雙語暢銷書《艾倫圖靈傳》第4章:彼岸新星(62)
The second problem, quite different, was the 'dull and elementary' one of actually doing the computation, with numbers substituted into the approximate formula, and worked out for thousands of different entries.
It so happened that the formula was rather like those which occurred in plotting the positions of the planets, because it was of the form of a sum of circular functions with different frequencies.
這個公式的形式是一系列不同頻率的周期函數的總和，類似於計算天體位置。It was for this reason that Titchmarsh had contrived to have the dull repetitive work of addition, multiplication, and of looking up of entries in cosine tables done by the same punched-card methods that were used in planetary astronomy.
這就是爲什麼蒂施馬奇要採用天文學中的打孔卡片，來做加法、乘法、查詢餘弦表這些重複而繁瑣的工作。
But it occurred to Alan that the problem was very similar to another kind of computation which was also done on a large practical scale, that of tide prediction.
在艾倫眼中，這個問題更像一個更大規模的問題──潮汐預測。Tides could also be regarded as the sum of a number of waves of different periods: daily, monthly, yearly oscillations of rise and fall.
潮汐可以看成是大量不同週期的波浪的總和。At Liverpool there was a machine which performed the summation automatically, by generating circular motions of the right frequencies and adding them up.
在利物浦，有一臺機器能自動地執行這樣的求和，它產生特定頻率的週期運動，並把它們疊加起來。It was a simple analogue machine; that is, it created a physical analogue of the mathematical function that had to be calculated.
這是一個簡單的模擬機，它爲需要計算的數學函數構造一個物理的模擬。This was a quite different idea from that of the Turing machine, which would work away on a finite, discrete, set of symbols.
這是和圖靈機很不一樣的想法，圖靈機是基於一套有限的、離散的符號集，This tide predicting machine, like a slide rule, depended not on symbols, but on the measurement of lengths.
而這個潮汐預測機則像是一把計算尺，它與符號無關，只依賴於長度的測量。
