Math

October 3, 2014

A Brief Note on Birds

The essence of Mathematics resides in its freedom
— George Cantor

There seems to be a tighter bond between math and poetry than between man and the mind in his head. Well known poets who have long since dead such as John Keats when he wrote Lamia, or Edgar Allan Poe when he worked on Sonnet — To Science, or Walt Whitman when crafting When I heard the learn’d astronomer, do not seem to have recognized this tight bond. The same goes for those who are living and think that math and poetry are two things that have developed at opposite poles, and because of this cancel each other out. A slightly better view, even though it is still shallow, will say that math and poetry, or literature, are not enemies, but these two things are not on the same level, and it is literature that is superior to, that is more amazing than, math. This second view can also be felt in the fat thick novel of the most famous Japanese contemporary writer, Haruki Murakami.

 1Q84 1

In the first part of his novel IQ84 whose launch was greeted with much fanfare in Europe and America, Murakami wrote the following on mathematics and literature:

Where mathematics was a magnificent imaginary building, the world of story as represented by Dickens was like a deep, magical forest for Tengo. When mathematics stretched infinitely upward toward the heavens, the forest spread out beneath his gaze in silence, its dark, sturdy roots stretching deep into the earth. In the forest there were no maps, no numbered doorways…. Tengo began deliberately to put some distance between himself and the world of mathematics, and instead the forest of story began to exert a stronger pull on his heart… Someday he might be able to decipher the spell. That possibility would gently warm his heart from within.

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Conjecture

January 11, 2009

Supercosmos Re-Creation?

Employing the evolution-given brain, humanity has succeeded so far in accumulating extraordinary amount of knowledge, including that of the natural universe. But that abundant pile is always haunted by epistemological anxiety regarding the truth, the consistency, and the completeness of the knowledge.

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Kurt Gödel and Albert Einstein, 1950. IAS Archives

Along with its assertion that the Platonic mathematical universe can never be reduced into a finite set of symbols and a bounded group of axioms, Gödel Theorem shows that a consistent knowledge is incomplete and a complete knowledge is inconsistent. For any consistent formal, recursively enumerable theory that proves basic arithmetical truths, an arithmetical statement that is true, but not provable in the theory, can be constructed. That is, any effectively generated theory capable of expressing elementary arithmetic cannot be both simultaneously consistent and complete.

How can humanity be rested assured of the accumulative knowledge on universe’s birth, when the incredibly vast distance of space and time makes it impossible for humanity to directly witness the birth of the universe?

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J. B. S. Haldane, 1941. Photo: Hans Wild/LIFE

“Now my own suspicion is that the Universe is not only queerer than we suppose, but queerer than we can suppose.” — Possible Worlds and Other Papers (1927), p. 286, J. B. S. Haldane.

How can human race complete the knowledge of the universe and all within, being aware of the impossibility of gaining complete knowledge of an object for one who is entrapped inside of it, while realizing the improbability of going outside of the universe he lives in?

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Epistemologi

September 23, 2008

Mencari Agama Merengkuh Sains

Hampir 100 tahun yang silam, tepatnya 30 Juni 1905, Albert Einstein menyerahkan draft paper, bukan sebuah buku tebal, yang ia kerjakan di waktu senggang. Kepada penerbitnya, Einstein bercanda semoga draft itu layak diumumkan, jika pun memang ada ruang yang sisa. Paper berkepala Zur Elektrodynamik Bewegter Körper (Tentang Elekrodinamika Benda-benda Bergerak) itu muncul di jurnal Annalen der Physik 17:891, 1905. Isinya terutama adalah reaksi terhadap eksperimen Michelson-Morley yang menguji keberadaan “luminiferous ether” sebagai medium penjalaran cahaya, sekaligus perluasan ide transformasi Lorentz dan teori gelombang elektromagnetik Maxwell. Di sana disimpulkan bahwa ether tak perlu ada, dan bahwa kecepatan cahaya selalu sama, tak peduli sumber cahaya atau si pengamat bergerak saling menjauh atau mendekat. Ringkasnya, paper itu berisi pemikiran yang meleceh akal sehat:  pandangan tentang ruang waktu nisbi yang mendobrak persepsi ruang-waktu mutlak Newtonian yang sudah berkuasa lebih dari 3 abad.

Quadran Taqi Al-Din. Sumber: muslimheritage.com

Ketika Einstein menyerahkan paper itu, ia hanyalah seorang pegawai culun di kantor paten Swiss. Ia bukan seorang professor dengan riwayat akademik yang mengesankan, dengan setumpuk buku tebal yang terbit mencantumkan namanya. Dan meski paper itu secara sempurna menghina akal sehat, menampik pandangan ruang-waktu yang tengah berkuasa, tak ada berita tentang kelompok ilmuwan yang merasa tersinggung oleh paper itu. Kita pun tak mendengar bahwa forum ilmuwan Jerman, Perancis dan Inggeris, bersama pimpinan sejumlah ormas, partai politik dan universitas paling berpengaruh di Eropa, bersatu lalu mengeluarkan fatwa hukuman mati. Tak ada catatan adanya kehebohan yang membuat mertua Einstein atau profesor pembimbing disertasinya, menegur Einstein dan mencoba memperbaiki sikap keilmuwannya. Juga tak ada keluhan mengapa Einstein menerbitkan papernya di jurnal berbahasa Jerman, mengapa bukan di jurnal berbahasa Inggeris: bukankah paper itu merongrong persepsi ruang waktu Newton yang Inggeris itu?

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Epistemologi

September 22, 2008

Imajinasi Ilahi

Imajinasi jauh lebih penting dari Agama. Imagination is much more important than Religion. Saya bayangkan bertahun-tahun kelak, kalimat ini terpampang sebagai semboyan di pintu gerbang kampus-kampus berbasis agama, di rumah-rumah ibadah, atau di kamar-kamar belajar para cendekia yang berkerja memautkan ilmu pengetahuan dan aspirasi religius.

Mereka yang mengenal sejarah perkembangan ilmu pengetahuan modern, akan tahu bahwa semboyan itu diilhami oleh salah satu dari tiga pernyataan Albert Einstein yang paling banyak dikutip dunia. Yaitu bahwa imajinasi jauh lebih penting dari ilmu pengetahuan. Dua pernyataan yang lain adalah: “ilmu tanpa agama akan buta, agama tanpa ilmu akan lumpuh”; dan “yang paling tak terpahamkan tentang alam semesta ini adalah bahwa ia ternyata bisa dipahami”.

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Novel

September 9, 2008

Poetic Time

For decades the world has been taught that Einstein’s Theory of Relativity is a set of extremely unfathomable complex mathematical concepts. The Theory of Relativity ― a superb orchestration of strokes of genius based upon Riemann’s geometric ideas which overthrew the Euclid’s 2300 year-old domination ― has become a sacred area of thought where those who are not brilliant in physics should not even think to lift a finger.

This novel by Alan Lightman, MIT professor in physics and director of the Program in Writing and Humanistic Studies, is enchanting because it transforms Einstein’s quest for the nature of time from pure mathematical abstractions into concrete human experiences. Time presented is the pulsing time inside every human being, constituting one as a true human. Instead of presenting a theoretical description about a very complex and subtle cosmic phenomenon that exist independent of human beings, Lightman offers a literary work to intensify the awareness of time that resides in every human’s heart and body. He illustrates the abstract concept of time through lenses of the pain of longing and the joy of passion, and in our aspiration to seek out our destiny and freedom.

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