大島さん http://d.hatena.ne.jp/squeaker/20080801#p1 に教えて頂いて、面白かったので気に入った部分をメモします。
For Richard a crazy idea was an opportunity to either prove it wrong or prove it right. Either way, he was interested.
リチャードにとって、気違いじみた考えは正しいか間違ってるかを確かめるチャンスで、どっちにせよ彼は興味を持った。
Every great man that I have known has had a certain time and place in their life that they use as a reference point; a time when things worked as they were supposed to and great things were accomplished. For Richard, that time was at Los Alamos during the Manhattan Project.
偉大な人というのははみんな良い仕事をして、後の参考になる時代というのがあって、リチャードの場合それはマンハッタンプロジェクトでのロスアラモス時代だった。
Consider the problem of finding the logarithm of a fractional number between 1.0 and 2.0 (the algorithm can be generalized without too much difficulty). Feynman observed that any such number can be uniquely represented as a product of numbers of the form 1 + 2-k, where k is an integer.
意味分かりませんでした。でもなんかすごそう。
Since the only computer language Richard was really familiar with was Basic, he made up a parallel version of Basic in which he wrote the program and then simulated it by hand to estimate how fast it would run on the Connection Machine.
リチャードが良く知っている言語は BASIC だけだったので、彼は並列 BASIC を作ってコネクションマシンで問題がどれくらい速く解けるか手で見積もった。
Our discrete analysis said we needed seven buffers per chip; Feynman's equations suggested that we only needed five. We decided to play it safe and ignore Feynman.
The decision to ignore Feynman's analysis was made in September, but by next spring we were up against a wall. The chips that we had designed were slightly too big to manufacture and the only way to solve the problem was to cut the number of buffers per chip back to five.
我々の別の離散的な分析ではチップ一つに着き七つのバッファが必要だったが、ファインマンの方程式が示すにたった五つで良いという事だった。我々は安全に振ってその結果を無視する事にした。
九月にファインマンの分析を無視しようと決めたが次の春には壁にぶち当たった。作ろうと思っていたチップが大きすぎて生産できない。解決する唯一の方法はファインマンの分析通りチップあたりのバッファを五つにする方法だった。
One of the simplest problems is just making the physics so that things look the same in every direction. The most obvious pattern of cellular automata, such as a fixed three-dimensional grid, has preferred directions along the axes of the grid. Is it possible to implement even Newtonian physics on a fixed lattice of automata?
(セルオートマトンで物理モデルを作る)一つの問題は、物理法則をどの方向でも同じように働かせる事だ。三次元格子を使うありがちなセルオートマトンでは、力が座標軸に偏ってしまう。ニュートンの法則を格子状のオートマトンで作るなんて出来るのだろうか？
His notion was that the underlying automata, rather than being connected in a regular lattice like a grid or a pattern of hexagons, might be randomly connected.
ファインマンの考えはセルを四角や六角に並べないで出鱈目に繋げる事だった。
For two-dimensional problems there was a neat solution to the anisotropy problem since Frisch, Hasslacher, Pomeau had shown that a hexagonal lattice with a simple set of rules produced isotropic behavior at the macro scale.
二次元を使ってこの異方性の素敵な解決が見つかった。 Frisch と Hasslacher と Pomeau が大まかに見るとどの方向にも同じように力が働くように見える六角形の格子と単純なルールを見つけたのだ。
I had written a program that simulated the evolution of populations of sexually reproducing creatures over hundreds of thousands of generations. The results were surprising in that the fitness of the population made progress in sudden leaps rather than by the expected steady improvement.
私は進化をシミュレートするために何万世代に及ぶ性生殖のプログラムを書いてみた。結果は驚くべきもので、進化はちょっとづつ起こるのではなく突然飛び跳ねるように起こることがわかった。
When I got back to Boston I went to the library and discovered a book by Kimura on the subject, and much to my disappointment, all of our "discoveries" were covered in the first few pages. When I called back and told Richard what I had found, he was elated. "Hey, we got it right!" he said. "Not bad for amateurs."
ボストンに帰って図書館で Kimura の本を読むと、我々の『発見』はものの最初数ページですでに発見されていてがっかりした。リチャードに電話すると、彼は喜んで言った。『ヘイ、合ってたじゃないか！素人にしては上出来だ。』
In retrospect I realize that in almost everything that we worked on together, we were both amateurs. In digital physics, neural networks, even parallel computing, we never really knew what we were doing. But the things that we studied were so new that no one else knew exactly what they were doing either. It was amateurs who made the progress.
思うに、共同研究者たちもみんな素人だった。デジタル物理やニューロネットワーク、分散コンピューティングまで、我々は自分で何をやっているか分かっていなかった。でも我々の研究は新しすぎて、本当の事はだれも分かるわけがないのだ。進歩を遂げるのは素人たちだった。
