carpentry and number theory
Category
🦄
CreativityTranscript
00:00:00Hello friends! Welcome to Fred and I Love Dunkley episode 205.3. Happy Sunday morning.
00:00:12Yeah, it's like 10.30 a.m. Yeah, I did some carpentry. Passed 2 hours.
00:00:23So, what I worked on is this, okay? Yeah, the top part of the pole, yeah, some gap filled in with the bolt and washer to fix it, to make it stable.
00:00:38That part done, yeah, drilling the hole and then bolts and nuts and washers. I'll show the photos later, okay?
00:00:45And then, at the bottom of the pole, the pole height is about 11 feet. Me, I'm about 5 feet, 10 inches. I'm less than 6 feet, okay?
00:00:58So, yeah, the pole is almost like twice as high as I am. Okay. It's tall, okay?
00:01:05Oh, yeah, I'll show the photos and that. So, after all this, okay, there's four metallic pipes and then two wooden sticks, wooden panels, okay?
00:01:16So, six parts, okay? And multiple parts, yeah, bolts and nuts drilled into the hole, right? Yeah, to conjoin them.
00:01:28After that, all the bolts and nuts are fastened. The very bottom part of that hole, it was uneven.
00:01:40I have to use this circular saw, make the cut to make it even. After that, with the grinding attachment to the drill, yeah, grinding.
00:01:53Yeah, that is like grinding stone, okay? To make it even, okay? Yeah, so it's done. It took me like two hours.
00:02:02I'll show the photos, okay? For now, let's do stretching. Okay? Yeah, cheers.
00:02:11Carpentry is fun, yeah. Very healthy hobby. Carpentry. Cheers.
00:02:18Okay. Oh, yeah.
00:02:23Oh, yeah.
00:02:25Uh.
00:02:27Uh.
00:02:37It's a good perfume, yeah.
00:02:39Okay.
00:02:43Okay.
00:02:46Okay.
00:02:47Okay.
00:02:48A minute.
00:02:53Okay.
00:02:58Okay,
00:02:59okay.
00:03:00Okay.
00:03:03You, you, you.
00:03:09Okay.
00:03:11Okay.
00:03:12Okay.
00:03:13� третьLab, вкусanism.
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00:04:15Okay, stretching.
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00:04:29You
00:04:48So circular so is you have to be very careful with that, okay
00:04:53So where are you so close or?
00:04:55To cut parts of that wood or metallic pipe for safety gear
00:05:02Goggles, eye goggles, gloves, earmugs, mask
00:05:12Okay, yeah
00:05:16Yeah, practice safety, okay
00:05:18Very important
00:05:24Very important
00:05:25Okay
00:05:26Okay
00:05:28Okay
00:05:32Okay
00:05:34Okay
00:05:38Okay
00:05:40Okay
00:05:48Okay
00:05:58Music
00:05:59Ah
00:08:27Now let's do martial arts, okay?
00:08:53Elbow.
00:08:55Jumping elbow.
00:09:00Five minutes.
00:09:16All right.
00:09:22Booyah.
00:09:24Oh.
00:09:26Okay.
00:09:30Whew.
00:09:32Thanks.
00:09:34Thanks.
00:09:36Yeah.
00:09:38Okay.
00:09:40Okay.
00:15:13Yeah, welcome to Friday Night Live Tonkily episode.
00:15:20Like 2 of 3.3, I guess.
00:15:24Oh, 2 of 5.3.
00:15:26Okay, okay.
00:15:27Yeah, let me show you some photos of the carpentry project.
00:15:31Yeah, let me show you some photos of the carpentry project.
00:15:35Yeah, still working on the pillar, central pillar.
00:15:37Yeah, after grinding with the grinding attachment to the drill.
00:15:54Before that, kind of rough on the edges, I did not use that one, I did not use that one.
00:16:04That one is just too weak.
00:16:06The one I used was most stone-based, cylinder, cylindrical stone-based too.
00:16:13Okay, okay, okay, okay, okay, okay, okay.
00:16:43So, okay, okay, okay, okay, okay.
00:16:55Well, okay.
00:16:57Okay, okay, okay, yeah.
00:16:57from the underness, inside, okay?
00:17:07Oratorial gesture.
00:17:20Yes, the joints.
00:17:27Washo as Getfellers.
00:17:33That's about there, okay?
00:17:34Yeah, nice.
00:17:37Okay.
00:17:57Okay.
00:18:28Let me start cooking my lunch by boiling the water and vegetables.
00:22:12Okay, so my lunch, some leftover bean soup and onions and four hot dog sausages, microwave,
00:22:28what about plastic jarred, okay?
00:22:30Yeah, nice.
00:26:33Okay.
00:26:41Okay.
00:26:42Okay.
00:27:13Okay.
00:27:14Okay.
00:27:15Yeah.
00:27:17Yeah.
00:27:18Yeah.
00:27:19Yeah.
00:27:20Yeah.
00:27:21After that, to fix that, to fix that, or fixate the central pole to the floor of the shed.
00:27:36Yeah.
00:27:37Yeah.
00:27:39Okay.
00:27:40The flooring of the shred is partially broken, so I kind of felt with my fingers some 2x4 wooden beams, perpendicular to the fascia.
00:27:54Good, that would be the attachment point.
00:28:00But yeah, the 2x4 wooden beam, that's actually, it's not 2 inch by 4 inches, it's like 1.5 inch by 3.5 inches.
00:28:14Bucharest? Yeah, let's play some guitar.
00:28:22Are you okay?
00:28:32Cheers.
00:28:52I forgot the fingering of G chord.
00:29:14Okay, good.
00:29:28Oouya.
00:29:33Mathematics, sure.
00:29:42So, yeah, the coprimes, I remember, about maybe 3 months ago, we did prove something.
00:29:57I mean, it's already proven in the internet, but we can't prove it on our own.
00:30:03Like, it's related to this.
00:30:07I mean, these are examples, okay, so of more.
00:30:11The coprime audition theorem, just like, if a and b are coprimes, that means a and a plus b are coprimes.
00:30:36Also, b and a plus b are coprimes as well.
00:30:43We proved this long time ago, maybe 3 months ago.
00:30:49And it's somewhere in some way for somewhere in this house, but I, it will take too much time to look for it.
00:30:59Okay.
00:31:00Okay.
00:31:01And.
00:31:02Yeah.
00:31:03I'm clipping my finger now.
00:31:06Okay.
00:31:07Okay.
00:31:08But let me try to look for that whiteboard.
00:31:13Oh.
00:31:14Oh.
00:31:15Oh, right here.
00:31:16Okay.
00:31:17Yeah.
00:31:18That was easy.
00:31:20Yeah.
00:31:21Yeah.
00:31:22Yeah.
00:31:23Yeah.
00:31:24Yeah.
00:31:25Yeah.
00:31:26Yeah.
00:31:27This whiteboard frame comes falling apart.
00:31:29Okay.
00:31:30Okay.
00:31:31Yeah.
00:31:32Yeah.
00:31:33Yeah.
00:31:34Yeah.
00:31:35Yeah.
00:31:36Yeah.
00:31:37Yeah.
00:31:38Yeah.
00:31:39Yeah.
00:31:40Yeah.
00:31:41Yeah.
00:31:42Yeah.
00:31:43Yeah.
00:31:44Yeah.
00:31:45Yeah.
00:31:46Yeah.
00:31:47This whiteboard frame comes falling apart.
00:31:49Okay.
00:31:50Okay.
00:31:51Okay.
00:31:52Okay.
00:31:53Yeah.
00:31:54Yeah.
00:31:55Yeah.
00:31:56That was easy.
00:31:57Yeah.
00:31:58This is it.
00:31:59If A and B are co-primes, then A and A plus B, and also B and B are co-primes.
00:32:16Okay.
00:32:17Proof.
00:32:18Proof.
00:32:19Proof by contradiction.
00:32:20Let's say A and A plus B, let's say they are not co-primes.
00:32:23That means they have common factors, which is not larger than 1.
00:32:29Okay.
00:32:30Okay.
00:32:31And then if this is false, then this is false.
00:32:34Contra-positive.
00:32:35We are proving contra-positive.
00:32:36That's like forced order logic.
00:32:37Okay.
00:32:38Yeah.
00:32:39That's what proof by contradiction is about.
00:32:40Okay.
00:32:41Yeah.
00:32:42Okay.
00:32:43Yeah.
00:32:44Yeah.
00:32:45Okay.
00:32:46Yeah.
00:32:47Yeah.
00:32:48Okay.
00:32:49Okay.
00:32:50Okay.
00:32:51Okay.
00:32:52Okay.
00:32:53Okay.
00:32:54Okay.
00:32:55Okay.
00:32:56Okay.
00:32:57Okay.
00:32:58Okay.
00:32:59Okay.
00:33:00Okay.
00:33:05Okay.
00:33:26Okay.
00:33:28yeah we did like proof by case but even and even even and odd but even it cannot be even
00:33:41and even right but even and even that means that they're not co-primes okay so
00:33:53yeah odd even and odd we kind of did that
00:34:14but maybe there's easier proof than this okay
00:34:19uh
00:34:23but let me check on my lunch okay okay
00:34:27you
00:34:53you
00:34:59you
00:35:05you
00:35:10you
00:35:16you
00:35:22you
00:35:27you
00:35:33you
00:35:34you
00:35:35you
00:35:41you
00:35:42you
00:35:43you
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00:35:47you
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00:35:56you
00:35:58you
00:35:59you
00:36:00you
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00:36:08you
00:36:22you
00:36:24you
00:36:26you
00:36:28you
00:36:29you
00:36:30you
00:36:31you
00:36:32you
00:36:54you
00:36:55you
00:36:56you
00:36:57you
00:36:58you
00:36:59you
00:37:02you
00:37:04you
00:37:20you
00:37:22you
00:37:24you
00:37:28you
00:37:30you
00:37:46you
00:37:48you
00:37:50you
00:38:04you
00:38:08you
00:38:10you
00:38:12you
00:38:12you
00:38:13you
00:38:14you
00:38:15you
00:38:38you
00:38:39you
00:38:40you
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00:39:06you
00:39:08you
00:39:26you
00:39:27you
00:39:28you
00:39:30you
00:39:32you
00:39:34yeah so proof by contradiction okay so these are common divisor and of a and a plus b
00:39:56you
00:40:04you
00:40:05you
00:40:07you
00:40:09you
00:40:11you
00:40:13you
00:40:15you
00:40:17you
00:40:18okay they are using like euclidean algorithm okay okay okay
00:40:22okay
00:40:24okay
00:40:27nice and that's a lot easier proof yeah
00:40:30good
00:40:32good
00:40:34okay so what website today cited
00:40:50okay so what website today cited
00:41:00okay
00:41:00okay
00:41:01mm-hmm
00:41:02yeah
00:41:07mm-hmm
00:41:08yeah
00:41:11yeah
00:41:11yeah
00:41:11yeah
00:41:12yeah
00:41:12yeah
00:41:13sure
00:41:13sure
00:41:13yeah
00:41:13they can't controversial website but yeah let's check them out
00:41:17This is not exactly what I was looking for, but...
00:41:47Okay.
00:42:12Okay.
00:42:17Let's look at this one.
00:42:33Let's get back to the basics, okay?
00:42:40Sure.
00:42:42Let's get back, okay?
00:42:45Let's get back to the basics.
00:42:55Number theory.
00:43:02Bickety whiteboards.
00:43:10The theorem that they use, lemma, whatever, and we'll prove it separately.
00:43:25If D divides X and D divides Y,
00:43:40then D divides X and D divides Y.
00:43:53Then D divides X minus Y.
00:44:00Okay.
00:44:06I'm assuming D...
00:44:13No, we don't have to assume D is more than one.
00:44:21But for our purposes, let's assume D is an integer more than one.
00:44:38Let's come up with a new notation convention, okay?
00:44:53It's an integer which is more than one, okay?
00:45:00Okay?
00:45:01Yeah.
00:45:02Nice.
00:45:03Yeah.
00:45:04Brand new notation convention, okay?
00:45:05It's an integer which is more than one, okay?
00:45:10Really?
00:45:11Yeah.
00:45:12Nice.
00:45:13Yeah.
00:45:14Brand new notation convention, okay?
00:45:15Yeah.
00:45:16Yeah.
00:45:17This is an integer which is more than one, larger than one, okay?
00:45:20Sure.
00:45:21Nice.
00:45:22At least we came up with a brand new notation convention there, okay?
00:45:25Okay.
00:45:26Okay.
00:45:27Yeah.
00:45:28Five minutes break, please.
00:45:30Okay.
00:45:31Okay.
00:45:32Okay.
00:45:33Yeah.
00:45:34Five minutes break, please.
00:45:36Okay.
00:45:37Okay.
00:45:38Okay.
00:45:39Okay.
00:45:40Okay.
00:45:41Okay.
00:45:42Okay.
00:45:43Okay.
00:45:45Nice.
00:45:51Yeah.
00:45:55Nice.
00:45:56Yeah.
00:45:57Yeah.
00:45:58Yeah.
00:46:00Yeah.
00:46:01Okay, all right.
00:46:02Yeah.
00:46:03Yeah.
00:46:04Yeah.
00:46:06Yeah.
00:46:07Yeah.
00:46:08Yeah, yeah, yeah, yeah.
00:48:50Okay.
00:48:52Fun mathematics, fun carpentry, good hobbies, very healthy, constructive hobbies.
00:49:02Yeah.
00:49:03Yeah.
00:49:04Okay.
00:49:05Okay.
00:49:07Yeah, me being streamer is like pro bono educational, free educational services.
00:49:25Very constructive, positive, healthy, educational.
00:49:32Healthy, good.
00:49:39Okay.
00:49:41Good.
00:49:42Transport complete.
00:49:44Good.
00:49:45Okay.
00:49:49Okay.
00:49:51Okay.
00:49:53Okay.
00:49:54Okay.
00:49:55You
00:50:25You
00:50:36You're stepping back into the basic back to the basics proofs because we may need the similar
00:50:44proof techniques
00:50:46Later on okay, so yeah
00:50:52Let's prove this okay, yeah
00:50:55uh d divides x
00:51:00Well
00:51:03Actually
00:51:06D x y they will positive integers larger than one okay
00:51:17X y t okay, so
00:51:22D x is equal to
00:51:25Well, I find that as well, okay
00:51:33Alpha times D
00:51:39Y is equal to
00:51:41beta times D
00:51:43x minus y is equal to y, okay, and then I, of course alpha is better, more than beta, okay, so
00:51:52x minus y is equal to y, okay, and then I, of course alpha is better, more than beta, okay, so
00:51:57Is it equal to, yeah, D times alpha minus beta okay, which means, yeah, D divides x minus y, it's a factor, okay, good
00:52:09So
00:52:10x is equal to x is more than y, okay, okay, and then, okay, and then I, of course alpha is better, okay, so
00:52:14x is more than y, okay, okay, and then I, of course alpha is better, more than beta, okay, so
00:52:15which means D divides x minus y is a factor, okay?
00:52:22Good.
00:52:24Now, given that, here are some assumptions, okay?
00:52:38We say a and b is positive integers larger than 1, okay?
00:52:52Good.
00:52:54Integers larger than 1, okay?
00:52:56So this is positive, okay?
00:53:02Now let's prove this, okay?
00:53:04Yeah.
00:53:06Q, let's do like a cursive style.
00:53:13Q, E, D?
00:53:20I don't know.
00:53:24Maybe it's like this.
00:53:30Q, E, D.
00:53:33There we go.
00:53:36Q, E, D.
00:53:38Now this.
00:53:39Q, E, D.
00:53:43Q, E, D.
00:53:45Q, E, D.
00:53:56Q, E, D.
00:53:58Q, E, D.
00:53:59Uh, proof by contradiction, OK?
00:54:18Assume they are not co-primes, OK?
00:54:25That means they are common divisor, OK?
00:54:28So, well, d, alpha, beta.
00:54:43They will, integers are larger than one, OK?
00:54:46So, OK.
00:54:49If this is false, if they are not co-primes,
00:54:52then it means that this and these are common divisors, OK?
00:54:55Yeah, so.
00:54:58A is d alpha.
00:55:08A plus b is d beta.
00:55:13OK?
00:55:24Now, subtract.
00:55:26And of course, alpha is, beta is more than alpha, OK?
00:55:36Yeah.
00:55:37Subtract.
00:55:49OK.
00:55:51And it's actually not that easy, OK?
00:56:04So, beta minus alpha, can it be 1?
00:56:14Yeah, it's actually not that easy, OK?
00:56:17So, beta minus alpha, can it be 1?
00:56:22Can it be 1?
00:56:34But whatever the case.
00:56:36It doesn't matter, OK?
00:56:48It doesn't matter, OK?
00:56:49Beta minus alpha, it can be 1, or it can be more than 1, OK?
00:56:52So, now, we have a contradiction here.
00:57:02Let's say beta minus alpha.
00:57:06How about this?
00:57:10If you want to, complete this proof, OK?
00:57:17Vocal rest necessary.
00:57:19OK.
00:57:205 minutes break.
00:57:21Time check.
00:57:22It's been less than 1 hour, OK?
00:57:23Yeah, we have plenty of time.
00:57:24OK?
00:57:25Yeah.
00:57:265 minutes break.
00:57:27If you want to complete this proof, go for it, OK?
00:57:29Vocal rest.
00:57:30Vocal rest.
00:57:31Yeah, 5 minutes, thank you.
00:57:32OK.
00:57:33Yeah, 5 minutes, thank you.
00:57:35It's been less than 1 hour, OK?
00:57:36Yeah, we have plenty of time.
00:57:37OK?
00:57:38Yeah.
00:57:395 minutes break.
00:57:40If you want to complete this proof, go for it, OK?
00:57:42Vocal rest.
00:57:43OK?
00:57:44Yeah, 5 minutes, thank you.
00:57:46Yeah, 5 minutes, thank you.
00:57:59OK.
00:58:01OK, let's get some ventilation.
00:58:11OK.
00:58:12OK.
00:58:13OK.
00:58:14Let's get some ventilation.
00:58:15OK.
00:58:16OK.
00:58:17OK.
00:58:18OK.
00:58:19OK.
00:58:20OK.
00:58:22OK.
00:58:24OK.
00:58:25OK.
00:58:26OK.
00:58:29OK.
00:58:30OK.
00:58:32Hey.
00:58:34Hey.
00:58:34OK.
00:58:35OK.
00:58:35Hey.
00:58:55OK.
00:58:56OK.
01:01:26diet and
01:01:28study, work, rest.
01:01:33Let's take a breath from mathematics a little bit.
01:01:36Saturday training, I looked it up in the internet like Wikipedia. Originally during World War II,
01:01:43British
01:01:44Air Force. Okay, yeah the pilots
01:01:48and later on adopted by other countries
01:01:52for pilots. Okay, yeah.
01:01:54Parachute whose
01:01:57airplane got shot during World War II. Yeah, behind the enemy line and so some ejection parachute now they need to survive
01:02:05to cross the enemy line
01:02:08to come to friendly territory. Okay, so
01:02:11it's like wilderness
01:02:14survival like how to procure food, water,
01:02:18shelter. Yeah, it's part of the training. Okay, very interesting.
01:02:24Okay, good. Cheers.
01:02:34Okay, now
01:02:38we have
01:02:40now D is a factor of A, D is also a factor of B.
01:02:44But
01:02:45So if this is false, then this is false because A and B have common factor of D.
01:02:52So they are not co-primes anymore. Okay, so if this is not co-primes, then this is not co-primes either.
01:02:58QED, okay, yeah.
01:03:00So basically we are saying therefore A and B, they are not co-primes. Okay, so contradiction.
01:03:17Q-E-D. Okay, good.
01:03:25Okay, good.
01:03:28That's bad. Nice.
01:03:30Good mathematics there. Yeah, we can reprove this.
01:03:39Got some help from internet. Yeah, AI, sure.
01:03:46Now let's
01:03:48put this behind us, okay? Let's just talk.
01:03:50Yeah.
01:04:00That's some room.
01:04:04Okay.
01:04:07Okay.
01:04:08Okay.
01:04:09Okay.
01:04:11Okay.
01:04:13Okay.
01:04:15Okay.
01:04:16Okay.
01:04:17Okay.
01:04:18Okay.
01:04:19Yeah, I'm hungry. My lunch is ready. So we'll keep it brief. Okay? Yeah.
01:04:25Let's talk.
01:04:34Yeah.
01:04:34My lunch is ready. I'm hungry. So we keep it brief. Okay. Cheers.
01:04:50Yeah. So last night I watched, after the show, I watched Twilight Zone episodes, season four. Interesting. Yeah.
01:04:55Yeah. And I can see the influence on other TV shows like X-Files. Okay. Yeah. There's one episode last night. Yeah. It's about like...
01:05:10Also, it influenced other Hollywood movies like Terminator. Okay. So one episode after his image. It's basically robotics. Okay. So yeah.
01:05:25This being, though, he's a human being, but he got some injury and looked at his arm is like robotic, like wires and small light bulbs and stuff. Okay.
01:05:39Electronics. Then he realized that he realized he's not a human being, he's a robot. Okay. And that kind of inspired the Terminator movie. Okay.
01:05:58James Cameron. Okay. And next episode, it's like the 30-fathom grave is about World War II sunken Navy, U.S. Navy submarine discovered 20 years later, but still like metallic.
01:06:28Clank and sound like... Okay. Okay. Yeah. That's commission. That inspired one episode in X-Files. Okay. Yeah. I can see those influences. Okay.
01:06:41Yeah.
01:06:45They kind of expanded on what they did in Blood Zone. Okay. So, okay.
01:06:52Developing more fully. Okay. Yeah.
01:06:55Progenix. Okay. Nice.
01:06:58So, as a humanologist, okay, we have many branding ideas.
01:07:28Okay. So, yeah. I mean, it's possible that we get to live forever in the future. Okay.
01:07:34Yeah. There's possibility. Forever young. Sure.
01:07:38So, medical breakthrough. Yeah. That's possible.
01:07:41And me? Yeah. I'm a survivalist. Yeah. Exercise, diet, stretching, healthy hobbies. Okay. Yeah.
01:07:53Yeah. I want to live forever young, of course. Yeah.
01:07:55And it's possible. Okay. Who knows? Yeah.
01:08:02At least I want to live more than 100 years. Okay. Yeah. So, continue to develop all the theories. Okay. Yeah.
01:08:10And, yeah. In humanology, we inspire people. We get inspired by other people. Like you. Thank you.
01:08:22If we inspire each other, we teach each other, learn from each other. Okay. So, yeah.
01:08:25We develop each other's ideas. Okay. Sure. Yeah.
01:08:30Knowledge share and place. Humanology. Okay. Yeah. Welcome to human knowledge school. Okay. Yeah.
01:08:35That's what I have to say. Okay. Yeah. Yeah.
01:08:38Yeah. And in humanology, yeah, longevity is a great virtue. Okay. So,
01:08:44like, in the future, when I'm 100 years old, it'll be interesting to see
01:08:50how healthy I am, how mobile I am. Yeah. Exercise and stretching, you know,
01:09:00large arts, dancing. Yeah. Healthy diet. Okay. Yeah.
01:09:06Yeah. Yeah. Mostly lean food. Okay. Yeah.
01:09:18Yeah. Oh, yeah.
01:09:24Mm-hmm.
01:09:33Mm-hmm.
01:09:36Mm-hmm.
01:09:38Okay.
01:09:41So, I continue to watch those. I'm going to watch every single episode in season four
01:09:46because season four, yeah, it's an exceptional season because each episode is one hour long,
01:09:52longer than other seasons. Okay. So, more in-depth. Yeah. Sometimes I'm kind of slow.
01:10:00Boring sometimes, but that's fine. It's nice and slow. Very friendly. No violence. Okay.
01:10:06Yeah. Yeah. Torazone. Yeah. I like it. Okay. All right. See you tonight. Okay. Thank you.
01:10:15Fantastic.
01:10:17Yeah.
01:10:18Yeah.