Tips memanfaatkan pikiran yang kosong

Ketika pikiran kosong, yag paling baik dilakukan adalah bekerja, karena pikiran yang kosong cenderung diisi hal-hal yang negatif dan keputus-asaan. Alihkan pikiran yang kosong untuk berkarya dengan lebih baik. Carilah kesibukan yang sesuai dengan kepribadian.

Pikiran yang kosong, terkadang juga bisa dijadikan tempat untuk merenung dan melakukan kontemplasi.
Selain itu, pikiran yang kosong bisa dilakukan untuk melatih memori, mengingat beberapa angka dan kata. Mengulang peristiwa, dsb. Yang jelas, jangan biarkan pikiran kita kosong atau menganggur, berpikirlah karena dengan berpikir, kamu ADA.

I'm Back!!

I'm sorry to keep you waiting, Othello. I got my passion back, and I'm gonna keep it.

My Exeption

My exception is something special.

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Sent from my Nokia Phone

My Inner Thinking, My Little Rascal

Once upon a time, when i was a child. I always ask, what is this? And what is that? My parents sometimes get mad, because i keep asking whatever i see, and touch. My mind works really fast. I can't make a differences between imagination and reality. I don't even know whether i'm lying or not. My inner thinking looks like a puzzle, trying to get the missing piece of a picture. When i'm an adult, my inner thinking begin to loose it shapes. I'm too easy at dealing everything. Not trying to search deeply and don't want to move on. I'm stuck in situation when i have to choose which way to go. I wish my inner thinking back to me, teach me again and show me another dimension of life. My inner thinking is my little rascal. It cause a mess in my inner thinking room. But, even so. I miss you anyway, my little rascal.

New beginning, hajimemashite

I'm alive once again, with my mobile phone. Lets see, how much it works. ^^

http://library.nu/

http://library.nu/

Miss Stalker

somehow i don't really know why everything turns out like this.
i never want to involved on others bussiness.

It's tho opposite the old me who lock my doors, never let someone going through my zone.
But, she is so weak that i can't let her alone, miss aloner.

she is so clingy and following me around quitely whenever i go.
just like a stalker, but she is a good stalker :)

Mr. Google

some say that experience is the best teacher. But, i think that Mr. Google is my best teacher.

Human learns very well, when they get excited. Once, You attach by something that stuck in your heads for a long time. Your brain is in the best condition.

When surfing, sometimes we forgot to eat, sleep, and rest.

You can search everything by networking.

But we have to be careful, not all the internet says is true. You have to compare the information with another one. So, You are not misunderstanding.

Internet is a part of y life.

Eventhough i live in top of mountain, Internet still the most source to gain knowledge (As long as people know how to use it well).

I want to say Thank Mr. Google. You give me a lot of thinks. :)

I've Return

It's been a long time i'm not update this blog. Well, many things happened since my graduation last February.

Start next moth, i'll concentrate in this blog. Fulfill one of my objections that I want to publish something useful for everyone.

Hope it will comes true.Insya Allah. Amin

Stuck At The Moments?

When you caught in difficult situations, my friends suggest to make an innocence face. Can you do that? Well, at the first, it's difficult. This is about acting and lying. But don't try this, it's a bad habit.

The best is be honest no matter what. :)

Now I' really wake up my mind!!

Thing to do is be HAPPY.

Are you HAPPY today?

well, if you're not then lets cheer up your self.

Don't be burden of uncertain things.

SMILE :) !!!

v(^o^)v

Belajar Bagaimana Mempelajari Sesuatu

Mempelajari bagaimana mempelajari sesuatu, hal yang mungkin kadang kita lupakan. Ini adalah sebuah proses bagaimana agar kita bisa menyerap ilmu dengan maksimal. Terlepas dari seberapa pandai seseorang itu. Saya mungkin bukan termasuk orang yang pandai. Tapi karena saya bisa dibilang cukup rajin. Saya bisa menutupi kekurangan saya dalam hal intelegensi yang sebagian orang ada yang mengatakan sebagai 'keturunan'. Di kelas saya dulu ada seorang anak yang pandai, tapi ia malas dan suka berisik. Tapi saat ujian nilainya yang paling bagus. Saya sangat dongkol. Bagaimana orang seperti ia bisa seperti itu. Alhasil belakangan saya ketahui, kedua orang tuanya adalah dokter yang handal.

Sejak saat itu, saya tidak pernah dongkol lagi dengannya. Saya melampiaskan kedongkolan saya dengan mencari cara bagimana saya bisa belajar dengan baik. Itu adalah pertama kalinya saya berpikir serius tentang cara belajar saya. Awalnya saya membuat semacam jadwal pelajaran yang harus saya ulang seuplang sekolah, dan saya juga menentukan jam-jam tertentu khusus untuk mengerjakan tugas dan PR. Mulanya cara ini berhasil, tapi lama-kelamaan saya jenuh dan bosan. Akhirnya saya tinggalkan jadwal-jadwal itu. Meskipun awalnya cara ini cukup berhasil mendongkrak nilai saya. Ya, dengan menjadi rajin.

Setelah strategi rajin selesai, saya mencoba strategi lain, strategi moody. Jadi saya hanya belajar saat pikiran dan energi saya mendukung. Ini strategi yang umum dipakai siswa pada umumnya. Tapi kalau dipikir saya juga tidak menggunakan strategi ini 100 % karena berlawanan dengan pribadi saya. Kemudian muncul ide untuk belajar bersama. Catatan untuk cara ini adalah berhasil jika ujian sudah dekat.

Saya bukan orang yang rajin membaca, namun jika sudah penasaran akan sesuatu, sesuatu itu menjadi addict yang berbahaya. Hasilnya saya kecanduan komik selama lebuh dari 7 tahun. Alhamdulillah sekarang sudah agak reda. Hal aneh yang sering teman-teman katakan adalah kebiasaan saya meminjam komik begitu banyak saat mau ujian. Kalau diingat-ingat dulu saat teman sekamar seriur belajar, saya asik baca komik. Ck ck ck, benar-benar tidak sopan. Mungkin komik adalah salah satu bentuk pelampiasan saya atas ketegangan otot untuk menghadapi ujian. Saya membaca beberapa komik baru kenudian belajar lagi bab baru. Mungkin bagi saya dulu komik adalah penawar rasa bosan membaca huruf teks yang berjejer rapi. Nilai saya cukup stabil pada level baik dengan cara ini.

Beberapa hal juga pernaah saya coba untuk meningkatkan isi atau volume otak yaitu dengan image training. Sebuah cara yang saya temukan di sebuah komik tentang kedokteran. yaitu menggunakan imajinasi untuk memperlebar daya ingat dan kemampuan abstraksi. Hasilnya nilai saya yang berkaitan dengan geometri atau apapun gambar minimal dapat A- (Kalau tidak salah).

 

How to find the Purpose of Life?

Sekedar berbagi ilmu dari seorang dosen tentang bagaimana mencari tujuan hidup. Ini salah satu catatan lama yang mungkin berguna bagi yang membutuhkan. Bagi yang masih belum menemukan tujuan hidupnya semoga tulisan sedikit ini dapat membantu.

Untuk memperoleh tujuan hidup yang sesuai, pertama kita harus mengetahui terlebih dahulu apa kelebihan dan kekurangan kita. Hal ini dapat menunjukan seberapa jauh kita mengenal diri kita sendiri. Kemudian coba deh susun daftar, apa yang ingin/dapat kita lakukan dalam jangka waktu 1 jam, 1 minggu, 1 bulan, dan seterusnya.

Setelah itu coba pikirkan, motif dominan kita itu apa? Apakah kekuasaan, persahabatan, atau prestasi? ciri-ciri tiap orang dengan motif dominan yang berbeda itu juga beda loh...misalnya orang yang motif dominannya persahabatan. Dia cenderung untuk berkumpul bersama teman2, supel, pendengar yang baik, dll. Kemudian orang yang motif dominannya kekuasaan, orang dengan motif ini cenderung pandai bicara, egois, suka mengatur, dll.

Meskipun motif kekuasaan mendapat pandangan negatif yang cukup besar, tak selamanya seperti itu. Seorang pemimpin yang baik, pasti bisa mengatur anak buahnya dengan baik kan? Selanjutnya orang yang motif dominannya prestasi, orang dengan motif ini cenderung untuk serius, punya rasa tanggung jawab yang besar, pandai mengatur waktu, dsb.

Nah sekarang coba pikirkan motif dominan apa yang ada dalam diri anda?

Number Sense

Have you ever heard about number sense? What's the meaning and how to use it?

Karena sedikit artikel yang mengulasnya dalam bahasa indonesia. Kali ini saya menggunakan bahasa indonesia, by the way saat ini saya dalam tahap peningkatan kemampuan bahasa inggris di sebuah lembaga. Semoga nanti membawa manfaat.

Number sense merupakan sebuah intuisi yang baik mengenai bilangan dan hal yang terkait dengan bilangan. Hal ini dapat didefinisikan secara luas sebagai pemahaman makna bilangan dan pemahaman hubungan anratbilangan (Malofeeva, Day, Saco, Young, & Ciancio, 2004). Kemampuan number sense meliputi kemampuan mengenal bilangan, mengidentifikasi nilai bilangan dan memahami bagaimana mengaplikasikannya dalam berbagai macam cara, seperti berhitung, perhitungan mental, pengukuran atau estimasi/penaksiran. (http://surfnetparents.com/math_glasarry.html).

Number sense dihasilkan oleh suatu approach/pendekatan yang dikembangkan di Belanda sejak tahun 1970-an; yaotu RME (Realistic Mathematics Education) oleh Institut Freudenthal. matematika sebagai aktivitas manusia berarti manusia harus diberi kesempatan untuk menemukan kembali ide dan konsep matematika dengan bimbingan orang dewasa (Gravemeijer, 1994). Upaya ini dilakukan melalui penjelajahan berbagai situasi dan persoalan realistik. Realistik dalam hal ini dimaksudkan tidak mengacu pada realitas tetapi pada sesuatu yang dibayangkan siswa. Prinsip penemuan kembali dapat diinspirasi oleh prosedur-prosedur pemecahan informal, sedangkan proses penemuan kembali menggunakan konsep matematisasi.

Number sense merupakan kesadaran akan jumlah, memberi makna pada bilangan dan mampu menghubungkannya dengan makna yang berbeda. Siswa menemukan cara yang lebih mudah dalam menghadapi suatu bilangan, dan dapat mengerti bahwa sebuah bilangan dapat direpresentasikan dengan cara yang berbeda.

Terdapat dua model dimensi number sense yaitu kemampuan dasar (Basic skill) dan aritmatika konvensional (Conventional arithmetic). Jordan, kaplan, Olah, dan Locuniak (2006) menggambarkan bahwa dimensi kemampuan dasar meliputi kemampuan berhitung, mengenali bilangan, mengetahui bilangan, perhitungan nonverbal, penaksiran, dan pola bilangan. Dimensi yang lain yaitu atirmatika konvensional meliputi, kombinasi bilangan dan soal cerita. Aspek penting tentang number sense dinyatakan oleh Jordan dan rekan-rekannya yang dirangkum dalam 5 elemen kunci number sense anak (Jordan, et al, 2006 : 154).

1. Berhitung : mengetahui korespondensi satu-satu, urutan yang stabil, pengetahuan tentang prinsip kardinalitas dan mengetahui barisan berhitung.
2. Pengetahuan bilangan : mendeskripsikan dan mengkoordinasikan besaran dan membuat perbandingan besaran bilangan.
3. Transformasi bilangan : transformasi bilangan dengan penjumlahan, pengurangan dan perhitungan dalam konteks verbal dan nonverbal, perhitungan dengan atau tanpa bantuan (fisik atau verbal).
4. Penaksiran : memperkirakan besarnya himpunan dan menggunakan referensi titik.
5. Pola bilangan : meniru pola bilangan, memperbesar pola bilangan dan melihat hubungan antarbilangan.

Referensi :
Malofeeva, E., J., Saco, X., Young L., & Ciancio, D. 2004. Construction and Evaluation of A Number Sense Test With Head Start children. Jurnal Pendidikan Psikologi, 96(4), 648-659.

Gravemeijer, K. P. E. 1994. Developing Realistic Mathematics Education. Netherlands. Utrecht : Freudenthal institute.

Jordan, N. C., Kaplan, D., Olah, A. N., & Locuniak, M. N. 2006. Number Sense Growth in Kindergarten: A Longitudinal Investigation of Children At Risk For Mathematics Difficulties. Jurnal Penelitian Perkembangan Anak, 77(1), 153-175.

The Foundations of Mathematics

What is the foundations of mathematics?
when i look at the foundations of mathematics books 1st edition (by Thomas Q. Sibley). The first chapter is about laguange, logic and set. The second is about proof.
If the foundations is like that, what's the reason?
I though, foundation is something that make it strong and enough to grew up. The principals are quite similar with the building of a house and all the materials support it to stand up. Language, logic, set, proof is essential part. We can't share mathematics idea without language. Logic is about studying the correct reason, it's true or false. Mathematics investigations is just about true or false, so i think it's relevan, since it was developed a long time ago by Aristotles. Set is the most fundamental concept in mathematics, it's about how to collect a distinct objects. It's also relevan. At the end, i agree with Mr. Sibley.

Foundations of mathematics is a term sometimes used for certain fields of mathematics, such as mathematical logic, axiomatic set theory, proof theory, model theory, and recursion theory.
From the philosophy it self. There are three school that very influent the mathematicians and philosophers at the first time.

1. Platonism: "Platonist, such as Kurt Godel, hold that numbers are abstrack, necessarily existing objects, independent of the human mind."
2. Formalism : "Formalists, such as David Hilbert, hold that mathematics is no more or less than mathematical language. It is simply a series of games..."
3. Intuitionism : "Intuitionist, such us L. E. J. Brouwer, hold that mathematics is a creation of the human mind. Numbers, like fairy tale characters, are merely mental entities, which would not exist if there were never any human minds to think about them."
   

Reference :
http://en.wikipedia.org/wiki/Foundations_of_mathematics

Mathematics Discoveries

In this time, there are three points that i want to write in this article:
1. The old mathematics discoveries which is still exist today.
2. The old mathematics discoveries which isn't exist today.
3. The new mathematics discoveries which unrelated to old mathematics.
The explanations is below :

1. The Old Mathematics discoveries Which is Still Exist Today

SEMPOA

Why i take sempoa as one of mathematics discoveries? Since it's calculations tool,i thought this is a great discoveries.

Sempoa is one of old calculations tool which is still exist today. Although there were so many invenstions in calculations tool like calculators and computers with many series, but sempoa still has their existance.

Where sempoa comes from is unknow because sempoa used by many cultures in the world. Some researchers said it was on Babylonia and Tiongkok about 2400 SM and 300 SM. In English, sempoa is well-know as abacus. This word used since 1387, comes from latin "abakos" which is taken from greek "abax" means calculation tables.

Why sempoa still exist today?
I used to watch a live program in one of tv station about someone who expert using sempoa. There were three persons that gave calculation problems with 12 numbers, example :
278673589835 + 675548770098 + 227648652202 = ??

One person using sempoa while others calculate by arithmetic algorithm. Everything goes right but there something strange with the person who use sempoa, he did't use sempoa at all. He just move his thumb and index finger to calculates the problem on the board. He calculate faster than the others and the answer is right. I think it awesome, since he can do it well and defeated others. It's one of the effect of something called "Image Training" i though. Since sempoa in his mind with perfect shape and he can use it anytime. In this case is by using sempoa in a long time and slowly the sempoa is escape phisicaly, thus sempoa is just imaginations.

Perhaps, this is one of the reason why sempoa still exist today. Honestly i love sempoa too when i was a child, but by the time goes on i'm not expert on it again. Hm... I need more practice. What about you? Do you have ever use sempoa? In Indonesia itself thera so many sempoa clubs, one of the famous is ASMA (Adil Sempoa Mandiri) who win Sempoa National Olympics on August 24 2008.

2. The Old Mathematics Discoveries which isn't Exist Today

I determine to take the contradiction of Euclid fifth's Postulate, I hope it's quite relevan to discussed.

Euclids fifth's Postulate / Parallel Postulate

"If two lines are intersect by a transversal in such a way that the sum of the degree measures of the two interior angels on one side of the transversal is less than 180 degrees, then the two lines meet on that side of the transversal."

Some mathematicians thought that this is not a postulate, since it can proved by another four postulates. There are some mathematicians who has some effort to prove Euclid's postulate. This work begin when Euclid still alive until 1820. Some of them are:

1. Proclus from Alexandria (410-485)
2. Girolamo Saccheri from Italia (1607-1733)
3. karl Frederich Gauss from Jermany (1777-1855)
4. Wolfgang(Farkas) Boylai from Hungaria (1775-1856) and His son Yanos Boylai (1802-1860)
5. Nicolai Ivanoviteh Lobacevsky (1793-1856)

None of them can prove it, :) Euclid is brilliant. But their effort wasn't useless, because it can find another geometry which called Non-Euclides Geometry.

Since this postulate is difficult to understand, there are some mathematicians who tried to change with another equal postulate. Here are some of them :

• Proclus' Axiom : "If a line intersect one of two parallel lines, both of which are coplanar with the original line, then it must intersect the other also".
• Playfair's Axiom : "Through any point in space, there is at most one straight line parallel to a given straight line".

At the end, what happen with the fifth postulate's Euclid? The discovery of non-Euclidean geometry finally allowed mathematicians to open up their study of this familiar round surface along with other, even stranger, surfaces. Then the expansion of Euclid's axioms led the way to examine what might happen if they were to be eliminated or change.


3. The New Mathematics Discoveries Which Unrelated to Old Mathematics

After a long time, at the end, I couldn't found mathematics discoveries which unrelated with the past discoveries. The new theory is developed from the previous axiom or formulas, for example Jean Christopher Yoccoz who recieved the greatest honour for his work on dynamical systems when he was awarded a Fields Medal, the theory of dynamical systems really began with Poincare who was studying the stability of the solar system. Maria Gaetana Agnesi began working on her most important work, Analytical Institutions, dealing with differential and integral calculus.

During the 20th century, there are so many development on mathematics and at the same time, deep discoveries were made about the limitations to mathematics, it was discovered the truth or falsity of all statement formulated. Some of the most profound discoveries is :

1. In a 1990 speech to the International Congress of Mathematicians, David Hilbert set out a list of 23 unsolved problems in mathematics.
2. In 1976, Wolfgang Haken and Kenneth Apple used a computer to prove the four color theorem.
3. In 1931, Kurt Godel found that this was not the case for natural numbers plus both addition and multiplication: this system, know as Peano arithmetic, was in fact incompletable.

There are also new antry areas of mathematics such as mathematical logic, topology, complexity theory, and game theory.

Reference :
http://id.wikipedia.org/wiki/Sempoa
http://turnbull.mcs.st-and.ac.uk/history/Timelines/TimelineG.html
http://www.mathworld.wolfram.com/PlayfairsAxiom.html
http://www.mathworld.wolfram.com/ProclusAxiom.html
http://en.wikipedia.org/wiki/History_of_mathematicians#20th_century
Moeharti Hw, 1986, Modul Materi Pokok : Sistem-Sistem Geometri, Publisher :karunika Jakarta Open University, Jakarta.

1736 - Leonhard Euler Solves The Problem of The Seven Bridges of Königsberg, In Effect Creating Graph Theory

Fig.1

Based of what i've read, the konigsberg's bridge problem is a unique case. No wonder Euler wouldbe interested on it. Konigsberg located in a strategic position on the river Pregel, that's whay it become a trading center and an importanr medieval city. the river Pregel also divided this area into four land, which is conected with seven bridge : Blacksmith's bridge, connecting's bridge, High bridge, Green bridge, Honey bridge, merchant's bridge and Wooden bridge. As illustrated on figure 1.

Konigsberg is a city with beautiful scenery, the citizens of konigsberg used to spend their sunday afternoons by walking around their city. i don't know why people always make a trouble for themself. The problem was to find a walk trough the city that would cross each bridge once and only once, and if possible, returning to their start point. None can solved it, but Konigsberg is near with St. Petersburg, where the famous mathematicians Euler stay.

I found on some mathematics books about Euler investigated the Konigsberg's bridge by drawing a graph of the city as the figure below :

Fig. 2

But, actually Euler didn't draw the graph. so what did Euler do?
In 1736, Euler wrote up his solution in the Commentarii Academiae Scientriarum Imperialis Petropolitanae under the title 'Solutio Problematis ad Geometrian situs pertinentis'. Euler's diagram of Konigsberg appears in figure 3 :

Fig.3

Altough dated 1736, Euler's paper wasn't actually published until 1741, and was reprented in the new edition on the Commenterii (Novi Acta Commentarii.... ) which is appeared in 1752.
Euler's paper divided into twenty-one numbered paragraph. In his paper, Euler generelized the problem : "Whatever be the arrangement and division of the river into branches, and however many bridges there be, can one find out wheter or possible to cross each bridge exactly once?".

At the first, Euler try to list the possible paths and find the tour which is suitable for Konigsberg's problem. but this method has many weakness, like there so many possible paths, it need a long time and it can't used for more bridges and lands. Hence, Euler decide to look for another method that can find the specific tour with simple step.

Euler use the letter A, B, C, and D to represented the land. If someone walk from A to B right across bridge a or b, the path is AB. A is the initial region and B is the final. In the same way, if someone walk from A to B, B to D and D to C, then the three trips can be represented as ABDC. A is the inital region and C is the final region. Since each land separate by river, this people need to cross 3 bridges. in the same way, if we cross 4 bridges, the path represented with 5 combination letters.

The generalization is, if we cross n bridges the the combination letters is n + 1. The Konigsberg has 7 bridges so the paths can be represented by 8 combination letters.
Euler ignore which bridge is used, as long as the property of initial region and the final region is complete. The Konigsberg's problem can be simplify to look for combination of 8 letters, from A, B, C, and D, and the pair of letters appears with certain frecuency. the region A and B in connected by 2 bridges, so A and B will be used twice, A and C also twice. but, for A and D, B and D, C and D just once.

Before going to the next steps, Euler try to find a formula to indicates wheather possible or not to find the tour. Euler developed the answer from a simpler example on the figure below :

Fig. 4

If A connected with 3 bridges then A will appears twice. If there are five bridges connected to A region, then A will appears 3 times. the generalization is :
if there is an odd number k of bridges, the letter must appear (k + 1 )/2 times.
Since kneiphof is connected by five bridges, the path must contain three As. Similarly. there must be two Bs, two Cs, and two Ds. See the table below:

Summing the final row of frequency gives 9 required letters, but Koingsberg has 7 bridges which exactly once can have only 8 letters. Thus there can be no Konigsberg tour.

Euler continued his analysis :
if there is an even number k of bridges connecting a land mass, then the corresponding letter appears (k / 2) + 1 times if the path begin in that region, and k /2 times otherwise.

Ok, that's all i know about Konigsberg. Thanks for read.

References :
http://www.gss.ucsb.edu/hopkins1.pdf
http://en.wikipedia.org/wiki/Seven_Bridges_of_K%C3%B6nigsberg
http://www.math.nmsu.edu/his_projects/Euler-Barnett.pdf

What's the relation between infinity and zero?

I've read some article about The mistery of Zero. It's not the title of a film. Zero is weak but have a big power. How can i say it? one is bigger than zero, but if you try to calculate one divided by zero, you'll get error sign or NaN or infinity, didn't you? zero is netral. Thats way i love it. When zero appear in the first time? Based on what i've read, it come up from india. Infinity is powerful and so infinitely free. It is bigger than any quantity that can be imagined, it's bigger than any finite number. Infinity is one of the fundamental axioms upon which contemporary mathematics is based.

Zero and infinity are perhaps two of the most unique concepts in math. It's like a follower, zero is the reason of the infinity. Infinity it self are uncalculated because it's special. None can solve it, that's why infinity figured with such notation like this :

The sleep eight, some people said eight is perfect or good number. So what's the meaning with this? I guess, eight is a balace. It's hasn't start point and "Futari" or "Berputar-putar" or "Endless point". This is the reason why infinity is figured by "the sleep eight". Perhaps, the true answer is unknown.

inspired by :
http://www.towardsanewera.net/infinity_and_zero.htm