Predictions for Scientific Computing Fifty Years From Now Lloyd N.Trefether Oxford University omputing Laboratory LNT@comlab.ox.ac.uh This essay is adopted from a talk given June 17,1998 at the conference "Numericnl Analysis and Computers-50 Years of Progress"held at the University of Manchester in commemoration of the 50th anniversary of the Mark 1 computer. omputingCa8isalog,loigtimcinaurytecdnologicaliddhourge own fieldof that had little in common with today's com ithms we on the whole changed numerica will doj My remarks cons t aim for these to orbit around a 1.We may not be here. In the 20th century,everything technological seemns to be changing exponentially. This raises a problem.Exponentials do not go on for ever;something happens to them. Now in my opinion,many of the exponentials we are sitting on have not yet started to level off.Here at the beginning of the third millennium,biology is just beginning its great explosion,and although electronics got a head start of a few decades,it is hardy Sowing down yet. of expo nentials all around us ove r shadows dwell for me of the ows,on iseviden that te vilisation时 o within fif My reasoning has nothing to do with any particular catadysm that may befall us. such as environmenta catastrophe or exhaustion of asteroid impact orbio The argument is more abstract,and it goes like this.The indus rial explosion on earth began just two or three hundred years ago Now if technologica civilisations can last tens of thousands of years,how do you explain the extraordinar coincidence that you were born in the first few generations of thisone in the very firs century of radio,television,light bulbs,telephones,phonogr aphs,lasers,refriger ators. 1Predictions for Scientic Computing Fifty Years From Now Lloyd N. Trefethen Oxford University Computing Laboratory LNT@comlab.ox.ac.uk This essay is adapted from a talk given June 17, 1998 at the conference \Numerical Analysis and Computers|50 Years of Progress" held at the University of Manchester in commemoration of the 50th anniversary of the Mark 1 computer. Fifty years is a long, long time in any technological eld. In our own eld of scientic computing or numerical analysis, think back to 1950. Around the world, numerical problems in 1950 were solved with slide rules and on paper, or with mechanical calculators that had little in common with today's computers. Some of the algorithms we use today were in existence then, but on the whole, the last fty years have changed numerical computing beyond recognition. The next fty will do it again. My remarks consist of twelve predictions. I did not aim for these to orbit around a unifying theme, but that is nevertheless what happened. 1. We may not be here. In the 20th century, everything technological seems to be changing exponentially. This raises a problem. Exponentials do not go on for ever; something happens to them. Now in my opinion, many of the exponentials we are sitting on have not yet started to level o. Here at the beginning of the third millennium, biology is just beginning its great explosion, and although electronics got a head start of a few decades, it is hardly slowing down yet. The presence of exponentials all around us overshadows any attempt to predict the future. I feel I must dwell for a moment on one of the shadows, one that has nothing specically to do with computing. In my opinion, our position on an exponential tra jectory is evidence that technological civilisations do not last very long. I do not claim that our civilisation must end within fty years, or ve hundred, but I do believe there is reason to doubt it can survive for, say, ten thousand years. My reasoning has nothing to do with any particular cataclysm that may befall us, such as environmental catastrophe or exhaustion of resources or asteroid impact or bio￾logical or nuclear war. The argument is more abstract, and it goes like this. The indus￾trial explosion on earth began just two or three hundred years ago. Now if technological civilisations can last tens of thousands of years, how do you explain the extraordinary coincidence that you were born in the rst few generations of this one? | in the very rst century of radio, television, light bulbs, telephones, phonographs, lasers, refrigerators, 1