Bidang riset saya adalah tentang coding theory. Secara singkat, teori ini membahas tentang bagaimana cara mengkodekan (encode) suatu pesan menjadi sinyal, sehingga katakanlah sinyal ini diganggu oleh noise, maka penerima akan tahu bahwa sinyal ini telah diganggu oleh noise. Bahkan, ada juga cara pengkodean, sehingga sinyal yang telah diganggu ini tetap bisa diterjemahkan (decode) menjadi pesan yang awalnya diinginkan.

Keliatannya kompleks? Ya, memang. Apalagi buat first year student seperti saya. Dasar yang dibutuhkan adalah aljabar abstrak (seperti group, ring, field *maaf ga tau bahasa indonesianya*) dan buat saya sebagai first year student, ya saya belom belajar lahh!

Catatan: Pengenalan pertama abstract algebra (group) itu pada semester 3, sedangkan Coding Theory itu sendiri diajarkan di NTU sebagai elective, tapi pada year 3/4. *mati*

Lah, ngapain ngambil ribet-ribet kalo gitu? Emang ga ada research lain apa?

Soalnya research yang lain itu gak menarik. Sebenernya saya pengen research game theory (awalnya), cuma professor yang ahli game theory-nya sedang benar-benar sibuk (banyak student di bawah dia), sehingga dia terpaksa menolak saya atau saya memang ditolak mentah-mentah. Jadi saya cari professor lain yang katanya senior juga bagus, jadi deh research coding theory. Professor lain di divisi Matematika sendiri kebanyakan researchnya tentang hal-hal yang lebih absurd lagi, jadi jauh-jauh deh. Coding theory saja sudah terdengar agak alien, meskipun keren. Mudah-mudahan level gaul gue naik satu.

Oke, kembali ke masalah, intinya, background saya sangat lemah di sini. Bisa dibilang, saya belajar benar-benar dari nol. Back to square one. Hampir sih, nggak bener-bener nol, soalnya ada beberapa hal yang bisa dianalogikan dengan pengalaman saya di olimpiade matematika.

Di sini, saya mulai dengan gak sabar, mencoba mencerna definisi-definisi baru. Definisi ini, mudah. Itu, mudah. Teorema ini, gampang. Iya, benar. Cepat sekali semuanya itu dibaca… Sampai stuck di satu teorema. Itu benar-benar bikin depresi. Ada teorema baru, tapi saya ga dapet feel-nya untuk teorema itu. Gak make sense rasanya. Buktinya juga sulit banget dipahami *lebay*. Rasanya saya benar-benar dibodoh-bodohin sama matematika ini.

Flashback dikit. Dulu, saya sempet ngajar, dan ngebantuin temen-temen yang lain. Sometimes, rada kesel juga kalau untuk ngajarin suatu cara untuk ngerjain soal. Paling gampang, permutasi-kombinasi deh. Itu kan benar-benar mikir, dan saya suka pusing 7 keliling untuk menjelaskan hal yang ini, karena emang ribet kalo ga dapet insight-nya. Dan sekarang saya disentak lagi. Kayak ditampar, cuma gak berbekas di pipi. Berbekas di hati. *galau*

Pada akhirnya, saya sadar kalau saya terlalu cepat; terlalu cepat melangkah ke teritori yang tak terjamah. Saya cuma membaca, tidak melakukan. Ini kesalahan fatal saya. Mathematics is not a spectator sport. You have to be involved in it. And I’ve been reduced to be a spectator, and only a spectator. Nothing more, nothing less. Ini fatal banget. Akibatnya, saya hilang di tengah jalan, entah ke mana. Karena saya gak dapet feel-nya. Kenapa gak dapet? Karena saya hanya membaca, tapi tidak terlibat. Dan saya sadar, saya harus menolkan diri saya dulu, sebelum masuk ke tempat yang baru ini.

Dan mulailah saya untuk menolkan diri. Semua definisi mulai dibaca perlahan-lahan tapi pasti. Kalimat demi kalimat, saya coba teliti. Saya mencoba untuk tidak mengabaikan hal-hal yang trivial, yang obvious. Saya tetap coba baca, saya lakukan sendiri kalau saya tidak yakin, dan mencoba kembali berlatih. Rasanya sudah lama banget saya gak latihan soal. Because I’ve been reduced to be a spectator and only a spectator. I feel grateful that I realized this soon.

Di sini, saya bisa bilang, research benar-benar bisa disebut research dalam kesempatan ini. Karena saya benar-benar mulai mencari ulang, apa itu matematika? This is what I called, researching and rediscovering mathematics.

Ketika saya mulai latihan dan mengerjakan soal-soal di bidang baru ini, saya merasa kalau saya memang belom dapet feel-nya. Mudah-mudahan dalam waktu dekat, saya dapat pencerahan, sehingga soal-soal di bidang yang baru ini (abstract algebra) dapat saya selesaikan.

Saya teringat blog post dari Terrence Tao. Buat yang nggak tau, Terrence Tao itu peraih medali emas termuda di IMO, pada umur 13 tahun, di IMO 1988, Australia. Sekarang beliau menjadi professor di UCLA, California. Beliau bilang, kalau pembelajaran matematika itu bisa dibagi menjadi 3 fase:

1. Fase pre-rigorous. Ini artinya, pembelajaran matematika tidak didasarkan pada definisi formal dan bukti-bukti yang rigorous, tapi lebih ditekankan pada intuisi.
2. Fase rigorous. Di mana, seorang student di-expect untuk belajar matematika dengan definisi-definisi formal, dan bukti-bukti. Kebanyakan, peralihan dari fase 1 ke fase 2 adalah yang berat bagi para student.
3. Fase post-rigorous. Di mana seseorang sudah dilengkapi dengan definisi rigorous dan bukti-bukti, dan berusaha untuk meng-improve intuisi yang didapat di fase pre-rigorous. Biasanya fase ini yang bisa dapat insight-insight bagus dalam mengerjakan soal.

Dalam matematika olimpiade, bolehlah dibilang saya sudah sampai fase tiga, karena olimpiade memang butuh insight-insight yang seperti itu, dan juga karena definisi-definisi dan teorema-nya tidak terlalu berat =)). Makanya, saya jadi besar kepala ketika masuk ke dalam bidang yang baru, karena saya menyangka saya sudah sampai fase 3 juga. Saya merasa bisa mendapatkan intuisi untuk mengerjakan soal, padahal fase 0 saja belum lewat. Seperti yang saya bilang, ini benar-benar ajaran yang baik untuk saya.

Bisa diambil kesimpulan, selalu ingat kalau kita harus mulai dari 0 pada awalnya. Tidak bisa kita mulai dari 1, 2, 3, atau bahkan . Harus dari 0. Kita semua harus humble dalam memulai sesuatu. Terutama saya.

Jadi, gimana rasanya ditampar di hati?

PS: Kemarin saya baru ketemu professor saya, untungnya so far so good. Dan karena kebiasaan saya mumbling “eto…” (bahasa Jepang, artinya kurang lebih ’let’s see’, iya bukan sih?) ketika lagi mikir, si professor nyangka saya bisa bahasa Jepang. Bisa kok, kalo cuma baka baka baka doang saya bisa. Konichiwa, und arigatou!

(versi tl;dr: FREAK LU, WANGSA!)

Anak-anak punk memang menjadi hot issue di Indonesia beberapa minggu belakangan ini. Dimulai dari penangkapan sekelompok anak-anak Punk di Aceh yang sedang asyik menonton konser oleh otoritas setempat, mereka semua ditangkap dan diberikan pelajaran moral dan siraman rohani oleh otoritas tersebut. Tujuannya, agar mengembalikan mereka ke jalan moral yang benar (setidaknya menurut pemerintah Aceh) dan tidak tersesat di dalam jalan punk. Kalau kalian mau tahu lebih lanjut, silahkan googling ya

Pertama-tama, asumsi saya di sini adalah punk bukan merupakan anggota publik yang hobi mendengarkan musik punk. Punk yang saya maksud di sini adalah sebuah gaya hidup, bukan sebagai pendengar musik. As quoted here,

“The presence of punks bothers the general public,” he said. “They are involved in theft, brawls, attacks and assaults in Banda Aceh and Aceh Besar. They are criminals. Their actions are against Acehnese culture and violate Islamic Shariah law.”

Jelas bahwa terjadi sesat pikir generalisasi di sini. Saya pura-pura tidak melihat kalimat terakhir. Di lain sisi,

“Punk kids are not criminals. We detest the stigma that has been laid on us,” he said, adding that Banda Aceh was home to more than 100 members of different punk communities.

Opini awal saya atas berita di atas? Terpecah.

Di satu sisi, saya tidak setuju atas paksaan re-edukasi oleh pemerintah Aceh. Menjadi punk adalah hak mereka, pilihan mereka. Ini adalah poin yang juga dikemukakan oleh beberapa komunitas punk lainnya, bahkan sampai ada dukungan dari komunitas punk di Rusia dan Amerika Serikat. Mereka mengatakan bahwa agar punk di Aceh terus berjuang untuk mengedepankan hak-hak mereka di hadapan pemerintah yang represif, seperti Aceh. Saya membayangkan proses penangkapan punk-punk, seperti membayangkan penangkapan kriminal. Hey, mereka bukan kriminal, itu pilihan mereka. Karena inilah, ada yang memandang penangkapan mereka sebagai pelanggaran HAM.

Di lain sisi, kalau kita melihat kenapa mereka menjadi punk, bisa dikatakan sebagai hasil chain of events, yang saya percaya awalnya terjadi ketika mereka tidak dididik dengan baik. Saya rasa ada sebagian dari mereka yang putus sekolah, dan akhirnya tinggal di jalanan. Posisi pemerintah di sini adalah sebagai pendidik yang mendidik rakyatnya. Pilihan mereka untuk menjadi punk, saya rasa tidak dipikirkan dengan masak-masak, karena mereka kurang beruntung dibandingkan kawan-kawan mereka yang bisa mengenyam pendidikan. Ditambah lagi, stigma masyarakat di sana menyatakan bahwa mereka adalah kotor dan harus disingkirkan.

Dan akhirnya saya melihat sesuatu, bahwa ada 2 masalah di sini, yaitu

• stigma masyarakat tentang punk sebagai komunitas yang harus dijauhi, dan
• reedukasi yang sebenarnya perlu dilakukan atau tidak.

Stigma yang negatif di mata masyarakat ataupun kepolisian, memicu penangkapan punk-punk ini. Idealnya, tidak boleh ada prejudis yang terjadi di masyarakat. Tapi, judging a book by its cover sudah menjadi hal yang dasar bagi setiap manusia. Setiap orang punya prejudis masing-masing, tapi hanya orang bodohlah yang mengemukakan itu di depan publik. Dan ketika kita mulai berinteraksi dengan orang-orang, prejudis itu perlahan-lahan hilang. Sebaliknya, ketika kita terus mengasingkan diri, prejudis dan stigma semakin kuat, dan timbullah insiden, seperti dalam kasus ini.

Masalah reedukasi, saya mengembalikan kepada opini saya yang masih terpecah. Masalah ini merupakan konflik kepentingan 2 hal, antara hak asasi manusia, dalam hal ini punk-punk yang menjadi korbannya, versus kepentingan dan kewajiban pemerintah dalam mendidik rakyatnya. Jujur, saya tidak memihak kedua pihak dalam masalah ini; keduanya benar. Tapi yang saya takutkan adalah apabila pemerintah pergi lebih jauh dari mendidik, dan malah menjadi bersifat represif. Di lain sisi, ketika HAM terus-terusan diutamakan, maka konflik antar hak setiap manusia jelas terjadi. Kita butuh keseimbangan antara 2 hal ini.

Bagaimana pendapat Anda? Isikan dalam poll di bawah ini.

Kembali ke awal berita yang saya lihat: apabila proses penangkapan punk-punk ini menyebar ke seluruh daerah di Indonesia (kita sudah melihat Kepulauan Riau sebagai contoh), maka bukan tidak mungkin yang saya takutkan terjadi. Pemerintah pun mulai bergerak dengan agresif, dan mulai menangkapi siapapun yang dirasa tidak pantas di pandangan publik. Bukan tidak mungkin, kita akan kembali ke jaman Soeharto, ketika tato menjadi sasaran tembak.

Pada akhirnya, kita cuma bisa berharap agar prejudis tidak terus tumbuh di masyarakat, dan stigma negatif atas beberapa komunitas bisa menghilang. Dengan demikian, masyarakat bisa tumbuh dan terus maju. Kalau tidak, lebih baik saya kabur ke Singapura saja.

Bagaimana pendapat Anda?

Saya adalah seorang pelajar di Nanyang Technological University, Singapura. Saya memilih Mathematical Sciences sebagai major saya, disebabkan oleh hanya satu alasan: saya hanya bisa matematika. Kalau saja ada major seni, saya mungkin akan mengambilnya, karena The Art of Doing Nothing adalah keahlian saya.

Sedikit peringatan: saya adalah orang yang sangat sinis dan penuh dengan sarkas. But I usually leave these comments inside my mind, but beware that I could use them in my writings. Jadi saya minta maaf terlebih dahulu ya?

Kurang lebih isi blog ini, seperti yang saya sudah katakan, sebagian adalahrefleksi kehidupan. Sometimes, mungkin saya menaruh hal-hal random. Yah, mari kita lihat saja nanti.

I am not a good writer, but hopefully these writings is readable (obviously, doh) and could be beneficial to you as the reader.

Regards,

Ivan Wangsa.

We had to get up early and go to the first excursion. We’re going to Den Haag.

First, was the long bus trip. Although it wasn’t as long as from Bremen to Wangerooge, it is still long, approximately 60 kilometres.

Then we got off to Den Haag, and Paul led us in Den Haag. To my surprise, we left most of the teams there, so we’re on our own. I was really worried we’re going to got lost, forgetting that we had Paul!

It was a short, nice stroll, deviating the main route, to see beautiful bridges and buildings. We even see another Indonesian restaurant there. Then we got back to meet some of the teams, which is waiting outside the Escher museum to open.

Escher in het Paleis is a museum dedicated to M.C. Escher, which uses a building which was a former Winter Palace of Queen Mother Emma of the Netherlands. This unique combination surprised me. The museum was small, and makes my mind confused, because Escher’s art is somewhat goes with the concept of infinity and impossibility. Take a look at this:

or this:

To be frank, I’m a little bit dizzy there. But his arts are beautiful, and considering they were made from carved wood, or maybe pencil sketch (I forgot what phrase they do to describe it), it’s just crazy, considering, for example, the latter picture, which is very, very intricate.

There was also a photo booth to take the picture. But, the result will be distorted from the original photo; the left side will be looked bigger, and the right side will be looked smaller. We tried this, and I’ve been trying to find the photograph. I’ll scan it and upload it here as soon as possible. It is really funny.

Then we got out, and we took a walk in Den Haag. Seeing the Parliament building, and then going to Madurodam, Netherlands’ smallest city. It was a miniature city, and it was really complex. They are scaled 1:25 to the real buildings. There are, for example, Utrecht train station, Amsterdam Airport Schiphol, the Vredespaleis in Den Haag, and many other buildings, from old to new. Even Unilever building is there.

I was even more impressed by the fact that the buildings are made to cope up with Dutch’s unpredictable weather; sometimes sunny and sometimes rainy. Those buildings could stand for 30 years, and they are maintaining it. There was, even, small miniature people to made the city more lively. And when I was visiting Madurodam, there was people maintaining some of the buildings, and placed the small people to the ground. Now I wish I could photograph that.

Then we went to the beach. It was really windy and cold. And there was people swimming and even wore bikinis. Maybe this is the new definition of Dress to Kill. I don’t even dare to move my hand out of my pocket for a few first minutes. Not for long though.

We choose to build something, made from sand, on the beach, along with almost all of Indonesian team. And that turned out to be, somewhat, good.

And Paul’s sleeping on the sand. We took a picture of him secretly, and I will upload it, along with the rest of all my pictures in my camera.

Then we took a bus ride back to Novotel. Really tiring. And what greet us at Novotel, is my score:

P1 P2 P3 P4 P5 P6
* – 1 – 0 – 7 – * – *

Where * is the undetermined score, yet. Tomorrow the scores for problem 1, 5, and 6 will be revealed. Fingers crossed.

I was really tired, because of the excursion. And I had to go (along with almost the rest of Indonesian team) to a lecture titled

Optimizing trips, trains, and tracks

In optimizing trips, there were 1 problem posed: How to find the shortest path from one place to another, which could be determined by Dijkstra’s algorithm, and the traveling salesman problem. Here, I quote the problem statement from Wikipedia

We denote by messenger problem (since in practice this question should be solved by each postman, anyway also by many travelers) the task to find, for finitely many points whose pairwise distances are known, the shortest route connecting the points. Of course, this problem is solvable by finitely many trials. Rules which would push the number of trials below the number of permutations of the given points, are not known. The rule that one first should go from the starting point to the closest point, then to the point closest to this, etc., in general does not yield the shortest route.

which is still a hard problem to do (no algorithm known yet).

The second topic was about the lecturer’s experience to create a train timetable for Dutch’s complex train system. With several rules and given travelling time between stations, and also the given transit time between 2 trains, all of these conditions given by the Dutch railway company must be satisfied with the timetable that would be constructed by mathematicians and programmers.

The third part was about Sam Loyd’s problem about trains. I’ll give you the video for you to enjoy

Well, that’s it from now. Sorry for delaying the updates, the excursions are just too many, I have little time to update my blog. I am still suffering jet flag from Amsterdam, and as such unable to write long posts, as my head is still somewhat dizzy.

I’m signing off from Jakarta, Indonesia.

No post for today. LOL, just kidding. Anyway, today is the day two of the contest, and what I’m expecting is an easy (or medium) geometry problem, because we haven’t had any geometry problem on day 1.

We start the day early, although we are going to go to the contest hall at 8 am, 30 minutes later than yesterday’s time. Breakfast was always the same, so no big deal there. Sun really shows its job today. It was really sunny, so it was hot. But it’s still windy, so it feels kinda weird. 8 am, we went to the contest site. No high hopes today, after yesterday’s disastrous problem.

Well, not really, because I’m still hoping for an easy/medium geometry. So how’s the problem?

Problem 4. Let $$n > 0$$ be an integer. We are given a balance and $$n$$ weights of weight $$2^0, 2^1, cdots, 2^{n-1}$$. We are to place each of the $$n$$ weights on the balance, one after another, in such a way that the right pan is never heavier than the left pan. At each step we choose one of the weights that has not yet been placed on the balance, and place it on either the left pan or the right pan, until all of the weights have been placed.
Determine the number of ways in which this can be done.

Problem 5. Let $$f$$ be a function from the set of integers to the set of positive integers. Suppose that, for any two integers m and n, the difference $$f(m) – f(n)$$ is divisible by $$f(m- n).$$ Prove that, for all integers $$m$$ and $$n$$ with $$f(m) leq f(n)$$, the number $$f(n)$$ is divisible by $$f(m).$$

Problem 6. Let $$ABC$$ be an acute triangle with circumcircle $$Gamma$$. Let $$ell$$ be a tangent line to $$Gamma$$, and let $$ell_a, ell_b$$ and $$ell_c$$ be the lines obtained by reflecting $$ell$$ in the lines $$BC$$, $$CA$$ and $$AB$$, respectively. Show that the circumcircle of the triangle determined by the lines $$ell_a, ell_b$$ and $$ell_c$$ is tangent to the circle $$Gamma$$.

One comment, when I saw the problem, is:

Why, oh why, combinatorics was put in problem 4? And, why geometry on number 6? This couldn’t go any worse, definitely. This IMO sucks, doesn’t give Indonesian any advantages at all. 2 combinatorics problem in a single IMO is something that hasn’t ever been done since 2002. It’s been 10 years that 2 combinatorial problems appeared. I hate combinatorics, and only one time I’ve experienced worse, which is at 2010 Zhautykov Olympiad (they have 3 combinatorial problems!)

This couldn’t go any worse, definitely.

That statement was wrong. It did go wrong horrendously. I thought that combi number 1 should be the easiest one, and so I look for easy recursions (first thing that came to my mind is recursion). However, instead of the easy recursion:

[T_n=(2n-1)T_{n-1}]

where $$T_n$$ denotes the number of ways to place the weights for a positive integer $$n$$, I, instead, got this recursion:

[T_n=sum_{k=1}^nT_{n-k}{n-1choose k-1}2^{k-1}(k-1)!]

which, if solved, would obtain the same answer

[T_n=(2n-1)(2n-3)cdots1]

which is what I got in 2 hours. I tried problem 5 immediately after that, and I got something, maybe worth of a value. There has been a trend in the IMO to provide some random functional equation, and then to prove the properties of function satisfying the functional equation (or function inequality!), instead finding all solutions to the functional equation. Maybe, for the participants, finding all solutions has been a routine problem, they must have tricks up their sleeves, so they switched to a new insight on the functional equation.

Problem 6 looks simple, but if only looks could determine the solution. I was convinced that the problem would have a hard solution (inversion, projective geometry, transformation), but after seeing the solution on Mathlinks, it was classical. I haven’t read it fully, but it seems that there’s no advanced technique needed. But why the PSC put it as G8, the hardest problem in the geometry shortlist? I don’t really know.

After the 2nd day of the contest, we were out and to be surprised that it was really sunny. And windy. It still feels weird, because we are not experiencing typical Dutch summer. Some of us are still wondering, why is it so hot, compared to yesterday, and the day before yesterday, and the day before the day before yesterday, and … (complete the sequence)

Thus we went back to Novotel, with the same transportation issue (there was not enough bus to take everyone back to Novotel in one sweep), although it was sunny so we don’t have to shelter ourselves. It was really nice weather. We arrived at Novotel, to be greeted with our leader who has just come from their secret location, somewhere in Eindhoven. They’re going to have a lot of work to do, so I wish them the best of luck (and hopefully try to raise my score until I get a medal). I have no hopes or whatsoever, considering the result of these 2 days of the contest.

Also, Mr. Hery told us during the lunch that there was 2 ALGEBRA problem in Day 1, something, that I believe, has not ever been done in the history of IMO. It seems that the jury wanted problem A1 badly (A1 is problem 1 of day 1) and G8 really badly, and also the combinatorics on day 1 so really badly (I forgot what Mr. Hery said, maybe C3 or C4) so they decided to put 2 algebra problem in day one. I don’t know any circumstances that forced them to do this, breaking an IMO tradition, because I wasn’t there at the jury meeting (obviously).

After that, it was free time for us. Syafri (IMO 2002 contestants, who happened to live here,  in the Netherlands) wants to take us to the city (with Paul, obviously), and so, off we go, by tram. Someone on our team exchanged 500 Euros for smaller denominations, and so he became our boss.

Tram was really nice, although quite long for the journey. By 2.60 Euro, you take the tram anywhere within one hour of purchase. Thus we are off to Amsterdam city.

When we arrived, there was a street performer at the city center. His name was Crystal Ball Paul or something like that, he speaks English, and he performs. He’s funny, although sometimes he makes a bad joke. But his action were cool. He played with fireballs and do several tricks. Too bad, the audience responses were not so lively. Perhaps it was really windy and cold in Amsterdam.

Then we got lost. Well, not exactly got lost, but it looks like that Syafri and Paul had some instincts to go somewhere in Amsterdam. I am not allowed to say where we went, because we are on a non-disclosure verbal agreement. Looks like you already know, but you might be wrong

Then after that, we went to this small restaurant. Well not exactly a restaurant, but a kiosk. And it is really small. Paul recommended this place to have kebab. I was expecting this:

But what came up is something completely different. It was placed on a plate, on the plate was a round bread, with chicken (because I ordered chicken kebab), and lettuce. I ordered a small size, but the cook was really generous to us, I think that’s too many chicken. We were shortly full. The place is small, but looks like it is famous, because there are pictures of the owner with some Caucasians (possibly celebrity). The chili sauce was really weird, I think they have the second weirdest chili sauce I’ve ever tasted (after Kazakh chili sauce, of course)

Then we got back to the Novotel, and I started blogging the whole thing today.

Tomorrow will be excursion (YES!), to Den Haag, the somewhat administrative city of the Netherlands. I don’t know the correct way to describe it, but it seems correct.

Today I am free from any weights remain. I do need some rest now.

I’m signing off from Amsterdam, the Netherlands.