Soal Minggu 28 Juli 2008

Misalkan diketahui:
3 # 4 > 5
5 # 6 > 1
1 # 2 > 9
8 # 4 > 0
Berdasarkan informasi tersebut tentukan:
6 # 2 > .....
4 # 1 > .....
3 # 7 > .....
5 # 5 > .....
9 # 0 > .....

Petunjuk:
Persoalan ini pertama kali muncul pada buku teks kelas 3 SD (Keahlian perhitungan apa yang dimiliki siswa kelas 3 SD)

Tentang Matematika

Bayangkan bagaimana dunia ini seandainya tidak ada matematika? Mungkin kita tidak akan pernah menonton TV, bermain game di komputer atau di game net, mengobrol lewat telpon atau sekedar sms-an menggunakan Hand Phone kita. Bayangkan apa yang akan terjadi jika orang tidak mengenal bilangan dan tidak bisa berhitung secara sederhana. Bayangkan betapa kacaunya kalau kita tidak bisa memahami ruang dimana kita berada, tidak bisa memahami harga barang di mall atau di supermarket.
Dari sini saja mestinya kita sudah tahu kalau matematika itu memang penting. Sudah tidak disangsikan lagi, matematika memegang peranan yang cukup penting dalam kehidupan manusia. Banyak yang telah disumbangkan matematika bagi perkembangan perababan manusia. Kemajuan sains dan teknologi yang begitu pesat dewasa ini tidak lepas dari peranan matematika. Boleh dikatakan landasan utama sains dan teknologi adalah matematika.

Namun demikian, kita juga tidak dapat mengingkari kenyataan bahwa sampai sekarang masih banyak orang yang mengalami kesulitan dalam mempelajari matematika. Bahkan tidak jarang matematika dianggap ‘momok’ atau hantu yang menakutkan, yang sebisa mungkin dihindari. Ketika mendengar kata matematika serta merta yang muncul di pikiran adalah identik dengan kata ‘sulit’.

Apa itu sebenarnya matematika?
Kata "matematika" berasal dari kata μάθημα(máthema) dalam bahasa Yunani yang diartikan sebagai "sains, ilmu pengetahuan, atau belajar", juga μαθηματικός (mathematikós) yang diartikan sebagai "suka belajar". Nah, jika menilik artinya secara harafiah, sebenarnya tidak ada alasan bagi kita untuk tidak suka atau takut dengan matematika. Karena kalau kita tidak suka matematika itu berarti kita tidak suka belajar! Kalau kita selama ini masih menganggap matematika itu sulit, mungkin sebenarnya kita belum mengenal apa itu matematika.
Untuk mengenal matematika lebih dekat, lebih dulu kita mesti mengetahui ciri-ciri atau mengenali sifat-sifatnya. Matematika itu memiliki beberapa ciri-ciri penting. Pertama, memiliki obyek yang abstrak. Berbeda dengan ilmu pengetahuan lain, matematika merupakan cabang ilmu yang spesifik. Matematika tidak mempelajari obyek-obyek yang secara langsung dapat ditangkap oleh indera manusia. Substansi matematika adalah benda-benda pikir yang bersifat abstrak. Walaupun pada awalnya matematika lahir dari hasil pengamatan empiris terhadap benda-benda konkret (geometri), namun dalam perkembangannya matematika lebih memasuki dunianya yang abstrak. Obyek matematika adalah fakta, konsep, operasi dan prinsip yang kesemuannya itu berperan dalam membentuk proses berpikir matematis, dengan salah satu cirinya adalah adanya alur penalaran yang logis.
Dan ciri yang kedua, memiliki pola pikir deduktif dan konsisten. Matematika dikembangkan melalui deduksi dari seperangkat anggapan-anggapan yang tidak dipersoalkan lagi nilai kebenarannya dan dianggap saja benar. Dalam matematika, anggapan-anggapan yang dianggap benar itu dikenal dengan sebutan aksioma. Sekumpulan aksioma ini dapat digunakan untuk menyimpulkan kebenaran suatu pernyataan lain, dan pernyataan ini disebut teorema. Dari aksioma dan teorema atau dari teorema dan teorema kemudian dapat diturunkan teorema lain. Akhirnya matematika merupakan kumpulan butir-butir pengetahuan benar yang hanya terdiri atas dua jenis kebenaran, yaitu aksioma dan teorema. Selebihnya, kalaulah ada pengetahuan yang tampaknya benar, namun belum dapat dibuktikan, maka butir pengetahuan itu belum dianggap kebenaran dan hanya berupa suatu "takhayul" yang masih perlu dibuktikan. (Andi Hakim Nasution, 2001). Dengan kata lain, kebenaran konsistensi matematika adalah kebenaran dari suatu pernyataan tertentu yang didasarkan pada kebenaran-kebenaran pernyataan terdahulu yang telah diterima sebelumnya. Sehingga satu sama lain tidak mengalami pertentangan.
Disiplin utama dalam matematika awalnya didasarkan pada kebutuhan perhitungan dalam perdagangan, pengukuran tanah dan memprediksi peristiwa dalam astronomi. Ketiga kebutuhan ini secara umum berkaitan dengan ketiga pembagian umum bidang matematika, yaitu studi tentang struktur, ruang dan perubahan.
Studi tentang struktur dimulai dengan bilangan, seperti tentang bilangan asli dan bilangan bulat serta operasi arimetikanya, yang semuanya itu dijabarkan dalam aljabar dasar. Sedangkan teori bilangan, aljabar linier, aljabar abstrak, struktur aljabar merupakan bagian lanjut dari studi tentang struktur ini, yang akan dijumpai ketika seseorang studi lebih mendalam tentang matematika di perguruan tinggi.
Sedangkan ilmu tentang ruang berawal dari geometri, yaitu geometri Euclid dan trigonometri dari ruang tiga dimensi (yang juga dapat diterapkan ke dimensi lainnya), kemudian belakangan juga digeneralisasi ke geometri Non-euclid yang memegang peran sentral, salah satunya dalam teori relativitas umum.
Sementara kalkulus merupakan satu contoh bagian dari matematika yang digunakan untuk memahami dan mendiskripsikan perubahan pada kuantitas yang dapat dihitung. Konsep utama yang digunakan untuk menjelaskan perubahan variabel adalah fungsi. Banyak permasalahan yang berujung secara alamiah pada hubungan antara kuantitas dan laju perubahannya, dan metode untuk memecahkan masalah ini adalah topik bahasan dari persamaan differensial. Dan tentu masih banyak lagi yang lain seperti analisis real, analisis kompleks, maupun analisis fungsional yang belum akan dipelajari di bangku SMA.
Untuk menjelaskan dan menyelidiki dasar matematika, dikembangkan bidang teori pasti, logika matematika dan teori model. Saat pertama kali komputer disusun, beberapa konsep teori yang penting dibentuk oleh matematikawan dan telah memicu munculnya bidang teori komputabilitas, teori kompleksitas komputasional, teori informasi dan teori informasi algoritma. Nama umum untuk bidang-bidang penggunaan matematika dalam ilmu komputer ini adalah matematika diskret. Bidang-bidang penting dalam matematika terapan antara lain adalah statistik, yang menggunakan teori probabilitas sebagai alat untuk memberikan deskripsi, analisis dan perkiraan fenomena dan digunakan dalam hampir seluruh ilmu pengetahuan.

Untuk apa belajar matematika di sekolah?
Mungkin bagi kita cabang-cabang matematika yang disebutkan di atas masih terasa begitu asing. Soalnya itu memang merupakan bagian-bagian matematika yang tergolong tingkat tinggi dan hanya dipelajari ketika seseorang studi di jurusan matematika di perguruan tinggi. Tapi sekedar untuk memberi gambaran tentang lingkup matematika kiranya tidak ada salahnya. Kita menjadi lebih tahu, kalau sebenarnya matematika yang dipelajari di sekolah baik sekolah dasar maupun sekolah menengah boleh dikata belum seberapa, masih tergolong matematika yang levelnya rendah, seperti aljabar, trigonometri, aritmatika.
Secara umum tujuan diberikannya matematika di sekolah adalah untuk membantu siswa mempersiapkan diri agar sanggup menghadapi perubahan keadaan di dalam kehidupan dan di dunia yang selalu berkembang, melalui latihan bertindak atas dasar pemikiran secara logis, rasional, dan kritis. Serta mempersiapkan siswa agar dapat menggunakan matematika dan pola pikir matematika dalam kehidupan sehari-hari dan dalam mempelajari berbagai ilmu pengetahuan. Tujuan pendidikan matematika di sekolah lebih ditekankan pada penataan nalar, dasar dan pembentukan sikap, serta ketrampilan dalam penerapan matematika.

3D Visualisation Applet

It is no longer a question now, how visualisation is important in understanding 3 dimensional concepts? Recently, while exploring some software , I stumbled upon this interactive applet.
It is basically to have an idea of spatial geometry.
The title is Rotating Houses.
Try with kids. They will like to explore.

3 Hal Penting Tentang matematika

Ada 3 hal dasar yang mesti dipahami berkaitan dengan matematika.

Math is Not a Spectator Sport
“Matematika bukan olahraga tontonan” kira-kira begitulah terjemahan bebas dari sub judul di atas. Maksudnya begini, kita tidak bisa cuma menjadi penonton dalam pelajaran matematika. Kita tidak dapat belajar matematika hanya dengan datang di kelas, memperhatikan guru dan belajar di rumah dengan mengerjakan PR yang diberikan oleh guru. Sebaliknya, untuk dapat mempelajari matematika dengan baik kita harus secara aktif terlibat dalam proses pembelajaran matematika. Selain memberikan seluruh perhatian di dalam pelajaran matematika, kita harus mengembangkan apa yang sudah dipelajari. Kita mesti membuat catatan dengan baik, mengerjakan soal-soal atau PR, bahkan jika guru tidak memberi tugas sekalipun. Kita harus belajar dengan rutin dan terjadwal secara teratur, bukan hanya malam sebelum tes. Dengan kata lain, kita membutuhkan keterlibatan kita dalam seluruh proses pembelajaran matematika, baik saat pelajaran di sekolah maupun saat belajar sendiri di rumah.

Dalam kenyataannya, memang sebagian besar orang sungguh membutuhkan kerja keras untuk berhasil dalam pelajaran matematika, lebih-lebih untuk sungguh dapat menguasai pelajaran matematika dengan baik. Kita bisa mengecek, dengan bertanya pada orang-orang dekat di sekitar kita, entah bapak, ibu, saudara atau tetangga. Secara umum, orang butuh bekerja lebih keras untuk pelajaran matematika lebih daripada apa yang dilakukan untuk pelajaran lain. Jika kita tidak mau terlibat secara aktif dalam proses pembelajaran matematika, baik di dalam maupun di luar kelas, maka kita akan mengalami kesulitan dalam pelajaran matematika, dan kemungkinan untuk gagal atau tidak lulus dalam pelajaran matematika akan semakin besar.

Understand the Principles
Mungkin banyak orang dapat lulus dalam tes pelajaran sejarah dengan mudah hanya dengan menghafal tanggal, nama dan peristiwa-peristiwa. Namun untuk dapat lulus pelajaran matematika orang butuh melakukan lebih daripada sekedar menghafal kumpulan rumus-rumus, prinsip-prinsip atau konsep-konsep dalam matematika. Kita perlu memahami bagaimana menggunakan rumus-rumus tersebut, saat kapan rumus harus digunakan, dan hal itu seringkali jauh berbeda dari hanya sekedar menghafalnya.
Beberapa rumus memiliki batasan yang kita harus mengetahuinya secara benar dan cermat dalam menggunakannya. Dan kita perlu mengingat batasan-batasan tersebut atau kita akan kesulitan dalam mengerjakan soal atau memperoleh jawaban yang salah. Kadang kala juga rumus-rumus yang lain sangat umum dan memaksa kita untuk mengidentifikasi bagian-bagian dalam soal yang berhubungan dengan beberapa bagian dalam rumus itu. Hal itu mensyaratkan bahwa kita mesti mengetahui bagaimana prinsip dan cara kerja di balik rumus tersebut. Jika kita tidak menguasainya, maka seringkali hal itu dapat menyulitkan kita dalam menggunakan rumus tersebut. Sebagai contoh, dalam kalkulus tidak sulit untuk menghafal suatu rumus integral parsial. Namun, jika kita tidak mengerti bagaimana menggunakan rumus tersebut secara nyata dan tidak bisa mengidentifikasi pendekatan bagian-bagian integral itu, maka hafalan tentang rumus tersebut tidak akan cukup membantu atau tidak akan berguna sama sekali.

Mathematics is Cumulative
Yang juga perlu dipahami, matematika merupakan akumulasi atau kumpulan dari banyak materi. Seringkali apa yang sedang kita pelajari dalam pelajaran matematika sekarang bergantung pada pemahaman materi yang sudah dipelajari sebelumnya. Dengan kata lain, seringkali untuk memahami materi baru dibutuhkan pemahaman dari materi-materi pelajaran sebelumnya. Sebagai contoh, pelajaran tentang aljabar di SMA akan sangat sulit dipahami tanpa pengetahuan tentang aljabar yang sudah dipelajari di SMP. Pun kita tidak dapat mengerjakan kalkulus tanpa memahami aljabar dan trigonometri yang sudah dipelajari sebelumnya.

Beasiswa D-1 Bidang Migas

Buat yang masih berburu beasiswa, Kementrian Negara BUMN memberikan beasiswa D-1 untuk putra terbaik Indonesia untuk di didik untuk menjadi tenaga kerja siap pakai. Program beasiswa yang diperuntukkan bagi lulusan SMK jurusan listrik/kimia/Las/Mesin/Instrumentasi ini telah membuka pendaftaranya sejak 21 juli 2008 dan berkas lamaran beasiswa paling lambat diterima oleh panitia pada 1 Agustus 2008.

Mathematics in Playground

Students of grade 10 performed mathematics experiments in playground on calculating heights and distances using an isosceles right triangle. They used trigonometric ratios in calculating the height of basket ball pole and a building nearby the playground. It is amazing to share that they calculated the values corrected upto 2 decimal places.

• Firstly, they prepared their isosceles right triangles using a cardboard.
• They worked in groups and measured the heights of each group member using a measuring tape.

• They were told to hold t triangle with one edge parallel to the ground with hypotenuse angling up from their eye to the top of the object. They used the hypotenuse as the line of sight and moved backward/forward on the straight line drawn on the level ground, until the top of the object coincides with the top of the hypotenuse of right triangle.

It was altogether an enriching experience for me as a teacher because even in our school days we did not learn by these kinds of real experiments.

Awal Tahun Pelajaran

Tahun pelajaran 2007/2008 telah berakhir. Tangis, tawa, dan bahagia mewarnai perjalanan siswa/i selama mengikuti proses belajar selama 1 tahun yang lalu. Tahun pelajaran yang lalu tentu banyak menyisakan PR buat kita semua, hasil belajar yang buruk tentu harus menjadi pecut buat kita agar di tahun yang akan datang hasil belajarnya bisa lebih baik lagi. Buat yang prestasinya sudah baik, ehhm terus

Persamaan Sederhana

Hasil dari sebuah bilangan yang dikuadratkan biasanya punya nilai yang lebih besar dari bilngan itu sendiri ( misalnya 10² = 100 ) atau nilainya lebih kecil dari bilangan itu sendiri ( misalnya ( ½ )² = ¼ ), tetapi dapatkah anda menebak sebuah bilangan yang nilainya sama dengan kuadrat bilangan itu sendiri ? Permasalahan ini bisa kita misalkan dalam sebuah persamaan, misalkan bilangan tersebut

Creating aptitude puzzles

Mathematics learning is not just developing numerical solving skills of students. There are lot of skills like logical thinking, aptitude, knowledge and understanding enhancements which are an integral part of learning mathematics.

Here I am talking of developing aptitude in students of observing patterns and generating the next in steps. Children , specially of grade 6 to 8 love to do mathematical pattern based questions. I have created puzzles based on mathematical patterns and spatial arrangements . The images have been set to panorama view using an open source software Irfan view.

Following are some samples of playing with match sticks.

What we do with these pictures?

Show them to students and ask the following:

Guess the next figure and draw . Find a relationship between number of match sticks between consecutive steps . Try to formulate a general expression for the nth step.
Following are some samples of playing with unit cubes:

Guess the next figure and draw . Find a relationship between number of unit cubes between each consecutive steps . Try to formulate a general expression for the nth step.
Have fun learning mathematics using technology.

Beasiswa Trisakti

Yayasan Beasiswa Trisakti memberikan kesempatan kepada siswa/i SMA dan SMK yang baru saja lulus ujian akhir nasional Tahun 2008 untuk mendapatkan beasiswa penuh kuliah di Trisakti School of Management. Besar beasiswa yang diberikan maksimum selama empat tahun adalah sebesar biaya pendidikan yang diperlukan selama mahasiswa/i menempuh perkuliahan di TSM.Bagi siswa/i SMA dan SMK yang memenuhi

Soal Ujian Nasional ( Pembahasan Suku Banyak )

Kalau sebelumnya saya sudah membuat pembahasan tentang statistika, maka pembahasan soal - soal Ujian Nasional berikutnya yang saya buat adalah mengenai materi suku banyak. Seperti biasanya pemilihan materi suku banyak lebih karena jumlah soalnya yang relatif sedikit ( kalau tidak salah ada 8 soal ). Agak lama juga saya buat pembahasan materi suku banyak daripada pembahasan statistika, ini

Animated mathematical figures

In an e teaching workshop organised by CII Shiksha, I got to know about a cool animation tool UnFREEz. The addition of this e software to my directory helped me to add life to still mathematical figures. I experimented with this software in creating some animated mathematical stuff.
Have a look.

The following three figures are created to explain the properties of a rectangle viz. both pairs of opposite sides of a rectangle are equal, each angle of a rectangle is a right angle and diagonals of a rectangle are equal.

The figure given below may be used to understand the concept of vertices of a cube. Observe the pink dots. My students were making mathematics project on optical illusion . I thought of creating animated illusions using UnFRRez. Two parallel lines turning into a pair of intersecting lines ... Two equal lines turning into unequal lines...

Do you want to download it?

Here is the link.

Mathematics and image editing

Technology has given a magical toy in the hands of teachers and students to explore and learn interesting facts with ease. I have been exploring the internet based tools and softwares from past 2 years and had deeply felt its power in enriching learning level of students.

In our mathematics laboratory, we have been exploring on mathematics based activities using pictures. It is interesting to note that by using tech tools and softwares , we can do many mathematical experiments with a click of a mouse button. There are image editing tools and online programmes which can add/remove effects to a picture . This can bring in an incredible change in the existing image/picture leading to unusual results. I believe , a teacher or a student must take advantage of this facility . It would surely inculcate in learners the interest in the subject and developing creative skills. May be one day we may find a hidden mathematician.

Here I am sharing some interesting observations

• Transforming a tangram to a curvy tangram. I talked about this experiment in my previous post on image editing.
• Experimenting with illusions is an interesting activity which may be performed easily using image editors. Observe the given pictures... This is an optical illusion

In the above picture ,there are pink squares bounded by white and green squares. The presence of white and green boundaries around pink squares has changed the tone of pink shade. It is observed that when pink squares are bounded by green squares then they appear to be darker in shade. And when we remove all the green squares then we found that all the pink coloured squares are of same tone.

I was astonished to see this illusion. But you know, I wanted to try it for some other colour combinations. Manually, it is quite impossible to check on drawing, shading and then observing. So, an idea came to my mind to try using image editing tools. And here is the result...

I first tried with turning all pink squares to orange.

then to blue and so on I experimented with 5 different colours.The I tried to remove the green squares using eraser tool and got actually verified the result. In the figure given below, observe the part from where the green squares are completely removed. You will find that tone of blue colour is same . Ans there is a change in the tone of blue shade in the portion which is bounded by green squares.
The following pictures are edited using irfan view , a wonderful image editing tool. I took the following picture. I wanted to change the green coloured squares to some other colour to verify the experiment. Through Irfan view it was made posible. I edited the picture successfully.

Here is the result. I was amazed to see the fact that when green squares are turned to black, then also the illusion effect in yellow squares was there.Using a swap colour option, just by a click of mouse button, Yellow coloured squares are changed to blue. Exploring and learning the wonderful facts using technology is an enriching experience for me.

Check this one which I posted on Figures Speak.

Done, and Gets Things Smart

Disclaimer: I do not speak for Google! These are my own views and opinions, and are not endorsed in any way by my employer, nor anyone else, for that matter.

Everyone knows and quotes Joel's old chestnut, "Smart, and Gets Things Done." It was a blog, then a book, and now it's an aphorism.

People quote Joel's Proverb all the time because it gives us all such a nice snuggly feeling. Why? Because to be in this industry at all, even a bottom-feeder, you have to be smart. You were probably the top kid in your elementary school class. People probably picked on you. You were the geek back when geeks weren't popular. But now "smart" is fashionable.

That's right! All those loser kneebiter jocks in high school who played varsity and got all the girls and sported their big, winning, shark-white smiles as they barely jee-parlor-fran-saysed their way through the classes you coasted through: where are they now? A bunch of sorry-ass bank managers and failed insurance salesmen and suit-wearing stiffs at big law firms working for billion-dollar conglomerates where their daddies got them VP jobs where they just have to show up and putt against the other VPs on little astroturf greens in the hallways!

That's right, los... er, well, some of them are doing OK, I guess. "But they're not as rich as Bill Gates!" That's the other big tautology-cum-aphorism we geeks like to pull out when we're feeling insecure. Notwithstanding that Bill had a rich daddy and made his money through exactly the kind of corporate shenanigans that Big Meat is using on us today, with those selfsame jocks. We like to think the more important point is that Bill, Jobs, Bezos and the other tech billionaires (all fierce, business-savvy people) were geeks, and are thus evidence of the revenge of the nerds. And hey, tech did make a lot of money in the 80s and 90s. So "smart" is sort of in fashion now.

Unfortunately, "smart" is a generic enough concept that pretty much everyone in the world thinks they're smart. This is due to the Nobel-prize-winning Dunning-Kruger Effect, which says, in effect, that people don't know when they're not smart. (Note: people have pointed out that it was an Ig-Nobel. Me == Dumbass. Fortunately, "me == dumbass" was more or less the point of the article, so I'll let it stand.)

So looking for Smart is a bit problematic, since we aren't smart enough to distinguish it from B.S. The best we can do is find people who we think are smart because they're a bit like us.

Er, what about Gets Stuff Done, then? Well, the other qualification you need to be in this industry is that you have to have produced something. Anything at all. As soon as you write your first working program, you've gotten something done. And at that point you probably think of yourself as being a pretty hot market commodity, again because of the Dunning-Kruger Effect.

So, like, what kind of people is this Smart, and Gets Things Done adage actually hiring?

I've said it before: I thought I was a top-5% (or so) programmer for the first fifteen years I was coding. (1987-2002). Every time I learned something new, I thought "Gosh, I was really dumb for not knowing that, but now I'm definitely a superstar." It took me fifteen frigging years before I realized that there might in fact still be "one or two things" left to learn, at which point I started looking outward and finally discovered how absolutely bambi-esquely thumperly incompetently clueless I really am. Fifteen years!

But hell, let's be honest here: I still think I'm smart. We all do. Sure, I've managed to figure out, at least partly, just how un-smart I am, but I've got the whole "I'm smart" thing so hardwired from when I was a kid surrounded by "dolts" who couldn't memorize things as fast as I could, or predict the teacher's punch line way in advance, or whatever questionable heuristic I was using for measuring my own smartness, that it's hard not to think that way. And of course the "dolts" were way better than me at just about everything else. And they think they're pretty smart too! Definitely above average, anyway.

Squaaaaawk

So we all think we're smart for different reasons. Mine was memorization. Smart, eh? In reality I was just a giant, uncomprehending parrot. I got my first big nasty surprise when I was in the Navy Nuclear Power School program in Orlando, Florida, and I was setting historical records for the highest scores on their exams. The courses and exams had been carefully designed over some 30 years to maximize and then test "literal retention" of the material. They gave you all the material in outline form, and made you write it in your notebook, and your test answers were graded on edit-distance from the original notes. (I'm not making this up or exaggerating in the slightest.) They had set up the ultimate parrot game, and I happily accepted. I memorized the entire notebooks word-for-word, and aced their tests.

They treated me like some sort of movie star — that is, until the Radar final lab exam in electronics school, in which we had to troubleshoot an actual working (well, technically, not-working) radar system. I failed spectacularly: I'd arguably set another historical record, because I had no idea what to do. I just stood there hemming and hawing and pooing myself for three hours. I hadn't understood a single thing I'd memorized. Hey man, I was just playing their game! But I lost. I mean, I still made it through just fine, but I lost the celebrity privileges in a big way.

Having a good memory is a serious impediment to understanding. It lets you cheat your way through life. I've never learned to read sheet music to anywhere near the level I can play (for both guitar and piano.) I have large-ish repertoires and, at least for guitar, good technique from lots of lessons, but since I could memorize the sheet music in one sitting, I never learned how to read it faster than about a measure a minute. (It's not a photographic memory - I have to work a little to commit it to memory. But it was a lot less work than learning to read the music.) And as a result, my repertoire is only a thousandth what it could be if I knew how to read.

My memory (and, you know, overall laziness) has made me musically illiterate.

But when you combine the Dunning-Kruger effect (which affects me just as much as it does you) with having one or two things I've been good at in the past, it's all too easy to fall into the trap of thinking of myself as "smart", even if I know better now. All you have to do, to be "smart", is have a little competency at something, anything at all, just enough to be dangerous, and then the Dunning-Kruger Effect makes you think you're God's gift to that field, discipline, or what have you.

This is why everyone loves Smart, and Gets Things Done, which Joel always writes in boldface. We love it because right from the start it has the yummy baked-in assumption that you are smart, and that you get things done. And it also tacitly assumes that you know how to identify other people with the same qualities!

But... you don't.

It sucks, but the Dunning-Kruger Effect is frighteningly universal. It's a devil's pitchfork two horrible, boldfaced prongs. First:

Incompetent people grossly overestimate their own competence

We already talked about that, right? You're a good programmer! Heck, you're a great programmer! You're "smart", so anything you don't know you can go look up if you need it! Right?

Welcome to incompetence.

The second prong is a bit longer, and has a barbed poison tip:

Incompetent people fail to recognize genuine skill in others

Both prongs are intrinsically funny when you're watching them in action in someone else, and they're incomprehensible when anyone tries to poke you with them. Not necessarily offensive, mind you: you might get offended if someone tries to imply that you're not as competent as you feel you are, but it's more likely (per the D-K effect) that you'll simply not believe them. Not even close. You're smart! They're just wrong! Gosh!

The second prong, that of the ability to recognize true competence, has major ramifications when we conduct interviews. That's what Joel was writing about in Smart and Gets Things Done, you know: conducting technical interviews.

How do you hire someone who's smarter than you? How do you tell if someone's smarter than you?

This is a problem I've thought about, over nearly twenty years of interviewing, and it appears that the answer is: you can't. You just have to get lucky.

It's easy for a candidate to sound smart. Anyone can use big jargon-y words and talk the talk like nobody's business, but I'm living, breathing proof that articulacy doesn't connote any other form of intelligence. Heck, the Markov-chain synopses of my blogs that people post in quasi-jest tend to look like I wrote them.

All too often I find myself on interview loops where the candidate knows a seemingly astounding amount about coding, computer science, software engineering, and general industry topics, but we find out at the last minute that they can't code Hello, World in any language.

This is, of course, one of the failure-patterns that Joel's Get Things Done clause is designed to catch. But interviews are conducted under pretty artificial conditions, and as a result they wind up being most effective at hiring people who are good at interviewing. This is a special breed of parrot, in a way. Interviewing isn't a particularly good predictor of performance, any more than your rank in a coding competition is a predictor of real-world performance. In fact, somewhat depressingly, there's almost no correlation whatsoever.

If interviews suck, then why do we still do them this way?

Lots of reasons. One is just history: everyone else does it that way. Companies tend to hire pretty similar HR departments, and HR tends to guide companies towards doing it the way everyone else does it. Same goes for technical management, which is all too often HR-driven as the company grows.

Another is that interviewing is already a fairly time-intrusive function for the interviewers, and it tends to be miserable for the interviewees. Trying to make the process somehow more rigorous or accurate just exacerbates these side effects.

Another is the "rite of passage" phenomenon, wherein engineers feel that if they had to go through the gauntlet, then everyone else should, too.

So for the most part, everyone does the same non-working variety of interviews, and hopes for the best.

As far as identifying good people goes, the best solution I've ever seen was at Geoworks, where you were required to do a six-month internship before you could get hired full-time. This seems to be the norm in non-tech departments at most tech companies. They often substitute "contractor" for "intern", but it works out roughly the same. Geoworks is the only company I've seen stick to their guns and make it mandatory for engineers.

However, I'm convinced that it only worked because Geoworks seeded the engineering staff with great people. The founding engineers set up a truly beautiful software engineering environment, with lots of focus on tools, mentoring, continuing education, "anarchy projects" to let off steam and encourage innovation, and a host of other goodnesses.

I've been a contractor at companies that had no good engineers at all, literally none whatsoever. A mandatory six-month internship at such companies would only serve to lower their average bar, since anybody competent would leave after the six months was up. This doesn't contradict the D/K Effect. It's easy to spot lackluster, soulless engineering organizations, and doing so doesn't imply that you're especially smart.

The "Extended Interview"

Anyway, I've often wondered where the Geoworks founders found such great engineers. The short answer is: "Berkeley", but I'm really looking for something deeper than that; namely: how did they know?

Along similar lines, I've long felt that Amazon's success was due in no small part to Bezos having seeded his tech staff with great engineers. World-class great. I don't know where or how he found them, since, again, how do you hire someone who's smarter than you? He's a brilliant guy, but his original choices (ex-Lucid folks, by and large) seem a stroke of blind luck that's hard to attribute to mere genius. I'll probably never know how it happened. Wish I did!

They weren't too big on software engineering, though, or more likely they all felt that time-to-market trumped everything else (and were correct, at least in their case), so Amazon is successful but lacks a high-quality software engineering culture. It's gotten much better over the years, of course, but it's a far cry from Geoworks. It's largely up to individual teams at Amazon to decide how much engineering to sprinkle into their coding. There's no central group (or distributed peer group) who can tell any team how to build their software. This is effectively mandated from the top, in fact.

But time-to-market is a pretty powerful business force. Maybe that's the missing link? Lucid was founded by Dick Gabriel, the "worse is better" guy, and Amazon took the "worse is better" idea (internally) to untold new extremes.

Dunno! But it sure worked for them.

Google has a process similar to the Geoworks 6-month internship idea. Geoworks's internship was a form of "extended interview", since it was obvious even in the 1980s that the classic interview format isn't a very good predictor of performance. At Google, you don't have to do an internship. However, unlike at most other companies, you're not "slotted" into a real position on the tech ladder until you've been on the job at least six months. During that time you need to prove that you can function at the level you were hired for, and if it's wrong in either direction your level is adjusted at slotting time.

The "extended interview" (in any form) is the only solution I've ever seen to the horrible dilemma, How do you hire someone smarter than you? Or even the simpler problem, How do you identify someone who's actually Smart, and Gets Things Done? Interviews alone just don't cut it.

Let me say it more directly, for those of you who haven't taken this personally yet: you can't do what Joel is asking you to do. You're not qualified. The Smart and Gets Things Done approach to interviewing will only get you copies of yourself, and the work of Dunning and Kruger implies that if you hire someone better than you are, then it's entirely accidental.

Don't get me wrong: you should still try! Don't throw the bath and baby away. Smart and Gets Things Done is a good weeder function to filter out some of the common "epic fail" types.

But realize that this approach has a cost: it will also filter out some people who are just as good as you, if not better, or even way better, along dimensions that are entirely invisible to you due to Dunning-Kruger forces mostly beyond your control.

So there's this related interviewing/hiring heuristic that I think may better approximate the kinds of people you really want to hire: Done, and Gets Things Smart.

I'll take Joel's cue and write it in bold so you know it's important. It's not condescending or anything. Really. Let's all recite it together, to make it catchy and stuff. Maybe we should have a little ditty for it, so it sticks in our heads annoyingly, forever. I think the Happy Birthday song will do nicely:

Hap-py Birth-day To Yooooooou,
Done-and Geh-ets Things Smaaaart
Hmmm hmm HMMMMM Hmmmm Hmmmm whoeeeeeever
Done and geh-eeeeeets thiiiiiings Smaaaaaaaart *clap* *clap*

There! You'll remember it every time anyone has a birthday.

Done, and Gets Things Smart

All gentle faux-condescension aside (or as the classroom jocks would have read, "fox condesomething"), Joel's Smart, and Gets Things Done heuristic seems really obvious to everyone. It has this magical "we're all smart in this together" appeal. But sadly, for the reasons I've outlined, almost everyone interprets it to mean "Carbon Copy, of Myself". Great guidance gone astray!

The Done, and Gets Things Smart approach is also a way of finding great people, but it recognizes that the Dunning-Kruger Effect requires some countermeasures. It's modeled on the early successes I've witnessed at Geoworks, Amazon, and Google, all of whom had one thing in common: they hired brilliant seed engineers. This boldface is really addictive when you get started on it!

They all managed to continue hiring great people afterwards, but the seed engineers were the most important. I'm hoping that this is intuitively obvious in much the same way that wanting smart people who get things done is intuitively obvious.

I think you really, really want great seed engineers, and that this is a different class of engineer from the "pretty darn good" engineer we typically hire using Joel's oft-misinterpreted advice.

Seed engineers. It's key. You can apply the "I want ideal seed engineers" rule recursively to an organization, a department, a project, a team, and even your officemates. We're not just talking about startups.

Let me ask you a brutally honest question: since you began interviewing, how many of the engineers you've voted thumbs-up on (i.e. "hire!"), are engineers you'd personally hire to work with you in your first startup company? Let's say this is a hypothetical company you're going to found someday when you have just a little more financial freedom and a great idea.

I posit that most of you, willing to admit it or not, have a lower bar for your current company than you would for your own personal startup company.

The people you'd want to be in your startup are not of the Smart and Gets Things Done variety.

For your startup (or, applying the recursion, for your new project at your current company), you don't want someone who's "smart". You're not looking for "eager to learn", "picks things up quickly", "proven track record of ramping up fast".

No! Screw that. You want someone who's superhumanly godlike. Someone who can teach you a bunch of stuff. Someone you admire and wish you could emulate, not someone who you think will admire and emulate you.

You want someone who, when you give them a project to research, will come in on Monday and say: "I'm Done, and by the way I improved the existing infrastructure while I was at it."

Someone who always seems to be finishing stuff so fast it makes your head spin. That's what my Done clause means. It means they're frigging done all the time.

I met my first Done, and Gets Things Smart engineers back at Geoworks. This was looong before I had any sort of a clue that I suck as an engineer, but these folks (Andrew Wilson and Chris Thomas, if you really must know) were weird. They never seemed to be working that hard, but they were not only 10x as productive as their peers, they also managed technical feats that were quite frankly too scary for anyone else. They could (as just one trait) dive in and learn new languages and make fixes to tools that the rest of us assumed were, I dunno, stuff you'd normally pay a vendor to fix. They dove into the hairiest depths of every code base they encountered and didn't just add features and make fixes; they waved some sort of magic wand and improved the system while they were in there: they would Get Things Smart. Make the systems smarter, that is. Sort of like getting your act together, but they'd do it for your code.

I've met many more such engineers along the way. They're out there. They're better than you. They were better twenty years ago than I am today or ever will be. Maybe it's natural ability. Maybe it's luck in education or upbringing. Maybe they have a secret recipe for improving rapidly and learning utter fearlessness. I don't know. But I've met 'em, and they aren't "smart". They're abso-flutely fugging brilliant.

You can't interview these people. For starters, they're not interested; these are the people that companies hold on to as long as humanly or companyly possible. The kinds of people that companies file lawsuits over when they're recruited away.

You can only find Done, and Gets Things Smart people in two ways, and one of them I still don't understand very well.

The first way is to get real lucky and have one as a coworker or classmate. You work with them for a few years and come to realize they're just cut from a finer cloth than you and your other unwashed cohorts. You may be friends with some of them, which helps with the recruiting a little, but not necessarily. The important thing is that you recognize them, even if you don't know what makes them tick.

This is the one great hope we programmers have for fighting the Dunning-Kruger Effect, the one hope we have for getting something better than the average "just like me" Solid Plugger Joe Nobody you pick up with the Smart, and Gets Things Done approach. Our only "out" is that working side-by-side with someone will show us clearly when they vastly outclass us.

Your devious little mind will come up with all sorts of rationalizations for why they're so damn good, so you can continue to think of yourself as Smart, and Gets Things Done material. You may conclude that they're just a genetic anomaly, and it's no fair even trying to compare yourself to someone who obviously has an unfair gift from the heavens. Or you may tell yourself that they're just a domain expert in various domains that you don't "need" right now. Or you may simply choose not to think about it too much. Good Old Compartmentalization to the rescue!

But working with them directly will show you when they're better. It's the only way. You'll gradually realize that your math deficiencies aren't just something that you might need to beef up on if you ever "need to"; you'll see that virtually every problem space has a mathematical modeling component that you were blissfully unaware of until Done, and Gets Things Smart gal points it out to you and says, "There's an infinitely smarter approach, which by the way I implemented over the weekend." You stare slack-jawed for a little while, and then she says: "Here's a ball. Why don't you go bounce it?"

These people aren't just pure gold; they're golden-egg-laying geese. They are the ones you want to bring with you to your own startup. Not the Smart, and Gets Things Done, Just As Soon As I Read Up On The Subject, On The Company's Dime riff-raff like you and me. No. They're your seed engineers: the ones who will make or break your company with both their initial technical output and the engineering-culture decisions they put into place — decisions that will largely determine how the company works for the next twenty years.

I've been debating whether to say this, since it'll smack vaguely of obsequiousness, but I've realized that one of the Google seed engineers (exactly one) is almost singlehandedly responsible for the amazing quality of Google's engineering culture. And I mean both in the sense of having established it, and also in the sense of keeping the wheel spinning. I won't name the person, and for the record he almost certainly loathes me, for reasons that are my own damn fault. But I'd hire him in a heartbeat: more evidence, I think, that the Done, and Gets Things Smart folks aren't necessarily your friends. They're just people you're lucky enough to have worked with.

At first it's entirely non-obvious who's responsible for Google's culture of engineering discipline: the design docs, audited code reviews, early design reviews, readability reviews, resisting introduction of new languages, unit testing and code coverage, profiling and performance testing, etc. You know. The whole gamut of processes and tools that quality engineering organizations use to ensure that code is open, readable, documented, and generally non-shoddy work.

But if you keep an eye on the emails that go out to Google's engineering staff, over time a pattern emerges: there's one superheroic dude who's keeping us all in line.

How do you interview for such a person? You can't! Everyone will tell you they're God's Gift to engineering quality. Everyone knows how to give it impressive lip service. Heck, there are lots of people who take it way too far and try to gridlock the organization in their over-enthusiasm, when what you really want is a balanced and pragmatic approach. I'd argue that it's virtually impossible to detect these "soft skills" in a classic interview setting, except to the extent that you're hiring your own clone, which according to our thesis here, is NOT what you want. You want Done, and Gets Things Smart: done faster than you, and made your system smarter!

I'm guessing that Google's founders worked with this person in school, enough to recognize his valuable talents. Hence they used Identification Approach #1: get lucky in who you work with.

Incidentally, they hired plenty of other brilliant seed engineers who were equally responsible for Google's great technical infrastructure. I'm just using this one guy as an illustrative example. But you really want the Done, and Gets Things Smart people on every team. If you could mix in one Done, and Gets Things Smart person with every five to ten Smart, and Gets Things Done people, then you'd be in good shape, since the latter, being "smart", can hopefully learn a lot from the former.

But when you're starting a company, or an organization, or a big project, the need for Done, and Gets Things Smart seed engineers is desperate. It's dire, in the sense that if you don't get the right seed people in place, you're dooming your organization to mediocrity, if you manage to succeed at all.

And it's direst when you're in a startup, because you can't pillage people from elsewhere in your organization who you know are good. And because Done, and Gets Things Smart people are worth their weight in refined plutonium, they're probably reasonably happy in their current position.

So let's assume you're looking at the vast ocean of programmers, all of whom are self-professed superstars who've gotten lots of "stuff" done, and you want to identify not the superstars, but the super-heroes.

How do you do it? Well, Brian Dougherty of Geoworks did it somehow. Jeff Bezos did it somehow. Larry and Sergey did it somehow. I'm willing to bet good money that every successful tech company out there had some freakishly good seed engineers. But a lot of company heads who make these decisions aren't necessarily industry programmers, and they still manage to find some world-class people in all the noise. So there must be a second way to identify Done, and Gets Things Smart.

I think Identification Approach #2, and this is the one I don't understand very well, is that you "ask around". You know. You manually perform the graph build-and-traversal done by the Facebook "Smartest Friend" plug-in, where you ask everyone to name the best engineer they know, and continue doing that until it converges.

I think this might work, assuming you have lots of connections initially (lots of roots for your graph), so you don't get stuck in some slummy local minimum.

I've seen companies go to university professors and ask them who their brightest students are; that's a variant of this approach, although it usually only turns up future Done, and Gets Things Smart engineers. Every once in a very rare while you'll get a recent college grad in this category, but I think more often they tend to be experienced enough to make Gandalf feel young again.

Because technical brilliance, seemingly superhuman productivity, and near-militaristic adherence to software discipline aren't enough. They also need leadership skills. They don't have to be great leaders; in fact in a pinch, just being bossy might work for a while, as long as they're bossing people in the right directions. But they need to have the ability to guide the organization (or new team, or whatever) in uniformly excellent directions, which requires some leadership, even if it's bad or amateurish leadership.

As much as I suspect Approach #2 may work, I think Approach #1 is probably more reliable. Take a closer look at your coworkers who are doing things that you "could learn if you ever need it". Read up on the old Dunning-Kruger Effect. I recommend it with irony dialed at 11, since personally I have yet to read more than the Wikipedia article and a few other articles here and there. I'll read it if I "need to". Psh.

Done, and Gets Things Smart

Not superstars: superheroes! People who are freakishly good at what they do. People who finish things so fast that they seem to have paranormal assistance. People who can take in any new system or design for all intents instantaneously, with no "ramp-up", and who can immediately bring insights to bear that are quite simply beyond your rustic abilities.

Those are the folks you want. I'm not going to tell you: "Don't settle for less." Far from it. You still want to hire the Smart, and Gets Things Done folks. But those folks have a long way to grow, and they probably have absolutely no idea just how far it is. So you want some Done, and Gets Things Smart people to guide them.

And now, to play us out...

Dooooone and Ge-ets Things Smart,
Done and Ge-ets Things Smart,
Done and Geeee-eeeets Thiiings Smaaaa-aaaart,
Done and Ge-ets Things Smart!

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