Mathematics Today April 2000 53 Predictions for Scientific Computing Fifty Years From Now LLOYD N TREFETHEN Oxford University Computing Laboratory this one?-in the very first century of radio.television.light bulbs,telephones,phonographs,lasers,refrigerators,automo biles,airplanes,space a,computers,nuclear power,nuclear hat the nton of our in his fty in any technological field.In 950g tymay be that it is not so special after all,because tends not to problems in 1950 were solved with slide rules and on paper,or wn a Fermi's paradox,that also suggests that technological civilisa oday'scomputers ome of ay were oare short-lived changed numerical computing beyond recognition.The next tens of thousands of years?An 二 ecause it can.(Don t ask 1.WE MAY NOT BE HERE millions are so rare as to arise on only Ibelieve that the explanation of the there may be that tec level off Here at the beginning of the third perish in a cataclysm so great as to take the galaxy with them Suddenly the problem of predicting fifty years of scienific computing begins to look easy!Let's get down to it. The presene 2.WE'LL TALK TO COMPUTERS MORE OFTEN THAN TYPE TO THEM,AND trajectory is evidence that technological civilisations do no THEY'LL RESPOND WITH PICTURES ast very long.I do not MORE OFTEN THAN NUMBERS A big change in the last twenty years has been the arrival of graphical interfaces.When I was agraduate studentat Stanford phe c round 1980,we played with some Alto machines donared party tricks,to gimmickyto undre years Now i te oaythe descendants of the AotoMathematics Today April 2000 53 Predictions for Scientific Computing Fifty Years From Now LLOYD N TREFETHEN Oxford University Computing Laboratory This cs.;;iy 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 anniver￾sary of the Mark 1 comprlter. F ifty years is a long, long time in any technological field. In our own field of scientific computing or numerical analy￾sis, think hack to 1950. Around the world, numerical p~.ohlerns in 1950 were solved with slide nlles 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, hilt on the whole, the Iast fifty years have changed ni~merical computing beyond recognition. The next fifty will do it again. My remarks consist of twelve predictions. I did not aim for these to orhit ;iround a unifying theme, hut that is nevertheless w11;it happened. 1. WE MAY NOT BE HERE In the 20th century, everytl~ing technological seems to he changing e~ponentiall~. 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 heginning of the third millennium, hiology is just beginning its great explosion, and although electronics got a head start of a few decades, it is hardlv slowing down yet. The presence of exponentials all around us overshadows any attempt to predict the future. 1 feel 1 must dwell for a moment on one of the shadows, one that has nothing specifically to do with computing. In my opinion, our position on an exponential trajectory is evidence that technological civilisations do not Iast very long. I do not claim that our civilisation must end within fifty years, or five hundred, hut I do believe there is reason to douht it can survive for, say, ten thousand years. My reasoning has nothing to do with any particular cata￾clysm that may hefall us, such as environmental catastrophe or exhaustion of resources or asteroid impact or hiological or nu￾clear war. The argument is more ahstract, and it goes like this. The industrial 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 yoi~ were horn in the first few generations of this one? - in the very first century of radio, television, light hulhs, telephones, phonographs, lasers, refrigerators, automo￾biles, airplanes, spacecraft, computers, nuclear power, nuclear weapons, plastics, antihiotics, and genetic engineering? I helieve that the explanation of our special position in his￾tory may he that it is not so special after all, hecause history tends not to last very long. This argument has heen called the Copernican Principle hy J R Gott of Princeton University. There is a second line of evidence, sometimes known as Fermi's paradox, that also suggests that technological civilisa￾tions are short-lived. The human race is not an outpost of a ga￾lactic society; it is a domestic product. How can we explain this if technological civilisations Iast tens of thousands of years? An ages-old technological civilisation will expand across its galaxy, simply because it can. (Don't ask why, for expanding is what life does. If one species doesn't, another will replace it.) Yet in 100,000 years of expanding at one hundredth the speed of light, a civilisation can spread one thousand light years, a distance encompassing millions ofstars. Is it plausible that technological civilisations are so rare as to arise on only one star among millions? I helieve that the explanation of the emptiness out there may he that technological civilisations perish hefore they start to spread across their galaxy -or that they start spreading, then perish in a cataclysm so great as to take the galaxy with them. Suddenly the problem of predicting fifty years of scientific computing hegins to look easy! Let's get down to it. 2. WE'LL TALK TO COMPUTERS MORE OFTEN THAN TYPE TO THEM, AND THEY'LL RESPOND WITH PICTURES MORE OFTEN THAN NUMBERS A hig change in the last twenty years has heen the arrival of graphical interfaces. When 1 was a graduate student at Stanford around 1980, we played with some Alto machines donated hy Xerox, early workstations featuring windows, icons, mice and pointers, hut I thought these were party tricks, too gimmicky to catch on. Today the descendants of the Altos have driven other machines to extinction. It takes no special insight to predict that soon, an equally great change will occur as we take to interacting with computers hy speech. It has heen a long time