Category
🦄
CreativityTranscript
00:00:00Hello friends. Yeah, welcome to Friday Night Live. Welcome to the episode. 164.5. Yeah
00:00:10I took a bath. Long bath. And so, yeah. We can routine, right? Yeah. Okay. All right.
00:00:20What exercise? How about push-ups? We'll do 10 finger push-ups, okay?
00:00:42Okay. Very good. Wow. That's good. Okay. Five minutes break, please. Thank you.
00:01:12Okay.
00:01:42Okay.
00:02:12Okay.
00:02:42Okay.
00:03:12Okay.
00:03:42Okay.
00:04:12Okay.
00:04:42Okay.
00:05:12Okay.
00:05:42Okay.
00:06:13Okay.
00:06:15Okay. Welcome to the show.
00:06:21Happy Sunday evening.
00:06:27Okay, so.
00:06:31Yeah, like doing the Instagram live and also in Dailymotion, we talked about that incident.
00:06:37It helps.
00:06:39I mean, getting the feelings out
00:06:42you know, just talking about it.
00:06:44It's therapeutic, okay?
00:06:46Because it's traumatic.
00:06:48Just watching the horrible news like that.
00:06:50Yeah.
00:06:52So talking about it, it does help.
00:06:54Yeah.
00:06:56Yeah.
00:06:58Yeah.
00:07:02Okay.
00:07:04Now.
00:07:06Mathematics?
00:07:08Sure.
00:07:11Let me put some more layers.
00:07:15Silly.
00:07:41Okay.
00:07:43Okay.
00:07:45Okay.
00:07:47Okay.
00:07:49Okay.
00:07:51Okay.
00:07:53Okay.
00:07:55Okay.
00:07:57Okay.
00:07:59Okay.
00:08:01Okay.
00:08:03Okay.
00:08:05Okay.
00:08:07Okay.
00:08:10Okay.
00:08:12Okay.
00:08:14Okay.
00:08:16Okay.
00:08:18Okay.
00:08:20Okay.
00:08:22Okay.
00:08:24Okay.
00:08:26Okay.
00:08:28Let's take a look at this old whiteboard
00:08:30where we did
00:08:32that coefficient for
00:08:34base 2 and base 3.
00:08:37That was like
00:08:39two months ago, maybe a month ago.
00:08:41It's quite a while ago.
00:08:43Okay.
00:08:45Yeah.
00:08:47So.
00:08:53Let's look at it together.
00:08:55Okay.
00:08:59Ugh.
00:09:01Ugh.
00:09:23Ah.
00:09:27We need to redo this, okay?
00:09:29Because
00:09:31the way we did it here, we only did the
00:09:33we have base 2, right?
00:09:35And the other number
00:09:37we only did for the prime numbers.
00:09:41It's not necessary, okay?
00:09:43It can be any number bigger than 2.
00:09:45We need to redo this, okay?
00:09:49But base 3,
00:09:51same thing.
00:09:53Ah.
00:09:59Okay.
00:10:09Okay.
00:10:19Um.
00:10:23That means we need to grab our whiteboard, okay?
00:10:25So.
00:10:27Sure.
00:10:33Yeah.
00:10:35Let's grab our whiteboard and
00:10:39do it again. Sure.
00:10:41Uh.
00:10:57Uh.
00:11:23Go across to this one.
00:11:27Okay.
00:11:47Let's
00:11:49recall how we did
00:11:51as a coefficient for
00:11:53base 5.
00:11:57Uh.
00:12:01Greatest common divisor
00:12:03between 5 and 6.
00:12:051, right?
00:12:07Ah, I see.
00:12:09I see. So
00:12:11we did calculate
00:12:13Oh, okay.
00:12:15I see. I see. I see.
00:12:17There's some
00:12:19Uh.
00:12:23Okay.
00:12:25Okay. Our formula may not be
00:12:27quite complete, okay? Because
00:12:33we skipped
00:12:39numbers
00:12:41when the bigger number is
00:12:43we call it left number, okay?
00:12:45Left number is
00:12:47multiple of 5.
00:12:51Like 5 and 10, for example.
00:12:53Okay.
00:13:01Yeah, we need to modify our formula
00:13:03a little bit, okay? So, um.
00:13:05Okay.
00:13:21Well, we can qualify our formula
00:13:23so that this N
00:13:25the larger number
00:13:27is not a multiple
00:13:29of 5, okay? Then, then
00:13:31you'll be fine, okay? So
00:13:33Yeah, we can qualify like that, okay?
00:13:37Because if it is multiple of 5
00:13:39like 10 and 5
00:13:41then, um
00:13:43it's trivial, okay?
00:13:47We're only looking at
00:13:49non-trivial cases.
00:13:515 and multiple of 5 was
00:13:53greatest common divisor. 5, right?
00:13:55Yeah. So you don't really
00:13:57need to worry about those
00:13:59cases, okay?
00:14:01Okay.
00:14:11Okay.
00:14:15And
00:14:21Well, I kind of
00:14:23want to still make it work, though.
00:14:25I mean
00:14:31I
00:14:33I
00:14:35I
00:14:37I
00:14:39I
00:14:41I
00:14:43I
00:14:45I
00:14:47I
00:14:51I
00:14:53I
00:14:55I
00:14:57I
00:14:59I
00:15:01I
00:15:03I
00:15:05I
00:15:07I
00:15:09I
00:15:11I
00:15:13I
00:15:15I
00:15:17I
00:15:19I
00:15:21I
00:15:23I
00:15:25I
00:15:27I
00:15:29I
00:15:31I
00:15:33I
00:15:35I
00:15:37I
00:15:39I
00:15:41I
00:15:43I
00:15:45I
00:15:47I
00:15:49I
00:15:51I
00:15:53I
00:15:55I
00:15:57I
00:15:59I
00:16:01I
00:16:03I
00:16:05I
00:16:07I
00:16:09I
00:16:11If it does not work, that's fine.
00:16:23Uh
00:16:29Okay. You're qualified, but
00:16:31let's see what happens when it is 5, okay?
00:16:33So
00:16:472.5
00:16:492, so this one is 0
00:16:53Uh
00:16:592.5
00:17:012
00:17:030
00:17:052.52
00:17:11Okay
00:17:192.5
00:17:232.52
00:17:250
00:17:271
00:17:33Okay
00:17:35Now
00:17:37Gamma
00:17:39of
00:17:4110
00:17:435 is
00:17:45supposed to be 5
00:17:475
00:17:51Left number
00:17:53minus 2
00:17:55Right number
00:17:571
00:18:03Minus 15
00:18:05So yeah, it does not hold true
00:18:07but that's fine, okay?
00:18:09Why? We just qualified
00:18:11and it's not
00:18:13multiple of 5, okay?
00:18:15These cases are just too trivial
00:18:17Okay? We know what
00:18:19great common divisor is
00:18:21it's just 5, right?
00:18:23Basic coefficient for this
00:18:25would be
00:18:2910 times
00:18:331 plus
00:18:355 times minus 1, okay?
00:18:39Yeah
00:18:42How about
00:18:44greatest common divisor
00:18:465 and 5
00:18:48it's just 5
00:18:50I guess this would be 5 times 0
00:18:52plus 5 times 1
00:18:54and greatest common divisor
00:18:56is 15 and 5
00:18:58just 5
00:19:0010 times
00:19:0215 times
00:19:061 plus
00:19:085 times minus 2
00:19:11Basic coefficient for multiples
00:19:13it's just easy
00:19:15Okay?
00:19:17Yeah
00:19:21What is it?
00:19:30Okay, so
00:19:32let's do this
00:19:40Okay
00:20:04Okay?
00:20:06Yeah
00:20:08So 1 and minus
00:20:10k minus 1, okay?
00:20:12That's the basic coefficient for
00:20:14multiples of 5
00:20:16That's too trivial, okay?
00:20:18That's why we don't need to do this
00:20:20Okay?
00:20:22We only take care of
00:20:24non-trivial cases
00:20:26But, good to know
00:20:28Okay?
00:20:30Yeah
00:20:38Okay
00:21:08Yeah, so
00:21:18Okay, so we got formula for that
00:21:20That's good
00:21:28And to summarize
00:21:30this
00:21:32When
00:21:34n rho
00:21:365 is 0
00:22:06Okay
00:22:16Okay
00:22:18There we go
00:22:20Yeah, we didn't deal with this
00:22:22because it's just too easy
00:22:24to make it complete, okay?
00:22:26Good, good
00:22:36Okay
00:22:44We can combine the whole thing
00:22:46using eigenvectors and brackets, okay?
00:22:48But, yeah
00:22:50It's not totally necessary, okay?
00:23:02Okay
00:23:04Okay
00:23:06Now
00:23:10Let's
00:23:12take 5 minutes break
00:23:14and then
00:23:16we go back to the case
00:23:18where base
00:23:20Bazoo base
00:23:22is 2, okay?
00:23:24Yeah, and also Bazoo base is 3
00:23:26Yeah
00:23:30Sure
00:23:34Okay
00:23:42You know what?
00:23:445 minutes break, thank you
00:23:46Okay
00:23:50Yeah
00:23:54There we go
00:23:58It is silly
00:24:00Yeah, 5 minutes, thank you
00:24:30Okay
00:24:32Thank you
00:24:34Thank you
00:24:36Thank you
00:24:38Thank you
00:24:40Thank you
00:24:42Thank you
00:24:44Thank you
00:24:46Thank you
00:24:48Thank you
00:24:50Thank you
00:24:52Thank you
00:24:54Thank you
00:24:56Thank you
00:24:58Thank you
00:25:00Thank you
00:25:02Thank you
00:25:04Thank you
00:25:06Thank you
00:25:08Thank you
00:25:10Thank you
00:25:12Thank you
00:25:14Thank you
00:25:16Thank you
00:25:18Thank you
00:25:20Thank you
00:25:22Thank you
00:25:24Thank you
00:25:26Thank you
00:25:28Thank you
00:25:30Thank you
00:25:32Thank you
00:25:34Thank you
00:25:36Thank you
00:25:38Thank you
00:25:40Thank you
00:25:42Thank you
00:25:44Thank you
00:25:46Thank you
00:25:48Thank you
00:25:50Thank you
00:25:52Thank you
00:25:54Thank you
00:25:56Thank you
00:25:58Thank you
00:26:00Thank you
00:26:02Thank you
00:26:04Thank you
00:26:06Thank you
00:26:08Thank you
00:26:10Thank you
00:26:12Thank you
00:26:14Thank you
00:26:16Thank you
00:26:18Thank you
00:26:20Thank you
00:26:22Thank you
00:26:24Thank you
00:26:26Thank you
00:26:28Thank you
00:26:30Thank you
00:26:32Thank you
00:26:34Thank you
00:26:36Thank you
00:26:38Thank you
00:26:40Thank you
00:26:42Thank you
00:26:44Thank you
00:26:46Thank you
00:26:48Thank you
00:26:50Thank you
00:26:52Thank you
00:26:54Thank you
00:26:56Thank you
00:26:58Thank you
00:27:00Thank you
00:27:02Thank you
00:27:04Thank you
00:27:06Thank you
00:27:08Thank you
00:27:10Thank you
00:27:12Thank you
00:27:14Thank you
00:27:16Thank you
00:27:18Thank you
00:27:20Thank you
00:27:22Thank you
00:27:24Thank you
00:27:26Thank you
00:27:28Thank you
00:27:30Thank you
00:27:32Thank you
00:27:34Thank you
00:27:36Thank you
00:27:38Thank you
00:27:40Thank you
00:27:42Thank you
00:27:44Thank you
00:27:46Thank you
00:27:48Thank you
00:27:50Thank you
00:27:52Thank you
00:27:54Thank you
00:27:56Thank you
00:27:58Thank you
00:28:00Thank you
00:28:02Thank you
00:28:04Thank you
00:28:06Thank you
00:28:08Thank you
00:28:10Thank you
00:28:12Thank you
00:28:14Thank you
00:28:16Thank you
00:28:18Thank you
00:28:20Thank you
00:28:22Thank you
00:28:24Thank you
00:28:26Thank you
00:28:28Thank you
00:28:30Thank you
00:28:32Thank you
00:28:34Thank you
00:28:36Thank you
00:28:38Thank you
00:28:40Thank you
00:28:42Thank you
00:28:44Thank you
00:28:46Thank you
00:28:48Thank you
00:28:50Thank you
00:28:52Thank you
00:28:54Thank you
00:28:56Thank you
00:28:58Thank you
00:29:00Thank you
00:29:02Thank you
00:29:04Thank you
00:29:06Thank you
00:29:08Thank you
00:29:10Thank you
00:29:12Thank you
00:29:14Thank you
00:29:16Thank you
00:29:18Thank you
00:29:20Thank you
00:29:22Thank you
00:29:24Thank you
00:29:26Thank you
00:29:28Thank you
00:29:30Thank you
00:29:32Thank you
00:29:34Thank you
00:29:36Thank you
00:29:38Thank you
00:29:40Thank you
00:29:42Thank you
00:29:44Thank you
00:29:46Thank you
00:29:48Thank you
00:29:50Thank you
00:29:52Thank you
00:29:54Thank you
00:29:56Thank you
00:29:58Thank you
00:30:00Thank you
00:30:02Thank you
00:30:04Thank you
00:30:06Thank you
00:30:08Thank you
00:30:10Thank you
00:30:12Thank you
00:30:14Thank you
00:30:16Thank you
00:30:18Thank you
00:30:20Thank you
00:30:22Thank you
00:30:24Thank you
00:30:26Thank you
00:30:28Thank you
00:30:30Thank you
00:30:32Thank you
00:30:34Let's say 2k plus 1
00:30:52Minus k
00:30:58Yeah
00:31:00So
00:31:02Left
00:31:04number
00:31:06when base is 2
00:31:08and 2k plus 1
00:31:10is equal to
00:31:121
00:31:14Now
00:31:16right value coefficient
00:31:18when base is 2
00:31:22Minus k
00:31:24Good
00:31:26Easy
00:31:28How about
00:31:34when the argument
00:31:36is multiple of 2
00:31:38when argument is a multiple of 2.
00:32:08Okay, now gamma 2k, 2 is equal to 2k times 1 plus 2 times minus k minus 1, okay?
00:32:37So left base coefficient for 2k when base is 2 is equal to 1, right base coefficient
00:32:52of 2k when base is 2 is equal to minus k plus 1, okay?
00:33:00Good.
00:33:01It's easy, right?
00:33:08Okay.
00:33:16I'm kind of wondering when base is 5, why is formula so difficult?
00:33:24Kind of wondering.
00:33:29Now let's take 5 minutes break and then let's see when
00:33:32base coefficient for when the base is 3, okay?
00:33:38Cheers, yeah.
00:33:43Because we took a break from mathematics, now we are enjoying this, okay?
00:33:47It's good to take a break, okay?
00:33:49Cheers.
00:33:53Yeah, nice.
00:33:59Let's take 5 minutes break.
00:34:00Yep, very cool.
00:34:02Awesome.
00:34:10There we go, okay.
00:37:32Yeah, now I'm just drinking water because I control my drinking, okay?
00:37:58So, yeah.
00:38:07Let me go grab some more water then, okay?
00:38:12Okay.
00:38:28Oh, water is good.
00:38:42Okay.
00:38:49Base 3, let's go.
00:39:28Oh.
00:39:58Yeah, I'm copying from over there.
00:40:28Okay.
00:40:58Okay.
00:41:29Okay, there's definitely a pattern here.
00:41:45Okay.
00:41:54Oh.
00:42:16Okay, so we have this sequence, right?
00:42:241 minus 1, 1 minus, that's just too easy, okay?
00:42:26So, but we have here gamma 3 plus n
00:42:46minus 1.
00:42:48Okay.
00:42:50Okay.
00:42:52Okay.
00:42:54Okay.
00:42:56Okay.
00:42:58Okay.
00:43:00Okay.
00:43:18So, assume n row 3 is not equal to 0, okay?
00:43:26So N is not multiple of 3, okay?
00:44:00you
00:44:30you
00:44:32you
00:44:34you
00:44:36you
00:44:38you
00:44:58Okay, we have a sequence n n is equal to 1 2
00:45:054
00:45:07um
00:45:11Five
00:45:14Seven eight
00:45:18Ten
00:45:22You
00:45:37You
00:45:44And this maps to one two
00:45:54Three
00:45:57And four okay, and we need to find function for that okay, if you can go for it, okay, yeah
00:46:07Should be difficult. It's it will be like
00:46:10This number divide by three and then floor plus one you look something like that. Okay, so, okay
00:46:17Yeah, if you want to find a function that maps this like a
00:46:21Groups to this number. Okay. Yeah. Okay. Yeah, we'll take five minutes. Okay. Thank you
00:46:28Okay
00:46:31All right, okay
00:46:33Okay
00:46:35There we go, thank you
00:46:41Interesting
00:46:53You
00:47:03You
00:47:33You
00:48:03You
00:48:33You
00:49:03You
00:49:33You
00:49:36Okay
00:49:46Oh
00:49:56Okay, let's see
00:50:03You let me stop drinking a little bit, okay, so let me get some Tom's
00:50:28All right
00:50:31Let's enjoy this moment, okay, let's have some fun
00:50:38Yeah
00:50:57Okay
00:51:00You
00:51:06Yes, happy Sunday evening
00:51:14Having fun with mathematics
00:51:30You
00:52:00You
00:52:04So here's n
00:52:07Okay
00:52:09if we
00:52:11n plus 1
00:52:15Because 9 and 11, right
00:52:30You
00:52:34Divide by 3
00:52:41Plus 1, okay
00:52:51You have 6 and 8
00:52:55Divide by 3
00:52:58Floor then it becomes 2
00:53:042 plus 1, 3. Okay, it works. Okay, so we have
00:53:21Okay, good
00:53:27You
00:53:30Now
00:53:33I'm wondering
00:53:36If we can combine
00:53:40This argument when the argument is
00:53:43Known multiple of 3. That's what we did. Okay, but can we combine when argument is
00:53:49No multiple of 3 and also multiple of 3
00:53:53Let's look at the possibility. Okay
00:53:58You
00:54:04Let's see what happens, okay, so
00:54:13You
00:54:27You
00:54:57You
00:55:07What
00:55:12Yeah, you better separate that out why because it becomes too disruptive
00:55:18Okay, it becomes like 1 2 1 2
00:55:22then 3 2 3
00:55:25then 4 3 4
00:55:27Yeah, it's it's a mess
00:55:30You better just separate them out. Okay, so
00:55:33Okay
00:55:34That's fine
00:55:37No, yeah
00:55:41Okay, and then
00:55:51Gamma
00:55:533 plus 3 K
00:55:57You
00:56:22Okay, yeah
00:56:28You
00:56:30That's when n is 3 K so
00:56:35Meaning like n rho 3 is 0. Okay. Yeah. Okay. We better separate them out
00:56:42Okay. Yeah, there's absolutely no need to combine them. Okay, we can use Iverson-Broken and combine the two. Okay. Yeah, but
00:56:49That's too easy. So we are not going to write it out. Okay. Cheers. Yeah, okay
00:56:54You
00:57:03Mm-hmm
00:57:09Mm-hmm
00:57:18Time to go
00:57:24It's been almost one hour Wow time flies on Wow, okay now
00:57:34We looked at base 2 base 3 and base 5 and they were prime numbers
00:57:41Now let's venture out and let's look at when base is composite number
00:57:48Okay, the very first composite number 4
00:57:52Okay, let's see what it looks like that that's devil more tricky I think okay
00:58:02But
00:58:06It's yeah
00:58:13It's a little bit daunting to me a little bit scary, okay
00:58:22Ah
00:58:24but
00:58:26We have one hour, okay, so
00:58:30We may as well just do it I'm very refreshed
00:58:35It's good good nap and
00:58:38Took a bath. So and we took a long break from mathematics, right? So I think it's good time to do it
00:58:45Okay, let's take five minutes break and then we'll go ahead and
00:58:51Calculate best coefficients for base 4. Okay. Yeah
00:59:05It's good time to do it, okay. Yeah, sure. Let's go for it. Okay
00:59:13Okay, fine me thank you. Yeah
00:59:17Yeah, I
00:59:20Could have a new iPod. So, okay
00:59:26There we go
00:59:31Okay, cool
00:59:49You
01:00:19You
01:00:49You
01:01:19You
01:01:49You
01:02:20Okay
01:02:27Ah
01:02:35This is old whiteboard, so I'm not sure how easily this can be erased
01:02:43It's even missing a bottom frame
01:02:49You see doesn't erase at all
01:02:54Okay
01:03:13Where is that index?
01:03:20You
01:03:33Oh
01:03:42Where's the index
01:03:49You
01:04:19You
01:04:35You thought it doesn't even work dude
01:04:45Okay
01:04:50You
01:05:08Oh nice
01:05:19You
01:05:22You
01:05:48Hahahaha
01:05:5150% done. Okay. Works well.
01:06:06Little things in life.
01:06:13Oh
01:06:21This is fun.
01:06:35What do I do?
01:06:37Quite a workout.
01:06:39Okay.
01:06:55Now let's try this.
01:07:09Okay.
01:07:19Let me wash my hands.
01:07:23Wow.
01:07:25Wow.
01:07:49I hope this one is magnetic.
01:07:53How much time do I have?
01:08:07Okay. It's been more than one hour.
01:08:09Okay. So when
01:08:11Baseball, I'm not quite sure
01:08:13if I want to do it now.
01:08:15But
01:08:17It's been more than one hour. Okay.
01:08:19So we will do just a little bit. Okay.
01:08:21Some idea. Okay. Yeah.
01:08:23Just a little bit.
01:08:33Just a little bit.
01:08:35Let's exercise
01:08:37some kilojoules, you know.
01:08:39Cheers.
01:08:51Okay.
01:09:13Credit
01:09:15common divisor of
01:09:17Cool.
01:09:47Eight is
01:09:49multiple of four. So
01:09:51common, credit common divisor of
01:09:53eight and four is four. Okay. So
01:09:55we're not going to do that. Okay.
01:09:57It's too trivial. We'll just do it
01:09:59separately. Okay. Yeah.
01:10:17Okay.
01:10:47Okay.
01:11:17We'll keep going like this until we see your pattern. Okay.
01:11:37Okay.
01:11:39We'll keep
01:11:41going like this until we see your pattern.
01:11:43We'll keep going like this until we see your pattern.
01:11:45You
01:12:15You
01:12:20I thought you'd be no trivial. Okay, so cheers. Yeah
01:12:28Because when we dealt with
01:12:32prime number base
01:12:35Greatest common divisor is it's like a one right because this prime number. Okay, but when the basis
01:12:43The composite number then the greatest common divisor can be sometimes one and sometimes it's two
01:12:52Okay, yeah
01:12:55Yeah, that's why it's non-trivial, okay, so but
01:13:03Yeah, we keep doing this on to be self error, okay
01:13:13You
01:13:17We finish this column, okay
01:13:22It is pretty just solitaire
01:13:28Solo card game
01:13:30Airplane they have it. Okay
01:13:42You
01:14:06Okay
01:14:13Oh
01:14:17Tony is much powerful. You skip that
01:14:32You
01:14:42You
01:14:58No
01:15:00We finish the column and then we take five sir. Okay, so if you can spot a pattern go for it, okay
01:15:12You
01:15:31You
01:15:42You
01:15:49You
01:16:03Uh, I made a mistake here
01:16:07Okay, now I see a panel good
01:16:10Very good
01:16:16Yeah, we found a parallel, okay
01:16:19Do you see a panel? Yeah, go look for it. If you want to okay, we'll take 500. This is fun
01:16:27Now that's better than I thought it would be okay
01:16:32It's different kind of pattern but parallel nonetheless, okay
01:16:37This is nice, okay, let's take five minutes break. Thank you. Yep. Very good. Very good. I'm glad we're doing this
01:16:48Fun fun fun. There we go five minutes. Thank you
01:17:01You
01:17:06You
01:17:36You
01:18:06You
01:18:36You
01:19:06You
01:19:37You
01:19:42Okay
01:19:47Wow
01:19:50How interesting
01:19:52Now that we spotted a pattern, we can come up with a formula
01:19:56That's how Modus apparently this way. Okay. Well, it's
01:20:00Systematic
01:20:02Enumeration methods we did that long long time ago. I mean since long time ago. Okay, like go to bus connect your
01:20:10Stuff. Okay. There's a five years ago. Okay, so we've been doing this
01:20:15for years
01:20:17Yeah, cheers. Yeah
01:20:23What is that on one one minus one one one minus one, right
01:20:28Then you have
01:20:30Two minus minus two minus two minus two three minus three minus three four minus three minus four minus four blah blah blah
01:20:37Okay. Yeah
01:20:39Good
01:20:42Yeah
01:20:51So
01:20:57Now the mapping, okay
01:21:09This is the fun part
01:21:16Mapping by mapping I mean function. Okay. So yeah. Yeah Cheers
01:21:21You
01:21:26Time to look
01:21:34We have more than 30 minutes left, okay good now we need to introduce some artificial controls on your guess so
01:21:43We have gamma
01:21:45You
01:21:49Four plus n, okay, come on four now
01:22:01One minus one yeah, we chose one. Okay, it's artificial control construction
01:22:15You
01:22:27Okay, and index starting from zero
01:22:45Oh
01:22:51My bad
01:23:05We skip the multiple of four, okay
01:23:15You
01:23:43What
01:23:46You
01:23:50Huh
01:23:54I'm sorry, it's too small. Okay, but you can take a screenshot enlarge it. Okay. Yeah
01:24:10Now we need to find a function
01:24:13Okay, this is n
01:24:23And that is like it let's say
01:24:32E of n, okay, how about that? It's dysfunctional van. Okay, so
01:24:37You
01:24:41Mapping
01:24:45They won't be difficult if it's similar, okay like
01:24:49And
01:24:50Divide by four then flooring and plus one something like that. That's tough. Okay, so
01:24:58By now we are used to it. Okay, so it's similar pattern
01:25:02Later on we unify all those formulas and come up with one formula that works for everything. Okay, but that's our goal. Okay
01:25:10All one constant time algorithm formula for best coefficients, okay
01:25:16Currently they have all log n algorithms
01:25:19Yeah, okay
01:25:21We're heading the right direction. Okay Cheers
01:25:25Hmm
01:25:31We are
01:25:37So we group them
01:25:41About plus minus sign you worry about that. That's easy. Okay, so
01:25:49Three by three, okay
01:25:57Okay
01:26:01You
01:26:31You
01:26:45Let's say the K
01:27:01You
01:27:07It seems to be
01:27:16And plus one
01:27:19Divide by four
01:27:22flooring and
01:27:24then plus one
01:27:26That's what it seems
01:27:32Oh, yeah
01:27:37Three five six becomes four six seven
01:27:43Divide by four and then flooring becomes one then plus one truth. Okay. Yeah
01:27:50Seven nine ten becomes eight ten eleven
01:27:54Okay, divide by four
01:27:57Floor and two. Okay, and then plus one it comes to you. Okay. Yeah. Yes. Yeah, it is same pattern. Good
01:28:04We found a parent. Okay. Nice
01:28:06Yeah, very nice
01:28:13Wow
01:28:16Yes, yeah
01:28:26Oh
01:28:31Let's say five minutes break, okay, and then after that
01:28:37If you want to yeah fine formula for yen, okay
01:28:41If you want to okay. Yeah, we'll take five minutes break. Thank you. Yeah, this is nice. Yeah
01:28:48You like marathon
01:28:53Yeah
01:28:56Oh
01:29:03Okay, very cool, yeah blindness, thank you
01:29:18All right
01:29:26You
01:29:56You
01:30:26You
01:30:56You
01:31:26You
01:31:56You
01:32:00Oh
01:32:07Okay
01:32:21All right, I come back we're back
01:32:27now
01:32:29Time to go
01:32:32Time flies when we into something right? Yeah
01:32:36We have more than 30 minutes
01:32:40Okay
01:32:46Very cool. Cheers. Yeah
01:32:57You
01:33:05Wow, so sign is a little bit tricky
01:33:11Plus minus minus plus minus minus plus minus minus. Okay. It's a little bit tricky. Okay. Hmm
01:33:26You
01:33:28You
01:33:55Cheers
01:33:58You
01:34:04Because it's quasi alternating
01:34:07Quasi alternation. Okay, that plus minus plus minus is not that it's plus minus minus plus minus minus. Okay
01:34:14So how do you devise that kind of formula here?
01:34:23How interesting
01:34:28You
01:34:43So we have to find a function that maps
01:34:48zero one two into
01:34:51One minus one minus one. Okay zero one two
01:34:54We just subject three and
01:34:56Subject six. Okay. No problem, but it all goes down to zero one two mapping to one minus one minus one
01:35:04Okay
01:35:05What kind of function it would be that so?
01:35:11We are mapping zero one two
01:35:24And this is an okay
01:35:30Mapping problem
01:35:39One minus one minus one
01:35:45It's looks easy, right
01:35:47But I do not know the answer yet. Okay, let's
01:35:50Relax, and we have time
01:35:54More than 20 minutes left actually
01:36:01Yeah, more than 20 minutes left, okay
01:36:04interesting
01:36:05Find a function that maps from zero one two to one minus one minus one. Okay
01:36:10You
01:36:23Cheers
01:36:35It will have to do with number three
01:36:38Right, yeah, like okay
01:36:46All these numbers yeah some number and row three, okay. Yeah
01:36:52Then it becomes zero one two and row and row three. Okay. Yeah
01:37:02Wait a minute not exactly
01:37:07You
01:37:09But we'll deal with that later, okay, it's not n or three not really
01:37:37You
01:37:52Yeah
01:38:07You
01:38:16You
01:38:30You
01:38:37Actually
01:38:42The index here should be minus one, okay
01:38:58Okay
01:39:01You
01:39:03You have three and five seven and nine eleven and thirteen it's like skips right? Yeah. Okay. Yeah, okay
01:39:11With the dot is still true. It does this for us to work
01:39:19Yeah, it does okay good
01:39:30You
01:39:53Looks like an easy problem, but it's a little bit tricky. It should not be too difficult
01:39:59I don't think it would be but
01:40:02It does require some thinking and I do not have answer yet
01:40:10Very interesting
01:40:14You
01:40:29Yeah from first set to second set yeah, just add four to each element
01:40:33Okay, and then add four add four then we got the same thing. Okay. Okay
01:40:54Who
01:40:57It's like let me do both for
01:41:03Three one two
01:41:05Three one two. Okay. Okay
01:41:08so
01:41:11Three one two
01:41:15And row four, okay. Yeah
01:41:19They met two one minus one minus one because you're not even positive number, okay, so
01:41:26Okay
01:41:29We call it geocastle
01:41:37Okay
01:41:47You
01:41:56You
01:42:00Yes
01:42:26You
01:42:28We may have to resort to Iverson bracket, okay, if she's like come to programming, okay, if then I have statement
01:42:35Okay, that's why I was bracket is about. Okay, so
01:42:40Then it's easy, okay, but to express this in traditional
01:42:45mathematical language
01:42:47That can be more challenging. Okay, but we don't have to we can use our person record. That's fine. Okay
01:42:57You
01:43:09We have more than 10 minutes left, okay, let's take two minutes break, okay, and
01:43:15then we express
01:43:16yen
01:43:17in terms of I was in bracket, okay, and
01:43:21Then we'll try to find out
01:43:24What traditional way of expressing it, okay
01:43:28Five minutes broken. Thank you. Three minutes break. Thank you
01:43:33Okay, how interesting
01:43:37Yep
01:43:39Yeah, oh
01:43:43Okay
01:43:46Three minutes break. Thank you. Yep
01:43:53You
01:43:57All right
01:44:23You
01:44:53You
01:45:23You
01:45:53You
01:46:24All right, welcome back
01:46:38So Iverson bracket, this Wikipedia article is about computer programming, if-then-else statement
01:46:47It's generalization of Kronecker data, okay, Kronecker is a mathematician, okay, so yeah
01:46:56And Iverson, Mr. Iverson is like a computer scientist, okay, he invented the computer-prone language
01:47:05Whose name I do not recall
01:47:09Yeah, professor of computer science
01:47:12Stanford
01:47:14Mr. Professor Donald Knuth, he kind of popularized the idea, okay. Yeah, he's a good mathematician as well, okay
01:47:24Cheers
01:47:27Hmm
01:47:42So using Iverson bracket, it's kind of a short code, okay, but it's legit
01:47:47You
01:47:51Do not very widely accepted notation convention in mathematics, okay, so it doesn't matter
01:48:02I majored in computer science, I did not major or even minor in mathematics, okay
01:48:10Let's go
01:48:14You
01:48:17You
01:48:26Iverson bracket, okay
01:48:33If n row 4
01:48:43Is
01:48:45If n row 4 is less than 3, because we have to group this, okay, 1 and 2, then
01:48:56If that's true
01:49:00Then
01:49:04Multiply minus 1, okay, 2, this one
01:49:16And if n row 4
01:49:31Is, well, let's do this
01:49:38If n row 4 is not equal to 3, okay, then that
01:49:45If n row 4 is equal to 3
01:49:51Okay, then yeah, plus 1, okay, so
01:49:58Okay
01:50:02Multiply by
01:50:09This one
01:50:16You
01:50:18Okay
01:50:21Yeah, there we go
01:50:28Okay
01:50:33It's boolean, okay. Yeah time check
01:50:37Two full hours of mathematics, we do that every now and then, okay. We have less than 10 minutes left, okay?
01:50:52Okay, good enough, okay
01:51:02Okay
01:51:05You
01:51:07Yeah, cheers
01:51:19Yeah, it's like if this is true, this is false. If this is false, this is true, because it's very boolean, okay
01:51:26Binary, okay. Yeah
01:51:35You
01:51:37Can we express this without Iverson bracket?
01:51:43It's possible, but I do not know yet
01:51:51I'm not sure if there is traditional mathematics
01:51:55Without using Iverson bracket, this function. I do not know how to do that yet, but maybe there is
01:52:05Okay
01:52:07Yeah
01:52:35You
01:52:40Well, the equivalent problem would be this
01:52:45If you reduce this by one, okay
01:52:47You
01:53:03It's a very equivalent problem, okay
01:53:17You
01:53:21Okay
01:53:34Then how about this?
01:53:40We want to group this one and two together and single out three, okay, so
01:53:46There is a way to do that
01:53:50If we divide this number by three
01:53:58Okay
01:54:03And then floor it
01:54:06Okay
01:54:10So
01:54:16You
01:54:18Forget about this one, okay, so we don't really need that
01:54:28And divide by three and floor it
01:54:35And then becomes one
01:54:37zero zero
01:54:39Now we successfully grouped this one and two, okay, very good
01:54:43And
01:54:46Then one minus one minus one we got it, okay, it's good
01:54:59So this function g of n is equal to minus one
01:55:10To the
01:55:13You
01:55:19Yeah, we're flipping the sign, right, yeah
01:55:31Yeah, we got it
01:55:37We will have five minutes left, okay, so
01:55:40The e of n without using I was American would be
01:55:53You
01:56:09You
01:56:19Oh, there we go, we got it
01:56:29Tomorrow
01:56:30We'll check this formula. We'll verify making some examples to see if this formula is
01:56:36Correct if there are some errors we correct it
01:56:40Okay. Yeah, I'll see you tomorrow. Okay. Thank you. Thank you. Thank you. Yeah
01:56:44Even I will I digitize this in Zoom software and then upload to Dailymotion and then
01:56:52After that, we'll do Instagram live together, you know, Dailymotion as well. Okay. Yeah
01:56:56Yeah, I'll see you soon or I'll see you in maybe 10 minutes or I'll see you tomorrow. Okay. Thank you. Yeah, good night. Yeah
01:57:03Fantastic