
00:35:59Is equal to,
00:36:04well, that's three, which is two plus one,
00:36:13which is 12 quotient five, that's two, and plus one, okay? That's
00:36:29two.
00:36:39If the denominator is multiple of five, then we add zero, otherwise we add one, okay? So yeah,
00:36:52we have done this before, okay?
00:36:59So,
00:37:07okay.
00:37:27Something like that.
00:37:30In this case,
00:37:37okay?
00:37:52I think I think it's
00:38:07okay.
00:38:09Okay.
00:38:12Yeah.
00:38:14Okay.
00:38:20So, this is equal to x quotient y plus
00:38:29plus x rho y divided by y ceiling.
00:38:44I mean, it does not quite get rid of the ceiling, okay? So, and it's actually more
00:38:51complicated expression than that, so I'm not sure if this is going to help us here.
00:39:00But it might help us.
00:39:18I don't know.
00:39:24Yes, cheers.
00:39:59Yeah.
00:40:29So,
00:40:46let's say five is great, okay? Yeah, and then we'll use this formula to this,
00:40:52because I'm not sure if it's going to help us or not. I do not know, but I think it was worth a try.
00:41:02Yeah, sure.
00:41:08You want to prove this? Go for it, okay? Yeah, yeah.
00:41:15Five is great, thank you. Yeah, how interesting.
00:41:19Yeah.
00:41:28Very cool. Okay, five minutes, thank you.
00:41:39There we go.
00:41:43Okay.
00:41:49So,
00:42:19you
00:42:49know,
00:43:19you
00:43:49know,
00:44:19you
00:44:49know,
00:45:19you
00:45:49know,
00:46:19you
00:46:27Okay.
00:46:31Well, let's use this formula and let's see what happens. I don't know if it's going to help us or
00:46:36not, but well, worth a try, I think.
00:46:43Okay, so this left-hand side,
00:46:50right-hand side. Let's do easy one first, okay? Right-hand side.
00:47:06Let me take out my laundry, okay, so the dryer. Let me see if it's dry. Okay.
00:47:36So,
00:47:55I think that's dry, so good.
00:47:56Ah, okay, so we have that. Now, left-hand side. Yes.
00:48:16Aye, aye, aye.
00:48:20Aye, aye, aye.
00:48:43Okay.
00:48:43We'll call this R, okay? Yeah. Otherwise, it becomes too complicated, okay?
00:49:14So,
00:49:26yes.
00:49:43Aye, aye, aye.
00:50:07Now,
00:50:13aye, aye, aye.
00:50:19Aye, aye, aye.
00:50:25Aye, aye, aye.
00:50:31Aye, aye, aye.
00:50:37Aye, aye, aye.
00:50:41Aye, aye, aye.
00:50:47Aye, aye, aye.
00:50:53Aye, aye, aye.
00:50:59Aye, aye, aye.
00:51:05Aye, aye, aye.
00:51:09Wow, this is a lot.
00:51:14I did not expect it would be this difficult, okay.
00:51:36And I think this is same as
00:51:39I don't think this is helping, okay, it's making things more complicated than necessary, okay, so
00:51:57but it's worthwhile to check. Okay, now let's get back to this example. It's interesting and
00:52:09let's try to understand what's going on.
00:52:21Time check real quick.
00:52:32Time check.
00:52:39It's been less than one hour, okay, okay.
00:53:09Okay.
00:54:39We'll get there, okay, maybe not tonight.
00:55:09Time check.
00:55:33Okay, there's some jumping going on here.
00:55:39Just like there, okay. All right.
00:55:55Time check real quick.
00:56:03It's been less than one hour, okay, okay.
00:56:09B is just, you know, integers.
00:56:29And we divide by five, then ceiling.
00:56:39And
00:56:55we add two numbers.
00:57:09And then we divide by six and then ceiling.
00:57:39I don't know, okay.
00:57:55Let's take five minutes break, okay. You know, I
00:58:02I think I'm a decent, competent mathematician, okay. I've been doing mathematics for a very long time.
00:58:12But this, I do not understand what's going on, okay. It's number theory, right?
00:58:22Number theory, it looks easy, but it can be quite difficult, okay, yeah.
00:58:32So what works in mathematics? Yeah, take your break from mathematics, okay, yeah.
00:58:40Then, with fresh energy, yeah, we can get back to it, okay, but, yeah.
00:58:48Let's take five minutes break, okay.
00:58:50Wow.
00:58:52Oof.
00:58:58Five minutes, okay, thank you, yeah.
00:59:00Wow.
00:59:06Wow.
00:59:08It's surprisingly difficult.
00:59:14Yeah.
00:59:16Unexpectedly.
00:59:18Okay, five minutes, thank you.
00:59:20Okay.
00:59:28Okay.
00:59:50Okay.
00:59:52Okay.
00:59:54Okay.
00:59:56Okay.
00:59:58Okay.
01:00:00Okay.
01:00:02Okay.
01:00:04Okay.
01:00:06Okay.
01:00:08Okay.
01:00:10Okay.
01:00:12Okay.
01:00:14Okay.
01:00:16Okay.
01:00:18Okay.
01:00:20Okay.
01:00:22Okay.
01:00:24Okay.
01:00:26Okay.
01:00:28Okay.
01:00:30Okay.
01:00:32Okay.
01:00:34Okay.
01:00:36Okay.
01:00:38Okay.
01:00:40Okay.
01:00:42Okay.
01:00:44Okay.
01:00:46Okay.
01:00:48Okay.
01:00:50Okay.
01:00:52Okay.
01:00:54Okay.
01:00:56Okay.
01:00:58Okay.
01:01:00Okay.
01:01:02Okay.
01:01:04Okay.
01:01:06Okay.
01:01:08Okay.
01:01:10Okay.
01:01:12Okay.
01:01:14Okay.
01:01:16Okay.
01:01:18Okay.
01:01:20Okay.
01:01:22Okay.
01:01:24Okay.
01:01:26Okay.
01:01:28Okay.
01:01:30Okay.
01:01:32Okay.
01:01:34Okay.
01:01:36Okay.
01:01:38Okay.
01:01:40Okay.
01:01:42Okay.
01:01:44Okay.
01:01:47Okay.
01:01:49Okay.
01:01:51Okay.
01:01:53Okay.
01:01:55Okay.
01:01:57Okay.
01:01:59Okay.
01:02:01Okay.
01:02:03So it's been one hour.
01:02:05So let's wrap up for this episode.
01:02:08Sure, great. See you soon. Thank you. Yep. I got to think about this. Okay. Yeah