humanology 2071.1 .

  • 2 months ago
Transcript
00:00:00Hello friends, welcome to HumanRG 2071.
00:00:15Alright, alright, okay.
00:00:18Okay, let's do some dumbbells to strengthen.
00:00:24Forearm, bicep, shoulder.
00:00:28Okay.
00:00:35Let me tighten.
00:00:40Screws here.
00:00:42Okay, let's go.
00:00:57Okay, I think that's good because I'm still recovering from my right shoulder injury.
00:01:11Gradually, slowly build up.
00:01:14Okay.
00:01:16Now.
00:01:21Let's do some swing kicks.
00:01:28Okay.
00:01:32Okay, good.
00:01:34Five minutes break please, thank you.
00:01:37Good exercise there, nice.
00:01:41Happy Thursday.
00:01:48Okay, five minutes, thank you.
00:01:57Thank you.
00:02:27Thank you.
00:02:57Thank you.
00:03:27Thank you.
00:03:57Thank you.
00:04:27Okay.
00:04:57Thank you.
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00:05:57Thank you.
00:06:00Thank you.
00:06:07Oh.
00:06:10Yeah, I'm done running low on fat carbs, so let me have a go.
00:06:27you
00:06:57You
00:07:08Okay
00:07:15Oh
00:07:17You
00:07:24Let's get back to mathematics, okay. Yeah, let's exercise some diligence and then
00:07:31We'll
00:07:34Yeah
00:07:40Yeah, we verify this
00:07:42Ah
00:08:00It's kind of tedious that's why I don't feel like doing it but
00:08:07It's something I have to do
00:08:12Let me get some vodka here
00:08:24You
00:08:42You
00:08:52So, by the way
00:08:54I will if we find finalize this algorithm. Okay, our algorithm will be
00:09:00slightly more efficient than
00:09:03Utilitarian algorithm. Okay. So yeah that showed us grace and save this project
00:09:13The Euclidean algorithm it will be it's complexity is
00:09:18To find greatest common divisor
00:09:21It will be
00:09:26N is the input number. Okay. Yeah the two inputs right? Yes a bigger bigger one. Okay, so and
00:09:33Number of digits or that number. Yeah, look tap look and base 10. Okay. Yeah, so and
00:09:40And in Euclidean algorithm they do subtraction
00:09:45Okay, n times
00:09:49Log n times, okay
00:09:52This complexity will be
00:10:00Okay, because in each step yeah subtraction that's log n algorithm, okay, yeah and this is bigger than
00:10:08Once we find this
00:10:13Algorithm our formula there is some divisions and division is
00:10:21When n is the that was the confusion when n is the number of digits then n log n, okay, that's
00:10:28Division algorithm complexity. Okay, so so you will be but here n is our input number. Okay, so it will be
00:10:35Log n times
00:10:55Log of log n, okay
00:10:57You
00:11:04And log n is smaller than n
00:11:12That's why our
00:11:14Future I suppose the algorithm that we are looking for. Okay, if we find it, yeah, you'll be more efficient than
00:11:22Euclidean algorithm
00:11:23Slightly. Okay. Yeah
00:11:26But still okay
00:11:30Okay now I
00:11:33In the morning, yeah, I woke up and on my bed. I did some
00:11:37Some of this. Okay that share that with you
00:11:40When the time comes, okay
00:11:46Cheers, yeah, happy Thursday. Yeah
00:11:51Mm-hmm
00:11:54Lived a little bit
00:11:56You
00:11:58You
00:12:21What
00:12:24Okay
00:12:25Now I have to wash my hands
00:12:28No problem, let me watch this club as well
00:12:58You
00:13:06Okay, now let me have some dragon drinks
00:13:11Cheers
00:13:13I'll name them for
00:13:16Our sconces in Bosco
00:13:25You
00:13:28You
00:13:31Cheers happy Thursday
00:13:36Mm-hmm
00:13:42Okay, do you need this
00:13:50We don't we can't do okay, so
00:13:56Now
00:13:58You
00:14:04L1
00:14:14It's rather long formula
00:14:22Well, what am I doing
00:14:26L1 okay
00:14:28You
00:14:30L1
00:14:33This whole thing becomes 0
00:14:36So 1 plus
00:14:42This is 0 this is 0
00:14:46So this whole thing becomes 0
00:14:50So just error is minus 1, okay
00:14:55R1
00:14:59That's 1 this is 0 1
00:15:05Okay
00:15:07Then
00:15:10Gamma
00:15:125 plus 1 that's 6
00:15:176 and 5
00:15:21Create a common design in 6 and 5 1 right now does this formula work
00:15:29You
00:15:32Okay, you have 6 here
00:15:352 minus 6
00:15:38R
00:15:401
00:15:41plus 5
00:15:44Minus 1 so it did not work. Okay. I think this fix this problem
00:15:53Somewhere
00:15:56You okay, so let me look for bracket formula for base 5, okay
00:16:16Yeah
00:16:26You
00:16:39What
00:16:55Yeah
00:17:22Yeah
00:17:25You
00:17:55You
00:18:20Ah, maybe we never fix this I don't know
00:18:25But if you did not fix this we fix it because we made a similar error before right so
00:18:38There's so many whiteboards the shop of the shop all
00:18:49Yeah
00:18:55You
00:19:25You
00:19:55You
00:20:16Okay, you know what let's just redo this, okay
00:20:22Yeah
00:20:24Yeah, I could have whiteboard and we just redo this, okay, yeah and because
00:20:32just looking for like previous whiteboards and
00:20:35not necessary because
00:20:37We know how to do this quite efficiently these days. Okay. Yeah
00:20:45Okay, yeah, let's take final spread, okay, thank you
00:20:52Okay, okay
00:20:58Mm-hmm five minutes, thank you
00:21:22You
00:21:52You
00:22:22You
00:22:52You
00:23:00You
00:23:08You
00:23:22You
00:23:52You
00:24:22You
00:24:37You
00:24:53You
00:25:08Okay
00:25:10You
00:25:20Well, let's not reinvent the wheel let's look at the what we did and Jackson memory there
00:25:29Okay
00:25:33Step by step, okay, we start with visual
00:25:37expression
00:25:39the linear combination for
00:25:41great common divisor
00:25:44Okay
00:25:46Yeah
00:25:49Cheers
00:25:53Yeah, my hands were kind of shaky because I
00:25:56Felt kind of weak on my arm muscle. Yeah, that's why it was time to do some arm exercise and now it's no longer shaky
00:26:04Okay, good
00:26:07Problem solved. Okay, what we have here is
00:26:15Visual expression, the linear combination of two inputs to express a great common divisor, okay. Yeah
00:26:27Excluding
00:26:28multiples of five
00:26:30Multiple of five and five great common divisor five
00:26:34We combine them if we can integrate that and make one formula, but for now
00:26:40all the greatest common divisor between five and
00:26:44No multiple of five it should be one
00:26:48Okay, so add up to one. So
00:26:51we have
00:26:53minus one three minus three two minus two blah blah blah, right and
00:26:58And
00:26:59We are ignoring the signs
00:27:02Okay
00:27:04So we extract and we ignore the
00:27:08Repetition, okay, we extract just one three two five three seven blah blah blah. Okay. Yeah
00:27:19And
00:27:21But the way we did it here is kind of inefficient, okay because we come up with better method, okay
00:27:27So let's go ahead and grab a new iPod. Okay, and kind of redo this a little bit. Okay
00:27:34Because
00:27:36We know a lot better now, a lot more now, okay. Yeah, maybe we come up with a better
00:27:42more simplified formula
00:27:44possibly
00:27:57You
00:28:20You
00:28:27Okay, let's use this one
00:28:31Okay
00:28:33Wow
00:28:36All right, oh
00:28:41Then we got some water
00:28:57You
00:29:04Oh
00:29:07Okay, let's erase this
00:29:18You
00:29:27You
00:29:33Yeah, yesterday
00:29:35A lot of our friends joined us in the Instagram live. Yeah, the future leaders that might trust. Where's my people?
00:29:41Mm-hmm. It was very nice
00:29:46Yeah, so
00:29:54You
00:29:57You
00:30:17One three two five three seven
00:30:23You
00:30:25Four nine five eleven, okay
00:30:31So, yeah skipping method
00:30:38Right
00:30:41We did this before so that's why we can do it replicated easily, okay, so
00:30:53You
00:30:57Okay, let's say this is a an a.m. this pain is running out, okay
00:31:05You
00:31:20Oh, this one's good nice, okay
00:31:25You
00:31:3311 so n
00:31:48But
00:31:50To remind us actually this is not M. Okay, so let's call it M instead
00:31:57Because otherwise we'll be confused. Okay, there's probably a source of error. Yeah, the obvious of notation, right?
00:32:03Yeah, there's Wikipedia article about it. Okay, so we have to be very careful. Okay. Yeah, sirs
00:32:12If that they're different indices then we should assign different letters, okay
00:32:16Yes
00:32:20Okay
00:32:44Let's extract this
00:32:46You
00:32:56Okay
00:33:01So
00:33:05Let's say this is K
00:33:09Okay
00:33:11M is equal to
00:33:142k minus 1
00:33:18K is equal to
00:33:22M plus 1 divided by 2, okay
00:33:29When
00:33:31You
00:33:40When M is odd number, okay. Yeah Cheers
00:33:53Better okay
00:33:58Now
00:34:02You let's extract the other one
00:34:15You
00:34:31We call this
00:34:42Take it we call this L. Okay
00:34:49And the corresponding index M
00:35:01You
00:35:07When
00:35:12M is even okay. Yeah Cheers
00:35:25Hmm
00:35:27You
00:35:30This is an index transformation, okay. Yeah. Now what's the relation between the two? Yeah, is it?
00:35:44Why not
00:35:50Okay
00:35:54Yeah
00:35:57You
00:36:04To combine this
00:36:07Okay
00:36:11If you want to go for it, we'll take five minutes, okay
00:36:17A.m. Is equal to
00:36:28Oh some functional way, okay. Yeah, if you want to okay. Yeah, that's a fine respect. Okay, this is fun
00:36:38Good we started this for like two months by now. So we are very good at it. Okay. Yeah
00:36:47Great
00:36:53Five minutes. Thank you. Yep
00:36:56Yeah, if you want to fun function for a.m. Go for it, okay function over. Okay
00:37:10No
00:37:22Hmm
00:37:25You
00:37:55You
00:38:25You
00:38:55You
00:39:25You
00:39:55You
00:40:03You
00:40:10You
00:40:20You
00:40:25You
00:40:56You
00:41:06Up
00:41:16You
00:41:26You
00:41:37Okay
00:41:43You more time and I do let's relax
00:41:50Weekend is coming already. Yeah time flies. Oh, yeah. Sure. Sure
00:41:55You
00:41:59Hmm
00:42:04Cheers
00:42:09Mm-hmm
00:42:12So
00:42:16Well, let's stop I wasn't broken, okay, yeah
00:42:22If
00:42:26You
00:42:31M is a odd number
00:42:36Then
00:42:45You
00:42:55You
00:42:58Yeah, okay and plus one divided by two, okay plus
00:43:05When M is
00:43:08Even number
00:43:22And plus one, okay
00:43:26Now let's get rid of let's get rid of I was working, okay
00:43:34Meaning we will convert I wasn't bracket to regular algebra algebraic expression. Okay
00:43:49Yeah
00:43:55You
00:43:59Okay, if this is one yeah, then this if it is zero then
00:44:05Falls to zero. Okay. Yeah
00:44:09Now here we need to invert this, okay. Yeah
00:44:14You
00:44:24When this is zero
00:44:27It should be one. So this is zero. So one minus zero one. Okay, when this is one
00:44:35Then this should be zero right so if this is one one minus one zero, okay. Yeah, that's true. Okay. Yeah, we come on with
00:44:44It was a function, okay good
00:44:51Now next step
00:45:03You
00:45:13You
00:45:22One three, two five three three
00:45:37Do they repeat like that? Okay, and then actually
00:45:40Let's
00:45:44You know the signing first
00:45:47Okay now indexation
00:45:51Okay, so just let's say this is a b of n. Okay. Now we are using actual index n. Okay
00:45:59and
00:46:02If zero that's fictional, okay, so
00:46:09You
00:46:22Oh made the same mistake we skip multiple of five
00:46:37Then
00:46:40Index type from minus one. Okay. Yeah
00:46:42You
00:46:44You
00:47:09Yeah, it's tricky cheers
00:47:15We learn from our mistakes, okay, okay
00:47:35The way to group this
00:47:45You
00:47:52Oh, right
00:48:04And we have M well there
00:48:14You
00:48:27Okay, it's in index conversion index transformation, okay, so yeah
00:48:39Our next step
00:48:45The final function
00:48:48That describe the relationship between n and M
00:48:53Okay, yeah
00:48:56And vice versa
00:49:12You
00:49:14You
00:49:16Final function such that
00:49:20F of n
00:49:23Is equal to M
00:49:25Okay
00:49:27This is the ends. These are the M's
00:49:30The final function so that the fun f of n becomes M. Okay. Yeah, it's a mapping problem. Okay
00:49:40Now time to look at
00:49:45You
00:49:49Mathematical marathon. Yeah, it's been
00:49:56Less than one hour. Okay
00:50:00Okay, good let it finally spread. Okay. Thank you
00:50:07Yeah, it's a lot
00:50:09You
00:50:13But
00:50:14I'm glad we are redoing this because
00:50:17When we did this first time we are not familiar with this. Now. We are we did more. Okay good
00:50:25Okay, five minutes, thank you, okay, this is fun
00:50:31Okay, ah
00:50:35Okay, thank you
00:50:37Wow
00:51:07You
00:51:37You
00:52:07You
00:52:38You
00:52:50Okay, let's go
00:52:53You
00:53:03The best thing to learn from mathematics, okay, so the Republican Party
00:53:08Yeah, now they are on full
00:53:11like
00:53:14Criticism on
00:53:16You
00:53:18Kamala Harris
00:53:19Because they feel very threatened by her. So they're talking about
00:53:24Okay, it used to be a Bordeaux
00:53:27child Bordeaux's are
00:53:29The Bordeaux King Queen Bordeaux Queen. Yeah, like you're in charge of the Bordeaux situation
00:53:35but you didn't do anything as vice president, so
00:53:39But I don't know if that allegation is true or not. I don't know. I don't remember
00:53:44Okay
00:53:47But the thing is this okay, I mean
00:53:50Vice president doesn't have that much authority. She has to obey
00:53:54President Biden, so she cannot do her own things. Okay, and
00:53:59It's not her fault that she did not build a southern border wall
00:54:05it's Biden and
00:54:07More than that is Democratic Party because building southern border wall that's Donald Trump's idea Republican Party idea
00:54:13Okay, they know if that's the right idea
00:54:17It's common sense
00:54:19but
00:54:20Because if their idea came from Republican Party, that was a Trump. That's why they didn't do it
00:54:26In the southern border wall. Okay. Yes, so she's not to blame. Okay
00:54:33Mm-hmm. It's just party politics. Okay
00:54:39Yeah
00:54:43You
00:54:45Okay
00:54:53Let's grab more glass
00:55:09Yeah
00:55:14Okay
00:55:19Dragon lift drink. Alaskan spring bird
00:55:31Okay, cheers. Welcome to Humanology. Yeah, happy Thursday
00:55:37Oh
00:55:42It's good, okay. Okay. So mapping problem
00:55:52Minus one become one two and three become two four and six become three. Okay. All right
00:56:03Mm-hmm
00:56:07You
00:56:27I think it's just
00:56:38Uh
00:56:58We have two cases, okay
00:57:00Two and three they are consecutive four and six
00:57:03They are not consecutive, okay. Yeah
00:57:08Seven eight consecutive nine eleven not consecutive. Okay. So, okay. Okay
00:57:15Uh
00:57:33You
00:58:03You
00:58:14Let's do step by step
00:58:24We want to map this one two, three, four five blah blah M we want to map this to
00:58:33You a
00:58:3710
00:58:4012
00:58:55Uh
00:58:59It is 2m, okay. Yeah
00:59:03You put on them
00:59:08It's a little bit tricky, okay
00:59:16Let's take time on this
00:59:21Cheers again
00:59:33You
00:59:51Oh
01:00:03You
01:00:33You
01:00:42Well, maybe there's better way to do it but one easy way to do it is this yeah skipping method
01:00:50Alternate thing method. Okay
01:00:52We just skip
01:00:55Hop hop hop it method. Okay. Yeah like
01:01:01When we do
01:01:03If we do
01:01:33You
01:01:38Let's take a easy case easier case for first, okay, so if we do
01:01:45And
01:01:59You are by two
01:02:03Glory
01:02:06Plus one
01:02:09Okay
01:02:19Yeah
01:02:29Uh
01:02:34And divide by two seal it
01:02:48We are looking like two four six eight ten, okay. Yeah alternate it. Okay skipping happen
01:02:55Uh
01:03:01Yeah, it's not quite working, okay
01:03:16Wow, what a challenging problem this is
01:03:24You
01:03:33Yeah
01:03:44You
01:03:54You
01:04:25You even index when M is even okay
01:04:41Wow
01:04:54You
01:04:58Yeah here yeah and and divide by two
01:05:04Ceiling but here and divide by two flooring
01:05:10Okay
01:05:12It still automates. Okay. All right
01:05:17Wow
01:05:24You
01:05:36This is challenging, yeah
01:05:48You
01:05:54You
01:06:24You
01:06:54You
01:07:24You
01:07:54You
01:07:56You
01:08:23Maybe I should divide by three instead of two. Okay
01:08:26Okay
01:08:50Hmm
01:08:56You
01:09:26You
01:09:56You
01:10:01You
01:10:26You
01:10:33Mm-hmm
01:10:45Yeah, I'm not making a progress okay, ah
01:10:51Yeah, I'm kind of today was busy too at work, okay and
01:10:57I
01:11:00Do go to work a little earlier than usual and I have to stay
01:11:06later than usual at work was busy their work and
01:11:10I'm kind of drunk and
01:11:12we enough mathematical tonight, okay, so
01:11:16but
01:11:18Let's take five minutes break. Okay, and then
01:11:23Well, no, uh, let's just
01:11:26Wrap up this wrap it up for this episode. Okay, because uh,
01:11:32I'm kind of tired. Okay. Yeah, and
01:11:36We did good mathematics tonight, okay, so
01:11:41Let's finish up for this episode and then we take five minutes break and then
01:11:45We'll go Instagram live together at the finest broken
01:11:50Yeah, it's been a long day today for me, okay, so, okay
01:11:55We'll pick this up tomorrow. Okay. Yeah. Thank you. Yeah. Yeah, I'll see you
01:12:02Tomorrow we'll do Instagram live together after 10 minutes. Okay. Yeah. Thank you. Yeah
01:12:08Good night. Yeah. Thank you