中央大學數據分析方法研究中心主任
美國國家工程學院院士
中央研究院院士

The Earth has experienced an anthropogenic mean temperature increase at an unprecedented rate. Even though the total temperature increase of 0.8oC over the last hundred years seems to be insignificant, the fast rate bodes for dire consequences in the years to come. International efforts have been mobilized, conferences have been organized, resolutions have been adopted all aiming to fight the hazards associated with this anthropogenic climate change. So far, most of the attention has been centered on carbon consumption limitation or capping. As the CO2 already in the atmosphere will stay for 50 years or more, even if we stop carbon consumption right now, the effect of the past carbon consumption would stay with us for a long period.

Global warming is a scientific problem. The past, present and future of the scientific issue would be reviewed. To face the future, however, we have to go beyond science and consider economical and social issues. Based on a recent report released by United Nations and World Bank, existing data indicate that though the number of natural disasters might have increased drastic in tandem with the global temperature increase, population growth and economic development, the casualty from those natural disasters has actually decreased drastically over the last century. Reduction of casualty should be the central goal of hazard mitigation, for life is priceless. Thus, the data from the United Nations and the World Bank suggest that the more effective way for fighting the threatening hazards associated with global warming should be sustainable economic development. Only with the economic development can we have the means to fight against the potential hazards.

地球已在經歷人為的平均氣溫的增高，其速率是前所未見的。即使在過去的數百年內總增溫0.8oC，看起來沒什麼緊要，但是快速的增溫卻預告未來年代的可怕結果。國際上的各方努力已經動員起來，組織研討會，採取解決方案，皆指向對抗人為的氣候變化所招致的災害。至今，大部分的關注都聚焦在碳耗量的限制或定額。早已存在大氣中的CO2，將繼續停留50年之久或更長，即使我們現在就停止碳消耗，過去的碳消耗所產生的效應，也會跟著我們一段相當長的時間。

全球暖化是一個科學問題。過去、現在、和未來的科學論題都需檢視。面對未來，我們必須跳脫科學之外，考慮經濟和社會議題。根據聯合國和世界銀行新近發布的報告，現有的數據顯示自然災害的次數雖然緊隨著全球暖化、人口成長、和經濟發展而激增，但是自然災害招致的傷亡人數在上一世紀內，卻是急遽地下降。減少傷亡應該是減災規畫的首要目標，因為生命是無價的。因此，來自聯合國和世界銀行的報告建議：為了對抗與全球暖化相關聯的威脅性災害，較有效的解決之道應該是能永續經營的經濟發展。只有依靠經濟發展，我們才有辦法來防治潛在的災害。

Ever since Fourier Transform is widely applied in data analysis, people tend to think every change in terms of waves. Then, the notion of frequency becomes an indispensible quantity to specify the characteristics of complicate data, for the data are invariably transformed into frequency domain when the variation of the data in the time domain becomes too confused or random to track. Unfortunately, Fourier analysis is based on the underlying stationary and linear assumptions. As a result, the frequency (or wave number) are always independent of temporal or spatial variations. In reality, physical processes are highly variable, which call for the true frequency be a function of both time and location variables. These instantaneous frequency values contain rich information of the underlying properties of the data. In order to define such a versatile frequency values, we have to give up the comfort of a priori basis and develop a totally new adaptive data analysis approach. Indeed, many of the difficulties we encounter in data analysis could actually be traced back to the lack of correct definition for frequency, the critical physical quantity. In fact, once the frequency can be properly extracted from the data, many difficulties such as quantification of degree of nonlinearity and nonstationarity could be achieved easily.

Furthermore, the elusive definition and the method of determination the trend of a given data set can also be accomplished. A rigorous and logic definition of frequency will be given, and a new data analysis method would be introduced in this presentation. Examples of various nonstationary and nonlinear process would be used to illustrate the new view of data that would conform with physical perception rather than abstract mathematical views.

自從傅立葉變換廣泛地應用於數據分析以來，人們傾向於以波動來想像每一個變化。於是，頻率的概念變成不可或缺的物理量，用於標明複雜數據的特性，因為當數據在時域中的變化呈現過於混亂或無規可循時，數據可以不變地轉換為頻域。可惜的是，傅立葉分析是建立在靜止和線性的假設上。結果是頻率(或波數)總是和時間或空間的變化無關。實際上，物理過程是高度可變的，這就要求真正的頻率是時間和位置變數的函數。瞬時的頻率值含有數據潛在性質的豐富資訊。為了定義如此多功能的頻率值，我們不能安於既有的先驗基礎，而必須發展出一個全新適應的數據分析方法。確實的，在數據分析中我們所遭遇的許多困難，都源自於欠缺對頻率的正確定義，頻率是一個關鍵性的物理量。事實上，一旦頻率能從數據中適當地抽取出來，許多問題例如非線性和非靜止程度的量化皆可輕易得出。

甚且，定義一組已知數據和定出其趨勢的方法，一般捉摸不定，現也可以完成。在本演講中，我會對頻率給予一個嚴謹且合乎邏輯的定義，並介紹一種新的數據分析方法。各種非靜止和非線性過程的例子，將被用來闡述數據的新觀點，合乎身體感覺，而不是抽象的數學觀點。