• 3 months ago
Transcript
00:00Hello friends, welcome to Humanize 2084. Happy Monday.
00:12Ah, whatever.
00:15Okay.
00:25Let's see.
00:26Okay.
00:29Let's do exercise.
00:37How about knee exercise, huh? Yeah, sure.
00:40Ah, ah, ah.
00:55Okay, good enough.
00:57Five minutes break, please. Thank you.
01:10Good.
01:40Five minutes break.
02:10Five minutes break.
02:40Five minutes break.
03:10Five minutes break.
03:40Five minutes break.
04:10Five minutes break.
04:40Five minutes break.
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06:10Five minutes break.
06:40Welcome to Humanology.
07:06Welcome to Humanology.
07:12Yeah.
07:14So I noticed that Dailymotion
07:16maybe system upgrade
07:18their webpage is not
07:20available.
07:22Yeah.
07:24Hopefully
07:26it get resolved soon because I cannot
07:28access their webpage.
07:30Okay, so.
07:32Yeah, hopefully it get resolved soon
07:34so I can upload this to Dailymotion.
07:36Yeah.
07:38Okay.
07:40Happy Monday.
07:42And
07:44Mathematics, I kind of thought about it.
07:48Yeah.
07:50By the way, during the lunch time
07:52I typically run.
07:54I don't run like this.
07:56Underneath, I have T-shirt
07:58and short pants.
08:00So that's what I run with
08:02After that,
08:04after my body cool down, I
08:08put all this back on.
08:14Yeah.
08:18Yeah. Happy Monday.
08:20Yeah.
08:22Let's get back to Mathematics.
08:26Okay.
08:32I thought about it.
08:38Okay.
08:46We
08:48probably need another whiteboard but
08:50for now,
08:52let's use
08:54this little space here.
09:02Here.
09:08And here.
09:12Okay.
09:14So the applications.
09:16Hmm.
09:30Hmm.
09:46Hmm.
10:00Cheers.
10:06Hmm.
10:16Hmm.
10:24Hmm.
10:32Hmm.
10:38Hmm.
10:40we need to prove this okay
10:56we have an easier case
11:08n is 2 okay
11:26oops
11:56um I do not know whether this kind of equation already has been discovered or
12:03not I don't know okay let's check
12:12in the internet okay yeah because it's not a very very difficult equation right
12:19so who knows maybe somebody will discover that prove it right
12:45you're doing the ceiling function
12:49you
13:08uh let me start thinking a little bit okay yeah let's enjoy this
13:19you
13:43okay there's some whiskey
13:49you
13:58yes
14:19Yeah, maybe some of these properties may be useful, okay?
14:30It's possible.
14:31Potion?
14:32Yeah, we'll come dealing with that.
14:34Do you see this?
14:40Isn't it what we have?
14:48It kind of looks like what we have.
15:01Huh?
15:32Very similar.
15:40But not exactly the same.
15:42But we may be able to use this, okay?
15:47You see this?
16:17Okay, we have another potentially useful one here.
16:45Something that might solve us, you know?
16:54Yeah, mild operator, yes.
17:19Unsolved problem.
17:27Okay, so let's write down two equations that might help us, okay?
17:34It's good that we are checking this, okay?
17:37They don't have the exact same formula as we do, so it could be a brand new discovery.
17:42But, okay, so let me write it down.
18:12Yeah.
18:36Yeah, Professor Donald Knuth.
18:40He was a mathematician as well, yeah, of Stanford.
18:45Okay.
18:48Yeah, I bought his books, though I didn't quite study.
18:53I like him quite a bit, yeah.
19:01Although I don't always agree with him.
19:05Cool, Donald Knuth.
19:21Yeah.
19:51Okay.
19:59Okay.
20:05Okay.
20:07Very cool.
20:08Let's take five minutes break, okay?
20:10And then let's see if we can use this.
20:14What's like this one, okay?
20:17Yeah, sure.
20:20How interesting, huh?
20:33Okay, five minutes, okay?
20:35Wow.
20:37That's cool.
20:42Okay, very cool.
20:47Yeah.
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24:39So, cheers.
24:42According to this formula...
24:58What you are saying is, this is MS?
25:20Yeah, that is correct, ok, ok, so it's good, it's, basically we proved it, ok, based on
25:43this one, ok?
25:44Good, good, good.
25:45So it's kind of corollary of existing theorem, ok, it's easily derivable from what's already
25:52known.
25:53Ok, so our discovery, although it's new, it's not too new-new, ok, ok, no problem, that's
25:59fine, cheers, yeah.
26:10Now let's try to understand why this is the case.
26:22That's not obvious at all.
26:29It's good time to create a brand new iPod, ok, yeah, yeah, but we got it, ok, yeah, sure,
26:41so that we can move on, you know, yeah, nice, yeah, cheers, and let's take 5 minutes, ok,
26:49and I create a new iPod, ok, yeah, cheers, mmm, excellent, ok, yeah, yeah, yeah, yeah,
26:59yeah, yeah, Prof. Donald Kluse was on Stanford GS, never met him, ok, but I guess we're getting
27:08help from him, sure, that's cool, yeah, I like it, ok.
27:135 minutes, thank you.
27:17Yeah, he's a good mathematician, yeah.
27:27Capra Sanctus.
27:30Okay.
27:47Okay.
28:15Okay.
28:45Okay.
29:13Okay.
29:18Okay.
29:43Yeah, now we can move on.
29:49Good.
29:50That's good.
30:03Okay.
30:08This wiper is very heavy.
30:12Good.
30:18It's like weightlifting.
30:23Yeah.
30:30Yeah, that's like something very large plus transformation or something.
30:36Yeah, that was studied a long time ago.
30:39True.
30:40Earlier this year, I think.
30:42Yeah.
30:43I mean, we might have parts of the project.
30:46It's very educational.
30:47We learn different parts of mathematics, like Fourier transform, Laplace transform, and stuff.
30:54Yeah, so it was nice.
30:57Yeah.
30:59Earlier this year, right?
31:06Okay.
31:10Beautiful whiteboard.
31:11Brand new.
31:13Relatively.
31:35Okay.
31:37So, let's try to understand why this is the case, okay?
32:06That's nice.
32:07Yeah, I'm glad that they found this.
32:10Otherwise, I...
32:14Yeah, the proving is very trivial, okay?
32:16Yeah.
32:17Cheers.
32:18Yeah.
32:31Let's make some example.
32:38Let's say...
32:43Okay, that's 0.5 plus...
32:48This is 2 over 3.
32:57Well, special case.
32:58Let's make it easy.
33:14Okay.
33:31Okay.
33:43Yeah.
33:51That part is easy.
33:54Cheers.
33:58That's when n is 1, okay?
34:01Special case.
34:09Yeah.
34:15But what's not obvious at all is that when n is not 1, when...
34:27Yeah, m and n, they're both integers, okay?
34:30Well, let's say positive integers for now, okay?
34:33So...
34:39So, we need to understand why this is the case.
34:45Yeah, cheers.
34:54Let's see.
35:00X, 0.5, m, 1, n, 2.
35:21Okay.
35:24Now...
35:49Mm-hmm.
35:53It works out magically.
36:20Well, we know...
36:39We know that much, okay?
36:40Yeah.
36:44That's obvious.
36:45Now, from here, we need to prove this, okay?
37:16Which is easy, actually.
37:23Given this, okay?
37:37Well, actually, it's not that obvious, huh?
37:39Okay, okay, okay, okay, okay, okay.
37:46Ah, it's not that obvious, huh?
38:00Well...
38:08Cheers.
38:26Because ceiling function is...
38:27You cannot distribute, like, upstairs, downstairs, you know?
38:34Or can we?
38:36I doubt it.
38:42I don't think so.
38:43Okay.
39:12Yeah.
39:43Now, let's go back to that Wikipedia, okay?
39:51Yeah.
40:07Looks like they wrote a book together.
40:24What book did they write?
40:28I don't think I'm going to buy that book, though.
40:46There's some Internet outage.
40:53My apologies.
40:54Yeah, Internet was out briefly, so hopefully I didn't lose any footage.
41:00Well, it happened before, but we'll just continue, okay?
41:05Yeah.
41:09Yep.
41:26Well, yeah, hopefully we didn't lose any footage, okay?
41:29And I don't know what time we started.
41:32So how about this, okay?
41:35Let's restart it, okay?
41:36To be safe, okay?
41:37Yeah.
41:38Yeah.
41:39See you soon.