56 Mathematics Today April 2000 will make discoveries that transform our methods of paralle ck th n;or,just as like of upheaval.The tomo take anoth her generatior ut it will come 1940-1970 point arithmetic onand Crick.we have nown this must be true.and in 1995 eelermeihn the first genome of a free-standing organism was sequenced ide this is gh for 1970-2000 wton iterations u-macroglobulin proteinase inhibi or of Oc 54 bro 2002-2050 11.OUR METHODS OF PROGRAMMING WILL HAVE BEEN BLOWN OPEN BY IDEAS RELATED TO GENOMES AND NATURAL SELECTION nputer programs are strangely analo tingmade by ideas related to Genetic programs and c h are made poibe byids relted to and no othe 10.THE PROBLEM OF MASSIVELY genomics,thinking g digi PARALLEL COMPUTING WILL HAVE BEEN BLOWN OPEN BY IDEAS RELATED TO THE en in ad HUMAN BRAIN There's a program ner in the The information revolution is well underway,but the revolu mention mments!).Yet it is n ble that nowada big to be tific life is that the problem of massively verified,and indeed,the pr cess of industrial 1 as ated by an unending p riment and test code and computing nowadays is a cl correct,a process in which individua human intelligen ced as eve one expected a decadego rom ones eration to the next.and they are pever perfect. but they work to some computer scien nda the two prediction,jut revolutions in store will somehow be linked.Brain researchers pious wish ~ 56 Mathematics Today April 2000 Table 1. Some Past and Future Developments in Scientific Computing. The Asterisks Mark Items Summarised by (*). Refore 1940 Newton's method Gaussian elimination Gauss quadrature least-squares fitting Adams and Runge-Kutta formulas Richardson extrapolation 1940-1970 floating point arithmetic Fortran finite differences finite elements simplex algorithm Monte Carlo orthogonal linear algebra splines FFT 1970-2000 quasi-Newton iterations adaptivity stiff ODE solvers sottware libraries Mat lab multigrid sparscl and iterative linear algebra spectral methods interior point methods wavelets 2000-20.50 linear algebra in O(JV") flops multipole methods breakthroughs in preconditioners, spectral methods, time stepping for PDE speech and graphics everywhere fully intelligent, adaptive numerics * loss of determinism seamless interoperabi lity *massively parallel computing made possible by ideas related to the human brain *new programming methods made possible by ideas related to natural selection 1 10. THE PROBLEM OF MASSIVELY l PARALLEL COMPUTING WILL HAVE BEEN 1 , BLOWN OPEN BY IDEAS RELATED TO THE HUMAN BRAIN The informat~on revolution is well underway, hut the revolu￾tion in understanding the human hrain has not arrived yet. Some key idea is missing. Another fact ofscientific life is that the problem ofmassively parallel computing is stalled. For decades it has seemed plain that eventually, serial computers must run up against the con￾straints of the speed of light and the size of atoms, at which point further increases in power must come about through parallel￾ism. Yet parallel computing nowadays is a clumsy business, hogged down in communication problems, nowhere near as advanced as everyone expected a decade ago. I helieve that the dream of parallel computing will he ful￾filled. And it is hard to avoid the thought that if parallel com￾puting and the human hrain are both on the agenda, the two revolutions in store will somehow he linked. Brain researchers will make discoveries that transform our methods of parallel computing; or computer scientists will make discoveries that unlock the secrets of the brain; or, just as likely, the two fields will change in tandem, perhaps during an astonishing ten years of upheaval. The upheaval could hegin tomorrow, or it might take another generation, hut it will come hefore 2050. Meanwhile, another revolution in hiology is already happening: the working out of DNA/RNA genomes and their implications. Every organism from virus to man is specified by a program written in the alphahet of the nucleotides. Since Wat￾son and Crick, we have known this must he true, and in 1995, the first genome of a free-standing organism was sequenced. Since then, dozens more have followed, with the human ge￾nome itself now nearly complete, and everything in hiology, from development to drug design, is being reinvented as we watch. If I give you the sequence KPSGCGEQNMINFYPNVL in the standard code for the amino acids, this is enough for you to determine in a few seconds that 1 am speaking of an a-macroglohulin proteinase inhibitor of Octopus wlpris, and to locate related enzymes in ten other species. Just point your hrowser to http://www.ncbi.nlm.nih.gov and run hlnstp. I helieve that this drama has implicaticms for computing. 1 1. OUR METHODS OF PROGRAMMING WILL HAVE BEEN BLOWN OPEN BY IDEAS RELATED TO GENOMES AND NATURAL SELECTION Genetic programs and computer programs are strangely analo￾gous. Both are ahsolutely precise digital codcs, and no other codes that we know of have anything like the complexity of these two, with the size of a genome being of roughly the same order of magnitude (3 X 109 nucleotides for Homo sapiens) as the size of an operating system (2 X 10" hits for Windows 98). As a generation of engineers grows up with genomics, thinking digi￾tally about the evolution of life on earth, our methods of com￾puter programming will change. (Some ideas in this direction are already with us.) Traditionally, computer programs arc writ￾ten in a different way from biological ones. There's a program￾mer in the loop, an intelligence, which gives computer programs a logical structure that biological programs lack (not to mention comments!). Yet it is notahle that nowadays, large-scale software systems are too hig to he understood in detail by any individual, let alone mechanically analysed or verified, and indeed, the process of industrial software design already seems as close to evolution by natural selection as to mathematical logic. Software at a place like Microsoft is gencr￾ated hy an unending process of experiment and test, code and correct, a process in which individual human intelligences seem less important than they used to. Software systems evolve from one generation to the next, and they are never perfect, hut they work. The process is repugnant to some computer scien￾tists, hut it is scalable and i~nstoppahle. Finally, a prediction that is not really a prediction, just a pious wish