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00:00:00Hello friends, welcome to Human Learning Analogy 2107.
00:00:07Very cool.
00:00:09Let's see.
00:00:30Martial arts. Let's do a jump front push kick, okay?
00:00:46Okay? Good, good, good.
00:00:48Very good, yeah. Five minutes break, please. Thank you.
00:00:52Good exercise.
00:01:00We'll get some water.
00:01:11Ah.
00:01:16Very good.
00:01:45Okay.
00:02:10Okay.
00:02:30Okay.
00:02:59Okay.
00:03:24Okay.
00:03:49Welcome. Happy Monday.
00:03:53Ah, we'll get some tongs.
00:04:12Hello.
00:04:14Yeah. Welcome. Happy Monday.
00:04:16You?
00:04:18Mm-hmm.
00:04:19Yeah.
00:04:21To brighten the Monday, bright color.
00:04:26Yeah.
00:04:28Ah.
00:04:30You need to get some whiteboard, huh? Sure.
00:04:33Okay.
00:04:53Okay.
00:05:13Mm-hmm. Good.
00:05:42Let's erase this one.
00:05:52It's not published, but I don't think it's very difficult concept here.
00:06:02I don't remember. I don't even remember what this is about.
00:06:05It's not published, but I think we can erase this because if we need to,
00:06:10yeah, we can duplicate this. I don't think it's a very difficult concept here.
00:06:13Okay.
00:06:15Let's move on.
00:06:21And in a long time, yeah, we do some geometry a little bit, okay?
00:06:30Yeah.
00:06:59Okay.
00:07:00Yeah.
00:07:02And two people have equal distance.
00:07:05Okay.
00:07:07And I'm a mathematician.
00:07:11I thought, is that possible?
00:07:13What do you think?
00:07:16Well, when there are three people, is this possible?
00:07:20Yeah.
00:07:21Equilateral triangle, okay.
00:07:23Other than that, it's not possible.
00:07:25Let's prove that.
00:07:26Okay.
00:07:27In my head.
00:07:28Okay.
00:07:29It's an easy concept.
00:07:32Well, in three-dimensional fashion, yeah, tetrahedral with four people,
00:07:36but the person should be upstairs, not in the same location.
00:07:44Oh, water.
00:07:46Grab some water.
00:07:47Let me grab some water.
00:08:05Yeah.
00:08:07Cheers.
00:08:11So, I also looked at the biography of Euclid.
00:08:17He's like, he's not very well-known during his time, it seems, okay,
00:08:23because his life history is not very well-known.
00:08:26Okay?
00:08:27Surprisingly.
00:08:32But scholars speculate that he probably learned from Plato's students.
00:08:41Yeah.
00:08:43Yeah, Plato, he emphasized geometry and mathematics.
00:08:47He did, okay, as well as his philosophy, okay?
00:08:51Yeah.
00:08:54But Euclid, I think in his time, he was not well-known at all, it seems.
00:08:59That's what it seems, okay?
00:09:02Because nobody knows too much about him, okay?
00:09:07Yeah, he's a good mathematician, yeah.
00:09:09Don't get me wrong.
00:09:11I just think that it's about time after more than what, he was like 300 BC,
00:09:16like after Plato's time and before Archimedes' time, okay?
00:09:20Yeah.
00:09:21He's a great mathematician, yeah.
00:09:23It's just that it's time to do better than he, that's all, okay?
00:09:30Now, geometry, okay.
00:09:38Okay.
00:09:42Equilateral triangle.
00:09:46Let's say A, B, C.
00:09:50And, yeah.
00:09:54Pick any two people out of three people.
00:09:57Then they have the same distance, right?
00:10:00Yeah.
00:10:01A, B, A, C, C, B, okay?
00:10:05Now, proof by contradiction.
00:10:09Let's say there are four people on this plane.
00:10:13Yeah, not tetrahedron, the three-dimensional, not like that.
00:10:16But in this plane, is it possible to come up with the fourth point where,
00:10:21let's say D, and distance between D and all the others are same as all the others,
00:10:29two people distance, okay?
00:10:32If that's true,
00:10:40that person D, unless the distance is one, you know, okay?
00:10:44Yeah.
00:10:47Then distance between C and D should be one as well.
00:10:51So D must be inside of this circle.
00:11:07Centering C.
00:11:13Why?
00:11:15Because distance between C and D must be one.
00:11:20So, yeah.
00:11:22D must be in this, on the circumference of the circle, centering C.
00:11:27Okay?
00:11:28Yeah.
00:11:30Now, because the distance between D and A and D and B should be the same,
00:11:39D should be either here or here.
00:11:53D.
00:11:55D prime.
00:11:57So that distance between A and D is the same as distance between D and B.
00:12:14Okay?
00:12:18But if this D prime is the location, then the distance between A and D prime is longer than one.
00:12:31So this cannot be true.
00:12:33Now, distance between D and A, that's, again, is smaller than one.
00:12:43Okay?
00:12:45That's why it is impossible to have D in the same plane as A, B, C.
00:12:50D has to be above them, upstairs or downstairs.
00:12:55The fourth point in tetrahedron.
00:12:57Tetrahedron is a three-dimensional object with four dots, four vertices.
00:13:08And how many planes?
00:13:11Four of them.
00:13:13Okay?
00:13:14Yeah.
00:13:15It's like triangular pyramids.
00:13:16Okay?
00:13:17Yeah.
00:13:18You have dot here, D, and then you have the bottom plane and then three triangular side
00:13:25planes.
00:13:26Okay?
00:13:27Yeah.
00:13:28Tetrahedron.
00:13:29It's Wikipedia.
00:13:30Okay?
00:13:31Yeah.
00:13:32So we proved that.
00:13:34Okay?
00:13:36In a two-dimensional plane, the maximum number of people, the maximum number of dots that
00:13:44can have equal length, distance between them, is three.
00:13:49Three or two?
00:13:51In one-dimensional line, yeah, just two.
00:13:54Okay?
00:13:55Yeah.
00:13:56Three-dimensional space?
00:13:59Four.
00:14:01Four points.
00:14:02Then you can have exact distance between any two dots.
00:14:08Maximum?
00:14:09Four people.
00:14:10In a three-dimensional space.
00:14:13Okay?
00:14:14Yeah.
00:14:15And nice and easy, right?
00:14:16Yeah, sure.
00:14:17Okay.
00:14:18It's good to do some geometry in a long time, huh?
00:14:23Sure.
00:14:24Yeah.
00:14:25Okay.
00:14:26Yeah.
00:14:28Yeah.
00:14:31And also, our wonderful friend in Instagram Live mentioned least common multiple, right?
00:14:39Yeah.
00:14:40Yeah.
00:14:41And we are dealing with the greatest common divisor these days.
00:14:44Okay?
00:14:45Yeah.
00:14:46Oh, yeah.
00:14:47In Wikipedia, they are like interrelated.
00:14:49Okay?
00:14:50Sure.
00:14:51Yeah.
00:14:52Cool.
00:14:53Yeah.
00:14:55Yeah.
00:14:56Yeah.
00:14:57Okay.
00:14:58Very cool.
00:15:00You too.
00:15:01Okay.
00:15:02It's a cool story.
00:15:04You're welcome.
00:15:05Okay.
00:15:06Very cool.
00:15:07Okay.
00:15:08Yeah.
00:15:09Mm-hmm.
00:15:10Yeah.
00:15:15You
00:15:45You
00:16:15You
00:16:45You
00:17:15You
00:17:45You
00:17:52You
00:18:04You
00:18:15You
00:18:25You
00:18:33You
00:18:35You
00:18:44So, uh, i'm very sorry about this, uh
00:18:47hurricane in the eastern coast, uh, actually
00:18:50Nashville north carolina i've been to that town is beautiful town and with wonderful people like southern hospitality
00:18:57Okay, I traveled there once and then great time. Yeah, i'm very sorry about that
00:19:03Uh flooding situation
00:19:09Yeah
00:19:12Yeah, but yeah
00:19:14if i'm president I get out I direct scientists to uh
00:19:20come with a way to
00:19:22Neutralize hurricane before you use the land like that's when you salt palm or something in the middle
00:19:29In the eye of hurricane, okay
00:19:31Yeah, okay experiments
00:19:34Okay, yeah the government's funding of course
00:19:38But he will save a lot of money government money, okay
00:19:43Yeah, okay
00:19:47And
00:19:55Let's continue. Okay. Yeah cheers. Yeah
00:20:01Hmm
00:20:06Yeah base 11
00:20:22Um
00:20:31You
00:20:47Okay, 13 26 39
00:20:53You
00:21:00Oops no
00:21:1036 39
00:21:14452
00:21:18This is gonna be tricky, okay
00:21:21Uh
00:21:27Cheers
00:21:38Uh 39
00:21:4852
00:21:51You
00:22:03And 65
00:22:07All right, okay, so
00:22:11Times five
00:22:13You
00:22:20Okay
00:22:30Uh 28
00:22:4142
00:22:43You
00:22:5156
00:22:54Bingo
00:23:11Uh, sorry 45, okay
00:23:24Does sign always alternate
00:23:37Well, what 45
00:23:44Uh
00:23:4730 45
00:23:53You
00:23:58Does that always alternate
00:24:03Not always, okay. Yeah, I don't have to alternate. Okay
00:24:14Okay, good
00:24:19Yeah, cheers
00:24:24Um
00:24:4232
00:24:54You
00:24:56One two, three, four five then I it will start to uh be symmetric, okay, so
00:25:0934 yeah
00:25:1434
00:25:20You see yeah, it will start to be symmetric
00:25:24You
00:25:27Even minus three, okay
00:25:30We proved why it's symmetric, okay. Yeah cheers
00:25:40It's like roll crawl out theorem
00:25:44Result from that. Okay, so yeah 54
00:25:53You
00:26:00Every minus four, okay
00:26:0776
00:26:24You
00:26:35It would be five yeah 100
00:26:42Okay
00:26:45You
00:26:52You minus one
00:27:01Okay, yeah nice
00:27:06Okay, so, uh, yeah, we'll do 12 13 14 and so on and you only do the half of it, okay, so because
00:27:14The other half is just symmetric like palindrome. Okay. So yeah with the opposite sign. Okay, sure
00:27:25Good
00:27:33Mm-hmm
00:27:44Let's take five minutes break
00:27:47It's tedious it is but
00:27:51We got a short cut now. Yeah, we only need to do one half of them. Okay, so
00:27:56Sure, it's not too bad
00:28:08Nothing if you want to work out yourself, yeah
00:28:14I started
00:28:18Just with one line
00:28:23Okay, if you're completely go for it, okay if you want, okay, yeah
00:28:27Okay. Bye miss. Thank you
00:28:29Yeah
00:28:30Yeah, it's nice
00:28:33You
00:28:37That's why I drink alcohol when I do mathematics
00:28:40Well, sometimes because i'm excited out of time because i'm so enjoying it other times. It's kind of boring. Okay, so is the world
00:28:47Okay. Yeah
00:28:48Yeah, bye. Thank you
00:29:02You
00:29:32You
00:30:02You
00:30:32You
00:31:02You
00:31:11So I looked at some wikipedia like more like geometry figures like platonic solids whatnot just interesting
00:31:21Yeah geometry sure cheers
00:31:23Me
00:31:30Let's continue
00:31:45Yeah, we'll just do six of them
00:31:49Booyah
00:31:53You
00:32:23You
00:32:40Interesting
00:32:54It's fun actually
00:33:01Actually, it's four wow
00:33:06It's just easy
00:33:09You
00:33:2117 34
00:33:29Cheers yeah
00:33:33We're looking for multiple of seven that is
00:33:36One less or one more than multiple of 12, okay. Yeah
00:33:43Uh
00:33:4734
00:33:5334 36 34
00:34:0051
00:34:06Uh 48 60, okay
00:34:15Uh 68
00:34:21Okay
00:34:2460 72, okay
00:34:27Uh at 17, okay 85
00:34:33Um
00:34:3612
00:34:3812 times 7
00:34:44Yeah, 84, okay, we got it 17
00:34:50Times
00:34:52Five
00:34:56Plus 12 times minus 7
00:35:03Okay, yeah
00:35:06Uh, one two, three, four five six
00:35:15Okay
00:35:18Just one more, okay
00:35:23Um
00:35:30Six okay. Yeah
00:35:32Yeah
00:35:34It will be minus five, okay. Yeah
00:35:40Okay, that's 90. Okay 96 sure. Yeah
00:35:49Uh
00:35:52Nine 96 or uh 70 uh 80
00:35:59Uh four
00:36:03Uh
00:36:1612 times
00:36:21It is both of them, okay, but um
00:36:24Um
00:36:31So we have minus
00:36:33Of that and then so you should be now into six. Okay, so
00:36:38uh
00:36:3912 times eight, okay
00:36:44Cheers
00:36:54So
00:37:06Ninety
00:37:1084 yeah, there's some problem here because
00:37:19This is actually um
00:37:24Principle pair the when it comes to the
00:37:28Absolute value. This is smaller than that seven is smaller than eight, you know
00:37:33Okay
00:37:36Yeah, there's some issue here, okay
00:37:42Okay, give us a uh dehumidifier yeah, I just empty the water
00:37:54You
00:38:24You
00:38:54You
00:38:58Okay
00:39:08Yeah
00:39:13Well, that's interesting
00:39:19Ah
00:39:24So
00:39:39I'm looking at the other way forward. I'm looking to see if
00:39:45Similar problem exists in other bases. Okay, so
00:39:49Yeah
00:39:51Yeah, cheers. Yep
00:39:58Yeah
00:40:07Okay, we'll put my some more drinks
00:40:21You
00:40:30Cheers
00:40:49Hmm
00:40:52You
00:41:03Um
00:41:21You
00:41:26Well, I don't think it's such a big problem, okay because
00:41:34What we are after is this, okay we want to find some pattern
00:41:41uh, eventual formula, uh for this like a
00:41:45Uh
00:41:47Half first half of less
00:41:50left
00:41:51casual principle coefficients
00:41:54Okay, so the other half yeah, it's kind of symmetric. So it's not that important
00:42:00For our purposes. Okay. Yeah
00:42:06Okay
00:42:09Hmm
00:42:14Yeah, cheers, yeah, but it's interesting though, yeah, it's good that we
00:42:21Found this
00:42:24Yeah, cheers
00:42:30Hmm
00:42:36Okay
00:42:38Yeah
00:42:42But let's move on okay, yeah because we gotta we are long way to go, okay
00:42:52Yeah, like 13 14 15 16 17 18 19
00:42:5620 right
00:42:58Uh, we don't have to do it to all that stuff tonight
00:43:03All right, but uh, we do need to make some
00:43:06Progress there. Yeah
00:43:10Yeah, we may continue tomorrow, you know
00:43:13Yeah, it's been less than one hour. Okay, bye. Okay. Thank you. Yeah
00:43:25There we go, thank you
00:43:36You
00:44:03But
00:44:06But
00:44:22Yeah
00:44:36You
00:45:06You
00:45:36You
00:46:06You
00:46:17You
00:46:36You
00:46:42Yeah
00:46:56Yeah, so I took a shower yeah shower is so good yeah, I enjoy that yeah, okay
00:47:06Like this that switch, you know
00:47:09Okay
00:47:15Serious yeah
00:47:21Always happy always smiling laughing. Okay. Yeah
00:47:33Okay, let's go to start him
00:47:36Ah
00:48:01You
00:48:06You
00:48:0915
00:48:12Uh
00:48:15Maybe that's easier way. Okay, uh 15 is equal to uh
00:48:2313 plus 2. Okay, and we want to find uh, the multiple 15
00:48:31uh
00:48:32Such that uh, it would be one more or one less than a multiple 13
00:48:39Okay
00:48:50Okay
00:48:55So maybe we just deal with two
00:48:58Oh
00:49:00Instead of 15, okay
00:49:06Uh
00:49:10Multiple of two
00:49:14Being one more or one less than multiple 13, okay, how about
00:49:22Uh
00:49:25Six
00:49:28Yeah, yeah six times two twelve one less than 13, okay
00:49:40Uh, so
00:49:42But that's quite a little
00:49:4515 times
00:49:486
00:49:5090
00:49:54Right
00:49:56Multiple of 13
00:50:01Cheers
00:50:0891
00:50:1113 times 7
00:50:15Sure
00:50:16Now is there a number that's smaller than six though? Okay, let's let's look at it. Okay, so 15
00:50:26Uh
00:50:2930
00:50:3145
00:50:34Uh 39, uh
00:50:3839 and uh 52
00:50:45Okay
00:50:47Okay, then uh 60
00:50:51And next one will be 65
00:50:54Uh, yeah multiple 13 multiple 15, okay. Yeah, then you have 75
00:51:02And you have uh
00:51:0578
00:51:10Okay
00:51:16And then 80
00:51:24And then 91
00:51:39I'm sorry
00:51:4190 okay
00:51:45Yes, it looks like our method method worked
00:51:50Okay, cool
00:51:53So 50 times
00:51:59Uh
00:52:01To make it 90. Yeah six
00:52:07Well, we minus six
00:52:11Plus 13 times
00:52:14Uh
00:52:16seven
00:52:19All right
00:52:22Okay
00:52:27I think that's the most number
00:52:31Yeah here you leap from one to five here you're leaping from one to six so yeah, it's not unprecedented
00:52:38Okay. Yeah
00:52:40Okay. Okay. So now we have a method that
00:52:44That works good
00:52:47Yeah, we're getting better at it
00:52:50We need to take up something something brand new, okay. Yeah. Cheers. Yeah using the power logic, okay. Yeah
00:53:06Using the same methodology
00:53:20Okay
00:53:22Uh 16 is equal to
00:53:2513 plus 3 now
00:53:29Find a multiple of 3
00:53:32Which is one less or one more than multiple of 13. Okay. Yeah 12
00:53:38Okay, yeah
00:53:45So
00:53:47Yeah
00:53:49Uh
00:53:53Yeah, 12 is 3 times 4, okay, yeah 16 times 4
00:54:00Uh 64, okay
00:54:07Uh
00:54:10And um
00:54:1313 times 5 65. Okay, so it works
00:54:17Okay, there will be minus 4
00:54:26Okay
00:54:28Now is there a number less than that? Well, let's look at it 16 32
00:54:35Uh
00:54:3748 that's 64. Okay, and 13
00:54:47No, this is smallest one good very cool
00:54:54Awesome
00:54:59Yeah, cheers, yeah very good
00:55:07Then actually we can come up with a formula
00:55:11Without making more examples
00:55:14How cool is that
00:55:20You don't come with formula go for it, okay. Yeah
00:55:28Now now we discovered this after working up these examples, right? Yeah, so, uh
00:55:36Now we know what mechanism is behind this
00:55:44Hmm
00:55:48Nice so we don't have to make any more examples
00:55:53Example is induction, right?
00:55:55It's easier than deduction in many times many cases
00:55:59Now we'll do this deduction because we understand what's going on
00:56:04Yeah
00:56:05Induction making a lot of examples deduction. Uh, if you understand what's going on behind the scene that's deduction
00:56:13Okay, it's good time to do this option
00:56:16Okay, uh unified formula
00:56:19Principal left best coefficient go for it. Okay
00:56:25Okay, yeah progress. Okay. Thank you. Yeah now we know what's going on
00:56:33Yeah, fantastic
00:56:39Okay, there we go, thank you
00:56:43Yeah
00:56:45nice
00:57:13You
00:57:43You
00:58:13You
00:58:39You
00:58:43You
00:58:54Okay, welcome back we are back
00:58:59How nice great progress here
00:59:03Yeah
00:59:06So we paid off right yeah all this hard work
00:59:09legwork
00:59:11tedious laborious job
00:59:14Yeah, very worthwhile. Yeah. Cheers. We found it. Okay
00:59:20Hmm
00:59:25Yeah
00:59:29So
00:59:30uh
00:59:32Wikipedia about article about polyhedron. Okay. This is quite lengthy article. Okay, so
00:59:39Um, it does have some application to other branches of science to like chemistry like
00:59:47Ammonium iron ammonia iron. Okay, so
00:59:50Yeah, it's just
00:59:52Tetrahedral. Yeah, sure some chemistry. Yeah
00:59:56Cheers
01:00:02So
01:00:09I mean
01:00:12Mathematicians they study those things that
01:00:16At first
01:00:17Look, it doesn't seem very important
01:00:21Okay, so mathematics it's like other science branches. Okay. Well a little bit more so
01:00:28Well, it's driven by intellectual curiosity
01:00:31Okay
01:00:33Uh, look there's a coefficient not many people study this
01:00:38Okay
01:00:40Not very well-known well studied area. Yeah. Okay. Yeah
01:00:46It's like gold mine, okay, so yeah, sure
01:00:52Hmm
01:00:55Yeah
01:00:58Yeah, i've seen some web pages informal web pages, uh talk about talking about uh, there's coefficients but uh
01:01:06Not this one though
01:01:08This one was like a branding discovery
01:01:11Okay
01:01:12So some narrative mathematics, it's like this. It's god created mathematical universe like long time ago. It's true
01:01:20truth
01:01:21We're just as human beings. We're discovering it as mathematicians
01:01:26but
01:01:28This has always been true
01:01:31Since the beginning of the universe
01:01:34Okay, yeah
01:01:36It's just discovering it we are not making this up
01:01:41This went through full time
01:01:45Uh with
01:01:47God gave us great honor and privilege to discover this for the very first time in human history
01:01:55Okay, yeah cheers, yeah, welcome to human
01:02:06Has somebody discovered this before uh, it's possible, but I doubt it. Okay. Yeah because
01:02:13If it has been discovered, yeah, probably it will be in your wikipedia because this is very significant. It's
01:02:19Extraordinarily beautiful too. Okay. Yeah
01:02:23Yeah
01:02:26Yeah, seriously
01:02:28Yeah
01:02:32Of course jazzy guy right nicely dressed up and doing mathematics alone
01:02:40Monday evening
01:02:45Good times
01:02:47Yeah
01:02:55Oh, yeah
01:02:58Yeah
01:03:02So, uh time check
01:03:10It's been more than one hour, okay, so, uh, let's uh,
01:03:13Wrap up with this episode. Okay. Let me digitize this and i'll look into this
01:03:18a little bit more
01:03:19during the digitization and
01:03:22After that, we'll go to instagram live. Okay, because we didn't know
01:03:26Okay, what tonight okay, yeah five or ten minutes bro, okay. Yeah. Thank you. Yeah. Happy monday. Yeah
01:03:34Very productive. Yeah, nice